From a8ca18b4b815a2abdbecb958ee5f4c542d69aac7 Mon Sep 17 00:00:00 2001
From: Georgi Gerganov <ggerganov@gmail.com>
Date: Tue, 28 Oct 2025 19:41:43 +0200
Subject: [PATCH 001/185] llama-bench : clarify benchmarked parts of the
 computation (#16823)

---
 tools/llama-bench/README.md | 5 ++++-
 1 file changed, 4 insertions(+), 1 deletion(-)

diff --git a/tools/llama-bench/README.md b/tools/llama-bench/README.md
index ead4da45e29..87d9c0a219b 100644
--- a/tools/llama-bench/README.md
+++ b/tools/llama-bench/README.md
@@ -82,6 +82,9 @@ Using the `-d <n>` option, each test can be run at a specified context depth, pr
 
 For a description of the other options, see the [main example](../main/README.md).
 
+> [!NOTE]
+> The measurements with `llama-bench` do not include the times for tokenization and for sampling.
+
 ## Examples
 
 ### Text generation with different models
@@ -131,7 +134,7 @@ $ ./llama-bench -n 0 -n 16 -p 64 -t 1,2,4,8,16,32
 | llama 7B mostly Q4_0           |   3.56 GiB |     6.74 B | CPU        |         16 | pp 64      |     33.52 ± 0.03 |
 | llama 7B mostly Q4_0           |   3.56 GiB |     6.74 B | CPU        |         16 | tg 16      |     15.32 ± 0.05 |
 | llama 7B mostly Q4_0           |   3.56 GiB |     6.74 B | CPU        |         32 | pp 64      |     59.00 ± 1.11 |
-| llama 7B mostly Q4_0           |   3.56 GiB |     6.74 B | CPU        |         32 | tg 16      |     16.41 ± 0.79 ||
+| llama 7B mostly Q4_0           |   3.56 GiB |     6.74 B | CPU        |         32 | tg 16      |     16.41 ± 0.79 |
 
 ### Different numbers of layers offloaded to the GPU
 

From 85a7d8677bf2200981e52f744a21d5267964ffcf Mon Sep 17 00:00:00 2001
From: Georgi Gerganov <ggerganov@gmail.com>
Date: Tue, 28 Oct 2025 20:19:44 +0200
Subject: [PATCH 002/185] memory : remove KV cache size padding (#16812)

* memory : remove KV cache size padding

* cont : restore padding for n_kv tensor shape

* server : use slot context size instead of training context size

* server : simplify context limit logic
---
 src/llama-kv-cache.cpp                    | 11 +++++----
 src/llama-kv-cache.h                      |  2 --
 src/llama-model.cpp                       | 23 ++++---------------
 src/llama-model.h                         |  3 +--
 tools/server/server.cpp                   | 27 +++--------------------
 tools/server/tests/unit/test_ctx_shift.py |  2 +-
 6 files changed, 14 insertions(+), 54 deletions(-)

diff --git a/src/llama-kv-cache.cpp b/src/llama-kv-cache.cpp
index add74391f0c..6d5dd6051e7 100644
--- a/src/llama-kv-cache.cpp
+++ b/src/llama-kv-cache.cpp
@@ -961,10 +961,14 @@ bool llama_kv_cache::get_has_shift() const {
 uint32_t llama_kv_cache::get_n_kv(const slot_info & sinfo) const {
     uint32_t result = 0;
 
+    // pad the n_kv value so that the graph remains constant across batches and can be reused
+    // note: this also helps some backends with performance (f.ex https://github.com/ggml-org/llama.cpp/pull/16812#issuecomment-3455112220)
+    const uint32_t n_pad_cur = std::max(n_pad, 256u);
+
     for (uint32_t s = 0; s < sinfo.n_stream(); ++s) {
         const auto & cells = v_cells[sinfo.strm[s]];
 
-        result = std::max(std::min(cells.size(), std::max(n_pad, GGML_PAD(cells.used_max_p1(), n_pad))), result);
+        result = std::max(std::min(cells.size(), std::max(n_pad_cur, GGML_PAD(cells.used_max_p1(), n_pad_cur))), result);
     }
 
     return result;
@@ -2014,8 +2018,3 @@ void llama_kv_cache_context::set_input_kq_mask(ggml_tensor * dst, const llama_ub
 void llama_kv_cache_context::set_input_pos_bucket(ggml_tensor * dst, const llama_ubatch * ubatch) const {
     kv->set_input_pos_bucket(dst, ubatch);
 }
-
-uint32_t llama_kv_cache::get_padding(const llama_cparams & cparams) {
-    // the FA kernels require padding to avoid extra runtime boundary checks
-    return cparams.flash_attn ? 256u : 32u;
-}
diff --git a/src/llama-kv-cache.h b/src/llama-kv-cache.h
index 150e2825962..bf7821c07ca 100644
--- a/src/llama-kv-cache.h
+++ b/src/llama-kv-cache.h
@@ -19,8 +19,6 @@ struct llama_context;
 
 class llama_kv_cache : public llama_memory_i {
 public:
-    static uint32_t get_padding(const llama_cparams & cparams);
-
     struct stream_copy_info {
         bool empty() const {
             assert(ssrc.size() == sdst.size());
diff --git a/src/llama-model.cpp b/src/llama-model.cpp
index bb83a04e960..ea6f59ed482 100644
--- a/src/llama-model.cpp
+++ b/src/llama-model.cpp
@@ -19641,7 +19641,7 @@ struct llm_build_apertus : public llm_graph_context {
     }
 };
 
-llama_memory_i * llama_model::create_memory(const llama_memory_params & params, llama_cparams & cparams) const {
+llama_memory_i * llama_model::create_memory(const llama_memory_params & params, const llama_cparams & cparams) const {
     llama_memory_i * res;
 
     switch (arch) {
@@ -19692,17 +19692,13 @@ llama_memory_i * llama_model::create_memory(const llama_memory_params & params,
                         };
                     }
 
-                    const auto padding = llama_kv_cache::get_padding(cparams);
-
-                    cparams.n_ctx = GGML_PAD(cparams.n_ctx, padding);
-
                     res = new llama_memory_hybrid(
                         /* model             */ *this,
                         /* attn_type_k       */ params.type_k,
                         /* attn_type_v       */ params.type_v,
                         /* attn_v_trans      */ !cparams.flash_attn,
                         /* attn_kv_size      */ cparams.n_ctx,
-                        /* attn_n_pad        */ padding,
+                        /* attn_n_pad        */ 1,
                         /* attn_n_swa        */ hparams.n_swa,
                         /* attn_swa_type     */ hparams.swa_type,
                         /* recurrent_type_k  */ GGML_TYPE_F32,
@@ -19714,23 +19710,12 @@ llama_memory_i * llama_model::create_memory(const llama_memory_params & params,
                         /* filter_attn       */ std::move(filter_attn),
                         /* filter_recr       */ std::move(filter_recr));
                 } else {
-                    const auto padding = llama_kv_cache::get_padding(cparams);
-
                     uint32_t n_ctx_per_stream = cparams.n_ctx;
 
                     if (!cparams.kv_unified) {
                         n_ctx_per_stream = (cparams.n_ctx + cparams.n_seq_max - 1)/cparams.n_seq_max;
-                        n_ctx_per_stream = GGML_PAD(n_ctx_per_stream, padding);
-
-                        cparams.n_ctx = n_ctx_per_stream*cparams.n_seq_max;
-                    } else {
-                        n_ctx_per_stream = GGML_PAD(n_ctx_per_stream, padding);
-
-                        cparams.n_ctx = n_ctx_per_stream;
                     }
 
-                    LLAMA_LOG_DEBUG("%s: n_ctx = %u (padded)\n", __func__, cparams.n_ctx);
-
                     llama_memory_i::layer_reuse_cb reuse = nullptr;
 
                     if (arch == LLM_ARCH_GEMMA3N) {
@@ -19757,7 +19742,7 @@ llama_memory_i * llama_model::create_memory(const llama_memory_params & params,
                                 n_ctx_per_stream,
                                 cparams.n_seq_max,
                                 cparams.n_ubatch,
-                                padding,
+                                1,
                                 nullptr,
                                 reuse);
                     } else {
@@ -19772,7 +19757,7 @@ llama_memory_i * llama_model::create_memory(const llama_memory_params & params,
                                 cparams.kv_unified,
                                 n_ctx_per_stream,
                                 cparams.n_seq_max,
-                                padding,
+                                1,
                                 hparams.n_swa,
                                 hparams.swa_type,
                                 nullptr,
diff --git a/src/llama-model.h b/src/llama-model.h
index 248f854101c..1ab1cf7f8e9 100644
--- a/src/llama-model.h
+++ b/src/llama-model.h
@@ -500,9 +500,8 @@ struct llama_model {
 
     ggml_tensor * get_rope_factors(const llama_cparams & cparams, int il) const;
 
-    // note: can mutate `cparams`
     // TODO: move this to new llm_arch_model_i interface
-    llama_memory_i * create_memory(const llama_memory_params & params, llama_cparams & cparams) const;
+    llama_memory_i * create_memory(const llama_memory_params & params, const llama_cparams & cparams) const;
 
     // TODO: move this to new llm_arch_model_i interface
     ggml_cgraph * build_graph(const llm_graph_params & params) const;
diff --git a/tools/server/server.cpp b/tools/server/server.cpp
index 4124bffa40f..cb794ab647e 100644
--- a/tools/server/server.cpp
+++ b/tools/server/server.cpp
@@ -2866,10 +2866,12 @@ struct server_context {
 
         // if context shifting is disabled, make sure that we don't run out of context
         if (!params_base.ctx_shift && slot.n_past + 1 >= slot.n_ctx) {
+            slot.truncated      = true;
             slot.stop           = STOP_TYPE_LIMIT;
             slot.has_next_token = false;
 
-            SLT_DBG(slot, "stopped due to running out of context, n_past = %d, n_ctx = %d\n", slot.n_past, slot.n_ctx);
+            SLT_DBG(slot, "stopped due to running out of context capacity, n_past = %d, n_prompt_tokens = %d, n_decoded = %d, n_ctx = %d\n",
+                    slot.n_decoded, slot.n_prompt_tokens(), slot.n_past, slot.n_ctx);
         }
 
         // check the limits
@@ -2929,16 +2931,6 @@ struct server_context {
             }
         }
 
-        // if context shift is disabled, we stop when it reaches the context limit
-        if (slot.n_past >= slot.n_ctx) {
-            slot.truncated      = true;
-            slot.stop           = STOP_TYPE_LIMIT;
-            slot.has_next_token = false;
-
-            SLT_DBG(slot, "stopped due to running out of context capacity, n_past = %d, n_prompt_tokens = %d, n_decoded = %d, n_ctx = %d\n",
-                    slot.n_decoded, slot.n_prompt_tokens(), slot.n_past, slot.n_ctx);
-        }
-
         if (llama_vocab_is_eog(vocab, result.tok)) {
             slot.stop           = STOP_TYPE_EOS;
             slot.has_next_token = false;
@@ -2946,19 +2938,6 @@ struct server_context {
             SLT_DBG(slot, "%s", "stopped by EOS\n");
         }
 
-        const auto n_ctx_train = llama_model_n_ctx_train(model);
-
-        if (slot.task->params.n_predict < 1 && slot.n_prompt_tokens() + slot.n_decoded >= n_ctx_train) {
-            slot.truncated      = true;
-            slot.stop           = STOP_TYPE_LIMIT;
-            slot.has_next_token = false; // stop prediction
-
-            SLT_WRN(slot,
-                    "n_predict (%d) is set for infinite generation. "
-                    "Limiting generated tokens to n_ctx_train (%d) to avoid EOS-less generation infinite loop\n",
-                    slot.task->params.n_predict, n_ctx_train);
-        }
-
         SLT_DBG(slot, "n_decoded = %d, n_remaining = %d, next token: %5d '%s'\n", slot.n_decoded, slot.n_remaining, result.tok, token_str.c_str());
 
         return slot.has_next_token; // continue
diff --git a/tools/server/tests/unit/test_ctx_shift.py b/tools/server/tests/unit/test_ctx_shift.py
index 4adbbde64f5..7b047b7b3b7 100644
--- a/tools/server/tests/unit/test_ctx_shift.py
+++ b/tools/server/tests/unit/test_ctx_shift.py
@@ -45,7 +45,7 @@ def test_ctx_shift_enabled():
 
 @pytest.mark.parametrize("n_predict,n_token_output,truncated", [
     (64, 64, False),
-    (-1, 120, True),
+    (-1, 248, True), # 8 tokens prompt + 248 tokens generated = 256 tokens total
 ])
 def test_ctx_shift_disabled_short_prompt(n_predict: int, n_token_output: int, truncated: bool):
     global server

From 851553ea6b24cb39fd5fd188b437d777cb411de8 Mon Sep 17 00:00:00 2001
From: YaelGitAccount <38328157276@mby.co.il>
Date: Tue, 28 Oct 2025 21:10:28 +0200
Subject: [PATCH 003/185] cuda: add SET operation support (#16804)
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

* feat(cuda): add GGML_OP_SET support

Implement CUDA kernel for SET operation with f32 support.

All tests passing (14598/14598).

* cuda(set): add I32 support; keep F32

* refactor(cuda): use ggml_cuda_cpy to unify SET operator logic and remove code duplication

* Update ggml/src/ggml-cuda/ggml-cuda.cu

Co-authored-by: Sigbjørn Skjæret <sigbjorn.skjaeret@scala.com>

* Update ggml/src/ggml-cuda/set.cu

Co-authored-by: Sigbjørn Skjæret <sigbjorn.skjaeret@scala.com>

---------

Co-authored-by: Sigbjørn Skjæret <sigbjorn.skjaeret@scala.com>
---
 ggml/src/ggml-cuda/ggml-cuda.cu | 11 ++++++++++
 ggml/src/ggml-cuda/set.cu       | 39 +++++++++++++++++++++++++++++++++
 ggml/src/ggml-cuda/set.cuh      |  7 ++++++
 3 files changed, 57 insertions(+)
 create mode 100644 ggml/src/ggml-cuda/set.cu
 create mode 100644 ggml/src/ggml-cuda/set.cuh

diff --git a/ggml/src/ggml-cuda/ggml-cuda.cu b/ggml/src/ggml-cuda/ggml-cuda.cu
index 94ab1ec0f5a..be505748af5 100644
--- a/ggml/src/ggml-cuda/ggml-cuda.cu
+++ b/ggml/src/ggml-cuda/ggml-cuda.cu
@@ -50,6 +50,7 @@
 #include "ggml-cuda/upscale.cuh"
 #include "ggml-cuda/wkv.cuh"
 #include "ggml-cuda/gla.cuh"
+#include "ggml-cuda/set.cuh"
 #include "ggml-cuda/set-rows.cuh"
 #include "ggml-cuda/pad_reflect_1d.cuh"
 #include "ggml.h"
@@ -2416,6 +2417,9 @@ static bool ggml_cuda_compute_forward(ggml_backend_cuda_context & ctx, struct gg
         case GGML_OP_SET_ROWS:
             ggml_cuda_op_set_rows(ctx, dst);
             break;
+        case GGML_OP_SET:
+            ggml_cuda_op_set(ctx, dst);
+            break;
         case GGML_OP_DUP:
             ggml_cuda_dup(ctx, dst);
             break;
@@ -3842,6 +3846,13 @@ static bool ggml_backend_cuda_device_supports_op(ggml_backend_dev_t dev, const g
                        op->src[0]->type == GGML_TYPE_F32 &&
                        (op->src[1]->type == GGML_TYPE_I64 || op->src[1]->type == GGML_TYPE_I32);
             } break;
+        case GGML_OP_SET:
+            {
+                const ggml_type t = op->type;
+                return (t == GGML_TYPE_F32 || t == GGML_TYPE_I32) &&
+                    t == op->src[0]->type &&
+                    t == op->src[1]->type;
+            } break;
         case GGML_OP_CPY:
             {
                 ggml_type src0_type = op->src[0]->type;
diff --git a/ggml/src/ggml-cuda/set.cu b/ggml/src/ggml-cuda/set.cu
new file mode 100644
index 00000000000..04bfe07ba03
--- /dev/null
+++ b/ggml/src/ggml-cuda/set.cu
@@ -0,0 +1,39 @@
+#include "set.cuh"
+#include "cpy.cuh"
+
+void ggml_cuda_op_set(ggml_backend_cuda_context & ctx, ggml_tensor * dst) {
+    const ggml_tensor * src0 = dst->src[0];
+    const ggml_tensor * src1 = dst->src[1];
+
+    GGML_ASSERT((src0->type == GGML_TYPE_F32 || src0->type == GGML_TYPE_I32));
+    GGML_ASSERT(src1->type == src0->type);
+    GGML_ASSERT(dst ->type == src0->type);
+
+    GGML_ASSERT(ggml_is_contiguous(dst));
+    GGML_ASSERT(ggml_is_contiguous(src0));
+    GGML_ASSERT(ggml_is_contiguous(src1));
+
+    const size_t nb1    = ((int32_t *) dst->op_params)[0];
+    const size_t nb2    = ((int32_t *) dst->op_params)[1];
+    const size_t nb3    = ((int32_t *) dst->op_params)[2];
+    const size_t offset = ((int32_t *) dst->op_params)[3];
+    const bool   inplace= (bool)     ((int32_t *) dst->op_params)[4];
+
+    if (!inplace) {
+        ggml_cuda_cpy(ctx, src0, dst);
+    }
+
+    ggml_tensor dst_view = *dst;
+    dst_view.data  = (void *)((char *)dst->data + offset);
+    dst_view.ne[0] = src1->ne[0];
+    dst_view.ne[1] = src1->ne[1];
+    dst_view.ne[2] = src1->ne[2];
+    dst_view.ne[3] = src1->ne[3];
+
+    dst_view.nb[0] = ggml_element_size(dst);
+    dst_view.nb[1] = nb1;
+    dst_view.nb[2] = nb2;
+    dst_view.nb[3] = nb3;
+
+    ggml_cuda_cpy(ctx, src1, &dst_view);
+}
diff --git a/ggml/src/ggml-cuda/set.cuh b/ggml/src/ggml-cuda/set.cuh
new file mode 100644
index 00000000000..dd09529f3e4
--- /dev/null
+++ b/ggml/src/ggml-cuda/set.cuh
@@ -0,0 +1,7 @@
+#pragma once
+
+#include "common.cuh"
+
+#define CUDA_SET_BLOCK_SIZE 256
+
+void ggml_cuda_op_set(ggml_backend_cuda_context & ctx, ggml_tensor * dst);

From 338074c383c81366320d176d83b94b0a567ee0c2 Mon Sep 17 00:00:00 2001
From: YaelLogic <y0548591250@gmail.com>
Date: Wed, 29 Oct 2025 08:14:39 +0200
Subject: [PATCH 004/185] sycl: add RMS_NORM_BACK operation support (#16808)

* sycl: add RMS_NORM_BACK operation support

* sycl: rms_norm_back: add dual reduction paths (FP64 and FP32) and savepoint before further changes

* sycl: add RMS_NORM_BACK support

Implement RMS_NORM_BACK for the SYCL backend using FP32 compensated parallel reduction. Minimal docs updates (ops.md / SYCL.csv).

* revert: restore .gitignore and tools/run/CMakeLists.txt to upstream

* revert: restore tests/CMakeLists.txt to upstream

* sycl: optimize rms_norm_back

* fix: restore SYCL.csv to correct state with RMS_NORM_BACK support

* Update ggml/src/ggml-sycl/norm.cpp

Co-authored-by: Neo Zhang Jianyu <jianyu.zhang@intel.com>

* fix: remove trailing whitespace and add missing newline (EditorConfig)

---------

Co-authored-by: Neo Zhang Jianyu <jianyu.zhang@intel.com>
---
 docs/ops.md                      |   2 +-
 docs/ops/SYCL.csv                |   8 +-
 ggml/src/ggml-sycl/ggml-sycl.cpp |  11 +++
 ggml/src/ggml-sycl/norm.cpp      | 156 +++++++++++++++++++++++++++++++
 ggml/src/ggml-sycl/norm.hpp      |   2 +
 5 files changed, 174 insertions(+), 5 deletions(-)

diff --git a/docs/ops.md b/docs/ops.md
index dfd1cfab6a8..3738a480728 100644
--- a/docs/ops.md
+++ b/docs/ops.md
@@ -79,7 +79,7 @@ Legend:
 |                           REPEAT | ❌ | ✅ | ✅ | 🟡 | ✅ | 🟡 | ✅ | 🟡 | ❌ |
 |                      REPEAT_BACK | ❌ | ❌ | ✅ | ✅ | ❌ | ❌ | ❌ | ✅ | ❌ |
 |                         RMS_NORM | ❌ | ✅ | ✅ | ✅ | 🟡 | ✅ | ✅ | ✅ | ❌ |
-|                    RMS_NORM_BACK | ❌ | ❌ | ✅ | ✅ | ❌ | ❌ | ❌ | ✅ | ❌ |
+|                    RMS_NORM_BACK | ❌ | ❌ | ✅ | ✅ | ❌ | ❌ | ✅ | ✅ | ❌ |
 |                 RMS_NORM_MUL_ADD | ❌ | ✅ | ✅ | ✅ | ✅ | ✅ | ✅ | ✅ | ❌ |
 |                             ROLL | ❌ | ❌ | ✅ | ❌ | ❌ | ❌ | ❌ | ✅ | ❌ |
 |                             ROPE | ❌ | 🟡 | ✅ | ✅ | ✅ | ✅ | ✅ | ✅ | ❌ |
diff --git a/docs/ops/SYCL.csv b/docs/ops/SYCL.csv
index fe6876357f3..101e80f64c6 100644
--- a/docs/ops/SYCL.csv
+++ b/docs/ops/SYCL.csv
@@ -5637,25 +5637,25 @@
 "SYCL0","RMS_NORM","type=f32,ne=[64,5,4,3],v=0,eps=0.000000,inplace=0","support","1","yes","SYCL"
 "SYCL0","NORM","type=f32,ne=[64,5,4,3],v=1,eps=0.000000","support","1","yes","SYCL"
 "SYCL0","RMS_NORM","type=f32,ne=[64,5,4,3],v=1,eps=0.000000,inplace=0","support","1","yes","SYCL"
-"SYCL0","RMS_NORM_BACK","type=f32,ne=[64,5,4,3],eps=0.000000","support","0","no","SYCL"
+"SYCL0","RMS_NORM_BACK","type=f32,ne=[64,5,4,3],eps=0.000000","support","1","yes","SYCL"
 "SYCL0","L2_NORM","type=f32,ne=[64,5,4,3]","support","1","yes","SYCL"
 "SYCL0","NORM","type=f32,ne=[64,5,4,3],v=0,eps=0.000001","support","1","yes","SYCL"
 "SYCL0","RMS_NORM","type=f32,ne=[64,5,4,3],v=0,eps=0.000001,inplace=0","support","1","yes","SYCL"
 "SYCL0","NORM","type=f32,ne=[64,5,4,3],v=1,eps=0.000001","support","1","yes","SYCL"
 "SYCL0","RMS_NORM","type=f32,ne=[64,5,4,3],v=1,eps=0.000001,inplace=0","support","1","yes","SYCL"
-"SYCL0","RMS_NORM_BACK","type=f32,ne=[64,5,4,3],eps=0.000001","support","0","no","SYCL"
+"SYCL0","RMS_NORM_BACK","type=f32,ne=[64,5,4,3],eps=0.000001","support","1","yes","SYCL"
 "SYCL0","L2_NORM","type=f32,ne=[64,5,4,3]","support","1","yes","SYCL"
 "SYCL0","NORM","type=f32,ne=[64,5,4,3],v=0,eps=0.000100","support","1","yes","SYCL"
 "SYCL0","RMS_NORM","type=f32,ne=[64,5,4,3],v=0,eps=0.000100,inplace=0","support","1","yes","SYCL"
 "SYCL0","NORM","type=f32,ne=[64,5,4,3],v=1,eps=0.000100","support","1","yes","SYCL"
 "SYCL0","RMS_NORM","type=f32,ne=[64,5,4,3],v=1,eps=0.000100,inplace=0","support","1","yes","SYCL"
-"SYCL0","RMS_NORM_BACK","type=f32,ne=[64,5,4,3],eps=0.000100","support","0","no","SYCL"
+"SYCL0","RMS_NORM_BACK","type=f32,ne=[64,5,4,3],eps=0.000100","support","1","yes","SYCL"
 "SYCL0","L2_NORM","type=f32,ne=[64,5,4,3]","support","1","yes","SYCL"
 "SYCL0","NORM","type=f32,ne=[64,5,4,3],v=0,eps=0.100000","support","1","yes","SYCL"
 "SYCL0","RMS_NORM","type=f32,ne=[64,5,4,3],v=0,eps=0.100000,inplace=0","support","1","yes","SYCL"
 "SYCL0","NORM","type=f32,ne=[64,5,4,3],v=1,eps=0.100000","support","1","yes","SYCL"
 "SYCL0","RMS_NORM","type=f32,ne=[64,5,4,3],v=1,eps=0.100000,inplace=0","support","1","yes","SYCL"
-"SYCL0","RMS_NORM_BACK","type=f32,ne=[64,5,4,3],eps=0.100000","support","0","no","SYCL"
+"SYCL0","RMS_NORM_BACK","type=f32,ne=[64,5,4,3],eps=0.100000","support","1","yes","SYCL"
 "SYCL0","L2_NORM","type=f32,ne=[64,5,4,3]","support","1","yes","SYCL"
 "SYCL0","RMS_NORM","type=f32,ne=[64,5,4,3],v=0,eps=0.000001,inplace=1","support","1","yes","SYCL"
 "SYCL0","RMS_NORM_MUL_ADD","type=f32,ne=[64,5,4,3],eps=0.000000,broadcast=0,multi_add=0","support","1","yes","SYCL"
diff --git a/ggml/src/ggml-sycl/ggml-sycl.cpp b/ggml/src/ggml-sycl/ggml-sycl.cpp
index 328d1a71b75..c97c5899435 100644
--- a/ggml/src/ggml-sycl/ggml-sycl.cpp
+++ b/ggml/src/ggml-sycl/ggml-sycl.cpp
@@ -42,6 +42,7 @@
 #include "ggml-sycl/backend.hpp"
 #include "ggml-sycl/common.hpp"
 #include "ggml-sycl/element_wise.hpp"
+#include "ggml-sycl/norm.hpp"
 #include "ggml-sycl/presets.hpp"
 #include "ggml-sycl/gemm.hpp"
 #include "ggml-sycl/set_rows.hpp"
@@ -2637,6 +2638,11 @@ static void ggml_sycl_rms_norm(ggml_backend_sycl_context & ctx, ggml_tensor * ds
     ggml_sycl_op_rms_norm(ctx, dst);
 }
 
+static void ggml_sycl_rms_norm_back(ggml_backend_sycl_context & ctx, ggml_tensor * dst) {
+    scope_op_debug_print scope_dbg_print(__func__, dst, /*num_src=*/2);
+    ggml_sycl_op_rms_norm_back(ctx, dst);
+}
+
 static void ggml_sycl_l2_norm(ggml_backend_sycl_context & ctx, ggml_tensor * dst) {
     scope_op_debug_print scope_dbg_print(__func__, dst, /*num_src=*/1);
     ggml_sycl_op_l2_norm(ctx, dst);
@@ -3827,6 +3833,9 @@ static bool ggml_sycl_compute_forward(ggml_backend_sycl_context & ctx, struct gg
         case GGML_OP_LEAKY_RELU:
             ggml_sycl_leaky_relu(ctx, dst);
             break;
+        case GGML_OP_RMS_NORM_BACK:
+            ggml_sycl_rms_norm_back(ctx, dst);
+            break;
         case GGML_OP_RMS_NORM:
             ggml_sycl_rms_norm(ctx, dst);
             break;
@@ -4571,6 +4580,8 @@ static bool ggml_backend_sycl_device_supports_op(ggml_backend_dev_t dev, const g
             return ggml_is_contiguous(op->src[0]);
         case GGML_OP_RMS_NORM:
             return ((op->src[0]->ne[0] % WARP_SIZE) == 0);
+        case GGML_OP_RMS_NORM_BACK:
+            return ((op->src[0]->ne[0] % WARP_SIZE) == 0);
         case GGML_OP_SCALE:
             return true;
         case GGML_OP_CONT:
diff --git a/ggml/src/ggml-sycl/norm.cpp b/ggml/src/ggml-sycl/norm.cpp
index 4ec1416849c..823d3a4828c 100644
--- a/ggml/src/ggml-sycl/norm.cpp
+++ b/ggml/src/ggml-sycl/norm.cpp
@@ -480,6 +480,162 @@ void ggml_sycl_op_rms_norm(ggml_backend_sycl_context & ctx, ggml_tensor * dst) {
     rms_norm_f32_sycl(src0_dd, dst_dd, ne00, ne01, ne02, ne03, s01, s02, s03, eps, main_stream, ctx.device);
 }
 
+void ggml_sycl_op_rms_norm_back(ggml_backend_sycl_context & ctx, ggml_tensor * dst) {
+    scope_op_debug_print scope_dbg_print(__func__, dst, /*num_src=*/2);
+
+    GGML_ASSERT(dst->src[0]->type == GGML_TYPE_F32); // dz
+    GGML_ASSERT(dst->src[1]->type == GGML_TYPE_F32); // x
+    GGML_ASSERT(dst->type         == GGML_TYPE_F32);
+
+    float eps = 1e-5f;
+    std::memcpy(&eps, dst->op_params, sizeof(float));
+    if (!(eps > 0.0f) || !std::isfinite(eps)) eps = 1e-5f;
+
+    const float * g_base  = static_cast<const float *>(dst->src[0]->data); // dz
+    const float * x_base  = static_cast<const float *>(dst->src[1]->data); // x
+          float * dx_base = static_cast<      float *>(dst->data);
+
+    const int64_t D  = dst->ne[0];
+    const int64_t n1 = dst->ne[1], n2 = dst->ne[2], n3 = dst->ne[3]; (void) n3;
+    const int64_t N  = ggml_nrows(dst);
+    if (D == 0 || N == 0) return;
+
+    const ggml_tensor *G = dst->src[0];
+    const ggml_tensor *X = dst->src[1];
+    const int ts = (int) ggml_type_size(X->type);
+    GGML_ASSERT((size_t) X->nb[0]   == (size_t) ts);
+    GGML_ASSERT((size_t) G->nb[0]   == (size_t) ts);
+    GGML_ASSERT((size_t) dst->nb[0] == (size_t) ts);
+
+    const int64_t xs1 = X->nb[1] / ts, xs2 = X->nb[2] / ts, xs3 = X->nb[3] / ts;
+    const int64_t gs1 = G->nb[1] / ts, gs2 = G->nb[2] / ts, gs3 = G->nb[3] / ts;
+    const int64_t ds1 = dst->nb[1] / ts, ds2 = dst->nb[2] / ts, ds3 = dst->nb[3] / ts;
+
+    dpct::queue_ptr q = ctx.stream();
+
+    // work-group size: multiple of WARP_SIZE, capped by device and 256, and not larger than D
+    const int device_max_wg = ggml_sycl_info().max_work_group_sizes[ctx.device];
+    auto roundup = [](int v, int m) { return ((v + m - 1) / m) * m; };
+    int wg_cap = 256;
+    if (device_max_wg > 0) wg_cap = std::min(wg_cap, device_max_wg);
+    int WG = std::max(WARP_SIZE, std::min(roundup((int)std::min<int64_t>(D, wg_cap), WARP_SIZE), wg_cap));
+
+    // FP32 path: per-thread compensated accumulation + hierarchical reduction
+    q->submit([&](sycl::handler &cgh) {
+        const int nwarps_loc = std::max(1, WG / WARP_SIZE);
+        // store one partial value per warp (xx and xg) for cross-warp reduction
+        auto l_xx   = sycl::local_accessor<sycl::float2, 1>(sycl::range<1>(nwarps_loc), cgh);
+        auto l_xg   = sycl::local_accessor<sycl::float2, 1>(sycl::range<1>(nwarps_loc), cgh);
+
+        cgh.parallel_for(
+            sycl::nd_range<3>(sycl::range<3>(1, 1, N) * sycl::range<3>(1, 1, WG),
+                              sycl::range<3>(1, 1, WG)),
+            [=](sycl::nd_item<3> item_ct1) [[sycl::reqd_sub_group_size(WARP_SIZE)]] {
+                const int row = item_ct1.get_group(2);
+                const int tid = item_ct1.get_local_id(2);
+
+                const int64_t i1 = row % n1;
+                const int64_t i2 = (row / n1) % n2;
+                const int64_t i3 = row / (n1 * n2);
+
+                const float *__restrict x_row = x_base + i3 * xs3 + i2 * xs2 + i1 * xs1;
+                const float *__restrict g_row = g_base + i3 * gs3 + i2 * gs2 + i1 * gs1;
+                float *__restrict d_row       = dx_base + i3 * ds3 + i2 * ds2 + i1 * ds1;
+
+                // per-thread accumulation (compensated by default)
+                float sum_xx = 0.f, sum_xg = 0.f;
+#ifndef GGML_SYCL_RMS_BACK_FAST
+                float c_xx = 0.f, c_xg = 0.f;
+#endif
+                for (int64_t col = tid; col < D; col += WG) {
+                    const float xv = x_row[col];
+                    const float gv = g_row[col];
+#ifdef GGML_SYCL_RMS_BACK_FAST
+                    sum_xx += xv * xv;
+                    sum_xg += xv * gv;
+#else
+                    float y1 = xv * xv - c_xx;
+                    float t1 = sum_xx + y1;
+                    c_xx = (t1 - sum_xx) - y1;
+                    sum_xx = t1;
+
+                    float y2 = xv * gv - c_xg;
+                    float t2 = sum_xg + y2;
+                    c_xg = (t2 - sum_xg) - y2;
+                    sum_xg = t2;
+#endif
+                }
+
+                // warp-level reduction
+                sycl::float2 xx = sycl::float2(sum_xx,
+#ifndef GGML_SYCL_RMS_BACK_FAST
+                    c_xx
+#else
+                    0.f
+#endif
+                );
+                sycl::float2 xg = sycl::float2(sum_xg,
+#ifndef GGML_SYCL_RMS_BACK_FAST
+                    c_xg
+#else
+                    0.f
+#endif
+                );
+                xx = warp_reduce_sum(xx, item_ct1);
+                xg = warp_reduce_sum(xg, item_ct1);
+
+                // cross-warp reduction using local memory (single barrier)
+                const auto sub_group = item_ct1.get_sub_group();
+                const auto sg_id     = sub_group.get_group_linear_id();
+                const auto wi_in_sg  = sub_group.get_local_linear_id();
+                const int nthreads   = item_ct1.get_local_range(2);
+                const int nwarps     = nthreads / WARP_SIZE;
+
+                sycl::float2 xx_total = xx;
+                sycl::float2 xg_total = xg;
+                if (nwarps > 1) {
+                    if (wi_in_sg == 0) {
+                        l_xx[sg_id] = xx;
+                        l_xg[sg_id] = xg;
+                    }
+                    item_ct1.barrier(sycl::access::fence_space::local_space);
+
+                    if (sg_id == 0) {
+                        const unsigned wi_u = wi_in_sg;
+                        sycl::float2 xx_first = (wi_u < static_cast<unsigned>(nwarps)) ? l_xx[wi_u] : sycl::float2(0.f, 0.f);
+                        sycl::float2 xg_first = (wi_u < static_cast<unsigned>(nwarps)) ? l_xg[wi_u] : sycl::float2(0.f, 0.f);
+                        xx_total = warp_reduce_sum(xx_first, item_ct1);
+                        xg_total = warp_reduce_sum(xg_first, item_ct1);
+                    } else {
+                        // other subgroups keep their local totals; they'll be ignored
+                        xx_total = xx;
+                        xg_total = xg;
+                    }
+                    // ensure all threads see the first-subgroup result via broadcast below
+                }
+
+                // compute inv_r and coeff once per row and broadcast to the whole work-group
+                float inv_r = 0.f;
+                float coeff = 0.f;
+                if (tid == 0) {
+                    const float sum_xx_f  = xx_total.x() + xx_total.y();
+                    const float sum_xdz_f = xg_total.x() + xg_total.y();
+                    const float mean_eps  = sum_xx_f / (float) D + eps;
+                    const float sum_eps   = sum_xx_f + eps * (float) D;
+                    inv_r = sycl::rsqrt(mean_eps);
+                    coeff = -sum_xdz_f / sum_eps;
+                }
+                inv_r = sycl::group_broadcast(item_ct1.get_group(), inv_r);
+                coeff = sycl::group_broadcast(item_ct1.get_group(), coeff);
+
+                for (int64_t col = tid; col < D; col += WG) {
+                    d_row[col] = (g_row[col] + coeff * x_row[col]) * inv_r;
+                }
+            });
+    });
+
+}
+
 void ggml_sycl_op_l2_norm(ggml_backend_sycl_context& ctx, ggml_tensor* dst) {
 
     GGML_ASSERT(dst->src[0]->type == GGML_TYPE_F32);
diff --git a/ggml/src/ggml-sycl/norm.hpp b/ggml/src/ggml-sycl/norm.hpp
index 612cd67cf91..8cb885eb2ee 100644
--- a/ggml/src/ggml-sycl/norm.hpp
+++ b/ggml/src/ggml-sycl/norm.hpp
@@ -19,6 +19,8 @@ void ggml_sycl_op_norm(ggml_backend_sycl_context& ctx, ggml_tensor* dst);
 
 void ggml_sycl_op_rms_norm(ggml_backend_sycl_context& ctx, ggml_tensor* dst);
 
+void ggml_sycl_op_rms_norm_back(ggml_backend_sycl_context& ctx, ggml_tensor* dst);
+
 void ggml_sycl_op_group_norm(ggml_backend_sycl_context& ctx, ggml_tensor* dst);
 
 void ggml_sycl_op_l2_norm(ggml_backend_sycl_context& ctx, ggml_tensor* dst);

From 9a3ea685b937c0f0cbfda2e50004ea54bf187512 Mon Sep 17 00:00:00 2001
From: Aman Gupta <amangupta052@gmail.com>
Date: Wed, 29 Oct 2025 15:55:06 +0800
Subject: [PATCH 005/185] CUDA: Fix bug in topk-moe for gpt-oss (#16821)

* CUDA: Fix bug in topk-moe for gpt-oss

When using ggml_can_fuse_subgraph, the output nodes which are passed are wrong. This causes `test-backend-ops` to still fuse ndoes (because the nodes are not used elsewhere in the graph),
but it actually doesn't fuse in the actual gpt-oss

* fix for qwen3 too

* change ifndef to ifdef
---
 ggml/src/ggml-cuda/ggml-cuda.cu | 15 +++++++++++++--
 1 file changed, 13 insertions(+), 2 deletions(-)

diff --git a/ggml/src/ggml-cuda/ggml-cuda.cu b/ggml/src/ggml-cuda/ggml-cuda.cu
index be505748af5..fcff5d7cdc1 100644
--- a/ggml/src/ggml-cuda/ggml-cuda.cu
+++ b/ggml/src/ggml-cuda/ggml-cuda.cu
@@ -2978,7 +2978,7 @@ static bool ggml_cuda_can_fuse(const struct ggml_cgraph * cgraph, int node_idx,
         ggml_cuda_topk_moe_ops(/*with_norm=*/false, /*delayed_softmax=*/true);
 
     if (ops.size() == topk_moe_ops_with_norm.size() &&
-        ggml_can_fuse_subgraph(cgraph, node_idx, ops, { node_idx + 3, node_idx + 8 })) {
+        ggml_can_fuse_subgraph(cgraph, node_idx, ops, { node_idx + 3, node_idx + 9 })) {
         ggml_tensor * softmax = cgraph->nodes[node_idx];
         ggml_tensor * weights = cgraph->nodes[node_idx + 9];
 
@@ -2997,7 +2997,7 @@ static bool ggml_cuda_can_fuse(const struct ggml_cgraph * cgraph, int node_idx,
     }
 
     if (ops.size() == topk_moe_ops_delayed_softmax.size() &&
-        ggml_can_fuse_subgraph(cgraph, node_idx, ops, { node_idx + 2, node_idx + 5 })) {
+        ggml_can_fuse_subgraph(cgraph, node_idx, ops, { node_idx + 1, node_idx + 5 })) {
         ggml_tensor * softmax = cgraph->nodes[node_idx + 4];
         ggml_tensor * weights = cgraph->nodes[node_idx + 5];
 
@@ -3118,9 +3118,20 @@ static void evaluate_and_capture_cuda_graph(ggml_backend_cuda_context * cuda_ctx
         // With the use of CUDA graphs, the execution will be performed by the graph launch.
         if (!use_cuda_graph || cuda_graph_update_required) {
 
+            [[maybe_unused]] int prev_i = 0;
+
             for (int i = 0; i < cgraph->n_nodes; i++) {
                 ggml_tensor * node = cgraph->nodes[i];
 
+
+#ifdef GGML_CUDA_DEBUG
+                const int nodes_fused = i - prev_i - 1;
+                prev_i = i;
+                if (nodes_fused > 0) {
+                    GGML_LOG_INFO("nodes_fused: %d\n", nodes_fused);
+                }
+#endif
+
                 if (ggml_is_empty(node) || node->op == GGML_OP_RESHAPE || node->op == GGML_OP_TRANSPOSE || node->op == GGML_OP_VIEW || node->op == GGML_OP_PERMUTE || node->op == GGML_OP_NONE) {
                     continue;
                 }

From f549b0007dbdd683215820f7229ce180a12b191d Mon Sep 17 00:00:00 2001
From: Jeff Bolz <jbolz@nvidia.com>
Date: Wed, 29 Oct 2025 03:53:04 -0500
Subject: [PATCH 006/185] vulkan: Call ggml_vk_buffer_write_2d from
 ggml_vk_buffer_copy (#16793)

This lets the copy to the destination device use the host-visible
vidmem optimization.
---
 ggml/src/ggml-vulkan/ggml-vulkan.cpp | 5 +----
 1 file changed, 1 insertion(+), 4 deletions(-)

diff --git a/ggml/src/ggml-vulkan/ggml-vulkan.cpp b/ggml/src/ggml-vulkan/ggml-vulkan.cpp
index 173677a2637..5caf37d4030 100644
--- a/ggml/src/ggml-vulkan/ggml-vulkan.cpp
+++ b/ggml/src/ggml-vulkan/ggml-vulkan.cpp
@@ -5652,14 +5652,11 @@ static void ggml_vk_buffer_copy(vk_buffer& dst, size_t dst_offset, vk_buffer& sr
         VK_LOG_DEBUG("ggml_vk_buffer_copy(MULTI_DEVICE, " << size << ")");
         // Copy device to device
         ggml_vk_ensure_sync_staging_buffer(src->device, size);
-        ggml_vk_ensure_sync_staging_buffer(dst->device, size);
 
         // Copy to src staging buffer
         ggml_vk_buffer_copy(src->device->sync_staging, 0, src, src_offset, size);
-        // memcpy to dst staging buffer
-        memcpy(dst->device->sync_staging->ptr, src->device->sync_staging->ptr, size);
         // Copy to dst buffer
-        ggml_vk_buffer_copy(dst, dst_offset, dst->device->sync_staging, 0, size);
+        ggml_vk_buffer_write_2d(dst, dst_offset, src->device->sync_staging->ptr, 0, size, 1);
     }
 }
 

From 144a4ce824b6bd0e48d62009d10cae1daf5308db Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sigbj=C3=B8rn=20Skj=C3=A6ret?= <sigbjorn.skjaeret@scala.com>
Date: Wed, 29 Oct 2025 14:09:50 +0100
Subject: [PATCH 007/185] vendor : sync minja (#16500)

* sync minja.hpp

Adds Call/EndCall support, used in MiniCPM3 and MiniCPM4-MCP.

* remove spurious semicolon

* sync from ochafik/minja
---
 vendor/minja/minja.hpp | 111 +++++++++++++++++++++++++++++++++++------
 1 file changed, 96 insertions(+), 15 deletions(-)

diff --git a/vendor/minja/minja.hpp b/vendor/minja/minja.hpp
index dad75efbba5..57b138add6a 100644
--- a/vendor/minja/minja.hpp
+++ b/vendor/minja/minja.hpp
@@ -55,7 +55,7 @@ inline std::string normalize_newlines(const std::string & s) {
 }
 
 /* Values that behave roughly like in Python. */
-class Value : public std::enable_shared_from_this<Value> {
+class Value {
 public:
   using CallableType = std::function<Value(const std::shared_ptr<Context> &, ArgumentsValue &)>;
   using FilterType = std::function<Value(const std::shared_ptr<Context> &, ArgumentsValue &)>;
@@ -158,12 +158,14 @@ class Value : public std::enable_shared_from_this<Value> {
   Value(const json & v) {
     if (v.is_object()) {
       auto object = std::make_shared<ObjectType>();
+      object->reserve(v.size());
       for (auto it = v.begin(); it != v.end(); ++it) {
-        (*object)[it.key()] = it.value();
+        object->emplace_back(it.key(), Value(it.value()));
       }
       object_ = std::move(object);
     } else if (v.is_array()) {
       auto array = std::make_shared<ArrayType>();
+      array->reserve(v.size());
       for (const auto& item : v) {
         array->push_back(Value(item));
       }
@@ -610,7 +612,7 @@ static std::string error_location_suffix(const std::string & source, size_t pos)
   return out.str();
 }
 
-class Context : public std::enable_shared_from_this<Context> {
+class Context {
   protected:
     Value values_;
     std::shared_ptr<Context> parent_;
@@ -706,7 +708,7 @@ enum SpaceHandling { Keep, Strip, StripSpaces, StripNewline };
 
 class TemplateToken {
 public:
-    enum class Type { Text, Expression, If, Else, Elif, EndIf, For, EndFor, Generation, EndGeneration, Set, EndSet, Comment, Macro, EndMacro, Filter, EndFilter, Break, Continue };
+    enum class Type { Text, Expression, If, Else, Elif, EndIf, For, EndFor, Generation, EndGeneration, Set, EndSet, Comment, Macro, EndMacro, Filter, EndFilter, Break, Continue, Call, EndCall };
 
     static std::string typeToString(Type t) {
         switch (t) {
@@ -729,6 +731,8 @@ class TemplateToken {
             case Type::EndGeneration: return "endgeneration";
             case Type::Break: return "break";
             case Type::Continue: return "continue";
+            case Type::Call: return "call";
+            case Type::EndCall: return "endcall";
         }
         return "Unknown";
     }
@@ -846,6 +850,17 @@ struct LoopControlTemplateToken : public TemplateToken {
     LoopControlTemplateToken(const Location & loc, SpaceHandling pre, SpaceHandling post, LoopControlType control_type) : TemplateToken(Type::Break, loc, pre, post), control_type(control_type) {}
 };
 
+struct CallTemplateToken : public TemplateToken {
+    std::shared_ptr<Expression> expr;
+    CallTemplateToken(const Location & loc, SpaceHandling pre, SpaceHandling post, std::shared_ptr<Expression> && e)
+        : TemplateToken(Type::Call, loc, pre, post), expr(std::move(e)) {}
+};
+
+struct EndCallTemplateToken : public TemplateToken {
+    EndCallTemplateToken(const Location & loc, SpaceHandling pre, SpaceHandling post)
+        : TemplateToken(Type::EndCall, loc, pre, post) {}
+};
+
 class TemplateNode {
     Location location_;
 protected:
@@ -1047,36 +1062,48 @@ class MacroNode : public TemplateNode {
           }
         }
     }
-    void do_render(std::ostringstream &, const std::shared_ptr<Context> & macro_context) const override {
+    void do_render(std::ostringstream &, const std::shared_ptr<Context> & context) const override {
         if (!name) throw std::runtime_error("MacroNode.name is null");
         if (!body) throw std::runtime_error("MacroNode.body is null");
-        auto callable = Value::callable([&](const std::shared_ptr<Context> & context, ArgumentsValue & args) {
-            auto call_context = macro_context;
+
+        // Use init-capture to avoid dangling 'this' pointer and circular references
+        auto callable = Value::callable([weak_context = std::weak_ptr<Context>(context),
+                                         name = name, params = params, body = body,
+                                         named_param_positions = named_param_positions]
+                                        (const std::shared_ptr<Context> & call_context, ArgumentsValue & args) {
+            auto context_locked = weak_context.lock();
+            if (!context_locked) throw std::runtime_error("Macro context no longer valid");
+            auto execution_context = Context::make(Value::object(), context_locked);
+
+            if (call_context->contains("caller")) {
+                execution_context->set("caller", call_context->get("caller"));
+            }
+
             std::vector<bool> param_set(params.size(), false);
             for (size_t i = 0, n = args.args.size(); i < n; i++) {
                 auto & arg = args.args[i];
                 if (i >= params.size()) throw std::runtime_error("Too many positional arguments for macro " + name->get_name());
                 param_set[i] = true;
-                auto & param_name = params[i].first;
-                call_context->set(param_name, arg);
+                const auto & param_name = params[i].first;
+                execution_context->set(param_name, arg);
             }
             for (auto & [arg_name, value] : args.kwargs) {
                 auto it = named_param_positions.find(arg_name);
                 if (it == named_param_positions.end()) throw std::runtime_error("Unknown parameter name for macro " + name->get_name() + ": " + arg_name);
 
-                call_context->set(arg_name, value);
+                execution_context->set(arg_name, value);
                 param_set[it->second] = true;
             }
             // Set default values for parameters that were not passed
             for (size_t i = 0, n = params.size(); i < n; i++) {
                 if (!param_set[i] && params[i].second != nullptr) {
-                    auto val = params[i].second->evaluate(context);
-                    call_context->set(params[i].first, val);
+                    auto val = params[i].second->evaluate(call_context);
+                    execution_context->set(params[i].first, val);
                 }
             }
-            return body->render(call_context);
+            return body->render(execution_context);
         });
-        macro_context->set(name->get_name(), callable);
+        context->set(name->get_name(), callable);
     }
 };
 
@@ -1611,6 +1638,44 @@ class CallExpr : public Expression {
     }
 };
 
+class CallNode : public TemplateNode {
+    std::shared_ptr<Expression> expr;
+    std::shared_ptr<TemplateNode> body;
+
+public:
+    CallNode(const Location & loc, std::shared_ptr<Expression> && e, std::shared_ptr<TemplateNode> && b)
+        : TemplateNode(loc), expr(std::move(e)), body(std::move(b)) {}
+
+    void do_render(std::ostringstream & out, const std::shared_ptr<Context> & context) const override {
+        if (!expr) throw std::runtime_error("CallNode.expr is null");
+        if (!body) throw std::runtime_error("CallNode.body is null");
+
+        // Use init-capture to avoid dangling 'this' pointer and circular references
+        auto caller = Value::callable([weak_context = std::weak_ptr<Context>(context), body=body]
+                                      (const std::shared_ptr<Context> &, ArgumentsValue &) -> Value {
+            auto context_locked = weak_context.lock();
+            if (!context_locked) throw std::runtime_error("Caller context no longer valid");
+            return Value(body->render(context_locked));
+        });
+
+        context->set("caller", caller);
+
+        auto call_expr = dynamic_cast<CallExpr*>(expr.get());
+        if (!call_expr) {
+            throw std::runtime_error("Invalid call block syntax - expected function call");
+        }
+
+        Value function = call_expr->object->evaluate(context);
+        if (!function.is_callable()) {
+            throw std::runtime_error("Call target must be callable: " + function.dump());
+        }
+        ArgumentsValue args = call_expr->args.evaluate(context);
+
+        Value result = function.call(context, args);
+        out << result.to_str();
+    }
+};
+
 class FilterExpr : public Expression {
     std::vector<std::shared_ptr<Expression>> parts;
 public:
@@ -2320,7 +2385,7 @@ class Parser {
       static std::regex comment_tok(R"(\{#([-~]?)([\s\S]*?)([-~]?)#\})");
       static std::regex expr_open_regex(R"(\{\{([-~])?)");
       static std::regex block_open_regex(R"(^\{%([-~])?\s*)");
-      static std::regex block_keyword_tok(R"((if|else|elif|endif|for|endfor|generation|endgeneration|set|endset|block|endblock|macro|endmacro|filter|endfilter|break|continue)\b)");
+      static std::regex block_keyword_tok(R"((if|else|elif|endif|for|endfor|generation|endgeneration|set|endset|block|endblock|macro|endmacro|filter|endfilter|break|continue|call|endcall)\b)");
       static std::regex non_text_open_regex(R"(\{\{|\{%|\{#)");
       static std::regex expr_close_regex(R"(\s*([-~])?\}\})");
       static std::regex block_close_regex(R"(\s*([-~])?%\})");
@@ -2443,6 +2508,15 @@ class Parser {
             } else if (keyword == "endmacro") {
               auto post_space = parseBlockClose();
               tokens.push_back(std::make_unique<EndMacroTemplateToken>(location, pre_space, post_space));
+            } else if (keyword == "call") {
+              auto expr = parseExpression();
+              if (!expr) throw std::runtime_error("Expected expression in call block");
+
+              auto post_space = parseBlockClose();
+              tokens.push_back(std::make_unique<CallTemplateToken>(location, pre_space, post_space, std::move(expr)));
+            } else if (keyword == "endcall") {
+              auto post_space = parseBlockClose();
+              tokens.push_back(std::make_unique<EndCallTemplateToken>(location, pre_space, post_space));
             } else if (keyword == "filter") {
               auto filter = parseExpression();
               if (!filter) throw std::runtime_error("Expected expression in filter block");
@@ -2575,6 +2649,12 @@ class Parser {
                   throw unterminated(**start);
               }
               children.emplace_back(std::make_shared<MacroNode>(token->location, std::move(macro_token->name), std::move(macro_token->params), std::move(body)));
+          } else if (auto call_token = dynamic_cast<CallTemplateToken*>(token.get())) {
+            auto body = parseTemplate(begin, it, end);
+            if (it == end || (*(it++))->type != TemplateToken::Type::EndCall) {
+                throw unterminated(**start);
+            }
+            children.emplace_back(std::make_shared<CallNode>(token->location, std::move(call_token->expr), std::move(body)));
           } else if (auto filter_token = dynamic_cast<FilterTemplateToken*>(token.get())) {
               auto body = parseTemplate(begin, it, end);
               if (it == end || (*(it++))->type != TemplateToken::Type::EndFilter) {
@@ -2588,6 +2668,7 @@ class Parser {
           } else if (dynamic_cast<EndForTemplateToken*>(token.get())
                   || dynamic_cast<EndSetTemplateToken*>(token.get())
                   || dynamic_cast<EndMacroTemplateToken*>(token.get())
+                  || dynamic_cast<EndCallTemplateToken*>(token.get())
                   || dynamic_cast<EndFilterTemplateToken*>(token.get())
                   || dynamic_cast<EndIfTemplateToken*>(token.get())
                   || dynamic_cast<ElseTemplateToken*>(token.get())

From e41bcce8f0b53032a1fed275cd253e931c041cf6 Mon Sep 17 00:00:00 2001
From: Aman Gupta <amangupta052@gmail.com>
Date: Wed, 29 Oct 2025 21:11:53 +0800
Subject: [PATCH 008/185] CUDA: use fastdiv in set-rows (#16834)

* CUDA: use fastdiv in set-rows

* add assert about value fitting in u32
---
 ggml/src/ggml-cuda/common.cuh  |   7 +-
 ggml/src/ggml-cuda/set-rows.cu | 148 ++++++++++++++++++++++-----------
 2 files changed, 106 insertions(+), 49 deletions(-)

diff --git a/ggml/src/ggml-cuda/common.cuh b/ggml/src/ggml-cuda/common.cuh
index 1af23588301..6a472be7fbb 100644
--- a/ggml/src/ggml-cuda/common.cuh
+++ b/ggml/src/ggml-cuda/common.cuh
@@ -625,8 +625,11 @@ static __device__ __forceinline__ float ggml_cuda_e8m0_to_fp32(uint8_t x) {
 // and a shift:
 //
 // n/d = (mulhi(n, mp) + n) >> L;
-static const uint3 init_fastdiv_values(uint32_t d) {
-    GGML_ASSERT(d != 0);
+static const uint3 init_fastdiv_values(uint64_t d_64) {
+    GGML_ASSERT(d_64 != 0);
+    GGML_ASSERT(d_64 <= std::numeric_limits<uint32_t>::max());
+
+    uint32_t d = (uint32_t)d_64;
 
     // compute L = ceil(log2(d));
     uint32_t L = 0;
diff --git a/ggml/src/ggml-cuda/set-rows.cu b/ggml/src/ggml-cuda/set-rows.cu
index 1525a159527..631de7e8fa5 100644
--- a/ggml/src/ggml-cuda/set-rows.cu
+++ b/ggml/src/ggml-cuda/set-rows.cu
@@ -4,30 +4,53 @@
 typedef void (*set_rows_kernel_t)(const char * src, char * dst);
 
 // Generic quantized set_rows kernel template
-template<typename idx_t, typename block_type, int qk, void (*quantize_func)(const float*, block_type*)>
-static __global__ void k_set_rows_quant(
-        const float * __restrict__ src0, const idx_t * __restrict__ src1, block_type * __restrict__ dst,
-        const int64_t ne00, const int64_t ne01, const int64_t ne02, const int64_t ne03,
-        const int64_t ne10, const int64_t ne11, const int64_t ne12, const int64_t ne13,
-        const int64_t s01, const int64_t s02, const int64_t s03,
-        const int64_t s10, const int64_t s11, const int64_t s12,
-        const int64_t s1, const int64_t s2, const int64_t s3) {
-
+template <typename idx_t, typename block_type, int qk, void (*quantize_func)(const float *, block_type *)>
+static __global__ void k_set_rows_quant(const float * __restrict__ src0,
+                                        const idx_t * __restrict__ src1,
+                                        block_type * __restrict__ dst,
+                                        const int64_t ne_total,
+                                        const int64_t ne10,
+                                        const int64_t ne11,
+                                        const int64_t ne12,
+                                        const int64_t ne13,
+                                        const int64_t s01,
+                                        const int64_t s02,
+                                        const int64_t s03,
+                                        const int64_t s10,
+                                        const int64_t s11,
+                                        const int64_t s12,
+                                        const int64_t s1,
+                                        const int64_t s2,
+                                        const int64_t s3,
+                                        const uint3   ne00,
+                                        const uint3   ne01,
+                                        const uint3   ne02,
+                                        const uint3   ne11_fd,
+                                        const uint3   ne12_fd) {
     const int64_t i = int64_t(blockDim.x) * blockIdx.x + threadIdx.x;
-    const int64_t ne_total = (ne00 * ne01 * ne02 * ne03) / qk;
 
     if (i >= ne_total) {
         return;
     }
 
     const int64_t i_base = i * qk;
-    const int64_t i03 = i_base / (ne00 * ne01 * ne02);
-    const int64_t i02 = (i_base - i03 * ne00 * ne01 * ne02) / (ne00 * ne01);
-    const int64_t i01 = (i_base - i03 * ne00 * ne01 * ne02 - i02 * ne00 * ne01) / ne00;
-    const int64_t i00 = i_base - i03 * ne00 * ne01 * ne02 - i02 * ne00 * ne01 - i01 * ne00;
+    uint32_t      tmp    = (uint32_t) i_base;
+    uint2         div_mod;
+
+    div_mod           = fast_div_modulo(tmp, ne00);
+    const int64_t i00 = div_mod.y;
+    tmp               = div_mod.x;
 
-    const int64_t i12 = i03 % ne12;
-    const int64_t i11 = i02 % ne11;
+    div_mod           = fast_div_modulo(tmp, ne01);
+    const int64_t i01 = div_mod.y;
+    tmp               = div_mod.x;
+
+    div_mod           = fast_div_modulo(tmp, ne02);
+    const int64_t i02 = div_mod.y;
+    const int64_t i03 = div_mod.x;
+
+    const int64_t i12 = fastmodulo((uint32_t) i03, ne12_fd);
+    const int64_t i11 = fastmodulo((uint32_t) i02, ne11_fd);
     const int64_t i10 = i01;
 
     const int64_t dst_row = *(src1 + i10*s10 + i11*s11 + i12*s12);
@@ -41,6 +64,8 @@ static __global__ void k_set_rows_quant(
     quantize_func(src_block, dst_block);
 
     GGML_UNUSED(ne10);
+    GGML_UNUSED(ne11);
+    GGML_UNUSED(ne12);
     GGML_UNUSED(ne13);
 }
 
@@ -71,40 +96,65 @@ static void set_rows_cuda_quant(
     const int64_t s2  = nb2;
     const int64_t s3  = nb3;
 
-    if (ne_total > 0) {
+    if (ne_total > 0 && ne00 > 0 && ne01 > 0 && ne02 > 0 && ne11 > 0 && ne12 > 0) {
+        const uint3 ne00_fd = init_fastdiv_values((uint32_t) ne00);
+        const uint3 ne01_fd = init_fastdiv_values((uint32_t) ne01);
+        const uint3 ne02_fd = init_fastdiv_values((uint32_t) ne02);
+        const uint3 ne11_fd = init_fastdiv_values((uint32_t) ne11);
+        const uint3 ne12_fd = init_fastdiv_values((uint32_t) ne12);
+
         k_set_rows_quant<idx_t, block_type, qk, quantize_func><<<grid_size, block_size, 0, stream>>>(
-            src0_d, src1_d, dst_d,
-            ne00, ne01, ne02, ne03,
-            ne10, ne11, ne12, ne13,
-            s01, s02, s03,
-            s10, s11, s12,
-            s1, s2, s3);
+            src0_d, src1_d, dst_d, ne_total, ne10, ne11, ne12, ne13, s01, s02, s03, s10, s11, s12, s1, s2, s3, ne00_fd,
+            ne01_fd, ne02_fd, ne11_fd, ne12_fd);
     }
 }
 
-template<typename src_t, typename idx_t, typename dst_t>
-static __global__ void k_set_rows(
-        const src_t * __restrict__ src0, const idx_t * __restrict__ src1, dst_t * __restrict__ dst,
-        const int64_t ne00, const int64_t ne01, const int64_t ne02, const int64_t ne03,
-        const int64_t ne10, const int64_t ne11, const int64_t ne12, const int64_t ne13,
-        const int64_t s01, const int64_t s02, const int64_t s03,
-        const int64_t s10, const int64_t s11, const int64_t s12,
-        const int64_t s1, const int64_t s2, const int64_t s3) {
-
+template <typename src_t, typename idx_t, typename dst_t>
+static __global__ void k_set_rows(const src_t * __restrict__ src0,
+                                  const idx_t * __restrict__ src1,
+                                  dst_t * __restrict__ dst,
+                                  const int64_t ne_total,
+                                  const int64_t ne10,
+                                  const int64_t ne11,
+                                  const int64_t ne12,
+                                  const int64_t ne13,
+                                  const int64_t s01,
+                                  const int64_t s02,
+                                  const int64_t s03,
+                                  const int64_t s10,
+                                  const int64_t s11,
+                                  const int64_t s12,
+                                  const int64_t s1,
+                                  const int64_t s2,
+                                  const int64_t s3,
+                                  const uint3   ne00,
+                                  const uint3   ne01,
+                                  const uint3   ne02,
+                                  const uint3   ne11_fd,
+                                  const uint3   ne12_fd) {
     const int64_t i = int64_t(blockDim.x) * blockIdx.x + threadIdx.x;
-    const int64_t ne_total = ne00 * ne01 * ne02 * ne03;
 
     if (i >= ne_total) {
         return;
     }
 
-    const int64_t i03 = i / (ne00 * ne01 * ne02);
-    const int64_t i02 = (i - i03 * ne00 * ne01 * ne02) / (ne00 * ne01);
-    const int64_t i01 = (i - i03 * ne00 * ne01 * ne02 - i02 * ne00 * ne01) / ne00;
-    const int64_t i00 = i - i03 * ne00 * ne01 * ne02 - i02 * ne00 * ne01 - i01 * ne00;
+    uint32_t tmp = (uint32_t) i;
+    uint2    div_mod;
+
+    div_mod           = fast_div_modulo(tmp, ne00);
+    const int64_t i00 = div_mod.y;
+    tmp               = div_mod.x;
 
-    const int64_t i12 = i03 % ne12;
-    const int64_t i11 = i02 % ne11;
+    div_mod           = fast_div_modulo(tmp, ne01);
+    const int64_t i01 = div_mod.y;
+    tmp               = div_mod.x;
+
+    div_mod           = fast_div_modulo(tmp, ne02);
+    const int64_t i02 = div_mod.y;
+    const int64_t i03 = div_mod.x;
+
+    const int64_t i12 = fastmodulo((uint32_t) i03, ne12_fd);
+    const int64_t i11 = fastmodulo((uint32_t) i02, ne11_fd);
     const int64_t i10 = i01;
 
     const int64_t dst_row = *(src1 + i10*s10 + i11*s11 + i12*s12);
@@ -115,6 +165,8 @@ static __global__ void k_set_rows(
     dst_row_ptr[i00] = ggml_cuda_cast<dst_t>(src0_row[i00]);
 
     GGML_UNUSED(ne10);
+    GGML_UNUSED(ne11);
+    GGML_UNUSED(ne12);
     GGML_UNUSED(ne13);
 }
 
@@ -144,14 +196,16 @@ static void set_rows_cuda(
     const int64_t s2  = nb2/sizeof(dst_t);
     const int64_t s3  = nb3/sizeof(dst_t);
 
-    if (ne_total > 0) {
-        k_set_rows<<<grid_size, block_size, 0, stream>>>(
-            src0_d, src1_d, dst_d,
-            ne00, ne01, ne02, ne03,
-            ne10, ne11, ne12, ne13,
-            s01, s02, s03,
-            s10, s11, s12,
-            s1, s2, s3);
+    if (ne_total > 0 && ne00 > 0 && ne01 > 0 && ne02 > 0 && ne11 > 0 && ne12 > 0) {
+        const uint3 ne00_fd = init_fastdiv_values((uint32_t) ne00);
+        const uint3 ne01_fd = init_fastdiv_values((uint32_t) ne01);
+        const uint3 ne02_fd = init_fastdiv_values((uint32_t) ne02);
+        const uint3 ne11_fd = init_fastdiv_values((uint32_t) ne11);
+        const uint3 ne12_fd = init_fastdiv_values((uint32_t) ne12);
+
+        k_set_rows<<<grid_size, block_size, 0, stream>>>(src0_d, src1_d, dst_d, ne_total, ne10, ne11, ne12, ne13, s01,
+                                                         s02, s03, s10, s11, s12, s1, s2, s3, ne00_fd, ne01_fd, ne02_fd,
+                                                         ne11_fd, ne12_fd);
     }
 }
 

From 3eb2be1ca5f37480aeb16102970d9e65f43347fe Mon Sep 17 00:00:00 2001
From: Max Krasnyansky <maxk@qti.qualcomm.com>
Date: Wed, 29 Oct 2025 06:29:12 -0700
Subject: [PATCH 009/185] Hexagon Op queue & dispatch optimizations (#16820)

* hexagon: remove dspqueue callbacks and do all read processing inplace

* hexagon: there is no need to ref/deref the buffers at this point

We're not going to release the buffers without flushing the session queue.
So there is no need to inc/dec the refcounts for every request.
We also don't need to include those bufs in the response.

* hexagon: bump the thread count in the adb wrapper scripts

We can use more CPU cores now that the dedicated dspqueue polling threads are not used (ie no contention).
Also enable more agressive polling for now since we still map Flash Attention (and a few other kernels) to
the CPU and those dspqueue threads were keeping the CPU cores are higher clock freqs.

* hexagon: add lhez as the second code owner
---
 CODEOWNERS                             |   2 +-
 ggml/src/ggml-hexagon/ggml-hexagon.cpp | 270 ++++++++-----------------
 ggml/src/ggml-hexagon/htp/main.c       | 216 +++++---------------
 scripts/snapdragon/adb/run-bench.sh    |   3 +-
 scripts/snapdragon/adb/run-cli.sh      |   7 +-
 5 files changed, 136 insertions(+), 362 deletions(-)

diff --git a/CODEOWNERS b/CODEOWNERS
index 53d2e1e7ed4..bacc86cbbd6 100644
--- a/CODEOWNERS
+++ b/CODEOWNERS
@@ -65,7 +65,7 @@
 /ggml/src/ggml-impl.h                   @ggerganov @slaren
 /ggml/src/ggml-metal/                   @ggerganov
 /ggml/src/ggml-opencl/                  @lhez @max-krasnyansky
-/ggml/src/ggml-hexagon/                 @max-krasnyansky
+/ggml/src/ggml-hexagon/                 @max-krasnyansky @lhez
 /ggml/src/ggml-opt.cpp                  @JohannesGaessler
 /ggml/src/ggml-quants.*                 @ggerganov
 /ggml/src/ggml-rpc/                     @rgerganov
diff --git a/ggml/src/ggml-hexagon/ggml-hexagon.cpp b/ggml/src/ggml-hexagon/ggml-hexagon.cpp
index 5e3dc0a3d0c..2d376a6025c 100644
--- a/ggml/src/ggml-hexagon/ggml-hexagon.cpp
+++ b/ggml/src/ggml-hexagon/ggml-hexagon.cpp
@@ -217,6 +217,9 @@ struct ggml_hexagon_session {
     void allocate(int dev_id) noexcept(false);
     void release() noexcept(true);
 
+    void enqueue(struct htp_general_req &req, struct dspqueue_buffer *bufs, uint32_t n_bufs, bool sync = false);
+    void flush();
+
     ggml_backend_buffer_type buffer_type;
     ggml_backend_buffer_type repack_buffer_type;
 
@@ -237,15 +240,37 @@ struct ggml_hexagon_session {
     uint32_t         prof_pkts;
 };
 
-// Packet callback
-static void htp_packet_callback(dspqueue_t queue, AEEResult error, void * context) {
-    auto sess = static_cast<ggml_hexagon_session *>(context);
+void ggml_hexagon_session::enqueue(struct htp_general_req &req, struct dspqueue_buffer *bufs, uint32_t n_bufs, bool sync) {
+    // Bump pending flag (cleared in the session::flush once we get the responce)
+    this->op_pending++;  // atomic inc
+
+    int err = dspqueue_write(this->queue,
+                             0,                       // flags - the framework will autoset this
+                             n_bufs,                  // number of buffers
+                             bufs,                    // buffer references
+                             sizeof(req),
+                             (const uint8_t *) &req,  // Message
+                             1000000                  // Timeout
+    );
+
+    if (err != 0) {
+        GGML_ABORT("ggml-hex: %s dspqueue_write failed: 0x%08x\n", this->name.c_str(), (unsigned) err);
+    }
+
+    if (sync) {
+        flush();
+    }
+}
+
+// Flush HTP response queue i.e wait for all outstanding requests to complete
+void ggml_hexagon_session::flush() {
+    dspqueue_t q = this->queue;
 
     // Repeatedly read packets from the queue until it's empty. We don't
     // necessarily get a separate callback for each packet, and new packets
     // may arrive while we're processing the previous one.
 
-    while (1) {
+    while (this->op_pending) {
         struct htp_general_rsp rsp;
         uint32_t               rsp_size;
         uint32_t               flags;
@@ -253,22 +278,23 @@ static void htp_packet_callback(dspqueue_t queue, AEEResult error, void * contex
         struct dspqueue_buffer bufs[HTP_MAX_PACKET_BUFFERS];
         uint32_t               n_bufs;
 
-        // Read packet from queue
-        int err = dspqueue_read_noblock(queue, &flags,
-                                        HTP_MAX_PACKET_BUFFERS,  // Maximum number of buffer references
-                                        &n_bufs,                 // Number of buffer references
-                                        bufs,                    // Buffer references
-                                        sizeof(rsp),             // Max message length
-                                        &rsp_size,               // Message length
-                                        (uint8_t *) &rsp);
-
-        if (err == AEE_EWOULDBLOCK) {
-            // Consumed all packets available for now
-            return;
+        // Read response packet from queue
+        int err = dspqueue_read(q, &flags,
+                                   HTP_MAX_PACKET_BUFFERS,  // Maximum number of buffer references
+                                   &n_bufs,                 // Number of buffer references
+                                   bufs,                    // Buffer references
+                                   sizeof(rsp),             // Max message length
+                                   &rsp_size,               // Message length
+                                   (uint8_t *) &rsp,
+                                   1000000);                // Timeout
+
+        if (err == AEE_EEXPIRED) {
+            // TODO: might need to bail out if the HTP is stuck on something
+            continue;
         }
 
         if (err != 0) {
-            GGML_ABORT("ggml-hex: dspqueue_read_noblock failed: 0x%08x\n", (unsigned) err);
+            GGML_ABORT("ggml-hex: dspqueue_read failed: 0x%08x\n", (unsigned) err);
         }
 
         // Basic sanity checks
@@ -281,21 +307,15 @@ static void htp_packet_callback(dspqueue_t queue, AEEResult error, void * contex
             // TODO: handle errors
         }
 
-        // FIXME: update profiling implementation
-        sess->prof_usecs  = rsp.prof_usecs;
-        sess->prof_cycles = rsp.prof_cycles;
-        sess->prof_pkts   = rsp.prof_pkts;
+        // TODO: update profiling implementation, currently only works for opt_opsync mode
+        this->prof_usecs  = rsp.prof_usecs;
+        this->prof_cycles = rsp.prof_cycles;
+        this->prof_pkts   = rsp.prof_pkts;
 
-        sess->op_pending--;  // atomic dec
+        this->op_pending--;  // atomic dec
     }
 }
 
-// Error callback - simply terminates with an error. Used where we don't
-// expect errors.
-[[noreturn]] static void htp_error_callback(dspqueue_t queue, AEEResult error, void * context) {
-    GGML_ABORT("ggml-hex: dspcall general error 0x%x: for queue %p\n", error, (void *) queue);
-}
-
 // ** backend buffers
 
 struct ggml_backend_hexagon_buffer_type_context {
@@ -1564,7 +1584,8 @@ void ggml_hexagon_session::allocate(int dev_id) noexcept(false) {
                           0,              // Flags
                           128 * 1024,     // Request  queue size (in bytes)
                           64 * 1024,      // Response queue size (in bytes)
-                          htp_packet_callback, htp_error_callback,
+                          nullptr,        // Read packet callback (we handle reads explicitly)
+                          nullptr,        // Error callback (we handle errors during reads)
                           (void *) this,  // Callback context
                           &queue);
     if (err != 0) {
@@ -2205,7 +2226,7 @@ static void ggml_hexagon_mul_mat(const struct ggml_tensor * op, uint32_t flags)
     bufs[0].ptr    = src0->data;
     bufs[0].offset = (uint8_t *) src0->data - src0_buf->base;
     bufs[0].size   = ggml_nbytes(src0);
-    bufs[0].flags  = DSPQUEUE_BUFFER_FLAG_REF;
+    bufs[0].flags  = 0;
 
     // Second buffer Input Activations. This is a buffer that the CPU
     // writes and the DSP reads, so we'll need to flush CPU caches and
@@ -2215,8 +2236,7 @@ static void ggml_hexagon_mul_mat(const struct ggml_tensor * op, uint32_t flags)
     bufs[1].ptr    = src1->data;
     bufs[1].offset = (uint8_t *) src1->data - src1_buf->base;
     bufs[1].size   = ggml_nbytes(src1);
-    bufs[1].flags  = (DSPQUEUE_BUFFER_FLAG_REF |                   // Take a reference
-                     DSPQUEUE_BUFFER_FLAG_FLUSH_SENDER |          // Flush CPU
+    bufs[1].flags  = (DSPQUEUE_BUFFER_FLAG_FLUSH_SENDER |         // Flush CPU
                      DSPQUEUE_BUFFER_FLAG_INVALIDATE_RECIPIENT);  // Invalidate DSP
 
     // Third buffer Output Activations. We'll handle DSP
@@ -2227,7 +2247,7 @@ static void ggml_hexagon_mul_mat(const struct ggml_tensor * op, uint32_t flags)
     bufs[2].ptr    = dst->data;
     bufs[2].offset = (uint8_t *) dst->data - dst_buf->base;
     bufs[2].size   = ggml_nbytes(dst);
-    bufs[2].flags  = (DSPQUEUE_BUFFER_FLAG_REF | DSPQUEUE_BUFFER_FLAG_FLUSH_SENDER);
+    bufs[2].flags  = (DSPQUEUE_BUFFER_FLAG_FLUSH_SENDER);
 
     // Primary DSP session from the src0 (normally weight) tensor
     auto sess = src0_buf->sess;
@@ -2255,27 +2275,7 @@ static void ggml_hexagon_mul_mat(const struct ggml_tensor * op, uint32_t flags)
     }
 
     if ((opt_opmask & HTP_OPMASK_QUEUE)) {
-        // Bump pending flag (cleared in the callback once we get the responce)
-        sess->op_pending++;  // atomic inc
-
-        int err = dspqueue_write(sess->queue,
-                                 0,                       // flags - the framework will autoset this
-                                 3,                       // number of buffers
-                                 bufs,                    // buffer references
-                                 sizeof(req),
-                                 (const uint8_t *) &req,  // Message
-                                 1000000                  // Timeout
-        );
-
-        if (err != 0) {
-            GGML_ABORT("ggml-hex: %s dspqueue_write failed: 0x%08x\n", sess->name.c_str(), (unsigned) err);
-        }
-    }
-
-    if (opt_opsync) {
-        while (sess->op_pending) {
-            ;
-        }
+        sess->enqueue(req, bufs, 3, opt_opsync);
     }
 
     t2 = ggml_time_us();
@@ -2331,7 +2331,7 @@ static void ggml_hexagon_mul_mat_id(const struct ggml_tensor * op, uint32_t flag
     bufs[0].ptr    = src0->data;
     bufs[0].offset = (uint8_t *) src0->data - src0_buf->base;
     bufs[0].size   = ggml_nbytes(src0);
-    bufs[0].flags  = DSPQUEUE_BUFFER_FLAG_REF;
+    bufs[0].flags  = 0;
 
     // Second buffer Input Activations. This is a buffer that the CPU
     // writes and the DSP reads, so we'll need to flush CPU caches and
@@ -2341,8 +2341,7 @@ static void ggml_hexagon_mul_mat_id(const struct ggml_tensor * op, uint32_t flag
     bufs[1].ptr    = src1->data;
     bufs[1].offset = (uint8_t *) src1->data - src1_buf->base;
     bufs[1].size   = ggml_nbytes(src1);
-    bufs[1].flags  = (DSPQUEUE_BUFFER_FLAG_REF |                   // Take a reference
-                     DSPQUEUE_BUFFER_FLAG_FLUSH_SENDER |          // Flush CPU
+    bufs[1].flags  = (DSPQUEUE_BUFFER_FLAG_FLUSH_SENDER |         // Flush CPU
                      DSPQUEUE_BUFFER_FLAG_INVALIDATE_RECIPIENT);  // Invalidate DSP
 
     // Third buffer expert IDs. This is a buffer that the CPU
@@ -2353,8 +2352,7 @@ static void ggml_hexagon_mul_mat_id(const struct ggml_tensor * op, uint32_t flag
     bufs[2].ptr    = src2->data;
     bufs[2].offset = (uint8_t *) src2->data - src2_buf->base;
     bufs[2].size   = ggml_nbytes(src2);
-    bufs[2].flags  = (DSPQUEUE_BUFFER_FLAG_REF |                   // Take a reference
-                     DSPQUEUE_BUFFER_FLAG_FLUSH_SENDER |          // Flush CPU
+    bufs[2].flags  = (DSPQUEUE_BUFFER_FLAG_FLUSH_SENDER |         // Flush CPU
                      DSPQUEUE_BUFFER_FLAG_INVALIDATE_RECIPIENT);  // Invalidate DSP
 
     // Forth buffer Output Activations. We'll handle DSP
@@ -2365,7 +2363,7 @@ static void ggml_hexagon_mul_mat_id(const struct ggml_tensor * op, uint32_t flag
     bufs[3].ptr    = dst->data;
     bufs[3].offset = (uint8_t *) dst->data - dst_buf->base;
     bufs[3].size   = ggml_nbytes(dst);
-    bufs[3].flags  = (DSPQUEUE_BUFFER_FLAG_REF | DSPQUEUE_BUFFER_FLAG_FLUSH_SENDER);
+    bufs[3].flags  = (DSPQUEUE_BUFFER_FLAG_FLUSH_SENDER);
 
     // Primary DSP session from the src0 (normally weight) tensor
     auto sess = src0_buf->sess;
@@ -2394,27 +2392,7 @@ static void ggml_hexagon_mul_mat_id(const struct ggml_tensor * op, uint32_t flag
     }
 
     if ((opt_opmask & HTP_OPMASK_QUEUE)) {
-        // Bump pending flag (cleared in the callback once we get the responce)
-        sess->op_pending++;  // atomic inc
-
-        int err = dspqueue_write(sess->queue,
-                                 0,                       // flags - the framework will autoset this
-                                 4,                       // number of buffers
-                                 bufs,                    // buffer references
-                                 sizeof(req),
-                                 (const uint8_t *) &req,  // Message
-                                 1000000                  // Timeout
-        );
-
-        if (err != 0) {
-            GGML_ABORT("ggml-hex: %s dspqueue_write failed: 0x%08x\n", sess->name.c_str(), (unsigned) err);
-        }
-    }
-
-    if (opt_opsync) {
-        while (sess->op_pending) {
-            ;
-        }
+        sess->enqueue(req, bufs, 4, opt_opsync);
     }
 
     t2 = ggml_time_us();
@@ -2487,8 +2465,7 @@ static void ggml_hexagon_binary(const struct ggml_tensor * op, uint32_t flags) {
     bufs[0].ptr    = src0->data;
     bufs[0].offset = (uint8_t *) src0->data - src0_buf->base;
     bufs[0].size   = ggml_nbytes(src0);
-    bufs[0].flags  = (DSPQUEUE_BUFFER_FLAG_REF |                   // Take a reference
-                     DSPQUEUE_BUFFER_FLAG_FLUSH_SENDER |          // Flush CPU
+    bufs[0].flags  = (DSPQUEUE_BUFFER_FLAG_FLUSH_SENDER |         // Flush CPU
                      DSPQUEUE_BUFFER_FLAG_INVALIDATE_RECIPIENT);  // Invalidate DSP;
 
     // Second buffer = Second Operand of Binary op
@@ -2500,8 +2477,7 @@ static void ggml_hexagon_binary(const struct ggml_tensor * op, uint32_t flags) {
     bufs[1].ptr    = src1->data;
     bufs[1].offset = (uint8_t *) src1->data - src1_buf->base;
     bufs[1].size   = ggml_nbytes(src1);
-    bufs[1].flags  = (DSPQUEUE_BUFFER_FLAG_REF |                   // Take a reference
-                     DSPQUEUE_BUFFER_FLAG_FLUSH_SENDER |          // Flush CPU
+    bufs[1].flags  = (DSPQUEUE_BUFFER_FLAG_FLUSH_SENDER |         // Flush CPU
                      DSPQUEUE_BUFFER_FLAG_INVALIDATE_RECIPIENT);  // Invalidate DSP
 
     // Third buffer = Output Activations. We'll handle DSP
@@ -2512,7 +2488,7 @@ static void ggml_hexagon_binary(const struct ggml_tensor * op, uint32_t flags) {
     bufs[2].ptr    = dst->data;
     bufs[2].offset = (uint8_t *) dst->data - dst_buf->base;
     bufs[2].size   = ggml_nbytes(dst);
-    bufs[2].flags  = (DSPQUEUE_BUFFER_FLAG_REF | DSPQUEUE_BUFFER_FLAG_FLUSH_SENDER);
+    bufs[2].flags  = (DSPQUEUE_BUFFER_FLAG_FLUSH_SENDER);
 
     // Primary DSP session from the src0 tensor
     ggml_hexagon_session * sess = src0_buf->sess;
@@ -2540,26 +2516,7 @@ static void ggml_hexagon_binary(const struct ggml_tensor * op, uint32_t flags) {
     }
 
     if ((opt_opmask & HTP_OPMASK_QUEUE)) {
-        // Bump pending flag (cleared in the callback once we get the responce)
-        sess->op_pending++;  // atomic inc
-
-        int err = dspqueue_write(sess->queue,
-                                 0,                       // flags - the framework will autoset this
-                                 3,                       // number of buffers
-                                 bufs,                    // buffer references
-                                 sizeof(req),
-                                 (const uint8_t *) &req,  // Message
-                                 1000000);                // Timeout
-
-        if (0 != err) {
-            GGML_ABORT("ggml-hex: %s dspqueue_write failed: 0x%08x\n", sess->name.c_str(), (unsigned) err);
-        }
-    }
-
-    if (opt_opsync) {
-        while (sess->op_pending) {
-            ;
-        }
+        sess->enqueue(req, bufs, 3, opt_opsync);
     }
 
     t2 = ggml_time_us();
@@ -2624,8 +2581,7 @@ static void ggml_hexagon_add_id(const struct ggml_tensor * op, uint32_t flags) {
     bufs[0].ptr    = src0->data;
     bufs[0].offset = (uint8_t *) src0->data - src0_buf->base;
     bufs[0].size   = ggml_nbytes(src0);
-    bufs[0].flags  = (DSPQUEUE_BUFFER_FLAG_REF |                   // Take a reference
-                     DSPQUEUE_BUFFER_FLAG_FLUSH_SENDER |          // Flush CPU
+    bufs[0].flags  = (DSPQUEUE_BUFFER_FLAG_FLUSH_SENDER |         // Flush CPU
                      DSPQUEUE_BUFFER_FLAG_INVALIDATE_RECIPIENT);  // Invalidate DSP;
 
     // Second buffer = experts bias
@@ -2633,8 +2589,7 @@ static void ggml_hexagon_add_id(const struct ggml_tensor * op, uint32_t flags) {
     bufs[1].ptr    = src1->data;
     bufs[1].offset = (uint8_t *) src1->data - src1_buf->base;
     bufs[1].size   = ggml_nbytes(src1);
-    bufs[1].flags  = (DSPQUEUE_BUFFER_FLAG_REF |                   // Take a reference
-                     DSPQUEUE_BUFFER_FLAG_FLUSH_SENDER |          // Flush CPU
+    bufs[1].flags  = (DSPQUEUE_BUFFER_FLAG_FLUSH_SENDER |         // Flush CPU
                      DSPQUEUE_BUFFER_FLAG_INVALIDATE_RECIPIENT);  // Invalidate DSP
 
     // Third buffer = activated experts
@@ -2642,8 +2597,7 @@ static void ggml_hexagon_add_id(const struct ggml_tensor * op, uint32_t flags) {
     bufs[2].ptr    = src2->data;
     bufs[2].offset = (uint8_t *) src2->data - src2_buf->base;
     bufs[2].size   = ggml_nbytes(src2);
-    bufs[2].flags  = (DSPQUEUE_BUFFER_FLAG_REF |                   // Take a reference
-                     DSPQUEUE_BUFFER_FLAG_FLUSH_SENDER |          // Flush CPU
+    bufs[2].flags  = (DSPQUEUE_BUFFER_FLAG_FLUSH_SENDER |         // Flush CPU
                      DSPQUEUE_BUFFER_FLAG_INVALIDATE_RECIPIENT);  // Invalidate DSP
 
     // Forth buffer = output activations
@@ -2651,7 +2605,7 @@ static void ggml_hexagon_add_id(const struct ggml_tensor * op, uint32_t flags) {
     bufs[3].ptr    = dst->data;
     bufs[3].offset = (uint8_t *) dst->data - dst_buf->base;
     bufs[3].size   = ggml_nbytes(dst);
-    bufs[3].flags  = (DSPQUEUE_BUFFER_FLAG_REF | DSPQUEUE_BUFFER_FLAG_FLUSH_SENDER);
+    bufs[3].flags  = (DSPQUEUE_BUFFER_FLAG_FLUSH_SENDER);
 
     // Primary DSP session from the src0 tensor
     ggml_hexagon_session * sess = src0_buf->sess;
@@ -2681,26 +2635,7 @@ static void ggml_hexagon_add_id(const struct ggml_tensor * op, uint32_t flags) {
     }
 
     if ((opt_opmask & HTP_OPMASK_QUEUE)) {
-        // Bump pending flag (cleared in the callback once we get the responce)
-        sess->op_pending++;  // atomic inc
-
-        int err = dspqueue_write(sess->queue,
-                                 0,                       // flags - the framework will autoset this
-                                 4,                       // number of buffers
-                                 bufs,                    // buffer references
-                                 sizeof(req),
-                                 (const uint8_t *) &req,  // Message
-                                 1000000);                // Timeout
-
-        if (0 != err) {
-            GGML_ABORT("ggml-hex: %s dspqueue_write failed: 0x%08x\n", sess->name.c_str(), (unsigned) err);
-        }
-    }
-
-    if (opt_opsync) {
-        while (sess->op_pending) {
-            ;
-        }
+        sess->enqueue(req, bufs, 4, opt_opsync);
     }
 
     t2 = ggml_time_us();
@@ -2798,8 +2733,7 @@ static void ggml_hexagon_unary(const struct ggml_tensor * op, uint32_t flags) {
     bufs[n_bufs].ptr    = src0->data;
     bufs[n_bufs].offset = (uint8_t *) src0->data - src0_buf->base;
     bufs[n_bufs].size   = ggml_nbytes(src0);
-    bufs[n_bufs].flags  = (DSPQUEUE_BUFFER_FLAG_REF |                   // Take a reference
-                          DSPQUEUE_BUFFER_FLAG_FLUSH_SENDER |          // Flush CPU
+    bufs[n_bufs].flags  = (DSPQUEUE_BUFFER_FLAG_FLUSH_SENDER |         // Flush CPU
                           DSPQUEUE_BUFFER_FLAG_INVALIDATE_RECIPIENT);  // Invalidate DSP;
     ++n_bufs;
 
@@ -2814,8 +2748,7 @@ static void ggml_hexagon_unary(const struct ggml_tensor * op, uint32_t flags) {
         bufs[n_bufs].ptr    = src1->data;
         bufs[n_bufs].offset = (uint8_t *) src1->data - src1_buf->base;
         bufs[n_bufs].size   = ggml_nbytes(src1);
-        bufs[n_bufs].flags  = (DSPQUEUE_BUFFER_FLAG_REF |                   // Take a reference
-                              DSPQUEUE_BUFFER_FLAG_FLUSH_SENDER |          // Flush CPU
+        bufs[n_bufs].flags  = (DSPQUEUE_BUFFER_FLAG_FLUSH_SENDER |         // Flush CPU
                               DSPQUEUE_BUFFER_FLAG_INVALIDATE_RECIPIENT);  // Invalidate DSP
         ++n_bufs;
     }
@@ -2830,7 +2763,7 @@ static void ggml_hexagon_unary(const struct ggml_tensor * op, uint32_t flags) {
     bufs[n_bufs].ptr    = dst->data;
     bufs[n_bufs].offset = (uint8_t *) dst->data - dst_buf->base;
     bufs[n_bufs].size   = ggml_nbytes(dst);
-    bufs[n_bufs].flags  = (DSPQUEUE_BUFFER_FLAG_REF | DSPQUEUE_BUFFER_FLAG_FLUSH_SENDER);
+    bufs[n_bufs].flags  = (DSPQUEUE_BUFFER_FLAG_FLUSH_SENDER);
     ++n_bufs;
 
     // Primary DSP session from the src0 tensor
@@ -2863,26 +2796,7 @@ static void ggml_hexagon_unary(const struct ggml_tensor * op, uint32_t flags) {
     }
 
     if ((opt_opmask & HTP_OPMASK_QUEUE)) {
-        // Bump pending flag (cleared in the callback once we get the responce)
-        sess->op_pending++;  // atomic inc
-
-        int err = dspqueue_write(sess->queue,
-                                 0,                       // flags - the framework will autoset this
-                                 n_bufs,                  // number of buffers
-                                 bufs,                    // buffer references
-                                 sizeof(req),
-                                 (const uint8_t *) &req,  // Message
-                                 1000000);                // Timeout
-
-        if (0 != err) {
-            GGML_ABORT("ggml-hex: %s dspqueue_write failed: 0x%08x\n", sess->name.c_str(), (unsigned) err);
-        }
-    }
-
-    if (opt_opsync) {
-        while (sess->op_pending) {
-            ;
-        }
+        sess->enqueue(req, bufs, n_bufs, opt_opsync);
     }
 
     t2 = ggml_time_us();
@@ -2956,8 +2870,7 @@ static void ggml_hexagon_rope(const struct ggml_tensor * op, uint32_t flags) {
     bufs[n_bufs].ptr    = src0->data;
     bufs[n_bufs].offset = (uint8_t *) src0->data - src0_buf->base;
     bufs[n_bufs].size   = ggml_nbytes(src0);
-    bufs[n_bufs].flags  = (DSPQUEUE_BUFFER_FLAG_REF |                   // Take a reference
-                          DSPQUEUE_BUFFER_FLAG_FLUSH_SENDER |          // Flush CPU
+    bufs[n_bufs].flags  = (DSPQUEUE_BUFFER_FLAG_FLUSH_SENDER |         // Flush CPU
                           DSPQUEUE_BUFFER_FLAG_INVALIDATE_RECIPIENT);  // Invalidate DSP;
     ++n_bufs;
 
@@ -2971,8 +2884,7 @@ static void ggml_hexagon_rope(const struct ggml_tensor * op, uint32_t flags) {
     bufs[n_bufs].ptr    = src1->data;
     bufs[n_bufs].offset = (uint8_t *) src1->data - src1_buf->base;
     bufs[n_bufs].size   = ggml_nbytes(src1);
-    bufs[n_bufs].flags  = (DSPQUEUE_BUFFER_FLAG_REF |                   // Take a reference
-                          DSPQUEUE_BUFFER_FLAG_FLUSH_SENDER |          // Flush CPU
+    bufs[n_bufs].flags  = (DSPQUEUE_BUFFER_FLAG_FLUSH_SENDER |         // Flush CPU
                           DSPQUEUE_BUFFER_FLAG_INVALIDATE_RECIPIENT);  // Invalidate DSP
     ++n_bufs;
 
@@ -2987,8 +2899,7 @@ static void ggml_hexagon_rope(const struct ggml_tensor * op, uint32_t flags) {
         bufs[n_bufs].ptr    = src2->data;
         bufs[n_bufs].offset = (uint8_t *) src2->data - src2_buf->base;
         bufs[n_bufs].size   = ggml_nbytes(src2);
-        bufs[n_bufs].flags  = (DSPQUEUE_BUFFER_FLAG_REF |                   // Take a reference
-                              DSPQUEUE_BUFFER_FLAG_FLUSH_SENDER |          // Flush CPU
+        bufs[n_bufs].flags  = (DSPQUEUE_BUFFER_FLAG_FLUSH_SENDER |         // Flush CPU
                               DSPQUEUE_BUFFER_FLAG_INVALIDATE_RECIPIENT);  // Invalidate DSP
         ++n_bufs;
     }
@@ -3003,7 +2914,7 @@ static void ggml_hexagon_rope(const struct ggml_tensor * op, uint32_t flags) {
     bufs[n_bufs].ptr    = dst->data;
     bufs[n_bufs].offset = (uint8_t *) dst->data - dst_buf->base;
     bufs[n_bufs].size   = ggml_nbytes(dst);
-    bufs[n_bufs].flags  = (DSPQUEUE_BUFFER_FLAG_REF | DSPQUEUE_BUFFER_FLAG_FLUSH_SENDER);
+    bufs[n_bufs].flags  = (DSPQUEUE_BUFFER_FLAG_FLUSH_SENDER);
     ++n_bufs;
 
     // Primary DSP session from the src0 tensor
@@ -3036,26 +2947,7 @@ static void ggml_hexagon_rope(const struct ggml_tensor * op, uint32_t flags) {
     }
 
     if ((opt_opmask & HTP_OPMASK_QUEUE)) {
-        // Bump pending flag (cleared in the callback once we get the responce)
-        sess->op_pending++;  // atomic inc
-
-        int err = dspqueue_write(sess->queue,
-                                 0,                       // flags - the framework will autoset this
-                                 n_bufs,                  // number of buffers
-                                 bufs,                    // buffer references
-                                 sizeof(req),
-                                 (const uint8_t *) &req,  // Message
-                                 1000000);                // Timeout
-
-        if (0 != err) {
-            GGML_ABORT("ggml-hex: %s dspqueue_write failed: 0x%08x\n", sess->name.c_str(), (unsigned) err);
-        }
-    }
-
-    if (opt_opsync) {
-        while (sess->op_pending) {
-            ;
-        }
+        sess->enqueue(req, bufs, n_bufs, opt_opsync);
     }
 
     t2 = ggml_time_us();
@@ -3200,9 +3092,7 @@ static ggml_status ggml_backend_hexagon_graph_compute(ggml_backend_t backend, gg
     }
 
     // Wait until all pending ops complete
-    while (sess->op_pending) {
-        ;
-    }
+    sess->flush();
 
     return GGML_STATUS_SUCCESS;
 }
@@ -3213,9 +3103,7 @@ static void ggml_backend_hexagon_synchronize(ggml_backend_t backend) {
     HEX_VERBOSE("ggml-hex: %s synchronize\n", sess->name.c_str());
 
     // Wait until all pending ops complete
-    while (sess->op_pending) {
-        ;
-    }
+    sess->flush();
 }
 
 struct node_info {
diff --git a/ggml/src/ggml-hexagon/htp/main.c b/ggml/src/ggml-hexagon/htp/main.c
index e35ea3b0211..10e27333243 100644
--- a/ggml/src/ggml-hexagon/htp/main.c
+++ b/ggml/src/ggml-hexagon/htp/main.c
@@ -395,28 +395,14 @@ static void proc_matmul_req(struct htp_context *     ctx,
                             struct htp_general_req * req,
                             struct dspqueue_buffer * bufs,
                             size_t                   n_bufs) {
-    // Prep response buffer structs (needed for error responses, etc)
-    struct dspqueue_buffer rsp_bufs[HTP_MAX_PACKET_BUFFERS];
-    memset(rsp_bufs, 0, sizeof(rsp_bufs));
-    rsp_bufs[0].fd     = bufs[0].fd;
-    rsp_bufs[0].ptr    = bufs[0].ptr;
-    rsp_bufs[0].size   = bufs[0].size;
-    rsp_bufs[0].offset = bufs[0].offset;
-    rsp_bufs[0].flags  = DSPQUEUE_BUFFER_FLAG_DEREF;  // Release reference
-
-    rsp_bufs[1].fd     = bufs[1].fd;
-    rsp_bufs[1].ptr    = bufs[1].ptr;
-    rsp_bufs[1].size   = bufs[1].size;
-    rsp_bufs[1].offset = bufs[1].offset;
-    rsp_bufs[1].flags  = DSPQUEUE_BUFFER_FLAG_DEREF;  // Release reference
+    struct dspqueue_buffer rsp_bufs[1];
 
     // We had written to the output buffer, we'd also need to flush it
-    rsp_bufs[2].fd     = bufs[2].fd;
-    rsp_bufs[2].ptr    = bufs[2].ptr;
-    rsp_bufs[2].size   = bufs[2].size;
-    rsp_bufs[2].offset = bufs[2].offset;
-    rsp_bufs[2].flags  = (DSPQUEUE_BUFFER_FLAG_DEREF |                 // Release reference
-                         DSPQUEUE_BUFFER_FLAG_FLUSH_SENDER |          // Flush NSP
+    rsp_bufs[0].fd     = bufs[2].fd;
+    rsp_bufs[0].ptr    = bufs[2].ptr;
+    rsp_bufs[0].size   = bufs[2].size;
+    rsp_bufs[0].offset = bufs[2].offset;
+    rsp_bufs[0].flags  = (DSPQUEUE_BUFFER_FLAG_FLUSH_SENDER |         // Flush HTP
                          DSPQUEUE_BUFFER_FLAG_INVALIDATE_RECIPIENT);  // Invalidate CPU
 
     // Setup Op context
@@ -444,41 +430,21 @@ static void proc_matmul_req(struct htp_context *     ctx,
     }
 
     profile_stop(&prof);
-    send_htp_rsp(ctx, req->op, rsp_status, rsp_bufs, 3, &prof);
+    send_htp_rsp(ctx, req->op, rsp_status, rsp_bufs, 1, &prof);
 }
 
 static void proc_matmul_id_req(struct htp_context *     ctx,
                                struct htp_general_req * req,
                                struct dspqueue_buffer * bufs,
                                size_t                   n_bufs) {
-    // Prep response buffer structs (needed for error responses, etc)
-    struct dspqueue_buffer rsp_bufs[HTP_MAX_PACKET_BUFFERS];
-    memset(rsp_bufs, 0, sizeof(rsp_bufs));
-    rsp_bufs[0].fd     = bufs[0].fd;
-    rsp_bufs[0].ptr    = bufs[0].ptr;
-    rsp_bufs[0].size   = bufs[0].size;
-    rsp_bufs[0].offset = bufs[0].offset;
-    rsp_bufs[0].flags  = DSPQUEUE_BUFFER_FLAG_DEREF;  // Release reference
-
-    rsp_bufs[1].fd     = bufs[1].fd;
-    rsp_bufs[1].ptr    = bufs[1].ptr;
-    rsp_bufs[1].size   = bufs[1].size;
-    rsp_bufs[1].offset = bufs[1].offset;
-    rsp_bufs[1].flags  = DSPQUEUE_BUFFER_FLAG_DEREF;  // Release reference
-
-    rsp_bufs[2].fd     = bufs[2].fd;
-    rsp_bufs[2].ptr    = bufs[2].ptr;
-    rsp_bufs[2].size   = bufs[2].size;
-    rsp_bufs[2].offset = bufs[2].offset;
-    rsp_bufs[2].flags  = DSPQUEUE_BUFFER_FLAG_DEREF;  // Release reference
+    struct dspqueue_buffer rsp_bufs[1];
 
     // We had written to the output buffer, we'd also need to flush it
-    rsp_bufs[3].fd     = bufs[3].fd;
-    rsp_bufs[3].ptr    = bufs[3].ptr;
-    rsp_bufs[3].size   = bufs[3].size;
-    rsp_bufs[3].offset = bufs[3].offset;
-    rsp_bufs[3].flags  = (DSPQUEUE_BUFFER_FLAG_DEREF |                 // Release reference
-                         DSPQUEUE_BUFFER_FLAG_FLUSH_SENDER |          // Flush NSP
+    rsp_bufs[0].fd     = bufs[3].fd;
+    rsp_bufs[0].ptr    = bufs[3].ptr;
+    rsp_bufs[0].size   = bufs[3].size;
+    rsp_bufs[0].offset = bufs[3].offset;
+    rsp_bufs[0].flags  = (DSPQUEUE_BUFFER_FLAG_FLUSH_SENDER |         // Flush HTP
                          DSPQUEUE_BUFFER_FLAG_INVALIDATE_RECIPIENT);  // Invalidate CPU
 
     // Setup Op context
@@ -508,32 +474,18 @@ static void proc_matmul_id_req(struct htp_context *     ctx,
     }
 
     profile_stop(&prof);
-    send_htp_rsp(ctx, req->op, rsp_status, rsp_bufs, 4, &prof);
+    send_htp_rsp(ctx, req->op, rsp_status, rsp_bufs, 1, &prof);
 }
 
 static void proc_binary_req(struct htp_context * ctx, struct htp_general_req * req, struct dspqueue_buffer * bufs) {
-    struct dspqueue_buffer rsp_bufs[HTP_MAX_PACKET_BUFFERS];
-    memset(rsp_bufs, 0, sizeof(rsp_bufs));
-
-    rsp_bufs[0].fd     = bufs[0].fd;
-    rsp_bufs[0].ptr    = bufs[0].ptr;
-    rsp_bufs[0].offset = bufs[0].offset;
-    rsp_bufs[0].size   = bufs[0].size;
-    rsp_bufs[0].flags  = DSPQUEUE_BUFFER_FLAG_DEREF;  // Release reference
-
-    rsp_bufs[1].fd     = bufs[1].fd;
-    rsp_bufs[1].ptr    = bufs[1].ptr;
-    rsp_bufs[1].offset = bufs[1].offset;
-    rsp_bufs[1].size   = bufs[1].size;
-    rsp_bufs[1].flags  = DSPQUEUE_BUFFER_FLAG_DEREF;  // Release reference
+    struct dspqueue_buffer rsp_bufs[1];
 
     // We had written to the output buffer, we'd also need to flush it
-    rsp_bufs[2].fd     = bufs[2].fd;
-    rsp_bufs[2].ptr    = bufs[2].ptr;
-    rsp_bufs[2].offset = bufs[2].offset;
-    rsp_bufs[2].size   = bufs[2].size;
-    rsp_bufs[2].flags  = (DSPQUEUE_BUFFER_FLAG_DEREF |                 // Release reference
-                         DSPQUEUE_BUFFER_FLAG_FLUSH_SENDER |          // Flush NSP
+    rsp_bufs[0].fd     = bufs[2].fd;
+    rsp_bufs[0].ptr    = bufs[2].ptr;
+    rsp_bufs[0].offset = bufs[2].offset;
+    rsp_bufs[0].size   = bufs[2].size;
+    rsp_bufs[0].flags  = (DSPQUEUE_BUFFER_FLAG_FLUSH_SENDER |         // Flush HTP
                          DSPQUEUE_BUFFER_FLAG_INVALIDATE_RECIPIENT);  // Invalidate CPU
 
     // Setup Op context
@@ -561,38 +513,18 @@ static void proc_binary_req(struct htp_context * ctx, struct htp_general_req * r
     }
 
     profile_stop(&prof);
-    send_htp_rsp(ctx, req->op, rsp_status, rsp_bufs, 3, &prof);
+    send_htp_rsp(ctx, req->op, rsp_status, rsp_bufs, 1, &prof);
 }
 
 static void proc_add_id_req(struct htp_context * ctx, struct htp_general_req * req, struct dspqueue_buffer * bufs) {
-    struct dspqueue_buffer rsp_bufs[HTP_MAX_PACKET_BUFFERS];
-    memset(rsp_bufs, 0, sizeof(rsp_bufs));
-
-    rsp_bufs[0].fd     = bufs[0].fd;
-    rsp_bufs[0].ptr    = bufs[0].ptr;
-    rsp_bufs[0].offset = bufs[0].offset;
-    rsp_bufs[0].size   = bufs[0].size;
-    rsp_bufs[0].flags  = DSPQUEUE_BUFFER_FLAG_DEREF;  // Release reference
-
-    rsp_bufs[1].fd     = bufs[1].fd;
-    rsp_bufs[1].ptr    = bufs[1].ptr;
-    rsp_bufs[1].offset = bufs[1].offset;
-    rsp_bufs[1].size   = bufs[1].size;
-    rsp_bufs[1].flags  = DSPQUEUE_BUFFER_FLAG_DEREF;  // Release reference
-
-    rsp_bufs[2].fd     = bufs[2].fd;
-    rsp_bufs[2].ptr    = bufs[2].ptr;
-    rsp_bufs[2].offset = bufs[2].offset;
-    rsp_bufs[2].size   = bufs[2].size;
-    rsp_bufs[2].flags  = DSPQUEUE_BUFFER_FLAG_DEREF;  // Release reference
+    struct dspqueue_buffer rsp_bufs[1];
 
     // We had written to the output buffer, we'd also need to flush it
-    rsp_bufs[3].fd     = bufs[3].fd;
-    rsp_bufs[3].ptr    = bufs[3].ptr;
-    rsp_bufs[3].offset = bufs[3].offset;
-    rsp_bufs[3].size   = bufs[3].size;
-    rsp_bufs[3].flags  = (DSPQUEUE_BUFFER_FLAG_DEREF |                 // Release reference
-                         DSPQUEUE_BUFFER_FLAG_FLUSH_SENDER |          // Flush NSP
+    rsp_bufs[0].fd     = bufs[3].fd;
+    rsp_bufs[0].ptr    = bufs[3].ptr;
+    rsp_bufs[0].offset = bufs[3].offset;
+    rsp_bufs[0].size   = bufs[3].size;
+    rsp_bufs[0].flags  = (DSPQUEUE_BUFFER_FLAG_FLUSH_SENDER |         // Flush HTP
                          DSPQUEUE_BUFFER_FLAG_INVALIDATE_RECIPIENT);  // Invalidate CPU
 
     // Setup Op context
@@ -622,26 +554,18 @@ static void proc_add_id_req(struct htp_context * ctx, struct htp_general_req * r
     }
 
     profile_stop(&prof);
-    send_htp_rsp(ctx, req->op, rsp_status, rsp_bufs, 4, &prof);
+    send_htp_rsp(ctx, req->op, rsp_status, rsp_bufs, 1, &prof);
 }
 
 static void proc_unary_req(struct htp_context * ctx, struct htp_general_req * req, struct dspqueue_buffer * bufs) {
     struct dspqueue_buffer rsp_bufs[HTP_MAX_PACKET_BUFFERS];
-    memset(rsp_bufs, 0, sizeof(rsp_bufs));
-
-    rsp_bufs[0].fd     = bufs[0].fd;
-    rsp_bufs[0].ptr    = bufs[0].ptr;
-    rsp_bufs[0].offset = bufs[0].offset;
-    rsp_bufs[0].size   = bufs[0].size;
-    rsp_bufs[0].flags  = DSPQUEUE_BUFFER_FLAG_DEREF;  // Release reference
 
     // We had written to the output buffer, we'd also need to flush it
-    rsp_bufs[1].fd     = bufs[1].fd;
-    rsp_bufs[1].ptr    = bufs[1].ptr;
-    rsp_bufs[1].offset = bufs[1].offset;
-    rsp_bufs[1].size   = bufs[1].size;
-    rsp_bufs[1].flags  = (DSPQUEUE_BUFFER_FLAG_DEREF |                 // Release reference
-                         DSPQUEUE_BUFFER_FLAG_FLUSH_SENDER |          // Flush NSP
+    rsp_bufs[0].fd     = bufs[1].fd;
+    rsp_bufs[0].ptr    = bufs[1].ptr;
+    rsp_bufs[0].offset = bufs[1].offset;
+    rsp_bufs[0].size   = bufs[1].size;
+    rsp_bufs[0].flags  = (DSPQUEUE_BUFFER_FLAG_FLUSH_SENDER |         // Flush HTP
                          DSPQUEUE_BUFFER_FLAG_INVALIDATE_RECIPIENT);  // Invalidate CPU
 
     // Setup Op context
@@ -669,7 +593,7 @@ static void proc_unary_req(struct htp_context * ctx, struct htp_general_req * re
     }
 
     profile_stop(&prof);
-    send_htp_rsp(ctx, req->op, rsp_status, rsp_bufs, 2, &prof);
+    send_htp_rsp(ctx, req->op, rsp_status, rsp_bufs, 1, &prof);
 }
 
 static void proc_activations_req(struct htp_context *     ctx,
@@ -677,33 +601,16 @@ static void proc_activations_req(struct htp_context *     ctx,
                                  struct dspqueue_buffer * bufs,
                                  uint32_t                 n_bufs) {
     struct dspqueue_buffer rsp_bufs[HTP_MAX_PACKET_BUFFERS];
-    memset(rsp_bufs, 0, sizeof(rsp_bufs));
-
-    rsp_bufs[0].fd     = bufs[0].fd;
-    rsp_bufs[0].ptr    = bufs[0].ptr;
-    rsp_bufs[0].offset = bufs[0].offset;
-    rsp_bufs[0].size   = bufs[0].size;
-    rsp_bufs[0].flags  = DSPQUEUE_BUFFER_FLAG_DEREF;  // Release reference
 
-    int write_idx = 1;
-    if (3 == n_bufs) {
-        rsp_bufs[1].fd     = bufs[1].fd;
-        rsp_bufs[1].ptr    = bufs[1].ptr;
-        rsp_bufs[1].offset = bufs[1].offset;
-        rsp_bufs[1].size   = bufs[1].size;
-        rsp_bufs[1].flags  = DSPQUEUE_BUFFER_FLAG_DEREF;  // Release reference
-
-        write_idx = 2;
-    }
+    int write_idx = (n_bufs == 3) ? 2 : 1;
 
     // We had written to the output buffer, we'd also need to flush it
-    rsp_bufs[write_idx].fd     = bufs[write_idx].fd;
-    rsp_bufs[write_idx].ptr    = bufs[write_idx].ptr;
-    rsp_bufs[write_idx].offset = bufs[write_idx].offset;
-    rsp_bufs[write_idx].size   = bufs[write_idx].size;
-    rsp_bufs[write_idx].flags  = (DSPQUEUE_BUFFER_FLAG_DEREF |                 // Release reference
-                                 DSPQUEUE_BUFFER_FLAG_FLUSH_SENDER |          // Flush NSP
-                                 DSPQUEUE_BUFFER_FLAG_INVALIDATE_RECIPIENT);  // Invalidate CPU
+    rsp_bufs[0].fd     = bufs[write_idx].fd;
+    rsp_bufs[0].ptr    = bufs[write_idx].ptr;
+    rsp_bufs[0].offset = bufs[write_idx].offset;
+    rsp_bufs[0].size   = bufs[write_idx].size;
+    rsp_bufs[0].flags  = (DSPQUEUE_BUFFER_FLAG_FLUSH_SENDER |         // Flush HTP
+                          DSPQUEUE_BUFFER_FLAG_INVALIDATE_RECIPIENT); // Invalidate CPU
 
     // Setup Op context
     struct htp_ops_context octx = { 0 };
@@ -742,7 +649,7 @@ static void proc_activations_req(struct htp_context *     ctx,
     }
 
     profile_stop(&prof);
-    send_htp_rsp(ctx, req->op, rsp_status, rsp_bufs, n_bufs, &prof);
+    send_htp_rsp(ctx, req->op, rsp_status, rsp_bufs, 1, &prof);
 }
 
 static void proc_rope_req(struct htp_context *     ctx,
@@ -750,39 +657,16 @@ static void proc_rope_req(struct htp_context *     ctx,
                           struct dspqueue_buffer * bufs,
                           uint32_t                 n_bufs) {
     struct dspqueue_buffer rsp_bufs[HTP_MAX_PACKET_BUFFERS];
-    memset(rsp_bufs, 0, sizeof(rsp_bufs));
-
-    rsp_bufs[0].fd     = bufs[0].fd;
-    rsp_bufs[0].ptr    = bufs[0].ptr;
-    rsp_bufs[0].offset = bufs[0].offset;
-    rsp_bufs[0].size   = bufs[0].size;
-    rsp_bufs[0].flags  = DSPQUEUE_BUFFER_FLAG_DEREF;  // Release reference
 
-    rsp_bufs[1].fd     = bufs[1].fd;
-    rsp_bufs[1].ptr    = bufs[1].ptr;
-    rsp_bufs[1].offset = bufs[1].offset;
-    rsp_bufs[1].size   = bufs[1].size;
-    rsp_bufs[1].flags  = DSPQUEUE_BUFFER_FLAG_DEREF;  // Release reference
-
-    int write_idx = 2;
-    if (4 == n_bufs) {
-        rsp_bufs[write_idx].fd     = bufs[write_idx].fd;
-        rsp_bufs[write_idx].ptr    = bufs[write_idx].ptr;
-        rsp_bufs[write_idx].offset = bufs[write_idx].offset;
-        rsp_bufs[write_idx].size   = bufs[write_idx].size;
-        rsp_bufs[write_idx].flags  = DSPQUEUE_BUFFER_FLAG_DEREF;  // Release reference
-
-        write_idx++;
-    }
+    int write_idx = (n_bufs == 4) ? 3 : 2;
 
     // We had written to the output buffer, we'd also need to flush it
-    rsp_bufs[write_idx].fd     = bufs[write_idx].fd;
-    rsp_bufs[write_idx].ptr    = bufs[write_idx].ptr;
-    rsp_bufs[write_idx].offset = bufs[write_idx].offset;
-    rsp_bufs[write_idx].size   = bufs[write_idx].size;
-    rsp_bufs[write_idx].flags  = (DSPQUEUE_BUFFER_FLAG_DEREF |                 // Release reference
-                                 DSPQUEUE_BUFFER_FLAG_FLUSH_SENDER |          // Flush NSP
-                                 DSPQUEUE_BUFFER_FLAG_INVALIDATE_RECIPIENT);  // Invalidate CPU
+    rsp_bufs[0].fd     = bufs[write_idx].fd;
+    rsp_bufs[0].ptr    = bufs[write_idx].ptr;
+    rsp_bufs[0].offset = bufs[write_idx].offset;
+    rsp_bufs[0].size   = bufs[write_idx].size;
+    rsp_bufs[0].flags  = (DSPQUEUE_BUFFER_FLAG_FLUSH_SENDER |         // Flush HTP
+                          DSPQUEUE_BUFFER_FLAG_INVALIDATE_RECIPIENT); // Invalidate CPU
 
     // Setup Op context
     struct htp_ops_context octx = { 0 };
@@ -819,7 +703,7 @@ static void proc_rope_req(struct htp_context *     ctx,
     }
 
     profile_stop(&prof);
-    send_htp_rsp(ctx, req->op, rsp_status, rsp_bufs, n_bufs, &prof);
+    send_htp_rsp(ctx, req->op, rsp_status, rsp_bufs, 1, &prof);
 }
 
 static void htp_packet_callback(dspqueue_t queue, int error, void * context) {
diff --git a/scripts/snapdragon/adb/run-bench.sh b/scripts/snapdragon/adb/run-bench.sh
index 25e0662016c..b2e651e7493 100755
--- a/scripts/snapdragon/adb/run-bench.sh
+++ b/scripts/snapdragon/adb/run-bench.sh
@@ -35,5 +35,6 @@ adb $adbserial shell " \
   LD_LIBRARY_PATH=$basedir/$branch/lib   \
   ADSP_LIBRARY_PATH=$basedir/$branch/lib \
     $ndev $nhvx $opmask ./$branch/bin/llama-bench --device $device --mmap 0 -m $basedir/../gguf/$model \
-        -t 4 --batch-size 128 -ngl 99 $@ \
+        --poll 1000 -t 6 --cpu-mask 0xfc --cpu-strict 1 \
+        --batch-size 128 -ngl 99 $@ \
 "
diff --git a/scripts/snapdragon/adb/run-cli.sh b/scripts/snapdragon/adb/run-cli.sh
index 763482e55ab..ab8d6d49a24 100755
--- a/scripts/snapdragon/adb/run-cli.sh
+++ b/scripts/snapdragon/adb/run-cli.sh
@@ -45,8 +45,9 @@ adb $adbserial shell " \
   cd $basedir; ulimit -c unlimited;        \
     LD_LIBRARY_PATH=$basedir/$branch/lib   \
     ADSP_LIBRARY_PATH=$basedir/$branch/lib \
-    $verbose $experimental $sched $opmask $profile $nhvx $ndev           \
-      ./$branch/bin/llama-cli --no-mmap -m $basedir/../gguf/$model       \
-         -t 4 --ctx-size 8192 --batch-size 128 -ctk q8_0 -ctv q8_0 -fa on \
+    $verbose $experimental $sched $opmask $profile $nhvx $ndev       \
+      ./$branch/bin/llama-cli --no-mmap -m $basedir/../gguf/$model   \
+         --poll 1000 -t 6 --cpu-mask 0xfc --cpu-strict 1             \
+         --ctx-size 8192 --batch-size 128 -ctk q8_0 -ctv q8_0 -fa on \
          -ngl 99 --device $device $cli_opts $@ \
 "

From bcf5bda6f5df559565d11d7c8e8295c1159a85ec Mon Sep 17 00:00:00 2001
From: Ruben Ortlam <picard12@live.de>
Date: Wed, 29 Oct 2025 14:39:03 +0100
Subject: [PATCH 010/185] Vulkan MMQ Integer Dot Refactor and K-Quant support
 (#16536)

* vulkan: add mmq q2_k integer dot support

* Refactor mmq caching

* Reduce mmq register use

* Load 4 quant blocks into shared memory in one step

* Pack q2_k blocks into caches of 32

* Use 32-bit accumulators for integer dot matmul

* Add q4_k mmq

* Add q3_k mmq

* Add q5_k mmq

* Add q6_k mmq

* Add mxfp4 mmq, enable MMQ MUL_MAT_ID

* Fix mmv dm loads
---
 ggml/src/ggml-vulkan/ggml-vulkan.cpp          | 165 +++++-
 .../vulkan-shaders/dequant_funcs.glsl         |  10 +-
 .../vulkan-shaders/dequant_funcs_cm2.glsl     |   6 +-
 .../vulkan-shaders/dequant_mxfp4.comp         |   4 +-
 .../vulkan-shaders/dequant_q2_k.comp          |   4 +-
 .../vulkan-shaders/dequant_q4_k.comp          |   4 +-
 .../vulkan-shaders/dequant_q5_k.comp          |   4 +-
 .../vulkan-shaders/mul_mat_vec_q2_k.comp      |   6 +-
 .../vulkan-shaders/mul_mat_vec_q4_k.comp      |   6 +-
 .../vulkan-shaders/mul_mat_vec_q5_k.comp      |   6 +-
 .../ggml-vulkan/vulkan-shaders/mul_mm.comp    |  72 +--
 .../vulkan-shaders/mul_mm_funcs.glsl          |  14 +-
 .../vulkan-shaders/mul_mm_id_funcs.glsl       |  70 +++
 .../ggml-vulkan/vulkan-shaders/mul_mmq.comp   | 288 +++-------
 .../vulkan-shaders/mul_mmq_funcs.glsl         | 538 ++++++++++++++++--
 .../vulkan-shaders/mul_mmq_shmem_types.glsl   |  78 +++
 .../src/ggml-vulkan/vulkan-shaders/types.glsl |  53 +-
 .../vulkan-shaders/vulkan-shaders-gen.cpp     |   5 +-
 18 files changed, 928 insertions(+), 405 deletions(-)
 create mode 100644 ggml/src/ggml-vulkan/vulkan-shaders/mul_mm_id_funcs.glsl
 create mode 100644 ggml/src/ggml-vulkan/vulkan-shaders/mul_mmq_shmem_types.glsl

diff --git a/ggml/src/ggml-vulkan/ggml-vulkan.cpp b/ggml/src/ggml-vulkan/ggml-vulkan.cpp
index 5caf37d4030..3d10aa07b08 100644
--- a/ggml/src/ggml-vulkan/ggml-vulkan.cpp
+++ b/ggml/src/ggml-vulkan/ggml-vulkan.cpp
@@ -486,6 +486,7 @@ struct vk_device_struct {
     vk_matmul_pipeline2 pipeline_matmul_id_f16_f32;
 
     vk_matmul_pipeline2 pipeline_dequant_mul_mat_mat_id[GGML_TYPE_COUNT];
+    vk_matmul_pipeline2 pipeline_dequant_mul_mat_mat_id_q8_1[GGML_TYPE_COUNT];
 
     vk_pipeline pipeline_matmul_split_k_reduce;
     vk_pipeline pipeline_quantize_q8_1;
@@ -2448,8 +2449,11 @@ static void ggml_vk_load_shaders(vk_device& device) {
                           l_warptile_id, m_warptile_id, s_warptile_id,
                           l_warptile_mmq, m_warptile_mmq, s_warptile_mmq,
                           l_warptile_mmq_int, m_warptile_mmq_int, s_warptile_mmq_int,
+                          l_warptile_mmq_int_k, m_warptile_mmq_int_k, s_warptile_mmq_int_k,
                           l_warptile_mmq_k, m_warptile_mmq_k, s_warptile_mmq_k,
-                          l_warptile_mmqid, m_warptile_mmqid, s_warptile_mmqid;
+                          l_warptile_mmqid, m_warptile_mmqid, s_warptile_mmqid,
+                          l_warptile_mmqid_int, m_warptile_mmqid_int, s_warptile_mmqid_int,
+                          l_warptile_mmqid_int_k, m_warptile_mmqid_int_k, s_warptile_mmqid_int_k;
     std::array<uint32_t, 3> l_wg_denoms, m_wg_denoms, s_wg_denoms,
                             l_mmq_wg_denoms, m_mmq_wg_denoms, s_mmq_wg_denoms,
                             l_mmq_wg_denoms_k, m_mmq_wg_denoms_k, s_mmq_wg_denoms_k,
@@ -2512,10 +2516,16 @@ static void ggml_vk_load_shaders(vk_device& device) {
         m_warptile_mmq = { 128,  64,  64, 32, subgroup_size_8, 32, 2, tm_m, tn_m, tk_m, subgroup_size_8 };
         s_warptile_mmq = { subgroup_size_32, 32, 32, 32, 32, 32, 2, tm_s, tn_s, tk_s, subgroup_size_8 };
 
+        // Integer MMQ has a smaller shared memory profile, but heavier register use
         l_warptile_mmq_int = { 128, 128, 128, 32, subgroup_size_8 * 2, 64, 2, 4, 4, 1, subgroup_size_8 };
         m_warptile_mmq_int = { 128,  64,  64, 32, subgroup_size_8,     32, 2, 2, 2, 1, subgroup_size_8 };
         s_warptile_mmq_int = { subgroup_size_32, 32, 32, 32, 32,       32, 2, 2, 1, 1, subgroup_size_8 };
 
+        // K-quants use even more registers, mitigate by setting WMITER to 1
+        l_warptile_mmq_int_k = { 128, 128, 128, 32, subgroup_size_8 * 2, 64, 1, 4, 4, 1, subgroup_size_8 };
+        m_warptile_mmq_int_k = { 128,  64,  64, 32, subgroup_size_8,     32, 1, 2, 2, 1, subgroup_size_8 };
+        s_warptile_mmq_int_k = { subgroup_size_32, 32, 32, 32, 32,       32, 1, 2, 1, 1, subgroup_size_8 };
+
         l_warptile_id = { 128, 128, 128, 16, mul_mat_subgroup_size_16 * 2, 64, 2, tm_l, tn_l, tk_l, mul_mat_subgroup_size_16 };
         m_warptile_id = { 128,  64,  64, 16, mul_mat_subgroup_size_16, 32, 2, tm_m, tn_m, tk_m, mul_mat_subgroup_size_16 };
         s_warptile_id = { mul_mat_subgroup_size_16, 32, 32, 16, 32, 32, 2, tm_s, tn_s, tk_s, mul_mat_subgroup_size_16 };
@@ -2524,10 +2534,18 @@ static void ggml_vk_load_shaders(vk_device& device) {
         m_warptile_mmqid = { 128,  64,  64, 32, mul_mat_subgroup_size_8, 32, 2, tm_m, tn_m, tk_m, mul_mat_subgroup_size_8 };
         s_warptile_mmqid = { mul_mat_subgroup_size_32, 32, 32, 32, 32, 32, 2, tm_s, tn_s, tk_s, mul_mat_subgroup_size_8 };
 
+        l_warptile_mmqid_int = { 128, 128, 128, 32, mul_mat_subgroup_size_8 * 2, 64, 2, 4, 4, 1, mul_mat_subgroup_size_8 };
+        m_warptile_mmqid_int = { 128,  64,  64, 32, mul_mat_subgroup_size_8,     32, 2, 2, 2, 1, mul_mat_subgroup_size_8 };
+        s_warptile_mmqid_int = { mul_mat_subgroup_size_32, 32, 32, 32, 32,       32, 2, 2, 1, 1, mul_mat_subgroup_size_8 };
+
+        l_warptile_mmqid_int_k = { 128, 128, 128, 32, mul_mat_subgroup_size_16 * 2, 64, 1, 4, 4, 1, mul_mat_subgroup_size_16 };
+        m_warptile_mmqid_int_k = { 128,  64,  64, 32, mul_mat_subgroup_size_16,     32, 1, 2, 2, 1, mul_mat_subgroup_size_16 };
+        s_warptile_mmqid_int_k = { mul_mat_subgroup_size_32, 32, 32, 32, 32,       32, 1, 2, 1, 1, mul_mat_subgroup_size_16 };
+
         // chip specific tuning
         if ((device->architecture == AMD_GCN) && (device->driver_id != vk::DriverId::eAmdProprietary)) {
             m_warptile_mmq = m_warptile_mmq_int = { 256, 64, 64, 32, 16, 16, 2, 2, 2, 1, 16 };
-            m_warptile_mmqid = { 256, 64, 64, 32, 16, 16, 2, 2, 2, 1, 16 };
+            m_warptile_mmqid = m_warptile_mmqid_int = { 256, 64, 64, 32, 16, 16, 2, 2, 2, 1, 16 };
         }
 
         l_mmq_wg_denoms = l_wg_denoms = {128, 128, 1 };
@@ -2912,18 +2930,15 @@ static void ggml_vk_load_shaders(vk_device& device) {
         if (device->mul_mat ## ID ## _s[TYPE]) \
             ggml_vk_create_pipeline(device, device-> PIPELINE_NAME ->a_s, #NAMELC #F16ACC "_aligned_s", NAMELC ## _aligned ## F16ACC ## _len, NAMELC ## _aligned ## F16ACC ## _data, "main", PARAMCOUNT, sizeof(PUSHCONST), s_ ## WG_DENOMS, s_ ## WARPTILE, s_align, false, REQSUBGROUPSIZE > 0, REQSUBGROUPSIZE);   \
 
-#define CREATE_MMQ(TYPE, PIPELINE_NAME, NAMELC, WG_DENOMS, WARPTILE, PUSHCONST, PARAMCOUNT, ID) \
+#define CREATE_MMQ(TYPE, PIPELINE_NAME, NAMELC, WG_DENOMS, WARPTILE, PUSHCONST, PARAMCOUNT, ID, REQSUBGROUPSIZE) \
         if (device->mul_mat ## ID ## _l[TYPE]) { \
-            ggml_vk_create_pipeline(device, device-> PIPELINE_NAME .f16acc->l, #NAMELC "_f16acc_l", NAMELC ## _f16acc_len, NAMELC ##  _f16acc_data, "main", PARAMCOUNT, sizeof(PUSHCONST), l_ ## WG_DENOMS, l_ ## WARPTILE, 1);   \
-            ggml_vk_create_pipeline(device, device-> PIPELINE_NAME .f32acc->l, #NAMELC        "_l", NAMELC ## _len,        NAMELC ##  _data,        "main", PARAMCOUNT, sizeof(PUSHCONST), l_ ## WG_DENOMS, l_ ## WARPTILE, 1);   \
+            ggml_vk_create_pipeline(device, device-> PIPELINE_NAME .f32acc->l, #NAMELC        "_l", NAMELC ## _len,        NAMELC ##  _data,        "main", PARAMCOUNT, sizeof(PUSHCONST), l_ ## WG_DENOMS, l_ ## WARPTILE, 1, false, REQSUBGROUPSIZE > 0, REQSUBGROUPSIZE);   \
         } \
         if (device->mul_mat ## ID ## _m[TYPE]) { \
-            ggml_vk_create_pipeline(device, device-> PIPELINE_NAME .f16acc->m, #NAMELC "_f16acc_m", NAMELC ## _f16acc_len, NAMELC ##  _f16acc_data, "main", PARAMCOUNT, sizeof(PUSHCONST), m_ ## WG_DENOMS, m_ ## WARPTILE, 1);   \
-            ggml_vk_create_pipeline(device, device-> PIPELINE_NAME .f32acc->m, #NAMELC        "_m", NAMELC ## _len,        NAMELC ##  _data,        "main", PARAMCOUNT, sizeof(PUSHCONST), m_ ## WG_DENOMS, m_ ## WARPTILE, 1);   \
+            ggml_vk_create_pipeline(device, device-> PIPELINE_NAME .f32acc->m, #NAMELC        "_m", NAMELC ## _len,        NAMELC ##  _data,        "main", PARAMCOUNT, sizeof(PUSHCONST), m_ ## WG_DENOMS, m_ ## WARPTILE, 1, false, REQSUBGROUPSIZE > 0, REQSUBGROUPSIZE);   \
         } \
         if (device->mul_mat ## ID ## _s[TYPE]) { \
-            ggml_vk_create_pipeline(device, device-> PIPELINE_NAME .f16acc->s, #NAMELC "_f16acc_s", NAMELC ## _f16acc_len, NAMELC ##  _f16acc_data, "main", PARAMCOUNT, sizeof(PUSHCONST), s_ ## WG_DENOMS, s_ ## WARPTILE, 1);   \
-            ggml_vk_create_pipeline(device, device-> PIPELINE_NAME .f32acc->s, #NAMELC        "_s", NAMELC ## _len,        NAMELC ##  _data,        "main", PARAMCOUNT, sizeof(PUSHCONST), s_ ## WG_DENOMS, s_ ## WARPTILE, 1);   \
+            ggml_vk_create_pipeline(device, device-> PIPELINE_NAME .f32acc->s, #NAMELC        "_s", NAMELC ## _len,        NAMELC ##  _data,        "main", PARAMCOUNT, sizeof(PUSHCONST), s_ ## WG_DENOMS, s_ ## WARPTILE, 1, false, REQSUBGROUPSIZE > 0, REQSUBGROUPSIZE);   \
         } \
 
         // Create 2 variants, {f16,f32} accumulator
@@ -2962,11 +2977,19 @@ static void ggml_vk_load_shaders(vk_device& device) {
 
 #if defined(GGML_VULKAN_INTEGER_DOT_GLSLC_SUPPORT)
         if (device->integer_dot_product) {
-            CREATE_MMQ(GGML_TYPE_Q4_0, pipeline_dequant_mul_mat_mat_q8_1[GGML_TYPE_Q4_0], matmul_q4_0_q8_1, mmq_wg_denoms, warptile_mmq_int, vk_mat_mat_push_constants, 3, );
-            CREATE_MMQ(GGML_TYPE_Q4_1, pipeline_dequant_mul_mat_mat_q8_1[GGML_TYPE_Q4_1], matmul_q4_1_q8_1, mmq_wg_denoms, warptile_mmq_int, vk_mat_mat_push_constants, 3, );
-            CREATE_MMQ(GGML_TYPE_Q5_0, pipeline_dequant_mul_mat_mat_q8_1[GGML_TYPE_Q5_0], matmul_q5_0_q8_1, mmq_wg_denoms, warptile_mmq_int, vk_mat_mat_push_constants, 3, );
-            CREATE_MMQ(GGML_TYPE_Q5_1, pipeline_dequant_mul_mat_mat_q8_1[GGML_TYPE_Q5_1], matmul_q5_1_q8_1, mmq_wg_denoms, warptile_mmq_int, vk_mat_mat_push_constants, 3, );
-            CREATE_MMQ(GGML_TYPE_Q8_0, pipeline_dequant_mul_mat_mat_q8_1[GGML_TYPE_Q8_0], matmul_q8_0_q8_1, mmq_wg_denoms, warptile_mmq_int, vk_mat_mat_push_constants, 3, );
+            CREATE_MMQ(GGML_TYPE_Q4_0, pipeline_dequant_mul_mat_mat_q8_1[GGML_TYPE_Q4_0], matmul_q4_0_q8_1, mmq_wg_denoms, warptile_mmq_int, vk_mat_mat_push_constants, 3, , 0);
+            CREATE_MMQ(GGML_TYPE_Q4_1, pipeline_dequant_mul_mat_mat_q8_1[GGML_TYPE_Q4_1], matmul_q4_1_q8_1, mmq_wg_denoms, warptile_mmq_int, vk_mat_mat_push_constants, 3, , 0);
+            CREATE_MMQ(GGML_TYPE_Q5_0, pipeline_dequant_mul_mat_mat_q8_1[GGML_TYPE_Q5_0], matmul_q5_0_q8_1, mmq_wg_denoms, warptile_mmq_int, vk_mat_mat_push_constants, 3, , 0);
+            CREATE_MMQ(GGML_TYPE_Q5_1, pipeline_dequant_mul_mat_mat_q8_1[GGML_TYPE_Q5_1], matmul_q5_1_q8_1, mmq_wg_denoms, warptile_mmq_int, vk_mat_mat_push_constants, 3, , 0);
+            CREATE_MMQ(GGML_TYPE_Q8_0, pipeline_dequant_mul_mat_mat_q8_1[GGML_TYPE_Q8_0], matmul_q8_0_q8_1, mmq_wg_denoms, warptile_mmq_int, vk_mat_mat_push_constants, 3, , 0);
+
+            CREATE_MMQ(GGML_TYPE_MXFP4, pipeline_dequant_mul_mat_mat_q8_1[GGML_TYPE_MXFP4], matmul_mxfp4_q8_1, mmq_wg_denoms, warptile_mmq_int, vk_mat_mat_push_constants, 3, , 0);
+
+            CREATE_MMQ(GGML_TYPE_Q2_K, pipeline_dequant_mul_mat_mat_q8_1[GGML_TYPE_Q2_K], matmul_q2_k_q8_1, mmq_wg_denoms, warptile_mmq_int_k, vk_mat_mat_push_constants, 3, , 0);
+            CREATE_MMQ(GGML_TYPE_Q3_K, pipeline_dequant_mul_mat_mat_q8_1[GGML_TYPE_Q3_K], matmul_q3_k_q8_1, mmq_wg_denoms, warptile_mmq_int_k, vk_mat_mat_push_constants, 3, , 0);
+            CREATE_MMQ(GGML_TYPE_Q4_K, pipeline_dequant_mul_mat_mat_q8_1[GGML_TYPE_Q4_K], matmul_q4_k_q8_1, mmq_wg_denoms, warptile_mmq_int_k, vk_mat_mat_push_constants, 3, , 0);
+            CREATE_MMQ(GGML_TYPE_Q5_K, pipeline_dequant_mul_mat_mat_q8_1[GGML_TYPE_Q5_K], matmul_q5_k_q8_1, mmq_wg_denoms, warptile_mmq_int_k, vk_mat_mat_push_constants, 3, , 0);
+            CREATE_MMQ(GGML_TYPE_Q6_K, pipeline_dequant_mul_mat_mat_q8_1[GGML_TYPE_Q6_K], matmul_q6_k_q8_1, mmq_wg_denoms, warptile_mmq_int_k, vk_mat_mat_push_constants, 3, , 0);
         }
 #endif
 
@@ -2996,6 +3019,24 @@ static void ggml_vk_load_shaders(vk_device& device) {
             CREATE_MM2(GGML_TYPE_IQ4_XS,  pipeline_dequant_mul_mat_mat_id[GGML_TYPE_IQ4_XS],  matmul_id_subgroup_iq4_xs_f32,  mmq_wg_denoms, warptile_mmqid, vk_mat_mat_id_push_constants, 4, _id, mul_mat_subgroup_size);
             CREATE_MM2(GGML_TYPE_IQ4_NL,  pipeline_dequant_mul_mat_mat_id[GGML_TYPE_IQ4_NL],  matmul_id_subgroup_iq4_nl_f32,  mmq_wg_denoms, warptile_mmqid, vk_mat_mat_id_push_constants, 4, _id, mul_mat_subgroup_size);
             CREATE_MM2(GGML_TYPE_MXFP4,   pipeline_dequant_mul_mat_mat_id[GGML_TYPE_MXFP4],   matmul_id_subgroup_mxfp4_f32,   mmq_wg_denoms, warptile_mmqid, vk_mat_mat_id_push_constants, 4, _id, mul_mat_subgroup_size);
+
+#if defined(GGML_VULKAN_INTEGER_DOT_GLSLC_SUPPORT)
+            if (device->integer_dot_product) {
+                CREATE_MMQ(GGML_TYPE_Q4_0, pipeline_dequant_mul_mat_mat_id_q8_1[GGML_TYPE_Q4_0], matmul_id_subgroup_q4_0_q8_1, mmq_wg_denoms, warptile_mmqid_int,   vk_mat_mat_id_push_constants, 4, _id, mul_mat_subgroup_size);
+                CREATE_MMQ(GGML_TYPE_Q4_1, pipeline_dequant_mul_mat_mat_id_q8_1[GGML_TYPE_Q4_1], matmul_id_subgroup_q4_1_q8_1, mmq_wg_denoms, warptile_mmqid_int,   vk_mat_mat_id_push_constants, 4, _id, mul_mat_subgroup_size);
+                CREATE_MMQ(GGML_TYPE_Q5_0, pipeline_dequant_mul_mat_mat_id_q8_1[GGML_TYPE_Q5_0], matmul_id_subgroup_q5_0_q8_1, mmq_wg_denoms, warptile_mmqid_int,   vk_mat_mat_id_push_constants, 4, _id, mul_mat_subgroup_size);
+                CREATE_MMQ(GGML_TYPE_Q5_1, pipeline_dequant_mul_mat_mat_id_q8_1[GGML_TYPE_Q5_1], matmul_id_subgroup_q5_1_q8_1, mmq_wg_denoms, warptile_mmqid_int,   vk_mat_mat_id_push_constants, 4, _id, mul_mat_subgroup_size);
+                CREATE_MMQ(GGML_TYPE_Q8_0, pipeline_dequant_mul_mat_mat_id_q8_1[GGML_TYPE_Q8_0], matmul_id_subgroup_q8_0_q8_1, mmq_wg_denoms, warptile_mmqid_int,   vk_mat_mat_id_push_constants, 4, _id, mul_mat_subgroup_size);
+
+                CREATE_MMQ(GGML_TYPE_MXFP4, pipeline_dequant_mul_mat_mat_id_q8_1[GGML_TYPE_MXFP4], matmul_id_subgroup_mxfp4_q8_1, mmq_wg_denoms, warptile_mmqid_int,   vk_mat_mat_id_push_constants, 4, _id, mul_mat_subgroup_size);
+
+                CREATE_MMQ(GGML_TYPE_Q2_K, pipeline_dequant_mul_mat_mat_id_q8_1[GGML_TYPE_Q2_K], matmul_id_subgroup_q2_k_q8_1, mmq_wg_denoms, warptile_mmqid_int_k, vk_mat_mat_id_push_constants, 4, _id, mul_mat_subgroup_size_16);
+                CREATE_MMQ(GGML_TYPE_Q3_K, pipeline_dequant_mul_mat_mat_id_q8_1[GGML_TYPE_Q3_K], matmul_id_subgroup_q3_k_q8_1, mmq_wg_denoms, warptile_mmqid_int_k, vk_mat_mat_id_push_constants, 4, _id, mul_mat_subgroup_size_16);
+                CREATE_MMQ(GGML_TYPE_Q4_K, pipeline_dequant_mul_mat_mat_id_q8_1[GGML_TYPE_Q4_K], matmul_id_subgroup_q4_k_q8_1, mmq_wg_denoms, warptile_mmqid_int_k, vk_mat_mat_id_push_constants, 4, _id, mul_mat_subgroup_size_16);
+                CREATE_MMQ(GGML_TYPE_Q5_K, pipeline_dequant_mul_mat_mat_id_q8_1[GGML_TYPE_Q5_K], matmul_id_subgroup_q5_k_q8_1, mmq_wg_denoms, warptile_mmqid_int_k, vk_mat_mat_id_push_constants, 4, _id, mul_mat_subgroup_size_16);
+                CREATE_MMQ(GGML_TYPE_Q6_K, pipeline_dequant_mul_mat_mat_id_q8_1[GGML_TYPE_Q6_K], matmul_id_subgroup_q6_k_q8_1, mmq_wg_denoms, warptile_mmqid_int_k, vk_mat_mat_id_push_constants, 4, _id, mul_mat_subgroup_size_16);
+            }
+#endif
         } else {
             CREATE_MM(GGML_TYPE_F32, pipeline_matmul_id_f32, matmul_id_f32_f32, , wg_denoms, warptile, vk_mat_mat_push_constants, 4, _id, 0);
             CREATE_MM2(GGML_TYPE_F16, pipeline_matmul_id_f16, matmul_id_f16, wg_denoms, warptile, vk_mat_mat_push_constants, 4, _id, 0);
@@ -3022,6 +3063,24 @@ static void ggml_vk_load_shaders(vk_device& device) {
             CREATE_MM2(GGML_TYPE_IQ4_XS,  pipeline_dequant_mul_mat_mat_id[GGML_TYPE_IQ4_XS],  matmul_id_iq4_xs_f32,  mmq_wg_denoms, warptile_mmqid, vk_mat_mat_id_push_constants, 4, _id, 0);
             CREATE_MM2(GGML_TYPE_IQ4_NL,  pipeline_dequant_mul_mat_mat_id[GGML_TYPE_IQ4_NL],  matmul_id_iq4_nl_f32,  mmq_wg_denoms, warptile_mmqid, vk_mat_mat_id_push_constants, 4, _id, 0);
             CREATE_MM2(GGML_TYPE_MXFP4,   pipeline_dequant_mul_mat_mat_id[GGML_TYPE_MXFP4],   matmul_id_mxfp4_f32,   mmq_wg_denoms, warptile_mmqid, vk_mat_mat_id_push_constants, 4, _id, 0);
+
+#if defined(GGML_VULKAN_INTEGER_DOT_GLSLC_SUPPORT)
+            if (device->integer_dot_product) {
+                CREATE_MMQ(GGML_TYPE_Q4_0, pipeline_dequant_mul_mat_mat_id_q8_1[GGML_TYPE_Q4_0], matmul_id_q4_0_q8_1, mmq_wg_denoms, warptile_mmqid_int,   vk_mat_mat_id_push_constants, 4, _id, 0);
+                CREATE_MMQ(GGML_TYPE_Q4_1, pipeline_dequant_mul_mat_mat_id_q8_1[GGML_TYPE_Q4_1], matmul_id_q4_1_q8_1, mmq_wg_denoms, warptile_mmqid_int,   vk_mat_mat_id_push_constants, 4, _id, 0);
+                CREATE_MMQ(GGML_TYPE_Q5_0, pipeline_dequant_mul_mat_mat_id_q8_1[GGML_TYPE_Q5_0], matmul_id_q5_0_q8_1, mmq_wg_denoms, warptile_mmqid_int,   vk_mat_mat_id_push_constants, 4, _id, 0);
+                CREATE_MMQ(GGML_TYPE_Q5_1, pipeline_dequant_mul_mat_mat_id_q8_1[GGML_TYPE_Q5_1], matmul_id_q5_1_q8_1, mmq_wg_denoms, warptile_mmqid_int,   vk_mat_mat_id_push_constants, 4, _id, 0);
+                CREATE_MMQ(GGML_TYPE_Q8_0, pipeline_dequant_mul_mat_mat_id_q8_1[GGML_TYPE_Q8_0], matmul_id_q8_0_q8_1, mmq_wg_denoms, warptile_mmqid_int,   vk_mat_mat_id_push_constants, 4, _id, 0);
+
+                CREATE_MMQ(GGML_TYPE_MXFP4, pipeline_dequant_mul_mat_mat_id_q8_1[GGML_TYPE_MXFP4], matmul_id_mxfp4_q8_1, mmq_wg_denoms, warptile_mmqid_int,   vk_mat_mat_id_push_constants, 4, _id, 0);
+
+                CREATE_MMQ(GGML_TYPE_Q2_K, pipeline_dequant_mul_mat_mat_id_q8_1[GGML_TYPE_Q2_K], matmul_id_q2_k_q8_1, mmq_wg_denoms, warptile_mmqid_int_k, vk_mat_mat_id_push_constants, 4, _id, 0);
+                CREATE_MMQ(GGML_TYPE_Q3_K, pipeline_dequant_mul_mat_mat_id_q8_1[GGML_TYPE_Q3_K], matmul_id_q3_k_q8_1, mmq_wg_denoms, warptile_mmqid_int_k, vk_mat_mat_id_push_constants, 4, _id, 0);
+                CREATE_MMQ(GGML_TYPE_Q4_K, pipeline_dequant_mul_mat_mat_id_q8_1[GGML_TYPE_Q4_K], matmul_id_q4_k_q8_1, mmq_wg_denoms, warptile_mmqid_int_k, vk_mat_mat_id_push_constants, 4, _id, 0);
+                CREATE_MMQ(GGML_TYPE_Q5_K, pipeline_dequant_mul_mat_mat_id_q8_1[GGML_TYPE_Q5_K], matmul_id_q5_k_q8_1, mmq_wg_denoms, warptile_mmqid_int_k, vk_mat_mat_id_push_constants, 4, _id, 0);
+                CREATE_MMQ(GGML_TYPE_Q6_K, pipeline_dequant_mul_mat_mat_id_q8_1[GGML_TYPE_Q6_K], matmul_id_q6_k_q8_1, mmq_wg_denoms, warptile_mmqid_int_k, vk_mat_mat_id_push_constants, 4, _id, 0);
+            }
+#endif
         }
 #undef CREATE_MM2
 #undef CREATE_MMQ
@@ -3086,6 +3145,12 @@ static void ggml_vk_load_shaders(vk_device& device) {
             CREATE_MMQ(GGML_TYPE_Q5_0, pipeline_dequant_mul_mat_mat_q8_1[GGML_TYPE_Q5_0].f32acc, matmul_q5_0_q8_1, mmq_wg_denoms, warptile_mmq_int, vk_mat_mat_push_constants, 3, );
             CREATE_MMQ(GGML_TYPE_Q5_1, pipeline_dequant_mul_mat_mat_q8_1[GGML_TYPE_Q5_1].f32acc, matmul_q5_1_q8_1, mmq_wg_denoms, warptile_mmq_int, vk_mat_mat_push_constants, 3, );
             CREATE_MMQ(GGML_TYPE_Q8_0, pipeline_dequant_mul_mat_mat_q8_1[GGML_TYPE_Q8_0].f32acc, matmul_q8_0_q8_1, mmq_wg_denoms, warptile_mmq_int, vk_mat_mat_push_constants, 3, );
+
+            CREATE_MMQ(GGML_TYPE_Q2_K, pipeline_dequant_mul_mat_mat_q8_1[GGML_TYPE_Q2_K].f32acc, matmul_q2_k_q8_1, mmq_wg_denoms, warptile_mmq_int_k, vk_mat_mat_push_constants, 3, );
+            CREATE_MMQ(GGML_TYPE_Q3_K, pipeline_dequant_mul_mat_mat_q8_1[GGML_TYPE_Q3_K].f32acc, matmul_q3_k_q8_1, mmq_wg_denoms, warptile_mmq_int_k, vk_mat_mat_push_constants, 3, );
+            CREATE_MMQ(GGML_TYPE_Q4_K, pipeline_dequant_mul_mat_mat_q8_1[GGML_TYPE_Q4_K].f32acc, matmul_q4_k_q8_1, mmq_wg_denoms, warptile_mmq_int_k, vk_mat_mat_push_constants, 3, );
+            CREATE_MMQ(GGML_TYPE_Q5_K, pipeline_dequant_mul_mat_mat_q8_1[GGML_TYPE_Q5_K].f32acc, matmul_q5_k_q8_1, mmq_wg_denoms, warptile_mmq_int_k, vk_mat_mat_push_constants, 3, );
+            CREATE_MMQ(GGML_TYPE_Q6_K, pipeline_dequant_mul_mat_mat_q8_1[GGML_TYPE_Q6_K].f32acc, matmul_q6_k_q8_1, mmq_wg_denoms, warptile_mmq_int_k, vk_mat_mat_push_constants, 3, );
         }
 #endif
 
@@ -3145,7 +3210,7 @@ static void ggml_vk_load_shaders(vk_device& device) {
     }
     // reusing CREATE_MM from the fp32 path
     if ((device->coopmat2 || device->coopmat_support)
-#if defined(GGML_VULKAN_INTEGER_DOT_GLSLC_SUPPORT)
+#if defined(GGML_VULKAN_BFLOAT16_GLSLC_SUPPORT)
         && !device->coopmat_bf16_support
 #endif
         ) {
@@ -4928,7 +4993,7 @@ static vk_matmul_pipeline ggml_vk_get_mul_mat_mat_pipeline(ggml_backend_vk_conte
 
     // MMQ
     if (src1_type == GGML_TYPE_Q8_1) {
-        vk_matmul_pipeline pipelines = (ctx->device->fp16 && prec == GGML_PREC_DEFAULT) ? ctx->device->pipeline_dequant_mul_mat_mat_q8_1[src0_type].f16acc : ctx->device->pipeline_dequant_mul_mat_mat_q8_1[src0_type].f32acc;
+        vk_matmul_pipeline pipelines = ctx->device->pipeline_dequant_mul_mat_mat_q8_1[src0_type].f32acc;
 
         if (pipelines->s == nullptr && pipelines->m == nullptr && pipelines->l == nullptr) {
             return nullptr;
@@ -5075,6 +5140,17 @@ static vk_matmul_pipeline ggml_vk_get_mul_mat_mat_id_pipeline(ggml_backend_vk_co
         }
     }
 
+    // MMQ
+    if (src1_type == GGML_TYPE_Q8_1) {
+        vk_matmul_pipeline pipelines = ctx->device->pipeline_dequant_mul_mat_mat_id_q8_1[src0_type].f32acc;
+
+        if (pipelines->s == nullptr && pipelines->m == nullptr && pipelines->l == nullptr) {
+            return nullptr;
+        }
+
+        return pipelines;
+    }
+
     GGML_ASSERT(src1_type == GGML_TYPE_F32 || (ctx->device->coopmat2 && src1_type == GGML_TYPE_F16));
 
     switch (src0_type) {
@@ -6877,10 +6953,19 @@ static void ggml_vk_mul_mat_id_q_f16(ggml_backend_vk_context * ctx, vk_context&
 
     const bool y_f32_kernel = src1->type == GGML_TYPE_F32 && !y_non_contig;
 
-    vk_matmul_pipeline mmp = ggml_vk_get_mul_mat_mat_id_pipeline(ctx, src0->type, y_non_contig ? f16_type : src1->type, (ggml_prec)dst->op_params[0]);
+    bool quantize_y = ctx->device->integer_dot_product && src1->type == GGML_TYPE_F32 && ggml_is_contiguous(src1) && (ne11 * ne10) % 4 == 0;
+
+    // Check for mmq first
+    vk_matmul_pipeline mmp = quantize_y ? ggml_vk_get_mul_mat_mat_id_pipeline(ctx, src0->type, GGML_TYPE_Q8_1, (ggml_prec)dst->op_params[0]) : nullptr;
+
+    if (mmp == nullptr) {
+        // Fall back to f16 dequant mul mat
+        mmp = ggml_vk_get_mul_mat_mat_id_pipeline(ctx, src0->type, y_non_contig ? f16_type : src1->type, (ggml_prec)dst->op_params[0]);
+        quantize_y = false;
+    }
 
     const bool qx_needs_dequant = mmp == nullptr || x_non_contig;
-    const bool qy_needs_dequant = (src1->type != f16_type && !y_f32_kernel) || y_non_contig;
+    const bool qy_needs_dequant = !quantize_y && ((src1->type != f16_type && !y_f32_kernel) || y_non_contig);
 
     if (qx_needs_dequant) {
         // Fall back to dequant + f16 mulmat
@@ -6890,8 +6975,8 @@ static void ggml_vk_mul_mat_id_q_f16(ggml_backend_vk_context * ctx, vk_context&
     // Not implemented
     GGML_ASSERT(y_non_contig || !qy_needs_dequant);  // NOLINT
 
-    const uint32_t kpad = ggml_vk_align_size(ne10, ggml_vk_guess_matmul_id_pipeline_align(ctx, mmp, ne01, nei1, qx_needs_dequant ? f16_type : src0->type));
-    const bool aligned = ne10 == kpad && ne01 > 8 && nei1 > 8;
+    const uint32_t kpad = quantize_y ? 0 : ggml_vk_align_size(ne10, ggml_vk_guess_matmul_id_pipeline_align(ctx, mmp, ne01, nei1, qx_needs_dequant ? f16_type : src0->type));
+    const bool aligned = !quantize_y && ne10 == kpad && ne01 > 8 && nei1 > 8;
 
     vk_pipeline pipeline = ggml_vk_guess_matmul_id_pipeline(ctx, mmp, ne01, nei1, aligned, qx_needs_dequant ? f16_type : src0->type);
 
@@ -6904,12 +6989,13 @@ static void ggml_vk_mul_mat_id_q_f16(ggml_backend_vk_context * ctx, vk_context&
     const uint64_t qx_sz = ggml_type_size(src0->type) * x_ne / ggml_blck_size(src0->type);
     const uint64_t qy_sz = ggml_type_size(src1->type) * y_ne / ggml_blck_size(src1->type);
     const uint64_t x_sz = !qx_needs_dequant ? qx_sz : sizeof(ggml_fp16_t) * x_ne;
-    const uint64_t y_sz = y_f32_kernel ? sizeof(float) * y_ne : sizeof(ggml_fp16_t) * y_ne;
+    const uint64_t y_sz = quantize_y ? (y_ne * ggml_type_size(GGML_TYPE_Q8_1) / ggml_blck_size(GGML_TYPE_Q8_1)) : (y_f32_kernel ? sizeof(float) * y_ne : sizeof(ggml_fp16_t) * y_ne);
     const uint64_t ids_sz = nbi2;
     const uint64_t d_sz = sizeof(float) * d_ne;
 
     vk_pipeline to_fp16_vk_0 = nullptr;
     vk_pipeline to_fp16_vk_1 = nullptr;
+    vk_pipeline to_q8_1 = nullptr;
 
     if (x_non_contig) {
         to_fp16_vk_0 = ggml_vk_get_cpy_pipeline(ctx, src0, nullptr, f16_type);
@@ -6924,9 +7010,16 @@ static void ggml_vk_mul_mat_id_q_f16(ggml_backend_vk_context * ctx, vk_context&
     GGML_ASSERT(!qx_needs_dequant || to_fp16_vk_0 != nullptr);  // NOLINT
     GGML_ASSERT(!qy_needs_dequant || to_fp16_vk_1 != nullptr);  // NOLINT
 
+    if (quantize_y) {
+        to_q8_1 = ggml_vk_get_quantize_pipeline(ctx, GGML_TYPE_Q8_1, true);
+    }
+
     if (dryrun) {
         const uint64_t x_sz_upd = x_sz * ne02 * ne03;
-        const uint64_t y_sz_upd = y_sz * ne12 * ne13;
+        uint64_t y_sz_upd = y_sz * ne12 * ne13;
+        if (quantize_y) {
+            y_sz_upd = CEIL_DIV(y_sz_upd, 144) * 144;
+        }
         if (
                 (qx_needs_dequant && x_sz_upd > ctx->device->properties.limits.maxStorageBufferRange) ||
                 (qy_needs_dequant && y_sz_upd > ctx->device->properties.limits.maxStorageBufferRange)) {
@@ -6935,7 +7028,7 @@ static void ggml_vk_mul_mat_id_q_f16(ggml_backend_vk_context * ctx, vk_context&
         if (qx_needs_dequant && ctx->prealloc_size_x < x_sz_upd) {
             ctx->prealloc_size_x = x_sz_upd;
         }
-        if (qy_needs_dequant && ctx->prealloc_size_y < y_sz_upd) {
+        if ((qy_needs_dequant || quantize_y) && ctx->prealloc_size_y < y_sz_upd) {
             ctx->prealloc_size_y = y_sz_upd;
         }
 
@@ -6947,6 +7040,9 @@ static void ggml_vk_mul_mat_id_q_f16(ggml_backend_vk_context * ctx, vk_context&
         if (qy_needs_dequant) {
             ggml_pipeline_request_descriptor_sets(ctx, to_fp16_vk_1, 1);
         }
+        if (quantize_y) {
+            ggml_pipeline_request_descriptor_sets(ctx, to_q8_1, 1);
+        }
         return;
     }
 
@@ -6983,6 +7079,9 @@ static void ggml_vk_mul_mat_id_q_f16(ggml_backend_vk_context * ctx, vk_context&
     if (qy_needs_dequant) {
         d_Y = ctx->prealloc_y;
         GGML_ASSERT(d_Y->size >= y_sz * ne12 * ne13);
+    } else if (quantize_y) {
+        d_Y = ctx->prealloc_y;
+        GGML_ASSERT(d_Y->size >= CEIL_DIV(y_sz * ne12 * ne13, 144) * 144);
     } else {
         d_Y = d_Qy;
         y_buf_offset = qy_buf_offset;
@@ -7014,6 +7113,17 @@ static void ggml_vk_mul_mat_id_q_f16(ggml_backend_vk_context * ctx, vk_context&
             ctx->prealloc_y_last_tensor_used = src1;
         }
     }
+    if (quantize_y) {
+        if (ctx->prealloc_y_last_pipeline_used != to_q8_1.get() ||
+            ctx->prealloc_y_last_tensor_used != src1) {
+            if (ctx->prealloc_y_need_sync) {
+                ggml_vk_sync_buffers(ctx, subctx);
+            }
+            ggml_vk_quantize_q8_1(ctx, subctx, ggml_vk_subbuffer(ctx, d_Qy, qy_buf_offset), ggml_vk_subbuffer(ctx, d_Y, 0), y_ne * ne12 * ne13, true);
+            ctx->prealloc_y_last_pipeline_used = to_q8_1.get();
+            ctx->prealloc_y_last_tensor_used = src1;
+        }
+    }
 
     uint32_t stride_batch_x = ne00*ne01;
     uint32_t stride_batch_y = ne10*ne11;
@@ -7022,14 +7132,19 @@ static void ggml_vk_mul_mat_id_q_f16(ggml_backend_vk_context * ctx, vk_context&
         stride_batch_x = src0->nb[0] / ggml_type_size(src0->type);
     }
 
-    if (!ggml_vk_dim01_contiguous(src1) && !qy_needs_dequant) {
+    if (!ggml_vk_dim01_contiguous(src1) && !qy_needs_dequant && !quantize_y) {
         stride_batch_y = src1->nb[0] / ggml_type_size(src1->type);
     }
 
+    uint32_t y_sz_total = y_sz * ne12 * ne13;
+    if (quantize_y) {
+        y_sz_total = CEIL_DIV(y_sz_total, 144) * 144;
+    }
+
     // compute
     ggml_vk_matmul_id(
         ctx, subctx, pipeline,
-        { d_X, x_buf_offset, x_sz * ne02 * ne03 }, { d_Y, y_buf_offset, y_sz * ne12 * ne13 },
+        { d_X, x_buf_offset, x_sz * ne02 * ne03 }, { d_Y, y_buf_offset, y_sz_total },
         { d_D, d_buf_offset, d_sz * ne22 * ne23 }, { d_ids, ids_buf_offset, ids_sz },
         ne01, ne21, ne10, ne10, ne10, ne01,
         stride_batch_x, stride_batch_y, ne20*ne21,
diff --git a/ggml/src/ggml-vulkan/vulkan-shaders/dequant_funcs.glsl b/ggml/src/ggml-vulkan/vulkan-shaders/dequant_funcs.glsl
index 0d98f5a9d6b..09676a623ba 100644
--- a/ggml/src/ggml-vulkan/vulkan-shaders/dequant_funcs.glsl
+++ b/ggml/src/ggml-vulkan/vulkan-shaders/dequant_funcs.glsl
@@ -437,7 +437,7 @@ vec4 dequantize4(uint ib, uint iqs, uint a_offset) {
 #if defined(DATA_A_MXFP4)
 vec2 dequantize(uint ib, uint iqs, uint a_offset) {
     const uint vui = uint(data_a[a_offset + ib].qs[iqs]);
-    return vec2(kvalues_mxfp4[vui & 0xF], kvalues_mxfp4[vui >> 4]);
+    return vec2(kvalues_mxfp4[vui & 0xF], kvalues_mxfp4[vui >> 4]) * 0.5;
 }
 vec4 dequantize4(uint ib, uint iqs, uint a_offset) {
     vec2 v0 = dequantize(ib, iqs, a_offset);
@@ -488,9 +488,9 @@ vec2 dequantize(uint ib, uint iqs, uint a_offset) {
 
     const uvec2 qs = uvec2(data_a[a_offset + ib].qs[qsi], data_a[a_offset + ib].qs[qsi + 1]);
     const uint scales = data_a[a_offset + ib].scales[scalesi];
-    const vec2 d = vec2(data_a[a_offset + ib].d);
+    const vec2 dm = vec2(data_a[a_offset + ib].dm);
 
-    return d.x * float(scales & 0xF) * vec2((qs >> qsshift) & 3) - d.y * float(scales >> 4);
+    return dm.x * float(scales & 0xF) * vec2((qs >> qsshift) & 3) - dm.y * float(scales >> 4);
 }
 vec2 get_dm(uint ib, uint a_offset) {
     return vec2(1, 0);
@@ -529,7 +529,7 @@ vec2 dequantize(uint ib, uint iqs, uint a_offset) {
     const uint is = 2 * n + b;                 // 0..7
     const uint qsi = n * 32 + (iqs % 16) * 2;  // 0,2,4..126
 
-    const vec2 loadd = vec2(data_a[a_offset + ib].d);
+    const vec2 loadd = vec2(data_a[a_offset + ib].dm);
 
     const uint scidx0 = (is < 4) ? is : (is + 4);
     const uint scidx1 = (is < 4) ? is : (is - 4);
@@ -567,7 +567,7 @@ vec2 dequantize(uint ib, uint iqs, uint a_offset) {
 
     const uint8_t hm = uint8_t(1 << (iqs / 16));
 
-    const vec2 loadd = vec2(data_a[a_offset + ib].d);
+    const vec2 loadd = vec2(data_a[a_offset + ib].dm);
 
     const uint scidx0 = (is < 4) ? is : (is + 4);
     const uint scidx1 = (is < 4) ? is : (is - 4);
diff --git a/ggml/src/ggml-vulkan/vulkan-shaders/dequant_funcs_cm2.glsl b/ggml/src/ggml-vulkan/vulkan-shaders/dequant_funcs_cm2.glsl
index 67baedf7c61..8ac6482dc94 100644
--- a/ggml/src/ggml-vulkan/vulkan-shaders/dequant_funcs_cm2.glsl
+++ b/ggml/src/ggml-vulkan/vulkan-shaders/dequant_funcs_cm2.glsl
@@ -120,7 +120,7 @@ layout(buffer_reference, std430, buffer_reference_align = 16) buffer decodeBufQ2
 float16_t dequantFuncQ2_K(const in decodeBufQ2_K bl, const in uint blockCoords[2], const in uint coordInBlock[2])
 {
     decodeBufQ2_K_packed16 bl16 = decodeBufQ2_K_packed16(bl);
-    const f16vec2 d = bl.block.d;
+    const f16vec2 dm = bl.block.dm;
     const uint idx = coordInBlock[1];
 
     const uint scalesi = (idx & 0xF0) >> 4;             // 0..15
@@ -131,7 +131,7 @@ float16_t dequantFuncQ2_K(const in decodeBufQ2_K bl, const in uint blockCoords[2
     qs = unpack8(qs)[idx & 1];
 
     const uint scales = bl.block.scales[scalesi];
-    float16_t ret = d.x * float16_t(scales & 0xF) * float16_t(qs) - d.y * float16_t(scales >> 4);
+    float16_t ret = dm.x * float16_t(scales & 0xF) * float16_t(qs) - dm.y * float16_t(scales >> 4);
     return ret;
 }
 
@@ -680,7 +680,7 @@ float16_t dequantFuncMXFP4(const in decodeBufMXFP4 bl, const in uint blockCoords
     uint32_t qs = bl.block.qs[iqs];
     qs >>= shift;
     qs &= 0xF;
-    float16_t ret = float16_t(kvalues_mxfp4[qs] * d);
+    float16_t ret = float16_t(kvalues_mxfp4[qs] * d * 0.5);
     return ret;
 }
 #endif
diff --git a/ggml/src/ggml-vulkan/vulkan-shaders/dequant_mxfp4.comp b/ggml/src/ggml-vulkan/vulkan-shaders/dequant_mxfp4.comp
index ffba5a77ddf..3194ba291f3 100644
--- a/ggml/src/ggml-vulkan/vulkan-shaders/dequant_mxfp4.comp
+++ b/ggml/src/ggml-vulkan/vulkan-shaders/dequant_mxfp4.comp
@@ -26,7 +26,7 @@ void main() {
     const float d = e8m0_to_fp32(data_a[ib].e);
 
     [[unroll]] for (uint l = 0; l < 8; ++l) {
-        data_b[b_idx + l +  0] = D_TYPE(d * kvalues_mxfp4[data_a[ib].qs[q_idx + l] & 0xF]);
-        data_b[b_idx + l + 16] = D_TYPE(d * kvalues_mxfp4[data_a[ib].qs[q_idx + l] >>  4]);
+        data_b[b_idx + l +  0] = D_TYPE(d * 0.5 * float(kvalues_mxfp4[data_a[ib].qs[q_idx + l] & 0xF]));
+        data_b[b_idx + l + 16] = D_TYPE(d * 0.5 * float(kvalues_mxfp4[data_a[ib].qs[q_idx + l] >>  4]));
     }
 }
diff --git a/ggml/src/ggml-vulkan/vulkan-shaders/dequant_q2_k.comp b/ggml/src/ggml-vulkan/vulkan-shaders/dequant_q2_k.comp
index 58dc2e5dfde..dc05a783489 100644
--- a/ggml/src/ggml-vulkan/vulkan-shaders/dequant_q2_k.comp
+++ b/ggml/src/ggml-vulkan/vulkan-shaders/dequant_q2_k.comp
@@ -24,8 +24,8 @@ void main() {
         const uint ql_idx = 32 * ip + il;
         const uint8_t qs = data_a[i].qs[32 * ip + il];
 
-        FLOAT_TYPE dall = FLOAT_TYPE(data_a[i].d.x);
-        FLOAT_TYPE dmin = FLOAT_TYPE(data_a[i].d.y);
+        FLOAT_TYPE dall = FLOAT_TYPE(data_a[i].dm.x);
+        FLOAT_TYPE dmin = FLOAT_TYPE(data_a[i].dm.y);
         data_b[y_idx +  0] = D_TYPE(dall * FLOAT_TYPE((data_a[i].scales[is+0] & 0xF) * ((qs >> 0) & 3)) - dmin * FLOAT_TYPE(data_a[i].scales[is+0] >> 4));
         data_b[y_idx + 32] = D_TYPE(dall * FLOAT_TYPE((data_a[i].scales[is+2] & 0xF) * ((qs >> 2) & 3)) - dmin * FLOAT_TYPE(data_a[i].scales[is+2] >> 4));
         data_b[y_idx + 64] = D_TYPE(dall * FLOAT_TYPE((data_a[i].scales[is+4] & 0xF) * ((qs >> 4) & 3)) - dmin * FLOAT_TYPE(data_a[i].scales[is+4] >> 4));
diff --git a/ggml/src/ggml-vulkan/vulkan-shaders/dequant_q4_k.comp b/ggml/src/ggml-vulkan/vulkan-shaders/dequant_q4_k.comp
index 8b7be557e95..0f23dc0a349 100644
--- a/ggml/src/ggml-vulkan/vulkan-shaders/dequant_q4_k.comp
+++ b/ggml/src/ggml-vulkan/vulkan-shaders/dequant_q4_k.comp
@@ -20,8 +20,8 @@ void main() {
         const uint is = 2 * il;
         const uint n = 4;
 
-        const FLOAT_TYPE dall = FLOAT_TYPE(data_a[ib].d.x);
-        const FLOAT_TYPE dmin = FLOAT_TYPE(data_a[ib].d.y);
+        const FLOAT_TYPE dall = FLOAT_TYPE(data_a[ib].dm.x);
+        const FLOAT_TYPE dmin = FLOAT_TYPE(data_a[ib].dm.y);
 
         const uint y_idx = ib * QUANT_K + 64 * il + n * ir;
         const uint qs_idx = 32*il + n * ir;
diff --git a/ggml/src/ggml-vulkan/vulkan-shaders/dequant_q5_k.comp b/ggml/src/ggml-vulkan/vulkan-shaders/dequant_q5_k.comp
index 6bc04670fc5..970469a601c 100644
--- a/ggml/src/ggml-vulkan/vulkan-shaders/dequant_q5_k.comp
+++ b/ggml/src/ggml-vulkan/vulkan-shaders/dequant_q5_k.comp
@@ -19,8 +19,8 @@ void main() {
         const uint ir = tid % 16;
         const uint is = 2 * il;
 
-        const FLOAT_TYPE dall = FLOAT_TYPE(data_a[ib].d.x);
-        const FLOAT_TYPE dmin = FLOAT_TYPE(data_a[ib].d.y);
+        const FLOAT_TYPE dall = FLOAT_TYPE(data_a[ib].dm.x);
+        const FLOAT_TYPE dmin = FLOAT_TYPE(data_a[ib].dm.y);
 
         const uint y_idx = ib * QUANT_K + 64 * il + 2 * ir;
         const uint qs_idx = 32*il + 2 * ir;
diff --git a/ggml/src/ggml-vulkan/vulkan-shaders/mul_mat_vec_q2_k.comp b/ggml/src/ggml-vulkan/vulkan-shaders/mul_mat_vec_q2_k.comp
index 03ed25d3bfe..14093c0de5a 100644
--- a/ggml/src/ggml-vulkan/vulkan-shaders/mul_mat_vec_q2_k.comp
+++ b/ggml/src/ggml-vulkan/vulkan-shaders/mul_mat_vec_q2_k.comp
@@ -41,9 +41,7 @@ void calc_superblock(const uint a_offset, const uint b_offset, const uint itid,
         const vec4 qs_u32_4 = vec4(unpack8((qs_u32 >> 4) & 0x03030303));
         const vec4 qs_u32_6 = vec4(unpack8((qs_u32 >> 6) & 0x03030303));
 
-        vec2 d = vec2(data_a[ib0 + i].d);
-        const FLOAT_TYPE dall = FLOAT_TYPE(d.x);
-        const FLOAT_TYPE dmin = FLOAT_TYPE(d.y);
+        const FLOAT_TYPE_VEC2 dm = vec2(data_a[ib0 + i].dm);
 
         [[unroll]] for (uint j = 0; j < NUM_COLS; ++j) {
             vec2 b0 =   vec2(data_b_v2[(j*p.batch_stride_b + b_offset + y_idx) / 2 +  0]);
@@ -75,7 +73,7 @@ void calc_superblock(const uint a_offset, const uint b_offset, const uint itid,
                        fma(FLOAT_TYPE(b96[l]),  sccache2[csel][ix][6 + 8*v_im],
                        fma(FLOAT_TYPE(b112[l]), sccache2[csel][ix][7 + 8*v_im], sum2))))))));
             }
-            temp[j][n] = fma(dall, sum1, fma(-dmin, sum2, temp[j][n]));
+            temp[j][n] = fma(dm.x, sum1, fma(-dm.y, sum2, temp[j][n]));
         }
     }
 }
diff --git a/ggml/src/ggml-vulkan/vulkan-shaders/mul_mat_vec_q4_k.comp b/ggml/src/ggml-vulkan/vulkan-shaders/mul_mat_vec_q4_k.comp
index 21d07d2e509..49d91ad5910 100644
--- a/ggml/src/ggml-vulkan/vulkan-shaders/mul_mat_vec_q4_k.comp
+++ b/ggml/src/ggml-vulkan/vulkan-shaders/mul_mat_vec_q4_k.comp
@@ -14,9 +14,7 @@ void calc_superblock(const uint a_offset, const uint b_offset, const uint v_im,
 
     [[unroll]] for (uint n = 0; n < num_rows; ++n) {
         const uint ib0 = a_offset / QUANT_K + (first_row+n)*num_blocks_per_row;
-        vec2 d = vec2(data_a[ib0 + i].d);
-        const FLOAT_TYPE dall = FLOAT_TYPE(d.x);
-        const FLOAT_TYPE dmin = FLOAT_TYPE(d.y);
+        const FLOAT_TYPE_VEC2 dm = FLOAT_TYPE_VEC2(data_a[ib0 + i].dm);
 
         const uint32_t scale0_u32 = data_a_packed16[ib0 + i].scales[v_im    ];
         const uint32_t scale4_u32 = data_a_packed16[ib0 + i].scales[v_im + 2];
@@ -81,7 +79,7 @@ void calc_superblock(const uint a_offset, const uint b_offset, const uint v_im,
                 fma(FLOAT_TYPE(by10.y), sc2, fma(FLOAT_TYPE(by132.y), sc3, fma(FLOAT_TYPE(by20.y), sc6, fma(FLOAT_TYPE(by232.y), sc7,
                 fma(FLOAT_TYPE(by10.z), sc2, fma(FLOAT_TYPE(by132.z), sc3, fma(FLOAT_TYPE(by20.z), sc6, fma(FLOAT_TYPE(by232.z), sc7,
                 fma(FLOAT_TYPE(by10.w), sc2, fma(FLOAT_TYPE(by132.w), sc3, fma(FLOAT_TYPE(by20.w), sc6,     FLOAT_TYPE(by232.w) * sc7)))))))))))))));
-            temp[j][n] = fma(dall, fma(sx, sc0, fma(sy, sc1, fma(sz, sc4, sw * sc5))), fma(-dmin, smin, temp[j][n]));
+            temp[j][n] = fma(dm.x, fma(sx, sc0, fma(sy, sc1, fma(sz, sc4, sw * sc5))), fma(-dm.y, smin, temp[j][n]));
         }
     }
 }
diff --git a/ggml/src/ggml-vulkan/vulkan-shaders/mul_mat_vec_q5_k.comp b/ggml/src/ggml-vulkan/vulkan-shaders/mul_mat_vec_q5_k.comp
index 9e46c89a11f..0d61b4966ec 100644
--- a/ggml/src/ggml-vulkan/vulkan-shaders/mul_mat_vec_q5_k.comp
+++ b/ggml/src/ggml-vulkan/vulkan-shaders/mul_mat_vec_q5_k.comp
@@ -14,9 +14,7 @@ void calc_superblock(const uint a_offset, const uint b_offset, const uint v_im,
 
     [[unroll]] for (uint n = 0; n < num_rows; ++n) {
         const uint ib0 = a_offset / QUANT_K + (first_row+n)*num_blocks_per_row;
-        vec2 d = vec2(data_a[ib0 + i].d);
-        const FLOAT_TYPE dall = FLOAT_TYPE(d.x);
-        const FLOAT_TYPE dmin = FLOAT_TYPE(d.y);
+        const FLOAT_TYPE_VEC2 dm = FLOAT_TYPE_VEC2(data_a[ib0 + i].dm);
 
         const uint32_t scale0_u32 = data_a_packed16[ib0 + i].scales[v_im    ];
         const uint32_t scale4_u32 = data_a_packed16[ib0 + i].scales[v_im + 2];
@@ -113,7 +111,7 @@ void calc_superblock(const uint a_offset, const uint b_offset, const uint v_im,
               fma(FLOAT_TYPE(by132.x) + FLOAT_TYPE(by132.y) + FLOAT_TYPE(by148.x) + FLOAT_TYPE(by148.y), sc3,
               fma(FLOAT_TYPE(by20.x) + FLOAT_TYPE(by20.y) + FLOAT_TYPE(by216.x) + FLOAT_TYPE(by216.y), sc6,
                   (FLOAT_TYPE(by232.x) + FLOAT_TYPE(by232.y) + FLOAT_TYPE(by248.x) + FLOAT_TYPE(by248.y)) * sc7)));
-            temp[j][n] = fma(dall, fma(sx, sc0, fma(sy, sc1, fma(sz, sc4, sw * sc5))), fma(-dmin, smin, temp[j][n]));
+            temp[j][n] = fma(dm.x, fma(sx, sc0, fma(sy, sc1, fma(sz, sc4, sw * sc5))), fma(-dm.y, smin, temp[j][n]));
         }
     }
 }
diff --git a/ggml/src/ggml-vulkan/vulkan-shaders/mul_mm.comp b/ggml/src/ggml-vulkan/vulkan-shaders/mul_mm.comp
index a20788c4b51..d260969f07e 100644
--- a/ggml/src/ggml-vulkan/vulkan-shaders/mul_mm.comp
+++ b/ggml/src/ggml-vulkan/vulkan-shaders/mul_mm.comp
@@ -120,81 +120,11 @@ shared FLOAT_TYPE_VEC2 buf_b[BN * SHMEM_STRIDE];
 
 #define NUM_WARPS (BLOCK_SIZE / WARP)
 
-#ifdef MUL_MAT_ID
-shared u16vec2 row_ids[BN];
-uint _ne1;
-
-#ifdef MUL_MAT_ID_USE_SUBGROUPS
-shared uvec4 ballots_sh[NUM_WARPS];
-
-void load_row_ids(uint expert_idx, bool nei0_is_pow2, uint ic) {
-    _ne1 = 0;
-    uint num_elements = p.nei1 * p.nei0;
-    uint nei0shift = findLSB(p.nei0);
-
-    uint ids[16];
-    uint iter = 0;
-
-    for (uint j = 0; j < num_elements; j += BLOCK_SIZE) {
-        // prefetch up to 16 elements
-        if (iter == 0) {
-            [[unroll]] for (uint k = 0; k < 16; ++k) {
-                uint i = j + gl_LocalInvocationIndex + k*BLOCK_SIZE;
-                bool in_range = i < num_elements;
-                uint ii1;
-                if (nei0_is_pow2) {
-                    ii1 = i >> nei0shift;
-                } else {
-                    ii1 = i / p.nei0;
-                }
-                uint ii0 = i - ii1 * p.nei0;
-                ids[k] = in_range ? data_ids[ii1*p.nbi1 + ii0] : 0;
-            }
-        }
-        uint i = j + gl_LocalInvocationIndex;
-        bool in_range = i < num_elements;
-        uint ii1;
-        if (nei0_is_pow2) {
-            ii1 = i >> nei0shift;
-        } else {
-            ii1 = i / p.nei0;
-        }
-        uint ii0 = i - ii1 * p.nei0;
-        uint id = ids[iter++];
-        uvec4 ballot = subgroupBallot(in_range && id == expert_idx);
-
-        ballots_sh[gl_SubgroupID] = ballot;
-        barrier();
-
-        uint subgroup_base = 0;
-        uint total = 0;
-        for (uint k = 0; k < gl_NumSubgroups; ++k) {
-            if (k == gl_SubgroupID) {
-                subgroup_base = total;
-            }
-            total += subgroupBallotBitCount(ballots_sh[k]);
-        }
-        barrier();
-
-        uint idx = subgroup_base + subgroupBallotExclusiveBitCount(ballot);
-        if (in_range && id == expert_idx && _ne1 + idx >= ic * BN && _ne1 + idx < (ic + 1) * BN) {
-            row_ids[_ne1 + idx - ic * BN] = u16vec2(ii0, ii1);
-        }
-        _ne1 += total;
-        iter &= 15;
-        if (_ne1 >= (ic + 1) * BN) {
-            break;
-        }
-    }
-    barrier();
-}
-#endif // MUL_MAT_ID_USE_SUBGROUPS
-#endif // MUL_MAT_ID
-
 #ifdef COOPMAT
 shared ACC_TYPE coopmat_stage[TM * TN * NUM_WARPS];
 #endif
 
+#include "mul_mm_id_funcs.glsl"
 #include "mul_mm_funcs.glsl"
 
 void main() {
diff --git a/ggml/src/ggml-vulkan/vulkan-shaders/mul_mm_funcs.glsl b/ggml/src/ggml-vulkan/vulkan-shaders/mul_mm_funcs.glsl
index 0ebfbd6462c..ee5ded2e8d3 100644
--- a/ggml/src/ggml-vulkan/vulkan-shaders/mul_mm_funcs.glsl
+++ b/ggml/src/ggml-vulkan/vulkan-shaders/mul_mm_funcs.glsl
@@ -134,15 +134,15 @@ void load_a_to_shmem(const uint pos_a, const uint row, const uint col, const uin
             const uint ib = idx / 128;                         // 2 values per idx
             const uint iqs = idx % 128;                        // 0..127
 
-            const uint qsi = (iqs / 64) * 32 + (iqs % 16) * 2; // 0,2,4..30
+            const uint qsi = (iqs / 64) * 16 + (iqs % 16);     // 0..15
             const uint scalesi = iqs / 8;                      // 0..15
             const uint qsshift = ((iqs % 64) / 16) * 2;        // 0,2,4,6
 
-            const uvec2 qs = uvec2(data_a[ib].qs[qsi], data_a[ib].qs[qsi + 1]);
+            const uvec2 qs = uvec2(unpack8(data_a_packed16[ib].qs[qsi]));
             const uint scales = data_a[ib].scales[scalesi];
-            const vec2 d = vec2(data_a[ib].d);
+            const vec2 dm = vec2(data_a[ib].dm);
 
-            const vec2 v = d.x * float(scales & 0xF) * vec2((qs >> qsshift) & 3) - d.y * float(scales >> 4);
+            const vec2 v = dm.x * float(scales & 0xF) * vec2((qs >> qsshift) & 3) - dm.y * float(scales >> 4);
 
             buf_a[buf_idx] = FLOAT_TYPE_VEC2(v.xy);
 #elif defined(DATA_A_Q3_K)
@@ -179,7 +179,7 @@ void load_a_to_shmem(const uint pos_a, const uint row, const uint col, const uin
             const uint is = 2 * n + b;                 // 0..7
             const uint qsi = n * 32 + (iqs % 16) * 2;  // 0,2,4..126
 
-            const vec2 loadd = vec2(data_a[ib].d);
+            const vec2 loadd = vec2(data_a[ib].dm);
 
             const uint scidx0 = (is < 4) ? is : (is + 4);
             const uint scidx1 = (is < 4) ? is : (is - 4);
@@ -215,7 +215,7 @@ void load_a_to_shmem(const uint pos_a, const uint row, const uint col, const uin
 
             const uint8_t hm = uint8_t(1 << (iqs / 16));
 
-            const vec2 loadd = vec2(data_a[ib].d);
+            const vec2 loadd = vec2(data_a[ib].dm);
 
             const uint scidx0 = (is < 4) ? is : (is + 4);
             const uint scidx1 = (is < 4) ? is : (is - 4);
@@ -468,7 +468,7 @@ void load_a_to_shmem(const uint pos_a, const uint row, const uint col, const uin
             const uint ib = idx / 8;
             const uint iqs = (idx & 0x07) * 2;
 
-            const float d = e8m0_to_fp32(data_a[ib].e);
+            const float d = e8m0_to_fp32(data_a[ib].e) * 0.5;
             const uint vui = uint(data_a[ib].qs[iqs]);
             const uint vui2 = uint(data_a[ib].qs[iqs+1]);
 
diff --git a/ggml/src/ggml-vulkan/vulkan-shaders/mul_mm_id_funcs.glsl b/ggml/src/ggml-vulkan/vulkan-shaders/mul_mm_id_funcs.glsl
new file mode 100644
index 00000000000..1d0e84ac942
--- /dev/null
+++ b/ggml/src/ggml-vulkan/vulkan-shaders/mul_mm_id_funcs.glsl
@@ -0,0 +1,70 @@
+#ifdef MUL_MAT_ID
+shared u16vec2 row_ids[BN];
+uint _ne1;
+
+#ifdef MUL_MAT_ID_USE_SUBGROUPS
+shared uvec4 ballots_sh[NUM_WARPS];
+
+void load_row_ids(uint expert_idx, bool nei0_is_pow2, uint ic) {
+    _ne1 = 0;
+    uint num_elements = p.nei1 * p.nei0;
+    uint nei0shift = findLSB(p.nei0);
+
+    uint ids[16];
+    uint iter = 0;
+
+    for (uint j = 0; j < num_elements; j += BLOCK_SIZE) {
+        // prefetch up to 16 elements
+        if (iter == 0) {
+            [[unroll]] for (uint k = 0; k < 16; ++k) {
+                uint i = j + gl_LocalInvocationIndex + k*BLOCK_SIZE;
+                bool in_range = i < num_elements;
+                uint ii1;
+                if (nei0_is_pow2) {
+                    ii1 = i >> nei0shift;
+                } else {
+                    ii1 = i / p.nei0;
+                }
+                uint ii0 = i - ii1 * p.nei0;
+                ids[k] = in_range ? data_ids[ii1*p.nbi1 + ii0] : 0;
+            }
+        }
+        uint i = j + gl_LocalInvocationIndex;
+        bool in_range = i < num_elements;
+        uint ii1;
+        if (nei0_is_pow2) {
+            ii1 = i >> nei0shift;
+        } else {
+            ii1 = i / p.nei0;
+        }
+        uint ii0 = i - ii1 * p.nei0;
+        uint id = ids[iter++];
+        uvec4 ballot = subgroupBallot(in_range && id == expert_idx);
+
+        ballots_sh[gl_SubgroupID] = ballot;
+        barrier();
+
+        uint subgroup_base = 0;
+        uint total = 0;
+        for (uint k = 0; k < gl_NumSubgroups; ++k) {
+            if (k == gl_SubgroupID) {
+                subgroup_base = total;
+            }
+            total += subgroupBallotBitCount(ballots_sh[k]);
+        }
+        barrier();
+
+        uint idx = subgroup_base + subgroupBallotExclusiveBitCount(ballot);
+        if (in_range && id == expert_idx && _ne1 + idx >= ic * BN && _ne1 + idx < (ic + 1) * BN) {
+            row_ids[_ne1 + idx - ic * BN] = u16vec2(ii0, ii1);
+        }
+        _ne1 += total;
+        iter &= 15;
+        if (_ne1 >= (ic + 1) * BN) {
+            break;
+        }
+    }
+    barrier();
+}
+#endif // MUL_MAT_ID_USE_SUBGROUPS
+#endif // MUL_MAT_ID
diff --git a/ggml/src/ggml-vulkan/vulkan-shaders/mul_mmq.comp b/ggml/src/ggml-vulkan/vulkan-shaders/mul_mmq.comp
index b5d761c0bab..8b238ac4bc1 100644
--- a/ggml/src/ggml-vulkan/vulkan-shaders/mul_mmq.comp
+++ b/ggml/src/ggml-vulkan/vulkan-shaders/mul_mmq.comp
@@ -10,10 +10,9 @@
 #extension GL_EXT_shader_explicit_arithmetic_types_float16 : require
 #endif
 
-#ifdef COOPMAT
-#extension GL_KHR_cooperative_matrix : enable
-#extension GL_KHR_memory_scope_semantics : enable
+#if defined(MUL_MAT_ID_USE_SUBGROUPS)
 #extension GL_KHR_shader_subgroup_basic : enable
+#extension GL_KHR_shader_subgroup_ballot : enable
 #endif
 
 #ifdef MUL_MAT_ID
@@ -24,7 +23,10 @@
 
 layout(local_size_x_id = 0, local_size_y = 1, local_size_z = 1) in;
 
-layout (binding = 0) readonly buffer A {A_TYPE_PACKED16 data_a[];};
+layout (binding = 0) readonly buffer A {A_TYPE data_a[];};
+#if defined(A_TYPE_PACKED16)
+layout (binding = 0) readonly buffer A_PACKED16 {A_TYPE_PACKED16 data_a_packed16[];};
+#endif
 #if defined(A_TYPE_PACKED32)
 layout (binding = 0) readonly buffer A_PACKED32 {A_TYPE_PACKED32 data_a_packed32[];};
 #endif
@@ -76,40 +78,27 @@ layout (constant_id = 10) const uint WARP = 32;
 
 #define BK 32
 
-#ifdef COOPMAT
-#define SHMEM_STRIDE (BK / 4 + 4)
-#else
-#define SHMEM_STRIDE (BK / 4 + 1)
-#endif
+#define MMQ_SHMEM
 
-shared int32_t buf_a_qs[BM * SHMEM_STRIDE];
+#include "mul_mmq_shmem_types.glsl"
 
-#ifndef COOPMAT
-#if QUANT_AUXF == 1
-shared FLOAT_TYPE buf_a_dm[BM];
-#else
-shared FLOAT_TYPE_VEC2 buf_a_dm[BM];
-#endif
+#ifndef BK_STEP
+#define BK_STEP 4
 #endif
 
-shared int32_t buf_b_qs[BN * SHMEM_STRIDE];
-#ifndef COOPMAT
-shared FLOAT_TYPE_VEC2 buf_b_ds[BN];
-#endif
+// Shared memory cache
+shared block_a_cache buf_a[BM * BK_STEP];
+shared block_b_cache buf_b[BN * BK_STEP];
+// Register cache
+block_a_cache cache_a[WMITER * TM];
+block_b_cache cache_b;
 
-#define LOAD_VEC_A (4 * QUANT_R)
+#define LOAD_VEC_A (4 * QUANT_R_MMQ)
 #define LOAD_VEC_B 16
 
-#ifdef MUL_MAT_ID
-shared u16vec2 row_ids[4096];
-#endif // MUL_MAT_ID
-
 #define NUM_WARPS (BLOCK_SIZE / WARP)
 
-#ifdef COOPMAT
-shared ACC_TYPE coopmat_stage[TM * TN * NUM_WARPS];
-#endif
-
+#include "mul_mm_id_funcs.glsl"
 #include "mul_mmq_funcs.glsl"
 
 void main() {
@@ -139,26 +128,12 @@ void main() {
     const uint WNITER = (WM * WN) / (WARP * TM * TN * WMITER);
     const uint WSUBM = WM / WMITER;
     const uint WSUBN = WN / WNITER;
-
-#ifdef COOPMAT
-    const uint warp_i = gl_SubgroupID;
-
-    const uint tiw = gl_SubgroupInvocationID;
-
-    const uint cms_per_row = WM / TM;
-    const uint cms_per_col = WN / TN;
-
-    const uint storestride = WARP / TM;
-    const uint store_r = tiw % TM;
-    const uint store_c = tiw / TM;
-#else
     const uint warp_i = gl_LocalInvocationID.x / WARP;
 
     const uint tiw = gl_LocalInvocationID.x % WARP;
 
     const uint tiwr = tiw % (WSUBM / TM);
     const uint tiwc = tiw / (WSUBM / TM);
-#endif
 
     const uint warp_r = warp_i % (BM / WM);
     const uint warp_c = warp_i / (BM / WM);
@@ -172,17 +147,27 @@ void main() {
     const uint loadstride_b = BLOCK_SIZE * LOAD_VEC_B / BK;
 
 #ifdef MUL_MAT_ID
-    uint _ne1 = 0;
-    for (uint ii1 = 0; ii1 < p.nei1; ii1++) {
-        for (uint ii0 = 0; ii0 < p.nei0; ii0++) {
+#ifdef MUL_MAT_ID_USE_SUBGROUPS
+    if (bitCount(p.nei0) == 1) {
+        load_row_ids(expert_idx, true, ic);
+    } else {
+        load_row_ids(expert_idx, false, ic);
+    }
+#else
+    _ne1 = 0;
+    for (uint ii1 = 0; ii1 < p.nei1 && _ne1 < (ic + 1) * BN; ii1++) {
+        for (uint ii0 = 0; ii0 < p.nei0 && _ne1 < (ic + 1) * BN; ii0++) {
             if (data_ids[ii1*p.nbi1 + ii0] == expert_idx) {
-                row_ids[_ne1] = u16vec2(ii0, ii1);
+                if (_ne1 >= ic * BN) {
+                    row_ids[_ne1 - ic * BN] = u16vec2(ii0, ii1);
+                }
                 _ne1++;
             }
         }
     }
 
     barrier();
+#endif
 
     // Workgroup has no work
     if (ic * BN >= _ne1) return;
@@ -209,159 +194,70 @@ void main() {
     uint pos_b_ib = (batch_idx * p.batch_stride_b + ic * BN * p.stride_b + start_k) / BK;
 #endif
 
-#ifdef COOPMAT
-    coopmat<int8_t, gl_ScopeSubgroup, TM, TK, gl_MatrixUseA> cache_a;
-    coopmat<int8_t, gl_ScopeSubgroup, TK, TN, gl_MatrixUseB> cache_b;
-    coopmat<int32_t, gl_ScopeSubgroup, TM, TN, gl_MatrixUseAccumulator> cm_result;
-
-    coopmat<ACC_TYPE, gl_ScopeSubgroup, TM, TN, gl_MatrixUseAccumulator> factors[cms_per_row * cms_per_col];
-
-    coopmat<ACC_TYPE, gl_ScopeSubgroup, TM, TN, gl_MatrixUseAccumulator> sums[cms_per_row * cms_per_col];
-
-    [[unroll]] for (uint i = 0; i < cms_per_row * cms_per_col; i++) {
-        sums[i] = coopmat<ACC_TYPE, gl_ScopeSubgroup, TM, TN, gl_MatrixUseAccumulator>(0.0f);
-    }
-#else
-    int32_t cache_a_qs[WMITER * TM * BK / 4];
-
-    int32_t cache_b_qs[TN * BK / 4];
-
     ACC_TYPE sums[WMITER * TM * WNITER * TN];
 
     [[unroll]] for (uint i = 0; i < WMITER*TM*WNITER*TN; i++) {
         sums[i] = ACC_TYPE(0.0f);
     }
-#endif
 
-#if QUANT_AUXF == 1
-    FLOAT_TYPE cache_a_dm[WMITER * TM];
-#else
-    FLOAT_TYPE_VEC2 cache_a_dm[WMITER * TM];
-#endif
-
-    FLOAT_TYPE_VEC2 cache_b_ds[TN];
-
-    for (uint block = start_k; block < end_k; block += BK) {
+    for (uint block = start_k; block < end_k; block += BK * BK_STEP) {
         [[unroll]] for (uint l = 0; loadc_a + l < BM; l += loadstride_a) {
-            const uint ib = pos_a_ib + (loadc_a + l) * p.stride_a / BK;
-            const uint iqs = loadr_a;
             const uint buf_ib = loadc_a + l;
+            const uint ib = pos_a_ib + buf_ib * p.stride_a / BK;
+            const uint iqs = loadr_a;
 
-            if (iqs == 0) {
-#if QUANT_AUXF == 1
-                buf_a_dm[buf_ib] = get_d(ib);
-#else
-                buf_a_dm[buf_ib] = get_dm(ib);
-#endif
+            [[unroll]] for (uint k_step = 0; k_step < BK_STEP; k_step++) {
+                block_a_to_shmem(k_step * BM + buf_ib, ib + k_step, iqs);
             }
-#if QUANT_R == 1
-            buf_a_qs[buf_ib * SHMEM_STRIDE + iqs] = repack(ib, iqs);
-#else
-            const i32vec2 vals = repack(ib, iqs);
-            buf_a_qs[buf_ib * SHMEM_STRIDE + iqs    ] = vals.x;
-            buf_a_qs[buf_ib * SHMEM_STRIDE + iqs + 4] = vals.y;
-#endif
         }
         [[unroll]] for (uint l = 0; loadc_b + l < BN; l += loadstride_b) {
+            const uint buf_ib = loadc_b + l;
+
 #ifdef MUL_MAT_ID
-            const u16vec2 row_idx = row_ids[ic * BN + loadc_b + l];
-            const uint idx = pos_b_ib + row_idx.y * p.batch_stride_b / LOAD_VEC_B + (row_idx.x % p.ne11) * p.stride_b / LOAD_VEC_B + loadr_b;
-            const uint ib = idx / 8;
-            const uint iqs = idx & 0x7;
+            const u16vec2 row_idx = row_ids[buf_ib];
+            const uint ib = pos_b_ib + row_idx.y * p.batch_stride_b / BK + (row_idx.x % p.ne11) * p.stride_b / BK;
 #else
-            const uint ib = pos_b_ib + (loadc_b + l) * p.stride_b / BK;
-            const uint ib_outer = ib / 4;
-            const uint ib_inner = ib % 4;
-
-            const uint iqs = loadr_b;
+            const uint ib = pos_b_ib + buf_ib * p.stride_b / BK;
 #endif
+            const uint iqs = loadr_b;
 
-            const uint buf_ib = loadc_b + l;
-
-            if (iqs == 0) {
-                buf_b_ds[buf_ib] = FLOAT_TYPE_VEC2(data_b[ib_outer].ds[ib_inner]);
+            [[unroll]] for (uint k_step = 0; k_step < BK_STEP; k_step++) {
+                block_b_to_shmem(k_step * BN + buf_ib, ib + k_step, iqs);
             }
-            const ivec4 values = data_b[ib_outer].qs[ib_inner * 2 + iqs];
-            buf_b_qs[buf_ib * SHMEM_STRIDE + iqs * 4    ] = values.x;
-            buf_b_qs[buf_ib * SHMEM_STRIDE + iqs * 4 + 1] = values.y;
-            buf_b_qs[buf_ib * SHMEM_STRIDE + iqs * 4 + 2] = values.z;
-            buf_b_qs[buf_ib * SHMEM_STRIDE + iqs * 4 + 3] = values.w;
         }
 
         barrier();
 
-        pos_a_ib += 1;
-        pos_b_ib += 1;
+        pos_a_ib += BK_STEP;
+        pos_b_ib += BK_STEP;
 
-#ifdef COOPMAT
-        [[unroll]] for (uint cm_row = 0; cm_row < cms_per_row; cm_row++) {
-            const uint ib_a = warp_r * WM + cm_row * TM;
+        for (uint k_step = 0; k_step < BK_STEP; k_step++) {
             // Load from shared into cache
-            coopMatLoad(cache_a, buf_a_qs, ib_a * SHMEM_STRIDE, SHMEM_STRIDE, gl_CooperativeMatrixLayoutRowMajor);
-
-            // TODO: only cache values that are actually needed
-            [[unroll]] for (uint t_idx = 0; t_idx < TM; t_idx++) {
-                cache_a_dm[t_idx] = buf_a_dm[ib_a + t_idx];
-            }
-
-            [[unroll]] for (uint cm_col = 0; cm_col < cms_per_col; cm_col++) {
-                const uint ib_b = warp_c * WN + cm_col * TN;
-                coopMatLoad(cache_b, buf_b_qs, ib_b * SHMEM_STRIDE, SHMEM_STRIDE, gl_CooperativeMatrixLayoutColumnMajor);
-
-                // TODO: only cache values that are actually needed
-                [[unroll]] for (uint t_idx = 0; t_idx < TN; t_idx++) {
-                    cache_b_dm[t_idx] = buf_b_d[ib_b + t_idx];
-                }
-
-                cm_result = coopmat<int32_t, gl_ScopeSubgroup, TM, TN, gl_MatrixUseAccumulator>(0);
-                cm_result = coopMatMulAdd(cache_a, cache_b, cm_result);
-
-                [[unroll]] for (uint col = 0; col < TN; col += storestride) {
-                    coopmat_stage[warp_i * TM * TN + (store_c + col) * TM + store_r] = ACC_TYPE(float(cache_a_d[store_r]) * float(cache_b_d[store_c + col]));
-                }
-
-                coopMatLoad(factors, coopmat_stage, warp_i * TM * TN, TM, gl_CooperativeMatrixLayoutColumnMajor);
-                sums[cm_col * cms_per_row + cm_row] += factors * coopmat<ACC_TYPE, gl_ScopeSubgroup, TM, TN, gl_MatrixUseAccumulator>(cm_result);
-            }
-        }
-#else
-        // Load from shared into cache
-        [[unroll]] for (uint wsir = 0; wsir < WMITER; wsir++) {
-            [[unroll]] for (uint cr = 0; cr < TM; cr++) {
-                const uint ib = warp_r * WM + wsir * WSUBM + tiwr * TM + cr;
-                cache_a_dm[wsir * TM + cr] = buf_a_dm[ib];
-                [[unroll]] for (uint idx_k = 0; idx_k < BK / 4; idx_k++) {
-                    cache_a_qs[(wsir * TM + cr) * (BK / 4) + idx_k] = buf_a_qs[ib * SHMEM_STRIDE + idx_k];
-                }
-            }
-        }
+            [[unroll]] for (uint wsir = 0; wsir < WMITER; wsir++) {
+                [[unroll]] for (uint cr = 0; cr < TM; cr++) {
+                    const uint reg_ib = wsir * TM + cr;
+                    const uint buf_ib = warp_r * WM + wsir * WSUBM + tiwr * TM + cr;
 
-        [[unroll]] for (uint wsic = 0; wsic < WNITER; wsic++) {
-            [[unroll]] for (uint cc = 0; cc < TN; cc++) {
-                const uint ib = warp_c * WN + wsic * WSUBN + tiwc * TN + cc;
-                cache_b_ds[cc] = buf_b_ds[ib];
-                [[unroll]] for (uint idx_k = 0; idx_k < BK / 4; idx_k++) {
-                    cache_b_qs[cc * (BK / 4) + idx_k] = buf_b_qs[ib * SHMEM_STRIDE + idx_k];
+                    block_a_to_registers(reg_ib, k_step * BM + buf_ib);
                 }
             }
 
-            [[unroll]] for (uint wsir = 0; wsir < WMITER; wsir++) {
+            [[unroll]] for (uint wsic = 0; wsic < WNITER; wsic++) {
                 [[unroll]] for (uint cc = 0; cc < TN; cc++) {
-                    [[unroll]] for (uint cr = 0; cr < TM; cr++) {
-                        const uint cache_a_idx = wsir * TM + cr;
-                        const uint sums_idx = (wsic * TN + cc) * (WMITER * TM) + wsir * TM + cr;
-                        int32_t q_sum = 0;
-                        [[unroll]] for (uint idx_k = 0; idx_k < BK / 4; idx_k++) {
-                            q_sum += dotPacked4x8EXT(cache_a_qs[cache_a_idx * (BK / 4) + idx_k],
-                                                     cache_b_qs[cc * (BK / 4) + idx_k]);
-                        }
+                    const uint ib = k_step * BN + warp_c * WN + wsic * WSUBN + tiwc * TN + cc;
+                    block_b_to_registers(ib);
 
-                        sums[sums_idx] += mul_q8_1(q_sum, cache_a_dm[cache_a_idx], cache_b_ds[cc], 1);
+                    [[unroll]] for (uint wsir = 0; wsir < WMITER; wsir++) {
+                        [[unroll]] for (uint cr = 0; cr < TM; cr++) {
+                            const uint cache_a_idx = wsir * TM + cr;
+                            const uint sums_idx = (wsic * TN + cc) * (WMITER * TM) + wsir * TM + cr;
+
+                            sums[sums_idx] += mmq_dot_product(cache_a_idx);
+                        }
                     }
                 }
             }
         }
-#endif
 
         barrier();
     }
@@ -373,54 +269,6 @@ void main() {
     const uint offsets = batch_idx * p.batch_stride_d + ik * p.batch_stride_d * gl_NumWorkGroups.z;
 #endif
 
-#ifdef COOPMAT
-#ifdef MUL_MAT_ID
-    [[unroll]] for (uint cm_row = 0; cm_row < cms_per_row; cm_row++) {
-        [[unroll]] for (uint cm_col = 0; cm_col < cms_per_col; cm_col++) {
-            coopMatStore(sums[cm_col * cms_per_row + cm_row], coopmat_stage, warp_i * TM * TN, TM, gl_CooperativeMatrixLayoutColumnMajor);
-
-            [[unroll]] for (uint col = 0; col < BN; col += storestride) {
-                const uint row_i = dc + cm_col * TN + col + store_c;
-                if (row_i >= _ne1) break;
-
-                const u16vec2 row_idx = row_ids[row_i];
-
-                data_d[row_idx.y * p.batch_stride_d + row_idx.x * p.stride_d + dr + cm_row * TM + store_r] = D_TYPE(coopmat_stage[warp_i * TM * TN + (col + store_c) * TM + store_r]);
-            }
-        }
-    }
-#else
-    const bool is_aligned = p.stride_d % 4 == 0;  // Assumption: D_TYPE == float
-
-    [[unroll]] for (uint cm_row = 0; cm_row < cms_per_row; cm_row++) {
-        [[unroll]] for (uint cm_col = 0; cm_col < cms_per_col; cm_col++) {
-            const bool is_in_bounds = dr + (cm_row + 1) * TM <= p.M && dc + (cm_col + 1) * TN <= p.N;
-
-            if (is_aligned && is_in_bounds) {
-                // Full coopMat is within bounds and stride_d is aligned with 16B
-                coopmat<D_TYPE, gl_ScopeSubgroup, TM, TN, gl_MatrixUseAccumulator> cm_dtype = coopmat<D_TYPE, gl_ScopeSubgroup, TM, TN, gl_MatrixUseAccumulator>(sums[cm_col * cms_per_row + cm_row]);
-                coopMatStore(cm_dtype, data_d, offsets + (dc + cm_col * TN) * p.stride_d + dr + cm_row * TM, p.stride_d, gl_CooperativeMatrixLayoutColumnMajor);
-            } else if (is_in_bounds) {
-                // Full coopMat is within bounds, but stride_d is not aligned
-                coopMatStore(sums[cm_col * cms_per_row + cm_row], coopmat_stage, warp_i * TM * TN, TM, gl_CooperativeMatrixLayoutColumnMajor);
-
-                [[unroll]] for (uint col = 0; col < TN; col += storestride) {
-                    data_d[offsets + (dc + cm_col * TN + col + store_c) * p.stride_d + dr + cm_row * TM + store_r] = D_TYPE(coopmat_stage[warp_i * TM * TN + (col + store_c) * TM + store_r]);
-                }
-            } else if (dr + cm_row * TM < p.M && dc + cm_col * TN < p.N) {
-                // Partial coopMat is within bounds
-                coopMatStore(sums[cm_col * cms_per_row + cm_row], coopmat_stage, warp_i * TM * TN, TM, gl_CooperativeMatrixLayoutColumnMajor);
-
-                [[unroll]] for (uint col = 0; col < TN; col += storestride) {
-                    if (dr + cm_row * TM + store_r < p.M && dc + cm_col * TN + col + store_c < p.N) {
-                        data_d[offsets + (dc + cm_col * TN + col + store_c) * p.stride_d + dr + cm_row * TM + store_r] = D_TYPE(coopmat_stage[warp_i * TM * TN + (col + store_c) * TM + store_r]);
-                    }
-                }
-            }
-        }
-    }
-#endif // MUL_MAT_ID
-#else
     [[unroll]] for (uint wsic = 0; wsic < WNITER; wsic++) {
         [[unroll]] for (uint wsir = 0; wsir < WMITER; wsir++) {
 
@@ -431,19 +279,21 @@ void main() {
                 const uint row_i = dc_warp + cc;
                 if (row_i >= _ne1) break;
 
-                const u16vec2 row_idx = row_ids[row_i];
+                const u16vec2 row_idx = row_ids[row_i - ic * BN];
 #endif // MUL_MAT_ID
                 [[unroll]] for (uint cr = 0; cr < TM; cr++) {
+                    const uint sums_idx = (wsic * TN + cc) * WMITER * TM + wsir * TM + cr;
 #ifdef MUL_MAT_ID
-                    data_d[row_idx.y * p.batch_stride_d + row_idx.x * p.stride_d + dr_warp + cr] = D_TYPE(sums[(wsic * TN + cc) * (WMITER * TM) + wsir * TM + cr]);
+                    if (dr_warp + cr < p.M) {
+                        data_d[row_idx.y * p.batch_stride_d + row_idx.x * p.stride_d + dr_warp + cr] = D_TYPE(sums[sums_idx].x);
+                    }
 #else
                     if (dr_warp + cr < p.M && dc_warp + cc < p.N) {
-                        data_d[offsets + (dc_warp + cc) * p.stride_d + dr_warp + cr] = D_TYPE(sums[(wsic * TN + cc) * (WMITER * TM) + wsir * TM + cr]);
+                        data_d[offsets + (dc_warp + cc) * p.stride_d + dr_warp + cr] = D_TYPE(sums[sums_idx].x);
                     }
 #endif // MUL_MAT_ID
                 }
             }
         }
     }
-#endif // COOPMAT
 }
diff --git a/ggml/src/ggml-vulkan/vulkan-shaders/mul_mmq_funcs.glsl b/ggml/src/ggml-vulkan/vulkan-shaders/mul_mmq_funcs.glsl
index fe71eb131c8..c0c03fedcc2 100644
--- a/ggml/src/ggml-vulkan/vulkan-shaders/mul_mmq_funcs.glsl
+++ b/ggml/src/ggml-vulkan/vulkan-shaders/mul_mmq_funcs.glsl
@@ -6,41 +6,89 @@
 
 // Each iqs value maps to a 32-bit integer
 
-#if defined(DATA_A_Q4_0)
+#if defined(DATA_A_Q4_0) || defined(DATA_A_Q4_1)
+// 2-byte loads for Q4_0 blocks (18 bytes)
+// 4-byte loads for Q4_1 blocks (20 bytes)
 i32vec2 repack(uint ib, uint iqs) {
-    // Use 2-byte loads since a q4_0 block (18 bytes) is not divisible by 4
-    const u16vec2 quants = u16vec2(data_a[ib].qs[iqs * 2    ],
-                                   data_a[ib].qs[iqs * 2 + 1]);
+#ifdef DATA_A_Q4_0
+    const u16vec2 quants = u16vec2(data_a_packed16[ib].qs[iqs * 2    ],
+                                   data_a_packed16[ib].qs[iqs * 2 + 1]);
     const uint32_t vui = pack32(quants);
     return i32vec2( vui       & 0x0F0F0F0F,
                    (vui >> 4) & 0x0F0F0F0F);
+#else // DATA_A_Q4_1
+    const uint32_t vui = data_a_packed32[ib].qs[iqs];
+    return i32vec2( vui       & 0x0F0F0F0F,
+                   (vui >> 4) & 0x0F0F0F0F);
+#endif
 }
 
+#ifdef DATA_A_Q4_0
 ACC_TYPE mul_q8_1(const int32_t q_sum, const float da, const vec2 dsb, const int32_t sum_divisor) {
     return ACC_TYPE(da * (float(q_sum) * dsb.x - (8 / sum_divisor) * dsb.y));
 }
+#else // DATA_A_Q4_1
+ACC_TYPE mul_q8_1(const int32_t q_sum, const vec2 dma, const vec2 dsb, const int32_t sum_divisor) {
+    return ACC_TYPE(float(q_sum) * dma.x * dsb.x + dma.y * dsb.y / sum_divisor);
+}
 #endif
 
-#if defined(DATA_A_Q4_1)
-i32vec2 repack(uint ib, uint iqs) {
-    // Use 4-byte loads since a q4_1 block (20 bytes) is divisible by 4
-    const uint32_t vui = data_a_packed32[ib].qs[iqs];
-    return i32vec2( vui       & 0x0F0F0F0F,
-                   (vui >> 4) & 0x0F0F0F0F);
+#ifdef MMQ_SHMEM
+void block_a_to_shmem(const uint buf_ib, const uint ib, const uint iqs) {
+#ifdef DATA_A_Q4_0
+    buf_a[buf_ib].qs[iqs] = pack32(u16vec2(data_a_packed16[ib].qs[iqs * 2],
+                                           data_a_packed16[ib].qs[iqs * 2 + 1]));
+
+    if (iqs == 0) {
+        buf_a[buf_ib].dm = FLOAT_TYPE(data_a_packed16[ib].d);
+    }
+#else // DATA_A_Q4_1
+    buf_a[buf_ib].qs[iqs] = data_a_packed32[ib].qs[iqs];
+
+    if (iqs == 0) {
+        buf_a[buf_ib].dm = FLOAT_TYPE_VEC2(data_a_packed32[ib].dm);
+    }
+#endif
 }
 
-ACC_TYPE mul_q8_1(const int32_t q_sum, const vec2 dma, const vec2 dsb, const int32_t sum_divisor) {
-    return ACC_TYPE(float(q_sum) * dma.x * dsb.x + dma.y * dsb.y / sum_divisor);
+void block_a_to_registers(const uint reg_ib, const uint buf_ib) {
+    cache_a[reg_ib].dm = buf_a[buf_ib].dm;
+
+    [[unroll]] for (uint iqs = 0; iqs < 4; iqs++) {
+        cache_a[reg_ib].qs[iqs] = buf_a[buf_ib].qs[iqs];
+    }
 }
-#endif
 
-#if defined(DATA_A_Q5_0)
+ACC_TYPE mmq_dot_product(const uint ib_a) {
+    int32_t q_sum = 0;
+    [[unroll]] for (uint iqs = 0; iqs < 4; iqs++) {
+        const uint32_t vui = cache_a[ib_a].qs[iqs];
+        const i32vec2 qs_a = i32vec2( vui       & 0x0F0F0F0F,
+                                     (vui >> 4) & 0x0F0F0F0F);
+
+        const int32_t qs_b0 = cache_b.qs[iqs];
+        const int32_t qs_b1 = cache_b.qs[iqs + 4];
+
+        q_sum += dotPacked4x8EXT(qs_a.x, qs_b0);
+        q_sum += dotPacked4x8EXT(qs_a.y, qs_b1);
+    }
+
+    return mul_q8_1(q_sum, cache_a[ib_a].dm, cache_b.ds, 1);
+}
+#endif // MMQ_SHMEM
+
+#elif defined(DATA_A_Q5_0) || defined(DATA_A_Q5_1)
+// 2-byte loads for Q5_0 blocks (22 bytes)
+// 4-byte loads for Q5_1 blocks (24 bytes)
 i32vec2 repack(uint ib, uint iqs) {
-    // Use 2-byte loads since a q5_0 block (22 bytes) is not divisible by 4
-    const u16vec2 quants = u16vec2(data_a[ib].qs[iqs * 2    ],
-                                   data_a[ib].qs[iqs * 2 + 1]);
+    const u16vec2 quants = u16vec2(data_a_packed16[ib].qs[iqs * 2    ],
+                                   data_a_packed16[ib].qs[iqs * 2 + 1]);
     const uint32_t vui = pack32(quants);
-    const int32_t qh = int32_t((uint32_t(data_a[ib].qh[1]) << 16 | data_a[ib].qh[0]) >> (4 * iqs));
+#ifdef DATA_A_Q5_0
+    const int32_t qh = int32_t((uint32_t(data_a_packed16[ib].qh[1]) << 16 | data_a_packed16[ib].qh[0]) >> (4 * iqs));
+#else // DATA_A_Q5_1
+    const int32_t qh = int32_t(data_a_packed32[ib].qh >> (4 * iqs));
+#endif
     const int32_t v0 = int32_t(vui & 0x0F0F0F0F)
                      | ((qh & 0xF) * 0x02040810) & 0x10101010; // (0,1,2,3) -> (4,12,20,28)
 
@@ -50,40 +98,457 @@ i32vec2 repack(uint ib, uint iqs) {
     return i32vec2(v0, v1);
 }
 
+#ifdef DATA_A_Q5_0
 ACC_TYPE mul_q8_1(const int32_t q_sum, const float da, const vec2 dsb, const int32_t sum_divisor) {
     return ACC_TYPE(da * (float(q_sum) * dsb.x - (16 / sum_divisor) * dsb.y));
 }
+#else // DATA_A_Q5_1
+ACC_TYPE mul_q8_1(const int32_t q_sum, const vec2 dma, const vec2 dsb, const int32_t sum_divisor) {
+    return ACC_TYPE(float(q_sum) * dma.x * dsb.x + dma.y * dsb.y / sum_divisor);
+}
 #endif
 
-#if defined(DATA_A_Q5_1)
-i32vec2 repack(uint ib, uint iqs) {
-    // Use 4-byte loads since a q5_1 block (24 bytes) is divisible by 4
-    const uint32_t vui = data_a_packed32[ib].qs[iqs];
-    const int32_t qh = int32_t(data_a_packed32[ib].qh >> (4 * iqs));
-    const int32_t v0 = int32_t(vui & 0x0F0F0F0F)
-                     | ((qh & 0xF) * 0x02040810) & 0x10101010; // (0,1,2,3) -> (4,12,20,28)
+#ifdef MMQ_SHMEM
+void block_a_to_shmem(const uint buf_ib, const uint ib, const uint iqs) {
+#ifdef DATA_A_Q5_0
+    buf_a[buf_ib].qs[iqs] = pack32(u16vec2(data_a_packed16[ib].qs[iqs * 2],
+                                           data_a_packed16[ib].qs[iqs * 2 + 1]));
 
-    const int32_t v1 = int32_t((vui >> 4) & 0x0F0F0F0F)
-                     | (((qh >> 16) & 0xF) * 0x02040810) & 0x10101010; // (16,17,18,19) -> (4,12,20,28)
+    if (iqs == 0) {
+        buf_a[buf_ib].dm = FLOAT_TYPE(data_a_packed16[ib].d);
+        buf_a[buf_ib].qh = pack32(u16vec2(data_a_packed16[ib].qh[0], data_a_packed16[ib].qh[1]));
+    }
+#else // DATA_A_Q5_1
+    buf_a[buf_ib].qs[iqs] = data_a_packed32[ib].qs[iqs];
 
-    return i32vec2(v0, v1);
+    if (iqs == 0) {
+        buf_a[buf_ib].dm = FLOAT_TYPE_VEC2(data_a_packed32[ib].dm);
+        buf_a[buf_ib].qh = data_a_packed32[ib].qh;
+    }
+#endif
 }
 
-ACC_TYPE mul_q8_1(const int32_t q_sum, const vec2 dma, const vec2 dsb, const int32_t sum_divisor) {
-    return ACC_TYPE(float(q_sum) * dma.x * dsb.x + dma.y * dsb.y / sum_divisor);
+void block_a_to_registers(const uint reg_ib, const uint buf_ib) {
+    cache_a[reg_ib].dm = buf_a[buf_ib].dm;
+    cache_a[reg_ib].qh = buf_a[buf_ib].qh;
+
+    [[unroll]] for (uint iqs = 0; iqs < 4; iqs++) {
+        cache_a[reg_ib].qs[iqs] = buf_a[buf_ib].qs[iqs];
+    }
 }
+
+ACC_TYPE mmq_dot_product(const uint ib_a) {
+    int32_t q_sum = 0;
+    [[unroll]] for (uint iqs = 0; iqs < 4; iqs++) {
+        const uint32_t vui = cache_a[ib_a].qs[iqs];
+        const int32_t qh = int32_t(cache_a[ib_a].qh >> (4 * iqs));
+        const int32_t qs_a0 = int32_t(vui & 0x0F0F0F0F)
+                         | ((qh & 0xF) * 0x02040810) & 0x10101010; // (0,1,2,3) -> (4,12,20,28)
+        const int32_t qs_a1 = int32_t((vui >> 4) & 0x0F0F0F0F)
+                         | (((qh >> 16) & 0xF) * 0x02040810) & 0x10101010; // (16,17,18,19) -> (4,12,20,28)
+
+        const int32_t qs_b0 = cache_b.qs[iqs];
+        const int32_t qs_b1 = cache_b.qs[iqs + 4];
+
+        q_sum += dotPacked4x8EXT(qs_a0, qs_b0);
+        q_sum += dotPacked4x8EXT(qs_a1, qs_b1);
+    }
+
+    return mul_q8_1(q_sum, cache_a[ib_a].dm, cache_b.ds, 1);
+}
+#endif // MMQ_SHMEM
 #endif
 
 #if defined(DATA_A_Q8_0)
+// 2-byte loads for Q8_0 blocks (34 bytes)
 int32_t repack(uint ib, uint iqs) {
-    // Use 2-byte loads since a q8_0 block (34 bytes) is not divisible by 4
-    return pack32(i16vec2(data_a[ib].qs[iqs * 2    ],
-                          data_a[ib].qs[iqs * 2 + 1]));
+    return pack32(i16vec2(data_a_packed16[ib].qs[iqs * 2    ],
+                          data_a_packed16[ib].qs[iqs * 2 + 1]));
 }
 
 ACC_TYPE mul_q8_1(const int32_t q_sum, const float da, const vec2 dsb, const int32_t sum_divisor) {
     return ACC_TYPE(float(q_sum) * da * dsb.x);
 }
+
+#ifdef MMQ_SHMEM
+void block_a_to_shmem(const uint buf_ib, const uint ib, const uint iqs) {
+    buf_a[buf_ib].qs[iqs] = pack32(i16vec2(data_a_packed16[ib].qs[iqs * 2],
+                                           data_a_packed16[ib].qs[iqs * 2 + 1]));
+
+    if (iqs == 0) {
+        buf_a[buf_ib].dm = FLOAT_TYPE(data_a_packed16[ib].d);
+    }
+}
+
+void block_a_to_registers(const uint reg_ib, const uint buf_ib) {
+    cache_a[reg_ib].dm = buf_a[buf_ib].dm;
+
+    [[unroll]] for (uint iqs = 0; iqs < 8; iqs++) {
+        cache_a[reg_ib].qs[iqs] = buf_a[buf_ib].qs[iqs];
+    }
+}
+
+ACC_TYPE mmq_dot_product(const uint ib_a) {
+    int32_t q_sum = 0;
+    [[unroll]] for (uint iqs = 0; iqs < 8; iqs++) {
+        const int32_t qs_a = cache_a[ib_a].qs[iqs];
+        const int32_t qs_b = cache_b.qs[iqs];
+
+        q_sum += dotPacked4x8EXT(qs_a, qs_b);
+    }
+
+    return mul_q8_1(q_sum, cache_a[ib_a].dm, cache_b.ds, 1);
+}
+#endif // MMQ_SHMEM
+#endif
+
+#if defined(DATA_A_MXFP4)
+// 1-byte loads for mxfp4 blocks (17 bytes)
+i32vec2 repack(uint ib, uint iqs) {
+    const uint32_t quants = pack32(u8vec4(data_a[ib].qs[iqs * 4    ],
+                                          data_a[ib].qs[iqs * 4 + 1],
+                                          data_a[ib].qs[iqs * 4 + 2],
+                                          data_a[ib].qs[iqs * 4 + 3]));
+
+    return i32vec2( quants       & 0x0F0F0F0F,
+                   (quants >> 4) & 0x0F0F0F0F);
+}
+
+ACC_TYPE mul_q8_1(const int32_t q_sum, const float da, const vec2 dsb, const int32_t sum_divisor) {
+    return ACC_TYPE(da * dsb.x * float(q_sum));
+}
+
+#ifdef MMQ_SHMEM
+void block_a_to_shmem(const uint buf_ib, const uint ib, const uint iqs) {
+    const uint32_t qs = pack32(u8vec4(data_a[ib].qs[iqs * 4    ],
+                                      data_a[ib].qs[iqs * 4 + 1],
+                                      data_a[ib].qs[iqs * 4 + 2],
+                                      data_a[ib].qs[iqs * 4 + 3]));
+
+    const u8vec4 i_a0 = unpack8( qs       & 0x0F0F0F0F);
+    const u8vec4 i_a1 = unpack8((qs >> 4) & 0x0F0F0F0F);
+
+    buf_a[buf_ib].qs[iqs    ] = pack32(i8vec4(kvalues_mxfp4[i_a0.x], kvalues_mxfp4[i_a0.y], kvalues_mxfp4[i_a0.z], kvalues_mxfp4[i_a0.w]));
+    buf_a[buf_ib].qs[iqs + 4] = pack32(i8vec4(kvalues_mxfp4[i_a1.x], kvalues_mxfp4[i_a1.y], kvalues_mxfp4[i_a1.z], kvalues_mxfp4[i_a1.w]));
+
+    if (iqs == 0) {
+        buf_a[buf_ib].d = FLOAT_TYPE(e8m0_to_fp32(data_a[ib].e) * 0.5);
+    }
+}
+
+void block_a_to_registers(const uint reg_ib, const uint buf_ib) {
+    cache_a[reg_ib].d = buf_a[buf_ib].d;
+
+    [[unroll]] for (uint iqs = 0; iqs < 8; iqs++) {
+        cache_a[reg_ib].qs[iqs] = buf_a[buf_ib].qs[iqs];
+    }
+}
+
+ACC_TYPE mmq_dot_product(const uint ib_a) {
+    int32_t q_sum = 0;
+    [[unroll]] for (uint iqs = 0; iqs < 8; iqs++) {
+        const int32_t qs_a = cache_a[ib_a].qs[iqs];
+
+        q_sum += dotPacked4x8EXT(qs_a, cache_b.qs[iqs]);
+    }
+
+    return mul_q8_1(q_sum, cache_a[ib_a].d, cache_b.ds, 1);
+}
+#endif // MMQ_SHMEM
+#endif
+
+// For k-quants, ib and iqs still assume 32-wide blocks, but k-quants are 256-wide
+// iqs still refers to a 32-bit integer, meaning 0..7 for 32-wide quants
+#if defined(DATA_A_Q2_K)
+// 4-byte loads for Q2_K blocks (84 bytes)
+int32_t repack(uint ib, uint iqs) {
+    const uint ib_k = ib / 8;
+    const uint iqs_k = (ib % 8) * 8 + iqs;
+
+    const uint qs_idx = (iqs_k / 32) * 8 + (iqs_k % 8);
+    const uint qs_shift = ((iqs_k % 32) / 8) * 2;
+
+    return int32_t((data_a_packed32[ib_k].qs[qs_idx] >> qs_shift) & 0x03030303);
+}
+
+uint8_t get_scale(uint ib, uint iqs) {
+    const uint ib_k = ib / 8;
+    const uint iqs_k = (ib % 8) * 8 + iqs;
+
+    return data_a[ib_k].scales[iqs_k / 4];
+}
+
+ACC_TYPE mul_q8_1(const int32_t sum_d, const int32_t sum_m, const vec2 dma, const vec2 dsb, const int32_t sum_divisor) {
+    return ACC_TYPE(dsb.x * (dma.x * float(sum_d) - dma.y * float(sum_m)));
+}
+
+#ifdef MMQ_SHMEM
+void block_a_to_shmem(const uint buf_ib, const uint ib, const uint iqs) {
+    const uint ib_k = ib / 8;
+    const uint iqs_k = (ib % 8) * 8 + iqs * QUANT_R_MMQ;
+
+    const uint qs_idx = (iqs_k / 32) * 8 + (iqs_k % 8);
+    const uint qs_shift = ((iqs_k % 32) / 8) * 2;
+
+    // Repack 4x4 quants into one int
+    const uint32_t vals0 = (data_a_packed32[ib_k].qs[qs_idx    ] >> qs_shift) & 0x03030303;
+    const uint32_t vals1 = (data_a_packed32[ib_k].qs[qs_idx + 1] >> qs_shift) & 0x03030303;
+    const uint32_t vals2 = (data_a_packed32[ib_k].qs[qs_idx + 2] >> qs_shift) & 0x03030303;
+    const uint32_t vals3 = (data_a_packed32[ib_k].qs[qs_idx + 3] >> qs_shift) & 0x03030303;
+
+    buf_a[buf_ib].qs[iqs] = vals0 | (vals1 << 2) | (vals2 << 4) | (vals3 << 6);
+
+    if (iqs == 0) {
+        buf_a[buf_ib].dm = FLOAT_TYPE_VEC2(data_a_packed32[ib_k].dm);
+        buf_a[buf_ib].scales = unpack8(data_a_packed16[ib_k].scales[iqs_k / 8]);
+    }
+}
+
+void block_a_to_registers(const uint reg_ib, const uint buf_ib) {
+    cache_a[reg_ib].dm = buf_a[buf_ib].dm;
+    cache_a[reg_ib].scales = buf_a[buf_ib].scales;
+
+    [[unroll]] for (uint iqs = 0; iqs < 2; iqs++) {
+        cache_a[reg_ib].qs[iqs] = buf_a[buf_ib].qs[iqs];
+    }
+}
+
+ACC_TYPE mmq_dot_product(const uint ib_a) {
+    int32_t sum_d = 0;
+    int32_t sum_m = 0;
+
+    [[unroll]] for (uint iqs = 0; iqs < 8; iqs++) {
+        const uint8_t scale = cache_a[ib_a].scales[iqs / 4];
+        const int32_t scale_m = int32_t(scale >> 4) * 0x01010101; // Duplicate 8-bit value across 32-bits.
+        const int32_t qs_a = int32_t((cache_a[ib_a].qs[iqs / 4] >> ((iqs % 4) * 2)) & 0x03030303);
+
+        sum_d += dotPacked4x8EXT(qs_a, cache_b.qs[iqs]) * (scale & 0xF);
+        sum_m += dotPacked4x8EXT(scale_m, cache_b.qs[iqs]);
+    }
+
+    return mul_q8_1(sum_d, sum_m, cache_a[ib_a].dm, cache_b.ds, 1);
+}
+#endif // MMQ_SHMEM
+#endif
+
+#if defined(DATA_A_Q3_K)
+// 2-byte loads for Q3_K blocks (110 bytes)
+#ifdef MMQ_SHMEM
+void block_a_to_shmem(const uint buf_ib, const uint ib, const uint iqs) {
+    const uint ib_k = ib / 8;
+    const uint hm_idx = iqs * QUANT_R_MMQ;
+    const uint iqs_k = (ib % 8) * 8 + hm_idx;
+
+    const uint qs_idx = (iqs_k / 32) * 8 + (iqs_k % 8);
+    const uint qs_shift = ((iqs_k % 32) / 8) * 2;
+    const uint hm_shift = iqs_k / 8;
+
+    // Repack 2x4 quants into one int
+    // Add the 3rd bit instead of subtracting it to allow packing the quants
+    const i8vec2 vals00 = unpack8(int16_t((data_a_packed16[ib_k].qs[qs_idx * 2        ] >> qs_shift) & uint16_t(0x0303))) |
+                          unpack8(int16_t(((data_a_packed16[ib_k].hmask[hm_idx * 2    ] >> hm_shift) & uint16_t(0x0101)) << 2));
+    const i8vec2 vals01 = unpack8(int16_t((data_a_packed16[ib_k].qs[qs_idx * 2 + 1    ] >> qs_shift) & uint16_t(0x0303))) |
+                          unpack8(int16_t(((data_a_packed16[ib_k].hmask[hm_idx * 2 + 1] >> hm_shift) & uint16_t(0x0101)) << 2));
+    const i8vec2 vals10 = unpack8(int16_t((data_a_packed16[ib_k].qs[qs_idx * 2 + 2    ] >> qs_shift) & uint16_t(0x0303))) |
+                          unpack8(int16_t(((data_a_packed16[ib_k].hmask[hm_idx * 2 + 2] >> hm_shift) & uint16_t(0x0101)) << 2));
+    const i8vec2 vals11 = unpack8(int16_t((data_a_packed16[ib_k].qs[qs_idx * 2 + 3    ] >> qs_shift) & uint16_t(0x0303))) |
+                          unpack8(int16_t(((data_a_packed16[ib_k].hmask[hm_idx * 2 + 3] >> hm_shift) & uint16_t(0x0101)) << 2));
+    buf_a[buf_ib].qs[iqs] = pack32(u8vec4(vals00.x, vals00.y, vals01.x, vals01.y)) |
+                           (pack32(u8vec4(vals10.x, vals10.y, vals11.x, vals11.y)) << 4);
+
+    if (iqs == 0) {
+        const uint is = iqs_k / 4;
+        const i8vec2 scales = i8vec2(unpack8(((data_a_packed16[ib_k].scales[(is % 8      ) / 2] >> (4 * (is / 8))) & 0x0F0F) |
+                                            (((data_a_packed16[ib_k].scales[(8 + (is % 4)) / 2] >> (2 * (is / 4))) & 0x0303) << 4)));
+
+        buf_a[buf_ib].d_scales = FLOAT_TYPE(data_a_packed16[ib_k].d) * FLOAT_TYPE_VEC2(scales - 32);
+    }
+}
+
+void block_a_to_registers(const uint reg_ib, const uint buf_ib) {
+    cache_a[reg_ib].d_scales = buf_a[buf_ib].d_scales;
+
+    [[unroll]] for (uint iqs = 0; iqs < 4; iqs++) {
+        cache_a[reg_ib].qs[iqs] = buf_a[buf_ib].qs[iqs];
+    }
+}
+
+ACC_TYPE mmq_dot_product(const uint ib_a) {
+    float result = 0.0;
+    int32_t q_sum = 0;
+
+    [[unroll]] for (uint iqs = 0; iqs < 4; iqs++) {
+        // Subtract 4 from the quants to correct the 3rd bit offset
+        const int32_t qs_a = pack32(unpack8(int32_t((cache_a[ib_a].qs[iqs / 2] >> ((iqs % 2) * 4)) & 0x0F0F0F0F)) - int8_t(4));
+
+        q_sum += dotPacked4x8EXT(qs_a, cache_b.qs[iqs]);
+    }
+    result += float(cache_a[ib_a].d_scales[0]) * float(q_sum);
+    q_sum = 0;
+
+    [[unroll]] for (uint iqs = 4; iqs < 8; iqs++) {
+        const int32_t qs_a = pack32(unpack8(int32_t((cache_a[ib_a].qs[iqs / 2] >> ((iqs % 2) * 4)) & 0x0F0F0F0F)) - int8_t(4));
+
+        q_sum += dotPacked4x8EXT(qs_a, cache_b.qs[iqs]);
+    }
+    result += float(cache_a[ib_a].d_scales[1]) * float(q_sum);
+
+    return ACC_TYPE(cache_b.ds.x * result);
+}
+#endif // MMQ_SHMEM
+#endif
+
+#if defined(DATA_A_Q4_K) || defined(DATA_A_Q5_K)
+// 4-byte loads for Q4_K blocks (144 bytes) and Q5_K blocks (176 bytes)
+ACC_TYPE mul_q8_1(const int32_t q_sum, const vec2 dma, const vec2 dsb, const int32_t sum_divisor) {
+    return ACC_TYPE(dsb.x * dma.x * float(q_sum) - dma.y * dsb.y);
+}
+
+#ifdef MMQ_SHMEM
+void block_a_to_shmem(const uint buf_ib, const uint ib, const uint iqs) {
+    const uint ib_k = ib / 8;
+    const uint iqs_k = (ib % 8) * 8 + iqs * QUANT_R_MMQ;
+
+    const uint qs_idx = (iqs_k / 16) * 8 + (iqs_k % 8);
+    const uint qs_shift = ((iqs_k % 16) / 8) * 4;
+
+    // Repack 2x4 quants into one int
+#if defined(DATA_A_Q4_K)
+    const uint32_t vals0 = (data_a_packed32[ib_k].qs[qs_idx    ] >> qs_shift) & 0x0F0F0F0F;
+    const uint32_t vals1 = (data_a_packed32[ib_k].qs[qs_idx + 1] >> qs_shift) & 0x0F0F0F0F;
+
+    buf_a[buf_ib].qs[iqs] = vals0 | (vals1 << 4);
+#else // defined(DATA_A_Q5_K)
+    const uint qh_idx = iqs * QUANT_R_MMQ;
+    const uint qh_shift = iqs_k / 8;
+
+    buf_a[buf_ib].qs[iqs] = int32_t(((data_a_packed32[ib_k].qs[qs_idx] >> qs_shift) & 0x0F0F0F0F) |
+                                   (((data_a_packed32[ib_k].qh[qh_idx] >> qh_shift) & 0x01010101) << 4));
+#endif
+
+
+    if (iqs == 0) {
+        // Scale index
+        const uint is = iqs_k / 8;
+        u8vec2 scale_dm;
+        if (is < 4) {
+            scale_dm = u8vec2(data_a[ib_k].scales[is] & 0x3F, data_a[ib_k].scales[is + 4] & 0x3F);
+        } else {
+            scale_dm = u8vec2((data_a[ib_k].scales[is+4] & 0xF) | ((data_a[ib_k].scales[is-4] & 0xC0) >> 2),
+                              (data_a[ib_k].scales[is+4] >>  4) | ((data_a[ib_k].scales[is  ] & 0xC0) >> 2));
+        }
+
+        buf_a[buf_ib].dm = FLOAT_TYPE_VEC2(data_a_packed32[ib_k].dm) * FLOAT_TYPE_VEC2(scale_dm);
+    }
+}
+
+void block_a_to_registers(const uint reg_ib, const uint buf_ib) {
+    cache_a[reg_ib].dm = buf_a[buf_ib].dm;
+
+    [[unroll]] for (uint iqs = 0; iqs < 8 / QUANT_R_MMQ; iqs++) {
+        cache_a[reg_ib].qs[iqs] = buf_a[buf_ib].qs[iqs];
+    }
+}
+
+ACC_TYPE mmq_dot_product(const uint ib_a) {
+    int32_t q_sum = 0;
+
+    [[unroll]] for (uint iqs = 0; iqs < 8; iqs++) {
+#if defined(DATA_A_Q4_K)
+        const int32_t qs_a = int32_t((cache_a[ib_a].qs[iqs / 2] >> ((iqs % 2) * 4)) & 0x0F0F0F0F);
+#else // defined(DATA_A_Q5_K)
+        const int32_t qs_a = cache_a[ib_a].qs[iqs];
+#endif
+
+        q_sum += dotPacked4x8EXT(qs_a, cache_b.qs[iqs]);
+    }
+
+    return mul_q8_1(q_sum, cache_a[ib_a].dm, cache_b.ds, 1);
+}
+#endif // MMQ_SHMEM
+#endif
+
+#ifdef MMQ_SHMEM
+void block_b_to_shmem(const uint buf_ib, const uint ib, const uint iqs) {
+    const uint ib_outer = ib / 4;
+    const uint ib_inner = ib % 4;
+
+    if (iqs == 0) {
+        buf_b[buf_ib].ds = FLOAT_TYPE_VEC2(data_b[ib_outer].ds[ib_inner]);
+    }
+
+    const ivec4 values = data_b[ib_outer].qs[ib_inner * 2 + iqs];
+    buf_b[buf_ib].qs[iqs * 4    ] = values.x;
+    buf_b[buf_ib].qs[iqs * 4 + 1] = values.y;
+    buf_b[buf_ib].qs[iqs * 4 + 2] = values.z;
+    buf_b[buf_ib].qs[iqs * 4 + 3] = values.w;
+}
+
+void block_b_to_registers(const uint ib) {
+    cache_b.ds = buf_b[ib].ds;
+    [[unroll]] for (uint iqs = 0; iqs < BK / 4; iqs++) {
+        cache_b.qs[iqs] = buf_b[ib].qs[iqs];
+    }
+}
+#endif
+
+#if defined(DATA_A_Q6_K)
+// 2-byte loads for Q6_K blocks (210 bytes)
+#ifdef MMQ_SHMEM
+void block_a_to_shmem(const uint buf_ib, const uint ib, const uint iqs) {
+    const uint ib_k = ib / 8;
+    const uint iqs_k = (ib % 8) * 8 + iqs;
+
+    const uint ql_idx = (iqs_k / 32) * 16 + iqs_k % 16;
+    const uint ql_shift = ((iqs_k % 32) / 16) * 4;
+
+    const uint qh_idx = (iqs_k / 32) * 8 + iqs;
+    const uint qh_shift = ((iqs_k % 32) / 8) * 2;
+
+    const i8vec2 vals00 = (unpack8(int16_t((data_a_packed16[ib_k].ql[ql_idx * 2    ] >> ql_shift) & uint16_t(0x0F0F))) |
+                          unpack8(int16_t(((data_a_packed16[ib_k].qh[qh_idx * 2    ] >> qh_shift) & uint16_t(0x0303)) << 4))) - int8_t(32);
+    const i8vec2 vals01 = (unpack8(int16_t((data_a_packed16[ib_k].ql[ql_idx * 2 + 1] >> ql_shift) & uint16_t(0x0F0F))) |
+                          unpack8(int16_t(((data_a_packed16[ib_k].qh[qh_idx * 2 + 1] >> qh_shift) & uint16_t(0x0303)) << 4))) - int8_t(32);
+    buf_a[buf_ib].qs[iqs] = pack32(i8vec4(vals00.x, vals00.y, vals01.x, vals01.y));
+
+    if (iqs == 0) {
+        const uint is = iqs_k / 4;
+        const i8vec2 scales = unpack8(data_a_packed16[ib_k].scales[is / 2]);
+
+        buf_a[buf_ib].d_scales = FLOAT_TYPE(data_a_packed16[ib_k].d) * FLOAT_TYPE_VEC2(scales);
+    }
+}
+
+void block_a_to_registers(const uint reg_ib, const uint buf_ib) {
+    cache_a[reg_ib].d_scales = buf_a[buf_ib].d_scales;
+
+    [[unroll]] for (uint iqs = 0; iqs < 8; iqs++) {
+        cache_a[reg_ib].qs[iqs] = buf_a[buf_ib].qs[iqs];
+    }
+}
+
+ACC_TYPE mmq_dot_product(const uint ib_a) {
+    float result = 0.0;
+    int32_t q_sum = 0;
+
+    [[unroll]] for (uint iqs = 0; iqs < 4; iqs++) {
+        const int32_t qs_a = cache_a[ib_a].qs[iqs];
+
+        q_sum += dotPacked4x8EXT(qs_a, cache_b.qs[iqs]);
+    }
+    result += float(cache_a[ib_a].d_scales[0]) * float(q_sum);
+    q_sum = 0;
+
+    [[unroll]] for (uint iqs = 4; iqs < 8; iqs++) {
+        const int32_t qs_a = cache_a[ib_a].qs[iqs];
+
+        q_sum += dotPacked4x8EXT(qs_a, cache_b.qs[iqs]);
+    }
+    result += float(cache_a[ib_a].d_scales[1]) * float(q_sum);
+
+    return ACC_TYPE(cache_b.ds.x * result);
+}
+#endif // MMQ_SHMEM
 #endif
 
 #if defined(DATA_A_Q4_0) || defined(DATA_A_Q5_0) || defined(DATA_A_Q8_0) || defined(DATA_A_IQ1_S) || defined(DATA_A_IQ2_XXS) || defined(DATA_A_IQ2_XS) || defined(DATA_A_IQ2_S) || defined(DATA_A_IQ3_XXS) || defined(DATA_A_IQ3_S) || defined(DATA_A_IQ4_XS) || defined(DATA_A_IQ4_NL)
@@ -103,3 +568,10 @@ FLOAT_TYPE_VEC2 get_dm(uint ib) {
     return FLOAT_TYPE_VEC2(data_a_packed32[ib].dm);
 }
 #endif
+
+#if defined(DATA_A_Q2_K)
+FLOAT_TYPE_VEC2 get_dm(uint ib) {
+    const uint ib_k = ib / 8;
+    return FLOAT_TYPE_VEC2(data_a_packed32[ib_k].dm);
+}
+#endif
diff --git a/ggml/src/ggml-vulkan/vulkan-shaders/mul_mmq_shmem_types.glsl b/ggml/src/ggml-vulkan/vulkan-shaders/mul_mmq_shmem_types.glsl
new file mode 100644
index 00000000000..72fec440490
--- /dev/null
+++ b/ggml/src/ggml-vulkan/vulkan-shaders/mul_mmq_shmem_types.glsl
@@ -0,0 +1,78 @@
+#if defined(DATA_A_Q4_0)
+#define QUANT_R_MMQ 2
+struct block_a_cache {
+    uint32_t qs[16/4];
+    FLOAT_TYPE dm;
+};
+#elif defined(DATA_A_Q4_1)
+#define QUANT_R_MMQ 2
+struct block_a_cache {
+    uint32_t qs[16/4];
+    FLOAT_TYPE_VEC2 dm;
+};
+#elif defined(DATA_A_Q5_0)
+#define QUANT_R_MMQ 2
+struct block_a_cache {
+    uint32_t qs[16/4];
+    uint32_t qh;
+    FLOAT_TYPE dm;
+};
+#elif defined(DATA_A_Q5_1)
+#define QUANT_R_MMQ 2
+struct block_a_cache {
+    uint32_t qs[16/4];
+    uint32_t qh;
+    FLOAT_TYPE_VEC2 dm;
+};
+#elif defined(DATA_A_Q8_0)
+#define QUANT_R_MMQ 1
+// AMD likes 4, Intel likes 1 and Nvidia likes 2
+#define BK_STEP 1
+struct block_a_cache {
+    int32_t qs[32/4];
+    FLOAT_TYPE dm;
+};
+#elif defined(DATA_A_MXFP4)
+#define QUANT_R_MMQ 2
+struct block_a_cache {
+    int32_t qs[8];
+    FLOAT_TYPE d;
+};
+#elif defined(DATA_A_Q2_K)
+#define QUANT_R_MMQ 4
+struct block_a_cache {
+    uint32_t qs[2];
+    u8vec2 scales;
+    FLOAT_TYPE_VEC2 dm;
+};
+#elif defined(DATA_A_Q3_K)
+#define QUANT_R_MMQ 2
+struct block_a_cache {
+    uint32_t qs[4];
+    FLOAT_TYPE_VEC2 d_scales;
+};
+#elif defined(DATA_A_Q4_K)
+#define QUANT_R_MMQ 2
+struct block_a_cache {
+    uint32_t qs[4];
+    FLOAT_TYPE_VEC2 dm;
+};
+#elif defined(DATA_A_Q5_K)
+#define QUANT_R_MMQ 1
+struct block_a_cache {
+    int32_t qs[8];
+    FLOAT_TYPE_VEC2 dm;
+};
+#elif defined(DATA_A_Q6_K)
+#define QUANT_R_MMQ 1
+struct block_a_cache {
+    int32_t qs[8];
+    FLOAT_TYPE_VEC2 d_scales;
+};
+#endif
+
+struct block_b_cache
+{
+    int32_t qs[8];
+    FLOAT_TYPE_VEC2 ds;
+};
diff --git a/ggml/src/ggml-vulkan/vulkan-shaders/types.glsl b/ggml/src/ggml-vulkan/vulkan-shaders/types.glsl
index 2fa54ce51fc..02578c77c4f 100644
--- a/ggml/src/ggml-vulkan/vulkan-shaders/types.glsl
+++ b/ggml/src/ggml-vulkan/vulkan-shaders/types.glsl
@@ -66,6 +66,7 @@ struct block_q4_0_packed16
 #define QUANT_AUXF 1
 #define A_TYPE block_q4_0
 #define A_TYPE_PACKED16 block_q4_0_packed16
+#define DATA_A_QUANT_LEGACY
 #endif
 
 #define QUANT_K_Q4_1 32
@@ -98,6 +99,7 @@ struct block_q4_1_packed32
 #define A_TYPE block_q4_1
 #define A_TYPE_PACKED16 block_q4_1_packed16
 #define A_TYPE_PACKED32 block_q4_1_packed32
+#define DATA_A_QUANT_LEGACY
 #endif
 
 #define QUANT_K_Q5_0 32
@@ -123,6 +125,7 @@ struct block_q5_0_packed16
 #define QUANT_AUXF 1
 #define A_TYPE block_q5_0
 #define A_TYPE_PACKED16 block_q5_0_packed16
+#define DATA_A_QUANT_LEGACY
 #endif
 
 #define QUANT_K_Q5_1 32
@@ -158,6 +161,7 @@ struct block_q5_1_packed32
 #define A_TYPE block_q5_1
 #define A_TYPE_PACKED16 block_q5_1_packed16
 #define A_TYPE_PACKED32 block_q5_1_packed32
+#define DATA_A_QUANT_LEGACY
 #endif
 
 #define QUANT_K_Q8_0 32
@@ -186,6 +190,7 @@ struct block_q8_0_packed32
 #define A_TYPE block_q8_0
 #define A_TYPE_PACKED16 block_q8_0_packed16
 #define A_TYPE_PACKED32 block_q8_0_packed32
+#define DATA_A_QUANT_LEGACY
 #endif
 
 #define QUANT_K_Q8_1 32
@@ -226,21 +231,21 @@ struct block_q2_K
 {
     uint8_t scales[QUANT_K_Q2_K/16];
     uint8_t qs[QUANT_K_Q2_K/4];
-    f16vec2 d;
+    f16vec2 dm;
 };
 
 struct block_q2_K_packed16
 {
     uint16_t scales[QUANT_K_Q2_K/16/2];
     uint16_t qs[QUANT_K_Q2_K/4/2];
-    f16vec2 d;
+    f16vec2 dm;
 };
 
 struct block_q2_K_packed32
 {
     uint32_t scales[QUANT_K_Q2_K/16/4];
     uint32_t qs[QUANT_K_Q2_K/4/4];
-    f16vec2 d;
+    f16vec2 dm;
 };
 
 #if defined(DATA_A_Q2_K)
@@ -249,6 +254,8 @@ struct block_q2_K_packed32
 #define A_TYPE block_q2_K
 #define A_TYPE_PACKED16 block_q2_K_packed16
 #define A_TYPE_PACKED32 block_q2_K_packed32
+#define SCALES_PER_32 2
+#define DATA_A_QUANT_K
 #endif
 
 #define QUANT_K_Q3_K 256
@@ -274,27 +281,28 @@ struct block_q3_K_packed16
 #define QUANT_R 1
 #define A_TYPE block_q3_K
 #define A_TYPE_PACKED16 block_q3_K_packed16
+#define DATA_A_QUANT_K
 #endif
 
 #define QUANT_K_Q4_K 256
 
 struct block_q4_K
 {
-    f16vec2 d;
+    f16vec2 dm;
     uint8_t scales[3*QUANT_K_Q4_K/64];
     uint8_t qs[QUANT_K_Q4_K/2];
 };
 
 struct block_q4_K_packed16
 {
-    f16vec2 d;
+    f16vec2 dm;
     uint16_t scales[3*QUANT_K_Q4_K/64/2];
     uint16_t qs[QUANT_K_Q4_K/2/2];
 };
 
 struct block_q4_K_packed32
 {
-    f16vec2 d;
+    f16vec2 dm;
     uint32_t scales[3*QUANT_K_Q4_K/64/4];
     uint32_t qs[QUANT_K_Q4_K/2/4];
 };
@@ -310,13 +318,14 @@ struct block_q4_K_packed128
 #define A_TYPE block_q4_K
 #define A_TYPE_PACKED16 block_q4_K_packed16
 #define A_TYPE_PACKED32 block_q4_K_packed32
+#define DATA_A_QUANT_K
 #endif
 
 #define QUANT_K_Q5_K 256
 
 struct block_q5_K
 {
-    f16vec2 d;
+    f16vec2 dm;
     uint8_t scales[12];
     uint8_t qh[QUANT_K_Q5_K/8];
     uint8_t qs[QUANT_K_Q5_K/2];
@@ -324,12 +333,20 @@ struct block_q5_K
 
 struct block_q5_K_packed16
 {
-    f16vec2 d;
+    f16vec2 dm;
     uint16_t scales[12/2];
     uint16_t qh[QUANT_K_Q5_K/8/2];
     uint16_t qs[QUANT_K_Q5_K/2/2];
 };
 
+struct block_q5_K_packed32
+{
+    f16vec2 dm;
+    uint32_t scales[12/4];
+    uint32_t qh[QUANT_K_Q5_K/8/4];
+    uint32_t qs[QUANT_K_Q5_K/2/4];
+};
+
 struct block_q5_K_packed128
 {
     uvec4 q5k[11];
@@ -340,6 +357,8 @@ struct block_q5_K_packed128
 #define QUANT_R 1
 #define A_TYPE block_q5_K
 #define A_TYPE_PACKED16 block_q5_K_packed16
+#define A_TYPE_PACKED32 block_q5_K_packed32
+#define DATA_A_QUANT_K
 #endif
 
 #define QUANT_K_Q6_K 256
@@ -356,7 +375,7 @@ struct block_q6_K_packed16
 {
     uint16_t ql[QUANT_K_Q6_K/2/2];
     uint16_t qh[QUANT_K_Q6_K/4/2];
-    int8_t scales[QUANT_K_Q6_K/16];
+    int16_t scales[QUANT_K_Q6_K/16/2];
     float16_t d;
 };
 
@@ -365,6 +384,7 @@ struct block_q6_K_packed16
 #define QUANT_R 1
 #define A_TYPE block_q6_K
 #define A_TYPE_PACKED16 block_q6_K_packed16
+#define DATA_A_QUANT_K
 #endif
 
 // IQuants
@@ -1363,18 +1383,11 @@ struct block_mxfp4
     uint8_t qs[QUANT_K_MXFP4/2];
 };
 
-//struct block_mxfp4_packed16
-//{
-//    uint8_t e;
-//    uint16_t qs[QUANT_K_MXFP4/2/2];
-//};
-
 #if defined(DATA_A_MXFP4)
 #define QUANT_K QUANT_K_MXFP4
 #define QUANT_R QUANT_R_MXFP4
 #define QUANT_AUXF 1
 #define A_TYPE block_mxfp4
-//#define A_TYPE_PACKED16 block_mxfp4_packed16
 #endif
 
 #if defined(DATA_A_IQ4_NL) || defined(DATA_A_IQ4_XS)
@@ -1397,12 +1410,12 @@ void init_iq_shmem(uvec3 wgsize)
 #endif
 
 #if defined(DATA_A_MXFP4)
-const FLOAT_TYPE kvalues_mxfp4_const[16] = {
-    FLOAT_TYPE(0.0f), FLOAT_TYPE(0.5f), FLOAT_TYPE(1.0f), FLOAT_TYPE(1.5f), FLOAT_TYPE(2.0f), FLOAT_TYPE(3.0f), FLOAT_TYPE(4.0f), FLOAT_TYPE(6.0f),
-    FLOAT_TYPE(-0.0f), FLOAT_TYPE(-0.5f), FLOAT_TYPE(-1.0f), FLOAT_TYPE(-1.5f), FLOAT_TYPE(-2.0f), FLOAT_TYPE(-3.0f), FLOAT_TYPE(-4.0f), FLOAT_TYPE(-6.0f)
+const int8_t kvalues_mxfp4_const[16] = {
+    int8_t(0), int8_t(1), int8_t(2), int8_t(3), int8_t(4), int8_t(6), int8_t(8), int8_t(12),
+    int8_t(0), int8_t(-1), int8_t(-2), int8_t(-3), int8_t(-4), int8_t(-6), int8_t(-8), int8_t(-12),
 };
 
-shared FLOAT_TYPE kvalues_mxfp4[16];
+shared int8_t kvalues_mxfp4[16];
 
 #define NEEDS_INIT_IQ_SHMEM
 void init_iq_shmem(uvec3 wgsize)
diff --git a/ggml/src/ggml-vulkan/vulkan-shaders/vulkan-shaders-gen.cpp b/ggml/src/ggml-vulkan/vulkan-shaders/vulkan-shaders-gen.cpp
index 0f25ba34530..03fa016398c 100644
--- a/ggml/src/ggml-vulkan/vulkan-shaders/vulkan-shaders-gen.cpp
+++ b/ggml/src/ggml-vulkan/vulkan-shaders/vulkan-shaders-gen.cpp
@@ -566,7 +566,8 @@ void matmul_shaders(bool fp16, MatMulIdType matmul_id_type, bool coopmat, bool c
         }
 
 #if defined(GGML_VULKAN_INTEGER_DOT_GLSLC_SUPPORT)
-        if (!coopmat && !coopmat2 && matmul_id_type == MatMulIdType::NONE && is_legacy_quant(tname)) {
+        // Integer dot mmq performs better with f32 accumulators
+        if (!f16acc && !coopmat && !coopmat2 && (is_legacy_quant(tname) || is_k_quant(tname) || tname == "mxfp4")) {
             string_to_spv(shader_name + "_" + tname + "_q8_1", "mul_mmq.comp", merge_maps(merge_maps(base_dict, float_type_dict), {{data_a_key, "1"}, {"D_TYPE", "float"},}), fp16, coopmat, coopmat2, f16acc);
         }
 #endif
@@ -574,7 +575,7 @@ void matmul_shaders(bool fp16, MatMulIdType matmul_id_type, bool coopmat, bool c
 }
 
 void process_shaders() {
-    std::map<std::string, std::string> base_dict = {{"FLOAT_TYPE", "float"}};
+    std::map<std::string, std::string> base_dict = {{"FLOAT_TYPE", "float"}, {"FLOAT_TYPE_VEC2", "vec2"}};
 
     // matmul
     for (const MatMulIdType& matmul_id_type : {MatMulIdType::NONE, MatMulIdType::DEFAULT, MatMulIdType::SUBGROUP}) {

From 10fcc41290e233788f5a4215314156e8e023eb92 Mon Sep 17 00:00:00 2001
From: Jeff Bolz <jbolz@nvidia.com>
Date: Wed, 29 Oct 2025 08:44:29 -0500
Subject: [PATCH 011/185] vulkan: Update topk_moe fusion to handle gpt's late
 softmax (#16656)

* vulkan: Update topk_moe fusion to handle gpt's late softmax

Based on #16649.

* Add ggml_check_edges

* Add sync logging to show fusion effects

* handle clamp added in #16655

* Update ggml/src/ggml-impl.h

Co-authored-by: Diego Devesa <slarengh@gmail.com>
---
 ggml/src/ggml-impl.h                          |  16 +
 ggml/src/ggml-vulkan/ggml-vulkan.cpp          | 304 +++++++++++-------
 .../ggml-vulkan/vulkan-shaders/topk_moe.comp  |  90 ++++--
 3 files changed, 272 insertions(+), 138 deletions(-)

diff --git a/ggml/src/ggml-impl.h b/ggml/src/ggml-impl.h
index e9201cdc685..ec37a25337b 100644
--- a/ggml/src/ggml-impl.h
+++ b/ggml/src/ggml-impl.h
@@ -682,6 +682,7 @@ static inline bool ggml_can_fuse_subgraph(const struct ggml_cgraph * cgraph,
 #endif
 
 #ifdef __cplusplus
+#include <array>
 #include <initializer_list>
 #include <vector>
 
@@ -697,6 +698,21 @@ inline bool ggml_can_fuse_subgraph(const struct ggml_cgraph *          cgraph,
     return ggml_can_fuse_subgraph(cgraph, start_idx, ops.size(), ops.begin(), outputs.begin(), outputs.size());
 }
 
+// Return true if the edges in the graph match expectations.
+inline bool ggml_check_edges(const struct ggml_cgraph *                cgraph,
+                             int                                       start_idx,
+                             std::initializer_list<std::array<int, 3>> edges) {
+    for (const auto & edge : edges) {
+        int dst_node = edge[0];
+        int src_idx  = edge[1];
+        int src_node = edge[2];
+        if (cgraph->nodes[start_idx + dst_node]->src[src_idx] != cgraph->nodes[start_idx + src_node]) {
+            return false;
+        }
+    }
+    return true;
+}
+
 // expose GGUF internals for test code
 GGML_API size_t gguf_type_size(enum gguf_type type);
 GGML_API struct gguf_context * gguf_init_from_file_impl(FILE * file, struct gguf_init_params params);
diff --git a/ggml/src/ggml-vulkan/ggml-vulkan.cpp b/ggml/src/ggml-vulkan/ggml-vulkan.cpp
index 3d10aa07b08..50e7922dc60 100644
--- a/ggml/src/ggml-vulkan/ggml-vulkan.cpp
+++ b/ggml/src/ggml-vulkan/ggml-vulkan.cpp
@@ -385,12 +385,76 @@ static constexpr uint32_t num_argsort_pipelines = 11;
 static constexpr uint32_t max_argsort_cols = 1 << (num_argsort_pipelines-1);
 static constexpr uint32_t num_topk_moe_pipelines = 10;
 
-static constexpr std::array topk_moe_norm{ GGML_OP_SOFT_MAX, GGML_OP_RESHAPE,  GGML_OP_ARGSORT,
-                                           GGML_OP_VIEW,     GGML_OP_GET_ROWS, GGML_OP_RESHAPE,
-                                           GGML_OP_SUM_ROWS, GGML_OP_DIV,      GGML_OP_RESHAPE };
-static constexpr std::array topk_moe     { GGML_OP_SOFT_MAX, GGML_OP_RESHAPE,  GGML_OP_ARGSORT,
-                                           GGML_OP_VIEW,     GGML_OP_GET_ROWS };
+static constexpr std::initializer_list<ggml_op> topk_moe_early_softmax_norm{ GGML_OP_SOFT_MAX, GGML_OP_RESHAPE,  GGML_OP_ARGSORT,
+                                                                             GGML_OP_VIEW,     GGML_OP_GET_ROWS, GGML_OP_RESHAPE,
+                                                                             GGML_OP_SUM_ROWS, GGML_OP_CLAMP,    GGML_OP_DIV,
+                                                                             GGML_OP_RESHAPE };
+static constexpr std::initializer_list<ggml_op> topk_moe_early_softmax     { GGML_OP_SOFT_MAX, GGML_OP_RESHAPE,  GGML_OP_ARGSORT,
+                                                                             GGML_OP_VIEW,     GGML_OP_GET_ROWS };
+static constexpr std::initializer_list<ggml_op> topk_moe_late_softmax      { GGML_OP_ARGSORT,  GGML_OP_VIEW,
+                                                                             GGML_OP_GET_ROWS, GGML_OP_RESHAPE,
+                                                                             GGML_OP_SOFT_MAX, GGML_OP_RESHAPE };
+
+//node #978 (  SOFT_MAX):     ffn_moe_probs-15 (   0K) [Vulka         ] use=2:    ffn_moe_logits-15 (   0K) [Vulka         ]
+//node #979 (   RESHAPE): ffn_moe_probs-15 (re (   0K) [Vulka         ] use=1:     ffn_moe_probs-15 (   0K) [Vulka         ]
+//node #980 (   ARGSORT):   ffn_moe_argsort-15 (   0K) [Vulka         ] use=1:     ffn_moe_probs-15 (   0K) [Vulka         ]
+//node #981 (      VIEW):      ffn_moe_topk-15 (   0K) [Vulka         ] use=4:   ffn_moe_argsort-15 (   0K) [Vulka         ]
+//node #982 (  GET_ROWS):   ffn_moe_weights-15 (   0K) [Vulka         ] use=1: ffn_moe_probs-15 (re (   0K) [Vulka         ]      ffn_moe_topk-15 (   0K) [Vulka         ]
+//node #983 (   RESHAPE): ffn_moe_weights-15 ( (   0K) [Vulka         ] use=2:   ffn_moe_weights-15 (   0K) [Vulka         ]
+//node #984 (  SUM_ROWS): ffn_moe_weights_sum- (   0K) [Vulka         ] use=1: ffn_moe_weights-15 ( (   0K) [Vulka         ]
+//node #985 (     CLAMP): ffn_moe_weights_sum_ (   0K) [Vulka         ] use=1: ffn_moe_weights_sum- (   0K) [Vulka         ]
+//node #986 (       DIV): ffn_moe_weights_norm (   0K) [Vulka         ] use=1: ffn_moe_weights-15 ( (   0K) [Vulka         ] ffn_moe_weights_sum_ (   0K) [Vulka         ]
+//node #987 (   RESHAPE): ffn_moe_weights_norm (   0K) [Vulka         ] use=1: ffn_moe_weights_norm (   0K) [Vulka         ]
+static constexpr std::initializer_list<std::array<int, 3>> topk_moe_early_softmax_norm_edges {
+    { 1, 0, 0 }, // reshape->src[0]  == softmax
+    { 2, 0, 0 }, // argsort->src[0]  == softmax
+    { 3, 0, 2 }, // view->src[0]     == argsort
+    { 4, 0, 1 }, // get_rows->src[0] == reshape
+    { 4, 1, 3 }, // get_rows->src[1] == view
+    { 5, 0, 4 }, // reshape->src[0]  == get_rows
+    { 6, 0, 5 }, // sum_rows->src[0] == reshape
+    { 7, 0, 6 }, // clamp->src[0]    == sum_rows
+    { 8, 0, 5 }, // div->src[0]      == reshape
+    { 8, 1, 7 }, // div->src[1]      == clamp
+    { 9, 0, 8 }, // reshape->src[0]  == div
+};
+
+// same as early_softmax_norm but ending after the get_rows
+static constexpr std::initializer_list<std::array<int, 3>> topk_moe_early_softmax_edges {
+    { 1, 0, 0 }, // reshape->src[0]  == softmax
+    { 2, 0, 0 }, // argsort->src[0]  == softmax
+    { 3, 0, 2 }, // view->src[0]     == argsort
+    { 4, 0, 1 }, // get_rows->src[0] == reshape
+    { 4, 1, 3 }, // get_rows->src[1] == view
+};
 
+//node #652 (   ARGSORT):   ffn_moe_argsort-11 (   0K) [Vulka         ] use=1:     ffn_moe_probs-11 (   0K) [Vulka         ]
+//node #653 (      VIEW):      ffn_moe_topk-11 (   0K) [Vulka         ] use=7:   ffn_moe_argsort-11 (   0K) [Vulka         ]
+//node #654 (  GET_ROWS):   ffn_moe_weights-11 (   0K) [Vulka         ] use=1: ffn_moe_probs-11 (re (   0K) [Vulka         ]      ffn_moe_topk-11 (   0K) [Vulka         ]
+//node #655 (   RESHAPE): ffn_moe_weights-11 ( (   0K) [Vulka         ] use=1:   ffn_moe_weights-11 (   0K) [Vulka         ]
+//node #656 (  SOFT_MAX):             node_656 (   0K) [Vulka         ] use=1: ffn_moe_weights-11 ( (   0K) [Vulka         ]
+//node #657 (   RESHAPE): ffn_moe_weights_soft (   0K) [Vulka         ] use=1:             node_656 (   0K) [Vulka         ]
+static constexpr std::initializer_list<std::array<int, 3>> topk_moe_late_softmax_edges {
+    { 1, 0, 0 }, // view->src[0]     == argsort
+    { 2, 1, 1 }, // get_rows->src[1] == view
+    { 3, 0, 2 }, // reshape->src[0]  == get_rows
+    { 4, 0, 3 }, // soft_max->src[0] == reshape
+    { 5, 0, 4 }, // reshape->src[0]  == soft_max
+};
+
+enum topk_moe_mode {
+    TOPK_MOE_EARLY_SOFTMAX,
+    TOPK_MOE_EARLY_SOFTMAX_NORM,
+    TOPK_MOE_LATE_SOFTMAX,
+    TOPK_MOE_COUNT,
+};
+
+static topk_moe_mode ggml_vk_num_additional_ops_to_topk_moe_mode(uint32_t num) {
+    topk_moe_mode mode = num == topk_moe_early_softmax_norm.size() - 1 ? TOPK_MOE_EARLY_SOFTMAX_NORM :
+                         num == topk_moe_early_softmax.size() - 1      ? TOPK_MOE_EARLY_SOFTMAX :
+                                                                         TOPK_MOE_LATE_SOFTMAX;
+    return mode;
+}
 
 struct vk_device_struct {
     std::recursive_mutex mutex;
@@ -605,8 +669,7 @@ struct vk_device_struct {
 
     vk_pipeline pipeline_flash_attn_split_k_reduce;
 
-    // [2] is {!norm, norm}
-    vk_pipeline pipeline_topk_moe[num_topk_moe_pipelines][2];
+    vk_pipeline pipeline_topk_moe[num_topk_moe_pipelines][TOPK_MOE_COUNT];
 
     std::vector<vk_pipeline_ref> all_pipelines;
 
@@ -954,6 +1017,8 @@ static_assert(sizeof(vk_op_multi_add_push_constants) <= 256);
 struct vk_op_topk_moe_push_constants {
     uint32_t n_rows;
     uint32_t n_expert_used;
+    float clamp_min;
+    float clamp_max;
 };
 
 struct vk_op_add_id_push_constants {
@@ -3804,8 +3869,9 @@ static void ggml_vk_load_shaders(vk_device& device) {
     ggml_vk_create_pipeline(device, device->pipeline_conv2d_dw_cwhn_f16_f32, "conv2d_dw_cwhn_f16_f32", conv2d_dw_cwhn_f16_f32_len, conv2d_dw_cwhn_f16_f32_data, "main", 3, sizeof(vk_op_conv2d_dw_push_constants), {512, 1, 1}, {}, 1);
 
     for (uint32_t i = 0; i < num_topk_moe_pipelines; ++i) {
-        ggml_vk_create_pipeline2(device, device->pipeline_topk_moe[i][0], "topk_moe_f32_"+std::to_string(i),   topk_moe_f32_len, topk_moe_f32_data, "main", 3, sizeof(vk_op_topk_moe_push_constants), {1, 1, 1}, {device->subgroup_size, 1u<<i, 0}, 1, true, true);
-        ggml_vk_create_pipeline2(device, device->pipeline_topk_moe[i][1], "topk_moe_f32_"+std::to_string(i),   topk_moe_f32_len, topk_moe_f32_data, "main", 3, sizeof(vk_op_topk_moe_push_constants), {1, 1, 1}, {device->subgroup_size, 1u<<i, 1}, 1, true, true);
+        ggml_vk_create_pipeline2(device, device->pipeline_topk_moe[i][TOPK_MOE_EARLY_SOFTMAX],      "topk_moe_f32_early_softmax_"+std::to_string(i),       topk_moe_f32_len, topk_moe_f32_data, "main", 3, sizeof(vk_op_topk_moe_push_constants), {1, 1, 1}, {device->subgroup_size, 1u<<i, 0, 0}, 1, true, true);
+        ggml_vk_create_pipeline2(device, device->pipeline_topk_moe[i][TOPK_MOE_EARLY_SOFTMAX_NORM], "topk_moe_f32_early_softmax_norm"+std::to_string(i),   topk_moe_f32_len, topk_moe_f32_data, "main", 3, sizeof(vk_op_topk_moe_push_constants), {1, 1, 1}, {device->subgroup_size, 1u<<i, 1, 0}, 1, true, true);
+        ggml_vk_create_pipeline2(device, device->pipeline_topk_moe[i][TOPK_MOE_LATE_SOFTMAX],       "topk_moe_f32_late_softmax"+std::to_string(i),         topk_moe_f32_len, topk_moe_f32_data, "main", 3, sizeof(vk_op_topk_moe_push_constants), {1, 1, 1}, {device->subgroup_size, 1u<<i, 0, 1}, 1, true, true);
     }
 
     for (auto &c : compiles) {
@@ -8083,8 +8149,8 @@ static vk_pipeline ggml_vk_op_get_pipeline(ggml_backend_vk_context * ctx, const
         if (ctx->num_additional_fused_ops) {
             uint32_t idx = (uint32_t)ceilf(log2f(float(dst->ne[0])));
             GGML_ASSERT(idx < num_topk_moe_pipelines);
-            bool with_norm = ctx->num_additional_fused_ops == topk_moe_norm.size() - 1;
-            return ctx->device->pipeline_topk_moe[idx][with_norm];
+            topk_moe_mode mode = ggml_vk_num_additional_ops_to_topk_moe_mode(ctx->num_additional_fused_ops);
+            return ctx->device->pipeline_topk_moe[idx][mode];
         }
 
         if (src0->type == GGML_TYPE_F32 && (src1 == nullptr || src1->type == GGML_TYPE_F32) && dst->type == GGML_TYPE_F32) {
@@ -8139,6 +8205,13 @@ static vk_pipeline ggml_vk_op_get_pipeline(ggml_backend_vk_context * ctx, const
             return nullptr;
         }
     case GGML_OP_ARGSORT:
+        if (ctx->num_additional_fused_ops) {
+            uint32_t idx = (uint32_t)ceilf(log2f(float(dst->ne[0])));
+            GGML_ASSERT(idx < num_topk_moe_pipelines);
+            topk_moe_mode mode = ggml_vk_num_additional_ops_to_topk_moe_mode(ctx->num_additional_fused_ops);
+            return ctx->device->pipeline_topk_moe[idx][mode];
+        }
+
         if (src0->type == GGML_TYPE_F32 && dst->type == GGML_TYPE_I32) {
             uint32_t idx = (uint32_t)ceilf(log2f(float(dst->ne[0])));
             return ctx->device->pipeline_argsort_f32[idx];
@@ -9678,10 +9751,12 @@ static void ggml_vk_soft_max_back(ggml_backend_vk_context * ctx, vk_context& sub
 
 static void ggml_vk_topk_moe(ggml_backend_vk_context * ctx, vk_context& subctx, ggml_cgraph * cgraph, int node_idx, bool dryrun = false) {
 
-    bool with_norm = ctx->num_additional_fused_ops == topk_moe_norm.size() - 1;
+    topk_moe_mode mode = ggml_vk_num_additional_ops_to_topk_moe_mode(ctx->num_additional_fused_ops);
     ggml_tensor * logits = cgraph->nodes[node_idx + 0]->src[0];
-    ggml_tensor * weights = with_norm ? cgraph->nodes[node_idx + 8] : cgraph->nodes[node_idx + 4];
-    ggml_tensor * ids = cgraph->nodes[node_idx + 3];
+    ggml_tensor * weights = (mode == TOPK_MOE_EARLY_SOFTMAX_NORM) ? cgraph->nodes[node_idx + 9] :
+                            (mode == TOPK_MOE_EARLY_SOFTMAX)      ? cgraph->nodes[node_idx + 4] :
+                                                                    cgraph->nodes[node_idx + 5];
+    ggml_tensor * ids = (mode == TOPK_MOE_LATE_SOFTMAX) ? cgraph->nodes[node_idx + 1] : cgraph->nodes[node_idx + 3];
 
     GGML_ASSERT(logits->type == GGML_TYPE_F32);
     GGML_ASSERT(weights->type == GGML_TYPE_F32);
@@ -9740,9 +9815,14 @@ static void ggml_vk_topk_moe(ggml_backend_vk_context * ctx, vk_context& subctx,
         GGML_ASSERT(d_ids != nullptr);
     }
 
-    vk_op_topk_moe_push_constants pc;
+    vk_op_topk_moe_push_constants pc {};
     pc.n_rows = n_rows;
     pc.n_expert_used = n_expert_used;
+    if (mode == TOPK_MOE_EARLY_SOFTMAX_NORM) {
+        ggml_tensor * clamp = cgraph->nodes[node_idx + 7];
+        pc.clamp_min = ggml_get_op_params_f32(clamp, 0);
+        pc.clamp_max = ggml_get_op_params_f32(clamp, 1);
+    }
 
     GGML_ASSERT(n_expert_used <= n_experts);
 
@@ -11337,7 +11417,13 @@ static bool ggml_vk_build_graph(ggml_backend_vk_context * ctx, ggml_cgraph * cgr
                 }
             }
         }
+
+#define ENABLE_SYNC_LOGGING 0
+
         if (need_sync) {
+#if ENABLE_SYNC_LOGGING
+            std::cerr <<  "sync" << std::endl;
+#endif
             ctx->unsynced_nodes_written.clear();
             ctx->unsynced_nodes_read.clear();
             ggml_vk_sync_buffers(ctx, compute_ctx);
@@ -11355,6 +11441,18 @@ static bool ggml_vk_build_graph(ggml_backend_vk_context * ctx, ggml_cgraph * cgr
             }
         }
     }
+#if ENABLE_SYNC_LOGGING
+    if (!dryrun) {
+        for (int i = 0; i < ctx->num_additional_fused_ops + 1; ++i) {
+            auto *n = cgraph->nodes[node_idx + i];
+            std::cerr << node_idx + i << " " << ggml_op_name(n->op) << " " <<  n->name;
+            if (n->op == GGML_OP_GLU) {
+                std::cerr << " " << ggml_glu_op_name(ggml_get_glu_op(n)) << " " << (n->src[1] ? "split" : "single") << " ";
+            }
+            std::cerr << std::endl;
+        }
+    }
+#endif
 
     switch (node->op) {
     case GGML_OP_REPEAT:
@@ -11533,7 +11631,11 @@ static bool ggml_vk_build_graph(ggml_backend_vk_context * ctx, ggml_cgraph * cgr
 
         break;
     case GGML_OP_ARGSORT:
-        ggml_vk_argsort(ctx, compute_ctx, src0, node, dryrun);
+        if (ctx->num_additional_fused_ops) {
+            ggml_vk_topk_moe(ctx, compute_ctx, cgraph, node_idx, dryrun);
+        } else {
+            ggml_vk_argsort(ctx, compute_ctx, src0, node, dryrun);
+        }
 
         break;
     case GGML_OP_SUM:
@@ -12306,30 +12408,27 @@ static bool ggml_vk_can_fuse(const struct ggml_cgraph * cgraph, int node_idx, st
 }
 
 static bool ggml_vk_can_fuse_topk_moe(ggml_backend_vk_context * ctx, const struct ggml_cgraph * cgraph,
-                                      int node_idx, bool with_norm) {
+                                      int node_idx, topk_moe_mode mode) {
 
-    if (with_norm) {
-        if (node_idx + (int)topk_moe_norm.size() > cgraph->n_nodes) {
-            return false;
-        }
-        for (size_t i = 0; i < topk_moe_norm.size(); ++i) {
-            if (cgraph->nodes[node_idx + i]->op != topk_moe_norm[i]) {
-                return false;
-            }
-        }
-    } else {
-        if (node_idx + (int)topk_moe.size() > cgraph->n_nodes) {
-            return false;
-        }
-        for (size_t i = 0; i < topk_moe.size(); ++i) {
-            if (cgraph->nodes[node_idx + i]->op != topk_moe[i]) {
-                return false;
-            }
-        }
-    }
+    const ggml_tensor * softmax;
+    const ggml_tensor * weights;
 
-    const ggml_tensor * softmax =  cgraph->nodes[node_idx + 0];
-    const ggml_tensor * weights = with_norm ? cgraph->nodes[node_idx + 8] : cgraph->nodes[node_idx + 4];
+    switch (mode) {
+    case TOPK_MOE_EARLY_SOFTMAX_NORM:
+        softmax = cgraph->nodes[node_idx + 0];
+        weights = cgraph->nodes[node_idx + 9];
+        break;
+    case TOPK_MOE_EARLY_SOFTMAX:
+        softmax = cgraph->nodes[node_idx + 0];
+        weights = cgraph->nodes[node_idx + 4];
+        break;
+    case TOPK_MOE_LATE_SOFTMAX:
+        softmax = cgraph->nodes[node_idx + 4];
+        weights = cgraph->nodes[node_idx + 5];
+        break;
+    default:
+        return false;
+    }
 
     const float * op_params = (const float *)softmax->op_params;
 
@@ -12355,60 +12454,6 @@ static bool ggml_vk_can_fuse_topk_moe(ggml_backend_vk_context * ctx, const struc
         return false;
     }
 
-    // Check that the nodes don't have any unexpected uses
-    const ggml_tensor * reshape1 =  cgraph->nodes[node_idx + 1];
-    const ggml_tensor * argsort =   cgraph->nodes[node_idx + 2];
-    const ggml_tensor * view =      cgraph->nodes[node_idx + 3];
-    const ggml_tensor * get_rows =  cgraph->nodes[node_idx + 4];
-    const ggml_tensor * reshape5 =  with_norm ? cgraph->nodes[node_idx + 5] : nullptr;
-    const ggml_tensor * sum_rows =  with_norm ? cgraph->nodes[node_idx + 6] : nullptr;
-    const ggml_tensor * div =       with_norm ? cgraph->nodes[node_idx + 7] : nullptr;
-    const ggml_tensor * reshape8 =  with_norm ? cgraph->nodes[node_idx + 8] : nullptr;
-
-    // softmax is used by reshape and argsort
-    if (ggml_node_get_use_count(cgraph, node_idx) != 2 ||
-        reshape1->src[0] != softmax ||
-        argsort->src[0] != softmax) {
-        return false;
-    }
-    // reshape is used by get_rows
-    if (ggml_node_get_use_count(cgraph, node_idx + 1) != 1 ||
-        get_rows->src[0] != reshape1) {
-        return false;
-    }
-    // argsort is used by view
-    if (ggml_node_get_use_count(cgraph, node_idx + 2) != 1 ||
-        view->src[0] != argsort) {
-        return false;
-    }
-    // view is written (via argsort), we can skip checking it
-
-    if (with_norm) {
-        // get_rows is used by reshape
-        if (ggml_node_get_use_count(cgraph, node_idx + 4) != 1 ||
-            reshape5->src[0] != get_rows) {
-            return false;
-        }
-
-        // reshape is used by sum_rows and div
-        if (ggml_node_get_use_count(cgraph, node_idx + 5) != 2 ||
-            sum_rows->src[0] != reshape5 ||
-            div->src[0] != reshape5) {
-            return false;
-        }
-
-        // sum_rows is used by div
-        if (ggml_node_get_use_count(cgraph, node_idx + 6) != 1 ||
-            div->src[1] != sum_rows) {
-            return false;
-        }
-
-        // div/reshape are written
-        if (reshape8->src[0] != div) {
-            return false;
-        }
-    }
-
     if (!ctx->device->subgroup_arithmetic ||
         !ctx->device->subgroup_shuffle ||
         !ctx->device->subgroup_require_full_support ||
@@ -12494,10 +12539,18 @@ static ggml_status ggml_backend_vk_graph_compute(ggml_backend_t backend, ggml_cg
                 ctx->num_additional_fused_ops = num_adds - 1;
             } else if (ggml_vk_can_fuse(cgraph, i, { GGML_OP_RMS_NORM, GGML_OP_MUL })) {
                 ctx->num_additional_fused_ops = 1;
-            } else if (ggml_vk_can_fuse_topk_moe(ctx, cgraph, i, true)) {
-                ctx->num_additional_fused_ops = topk_moe_norm.size() - 1;
-            } else if (ggml_vk_can_fuse_topk_moe(ctx, cgraph, i, false)) {
-                ctx->num_additional_fused_ops = topk_moe.size() - 1;
+            } else if (ggml_can_fuse_subgraph(cgraph, i, topk_moe_early_softmax_norm, { i + 3, i + 9 }) &&
+                       ggml_check_edges(cgraph, i, topk_moe_early_softmax_norm_edges) &&
+                       ggml_vk_can_fuse_topk_moe(ctx, cgraph, i, TOPK_MOE_EARLY_SOFTMAX_NORM)) {
+                ctx->num_additional_fused_ops = topk_moe_early_softmax_norm.size() - 1;
+            } else if (ggml_can_fuse_subgraph(cgraph, i, topk_moe_early_softmax, { i + 3, i + 4 }) &&
+                       ggml_check_edges(cgraph, i, topk_moe_early_softmax_edges) &&
+                       ggml_vk_can_fuse_topk_moe(ctx, cgraph, i, TOPK_MOE_EARLY_SOFTMAX)) {
+                ctx->num_additional_fused_ops = topk_moe_early_softmax.size() - 1;
+            } else if (ggml_can_fuse_subgraph(cgraph, i, topk_moe_late_softmax, { i + 1, i + 5 }) &&
+                       ggml_check_edges(cgraph, i, topk_moe_late_softmax_edges) &&
+                       ggml_vk_can_fuse_topk_moe(ctx, cgraph, i, TOPK_MOE_LATE_SOFTMAX)) {
+                ctx->num_additional_fused_ops = topk_moe_late_softmax.size() - 1;
             }
         }
         ggml_vk_build_graph(ctx, cgraph, i, nullptr, 0, true, false, false, false);
@@ -12595,10 +12648,18 @@ static ggml_status ggml_backend_vk_graph_compute(ggml_backend_t backend, ggml_cg
                 ctx->num_additional_fused_ops = num_adds - 1;
             } else if (ggml_vk_can_fuse(cgraph, i, { GGML_OP_RMS_NORM, GGML_OP_MUL })) {
                 ctx->num_additional_fused_ops = 1;
-            } else if (ggml_vk_can_fuse_topk_moe(ctx, cgraph, i, true)) {
-                ctx->num_additional_fused_ops = topk_moe_norm.size() - 1;
-            } else if (ggml_vk_can_fuse_topk_moe(ctx, cgraph, i, false)) {
-                ctx->num_additional_fused_ops = topk_moe.size() - 1;
+            } else if (ggml_can_fuse_subgraph(cgraph, i, topk_moe_early_softmax_norm, { i + 3, i + 9 }) &&
+                       ggml_check_edges(cgraph, i, topk_moe_early_softmax_norm_edges) &&
+                       ggml_vk_can_fuse_topk_moe(ctx, cgraph, i, TOPK_MOE_EARLY_SOFTMAX_NORM)) {
+                ctx->num_additional_fused_ops = topk_moe_early_softmax_norm.size() - 1;
+            } else if (ggml_can_fuse_subgraph(cgraph, i, topk_moe_early_softmax, { i + 3, i + 4 }) &&
+                       ggml_check_edges(cgraph, i, topk_moe_early_softmax_edges) &&
+                       ggml_vk_can_fuse_topk_moe(ctx, cgraph, i, TOPK_MOE_EARLY_SOFTMAX)) {
+                ctx->num_additional_fused_ops = topk_moe_early_softmax.size() - 1;
+            } else if (ggml_can_fuse_subgraph(cgraph, i, topk_moe_late_softmax, { i + 1, i + 5 }) &&
+                       ggml_check_edges(cgraph, i, topk_moe_late_softmax_edges) &&
+                       ggml_vk_can_fuse_topk_moe(ctx, cgraph, i, TOPK_MOE_LATE_SOFTMAX)) {
+                ctx->num_additional_fused_ops = topk_moe_late_softmax.size() - 1;
             }
         }
 
@@ -12730,25 +12791,44 @@ static void ggml_vk_graph_optimize(ggml_backend_t backend, struct ggml_cgraph *
     while (first_unused < graph->n_nodes) {
         std::vector<int> current_set;
 
-        // Avoid reordering topk_moe_norm
-        if (first_unused + (int)topk_moe_norm.size() <= graph->n_nodes) {
-            bool is_topk_moe_norm = true;
-            for (size_t j = 0; j < topk_moe_norm.size(); ++j) {
-                if (graph->nodes[first_unused + j]->op != topk_moe_norm[j] || used[first_unused + j]) {
-                    is_topk_moe_norm = false;
+        // Check for fusion patterns and avoid reordering them
+        auto const &match_pattern = [&](const std::initializer_list<ggml_op> &pattern, int start) -> bool {
+            if (start + (int)pattern.size() <= graph->n_nodes) {
+                bool is_pattern = true;
+                for (size_t j = 0; j < pattern.size(); ++j) {
+                    if (graph->nodes[start + j]->op != pattern.begin()[j] || used[start + j]) {
+                        is_pattern = false;
+                    }
                 }
+                return is_pattern;
             }
-            if (is_topk_moe_norm) {
-                for (size_t j = 0; j < topk_moe_norm.size(); ++j) {
+            return false;
+        };
+
+        auto const &keep_pattern = [&](const std::initializer_list<ggml_op> &pattern) -> bool {
+            if (match_pattern(pattern, first_unused)) {
+                for (size_t j = 0; j < pattern.size(); ++j) {
                     new_order.push_back(graph->nodes[first_unused + j]);
                     used[first_unused + j] = true;
                 }
                 while (first_unused < graph->n_nodes && used[first_unused]) {
                     first_unused++;
                 }
-                continue;
+                return true;
             }
+            return false;
+        };
+
+        if (keep_pattern(topk_moe_early_softmax_norm)) {
+            continue;
+        }
+        if (keep_pattern(topk_moe_early_softmax)) {
+            continue;
         }
+        if (keep_pattern(topk_moe_late_softmax)) {
+            continue;
+        }
+
         // First, grab the next unused node.
         current_set.push_back(first_unused);
 
@@ -12766,6 +12846,12 @@ static void ggml_vk_graph_optimize(ggml_backend_t backend, struct ggml_cgraph *
             if (is_empty(graph->nodes[j])) {
                 continue;
             }
+            // Don't pull forward nodes from fusion patterns
+            if (match_pattern(topk_moe_early_softmax_norm, j) ||
+                match_pattern(topk_moe_early_softmax, j) ||
+                match_pattern(topk_moe_late_softmax, j)) {
+                continue;
+            }
             bool ok = true;
             for (int c = first_unused; c < j; ++c) {
                 if (!used[c] &&
diff --git a/ggml/src/ggml-vulkan/vulkan-shaders/topk_moe.comp b/ggml/src/ggml-vulkan/vulkan-shaders/topk_moe.comp
index 9e56d5f8a3c..bc1c278bf49 100644
--- a/ggml/src/ggml-vulkan/vulkan-shaders/topk_moe.comp
+++ b/ggml/src/ggml-vulkan/vulkan-shaders/topk_moe.comp
@@ -11,6 +11,8 @@ layout (push_constant) uniform parameter
 {
     uint n_rows;
     uint n_expert_used;
+    float clamp_min;
+    float clamp_max;
 };
 
 layout(local_size_x_id = 0, local_size_y = 4, local_size_z = 1) in;
@@ -18,6 +20,7 @@ layout(local_size_x_id = 0, local_size_y = 4, local_size_z = 1) in;
 layout(constant_id = 0) const uint WARP_SIZE = 32;
 layout(constant_id = 1) const uint n_experts = 512;
 layout(constant_id = 2) const bool with_norm = true;
+layout(constant_id = 3) const bool late_softmax = false;
 
 const uint experts_per_thread = (n_experts > WARP_SIZE) ? n_experts / WARP_SIZE : 1;
 
@@ -25,53 +28,72 @@ layout (binding = 0, std430) readonly buffer Logits {float logits[];};
 layout (binding = 1, std430) writeonly buffer Weights {float weights[];};
 layout (binding = 2, std430) writeonly buffer Ids {uint ids[];};
 
-void main() {
-    const uint row = gl_WorkGroupID.x * gl_WorkGroupSize.y + gl_LocalInvocationID.y;
-    if (row >= n_rows) {
-        return;
-    }
+const float INFINITY = 1.0 / 0.0;
 
-    const uint logits_offset = n_experts * row;
-    const uint weights_offset = n_expert_used * row;
-    const uint ids_offset = n_experts * row;
-
-    float logits_r[experts_per_thread];
-
-    const float INFINITY = 1.0 / 0.0;
+// Warp-local softmax used for both the pre-top-k logits and the post-top-k delayed path.
+void softmax_warp_inplace(inout float vals[experts_per_thread], const uint limit, const uint lane, const bool use_limit) {
+    float max_val = -INFINITY;
 
     [[unroll]]
-    for (uint i = 0; i < n_experts; i += WARP_SIZE) {
-        const uint expert        = i + gl_LocalInvocationID.x;
-        logits_r[i / WARP_SIZE] = n_experts % WARP_SIZE == 0 || expert < n_experts ? logits[logits_offset + expert] : -INFINITY;
+    for (int i = 0; i < experts_per_thread; i++) {
+        const uint idx       = lane + i * WARP_SIZE;
+        const bool is_active = !use_limit || (idx < limit);
+        if (is_active) {
+            max_val = max(max_val, vals[i]);
+        }
     }
 
-    float max_val = logits_r[0];
+    max_val = subgroupMax(max_val);
+
+    float sum = 0.f;
 
     [[unroll]]
-    for (int i = 1; i < experts_per_thread; i++) {
-        const float val = logits_r[i];
-        max_val         = max(val, max_val);
+    for (int i = 0; i < experts_per_thread; i++) {
+        const uint idx       = lane + i * WARP_SIZE;
+        const bool is_active = !use_limit || (idx < limit);
+        if (is_active) {
+            const float val = exp(vals[i] - max_val);
+            vals[i]         = val;
+            sum += val;
+        } else {
+            vals[i] = 0.f;
+        }
     }
 
-    max_val = subgroupMax(max_val);
+    sum = subgroupAdd(sum);
 
-    float wt[experts_per_thread];
-    float tmp = 0.f;
+    const float inv_sum = 1.0f / sum;
 
     [[unroll]]
     for (int i = 0; i < experts_per_thread; i++) {
-        const float val = logits_r[i];
-        wt[i]           = exp(val - max_val);
-        tmp += wt[i];
+        const uint idx       = lane + i * WARP_SIZE;
+        const bool is_active = !use_limit || (idx < limit);
+        if (is_active) {
+            vals[i] *= inv_sum;
+        }
     }
+}
 
-    tmp = subgroupAdd(tmp);
+void main() {
+    const uint row = gl_WorkGroupID.x * gl_WorkGroupSize.y + gl_LocalInvocationID.y;
+    if (row >= n_rows) {
+        return;
+    }
 
-    const float inv_sum = 1.0f / tmp;
+    const uint logits_offset = n_experts * row;
+    const uint weights_offset = n_expert_used * row;
+    const uint ids_offset = n_experts * row;
+
+    float wt[experts_per_thread];
 
     [[unroll]]
-    for (int i = 0; i < experts_per_thread; i++) {
-        wt[i] = wt[i] * inv_sum;
+    for (uint i = 0; i < n_experts; i += WARP_SIZE) {
+        const uint expert = i + gl_LocalInvocationID.x;
+        wt[i / WARP_SIZE] = (n_experts % WARP_SIZE == 0 || expert < n_experts) ? logits[logits_offset + expert] : -INFINITY;
+    }
+
+    if (!late_softmax) {
+        softmax_warp_inplace(wt, n_experts, gl_LocalInvocationID.x, false);
     }
 
     // at this point, each thread holds a portion of softmax,
@@ -82,6 +104,11 @@ void main() {
 
     float output_weights[experts_per_thread];
 
+    [[unroll]]
+    for (int i = 0; i < experts_per_thread; i++) {
+        output_weights[i] = 0.f;
+    }
+
     for (int k = 0; k < n_expert_used; k++) {
         float max_val    = wt[0];
         uint   max_expert = gl_LocalInvocationID.x;
@@ -121,6 +148,7 @@ void main() {
 
     if (with_norm) {
         wt_sum              = subgroupAdd(wt_sum);
+        wt_sum              = clamp(wt_sum, clamp_min, clamp_max);
         const float inv_sum = 1.0f / wt_sum;
 
         [[unroll]]
@@ -129,6 +157,10 @@ void main() {
         }
     }
 
+    if (late_softmax) {
+        softmax_warp_inplace(output_weights, n_expert_used, gl_LocalInvocationID.x, true);
+    }
+
     [[unroll]]
     for (uint i = 0; i < experts_per_thread; ++i) {
         uint idx = i * WARP_SIZE + gl_LocalInvocationID.x;

From e3af5563bd049141e036b50f843196db33d23e97 Mon Sep 17 00:00:00 2001
From: Xuan-Son Nguyen <son@huggingface.co>
Date: Wed, 29 Oct 2025 18:09:18 +0100
Subject: [PATCH 012/185] llama: store mrope data in KV cell (#16825)

* llama: store mrope data in KV cell

* correct x,y ordering

* address review comments

* add consistency checks

* Update src/llama-kv-cache.cpp

Co-authored-by: Georgi Gerganov <ggerganov@gmail.com>

* add TODO

* fix asan error

* kv-cells : improve ext handling

* cont : fix headers

---------

Co-authored-by: Georgi Gerganov <ggerganov@gmail.com>
---
 src/llama-batch.cpp    | 67 ++++++++++++++++++++++++++----------------
 src/llama-batch.h      | 13 +++++++-
 src/llama-kv-cache.cpp | 32 ++++++++++++++++++++
 src/llama-kv-cells.h   | 46 +++++++++++++++++++++++++++--
 tools/mtmd/mtmd.cpp    | 13 +++++++-
 tools/mtmd/mtmd.h      |  4 +--
 6 files changed, 143 insertions(+), 32 deletions(-)

diff --git a/src/llama-batch.cpp b/src/llama-batch.cpp
index 55d89eca0ad..6cb118f684e 100644
--- a/src/llama-batch.cpp
+++ b/src/llama-batch.cpp
@@ -215,6 +215,7 @@ bool llama_batch_allocr::init(
             /*.n_seq_tokens =*/ (uint32_t) 1,
             /*.n_seqs       =*/ (uint32_t) batch.n_tokens,
             /*.n_seqs_unq   =*/ (uint32_t) this->seq_id_unq.size(),
+            /*.n_pos        =*/ n_pos_per_embd,
             /*.token        =*/ batch.token,
             /*.embd         =*/ batch.embd,
             /*.pos          =*/ batch.pos,
@@ -251,46 +252,58 @@ bool llama_batch_allocr::init(
     // consistency checks
     //
 
-    for (uint32_t s = 0; s < n_seq_max; ++s) {
-        if (seq_pos[s].empty()) {
-            continue;
+    if (n_pos_per_embd > 1) {
+        // M-RoPE case: allow position to "jump" forward only (non-continuous positions are allowed)
+        for (uint32_t s = 0; s < n_seq_max; ++s) {
+            if (seq_pos[s].empty()) {
+                continue;
+            }
+
+            const llama_pos p0 = memory ? memory->seq_pos_max(s) : -1;
+
+            if (p0 >= 0 && p0 >= seq_pos_min(s)) {
+                LLAMA_LOG_ERROR(
+                        "%s: the tokens of sequence %d in the input batch have inconsistent sequence positions:\n"
+                        " - the last position stored in the memory module of the context (i.e. the KV cache) for sequence %d is X = %d\n"
+                        " - the tokens for sequence %d in the input batch have a starting position of Y = %d\n"
+                        " for M-RoPE, it is required that the position satisfies: X < Y\n",
+                        __func__, s, s, p0, s, seq_pos_min(s));
+
+                return false;
+            }
         }
+    } else {
+        for (uint32_t s = 0; s < n_seq_max; ++s) {
+            if (seq_pos[s].empty()) {
+                continue;
+            }
 
-        const llama_pos p0 = memory ? memory->seq_pos_max(s) : -1;
+            const llama_pos p0 = memory ? memory->seq_pos_max(s) : -1;
 
-        if (p0 >= 0) {
-            bool ok = true;
+            if (p0 >= 0) {
+                bool ok = true;
 
-            if (batch.token) {
                 if (seq_pos_min(s) != p0 + 1) {
                     ok = false;
                 }
-            } else {
-                assert(batch.embd);
 
-                // for embeddings (typically used as vision input), we allow them to have repeating positions
-                // ref: https://github.com/ggml-org/llama.cpp/issues/13694#issuecomment-2983871762
-                if (seq_pos_min(s) != p0 && seq_pos_min(s) != p0 + 1) {
-                    ok = false;
+                if (!ok) {
+                    LLAMA_LOG_ERROR(
+                            "%s: the tokens of sequence %d in the input batch have inconsistent sequence positions:\n"
+                            " - the last position stored in the memory module of the context (i.e. the KV cache) for sequence %d is X = %d\n"
+                            " - the tokens for sequence %d in the input batch have a starting position of Y = %d\n"
+                            " it is required that the sequence positions remain consecutive: Y = X + 1\n",
+                            __func__, s, s, p0, s, seq_pos_min(s));
+
+                    return false;
                 }
             }
 
-            if (!ok) {
-                LLAMA_LOG_ERROR(
-                        "%s: the tokens of sequence %d in the input batch have inconsistent sequence positions:\n"
-                        " - the last position stored in the memory module of the context (i.e. the KV cache) for sequence %d is X = %d\n"
-                        " - the tokens for sequence %d in the input batch have a starting position of Y = %d\n"
-                        " it is required that the sequence positions remain consecutive: Y = X + 1\n",
-                        __func__, s, s, p0, s, seq_pos_min(s));
-
+            if (seq_pos_max(s) - seq_pos_min(s) + 1 > (int) seq_pos[s].size()) {
+                LLAMA_LOG_ERROR("%s: sequence %d positions are not continuous\n", __func__, s);
                 return false;
             }
         }
-
-        if (seq_pos_max(s) - seq_pos_min(s) + 1 > (int) seq_pos[s].size()) {
-            LLAMA_LOG_ERROR("%s: sequence %d positions are not continuous\n", __func__, s);
-            return false;
-        }
     }
 
     if (memory) {
@@ -389,6 +402,7 @@ llama_ubatch llama_batch_allocr::ubatch_reserve(uint32_t n_seq_tokens, uint32_t
         /*.n_seq_tokens =*/ n_seq_tokens,
         /*.n_seqs       =*/ n_seqs,
         /*.n_seqs_unq   =*/ n_seqs,
+        /*.n_pos        =*/ n_pos_per_embd,
 
         /*.token        =*/ udata->token.data(),
         /*.embd         =*/ nullptr,
@@ -710,6 +724,7 @@ llama_ubatch llama_batch_allocr::ubatch_add(const std::vector<int32_t> & idxs, u
         /*.n_seq_tokens =*/ n_tokens/n_seqs,
         /*.n_seqs       =*/ n_seqs,
         /*.n_seqs_unq   =*/ (uint32_t) udata->seq_id_unq.size(),
+        /*.n_pos        =*/ n_pos_per_embd,
 
         /*.token        =*/ batch.token ? udata->token.data() : nullptr,
         /*.embd         =*/ batch.embd ? udata->embd.data() : nullptr,
diff --git a/src/llama-batch.h b/src/llama-batch.h
index 0dc8cebd2a7..209cf3699de 100644
--- a/src/llama-batch.h
+++ b/src/llama-batch.h
@@ -17,6 +17,16 @@ struct llama_ubatch {
         return b_equal_seqs != 0;
     }
 
+    // typical for M-RoPE cases:
+    //   0 - sequantial position of the tokens/embeddings in the sequence
+    //   1 - y position in the image
+    //   2 - x position in the image
+    //   3 - other
+    bool is_pos_2d() const {
+        // TODO @ngxson : we may need to check for model arch when more models use >1 positions
+        return n_pos >= 3;
+    }
+
     uint32_t b_equal_seqs; // note: this is a boolean, but we use an int32_t for alignment
                            //       otherwise address sanitizer complains
     // TODO: whole_seqs for embeddings?
@@ -25,6 +35,7 @@ struct llama_ubatch {
     uint32_t n_seq_tokens; // tokens per sequence set
     uint32_t n_seqs;       // sequence sets in the ubatch
     uint32_t n_seqs_unq;   // unique sequence ids in the ubatch
+    uint32_t n_pos;        // number of position inputs for each token/embedding
 
     // seq_id_unq: unique sequence ids in the ubatch
     // seq_idx:    indices of the unique sequence ids in the ubatch in [0, n_seqs_unq)
@@ -33,7 +44,7 @@ struct llama_ubatch {
     //                          // size               | idx | val
     llama_token  *  token;      // [n_tokens]         | i   | id, token
     float        *  embd;       // [n_embd, n_tokens] | i   | embd
-    llama_pos    *  pos;        // [n_tokens]         | i   | pos
+    llama_pos    *  pos;        // [n_tokens*n_pos]   | i   | pos
     int32_t      *  n_seq_id;   // [n_tokens]         | i   | -
     llama_seq_id ** seq_id;     // [n_tokens]         | s   | s0, s1, seq_id
     llama_seq_id *  seq_id_unq; // [n_seqs_unq]       | s   | seq_id
diff --git a/src/llama-kv-cache.cpp b/src/llama-kv-cache.cpp
index 6d5dd6051e7..17627b6ccbb 100644
--- a/src/llama-kv-cache.cpp
+++ b/src/llama-kv-cache.cpp
@@ -338,6 +338,8 @@ void llama_kv_cache::seq_cp(llama_seq_id seq_id_src, llama_seq_id seq_id_dst, ll
             llama_pos pos   = v_cells[s0].pos_get(i);
             llama_pos shift = v_cells[s0].get_shift(i);
 
+            llama_kv_cell_ext ext = v_cells[s0].ext_get(i);
+
             if (shift != 0) {
                 pos -= shift;
                 assert(pos >= 0);
@@ -349,6 +351,8 @@ void llama_kv_cache::seq_cp(llama_seq_id seq_id_src, llama_seq_id seq_id_dst, ll
             if (shift != 0) {
                 v_cells[s1].pos_add(i, shift);
             }
+
+            v_cells[s1].ext_set(i, ext);
         }
     }
 
@@ -383,6 +387,7 @@ void llama_kv_cache::seq_keep(llama_seq_id seq_id) {
 
 void llama_kv_cache::seq_add(llama_seq_id seq_id, llama_pos p0, llama_pos p1, llama_pos shift) {
     GGML_ASSERT(seq_id >= 0 && (size_t) seq_id < seq_to_stream.size());
+    GGML_ASSERT(hparams.n_pos_per_embd() == 1 && "seq_add() is only supported for n_pos_per_embd() == 1");
 
     auto & cells = v_cells[seq_to_stream[seq_id]];
     auto & head  = v_heads[seq_to_stream[seq_id]];
@@ -427,6 +432,7 @@ void llama_kv_cache::seq_add(llama_seq_id seq_id, llama_pos p0, llama_pos p1, ll
 
 void llama_kv_cache::seq_div(llama_seq_id seq_id, llama_pos p0, llama_pos p1, int d) {
     GGML_ASSERT(seq_id >= 0 && (size_t) seq_id < seq_to_stream.size());
+    GGML_ASSERT(hparams.n_pos_per_embd() == 1 && "seq_div() is only supported for n_pos_per_embd() == 1");
 
     auto & cells = v_cells[seq_to_stream[seq_id]];
 
@@ -900,6 +906,14 @@ void llama_kv_cache::apply_ubatch(const slot_info & sinfo, const llama_ubatch &
 
             cells.pos_set(idx, ubatch.pos[i]);
 
+            if (ubatch.is_pos_2d()) {
+                llama_kv_cell_ext ext {
+                    /*.x =*/ ubatch.pos[i + ubatch.n_tokens*2],
+                    /*.y =*/ ubatch.pos[i + ubatch.n_tokens],
+                };
+                cells.ext_set(idx, ext);
+            }
+
             for (int32_t s = 0; s < ubatch.n_seq_id[i]; s++) {
                 cells.seq_add(idx, ubatch.seq_id[i][s]);
             }
@@ -1247,6 +1261,11 @@ void llama_kv_cache::set_input_kq_mask(ggml_tensor * dst, const llama_ubatch * u
 
                 const llama_pos p1 = ubatch->pos[i];
 
+                // for M-RoPE
+                const bool is_2d = ubatch->is_pos_2d();
+                const llama_pos p1_x = is_2d ? ubatch->pos[i + ubatch->n_tokens*2] : 0;
+                const llama_pos p1_y = is_2d ? ubatch->pos[i + ubatch->n_tokens]   : 0;
+
                 const uint64_t idst = n_kv*(h*n_stream*n_tps_pad + s*n_tps_pad + ii);
 
                 for (uint32_t j = 0; j < n_kv; ++j) {
@@ -1266,6 +1285,14 @@ void llama_kv_cache::set_input_kq_mask(ggml_tensor * dst, const llama_ubatch * u
                         continue;
                     }
 
+                    // M-RoPE causal mask
+                    if (causal_attn && is_2d && p0 == p1) {
+                        const auto & p0_ext = cells.ext_get(j);
+                        if (p0_ext.is_2d_gt(p1_x, p1_y)) {
+                            continue;
+                        }
+                    }
+
                     // apply SWA if any
                     if (is_masked_swa(p0, p1)) {
                         continue;
@@ -1559,6 +1586,9 @@ void llama_kv_cache::state_write_meta(llama_io_write_i & io, const cell_ranges_t
             io.write(&pos,      sizeof(pos));
             io.write(&n_seq_id, sizeof(n_seq_id));
 
+            // TODO: we also need to save llama_kv_cell_ext when apply_ubatch() support loading it
+            //       see: https://github.com/ggml-org/llama.cpp/pull/16825#issuecomment-3460868350
+
             for (const auto & seq_id : seq_ids) {
                 io.write(&seq_id, sizeof(seq_id));
             }
@@ -1704,6 +1734,8 @@ bool llama_kv_cache::state_read_meta(llama_io_read_i & io, uint32_t strm, uint32
             return false;
         }
 
+        // TODO: we cannot yet restore llama_kv_cell_ext as the apply_ubatch() does not support it yet
+        //       see: https://github.com/ggml-org/llama.cpp/pull/16825#issuecomment-3460868350
         apply_ubatch(sinfo, ubatch);
 
         const auto head_cur = sinfo.head();
diff --git a/src/llama-kv-cells.h b/src/llama-kv-cells.h
index 8f6bf01456c..10063bf4272 100644
--- a/src/llama-kv-cells.h
+++ b/src/llama-kv-cells.h
@@ -5,9 +5,27 @@
 
 #include <bitset>
 #include <cassert>
-#include <vector>
-#include <set>
+#include <cstring>
 #include <map>
+#include <set>
+#include <vector>
+
+struct llama_kv_cell_ext {
+    // 2D spatial positions, typically used for M-RoPE
+    llama_pos x = 0;
+    llama_pos y = 0;
+
+    // return true if the current 2D spatial position is greater than other
+    bool is_2d_gt(llama_pos ox, llama_pos oy) const {
+        return (y > oy) || (y == oy && x > ox);
+    }
+
+    void reset() {
+        static_assert(std::is_trivially_copyable_v<llama_kv_cell_ext>);
+
+        memset(this, 0, sizeof(*this));
+    }
+};
 
 // meta information about KV cells that can be part of multiple sequences at the same time
 // TODO: add unit tests
@@ -16,6 +34,7 @@ class llama_kv_cells {
     void reset() {
         for (uint32_t i = 0; i < pos.size(); ++i) {
             pos[i]   = -1;
+            ext[i].reset();
             shift[i] =  0;
             seq[i].reset();
         }
@@ -43,6 +62,7 @@ class llama_kv_cells {
 
     void resize(uint32_t n) {
         pos.resize(n);
+        ext.resize(n);
         shift.resize(n);
         seq.resize(n);
 
@@ -108,6 +128,7 @@ class llama_kv_cells {
             const auto idx = i + j;
 
             res.pos[j] = pos[idx];
+            res.ext[j] = ext[idx];
             res.seq[j] = seq[idx];
 
             assert(shift[idx] == 0);
@@ -126,6 +147,7 @@ class llama_kv_cells {
             const auto idx = idxs[j];
 
             res.pos[j] = pos[idx];
+            res.ext[j] = ext[idx];
             res.seq[j] = seq[idx];
 
             assert(shift[idx] == 0);
@@ -154,6 +176,7 @@ class llama_kv_cells {
             }
 
             pos[idx] = other.pos[j];
+            ext[idx] = other.ext[j];
             seq[idx] = other.seq[j];
 
             if (pos[idx] != -1) {
@@ -184,6 +207,7 @@ class llama_kv_cells {
             }
 
             pos[idx] = other.pos[j];
+            ext[idx] = other.ext[j];
             seq[idx] = other.seq[j];
 
             if (pos[idx] != -1) {
@@ -203,6 +227,7 @@ class llama_kv_cells {
         seq[i].reset();
 
         pos[i] = -1;
+        ext[i].reset();
         shift[i] = 0;
 
         used.erase(i);
@@ -221,6 +246,7 @@ class llama_kv_cells {
 
         if (seq[i].none()) {
             pos[i] = -1;
+            ext[i].reset();
             shift[i] = 0;
 
             used.erase(i);
@@ -250,6 +276,7 @@ class llama_kv_cells {
             seq[i].reset();
 
             pos[i] = -1;
+            ext[i].reset();
             shift[i] = 0;
 
             used.erase(i);
@@ -340,6 +367,13 @@ class llama_kv_cells {
         return pos[i];
     }
 
+    const llama_kv_cell_ext & ext_get(uint32_t i) const {
+        assert(i < pos.size());
+        assert(pos[i] != -1);
+
+        return ext[i];
+    }
+
     // note: call only if the cell is not empty
     llama_pos get_shift(uint32_t i) const {
         assert(i < pos.size());
@@ -368,6 +402,11 @@ class llama_kv_cells {
         used.insert(i);
     }
 
+    void ext_set(uint32_t i, llama_kv_cell_ext p) {
+        assert(i < ext.size());
+        ext[i] = p;
+    }
+
     // pos[i] = pos[i] + d
     // sets "has_shift" to true
     // note: call only if the cell is not empty
@@ -424,6 +463,9 @@ class llama_kv_cells {
 
     std::vector<llama_pos> pos;
 
+    // stores extra info per cell
+    std::vector<llama_kv_cell_ext> ext;
+
     // this array accumulates any applied shifts to the pos array since the last reset_shift() call
     // this is used to queue multiple updates to the pos array, which in the end can be applied in one go:
     //
diff --git a/tools/mtmd/mtmd.cpp b/tools/mtmd/mtmd.cpp
index 3b901bfac82..1a48f903efa 100644
--- a/tools/mtmd/mtmd.cpp
+++ b/tools/mtmd/mtmd.cpp
@@ -5,6 +5,15 @@
 
 #include "llama.h"
 
+// fix problem with std::min and std::max
+#if defined(_WIN32)
+#define WIN32_LEAN_AND_MEAN
+#ifndef NOMINMAX
+#   define NOMINMAX
+#endif
+#include <windows.h>
+#endif
+
 #include <algorithm>
 #include <cerrno>
 #include <cstdio>
@@ -1031,7 +1040,9 @@ const char * mtmd_image_tokens_get_id(const mtmd_image_tokens * image_tokens) {
 
 llama_pos mtmd_image_tokens_get_n_pos(const mtmd_image_tokens * image_tokens) {
     if (image_tokens->use_mrope_pos) {
-        return 1; // for M-RoPE, the whole image is 1 in temporal dimension
+        // for M-RoPE, temporal dimension = max(t,h,w)
+        // t is omitted as we don't support video input
+        return std::max(image_tokens->nx, image_tokens->ny);
     }
     return image_tokens->n_tokens();
 }
diff --git a/tools/mtmd/mtmd.h b/tools/mtmd/mtmd.h
index f4ea07d3ad5..0b5d2ba0c76 100644
--- a/tools/mtmd/mtmd.h
+++ b/tools/mtmd/mtmd.h
@@ -153,7 +153,7 @@ MTMD_API const mtmd_image_tokens *  mtmd_input_chunk_get_tokens_image(const mtmd
 MTMD_API size_t                     mtmd_input_chunk_get_n_tokens    (const mtmd_input_chunk * chunk);
 // returns nullptr for ID on text chunk
 MTMD_API const char *               mtmd_input_chunk_get_id          (const mtmd_input_chunk * chunk);
-// number of temporal positions (always 1 for M-RoPE, n_tokens otherwise)
+// number of temporal positions (equals to max(t,h,w) for M-RoPE; equals to n_tokens otherwise)
 MTMD_API llama_pos                  mtmd_input_chunk_get_n_pos       (const mtmd_input_chunk * chunk);
 
 // in case you want to use custom logic to handle the chunk (i.e. KV cache management)
@@ -171,7 +171,7 @@ MTMD_API size_t       mtmd_image_tokens_get_n_tokens(const mtmd_image_tokens * i
 MTMD_API size_t       mtmd_image_tokens_get_nx      (const mtmd_image_tokens * image_tokens);
 MTMD_API size_t       mtmd_image_tokens_get_ny      (const mtmd_image_tokens * image_tokens);
 MTMD_API const char * mtmd_image_tokens_get_id      (const mtmd_image_tokens * image_tokens); // TODO: deprecate
-// number of temporal positions (always 1 for M-RoPE, n_tokens otherwise)
+// number of temporal positions (equals to max(t,h,w) for M-RoPE; equals to n_tokens otherwise)
 MTMD_API llama_pos    mtmd_image_tokens_get_n_pos   (const mtmd_image_tokens * image_tokens); // TODO: deprecate
 
 // tokenize an input text prompt and a list of bitmaps (images/audio)

From 3464bdac37027c5e9661621fc75ffcef3c19c6ef Mon Sep 17 00:00:00 2001
From: Xuan-Son Nguyen <son@huggingface.co>
Date: Wed, 29 Oct 2025 20:11:39 +0100
Subject: [PATCH 013/185] llama: fix ASAN error with M-RoPE (#16848)

---
 src/llama-batch.cpp | 13 ++++++++-----
 1 file changed, 8 insertions(+), 5 deletions(-)

diff --git a/src/llama-batch.cpp b/src/llama-batch.cpp
index 6cb118f684e..0d4939fdb01 100644
--- a/src/llama-batch.cpp
+++ b/src/llama-batch.cpp
@@ -669,10 +669,8 @@ llama_ubatch llama_batch_allocr::ubatch_add(const std::vector<int32_t> & idxs, u
 
     auto udata = std::make_shared<llama_ubatch::data_t>();
 
-    const int32_t n_pos_cur = batch.embd ? n_pos_per_embd : 1;
-
     const int64_t n_embd_all = batch.embd ? (int64_t) n_tokens*n_embd : 0;
-    const int64_t n_pos_all  =              (int64_t) n_tokens*n_pos_cur;
+    const int64_t n_pos_all  =              (int64_t) n_tokens*n_pos_per_embd;
 
     udata->token     .resize(n_tokens);
     udata->embd      .resize(n_embd_all);
@@ -694,8 +692,13 @@ llama_ubatch llama_batch_allocr::ubatch_add(const std::vector<int32_t> & idxs, u
             memcpy(udata->embd.data() + i*n_embd, batch.embd + (int64_t) idxs[i]*n_embd, n_embd*sizeof(float));
         }
 
-        for (int j = 0; j < n_pos_cur; ++j) {
-            udata->pos[j*n_tokens + i] = batch.pos[j*batch.n_tokens + idxs[i]];
+        for (size_t j = 0; j < (size_t)n_pos_per_embd; ++j) {
+            // if we are using M-RoPE
+            //     if the current batch is text, we need to broadcast the same position across all RoPE sections
+            //     otherwise, the input batch is image embeddings, we copy the positions as-is
+            // if we are not using M-RoPE, there is only one position per token (this loop runs only once)
+            size_t src_off = batch.token ? 0 : j*batch.n_tokens;
+            udata->pos[j*n_tokens + i] = batch.pos[src_off + idxs[i]];
         }
 
         udata->n_seq_id[i] = batch.n_seq_id[idxs[i]];

From b9ce94017729465895402cbcfffb51fa926c15e3 Mon Sep 17 00:00:00 2001
From: Jeff Bolz <jbolz@nvidia.com>
Date: Wed, 29 Oct 2025 15:13:10 -0500
Subject: [PATCH 014/185] vulkan: Fuse rope+set_rows (#16769)

This pattern appears in a lot of models, the rope operation is applied right
before storing into the KV cache (usually on the K tensor).

Add a path to some of the rope shaders that computes the destination address
based on the set_rows tensor. Compile variants of the shader with D_TYPE of
f16 (the usual KV cache type).

Add a src3 operand to ggml_vk_op_f32 - sometimes rope uses three srcs and needs
the fourth for the row indices.

Add fused_ops_write_mask to indicate which intermediate tensors need to write
their results to memory. Skipping writing the roped K value helps to allow more
nodes to run concurrently.

Add logic to ggml_vk_graph_optimize to make ROPE+VIEW+SET_ROWS consecutive. It
rarely starts out that way in the graph.

Add new backend tests.
---
 ggml/src/ggml-vulkan/ggml-vulkan.cpp          | 334 +++++++++++++-----
 .../ggml-vulkan/vulkan-shaders/rope_head.glsl |   2 +
 .../ggml-vulkan/vulkan-shaders/rope_neox.comp |  13 +-
 .../ggml-vulkan/vulkan-shaders/rope_norm.comp |  13 +-
 .../vulkan-shaders/vulkan-shaders-gen.cpp     |   4 +
 tests/test-backend-ops.cpp                    | 122 +++++--
 6 files changed, 371 insertions(+), 117 deletions(-)

diff --git a/ggml/src/ggml-vulkan/ggml-vulkan.cpp b/ggml/src/ggml-vulkan/ggml-vulkan.cpp
index 50e7922dc60..8a9f5980ea8 100644
--- a/ggml/src/ggml-vulkan/ggml-vulkan.cpp
+++ b/ggml/src/ggml-vulkan/ggml-vulkan.cpp
@@ -456,6 +456,11 @@ static topk_moe_mode ggml_vk_num_additional_ops_to_topk_moe_mode(uint32_t num) {
     return mode;
 }
 
+static constexpr std::initializer_list<std::array<int, 3>> rope_view_set_rows_edges {
+    { 1, 0, 0 }, // view->src[0]     == rope
+    { 2, 0, 1 }, // set_rows->src[0] == view
+};
+
 struct vk_device_struct {
     std::recursive_mutex mutex;
 
@@ -638,8 +643,8 @@ struct vk_device_struct {
     vk_pipeline pipeline_soft_max_f32, pipeline_soft_max_f32_f16;
     vk_pipeline pipeline_soft_max_f32_wg512, pipeline_soft_max_f32_f16_wg512;
     vk_pipeline pipeline_soft_max_back_f32;
-    vk_pipeline pipeline_rope_norm_f32, pipeline_rope_norm_f16;
-    vk_pipeline pipeline_rope_neox_f32, pipeline_rope_neox_f16;
+    vk_pipeline pipeline_rope_norm_f32, pipeline_rope_norm_f16, pipeline_rope_norm_f32_f16;
+    vk_pipeline pipeline_rope_neox_f32, pipeline_rope_neox_f16, pipeline_rope_neox_f32_f16;
     vk_pipeline pipeline_rope_multi_f32, pipeline_rope_multi_f16;
     vk_pipeline pipeline_rope_vision_f32, pipeline_rope_vision_f16;
     vk_pipeline pipeline_argsort_f32[num_argsort_pipelines];
@@ -1052,6 +1057,7 @@ struct vk_op_rope_push_constants {
     uint32_t s2;
     int32_t sections[4];
     uint32_t is_back;
+    uint32_t set_rows_stride;
 };
 
 struct vk_op_soft_max_push_constants {
@@ -1562,6 +1568,10 @@ struct ggml_backend_vk_context {
     // number of additional consecutive nodes that are being fused with the
     // node currently being processed
     int num_additional_fused_ops {};
+    // Bitmask of which fused ops need to write an intermediate value to memory.
+    // Bit 'i' means nodes[start_of_fusion + i] writes to memory.
+    // If there's no fusion, bit 0 is still set.
+    int fused_ops_write_mask {};
 };
 
 static void * const vk_ptr_base = (void *)(uintptr_t) 0x1000;  // NOLINT
@@ -3695,21 +3705,27 @@ static void ggml_vk_load_shaders(vk_device& device) {
     ggml_vk_create_pipeline(device, device->pipeline_soft_max_f32_f16_wg512, "soft_max_f32_f16_wg512", soft_max_f32_f16_len, soft_max_f32_f16_data, "main", 4, sizeof(vk_op_soft_max_push_constants), {1, 1, 1}, { 512 }, 1);
     ggml_vk_create_pipeline(device, device->pipeline_soft_max_back_f32, "soft_max_back_f32", soft_max_back_f32_len, soft_max_back_f32_data, "main", 3, sizeof(vk_op_push_constants), {1, 1, 1}, { device->subgroup_size }, 1, true);
 
-    ggml_vk_create_pipeline(device, device->pipeline_rope_norm_f32, "rope_norm_f32", rope_norm_f32_len, rope_norm_f32_data, "main", 4, sizeof(vk_op_rope_push_constants), {1, 512, 1}, {}, 1);
-    ggml_vk_create_pipeline(device, device->pipeline_rope_neox_f32, "rope_neox_f32", rope_neox_f32_len, rope_neox_f32_data, "main", 4, sizeof(vk_op_rope_push_constants), {1, 512, 1}, {}, 1);
-    ggml_vk_create_pipeline(device, device->pipeline_rope_multi_f32, "rope_multi_f32", rope_multi_f32_len, rope_multi_f32_data, "main", 4, sizeof(vk_op_rope_push_constants), {1, 512, 1}, {}, 1);
-    ggml_vk_create_pipeline(device, device->pipeline_rope_vision_f32, "rope_vision_f32", rope_vision_f32_len, rope_vision_f32_data, "main", 4, sizeof(vk_op_rope_push_constants), {1, 512, 1}, {}, 1);
+    ggml_vk_create_pipeline(device, device->pipeline_rope_norm_f32, "rope_norm_f32", rope_norm_f32_len, rope_norm_f32_data, "main", 5, sizeof(vk_op_rope_push_constants), {1, 512, 1}, {}, 1);
+    ggml_vk_create_pipeline(device, device->pipeline_rope_neox_f32, "rope_neox_f32", rope_neox_f32_len, rope_neox_f32_data, "main", 5, sizeof(vk_op_rope_push_constants), {1, 512, 1}, {}, 1);
+    ggml_vk_create_pipeline(device, device->pipeline_rope_multi_f32, "rope_multi_f32", rope_multi_f32_len, rope_multi_f32_data, "main", 5, sizeof(vk_op_rope_push_constants), {1, 512, 1}, {}, 1);
+    ggml_vk_create_pipeline(device, device->pipeline_rope_vision_f32, "rope_vision_f32", rope_vision_f32_len, rope_vision_f32_data, "main", 5, sizeof(vk_op_rope_push_constants), {1, 512, 1}, {}, 1);
 
     if (device->float_controls_rte_fp16) {
-        ggml_vk_create_pipeline(device, device->pipeline_rope_norm_f16, "rope_norm_f16", rope_norm_f16_rte_len, rope_norm_f16_rte_data, "main", 4, sizeof(vk_op_rope_push_constants), {1, 512, 1}, {}, 1);
-        ggml_vk_create_pipeline(device, device->pipeline_rope_neox_f16, "rope_neox_f16", rope_neox_f16_rte_len, rope_neox_f16_rte_data, "main", 4, sizeof(vk_op_rope_push_constants), {1, 512, 1}, {}, 1);
-        ggml_vk_create_pipeline(device, device->pipeline_rope_multi_f16, "rope_multi_f16", rope_multi_f16_rte_len, rope_multi_f16_rte_data, "main", 4, sizeof(vk_op_rope_push_constants), {1, 512, 1}, {}, 1);
-        ggml_vk_create_pipeline(device, device->pipeline_rope_vision_f16, "rope_vision_f16", rope_vision_f16_rte_len, rope_vision_f16_rte_data, "main", 4, sizeof(vk_op_rope_push_constants), {1, 512, 1}, {}, 1);
+        ggml_vk_create_pipeline(device, device->pipeline_rope_norm_f16, "rope_norm_f16", rope_norm_f16_rte_len, rope_norm_f16_rte_data, "main", 5, sizeof(vk_op_rope_push_constants), {1, 512, 1}, {}, 1);
+        ggml_vk_create_pipeline(device, device->pipeline_rope_neox_f16, "rope_neox_f16", rope_neox_f16_rte_len, rope_neox_f16_rte_data, "main", 5, sizeof(vk_op_rope_push_constants), {1, 512, 1}, {}, 1);
+        ggml_vk_create_pipeline(device, device->pipeline_rope_multi_f16, "rope_multi_f16", rope_multi_f16_rte_len, rope_multi_f16_rte_data, "main", 5, sizeof(vk_op_rope_push_constants), {1, 512, 1}, {}, 1);
+        ggml_vk_create_pipeline(device, device->pipeline_rope_vision_f16, "rope_vision_f16", rope_vision_f16_rte_len, rope_vision_f16_rte_data, "main", 5, sizeof(vk_op_rope_push_constants), {1, 512, 1}, {}, 1);
+
+        ggml_vk_create_pipeline(device, device->pipeline_rope_norm_f32_f16, "rope_norm_f32_f16", rope_norm_f32_f16_rte_len, rope_norm_f32_f16_rte_data, "main", 5, sizeof(vk_op_rope_push_constants), {1, 512, 1}, {}, 1);
+        ggml_vk_create_pipeline(device, device->pipeline_rope_neox_f32_f16, "rope_neox_f32_f16", rope_neox_f32_f16_rte_len, rope_neox_f32_f16_rte_data, "main", 5, sizeof(vk_op_rope_push_constants), {1, 512, 1}, {}, 1);
     } else {
-        ggml_vk_create_pipeline(device, device->pipeline_rope_norm_f16, "rope_norm_f16", rope_norm_f16_len, rope_norm_f16_data, "main", 4, sizeof(vk_op_rope_push_constants), {1, 512, 1}, {}, 1);
-        ggml_vk_create_pipeline(device, device->pipeline_rope_neox_f16, "rope_neox_f16", rope_neox_f16_len, rope_neox_f16_data, "main", 4, sizeof(vk_op_rope_push_constants), {1, 512, 1}, {}, 1);
-        ggml_vk_create_pipeline(device, device->pipeline_rope_multi_f16, "rope_multi_f16", rope_multi_f16_len, rope_multi_f16_data, "main", 4, sizeof(vk_op_rope_push_constants), {1, 512, 1}, {}, 1);
-        ggml_vk_create_pipeline(device, device->pipeline_rope_vision_f16, "rope_vision_f16", rope_vision_f16_len, rope_vision_f16_data, "main", 4, sizeof(vk_op_rope_push_constants), {1, 512, 1}, {}, 1);
+        ggml_vk_create_pipeline(device, device->pipeline_rope_norm_f16, "rope_norm_f16", rope_norm_f16_len, rope_norm_f16_data, "main", 5, sizeof(vk_op_rope_push_constants), {1, 512, 1}, {}, 1);
+        ggml_vk_create_pipeline(device, device->pipeline_rope_neox_f16, "rope_neox_f16", rope_neox_f16_len, rope_neox_f16_data, "main", 5, sizeof(vk_op_rope_push_constants), {1, 512, 1}, {}, 1);
+        ggml_vk_create_pipeline(device, device->pipeline_rope_multi_f16, "rope_multi_f16", rope_multi_f16_len, rope_multi_f16_data, "main", 5, sizeof(vk_op_rope_push_constants), {1, 512, 1}, {}, 1);
+        ggml_vk_create_pipeline(device, device->pipeline_rope_vision_f16, "rope_vision_f16", rope_vision_f16_len, rope_vision_f16_data, "main", 5, sizeof(vk_op_rope_push_constants), {1, 512, 1}, {}, 1);
+
+        ggml_vk_create_pipeline(device, device->pipeline_rope_norm_f32_f16, "rope_norm_f32_f16", rope_norm_f32_f16_len, rope_norm_f32_f16_data, "main", 5, sizeof(vk_op_rope_push_constants), {1, 512, 1}, {}, 1);
+        ggml_vk_create_pipeline(device, device->pipeline_rope_neox_f32_f16, "rope_neox_f32_f16", rope_neox_f32_f16_len, rope_neox_f32_f16_data, "main", 5, sizeof(vk_op_rope_push_constants), {1, 512, 1}, {}, 1);
     }
 
     for (uint32_t i = 0; i < num_argsort_pipelines; ++i) {
@@ -8168,7 +8184,8 @@ static vk_pipeline ggml_vk_op_get_pipeline(ggml_backend_vk_context * ctx, const
     case GGML_OP_ROPE:
     case GGML_OP_ROPE_BACK:
         {
-            const int mode = ((const int32_t *) dst->op_params)[2];
+            const ggml_tensor *rope = ctx->num_additional_fused_ops == 2 ? dst->src[0]->src[0] : dst;
+            const int mode = ((const int32_t *) rope->op_params)[2];
             const bool is_neox = mode & GGML_ROPE_TYPE_NEOX;
             const bool is_mrope = mode & GGML_ROPE_TYPE_MROPE;
             const bool is_vision = mode == GGML_ROPE_TYPE_VISION;
@@ -8177,6 +8194,9 @@ static vk_pipeline ggml_vk_op_get_pipeline(ggml_backend_vk_context * ctx, const
                 if (src0->type == GGML_TYPE_F32 && dst->type == GGML_TYPE_F32) {
                     return ctx->device->pipeline_rope_neox_f32;
                 }
+                if (src0->type == GGML_TYPE_F32 && dst->type == GGML_TYPE_F16) {
+                    return ctx->device->pipeline_rope_neox_f32_f16;
+                }
                 if (src0->type == GGML_TYPE_F16 && dst->type == GGML_TYPE_F16) {
                     return ctx->device->pipeline_rope_neox_f16;
                 }
@@ -8198,6 +8218,9 @@ static vk_pipeline ggml_vk_op_get_pipeline(ggml_backend_vk_context * ctx, const
                 if (src0->type == GGML_TYPE_F32 && dst->type == GGML_TYPE_F32) {
                     return ctx->device->pipeline_rope_norm_f32;
                 }
+                if (src0->type == GGML_TYPE_F32 && dst->type == GGML_TYPE_F16) {
+                    return ctx->device->pipeline_rope_norm_f32_f16;
+                }
                 if (src0->type == GGML_TYPE_F16 && dst->type == GGML_TYPE_F16) {
                     return ctx->device->pipeline_rope_norm_f16;
                 }
@@ -8407,20 +8430,22 @@ static uint32_t get_misalign_bytes(ggml_backend_vk_context * ctx, const ggml_ten
     return ((vk_tensor_offset(t) + t->view_offs) & (ctx->device->properties.limits.minStorageBufferOffsetAlignment - 1));;
 }
 
-template <typename T> void init_pushconst_tensor_offsets(ggml_backend_vk_context * ctx, T &p, const ggml_tensor * src0, const ggml_tensor * src1, const ggml_tensor * src2, ggml_tensor * dst) {
+template <typename T> void init_pushconst_tensor_offsets(ggml_backend_vk_context * ctx, T &p, const ggml_tensor * src0, const ggml_tensor * src1, const ggml_tensor * src2, const ggml_tensor * src3, ggml_tensor * dst) {
     GGML_UNUSED(p);
     GGML_UNUSED(src0);
     GGML_UNUSED(src1);
     GGML_UNUSED(src2);
+    GGML_UNUSED(src3);
     GGML_UNUSED(dst);
     static_assert(!std::is_const<T>::value, "unexpected type");
     GGML_ASSERT(!src0 || get_misalign_bytes(ctx, src0) == 0);
     GGML_ASSERT(!src1 || get_misalign_bytes(ctx, src1) == 0);
     GGML_ASSERT(!src2 || get_misalign_bytes(ctx, src2) == 0);
+    GGML_ASSERT(!src3 || get_misalign_bytes(ctx, src3) == 0);
     GGML_ASSERT(!dst  || get_misalign_bytes(ctx, dst) == 0);
 }
 
-template <> void init_pushconst_tensor_offsets(ggml_backend_vk_context * ctx, vk_op_unary_push_constants &p, const ggml_tensor * src0, const ggml_tensor * src1, const ggml_tensor * src2, ggml_tensor * dst) {
+template <> void init_pushconst_tensor_offsets(ggml_backend_vk_context * ctx, vk_op_unary_push_constants &p, const ggml_tensor * src0, const ggml_tensor * src1, const ggml_tensor * src2, const ggml_tensor * src3, ggml_tensor * dst) {
     const uint32_t a_offset = get_misalign_bytes(ctx, src0) / ggml_type_size(src0->type);
     const uint32_t d_offset = get_misalign_bytes(ctx, dst) / ggml_type_size(dst->type);
 
@@ -8428,9 +8453,10 @@ template <> void init_pushconst_tensor_offsets(ggml_backend_vk_context * ctx, vk
 
     GGML_UNUSED(src1);
     GGML_UNUSED(src2);
+    GGML_UNUSED(src3);
 }
 
-template <> void init_pushconst_tensor_offsets(ggml_backend_vk_context * ctx, vk_op_sum_rows_push_constants &p, const ggml_tensor * src0, const ggml_tensor * src1, const ggml_tensor * src2, ggml_tensor * dst) {
+template <> void init_pushconst_tensor_offsets(ggml_backend_vk_context * ctx, vk_op_sum_rows_push_constants &p, const ggml_tensor * src0, const ggml_tensor * src1, const ggml_tensor * src2, const ggml_tensor * src3, ggml_tensor * dst) {
     const uint32_t a_offset = get_misalign_bytes(ctx, src0) / ggml_type_size(src0->type);
     const uint32_t d_offset = get_misalign_bytes(ctx, dst) / ggml_type_size(dst->type);
 
@@ -8438,9 +8464,10 @@ template <> void init_pushconst_tensor_offsets(ggml_backend_vk_context * ctx, vk
 
     GGML_UNUSED(src1);
     GGML_UNUSED(src2);
+    GGML_UNUSED(src3);
 }
 
-template <> void init_pushconst_tensor_offsets(ggml_backend_vk_context * ctx, vk_op_pad_push_constants &p, const ggml_tensor * src0, const ggml_tensor * src1, const ggml_tensor * src2, ggml_tensor * dst) {
+template <> void init_pushconst_tensor_offsets(ggml_backend_vk_context * ctx, vk_op_pad_push_constants &p, const ggml_tensor * src0, const ggml_tensor * src1, const ggml_tensor * src2, const ggml_tensor * src3, ggml_tensor * dst) {
     const uint32_t a_offset = get_misalign_bytes(ctx, src0) / ggml_type_size(src0->type);
     const uint32_t d_offset = get_misalign_bytes(ctx, dst) / ggml_type_size(dst->type);
 
@@ -8448,9 +8475,10 @@ template <> void init_pushconst_tensor_offsets(ggml_backend_vk_context * ctx, vk
 
     GGML_UNUSED(src1);
     GGML_UNUSED(src2);
+    GGML_UNUSED(src3);
 }
 
-template <> void init_pushconst_tensor_offsets(ggml_backend_vk_context * ctx, vk_op_im2col_3d_push_constants &p, const ggml_tensor * src0, const ggml_tensor * src1, const ggml_tensor * src2, ggml_tensor * dst) {
+template <> void init_pushconst_tensor_offsets(ggml_backend_vk_context * ctx, vk_op_im2col_3d_push_constants &p, const ggml_tensor * src0, const ggml_tensor * src1, const ggml_tensor * src2, const ggml_tensor * src3, ggml_tensor * dst) {
     const uint32_t a_offset = get_misalign_bytes(ctx, src1) / ggml_type_size(src1->type);
     const uint32_t d_offset = get_misalign_bytes(ctx, dst) / ggml_type_size(dst->type);
 
@@ -8458,9 +8486,10 @@ template <> void init_pushconst_tensor_offsets(ggml_backend_vk_context * ctx, vk
 
     GGML_UNUSED(src0);
     GGML_UNUSED(src2);
+    GGML_UNUSED(src3);
 }
 
-template <> void init_pushconst_tensor_offsets(ggml_backend_vk_context * ctx, vk_op_binary_push_constants &p, const ggml_tensor * src0, const ggml_tensor * src1, const ggml_tensor * src2, ggml_tensor * dst) {
+template <> void init_pushconst_tensor_offsets(ggml_backend_vk_context * ctx, vk_op_binary_push_constants &p, const ggml_tensor * src0, const ggml_tensor * src1, const ggml_tensor * src2, const ggml_tensor * src3, ggml_tensor * dst) {
     const uint32_t a_offset = get_misalign_bytes(ctx, src0) / ggml_type_size(src0->type);
     const uint32_t b_offset = get_misalign_bytes(ctx, src1) / ggml_type_size(src1->type);
     const uint32_t d_offset = get_misalign_bytes(ctx, dst) / ggml_type_size(dst->type);
@@ -8470,9 +8499,10 @@ template <> void init_pushconst_tensor_offsets(ggml_backend_vk_context * ctx, vk
     p.misalign_offsets = (a_offset << 16) | (b_offset << 8) | d_offset;
 
     GGML_UNUSED(src2);
+    GGML_UNUSED(src3);
 }
 
-template <> void init_pushconst_tensor_offsets(ggml_backend_vk_context * ctx, vk_op_upscale_push_constants &p, const ggml_tensor * src0, const ggml_tensor * src1, const ggml_tensor * src2, ggml_tensor * dst) {
+template <> void init_pushconst_tensor_offsets(ggml_backend_vk_context * ctx, vk_op_upscale_push_constants &p, const ggml_tensor * src0, const ggml_tensor * src1, const ggml_tensor * src2, const ggml_tensor * src3, ggml_tensor * dst) {
     const uint32_t a_offset = get_misalign_bytes(ctx, src0) / ggml_type_size(src0->type);
     const uint32_t d_offset = get_misalign_bytes(ctx, dst) / ggml_type_size(dst->type);
 
@@ -8481,10 +8511,11 @@ template <> void init_pushconst_tensor_offsets(ggml_backend_vk_context * ctx, vk
 
     GGML_UNUSED(src1);
     GGML_UNUSED(src2);
+    GGML_UNUSED(src3);
 }
 
 template<typename PC>
-static void ggml_vk_op_f32(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, const ggml_tensor * src2, ggml_tensor * dst, ggml_op op, PC&& pc, bool dryrun = false) {
+static void ggml_vk_op_f32(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, const ggml_tensor * src2, const ggml_tensor * src3, ggml_tensor * dst, ggml_op op, PC&& pc, bool dryrun = false) {
     VK_LOG_DEBUG("ggml_vk_op_f32((" << src0 << ", name=" << src0->name << ", type=" << src0->type << ", ne0=" << src0->ne[0] << ", ne1=" << src0->ne[1] << ", ne2=" << src0->ne[2] << ", ne3=" << src0->ne[3] << ", nb0=" << src0->nb[0] << ", nb1=" << src0->nb[1] << ", nb2=" << src0->nb[2] << ", nb3=" << src0->nb[3];
     if (src1 != nullptr) {
         std::cerr << "), (" << src1 << ", name=" << src1->name << ", type=" << src1->type << ", ne0=" << src1->ne[0] << ", ne1=" << src1->ne[1] << ", ne2=" << src1->ne[2] << ", ne3=" << src1->ne[3] << ", nb0=" << src1->nb[0] << ", nb1=" << src1->nb[1] << ", nb2=" << src1->nb[2] << ", nb3=" << src1->nb[3];
@@ -8492,6 +8523,9 @@ static void ggml_vk_op_f32(ggml_backend_vk_context * ctx, vk_context& subctx, co
     if (src2 != nullptr) {
         std::cerr << "), (" << src2 << ", name=" << src2->name << ", type=" << src2->type << ", ne0=" << src2->ne[0] << ", ne1=" << src2->ne[1] << ", ne2=" << src2->ne[2] << ", ne3=" << src2->ne[3] << ", nb0=" << src2->nb[0] << ", nb1=" << src2->nb[1] << ", nb2=" << src2->nb[2] << ", nb3=" << src2->nb[3];
     }
+    if (src3 != nullptr) {
+        std::cerr << "), (" << src3 << ", name=" << src3->name << ", type=" << src3->type << ", ne0=" << src3->ne[0] << ", ne1=" << src3->ne[1] << ", ne2=" << src3->ne[2] << ", ne3=" << src3->ne[3] << ", nb0=" << src3->nb[0] << ", nb1=" << src3->nb[1] << ", nb2=" << src3->nb[2] << ", nb3=" << src3->nb[3];
+    }
     std::cerr << "), (" << dst << ", name=" << dst->name << ", type=" << dst->type << ", ne0=" << dst->ne[0] << ", ne1=" << dst->ne[1] << ", ne2=" << dst->ne[2] << ", ne3=" << dst->ne[3] << ", nb0=" << dst->nb[0] << ", nb1=" << dst->nb[1] << ", nb2=" << dst->nb[2] << ", nb3=" << dst->nb[3];
     std::cerr << "), " << ggml_op_name(op) << ", " << (dryrun ? "dryrun" : "") << ")");
     GGML_ASSERT(op == GGML_OP_GET_ROWS || op == GGML_OP_CPY || (!ggml_is_quantized(src0->type) && (src1 == nullptr || !ggml_is_quantized(src1->type))));  // NOLINT
@@ -8518,6 +8552,13 @@ static void ggml_vk_op_f32(ggml_backend_vk_context * ctx, vk_context& subctx, co
     const uint64_t ne23 = use_src2 ? src2->ne[3] : 0;
     const uint64_t ne2 = ne20 * ne21;
 
+    const bool use_src3 = src3 != nullptr;
+    const uint64_t ne30 = use_src3 ? src3->ne[0] : 0;
+    const uint64_t ne31 = use_src3 ? src3->ne[1] : 0;
+    const uint64_t ne32 = use_src3 ? src3->ne[2] : 0;
+    const uint64_t ne33 = use_src3 ? src3->ne[3] : 0;
+    const uint64_t ne3 = ne30 * ne31;
+
     const uint64_t ned0 = dst->ne[0];
     const uint64_t ned1 = dst->ne[1];
     const uint64_t ned2 = dst->ne[2];
@@ -8548,6 +8589,7 @@ static void ggml_vk_op_f32(ggml_backend_vk_context * ctx, vk_context& subctx, co
     ggml_backend_vk_buffer_context * src0_buf_ctx = (ggml_backend_vk_buffer_context *)src0->buffer->context;
     ggml_backend_vk_buffer_context * src1_buf_ctx = use_src1 ? (ggml_backend_vk_buffer_context *)src1->buffer->context : nullptr;
     ggml_backend_vk_buffer_context * src2_buf_ctx = use_src2 ? (ggml_backend_vk_buffer_context *)src2->buffer->context : nullptr;
+    ggml_backend_vk_buffer_context * src3_buf_ctx = use_src3 ? (ggml_backend_vk_buffer_context *)src3->buffer->context : nullptr;
 
     vk_buffer d_X = nullptr;
     size_t x_buf_offset = 0;
@@ -8555,10 +8597,13 @@ static void ggml_vk_op_f32(ggml_backend_vk_context * ctx, vk_context& subctx, co
     size_t y_buf_offset = 0;
     vk_buffer d_Z = nullptr;
     size_t z_buf_offset = 0;
+    vk_buffer d_W = nullptr;
+    size_t w_buf_offset = 0;
 
     bool src0_uma = false;
     bool src1_uma = false;
     bool src2_uma = false;
+    bool src3_uma = false;
 
     if (ctx->device->uma) {
         ggml_vk_host_get(ctx->device, src0->data, d_X, x_buf_offset);
@@ -8571,6 +8616,10 @@ static void ggml_vk_op_f32(ggml_backend_vk_context * ctx, vk_context& subctx, co
             ggml_vk_host_get(ctx->device, src2->data, d_Z, z_buf_offset);
             src2_uma = d_Z != nullptr;
         }
+        if (use_src3) {
+            ggml_vk_host_get(ctx->device, src3->data, d_W, w_buf_offset);
+            src3_uma = d_W != nullptr;
+        }
     }
 
     vk_buffer d_D = dst_buf_ctx->dev_buffer;
@@ -8592,11 +8641,17 @@ static void ggml_vk_op_f32(ggml_backend_vk_context * ctx, vk_context& subctx, co
         z_buf_offset = vk_tensor_offset(src2) + src2->view_offs;
         GGML_ASSERT(d_Z != nullptr);
     }
+    if (use_src3 && !src3_uma) {
+        d_W = src3_buf_ctx->dev_buffer;
+        w_buf_offset = vk_tensor_offset(src3) + src3->view_offs;
+        GGML_ASSERT(d_W != nullptr);
+    }
     // Compute misalignment offset for descriptors and store it in in push constants, then align the descriptor offsets.
-    init_pushconst_tensor_offsets(ctx, pc, src0, src1, src2, dst);
+    init_pushconst_tensor_offsets(ctx, pc, src0, src1, src2, src3, dst);
     x_buf_offset &= ~(ctx->device->properties.limits.minStorageBufferOffsetAlignment - 1);
     y_buf_offset &= ~(ctx->device->properties.limits.minStorageBufferOffsetAlignment - 1);
     z_buf_offset &= ~(ctx->device->properties.limits.minStorageBufferOffsetAlignment - 1);
+    w_buf_offset &= ~(ctx->device->properties.limits.minStorageBufferOffsetAlignment - 1);
     d_buf_offset &= ~(ctx->device->properties.limits.minStorageBufferOffsetAlignment - 1);
 
     std::array<uint32_t, 3> elements;
@@ -8797,12 +8852,13 @@ static void ggml_vk_op_f32(ggml_backend_vk_context * ctx, vk_context& subctx, co
         break;
     }
 
-    uint64_t x_sz, y_sz, z_sz, d_sz;
+    uint64_t x_sz, y_sz, z_sz, w_sz, d_sz;
 
     if (op_supports_incontiguous) {
         x_sz = ggml_nbytes(src0) + get_misalign_bytes(ctx, src0);
         y_sz = use_src1 ? ggml_nbytes(src1) + get_misalign_bytes(ctx, src1) : 0;
         z_sz = use_src2 ? ggml_nbytes(src2) + get_misalign_bytes(ctx, src2) : 0;
+        w_sz = use_src3 ? ggml_nbytes(src3) + get_misalign_bytes(ctx, src3) : 0;
         d_sz = ggml_nbytes(dst) + get_misalign_bytes(ctx, dst);
 
         if (x_buf_offset + x_sz >= d_X->size) {
@@ -8814,6 +8870,9 @@ static void ggml_vk_op_f32(ggml_backend_vk_context * ctx, vk_context& subctx, co
         if (use_src2 && z_buf_offset + z_sz >= d_Z->size) {
             z_sz = ggml_vk_get_max_buffer_range(ctx, d_Z, z_buf_offset);
         }
+        if (use_src3 && w_buf_offset + w_sz >= d_W->size) {
+            w_sz = ggml_vk_get_max_buffer_range(ctx, d_W, w_buf_offset);
+        }
         if (d_buf_offset + d_sz >= d_D->size) {
             d_sz = ggml_vk_get_max_buffer_range(ctx, d_D, d_buf_offset);
         }
@@ -8821,6 +8880,7 @@ static void ggml_vk_op_f32(ggml_backend_vk_context * ctx, vk_context& subctx, co
         x_sz = ggml_type_size(src0->type)/ggml_blck_size(src0->type) * ne0 * ne02 * ne03;
         y_sz = use_src1 ? ggml_type_size(src1->type) * ne1 * ne12 * ne13 : 0;
         z_sz = use_src2 ? ggml_type_size(src2->type) * ne2 * ne22 * ne23 : 0;
+        w_sz = use_src3 ? ggml_type_size(src3->type) * ne3 * ne32 * ne33 : 0;
         d_sz = ggml_type_size(dst->type) * ned * ned2 * ned3;
     }
 
@@ -8862,14 +8922,19 @@ static void ggml_vk_op_f32(ggml_backend_vk_context * ctx, vk_context& subctx, co
         ggml_vk_dispatch_pipeline(ctx, subctx, pipeline, { vk_subbuffer{ d_X, x_buf_offset, x_sz }, subbuf_y, subbuf_z, vk_subbuffer{ d_D, d_buf_offset, d_sz } }, pc, elements);
     } else if (op == GGML_OP_ROPE || op == GGML_OP_ROPE_BACK) {
         // Empty src2 is possible in rope, but the shader needs a buffer
-        vk_subbuffer subbuf_z;
+        vk_subbuffer subbuf_z, subbuf_w;
         if (use_src2) {
             subbuf_z = { d_Z, z_buf_offset, z_sz };
         } else {
             subbuf_z = { d_X, 0, x_sz };
         }
+        if (use_src3) {
+            subbuf_w = { d_W, w_buf_offset, w_sz };
+        } else {
+            subbuf_w = { d_X, 0, x_sz };
+        }
 
-        ggml_vk_dispatch_pipeline(ctx, subctx, pipeline, { vk_subbuffer{ d_X, x_buf_offset, x_sz }, vk_subbuffer{ d_Y, y_buf_offset, y_sz }, subbuf_z, vk_subbuffer{ d_D, d_buf_offset, d_sz } }, pc, elements);
+        ggml_vk_dispatch_pipeline(ctx, subctx, pipeline, { vk_subbuffer{ d_X, x_buf_offset, x_sz }, vk_subbuffer{ d_Y, y_buf_offset, y_sz }, subbuf_z, vk_subbuffer{ d_D, d_buf_offset, d_sz }, subbuf_w }, pc, elements);
     } else if (op == GGML_OP_IM2COL || op == GGML_OP_IM2COL_3D) {
         if (ctx->device->shader_int64 && ctx->device->buffer_device_address) {
             // buffer device address path doesn't use dst buffer
@@ -8885,6 +8950,8 @@ static void ggml_vk_op_f32(ggml_backend_vk_context * ctx, vk_context& subctx, co
     } else if (op == GGML_OP_OPT_STEP_SGD) {
         // OPT_STEP_SGD works on src0, it does not need dst
         ggml_vk_dispatch_pipeline(ctx, subctx, pipeline, { vk_subbuffer{ d_X, x_buf_offset, x_sz }, vk_subbuffer{ d_Y, y_buf_offset, y_sz }, vk_subbuffer{ d_Z, z_buf_offset, z_sz } }, pc, elements);
+    } else if (use_src3) {
+        ggml_vk_dispatch_pipeline(ctx, subctx, pipeline, { vk_subbuffer{ d_X, x_buf_offset, x_sz }, vk_subbuffer{ d_Y, y_buf_offset, y_sz }, vk_subbuffer{ d_Z, z_buf_offset, z_sz }, vk_subbuffer{ d_W, w_buf_offset, w_sz }, vk_subbuffer{ d_D, d_buf_offset, d_sz } }, pc, elements);
     } else if (use_src2) {
         ggml_vk_dispatch_pipeline(ctx, subctx, pipeline, { vk_subbuffer{ d_X, x_buf_offset, x_sz }, vk_subbuffer{ d_Y, y_buf_offset, y_sz }, vk_subbuffer{ d_Z, z_buf_offset, z_sz }, vk_subbuffer{ d_D, d_buf_offset, d_sz } }, pc, elements);
     } else if (use_src1) {
@@ -8899,7 +8966,7 @@ static void ggml_vk_get_rows(ggml_backend_vk_context * ctx, vk_context& subctx,
     const uint32_t src1_type_size = ggml_type_size(src1->type);
     const uint32_t dst_type_size = ggml_type_size(dst->type);
 
-    ggml_vk_op_f32<vk_op_binary_push_constants>(ctx, subctx, src0, src1, nullptr, dst, GGML_OP_GET_ROWS, {
+    ggml_vk_op_f32<vk_op_binary_push_constants>(ctx, subctx, src0, src1, nullptr, nullptr, dst, GGML_OP_GET_ROWS, {
         (uint32_t)ggml_nelements(src0),
         (uint32_t)src0->ne[0], (uint32_t)src0->ne[1], (uint32_t)src0->ne[2],(uint32_t)src0->ne[3], (uint32_t)src0->nb[0] / src0_type_size, (uint32_t)src0->nb[1] / src0_type_size, (uint32_t)src0->nb[2] / src0_type_size, (uint32_t)src0->nb[3] / src0_type_size,
         (uint32_t)src1->ne[0], (uint32_t)src1->ne[1], (uint32_t)src1->ne[2],(uint32_t)src1->ne[3], (uint32_t)src1->nb[0] / src1_type_size, (uint32_t)src1->nb[1] / src1_type_size, (uint32_t)src1->nb[2] / src1_type_size, (uint32_t)src1->nb[3] / src1_type_size,
@@ -8919,7 +8986,7 @@ static void ggml_vk_acc(ggml_backend_vk_context * ctx, vk_context& subctx, const
     // int nb3 = dst->op_params[2] / 4; // 4 bytes of float32 - unused
     int offset = dst->op_params[3] / 4; // offset in bytes
 
-    ggml_vk_op_f32<vk_op_binary_push_constants>(ctx, subctx, src0, src1, nullptr, dst, GGML_OP_ACC, {
+    ggml_vk_op_f32<vk_op_binary_push_constants>(ctx, subctx, src0, src1, nullptr, nullptr, dst, GGML_OP_ACC, {
         (uint32_t)ggml_nelements(src0),
         (uint32_t)src0->ne[0], (uint32_t)src0->ne[1], (uint32_t)src0->ne[2],(uint32_t)src0->ne[3], (uint32_t)src0->nb[0] / src0_type_size, (uint32_t)nb1, (uint32_t)nb2, (uint32_t)src0->nb[3] / src0_type_size,
         (uint32_t)src1->ne[0], (uint32_t)src1->ne[1], (uint32_t)src1->ne[2],(uint32_t)src1->ne[3], (uint32_t)src1->nb[0] / src1_type_size, (uint32_t)src1->nb[1] / src1_type_size, (uint32_t)src1->nb[2] / src1_type_size, (uint32_t)src1->nb[3] / src1_type_size,
@@ -9044,7 +9111,7 @@ static void ggml_vk_add(ggml_backend_vk_context * ctx, vk_context& subctx, const
     const uint32_t src1_type_size = ggml_type_size(src1->type);
     const uint32_t dst_type_size = ggml_type_size(dst->type);
 
-    ggml_vk_op_f32<vk_op_binary_push_constants>(ctx, subctx, src0, src1, nullptr, dst, GGML_OP_ADD, {
+    ggml_vk_op_f32<vk_op_binary_push_constants>(ctx, subctx, src0, src1, nullptr, nullptr, dst, GGML_OP_ADD, {
         (uint32_t)ggml_nelements(src0),
         (uint32_t)src0->ne[0], (uint32_t)src0->ne[1], (uint32_t)src0->ne[2],(uint32_t)src0->ne[3], (uint32_t)src0->nb[0] / src0_type_size, (uint32_t)src0->nb[1] / src0_type_size, (uint32_t)src0->nb[2] / src0_type_size, (uint32_t)src0->nb[3] / src0_type_size,
         (uint32_t)src1->ne[0], (uint32_t)src1->ne[1], (uint32_t)src1->ne[2],(uint32_t)src1->ne[3], (uint32_t)src1->nb[0] / src1_type_size, (uint32_t)src1->nb[1] / src1_type_size, (uint32_t)src1->nb[2] / src1_type_size, (uint32_t)src1->nb[3] / src1_type_size,
@@ -9059,7 +9126,7 @@ static void ggml_vk_sub(ggml_backend_vk_context * ctx, vk_context& subctx, const
     const uint32_t src1_type_size = ggml_type_size(src1->type);
     const uint32_t dst_type_size = ggml_type_size(dst->type);
 
-    ggml_vk_op_f32<vk_op_binary_push_constants>(ctx, subctx, src0, src1, nullptr, dst, GGML_OP_SUB, {
+    ggml_vk_op_f32<vk_op_binary_push_constants>(ctx, subctx, src0, src1, nullptr, nullptr, dst, GGML_OP_SUB, {
         (uint32_t)ggml_nelements(src0),
         (uint32_t)src0->ne[0], (uint32_t)src0->ne[1], (uint32_t)src0->ne[2],(uint32_t)src0->ne[3], (uint32_t)src0->nb[0] / src0_type_size, (uint32_t)src0->nb[1] / src0_type_size, (uint32_t)src0->nb[2] / src0_type_size, (uint32_t)src0->nb[3] / src0_type_size,
         (uint32_t)src1->ne[0], (uint32_t)src1->ne[1], (uint32_t)src1->ne[2],(uint32_t)src1->ne[3], (uint32_t)src1->nb[0] / src1_type_size, (uint32_t)src1->nb[1] / src1_type_size, (uint32_t)src1->nb[2] / src1_type_size, (uint32_t)src1->nb[3] / src1_type_size,
@@ -9074,7 +9141,7 @@ static void ggml_vk_mul(ggml_backend_vk_context * ctx, vk_context& subctx, const
     const uint32_t src1_type_size = ggml_type_size(src1->type);
     const uint32_t dst_type_size = ggml_type_size(dst->type);
 
-    ggml_vk_op_f32<vk_op_binary_push_constants>(ctx, subctx, src0, src1, nullptr, dst, GGML_OP_MUL, {
+    ggml_vk_op_f32<vk_op_binary_push_constants>(ctx, subctx, src0, src1, nullptr, nullptr, dst, GGML_OP_MUL, {
         (uint32_t)ggml_nelements(src0),
         (uint32_t)src0->ne[0], (uint32_t)src0->ne[1], (uint32_t)src0->ne[2],(uint32_t)src0->ne[3], (uint32_t)src0->nb[0] / src0_type_size, (uint32_t)src0->nb[1] / src0_type_size, (uint32_t)src0->nb[2] / src0_type_size, (uint32_t)src0->nb[3] / src0_type_size,
         (uint32_t)src1->ne[0], (uint32_t)src1->ne[1], (uint32_t)src1->ne[2],(uint32_t)src1->ne[3], (uint32_t)src1->nb[0] / src1_type_size, (uint32_t)src1->nb[1] / src1_type_size, (uint32_t)src1->nb[2] / src1_type_size, (uint32_t)src1->nb[3] / src1_type_size,
@@ -9089,7 +9156,7 @@ static void ggml_vk_div(ggml_backend_vk_context * ctx, vk_context& subctx, const
     const uint32_t src1_type_size = ggml_type_size(src1->type);
     const uint32_t dst_type_size = ggml_type_size(dst->type);
 
-    ggml_vk_op_f32<vk_op_binary_push_constants>(ctx, subctx, src0, src1, nullptr, dst, GGML_OP_DIV, {
+    ggml_vk_op_f32<vk_op_binary_push_constants>(ctx, subctx, src0, src1, nullptr, nullptr, dst, GGML_OP_DIV, {
         (uint32_t)ggml_nelements(src0),
         (uint32_t)src0->ne[0], (uint32_t)src0->ne[1], (uint32_t)src0->ne[2],(uint32_t)src0->ne[3], (uint32_t)src0->nb[0] / src0_type_size, (uint32_t)src0->nb[1] / src0_type_size, (uint32_t)src0->nb[2] / src0_type_size, (uint32_t)src0->nb[3] / src0_type_size,
         (uint32_t)src1->ne[0], (uint32_t)src1->ne[1], (uint32_t)src1->ne[2],(uint32_t)src1->ne[3], (uint32_t)src1->nb[0] / src1_type_size, (uint32_t)src1->nb[1] / src1_type_size, (uint32_t)src1->nb[2] / src1_type_size, (uint32_t)src1->nb[3] / src1_type_size,
@@ -9104,7 +9171,7 @@ static void ggml_vk_add_id(ggml_backend_vk_context * ctx, vk_context& subctx, co
     const uint32_t src1_type_size = ggml_type_size(src1->type);
     const uint32_t src2_type_size = ggml_type_size(src2->type);
 
-    ggml_vk_op_f32<vk_op_add_id_push_constants>(ctx, subctx, src0, src1, src2, dst, GGML_OP_ADD_ID, {
+    ggml_vk_op_f32<vk_op_add_id_push_constants>(ctx, subctx, src0, src1, src2, nullptr, dst, GGML_OP_ADD_ID, {
         (uint32_t)dst->ne[0],
         (uint32_t)dst->ne[1],
         (uint32_t)src0->nb[1] / src0_type_size,
@@ -9337,7 +9404,7 @@ static void ggml_vk_ssm_conv(ggml_backend_vk_context * ctx, vk_context& subctx,
     const ggml_tensor * src0 = dst->src[0];
     const ggml_tensor * src1 = dst->src[1];
 
-    ggml_vk_op_f32<vk_op_ssm_conv_push_constants>(ctx, subctx, src0, src1, nullptr, dst, GGML_OP_SSM_CONV, {
+    ggml_vk_op_f32<vk_op_ssm_conv_push_constants>(ctx, subctx, src0, src1, nullptr, nullptr, dst, GGML_OP_SSM_CONV, {
         (uint32_t)src0->nb[1], (uint32_t)src0->nb[2],
         (uint32_t)src1->nb[1],
         (uint32_t)dst->nb[0], (uint32_t)dst->nb[1], (uint32_t)dst->nb[2],
@@ -9455,7 +9522,7 @@ static void ggml_vk_opt_step_adamw(ggml_backend_vk_context * ctx, vk_context& su
 static void ggml_vk_opt_step_sgd(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, const ggml_tensor * src2, ggml_tensor * dst, bool dryrun = false) {
     const size_t n = ggml_nelements(dst->src[0]);
 
-    ggml_vk_op_f32<vk_op_push_constants>(ctx, subctx, src0, src1, src2, dst, GGML_OP_OPT_STEP_SGD, { (uint32_t)n, 0, 0.0f, 0.0f }, dryrun);
+    ggml_vk_op_f32<vk_op_push_constants>(ctx, subctx, src0, src1, src2, nullptr, dst, GGML_OP_OPT_STEP_SGD, { (uint32_t)n, 0, 0.0f, 0.0f }, dryrun);
 }
 
 static void ggml_vk_concat(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, ggml_tensor * dst, bool dryrun = false) {
@@ -9465,7 +9532,7 @@ static void ggml_vk_concat(ggml_backend_vk_context * ctx, vk_context& subctx, co
     const uint32_t src1_type_size = ggml_type_size(src1->type);
     const uint32_t dst_type_size = ggml_type_size(dst->type);
 
-    ggml_vk_op_f32<vk_op_binary_push_constants>(ctx, subctx, src0, src1, nullptr, dst, GGML_OP_CONCAT, {
+    ggml_vk_op_f32<vk_op_binary_push_constants>(ctx, subctx, src0, src1, nullptr, nullptr, dst, GGML_OP_CONCAT, {
         (uint32_t)ggml_nelements(dst),
         (uint32_t)src0->ne[0], (uint32_t)src0->ne[1], (uint32_t)src0->ne[2],(uint32_t)src0->ne[3], (uint32_t)src0->nb[0] / src0_type_size, (uint32_t)src0->nb[1] / src0_type_size, (uint32_t)src0->nb[2] / src0_type_size, (uint32_t)src0->nb[3] / src0_type_size,
         (uint32_t)src1->ne[0], (uint32_t)src1->ne[1], (uint32_t)src1->ne[2],(uint32_t)src1->ne[3], (uint32_t)src1->nb[0] / src1_type_size, (uint32_t)src1->nb[1] / src1_type_size, (uint32_t)src1->nb[2] / src1_type_size, (uint32_t)src1->nb[3] / src1_type_size,
@@ -9493,7 +9560,7 @@ static void ggml_vk_upscale(ggml_backend_vk_context * ctx, vk_context& subctx, c
         pixel_offset = 0.0f;
     }
 
-    ggml_vk_op_f32<vk_op_upscale_push_constants>(ctx, subctx, src0, nullptr, nullptr, dst, GGML_OP_UPSCALE, {
+    ggml_vk_op_f32<vk_op_upscale_push_constants>(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_UPSCALE, {
         (uint32_t)ggml_nelements(dst), 0, 0,
         (uint32_t)ne00, (uint32_t)ne01,
         (uint32_t)nb00 / src0_type_size, (uint32_t)nb01 / src0_type_size, (uint32_t)nb02 / src0_type_size, (uint32_t)nb03 / src0_type_size,
@@ -9507,23 +9574,23 @@ static void ggml_vk_scale(ggml_backend_vk_context * ctx, vk_context& subctx, con
     p.param1 = ggml_get_op_params_f32(dst, 0);
     p.param2 = ggml_get_op_params_f32(dst, 1);
 
-    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, dst, GGML_OP_SCALE, std::move(p), dryrun);
+    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_SCALE, std::move(p), dryrun);
 }
 
 static void ggml_vk_sqr(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst, bool dryrun = false) {
-    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, dst, GGML_OP_SQR, vk_op_unary_push_constants_init(src0, dst), dryrun);
+    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_SQR, vk_op_unary_push_constants_init(src0, dst), dryrun);
 }
 
 static void ggml_vk_sqrt(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst, bool dryrun = false) {
-    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, dst, GGML_OP_SQRT, vk_op_unary_push_constants_init(src0, dst), dryrun);
+    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_SQRT, vk_op_unary_push_constants_init(src0, dst), dryrun);
 }
 
 static void ggml_vk_sin(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst, bool dryrun = false) {
-    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, dst, GGML_OP_SIN, vk_op_unary_push_constants_init(src0, dst), dryrun);
+    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_SIN, vk_op_unary_push_constants_init(src0, dst), dryrun);
 }
 
 static void ggml_vk_cos(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst, bool dryrun = false) {
-    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, dst, GGML_OP_COS, vk_op_unary_push_constants_init(src0, dst), dryrun);
+    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_COS, vk_op_unary_push_constants_init(src0, dst), dryrun);
 }
 
 static void ggml_vk_clamp(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst, bool dryrun = false) {
@@ -9531,12 +9598,12 @@ static void ggml_vk_clamp(ggml_backend_vk_context * ctx, vk_context& subctx, con
     p.param1 = ggml_get_op_params_f32(dst, 0);
     p.param2 = ggml_get_op_params_f32(dst, 1);
 
-    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, dst, GGML_OP_CLAMP, std::move(p), dryrun);
+    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_CLAMP, std::move(p), dryrun);
 }
 
 static void ggml_vk_pad(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst, bool dryrun = false) {
     vk_op_pad_push_constants p = vk_op_pad_push_constants_init(src0, dst);
-    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, dst, GGML_OP_PAD, std::move(p), dryrun);
+    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_PAD, std::move(p), dryrun);
 }
 
 static void ggml_vk_roll(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst, bool dryrun = false) {
@@ -9551,17 +9618,17 @@ static void ggml_vk_roll(ggml_backend_vk_context * ctx, vk_context& subctx, cons
     memcpy(&p.param1, &s01_packed, sizeof(float));
     memcpy(&p.param2, &s23_packed, sizeof(float));
 
-    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, dst, GGML_OP_ROLL, std::move(p), dryrun);
+    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_ROLL, std::move(p), dryrun);
 }
 
 static void ggml_vk_repeat(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst, bool dryrun = false) {
     vk_op_unary_push_constants p = vk_op_unary_push_constants_init(src0, dst, ggml_nelements(dst));
-    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, dst, GGML_OP_REPEAT, std::move(p), dryrun);
+    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_REPEAT, std::move(p), dryrun);
 }
 
 static void ggml_vk_repeat_back(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst, bool dryrun = false) {
     vk_op_unary_push_constants p = vk_op_unary_push_constants_init(src0, dst, ggml_nelements(dst));
-    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, dst, GGML_OP_REPEAT_BACK, std::move(p), dryrun);
+    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_REPEAT_BACK, std::move(p), dryrun);
 }
 
 static void ggml_vk_cpy(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst, bool dryrun = false) {
@@ -9577,7 +9644,7 @@ static void ggml_vk_cpy(ggml_backend_vk_context * ctx, vk_context& subctx, const
     }
 
     vk_op_unary_push_constants p = vk_op_unary_push_constants_init(src0, dst, ne);
-    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, dst, GGML_OP_CPY, std::move(p), dryrun);
+    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_CPY, std::move(p), dryrun);
 }
 
 static void ggml_vk_set_rows(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, ggml_tensor * dst, bool dryrun = false) {
@@ -9592,7 +9659,7 @@ static void ggml_vk_set_rows(ggml_backend_vk_context * ctx, vk_context& subctx,
         return;
     }
 
-    ggml_vk_op_f32<vk_op_binary_push_constants>(ctx, subctx, src0, src1, nullptr, dst, GGML_OP_SET_ROWS, {
+    ggml_vk_op_f32<vk_op_binary_push_constants>(ctx, subctx, src0, src1, nullptr, nullptr, dst, GGML_OP_SET_ROWS, {
         (uint32_t)ggml_nelements(src0),
         (uint32_t)src0->ne[0], (uint32_t)src0->ne[1], (uint32_t)src0->ne[2],(uint32_t)src0->ne[3], (uint32_t)src0->nb[0] / src0_type_size, (uint32_t)src0->nb[1] / src0_type_size, (uint32_t)src0->nb[2] / src0_type_size, (uint32_t)src0->nb[3] / src0_type_size,
         (uint32_t)src1->ne[0], (uint32_t)src1->ne[1], (uint32_t)src1->ne[2],(uint32_t)src1->ne[3], (uint32_t)src1->nb[0] / src1_type_size, (uint32_t)src1->nb[1] / src1_type_size, (uint32_t)src1->nb[2] / src1_type_size, (uint32_t)src1->nb[3] / src1_type_size,
@@ -9603,13 +9670,13 @@ static void ggml_vk_set_rows(ggml_backend_vk_context * ctx, vk_context& subctx,
 }
 
 static void ggml_vk_silu_back(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, ggml_tensor * dst, bool dryrun = false) {
-    ggml_vk_op_f32<vk_op_push_constants>(ctx, subctx, src0, src1, nullptr, dst, GGML_OP_SILU_BACK, { (uint32_t)ggml_nelements(src0), 0, 0.0f, 0.0f }, dryrun);
+    ggml_vk_op_f32<vk_op_push_constants>(ctx, subctx, src0, src1, nullptr, nullptr, dst, GGML_OP_SILU_BACK, { (uint32_t)ggml_nelements(src0), 0, 0.0f, 0.0f }, dryrun);
 }
 
 static void ggml_vk_norm(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst, bool dryrun = false) {
     float * op_params = (float *)dst->op_params;
 
-    ggml_vk_op_f32<vk_op_push_constants>(ctx, subctx, src0, nullptr, nullptr, dst, GGML_OP_NORM, { (uint32_t)src0->ne[0], (uint32_t)src0->ne[1], op_params[0], 0.0f }, dryrun);
+    ggml_vk_op_f32<vk_op_push_constants>(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_NORM, { (uint32_t)src0->ne[0], (uint32_t)src0->ne[1], op_params[0], 0.0f }, dryrun);
 }
 
 static void ggml_vk_group_norm(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst, bool dryrun = false) {
@@ -9620,7 +9687,7 @@ static void ggml_vk_group_norm(ggml_backend_vk_context * ctx, vk_context& subctx
     const float eps = float_op_params[1];
     const uint32_t group_size = src0->ne[0] * src0->ne[1] * ((src0->ne[2] + num_groups - 1) / num_groups);
 
-    ggml_vk_op_f32<vk_op_push_constants>(ctx, subctx, src0, nullptr, nullptr, dst, GGML_OP_GROUP_NORM, { group_size, 0, eps, 0.0f }, dryrun);
+    ggml_vk_op_f32<vk_op_push_constants>(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_GROUP_NORM, { group_size, 0, eps, 0.0f }, dryrun);
 }
 
 static uint32_t ggml_vk_rms_num_partials(ggml_backend_vk_context * ctx, const ggml_tensor *node) {
@@ -9643,7 +9710,7 @@ static void ggml_vk_rms_norm(ggml_backend_vk_context * ctx, vk_context& subctx,
 
     uint32_t param3 = ctx->do_add_rms_partials ? ggml_vk_rms_num_partials(ctx, dst) : 0;
 
-    ggml_vk_op_f32<vk_op_binary_push_constants>(ctx, subctx, src0, src1, nullptr, dst, GGML_OP_RMS_NORM, {
+    ggml_vk_op_f32<vk_op_binary_push_constants>(ctx, subctx, src0, src1, nullptr, nullptr, dst, GGML_OP_RMS_NORM, {
         (uint32_t)ggml_nelements(src0),
         (uint32_t)src0->ne[0], (uint32_t)src0->ne[1], (uint32_t)src0->ne[2],(uint32_t)src0->ne[3], (uint32_t)src0->nb[0] / src0_type_size, (uint32_t)src0->nb[1] / src0_type_size, (uint32_t)src0->nb[2] / src0_type_size, (uint32_t)src0->nb[3] / src0_type_size,
         (uint32_t)src1->ne[0], (uint32_t)src1->ne[1], (uint32_t)src1->ne[2],(uint32_t)src1->ne[3], (uint32_t)src1->nb[0] / src1_type_size, (uint32_t)src1->nb[1] / src1_type_size, (uint32_t)src1->nb[2] / src1_type_size, (uint32_t)src1->nb[3] / src1_type_size,
@@ -9660,16 +9727,16 @@ static void ggml_vk_rms_norm(ggml_backend_vk_context * ctx, vk_context& subctx,
 
 static void ggml_vk_rms_norm_back(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, ggml_tensor * dst, bool dryrun = false) {
     float * op_params = (float *)dst->op_params;
-    ggml_vk_op_f32<vk_op_push_constants>(ctx, subctx, src0, src1, nullptr, dst, GGML_OP_RMS_NORM_BACK, { (uint32_t)src0->ne[0], (uint32_t)src0->ne[1], op_params[0], 0.0f }, dryrun);
+    ggml_vk_op_f32<vk_op_push_constants>(ctx, subctx, src0, src1, nullptr, nullptr, dst, GGML_OP_RMS_NORM_BACK, { (uint32_t)src0->ne[0], (uint32_t)src0->ne[1], op_params[0], 0.0f }, dryrun);
 }
 
 static void ggml_vk_l2_norm(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst, bool dryrun = false) {
     float * op_params = (float *)dst->op_params;
-    ggml_vk_op_f32<vk_op_push_constants>(ctx, subctx, src0, nullptr, nullptr, dst, GGML_OP_L2_NORM, { (uint32_t)src0->ne[0], (uint32_t)src0->ne[1], op_params[0], 0.0f }, dryrun);
+    ggml_vk_op_f32<vk_op_push_constants>(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_L2_NORM, { (uint32_t)src0->ne[0], (uint32_t)src0->ne[1], op_params[0], 0.0f }, dryrun);
 }
 
 static void ggml_vk_unary(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst, bool dryrun = false) {
-    ggml_vk_op_f32<vk_op_push_constants>(ctx, subctx, src0, nullptr, nullptr, dst, GGML_OP_UNARY, { (uint32_t)ggml_nelements(src0), 0, 0.0f, 0.0f }, dryrun);
+    ggml_vk_op_f32<vk_op_push_constants>(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_UNARY, { (uint32_t)ggml_nelements(src0), 0, 0.0f, 0.0f }, dryrun);
 }
 
 static void ggml_vk_glu(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, ggml_tensor * dst, bool dryrun = false) {
@@ -9692,7 +9759,7 @@ static void ggml_vk_glu(ggml_backend_vk_context * ctx, vk_context& subctx, const
 
     const uint32_t mode = split ? 2 : (swapped ? 1 : 0);
 
-    ggml_vk_op_f32<vk_op_glu_push_constants>(ctx, subctx, src0, src1, nullptr, dst, GGML_OP_GLU,
+    ggml_vk_op_f32<vk_op_glu_push_constants>(ctx, subctx, src0, src1, nullptr, nullptr, dst, GGML_OP_GLU,
         {
             (uint32_t)ggml_nelements(dst),
             (uint32_t)src0->ne[0],
@@ -9705,7 +9772,7 @@ static void ggml_vk_glu(ggml_backend_vk_context * ctx, vk_context& subctx, const
 
 static void ggml_vk_diag_mask_inf(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst, bool dryrun = false) {
     int32_t * op_params = (int32_t *)dst->op_params;
-    ggml_vk_op_f32<vk_op_diag_mask_push_constants>(ctx, subctx, src0, nullptr, nullptr, dst, GGML_OP_DIAG_MASK_INF, { (uint32_t)src0->ne[0], (uint32_t)src0->ne[1], op_params[0] }, dryrun);
+    ggml_vk_op_f32<vk_op_diag_mask_push_constants>(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_DIAG_MASK_INF, { (uint32_t)src0->ne[0], (uint32_t)src0->ne[1], op_params[0] }, dryrun);
 }
 
 static void ggml_vk_soft_max(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, const ggml_tensor * src2, ggml_tensor * dst, bool dryrun = false) {
@@ -9730,7 +9797,7 @@ static void ggml_vk_soft_max(ggml_backend_vk_context * ctx, vk_context& subctx,
     const float m0 = powf(2.0f, -(max_bias       ) / n_head_log2);
     const float m1 = powf(2.0f, -(max_bias / 2.0f) / n_head_log2);
 
-    ggml_vk_op_f32<vk_op_soft_max_push_constants>(ctx, subctx, src0, src1, src2, dst, GGML_OP_SOFT_MAX, {
+    ggml_vk_op_f32<vk_op_soft_max_push_constants>(ctx, subctx, src0, src1, src2, nullptr, dst, GGML_OP_SOFT_MAX, {
         ncols,
         src1 != nullptr ? nrows_y : (uint32_t)0,
         (uint32_t)src0->ne[0], (uint32_t)src0->ne[1], (uint32_t)src0->ne[2],
@@ -9746,7 +9813,7 @@ static void ggml_vk_soft_max(ggml_backend_vk_context * ctx, vk_context& subctx,
 
 static void ggml_vk_soft_max_back(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, ggml_tensor * dst, bool dryrun = false) {
     float * op_params = (float *)dst->op_params;
-    ggml_vk_op_f32<vk_op_push_constants>(ctx, subctx, src0, src1, nullptr, dst, GGML_OP_SOFT_MAX_BACK, { (uint32_t)src0->ne[0], (uint32_t)ggml_nrows(src0), op_params[0], op_params[1] }, dryrun);
+    ggml_vk_op_f32<vk_op_push_constants>(ctx, subctx, src0, src1, nullptr, nullptr, dst, GGML_OP_SOFT_MAX_BACK, { (uint32_t)src0->ne[0], (uint32_t)ggml_nrows(src0), op_params[0], op_params[1] }, dryrun);
 }
 
 static void ggml_vk_topk_moe(ggml_backend_vk_context * ctx, vk_context& subctx, ggml_cgraph * cgraph, int node_idx, bool dryrun = false) {
@@ -9837,7 +9904,12 @@ static void ggml_vk_topk_moe(ggml_backend_vk_context * ctx, vk_context& subctx,
         }, pc, elements);
 }
 
-static void ggml_vk_rope(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, const ggml_tensor * src2, ggml_tensor * dst, bool backprop, bool dryrun = false) {
+static void ggml_vk_rope(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_cgraph * cgraph, int node_idx, bool backprop, bool dryrun = false) {
+    ggml_tensor * dst = cgraph->nodes[node_idx];
+    const ggml_tensor * src0 = dst->src[0];
+    const ggml_tensor * src1 = dst->src[1];
+    const ggml_tensor * src2 = dst->src[2];
+    const ggml_tensor * src3 = nullptr;
     const int n_dims        = ((int32_t *) dst->op_params)[1];
     const int mode          = ((int32_t *) dst->op_params)[2];
     // const int n_ctx         = ((int32_t *) dst->op_params)[3];
@@ -9861,11 +9933,20 @@ static void ggml_vk_rope(ggml_backend_vk_context * ctx, vk_context& subctx, cons
     uint32_t s1 = src0->nb[1] / ggml_type_size(src0->type);
     uint32_t s2 = src0->nb[2] / ggml_type_size(src0->type);
 
-    ggml_vk_op_f32<vk_op_rope_push_constants>(ctx, subctx, src0, src1, src2, dst, GGML_OP_ROPE, {
+    uint32_t set_rows_stride = 0;
+    // Fused rope + view + set_rows passes the set_rows destination stride in set_rows_stride
+    // and overrides the dst and sets src3=row_indices
+    if (ctx->num_additional_fused_ops > 0) {
+        set_rows_stride = cgraph->nodes[node_idx + 2]->nb[1] / ggml_type_size(cgraph->nodes[node_idx + 2]->type);
+        src3 = cgraph->nodes[node_idx + 2]->src[1];
+        dst = cgraph->nodes[node_idx + 2];
+    }
+
+    ggml_vk_op_f32<vk_op_rope_push_constants>(ctx, subctx, src0, src1, src2, src3, dst, GGML_OP_ROPE, {
         (uint32_t)src0->ne[0], (uint32_t)n_dims, freq_scale, (uint32_t)src0->ne[1],
         freq_base, ext_factor, attn_factor, {corr_dims[0], corr_dims[1]}, theta_scale,
         src2 != nullptr, (uint32_t)src0->ne[2], s1, s2,
-        { sections[0], sections[1], sections[2], sections[3] }, backprop
+        { sections[0], sections[1], sections[2], sections[3] }, backprop, set_rows_stride,
     }, dryrun);
 }
 
@@ -9874,7 +9955,7 @@ static void ggml_vk_argsort(ggml_backend_vk_context * ctx, vk_context& subctx, c
 
     uint32_t ncols = src0->ne[0];
 
-    ggml_vk_op_f32<vk_op_argsort_push_constants>(ctx, subctx, src0, nullptr, nullptr, dst, GGML_OP_ARGSORT, {
+    ggml_vk_op_f32<vk_op_argsort_push_constants>(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_ARGSORT, {
         ncols,
         op_params[0],
     }, dryrun);
@@ -9882,26 +9963,26 @@ static void ggml_vk_argsort(ggml_backend_vk_context * ctx, vk_context& subctx, c
 
 static void ggml_vk_sum(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst, bool dryrun = false) {
     vk_op_sum_rows_push_constants p = vk_op_sum_rows_push_constants_init(src0, dst, ggml_nelements(src0));
-    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, dst, GGML_OP_SUM, p, dryrun);
+    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_SUM, p, dryrun);
 }
 
 static void ggml_vk_sum_rows(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst, bool dryrun = false) {
     vk_op_sum_rows_push_constants p = vk_op_sum_rows_push_constants_init(src0, dst, src0->ne[0]);
-    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, dst, GGML_OP_SUM_ROWS, p, dryrun);
+    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_SUM_ROWS, p, dryrun);
 }
 
 static void ggml_vk_mean(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst, bool dryrun = false) {
     vk_op_sum_rows_push_constants p = vk_op_sum_rows_push_constants_init(src0, dst, src0->ne[0]);
     p.weight = 1.0f / (float)src0->ne[0];
-    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, dst, GGML_OP_MEAN, p, dryrun);
+    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_MEAN, p, dryrun);
 }
 
 static void ggml_vk_argmax(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst, bool dryrun = false) {
-    ggml_vk_op_f32<vk_op_push_constants>(ctx, subctx, src0, nullptr, nullptr, dst, GGML_OP_ARGMAX, { (uint32_t)src0->ne[0], (uint32_t)src0->ne[1], 0.0f, 0.0f }, dryrun);
+    ggml_vk_op_f32<vk_op_push_constants>(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_ARGMAX, { (uint32_t)src0->ne[0], (uint32_t)src0->ne[1], 0.0f, 0.0f }, dryrun);
 }
 
 static void ggml_vk_count_equal(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, ggml_tensor * dst, bool dryrun = false) {
-    ggml_vk_op_f32<vk_op_push_constants>(ctx, subctx, src0, src1, nullptr, dst, GGML_OP_COUNT_EQUAL, { (uint32_t)ggml_nelements(src0), 0, 0.0f, 0.0f }, dryrun);
+    ggml_vk_op_f32<vk_op_push_constants>(ctx, subctx, src0, src1, nullptr, nullptr, dst, GGML_OP_COUNT_EQUAL, { (uint32_t)ggml_nelements(src0), 0, 0.0f, 0.0f }, dryrun);
 }
 
 static void ggml_vk_im2col(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, ggml_tensor * dst, bool dryrun = false) {
@@ -9934,7 +10015,7 @@ static void ggml_vk_im2col(ggml_backend_vk_context * ctx, vk_context& subctx, co
 
     const vk::DeviceAddress dst_addr = d_buf->bda_addr + vk_tensor_offset(dst) + dst->view_offs;
 
-    ggml_vk_op_f32<vk_op_im2col_push_constants>(ctx, subctx, src0, src1, nullptr, dst, GGML_OP_IM2COL, {
+    ggml_vk_op_f32<vk_op_im2col_push_constants>(ctx, subctx, src0, src1, nullptr, nullptr, dst, GGML_OP_IM2COL, {
         dst_addr,
         batch_offset, offset_delta,
         IC, IW, IH, OW, OH, KW, KH,
@@ -10007,7 +10088,7 @@ static void ggml_vk_im2col_3d(ggml_backend_vk_context * ctx, vk_context& subctx,
     pc.OH_OW_IC_KD_KH_KW = OH*OW*IC*KD*KH*KW;
     pc.OW_IC_KD_KH_KW = OW*IC*KD*KH*KW;
 
-    ggml_vk_op_f32<vk_op_im2col_3d_push_constants>(ctx, subctx, src0, src1, nullptr, dst, GGML_OP_IM2COL_3D, std::move(pc), dryrun);
+    ggml_vk_op_f32<vk_op_im2col_3d_push_constants>(ctx, subctx, src0, src1, nullptr, nullptr, dst, GGML_OP_IM2COL_3D, std::move(pc), dryrun);
 }
 
 static void ggml_vk_timestep_embedding(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst, bool dryrun = false) {
@@ -10015,7 +10096,7 @@ static void ggml_vk_timestep_embedding(ggml_backend_vk_context * ctx, vk_context
     const uint32_t max_period = dst->op_params[1];
     const uint32_t nb1 = dst->nb[1] / ggml_type_size(dst->type);
 
-    ggml_vk_op_f32<vk_op_timestep_embedding_push_constants>(ctx, subctx, src0, nullptr, nullptr, dst, GGML_OP_TIMESTEP_EMBEDDING, {
+    ggml_vk_op_f32<vk_op_timestep_embedding_push_constants>(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_TIMESTEP_EMBEDDING, {
         nb1, dim, max_period,
     }, dryrun);
 }
@@ -10048,7 +10129,7 @@ static void ggml_vk_conv_transpose_1d(ggml_backend_vk_context * ctx, vk_context&
     p.nb1 = static_cast<uint32_t>(nb1 / nb0);
     p.s0 = static_cast<uint32_t>(s0);
 
-    ggml_vk_op_f32(ctx, subctx, src0, src1, nullptr, dst, GGML_OP_CONV_TRANSPOSE_1D, std::move(p), dryrun);
+    ggml_vk_op_f32(ctx, subctx, src0, src1, nullptr, nullptr, dst, GGML_OP_CONV_TRANSPOSE_1D, std::move(p), dryrun);
 }
 
 static void ggml_vk_pool_2d(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst, bool dryrun = false) {
@@ -10071,7 +10152,7 @@ static void ggml_vk_pool_2d(ggml_backend_vk_context * ctx, vk_context& subctx, c
 
     const uint32_t parallel_elements = N * OC * OH * OW;
 
-    ggml_vk_op_f32<vk_op_pool2d_push_constants>(ctx, subctx, src0, nullptr, nullptr, dst, GGML_OP_POOL_2D, {
+    ggml_vk_op_f32<vk_op_pool2d_push_constants>(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_POOL_2D, {
         IW, IH, OW, OH, OC,
         parallel_elements,
         op,
@@ -10125,7 +10206,7 @@ static void ggml_vk_conv_2d(ggml_backend_vk_context * ctx, vk_context & subctx,
     GGML_ASSERT(ne03 == ne2);
     GGML_ASSERT(ne02 == ne12);
 
-    ggml_vk_op_f32(ctx, subctx, src0, src1, nullptr, dst, GGML_OP_CONV_2D, std::move(p), dryrun);
+    ggml_vk_op_f32(ctx, subctx, src0, src1, nullptr, nullptr, dst, GGML_OP_CONV_2D, std::move(p), dryrun);
 }
 
 static void ggml_vk_conv_transpose_2d(ggml_backend_vk_context * ctx, vk_context & subctx, const ggml_tensor * src0,
@@ -10174,7 +10255,7 @@ static void ggml_vk_conv_transpose_2d(ggml_backend_vk_context * ctx, vk_context
     GGML_ASSERT(ne02 == ne2);
     GGML_ASSERT(ne03 == ne12);
 
-    ggml_vk_op_f32(ctx, subctx, src0, src1, nullptr, dst, GGML_OP_CONV_TRANSPOSE_2D, std::move(p), dryrun);
+    ggml_vk_op_f32(ctx, subctx, src0, src1, nullptr, nullptr, dst, GGML_OP_CONV_TRANSPOSE_2D, std::move(p), dryrun);
 }
 
 static void ggml_vk_conv_2d_dw(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, ggml_tensor * dst, bool dryrun = false) {
@@ -10198,12 +10279,12 @@ static void ggml_vk_conv_2d_dw(ggml_backend_vk_context * ctx, vk_context& subctx
     GGML_ASSERT(src0->ne[3] == p.channels);
     GGML_ASSERT(src1->ne[3] == p.batches);
 
-    ggml_vk_op_f32(ctx, subctx, src0, src1, nullptr, dst, GGML_OP_CONV_2D_DW, std::move(p), dryrun);
+    ggml_vk_op_f32(ctx, subctx, src0, src1, nullptr, nullptr, dst, GGML_OP_CONV_2D_DW, std::move(p), dryrun);
 }
 
 static void ggml_vk_leaky_relu(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst, bool dryrun = false) {
     const float * op_params = (const float *)dst->op_params;
-    ggml_vk_op_f32<vk_op_push_constants>(ctx, subctx, src0, nullptr, nullptr, dst, GGML_OP_LEAKY_RELU, { (uint32_t)ggml_nelements(src0), 0, op_params[0], 0.0f }, dryrun);
+    ggml_vk_op_f32<vk_op_push_constants>(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_LEAKY_RELU, { (uint32_t)ggml_nelements(src0), 0, op_params[0], 0.0f }, dryrun);
 }
 
 #ifdef GGML_VULKAN_RUN_TESTS
@@ -11329,7 +11410,6 @@ static bool ggml_vk_build_graph(ggml_backend_vk_context * ctx, ggml_cgraph * cgr
         case GGML_OP_DIAG_MASK_INF:
         case GGML_OP_SOFT_MAX:
         case GGML_OP_SOFT_MAX_BACK:
-        case GGML_OP_ROPE:
         case GGML_OP_ROPE_BACK:
         case GGML_OP_ARGSORT:
         case GGML_OP_SUM:
@@ -11403,9 +11483,12 @@ static bool ggml_vk_build_graph(ggml_backend_vk_context * ctx, ggml_cgraph * cgr
         // nodes require synchronization.
         for (int32_t i = 0; i < ctx->num_additional_fused_ops + 1 && !need_sync; ++i) {
             const ggml_tensor *cur_node = cgraph->nodes[node_idx + i];
-            if (overlaps_unsynced(cur_node, ctx->unsynced_nodes_read) || overlaps_unsynced(cur_node, ctx->unsynced_nodes_written)) {
-                need_sync = true;
-                break;
+            // If the node actually writes to memory, then check if it needs to sync
+            if (ctx->fused_ops_write_mask & (1 << i)) {
+                if (overlaps_unsynced(cur_node, ctx->unsynced_nodes_read) || overlaps_unsynced(cur_node, ctx->unsynced_nodes_written)) {
+                    need_sync = true;
+                    break;
+                }
             }
             for (uint32_t j = 0; j < GGML_MAX_SRC; ++j) {
                 if (!cur_node->src[j]) {
@@ -11432,7 +11515,9 @@ static bool ggml_vk_build_graph(ggml_backend_vk_context * ctx, ggml_cgraph * cgr
         for (int32_t i = 0; i < ctx->num_additional_fused_ops + 1; ++i) {
             const ggml_tensor *cur_node = cgraph->nodes[node_idx + i];
             // Multiple outputs could be written, e.g. in topk_moe. Add them all to the list.
-            ctx->unsynced_nodes_written.push_back(cur_node);
+            if (ctx->fused_ops_write_mask & (1 << i)) {
+                ctx->unsynced_nodes_written.push_back(cur_node);
+            }
             for (uint32_t j = 0; j < GGML_MAX_SRC; ++j) {
                 if (!cur_node->src[j]) {
                     continue;
@@ -11623,11 +11708,11 @@ static bool ggml_vk_build_graph(ggml_backend_vk_context * ctx, ggml_cgraph * cgr
 
         break;
     case GGML_OP_ROPE:
-        ggml_vk_rope(ctx, compute_ctx, src0, src1, src2, node, false, dryrun);
+        ggml_vk_rope(ctx, compute_ctx, cgraph, node_idx, false, dryrun);
 
         break;
     case GGML_OP_ROPE_BACK:
-        ggml_vk_rope(ctx, compute_ctx, src0, src1, src2, node, true, dryrun);
+        ggml_vk_rope(ctx, compute_ctx, cgraph, node_idx, true, dryrun);
 
         break;
     case GGML_OP_ARGSORT:
@@ -12464,6 +12549,41 @@ static bool ggml_vk_can_fuse_topk_moe(ggml_backend_vk_context * ctx, const struc
     return true;
 }
 
+static bool ggml_vk_can_fuse_rope_set_rows(ggml_backend_vk_context * ctx, const struct ggml_cgraph * cgraph,
+                                           int node_idx) {
+    GGML_UNUSED(ctx);
+    const ggml_tensor *rope = cgraph->nodes[node_idx + 0];
+    const ggml_tensor *view = cgraph->nodes[node_idx + 1];
+    const ggml_tensor *set_rows = cgraph->nodes[node_idx + 2];
+
+    // ne3 not tested
+    if (rope->src[0]->ne[3] != 1) {
+        return false;
+    }
+
+    if (set_rows->type != GGML_TYPE_F32 && set_rows->type != GGML_TYPE_F16) {
+        return false;
+    }
+
+    if (set_rows->src[1]->type != GGML_TYPE_I64) {
+        return false;
+    }
+
+    // The view should flatten two dims of rope into one dim
+    if (!ggml_is_contiguous(view) ||
+        view->ne[0] != rope->ne[0] * rope->ne[1]) {
+        return false;
+    }
+
+    // Only norm/neox shaders have the fusion code
+    const int mode = ((const int32_t *) rope->op_params)[2];
+    if (mode != GGML_ROPE_TYPE_NORMAL && mode != GGML_ROPE_TYPE_NEOX) {
+        return false;
+    }
+
+    return true;
+}
+
 static uint32_t ggml_vk_fuse_multi_add(ggml_backend_vk_context * ctx, const struct ggml_cgraph * cgraph, int node_idx) {
 
     const ggml_tensor *first_node = cgraph->nodes[node_idx];
@@ -12539,6 +12659,10 @@ static ggml_status ggml_backend_vk_graph_compute(ggml_backend_t backend, ggml_cg
                 ctx->num_additional_fused_ops = num_adds - 1;
             } else if (ggml_vk_can_fuse(cgraph, i, { GGML_OP_RMS_NORM, GGML_OP_MUL })) {
                 ctx->num_additional_fused_ops = 1;
+            } else if (ggml_can_fuse_subgraph(cgraph, i, { GGML_OP_ROPE, GGML_OP_VIEW, GGML_OP_SET_ROWS }, { i + 2 }) &&
+                       ggml_check_edges(cgraph, i, rope_view_set_rows_edges) &&
+                       ggml_vk_can_fuse_rope_set_rows(ctx, cgraph, i)) {
+                ctx->num_additional_fused_ops = 2;
             } else if (ggml_can_fuse_subgraph(cgraph, i, topk_moe_early_softmax_norm, { i + 3, i + 9 }) &&
                        ggml_check_edges(cgraph, i, topk_moe_early_softmax_norm_edges) &&
                        ggml_vk_can_fuse_topk_moe(ctx, cgraph, i, TOPK_MOE_EARLY_SOFTMAX_NORM)) {
@@ -12648,20 +12772,31 @@ static ggml_status ggml_backend_vk_graph_compute(ggml_backend_t backend, ggml_cg
                 ctx->num_additional_fused_ops = num_adds - 1;
             } else if (ggml_vk_can_fuse(cgraph, i, { GGML_OP_RMS_NORM, GGML_OP_MUL })) {
                 ctx->num_additional_fused_ops = 1;
+            } else if (ggml_can_fuse_subgraph(cgraph, i, { GGML_OP_ROPE, GGML_OP_VIEW, GGML_OP_SET_ROWS }, { i + 2 }) &&
+                       ggml_check_edges(cgraph, i, rope_view_set_rows_edges) &&
+                       ggml_vk_can_fuse_rope_set_rows(ctx, cgraph, i)) {
+                ctx->num_additional_fused_ops = 2;
             } else if (ggml_can_fuse_subgraph(cgraph, i, topk_moe_early_softmax_norm, { i + 3, i + 9 }) &&
                        ggml_check_edges(cgraph, i, topk_moe_early_softmax_norm_edges) &&
                        ggml_vk_can_fuse_topk_moe(ctx, cgraph, i, TOPK_MOE_EARLY_SOFTMAX_NORM)) {
                 ctx->num_additional_fused_ops = topk_moe_early_softmax_norm.size() - 1;
+                // view of argsort writes to memory
+                ctx->fused_ops_write_mask |= 1 << 3;
             } else if (ggml_can_fuse_subgraph(cgraph, i, topk_moe_early_softmax, { i + 3, i + 4 }) &&
                        ggml_check_edges(cgraph, i, topk_moe_early_softmax_edges) &&
                        ggml_vk_can_fuse_topk_moe(ctx, cgraph, i, TOPK_MOE_EARLY_SOFTMAX)) {
                 ctx->num_additional_fused_ops = topk_moe_early_softmax.size() - 1;
+                // view of argsort writes to memory
+                ctx->fused_ops_write_mask |= 1 << 3;
             } else if (ggml_can_fuse_subgraph(cgraph, i, topk_moe_late_softmax, { i + 1, i + 5 }) &&
                        ggml_check_edges(cgraph, i, topk_moe_late_softmax_edges) &&
                        ggml_vk_can_fuse_topk_moe(ctx, cgraph, i, TOPK_MOE_LATE_SOFTMAX)) {
                 ctx->num_additional_fused_ops = topk_moe_late_softmax.size() - 1;
+                // view of argsort writes to memory
+                ctx->fused_ops_write_mask |= 1 << 1;
             }
         }
+        ctx->fused_ops_write_mask |= 1 << ctx->num_additional_fused_ops;
 
         // Signal the almost_ready fence when the graph is mostly complete (< 20% remaining)
         bool almost_ready = (cgraph->n_nodes - i) < cgraph->n_nodes / 5;
@@ -12707,6 +12842,7 @@ static ggml_status ggml_backend_vk_graph_compute(ggml_backend_t backend, ggml_cg
         }
         i += ctx->num_additional_fused_ops;
         ctx->num_additional_fused_ops = 0;
+        ctx->fused_ops_write_mask = 0;
     }
 
     if (vk_perf_logger_enabled) {
@@ -12863,6 +12999,32 @@ static void ggml_vk_graph_optimize(ggml_backend_t backend, struct ggml_cgraph *
             }
             if (ok) {
                 current_set.push_back(j);
+                // Look for ROPE + VIEW + SET_ROWS and make them consecutive
+                if (graph->nodes[j]->op == GGML_OP_ROPE) {
+                    int view_idx = -1;
+                    int set_rows_idx = -1;
+                    for (int k = j+1; k < std::min(j + 10, graph->n_nodes); ++k) {
+                        if (view_idx == -1 &&
+                            graph->nodes[k]->op == GGML_OP_VIEW &&
+                            graph->nodes[k]->src[0] == graph->nodes[j]) {
+                            view_idx = k;
+                            continue;
+                        }
+                        if (view_idx != -1 &&
+                            set_rows_idx == -1 &&
+                            graph->nodes[k]->op == GGML_OP_SET_ROWS &&
+                            graph->nodes[k]->src[0] == graph->nodes[view_idx]) {
+                            set_rows_idx = k;
+                            break;
+                        }
+                    }
+                    if (set_rows_idx != -1) {
+                        current_set.push_back(view_idx);
+                        current_set.push_back(set_rows_idx);
+                        used[view_idx] = true;
+                        used[set_rows_idx] = true;
+                    }
+                }
             }
         }
         // Second pass grabs view nodes.
diff --git a/ggml/src/ggml-vulkan/vulkan-shaders/rope_head.glsl b/ggml/src/ggml-vulkan/vulkan-shaders/rope_head.glsl
index 50fc1f1e2d2..0eda186c8a3 100644
--- a/ggml/src/ggml-vulkan/vulkan-shaders/rope_head.glsl
+++ b/ggml/src/ggml-vulkan/vulkan-shaders/rope_head.glsl
@@ -10,6 +10,7 @@ layout (binding = 0) readonly buffer X {A_TYPE data_a[];};
 layout (binding = 1) readonly buffer Y {int data_pos[];};
 layout (binding = 2) readonly buffer Z {float data_ff[];};
 layout (binding = 3) writeonly buffer D {D_TYPE data_d[];};
+layout (binding = 4) readonly buffer I {uvec2 data_i[];}; // indices for set_rows
 
 layout (push_constant) uniform parameter {
     uint ncols;
@@ -27,6 +28,7 @@ layout (push_constant) uniform parameter {
     uint s2;
     int sections[4];
     uint is_back;
+    uint set_rows_stride;
 } p;
 
 float rope_yarn_ramp(const float low, const float high, const uint i0) {
diff --git a/ggml/src/ggml-vulkan/vulkan-shaders/rope_neox.comp b/ggml/src/ggml-vulkan/vulkan-shaders/rope_neox.comp
index 06e095bef96..9f4538155a0 100644
--- a/ggml/src/ggml-vulkan/vulkan-shaders/rope_neox.comp
+++ b/ggml/src/ggml-vulkan/vulkan-shaders/rope_neox.comp
@@ -16,12 +16,19 @@ void main() {
     const uint row_x     = row_dst % ne1;
     const uint channel_x = row_dst / ne1;
 
-    const uint idst = row_dst*ne0 + i0/2;
+    uint idst = row_dst*ne0 + i0/2;
     const uint ix   = channel_x*p.s2 + row_x*p.s1 + i0/2;
 
+    // Fusion optimization: ROPE + VIEW + SET_ROWS..
+    // The rope output is viewed as a 1D tensor and offset based on a row index in data_i.
+    if (p.set_rows_stride != 0) {
+        idst = row_x*ne0 + i0/2;
+        idst += data_i[channel_x].x * p.set_rows_stride;
+    }
+
     if (i0 >= p.n_dims) {
-        data_d[idst + i0/2 + 0] = data_a[ix + i0/2 + 0];
-        data_d[idst + i0/2 + 1] = data_a[ix + i0/2 + 1];
+        data_d[idst + i0/2 + 0] = D_TYPE(data_a[ix + i0/2 + 0]);
+        data_d[idst + i0/2 + 1] = D_TYPE(data_a[ix + i0/2 + 1]);
 
         return;
     }
diff --git a/ggml/src/ggml-vulkan/vulkan-shaders/rope_norm.comp b/ggml/src/ggml-vulkan/vulkan-shaders/rope_norm.comp
index 6ba95754090..f4209ed9582 100644
--- a/ggml/src/ggml-vulkan/vulkan-shaders/rope_norm.comp
+++ b/ggml/src/ggml-vulkan/vulkan-shaders/rope_norm.comp
@@ -16,12 +16,19 @@ void main() {
     const uint row_x     = row_dst % ne1;
     const uint channel_x = row_dst / ne1;
 
-    const uint idst = row_dst*ne0 + i0;
+    uint idst = row_dst*ne0 + i0;
     const uint ix   = channel_x*p.s2 + row_x*p.s1 + i0;
 
+    // Fusion optimization: ROPE + VIEW + SET_ROWS..
+    // The rope output is viewed as a 1D tensor and offset based on a row index in data_i.
+    if (p.set_rows_stride != 0) {
+        idst = row_x*ne0 + i0;
+        idst += data_i[channel_x].x * p.set_rows_stride;
+    }
+
     if (i0 >= p.n_dims) {
-        data_d[idst + 0] = data_a[ix + 0];
-        data_d[idst + 1] = data_a[ix + 1];
+        data_d[idst + 0] = D_TYPE(data_a[ix + 0]);
+        data_d[idst + 1] = D_TYPE(data_a[ix + 1]);
 
         return;
     }
diff --git a/ggml/src/ggml-vulkan/vulkan-shaders/vulkan-shaders-gen.cpp b/ggml/src/ggml-vulkan/vulkan-shaders/vulkan-shaders-gen.cpp
index 03fa016398c..e6ec589fb84 100644
--- a/ggml/src/ggml-vulkan/vulkan-shaders/vulkan-shaders-gen.cpp
+++ b/ggml/src/ggml-vulkan/vulkan-shaders/vulkan-shaders-gen.cpp
@@ -842,10 +842,14 @@ void process_shaders() {
     string_to_spv("rope_norm_f32", "rope_norm.comp", {{"A_TYPE", "float"}, {"D_TYPE", "float"}});
     string_to_spv("rope_norm_f16", "rope_norm.comp", {{"A_TYPE", "float16_t"}, {"D_TYPE", "float16_t"}});
     string_to_spv("rope_norm_f16_rte", "rope_norm.comp", {{"A_TYPE", "float16_t"}, {"D_TYPE", "float16_t"}, {"RTE16", "1"}});
+    string_to_spv("rope_norm_f32_f16", "rope_norm.comp", {{"A_TYPE", "float"}, {"D_TYPE", "float16_t"}});
+    string_to_spv("rope_norm_f32_f16_rte", "rope_norm.comp", {{"A_TYPE", "float"}, {"D_TYPE", "float16_t"}, {"RTE16", "1"}});
 
     string_to_spv("rope_neox_f32", "rope_neox.comp", {{"A_TYPE", "float"}, {"D_TYPE", "float"}});
     string_to_spv("rope_neox_f16", "rope_neox.comp", {{"A_TYPE", "float16_t"}, {"D_TYPE", "float16_t"}});
     string_to_spv("rope_neox_f16_rte", "rope_neox.comp", {{"A_TYPE", "float16_t"}, {"D_TYPE", "float16_t"}, {"RTE16", "1"}});
+    string_to_spv("rope_neox_f32_f16", "rope_neox.comp", {{"A_TYPE", "float"}, {"D_TYPE", "float16_t"}});
+    string_to_spv("rope_neox_f32_f16_rte", "rope_neox.comp", {{"A_TYPE", "float"}, {"D_TYPE", "float16_t"}, {"RTE16", "1"}});
 
     string_to_spv("rope_multi_f32", "rope_multi.comp", {{"A_TYPE", "float"}, {"D_TYPE", "float"}});
     string_to_spv("rope_multi_f16", "rope_multi.comp", {{"A_TYPE", "float16_t"}, {"D_TYPE", "float16_t"}});
diff --git a/tests/test-backend-ops.cpp b/tests/test-backend-ops.cpp
index aee17301379..3139119af7a 100644
--- a/tests/test-backend-ops.cpp
+++ b/tests/test-backend-ops.cpp
@@ -2125,6 +2125,34 @@ struct test_get_rows_back : public test_case {
     }
 };
 
+static void init_set_rows_row_ids(ggml_tensor * t, int num_rows) {
+    std::random_device rd;
+    std::default_random_engine rng(rd());
+    for (int i2 = 0; i2 < t->ne[2]; i2++) {
+        for (int i1 = 0; i1 < t->ne[1]; i1++) {
+            // generate a shuffled subset of row indices
+            std::vector<int64_t> data(num_rows);
+            for (int i = 0; i < num_rows; i++) {
+                data[i] = i;
+            }
+            std::shuffle(data.begin(), data.end(), rng);
+            data.resize(t->ne[0]);
+
+            const size_t offs = i1*t->nb[1] + i2*t->nb[2];
+            if (t->type == GGML_TYPE_I32) {
+                // TODO: Make a template or something
+                std::vector<int32_t> data_i32(t->ne[0]);
+                for (int i = 0; i < t->ne[0]; i++) {
+                    data_i32[i] = static_cast<int32_t>(data[i]);
+                }
+                ggml_backend_tensor_set(t, data_i32.data(), offs, t->ne[0]*sizeof(int32_t));
+            } else {
+                ggml_backend_tensor_set(t, data.data(), offs, t->ne[0]*sizeof(int64_t));
+            }
+        }
+    }
+}
+
 // GGML_OP_SET_ROWS
 struct test_set_rows : public test_case {
     const ggml_type type;
@@ -2168,37 +2196,13 @@ struct test_set_rows : public test_case {
     }
 
     void initialize_tensors(ggml_context * ctx) override {
-        std::random_device rd;
-        std::default_random_engine rng(rd());
         for (ggml_tensor * t = ggml_get_first_tensor(ctx); t != NULL; t = ggml_get_next_tensor(ctx, t)) {
             if (t->type == GGML_TYPE_I64 || t->type == GGML_TYPE_I32) {
                 if (ggml_is_view_op(t->op)) {
                     continue;
                 }
 
-                for (int i2 = 0; i2 < t->ne[2]; i2++) {
-                    for (int i1 = 0; i1 < t->ne[1]; i1++) {
-                        // generate a shuffled subset of row indices
-                        std::vector<int64_t> data(ne[1]);
-                        for (int i = 0; i < ne[1]; i++) {
-                            data[i] = i;
-                        }
-                        std::shuffle(data.begin(), data.end(), rng);
-                        data.resize(t->ne[0]);
-
-                        const size_t offs = i1*t->nb[1] + i2*t->nb[2];
-                        if (t->type == GGML_TYPE_I32) {
-                            // TODO: Make a template or something
-                            std::vector<int32_t> data_i32(t->ne[0]);
-                            for (int i = 0; i < t->ne[0]; i++) {
-                                data_i32[i] = static_cast<int32_t>(data[i]);
-                            }
-                            ggml_backend_tensor_set(t, data_i32.data(), offs, t->ne[0]*sizeof(int32_t));
-                        } else {
-                            ggml_backend_tensor_set(t, data.data(), offs, t->ne[0]*sizeof(int64_t));
-                        }
-                    }
-                }
+                init_set_rows_row_ids(t, ne[1]);
             } else {
                 init_tensor_uniform(t);
             }
@@ -2227,6 +2231,67 @@ struct test_set_rows : public test_case {
     }
 };
 
+// GGML_OP_ROPE + GGML_OP_VIEW + GGML_OP_SET_ROWS
+struct test_rope_set_rows : public test_case {
+    const ggml_type type;
+    const ggml_type type_idx;
+    const std::array<int64_t, 4> ne;
+    int mode;
+
+    std::string vars() override {
+        return VARS_TO_STR4(type, type_idx, ne, mode);
+    }
+
+    std::string op_desc(ggml_tensor * t) override {
+        GGML_UNUSED(t);
+        return "ROPE_SET_ROWS";
+    }
+
+    bool run_whole_graph() override { return true; }
+
+    test_rope_set_rows(ggml_type type,
+            ggml_type type_idx,
+            std::array<int64_t, 4> ne,
+            int mode)
+        : type(type), type_idx(type_idx), ne(ne), mode(mode) {}
+
+    ggml_tensor * build_graph(ggml_context * ctx) override {
+        ggml_tensor * src = ggml_new_tensor_4d(ctx, GGML_TYPE_F32, ne[0], ne[1], ne[2], 1);
+        ggml_set_name(src, "src");
+
+        ggml_tensor * pos = ggml_new_tensor_1d(ctx, GGML_TYPE_I32, ne[2]);
+
+        ggml_tensor * rope = ggml_rope(ctx, src, pos, ne[0], mode);
+
+        ggml_tensor * view = ggml_view_2d(ctx, rope, ne[0] * ne[1], ne[2], rope->nb[2], 0);
+
+        ggml_tensor * dst = ggml_new_tensor_4d(ctx, type, ne[0] * ne[1], ne[2] * ne[3], 1, 1);
+        ggml_set_name(dst, "dst");
+
+        ggml_tensor * row_idxs = ggml_new_tensor_3d(ctx, type_idx, ne[2], 1, 1);
+        ggml_set_name(row_idxs, "row_idxs");
+
+        ggml_tensor * out = ggml_set_rows(ctx, dst, view, row_idxs);
+        ggml_set_name(out, "out");
+
+        return out;
+    }
+
+    void initialize_tensors(ggml_context * ctx) override {
+        for (ggml_tensor * t = ggml_get_first_tensor(ctx); t != NULL; t = ggml_get_next_tensor(ctx, t)) {
+            if (t->type == GGML_TYPE_I64 || t->type == GGML_TYPE_I32) {
+                if (ggml_is_view_op(t->op)) {
+                    continue;
+                }
+
+                init_set_rows_row_ids(t, ne[2]);
+            } else {
+                init_tensor_uniform(t);
+            }
+        }
+    }
+};
+
 // GGML_OP_ARGMAX
 struct test_argmax : public test_case {
     const ggml_type type;
@@ -6163,6 +6228,13 @@ static std::vector<std::unique_ptr<test_case>> make_test_cases_eval() {
         }
     }
 
+    for (int mode : { GGML_ROPE_TYPE_NORMAL, GGML_ROPE_TYPE_NEOX }) {
+        for (ggml_type type : {GGML_TYPE_F16, GGML_TYPE_F32}) {
+            test_cases.emplace_back(new test_rope_set_rows(type, GGML_TYPE_I64, { 128, 32, 1, 100 }, mode));
+            test_cases.emplace_back(new test_rope_set_rows(type, GGML_TYPE_I64, { 128, 32, 512, 1 }, mode));
+        }
+    }
+
     for (ggml_type type_input : {GGML_TYPE_F32}) {
         for (ggml_op_pool pool_type : {GGML_OP_POOL_AVG, GGML_OP_POOL_MAX}) {
             for (int k0 : {1, 3}) {

From 8b11deea4663f29d3e042ce1056ba643264cd5f1 Mon Sep 17 00:00:00 2001
From: Oliver Simons <osimons@nvidia.com>
Date: Thu, 30 Oct 2025 04:34:15 +0100
Subject: [PATCH 015/185] Hide latency of bias and gate-loading (#16847)

This is realised by loading them into registers before computation of
the dot-product, effectively batching them together with said
dot-product. As a lot of threads are alive here, the warp scheduler has
enough threads available to effectively hide the cost of additionally
loading those two floats.
---
 ggml/src/ggml-cuda/mmvq.cu | 20 ++++++++++++++++++--
 1 file changed, 18 insertions(+), 2 deletions(-)

diff --git a/ggml/src/ggml-cuda/mmvq.cu b/ggml/src/ggml-cuda/mmvq.cu
index be04a85cc55..07645ad9e71 100644
--- a/ggml/src/ggml-cuda/mmvq.cu
+++ b/ggml/src/ggml-cuda/mmvq.cu
@@ -190,12 +190,28 @@ static __global__ void mul_mat_vec_q(
 
     const uint32_t channel_bias = ids ? channel_x : channel_dst;
 
+    float x_biases[ncols_dst][rows_per_cuda_block]    = { { 0.0f } };
+    float gate_biases[ncols_dst][rows_per_cuda_block] = { { 0.0f } };
     if constexpr (has_fusion) {
         if (use_bias) {
             x_bias = x_bias + sample_dst*stride_sample_dst + channel_bias*stride_channel_dst + row0;
+            // 1. Hide latency by prefetching bias and gate here
+            // 2. load only on threads that won't die after partial sum calculation
+            if (threadIdx.x < rows_per_cuda_block && threadIdx.y == 0 &&
+                (rows_per_cuda_block == 1 || uint32_t(row0 + threadIdx.x) < stride_col_dst)) {
+                for (int j = 0; j < ncols_dst; ++j) {
+                    x_biases[j][threadIdx.x] = x_bias[j * stride_col_dst + threadIdx.x];
+                }
+            }
         }
         if (use_gate_bias) {
             gate_bias = gate_bias + sample_dst*stride_sample_dst + channel_bias*stride_channel_dst + row0;
+            if (threadIdx.x < rows_per_cuda_block && threadIdx.y == 0 &&
+                (rows_per_cuda_block == 1 || uint32_t(row0 + threadIdx.x) < stride_col_dst)) {
+                for (int j = 0; j < ncols_dst; ++j) {
+                    gate_biases[j][threadIdx.x] = gate_bias[j * stride_col_dst + threadIdx.x];
+                }
+            }
         }
     }
 
@@ -283,12 +299,12 @@ static __global__ void mul_mat_vec_q(
             float result = tmp[j][threadIdx.x];
             if constexpr (has_fusion) {
                 if (use_bias) {
-                    result += x_bias[j*stride_col_dst + threadIdx.x];
+                    result += x_biases[j][threadIdx.x];
                 }
                 if (use_gate) {
                     float gate_value = tmp_gate[j][threadIdx.x];
                     if (use_gate_bias) {
-                        gate_value += gate_bias[j*stride_col_dst + threadIdx.x];
+                        gate_value += gate_biases[j][threadIdx.x];
                     }
                     switch (active_glu) {
                         case GGML_GLU_OP_SWIGLU:

From 052df28b0e3ca0398e5928c61c7de40254317894 Mon Sep 17 00:00:00 2001
From: Jeff Bolz <jbolz@nvidia.com>
Date: Thu, 30 Oct 2025 01:27:41 -0500
Subject: [PATCH 016/185] vulkan: Handle argsort with a large number of rows
 (#16851)

---
 ggml/src/ggml-vulkan/ggml-vulkan.cpp             |  4 ++++
 ggml/src/ggml-vulkan/vulkan-shaders/argsort.comp | 16 ++++++++++++----
 2 files changed, 16 insertions(+), 4 deletions(-)

diff --git a/ggml/src/ggml-vulkan/ggml-vulkan.cpp b/ggml/src/ggml-vulkan/ggml-vulkan.cpp
index 8a9f5980ea8..d0976519f26 100644
--- a/ggml/src/ggml-vulkan/ggml-vulkan.cpp
+++ b/ggml/src/ggml-vulkan/ggml-vulkan.cpp
@@ -1082,6 +1082,7 @@ struct vk_op_soft_max_push_constants {
 
 struct vk_op_argsort_push_constants {
     uint32_t ncols;
+    uint32_t nrows;
     int32_t order;
 };
 
@@ -8708,6 +8709,7 @@ static void ggml_vk_op_f32(ggml_backend_vk_context * ctx, vk_context& subctx, co
         break;
     case GGML_OP_ARGSORT:
         elements = { (uint32_t)ne00, (uint32_t)ggml_nrows(src0), 1 };
+        elements[1] = std::min(elements[1], ctx->device->properties.limits.maxComputeWorkGroupCount[1]);
         break;
     case GGML_OP_IM2COL:
         {
@@ -9954,9 +9956,11 @@ static void ggml_vk_argsort(ggml_backend_vk_context * ctx, vk_context& subctx, c
     int32_t * op_params = (int32_t *)dst->op_params;
 
     uint32_t ncols = src0->ne[0];
+    uint32_t nrows = ggml_nrows(src0);
 
     ggml_vk_op_f32<vk_op_argsort_push_constants>(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_ARGSORT, {
         ncols,
+        nrows,
         op_params[0],
     }, dryrun);
 }
diff --git a/ggml/src/ggml-vulkan/vulkan-shaders/argsort.comp b/ggml/src/ggml-vulkan/vulkan-shaders/argsort.comp
index c81b84452e7..c4e68bc0237 100644
--- a/ggml/src/ggml-vulkan/vulkan-shaders/argsort.comp
+++ b/ggml/src/ggml-vulkan/vulkan-shaders/argsort.comp
@@ -14,6 +14,7 @@ layout (binding = 1)          buffer D {int data_d[];};
 
 layout (push_constant) uniform parameter {
     uint ncols;
+    uint nrows;
     uint order;
 } p;
 
@@ -26,10 +27,9 @@ void swap(uint idx0, uint idx1) {
     dst_row[idx1] = tmp;
 }
 
-void argsort(bool needs_bounds_check) {
+void argsort(bool needs_bounds_check, const uint row) {
     // bitonic sort
     const int col = int(gl_LocalInvocationID.x);
-    const uint row = gl_WorkGroupID.y;
 
     const uint row_offset = row * p.ncols;
 
@@ -72,8 +72,16 @@ void argsort(bool needs_bounds_check) {
 
 void main() {
     if (p.ncols == BLOCK_SIZE) {
-        argsort(false);
+        uint row = gl_WorkGroupID.y;
+        while (row < p.nrows) {
+            argsort(false, row);
+            row += gl_WorkGroupSize.y * gl_NumWorkGroups.y;
+        }
     } else {
-        argsort(true);
+        uint row = gl_WorkGroupID.y;
+        while (row < p.nrows) {
+            argsort(true, row);
+            row += gl_WorkGroupSize.y * gl_NumWorkGroups.y;
+        }
     }
 }

From d7395115baf395b75a73a17b0b796e746e468da9 Mon Sep 17 00:00:00 2001
From: Jan Boon <jan.boon@kaetemi.be>
Date: Thu, 30 Oct 2025 14:30:58 +0800
Subject: [PATCH 017/185] llama : use std::abs instead of abs (#16853)

---
 src/llama-graph.cpp | 2 +-
 src/llama-quant.cpp | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/src/llama-graph.cpp b/src/llama-graph.cpp
index 112d195f291..f9751b31836 100644
--- a/src/llama-graph.cpp
+++ b/src/llama-graph.cpp
@@ -2035,7 +2035,7 @@ int32_t llama_relative_position_bucket(llama_pos x, llama_pos y, uint64_t n_buck
 
     if (bidirectional) {
         relative_bucket += (relative_position > 0) * n_buckets;
-        relative_position = abs(relative_position);
+        relative_position = std::abs(relative_position);
     } else {
         relative_position = -std::min<int32_t>(relative_position, 0);
     }
diff --git a/src/llama-quant.cpp b/src/llama-quant.cpp
index 6dd40412b48..a56b2626ae1 100644
--- a/src/llama-quant.cpp
+++ b/src/llama-quant.cpp
@@ -653,7 +653,7 @@ static void llama_model_quantize_impl(const std::string & fname_inp, const std::
                 gguf_set_val_f32(ctx_out.get(), o.key, o.val_f64);
             } else if (o.tag == LLAMA_KV_OVERRIDE_TYPE_INT) {
                 // Setting type to UINT32. See https://github.com/ggml-org/llama.cpp/pull/14182 for context
-                gguf_set_val_u32(ctx_out.get(), o.key, (uint32_t)abs(o.val_i64));
+                gguf_set_val_u32(ctx_out.get(), o.key, (uint32_t)std::abs(o.val_i64));
             } else if (o.tag == LLAMA_KV_OVERRIDE_TYPE_BOOL) {
                 gguf_set_val_bool(ctx_out.get(), o.key, o.val_bool);
             } else if (o.tag == LLAMA_KV_OVERRIDE_TYPE_STR) {

From 229bf686287d18f82c44e89888cc662145ecfdb4 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sigbj=C3=B8rn=20Skj=C3=A6ret?= <sigbjorn.skjaeret@scala.com>
Date: Thu, 30 Oct 2025 08:56:28 +0100
Subject: [PATCH 018/185] cuda : fix argsort with 64k+ rows (#16849)

---
 ggml/src/ggml-cuda/argsort.cu | 4 ++--
 tests/test-backend-ops.cpp    | 3 ++-
 2 files changed, 4 insertions(+), 3 deletions(-)

diff --git a/ggml/src/ggml-cuda/argsort.cu b/ggml/src/ggml-cuda/argsort.cu
index 6e7b90d4278..3722cf3ab26 100644
--- a/ggml/src/ggml-cuda/argsort.cu
+++ b/ggml/src/ggml-cuda/argsort.cu
@@ -87,7 +87,7 @@ template<ggml_sort_order order>
 static __global__ void k_argsort_f32_i32(const float * x, int * dst, const int ncols, int ncols_pad) {
     // bitonic sort
     int col = threadIdx.x;
-    int row = blockIdx.y;
+    int row = blockIdx.x;
 
     if (col >= ncols_pad) {
         return;
@@ -151,7 +151,7 @@ static void argsort_f32_i32_cuda_bitonic(const float *   x,
     const int ncols_pad = next_power_of_2(ncols);
 
     const dim3 block_dims(ncols_pad, 1, 1);
-    const dim3 block_nums(1, nrows, 1);
+    const dim3 block_nums(nrows, 1, 1);
     const size_t shared_mem = ncols_pad * sizeof(int);
 
     // FIXME: this limit could be raised by ~2-4x on Ampere or newer
diff --git a/tests/test-backend-ops.cpp b/tests/test-backend-ops.cpp
index 3139119af7a..4b1304c2b89 100644
--- a/tests/test-backend-ops.cpp
+++ b/tests/test-backend-ops.cpp
@@ -7111,7 +7111,8 @@ static std::vector<std::unique_ptr<test_case>> make_test_cases_eval() {
         test_cases.emplace_back(new test_argsort(GGML_TYPE_F32, {16, 10, 10, 10}, order));
         test_cases.emplace_back(new test_argsort(GGML_TYPE_F32, {60, 10, 10, 10}, order)); // qwen
         test_cases.emplace_back(new test_argsort(GGML_TYPE_F32, {1024, 1, 1, 1}, order));
-        test_cases.emplace_back(new test_argsort(GGML_TYPE_F32, {16384, 1, 1, 1}, order)); // bailingmoe2 (group selection)
+        test_cases.emplace_back(new test_argsort(GGML_TYPE_F32, {16384, 1, 1, 1}, order)); // many backends only handle up to 1024
+        test_cases.emplace_back(new test_argsort(GGML_TYPE_F32, {2, 8, 8192, 1}, order)); // bailingmoe2 (group selection)
     }
 
     for (ggml_scale_mode mode : {GGML_SCALE_MODE_NEAREST, GGML_SCALE_MODE_BILINEAR}) {

From bacddc049a00786df44e682262f6e298742bfbc3 Mon Sep 17 00:00:00 2001
From: Tianyue-Zhao <zhaotianyue@outlook.com>
Date: Thu, 30 Oct 2025 07:18:50 -0400
Subject: [PATCH 019/185] model: Add support for CogVLM model (#15002)

* Added GGUF mappings for CogVLM model

* Add tensor mapping for CogVLM visual encoder

* Add CogVLM to conversion script, no vision part yet

* Added CogVLM vision model to conversion script

* Add graph for CogVLM CLIP model

* Add graph for CogVLM

* Fixes for CogVLM. Now compiles.

* Model now runs

* Fixes for cogvlm graph

* Account for graph context change after rebase

* Changes for whitespace

* Changes in convert script according to comments

* Switch CogVLM LLM graph to merged QKV tensor

* Use rope_type variable instead of direct definition

* Change CogVLM CLIP encoder to use SWIGLU

* Switch CogVLM CLIP to use merged QKV

* Apply rebase edits and remove ggml_cont call that is now unnecessary

* clean up

---------

Co-authored-by: Xuan Son Nguyen <son@huggingface.co>
---
 convert_hf_to_gguf.py          |  33 ++++++-
 gguf-py/gguf/constants.py      |  52 ++++++++++++
 gguf-py/gguf/tensor_mapping.py |  95 +++++++++++++++++----
 src/llama-arch.cpp             |  26 ++++++
 src/llama-arch.h               |   6 ++
 src/llama-model.cpp            | 146 +++++++++++++++++++++++++++++++
 src/llama-model.h              |   7 ++
 tools/mtmd/clip-impl.h         |  11 +++
 tools/mtmd/clip.cpp            | 151 ++++++++++++++++++++++++++++++---
 9 files changed, 501 insertions(+), 26 deletions(-)

diff --git a/convert_hf_to_gguf.py b/convert_hf_to_gguf.py
index b7593666843..0fd8d5681d7 100755
--- a/convert_hf_to_gguf.py
+++ b/convert_hf_to_gguf.py
@@ -1528,7 +1528,7 @@ def set_gguf_parameters(self):
             self.gguf_writer.add_vision_embedding_length(self.find_vparam(["hidden_size"]))
             self.gguf_writer.add_vision_feed_forward_length(self.find_vparam(["intermediate_size"]))
             self.gguf_writer.add_vision_block_count(self.find_vparam(self.n_block_keys))
-            self.gguf_writer.add_vision_head_count(self.find_vparam(["num_attention_heads"]))
+            self.gguf_writer.add_vision_head_count(self.find_vparam(["num_attention_heads", "num_heads"]))
 
             # preprocessor config
             image_mean = _MISTRAL_COMMON_DATASET_MEAN if self.is_mistral_format else self.preprocessor_config["image_mean"]
@@ -9493,6 +9493,37 @@ def modify_tensors(self, data_torch: Tensor, name: str, bid: int | None) -> Iter
 
         return [] # skip other tensors
 
+
+@ModelBase.register("CogVLMForCausalLM")
+class CogVLMVisionModel(MmprojModel):
+
+    def set_gguf_parameters(self):
+        super().set_gguf_parameters()
+        self.gguf_writer.add_vision_attention_layernorm_eps(self.hparams.get("layer_norm_eps", 1e-6))
+        self.gguf_writer.add_clip_projector_type(gguf.VisionProjectorType.COGVLM)
+
+    def modify_tensors(self, data_torch: Tensor, name: str, bid: int | None) -> Iterable[tuple[str, Tensor]]:
+        del bid  # unused
+
+        if not name.startswith("model.vision."):
+            return []
+
+        return [(self.map_tensor_name(name), data_torch)]
+
+
+@ModelBase.register("CogVLMForCausalLM")
+class CogVLMModel(LlamaModel):
+    model_arch = gguf.MODEL_ARCH.COGVLM
+
+    def modify_tensors(self, data_torch: Tensor, name: str, bid: int | None) -> Iterable[tuple[str, Tensor]]:
+        del bid  # unused
+
+        # block vision tensors
+        if name.startswith("model.vision."):
+            return []
+
+        return [(self.map_tensor_name(name), data_torch)]
+
 ###### CONVERSION LOGIC ######
 
 
diff --git a/gguf-py/gguf/constants.py b/gguf-py/gguf/constants.py
index 94fcfaf69cf..a0c08f69172 100644
--- a/gguf-py/gguf/constants.py
+++ b/gguf-py/gguf/constants.py
@@ -420,6 +420,7 @@ class MODEL_ARCH(IntEnum):
     SEED_OSS         = auto()
     GROVEMOE         = auto()
     APERTUS          = auto()
+    COGVLM           = auto()
 
 
 class VISION_PROJECTOR_TYPE(IntEnum):
@@ -430,6 +431,7 @@ class VISION_PROJECTOR_TYPE(IntEnum):
     GLM_EDGE  = auto()
     MERGER    = auto()
     GEMMA3    = auto()
+    COGVLM    = auto()
 
 
 class MODEL_TENSOR(IntEnum):
@@ -600,6 +602,11 @@ class MODEL_TENSOR(IntEnum):
     SHORTCONV_CONV       = auto()
     SHORTCONV_INPROJ     = auto()
     SHORTCONV_OUTPROJ    = auto()
+    VISEXP_ATTN_QKV      = auto()
+    VISEXP_ATTN_OUT      = auto()
+    VISEXP_GATE          = auto()
+    VISEXP_DOWN          = auto()
+    VISEXP_UP            = auto()
     # vision
     V_MMPROJ             = auto()
     V_MMPROJ_FC          = auto()
@@ -609,6 +616,7 @@ class MODEL_TENSOR(IntEnum):
     V_ENC_EMBD_PATCH     = auto()
     V_ENC_EMBD_POS       = auto()
     V_ENC_INPUT_NORM     = auto()
+    V_ENC_ATTN_QKV       = auto()
     V_ENC_ATTN_Q         = auto()
     V_ENC_ATTN_Q_NORM    = auto()
     V_ENC_ATTN_K         = auto()
@@ -640,6 +648,12 @@ class MODEL_TENSOR(IntEnum):
     V_RESMPL_QUERY       = auto() # minicpmv
     V_TOK_EMBD_IMG_BREAK = auto() # pixtral
     V_MM_PATCH_MERGER    = auto() # mistral small 3.1
+    V_MM_POST_FC_NORM    = auto() # cogvlm
+    V_MM_UP              = auto() # cogvlm
+    V_MM_DOWN            = auto() # cogvlm
+    V_MM_GATE            = auto() # cogvlm
+    V_TOK_BOI            = auto() # cogvlm
+    V_TOK_EOI            = auto() # cogvlm
     # audio (mtmd)
     A_ENC_EMBD_POS       = auto()
     A_ENC_CONV1D         = auto()
@@ -766,6 +780,7 @@ class MODEL_TENSOR(IntEnum):
     MODEL_ARCH.SEED_OSS:         "seed_oss",
     MODEL_ARCH.GROVEMOE:         "grovemoe",
     MODEL_ARCH.APERTUS:          "apertus",
+    MODEL_ARCH.COGVLM:           "cogvlm",
 }
 
 VISION_PROJECTOR_TYPE_NAMES: dict[VISION_PROJECTOR_TYPE, str] = {
@@ -946,6 +961,11 @@ class MODEL_TENSOR(IntEnum):
     MODEL_TENSOR.SHORTCONV_CONV:            "blk.{bid}.shortconv.conv",
     MODEL_TENSOR.SHORTCONV_INPROJ:          "blk.{bid}.shortconv.in_proj",
     MODEL_TENSOR.SHORTCONV_OUTPROJ:         "blk.{bid}.shortconv.out_proj",
+    MODEL_TENSOR.VISEXP_ATTN_QKV:           "blk.{bid}.vis_attn_qkv",
+    MODEL_TENSOR.VISEXP_ATTN_OUT:           "blk.{bid}.vis_attn_output",
+    MODEL_TENSOR.VISEXP_GATE:               "blk.{bid}.vis_gate",
+    MODEL_TENSOR.VISEXP_DOWN:               "blk.{bid}.vis_down",
+    MODEL_TENSOR.VISEXP_UP:                 "blk.{bid}.vis_up",
     # vision
     MODEL_TENSOR.V_MMPROJ:                  "mm.{bid}",
     MODEL_TENSOR.V_MMPROJ_FC:               "mm.model.fc",
@@ -954,6 +974,7 @@ class MODEL_TENSOR(IntEnum):
     MODEL_TENSOR.V_ENC_EMBD_CLS:            "v.class_embd",
     MODEL_TENSOR.V_ENC_EMBD_PATCH:          "v.patch_embd",
     MODEL_TENSOR.V_ENC_EMBD_POS:            "v.position_embd",
+    MODEL_TENSOR.V_ENC_ATTN_QKV:            "v.blk.{bid}.attn_qkv",
     MODEL_TENSOR.V_ENC_ATTN_Q:              "v.blk.{bid}.attn_q",
     MODEL_TENSOR.V_ENC_ATTN_Q_NORM:         "v.blk.{bid}.attn_q_norm",
     MODEL_TENSOR.V_ENC_ATTN_K:              "v.blk.{bid}.attn_k",
@@ -986,6 +1007,12 @@ class MODEL_TENSOR(IntEnum):
     MODEL_TENSOR.V_RESMPL_QUERY:            "resampler.query",
     MODEL_TENSOR.V_TOK_EMBD_IMG_BREAK:      "v.token_embd.img_break", # pixtral
     MODEL_TENSOR.V_MM_PATCH_MERGER:         "mm.patch_merger", # mistral small 3.1
+    MODEL_TENSOR.V_MM_POST_FC_NORM:         "mm.post_fc_norm", # cogvlm
+    MODEL_TENSOR.V_MM_UP:                   "mm.up",
+    MODEL_TENSOR.V_MM_DOWN:                 "mm.down",
+    MODEL_TENSOR.V_MM_GATE:                 "mm.gate",
+    MODEL_TENSOR.V_TOK_BOI:                 "v.boi",
+    MODEL_TENSOR.V_TOK_EOI:                 "v.eoi",
     # audio (mtmd)
     MODEL_TENSOR.A_ENC_EMBD_POS:            "a.position_embd",
     MODEL_TENSOR.A_ENC_CONV1D:              "a.conv1d.{bid}",
@@ -1023,6 +1050,7 @@ class MODEL_TENSOR(IntEnum):
         MODEL_TENSOR.V_ENC_EMBD_PATCH,
         MODEL_TENSOR.V_ENC_EMBD_POS,
         MODEL_TENSOR.V_ENC_INPUT_NORM,
+        MODEL_TENSOR.V_ENC_ATTN_QKV,
         MODEL_TENSOR.V_ENC_ATTN_Q,
         MODEL_TENSOR.V_ENC_ATTN_Q_NORM,
         MODEL_TENSOR.V_ENC_ATTN_K,
@@ -1054,6 +1082,12 @@ class MODEL_TENSOR(IntEnum):
         MODEL_TENSOR.V_RESMPL_QUERY,
         MODEL_TENSOR.V_TOK_EMBD_IMG_BREAK,
         MODEL_TENSOR.V_MM_PATCH_MERGER,
+        MODEL_TENSOR.V_MM_POST_FC_NORM,
+        MODEL_TENSOR.V_MM_UP,
+        MODEL_TENSOR.V_MM_DOWN,
+        MODEL_TENSOR.V_MM_GATE,
+        MODEL_TENSOR.V_TOK_BOI,
+        MODEL_TENSOR.V_TOK_EOI,
         # audio
         MODEL_TENSOR.A_ENC_EMBD_POS,
         MODEL_TENSOR.A_ENC_CONV1D,
@@ -2837,6 +2871,23 @@ class MODEL_TENSOR(IntEnum):
         MODEL_TENSOR.FFN_DOWN_CHEXP,
         MODEL_TENSOR.FFN_UP_CHEXP,
     ],
+    MODEL_ARCH.COGVLM: [
+        MODEL_TENSOR.TOKEN_EMBD,
+        MODEL_TENSOR.OUTPUT_NORM,
+        MODEL_TENSOR.OUTPUT,
+        MODEL_TENSOR.ATTN_NORM,
+        MODEL_TENSOR.ATTN_QKV,
+        MODEL_TENSOR.ATTN_OUT,
+        MODEL_TENSOR.FFN_NORM,
+        MODEL_TENSOR.FFN_GATE,
+        MODEL_TENSOR.FFN_DOWN,
+        MODEL_TENSOR.FFN_UP,
+        MODEL_TENSOR.VISEXP_ATTN_QKV,
+        MODEL_TENSOR.VISEXP_ATTN_OUT,
+        MODEL_TENSOR.VISEXP_GATE,
+        MODEL_TENSOR.VISEXP_UP,
+        MODEL_TENSOR.VISEXP_DOWN,
+    ],
     # TODO
 }
 
@@ -3063,6 +3114,7 @@ class VisionProjectorType:
     LFM2 = "lfm2"
     KIMIVL = "kimivl"
     LIGHTONOCR = "lightonocr"
+    COGVLM = "cogvlm"
 
 
 # Items here are (block size, type size)
diff --git a/gguf-py/gguf/tensor_mapping.py b/gguf-py/gguf/tensor_mapping.py
index d7dcd8efb84..37e6fc85d51 100644
--- a/gguf-py/gguf/tensor_mapping.py
+++ b/gguf-py/gguf/tensor_mapping.py
@@ -104,6 +104,7 @@ class TensorNameMap:
             "backbone.final_layer_norm",               # wavtokenizer
             "model.norm",                              # llama4
             "model.transformer.ln_f",                  # llada
+            "model.norm",                              # cogvlm
         ),
 
         # Rope frequencies
@@ -162,6 +163,7 @@ class TensorNameMap:
             "encoder.layer.{bid}.layer_norm_1",             # jina-v2-code
             "rwkv.blocks.{bid}.ln2",                        # rwkv6
             "model.layers.{bid}.ln2",                       # rwkv7
+            "model.layers.{bid}.post_attention_layernorm",  # cogvlm
         ),
 
         # Attention query-key-value
@@ -184,6 +186,7 @@ class TensorNameMap:
             "encoder.layers.{bid}.self_attention.query_key_value",                 # chatglm
             "transformer.layers.{bid}.attn.qkv_proj",                              # openelm
             "transformer_encoder.{bid}.qkv",                                       # neobert
+            "model.layers.{bid}.self_attn.language_expert_query_key_value",        # cogvlm
         ),
 
         # Attention query
@@ -279,6 +282,7 @@ class TensorNameMap:
             "model.transformer.blocks.{bid}.attn_out",                      # llada
             "layers.{bid}.self_attn.o_proj",                                # qwen3-embedding
             "backbone.layers.{bid}.mixer.o_proj",                           # nemotron-h
+            "model.layers.{bid}.self_attn.language_expert_dense",           # cogvlm
         ),
 
         # Attention output norm
@@ -418,6 +422,7 @@ class TensorNameMap:
             "model.transformer.blocks.{bid}.up_proj",                 # llada
             "layers.{bid}.mlp.up_proj",                               # qwen3-embedding
             "backbone.layers.{bid}.mixer.up_proj",                    # nemotron-h
+            "model.layers.{bid}.mlp.language_mlp.up_proj",            # cogvlm
         ),
 
         MODEL_TENSOR.FFN_UP_EXP: (
@@ -450,21 +455,22 @@ class TensorNameMap:
 
         # Feed-forward gate
         MODEL_TENSOR.FFN_GATE: (
-            "model.layers.{bid}.mlp.gate_proj",           # llama-hf refact olmo2
-            "layers.{bid}.mlp.gate_proj",                 # embeddinggemma
-            "layers.{bid}.feed_forward.w1",               # llama-pth
-            "transformer.h.{bid}.mlp.w2",                 # qwen
-            "transformer.h.{bid}.mlp.c_fc2",              # jais
-            "model.layers.layers.{bid}.mlp.gate_proj",    # plamo
-            "model.layers.{bid}.feed_forward.w1",         # internlm2
-            "encoder.layers.{bid}.mlp.fc12",              # nomic-bert
-            "encoder.layer.{bid}.mlp.gated_layers_w",     # jina-bert-v2 (split up/gate, no longer used)
-            "transformer.h.{bid}.mlp.linear_1",           # refact
-            "model.layers.{bid}.residual_mlp.w1",         # arctic
-            "transformer.h.{bid}.mlp.c_fc_0",             # exaone
-            "model.layers.{bid}.feed_forward.gate_proj",  # llama4 jamba granite-hybrid
-            "model.transformer.blocks.{bid}.ff_proj",     # llada
-            "layers.{bid}.mlp.gate_proj",                 # qwen3-embedding
+            "model.layers.{bid}.mlp.gate_proj",               # llama-hf refact olmo2
+            "layers.{bid}.mlp.gate_proj",                     # embeddinggemma
+            "layers.{bid}.feed_forward.w1",                   # llama-pth
+            "transformer.h.{bid}.mlp.w2",                     # qwen
+            "transformer.h.{bid}.mlp.c_fc2",                  # jais
+            "model.layers.layers.{bid}.mlp.gate_proj",        # plamo
+            "model.layers.{bid}.feed_forward.w1",             # internlm2
+            "encoder.layers.{bid}.mlp.fc12",                  # nomic-bert
+            "encoder.layer.{bid}.mlp.gated_layers_w",         # jina-bert-v2 (split up/gate, no longer used)
+            "transformer.h.{bid}.mlp.linear_1",               # refact
+            "model.layers.{bid}.residual_mlp.w1",             # arctic
+            "transformer.h.{bid}.mlp.c_fc_0",                 # exaone
+            "model.layers.{bid}.feed_forward.gate_proj",      # llama4 jamba granite-hybrid
+            "model.transformer.blocks.{bid}.ff_proj",         # llada
+            "layers.{bid}.mlp.gate_proj",                     # qwen3-embedding
+            "model.layers.{bid}.mlp.language_mlp.gate_proj",  # cogvlm
         ),
 
         MODEL_TENSOR.FFN_GATE_EXP: (
@@ -522,6 +528,7 @@ class TensorNameMap:
             "model.transformer.blocks.{bid}.ff_out",                  # llada
             "layers.{bid}.mlp.down_proj",                             # qwen3-embedding
             "backbone.layers.{bid}.mixer.down_proj",                  # nemotron-h
+            "model.layers.{bid}.mlp.language_mlp.down_proj",          # cogvlm
         ),
 
         MODEL_TENSOR.FFN_DOWN_EXP: (
@@ -1047,6 +1054,26 @@ class TensorNameMap:
             "encoder.block.{bid}.layer.1.DenseReluDense.wo", # t5
         ),
 
+        MODEL_TENSOR.VISEXP_UP: (
+            "model.layers.{bid}.mlp.vision_mlp.up_proj",  # cogvlm
+        ),
+
+        MODEL_TENSOR.VISEXP_GATE: (
+            "model.layers.{bid}.mlp.vision_mlp.gate_proj",  # cogvlm
+        ),
+
+        MODEL_TENSOR.VISEXP_DOWN: (
+            "model.layers.{bid}.mlp.vision_mlp.down_proj",  # cogvlm
+        ),
+
+        MODEL_TENSOR.VISEXP_ATTN_OUT: (
+            "model.layers.{bid}.self_attn.vision_expert_dense",  # cogvlm
+        ),
+
+        MODEL_TENSOR.VISEXP_ATTN_QKV: (
+            "model.layers.{bid}.self_attn.vision_expert_query_key_value",  # cogvlm
+        ),
+
         ############################################################################
         # TODO: these do not belong to block_mappings_cfg - move them to mappings_cfg
         MODEL_TENSOR.ENC_OUTPUT_NORM: (
@@ -1148,6 +1175,7 @@ class TensorNameMap:
 
         MODEL_TENSOR.V_MMPROJ_FC: (
             "model.connector.modality_projection.proj", # SmolVLM
+            "model.vision.linear_proj.linear_proj", # cogvlm
         ),
 
         MODEL_TENSOR.V_MMPROJ_MLP: (
@@ -1164,6 +1192,7 @@ class TensorNameMap:
             "vision_tower.vision_model.embeddings.class_embedding",
             "model.vision_tower.embeddings.cls_token", # Intern-S1
             "vision_model.class_embedding", # llama 4
+            "model.vision.patch_embedding.cls_embedding", # cogvlm
         ),
 
         MODEL_TENSOR.V_ENC_EMBD_PATCH: (
@@ -1176,6 +1205,7 @@ class TensorNameMap:
             "vision_model.patch_embedding.linear", # llama 4
             "visual.patch_embed.proj", # qwen2vl
             "vision_tower.patch_embed.proj", # kimi-vl
+            "model.vision.patch_embedding.proj", # cogvlm
         ),
 
         MODEL_TENSOR.V_ENC_EMBD_POS: (
@@ -1185,6 +1215,11 @@ class TensorNameMap:
             "model.vision_model.embeddings.position_embedding", # SmolVLM
             "vision_model.positional_embedding_vlm", # llama 4
             "vision_tower.patch_embed.pos_emb", # kimi-vl
+            "model.vision.patch_embedding.position_embedding", # cogvlm
+        ),
+
+        MODEL_TENSOR.V_ENC_ATTN_QKV: (
+            "model.vision.transformer.layers.{bid}.attention.query_key_value", # cogvlm
         ),
 
         MODEL_TENSOR.V_ENC_ATTN_Q: (
@@ -1244,6 +1279,7 @@ class TensorNameMap:
             "vision_model.model.layers.{bid}.input_layernorm", # llama4
             "visual.blocks.{bid}.norm1", # qwen2vl
             "vision_tower.encoder.blocks.{bid}.norm0", # kimi-vl (norm0/norm1)
+            "model.vision.transformer.layers.{bid}.input_layernorm", # cogvlm
         ),
 
         MODEL_TENSOR.V_ENC_ATTN_O: (
@@ -1257,6 +1293,7 @@ class TensorNameMap:
             "vision_encoder.transformer.layers.{bid}.attention.wo", # pixtral
             "visual.blocks.{bid}.attn.proj", # qwen2vl
             "vision_tower.encoder.blocks.{bid}.wo", # kimi-vl
+            "model.vision.transformer.layers.{bid}.attention.dense", # cogvlm
         ),
 
         MODEL_TENSOR.V_ENC_POST_ATTN_NORM: (
@@ -1270,6 +1307,7 @@ class TensorNameMap:
             "vision_encoder.transformer.layers.{bid}.ffn_norm", # pixtral
             "visual.blocks.{bid}.norm2", # qwen2vl
             "vision_tower.encoder.blocks.{bid}.norm1", # kimi-vl (norm0/norm1)
+            "model.vision.transformer.layers.{bid}.post_attention_layernorm", # cogvlm
         ),
 
         MODEL_TENSOR.V_ENC_FFN_UP: (
@@ -1283,6 +1321,7 @@ class TensorNameMap:
             "visual.blocks.{bid}.mlp.fc1", # qwen2vl
             "visual.blocks.{bid}.mlp.up_proj", # qwen2.5vl
             "vision_tower.encoder.blocks.{bid}.mlp.fc0", # kimi-vl (fc0/fc1)
+            "model.vision.transformer.layers.{bid}.mlp.fc1", # cogvlm
         ),
 
         MODEL_TENSOR.V_ENC_FFN_GATE: (
@@ -1302,6 +1341,7 @@ class TensorNameMap:
             "visual.blocks.{bid}.mlp.fc2", # qwen2vl
             "visual.blocks.{bid}.mlp.down_proj", # qwen2.5vl
             "vision_tower.encoder.blocks.{bid}.mlp.fc1", # kimi-vl (fc0/fc1)
+            "model.vision.transformer.layers.{bid}.mlp.fc2", # cogvlm
         ),
 
         MODEL_TENSOR.V_LAYER_SCALE_1: (
@@ -1338,6 +1378,7 @@ class TensorNameMap:
             "multi_modal_projector.layer_norm",
             "multi_modal_projector.pre_norm",
             "pre_mm_projector_norm",
+            "model.vision.linear_proj.norm1", # cogvlm
         ),
 
         MODEL_TENSOR.V_MM_SOFT_EMB_NORM: (
@@ -1397,6 +1438,30 @@ class TensorNameMap:
             "patch_merger.merging_layer", # mistral
         ),
 
+        MODEL_TENSOR.V_MM_POST_FC_NORM: (
+            "model.vision.linear_proj.norm1", # cogvlm
+        ),
+
+        MODEL_TENSOR.V_MM_UP: (
+            "model.vision.linear_proj.dense_h_to_4h", # cogvlm
+        ),
+
+        MODEL_TENSOR.V_MM_DOWN: (
+            "model.vision.linear_proj.dense_4h_to_h", # cogvlm
+        ),
+
+        MODEL_TENSOR.V_MM_GATE: (
+            "model.vision.linear_proj.gate_proj", # cogvlm
+        ),
+
+        MODEL_TENSOR.V_TOK_BOI: (
+            "model.vision.boi", # cogvlm
+        ),
+
+        MODEL_TENSOR.V_TOK_EOI: (
+            "model.vision.eoi", # cogvlm
+        ),
+
         # audio (mtmd)
 
         MODEL_TENSOR.A_ENC_EMBD_POS: (
diff --git a/src/llama-arch.cpp b/src/llama-arch.cpp
index 8ca769c5fd2..ba45e88c08e 100644
--- a/src/llama-arch.cpp
+++ b/src/llama-arch.cpp
@@ -103,6 +103,7 @@ static const std::map<llm_arch, const char *> LLM_ARCH_NAMES = {
     { LLM_ARCH_SEED_OSS,         "seed_oss"         },
     { LLM_ARCH_GROVEMOE,         "grovemoe"         },
     { LLM_ARCH_APERTUS,          "apertus"          },
+    { LLM_ARCH_COGVLM,           "cogvlm"           },
     { LLM_ARCH_UNKNOWN,          "(unknown)"        },
 };
 
@@ -2312,6 +2313,26 @@ static const std::map<llm_arch, std::map<llm_tensor, const char *>> LLM_TENSOR_N
             { LLM_TENSOR_FFN_UP_CHEXPS,      "blk.%d.ffn_up_chexps" },
         },
     },
+    {
+        LLM_ARCH_COGVLM,
+        {
+            { LLM_TENSOR_TOKEN_EMBD,      "token_embd" },
+            { LLM_TENSOR_OUTPUT_NORM,     "output_norm" },
+            { LLM_TENSOR_OUTPUT,          "output" },
+            { LLM_TENSOR_ATTN_NORM,       "blk.%d.attn_norm" },
+            { LLM_TENSOR_ATTN_QKV,        "blk.%d.attn_qkv" },
+            { LLM_TENSOR_ATTN_OUT,        "blk.%d.attn_output" },
+            { LLM_TENSOR_FFN_NORM,        "blk.%d.ffn_norm" },
+            { LLM_TENSOR_FFN_GATE,        "blk.%d.ffn_gate" },
+            { LLM_TENSOR_FFN_DOWN,        "blk.%d.ffn_down" },
+            { LLM_TENSOR_FFN_UP,          "blk.%d.ffn_up" },
+            { LLM_TENSOR_VISEXP_ATTN_QKV, "blk.%d.vis_attn_qkv" },
+            { LLM_TENSOR_VISEXP_ATTN_OUT, "blk.%d.vis_attn_output" },
+            { LLM_TENSOR_VISEXP_FFN_GATE, "blk.%d.vis_gate" },
+            { LLM_TENSOR_VISEXP_FFN_DOWN, "blk.%d.vis_down" },
+            { LLM_TENSOR_VISEXP_FFN_UP,   "blk.%d.vis_up" },
+        },
+    },
     {
         LLM_ARCH_UNKNOWN,
         {
@@ -2488,6 +2509,11 @@ static const std::map<llm_tensor, llm_tensor_info> LLM_TENSOR_INFOS = {
     {LLM_TENSOR_SHORTCONV_CONV,             {LLM_TENSOR_LAYER_REPEATING, GGML_OP_SSM_CONV}},
     {LLM_TENSOR_SHORTCONV_INPROJ,           {LLM_TENSOR_LAYER_REPEATING, GGML_OP_MUL_MAT}},
     {LLM_TENSOR_SHORTCONV_OUTPROJ,          {LLM_TENSOR_LAYER_REPEATING, GGML_OP_MUL_MAT}},
+    {LLM_TENSOR_VISEXP_ATTN_QKV,            {LLM_TENSOR_LAYER_REPEATING, GGML_OP_MUL_MAT}},
+    {LLM_TENSOR_VISEXP_ATTN_OUT,            {LLM_TENSOR_LAYER_REPEATING, GGML_OP_MUL_MAT}},
+    {LLM_TENSOR_VISEXP_FFN_GATE,            {LLM_TENSOR_LAYER_REPEATING, GGML_OP_MUL_MAT}},
+    {LLM_TENSOR_VISEXP_FFN_DOWN,            {LLM_TENSOR_LAYER_REPEATING, GGML_OP_MUL_MAT}},
+    {LLM_TENSOR_VISEXP_FFN_UP,              {LLM_TENSOR_LAYER_REPEATING, GGML_OP_MUL_MAT}},
     // NextN/MTP tensors are currently ignored (reserved for future MTP support)
     // These tensors only exist in the last layer(s) and are treated as output tensors
     {LLM_TENSOR_NEXTN_EH_PROJ,              {LLM_TENSOR_LAYER_OUTPUT, GGML_OP_MUL_MAT}},
diff --git a/src/llama-arch.h b/src/llama-arch.h
index dea725c1a75..3350e8b4315 100644
--- a/src/llama-arch.h
+++ b/src/llama-arch.h
@@ -107,6 +107,7 @@ enum llm_arch {
     LLM_ARCH_SEED_OSS,
     LLM_ARCH_GROVEMOE,
     LLM_ARCH_APERTUS,
+    LLM_ARCH_COGVLM,
     LLM_ARCH_UNKNOWN,
 };
 
@@ -455,6 +456,11 @@ enum llm_tensor {
     LLM_TENSOR_SHORTCONV_CONV,
     LLM_TENSOR_SHORTCONV_INPROJ,
     LLM_TENSOR_SHORTCONV_OUTPROJ,
+    LLM_TENSOR_VISEXP_ATTN_QKV,
+    LLM_TENSOR_VISEXP_ATTN_OUT,
+    LLM_TENSOR_VISEXP_FFN_GATE,
+    LLM_TENSOR_VISEXP_FFN_DOWN,
+    LLM_TENSOR_VISEXP_FFN_UP,
     LLM_TENSOR_NEXTN_EH_PROJ,
     LLM_TENSOR_NEXTN_EMBED_TOKENS,
     LLM_TENSOR_NEXTN_ENORM,
diff --git a/src/llama-model.cpp b/src/llama-model.cpp
index ea6f59ed482..35759a00aec 100644
--- a/src/llama-model.cpp
+++ b/src/llama-model.cpp
@@ -2124,6 +2124,14 @@ void llama_model::load_hparams(llama_model_loader & ml) {
                     default: type = LLM_TYPE_UNKNOWN;
                 }
             } break;
+        case LLM_ARCH_COGVLM:
+            {
+                ml.get_key(LLM_KV_ATTENTION_LAYERNORM_RMS_EPS, hparams.f_norm_rms_eps);
+                switch (hparams.n_layer) {
+                    case 32: type = LLM_TYPE_13B; break;
+                    default: type = LLM_TYPE_UNKNOWN;
+                }
+            } break;
         default: throw std::runtime_error("unsupported model architecture");
     }
 
@@ -6136,6 +6144,41 @@ bool llama_model::load_tensors(llama_model_loader & ml) {
                         layer.attn_k_norm_b = create_tensor(tn(LLM_TENSOR_ATTN_K_NORM, "bias",   i), { n_embd_head_k }, TENSOR_NOT_REQUIRED);
                     }
                 } break;
+            case LLM_ARCH_COGVLM:
+                {
+                    tok_embd = create_tensor(tn(LLM_TENSOR_TOKEN_EMBD, "weight"), {n_embd, n_vocab}, 0);
+
+                    // output
+                    output_norm = create_tensor(tn(LLM_TENSOR_OUTPUT_NORM, "weight"), {n_embd}, 0);
+                    output      = create_tensor(tn(LLM_TENSOR_OUTPUT,      "weight"), {n_embd, n_vocab}, TENSOR_NOT_REQUIRED);
+
+                    // if output is NULL, init from the input tok embed
+                    if (output == NULL) {
+                        output = create_tensor(tn(LLM_TENSOR_TOKEN_EMBD, "weight"), {n_embd, n_vocab}, TENSOR_DUPLICATED);
+                    }
+
+                    for (int i = 0; i < n_layer; ++i) {
+                        auto & layer = layers[i];
+
+                        layer.attn_norm = create_tensor(tn(LLM_TENSOR_ATTN_NORM, "weight", i), {n_embd}, 0);
+                        layer.wqkv = create_tensor(tn(LLM_TENSOR_ATTN_QKV, "weight", i), {n_embd, n_embd_head_k * n_head * 3}, 0);
+                        layer.wo = create_tensor(tn(LLM_TENSOR_ATTN_OUT, "weight", i), {n_embd_head_k * n_head, n_embd}, 0);
+
+                        layer.visexp_attn_wqkv = create_tensor(tn(LLM_TENSOR_VISEXP_ATTN_QKV, "weight", i), {n_embd, n_embd_head_k * n_head * 3}, 0);
+                        layer.visexp_attn_wo = create_tensor(tn(LLM_TENSOR_VISEXP_ATTN_OUT, "weight", i), {n_embd_head_k * n_head, n_embd}, 0);
+
+                        layer.rope_freqs = create_tensor(tn(LLM_TENSOR_ROPE_FREQS, "weight", i), {n_rot/2}, TENSOR_NOT_REQUIRED | (i != 0 ? TENSOR_DUPLICATED : 0));
+
+                        layer.ffn_norm = create_tensor(tn(LLM_TENSOR_FFN_NORM, "weight", i), {n_embd}, 0);
+                        layer.ffn_gate = create_tensor(tn(LLM_TENSOR_FFN_GATE, "weight", i), {n_embd,   n_ff}, 0);
+                        layer.ffn_down = create_tensor(tn(LLM_TENSOR_FFN_DOWN, "weight", i), {  n_ff, n_embd}, 0);
+                        layer.ffn_up   = create_tensor(tn(LLM_TENSOR_FFN_UP,   "weight", i), {n_embd,   n_ff}, 0);
+
+                        layer.visexp_ffn_gate = create_tensor(tn(LLM_TENSOR_VISEXP_FFN_GATE, "weight", i), {n_embd,   n_ff}, 0);
+                        layer.visexp_ffn_down = create_tensor(tn(LLM_TENSOR_VISEXP_FFN_DOWN, "weight", i), {  n_ff, n_embd}, 0);
+                        layer.visexp_ffn_up   = create_tensor(tn(LLM_TENSOR_VISEXP_FFN_UP,   "weight", i), {n_embd,   n_ff}, 0);
+                    }
+                } break;
             default:
                 throw std::runtime_error("unknown architecture");
         }
@@ -19641,6 +19684,104 @@ struct llm_build_apertus : public llm_graph_context {
     }
 };
 
+struct llm_build_cogvlm : public llm_graph_context {
+    llm_build_cogvlm(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+        const int64_t n_embd_head = hparams.n_embd_head_v;
+        float kq_scale = 1.0f / sqrtf(float(n_embd_head));
+
+        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+        GGML_ASSERT(n_embd_head == hparams.n_rot);
+
+        ggml_tensor * inpL, * cur;
+        inpL = build_inp_embd(model.tok_embd);
+
+        ggml_tensor * inp_pos = build_inp_pos();
+
+        auto * inp_attn = build_attn_inp_kv();
+
+        // check ubatch to see if we have input tokens (text)
+        // or an input embedding vector (image)
+        bool is_text;
+        if (ubatch.token) {
+            is_text = true;
+        } else {
+            is_text = false;
+        }
+
+        for (int il = 0; il < n_layer; ++il) {
+            // get either the text or image weight tensors
+            ggml_tensor * wqkv, * wo;
+            ggml_tensor * ffn_gate, * ffn_down, * ffn_up;
+
+            if (is_text) {
+                wqkv = model.layers[il].wqkv;
+                wo = model.layers[il].wo;
+                ffn_gate = model.layers[il].ffn_gate;
+                ffn_down = model.layers[il].ffn_down;
+                ffn_up = model.layers[il].ffn_up;
+            } else {
+                wqkv = model.layers[il].visexp_attn_wqkv;
+                wo = model.layers[il].visexp_attn_wo;
+                ffn_gate = model.layers[il].visexp_ffn_gate;
+                ffn_down = model.layers[il].visexp_ffn_down;
+                ffn_up = model.layers[il].visexp_ffn_up;
+            }
+
+            ggml_tensor * inpSA = inpL;
+            cur = build_norm(inpSA, model.layers[il].attn_norm, NULL, LLM_NORM_RMS, il);
+
+            // build self attention
+            {
+                ggml_tensor * qkv = build_lora_mm(wqkv, cur);
+
+                // split qkv into Q, K, V along the first dimension
+                ggml_tensor * Qcur = ggml_view_3d(ctx0, qkv, n_embd_head, n_head, n_tokens, n_embd_head * sizeof(float),
+                    qkv->nb[1], 0);
+                ggml_tensor * Kcur = ggml_view_3d(ctx0, qkv, n_embd_head, n_head_kv, n_tokens, n_embd_head * sizeof(float),
+                    qkv->nb[1], n_embd * ggml_element_size(qkv));
+                ggml_tensor * Vcur = ggml_view_3d(ctx0, qkv, n_embd_head, n_head_kv, n_tokens, n_embd_head * sizeof(float),
+                    qkv->nb[1], 2 * n_embd * ggml_element_size(qkv));
+
+                Qcur = ggml_rope(ctx0, Qcur, inp_pos, n_embd_head, rope_type);
+                Kcur = ggml_rope(ctx0, Kcur, inp_pos, n_embd_head, rope_type);
+
+                cur = build_attn(inp_attn, wo, nullptr, Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, kq_scale, il);
+                cb(cur, "attn_out", il);
+            }
+
+            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+            cb(ffn_inp, "ffn_inp", il);
+
+            cur = build_norm(ffn_inp, model.layers[il].ffn_norm, NULL, LLM_NORM_RMS, il);
+            cb(cur, "ffn_norm", il);
+
+            cur = build_ffn(cur,
+                    ffn_up,   NULL, NULL,
+                    ffn_gate, NULL, NULL,
+                    ffn_down, NULL, NULL,
+                    NULL,
+                    LLM_FFN_SILU, LLM_FFN_PAR, il);
+
+            cur = ggml_add(ctx0, cur, ffn_inp);
+            cb(cur, "ffn_out", il);
+
+            inpL = cur;
+        }
+
+        cur = inpL;
+
+        cur = build_norm(cur, model.output_norm, NULL, LLM_NORM_RMS, -1);
+        cb(cur, "result_norm", -1);
+        res->t_embd = cur;
+
+        cur = build_lora_mm(model.output, cur);
+        cb(cur, "result_output", -1);
+        res->t_logits = cur;
+        ggml_build_forward_expand(gf, cur);
+
+    }
+};
+
 llama_memory_i * llama_model::create_memory(const llama_memory_params & params, const llama_cparams & cparams) const {
     llama_memory_i * res;
 
@@ -20165,6 +20306,10 @@ ggml_cgraph * llama_model::build_graph(const llm_graph_params & params) const {
             {
                 llm = std::make_unique<llm_build_apertus>(*this, params);
             } break;
+        case LLM_ARCH_COGVLM:
+            {
+                llm = std::make_unique<llm_build_cogvlm>(*this, params);
+            } break;
         default:
             GGML_ABORT("fatal error");
     }
@@ -20382,6 +20527,7 @@ llama_rope_type llama_model_rope_type(const llama_model * model) {
         case LLM_ARCH_SEED_OSS:
         case LLM_ARCH_GROVEMOE:
         case LLM_ARCH_APERTUS:
+        case LLM_ARCH_COGVLM:
             return LLAMA_ROPE_TYPE_NEOX;
 
         case LLM_ARCH_QWEN2VL:
diff --git a/src/llama-model.h b/src/llama-model.h
index 1ab1cf7f8e9..a5affda1c99 100644
--- a/src/llama-model.h
+++ b/src/llama-model.h
@@ -384,6 +384,13 @@ struct llama_layer {
     // openai-moe
     struct ggml_tensor * attn_sinks = nullptr;
 
+    // cogvlm
+    struct ggml_tensor * visexp_attn_wqkv = nullptr;
+    struct ggml_tensor * visexp_attn_wo   = nullptr;
+    struct ggml_tensor * visexp_ffn_gate  = nullptr;
+    struct ggml_tensor * visexp_ffn_down  = nullptr;
+    struct ggml_tensor * visexp_ffn_up    = nullptr;
+
     // xIELU activation parameters for Apertus
     struct ggml_tensor * ffn_act_alpha_n = nullptr;
     struct ggml_tensor * ffn_act_alpha_p = nullptr;
diff --git a/tools/mtmd/clip-impl.h b/tools/mtmd/clip-impl.h
index ad2108d1798..d4b88cb6980 100644
--- a/tools/mtmd/clip-impl.h
+++ b/tools/mtmd/clip-impl.h
@@ -63,6 +63,7 @@
 #define TN_PATCH_EMBD      "v.patch_embd.weight"  // not rename tensor with ".0" postfix for backwrad compat
 #define TN_PATCH_EMBD_1    "v.patch_embd.weight.1"
 #define TN_PATCH_BIAS      "v.patch_embd.bias"
+#define TN_ATTN_QKV        "%s.blk.%d.attn_qkv.%s"
 #define TN_ATTN_K          "%s.blk.%d.attn_k.%s"
 #define TN_ATTN_Q          "%s.blk.%d.attn_q.%s"
 #define TN_ATTN_V          "%s.blk.%d.attn_v.%s"
@@ -116,6 +117,14 @@
 #define TN_MM_NORM_PRE  "mm.a.norm_pre.%s"
 #define TN_MM_NORM_MID  "mm.a.norm_mid.%s"
 
+// cogvlm
+#define TN_MM_POST_FC_NORM "mm.post_fc_norm.%s"
+#define TN_MM_H_TO_4H      "mm.up.%s"
+#define TN_MM_GATE         "mm.gate.%s"
+#define TN_MM_4H_TO_H      "mm.down.%s"
+#define TN_TOK_BOI         "v.boi"
+#define TN_TOK_EOI         "v.eoi"
+
 // align x to upper multiple of n
 #define CLIP_ALIGN(x, n) ((((x) + (n) - 1) / (n)) * (n))
 
@@ -141,6 +150,7 @@ enum projector_type {
     PROJECTOR_TYPE_KIMIVL,
     PROJECTOR_TYPE_LIGHTONOCR,
     PROJECTOR_TYPE_UNKNOWN,
+    PROJECTOR_TYPE_COGVLM,
 };
 
 static std::map<projector_type, std::string> PROJECTOR_TYPE_NAMES = {
@@ -163,6 +173,7 @@ static std::map<projector_type, std::string> PROJECTOR_TYPE_NAMES = {
     { PROJECTOR_TYPE_LFM2,      "lfm2"},
     { PROJECTOR_TYPE_KIMIVL,    "kimivl"},
     { PROJECTOR_TYPE_LIGHTONOCR,"lightonocr"},
+    { PROJECTOR_TYPE_COGVLM,    "cogvlm"},
 };
 
 static projector_type clip_projector_type_from_string(const std::string & str) {
diff --git a/tools/mtmd/clip.cpp b/tools/mtmd/clip.cpp
index b44f0a3a28a..a135ba0a2b3 100644
--- a/tools/mtmd/clip.cpp
+++ b/tools/mtmd/clip.cpp
@@ -214,6 +214,8 @@ struct clip_layer {
     ggml_tensor * q_b = nullptr;
     ggml_tensor * v_w = nullptr;
     ggml_tensor * v_b = nullptr;
+    ggml_tensor * qkv_w = nullptr;
+    ggml_tensor * qkv_b = nullptr;
 
     ggml_tensor * o_w = nullptr;
     ggml_tensor * o_b = nullptr;
@@ -286,8 +288,6 @@ struct clip_model {
     // GLMV-Edge projection
     ggml_tensor * mm_model_adapter_conv_w = nullptr;
     ggml_tensor * mm_model_adapter_conv_b = nullptr;
-    ggml_tensor * mm_glm_tok_boi = nullptr;
-    ggml_tensor * mm_glm_tok_eoi = nullptr;
 
     // MobileVLM projection
     ggml_tensor * mm_model_mlp_1_w = nullptr;
@@ -359,6 +359,15 @@ struct clip_model {
     ggml_tensor * mm_norm_pre_w = nullptr;
     ggml_tensor * mm_norm_mid_w = nullptr;
 
+    // cogvlm
+    ggml_tensor * mm_post_fc_norm_w = nullptr;
+    ggml_tensor * mm_post_fc_norm_b = nullptr;
+    ggml_tensor * mm_h_to_4h_w = nullptr;
+    ggml_tensor * mm_gate_w = nullptr;
+    ggml_tensor * mm_4h_to_h_w = nullptr;
+    ggml_tensor * mm_boi = nullptr;
+    ggml_tensor * mm_eoi = nullptr;
+
     bool audio_has_avgpool() const {
         return proj_type == PROJECTOR_TYPE_QWEN2A
             || proj_type == PROJECTOR_TYPE_VOXTRAL;
@@ -1494,8 +1503,8 @@ struct clip_graph {
             // note: these embeddings are not present in text model, hence we cannot process them as text tokens
             // see: https://huggingface.co/THUDM/glm-edge-v-2b/blob/main/siglip.py#L53
             {
-                embeddings = ggml_concat(ctx0, model.mm_glm_tok_boi, embeddings, 1); // BOI
-                embeddings = ggml_concat(ctx0, embeddings, model.mm_glm_tok_eoi, 1); // EOI
+                embeddings = ggml_concat(ctx0, model.mm_boi, embeddings, 1); // BOI
+                embeddings = ggml_concat(ctx0, embeddings, model.mm_eoi, 1); // EOI
             }
         }
 
@@ -1613,6 +1622,104 @@ struct clip_graph {
         return gf;
     }
 
+    // cogvlm vision encoder
+    ggml_cgraph * build_cogvlm() {
+        GGML_ASSERT(model.class_embedding != nullptr);
+        GGML_ASSERT(model.position_embeddings != nullptr);
+
+        const int n_pos = n_patches + 1; // +1 for [CLS]
+
+        // build input and concatenate class embedding
+        ggml_tensor * inp = build_inp();
+        inp = ggml_concat(ctx0, inp, model.class_embedding, 1);
+
+        inp = ggml_add(ctx0, inp, model.position_embeddings);
+        cb(inp, "inp_pos", -1);
+
+        ggml_tensor * inpL = inp;
+
+        for (int il = 0; il < n_layer; il++) {
+            auto & layer = model.layers[il];
+            ggml_tensor * cur = inpL;
+
+            cur = ggml_mul_mat(ctx0, layer.qkv_w, cur);
+
+            cur = ggml_add(ctx0, cur, layer.qkv_b);
+
+            ggml_tensor * Qcur = ggml_view_3d(ctx0, cur, d_head, n_head, n_pos, d_head*sizeof(float),
+                cur->nb[1], 0);
+            ggml_tensor * Kcur = ggml_view_3d(ctx0, cur, d_head, n_head, n_pos, d_head*sizeof(float),
+                cur->nb[1], n_embd * sizeof(float));
+            ggml_tensor * Vcur = ggml_view_3d(ctx0, cur, d_head, n_head, n_pos, d_head*sizeof(float),
+                cur->nb[1], 2 * n_embd * sizeof(float));
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(layer.o_w, layer.o_b,
+                Qcur, Kcur, Vcur, nullptr, kq_scale, il);
+            cb(cur, "attn_out", il);
+
+            cur = build_norm(cur, layer.ln_1_w, layer.ln_1_b, NORM_TYPE_NORMAL, eps, il);
+            cb(cur, "attn_post_norm", il);
+
+            cur = ggml_add(ctx0, cur, inpL);
+            inpL = cur;
+
+            cur = build_ffn(cur,
+                layer.ff_up_w, layer.ff_up_b,
+                layer.ff_gate_w, layer.ff_gate_b,
+                layer.ff_down_w, layer.ff_down_b,
+                hparams.ffn_op, il);
+
+            cb(cur, "ffn_out", il);
+
+            cur = build_norm(cur, layer.ln_2_w, layer.ln_2_b, NORM_TYPE_NORMAL, eps, il);
+            cb(cur, "ffn_post_norm", il);
+
+            cur = ggml_add(ctx0, cur, inpL);
+            cb(cur, "layer_out", il);
+            inpL = cur;
+
+        }
+
+        // remove CLS token (like build_llama4 does)
+        ggml_tensor * cur = ggml_view_2d(ctx0, inpL,
+            n_embd, n_patches,
+            ggml_row_size(inpL->type, n_embd), 0);
+
+        // Multiply with mm_model_proj
+        cur = ggml_mul_mat(ctx0, model.mm_model_proj, cur);
+
+        // Apply layernorm, weight, bias
+        cur = build_norm(cur, model.mm_post_fc_norm_w, model.mm_post_fc_norm_b, NORM_TYPE_NORMAL, 1e-5, -1);
+
+        // Apply GELU
+        cur = ggml_gelu_inplace(ctx0, cur);
+
+        // Branch 1: multiply with mm_h_to_4h_w
+        ggml_tensor * h_to_4h = ggml_mul_mat(ctx0, model.mm_h_to_4h_w, cur);
+
+        // Branch 2: multiply with mm_gate_w
+        ggml_tensor * gate = ggml_mul_mat(ctx0, model.mm_gate_w, cur);
+
+        // Apply silu
+        gate = ggml_swiglu_split(ctx0, gate, h_to_4h);
+
+        // Apply mm_4h_to_h_w
+        cur = ggml_mul_mat(ctx0, model.mm_4h_to_h_w, gate);
+
+        // Concatenate with boi and eoi
+        cur = ggml_concat(ctx0, model.mm_boi, cur, 1);
+        cur = ggml_concat(ctx0, cur, model.mm_eoi, 1);
+
+        // build the graph
+        ggml_build_forward_expand(gf, cur);
+
+        return gf;
+    }
+
 private:
     //
     // utility functions
@@ -2126,6 +2233,10 @@ static ggml_cgraph * clip_image_build_graph(clip_ctx * ctx, const clip_image_f32
             {
                 res = graph.build_kimivl();
             } break;
+        case PROJECTOR_TYPE_COGVLM:
+            {
+                res = graph.build_cogvlm();
+            } break;
         default:
             {
                 res = graph.build_llava();
@@ -2532,10 +2643,11 @@ struct clip_model_loader {
         model.layers.resize(hparams.n_layer);
         for (int il = 0; il < hparams.n_layer; ++il) {
             auto & layer = model.layers[il];
-            layer.k_w    = get_tensor(string_format(TN_ATTN_K,      prefix, il, "weight"));
-            layer.q_w    = get_tensor(string_format(TN_ATTN_Q,      prefix, il, "weight"));
-            layer.v_w    = get_tensor(string_format(TN_ATTN_V,      prefix, il, "weight"));
+            layer.k_w    = get_tensor(string_format(TN_ATTN_K,      prefix, il, "weight"), false);
+            layer.q_w    = get_tensor(string_format(TN_ATTN_Q,      prefix, il, "weight"), false);
+            layer.v_w    = get_tensor(string_format(TN_ATTN_V,      prefix, il, "weight"), false);
             layer.o_w    = get_tensor(string_format(TN_ATTN_OUTPUT, prefix, il, "weight"));
+            layer.qkv_w  = get_tensor(string_format(TN_ATTN_QKV,    prefix, il, "weight"), false);
             layer.k_norm = get_tensor(string_format(TN_ATTN_K_NORM, prefix, il, "weight"), false);
             layer.q_norm = get_tensor(string_format(TN_ATTN_Q_NORM, prefix, il, "weight"), false);
             layer.ln_1_w = get_tensor(string_format(TN_LN_1,        prefix, il, "weight"), false);
@@ -2547,6 +2659,7 @@ struct clip_model_loader {
             layer.q_b    = get_tensor(string_format(TN_ATTN_Q,      prefix, il, "bias"), false);
             layer.v_b    = get_tensor(string_format(TN_ATTN_V,      prefix, il, "bias"), false);
             layer.o_b    = get_tensor(string_format(TN_ATTN_OUTPUT, prefix, il, "bias"), false);
+            layer.qkv_b  = get_tensor(string_format(TN_ATTN_QKV,    prefix, il, "bias"), false);
             layer.ln_1_b = get_tensor(string_format(TN_LN_1,        prefix, il, "bias"), false);
             layer.ln_2_b = get_tensor(string_format(TN_LN_2,        prefix, il, "bias"), false);
 
@@ -2682,8 +2795,8 @@ struct clip_model_loader {
                     model.mm_model_mlp_1_w = get_tensor(string_format(TN_GLM_ADAPTER_D_H_2_4H, "weight"));
                     model.mm_model_mlp_2_w = get_tensor(string_format(TN_GLM_ADAPTER_GATE, "weight"));
                     model.mm_model_mlp_3_w = get_tensor(string_format(TN_GLM_ADAPTER_D_4H_2_H, "weight"));
-                    model.mm_glm_tok_boi = get_tensor(string_format(TN_TOK_GLM_BOI, "weight"));
-                    model.mm_glm_tok_eoi = get_tensor(string_format(TN_TOK_GLM_EOI, "weight"));
+                    model.mm_boi = get_tensor(string_format(TN_TOK_GLM_BOI, "weight"));
+                    model.mm_eoi = get_tensor(string_format(TN_TOK_GLM_EOI, "weight"));
                 } break;
             case PROJECTOR_TYPE_QWEN2VL:
             case PROJECTOR_TYPE_QWEN25VL:
@@ -2777,6 +2890,17 @@ struct clip_model_loader {
                     model.mm_model_mlp_1_w = get_tensor(string_format(TN_MVLM_PROJ_MLP, 1, "weight"));
                     model.mm_model_mlp_2_w = get_tensor(string_format(TN_MVLM_PROJ_MLP, 2, "weight"));
                 } break;
+            case PROJECTOR_TYPE_COGVLM:
+                {
+                    model.mm_model_proj     = get_tensor(TN_MM_PROJECTOR);
+                    model.mm_post_fc_norm_w = get_tensor(string_format(TN_MM_POST_FC_NORM, "weight"));
+                    model.mm_post_fc_norm_b = get_tensor(string_format(TN_MM_POST_FC_NORM, "bias"));
+                    model.mm_h_to_4h_w      = get_tensor(string_format(TN_MM_H_TO_4H,      "weight"));
+                    model.mm_gate_w         = get_tensor(string_format(TN_MM_GATE,         "weight"));
+                    model.mm_4h_to_h_w      = get_tensor(string_format(TN_MM_4H_TO_H,      "weight"));
+                    model.mm_boi            = get_tensor(TN_TOK_BOI);
+                    model.mm_eoi            = get_tensor(TN_TOK_EOI);
+                } break;
             default:
                 GGML_ASSERT(false && "unknown projector type");
         }
@@ -3825,7 +3949,7 @@ int clip_n_output_tokens(const struct clip_ctx * ctx, struct clip_image_f32 * im
         case PROJECTOR_TYPE_GLM_EDGE:
             {
                 n_patches /= 4;
-                if (ctx->model.mm_glm_tok_boi) {
+                if (ctx->model.mm_boi) {
                     n_patches += 2; // for BOI and EOI token embeddings
                 }
             } break;
@@ -3915,6 +4039,10 @@ int clip_n_output_tokens(const struct clip_ctx * ctx, struct clip_image_f32 * im
                     n_patches /= 2;
                 }
             } break;
+        case PROJECTOR_TYPE_COGVLM:
+            {
+                n_patches += 2; // for BOI and EOI token embeddings
+            } break;
         default:
             GGML_ABORT("unsupported projector type");
     }
@@ -4323,6 +4451,7 @@ bool clip_image_batch_encode(clip_ctx * ctx, const int n_threads, const clip_ima
         case PROJECTOR_TYPE_ULTRAVOX:
         case PROJECTOR_TYPE_LFM2:
         case PROJECTOR_TYPE_VOXTRAL:
+        case PROJECTOR_TYPE_COGVLM:
             {
                 // do nothing
             } break;
@@ -4427,6 +4556,8 @@ int clip_n_mmproj_embd(const struct clip_ctx * ctx) {
         case PROJECTOR_TYPE_LFM2:
         case PROJECTOR_TYPE_KIMIVL:
             return ctx->model.mm_2_w->ne[1];
+        case PROJECTOR_TYPE_COGVLM:
+            return ctx->model.mm_4h_to_h_w->ne[1];
         default:
             GGML_ABORT("Unknown projector type");
     }

From dcca0d3ab840ebe9b2ccd4719033d408eeb758d7 Mon Sep 17 00:00:00 2001
From: Max Krasnyansky <maxk@qti.qualcomm.com>
Date: Thu, 30 Oct 2025 05:26:05 -0700
Subject: [PATCH 020/185] cpu: introduce chunking for flash attention (#16829)

Factor out the core FA loop into flash_atten_f16_one_chunk and add an outter loop
on top that handles the chunks.
---
 ggml/src/ggml-cpu/ops.cpp | 106 ++++++++++++++++++++++++++++++++------
 1 file changed, 90 insertions(+), 16 deletions(-)

diff --git a/ggml/src/ggml-cpu/ops.cpp b/ggml/src/ggml-cpu/ops.cpp
index 3156bd60101..c17ab10245d 100644
--- a/ggml/src/ggml-cpu/ops.cpp
+++ b/ggml/src/ggml-cpu/ops.cpp
@@ -7909,10 +7909,10 @@ void ggml_compute_forward_argsort(
 
 // ggml_compute_forward_flash_attn_ext
 
-static void ggml_compute_forward_flash_attn_ext_f16(
+static void ggml_compute_forward_flash_attn_ext_f16_one_chunk(
         const ggml_compute_params * params,
-        ggml_tensor * dst) {
-
+        ggml_tensor * dst,
+        int ir0, int ir1) {
     const ggml_tensor * q     = dst->src[0];
     const ggml_tensor * k     = dst->src[1];
     const ggml_tensor * v     = dst->src[2];
@@ -7928,9 +7928,6 @@ static void ggml_compute_forward_flash_attn_ext_f16(
     GGML_TENSOR_LOCALS(int64_t, ne,  dst, ne)
     GGML_TENSOR_LOCALS(size_t,  nb,  dst, nb)
 
-    const int ith = params->ith;
-    const int nth = params->nth;
-
     const int64_t DK = nek0;
     const int64_t DV = nev0;
     const int64_t N  = neq1;
@@ -7964,16 +7961,6 @@ static void ggml_compute_forward_flash_attn_ext_f16(
 
     // parallelize by q rows using ggml_vec_dot_f32
 
-    // total rows in q
-    const int nr = neq1*neq2*neq3;
-
-    // rows per thread
-    const int dr = (nr + nth - 1)/nth;
-
-    // row range for this thread
-    const int ir0 = dr*ith;
-    const int ir1 = MIN(ir0 + dr, nr);
-
     float scale         = 1.0f;
     float max_bias      = 0.0f;
     float logit_softcap = 0.0f;
@@ -8000,6 +7987,8 @@ static void ggml_compute_forward_flash_attn_ext_f16(
     GGML_ASSERT((                            q_to_vec_dot) && "fattn: unsupported K-type");
     GGML_ASSERT((v->type == GGML_TYPE_F32 || v_to_float  ) && "fattn: unsupported V-type");
 
+    int ith = params->ith;
+
     // loop over n_batch and n_head
     for (int ir = ir0; ir < ir1; ++ir) {
         // q indices
@@ -8147,6 +8136,91 @@ static void ggml_compute_forward_flash_attn_ext_f16(
     }
 }
 
+static void ggml_compute_forward_flash_attn_ext_f16(
+        const ggml_compute_params * params,
+        ggml_tensor * dst) {
+
+    const ggml_tensor * q     = dst->src[0];
+    const ggml_tensor * k     = dst->src[1];
+    const ggml_tensor * v     = dst->src[2];
+
+    GGML_TENSOR_LOCALS(int64_t, neq, q,   ne)
+    GGML_TENSOR_LOCALS(size_t,  nbq, q,   nb)
+    GGML_TENSOR_LOCALS(int64_t, nek, k,   ne)
+    GGML_TENSOR_LOCALS(size_t,  nbk, k,   nb)
+    GGML_TENSOR_LOCALS(int64_t, nev, v,   ne)
+    GGML_TENSOR_LOCALS(size_t,  nbv, v,   nb)
+    GGML_TENSOR_LOCALS(int64_t, ne,  dst, ne)
+    GGML_TENSOR_LOCALS(size_t,  nb,  dst, nb)
+
+    const int64_t DK = nek0;
+    const int64_t DV = nev0;
+    const int64_t N  = neq1;
+
+    GGML_ASSERT(ne0 == DV);
+    GGML_ASSERT(ne2 == N);
+
+    // input tensor rows must be contiguous
+    GGML_ASSERT(nbq0 == ggml_type_size(q->type));
+    GGML_ASSERT(nbk0 == ggml_type_size(k->type));
+    GGML_ASSERT(nbv0 == ggml_type_size(v->type));
+
+    GGML_ASSERT(neq0 == DK);
+    GGML_ASSERT(nek0 == DK);
+    GGML_ASSERT(nev0 == DV);
+
+    GGML_ASSERT(neq1 == N);
+
+    // dst cannot be transposed or permuted
+    GGML_ASSERT(nb0 == sizeof(float));
+    GGML_ASSERT(nb0 <= nb1);
+    GGML_ASSERT(nb1 <= nb2);
+    GGML_ASSERT(nb2 <= nb3);
+
+    // parallelize by q rows using ggml_vec_dot_f32
+
+    // total rows in q
+    const int64_t nr = neq1*neq2*neq3;
+
+    // rows per thread
+    const int ith = params->ith;
+    const int nth = params->nth;
+
+    // disable for NUMA
+    const bool disable_chunking = ggml_is_numa();
+
+    // 4x chunks per thread
+    int nth_scaled = nth * 4;
+    int64_t chunk_size = (nr + nth_scaled - 1) / nth_scaled;
+    int64_t nchunk     = (nr + chunk_size - 1) / chunk_size;
+
+    if (nth == 1 || nchunk < nth || disable_chunking) {
+        nchunk = nth;
+    }
+
+    if (ith == 0) {
+        // Every thread starts at ith, so the first unprocessed chunk is nth.  This save a bit of coordination right at the start.
+        ggml_threadpool_chunk_set(params->threadpool, nth);
+    }
+
+    ggml_barrier(params->threadpool);
+
+    // The number of elements in each chunk
+    const int64_t dr = (nr + nchunk - 1) / nchunk;
+
+    // The first chunk comes from our thread_id, the rest will get auto-assigned.
+    int current_chunk = ith;
+
+    while (current_chunk < nchunk) {
+        const int64_t ir0 = dr * current_chunk;
+        const int64_t ir1 = MIN(ir0 + dr, nr);
+
+        ggml_compute_forward_flash_attn_ext_f16_one_chunk(params, dst, ir0, ir1);
+
+        current_chunk = ggml_threadpool_chunk_add(params->threadpool, 1);
+    }
+}
+
 void ggml_compute_forward_flash_attn_ext(
         const ggml_compute_params * params,
         ggml_tensor * dst) {

From d261223d24e97f2df50220e4a5b7f0adb69bba81 Mon Sep 17 00:00:00 2001
From: JJJYmmm <92386084+JJJYmmm@users.noreply.github.com>
Date: Thu, 30 Oct 2025 23:19:14 +0800
Subject: [PATCH 021/185] model: add support for qwen3vl series (#16780)
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

* support qwen3vl series.

Co-authored-by: Thireus ☠ <Thireus@users.noreply.github.com>
Co-authored-by: yairpatch <yairpatch@users.noreply.github.com>
Co-authored-by: LETS-BEE <LETS-BEE@users.noreply.github.com>

* bugfix: fix the arch check for qwen3vl-moe.

* use build_ffn

* optimize deepstack structure

* optimize deepstack feature saving

* Revert "optimize deepstack feature saving" for temporal fix

This reverts commit f321b9fdf13e59527408152e73b1071e19a87e71.

* code clean

* use fused qkv in clip

* clean up / rm is_deepstack_layers for simplification

* add test model

* move test model to "big" section

* fix imrope check

* remove trailing whitespace

* fix rope fail

* metal : add imrope support

* add imrope support for sycl

* vulkan: add imrope w/o check

* fix vulkan

* webgpu: add imrope w/o check

* Update gguf-py/gguf/tensor_mapping.py

Co-authored-by: Sigbjørn Skjæret <sigbjorn.skjaeret@scala.com>

* fix tensor mapping

---------

Co-authored-by: Thireus ☠ <Thireus@users.noreply.github.com>
Co-authored-by: yairpatch <yairpatch@users.noreply.github.com>
Co-authored-by: LETS-BEE <LETS-BEE@users.noreply.github.com>
Co-authored-by: Xuan Son Nguyen <son@huggingface.co>
Co-authored-by: Georgi Gerganov <ggerganov@gmail.com>
Co-authored-by: Sigbjørn Skjæret <sigbjorn.skjaeret@scala.com>
---
 convert_hf_to_gguf.py                         | 219 ++++++++++-
 ggml/include/ggml.h                           |   1 +
 ggml/src/ggml-cpu/ops.cpp                     |  36 +-
 ggml/src/ggml-cuda/rope.cu                    |  47 ++-
 ggml/src/ggml-metal/ggml-metal-device.cpp     |  13 +-
 ggml/src/ggml-metal/ggml-metal-impl.h         |   1 +
 ggml/src/ggml-metal/ggml-metal.metal          |  28 +-
 ggml/src/ggml-sycl/rope.cpp                   |  47 ++-
 ggml/src/ggml-vulkan/ggml-vulkan.cpp          |   5 +-
 .../ggml-vulkan/vulkan-shaders/rope_head.glsl |   1 +
 .../vulkan-shaders/rope_multi.comp            |  34 +-
 .../ggml-webgpu/wgsl-shaders/rope.tmpl.wgsl   |  49 ++-
 gguf-py/gguf/constants.py                     |  51 +++
 gguf-py/gguf/gguf_writer.py                   |   6 +
 gguf-py/gguf/tensor_mapping.py                |  16 +
 include/llama.h                               |   1 +
 src/llama-arch.cpp                            |  42 +++
 src/llama-arch.h                              |   3 +
 src/llama-hparams.cpp                         |   2 +-
 src/llama-hparams.h                           |   3 +
 src/llama-kv-cache.cpp                        |   2 +-
 src/llama-model.cpp                           | 352 +++++++++++++++++-
 tests/test-backend-ops.cpp                    |   7 +-
 tests/test-rope.cpp                           |   4 +-
 tools/mtmd/clip-impl.h                        |   6 +
 tools/mtmd/clip.cpp                           | 243 +++++++++++-
 tools/mtmd/mtmd.cpp                           |   2 +-
 tools/mtmd/tests.sh                           |   1 +
 28 files changed, 1125 insertions(+), 97 deletions(-)

diff --git a/convert_hf_to_gguf.py b/convert_hf_to_gguf.py
index 0fd8d5681d7..5abc1779588 100755
--- a/convert_hf_to_gguf.py
+++ b/convert_hf_to_gguf.py
@@ -3852,7 +3852,43 @@ def set_gguf_parameters(self):
     def modify_tensors(self, data_torch: Tensor, name: str, bid: int | None) -> Iterable[tuple[str, Tensor]]:
         # process the experts separately
         name = name.replace("language_model.", "") # InternVL
-        if name.startswith("mlp") or name.startswith("vision_model") or name.startswith("model.vision_tower") or name.startswith("model.multi_modal_projector"):
+
+        # handle aggregated expert tensors
+        # GGUF stores dimensions reversed from PyTorch, so:
+        # PyTorch (A,B,C) -> GGUF writes [C,B,A] -> GGML reads ne={C,B,A}
+        # Input shapes from HF: (n_expert, n_ff_exp, n_embd) or (n_expert, n_embd, n_ff_exp)
+        # Expected GGML ne: {n_embd, n_ff_exp, n_expert} for gate/up, {n_ff_exp, n_embd, n_expert} for down
+        if name.endswith("mlp.experts.down_proj") or name.endswith("mlp.experts.down_proj.weight"):
+            mapped = f"{name}.weight" if not name.endswith(".weight") else name
+            # Input: (n_expert=128, n_ff_exp=768, n_embd=2048)
+            # Want GGML ne: {n_ff_exp, n_embd, n_expert} = {768, 2048, 128}
+            # Need PyTorch: (128, 2048, 768) [reversed of GGML]
+            # So: permute(0, 2, 1): (128, 768, 2048) -> (128, 2048, 768)
+            permuted = data_torch.permute(0, 2, 1).contiguous()
+            return [(self.map_tensor_name(mapped), permuted)]
+
+        if name.endswith("mlp.experts.gate_up_proj") or name.endswith("mlp.experts.gate_up_proj.weight"):
+            if data_torch.ndim < 3 or data_torch.shape[-1] % 2 != 0:
+                raise ValueError(f"Unexpected gate_up_proj shape for {name}: {tuple(data_torch.shape)}")
+            split_dim = data_torch.shape[-1] // 2
+            gate = data_torch[..., :split_dim].contiguous()
+            up = data_torch[..., split_dim:].contiguous()
+            # Input gate/up: (n_expert=128, n_embd=2048, n_ff_exp=768)
+            # Want GGML ne: {n_embd, n_ff_exp, n_expert} = {2048, 768, 128}
+            # Need PyTorch: (128, 768, 2048) [reversed of GGML]
+            # So: permute(0, 2, 1): (128, 2048, 768) -> (128, 768, 2048)
+            base_name = name.removesuffix(".weight")
+            base = base_name.rsplit('.', 1)[0]
+            mapped_gate = f"{base}.gate_proj.weight"
+            mapped_up = f"{base}.up_proj.weight"
+            perm_gate = gate.permute(0, 2, 1).contiguous()
+            perm_up = up.permute(0, 2, 1).contiguous()
+            return [
+                (self.map_tensor_name(mapped_gate), perm_gate),
+                (self.map_tensor_name(mapped_up), perm_up),
+            ]
+
+        if name.startswith("mlp") or name.startswith("vision_model") or name.startswith("model.vision_tower") or name.startswith("model.multi_modal_projector") or name.startswith("model.visual"):
             # skip visual tensors
             return []
         if name.find("experts") != -1:
@@ -4004,6 +4040,187 @@ def set_vocab(self):
         super().set_vocab()
 
 
+@ModelBase.register("Qwen3VLForConditionalGeneration", "Qwen3VLMoeForConditionalGeneration")
+class Qwen3VLVisionModel(MmprojModel):
+    def __init__(self, *args, **kwargs):
+        super().__init__(*args, **kwargs)
+        assert self.hparams_vision is not None
+        # Compute image_size if not present
+        if "image_size" not in self.hparams_vision:
+            # For Qwen3VL/Qwen3VLMoe, compute from num_position_embeddings
+            num_pos = self.hparams_vision.get("num_position_embeddings", 2304)
+            patch_size = self.hparams_vision.get("patch_size", 16)
+            # num_position_embeddings = (image_size / patch_size) ** 2
+            # So image_size = sqrt(num_position_embeddings) * patch_size
+            image_size = int(num_pos**0.5 * patch_size)
+            self.hparams_vision["image_size"] = image_size
+
+        # Rename config values for compatibility
+        self.hparams_vision["num_attention_heads"] = self.hparams_vision.get("num_heads")
+        self.hparams_vision["num_hidden_layers"] = self.hparams_vision.get("depth")
+
+        self.is_deepstack_layers = [False] * int(self.hparams_vision["num_hidden_layers"] or 0)
+        for idx in self.hparams_vision.get("deepstack_visual_indexes", []):
+            self.is_deepstack_layers[idx] = True
+
+    def set_gguf_parameters(self):
+        super().set_gguf_parameters()
+        self.gguf_writer.add_clip_projector_type(gguf.VisionProjectorType.QWEN3VL)
+        self.gguf_writer.add_vision_use_gelu(True)
+
+        if self.hparams_vision is not None:
+            merge_size = self.hparams_vision.get("spatial_merge_size")
+            if merge_size is not None:
+                self.gguf_writer.add_vision_spatial_merge_size(int(merge_size))
+
+        # Use text config's rms_norm_eps for vision attention layernorm eps
+        rms_norm_eps = self.global_config.get("text_config", {}).get("rms_norm_eps", 1e-6)
+        self.gguf_writer.add_vision_attention_layernorm_eps(rms_norm_eps)
+
+        if self.is_deepstack_layers:
+            self.gguf_writer.add_vision_is_deepstack_layers(self.is_deepstack_layers)
+
+    def modify_tensors(self, data_torch: Tensor, name: str, bid: int | None) -> Iterable[tuple[str, Tensor]]:
+        assert self.hparams_vision is not None
+        # Skip text model tensors - they go in the text model file
+        if name.startswith("model.language_model.") or name.startswith("lm_head."):
+            return []
+
+        if name.startswith("model.visual."):
+            name = name.replace("model.visual.", "visual.", 1)
+
+        if name.startswith("visual.deepstack_merger_list."):
+            prefix, rest = name.split(".", maxsplit=3)[2:]
+            # prefix is the layer index, convert to absolute clip layer index!
+            idx = self.hparams_vision.get("deepstack_visual_indexes", [])[int(prefix)]
+            target = rest
+
+            tensor_type: gguf.MODEL_TENSOR
+            if target.startswith("norm."):
+                tensor_type = gguf.MODEL_TENSOR.V_DS_NORM
+                suffix = target.split(".", 1)[1]
+            elif target.startswith("linear_fc1."):
+                tensor_type = gguf.MODEL_TENSOR.V_DS_FC1
+                suffix = target.split(".", 1)[1]
+            elif target.startswith("linear_fc2."):
+                tensor_type = gguf.MODEL_TENSOR.V_DS_FC2
+                suffix = target.split(".", 1)[1]
+            else:
+                raise ValueError(f"Unexpected deepstack tensor: {name}")
+
+            new_name = self.format_tensor_name(tensor_type, idx, suffix=f".{suffix}")
+            return [(new_name, data_torch)]
+
+        if name.startswith("visual.merger."):
+            suffix = name.split(".", 2)[2]
+            if suffix.startswith("linear_fc"):
+                fc_idx_str, tail = suffix.split(".", 1)
+                fc_num = int(fc_idx_str.replace("linear_fc", ""))
+                # Qwen3VL has linear_fc1 and linear_fc2
+                # Map to indices 0 and 2 (matching Qwen2VL which uses indices 0 and 2)
+                if fc_num == 1:
+                    fc_idx = 0
+                elif fc_num == 2:
+                    fc_idx = 2
+                else:
+                    raise ValueError(f"unexpected fc index {fc_num} in {name}")
+                new_name = self.format_tensor_name(gguf.MODEL_TENSOR.V_MMPROJ, fc_idx, suffix=f".{tail}")
+            elif suffix.startswith("norm."):
+                new_name = self.format_tensor_name(gguf.MODEL_TENSOR.V_POST_NORM, suffix=f".{suffix.split('.', 1)[1]}")
+            else:
+                raise ValueError(f"Unexpected merger tensor: {name}")
+            return [(new_name, data_torch)]
+
+        if name == "visual.patch_embed.proj.weight":
+            # split Conv3D into Conv2Ds along temporal dimension
+            c1, c2, kt, _, _ = data_torch.shape
+            del c1, c2
+            if kt != 2:
+                raise ValueError("Current implementation only supports temporal_patch_size of 2")
+            return [
+                (gguf.TENSOR_NAMES[gguf.MODEL_TENSOR.V_ENC_EMBD_PATCH] + ".weight", data_torch[:, :, 0, ...]),
+                (gguf.TENSOR_NAMES[gguf.MODEL_TENSOR.V_ENC_EMBD_PATCH] + ".weight.1", data_torch[:, :, 1, ...]),
+            ]
+
+        if name == "visual.patch_embed.proj.bias":
+            # Include the bias - it's used by the C++ code
+            return [(gguf.TENSOR_NAMES[gguf.MODEL_TENSOR.V_ENC_EMBD_PATCH] + ".bias", data_torch)]
+
+        if name.startswith("visual."):
+            return [(self.map_tensor_name(name), data_torch)]
+
+        # Fall back to parent class for other tensors
+        return super().modify_tensors(data_torch, name, bid)
+
+
+@ModelBase.register("Qwen3VLForConditionalGeneration")
+class Qwen3VLTextModel(Qwen3Model):
+    model_arch = gguf.MODEL_ARCH.QWEN3VL
+
+    def set_gguf_parameters(self):
+        super().set_gguf_parameters()
+
+        # Handle MRoPE (Multi-axis Rotary Position Embedding) for Qwen3-VL
+        text_config = self.hparams.get("text_config", {})
+        # rope_scaling is deprecated in V5, use rope_parameters instead
+        rope_scaling = text_config.get("rope_scaling") or text_config.get("rope_parameters") or {}
+
+        if rope_scaling.get("mrope_section"):
+            # mrope_section contains [time, height, width] dimensions
+            mrope_section = rope_scaling["mrope_section"]
+            # Pad to 4 dimensions [time, height, width, extra]
+            while len(mrope_section) < 4:
+                mrope_section.append(0)
+            self.gguf_writer.add_rope_dimension_sections(mrope_section[:4])
+
+            logger.info(f"MRoPE sections: {mrope_section[:4]}")
+
+        vision_config = self.hparams.get("vision_config", {})
+        deepstack_layer_num = len(vision_config.get("deepstack_visual_indexes", []))
+        self.gguf_writer.add_num_deepstack_layers(deepstack_layer_num)
+
+    def modify_tensors(self, data_torch: Tensor, name: str, bid: int | None) -> Iterable[tuple[str, Tensor]]:
+        # Skip vision tensors - they go in the mmproj file
+        if name.startswith("model.visual."):
+            return []
+
+        return super().modify_tensors(data_torch, name, bid)
+
+
+@ModelBase.register("Qwen3VLMoeForConditionalGeneration")
+class Qwen3VLMoeTextModel(Qwen3MoeModel):
+    model_arch = gguf.MODEL_ARCH.QWEN3VLMOE
+
+    def set_gguf_parameters(self):
+        super().set_gguf_parameters()
+
+        # Handle MRoPE (Multi-axis Rotary Position Embedding) for Qwen3-VL
+        text_config = self.hparams.get("text_config", {})
+        # rope_scaling is deprecated in V5, use rope_parameters instead
+        rope_scaling = text_config.get("rope_scaling") or text_config.get("rope_parameters") or {}
+
+        if rope_scaling.get("mrope_section"):
+            # mrope_section contains [time, height, width] dimensions
+            mrope_section = rope_scaling["mrope_section"]
+            # Pad to 4 dimensions [time, height, width, extra]
+            while len(mrope_section) < 4:
+                mrope_section.append(0)
+            self.gguf_writer.add_rope_dimension_sections(mrope_section[:4])
+
+            logger.info(f"MRoPE sections: {mrope_section[:4]}")
+
+        vision_config = self.hparams.get("vision_config", {})
+        deepstack_layer_num = len(vision_config.get("deepstack_visual_indexes", []))
+        self.gguf_writer.add_num_deepstack_layers(deepstack_layer_num)
+
+    def modify_tensors(self, data_torch: Tensor, name: str, bid: int | None) -> Iterable[tuple[str, Tensor]]:
+        # Skip vision tensors - they go in the mmproj file
+        if name.startswith("model.visual."):
+            return []
+
+        return super().modify_tensors(data_torch, name, bid)
+
+
 @ModelBase.register("GPT2LMHeadModel")
 class GPT2Model(TextModel):
     model_arch = gguf.MODEL_ARCH.GPT2
diff --git a/ggml/include/ggml.h b/ggml/include/ggml.h
index d948b00cc7f..2311cdabe3b 100644
--- a/ggml/include/ggml.h
+++ b/ggml/include/ggml.h
@@ -242,6 +242,7 @@
 #define GGML_ROPE_TYPE_NEOX   2
 #define GGML_ROPE_TYPE_MROPE  8
 #define GGML_ROPE_TYPE_VISION 24
+#define GGML_ROPE_TYPE_IMROPE 40 // binary: 101000
 
 #define GGML_MROPE_SECTIONS   4
 
diff --git a/ggml/src/ggml-cpu/ops.cpp b/ggml/src/ggml-cpu/ops.cpp
index c17ab10245d..f66d36ff62c 100644
--- a/ggml/src/ggml-cpu/ops.cpp
+++ b/ggml/src/ggml-cpu/ops.cpp
@@ -5474,7 +5474,7 @@ static void ggml_rope_cache_init(
 }
 
 static void ggml_mrope_cache_init(
-     float theta_base_t, float theta_base_h, float theta_base_w, float theta_base_e, int sections[4], bool indep_sects,
+     float theta_base_t, float theta_base_h, float theta_base_w, float theta_base_e, int sections[4], bool is_imrope, bool indep_sects,
      float freq_scale, const float * freq_factors, float corr_dims[2], int64_t ne0, float ext_factor, float mscale,
      float * cache, float sin_sign, float theta_scale) {
     // ref: https://github.com/jquesnelle/yarn/blob/master/scaled_rope/LlamaYaRNScaledRotaryEmbedding.py
@@ -5509,14 +5509,26 @@ static void ggml_mrope_cache_init(
         }
 
         float theta = theta_t;
-        if (sector >= sections[0] && sector < sec_w) {
-            theta = theta_h;
-        }
-        else if (sector >= sec_w && sector < sec_w + sections[2]) {
-            theta = theta_w;
-        }
-        else if (sector >= sec_w + sections[2]) {
-            theta = theta_e;
+        if (is_imrope) { // qwen3vl apply interleaved mrope
+            if (sector % 3 == 1 && sector < 3 * sections[1]) {
+                theta = theta_h;
+            } else if (sector % 3 == 2 && sector < 3 * sections[2]) {
+                theta = theta_w;
+            } else if (sector % 3 == 0 && sector < 3 * sections[0]) {
+                theta = theta_t;
+            } else {
+                theta = theta_e;
+            }
+        } else {
+            if (sector >= sections[0] && sector < sec_w) {
+                theta = theta_h;
+            }
+            else if (sector >= sec_w && sector < sec_w + sections[2]) {
+                theta = theta_w;
+            }
+            else if (sector >= sec_w + sections[2]) {
+                theta = theta_e;
+            }
         }
 
         rope_yarn(
@@ -5589,6 +5601,7 @@ static void ggml_compute_forward_rope_f32(
 
     const bool is_neox = mode & GGML_ROPE_TYPE_NEOX;
     const bool is_mrope = mode & GGML_ROPE_TYPE_MROPE;  // ggml_rope_multi, multimodal rotary position embedding
+    const bool is_imrope = mode == GGML_ROPE_TYPE_IMROPE; // qwen3vl apply interleaved mrope
     const bool is_vision = mode == GGML_ROPE_TYPE_VISION;
 
     if (is_mrope) {
@@ -5627,7 +5640,7 @@ static void ggml_compute_forward_rope_f32(
                 const int64_t p_w = pos[i2 + ne2 * 2];
                 const int64_t p_e = pos[i2 + ne2 * 3];
                 ggml_mrope_cache_init(
-                    p_t, p_h, p_w, p_e, sections, is_vision,
+                    p_t, p_h, p_w, p_e, sections, is_imrope, is_vision,
                     freq_scale, freq_factors, corr_dims, ne0, ext_factor, attn_factor, cache, sin_sign, theta_scale);
             }
 
@@ -5775,6 +5788,7 @@ static void ggml_compute_forward_rope_f16(
 
     const bool is_neox = mode & GGML_ROPE_TYPE_NEOX;
     const bool is_mrope = mode & GGML_ROPE_TYPE_MROPE;
+    const bool is_imrope = mode == GGML_ROPE_TYPE_IMROPE;
     const bool is_vision = mode == GGML_ROPE_TYPE_VISION;
 
     if (is_mrope) {
@@ -5813,7 +5827,7 @@ static void ggml_compute_forward_rope_f16(
                 const int64_t p_w = pos[i2 + ne2 * 2];
                 const int64_t p_e = pos[i2 + ne2 * 3];
                 ggml_mrope_cache_init(
-                    p_t, p_h, p_w, p_e, sections, is_vision,
+                    p_t, p_h, p_w, p_e, sections, is_imrope, is_vision,
                     freq_scale, freq_factors, corr_dims, ne0, ext_factor, attn_factor, cache, sin_sign, theta_scale);
             }
 
diff --git a/ggml/src/ggml-cuda/rope.cu b/ggml/src/ggml-cuda/rope.cu
index d058504cd6c..78ed7f519ab 100644
--- a/ggml/src/ggml-cuda/rope.cu
+++ b/ggml/src/ggml-cuda/rope.cu
@@ -125,7 +125,7 @@ template<bool forward, bool has_ff, typename T>
 static __global__ void rope_multi(
         const T * x, T * dst, const int ne0, const int ne1, const int ne2, const int s1, const int s2,
         const int n_dims, const int32_t * pos, const float freq_scale, const float ext_factor, const float attn_factor,
-        const rope_corr_dims corr_dims, const float theta_scale, const float * freq_factors, const mrope_sections sections) {
+        const rope_corr_dims corr_dims, const float theta_scale, const float * freq_factors, const mrope_sections sections, const bool is_imrope) {
     const int i0 = 2*(blockDim.y*blockIdx.y + threadIdx.y);
 
     if (i0 >= ne0) {
@@ -152,17 +152,29 @@ static __global__ void rope_multi(
     const int sector = (i0 / 2) % sect_dims;
 
     float theta_base = 0.0;
-    if (sector < sections.v[0]) {
-        theta_base = pos[channel_x]*powf(theta_scale, i0/2.0f);
-    }
-    else if (sector >= sections.v[0] && sector < sec_w) {
-        theta_base = pos[channel_x + ne2 * 1]*powf(theta_scale, i0/2.0f);
-    }
-    else if (sector >= sec_w && sector < sec_w + sections.v[2]) {
-        theta_base = pos[channel_x + ne2 * 2]*powf(theta_scale, i0/2.0f);
-    }
-    else if (sector >= sec_w + sections.v[2]) {
-        theta_base = pos[channel_x + ne2 * 3]*powf(theta_scale, i0/2.0f);
+    if (is_imrope) {
+        if (sector % 3 == 1 && sector < 3 * sections.v[1]) { // h
+            theta_base = pos[channel_x + ne2 * 1]*powf(theta_scale, i0/2.0f);
+        } else if (sector % 3 == 2 && sector < 3 * sections.v[2]) { // w
+            theta_base = pos[channel_x + ne2 * 2]*powf(theta_scale, i0/2.0f);
+        } else if (sector % 3 == 0 && sector < 3 * sections.v[0]) { // t
+            theta_base = pos[channel_x]*powf(theta_scale, i0/2.0f);
+        } else {
+            theta_base = pos[channel_x + ne2 * 3]*powf(theta_scale, i0/2.0f);
+        }
+    } else {
+        if (sector < sections.v[0]) {
+            theta_base = pos[channel_x]*powf(theta_scale, i0/2.0f);
+        }
+        else if (sector >= sections.v[0] && sector < sec_w) {
+            theta_base = pos[channel_x + ne2 * 1]*powf(theta_scale, i0/2.0f);
+        }
+        else if (sector >= sec_w && sector < sec_w + sections.v[2]) {
+            theta_base = pos[channel_x + ne2 * 2]*powf(theta_scale, i0/2.0f);
+        }
+        else if (sector >= sec_w + sections.v[2]) {
+            theta_base = pos[channel_x + ne2 * 3]*powf(theta_scale, i0/2.0f);
+        }
     }
 
     const float freq_factor = has_ff ? freq_factors[i0/2] : 1.0f;
@@ -276,7 +288,7 @@ template<bool forward, typename T>
 static void rope_multi_cuda(
         const T * x, T * dst, const int ne0, const int ne1, const int ne2, const int s1, const int s2, const int n_dims, const int nr,
         const int32_t * pos, const float freq_scale, const float freq_base, const float ext_factor, const float attn_factor,
-        const rope_corr_dims corr_dims, const float * freq_factors, const mrope_sections sections, cudaStream_t stream) {
+        const rope_corr_dims corr_dims, const float * freq_factors, const mrope_sections sections, const bool is_imrope, cudaStream_t stream) {
     GGML_ASSERT(ne0 % 2 == 0);
     const dim3 block_dims(1, CUDA_ROPE_BLOCK_SIZE, 1);
     const int n_blocks_x = (ne0 + 2*CUDA_ROPE_BLOCK_SIZE - 1) / (2*CUDA_ROPE_BLOCK_SIZE);
@@ -287,11 +299,11 @@ static void rope_multi_cuda(
     if (freq_factors == nullptr) {
         rope_multi<forward, false, T><<<block_nums, block_dims, 0, stream>>>(
             x, dst, ne0, ne1, ne2, s1, s2, n_dims, pos, freq_scale, ext_factor,
-            attn_factor, corr_dims, theta_scale, freq_factors, sections);
+            attn_factor, corr_dims, theta_scale, freq_factors, sections, is_imrope);
     } else {
         rope_multi<forward, true, T><<<block_nums, block_dims, 0, stream>>>(
             x, dst, ne0, ne1, ne2, s1, s2, n_dims, pos, freq_scale, ext_factor,
-            attn_factor, corr_dims, theta_scale, freq_factors, sections);
+            attn_factor, corr_dims, theta_scale, freq_factors, sections, is_imrope);
     }
 }
 
@@ -369,6 +381,7 @@ void ggml_cuda_op_rope_impl(ggml_backend_cuda_context & ctx, ggml_tensor * dst)
 
     const bool is_neox = mode & GGML_ROPE_TYPE_NEOX;
     const bool is_mrope = mode & GGML_ROPE_TYPE_MROPE;
+    const bool is_imrope = mode == GGML_ROPE_TYPE_IMROPE;
     const bool is_vision = mode == GGML_ROPE_TYPE_VISION;
 
     if (is_mrope) {
@@ -406,11 +419,11 @@ void ggml_cuda_op_rope_impl(ggml_backend_cuda_context & ctx, ggml_tensor * dst)
         if (src0->type == GGML_TYPE_F32) {
             rope_multi_cuda<forward>(
                 (const float *) src0_d, (float *) dst_d, ne00, ne01, ne02, s01, s02, n_dims, nr, pos, freq_scale,
-                freq_base, ext_factor, attn_factor, corr_dims, freq_factors, sections, stream);
+                freq_base, ext_factor, attn_factor, corr_dims, freq_factors, sections, is_imrope, stream);
         } else if (src0->type == GGML_TYPE_F16) {
             rope_multi_cuda<forward>(
                 (const half *) src0_d, (half *) dst_d, ne00, ne01, ne02, s01, s02, n_dims, nr, pos, freq_scale,
-                freq_base, ext_factor, attn_factor, corr_dims, freq_factors, sections, stream);
+                freq_base, ext_factor, attn_factor, corr_dims, freq_factors, sections, is_imrope, stream);
         } else {
             GGML_ABORT("fatal error");
         }
diff --git a/ggml/src/ggml-metal/ggml-metal-device.cpp b/ggml/src/ggml-metal/ggml-metal-device.cpp
index 75811634227..1a3c7873b74 100644
--- a/ggml/src/ggml-metal/ggml-metal-device.cpp
+++ b/ggml/src/ggml-metal/ggml-metal-device.cpp
@@ -1332,11 +1332,12 @@ ggml_metal_pipeline_t ggml_metal_library_get_pipeline_rope(ggml_metal_library_t
 
     const bool is_neox   = mode & GGML_ROPE_TYPE_NEOX;
     const bool is_mrope  = mode & GGML_ROPE_TYPE_MROPE;
+    const bool is_imrope = mode == GGML_ROPE_TYPE_IMROPE;
     const bool is_vision = mode == GGML_ROPE_TYPE_VISION;
 
     if (is_neox) {
         snprintf(base, 256, "kernel_rope_neox_%s", ggml_type_name(op->src[0]->type));
-    } else if (is_mrope && !is_vision) {
+    } else if ((is_mrope || is_imrope) && !is_vision) {
         GGML_ASSERT(op->src[1]->ne[0]*4 >= op->src[0]->ne[2]); // need at least 4 pos per token
         snprintf(base, 256, "kernel_rope_multi_%s", ggml_type_name(op->src[0]->type));
     } else if (is_vision) {
@@ -1346,14 +1347,20 @@ ggml_metal_pipeline_t ggml_metal_library_get_pipeline_rope(ggml_metal_library_t
         snprintf(base, 256, "kernel_rope_norm_%s", ggml_type_name(op->src[0]->type));
     }
 
-    snprintf(name, 256, "%s", base);
+    snprintf(name, 256, "%s_imrope=%d", base, is_imrope ? 1 : 0);
 
     ggml_metal_pipeline_t res = ggml_metal_library_get_pipeline(lib, name);
     if (res) {
         return res;
     }
 
-    res = ggml_metal_library_compile_pipeline(lib, base, name, nullptr);
+    ggml_metal_cv_t cv = ggml_metal_cv_init();
+
+    ggml_metal_cv_set_bool(cv, is_imrope, FC_ROPE + 0);
+
+    res = ggml_metal_library_compile_pipeline(lib, base, name, cv);
+
+    ggml_metal_cv_free(cv);
 
     return res;
 }
diff --git a/ggml/src/ggml-metal/ggml-metal-impl.h b/ggml/src/ggml-metal/ggml-metal-impl.h
index 96f43d260a3..7a878a657bc 100644
--- a/ggml/src/ggml-metal/ggml-metal-impl.h
+++ b/ggml/src/ggml-metal/ggml-metal-impl.h
@@ -76,6 +76,7 @@
 #define FC_FLASH_ATTN_EXT_VEC_REDUCE   500
 #define FC_MUL_MV                      600
 #define FC_MUL_MM                      700
+#define FC_ROPE                        800
 
 // op-specific constants
 #define OP_FLASH_ATTN_EXT_NQPTG 8
diff --git a/ggml/src/ggml-metal/ggml-metal.metal b/ggml/src/ggml-metal/ggml-metal.metal
index 2c2f0141514..fa839a1df6e 100644
--- a/ggml/src/ggml-metal/ggml-metal.metal
+++ b/ggml/src/ggml-metal/ggml-metal.metal
@@ -3709,6 +3709,8 @@ template [[host_name("kernel_mul_mv_bf16_f32_short")]]  kernel mul_mv_t_t_short_
 template [[host_name("kernel_mul_mv_bf16_bf16_short")]] kernel mul_mv_t_t_short_t kernel_mul_mv_t_t_short<bfloat, bfloat>;
 #endif
 
+constant bool FC_rope_is_imrope [[function_constant(FC_ROPE + 0)]];
+
 static float rope_yarn_ramp(const float low, const float high, const int i0) {
     const float y = (i0 / 2 - low) / max(0.001f, high - low);
     return 1.0f - min(1.0f, max(0.0f, y));
@@ -3889,14 +3891,26 @@ kernel void kernel_rope_multi(
             const int sector    = ic % sect_dims;
 
             float theta_base;
-            if (sector < args.sect_0) {
-                theta_base = (float) pos[i2];
-            } else if (sector < sec_w01) {
-                theta_base = (float) pos[i2 + args.ne02];
-            } else if (sector < sec_w012) {
-                theta_base = (float) pos[i2 + args.ne02 * 2];
+            if (FC_rope_is_imrope) {
+                if (sector % 3 == 1 && sector < 3 * args.sect_1) { // h
+                    theta_base = (float) pos[i2 + args.ne02 * 1];
+                } else if (sector % 3 == 2 && sector < 3 * args.sect_2) { // w
+                    theta_base = (float) pos[i2 + args.ne02 * 2];
+                } else if (sector % 3 == 0 && sector < 3 * args.sect_0) { // t
+                    theta_base = (float) pos[i2 + args.ne02 * 0];
+                } else { // e
+                    theta_base = (float) pos[i2 + args.ne02 * 3];
+                }
             } else {
-                theta_base = (float) pos[i2 + args.ne02 * 3];
+                if (sector < args.sect_0) {
+                    theta_base = (float) pos[i2];
+                } else if (sector < sec_w01) {
+                    theta_base = (float) pos[i2 + args.ne02 * 1];
+                } else if (sector < sec_w012) {
+                    theta_base = (float) pos[i2 + args.ne02 * 2];
+                } else {
+                    theta_base = (float) pos[i2 + args.ne02 * 3];
+                }
             }
             // end of mrope
 
diff --git a/ggml/src/ggml-sycl/rope.cpp b/ggml/src/ggml-sycl/rope.cpp
index a3ab703d1f0..69140b19a4c 100644
--- a/ggml/src/ggml-sycl/rope.cpp
+++ b/ggml/src/ggml-sycl/rope.cpp
@@ -119,7 +119,7 @@ static void rope_multi(const T * x, T * dst, const int ne0, const int ne1, const
                         const size_t s2, const int n_dims, const int32_t * pos, const float freq_scale,
                         const float ext_factor, const float attn_factor, const rope_corr_dims corr_dims,
                         const float theta_scale, const float * freq_factors, const mrope_sections sections,
-                        const sycl::nd_item<3> & item_ct1) {
+                        const bool is_imrope, const sycl::nd_item<3> & item_ct1) {
     // get index pos
     const int i0 = 2 * (item_ct1.get_group(1) * item_ct1.get_local_range(1) + item_ct1.get_local_id(1));
     if (i0 >= ne0) {
@@ -143,17 +143,29 @@ static void rope_multi(const T * x, T * dst, const int ne0, const int ne1, const
 
 
     float theta_base = 0.0;
-    if (sector < sections.v[0]) {
-        theta_base = pos[channel_x]*sycl::pow(theta_scale, i0/2.0f);
-    }
-    else if (sector >= sections.v[0] && sector < sec_w) {
-        theta_base = pos[channel_x + ne2 * 1]*sycl::pow(theta_scale, i0/2.0f);
-    }
-    else if (sector >= sec_w && sector < sec_w + sections.v[2]) {
-        theta_base = pos[channel_x + ne2 * 2]*sycl::pow(theta_scale, i0/2.0f);
-    }
-    else if (sector >= sec_w + sections.v[2]) {
-        theta_base = pos[channel_x + ne2 * 3]*sycl::pow(theta_scale, i0/2.0f);
+    if (is_imrope) {
+        if (sector % 3 == 1 && sector < 3 * sections.v[1]) {
+            theta_base = pos[channel_x + ne2 * 1]*sycl::pow(theta_scale, i0/2.0f);
+        } else if (sector % 3 == 2 && sector < 3 * sections.v[2]) {
+            theta_base = pos[channel_x + ne2 * 2]*sycl::pow(theta_scale, i0/2.0f);
+        } else if (sector % 3 == 0 && sector < 3 * sections.v[0]) {
+            theta_base = pos[channel_x]*sycl::pow(theta_scale, i0/2.0f);
+        } else {
+            theta_base = pos[channel_x + ne2 * 3]*sycl::pow(theta_scale, i0/2.0f);
+        }
+    } else {
+        if (sector < sections.v[0]) {
+            theta_base = pos[channel_x]*sycl::pow(theta_scale, i0/2.0f);
+        }
+        else if (sector >= sections.v[0] && sector < sec_w) {
+            theta_base = pos[channel_x + ne2 * 1]*sycl::pow(theta_scale, i0/2.0f);
+        }
+        else if (sector >= sec_w && sector < sec_w + sections.v[2]) {
+            theta_base = pos[channel_x + ne2 * 2]*sycl::pow(theta_scale, i0/2.0f);
+        }
+        else if (sector >= sec_w + sections.v[2]) {
+            theta_base = pos[channel_x + ne2 * 3]*sycl::pow(theta_scale, i0/2.0f);
+        }
     }
 
     const float freq_factor = has_ff ? freq_factors[i0 / 2] : 1.0f;
@@ -281,7 +293,7 @@ static void rope_multi_sycl(const T * x, T * dst, const int ne0, const int ne1,
                              const size_t s2, const int n_dims, const int nr, const int32_t * pos,
                              const float freq_scale, const float freq_base, const float ext_factor,
                              const float attn_factor, const rope_corr_dims corr_dims, const float * freq_factors,
-                             const mrope_sections sections, queue_ptr stream) {
+                             const mrope_sections sections, const bool is_imrope, queue_ptr stream) {
     GGML_ASSERT(ne0 % 2 == 0);
     const sycl::range<3>    block_dims(1, SYCL_ROPE_BLOCK_SIZE, 1);
     const int               n_blocks_y = ceil_div(ne0, (2 * SYCL_ROPE_BLOCK_SIZE));
@@ -297,12 +309,12 @@ static void rope_multi_sycl(const T * x, T * dst, const int ne0, const int ne1,
     if (freq_factors == nullptr) {
         stream->parallel_for(nd_range, [=](sycl::nd_item<3> item_ct1) {
             rope_multi<T, false>(x, dst, ne0, ne1, ne2, s1, s2, n_dims, pos, freq_scale, ext_factor, attn_factor,
-                                  corr_dims, theta_scale, freq_factors, sections, item_ct1);
+                                  corr_dims, theta_scale, freq_factors, sections, is_imrope, item_ct1);
         });
     } else {
         stream->parallel_for(nd_range, [=](sycl::nd_item<3> item_ct1) {
             rope_multi<T, true>(x, dst, ne0, ne1, ne2, s1, s2, n_dims, pos, freq_scale, ext_factor, attn_factor,
-                                 corr_dims, theta_scale, freq_factors, sections, item_ct1);
+                                 corr_dims, theta_scale, freq_factors, sections, is_imrope, item_ct1);
         });
     }
 }
@@ -381,6 +393,7 @@ inline void ggml_sycl_op_rope(ggml_backend_sycl_context & ctx, ggml_tensor *dst)
 
     const bool is_neox = mode & GGML_ROPE_TYPE_NEOX;
     const bool is_mrope = mode & GGML_ROPE_TYPE_MROPE;
+    const bool is_imrope = mode == GGML_ROPE_TYPE_IMROPE;
     const bool is_vision = mode == GGML_ROPE_TYPE_VISION;
 
     if (is_mrope) {
@@ -422,11 +435,11 @@ inline void ggml_sycl_op_rope(ggml_backend_sycl_context & ctx, ggml_tensor *dst)
         if (dst->src[0]->type == GGML_TYPE_F16) {
             rope_multi_sycl((const sycl::half *)dst->src[0]->data, (sycl::half *)dst->data, ne00, ne01, ne02, s01,
                 s02, n_dims, nr, pos, freq_scale, freq_base, ext_factor, attn_factor, corr_dims,
-                freq_factors, sections, main_stream);
+                freq_factors, sections, is_imrope, main_stream);
         } else if (dst->src[0]->type == GGML_TYPE_F32) {
             rope_multi_sycl((const float *) dst->src[0]->data, (float *) dst->data, ne00, ne01, ne02, s01, s02, n_dims,
                              nr, pos, freq_scale, freq_base, ext_factor, attn_factor, corr_dims, freq_factors, sections,
-                             main_stream);
+                             is_imrope, main_stream);
         } else {
             GGML_ABORT("Fatal error: Tensor type unsupported!");
         }
diff --git a/ggml/src/ggml-vulkan/ggml-vulkan.cpp b/ggml/src/ggml-vulkan/ggml-vulkan.cpp
index d0976519f26..b61879aa5d3 100644
--- a/ggml/src/ggml-vulkan/ggml-vulkan.cpp
+++ b/ggml/src/ggml-vulkan/ggml-vulkan.cpp
@@ -1056,6 +1056,7 @@ struct vk_op_rope_push_constants {
     uint32_t s1;
     uint32_t s2;
     int32_t sections[4];
+    uint32_t is_imrope;
     uint32_t is_back;
     uint32_t set_rows_stride;
 };
@@ -9927,6 +9928,8 @@ static void ggml_vk_rope(ggml_backend_vk_context * ctx, vk_context& subctx, cons
         memcpy(sections, (int32_t *) dst->op_params + 11, sizeof(int)*4);
     }
 
+    const bool is_imrope = mode == GGML_ROPE_TYPE_IMROPE;
+
     float corr_dims[2];
     ggml_rope_yarn_corr_dims(n_dims, n_ctx_orig, freq_base, beta_fast, beta_slow, corr_dims);
 
@@ -9948,7 +9951,7 @@ static void ggml_vk_rope(ggml_backend_vk_context * ctx, vk_context& subctx, cons
         (uint32_t)src0->ne[0], (uint32_t)n_dims, freq_scale, (uint32_t)src0->ne[1],
         freq_base, ext_factor, attn_factor, {corr_dims[0], corr_dims[1]}, theta_scale,
         src2 != nullptr, (uint32_t)src0->ne[2], s1, s2,
-        { sections[0], sections[1], sections[2], sections[3] }, backprop, set_rows_stride,
+        { sections[0], sections[1], sections[2], sections[3] }, is_imrope, backprop, set_rows_stride,
     }, dryrun);
 }
 
diff --git a/ggml/src/ggml-vulkan/vulkan-shaders/rope_head.glsl b/ggml/src/ggml-vulkan/vulkan-shaders/rope_head.glsl
index 0eda186c8a3..fa2bb33394c 100644
--- a/ggml/src/ggml-vulkan/vulkan-shaders/rope_head.glsl
+++ b/ggml/src/ggml-vulkan/vulkan-shaders/rope_head.glsl
@@ -27,6 +27,7 @@ layout (push_constant) uniform parameter {
     uint s1;
     uint s2;
     int sections[4];
+    uint is_imrope;
     uint is_back;
     uint set_rows_stride;
 } p;
diff --git a/ggml/src/ggml-vulkan/vulkan-shaders/rope_multi.comp b/ggml/src/ggml-vulkan/vulkan-shaders/rope_multi.comp
index 111286b4988..54aabcf2228 100644
--- a/ggml/src/ggml-vulkan/vulkan-shaders/rope_multi.comp
+++ b/ggml/src/ggml-vulkan/vulkan-shaders/rope_multi.comp
@@ -32,17 +32,29 @@ void main() {
     const uint sector = (i0 / 2) % sect_dims;
 
     float theta_base = 0.0;
-    if (sector < p.sections[0]) {
-        theta_base = data_pos[channel_x]*pow(p.theta_scale, i0/2.0f);
-    }
-    else if (sector >= p.sections[0] && sector < sec_w) {
-        theta_base = data_pos[channel_x + ne2 * 1]*pow(p.theta_scale, i0/2.0f);
-    }
-    else if (sector >= sec_w && sector < sec_w + p.sections[2]) {
-        theta_base = data_pos[channel_x + ne2 * 2]*pow(p.theta_scale, i0/2.0f);
-    }
-    else if (sector >= sec_w + p.sections[2]) {
-        theta_base = data_pos[channel_x + ne2 * 3]*pow(p.theta_scale, i0/2.0f);
+    if (p.is_imrope != 0) {
+        if (sector % 3 == 1 && sector < 3 * p.sections[1]) {
+            theta_base = data_pos[channel_x + ne2 * 1]*pow(p.theta_scale, i0/2.0f);
+        } else if (sector % 3 == 2 && sector < 3 * p.sections[2]) {
+            theta_base = data_pos[channel_x + ne2 * 2]*pow(p.theta_scale, i0/2.0f);
+        } else if (sector % 3 == 0 && sector < 3 * p.sections[0]) {
+            theta_base = data_pos[channel_x]*pow(p.theta_scale, i0/2.0f);
+        } else {
+            theta_base = data_pos[channel_x + ne2 * 3]*pow(p.theta_scale, i0/2.0f);
+        }
+    } else {
+        if (sector < p.sections[0]) {
+            theta_base = data_pos[channel_x]*pow(p.theta_scale, i0/2.0f);
+        }
+        else if (sector >= p.sections[0] && sector < sec_w) {
+            theta_base = data_pos[channel_x + ne2 * 1]*pow(p.theta_scale, i0/2.0f);
+        }
+        else if (sector >= sec_w && sector < sec_w + p.sections[2]) {
+            theta_base = data_pos[channel_x + ne2 * 2]*pow(p.theta_scale, i0/2.0f);
+        }
+        else if (sector >= sec_w + p.sections[2]) {
+            theta_base = data_pos[channel_x + ne2 * 3]*pow(p.theta_scale, i0/2.0f);
+        }
     }
 
     const float freq_factor = p.has_ff != 0 ? data_ff[i0/2] : 1.0f;
diff --git a/ggml/src/ggml-webgpu/wgsl-shaders/rope.tmpl.wgsl b/ggml/src/ggml-webgpu/wgsl-shaders/rope.tmpl.wgsl
index 9a6ff41128b..84dc8dbff61 100644
--- a/ggml/src/ggml-webgpu/wgsl-shaders/rope.tmpl.wgsl
+++ b/ggml/src/ggml-webgpu/wgsl-shaders/rope.tmpl.wgsl
@@ -221,6 +221,7 @@ fn main(@builtin(global_invocation_id) gid: vec3<u32>) {
 
     let is_neox = bool(params.mode & 2);
     let is_mrope = bool(params.mode & 8);
+    let is_imrope = params.mode == 40;
     let is_vision = params.mode == 24;
 
     var i = gid.x * 2; // start index for this thread
@@ -248,24 +249,36 @@ fn main(@builtin(global_invocation_id) gid: vec3<u32>) {
         let sec_w = params.sections1 + params.sections0;
         let sec_e = params.sections2 + sec_w;
         let sector = (i0 / 2) % sect_dims;
-        if (sector >= params.sections0 && sector < sec_w) {
-            theta_base_mult = 1;
-            if (is_vision) {
-                theta_scale_pwr = sector - params.sections0;
-            }
-        } else if (sector >= sec_w && sector < sec_e) {
-            theta_base_mult = 2;
-            if (is_vision) {
-                theta_scale_pwr = sector - sec_w;
-            }
-        } else if (sector >= sec_e) {
-            if (is_vision) {
-                theta_scale_pwr = sector - sec_e;
-                theta_scale_pwr = (i0 / 2) % sec_e;
-            }
-            theta_base_mult = 3;
-        } else if (is_vision) {
-            theta_scale_pwr = sector;
+        if (is_imrope) {
+          if (sector % 3 == 1 && sector < 3 * params.sections1) {
+              theta_base_mult = 1;
+          } else if (sector % 3 == 2 && sector < 3 * params.sections2) {
+              theta_base_mult = 2;
+          } else if (sector % 3 == 0 && sector < 3 * params.sections0) {
+              theta_base_mult = 0;
+          } else {
+              theta_base_mult = 3;
+          }
+        } else {
+          if (sector >= params.sections0 && sector < sec_w) {
+              theta_base_mult = 1;
+              if (is_vision) {
+                  theta_scale_pwr = sector - params.sections0;
+              }
+          } else if (sector >= sec_w && sector < sec_e) {
+              theta_base_mult = 2;
+              if (is_vision) {
+                  theta_scale_pwr = sector - sec_w;
+              }
+          } else if (sector >= sec_e) {
+              if (is_vision) {
+                  theta_scale_pwr = sector - sec_e;
+                  theta_scale_pwr = (i0 / 2) % sec_e;
+              }
+              theta_base_mult = 3;
+          } else if (is_vision) {
+              theta_scale_pwr = sector;
+          }
         }
     }
     let theta_base = f32(src1[params.offset_src1 + i2 + params.ne2 * theta_base_mult]) * pow(params.theta_scale, f32(theta_scale_pwr));
diff --git a/gguf-py/gguf/constants.py b/gguf-py/gguf/constants.py
index a0c08f69172..d75ac704fed 100644
--- a/gguf-py/gguf/constants.py
+++ b/gguf-py/gguf/constants.py
@@ -111,6 +111,7 @@ class LLM:
         EXPERTS_PER_GROUP                 = "{arch}.experts_per_group"
         MOE_EVERY_N_LAYERS                = "{arch}.moe_every_n_layers"
         NEXTN_PREDICT_LAYERS              = "{arch}.nextn_predict_layers"
+        NUM_DEEPSTACK_LAYERS              = "{arch}.n_deepstack_layers"
         POOLING_TYPE                      = "{arch}.pooling_type"
         LOGIT_SCALE                       = "{arch}.logit_scale"
         DECODER_START_TOKEN_ID            = "{arch}.decoder_start_token_id"
@@ -277,6 +278,7 @@ class ClipVision:
         USE_GELU            = "clip.use_gelu"
         USE_SILU            = "clip.use_silu"
         N_WA_PATTERN        = "clip.vision.n_wa_pattern" # used by qwen2.5vl
+        IS_DEEPSTACK_LAYERS = "clip.vision.is_deepstack_layers"
 
         class Attention:
             HEAD_COUNT      = "clip.vision.attention.head_count"
@@ -350,6 +352,8 @@ class MODEL_ARCH(IntEnum):
     QWEN2VL          = auto()
     QWEN3            = auto()
     QWEN3MOE         = auto()
+    QWEN3VL          = auto()
+    QWEN3VLMOE       = auto()
     PHI2             = auto()
     PHI3             = auto()
     PHIMOE           = auto()
@@ -431,6 +435,7 @@ class VISION_PROJECTOR_TYPE(IntEnum):
     GLM_EDGE  = auto()
     MERGER    = auto()
     GEMMA3    = auto()
+    QWEN3VL   = auto()
     COGVLM    = auto()
 
 
@@ -648,6 +653,9 @@ class MODEL_TENSOR(IntEnum):
     V_RESMPL_QUERY       = auto() # minicpmv
     V_TOK_EMBD_IMG_BREAK = auto() # pixtral
     V_MM_PATCH_MERGER    = auto() # mistral small 3.1
+    V_DS_NORM            = auto() # qwen3vl
+    V_DS_FC1             = auto() # qwen3vl
+    V_DS_FC2             = auto() # qwen3vl
     V_MM_POST_FC_NORM    = auto() # cogvlm
     V_MM_UP              = auto() # cogvlm
     V_MM_DOWN            = auto() # cogvlm
@@ -709,6 +717,8 @@ class MODEL_TENSOR(IntEnum):
     MODEL_ARCH.QWEN2VL:          "qwen2vl",
     MODEL_ARCH.QWEN3:            "qwen3",
     MODEL_ARCH.QWEN3MOE:         "qwen3moe",
+    MODEL_ARCH.QWEN3VL:          "qwen3vl",
+    MODEL_ARCH.QWEN3VLMOE:       "qwen3vlmoe",
     MODEL_ARCH.PHI2:             "phi2",
     MODEL_ARCH.PHI3:             "phi3",
     MODEL_ARCH.PHIMOE:           "phimoe",
@@ -1007,6 +1017,9 @@ class MODEL_TENSOR(IntEnum):
     MODEL_TENSOR.V_RESMPL_QUERY:            "resampler.query",
     MODEL_TENSOR.V_TOK_EMBD_IMG_BREAK:      "v.token_embd.img_break", # pixtral
     MODEL_TENSOR.V_MM_PATCH_MERGER:         "mm.patch_merger", # mistral small 3.1
+    MODEL_TENSOR.V_DS_NORM:                 "v.deepstack.{bid}.norm",
+    MODEL_TENSOR.V_DS_FC1:                  "v.deepstack.{bid}.fc1",
+    MODEL_TENSOR.V_DS_FC2:                  "v.deepstack.{bid}.fc2",
     MODEL_TENSOR.V_MM_POST_FC_NORM:         "mm.post_fc_norm", # cogvlm
     MODEL_TENSOR.V_MM_UP:                   "mm.up",
     MODEL_TENSOR.V_MM_DOWN:                 "mm.down",
@@ -1082,6 +1095,9 @@ class MODEL_TENSOR(IntEnum):
         MODEL_TENSOR.V_RESMPL_QUERY,
         MODEL_TENSOR.V_TOK_EMBD_IMG_BREAK,
         MODEL_TENSOR.V_MM_PATCH_MERGER,
+        MODEL_TENSOR.V_DS_NORM,
+        MODEL_TENSOR.V_DS_FC1,
+        MODEL_TENSOR.V_DS_FC2,
         MODEL_TENSOR.V_MM_POST_FC_NORM,
         MODEL_TENSOR.V_MM_UP,
         MODEL_TENSOR.V_MM_DOWN,
@@ -1529,6 +1545,40 @@ class MODEL_TENSOR(IntEnum):
         MODEL_TENSOR.FFN_DOWN_EXP,
         MODEL_TENSOR.FFN_UP_EXP,
     ],
+    MODEL_ARCH.QWEN3VL: [
+        MODEL_TENSOR.TOKEN_EMBD,
+        MODEL_TENSOR.OUTPUT_NORM,
+        MODEL_TENSOR.OUTPUT,
+        MODEL_TENSOR.ROPE_FREQS,
+        MODEL_TENSOR.ATTN_NORM,
+        MODEL_TENSOR.ATTN_Q,
+        MODEL_TENSOR.ATTN_Q_NORM,
+        MODEL_TENSOR.ATTN_K,
+        MODEL_TENSOR.ATTN_K_NORM,
+        MODEL_TENSOR.ATTN_V,
+        MODEL_TENSOR.ATTN_OUT,
+        MODEL_TENSOR.FFN_NORM,
+        MODEL_TENSOR.FFN_GATE,
+        MODEL_TENSOR.FFN_DOWN,
+        MODEL_TENSOR.FFN_UP,
+    ],
+    MODEL_ARCH.QWEN3VLMOE: [
+        MODEL_TENSOR.TOKEN_EMBD,
+        MODEL_TENSOR.OUTPUT_NORM,
+        MODEL_TENSOR.OUTPUT,
+        MODEL_TENSOR.ATTN_NORM,
+        MODEL_TENSOR.ATTN_Q,
+        MODEL_TENSOR.ATTN_Q_NORM,
+        MODEL_TENSOR.ATTN_K,
+        MODEL_TENSOR.ATTN_K_NORM,
+        MODEL_TENSOR.ATTN_V,
+        MODEL_TENSOR.ATTN_OUT,
+        MODEL_TENSOR.FFN_NORM,
+        MODEL_TENSOR.FFN_GATE_INP,
+        MODEL_TENSOR.FFN_GATE_EXP,
+        MODEL_TENSOR.FFN_DOWN_EXP,
+        MODEL_TENSOR.FFN_UP_EXP,
+    ],
     MODEL_ARCH.PLAMO: [
         MODEL_TENSOR.TOKEN_EMBD,
         MODEL_TENSOR.OUTPUT_NORM,
@@ -3106,6 +3156,7 @@ class VisionProjectorType:
     LLAMA4 = "llama4"
     QWEN2VL = "qwen2vl_merger"
     QWEN25VL = "qwen2.5vl_merger"
+    QWEN3VL = "qwen3vl_merger"
     ULTRAVOX = "ultravox"
     INTERNVL = "internvl"
     QWEN2A = "qwen2a" # audio
diff --git a/gguf-py/gguf/gguf_writer.py b/gguf-py/gguf/gguf_writer.py
index d52d4f40f78..a051daeeb13 100644
--- a/gguf-py/gguf/gguf_writer.py
+++ b/gguf-py/gguf/gguf_writer.py
@@ -860,6 +860,9 @@ def add_attn_temperature_length(self, value: int) -> None:
     def add_pooling_type(self, value: PoolingType) -> None:
         self.add_uint32(Keys.LLM.POOLING_TYPE.format(arch=self.arch), value.value)
 
+    def add_num_deepstack_layers(self, count: int) -> None:
+        self.add_uint32(Keys.LLM.NUM_DEEPSTACK_LAYERS.format(arch=self.arch), count)
+
     def add_rope_dimension_count(self, count: int) -> None:
         self.add_uint32(Keys.Rope.DIMENSION_COUNT.format(arch=self.arch), count)
 
@@ -1071,6 +1074,9 @@ def add_vision_projector_scale_factor(self, value: int) -> None:
     def add_vision_n_wa_pattern(self, value: int) -> None:
         self.add_uint32(Keys.ClipVision.N_WA_PATTERN, value)
 
+    def add_vision_is_deepstack_layers(self, layers: Sequence[bool]) -> None:
+        self.add_array(Keys.ClipVision.IS_DEEPSTACK_LAYERS, layers)
+
     # audio models
 
     def add_audio_projection_dim(self, value: int) -> None:
diff --git a/gguf-py/gguf/tensor_mapping.py b/gguf-py/gguf/tensor_mapping.py
index 37e6fc85d51..6fe6f22358c 100644
--- a/gguf-py/gguf/tensor_mapping.py
+++ b/gguf-py/gguf/tensor_mapping.py
@@ -1215,10 +1215,12 @@ class TensorNameMap:
             "model.vision_model.embeddings.position_embedding", # SmolVLM
             "vision_model.positional_embedding_vlm", # llama 4
             "vision_tower.patch_embed.pos_emb", # kimi-vl
+            "visual.pos_embed", # qwen3vl
             "model.vision.patch_embedding.position_embedding", # cogvlm
         ),
 
         MODEL_TENSOR.V_ENC_ATTN_QKV: (
+            "visual.blocks.{bid}.attn.qkv", # qwen3vl
             "model.vision.transformer.layers.{bid}.attention.query_key_value", # cogvlm
         ),
 
@@ -1320,6 +1322,7 @@ class TensorNameMap:
             "vision_model.model.layers.{bid}.mlp.fc1", # llama4
             "visual.blocks.{bid}.mlp.fc1", # qwen2vl
             "visual.blocks.{bid}.mlp.up_proj", # qwen2.5vl
+            "visual.blocks.{bid}.mlp.linear_fc1", # qwen3vl
             "vision_tower.encoder.blocks.{bid}.mlp.fc0", # kimi-vl (fc0/fc1)
             "model.vision.transformer.layers.{bid}.mlp.fc1", # cogvlm
         ),
@@ -1340,6 +1343,7 @@ class TensorNameMap:
             "vision_model.model.layers.{bid}.mlp.fc2", # llama4
             "visual.blocks.{bid}.mlp.fc2", # qwen2vl
             "visual.blocks.{bid}.mlp.down_proj", # qwen2.5vl
+            "visual.blocks.{bid}.mlp.linear_fc2", # qwen3vl
             "vision_tower.encoder.blocks.{bid}.mlp.fc1", # kimi-vl (fc0/fc1)
             "model.vision.transformer.layers.{bid}.mlp.fc2", # cogvlm
         ),
@@ -1438,6 +1442,18 @@ class TensorNameMap:
             "patch_merger.merging_layer", # mistral
         ),
 
+        MODEL_TENSOR.V_DS_NORM: (
+            "model.visual.deepstack_merger_list.{bid}.norm", # deepstack in qwen3vl
+        ),
+
+        MODEL_TENSOR.V_DS_FC1: (
+            "model.visual.deepstack_merger_list.{bid}.linear_fc1", # deepstack in qwen3vl
+        ),
+
+        MODEL_TENSOR.V_DS_FC2: (
+            "model.visual.deepstack_merger_list.{bid}.linear_fc2", # deepstack in qwen3vl
+        ),
+
         MODEL_TENSOR.V_MM_POST_FC_NORM: (
             "model.vision.linear_proj.norm1", # cogvlm
         ),
diff --git a/include/llama.h b/include/llama.h
index a0a660bff88..08e2ffa34c9 100644
--- a/include/llama.h
+++ b/include/llama.h
@@ -83,6 +83,7 @@ extern "C" {
         LLAMA_ROPE_TYPE_NORM   = 0,
         LLAMA_ROPE_TYPE_NEOX   = GGML_ROPE_TYPE_NEOX,
         LLAMA_ROPE_TYPE_MROPE  = GGML_ROPE_TYPE_MROPE,
+        LLAMA_ROPE_TYPE_IMROPE = GGML_ROPE_TYPE_IMROPE,
         LLAMA_ROPE_TYPE_VISION = GGML_ROPE_TYPE_VISION,
     };
 
diff --git a/src/llama-arch.cpp b/src/llama-arch.cpp
index ba45e88c08e..ad2880034c2 100644
--- a/src/llama-arch.cpp
+++ b/src/llama-arch.cpp
@@ -32,6 +32,8 @@ static const std::map<llm_arch, const char *> LLM_ARCH_NAMES = {
     { LLM_ARCH_QWEN2VL,          "qwen2vl"          },
     { LLM_ARCH_QWEN3,            "qwen3"            },
     { LLM_ARCH_QWEN3MOE,         "qwen3moe"         },
+    { LLM_ARCH_QWEN3VL,          "qwen3vl"          },
+    { LLM_ARCH_QWEN3VLMOE,       "qwen3vlmoe"       },
     { LLM_ARCH_PHI2,             "phi2"             },
     { LLM_ARCH_PHI3,             "phi3"             },
     { LLM_ARCH_PHIMOE,           "phimoe"           },
@@ -146,6 +148,7 @@ static const std::map<llm_kv, const char *> LLM_KV_NAMES = {
     { LLM_KV_EXPERTS_PER_GROUP,                 "%s.experts_per_group"                 },
     { LLM_KV_MOE_EVERY_N_LAYERS,                "%s.moe_every_n_layers"                },
     { LLM_KV_NEXTN_PREDICT_LAYERS,              "%s.nextn_predict_layers"              },
+    { LLM_KV_NUM_DEEPSTACK_LAYERS,              "%s.n_deepstack_layers"                },
     { LLM_KV_POOLING_TYPE,                      "%s.pooling_type"                      },
     { LLM_KV_LOGIT_SCALE,                       "%s.logit_scale"                       },
     { LLM_KV_DECODER_START_TOKEN_ID,            "%s.decoder_start_token_id"            },
@@ -780,6 +783,45 @@ static const std::map<llm_arch, std::map<llm_tensor, const char *>> LLM_TENSOR_N
             { LLM_TENSOR_FFN_UP_EXPS,        "blk.%d.ffn_up_exps" },
         },
     },
+    {
+        LLM_ARCH_QWEN3VL,
+        {
+            { LLM_TENSOR_TOKEN_EMBD,      "token_embd" },
+            { LLM_TENSOR_OUTPUT_NORM,     "output_norm" },
+            { LLM_TENSOR_OUTPUT,          "output" },
+            { LLM_TENSOR_ATTN_NORM,       "blk.%d.attn_norm" },
+            { LLM_TENSOR_ATTN_Q,          "blk.%d.attn_q" },
+            { LLM_TENSOR_ATTN_Q_NORM,     "blk.%d.attn_q_norm" },
+            { LLM_TENSOR_ATTN_K,          "blk.%d.attn_k" },
+            { LLM_TENSOR_ATTN_K_NORM,     "blk.%d.attn_k_norm" },
+            { LLM_TENSOR_ATTN_V,          "blk.%d.attn_v" },
+            { LLM_TENSOR_ATTN_OUT,        "blk.%d.attn_output" },
+            { LLM_TENSOR_FFN_NORM,        "blk.%d.ffn_norm" },
+            { LLM_TENSOR_FFN_GATE,        "blk.%d.ffn_gate" },
+            { LLM_TENSOR_FFN_DOWN,        "blk.%d.ffn_down" },
+            { LLM_TENSOR_FFN_UP,          "blk.%d.ffn_up" },
+        },
+    },
+    {
+        LLM_ARCH_QWEN3VLMOE,
+        {
+            { LLM_TENSOR_TOKEN_EMBD,         "token_embd" },
+            { LLM_TENSOR_OUTPUT_NORM,        "output_norm" },
+            { LLM_TENSOR_OUTPUT,             "output" },
+            { LLM_TENSOR_ATTN_NORM,          "blk.%d.attn_norm" },
+            { LLM_TENSOR_ATTN_Q,             "blk.%d.attn_q" },
+            { LLM_TENSOR_ATTN_Q_NORM,        "blk.%d.attn_q_norm" },
+            { LLM_TENSOR_ATTN_K,             "blk.%d.attn_k" },
+            { LLM_TENSOR_ATTN_K_NORM,        "blk.%d.attn_k_norm" },
+            { LLM_TENSOR_ATTN_V,             "blk.%d.attn_v" },
+            { LLM_TENSOR_ATTN_OUT,           "blk.%d.attn_output" },
+            { LLM_TENSOR_FFN_NORM,           "blk.%d.ffn_norm" },
+            { LLM_TENSOR_FFN_GATE_INP,       "blk.%d.ffn_gate_inp" },
+            { LLM_TENSOR_FFN_GATE_EXPS,      "blk.%d.ffn_gate_exps" },
+            { LLM_TENSOR_FFN_DOWN_EXPS,      "blk.%d.ffn_down_exps" },
+            { LLM_TENSOR_FFN_UP_EXPS,        "blk.%d.ffn_up_exps" },
+        },
+    },
     {
         LLM_ARCH_PHI2,
         {
diff --git a/src/llama-arch.h b/src/llama-arch.h
index 3350e8b4315..4dae35e2923 100644
--- a/src/llama-arch.h
+++ b/src/llama-arch.h
@@ -36,6 +36,8 @@ enum llm_arch {
     LLM_ARCH_QWEN2VL,
     LLM_ARCH_QWEN3,
     LLM_ARCH_QWEN3MOE,
+    LLM_ARCH_QWEN3VL,
+    LLM_ARCH_QWEN3VLMOE,
     LLM_ARCH_PHI2,
     LLM_ARCH_PHI3,
     LLM_ARCH_PHIMOE,
@@ -150,6 +152,7 @@ enum llm_kv {
     LLM_KV_EXPERTS_PER_GROUP,
     LLM_KV_MOE_EVERY_N_LAYERS,
     LLM_KV_NEXTN_PREDICT_LAYERS,
+    LLM_KV_NUM_DEEPSTACK_LAYERS,
     LLM_KV_POOLING_TYPE,
     LLM_KV_LOGIT_SCALE,
     LLM_KV_DECODER_START_TOKEN_ID,
diff --git a/src/llama-hparams.cpp b/src/llama-hparams.cpp
index db65d69eabd..514d653844c 100644
--- a/src/llama-hparams.cpp
+++ b/src/llama-hparams.cpp
@@ -148,7 +148,7 @@ bool llama_hparams::is_recurrent(uint32_t il) const {
 }
 
 uint32_t llama_hparams::n_pos_per_embd() const {
-    return rope_type == LLAMA_ROPE_TYPE_MROPE ? 4 : 1;
+    return rope_type == LLAMA_ROPE_TYPE_MROPE || rope_type == LLAMA_ROPE_TYPE_IMROPE ? 4 : 1;
 }
 
 bool llama_hparams::is_swa(uint32_t il) const {
diff --git a/src/llama-hparams.h b/src/llama-hparams.h
index 6fcf91b7daa..539fecb3f78 100644
--- a/src/llama-hparams.h
+++ b/src/llama-hparams.h
@@ -183,6 +183,9 @@ struct llama_hparams {
     std::array<float, LLAMA_MAX_LAYERS> xielu_beta;
     std::array<float, LLAMA_MAX_LAYERS> xielu_eps;
 
+    // qwen3vl deepstack
+    uint32_t n_deepstack_layers = 0;
+
     // needed by encoder-decoder models (e.g. T5, FLAN-T5)
     // ref: https://github.com/ggerganov/llama.cpp/pull/8141
     llama_token dec_start_token_id = LLAMA_TOKEN_NULL;
diff --git a/src/llama-kv-cache.cpp b/src/llama-kv-cache.cpp
index 17627b6ccbb..e26385a1fea 100644
--- a/src/llama-kv-cache.cpp
+++ b/src/llama-kv-cache.cpp
@@ -1375,7 +1375,7 @@ ggml_tensor * llama_kv_cache::build_rope_shift(
     const auto & yarn_beta_slow  = cparams.yarn_beta_slow;
 
     const auto & n_rot     = hparams.n_rot;
-    const auto & rope_type = hparams.rope_type == LLAMA_ROPE_TYPE_MROPE
+    const auto & rope_type = hparams.rope_type == LLAMA_ROPE_TYPE_MROPE || hparams.rope_type == LLAMA_ROPE_TYPE_IMROPE
                                 // @ngxson : this is a workaround
                                 // for M-RoPE, we want to rotate the whole vector when doing KV shift
                                 // a normal RoPE should work, we just need to use the correct ordering
diff --git a/src/llama-model.cpp b/src/llama-model.cpp
index 35759a00aec..1e0680bee95 100644
--- a/src/llama-model.cpp
+++ b/src/llama-model.cpp
@@ -1025,6 +1025,21 @@ void llama_model::load_hparams(llama_model_loader & ml) {
                     default: type = LLM_TYPE_UNKNOWN;
                 }
             } break;
+        case LLM_ARCH_QWEN3VL:
+            {
+                ml.get_key(LLM_KV_NUM_DEEPSTACK_LAYERS, hparams.n_deepstack_layers, false);
+                ml.get_key_or_arr(LLM_KV_ROPE_DIMENSION_SECTIONS, hparams.rope_sections, 4, true);
+                ml.get_key(LLM_KV_ATTENTION_LAYERNORM_RMS_EPS, hparams.f_norm_rms_eps);
+                switch (hparams.n_layer) {
+                    case 28: type = LLM_TYPE_1_7B; break;
+                    case 36: type = hparams.n_embd == 2560 ? LLM_TYPE_4B : LLM_TYPE_8B; break;
+                    case 64: type = LLM_TYPE_32B; break;
+                    default: type = LLM_TYPE_UNKNOWN;
+                }
+                // since vision model stacks deepstack features along feature dim
+                // we also create a fake "n_embd" for text model to be the main embd + deepstack embds
+                hparams.n_embd *= hparams.n_deepstack_layers + 1;
+            } break;
         case LLM_ARCH_QWEN3MOE:
             {
                 ml.get_key(LLM_KV_EXPERT_FEED_FORWARD_LENGTH,        hparams.n_ff_exp, false);
@@ -1036,6 +1051,21 @@ void llama_model::load_hparams(llama_model_loader & ml) {
                     default: type = LLM_TYPE_UNKNOWN;
                 }
             } break;
+        case LLM_ARCH_QWEN3VLMOE:
+            {
+                ml.get_key(LLM_KV_NUM_DEEPSTACK_LAYERS, hparams.n_deepstack_layers, false);
+                ml.get_key_or_arr(LLM_KV_ROPE_DIMENSION_SECTIONS, hparams.rope_sections, 4, true);
+                ml.get_key(LLM_KV_EXPERT_FEED_FORWARD_LENGTH, hparams.n_ff_exp, false);
+                ml.get_key(LLM_KV_ATTENTION_LAYERNORM_RMS_EPS, hparams.f_norm_rms_eps);
+                switch (hparams.n_layer) {
+                    case 48: type = LLM_TYPE_30B_A3B; break;
+                    case 94: type = LLM_TYPE_235B_A22B; break;
+                    default: type = LLM_TYPE_UNKNOWN;
+                }
+                // since vision model stacks deepstack features along feature dim
+                // we also create a fake "n_embd" for text model to be the main embd + deepstack embds
+                hparams.n_embd *= hparams.n_deepstack_layers + 1;
+            } break;
         case LLM_ARCH_PHI2:
             {
                 ml.get_key(LLM_KV_ATTENTION_LAYERNORM_EPS, hparams.f_norm_eps);
@@ -3285,7 +3315,12 @@ bool llama_model::load_tensors(llama_model_loader & ml) {
                     }
                 } break;
             case LLM_ARCH_QWEN3:
+            case LLM_ARCH_QWEN3VL:
                 {
+                    // for model loading, the weights only have the main embd
+                    // so we need to divide by the number of deepstack layers + 1
+                    // n_embd is const int so we declare a new variable
+                    int64_t n_embd = hparams.n_embd / (hparams.n_deepstack_layers + 1);
                     tok_embd = create_tensor(tn(LLM_TENSOR_TOKEN_EMBD, "weight"), {n_embd, n_vocab}, 0);
 
                     // output
@@ -3319,7 +3354,12 @@ bool llama_model::load_tensors(llama_model_loader & ml) {
                     }
                 } break;
             case LLM_ARCH_QWEN3MOE:
+            case LLM_ARCH_QWEN3VLMOE:
                 {
+                    // for model loading, the weights only have the main embd
+                    // so we need to divide by the number of deepstack layers + 1
+                    // n_embd is const int so we declare a new variable
+                    int64_t n_embd = hparams.n_embd / (hparams.n_deepstack_layers + 1);
                     tok_embd = create_tensor(tn(LLM_TENSOR_TOKEN_EMBD, "weight"), {n_embd, n_vocab}, 0);
 
                     // output
@@ -6428,6 +6468,10 @@ void llama_model::print_info() const {
         LLAMA_LOG_INFO("%s: freq_scale_train = %g\n",     __func__, hparams.rope_freq_scale_train);
         LLAMA_LOG_INFO("%s: n_ctx_orig_yarn  = %u\n",     __func__, hparams.n_ctx_orig_yarn);
         LLAMA_LOG_INFO("%s: rope_finetuned   = %s\n",     __func__, hparams.rope_finetuned ? "yes" : "unknown");
+        // MRoPE (Multi-axis Rotary Position Embedding) sections
+        if (const auto & s = hparams.rope_sections; s[0] || s[1] || s[2] || s[3]) {
+            LLAMA_LOG_INFO("%s: mrope sections   = [%d, %d, %d, %d]\n", __func__, s[0], s[1], s[2], s[3]);
+        }
         if (!classifier_labels.empty()) {
             LLAMA_LOG_INFO("%s: n_cls_out        = %u\n", __func__, hparams.n_cls_out);
 
@@ -6493,7 +6537,7 @@ void llama_model::print_info() const {
         LLAMA_LOG_INFO("%s: n_ff_shexp       = %d\n",     __func__, hparams.n_ff_shexp);
     }
 
-    if (arch == LLM_ARCH_QWEN3MOE || arch == LLM_ARCH_OPENAI_MOE) {
+    if (arch == LLM_ARCH_QWEN3MOE || arch == LLM_ARCH_OPENAI_MOE || arch == LLM_ARCH_QWEN3VLMOE) {
         LLAMA_LOG_INFO("%s: n_ff_exp         = %d\n",     __func__, hparams.n_ff_exp);
     }
 
@@ -9655,6 +9699,301 @@ struct llm_build_qwen3moe : public llm_graph_context {
     }
 };
 
+struct llm_build_qwen3vl : public llm_graph_context {
+    llm_build_qwen3vl(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+
+        const int64_t n_embd_full = hparams.n_embd; // main embd + deepstack embds
+        const size_t n_deepstack_layers = hparams.n_deepstack_layers;
+        const int64_t n_embd = n_embd_full / (n_deepstack_layers + 1);
+        const int64_t n_embd_head = hparams.n_embd_head_v;
+
+
+        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+        GGML_ASSERT(n_embd_head == hparams.n_rot);
+
+        ggml_tensor * cur;
+        ggml_tensor * inpL;
+
+        inpL = build_inp_embd(model.tok_embd);
+
+        int sections[4];
+        std::copy(std::begin(hparams.rope_sections), std::begin(hparams.rope_sections) + 4, sections);
+
+        std::vector<ggml_tensor *> deepstack_features(n_deepstack_layers, nullptr);
+
+        if (ubatch.embd) {
+            // Image input: split main embd and deepstack embds
+            ggml_tensor * inpL_main = ggml_view_2d(ctx0, inpL, n_embd, n_tokens, inpL->nb[1], 0);
+            for (size_t i = 0; i < n_deepstack_layers; i++) {
+                deepstack_features[i] = ggml_view_2d(ctx0, inpL, n_embd, n_tokens, inpL->nb[1], (i + 1) * n_embd * sizeof(float));
+            }
+            inpL = inpL_main;
+        }
+
+        // inp_pos - contains the positions
+        ggml_tensor * inp_pos = build_inp_pos();
+
+        auto * inp_attn = build_attn_inp_kv();
+
+        ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+        for (int il = 0; il < n_layer; ++il) {
+            ggml_tensor * inpSA = inpL;
+
+            // norm
+            cur = build_norm(inpL,
+                    model.layers[il].attn_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "attn_norm", il);
+
+            // self-attention
+            {
+                // compute Q and K and RoPE them
+                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+                cb(Qcur, "Qcur", il);
+
+                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+                cb(Kcur, "Kcur", il);
+
+                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+                cb(Vcur, "Vcur", il);
+
+                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+                Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL, LLM_NORM_RMS, il);
+                cb(Qcur, "Qcur_normed", il);
+
+                Qcur = ggml_rope_multi(
+                        ctx0, Qcur, inp_pos, nullptr,
+                        n_rot, sections, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+                Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, NULL, LLM_NORM_RMS, il);
+                cb(Kcur, "Kcur_normed", il);
+
+                Kcur = ggml_rope_multi(
+                        ctx0, Kcur, inp_pos, nullptr,
+                        n_rot, sections, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+                cb(Qcur, "Qcur", il);
+                cb(Kcur, "Kcur", il);
+                cb(Vcur, "Vcur", il);
+
+                cur = build_attn(inp_attn,
+                        model.layers[il].wo, model.layers[il].bo,
+                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+            }
+
+            if (il == n_layer - 1 && inp_out_ids) {
+                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+            }
+
+            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+            cb(ffn_inp, "ffn_inp", il);
+
+            // feed-forward network
+            cur = build_norm(ffn_inp,
+                    model.layers[il].ffn_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "ffn_norm", il);
+
+            cur = build_ffn(cur,
+                    model.layers[il].ffn_up,   NULL, NULL,
+                    model.layers[il].ffn_gate, NULL, NULL,
+                    model.layers[il].ffn_down, NULL, NULL,
+                    NULL,
+                    LLM_FFN_SILU, LLM_FFN_PAR, il);
+            cb(cur, "ffn_out", il);
+
+            cur = ggml_add(ctx0, cur, ffn_inp);
+
+            cur = build_cvec(cur, il);
+            cb(cur, "l_out", il);
+
+            if (ubatch.embd && (size_t)il < n_deepstack_layers) {
+                cur = ggml_add(ctx0, cur, deepstack_features[il]);
+                cb(cur, "deepstack_out", il);
+            }
+
+            // input for next layer
+            inpL = cur;
+        }
+
+        cur = inpL;
+
+        cur = build_norm(cur,
+                model.output_norm, NULL,
+                LLM_NORM_RMS, -1);
+
+        cb(cur, "result_norm", -1);
+        res->t_embd = cur;
+
+        // lm_head
+        cur = build_lora_mm(model.output, cur);
+
+        cb(cur, "result_output", -1);
+        res->t_logits = cur;
+
+        ggml_build_forward_expand(gf, cur);
+    }
+};
+
+struct llm_build_qwen3vlmoe : public llm_graph_context {
+    llm_build_qwen3vlmoe(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+        const int64_t n_embd_full = hparams.n_embd; // main embd + deepstack embds
+        const size_t n_deepstack_layers = hparams.n_deepstack_layers;
+        const int64_t n_embd = n_embd_full / (n_deepstack_layers + 1);
+        const int64_t n_embd_head = hparams.n_embd_head_v;
+
+        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+        GGML_ASSERT(n_embd_head == hparams.n_rot);
+
+        ggml_tensor * cur;
+        ggml_tensor * inpL;
+
+        inpL = build_inp_embd(model.tok_embd);
+
+        int sections[4];
+        std::copy(std::begin(hparams.rope_sections), std::begin(hparams.rope_sections) + 4, sections);
+
+        std::vector<ggml_tensor *> deepstack_features(n_deepstack_layers, nullptr);
+
+        if (ubatch.embd) {
+            // Image input: split main embd and deepstack embds
+            ggml_tensor * inpL_main = ggml_view_2d(ctx0, inpL, n_embd, n_tokens, inpL->nb[1], 0);
+            for (size_t i = 0; i < n_deepstack_layers; i++) {
+                deepstack_features[i] = ggml_view_2d(ctx0, inpL, n_embd, n_tokens, inpL->nb[1], (i + 1) * n_embd * sizeof(float));
+            }
+            inpL = inpL_main;
+        }
+
+        // inp_pos - contains the positions
+        ggml_tensor * inp_pos = build_inp_pos();
+
+        auto * inp_attn = build_attn_inp_kv();
+
+        ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+        for (int il = 0; il < n_layer; ++il) {
+            ggml_tensor * inpSA = inpL;
+
+            // norm
+            cur = build_norm(inpL,
+                    model.layers[il].attn_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "attn_norm", il);
+
+            // self_attention
+            {
+                // compute Q and K and RoPE them
+                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+                cb(Qcur, "Qcur", il);
+
+                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+                cb(Kcur, "Kcur", il);
+
+                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+                cb(Vcur, "Vcur", il);
+
+                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+                Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL, LLM_NORM_RMS, il);
+                cb(Qcur, "Qcur_normed", il);
+
+                Qcur = ggml_rope_multi(
+                        ctx0, Qcur, inp_pos, nullptr,
+                        n_rot, sections, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+                Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, NULL, LLM_NORM_RMS, il);
+                cb(Kcur, "Kcur_normed", il);
+
+                Kcur = ggml_rope_multi(
+                        ctx0, Kcur, inp_pos, nullptr,
+                        n_rot, sections, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+                cb(Qcur, "Qcur", il);
+                cb(Kcur, "Kcur", il);
+                cb(Vcur, "Vcur", il);
+
+                cur = build_attn(inp_attn,
+                        model.layers[il].wo, model.layers[il].bo,
+                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+            }
+
+            if (il == n_layer - 1 && inp_out_ids) {
+                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+            }
+
+            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+            cb(ffn_inp, "ffn_inp", il);
+
+            // MoE branch
+            cur = build_norm(ffn_inp,
+                    model.layers[il].ffn_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "ffn_norm", il);
+
+            ggml_tensor * moe_out =
+                build_moe_ffn(cur,
+                        model.layers[il].ffn_gate_inp,
+                        model.layers[il].ffn_up_exps,
+                        model.layers[il].ffn_gate_exps,
+                        model.layers[il].ffn_down_exps,
+                        nullptr,
+                        n_expert, n_expert_used,
+                        LLM_FFN_SILU, true,
+                        false, 0.0,
+                        LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
+                        il);
+            cb(moe_out, "ffn_moe_out", il);
+            cur = moe_out;
+
+            cur = ggml_add(ctx0, cur, ffn_inp);
+
+            cur = build_cvec(cur, il);
+            cb(cur, "l_out", il);
+
+            if (ubatch.embd && (size_t)il < n_deepstack_layers) {
+                cur = ggml_add(ctx0, cur, deepstack_features[il]);
+                cb(cur, "deepstack_out", il);
+            }
+
+            // input for next layer
+            inpL = cur;
+        }
+
+        cur = inpL;
+
+        cur = build_norm(cur,
+                model.output_norm, NULL,
+                LLM_NORM_RMS, -1);
+
+        cb(cur, "result_norm", -1);
+        res->t_embd = cur;
+
+        // lm_head
+        cur = build_lora_mm(model.output, cur);
+
+        cb(cur, "result_output", -1);
+        res->t_logits = cur;
+
+        ggml_build_forward_expand(gf, cur);
+    }
+};
+
 struct llm_build_phi2 : public llm_graph_context {
     llm_build_phi2(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
         const int64_t n_embd_head = hparams.n_embd_head_v;
@@ -20014,6 +20353,14 @@ ggml_cgraph * llama_model::build_graph(const llm_graph_params & params) const {
             {
                 llm = std::make_unique<llm_build_qwen3moe>(*this, params);
             } break;
+        case LLM_ARCH_QWEN3VL:
+            {
+                llm = std::make_unique<llm_build_qwen3vl>(*this, params);
+            } break;
+        case LLM_ARCH_QWEN3VLMOE:
+            {
+                llm = std::make_unique<llm_build_qwen3vlmoe>(*this, params);
+            } break;
         case LLM_ARCH_PHI2:
             {
                 llm = std::make_unique<llm_build_phi2>(*this, params);
@@ -20532,6 +20879,9 @@ llama_rope_type llama_model_rope_type(const llama_model * model) {
 
         case LLM_ARCH_QWEN2VL:
             return LLAMA_ROPE_TYPE_MROPE;
+        case LLM_ARCH_QWEN3VL:
+        case LLM_ARCH_QWEN3VLMOE:
+            return LLAMA_ROPE_TYPE_IMROPE;
 
         // all model arches should be listed explicitly here
         case LLM_ARCH_UNKNOWN:
diff --git a/tests/test-backend-ops.cpp b/tests/test-backend-ops.cpp
index 4b1304c2b89..92361d6f0f4 100644
--- a/tests/test-backend-ops.cpp
+++ b/tests/test-backend-ops.cpp
@@ -7076,7 +7076,12 @@ static std::vector<std::unique_ptr<test_case>> make_test_cases_eval() {
                                     test_cases.emplace_back(new test_rope(type, {128,  28, 2, 1}, 128, GGML_ROPE_TYPE_MROPE,  512, fs, ef, af, ff, v, fw)); // rope_multi,m-rope (qwen2vl 7B)
                                     test_cases.emplace_back(new test_rope(type, {128,  12, 2, 1},  20, GGML_ROPE_TYPE_MROPE,  512, fs, ef, af, ff, v, fw));
                                     test_cases.emplace_back(new test_rope(type, {128,  28, 2, 1},  32, GGML_ROPE_TYPE_MROPE,  512, fs, ef, af, ff, v, fw));
+                                    test_cases.emplace_back(new test_rope(type, {128,  12, 2, 1}, 128, GGML_ROPE_TYPE_IMROPE,  512, fs, ef, af, ff, v, fw)); // rope_multi,imrope (qwen3vl 2B)
+                                    test_cases.emplace_back(new test_rope(type, {128,  28, 2, 1}, 128, GGML_ROPE_TYPE_IMROPE,  512, fs, ef, af, ff, v, fw)); // rope_multi,imrope (qwen3vl 7B)
+                                    test_cases.emplace_back(new test_rope(type, {128,  12, 2, 1},  20, GGML_ROPE_TYPE_IMROPE,  512, fs, ef, af, ff, v, fw));
+                                    test_cases.emplace_back(new test_rope(type, {128,  28, 2, 1},  32, GGML_ROPE_TYPE_IMROPE,  512, fs, ef, af, ff, v, fw));
                                     test_cases.emplace_back(new test_rope(type, { 80,  16, 2, 1},  80, GGML_ROPE_TYPE_VISION, 512, fs, ef, af, ff, v, fw)); // rope_multi,m-rope (qwen2vl ViT)
+                                    test_cases.emplace_back(new test_rope(type, {128,  16, 2, 1}, 128, GGML_ROPE_TYPE_IMROPE, 512, fs, ef, af, ff, v, fw)); // rope_multi,m-rope (qwen3vl)
                                 }
 
                                 test_cases.emplace_back(new test_rope(type, { 64, 128, 2, 1},  64, GGML_ROPE_TYPE_NEOX, 512, fs, ef, af, ff, v, fw)); // neox (falcon 40B)
@@ -7092,7 +7097,7 @@ static std::vector<std::unique_ptr<test_case>> make_test_cases_eval() {
 
     // single inplace test per type/mode/ff
     for (ggml_type type : {GGML_TYPE_F32, GGML_TYPE_F16}) {
-        for (int mode : {GGML_ROPE_TYPE_NORMAL, GGML_ROPE_TYPE_NEOX, GGML_ROPE_TYPE_MROPE, GGML_ROPE_TYPE_VISION}) {
+        for (int mode : {GGML_ROPE_TYPE_NORMAL, GGML_ROPE_TYPE_NEOX, GGML_ROPE_TYPE_MROPE, GGML_ROPE_TYPE_IMROPE, GGML_ROPE_TYPE_VISION}) {
             for (bool ff : {false, true}) {
                 test_cases.emplace_back(new test_rope(type, {128,  32, 2, 1}, 128, mode, 512, 1.4245f, 0.7465f, 1.4245f, ff, 0, true, true));
             }
diff --git a/tests/test-rope.cpp b/tests/test-rope.cpp
index 322b8bb99ec..22c51d81f60 100644
--- a/tests/test-rope.cpp
+++ b/tests/test-rope.cpp
@@ -138,7 +138,7 @@ int main(int /*argc*/, const char ** /*argv*/) {
     struct ggml_tensor * x;
 
     // rope f32
-    for (int m = 0; m < 5; ++m) {
+    for (int m = 0; m < 6; ++m) {
         const int ndims = 4;
 
         const int64_t n_rot = 128;
@@ -180,7 +180,7 @@ int main(int /*argc*/, const char ** /*argv*/) {
             struct ggml_tensor * p2 = ggml_new_tensor_1d(ctx0, GGML_TYPE_I32, ne[2] * 4);
 
             int sections[4] = {16, 24, 24, 0};
-            mode = (m == 3) ? GGML_ROPE_TYPE_MROPE : GGML_ROPE_TYPE_VISION;
+            mode = (m == 3) ? GGML_ROPE_TYPE_MROPE : (m == 4) ? GGML_ROPE_TYPE_VISION : GGML_ROPE_TYPE_IMROPE;
 
             for (int i = 0; i < ne[2]; ++i) {
                 for (int j = 0; j < 4; ++j) {
diff --git a/tools/mtmd/clip-impl.h b/tools/mtmd/clip-impl.h
index d4b88cb6980..311a4c9086a 100644
--- a/tools/mtmd/clip-impl.h
+++ b/tools/mtmd/clip-impl.h
@@ -39,6 +39,7 @@
 #define KEY_FEATURE_LAYER       "clip.vision.feature_layer"
 #define KEY_PROJ_SCALE_FACTOR   "clip.vision.projector.scale_factor"
 #define KEY_SPATIAL_MERGE_SIZE  "clip.vision.spatial_merge_size"
+#define KEY_IS_DEEPSTACK_LAYERS "clip.vision.is_deepstack_layers"
 
 #define KEY_MM_PATCH_MERGE_TYPE   "clip.vision.mm_patch_merge_type"
 #define KEY_IMAGE_GRID_PINPOINTS  "clip.vision.image_grid_pinpoints"
@@ -94,6 +95,9 @@
 #define TN_TOK_IMG_BREAK   "v.token_embd.img_break"     // pixtral
 #define TN_TOK_GLM_BOI     "adapter.boi"                // glm-edge (these embeddings are not in text model)
 #define TN_TOK_GLM_EOI     "adapter.eoi"                // glm-edge (these embeddings are not in text model)
+#define TN_DEEPSTACK_NORM  "v.deepstack.%d.norm.%s"     // qwen3vl deepstack
+#define TN_DEEPSTACK_FC1   "v.deepstack.%d.fc1.%s"      // qwen3vl deepstack
+#define TN_DEEPSTACK_FC2   "v.deepstack.%d.fc2.%s"      // qwen3vl deepstack
 
 // mimicpmv
 #define TN_MINICPMV_POS_EMBD_K "resampler.pos_embed_k"
@@ -136,6 +140,7 @@ enum projector_type {
     PROJECTOR_TYPE_MINICPMV,
     PROJECTOR_TYPE_GLM_EDGE,
     PROJECTOR_TYPE_QWEN2VL,
+    PROJECTOR_TYPE_QWEN3VL,
     PROJECTOR_TYPE_GEMMA3,
     PROJECTOR_TYPE_IDEFICS3,
     PROJECTOR_TYPE_PIXTRAL,
@@ -161,6 +166,7 @@ static std::map<projector_type, std::string> PROJECTOR_TYPE_NAMES = {
     { PROJECTOR_TYPE_GLM_EDGE,  "adapter"},
     { PROJECTOR_TYPE_QWEN2VL,   "qwen2vl_merger"},
     { PROJECTOR_TYPE_QWEN25VL,  "qwen2.5vl_merger"},
+    { PROJECTOR_TYPE_QWEN3VL,   "qwen3vl_merger"},
     { PROJECTOR_TYPE_GEMMA3,    "gemma3"},
     { PROJECTOR_TYPE_IDEFICS3,  "idefics3"},
     { PROJECTOR_TYPE_PIXTRAL,   "pixtral"},
diff --git a/tools/mtmd/clip.cpp b/tools/mtmd/clip.cpp
index a135ba0a2b3..b312fda637f 100644
--- a/tools/mtmd/clip.cpp
+++ b/tools/mtmd/clip.cpp
@@ -241,6 +241,18 @@ struct clip_layer {
     // layer scale (no bias)
     ggml_tensor * ls_1_w = nullptr;
     ggml_tensor * ls_2_w = nullptr;
+
+    // qwen3vl deepstack merger
+    ggml_tensor * deepstack_norm_w = nullptr;
+    ggml_tensor * deepstack_norm_b = nullptr;
+    ggml_tensor * deepstack_fc1_w = nullptr;
+    ggml_tensor * deepstack_fc1_b = nullptr;
+    ggml_tensor * deepstack_fc2_w = nullptr;
+    ggml_tensor * deepstack_fc2_b = nullptr;
+
+    bool has_deepstack() const {
+        return deepstack_fc1_w != nullptr;
+    }
 };
 
 struct clip_model {
@@ -260,6 +272,8 @@ struct clip_model {
 
     std::vector<clip_layer> layers;
 
+    int32_t n_deepstack_layers = 0; // used by Qwen3-VL, calculated from clip_layer
+
     ggml_tensor * post_ln_w;
     ggml_tensor * post_ln_b;
 
@@ -840,6 +854,189 @@ struct clip_graph {
         return gf;
     }
 
+    // Qwen3VL
+    ggml_cgraph * build_qwen3vl() {
+        GGML_ASSERT(model.patch_bias != nullptr);
+        GGML_ASSERT(model.position_embeddings != nullptr);
+        GGML_ASSERT(model.class_embedding == nullptr);
+
+        const int batch_size       = 1;
+        const int n_pos            = n_patches;
+        const int num_position_ids = n_pos * 4; // m-rope requires 4 dim per position
+
+        norm_type norm_t = NORM_TYPE_NORMAL;
+
+        int mrope_sections[4] = {d_head/4, d_head/4, d_head/4, d_head/4};
+
+        ggml_tensor * inp_raw = build_inp_raw();
+        ggml_tensor * inp = ggml_conv_2d(ctx0, model.patch_embeddings_0, inp_raw, patch_size, patch_size, 0, 0, 1, 1);
+
+        GGML_ASSERT(img.nx % (patch_size * 2) == 0);
+        GGML_ASSERT(img.ny % (patch_size * 2) == 0);
+
+        // second conv dimension
+        {
+            auto inp_1 = ggml_conv_2d(ctx0, model.patch_embeddings_1, inp_raw, patch_size, patch_size, 0, 0, 1, 1);
+            inp = ggml_add(ctx0, inp, inp_1);
+
+            inp = ggml_permute(ctx0, inp, 1, 2, 0, 3);  // [w, h, c, b] -> [c, w, h, b]
+            inp = ggml_cont_4d(
+                ctx0, inp,
+                n_embd * 2, n_patches_x / 2, n_patches_y, batch_size);
+            inp = ggml_reshape_4d(
+                ctx0, inp,
+                n_embd * 2, n_patches_x / 2, 2, batch_size * (n_patches_y / 2));
+            inp = ggml_permute(ctx0, inp, 0, 2, 1, 3);
+            inp = ggml_cont_3d(
+                ctx0, inp,
+                n_embd, n_patches_x * n_patches_y, batch_size);
+        }
+
+        // add patch bias
+        if (model.patch_bias != nullptr) {
+            inp = ggml_add(ctx0, inp, model.patch_bias);
+            cb(inp, "patch_bias", -1);
+        }
+
+        // calculate absolute position embedding and apply
+        ggml_tensor * learned_pos_embd = resize_position_embeddings();
+        learned_pos_embd = ggml_cont_4d(
+            ctx0, learned_pos_embd,
+            n_embd * 2, n_patches_x / 2, n_patches_y, batch_size);
+        learned_pos_embd = ggml_reshape_4d(
+            ctx0, learned_pos_embd,
+            n_embd * 2, n_patches_x / 2, 2, batch_size * (n_patches_y / 2));
+        learned_pos_embd = ggml_permute(ctx0, learned_pos_embd, 0, 2, 1, 3);
+        learned_pos_embd = ggml_cont_3d(
+            ctx0, learned_pos_embd,
+            n_embd, n_patches_x * n_patches_y, batch_size);
+        inp = ggml_add(ctx0, inp, learned_pos_embd);
+        cb(inp, "inp_pos_emb", -1);
+
+        ggml_tensor * inpL = inp;
+
+        ggml_tensor * positions = ggml_new_tensor_1d(ctx0, GGML_TYPE_I32, num_position_ids);
+        ggml_set_name(positions, "positions");
+        ggml_set_input(positions);
+
+        // pre-layernorm
+        if (model.pre_ln_w) {
+            inpL = build_norm(inpL, model.pre_ln_w, model.pre_ln_b, norm_t, eps, -1);
+        }
+
+        // deepstack features (stack along the feature dimension), [n_embd * len(deepstack_layers), n_patches_x * n_patches_y, batch_size]
+        ggml_tensor * deepstack_features = nullptr;
+        const int merge_factor = hparams.spatial_merge_size > 0 ? hparams.spatial_merge_size * hparams.spatial_merge_size : 4; // default 2x2=4 for qwen3vl
+
+        // loop over layers
+        for (int il = 0; il < n_layer; il++) {
+            auto & layer = model.layers[il];
+
+            ggml_tensor * cur = inpL; // inpL = residual, cur = hidden_states
+
+            // layernorm1
+            cur = build_norm(cur, layer.ln_1_w, layer.ln_1_b, norm_t, eps, il);
+            cb(cur, "ln1", il);
+
+            // self-attention
+            {
+                cur = ggml_mul_mat(ctx0, layer.qkv_w, cur);
+                cur = ggml_add(ctx0, cur, layer.qkv_b);
+
+                ggml_tensor * Qcur = ggml_view_3d(ctx0, cur, d_head, n_head, n_pos, d_head*sizeof(float),
+                    cur->nb[1], 0);
+                ggml_tensor * Kcur = ggml_view_3d(ctx0, cur, d_head, n_head, n_pos, d_head*sizeof(float),
+                    cur->nb[1], n_embd * sizeof(float));
+                ggml_tensor * Vcur = ggml_view_3d(ctx0, cur, d_head, n_head, n_pos, d_head*sizeof(float),
+                    cur->nb[1], 2 * n_embd * sizeof(float));
+
+                cb(Qcur, "Qcur", il);
+                cb(Kcur, "Kcur", il);
+                cb(Vcur, "Vcur", il);
+
+                // apply M-RoPE
+                Qcur = ggml_rope_multi(
+                    ctx0, Qcur, positions, nullptr,
+                    d_head/2, mrope_sections, GGML_ROPE_TYPE_VISION, 32768, 10000, 1, 0, 1, 32, 1);
+                Kcur = ggml_rope_multi(
+                    ctx0, Kcur, positions, nullptr,
+                    d_head/2, mrope_sections, GGML_ROPE_TYPE_VISION, 32768, 10000, 1, 0, 1, 32, 1);
+
+                cb(Qcur, "Qcur_rope", il);
+                cb(Kcur, "Kcur_rope", il);
+
+                cur = build_attn(layer.o_w, layer.o_b,
+                    Qcur, Kcur, Vcur, nullptr, kq_scale, il);
+                cb(cur, "attn_out", il);
+            }
+
+            // re-add the layer input, e.g., residual
+            cur = ggml_add(ctx0, cur, inpL);
+
+            inpL = cur; // inpL = residual, cur = hidden_states
+
+            cb(cur, "ffn_inp", il);
+
+            // layernorm2
+            cur = build_norm(cur, layer.ln_2_w, layer.ln_2_b, norm_t, eps, il);
+            cb(cur, "ffn_inp_normed", il);
+
+            // ffn
+            cur = build_ffn(cur,
+                layer.ff_up_w, layer.ff_up_b,
+                layer.ff_gate_w, layer.ff_gate_b,
+                layer.ff_down_w, layer.ff_down_b,
+                hparams.ffn_op, il);
+
+            cb(cur, "ffn_out", il);
+
+            // residual 2
+            cur = ggml_add(ctx0, inpL, cur);
+            cb(cur, "layer_out", il);
+
+            if (layer.has_deepstack()) {
+                ggml_tensor * feat = ggml_reshape_3d(ctx0, cur, n_embd * merge_factor, n_pos / merge_factor, batch_size);
+                feat = build_norm(feat, layer.deepstack_norm_w, layer.deepstack_norm_b, norm_t, eps, il);
+                feat = build_ffn(feat,
+                    layer.deepstack_fc1_w, layer.deepstack_fc1_b,
+                    nullptr, nullptr,
+                    layer.deepstack_fc2_w, layer.deepstack_fc2_b,
+                    ffn_op_type::FFN_GELU, il);
+
+                if(!deepstack_features) {
+                    deepstack_features = feat;
+                } else {
+                    // concat along the feature dimension
+                    deepstack_features = ggml_concat(ctx0, deepstack_features, feat, 0);
+                }
+            }
+
+            inpL = cur;
+        }
+
+        // post-layernorm
+        if (model.post_ln_w) {
+            inpL = build_norm(inpL, model.post_ln_w, model.post_ln_b, norm_t, eps, n_layer);
+        }
+
+        // multimodal projection
+        ggml_tensor * embeddings = inpL;
+        embeddings = ggml_reshape_3d(ctx0, embeddings, n_embd * 4, n_pos / 4, batch_size);
+
+        embeddings = build_ffn(embeddings,
+            model.mm_0_w, model.mm_0_b,
+            nullptr, nullptr,
+            model.mm_1_w, model.mm_1_b,
+            ffn_op_type::FFN_GELU, -1);
+
+        embeddings = ggml_concat(ctx0, embeddings, deepstack_features, 0); // concat along the feature dimension
+
+        // build the graph
+        ggml_build_forward_expand(gf, embeddings);
+
+        return gf;
+    }
+
     ggml_cgraph * build_minicpmv() {
         const int batch_size = 1;
 
@@ -2211,6 +2408,10 @@ static ggml_cgraph * clip_image_build_graph(clip_ctx * ctx, const clip_image_f32
             {
                 res = graph.build_qwen2vl();
             } break;
+        case PROJECTOR_TYPE_QWEN3VL:
+            {
+                res = graph.build_qwen3vl();
+            } break;
         case PROJECTOR_TYPE_MINICPMV:
             {
                 res = graph.build_minicpmv();
@@ -2534,6 +2735,12 @@ struct clip_model_loader {
                         hparams.warmup_image_size = hparams.patch_size * 8;
                         get_u32(KEY_WIN_ATTN_PATTERN, hparams.n_wa_pattern);
                     } break;
+                case PROJECTOR_TYPE_QWEN3VL:
+                    {
+                        hparams.image_size = 1024; // still need this?
+                        hparams.warmup_image_size = hparams.patch_size * 8;
+                        get_u32(KEY_SPATIAL_MERGE_SIZE, hparams.spatial_merge_size, false);
+                    } break;
                 case PROJECTOR_TYPE_LLAMA4:
                     {
                         hparams.rope_theta = 10000.0f;
@@ -2572,6 +2779,9 @@ struct clip_model_loader {
                 LOG_INF("%s: minicpmv_version:   %d\n", __func__, hparams.minicpmv_version);
                 LOG_INF("%s: proj_scale_factor:  %d\n", __func__, hparams.proj_scale_factor);
                 LOG_INF("%s: n_wa_pattern:       %d\n", __func__, hparams.n_wa_pattern);
+                if (hparams.spatial_merge_size > 0) {
+                    LOG_INF("%s: spatial_merge_size: %d\n", __func__, hparams.spatial_merge_size);
+                }
             } else if (is_audio) {
                 LOG_INF("\n--- audio hparams ---\n");
                 LOG_INF("%s: n_mel_bins:         %d\n", __func__, hparams.n_mel_bins);
@@ -2671,6 +2881,18 @@ struct clip_model_loader {
             layer.ff_down_w = get_tensor(string_format(TN_FFN_DOWN, prefix, il, "weight"));
             layer.ff_down_b = get_tensor(string_format(TN_FFN_DOWN, prefix, il, "bias"),   false);
 
+
+            // qwen3vl deepstack layer
+            layer.deepstack_norm_w = get_tensor(string_format(TN_DEEPSTACK_NORM, il, "weight"), false);
+            layer.deepstack_norm_b = get_tensor(string_format(TN_DEEPSTACK_NORM, il, "bias"), false);
+            layer.deepstack_fc1_w  = get_tensor(string_format(TN_DEEPSTACK_FC1,  il, "weight"), false);
+            layer.deepstack_fc1_b  = get_tensor(string_format(TN_DEEPSTACK_FC1,  il, "bias"), false);
+            layer.deepstack_fc2_w  = get_tensor(string_format(TN_DEEPSTACK_FC2,  il, "weight"), false);
+            layer.deepstack_fc2_b  = get_tensor(string_format(TN_DEEPSTACK_FC2,  il, "bias"), false);
+            if (layer.has_deepstack()) {
+                model.n_deepstack_layers++;
+            }
+
             // some models already exported with legacy (incorrect) naming which is quite messy, let's fix it here
             // note: Qwen model converted from the old surgery script has n_ff = 0, so we cannot use n_ff to check!
             bool is_ffn_swapped = (
@@ -2806,6 +3028,13 @@ struct clip_model_loader {
                     model.mm_1_w = get_tensor(string_format(TN_LLAVA_PROJ, 2, "weight"));
                     model.mm_1_b = get_tensor(string_format(TN_LLAVA_PROJ, 2, "bias"));
                 } break;
+            case PROJECTOR_TYPE_QWEN3VL:
+                {
+                    model.mm_0_w = get_tensor(string_format(TN_LLAVA_PROJ, 0, "weight"));
+                    model.mm_0_b = get_tensor(string_format(TN_LLAVA_PROJ, 0, "bias"));
+                    model.mm_1_w = get_tensor(string_format(TN_LLAVA_PROJ, 2, "weight"));
+                    model.mm_1_b = get_tensor(string_format(TN_LLAVA_PROJ, 2, "bias"));
+                } break;
             case PROJECTOR_TYPE_GEMMA3:
                 {
                     model.mm_input_proj_w = get_tensor(TN_MM_INP_PROJ);
@@ -3689,7 +3918,7 @@ bool clip_image_preprocess(struct clip_ctx * ctx, const clip_image_u8 * img, str
         res_imgs->grid_y = inst.grid_size.height;
         return true;
 
-    } else if (ctx->proj_type() == PROJECTOR_TYPE_QWEN2VL || ctx->proj_type() == PROJECTOR_TYPE_QWEN25VL) {
+    } else if (ctx->proj_type() == PROJECTOR_TYPE_QWEN2VL || ctx->proj_type() == PROJECTOR_TYPE_QWEN25VL || ctx->proj_type() == PROJECTOR_TYPE_QWEN3VL) {
         clip_image_u8 resized;
         auto patch_size = params.patch_size * 2;
         auto new_size = image_manipulation::calc_size_preserved_ratio(original_size, patch_size, params.image_size);
@@ -3915,7 +4144,7 @@ const char * clip_patch_merge_type(const struct clip_ctx * ctx) {
 int clip_n_output_tokens_x(const struct clip_ctx * ctx, struct clip_image_f32 * img) {
     const auto & params = ctx->model.hparams;
     const int n_total = clip_n_output_tokens(ctx, img);
-    if (ctx->proj_type() == PROJECTOR_TYPE_QWEN2VL || ctx->proj_type() == PROJECTOR_TYPE_QWEN25VL) {
+    if (ctx->proj_type() == PROJECTOR_TYPE_QWEN2VL || ctx->proj_type() == PROJECTOR_TYPE_QWEN25VL || ctx->proj_type() == PROJECTOR_TYPE_QWEN3VL) {
         return img->nx / (params.patch_size * 2) + (int)(img->nx % params.patch_size > 0);
     }
     return n_total;
@@ -3923,7 +4152,7 @@ int clip_n_output_tokens_x(const struct clip_ctx * ctx, struct clip_image_f32 *
 
 int clip_n_output_tokens_y(const struct clip_ctx * ctx, struct clip_image_f32 * img) {
     const auto & params = ctx->model.hparams;
-    if (ctx->proj_type() == PROJECTOR_TYPE_QWEN2VL || ctx->proj_type() == PROJECTOR_TYPE_QWEN25VL) {
+    if (ctx->proj_type() == PROJECTOR_TYPE_QWEN2VL || ctx->proj_type() == PROJECTOR_TYPE_QWEN25VL || ctx->proj_type() == PROJECTOR_TYPE_QWEN3VL) {
         return img->ny / (params.patch_size * 2) + (int)(img->ny % params.patch_size > 0);
     }
     return 1;
@@ -3979,6 +4208,7 @@ int clip_n_output_tokens(const struct clip_ctx * ctx, struct clip_image_f32 * im
             } break;
         case PROJECTOR_TYPE_QWEN2VL:
         case PROJECTOR_TYPE_QWEN25VL:
+        case PROJECTOR_TYPE_QWEN3VL:
             {
                 // dynamic size (2 conv, so double patch size)
                 int patch_size = params.patch_size * 2;
@@ -4292,6 +4522,7 @@ bool clip_image_batch_encode(clip_ctx * ctx, const int n_threads, const clip_ima
                 set_input_f32("pos_embed", pos_embed);
             } break;
         case PROJECTOR_TYPE_QWEN2VL:
+        case PROJECTOR_TYPE_QWEN3VL:
             {
                 const int merge_ratio = 2;
                 const int pw = image_size_width  / patch_size;
@@ -4540,6 +4771,9 @@ int clip_n_mmproj_embd(const struct clip_ctx * ctx) {
         case PROJECTOR_TYPE_QWEN2VL:
         case PROJECTOR_TYPE_QWEN25VL:
             return ctx->model.mm_1_b->ne[0];
+        case PROJECTOR_TYPE_QWEN3VL:
+            // main path + deepstack paths
+            return ctx->model.mm_1_b->ne[0] * (1 + ctx->model.n_deepstack_layers);
         case PROJECTOR_TYPE_GEMMA3:
             return ctx->model.mm_input_proj_w->ne[0];
         case PROJECTOR_TYPE_IDEFICS3:
@@ -4576,7 +4810,8 @@ bool clip_is_glm(const struct clip_ctx * ctx) {
 
 bool clip_is_qwen2vl(const struct clip_ctx * ctx) {
     return ctx->proj_type() == PROJECTOR_TYPE_QWEN2VL
-        || ctx->proj_type() == PROJECTOR_TYPE_QWEN25VL;
+        || ctx->proj_type() == PROJECTOR_TYPE_QWEN25VL
+        || ctx->proj_type() == PROJECTOR_TYPE_QWEN3VL;
 }
 
 bool clip_is_llava(const struct clip_ctx * ctx) {
diff --git a/tools/mtmd/mtmd.cpp b/tools/mtmd/mtmd.cpp
index 1a48f903efa..196641dd95e 100644
--- a/tools/mtmd/mtmd.cpp
+++ b/tools/mtmd/mtmd.cpp
@@ -267,7 +267,7 @@ struct mtmd_context {
             // https://github.com/huggingface/transformers/blob/1cd110c6cb6a6237614130c470e9a902dbc1a4bd/docs/source/en/model_doc/pixtral.md
             img_end = "[IMG_END]";
 
-        } else if (proj == PROJECTOR_TYPE_QWEN2VL || proj == PROJECTOR_TYPE_QWEN25VL) {
+        } else if (proj == PROJECTOR_TYPE_QWEN2VL || proj == PROJECTOR_TYPE_QWEN25VL || proj == PROJECTOR_TYPE_QWEN3VL) {
             // <|vision_start|> ... (image embeddings) ... <|vision_end|>
             img_beg = "<|vision_start|>";
             img_end = "<|vision_end|>";
diff --git a/tools/mtmd/tests.sh b/tools/mtmd/tests.sh
index c2270746360..472f7d821c2 100755
--- a/tools/mtmd/tests.sh
+++ b/tools/mtmd/tests.sh
@@ -84,6 +84,7 @@ if [ "$RUN_BIG_TESTS" = true ]; then
     add_test_vision "ggml-org/Qwen2-VL-7B-Instruct-GGUF:Q4_K_M"
     add_test_vision "ggml-org/Qwen2.5-VL-3B-Instruct-GGUF:Q4_K_M"
     add_test_vision "ggml-org/Qwen2.5-VL-7B-Instruct-GGUF:Q4_K_M"
+    add_test_vision "ggml-org/Qwen3-VL-2B-Instruct-GGUF:Q8_0"
     add_test_vision "ggml-org/InternVL3-8B-Instruct-GGUF:Q4_K_M"
     add_test_vision "ggml-org/InternVL3-14B-Instruct-GGUF:Q4_K_M"
     add_test_vision "ggml-org/Qwen2.5-Omni-7B-GGUF:Q4_K_M"

From 835e918d8428f5119927d7150bf5a26176dedda0 Mon Sep 17 00:00:00 2001
From: Shagun Bera <141054835+notV3NOM@users.noreply.github.com>
Date: Thu, 30 Oct 2025 21:17:31 +0530
Subject: [PATCH 022/185] common: fix typo in cli help text (#16864)

---
 common/arg.cpp | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/common/arg.cpp b/common/arg.cpp
index a465eb36234..e8941cda41c 100644
--- a/common/arg.cpp
+++ b/common/arg.cpp
@@ -3203,7 +3203,7 @@ common_params_context common_params_parser_init(common_params & params, llama_ex
     ).set_examples({LLAMA_EXAMPLE_IMATRIX}));
     add_opt(common_arg(
         {"--parse-special"},
-        string_format("prase special tokens (chat, tool, etc) (default: %s)", params.parse_special ? "true" : "false"),
+        string_format("parse special tokens (chat, tool, etc) (default: %s)", params.parse_special ? "true" : "false"),
         [](common_params & params) {
             params.parse_special = true;
         }

From 517b7170e1a4d733583c4b07c5b7a49acc05911c Mon Sep 17 00:00:00 2001
From: Max Krasnyansky <maxk@qti.qualcomm.com>
Date: Thu, 30 Oct 2025 09:06:13 -0700
Subject: [PATCH 023/185] cpu: introduce chunking for repack matmuls and enable
 matmul-id chunking on ARM64 (#16833)

Very similar implementation to the flash-attention chunking, with similar benefits.
---
 ggml/src/ggml-cpu/ggml-cpu.c |  5 ---
 ggml/src/ggml-cpu/repack.cpp | 78 ++++++++++++++++++++++++++----------
 2 files changed, 57 insertions(+), 26 deletions(-)

diff --git a/ggml/src/ggml-cpu/ggml-cpu.c b/ggml/src/ggml-cpu/ggml-cpu.c
index 9ec485cfa2f..b5466dd703d 100644
--- a/ggml/src/ggml-cpu/ggml-cpu.c
+++ b/ggml/src/ggml-cpu/ggml-cpu.c
@@ -1613,13 +1613,8 @@ static void ggml_compute_forward_mul_mat_id(
             chunk_size = 64;
         }
 
-#if defined(__aarch64__)
-        // disable for ARM
-        const bool disable_chunking = true;
-#else
         // disable for NUMA
         const bool disable_chunking = ggml_is_numa();
-#endif // defined(__aarch64__)
 
         int64_t nchunk0 = (nr0 + chunk_size - 1) / chunk_size;
         int64_t nchunk1 = (nr1 + chunk_size - 1) / chunk_size;
diff --git a/ggml/src/ggml-cpu/repack.cpp b/ggml/src/ggml-cpu/repack.cpp
index f531d21e232..8da1e0e9245 100644
--- a/ggml/src/ggml-cpu/repack.cpp
+++ b/ggml/src/ggml-cpu/repack.cpp
@@ -1600,6 +1600,32 @@ template <typename BLOC_TYPE, int64_t INTER_SIZE, int64_t NB_COLS, ggml_type PAR
         return false;
     }
 
+    void forward_mul_mat_one_chunk(ggml_compute_params * params, ggml_tensor * op, int64_t src0_start, int64_t src0_end) {
+        const ggml_tensor * src0 = op->src[0];
+        const ggml_tensor * src1 = op->src[1];
+        ggml_tensor *       dst  = op;
+
+        GGML_TENSOR_BINARY_OP_LOCALS
+
+        const void * src1_wdata      = params->wdata;
+        const size_t src1_col_stride = ggml_row_size(PARAM_TYPE, ne10);
+
+        // If there are more than three rows in src1, use gemm; otherwise, use gemv.
+        if (ne11 > 3) {
+            gemm<BLOC_TYPE, INTER_SIZE, NB_COLS, PARAM_TYPE>(ne00,
+                    (float *) ((char *) dst->data) + src0_start, ne01,
+                    (const char *) src0->data + src0_start * nb01,
+                    (const char *) src1_wdata, ne11 - ne11 % 4, src0_end - src0_start);
+        }
+        for (int iter = ne11 - ne11 % 4; iter < ne11; iter++) {
+            gemv<BLOC_TYPE, INTER_SIZE, NB_COLS, PARAM_TYPE>(ne00,
+                    (float *) ((char *) dst->data + (iter * nb1)) + src0_start, ne01,
+                    (const char *) src0->data + src0_start * nb01,
+                    (const char *) src1_wdata + (src1_col_stride * iter), 1,
+                    src0_end - src0_start);
+        }
+    }
+
     void forward_mul_mat(ggml_compute_params * params, ggml_tensor * op) {
         const ggml_tensor * src0 = op->src[0];
         const ggml_tensor * src1 = op->src[1];
@@ -1643,31 +1669,41 @@ template <typename BLOC_TYPE, int64_t INTER_SIZE, int64_t NB_COLS, ggml_type PAR
             from_float((float *) ((char *) src1->data + i11 * nb11), (void *) (wdata + i11 * nbw1), ne10);
         }
 
-        ggml_barrier(params->threadpool);
+        // disable for NUMA
+        const bool disable_chunking = ggml_is_numa();
 
-        const void * src1_wdata      = params->wdata;
-        const size_t src1_col_stride = ggml_row_size(PARAM_TYPE, ne10);
-        int64_t      src0_start      = (ith * ne01) / nth;
-        int64_t      src0_end        = ((ith + 1) * ne01) / nth;
-        src0_start = (src0_start % NB_COLS) ? src0_start + NB_COLS - (src0_start % NB_COLS) : src0_start;
-        src0_end   = (src0_end   % NB_COLS) ? src0_end   + NB_COLS - (src0_end   % NB_COLS) : src0_end;
-        if (src0_start >= src0_end) {
-            return;
+        // 4x chunks per thread
+        int64_t nr = ggml_nrows(op->src[0]);
+        int nth_scaled = nth * 4;
+        int64_t chunk_size = (nr + nth_scaled - 1) / nth_scaled;
+        int64_t nchunk     = (nr + chunk_size - 1) / chunk_size;
+
+        if (nth == 1 || nchunk < nth || disable_chunking) {
+            nchunk = nth;
         }
 
-        // If there are more than three rows in src1, use gemm; otherwise, use gemv.
-        if (ne11 > 3) {
-            gemm<BLOC_TYPE, INTER_SIZE, NB_COLS, PARAM_TYPE>(ne00,
-                    (float *) ((char *) dst->data) + src0_start, ne01,
-                    (const char *) src0->data + src0_start * nb01,
-                    (const char *) src1_wdata, ne11 - ne11 % 4, src0_end - src0_start);
+        if (ith == 0) {
+            // Every thread starts at ith, so the first unprocessed chunk is nth.  This save a bit of coordination right at the start.
+            ggml_threadpool_chunk_set(params->threadpool, nth);
         }
-        for (int iter = ne11 - ne11 % 4; iter < ne11; iter++) {
-            gemv<BLOC_TYPE, INTER_SIZE, NB_COLS, PARAM_TYPE>(ne00,
-                    (float *) ((char *) dst->data + (iter * nb1)) + src0_start, ne01,
-                    (const char *) src0->data + src0_start * nb01,
-                    (const char *) src1_wdata + (src1_col_stride * iter), 1,
-                    src0_end - src0_start);
+
+        ggml_barrier(params->threadpool);
+
+        // The first chunk comes from our thread_id, the rest will get auto-assigned.
+        int current_chunk = ith;
+
+        while (current_chunk < nchunk) {
+            int64_t src0_start = (current_chunk * ne01) / nchunk;
+            int64_t src0_end   = ((current_chunk + 1) * ne01) / nchunk;
+            src0_start = (src0_start % NB_COLS) ? src0_start + NB_COLS - (src0_start % NB_COLS) : src0_start;
+            src0_end   = (src0_end   % NB_COLS) ? src0_end   + NB_COLS - (src0_end   % NB_COLS) : src0_end;
+            if (src0_start >= src0_end) {
+                break;
+            }
+
+            forward_mul_mat_one_chunk(params, dst, src0_start, src0_end);
+
+            current_chunk = ggml_threadpool_chunk_add(params->threadpool, 1);
         }
     }
 

From b52edd25586fabb70f0c21b274473b307cf14499 Mon Sep 17 00:00:00 2001
From: Georgi Gerganov <ggerganov@gmail.com>
Date: Thu, 30 Oct 2025 18:42:57 +0200
Subject: [PATCH 024/185] server : remove n_past (#16818)

* server : remove n_past

* server : replace slot.n_prompt_tokens() with slot.task->n_tokens()

* server : fixes + clean-up

* cont : fix context shift

* server : add server_tokens::pos_next()

Co-authored-by: Xuan-Son Nguyen <son@huggingface.co>

* server : fix pos_next() usage

Co-authored-by: Xuan-Son Nguyen <son@huggingface.co>

---------

Co-authored-by: Xuan-Son Nguyen <son@huggingface.co>
---
 tools/server/README.md  |   4 +-
 tools/server/server.cpp | 220 ++++++++++++++++++++--------------------
 tools/server/utils.hpp  | 106 +++++++++++--------
 3 files changed, 177 insertions(+), 153 deletions(-)

diff --git a/tools/server/README.md b/tools/server/README.md
index f5ab9236d52..c16d0bd6dcd 100644
--- a/tools/server/README.md
+++ b/tools/server/README.md
@@ -587,7 +587,7 @@ These words will not be included in the completion, so make sure to add them to
   - `word`: Stopped due to encountering a stopping word from `stop` JSON array provided
 - `stopping_word`: The stopping word encountered which stopped the generation (or "" if not stopped due to a stopping word)
 - `timings`: Hash of timing information about the completion such as the number of tokens `predicted_per_second`
-- `tokens_cached`: Number of tokens from the prompt which could be re-used from previous completion (`n_past`)
+- `tokens_cached`: Number of tokens from the prompt which could be re-used from previous completion
 - `tokens_evaluated`: Number of tokens evaluated in total from the prompt
 - `truncated`: Boolean indicating if the context size was exceeded during generation, i.e. the number of tokens provided in the prompt (`tokens_evaluated`) plus tokens generated (`tokens predicted`) exceeded the context size (`n_ctx`)
 
@@ -1045,7 +1045,7 @@ Available metrics:
 - `llamacpp:kv_cache_tokens`: KV-cache tokens.
 - `llamacpp:requests_processing`: Number of requests processing.
 - `llamacpp:requests_deferred`: Number of requests deferred.
-- `llamacpp:n_past_max`: High watermark of the context size observed.
+- `llamacpp:n_tokens_max`: High watermark of the context size observed.
 
 ### POST `/slots/{id_slot}?action=save`: Save the prompt cache of the specified slot to a file.
 
diff --git a/tools/server/server.cpp b/tools/server/server.cpp
index cb794ab647e..d56468595dd 100644
--- a/tools/server/server.cpp
+++ b/tools/server/server.cpp
@@ -292,6 +292,10 @@ struct server_task {
 
     server_task(server_task_type type) : type(type) {}
 
+    int32_t n_tokens() const {
+        return tokens.size();
+    }
+
     static slot_params params_from_json_cmpl(
             const llama_context * ctx,
             const common_params & params_base,
@@ -1308,7 +1312,7 @@ struct server_task_result_metrics : server_task_result {
     uint64_t n_tokens_predicted_total        = 0;
     uint64_t t_tokens_generation_total       = 0;
 
-    uint64_t n_past_max = 0;
+    uint64_t n_tokens_max = 0;
 
     uint64_t n_prompt_tokens_processed = 0;
     uint64_t t_prompt_processing       = 0;
@@ -1335,7 +1339,7 @@ struct server_task_result_metrics : server_task_result {
             { "n_tokens_predicted_total",        n_tokens_predicted_total },
             { "t_prompt_processing_total",       t_prompt_processing_total },
 
-            { "n_past_max",                      n_past_max },
+            { "n_tokens_max",                    n_tokens_max },
 
             { "n_prompt_tokens_processed",       n_prompt_tokens_processed },
             { "t_prompt_processing",             t_prompt_processing },
@@ -1636,7 +1640,6 @@ struct server_slot {
 
     // generation props
     int32_t n_ctx       = 0;  // context size per slot
-    int32_t n_past      = 0;
     int32_t n_keep      = 0;
     int32_t n_decoded   = 0;
     int32_t n_remaining = -1;
@@ -1645,10 +1648,6 @@ struct server_slot {
     int32_t n_prompt_tokens_cache     = 0;
     int32_t n_prompt_tokens_processed = 0;
 
-    int32_t n_prompt_tokens() const {
-        return task->tokens.size();
-    }
-
     size_t last_nl_pos = 0;
 
     std::string  generated_text;
@@ -1733,7 +1732,6 @@ struct server_slot {
         truncated      = false;
         stop           = STOP_TYPE_NONE;
         stopping_word  = "";
-        n_past         = 0;
         n_sent_text    = 0;
         chat_format    = COMMON_CHAT_FORMAT_CONTENT_ONLY;
 
@@ -1818,7 +1816,7 @@ struct server_slot {
         if (is_processing()) {
             GGML_ASSERT(task);
 
-            SLT_INF(*this, "stop processing: n_past = %d, truncated = %d\n", n_past, truncated);
+            SLT_INF(*this, "stop processing: n_tokens = %d, truncated = %d\n", prompt.n_tokens(), truncated);
 
             t_last_used = ggml_time_us();
             t_token_generation = (ggml_time_us() - t_start_generation) / 1e3;
@@ -1970,7 +1968,7 @@ struct server_metrics {
     uint64_t n_tokens_predicted_total        = 0;
     uint64_t t_tokens_generation_total       = 0;
 
-    uint64_t n_past_max = 0;
+    uint64_t n_tokens_max = 0;
 
     uint64_t n_prompt_tokens_processed = 0;
     uint64_t t_prompt_processing       = 0;
@@ -1991,9 +1989,7 @@ struct server_metrics {
         t_prompt_processing             += slot.t_prompt_processing;
         t_prompt_processing_total       += slot.t_prompt_processing;
 
-        if (slot.n_past > 0) {
-            n_past_max = std::max(n_past_max, (uint64_t) slot.n_past);
-        }
+        n_tokens_max = std::max(n_tokens_max, (uint64_t) slot.prompt.n_tokens());
     }
 
     void on_prediction(const server_slot & slot) {
@@ -2009,9 +2005,7 @@ struct server_metrics {
             if (slot.is_processing()) {
                 n_busy_slots_total++;
             }
-            if (slot.n_past > 0) {
-                n_past_max = std::max(n_past_max, (uint64_t) slot.n_past);
-            }
+            n_tokens_max = std::max(n_tokens_max, (uint64_t) slot.prompt.n_tokens());
         }
     }
 
@@ -2865,13 +2859,13 @@ struct server_context {
         }
 
         // if context shifting is disabled, make sure that we don't run out of context
-        if (!params_base.ctx_shift && slot.n_past + 1 >= slot.n_ctx) {
+        if (!params_base.ctx_shift && slot.prompt.n_tokens() + 1 >= slot.n_ctx) {
             slot.truncated      = true;
             slot.stop           = STOP_TYPE_LIMIT;
             slot.has_next_token = false;
 
-            SLT_DBG(slot, "stopped due to running out of context capacity, n_past = %d, n_prompt_tokens = %d, n_decoded = %d, n_ctx = %d\n",
-                    slot.n_decoded, slot.n_prompt_tokens(), slot.n_past, slot.n_ctx);
+            SLT_DBG(slot, "stopped due to running out of context capacity, prompt.n_tokens() = %d, task.n_tokens = %d, n_decoded = %d, n_ctx = %d\n",
+                    slot.prompt.n_tokens(), slot.task->n_tokens(), slot.n_decoded, slot.n_ctx);
         }
 
         // check the limits
@@ -2998,7 +2992,7 @@ struct server_context {
     }
 
     void send_error(const server_slot & slot, const std::string & error, const enum error_type type = ERROR_TYPE_SERVER) {
-        send_error(slot.task->id, error, type, slot.n_prompt_tokens(), slot.n_ctx);
+        send_error(slot.task->id, error, type, slot.task->n_tokens(), slot.n_ctx);
     }
 
     void send_error(const int id_task, const std::string & error, const enum error_type type = ERROR_TYPE_SERVER, const int32_t n_prompt_tokens = 0, const int32_t n_ctx = 0) {
@@ -3035,7 +3029,7 @@ struct server_context {
 
         if (is_progress) {
             res->is_progress        = true;
-            res->progress.total     = slot.n_prompt_tokens();
+            res->progress.total     = slot.task->n_tokens();
             res->progress.cache     = slot.n_prompt_tokens_cache;
             res->progress.processed = slot.prompt.tokens.size();
             res->progress.time_ms   = (ggml_time_us() - slot.t_start_process_prompt / 1000);
@@ -3047,7 +3041,7 @@ struct server_context {
         }
 
         res->n_decoded           = slot.n_decoded;
-        res->n_prompt_tokens     = slot.n_prompt_tokens();
+        res->n_prompt_tokens     = slot.task->n_tokens();
         res->post_sampling_probs = slot.task->params.post_sampling_probs;
 
         res->verbose           = slot.task->params.verbose;
@@ -3083,8 +3077,8 @@ struct server_context {
 
         res->truncated           = slot.truncated;
         res->n_decoded           = slot.n_decoded;
-        res->n_prompt_tokens     = slot.n_prompt_tokens();
-        res->n_tokens_cached     = slot.n_past;
+        res->n_prompt_tokens     = slot.task->n_tokens();
+        res->n_tokens_cached     = slot.prompt.n_tokens();
         res->has_new_line        = slot.has_new_line;
         res->stopping_word       = slot.stopping_word;
         res->stop                = slot.stop;
@@ -3123,7 +3117,7 @@ struct server_context {
         auto res = std::make_unique<server_task_result_embd>();
         res->id        = slot.task->id;
         res->index     = slot.task->index;
-        res->n_tokens  = slot.n_prompt_tokens();
+        res->n_tokens  = slot.task->n_tokens();
         res->oaicompat = slot.task->params.oaicompat;
 
         const int n_embd = llama_model_n_embd(model);
@@ -3168,7 +3162,7 @@ struct server_context {
         auto res = std::make_unique<server_task_result_rerank>();
         res->id       = slot.task->id;
         res->index    = slot.task->index;
-        res->n_tokens = slot.n_prompt_tokens();
+        res->n_tokens = slot.task->n_tokens();
 
         for (int i = 0; i < batch.n_tokens; ++i) {
             if (!batch.logits[i] || batch.seq_id[i][0] != slot.id) {
@@ -3375,7 +3369,7 @@ struct server_context {
                     res->n_tokens_predicted_total        = metrics.n_tokens_predicted_total;
                     res->t_tokens_generation_total       = metrics.t_tokens_generation_total;
 
-                    res->n_past_max = metrics.n_past_max;
+                    res->n_tokens_max = metrics.n_tokens_max;
 
                     res->n_prompt_tokens_processed = metrics.n_prompt_tokens_processed;
                     res->t_prompt_processing       = metrics.t_prompt_processing;
@@ -3551,7 +3545,7 @@ struct server_context {
         // apply context-shift if needed
         // TODO: simplify and improve
         for (server_slot & slot : slots) {
-            if (slot.is_processing() && slot.n_past + 1 >= slot.n_ctx) {
+            if (slot.is_processing() && slot.prompt.n_tokens() + 1 >= slot.n_ctx) {
                 if (!params_base.ctx_shift) {
                     // this check is redundant (for good)
                     // we should never get here, because generation should already stopped in process_token()
@@ -3567,7 +3561,7 @@ struct server_context {
                 }
 
                 // Shift context
-                int n_keep = slot.task->params.n_keep < 0 ? slot.n_prompt_tokens() : slot.task->params.n_keep;
+                int n_keep = slot.task->params.n_keep < 0 ? slot.task->n_tokens() : slot.task->params.n_keep;
 
                 if (add_bos_token) {
                     n_keep += 1;
@@ -3575,28 +3569,30 @@ struct server_context {
 
                 n_keep = std::min(slot.n_ctx - 4, n_keep);
 
-                const int n_left    = slot.n_past - n_keep;
+                const int n_left    = slot.prompt.n_tokens() - n_keep;
                 const int n_discard = slot.task->params.n_discard ? slot.task->params.n_discard : (n_left / 2);
 
                 SLT_WRN(slot, "slot context shift, n_keep = %d, n_left = %d, n_discard = %d\n", n_keep, n_left, n_discard);
 
                 llama_memory_seq_rm (llama_get_memory(ctx), slot.id, n_keep            , n_keep + n_discard);
-                llama_memory_seq_add(llama_get_memory(ctx), slot.id, n_keep + n_discard, slot.n_past,        -n_discard);
+                llama_memory_seq_add(llama_get_memory(ctx), slot.id, n_keep + n_discard, slot.prompt.n_tokens(), -n_discard);
 
                 // add generated tokens to cache
+                // ref: https://github.com/ggml-org/llama.cpp/pull/16818#discussion_r2473269481
                 {
+                    GGML_ASSERT(!slot.prompt.tokens.has_mtmd);
+
                     llama_tokens new_tokens = slot.prompt.tokens.get_text_tokens(); // copy
                     for (size_t i = n_keep + n_discard; i < new_tokens.size(); i++) {
                         new_tokens[i - n_discard] = new_tokens[i];
                     }
 
                     new_tokens.resize(slot.prompt.tokens.size() - n_discard);
+
                     slot.prompt.tokens.clear();
                     slot.prompt.tokens.insert(new_tokens);
                 }
 
-                slot.n_past -= n_discard;
-
                 slot.truncated = true;
             }
         }
@@ -3627,13 +3623,12 @@ struct server_context {
 
             slot.i_batch = batch.n_tokens;
 
-            common_batch_add(batch, slot.sampled, slot.n_past, { slot.id }, true);
+            common_batch_add(batch, slot.sampled, slot.prompt.tokens.pos_next(), { slot.id }, true);
 
-            slot.n_past += 1;
             slot.prompt.tokens.push_back(slot.sampled);
 
-            SLT_DBG(slot, "slot decode token, n_ctx = %d, n_past = %d, n_cache_tokens = %d, truncated = %d\n",
-                    slot.n_ctx, slot.n_past, (int) slot.prompt.tokens.size(), slot.truncated);
+            SLT_DBG(slot, "slot decode token, n_ctx = %d, n_tokens = %d, truncated = %d\n",
+                    slot.n_ctx, slot.prompt.n_tokens(), slot.truncated);
         }
 
         // process in chunks of params.n_batch
@@ -3663,11 +3658,10 @@ struct server_context {
                         slot.t_start_process_prompt = ggml_time_us();
                         slot.t_start_generation = 0;
 
-                        slot.n_past = 0;
                         slot.state = SLOT_STATE_PROCESSING_PROMPT;
 
-                        SLT_INF(slot, "new prompt, n_ctx_slot = %d, n_keep = %d, n_prompt_tokens = %d\n",
-                                slot.n_ctx, slot.task->params.n_keep, slot.n_prompt_tokens());
+                        SLT_INF(slot, "new prompt, n_ctx_slot = %d, n_keep = %d, task.n_tokens = %d\n",
+                                slot.n_ctx, slot.task->params.n_keep, slot.task->n_tokens());
 
                         // print prompt tokens (for debugging)
                         /*if (1) {
@@ -3682,6 +3676,9 @@ struct server_context {
                             }
                         }*/
 
+                        // keep track how many tokens we can reuse from the previous state
+                        int n_past = 0;
+
                         // empty prompt passed -> release the slot and send empty response
                         if (input_tokens.empty()) {
                             SLT_WRN(slot, "%s", "empty prompt - releasing slot\n");
@@ -3701,19 +3698,19 @@ struct server_context {
                         }
 
                         if (!slot.can_split()) {
-                            if (slot.n_prompt_tokens() > n_ubatch) {
+                            if (slot.task->n_tokens() > n_ubatch) {
                                 send_error(slot, "input is too large to process. increase the physical batch size", ERROR_TYPE_SERVER);
                                 slot.release();
                                 continue;
                             }
 
-                            if (slot.n_prompt_tokens() > slot.n_ctx) {
+                            if (slot.task->n_tokens() > slot.n_ctx) {
                                 send_error(slot, "input is larger than the max context size. skipping", ERROR_TYPE_EXCEED_CONTEXT_SIZE);
                                 slot.release();
                                 continue;
                             }
                         } else {
-                            if (slot.n_prompt_tokens() >= slot.n_ctx) {
+                            if (slot.task->n_tokens() >= slot.n_ctx) {
                                 send_error(slot, "the request exceeds the available context size, try increasing it", ERROR_TYPE_EXCEED_CONTEXT_SIZE);
                                 slot.release();
                                 continue;
@@ -3721,32 +3718,34 @@ struct server_context {
 
                             if (slot.task->params.cache_prompt) {
                                 // reuse any previously computed tokens that are common with the new prompt
-                                slot.n_past = slot.prompt.tokens.get_common_prefix(input_tokens);
+                                n_past = slot.prompt.tokens.get_common_prefix(input_tokens);
 
                                 // if there is an alora invoked, don't cache after the invocation start
-                                if (slot.alora_invocation_start >= 0) {
-                                    SLT_DBG(slot, "only caching to alora invocation start (n_past=%d, alora_invocation_start=%d)\n", slot.n_past, slot.alora_invocation_start);
-                                    slot.n_past = std::min(slot.n_past, slot.alora_invocation_start - 1);
+                                if (slot.alora_invocation_start > 0) {
+                                    SLT_DBG(slot, "only caching to alora invocation start (n_past = %d, alora_invocation_start = %d)\n", n_past, slot.alora_invocation_start);
+                                    n_past = std::min(n_past, slot.alora_invocation_start - 1);
                                 }
 
                                 // reuse chunks from the cached prompt by shifting their KV cache in the new position
                                 if (params_base.n_cache_reuse > 0) {
-                                    size_t head_c = slot.n_past; // cache
-                                    size_t head_p = slot.n_past; // current prompt
+                                    GGML_ASSERT(!slot.prompt.tokens.has_mtmd);
+
+                                    size_t head_c = n_past; // cache
+                                    size_t head_p = n_past; // current prompt
 
                                     if (mctx) {
                                         // we should never reach this
                                         GGML_ABORT("not supported by multimodal");
                                     }
 
-                                    SLT_DBG(slot, "trying to reuse chunks with size > %d, slot.n_past = %d\n", params_base.n_cache_reuse, slot.n_past);
+                                    SLT_DBG(slot, "trying to reuse chunks with size > %d, n_past = %d\n", params_base.n_cache_reuse, n_past);
 
                                     while (head_c < slot.prompt.tokens.size() &&
                                            head_p < input_tokens.size()) {
 
                                         size_t n_match = 0;
                                         while (head_c + n_match < slot.prompt.tokens.size() &&
-                                               head_p + n_match < input_tokens.size()     &&
+                                               head_p + n_match < input_tokens.size()       &&
                                                slot.prompt.tokens[head_c + n_match] == input_tokens[head_p + n_match]) {
 
                                             n_match++;
@@ -3765,7 +3764,7 @@ struct server_context {
 
                                             for (size_t i = 0; i < n_match; i++) {
                                                 slot.prompt.tokens.set_token(head_p + i, slot.prompt.tokens[head_c + i]);
-                                                slot.n_past++;
+                                                n_past++;
                                             }
 
                                             head_c += n_match;
@@ -3775,31 +3774,31 @@ struct server_context {
                                         }
                                     }
 
-                                    SLT_DBG(slot, "after context reuse, new slot.n_past = %d\n", slot.n_past);
+                                    SLT_DBG(slot, "after context reuse, new n_past = %d\n", n_past);
                                 }
                             } else {
-                                // if we don't cache the prompt, we have to remove the entire KV cache
-                                slot.n_past = 0;
+                                // if we don't cache the prompt, we have to remove all previous tokens
+                                n_past = 0;
                             }
 
                             // note: when n_swa == 0, the model does not use SWA, which is equivalent to a window of 1
                             const auto n_swa = std::max(1, llama_model_n_swa(model));
 
                             // the largest pos_min required for a checkpoint to be useful
-                            const auto pos_min_thold = std::max(0, slot.n_past - n_swa);
+                            const auto pos_min_thold = std::max(0, n_past - n_swa);
 
-                            if (slot.n_past > 0 && slot.n_past < (int) slot.prompt.tokens.size()) {
+                            if (n_past > 0 && n_past < slot.prompt.n_tokens()) {
                                 const auto pos_min = llama_memory_seq_pos_min(llama_get_memory(ctx), slot.id);
                                 if (pos_min == -1) {
-                                    SLT_ERR(slot, "n_past = %d, slot.prompt.tokens.size() = %d, seq_id = %d, pos_min = %d\n", slot.n_past, (int) slot.prompt.tokens.size(), slot.id, pos_min);
+                                    SLT_ERR(slot, "n_past = %d, slot.prompt.tokens.size() = %d, seq_id = %d, pos_min = %d\n", n_past, (int) slot.prompt.tokens.size(), slot.id, pos_min);
                                     GGML_ABORT("pos_min == -1, but n_past > 0 - should not happen: https://github.com/ggml-org/llama.cpp/pull/13833#discussion_r2116181237");
                                 }
 
                                 // when the prompt prefix does not match, print the tokens around the mismatch
                                 // this is useful for debugging prompt caching
                                 {
-                                    const int np0 = std::max<int>(slot.n_past - 4, 0);
-                                    const int np1 = std::min<int>(slot.n_past + 6, std::min(slot.prompt.tokens.size(), slot.task->tokens.size()));
+                                    const int np0 = std::max<int>(n_past - 4, 0);
+                                    const int np1 = std::min<int>(n_past + 6, std::min(slot.prompt.tokens.size(), slot.task->tokens.size()));
 
                                     std::stringstream ss0;
                                     std::stringstream ss1;
@@ -3811,7 +3810,7 @@ struct server_context {
                                     ss1 << "new: ... ";
 
                                     for (int i = np0; i < np1; i++) {
-                                        if (i == slot.n_past) {
+                                        if (i == n_past) {
                                             ss0 << " | ";
                                             ss1 << " | ";
                                         }
@@ -3839,7 +3838,10 @@ struct server_context {
                                 }
 
                                 if (pos_min > pos_min_thold) {
-                                    SLT_WRN(slot, "n_past = %d, slot.prompt.tokens.size() = %d, seq_id = %d, pos_min = %d, n_swa = %d\n", slot.n_past, (int) slot.prompt.tokens.size(), slot.id, pos_min, n_swa);
+                                    // TODO: support can be added in the future when corresponding vision models get released
+                                    GGML_ASSERT(!slot.prompt.tokens.has_mtmd);
+
+                                    SLT_WRN(slot, "n_past = %d, slot.prompt.tokens.size() = %d, seq_id = %d, pos_min = %d, n_swa = %d\n", n_past, (int) slot.prompt.tokens.size(), slot.id, pos_min, n_swa);
 
                                     // search for a context checkpoint
                                     const auto it = std::find_if(
@@ -3863,7 +3865,7 @@ struct server_context {
                                             do_reset = true;
                                             //printf("[DEBUG] `do_reset` was set to `true` after failing to restore a checkpoint");
                                         } else {
-                                            slot.n_past = std::min(slot.n_past, std::max(it->pos_min + 1, it->pos_max));
+                                            n_past = std::min(n_past, std::max(it->pos_min + 1, it->pos_max));
                                             SLT_WRN(slot, "restored context checkpoint (pos_min = %d, pos_max = %d, size = %.3f MiB)\n", it->pos_min, it->pos_max, (float) checkpoint_size / 1024 / 1024);
                                         }
                                     }
@@ -3871,7 +3873,7 @@ struct server_context {
                                     if (do_reset) {
                                         SLT_WRN(slot, "forcing full prompt re-processing due to lack of cache data (likely due to SWA or hybrid/recurrent memory, see %s)\n",
                                                 "https://github.com/ggml-org/llama.cpp/pull/13194#issuecomment-2868343055");
-                                        slot.n_past = 0;
+                                        n_past = 0;
                                     }
                                 }
                             }
@@ -3891,43 +3893,44 @@ struct server_context {
                         }
 
                         // [TAG_PROMPT_LOGITS]
-                        if (slot.n_past == slot.n_prompt_tokens() && slot.n_past > 0) {
-                            SLT_WRN(slot, "need to evaluate at least 1 token for each active slot (n_past = %d, n_prompt_tokens = %d)\n", slot.n_past, slot.n_prompt_tokens());
-                            slot.n_past--;
-                            SLT_WRN(slot, "n_past was set to %d\n", slot.n_past);
+                        if (n_past == slot.task->n_tokens() && n_past > 0) {
+                            SLT_WRN(slot, "need to evaluate at least 1 token for each active slot (n_past = %d, task.n_tokens() = %d)\n", n_past, slot.task->n_tokens());
+                            n_past--;
+                            SLT_WRN(slot, "n_past was set to %d\n", n_past);
                         }
 
-                        slot.n_prompt_tokens_cache     = slot.n_past;
+                        slot.n_prompt_tokens_cache     = n_past;
                         slot.n_prompt_tokens_processed = 0;
+
+                        slot.prompt.tokens.keep_first(n_past);
                     }
 
                     if (!slot.can_split()) {
                         // cannot fit the prompt in the current batch - will try next iter
-                        if (batch.n_tokens + slot.n_prompt_tokens() > n_batch) {
+                        if (batch.n_tokens + slot.task->n_tokens() > n_batch) {
                             continue;
                         }
                     }
 
                     // truncate any tokens that are beyond n_past for this slot
-                    if (!llama_memory_seq_rm(llama_get_memory(ctx), slot.id, slot.n_past, -1)) {
-                        SLT_WRN(slot, "failed to truncate tokens beyond n_past = %d\n", slot.n_past);
+                    const llama_pos p0 = slot.prompt.tokens.pos_next();
+                    if (!llama_memory_seq_rm(llama_get_memory(ctx), slot.id, p0, -1)) {
+                        SLT_WRN(slot, "failed to truncate tokens with position >= %d\n", p0);
                         llama_memory_seq_rm(llama_get_memory(ctx), slot.id, -1, -1);
 
                         // there is no common part left
-                        slot.n_past                = 0;
                         slot.n_prompt_tokens_cache = 0;
-                    }
 
-                    SLT_INF(slot, "n_past = %d, memory_seq_rm [%d, end)\n", slot.n_past, slot.n_past);
+                        slot.prompt.tokens.clear();
+                    }
 
-                    // remove the non-common part from the cache
-                    slot.prompt.tokens.keep_first(slot.n_past);
+                    SLT_INF(slot, "n_tokens = %d, memory_seq_rm [%d, end)\n", slot.prompt.n_tokens(), p0);
 
                     // check if we should process the image
-                    if (slot.n_past < slot.n_prompt_tokens() && input_tokens[slot.n_past] == LLAMA_TOKEN_NULL) {
+                    if (slot.prompt.n_tokens() < slot.task->n_tokens() && input_tokens[slot.prompt.n_tokens()] == LLAMA_TOKEN_NULL) {
                         // process the image
-                        int32_t new_n_past;
-                        int32_t res = input_tokens.process_chunk(ctx, mctx, slot.n_past, slot.id, new_n_past);
+                        size_t n_tokens_out = 0;
+                        int32_t res = input_tokens.process_chunk(ctx, mctx, slot.prompt.n_tokens(), slot.prompt.tokens.pos_next(), slot.id, n_tokens_out);
                         if (res != 0) {
                             SLT_ERR(slot, "failed to process image, res = %d\n", res);
                             send_error(slot, "failed to process image", ERROR_TYPE_SERVER);
@@ -3935,16 +3938,13 @@ struct server_context {
                             continue;
                         }
 
+                        slot.n_prompt_tokens_processed += n_tokens_out;
+
                         // add the image chunk to cache
                         {
-                            const auto & chunk = input_tokens.find_chunk(slot.n_past);
+                            const auto & chunk = input_tokens.find_chunk(slot.prompt.n_tokens());
                             slot.prompt.tokens.push_back(chunk.get()); // copy
                         }
-
-                        const int32_t n_pos = new_n_past - slot.n_past;
-
-                        slot.n_past                    += n_pos;
-                        slot.n_prompt_tokens_processed += n_pos;
                     }
 
                     // If using an alora, there may be uncached tokens that come
@@ -3952,8 +3952,8 @@ struct server_context {
                     // tokens before the invocation sequence need to be
                     // processed without the adpter in a separate batch, then
                     // the adapter needs to be enabled for the remaining tokens.
-                    if (lora_all_alora(slot.lora) && slot.alora_invocation_start - 1 > slot.n_past) {
-                        SLT_DBG(slot, "processing pre-alora tokens without the adapter (n_past = %d, alora_invocation_start = %d)\n", slot.n_past, slot.alora_invocation_start);
+                    if (lora_all_alora(slot.lora) && slot.alora_invocation_start - 1 > slot.prompt.n_tokens()) {
+                        SLT_DBG(slot, "processing pre-alora tokens without the adapter (n_tokens = %d, alora_invocation_start = %d)\n", slot.prompt.n_tokens(), slot.alora_invocation_start);
                         const auto & enabled_loras = lora_get_enabled_ids(slot.lora);
                         GGML_ASSERT(enabled_loras.size() == 1);
                         alora_scale = slot.lora[enabled_loras[0]].scale;
@@ -3979,9 +3979,9 @@ struct server_context {
                             );
 
                     // add prompt tokens for processing in the current batch
-                    while (slot.n_past < slot.n_prompt_tokens() && batch.n_tokens < n_batch) {
+                    while (slot.prompt.n_tokens() < slot.task->n_tokens() && batch.n_tokens < n_batch) {
                         // get next token to process
-                        llama_token cur_tok = input_tokens[slot.n_past];
+                        llama_token cur_tok = input_tokens[slot.prompt.n_tokens()];
                         if (cur_tok == LLAMA_TOKEN_NULL) {
                             break; // end of text chunk
                         }
@@ -3989,30 +3989,33 @@ struct server_context {
                         // if this is an alora request with pre-invocation
                         // tokens that are not cached, we need to stop filling
                         // this batch at those pre-invocation tokens.
-                        if (alora_scale > 0 && slot.n_past == slot.alora_invocation_start - 1) {
-                            SLT_DBG(slot, "stop prompt batch filling at (n_past = %d, alora_invocation_start = %d)\n", slot.n_past, slot.alora_invocation_start);
+                        if (alora_scale > 0 && slot.prompt.n_tokens() == slot.alora_invocation_start - 1) {
+                            SLT_DBG(slot, "stop prompt batch filling at (n_tokens = %d, alora_invocation_start = %d)\n", slot.prompt.n_tokens(), slot.alora_invocation_start);
                             break;
                         }
 
                         // embedding requires all tokens in the batch to be output
-                        common_batch_add(batch, cur_tok, slot.n_past, { slot.id }, slot.need_embd());
+                        common_batch_add(batch,
+                            cur_tok,
+                            slot.prompt.tokens.pos_next(),
+                            { slot.id },
+                            slot.need_embd());
                         slot.prompt.tokens.push_back(cur_tok);
 
                         slot.n_prompt_tokens_processed++;
-                        slot.n_past++;
 
                         // process the last few tokens of the prompt separately in order to allow for a checkpoint to be created.
-                        if (do_checkpoint && slot.n_prompt_tokens() - slot.n_past == 64) {
+                        if (do_checkpoint && slot.task->n_tokens() - slot.prompt.n_tokens() == 64) {
                             break;
                         }
                     }
 
                     // SLT_INF(slot, "new slot.prompt.tokens: %s\n", slot.slot.prompt.tokens.str().c_str());
 
-                    SLT_INF(slot, "prompt processing progress, n_past = %d, n_tokens = %d, progress = %f\n", slot.n_past, batch.n_tokens, (float) slot.n_past / slot.n_prompt_tokens());
+                    SLT_INF(slot, "prompt processing progress, n_tokens = %d, batch.n_tokens = %d, progress = %f\n", slot.prompt.n_tokens(), batch.n_tokens, (float) slot.prompt.n_tokens() / slot.task->n_tokens());
 
                     // entire prompt has been processed
-                    if (slot.n_past == slot.n_prompt_tokens()) {
+                    if (slot.prompt.n_tokens() == slot.task->n_tokens()) {
                         slot.state = SLOT_STATE_DONE_PROMPT;
 
                         GGML_ASSERT(batch.n_tokens > 0);
@@ -4020,7 +4023,7 @@ struct server_context {
                         common_sampler_reset(slot.smpl);
 
                         // Process all prompt tokens through sampler system
-                        for (int i = 0; i < slot.n_prompt_tokens(); ++i) {
+                        for (int i = 0; i < slot.task->n_tokens(); ++i) {
                             llama_token id = input_tokens[i];
                             if (id != LLAMA_TOKEN_NULL) {
                                 common_sampler_accept(slot.smpl, id, false);
@@ -4033,7 +4036,7 @@ struct server_context {
                         slot.n_decoded = 0;
                         slot.i_batch   = batch.n_tokens - 1;
 
-                        SLT_INF(slot, "prompt done, n_past = %d, n_tokens = %d\n", slot.n_past, batch.n_tokens);
+                        SLT_INF(slot, "prompt done, n_tokens = %d, batch.n_tokens = %d\n", slot.prompt.n_tokens(), batch.n_tokens);
 
                         const auto pos_min = llama_memory_seq_pos_min(llama_get_memory(ctx), slot.id);
                         const auto pos_max = llama_memory_seq_pos_max(llama_get_memory(ctx), slot.id);
@@ -4253,9 +4256,9 @@ struct server_context {
                 // determine the max draft that fits the current slot state
                 int n_draft_max = slot.task->params.speculative.n_max;
 
-                // note: n_past is not yet increased for the `id` token sampled above
+                // note: slot.prompt is not yet expanded with the `id` token sampled above
                 //       also, need to leave space for 1 extra token to allow context shifts
-                n_draft_max = std::min(n_draft_max, slot.n_ctx - slot.n_past - 2);
+                n_draft_max = std::min(n_draft_max, slot.n_ctx - slot.prompt.n_tokens() - 2);
 
                 if (slot.n_remaining > 0) {
                     n_draft_max = std::min(n_draft_max, slot.n_remaining - 1);
@@ -4291,10 +4294,10 @@ struct server_context {
 
                 // construct the speculation batch
                 common_batch_clear(slot.batch_spec);
-                common_batch_add  (slot.batch_spec, id, slot.n_past, { slot.id }, true);
+                common_batch_add  (slot.batch_spec, id, slot.prompt.tokens.pos_next(), { slot.id }, true);
 
                 for (size_t i = 0; i < draft.size(); ++i) {
-                    common_batch_add(slot.batch_spec, draft[i], slot.n_past + 1 + i, { slot.id }, true);
+                    common_batch_add(slot.batch_spec, draft[i], slot.prompt.tokens.pos_next() + 1 + i, { slot.id }, true);
                 }
 
                 SLT_DBG(slot, "decoding speculative batch, size = %d\n", slot.batch_spec.n_tokens);
@@ -4304,7 +4307,6 @@ struct server_context {
                 // the accepted tokens from the speculation
                 const auto ids = common_sampler_sample_and_accept_n(slot.smpl, ctx, draft);
 
-                slot.n_past    += ids.size();
                 slot.n_decoded += ids.size();
 
                 // update how many tokens out of those tested were accepted
@@ -4313,7 +4315,7 @@ struct server_context {
                 slot.prompt.tokens.push_back(id);
                 slot.prompt.tokens.insert({ids.begin(), ids.end() - 1});
 
-                llama_memory_seq_rm(llama_get_memory(ctx), slot.id, slot.n_past, -1);
+                llama_memory_seq_rm(llama_get_memory(ctx), slot.id, slot.prompt.n_tokens(), -1);
 
                 for (size_t i = 0; i < ids.size(); ++i) {
                     completion_token_output result;
@@ -4334,7 +4336,7 @@ struct server_context {
                     }
                 }
 
-                SLT_DBG(slot, "accepted %d/%d draft tokens, new n_past = %d\n", (int) ids.size() - 1, (int) draft.size(), slot.n_past);
+                SLT_DBG(slot, "accepted %d/%d draft tokens, new n_tokens = %d\n", (int) ids.size() - 1, (int) draft.size(), slot.prompt.n_tokens());
             }
         }
 
@@ -4662,9 +4664,9 @@ int main(int argc, char ** argv) {
                     {"help",  "Total number of llama_decode() calls"},
                     {"value",  res_task->n_decode_total}
             }, {
-                    {"name",  "n_past_max"},
-                    {"help",  "Largest observed n_past."},
-                    {"value",  res_task->n_past_max}
+                    {"name",  "n_tokens_max"},
+                    {"help",  "Largest observed n_tokens."},
+                    {"value",  res_task->n_tokens_max}
             }, {
                     {"name",  "n_busy_slots_per_decode"},
                     {"help",  "Average number of busy slots per llama_decode() call"},
diff --git a/tools/server/utils.hpp b/tools/server/utils.hpp
index cc48f5a9d0a..fb95361b282 100644
--- a/tools/server/utils.hpp
+++ b/tools/server/utils.hpp
@@ -1080,19 +1080,22 @@ struct server_tokens {
 
 private: // disallow accessing these members directly, risking out-of-sync
 
-    // map a **start** position in tokens to the image chunk
-    std::unordered_map<llama_pos, mtmd::input_chunk_ptr> map_pos_to_media;
+    // map a **start** index in tokens to the image chunk
+    // note: the order need to be in-sync with tokens
+    std::map<size_t, mtmd::input_chunk_ptr> map_idx_to_media;
 
     // list of tokens
-    // it can include LLAMA_TOKEN_NULL, which is used to indicate a token that is not a text token
-    // a mtmd_input_chunk can occupy multiple tokens, one llama_token per **position**
-    // important: for models using mrope, an image can contain multiple tokens but will use only one **position**
+    //   if the token is LLAMA_TOKEN_NULL, it indicates that this position is occupied by media chunk
+    //   otherwise, it is a normal text token
+    // note: a non-text chunk can occupy multiple tokens (aka memory cells) in the token list
+    // note(2): for M-RoPE, an image can occupy different number of pos; do not assume 1-to-1 mapping tokens <-> pos
     llama_tokens tokens;
 
-    // for ex. with input of 5 text tokens and 2 images:
-    //      [0] [1] [2] [3] [4] [img0] [img0] [img0] [img1] [img1]
-    // pos  0   1   2   3   4   5      6      7      8      9
-    // map_pos_to_media will contain: {5, img0}, {8, img1}
+    // for ex. with input of 5 text tokens and 2 images (each image occupies 3 tokens and 2 pos):
+    //      [0] [1] [2] [3] [4] [img0] [img0] [img0] [img1] [img1] [img1]
+    // idx  0   1   2   3   4   5      6      7      8      9      10
+    // pos  0   1   2   3   4   5      5      5      7      7      7
+    // map_idx_to_media will contain: {5, img0}, {8, img1}
 
 public:
     server_tokens() = default;
@@ -1117,13 +1120,31 @@ struct server_tokens {
         }
     }
 
-    server_tokens(const llama_tokens & tokens, bool has_mtmd) : has_mtmd(has_mtmd), tokens(tokens) {}
+    server_tokens(const llama_tokens & tokens, bool has_mtmd) : has_mtmd(has_mtmd), tokens(tokens) {
+    }
+
+    llama_pos pos_next() const {
+        if (!has_mtmd) {
+            return tokens.size();
+        }
+
+        llama_pos res = tokens.size();
+
+        for (auto it = map_idx_to_media.begin(); it != map_idx_to_media.end(); ++it) {
+            const auto & chunk = it->second;
+            res += mtmd_input_chunk_get_n_pos(chunk.get()) - mtmd_input_chunk_get_n_tokens(chunk.get());
+        }
+
+        return res;
+    }
 
     // for debugging
     std::string str() const {
         std::ostringstream oss;
         oss << "tokens: ";
-        for (const auto & t : tokens) {
+        for (size_t idx = 0; idx < tokens.size(); ++idx) {
+            llama_token t = tokens[idx];
+            oss << "idx:" << idx << " ";
             if (t == LLAMA_TOKEN_NULL) {
                 oss << "<embd> ";
             } else {
@@ -1131,16 +1152,16 @@ struct server_tokens {
             }
         }
         oss << "\n";
-        oss << "image pos: ";
-        for (const auto & it : map_pos_to_media) {
+        oss << "image idx: ";
+        for (const auto & it : map_idx_to_media) {
             oss << it.first << ", ";
         }
         return oss.str();
     }
 
-    const mtmd::input_chunk_ptr & find_chunk(llama_pos pos) const {
-        auto it = map_pos_to_media.find(pos);
-        if (it != map_pos_to_media.end()) {
+    const mtmd::input_chunk_ptr & find_chunk(size_t idx) const {
+        auto it = map_idx_to_media.find(idx);
+        if (it != map_idx_to_media.end()) {
             return it->second;
         }
         throw std::runtime_error("Chunk not found");
@@ -1158,13 +1179,13 @@ struct server_tokens {
         auto type = mtmd_input_chunk_get_type(chunk);
         if (type == MTMD_INPUT_CHUNK_TYPE_IMAGE || type == MTMD_INPUT_CHUNK_TYPE_AUDIO) {
             GGML_ASSERT(has_mtmd);
-            const int n_pos = mtmd_input_chunk_get_n_pos(chunk);
-            llama_pos start_pos = tokens.size();
-            for (int i = 0; i < n_pos; ++i) {
+            const size_t n_tokens = mtmd_input_chunk_get_n_tokens(chunk);
+            size_t start_idx = tokens.size();
+            for (size_t i = 0; i < n_tokens; ++i) {
                 tokens.emplace_back(LLAMA_TOKEN_NULL);
             }
             mtmd::input_chunk_ptr new_chunk(mtmd_input_chunk_copy(chunk));
-            map_pos_to_media[start_pos] = std::move(new_chunk);
+            map_idx_to_media[start_idx] = std::move(new_chunk);
         } else if (type == MTMD_INPUT_CHUNK_TYPE_TEXT) {
             size_t n_tokens;
             const auto * text_tokens = mtmd_input_chunk_get_tokens_text(chunk, &n_tokens);
@@ -1178,7 +1199,7 @@ struct server_tokens {
 
     // appends server tokens, updates the media map. copies media chunks.
     void push_back(server_tokens & tokens) {
-        size_t start_pos = size();
+        size_t start_idx = size();
         for (size_t i = 0; i < tokens.size(); i++) {
             push_back(tokens[i]);
         }
@@ -1186,10 +1207,10 @@ struct server_tokens {
             // Assert if we are copying MTMD chunks to a server_tokens that does not have mtmd.
             // We could also just check, but this will prevent silently dropping MTMD data.
             GGML_ASSERT(has_mtmd);
-            for (auto it = tokens.map_pos_to_media.begin(); it != tokens.map_pos_to_media.end(); ) {
-                auto * chunk = tokens.map_pos_to_media[it->first].get();
+            for (auto it = tokens.map_idx_to_media.begin(); it != tokens.map_idx_to_media.end(); ) {
+                auto * chunk = tokens.map_idx_to_media[it->first].get();
                 mtmd::input_chunk_ptr new_chunk(mtmd_input_chunk_copy(chunk));
-                map_pos_to_media[start_pos+it->first] = std::move(new_chunk);
+                map_idx_to_media[start_idx+it->first] = std::move(new_chunk);
             }
         }
     }
@@ -1245,10 +1266,10 @@ struct server_tokens {
                 }
             }
             // remove all image chunks that are not used anymore
-            for (auto it = map_pos_to_media.begin(); it != map_pos_to_media.end(); ) {
-                llama_pos pos = it->first;
-                if (pos >= (llama_pos)n) {
-                    it = map_pos_to_media.erase(it);
+            for (auto it = map_idx_to_media.begin(); it != map_idx_to_media.end(); ) {
+                size_t idx = it->first;
+                if (idx >= n) {
+                    it = map_idx_to_media.erase(it);
                 } else {
                     ++it;
                 }
@@ -1296,12 +1317,12 @@ struct server_tokens {
                 const std::string id_ai = mtmd_input_chunk_get_id(a_chunk.get());
                 const std::string id_bi = mtmd_input_chunk_get_id(b_chunk.get());
 
-                const size_t pos_a = mtmd_input_chunk_get_n_pos(a_chunk.get());
-                const size_t pos_b = mtmd_input_chunk_get_n_pos(b_chunk.get());
+                const size_t n_tok_a = mtmd_input_chunk_get_n_tokens(a_chunk.get());
+                const size_t n_tok_b = mtmd_input_chunk_get_n_tokens(b_chunk.get());
 
-                if (id_ai == id_bi && pos_a == pos_b) {
-                    GGML_ASSERT(pos_a > 0 && "Invalid media chunk"); // should never happen
-                    i += pos_a - 1; // will be +1 by the for loop
+                if (id_ai == id_bi && n_tok_a == n_tok_b) {
+                    GGML_ASSERT(n_tok_a > 0 && "Invalid media chunk"); // should never happen
+                    i += n_tok_a - 1; // will be +1 by the for loop
                     continue;
                 }
 
@@ -1329,8 +1350,8 @@ struct server_tokens {
             if (t == LLAMA_TOKEN_NULL) {
                 try {
                     const auto & chunk = find_chunk(i);
-                    size_t n_pos = mtmd_input_chunk_get_n_pos(chunk.get());
-                    i += n_pos - 1; // will be +1 by the for loop
+                    size_t n_tokens = mtmd_input_chunk_get_n_tokens(chunk.get());
+                    i += n_tokens - 1; // will be +1 by the for loop
                 } catch (const std::exception & e) {
                     return false;
                 }
@@ -1345,19 +1366,20 @@ struct server_tokens {
     int32_t process_chunk(
                 llama_context * ctx,
                 mtmd_context * mctx,
-                llama_pos n_past,
+                size_t idx,
+                llama_pos pos,
                 int32_t seq_id,
-                llama_pos & n_pos_out) const {
-        const auto & chunk = find_chunk(n_past);
+                size_t & n_tokens_out) const {
+        const auto & chunk = find_chunk(idx);
         const char * name = mtmd_input_chunk_get_type(chunk.get()) == MTMD_INPUT_CHUNK_TYPE_IMAGE
                             ? "image" : "audio";
         SRV_INF("processing %s...\n", name);
         int32_t n_batch = llama_n_batch(ctx);
         int64_t t0 = ggml_time_ms();
-        llama_pos new_n_past = n_past;
+        llama_pos new_n_past; // unused for now
         int32_t result = mtmd_helper_eval_chunk_single(mctx, ctx,
             chunk.get(),
-            n_past,
+            pos,
             seq_id,
             n_batch,
             true, // logits last
@@ -1365,10 +1387,10 @@ struct server_tokens {
         SRV_INF("%s processed in %" PRId64 " ms\n", name, ggml_time_ms() - t0);
         if (result != 0) {
             LOG_ERR("mtmd_helper_eval failed with status %d", result);
-            n_pos_out = n_past;
+            n_tokens_out = 0;
             return result;
         }
-        n_pos_out = new_n_past;
+        n_tokens_out = mtmd_input_chunk_get_n_tokens(chunk.get());
         return 0;
     }
 };

From 16724b5b6836a2d4b8936a5824d2ff27c52b4517 Mon Sep 17 00:00:00 2001
From: chansikpark <chansik.park@gmail.com>
Date: Thu, 30 Oct 2025 14:22:23 -0400
Subject: [PATCH 025/185] server : bump request URI max length to 32768
 (#16862)

---
 tools/server/utils.hpp | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/tools/server/utils.hpp b/tools/server/utils.hpp
index fb95361b282..b6198edfc48 100644
--- a/tools/server/utils.hpp
+++ b/tools/server/utils.hpp
@@ -13,6 +13,8 @@
 #define CPPHTTPLIB_FORM_URL_ENCODED_PAYLOAD_MAX_LENGTH 1048576
 // increase backlog size to avoid connection resets for >> 1 slots
 #define CPPHTTPLIB_LISTEN_BACKLOG 512
+// increase max URI length to handle longer prompts in query string
+#define CPPHTTPLIB_REQUEST_URI_MAX_LENGTH 32768
 // disable Nagle's algorithm
 #define CPPHTTPLIB_TCP_NODELAY true
 #include <cpp-httplib/httplib.h>

From ce18efeaf1234bd08f25bc08f88ef95cf5d9e51f Mon Sep 17 00:00:00 2001
From: RodriMora <bullerwins@gmail.com>
Date: Thu, 30 Oct 2025 23:15:03 +0100
Subject: [PATCH 026/185] convert : update transformers requirements (#16866)
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

* Update requirements-convert_legacy_llama.txt

Updated requirements to support Qwen3-VL in transformers 4.57.1 version

* Update requirements/requirements-convert_legacy_llama.txt

Co-authored-by: Sigbjørn Skjæret <sigbjorn.skjaeret@scala.com>

---------

Co-authored-by: Sigbjørn Skjæret <sigbjorn.skjaeret@scala.com>
---
 requirements/requirements-convert_legacy_llama.txt | 9 +--------
 1 file changed, 1 insertion(+), 8 deletions(-)

diff --git a/requirements/requirements-convert_legacy_llama.txt b/requirements/requirements-convert_legacy_llama.txt
index f6076142cee..dbab3b9508f 100644
--- a/requirements/requirements-convert_legacy_llama.txt
+++ b/requirements/requirements-convert_legacy_llama.txt
@@ -1,14 +1,7 @@
 numpy~=1.26.4
 sentencepiece~=0.2.0
 
-# Embedding Gemma is currently a preview release:
-# https://github.com/huggingface/transformers/releases/tag/v4.56.0-Embedding-Gemma-preview
-
-# The version is needed to be able to convert Embedding Gemma models to GGUF format:
-git+https://github.com/huggingface/transformers@v4.56.0-Embedding-Gemma-preview
-
-# Once Embedding Gemma is officially released, we can switch to:
-#transformers>=4.57.1,<5.0.0
+transformers>=4.57.1,<5.0.0
 
 gguf>=0.1.0
 protobuf>=4.21.0,<5.0.0

From 9984cbb61d12491d604484fb38b678fa15064061 Mon Sep 17 00:00:00 2001
From: lhez <lih@qti.qualcomm.com>
Date: Thu, 30 Oct 2025 16:00:20 -0700
Subject: [PATCH 027/185] opencl: fix boundary handling for mul_mm (#16875)

---
 ggml/src/ggml-opencl/kernels/mul_mm_f16_f32_l4_lm.cl  | 6 +++---
 ggml/src/ggml-opencl/kernels/mul_mm_f32_f32_l4_lm.cl  | 4 ++--
 ggml/src/ggml-opencl/kernels/mul_mm_q8_0_f32_l4_lm.cl | 4 ++--
 3 files changed, 7 insertions(+), 7 deletions(-)

diff --git a/ggml/src/ggml-opencl/kernels/mul_mm_f16_f32_l4_lm.cl b/ggml/src/ggml-opencl/kernels/mul_mm_f16_f32_l4_lm.cl
index 1a1bfe144f6..6982f8f514d 100644
--- a/ggml/src/ggml-opencl/kernels/mul_mm_f16_f32_l4_lm.cl
+++ b/ggml/src/ggml-opencl/kernels/mul_mm_f16_f32_l4_lm.cl
@@ -79,8 +79,8 @@ kernel void kernel_mul_mm_f16_f32_l4_lm(
 
     for (int block = 0; block < ne00; block += BK) {
         for (int l = 0; l < BM; l += loadstride_a) {
-            if (loadc_a + l < ne01) {
-            const int idx = pos_a + (loadc_a + l) * stride_a / LOAD_VEC_A + loadr_a;
+            if (ir*BM + loadc_a + l < ne01) {
+                const int idx = pos_a + (loadc_a + l) * stride_a / LOAD_VEC_A + loadr_a;
                 buf_a[(loadr_a * LOAD_VEC_A + 0) * BM + loadc_a + l] = src0[idx].s0;
                 buf_a[(loadr_a * LOAD_VEC_A + 1) * BM + loadc_a + l] = src0[idx].s1;
                 buf_a[(loadr_a * LOAD_VEC_A + 2) * BM + loadc_a + l] = src0[idx].s2;
@@ -94,7 +94,7 @@ kernel void kernel_mul_mm_f16_f32_l4_lm(
         }
 
         for (int l = 0; l < BN; l += loadstride_b) {
-            if (loadc_b + l < ne11) {
+            if (ic*BN + loadc_b + l < ne11) {
                 const int idx = pos_b + (loadc_b + l) * stride_b / LOAD_VEC_B + loadr_b;
                 buf_b[(loadr_b * LOAD_VEC_B + 0) * BN + loadc_b + l] = src1[idx].s0;
                 buf_b[(loadr_b * LOAD_VEC_B + 1) * BN + loadc_b + l] = src1[idx].s1;
diff --git a/ggml/src/ggml-opencl/kernels/mul_mm_f32_f32_l4_lm.cl b/ggml/src/ggml-opencl/kernels/mul_mm_f32_f32_l4_lm.cl
index 39a5d4868ff..d7d5ba647e7 100644
--- a/ggml/src/ggml-opencl/kernels/mul_mm_f32_f32_l4_lm.cl
+++ b/ggml/src/ggml-opencl/kernels/mul_mm_f32_f32_l4_lm.cl
@@ -79,7 +79,7 @@ kernel void kernel_mul_mm_f32_f32_l4_lm(
 
     for (int block = 0; block < ne00; block += BK) {
         for (int l = 0; l < BM; l += loadstride_a) {
-            if (loadc_a + l < ne01) {
+            if (ir*BM + loadc_a + l < ne01) {
                 const int idx = pos_a + (loadc_a + l) * stride_a / LOAD_VEC_A + loadr_a;
                 buf_a[(loadr_a * LOAD_VEC_A + 0) * BM + loadc_a + l] = src0[idx].s0;
                 buf_a[(loadr_a * LOAD_VEC_A + 1) * BM + loadc_a + l] = src0[idx].s1;
@@ -94,7 +94,7 @@ kernel void kernel_mul_mm_f32_f32_l4_lm(
         }
 
         for (int l = 0; l < BN; l += loadstride_b) {
-            if (loadc_b + l < ne11) {
+            if (ic*BN + loadc_b + l < ne11) {
                 const int idx = pos_b + (loadc_b + l) * stride_b / LOAD_VEC_B + loadr_b;
                 buf_b[(loadr_b * LOAD_VEC_B + 0) * BN + loadc_b + l] = src1[idx].s0;
                 buf_b[(loadr_b * LOAD_VEC_B + 1) * BN + loadc_b + l] = src1[idx].s1;
diff --git a/ggml/src/ggml-opencl/kernels/mul_mm_q8_0_f32_l4_lm.cl b/ggml/src/ggml-opencl/kernels/mul_mm_q8_0_f32_l4_lm.cl
index fd47e8a89dc..147b66f6692 100644
--- a/ggml/src/ggml-opencl/kernels/mul_mm_q8_0_f32_l4_lm.cl
+++ b/ggml/src/ggml-opencl/kernels/mul_mm_q8_0_f32_l4_lm.cl
@@ -78,7 +78,7 @@ kernel void kernel_mul_mm_q8_0_f32_l4_lm(
 
     for (int block = 0; block < ne00; block += BK) {
         for (int l = 0; l < BM; l += loadstride_a) {
-            if (loadc_a + l < ne01) {
+            if (ir*BM + loadc_a + l < ne01) {
                 int idx = pos_a + (loadc_a + l) * stride_a / LOAD_VEC_A + loadr_a;
                 int ib  = idx / 8;
                 int iqs = idx % 8;
@@ -101,7 +101,7 @@ kernel void kernel_mul_mm_q8_0_f32_l4_lm(
         }
 
         for (int l = 0; l < BN; l += loadstride_b) {
-            if (loadc_b + l < ne11) {
+            if (ic*BN + loadc_b + l < ne11) {
                 int idx = pos_b + (loadc_b + l) * stride_b / LOAD_VEC_B + loadr_b;
                 buf_b[(loadr_b * LOAD_VEC_B + 0) * BN + loadc_b + l] = src1[idx].s0;
                 buf_b[(loadr_b * LOAD_VEC_B + 1) * BN + loadc_b + l] = src1[idx].s1;

From 6eb208d17ea29bb60295d9a2b5e7122dfb8f4b55 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sigbj=C3=B8rn=20Skj=C3=A6ret?= <sigbjorn.skjaeret@scala.com>
Date: Fri, 31 Oct 2025 00:34:27 +0100
Subject: [PATCH 028/185] ci : enable free-disk-space on cuda docker build
 (#16877)

---
 .github/workflows/docker.yml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/.github/workflows/docker.yml b/.github/workflows/docker.yml
index f73a2bc9f45..7ca11b1dffc 100644
--- a/.github/workflows/docker.yml
+++ b/.github/workflows/docker.yml
@@ -40,7 +40,7 @@ jobs:
           # https://github.com/ggml-org/llama.cpp/issues/11888
           #- { tag: "cpu", dockerfile: ".devops/cpu.Dockerfile", platforms: "linux/amd64,linux/arm64", full: true, light: true, server: true, free_disk_space: false }
           - { tag: "cpu",    dockerfile: ".devops/cpu.Dockerfile",    platforms: "linux/amd64", full: true, light: true, server: true, free_disk_space: false, runs_on: "ubuntu-22.04" }
-          - { tag: "cuda",   dockerfile: ".devops/cuda.Dockerfile",   platforms: "linux/amd64", full: true, light: true, server: true, free_disk_space: false, runs_on: "ubuntu-22.04" }
+          - { tag: "cuda",   dockerfile: ".devops/cuda.Dockerfile",   platforms: "linux/amd64", full: true, light: true, server: true, free_disk_space: true,  runs_on: "ubuntu-22.04" }
           - { tag: "musa",   dockerfile: ".devops/musa.Dockerfile",   platforms: "linux/amd64", full: true, light: true, server: true, free_disk_space: true,  runs_on: "ubuntu-22.04" }
           - { tag: "intel",  dockerfile: ".devops/intel.Dockerfile",  platforms: "linux/amd64", full: true, light: true, server: true, free_disk_space: true,  runs_on: "ubuntu-22.04" }
           - { tag: "vulkan", dockerfile: ".devops/vulkan.Dockerfile", platforms: "linux/amd64", full: true, light: true, server: true, free_disk_space: false, runs_on: "ubuntu-22.04" }

From 13002a08960e51a76c4d696165b5d7638d2f2b99 Mon Sep 17 00:00:00 2001
From: l3utterfly <gc.pthzfoldr@gmail.com>
Date: Fri, 31 Oct 2025 12:46:31 +0800
Subject: [PATCH 029/185] ggml-hexagon: respect input size when getting/setting
 tensor data (#16836)

* respect input size when getting/setting tensor data

allows partial repacking/copying when get tensor size is smaller than the actual tensor

* Removed duplicate repack_mxfp4_mxfp4x4x2 function
---
 ggml/src/ggml-hexagon/ggml-hexagon.cpp | 180 +++++++++++++++++++++++--
 1 file changed, 168 insertions(+), 12 deletions(-)

diff --git a/ggml/src/ggml-hexagon/ggml-hexagon.cpp b/ggml/src/ggml-hexagon/ggml-hexagon.cpp
index 2d376a6025c..945652263d4 100644
--- a/ggml/src/ggml-hexagon/ggml-hexagon.cpp
+++ b/ggml/src/ggml-hexagon/ggml-hexagon.cpp
@@ -676,6 +676,15 @@ static void repack_q4_0_q4x4x2(ggml_tensor * t, const void * data, size_t size)
     size_t row_size_pd = ggml_row_size(t->type, hex_round_up(t->ne[0], QK_Q4_0x4x2));  // extra elements for the pad
     size_t row_size_rp = row_size * 2;  // extra space for tmp pad (if any)
 
+    // Ensure we don't try to read more data than is available in the source buffer 'data'
+    // or write more than the tensor can hold.
+    const size_t total_tensor_size = (size_t)nrows * row_size;
+    const size_t n_bytes_to_copy = size < total_tensor_size ? size : total_tensor_size;
+
+    // Calculate how many full rows and how many remaining bytes we need to process.
+    const int64_t n_full_rows = n_bytes_to_copy / row_size;
+    const size_t  n_rem_bytes = n_bytes_to_copy % row_size;
+
     void * buf_pd = ggml_aligned_malloc(row_size_pd);
     GGML_ASSERT(buf_pd != NULL);
 
@@ -687,7 +696,8 @@ static void repack_q4_0_q4x4x2(ggml_tensor * t, const void * data, size_t size)
 
     init_row_q4x4x2((block_q4_0 *) buf_pd, t->ne[0]);  // init padded buffer to make sure the tail is all zeros
 
-    for (int64_t i = 0; i < nrows; i++) {
+    // 1. Process all the full rows
+    for (int64_t i = 0; i < n_full_rows; i++) {
         const uint8_t * src = (const uint8_t *) data + (i * row_size);
         uint8_t *       dst = (uint8_t *) t->data + (i * row_size);
 
@@ -696,6 +706,25 @@ static void repack_q4_0_q4x4x2(ggml_tensor * t, const void * data, size_t size)
         memcpy(dst, buf_rp, row_size);
     }
 
+    // 2. Process the final, potentially partial, row
+    if (n_rem_bytes > 0) {
+        const int64_t i = n_full_rows;
+        const uint8_t * src = (const uint8_t *) data + (i * row_size);
+        uint8_t *       dst = (uint8_t *) t->data + (i * row_size);
+
+        // re-init the row because we are potentially copying a partial row
+        init_row_q4x4x2((block_q4_0 *) buf_pd, t->ne[0]);
+
+        // Copy only the remaining bytes from the source.
+        memcpy(buf_pd, src, n_rem_bytes);
+
+        // Repack the entire buffer
+        repack_row_q4x4x2((uint8_t *) buf_rp, (const block_q4_0 *) buf_pd, t->ne[0]);
+
+        // Write only the corresponding remaining bytes to the destination tensor.
+        memcpy(dst, buf_rp, n_rem_bytes);
+    }
+
     ggml_aligned_free(buf_pd, row_size_pd);
     ggml_aligned_free(buf_rp, row_size_rp);
 }
@@ -708,6 +737,14 @@ static void repack_q4x4x2_q4_0(void * data, const ggml_tensor * t, size_t size)
     size_t row_size_pd = ggml_row_size(t->type, hex_round_up(t->ne[0], QK_Q4_0x4x2));  // extra elements for the pad
     size_t row_size_rp = row_size * 2;  // extra space for tmp pad (if any)
 
+    // Ensure we don't try to copy more data than the tensor actually contains.
+    const size_t total_tensor_size = (size_t)nrows * row_size;
+    const size_t n_bytes_to_copy = size < total_tensor_size ? size : total_tensor_size;
+
+    // Calculate how many full rows and how many remaining bytes we need to process.
+    const int64_t n_full_rows = n_bytes_to_copy / row_size;
+    const size_t  n_rem_bytes = n_bytes_to_copy % row_size;
+
     void * buf_pd = ggml_aligned_malloc(row_size_pd);
     GGML_ASSERT(buf_pd != NULL);
 
@@ -719,7 +756,8 @@ static void repack_q4x4x2_q4_0(void * data, const ggml_tensor * t, size_t size)
 
     memset(buf_pd, 0, row_size_pd);  // clear-out padded buffer to make sure the tail is all zeros
 
-    for (int64_t i = 0; i < nrows; i++) {
+    // 1. Process all the full rows
+    for (int64_t i = 0; i < n_full_rows; i++) {
         const uint8_t * src = (const uint8_t *) t->data + (i * row_size);
         uint8_t *       dst = (uint8_t *) data + (i * row_size);
 
@@ -728,6 +766,20 @@ static void repack_q4x4x2_q4_0(void * data, const ggml_tensor * t, size_t size)
         memcpy(dst, buf_rp, row_size);
     }
 
+    // 2. Process the final, potentially partial, row
+    if (n_rem_bytes > 0) {
+        const int64_t i = n_full_rows;
+        const uint8_t * src = (const uint8_t *) t->data + (i * row_size);
+        uint8_t *       dst = (uint8_t *) data + (i * row_size);
+
+        // We still need to read and unpack the entire source row because quantization is block-based.
+        memcpy(buf_pd, src, row_size);
+        unpack_row_q4x4x2((block_q4_0 *) buf_rp, (const uint8_t *) buf_pd, t->ne[0]);
+
+        // But we only copy the remaining number of bytes to the destination.
+        memcpy(dst, buf_rp, n_rem_bytes);
+    }
+
     ggml_aligned_free(buf_pd, row_size_pd);
     ggml_aligned_free(buf_rp, row_size_rp);
 }
@@ -950,6 +1002,15 @@ static void repack_q8_0_q8x4x2(ggml_tensor * t, const void * data, size_t size)
     size_t row_size_pd = ggml_row_size(t->type, hex_round_up(t->ne[0], QK_Q8_0x4x2));  // extra elements for the pad
     size_t row_size_rp = row_size * 2;  // extra space for tmp pad (if any)
 
+    // Ensure we don't try to read more data than is available in the source buffer 'data'
+    // or write more than the tensor can hold.
+    const size_t total_tensor_size = (size_t)nrows * row_size;
+    const size_t n_bytes_to_copy = size < total_tensor_size ? size : total_tensor_size;
+
+    // Calculate how many full rows and how many remaining bytes we need to process.
+    const int64_t n_full_rows = n_bytes_to_copy / row_size;
+    const size_t  n_rem_bytes = n_bytes_to_copy % row_size;
+
     void * buf_pd = ggml_aligned_malloc(row_size_pd);
     GGML_ASSERT(buf_pd != NULL);
 
@@ -961,7 +1022,8 @@ static void repack_q8_0_q8x4x2(ggml_tensor * t, const void * data, size_t size)
 
     init_row_q8x4x2((block_q8_0 *) buf_pd, t->ne[0]);  // init padded buffer to make sure the tail is all zeros
 
-    for (int64_t i = 0; i < nrows; i++) {
+    // 1. Process all the full rows
+    for (int64_t i = 0; i < n_full_rows; i++) {
         const uint8_t * src = (const uint8_t *) data + (i * row_size);
         uint8_t *       dst = (uint8_t *) t->data + (i * row_size);
 
@@ -970,6 +1032,25 @@ static void repack_q8_0_q8x4x2(ggml_tensor * t, const void * data, size_t size)
         memcpy(dst, buf_rp, row_size);
     }
 
+    // 2. Process the final, potentially partial, row
+    if (n_rem_bytes > 0) {
+        const int64_t i = n_full_rows;
+        const uint8_t * src = (const uint8_t *) data + (i * row_size);
+        uint8_t *       dst = (uint8_t *) t->data + (i * row_size);
+
+        // re-init the row because we are potentially copying a partial row
+        init_row_q8x4x2((block_q8_0 *) buf_pd, t->ne[0]);
+
+        // Copy only the remaining bytes from the source.
+        memcpy(buf_pd, src, n_rem_bytes);
+
+        // Repack the entire buffer
+        repack_row_q8x4x2((uint8_t *) buf_rp, (const block_q8_0 *) buf_pd, t->ne[0]);
+
+        // Write only the corresponding remaining bytes to the destination tensor.
+        memcpy(dst, buf_rp, n_rem_bytes);
+    }
+
     ggml_aligned_free(buf_pd, row_size_pd);
     ggml_aligned_free(buf_rp, row_size_rp);
 }
@@ -982,6 +1063,14 @@ static void repack_q8x4x2_q8_0(void * data, const ggml_tensor * t, size_t size)
     size_t row_size_pd = ggml_row_size(t->type, hex_round_up(t->ne[0], QK_Q8_0x4x2));  // extra elements for the pad
     size_t row_size_rp = row_size * 2;  // extra space for tmp pad (if any)
 
+    // Ensure we don't try to copy more data than the tensor actually contains.
+    const size_t total_tensor_size = (size_t)nrows * row_size;
+    const size_t n_bytes_to_copy = size < total_tensor_size ? size : total_tensor_size;
+
+    // Calculate how many full rows and how many remaining bytes we need to process.
+    const int64_t n_full_rows = n_bytes_to_copy / row_size;
+    const size_t  n_rem_bytes = n_bytes_to_copy % row_size;
+
     void * buf_pd = ggml_aligned_malloc(row_size_pd);
     GGML_ASSERT(buf_pd != NULL);
 
@@ -993,7 +1082,8 @@ static void repack_q8x4x2_q8_0(void * data, const ggml_tensor * t, size_t size)
 
     memset(buf_pd, 0, row_size_pd);  // clear-out padded buffer to make sure the tail is all zeros
 
-    for (int64_t i = 0; i < nrows; i++) {
+    // 1. Process all the full rows
+    for (int64_t i = 0; i < n_full_rows; i++) {
         const uint8_t * src = (const uint8_t *) t->data + (i * row_size);
         uint8_t *       dst = (uint8_t *) data + (i * row_size);
 
@@ -1002,6 +1092,20 @@ static void repack_q8x4x2_q8_0(void * data, const ggml_tensor * t, size_t size)
         memcpy(dst, buf_rp, row_size);
     }
 
+    // 2. Process the final, potentially partial, row
+    if (n_rem_bytes > 0) {
+        const int64_t i = n_full_rows;
+        const uint8_t * src = (const uint8_t *) t->data + (i * row_size);
+        uint8_t *       dst = (uint8_t *) data + (i * row_size);
+
+        // We still need to read and unpack the entire source row because quantization is block-based.
+        memcpy(buf_pd, src, row_size);
+        unpack_row_q8x4x2((block_q8_0 *) buf_rp, (const uint8_t *) buf_pd, t->ne[0]);
+
+        // But we only copy the remaining number of bytes to the destination.
+        memcpy(dst, buf_rp, n_rem_bytes);
+    }
+
     ggml_aligned_free(buf_pd, row_size_pd);
     ggml_aligned_free(buf_rp, row_size_rp);
 }
@@ -1249,6 +1353,15 @@ static void repack_mxfp4_mxfp4x4x2(ggml_tensor * t, const void * data, size_t si
     size_t row_size_pd = ggml_row_size(t->type, hex_round_up(t->ne[0], QK_MXFP4x4x2));  // extra elements for the pad
     size_t row_size_rp = row_size * 2;  // extra space for tmp pad (if any)
 
+    // Ensure we don't try to read more data than is available in the source buffer 'data'
+    // or write more than the tensor can hold.
+    const size_t total_tensor_size = (size_t)nrows * row_size;
+    const size_t n_bytes_to_copy = size < total_tensor_size ? size : total_tensor_size;
+
+    // Calculate how many full rows and how many remaining bytes we need to process.
+    const int64_t n_full_rows = n_bytes_to_copy / row_size;
+    const size_t  n_rem_bytes = n_bytes_to_copy % row_size;
+
     void * buf_pd = ggml_aligned_malloc(row_size_pd);
     GGML_ASSERT(buf_pd != NULL);
 
@@ -1260,7 +1373,8 @@ static void repack_mxfp4_mxfp4x4x2(ggml_tensor * t, const void * data, size_t si
 
     init_row_mxfp4x4x2((block_mxfp4 *) buf_pd, t->ne[0]);  // init padded buffer to make sure the tail is all zeros
 
-    for (int64_t i = 0; i < nrows; i++) {
+    // 1. Process all the full rows
+    for (int64_t i = 0; i < n_full_rows; i++) {
         const uint8_t * src = (const uint8_t *) data + (i * row_size);
         uint8_t *       dst = (uint8_t *) t->data + (i * row_size);
 
@@ -1269,6 +1383,25 @@ static void repack_mxfp4_mxfp4x4x2(ggml_tensor * t, const void * data, size_t si
         memcpy(dst, buf_rp, row_size);
     }
 
+    // 2. Process the final, potentially partial, row
+    if (n_rem_bytes > 0) {
+        const int64_t i = n_full_rows;
+        const uint8_t * src = (const uint8_t *) data + (i * row_size);
+        uint8_t *       dst = (uint8_t *) t->data + (i * row_size);
+
+        // re-init the row because we are potentially copying a partial row
+        init_row_mxfp4x4x2((block_mxfp4 *) buf_pd, t->ne[0]);
+
+        // Copy only the remaining bytes from the source.
+        memcpy(buf_pd, src, n_rem_bytes);
+
+        // Repack the entire buffer (partial data + zero padding).
+        repack_row_mxfp4x4x2((uint8_t *) buf_rp, (const block_mxfp4 *) buf_pd, t->ne[0]);
+
+        // Write only the corresponding remaining bytes to the destination tensor.
+        memcpy(dst, buf_rp, n_rem_bytes);
+    }
+
     ggml_aligned_free(buf_pd, row_size_pd);
     ggml_aligned_free(buf_rp, row_size_rp);
 }
@@ -1281,6 +1414,14 @@ static void repack_mxfp4x4x2_mxfp4(void * data, const ggml_tensor * t, size_t si
     size_t row_size_pd = ggml_row_size(t->type, hex_round_up(t->ne[0], QK_MXFP4x4x2));  // extra elements for the pad
     size_t row_size_rp = row_size * 2;  // extra space for tmp pad (if any)
 
+    // Ensure we don't try to copy more data than the tensor actually contains.
+    const size_t total_tensor_size = (size_t)nrows * row_size;
+    const size_t n_bytes_to_copy = size < total_tensor_size ? size : total_tensor_size;
+
+    // Calculate how many full rows and how many remaining bytes we need to process.
+    const int64_t n_full_rows = n_bytes_to_copy / row_size;
+    const size_t  n_rem_bytes = n_bytes_to_copy % row_size;
+
     void * buf_pd = ggml_aligned_malloc(row_size_pd);
     GGML_ASSERT(buf_pd != NULL);
 
@@ -1292,7 +1433,8 @@ static void repack_mxfp4x4x2_mxfp4(void * data, const ggml_tensor * t, size_t si
 
     memset(buf_pd, 0, row_size_pd);  // clear-out padded buffer to make sure the tail is all zeros
 
-    for (int64_t i = 0; i < nrows; i++) {
+    // 1. Process all the full rows
+    for (int64_t i = 0; i < n_full_rows; i++) {
         const uint8_t * src = (const uint8_t *) t->data + (i * row_size);
         uint8_t *       dst = (uint8_t *) data + (i * row_size);
 
@@ -1301,6 +1443,20 @@ static void repack_mxfp4x4x2_mxfp4(void * data, const ggml_tensor * t, size_t si
         memcpy(dst, buf_rp, row_size);
     }
 
+    // 2. Process the final, potentially partial, row
+    if (n_rem_bytes > 0) {
+        const int64_t i = n_full_rows;
+        const uint8_t * src = (const uint8_t *) t->data + (i * row_size);
+        uint8_t *       dst = (uint8_t *) data + (i * row_size);
+
+        // We still need to read and unpack the entire source row because the format is block-based.
+        memcpy(buf_pd, src, row_size);
+        unpack_row_mxfp4x4x2((block_mxfp4 *) buf_rp, (const uint8_t *) buf_pd, t->ne[0]);
+
+        // But we only copy the remaining number of bytes to the destination to respect the size limit.
+        memcpy(dst, buf_rp, n_rem_bytes);
+    }
+
     ggml_aligned_free(buf_pd, row_size_pd);
     ggml_aligned_free(buf_rp, row_size_rp);
 }
@@ -1319,19 +1475,19 @@ static void ggml_backend_hexagon_buffer_set_tensor(ggml_backend_buffer_t buffer,
     switch (tensor->type) {
         case GGML_TYPE_Q4_0:
             GGML_ASSERT(offset == 0);
-            GGML_ASSERT(size == ggml_nbytes(tensor));
+            GGML_ASSERT(offset + size <= ggml_nbytes(tensor));
             repack_q4_0_q4x4x2(tensor, data, size);
             break;
 
         case GGML_TYPE_Q8_0:
             GGML_ASSERT(offset == 0);
-            GGML_ASSERT(size == ggml_nbytes(tensor));
+            GGML_ASSERT(offset + size <= ggml_nbytes(tensor));
             repack_q8_0_q8x4x2(tensor, data, size);
             break;
 
         case GGML_TYPE_MXFP4:
             GGML_ASSERT(offset == 0);
-            GGML_ASSERT(size == ggml_nbytes(tensor));
+            GGML_ASSERT(offset + size <= ggml_nbytes(tensor));
             repack_mxfp4_mxfp4x4x2(tensor, data, size);
             break;
 
@@ -1355,19 +1511,19 @@ static void ggml_backend_hexagon_buffer_get_tensor(ggml_backend_buffer_t buffer,
     switch (tensor->type) {
         case GGML_TYPE_Q4_0:
             GGML_ASSERT(offset == 0);
-            GGML_ASSERT(size == ggml_nbytes(tensor));
+            GGML_ASSERT(offset + size <= ggml_nbytes(tensor));
             repack_q4x4x2_q4_0(data, tensor, size);
             break;
 
         case GGML_TYPE_Q8_0:
             GGML_ASSERT(offset == 0);
-            GGML_ASSERT(size == ggml_nbytes(tensor));
+            GGML_ASSERT(offset + size <= ggml_nbytes(tensor));
             repack_q8x4x2_q8_0(data, tensor, size);
             break;
 
         case GGML_TYPE_MXFP4:
             GGML_ASSERT(offset == 0);
-            GGML_ASSERT(size == ggml_nbytes(tensor));
+            GGML_ASSERT(offset + size <= ggml_nbytes(tensor));
             repack_mxfp4x4x2_mxfp4(data, tensor, size);
             break;
 

From d2a2673dd1c86a01ab010e18b13b8bb959968c48 Mon Sep 17 00:00:00 2001
From: Ruben Ortlam <picard12@live.de>
Date: Fri, 31 Oct 2025 08:14:49 +0100
Subject: [PATCH 030/185] vulkan: fix shmem overrun in mmq id shader (#16873)

* vulkan: fix shmem overrun in mmq id shader

* metal : fix mul_mm_id

---------

Co-authored-by: Georgi Gerganov <ggerganov@gmail.com>
---
 ggml/src/ggml-metal/ggml-metal-device.cpp                    | 2 +-
 ggml/src/ggml-vulkan/vulkan-shaders/mul_mmq.comp             | 4 ++++
 ggml/src/ggml-vulkan/vulkan-shaders/mul_mmq_shmem_types.glsl | 2 +-
 tests/test-backend-ops.cpp                                   | 3 +++
 4 files changed, 9 insertions(+), 2 deletions(-)

diff --git a/ggml/src/ggml-metal/ggml-metal-device.cpp b/ggml/src/ggml-metal/ggml-metal-device.cpp
index 1a3c7873b74..5607deaf414 100644
--- a/ggml/src/ggml-metal/ggml-metal-device.cpp
+++ b/ggml/src/ggml-metal/ggml-metal-device.cpp
@@ -677,7 +677,7 @@ ggml_metal_pipeline_t ggml_metal_library_get_pipeline_mul_mm_id_map0(ggml_metal_
     char name[256];
 
     snprintf(base, 256, "kernel_mul_mm_id_map0_ne20_%d", ne20);
-    snprintf(name, 256, "%s", base);
+    snprintf(name, 256, "%s_ne02=%d", base, ne02);
 
     ggml_metal_pipeline_t res = ggml_metal_library_get_pipeline(lib, name);
     if (res) {
diff --git a/ggml/src/ggml-vulkan/vulkan-shaders/mul_mmq.comp b/ggml/src/ggml-vulkan/vulkan-shaders/mul_mmq.comp
index 8b238ac4bc1..d955b4fc7af 100644
--- a/ggml/src/ggml-vulkan/vulkan-shaders/mul_mmq.comp
+++ b/ggml/src/ggml-vulkan/vulkan-shaders/mul_mmq.comp
@@ -82,9 +82,13 @@ layout (constant_id = 10) const uint WARP = 32;
 
 #include "mul_mmq_shmem_types.glsl"
 
+#ifdef MUL_MAT_ID
+#define BK_STEP 1
+#else
 #ifndef BK_STEP
 #define BK_STEP 4
 #endif
+#endif
 
 // Shared memory cache
 shared block_a_cache buf_a[BM * BK_STEP];
diff --git a/ggml/src/ggml-vulkan/vulkan-shaders/mul_mmq_shmem_types.glsl b/ggml/src/ggml-vulkan/vulkan-shaders/mul_mmq_shmem_types.glsl
index 72fec440490..1c0f5306f38 100644
--- a/ggml/src/ggml-vulkan/vulkan-shaders/mul_mmq_shmem_types.glsl
+++ b/ggml/src/ggml-vulkan/vulkan-shaders/mul_mmq_shmem_types.glsl
@@ -27,7 +27,7 @@ struct block_a_cache {
 #elif defined(DATA_A_Q8_0)
 #define QUANT_R_MMQ 1
 // AMD likes 4, Intel likes 1 and Nvidia likes 2
-#define BK_STEP 1
+// #define BK_STEP 1
 struct block_a_cache {
     int32_t qs[32/4];
     FLOAT_TYPE dm;
diff --git a/tests/test-backend-ops.cpp b/tests/test-backend-ops.cpp
index 92361d6f0f4..fa12c06ccdd 100644
--- a/tests/test-backend-ops.cpp
+++ b/tests/test-backend-ops.cpp
@@ -6880,6 +6880,9 @@ static std::vector<std::unique_ptr<test_case>> make_test_cases_eval() {
     test_cases.emplace_back(new test_mul_mat_id(GGML_TYPE_F16, GGML_TYPE_F32, 1, 1, false, 8, 16, 1));
     test_cases.emplace_back(new test_mul_mat_id(GGML_TYPE_F16, GGML_TYPE_F32, 16, 16, false, 32, 32, 32, 3));
 
+    // gpt-oss issue with Vulkan mmq_id
+    test_cases.emplace_back(new test_mul_mat_id(GGML_TYPE_MXFP4, GGML_TYPE_F32, 32, 2, false, 2880, 32, 2880));
+
     for (ggml_type type_a : base_types) {
         for (ggml_type type_b : {GGML_TYPE_F32 /*, GGML_TYPE_F16 */}) {
             for (int n_mats : {4, 8}) {

From 2976b0374d36609b0429dd6ce48807e2ad39a7c2 Mon Sep 17 00:00:00 2001
From: Masato Nakasaka <masato.nakasaka@intel.com>
Date: Fri, 31 Oct 2025 16:18:59 +0900
Subject: [PATCH 031/185] vulkan: Fix crash when FP16 mul_mat accumulation is
 not supported (#16796)

* Experimenting crash fix

* added assert for aborting and fixed comment

* changed to check if a pipeline is empty or not

* Moved function in class definition

* replaced with is_empty

* Modified is_empty to check only unaligned pipelines
---
 ggml/src/ggml-vulkan/ggml-vulkan.cpp | 20 +++++++++++++-------
 1 file changed, 13 insertions(+), 7 deletions(-)

diff --git a/ggml/src/ggml-vulkan/ggml-vulkan.cpp b/ggml/src/ggml-vulkan/ggml-vulkan.cpp
index b61879aa5d3..c3e5a9eccc3 100644
--- a/ggml/src/ggml-vulkan/ggml-vulkan.cpp
+++ b/ggml/src/ggml-vulkan/ggml-vulkan.cpp
@@ -145,8 +145,13 @@ static void ggml_vk_destroy_pipeline(vk::Device& device, vk_pipeline& pipeline);
 struct vk_matmul_pipeline_struct {
     vk_pipeline l, m, s;
     vk_pipeline a_l, a_m, a_s;
+    // Returns true when all unaligned pipelines are null.
+    // We only check for unaligned variants since one of the unaligned pipelines must exist
+    // while aligned pipelines are optional
+    bool is_empty() const {
+        return l == nullptr && m == nullptr && s == nullptr;
+    }
 };
-
 typedef std::shared_ptr<vk_matmul_pipeline_struct> vk_matmul_pipeline;
 
 struct vk_matmul_pipeline2 {
@@ -5079,7 +5084,7 @@ static vk_matmul_pipeline ggml_vk_get_mul_mat_mat_pipeline(ggml_backend_vk_conte
     if (src1_type == GGML_TYPE_Q8_1) {
         vk_matmul_pipeline pipelines = ctx->device->pipeline_dequant_mul_mat_mat_q8_1[src0_type].f32acc;
 
-        if (pipelines->s == nullptr && pipelines->m == nullptr && pipelines->l == nullptr) {
+        if (pipelines->is_empty()) {
             return nullptr;
         }
 
@@ -5228,7 +5233,7 @@ static vk_matmul_pipeline ggml_vk_get_mul_mat_mat_id_pipeline(ggml_backend_vk_co
     if (src1_type == GGML_TYPE_Q8_1) {
         vk_matmul_pipeline pipelines = ctx->device->pipeline_dequant_mul_mat_mat_id_q8_1[src0_type].f32acc;
 
-        if (pipelines->s == nullptr && pipelines->m == nullptr && pipelines->l == nullptr) {
+        if (pipelines->is_empty()) {
             return nullptr;
         }
 
@@ -5263,16 +5268,17 @@ static vk_matmul_pipeline ggml_vk_get_mul_mat_mat_id_pipeline(ggml_backend_vk_co
             return nullptr;
     }
 
+    vk_matmul_pipeline2& mmp = ctx->device->pipeline_dequant_mul_mat_mat_id[src0_type];
     // XXX TODO 'prec' is not actually allowed in mul_mat_id.
     bool prefer_fp16acc = ctx->device->fp16 /*&& prec == GGML_PREC_DEFAULT*/;
-    bool support_fp16acc = ctx->device->pipeline_dequant_mul_mat_mat_id[src0_type].f16acc != nullptr;
-    bool support_fp32acc = ctx->device->pipeline_dequant_mul_mat_mat_id[src0_type].f32acc != nullptr;
+    bool support_fp16acc = !mmp.f16acc->is_empty();
+    bool support_fp32acc = !mmp.f32acc->is_empty();
 
     if (support_fp16acc && (prefer_fp16acc || !support_fp32acc)) {
-        return ctx->device->pipeline_dequant_mul_mat_mat_id[src0_type].f16acc;
+        return mmp.f16acc;
     } else {
         GGML_ASSERT(support_fp32acc);
-        return ctx->device->pipeline_dequant_mul_mat_mat_id[src0_type].f32acc;
+        return mmp.f32acc;
     }
 }
 

From d2d931f173b8a736b08999436e9259aafddec718 Mon Sep 17 00:00:00 2001
From: Jeff Bolz <jbolz@nvidia.com>
Date: Fri, 31 Oct 2025 02:34:47 -0500
Subject: [PATCH 032/185] vulkan: disable spirv-opt for rope shaders (#16872)

---
 ggml/src/ggml-vulkan/vulkan-shaders/vulkan-shaders-gen.cpp | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/ggml/src/ggml-vulkan/vulkan-shaders/vulkan-shaders-gen.cpp b/ggml/src/ggml-vulkan/vulkan-shaders/vulkan-shaders-gen.cpp
index e6ec589fb84..bd178875d55 100644
--- a/ggml/src/ggml-vulkan/vulkan-shaders/vulkan-shaders-gen.cpp
+++ b/ggml/src/ggml-vulkan/vulkan-shaders/vulkan-shaders-gen.cpp
@@ -317,7 +317,8 @@ void string_to_spv_func(std::string name, std::string in_path, std::string out_p
 
     // disable spirv-opt for coopmat shaders for https://github.com/ggerganov/llama.cpp/issues/10734
     // disable spirv-opt for bf16 shaders for https://github.com/ggml-org/llama.cpp/issues/15344
-    std::string opt_level = (coopmat || name.find("bf16") != std::string::npos) ? "" : "-O";
+    // disable spirv-opt for rope shaders for https://github.com/ggml-org/llama.cpp/issues/16860
+    std::string opt_level = (coopmat || name.find("bf16") != std::string::npos || name.find("rope") != std::string::npos) ? "" : "-O";
 
     #ifdef _WIN32
         std::vector<std::string> cmd = {GLSLC, "-fshader-stage=compute", target_env, opt_level, "\"" + in_path + "\"", "-o", "\"" + out_path + "\""};

From 0f715b4e759acceccb9f437cfd2a988fff85514a Mon Sep 17 00:00:00 2001
From: Daniel Bevenius <daniel.bevenius@gmail.com>
Date: Fri, 31 Oct 2025 09:51:26 +0100
Subject: [PATCH 033/185] server : fix typos in server.cpp comments [no ci]
 (#16883)

---
 tools/server/server.cpp | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/tools/server/server.cpp b/tools/server/server.cpp
index d56468595dd..cb49254a1cc 100644
--- a/tools/server/server.cpp
+++ b/tools/server/server.cpp
@@ -3608,7 +3608,7 @@ struct server_context {
                 slot.task->params.sampling.preserved_tokens.find(token) != slot.task->params.sampling.preserved_tokens.end();
         };
 
-        // frist, add sampled tokens from any ongoing sequences
+        // first, add sampled tokens from any ongoing sequences
         for (auto & slot : slots) {
             if (slot.state != SLOT_STATE_GENERATING) {
                 continue;
@@ -3950,7 +3950,7 @@ struct server_context {
                     // If using an alora, there may be uncached tokens that come
                     // before the invocation sequence. When this happens, the
                     // tokens before the invocation sequence need to be
-                    // processed without the adpter in a separate batch, then
+                    // processed without the adapter in a separate batch, then
                     // the adapter needs to be enabled for the remaining tokens.
                     if (lora_all_alora(slot.lora) && slot.alora_invocation_start - 1 > slot.prompt.n_tokens()) {
                         SLT_DBG(slot, "processing pre-alora tokens without the adapter (n_tokens = %d, alora_invocation_start = %d)\n", slot.prompt.n_tokens(), slot.alora_invocation_start);

From c22473b580807929fd9e3a3344a48e8cfbe6c88f Mon Sep 17 00:00:00 2001
From: Georgi Gerganov <ggerganov@gmail.com>
Date: Fri, 31 Oct 2025 10:54:19 +0200
Subject: [PATCH 034/185] server : don't print user inputs to console (#16871)

---
 tools/server/server.cpp | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/tools/server/server.cpp b/tools/server/server.cpp
index cb49254a1cc..92d30664e41 100644
--- a/tools/server/server.cpp
+++ b/tools/server/server.cpp
@@ -3796,7 +3796,7 @@ struct server_context {
 
                                 // when the prompt prefix does not match, print the tokens around the mismatch
                                 // this is useful for debugging prompt caching
-                                {
+                                if (slots_debug) {
                                     const int np0 = std::max<int>(n_past - 4, 0);
                                     const int np1 = std::min<int>(n_past + 6, std::min(slot.prompt.tokens.size(), slot.task->tokens.size()));
 

From 8da3c0e200a586f768ada6f38745acb01380174c Mon Sep 17 00:00:00 2001
From: Georgi Gerganov <ggerganov@gmail.com>
Date: Fri, 31 Oct 2025 13:50:33 +0200
Subject: [PATCH 035/185] batch : fix consistency checks for the input
 positions (#16890)

---
 src/llama-batch.cpp | 30 ++++++++++++++++++++++--------
 1 file changed, 22 insertions(+), 8 deletions(-)

diff --git a/src/llama-batch.cpp b/src/llama-batch.cpp
index 0d4939fdb01..86a1a4ba187 100644
--- a/src/llama-batch.cpp
+++ b/src/llama-batch.cpp
@@ -261,15 +261,29 @@ bool llama_batch_allocr::init(
 
             const llama_pos p0 = memory ? memory->seq_pos_max(s) : -1;
 
-            if (p0 >= 0 && p0 >= seq_pos_min(s)) {
-                LLAMA_LOG_ERROR(
-                        "%s: the tokens of sequence %d in the input batch have inconsistent sequence positions:\n"
-                        " - the last position stored in the memory module of the context (i.e. the KV cache) for sequence %d is X = %d\n"
-                        " - the tokens for sequence %d in the input batch have a starting position of Y = %d\n"
-                        " for M-RoPE, it is required that the position satisfies: X < Y\n",
-                        __func__, s, s, p0, s, seq_pos_min(s));
+            if (batch.token) {
+                if (p0 >= 0 && p0 >= seq_pos_min(s)) {
+                    LLAMA_LOG_ERROR(
+                            "%s: the tokens of sequence %d in the input batch have inconsistent sequence positions:\n"
+                            " - the last position stored in the memory module of the context (i.e. the KV cache) for sequence %d is X = %d\n"
+                            " - the tokens for sequence %d in the input batch have a starting position of Y = %d\n"
+                            " for M-RoPE, it is required that the position satisfies: X < Y\n",
+                            __func__, s, s, p0, s, seq_pos_min(s));
 
-                return false;
+                    return false;
+                }
+            } else {
+                // embedding inputs can have overlapping positions
+                if (p0 >= 0 && p0 > seq_pos_min(s)) {
+                    LLAMA_LOG_ERROR(
+                            "%s: the tokens of sequence %d in the input batch have inconsistent sequence positions:\n"
+                            " - the last position stored in the memory module of the context (i.e. the KV cache) for sequence %d is X = %d\n"
+                            " - the tokens for sequence %d in the input batch have a starting position of Y = %d\n"
+                            " for M-RoPE, it is required that the position satisfies: X <= Y\n",
+                            __func__, s, s, p0, s, seq_pos_min(s));
+
+                    return false;
+                }
             }
         }
     } else {

From 4146d6a1a6228711a487a1e3e9ddd120f8d027d7 Mon Sep 17 00:00:00 2001
From: Aman Gupta <amangupta052@gmail.com>
Date: Fri, 31 Oct 2025 20:05:07 +0800
Subject: [PATCH 036/185] CUDA: add expert reduce kernel (#16857)
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

* CUDA: add expert reduce kernel

* contigous checks, better formatting, use std::vector instead of array

* use vector empty instead of size

Co-authored-by: Johannes Gäßler <johannesg@5d6.de>

---------

Co-authored-by: Johannes Gäßler <johannesg@5d6.de>
---
 ggml/src/ggml-cuda/ggml-cuda.cu          |  26 ++++
 ggml/src/ggml-cuda/moe-expert-reduce.cu  | 168 +++++++++++++++++++++++
 ggml/src/ggml-cuda/moe-expert-reduce.cuh |  11 ++
 tests/test-backend-ops.cpp               |  58 ++++++++
 4 files changed, 263 insertions(+)
 create mode 100644 ggml/src/ggml-cuda/moe-expert-reduce.cu
 create mode 100644 ggml/src/ggml-cuda/moe-expert-reduce.cuh

diff --git a/ggml/src/ggml-cuda/ggml-cuda.cu b/ggml/src/ggml-cuda/ggml-cuda.cu
index fcff5d7cdc1..61a8f1df87d 100644
--- a/ggml/src/ggml-cuda/ggml-cuda.cu
+++ b/ggml/src/ggml-cuda/ggml-cuda.cu
@@ -27,6 +27,7 @@
 #include "ggml-cuda/mmq.cuh"
 #include "ggml-cuda/mmvf.cuh"
 #include "ggml-cuda/mmvq.cuh"
+#include "ggml-cuda/moe-expert-reduce.cuh"
 #include "ggml-cuda/norm.cuh"
 #include "ggml-cuda/opt-step-adamw.cuh"
 #include "ggml-cuda/opt-step-sgd.cuh"
@@ -3169,6 +3170,31 @@ static void evaluate_and_capture_cuda_graph(ggml_backend_cuda_context * cuda_ctx
                         continue;
                     }
 
+                    if (node->op == GGML_OP_MUL) {
+                        int current_node = i + 1;
+                        int num_views    = 0;
+                        int num_adds     = 0;
+                        while (current_node < cgraph->n_nodes && cgraph->nodes[current_node]->op == GGML_OP_VIEW) {
+                            num_views++;
+                            current_node++;
+                        }
+
+                        while (current_node < cgraph->n_nodes && cgraph->nodes[current_node]->op == GGML_OP_ADD &&
+                                num_adds < num_views - 1) {
+                            num_adds++;
+                            current_node++;
+                        }
+
+                        if (num_adds == num_views - 1 && num_views > 0) {
+                            ggml_tensor * dst_node = cgraph->nodes[current_node - 1];
+                            if (ggml_cuda_should_use_moe_expert_reduce(cgraph, i, current_node)) {
+                                ggml_cuda_op_moe_expert_reduce(*cuda_ctx, node->src[0], node->src[1], dst_node);
+                                i += num_views + num_adds;
+                                continue;
+                            }
+                        }
+                    }
+
                     if (node->op == GGML_OP_ADD) {
                         int n_fuse = 0;
                         ggml_op ops[8];
diff --git a/ggml/src/ggml-cuda/moe-expert-reduce.cu b/ggml/src/ggml-cuda/moe-expert-reduce.cu
new file mode 100644
index 00000000000..a97c5d573bb
--- /dev/null
+++ b/ggml/src/ggml-cuda/moe-expert-reduce.cu
@@ -0,0 +1,168 @@
+#include "moe-expert-reduce.cuh"
+
+// This kernel is a fusion of the expert weight reduce, common in MoE models
+
+template <int n_expert_used_template>
+__global__ void moe_expert_reduce_cuda(const float * __restrict__ experts,
+                                       const float * __restrict__ weights,
+                                       float * __restrict__ dst,
+                                       const int n_expert_used,
+                                       const int n_cols) {
+    const int row = blockIdx.x;
+    const int col = blockIdx.y * blockDim.x + threadIdx.x;
+    if (col >= n_cols) {
+        return;
+    }
+
+    experts += row * n_cols * n_expert_used;
+    weights += row * n_expert_used;
+    dst += row * n_cols;
+
+    float acc = 0.f;
+    if constexpr (n_expert_used_template == 0) {
+        for (int expert = 0; expert < n_expert_used; ++expert) {
+            ggml_cuda_mad(acc, experts[col], weights[expert]);
+            experts += n_cols;
+        }
+        dst[col] = acc;
+    } else {
+#pragma unroll
+        for (int i = 0; i < n_expert_used_template; ++i) {
+            ggml_cuda_mad(acc, experts[col], weights[i]);
+            experts += n_cols;
+        }
+        dst[col] = acc;
+    }
+}
+
+static void launch_moe_expert_reduce(ggml_backend_cuda_context & ctx,
+                                     const float *               experts,
+                                     const float *               weights,
+                                     float *                     dst,
+                                     const int                   n_expert_used,
+                                     const int                   n_cols,
+                                     const int                   n_rows) {
+    const int block_size = 32;
+
+    const int n_blocks_x = n_rows;
+    const int n_blocks_y = (n_cols + block_size - 1) / block_size;
+
+    dim3 block_dims(block_size);
+    dim3 grid_dims(n_blocks_x, n_blocks_y);
+
+    cudaStream_t stream = ctx.stream();
+    switch (n_expert_used) {
+        case 1:
+            moe_expert_reduce_cuda<1>
+                <<<grid_dims, block_dims, 0, stream>>>(experts, weights, dst, n_expert_used, n_cols);
+            break;
+        case 2:
+            moe_expert_reduce_cuda<2>
+                <<<grid_dims, block_dims, 0, stream>>>(experts, weights, dst, n_expert_used, n_cols);
+            break;
+        case 4:
+            moe_expert_reduce_cuda<4>
+                <<<grid_dims, block_dims, 0, stream>>>(experts, weights, dst, n_expert_used, n_cols);
+            break;
+        case 6:
+            moe_expert_reduce_cuda<6>
+                <<<grid_dims, block_dims, 0, stream>>>(experts, weights, dst, n_expert_used, n_cols);
+            break;
+        case 8:
+            moe_expert_reduce_cuda<8>
+                <<<grid_dims, block_dims, 0, stream>>>(experts, weights, dst, n_expert_used, n_cols);
+            break;
+        case 16:
+            moe_expert_reduce_cuda<16>
+                <<<grid_dims, block_dims, 0, stream>>>(experts, weights, dst, n_expert_used, n_cols);
+            break;
+        case 32:
+            moe_expert_reduce_cuda<32>
+                <<<grid_dims, block_dims, 0, stream>>>(experts, weights, dst, n_expert_used, n_cols);
+            break;
+        case 64:
+            moe_expert_reduce_cuda<64>
+                <<<grid_dims, block_dims, 0, stream>>>(experts, weights, dst, n_expert_used, n_cols);
+            break;
+        case 128:
+            moe_expert_reduce_cuda<128>
+                <<<grid_dims, block_dims, 0, stream>>>(experts, weights, dst, n_expert_used, n_cols);
+            break;
+        default:
+            moe_expert_reduce_cuda<0>
+                <<<grid_dims, block_dims, 0, stream>>>(experts, weights, dst, n_expert_used, n_cols);
+            break;
+    }
+}
+
+bool ggml_cuda_should_use_moe_expert_reduce(const ggml_cgraph * cgraph, int start_index, int end_index) {
+    const ggml_tensor * mul = cgraph->nodes[start_index];
+
+    if (mul->op != GGML_OP_MUL || !ggml_is_contiguous(mul->src[0]) || !ggml_is_contiguous(mul->src[1])) {
+        return false;
+    }
+
+    int    current_node   = start_index + 1;
+    size_t current_offset = 0;
+
+    std::vector<const ggml_tensor *> view_nodes;
+    //check if all are views of the expert in increasing order
+    while (current_node < end_index && cgraph->nodes[current_node]->op == GGML_OP_VIEW) {
+        const ggml_tensor * node = cgraph->nodes[current_node];
+        if (node->view_src != mul) {
+            return false;
+        }
+        if (node->view_offs < current_offset) {
+            return false;
+        }
+        current_offset = node->view_offs;
+        current_node++;
+        view_nodes.push_back(node);
+    }
+
+    //check if all the adds are in increasing order
+    const ggml_tensor * prev_add_src = view_nodes.empty() ? nullptr : view_nodes[0];
+    int                 num_adds     = 0;
+    int                 num_views    = view_nodes.size();
+    while (current_node < end_index && cgraph->nodes[current_node]->op == GGML_OP_ADD) {
+        const ggml_tensor * add_node = cgraph->nodes[current_node];
+
+        bool is_first_op_ok  = num_views > num_adds ? add_node->src[0] == prev_add_src : false;
+        bool is_second_op_ok = num_views > num_adds ? add_node->src[1] == view_nodes[num_adds + 1] : false;
+
+        if (!is_first_op_ok || !is_second_op_ok) {
+            return false;
+        }
+        prev_add_src = add_node;
+
+        num_adds++;
+        current_node++;
+    }
+
+    if (num_views != num_adds + 1) {
+        return false;
+    }
+
+    return true;
+}
+
+void ggml_cuda_op_moe_expert_reduce(ggml_backend_cuda_context & ctx,
+                                    const ggml_tensor *         experts,
+                                    const ggml_tensor *         weights,
+                                    ggml_tensor *               dst) {
+    const int n_rows        = experts->ne[2];
+    const int n_expert_used = experts->ne[1];
+    const int n_cols        = experts->ne[0];
+
+    GGML_ASSERT(experts->type == GGML_TYPE_F32);
+    GGML_ASSERT(weights->type == GGML_TYPE_F32);
+    GGML_ASSERT(ggml_is_contiguous(experts));
+    GGML_ASSERT(ggml_is_contiguous(weights));
+    GGML_ASSERT(dst->type == GGML_TYPE_F32);
+
+    const float * experts_d = (const float *) experts->data;
+    const float * weights_d = (const float *) weights->data;
+    float *       dst_d     = (float *) dst->data;
+
+    launch_moe_expert_reduce(ctx, experts_d, weights_d, dst_d, n_expert_used, n_cols, n_rows);
+}
diff --git a/ggml/src/ggml-cuda/moe-expert-reduce.cuh b/ggml/src/ggml-cuda/moe-expert-reduce.cuh
new file mode 100644
index 00000000000..cafc50e104a
--- /dev/null
+++ b/ggml/src/ggml-cuda/moe-expert-reduce.cuh
@@ -0,0 +1,11 @@
+#include "common.cuh"
+#include "ggml.h"
+
+#include <initializer_list>
+
+void ggml_cuda_op_moe_expert_reduce(ggml_backend_cuda_context & ctx,
+                                    const ggml_tensor *         experts,
+                                    const ggml_tensor *         weights,
+                                    ggml_tensor *               dst);
+
+bool ggml_cuda_should_use_moe_expert_reduce(const ggml_cgraph * cgraph, int start_index, int end_index);
diff --git a/tests/test-backend-ops.cpp b/tests/test-backend-ops.cpp
index fa12c06ccdd..04fa1b62d3b 100644
--- a/tests/test-backend-ops.cpp
+++ b/tests/test-backend-ops.cpp
@@ -4807,6 +4807,60 @@ struct test_topk_moe: public test_case {
     }
 };
 
+struct test_moe_expert_reduce : public test_case {
+    const int64_t n_embd;
+    const int64_t n_tokens;
+    const int64_t n_expert_used;
+
+    test_moe_expert_reduce(int64_t n_embd = 64, int64_t n_tokens = 5, int64_t n_expert_used = 4)
+        : n_embd(n_embd), n_tokens(n_tokens), n_expert_used(n_expert_used) {
+        GGML_ASSERT(n_expert_used > 1);
+    }
+
+    std::string vars() override {
+        return VARS_TO_STR3(n_embd, n_tokens, n_expert_used);
+    }
+
+    std::string op_desc(ggml_tensor * t) override {
+        GGML_UNUSED(t);
+        return "MOE_EXPERT_REDUCE";
+    }
+
+    bool run_whole_graph() override { return true; }
+
+    ggml_tensor * build_graph(ggml_context * ctx) override {
+        ggml_tensor * experts = ggml_new_tensor_3d(ctx, GGML_TYPE_F32, n_embd, n_expert_used, n_tokens);
+        ggml_set_name(experts, "experts");
+
+        ggml_tensor * weights = ggml_new_tensor_3d(ctx, GGML_TYPE_F32, 1, n_expert_used, n_tokens);
+        ggml_set_name(weights, "weights");
+
+        ggml_tensor * weighted = ggml_mul(ctx, experts, weights);
+        ggml_set_name(weighted, "weighted_experts");
+
+        std::vector<ggml_tensor *> expert_views(n_expert_used);
+        for (int64_t i = 0; i < n_expert_used; ++i) {
+            expert_views[i] = ggml_view_2d(ctx, weighted, n_embd, n_tokens, weighted->nb[2], i * weighted->nb[1]);
+
+            std::string name = "expert_view_" + std::to_string(i);
+            ggml_set_name(expert_views[i], name.c_str());
+            ggml_build_forward_expand(gf, expert_views[i]);
+        }
+
+        ggml_tensor * moe_out = expert_views[0];
+        for (int64_t i = 1; i < n_expert_used; ++i) {
+            moe_out = ggml_add(ctx, moe_out, expert_views[i]);
+
+            std::string name = "expert_add_" + std::to_string(i - 1);
+            ggml_set_name(moe_out, name.c_str());
+        }
+
+        ggml_set_name(moe_out, "moe_out");
+
+        return moe_out;
+    }
+};
+
 struct test_mul_mat_vec_fusion : public test_case {
     const ggml_type type;
     const ggml_glu_op glu_op;
@@ -7260,6 +7314,10 @@ static std::vector<std::unique_ptr<test_case>> make_test_cases_eval() {
     test_cases.emplace_back(new test_topk_moe({ 8, 22, 1, 1 }, 4, /*with_norm*/ false, /*delayed_softmax*/ true));
     test_cases.emplace_back(new test_topk_moe({ 32, 22, 1, 1 }, 8, /*with_norm*/ false, /*delayed_softmax*/ true));
 
+    test_cases.emplace_back(new test_moe_expert_reduce(1024, 5, 4));
+    test_cases.emplace_back(new test_moe_expert_reduce(80, 3, 6));
+    test_cases.emplace_back(new test_moe_expert_reduce(80, 3, 7));
+
 #if 0
     // these tests are disabled to save execution time, sbut they can be handy for debugging
     test_cases.emplace_back(new test_llama(2, true));

From 6d39015a744b47bb7643ea73f412e6d64677f305 Mon Sep 17 00:00:00 2001
From: Georgi Gerganov <ggerganov@gmail.com>
Date: Fri, 31 Oct 2025 16:25:50 +0200
Subject: [PATCH 037/185] sync : ggml

---
 scripts/sync-ggml.last | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/scripts/sync-ggml.last b/scripts/sync-ggml.last
index 5e09de499e8..64a544d9110 100644
--- a/scripts/sync-ggml.last
+++ b/scripts/sync-ggml.last
@@ -1 +1 @@
-72632094336524a9c809e129e8b1c52154543a5a
+e02fb860ccbba8967905bceff23b677e88105280

From 31c511a968348281e11d590446bb815048a1e912 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Johannes=20G=C3=A4=C3=9Fler?= <johannesg@5d6.de>
Date: Fri, 31 Oct 2025 15:57:19 +0100
Subject: [PATCH 038/185] CUDA: Volta tensor core support for MMF (#16843)

* CUDA: Volta tensor core support for MMF

* more generic checks for hardware support

* Update ggml/src/ggml-cuda/mmf.cuh

Co-authored-by: Aman Gupta <amangupta052@gmail.com>

---------

Co-authored-by: Aman Gupta <amangupta052@gmail.com>
---
 ggml/src/ggml-cuda/common.cuh |  10 +-
 ggml/src/ggml-cuda/mma.cuh    | 237 ++++++++++++++++++++++++++++++----
 ggml/src/ggml-cuda/mmf.cu     |   2 +-
 ggml/src/ggml-cuda/mmf.cuh    |  41 ++++--
 4 files changed, 254 insertions(+), 36 deletions(-)

diff --git a/ggml/src/ggml-cuda/common.cuh b/ggml/src/ggml-cuda/common.cuh
index 6a472be7fbb..ca876459d40 100644
--- a/ggml/src/ggml-cuda/common.cuh
+++ b/ggml/src/ggml-cuda/common.cuh
@@ -224,6 +224,11 @@ static const char * cu_get_error_str(CUresult err) {
 #define AMD_MFMA_AVAILABLE
 #endif // defined(GGML_USE_HIP) && defined(CDNA) && !defined(GGML_HIP_NO_MMQ_MFMA)
 
+// The Volta instructions are in principle available on Turing or newer but they are effectively unusable:
+#if !defined(GGML_USE_HIP) && __CUDA_ARCH__ == GGML_CUDA_CC_VOLTA
+#define VOLTA_MMA_AVAILABLE
+#endif // !defined(GGML_USE_HIP) && __CUDA_ARCH__ == GGML_CUDA_CC_VOLTA
+
 #if !defined(GGML_USE_HIP) && __CUDA_ARCH__ >= GGML_CUDA_CC_TURING
 #define TURING_MMA_AVAILABLE
 #endif // !defined(GGML_USE_HIP) && __CUDA_ARCH__ >= GGML_CUDA_CC_TURING
@@ -278,7 +283,10 @@ static bool amd_mfma_available(const int cc) {
 #endif //!defined(GGML_HIP_NO_MMQ_MFMA)
 }
 
-// Volta technically had FP16 tensor cores but they work very differently compared to Turing and later.
+static bool volta_mma_available(const int cc) {
+    return GGML_CUDA_CC_IS_NVIDIA(cc) && ggml_cuda_highest_compiled_arch(cc) == GGML_CUDA_CC_VOLTA;
+}
+
 static bool turing_mma_available(const int cc) {
     return GGML_CUDA_CC_IS_NVIDIA(cc) && ggml_cuda_highest_compiled_arch(cc) >= GGML_CUDA_CC_TURING;
 }
diff --git a/ggml/src/ggml-cuda/mma.cuh b/ggml/src/ggml-cuda/mma.cuh
index c1f24243fe3..a7a28fd1ae6 100644
--- a/ggml/src/ggml-cuda/mma.cuh
+++ b/ggml/src/ggml-cuda/mma.cuh
@@ -18,6 +18,10 @@
 
 #include "common.cuh"
 
+// On Volta each warp is doing 4 8x8 mma operations in parallel.
+// The basic memory layout for a 32x8 output tile is to stack 4 input tiles in I direction and to mirror the B tile.
+// However, the i indices in this file are by default permuted to simplify the index calculations.
+// #define GGML_CUDA_MMA_NO_VOLTA_PERM
 
 #if CUDART_VERSION >= 11080
 
@@ -73,6 +77,15 @@ namespace ggml_cuda_mma {
         static constexpr int ne = I * J / 64;
         T x[ne] = {0};
 
+        static constexpr __device__ bool supported() {
+            if (I == 64 && J ==  2) return true;
+            if (I == 16 && J ==  8) return true;
+            if (I == 32 && J ==  4) return true;
+            if (I == 16 && J == 16) return true;
+            if (I == 32 && J == 32) return true;
+            return false;
+        }
+
         static __device__ __forceinline__ int get_i(const int l) {
             if constexpr (I == 64 && J == 2) { // Special tile size to load <16, 4> as <16, 8>
                 return threadIdx.x % 16;
@@ -85,7 +98,8 @@ namespace ggml_cuda_mma {
             } else if constexpr (I == 32 && J == 32) {
                 return 4 * (threadIdx.x / 32) + 8 * (l / 4) + (l % 4);
             } else {
-                static_assert(I == -1 && J == -1, "template specialization not implemented");
+                NO_DEVICE_CODE;
+                return -1;
             }
         }
 
@@ -101,22 +115,67 @@ namespace ggml_cuda_mma {
             } else if constexpr (I == 32 && J == 32) {
                 return threadIdx.x % 32;
             } else {
-                static_assert(I == -1 && J == -1, "template specialization not implemented");
+                NO_DEVICE_CODE;
+                return -1;
+            }
+        }
+#elif __CUDA_ARCH__ == GGML_CUDA_CC_VOLTA
+        static constexpr int ne = I * J / 32;
+        T x[ne] = {0};
+
+        static constexpr __device__ bool supported() {
+            if (I == 32 && J ==  8) return true;
+            return false;
+        }
+
+        static __device__ __forceinline__ int get_i(const int l) {
+            if constexpr (I == 32 && J == 8) {
+#ifdef GGML_CUDA_MMA_NO_VOLTA_PERM
+                return (((threadIdx.x % 16) / 4) * 8) | ((threadIdx.x / 16) * 4) | (l & 2) | (threadIdx.x % 2);
+#else
+                return (l & 2) | (threadIdx.x & ~2);
+#endif // GGML_CUDA_MMA_NO_VOLTA_PERM
+            } else {
+                NO_DEVICE_CODE;
+                return -1;
+            }
+        }
+
+        static __device__ __forceinline__ int get_j(const int l) {
+            if constexpr (I == 32 && J == 8) {
+                return (threadIdx.x & 2) | (l & (4 + 1));
+            } else {
+                NO_DEVICE_CODE;
+                return -1;
             }
         }
 #else
         static constexpr int ne = I * J / 32;
         T x[ne] = {0};
 
+        static constexpr __device__ bool supported() {
+            if (I ==  8 && J ==  4) return true;
+            if (I ==  8 && J ==  8) return true;
+            if (I == 16 && J ==  8) return true;
+            if (I == 16 && J == 16) return true;
+            if (I == 32 && J ==  8) return true;
+            return false;
+        }
+
         static __device__ __forceinline__ int get_i(const int l) {
-            if constexpr (I == 8 && (J == 4 || J == 8)) {
+            if constexpr (I == 8 && J == 4) {
+                return threadIdx.x / 4;
+            } else if constexpr (I == 8 && J == 8) {
                 return threadIdx.x / 4;
             } else if constexpr (I == 16 && J == 8) {
-                return (l / 2) * 8 + threadIdx.x / 4;
+                return ((l / 2) * 8) | (threadIdx.x / 4);
             } else if constexpr (I == 16 && J == 16) {
-                return ((l / 2) % 2) * 8 + threadIdx.x / 4;
+                return (((l / 2) % 2) * 8) | (threadIdx.x / 4);
+            } else if constexpr (I == 32 && J == 8) {
+                return tile<16, 8, T>::get_i(l); // Memory layout simply repeated with same pattern in i direction.
             } else {
-                static_assert(I == -1 && J == -1, "template specialization not implemented");
+                NO_DEVICE_CODE;
+                return -1;
             }
         }
 
@@ -124,13 +183,16 @@ namespace ggml_cuda_mma {
             if constexpr (I == 8 && J == 4) {
                 return threadIdx.x % 4;
             } else if constexpr (I == 8 && J == 8) {
-                return 4 * l + threadIdx.x % 4;
+                return (l * 4) | (threadIdx.x % 4);
             } else if constexpr (I == 16 && J == 8) {
-                return 2 * (threadIdx.x % 4) + l % 2;
+                return ((threadIdx.x % 4) * 2) | (l % 2);
             } else if constexpr (I == 16 && J == 16) {
-                return 8 * (l / 4) + 2 * (threadIdx.x % 4) + l % 2;
+                return ((l / 4) * 8) | ((threadIdx.x % 4) * 2) | (l % 2);
+            } else if constexpr (I == 32 && J == 8) {
+                return tile<16, 8, T>::get_j(l); // Memory layout simply repeated with same pattern in i direction.
             } else {
-                static_assert(I == -1 && J == -1, "template specialization not implemented");
+                NO_DEVICE_CODE;
+                return -1;
             }
         }
 #endif // defined(GGML_USE_HIP)
@@ -140,32 +202,83 @@ namespace ggml_cuda_mma {
     struct tile<I_, J_, half2> {
         static constexpr int I  = I_;
         static constexpr int J  = J_;
+
+#if __CUDA_ARCH__ == GGML_CUDA_CC_VOLTA
+        static constexpr int ne = I == 8 && J == 8 ? I * J / (WARP_SIZE/4) : I * J / WARP_SIZE;
+        half2 x[ne] = {{0.0f, 0.0f}};
+
+        static constexpr __device__ bool supported() {
+            if (I ==  8 && J ==  8) return true;
+            if (I == 32 && J ==  8) return true;
+            return false;
+        }
+
+        static __device__ __forceinline__ int get_i(const int l) {
+            if constexpr (I == 8 && J == 8) {
+                return ((threadIdx.x / 16) * 4) | (threadIdx.x % 4);
+            } else if constexpr (I == 32 && J == 8) {
+#ifdef GGML_CUDA_MMA_NO_VOLTA_PERM
+                return (((threadIdx.x % 16) / 4) * 8) | ((threadIdx.x / 16) * 4) | (threadIdx.x % 4);
+#else
+                return threadIdx.x;
+#endif // GGML_CUDA_MMA_NO_VOLTA_PERM
+            } else {
+                NO_DEVICE_CODE;
+                return -1;
+            }
+        }
+
+        static __device__ __forceinline__ int get_j(const int l) {
+            if constexpr ((I == 8 || I == 32) && J == 8) {
+                return l;
+            } else {
+                NO_DEVICE_CODE;
+                return -1;
+            }
+        }
+#else
         static constexpr int ne = I * J / WARP_SIZE;
         half2 x[ne] = {{0.0f, 0.0f}};
 
+        static constexpr __device__ bool supported() {
+            if (I ==  8 && J ==  4) return true;
+            if (I ==  8 && J ==  8) return true;
+            if (I == 16 && J ==  8) return true;
+            if (I == 16 && J == 16) return true;
+            if (I == 32 && J ==  8) return true;
+            return false;
+        }
+
         static __device__ __forceinline__ int get_i(const int l) {
             if constexpr (I == 8 && J == 8) {
                 return threadIdx.x / 4;
             } else if constexpr (I == 16 && J == 4) {
-                return l * 8 + threadIdx.x / 4;
+                return (l * 8) | (threadIdx.x / 4);
             } else if constexpr (I == 16 && J == 8) {
-                return (l % 2) * 8 + threadIdx.x / 4;
+                return ((l % 2) * 8) | (threadIdx.x / 4);
+            } else if constexpr (I == 32 && J == 8) {
+                return ((l / 4) * 16) | ((l % 2) * 8) | (threadIdx.x / 4);
             } else {
-                static_assert(I == -1 && J == -1, "template specialization not implemented");
+                NO_DEVICE_CODE;
+                return -1;
             }
         }
 
         static __device__ __forceinline__ int get_j(const int l) {
             if constexpr (I == 8 && J == 8) {
-                return l * 4 + threadIdx.x % 4;
+                return (l * 4) | (threadIdx.x % 4);
             } else if constexpr (I == 16 && J == 4) {
                 return threadIdx.x % 4;
             } else if constexpr (I == 16 && J == 8) {
-                return (l / 2) * 4 + threadIdx.x % 4;
+                return ((l / 2) * 4) | (threadIdx.x % 4);
+            } else if constexpr (I == 32 && J == 8) {
+                return ((l & 2) * 2) | (threadIdx.x % 4);
             } else {
-                static_assert(I == -1 && J == -1, "template specialization not implemented");
+                NO_DEVICE_CODE;
+                return -1;
             }
         }
+#endif // __CUDA_ARCH__ == GGML_CUDA_CC_VOLTA
     };
 
     template <int I_, int J_>
@@ -175,27 +288,36 @@ namespace ggml_cuda_mma {
         static constexpr int ne = I * J / WARP_SIZE;
         nv_bfloat162 x[ne] = {{0.0f, 0.0f}};
 
+        static constexpr __device__ bool supported() {
+            if (I ==  8 && J ==  8) return true;
+            if (I == 16 && J ==  4) return true;
+            if (I == 16 && J ==  8) return true;
+            return false;
+        }
+
         static __device__ __forceinline__ int get_i(const int l) {
             if constexpr (I == 8 && J == 8) {
                 return threadIdx.x / 4;
             } else if constexpr (I == 16 && J == 4) {
-                return l * 8 + threadIdx.x / 4;
+                return (l * 8) | (threadIdx.x / 4);
             } else if constexpr (I == 16 && J == 8) {
-                return (l % 2) * 8 + threadIdx.x / 4;
+                return ((l % 2) * 8) | (threadIdx.x / 4);
             } else {
-                static_assert(I == -1 && J == -1, "template specialization not implemented");
+                NO_DEVICE_CODE;
+                return -1;
             }
         }
 
         static __device__ __forceinline__ int get_j(const int l) {
             if constexpr (I == 8 && J == 8) {
-                return l * 4 + threadIdx.x % 4;
+                return (l * 4) | (threadIdx.x % 4);
             } else if constexpr (I == 16 && J == 4) {
                 return threadIdx.x % 4;
             } else if constexpr (I == 16 && J == 8) {
-                return (l / 2) * 4 + threadIdx.x % 4;
+                return ((l / 2) * 4) | (threadIdx.x % 4);
             } else {
-                static_assert(I == -1 && J == -1, "template specialization not implemented");
+                NO_DEVICE_CODE;
+                return -1;
             }
         }
     };
@@ -263,8 +385,12 @@ namespace ggml_cuda_mma {
             : "=r"(xi[0]), "=r"(xi[1])
             : "l"(xs));
 #else
-        load_generic(xs0, stride);
-        GGML_UNUSED(t);
+#if __CUDA_ARCH__ == GGML_CUDA_CC_VOLTA
+        GGML_UNUSED_VARS(t, xs0, stride);
+        NO_DEVICE_CODE;
+#else
+        load_generic(t, xs0, stride);
+#endif // __CUDA_ARCH__ == GGML_CUDA_CC_VOLTA
 #endif // TURING_MMA_AVAILABLE
     }
 
@@ -277,11 +403,35 @@ namespace ggml_cuda_mma {
         asm volatile("ldmatrix.sync.aligned.m8n8.x4.b16 {%0, %1, %2, %3}, [%4];"
             : "=r"(xi[0]), "=r"(xi[1]), "=r"(xi[2]), "=r"(xi[3])
             : "l"(xs));
+#else
+#if __CUDA_ARCH__ == GGML_CUDA_CC_VOLTA
+        GGML_UNUSED_VARS(t, xs0, stride);
+        NO_DEVICE_CODE;
 #else
         load_generic(t, xs0, stride);
+#endif // __CUDA_ARCH__ == GGML_CUDA_CC_VOLTA
 #endif // TURING_MMA_AVAILABLE
     }
 
+    template <typename T>
+    static __device__ __forceinline__ void load_ldmatrix(
+            tile<32, 8, T> & t, const T * __restrict__ xs0, const int stride) {
+#if __CUDA_ARCH__ == GGML_CUDA_CC_VOLTA
+#if 1
+        // TODO: more generic handling
+        static_assert(sizeof(T) == 4, "bad type size");
+        ggml_cuda_memcpy_1<4*sizeof(T)>(t.x + 0, xs0 + t.get_i(0)*stride + 0);
+        ggml_cuda_memcpy_1<4*sizeof(T)>(t.x + 4, xs0 + t.get_i(4)*stride + 4);
+#else
+        load_generic(t, xs0, stride);
+#endif // 1
+#else
+        tile<16, 8, T> * t16 = (tile<16, 8, T> *) &t;
+        load_ldmatrix(t16[0], xs0 +  0*stride, stride);
+        load_ldmatrix(t16[1], xs0 + 16*stride, stride);
+#endif // __CUDA_ARCH__ == GGML_CUDA_CC_VOLTA
+    }
+
     template <typename T>
     static __device__ __forceinline__ void load_ldmatrix_trans(
             tile<16, 8, T> & t, const T * __restrict__ xs0, const int stride) {
@@ -546,4 +696,43 @@ namespace ggml_cuda_mma {
         NO_DEVICE_CODE;
 #endif // AMD_MFMA_AVAILABLE
     }
+
+    template <typename T1, typename T2, int J, int K>
+    static __device__ __forceinline__ void mma(
+            tile<32, J, T1> & D, const tile<32, K, T2> & A, const tile<J, K, T2> & B) {
+        tile<16, J, T1> * D16 = (tile<16, J, T1> *) &D;
+        tile<16, K, T2> * A16 = (tile<16, K, T2> *) &A;
+        mma(D16[0], A16[0], B);
+        mma(D16[1], A16[1], B);
+    }
+
+    static __device__ __forceinline__ void mma(
+            tile<32, 8, float> & D, const tile<32, 8, half2> & A, const tile<8, 8, half2> & B) {
+#if __CUDA_ARCH__ == GGML_CUDA_CC_VOLTA
+        const int * Axi = (const int *) A.x;
+        const int * Bxi = (const int *) B.x;
+        int       * Dxi = (int       *) D.x;
+        asm("mma.sync.aligned.m8n8k4.row.col.f32.f16.f16.f32 "
+            "{%0, %1, %2, %3, %4, %5, %6, %7}, {%8, %9}, {%10, %11}, {%0, %1, %2, %3, %4, %5, %6, %7};"
+            : "+r"(Dxi[0]), "+r"(Dxi[1]), "+r"(Dxi[2]), "+r"(Dxi[3]), "+r"(Dxi[4]), "+r"(Dxi[5]), "+r"(Dxi[6]), "+r"(Dxi[7])
+            : "r"(Axi[0]), "r"(Axi[1]), "r"(Bxi[0]), "r"(Bxi[1]));
+        asm("mma.sync.aligned.m8n8k4.row.col.f32.f16.f16.f32 "
+            "{%0, %1, %2, %3, %4, %5, %6, %7}, {%8, %9}, {%10, %11}, {%0, %1, %2, %3, %4, %5, %6, %7};"
+            : "+r"(Dxi[0]), "+r"(Dxi[1]), "+r"(Dxi[2]), "+r"(Dxi[3]), "+r"(Dxi[4]), "+r"(Dxi[5]), "+r"(Dxi[6]), "+r"(Dxi[7])
+            : "r"(Axi[2]), "r"(Axi[3]), "r"(Bxi[2]), "r"(Bxi[3]));
+        asm("mma.sync.aligned.m8n8k4.row.col.f32.f16.f16.f32 "
+            "{%0, %1, %2, %3, %4, %5, %6, %7}, {%8, %9}, {%10, %11}, {%0, %1, %2, %3, %4, %5, %6, %7};"
+            : "+r"(Dxi[0]), "+r"(Dxi[1]), "+r"(Dxi[2]), "+r"(Dxi[3]), "+r"(Dxi[4]), "+r"(Dxi[5]), "+r"(Dxi[6]), "+r"(Dxi[7])
+            : "r"(Axi[4]), "r"(Axi[5]), "r"(Bxi[4]), "r"(Bxi[5]));
+        asm("mma.sync.aligned.m8n8k4.row.col.f32.f16.f16.f32 "
+            "{%0, %1, %2, %3, %4, %5, %6, %7}, {%8, %9}, {%10, %11}, {%0, %1, %2, %3, %4, %5, %6, %7};"
+            : "+r"(Dxi[0]), "+r"(Dxi[1]), "+r"(Dxi[2]), "+r"(Dxi[3]), "+r"(Dxi[4]), "+r"(Dxi[5]), "+r"(Dxi[6]), "+r"(Dxi[7])
+            : "r"(Axi[6]), "r"(Axi[7]), "r"(Bxi[6]), "r"(Bxi[7]));
+#else
+        tile<16, 8, float> * D16 = (tile<16, 8, float> *) &D;
+        tile<16, 8, half2> * A16 = (tile<16, 8, half2> *) &A;
+        mma(D16[0], A16[0], B);
+        mma(D16[1], A16[1], B);
+#endif // __CUDA_ARCH__ >= GGML_CUDA_CC_AMPERE
+    }
 }
diff --git a/ggml/src/ggml-cuda/mmf.cu b/ggml/src/ggml-cuda/mmf.cu
index 9e2aaf52d6c..2b0a61395b4 100644
--- a/ggml/src/ggml-cuda/mmf.cu
+++ b/ggml/src/ggml-cuda/mmf.cu
@@ -148,7 +148,7 @@ bool ggml_cuda_should_use_mmf(enum ggml_type type, int cc, int warp_size, const
         case GGML_TYPE_F32:
             return ampere_mma_available(cc);
         case GGML_TYPE_F16:
-            return turing_mma_available(cc);
+            return volta_mma_available(cc) || turing_mma_available(cc);
         case GGML_TYPE_BF16:
             return ampere_mma_available(cc);
         default:
diff --git a/ggml/src/ggml-cuda/mmf.cuh b/ggml/src/ggml-cuda/mmf.cuh
index 49d5295be0e..f7e46e2f63b 100644
--- a/ggml/src/ggml-cuda/mmf.cuh
+++ b/ggml/src/ggml-cuda/mmf.cuh
@@ -28,9 +28,19 @@ static __global__ void mul_mat_f(
         const int channel_ratio, const int stride_channel_x, const int stride_channel_y, const int stride_channel_dst,
         const int sample_ratio, const int stride_sample_x, const int stride_sample_y, const int stride_sample_dst) {
 #if !defined(GGML_USE_HIP) && !defined(GGML_USE_MUSA)
-    typedef tile<16, 8, T>     tile_A;
-    typedef tile< 8, 8, T>     tile_B;
-    typedef tile<16, 8, float> tile_C;
+    constexpr bool I_16_supported = tile<16, 8, T>::supported() && tile<16, 8, float>::supported();
+    constexpr bool I_32_supported = tile<32, 8, T>::supported() && tile<32, 8, float>::supported();
+
+    if (!I_16_supported && !I_32_supported) {
+        NO_DEVICE_CODE;
+        return;
+    }
+
+    constexpr int I_preferred = I_16_supported ? 16 : 32; // For Turing MMA both work but 16 is ~1% faster.
+
+    typedef tile<I_preferred, 8, T>     tile_A;
+    typedef tile<8,           8, T>     tile_B;
+    typedef tile<I_preferred, 8, float> tile_C;
 
     constexpr int warp_size = ggml_cuda_get_physical_warp_size();
     constexpr int tile_k_padded = warp_size + 4;
@@ -232,7 +242,6 @@ static __global__ void mul_mat_f(
 #endif // !defined(GGML_USE_HIP) && !defined(GGML_USE_MUSA)
 }
 
-
 //This kernel is for larger batch sizes of mul_mat_id
 template <typename T, int rows_per_block, int cols_per_block, int nwarps>
 __launch_bounds__(ggml_cuda_get_physical_warp_size()*nwarps, 1)
@@ -245,9 +254,19 @@ static __global__ void mul_mat_f_ids(
         const int sample_ratio, const int stride_sample_x, const int stride_sample_y, const int stride_sample_dst,
         const uint3 sis1_fd, const uint3 nch_fd) {
 #if !defined(GGML_USE_HIP) && !defined(GGML_USE_MUSA)
-    typedef tile<16, 8, T>     tile_A;
-    typedef tile< 8, 8, T>     tile_B;
-    typedef tile<16, 8, float> tile_C;
+    constexpr bool I_16_supported = tile<16, 8, T>::supported() && tile<16, 8, float>::supported();
+    constexpr bool I_32_supported = tile<32, 8, T>::supported() && tile<32, 8, float>::supported();
+
+    if (!I_16_supported && !I_32_supported) {
+        NO_DEVICE_CODE;
+        return;
+    }
+
+    constexpr int I_preferred = I_16_supported ? 16 : 32; // For Turing MMA both work butr 16 is ~1% faster.
+
+    typedef tile<I_preferred, 8, T>     tile_A;
+    typedef tile<8,           8, T>     tile_B;
+    typedef tile<I_preferred, 8, float> tile_C;
 
     constexpr int warp_size = ggml_cuda_get_physical_warp_size();
     constexpr int tile_k_padded = warp_size + 4;
@@ -533,7 +552,8 @@ void mul_mat_f_cuda(
         const int64_t stride_channel_x, const int64_t stride_channel_y, const int64_t stride_channel_dst, const int64_t nsamples_x,
         const int64_t nsamples_dst, const int64_t stride_sample_x, const int64_t stride_sample_y, const int64_t stride_sample_dst,
         cudaStream_t stream, const mmf_ids_data * ids_data) {
-    typedef tile<16, 8, T>     tile_A;
+    typedef tile<16, 8, T>     tile_A_16;
+    typedef tile<32, 8, T>     tile_A_32;
     typedef tile< 8, 8, T>     tile_B;
 
     GGML_ASSERT(ncols_x      % 2 == 0);
@@ -544,7 +564,8 @@ void mul_mat_f_cuda(
     const int64_t channel_ratio = nchannels_dst / nchannels_x;
     const int64_t sample_ratio  = nsamples_dst  / nsamples_x;
 
-    const int device = ggml_cuda_get_device();
+    const int device    = ggml_cuda_get_device();
+    const int cc        = ggml_cuda_info().devices[device].cc;
     const int warp_size = ggml_cuda_info().devices[device].warp_size;
 
     int64_t nwarps_best     = 1;
@@ -559,7 +580,7 @@ void mul_mat_f_cuda(
     }
 
     constexpr int rows_per_block = MMF_ROWS_PER_BLOCK;
-    const int nbytes_shared_iter = nwarps_best * tile_A::I * (warp_size + 4) * 4;
+    const int nbytes_shared_iter = nwarps_best * (volta_mma_available(cc) ? tile_A_32::I : tile_A_16::I) * (warp_size + 4) * 4;
     const int nbytes_shared_combine = GGML_PAD(cols_per_block, tile_B::I) * (nwarps_best*rows_per_block + 4) * 4;
     const int nbytes_shared = std::max(nbytes_shared_iter, nbytes_shared_combine);
     const int nbytes_slotmap = ids ? GGML_PAD(cols_per_block, 16) * sizeof(int) : 0;

From e58d585604bbbbbc24f8149effe444621b5191c6 Mon Sep 17 00:00:00 2001
From: Giuseppe Scrivano <gscrivan@redhat.com>
Date: Fri, 31 Oct 2025 21:20:07 +0100
Subject: [PATCH 039/185] model : add Granite Hybrid nano types (#16896)

Signed-off-by: Giuseppe Scrivano <gscrivan@redhat.com>
---
 src/llama-model.cpp | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/src/llama-model.cpp b/src/llama-model.cpp
index 1e0680bee95..89a6a51b2cc 100644
--- a/src/llama-model.cpp
+++ b/src/llama-model.cpp
@@ -1898,7 +1898,8 @@ void llama_model::load_hparams(llama_model_loader & ml) {
                 ml.get_key(LLM_KV_ATTENTION_LAYERNORM_RMS_EPS, hparams.f_norm_rms_eps);
 
                 switch (hparams.n_embd) {
-                    case 1536: type = LLM_TYPE_7B_A1B; break;
+                    case 768: type = LLM_TYPE_350M; break;
+                    case 1536: type = (hparams.n_embd == 2048 ? LLM_TYPE_7B_A1B : LLM_TYPE_1B); break;
                     case 2048: case 2560: type = LLM_TYPE_3B; break;
                     case 4096: type = LLM_TYPE_32B; break;
                     default: type = LLM_TYPE_UNKNOWN;

From 0de0a01576772032008a689afc4d7c80685074c4 Mon Sep 17 00:00:00 2001
From: "Piotr Wilkin (ilintar)" <piotr.wilkin@syndatis.com>
Date: Fri, 31 Oct 2025 21:20:47 +0100
Subject: [PATCH 040/185] model : Minimax M2 (#16831)
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

* Model: Minimax M2

* Cleanup

* Cleanup pt. 2

* Cleanup pt. 3

* Update convert_hf_to_gguf_update.py - merge catch blocks

Co-authored-by: Sigbjørn Skjæret <sigbjorn.skjaeret@scala.com>

* Remove vocab models and test

* Remove all redundant hparam settings covered by TextModel

* Move super to start, don't set block_count

* Update src/llama-model.cpp

Co-authored-by: Sigbjørn Skjæret <sigbjorn.skjaeret@scala.com>

* Update gguf-py/gguf/constants.py

Co-authored-by: Sigbjørn Skjæret <sigbjorn.skjaeret@scala.com>

---------

Co-authored-by: Sigbjørn Skjæret <sigbjorn.skjaeret@scala.com>
---
 convert_hf_to_gguf.py          |  61 ++++++++++++
 convert_hf_to_gguf_update.py   |   3 +-
 gguf-py/gguf/constants.py      |  20 ++++
 gguf-py/gguf/tensor_mapping.py |   1 +
 src/llama-arch.cpp             |  22 +++++
 src/llama-arch.h               |   1 +
 src/llama-model.cpp            | 170 +++++++++++++++++++++++++++++++++
 src/llama-model.h              |   1 +
 src/llama-vocab.cpp            |   5 +
 src/llama-vocab.h              |   1 +
 10 files changed, 284 insertions(+), 1 deletion(-)

diff --git a/convert_hf_to_gguf.py b/convert_hf_to_gguf.py
index 5abc1779588..f186c2167d7 100755
--- a/convert_hf_to_gguf.py
+++ b/convert_hf_to_gguf.py
@@ -1054,6 +1054,9 @@ def get_vocab_base_pre(self, tokenizer) -> str:
         if chkhsh == "53e325976a6e142379c19b09afcae354f2f496f147afa8f9e189a33fe4e3024e":
             # ref: https://huggingface.co/ibm-granite/granite-docling-258M
             res = "granite-docling"
+        if chkhsh == "f4f37b6c8eb9ea29b3eac6bb8c8487c5ab7885f8d8022e67edc1c68ce8403e95":
+            # ref: https://huggingface.co/MiniMaxAI/MiniMax-M2
+            res = "minimax-m2"
 
         if res is None:
             logger.warning("\n")
@@ -7126,6 +7129,64 @@ def prepare_tensors(self):
                 raise ValueError(f"Unprocessed experts: {experts}")
 
 
+@ModelBase.register("MiniMaxM2ForCausalLM")
+class MiniMaxM2Model(TextModel):
+    model_arch = gguf.MODEL_ARCH.MINIMAXM2
+    _experts_cache: dict[int, dict[str, Tensor]] = {}
+
+    def __init__(self, *args, **kwargs):
+        super().__init__(*args, **kwargs)
+        self.hparams["num_experts"] = self.hparams["num_local_experts"]
+
+    def set_gguf_parameters(self):
+        super().set_gguf_parameters()
+        if self.hparams["scoring_func"] == "sigmoid":
+            self.gguf_writer.add_expert_gating_func(gguf.ExpertGatingFuncType.SIGMOID)
+        elif self.hparams["scoring_func"] == "softmax":
+            self.gguf_writer.add_expert_gating_func(gguf.ExpertGatingFuncType.SOFTMAX)
+        else:
+            raise ValueError(f"Unsupported scoring_func value: {self.hparams['scoring_func']}")
+
+        self.gguf_writer.add_expert_feed_forward_length(self.find_hparam(["intermediate_size"]))
+        self.gguf_writer.add_rope_dimension_count(self.find_hparam(["rotary_dim"]))
+
+    def modify_tensors(self, data_torch: Tensor, name: str, bid: int | None):
+        if name.endswith("e_score_correction_bias"):
+            name = name.replace("e_score_correction_bias", "e_score_correction.bias")
+
+        # merge expert weights
+        if 'experts' in name:
+            n_experts = self.hparams["num_experts"]
+            assert bid is not None
+
+            expert_cache = self._experts_cache.setdefault(bid, {})
+            expert_cache[name] = data_torch
+            expert_weights = ["w1", "w2", "w3"]
+
+            # not enough expert weights to merge
+            if len(expert_cache) < n_experts * len(expert_weights):
+                return []
+
+            tensors: list[tuple[str, Tensor]] = []
+            for w_name in expert_weights:
+                datas: list[Tensor] = []
+
+                for xid in range(n_experts):
+                    ename = f"model.layers.{bid}.block_sparse_moe.experts.{xid}.{w_name}.weight"
+                    datas.append(expert_cache[ename])
+                    del expert_cache[ename]
+
+                data_torch = torch.stack(datas, dim=0)
+                merged_name = f"model.layers.{bid}.block_sparse_moe.experts.{w_name}.weight"
+                new_name = self.map_tensor_name(merged_name)
+                tensors.append((new_name, data_torch))
+
+            del self._experts_cache[bid]
+            return tensors
+
+        return super().modify_tensors(data_torch, name, bid)
+
+
 @ModelBase.register("Dots1ForCausalLM")
 class Dots1Model(Qwen2MoeModel):
     model_arch = gguf.MODEL_ARCH.DOTS1
diff --git a/convert_hf_to_gguf_update.py b/convert_hf_to_gguf_update.py
index 0ebc1b160f6..7df96eb0839 100755
--- a/convert_hf_to_gguf_update.py
+++ b/convert_hf_to_gguf_update.py
@@ -141,6 +141,7 @@ class TOKENIZER_TYPE(IntEnum):
     {"name": "mellum",           "tokt": TOKENIZER_TYPE.BPE, "repo": "https://huggingface.co/JetBrains/Mellum-4b-base", },
     {"name": "bailingmoe2",      "tokt": TOKENIZER_TYPE.BPE, "repo": "https://huggingface.co/inclusionAI/Ling-mini-base-2.0", },
     {"name": "granite-docling",  "tokt": TOKENIZER_TYPE.BPE, "repo": "https://huggingface.co/ibm-granite/granite-docling-258M", },
+    {"name": "minimax-m2",       "tokt": TOKENIZER_TYPE.BPE, "repo": "https://huggingface.co/MiniMaxAI/MiniMax-M2", },
 ]
 
 # some models are known to be broken upstream, so we will skip them as exceptions
@@ -435,7 +436,7 @@ def get_vocab_base_pre(self, tokenizer) -> str:
             tokenizer = AutoTokenizer.from_pretrained(f"models/tokenizers/{name}", use_fast=False)
         else:
             tokenizer = AutoTokenizer.from_pretrained(f"models/tokenizers/{name}")
-    except OSError as e:
+    except (OSError, TypeError) as e:
         logger.error(f"Failed to load tokenizer for model {name}. Error: {e}")
         continue  # Skip this model and continue with the next one in the loop
 
diff --git a/gguf-py/gguf/constants.py b/gguf-py/gguf/constants.py
index d75ac704fed..0d5afa01edf 100644
--- a/gguf-py/gguf/constants.py
+++ b/gguf-py/gguf/constants.py
@@ -425,6 +425,7 @@ class MODEL_ARCH(IntEnum):
     GROVEMOE         = auto()
     APERTUS          = auto()
     COGVLM           = auto()
+    MINIMAXM2        = auto()
 
 
 class VISION_PROJECTOR_TYPE(IntEnum):
@@ -790,6 +791,7 @@ class MODEL_TENSOR(IntEnum):
     MODEL_ARCH.SEED_OSS:         "seed_oss",
     MODEL_ARCH.GROVEMOE:         "grovemoe",
     MODEL_ARCH.APERTUS:          "apertus",
+    MODEL_ARCH.MINIMAXM2:        "minimax-m2",
     MODEL_ARCH.COGVLM:           "cogvlm",
 }
 
@@ -2921,6 +2923,24 @@ class MODEL_TENSOR(IntEnum):
         MODEL_TENSOR.FFN_DOWN_CHEXP,
         MODEL_TENSOR.FFN_UP_CHEXP,
     ],
+    MODEL_ARCH.MINIMAXM2: [
+        MODEL_TENSOR.TOKEN_EMBD,
+        MODEL_TENSOR.OUTPUT_NORM,
+        MODEL_TENSOR.OUTPUT,
+        MODEL_TENSOR.ATTN_NORM,
+        MODEL_TENSOR.ATTN_Q,
+        MODEL_TENSOR.ATTN_Q_NORM,
+        MODEL_TENSOR.ATTN_K,
+        MODEL_TENSOR.ATTN_K_NORM,
+        MODEL_TENSOR.ATTN_V,
+        MODEL_TENSOR.ATTN_OUT,
+        MODEL_TENSOR.FFN_NORM,
+        MODEL_TENSOR.FFN_GATE_INP,
+        MODEL_TENSOR.FFN_GATE_EXP,
+        MODEL_TENSOR.FFN_DOWN_EXP,
+        MODEL_TENSOR.FFN_UP_EXP,
+        MODEL_TENSOR.FFN_EXP_PROBS_B,
+    ],
     MODEL_ARCH.COGVLM: [
         MODEL_TENSOR.TOKEN_EMBD,
         MODEL_TENSOR.OUTPUT_NORM,
diff --git a/gguf-py/gguf/tensor_mapping.py b/gguf-py/gguf/tensor_mapping.py
index 6fe6f22358c..cef5acec758 100644
--- a/gguf-py/gguf/tensor_mapping.py
+++ b/gguf-py/gguf/tensor_mapping.py
@@ -381,6 +381,7 @@ class TensorNameMap:
             "model.layers.{bid}.mlp.moe_statics.e_score_correction",        # ernie4.5-moe
             "model.layers.{bid}.mlp.gate.expert_bias",                      # bailingmoe2
             "model.layers.{bid}.feed_forward.expert_bias",                  # lfm2moe
+            "model.layers.{bid}.block_sparse_moe.e_score_correction",       # minimax-m2
         ),
 
         # Feed-forward up
diff --git a/src/llama-arch.cpp b/src/llama-arch.cpp
index ad2880034c2..7c7953b83dd 100644
--- a/src/llama-arch.cpp
+++ b/src/llama-arch.cpp
@@ -105,6 +105,7 @@ static const std::map<llm_arch, const char *> LLM_ARCH_NAMES = {
     { LLM_ARCH_SEED_OSS,         "seed_oss"         },
     { LLM_ARCH_GROVEMOE,         "grovemoe"         },
     { LLM_ARCH_APERTUS,          "apertus"          },
+    { LLM_ARCH_MINIMAX_M2,       "minimax-m2"       },
     { LLM_ARCH_COGVLM,           "cogvlm"           },
     { LLM_ARCH_UNKNOWN,          "(unknown)"        },
 };
@@ -2355,6 +2356,27 @@ static const std::map<llm_arch, std::map<llm_tensor, const char *>> LLM_TENSOR_N
             { LLM_TENSOR_FFN_UP_CHEXPS,      "blk.%d.ffn_up_chexps" },
         },
     },
+    {
+        LLM_ARCH_MINIMAX_M2,
+        {
+            { LLM_TENSOR_TOKEN_EMBD,         "token_embd" },
+            { LLM_TENSOR_OUTPUT_NORM,        "output_norm" },
+            { LLM_TENSOR_OUTPUT,             "output" },
+            { LLM_TENSOR_ATTN_NORM,          "blk.%d.attn_norm" },
+            { LLM_TENSOR_ATTN_Q,             "blk.%d.attn_q" },
+            { LLM_TENSOR_ATTN_K,             "blk.%d.attn_k" },
+            { LLM_TENSOR_ATTN_V,             "blk.%d.attn_v" },
+            { LLM_TENSOR_ATTN_OUT,           "blk.%d.attn_output" },
+            { LLM_TENSOR_ATTN_Q_NORM,        "blk.%d.attn_q_norm" },
+            { LLM_TENSOR_ATTN_K_NORM,        "blk.%d.attn_k_norm" },
+            { LLM_TENSOR_FFN_NORM,           "blk.%d.ffn_norm" },
+            { LLM_TENSOR_FFN_GATE_INP,       "blk.%d.ffn_gate_inp" },
+            { LLM_TENSOR_FFN_GATE_EXPS,      "blk.%d.ffn_gate_exps" },
+            { LLM_TENSOR_FFN_DOWN_EXPS,      "blk.%d.ffn_down_exps" },
+            { LLM_TENSOR_FFN_UP_EXPS,        "blk.%d.ffn_up_exps" },
+            { LLM_TENSOR_FFN_EXP_PROBS_B,    "blk.%d.exp_probs_b" },
+        },
+    },
     {
         LLM_ARCH_COGVLM,
         {
diff --git a/src/llama-arch.h b/src/llama-arch.h
index 4dae35e2923..3f893a2dc69 100644
--- a/src/llama-arch.h
+++ b/src/llama-arch.h
@@ -109,6 +109,7 @@ enum llm_arch {
     LLM_ARCH_SEED_OSS,
     LLM_ARCH_GROVEMOE,
     LLM_ARCH_APERTUS,
+    LLM_ARCH_MINIMAX_M2,
     LLM_ARCH_COGVLM,
     LLM_ARCH_UNKNOWN,
 };
diff --git a/src/llama-model.cpp b/src/llama-model.cpp
index 89a6a51b2cc..db536525752 100644
--- a/src/llama-model.cpp
+++ b/src/llama-model.cpp
@@ -120,6 +120,7 @@ const char * llm_type_name(llm_type type) {
         case LLM_TYPE_30B_A3B:       return "30B.A3B";
         case LLM_TYPE_100B_A6B:      return "100B.A6B";
         case LLM_TYPE_106B_A12B:     return "106B.A12B";
+        case LLM_TYPE_230B_A10B:     return "230B.A10B";
         case LLM_TYPE_235B_A22B:     return "235B.A22B";
         case LLM_TYPE_300B_A47B:     return "300B.A47B";
         case LLM_TYPE_355B_A32B:     return "355B.A32B";
@@ -2155,6 +2156,17 @@ void llama_model::load_hparams(llama_model_loader & ml) {
                     default: type = LLM_TYPE_UNKNOWN;
                 }
             } break;
+        case LLM_ARCH_MINIMAX_M2:
+            {
+                ml.get_key(LLM_KV_ATTENTION_LAYERNORM_RMS_EPS,  hparams.f_norm_rms_eps);
+                ml.get_key(LLM_KV_EXPERT_FEED_FORWARD_LENGTH,   hparams.n_ff_exp);
+                ml.get_key(LLM_KV_EXPERT_GATING_FUNC,           hparams.expert_gating_func, false);
+
+                switch (hparams.n_layer) {
+                    case 62: type = LLM_TYPE_230B_A10B; break;
+                    default: type = LLM_TYPE_UNKNOWN;
+                }
+            } break;
         case LLM_ARCH_COGVLM:
             {
                 ml.get_key(LLM_KV_ATTENTION_LAYERNORM_RMS_EPS, hparams.f_norm_rms_eps);
@@ -6185,6 +6197,35 @@ bool llama_model::load_tensors(llama_model_loader & ml) {
                         layer.attn_k_norm_b = create_tensor(tn(LLM_TENSOR_ATTN_K_NORM, "bias",   i), { n_embd_head_k }, TENSOR_NOT_REQUIRED);
                     }
                 } break;
+            case LLM_ARCH_MINIMAX_M2:
+                {
+                    tok_embd = create_tensor(tn(LLM_TENSOR_TOKEN_EMBD, "weight"), {n_embd, n_vocab}, 0);
+
+                    // output
+                    output_norm = create_tensor(tn(LLM_TENSOR_OUTPUT_NORM, "weight"), {n_embd}, 0);
+                    output      = create_tensor(tn(LLM_TENSOR_OUTPUT,      "weight"), {n_embd, n_vocab}, 0);
+
+                    for (int i = 0; i < n_layer; ++i) {
+                        auto & layer = layers[i];
+
+                        layer.wq = create_tensor(tn(LLM_TENSOR_ATTN_Q, "weight", i), { n_embd, n_embd_head_k * n_head }, 0);
+                        layer.wk = create_tensor(tn(LLM_TENSOR_ATTN_K, "weight", i), { n_embd, n_embd_gqa }, 0);
+                        layer.wv = create_tensor(tn(LLM_TENSOR_ATTN_V, "weight", i), { n_embd, n_embd_gqa }, 0);
+                        layer.wo = create_tensor(tn(LLM_TENSOR_ATTN_OUT, "weight", i), { n_embd_head_k * n_head, n_embd }, 0);
+
+                        layer.attn_norm = create_tensor(tn(LLM_TENSOR_ATTN_NORM, "weight", i), {n_embd}, 0);
+                        layer.attn_q_norm = create_tensor(tn(LLM_TENSOR_ATTN_Q_NORM, "weight", i), {n_embd_head_k * n_head}, 0);
+                        layer.attn_k_norm = create_tensor(tn(LLM_TENSOR_ATTN_K_NORM, "weight", i), {n_embd_k_gqa}, 0);
+
+                        layer.ffn_norm = create_tensor(tn(LLM_TENSOR_FFN_NORM, "weight", i), {n_embd}, 0);
+
+                        layer.ffn_gate_inp = create_tensor(tn(LLM_TENSOR_FFN_GATE_INP, "weight", i), {n_embd, n_expert}, 0);
+                        layer.ffn_gate_exps = create_tensor(tn(LLM_TENSOR_FFN_GATE_EXPS, "weight", i), {n_embd, n_ff,   n_expert}, 0);
+                        layer.ffn_down_exps = create_tensor(tn(LLM_TENSOR_FFN_DOWN_EXPS, "weight", i), {n_ff,   n_embd, n_expert}, 0);
+                        layer.ffn_up_exps   = create_tensor(tn(LLM_TENSOR_FFN_UP_EXPS,   "weight", i), {n_embd, n_ff,   n_expert}, 0);
+                        layer.ffn_exp_probs_b = create_tensor(tn(LLM_TENSOR_FFN_EXP_PROBS_B, "bias", i), {n_expert}, 0);
+                    }
+                } break;
             case LLM_ARCH_COGVLM:
                 {
                     tok_embd = create_tensor(tn(LLM_TENSOR_TOKEN_EMBD, "weight"), {n_embd, n_vocab}, 0);
@@ -20024,6 +20065,130 @@ struct llm_build_apertus : public llm_graph_context {
     }
 };
 
+struct llm_build_minimax_m2 : public llm_graph_context {
+    llm_build_minimax_m2(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+        const int64_t n_embd_head = hparams.n_embd_head_v;
+
+        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+        // GGML_ASSERT(n_embd_head == hparams.n_rot); this is wrong in case of minimax, head_dim = 128, n_rot = 64
+
+        ggml_tensor * cur;
+        ggml_tensor * inpL;
+
+        inpL = build_inp_embd(model.tok_embd);
+
+        ggml_tensor * inp_pos = build_inp_pos();
+        auto inp_attn = build_attn_inp_kv();
+        ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+        for (int il = 0; il < n_layer; ++il) {
+            ggml_tensor * inpSA = inpL;
+
+            cur = inpL;
+
+            // self_attention
+            {
+                cur = build_norm(inpL, model.layers[il].attn_norm, NULL, LLM_NORM_RMS, il);
+                cb(cur, "attn_norm", il);
+
+                // compute Q and K and RoPE them
+                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+                cb(Qcur, "Qcur", il);
+
+                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+                cb(Kcur, "Kcur", il);
+
+                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+                cb(Vcur, "Vcur", il);
+
+                Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL,
+                        LLM_NORM_RMS, il);
+                cb(Qcur, "Qcur_normed", il);
+
+                Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, NULL,
+                        LLM_NORM_RMS, il);
+                cb(Kcur, "Kcur_normed", il);
+
+                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+                Qcur = ggml_rope_ext(
+                    ctx0, Qcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+                Kcur = ggml_rope_ext(
+                    ctx0, Kcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+                cb(Qcur, "Qcur", il);
+                cb(Kcur, "Kcur", il);
+                cb(Vcur, "Vcur", il);
+
+                cur = build_attn(inp_attn,
+                        model.layers[il].wo, NULL,
+                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+            }
+
+            if (il == n_layer - 1 && inp_out_ids) {
+                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+            }
+
+            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+            cb(ffn_inp, "ffn_inp", il);
+
+            // MoE branch
+            cur = build_norm(ffn_inp,
+                    model.layers[il].ffn_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "ffn_norm", il);
+
+            cur = build_moe_ffn(cur,
+                    model.layers[il].ffn_gate_inp,
+                    model.layers[il].ffn_up_exps,
+                    model.layers[il].ffn_gate_exps,
+                    model.layers[il].ffn_down_exps,
+                    model.layers[il].ffn_exp_probs_b,
+                    n_expert, n_expert_used,
+                    LLM_FFN_SILU, true,
+                    false, 0.0,
+                    (llama_expert_gating_func_type) hparams.expert_gating_func,
+                    il);
+            cb(cur, "ffn_moe_out", il);
+
+            cur = ggml_add(ctx0, cur, ffn_inp);
+
+            cur = build_cvec(cur, il);
+            cb(cur, "l_out", il);
+
+            // input for next layer
+            inpL = cur;
+        }
+
+        cur = inpL;
+
+        cur = build_norm(cur,
+                model.output_norm, NULL,
+                LLM_NORM_RMS, -1);
+
+        cb(cur, "result_norm", -1);
+        res->t_embd = cur;
+
+        // lm_head
+        cur = build_lora_mm(model.output, cur);
+
+        cb(cur, "result_output", -1);
+        res->t_logits = cur;
+
+        ggml_build_forward_expand(gf, cur);
+    }
+};
+
 struct llm_build_cogvlm : public llm_graph_context {
     llm_build_cogvlm(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
         const int64_t n_embd_head = hparams.n_embd_head_v;
@@ -20654,6 +20819,10 @@ ggml_cgraph * llama_model::build_graph(const llm_graph_params & params) const {
             {
                 llm = std::make_unique<llm_build_apertus>(*this, params);
             } break;
+        case LLM_ARCH_MINIMAX_M2:
+            {
+                llm = std::make_unique<llm_build_minimax_m2>(*this, params);
+            } break;
         case LLM_ARCH_COGVLM:
             {
                 llm = std::make_unique<llm_build_cogvlm>(*this, params);
@@ -20875,6 +21044,7 @@ llama_rope_type llama_model_rope_type(const llama_model * model) {
         case LLM_ARCH_SEED_OSS:
         case LLM_ARCH_GROVEMOE:
         case LLM_ARCH_APERTUS:
+        case LLM_ARCH_MINIMAX_M2:
         case LLM_ARCH_COGVLM:
             return LLAMA_ROPE_TYPE_NEOX;
 
diff --git a/src/llama-model.h b/src/llama-model.h
index a5affda1c99..71ff148e07d 100644
--- a/src/llama-model.h
+++ b/src/llama-model.h
@@ -114,6 +114,7 @@ enum llm_type {
     LLM_TYPE_30B_A3B,
     LLM_TYPE_100B_A6B,
     LLM_TYPE_106B_A12B, // GLM-4.5-Air
+    LLM_TYPE_230B_A10B, // Minimax M2
     LLM_TYPE_235B_A22B,
     LLM_TYPE_300B_A47B, // Ernie MoE big
     LLM_TYPE_355B_A32B, // GLM-4.5
diff --git a/src/llama-vocab.cpp b/src/llama-vocab.cpp
index 639fecbd317..735c5d547f9 100644
--- a/src/llama-vocab.cpp
+++ b/src/llama-vocab.cpp
@@ -401,6 +401,7 @@ struct llm_tokenizer_bpe : llm_tokenizer {
                 };
                 break;
             case LLAMA_VOCAB_PRE_TYPE_GPT4O:
+            case LLAMA_VOCAB_PRE_TYPE_MINIMAX_M2:
                 regex_exprs = {
                     // original regex from tokenizer.json
                     // "[^\\r\\n\\p{L}\\p{N}]?[\\p{Lu}\\p{Lt}\\p{Lm}\\p{Lo}\\p{M}]*[\\p{Ll}\\p{Lm}\\p{Lo}\\p{M}]+(?i:'s|'t|'re|'ve|'m|'ll|'d)?|[^\\r\\n\\p{L}\\p{N}]?[\\p{Lu}\\p{Lt}\\p{Lm}\\p{Lo}\\p{M}]+[\\p{Ll}\\p{Lm}\\p{Lo}\\p{M}]*(?i:'s|'t|'re|'ve|'m|'ll|'d)?|\\p{N}{1,3}| ?[^\\s\\p{L}\\p{N}]+[\\r\\n/]*|\\s*[\\r\\n]+|\\s+(?!\\S)|\\s+",
@@ -1992,6 +1993,10 @@ void llama_vocab::impl::load(llama_model_loader & ml, const LLM_KV & kv) {
                 tokenizer_pre == "grok-2") {
                 pre_type = LLAMA_VOCAB_PRE_TYPE_GROK_2;
                 clean_spaces = false;
+            } else if (
+                tokenizer_pre == "minimax-m2") {
+                pre_type = LLAMA_VOCAB_PRE_TYPE_MINIMAX_M2;
+                clean_spaces = false;
             } else {
                 throw std::runtime_error(format("unknown pre-tokenizer type: '%s'", tokenizer_pre.c_str()));
             }
diff --git a/src/llama-vocab.h b/src/llama-vocab.h
index 5e468675e44..1194ec473d0 100644
--- a/src/llama-vocab.h
+++ b/src/llama-vocab.h
@@ -49,6 +49,7 @@ enum llama_vocab_pre_type {
     LLAMA_VOCAB_PRE_TYPE_HUNYUAN_DENSE   = 38,
     LLAMA_VOCAB_PRE_TYPE_GROK_2          = 39,
     LLAMA_VOCAB_PRE_TYPE_GRANITE_DOCLING = 40,
+    LLAMA_VOCAB_PRE_TYPE_MINIMAX_M2      = 41,
 };
 
 struct LLM_KV;

From bea04522ff1a0d8559ccfd353aa018dcfbb608cc Mon Sep 17 00:00:00 2001
From: "Piotr Wilkin (ilintar)" <piotr.wilkin@syndatis.com>
Date: Fri, 31 Oct 2025 23:40:23 +0100
Subject: [PATCH 041/185] refactor : llama-model.cpp (#16252)
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

* Sqashed: llama-model.cpp refactoring

* Fix formatting of attn / ffn / ffn_moe calls

* Fix import regression / unify spacing in models.h

* totally DID NOT miss those!

* Add missing qwen3vl(moe) models

* Add missing new .cpp files to build

* Remove extra semicolons

* Editor checker

* Update src/models/models.h

Co-authored-by: Sigbjørn Skjæret <sigbjorn.skjaeret@scala.com>

---------

Co-authored-by: Sigbjørn Skjæret <sigbjorn.skjaeret@scala.com>
---
 src/CMakeLists.txt                 |    94 +
 src/llama-model.cpp                | 13565 +--------------------------
 src/models/apertus.cpp             |   125 +
 src/models/arcee.cpp               |   135 +
 src/models/arctic.cpp              |   138 +
 src/models/arwkv7.cpp              |    86 +
 src/models/baichuan.cpp            |   122 +
 src/models/bailingmoe.cpp          |   144 +
 src/models/bailingmoe2.cpp         |   135 +
 src/models/bert.cpp                |   176 +
 src/models/bitnet.cpp              |   160 +
 src/models/bloom.cpp               |   101 +
 src/models/chameleon.cpp           |   178 +
 src/models/chatglm.cpp             |   132 +
 src/models/codeshell.cpp           |   111 +
 src/models/cogvlm.cpp              |   100 +
 src/models/cohere2-iswa.cpp        |   131 +
 src/models/command-r.cpp           |   122 +
 src/models/dbrx.cpp                |   123 +
 src/models/deci.cpp                |   135 +
 src/models/deepseek.cpp            |   144 +
 src/models/deepseek2.cpp           |   236 +
 src/models/dots1.cpp               |   134 +
 src/models/dream.cpp               |   105 +
 src/models/ernie4-5-moe.cpp        |   150 +
 src/models/ernie4-5.cpp            |   111 +
 src/models/exaone.cpp              |   114 +
 src/models/exaone4.cpp             |   123 +
 src/models/falcon-h1.cpp           |   113 +
 src/models/falcon.cpp              |   120 +
 src/models/gemma-embedding.cpp     |   120 +
 src/models/gemma.cpp               |   112 +
 src/models/gemma2-iswa.cpp         |   125 +
 src/models/gemma3-iswa.cpp         |   131 +
 src/models/gemma3n-iswa.cpp        |   377 +
 src/models/glm4-moe.cpp            |   153 +
 src/models/glm4.cpp                |   127 +
 src/models/gpt2.cpp                |   105 +
 src/models/gptneox.cpp             |   144 +
 src/models/granite-hybrid.cpp      |   196 +
 src/models/granite.cpp             |   211 +
 src/models/graph-context-mamba.cpp |   283 +
 src/models/grok.cpp                |   160 +
 src/models/grovemoe.cpp            |   141 +
 src/models/hunyuan-dense.cpp       |   132 +
 src/models/hunyuan-moe.cpp         |   154 +
 src/models/internlm2.cpp           |   121 +
 src/models/jais.cpp                |    86 +
 src/models/jamba.cpp               |   107 +
 src/models/lfm2.cpp                |   173 +
 src/models/llada-moe.cpp           |   123 +
 src/models/llada.cpp               |   101 +
 src/models/llama-iswa.cpp          |   174 +
 src/models/llama.cpp               |   156 +
 src/models/mamba.cpp               |    55 +
 src/models/minicpm3.cpp            |   200 +
 src/models/minimax-m2.cpp          |   124 +
 src/models/models.h                |   477 +
 src/models/mpt.cpp                 |   126 +
 src/models/nemotron-h.cpp          |   121 +
 src/models/nemotron.cpp            |   122 +
 src/models/neo-bert.cpp            |   104 +
 src/models/olmo.cpp                |   121 +
 src/models/olmo2.cpp               |   151 +
 src/models/olmoe.cpp               |   124 +
 src/models/openai-moe-iswa.cpp     |   123 +
 src/models/openelm.cpp             |   124 +
 src/models/orion.cpp               |   123 +
 src/models/phi2.cpp                |   121 +
 src/models/phi3.cpp                |   153 +
 src/models/plamo.cpp               |   110 +
 src/models/plamo2.cpp              |   316 +
 src/models/plm.cpp                 |   168 +
 src/models/qwen.cpp                |   108 +
 src/models/qwen2.cpp               |   118 +
 src/models/qwen2moe.cpp            |   151 +
 src/models/qwen2vl.cpp             |   117 +
 src/models/qwen3.cpp               |   117 +
 src/models/qwen3moe.cpp            |   124 +
 src/models/qwen3vl-moe.cpp         |   150 +
 src/models/qwen3vl.cpp             |   144 +
 src/models/refact.cpp              |    94 +
 src/models/rwkv6-base.cpp          |   162 +
 src/models/rwkv6.cpp               |    94 +
 src/models/rwkv6qwen2.cpp          |    86 +
 src/models/rwkv7-base.cpp          |   135 +
 src/models/rwkv7.cpp               |    90 +
 src/models/seed-oss.cpp            |   124 +
 src/models/smallthinker.cpp        |   120 +
 src/models/smollm3.cpp             |   128 +
 src/models/stablelm.cpp            |   146 +
 src/models/starcoder.cpp           |   100 +
 src/models/starcoder2.cpp          |   121 +
 src/models/t5-dec.cpp              |   166 +
 src/models/t5-enc.cpp              |    96 +
 src/models/wavtokenizer-dec.cpp    |   149 +
 src/models/xverse.cpp              |   108 +
 97 files changed, 13423 insertions(+), 13563 deletions(-)
 create mode 100644 src/models/apertus.cpp
 create mode 100644 src/models/arcee.cpp
 create mode 100644 src/models/arctic.cpp
 create mode 100644 src/models/arwkv7.cpp
 create mode 100644 src/models/baichuan.cpp
 create mode 100644 src/models/bailingmoe.cpp
 create mode 100644 src/models/bailingmoe2.cpp
 create mode 100644 src/models/bert.cpp
 create mode 100644 src/models/bitnet.cpp
 create mode 100644 src/models/bloom.cpp
 create mode 100644 src/models/chameleon.cpp
 create mode 100644 src/models/chatglm.cpp
 create mode 100644 src/models/codeshell.cpp
 create mode 100644 src/models/cogvlm.cpp
 create mode 100644 src/models/cohere2-iswa.cpp
 create mode 100644 src/models/command-r.cpp
 create mode 100644 src/models/dbrx.cpp
 create mode 100644 src/models/deci.cpp
 create mode 100644 src/models/deepseek.cpp
 create mode 100644 src/models/deepseek2.cpp
 create mode 100644 src/models/dots1.cpp
 create mode 100644 src/models/dream.cpp
 create mode 100644 src/models/ernie4-5-moe.cpp
 create mode 100644 src/models/ernie4-5.cpp
 create mode 100644 src/models/exaone.cpp
 create mode 100644 src/models/exaone4.cpp
 create mode 100644 src/models/falcon-h1.cpp
 create mode 100644 src/models/falcon.cpp
 create mode 100644 src/models/gemma-embedding.cpp
 create mode 100644 src/models/gemma.cpp
 create mode 100644 src/models/gemma2-iswa.cpp
 create mode 100644 src/models/gemma3-iswa.cpp
 create mode 100644 src/models/gemma3n-iswa.cpp
 create mode 100644 src/models/glm4-moe.cpp
 create mode 100644 src/models/glm4.cpp
 create mode 100644 src/models/gpt2.cpp
 create mode 100644 src/models/gptneox.cpp
 create mode 100644 src/models/granite-hybrid.cpp
 create mode 100644 src/models/granite.cpp
 create mode 100644 src/models/graph-context-mamba.cpp
 create mode 100644 src/models/grok.cpp
 create mode 100644 src/models/grovemoe.cpp
 create mode 100644 src/models/hunyuan-dense.cpp
 create mode 100644 src/models/hunyuan-moe.cpp
 create mode 100644 src/models/internlm2.cpp
 create mode 100644 src/models/jais.cpp
 create mode 100644 src/models/jamba.cpp
 create mode 100644 src/models/lfm2.cpp
 create mode 100644 src/models/llada-moe.cpp
 create mode 100644 src/models/llada.cpp
 create mode 100644 src/models/llama-iswa.cpp
 create mode 100644 src/models/llama.cpp
 create mode 100644 src/models/mamba.cpp
 create mode 100644 src/models/minicpm3.cpp
 create mode 100644 src/models/minimax-m2.cpp
 create mode 100644 src/models/models.h
 create mode 100644 src/models/mpt.cpp
 create mode 100644 src/models/nemotron-h.cpp
 create mode 100644 src/models/nemotron.cpp
 create mode 100644 src/models/neo-bert.cpp
 create mode 100644 src/models/olmo.cpp
 create mode 100644 src/models/olmo2.cpp
 create mode 100644 src/models/olmoe.cpp
 create mode 100644 src/models/openai-moe-iswa.cpp
 create mode 100644 src/models/openelm.cpp
 create mode 100644 src/models/orion.cpp
 create mode 100644 src/models/phi2.cpp
 create mode 100644 src/models/phi3.cpp
 create mode 100644 src/models/plamo.cpp
 create mode 100644 src/models/plamo2.cpp
 create mode 100644 src/models/plm.cpp
 create mode 100644 src/models/qwen.cpp
 create mode 100644 src/models/qwen2.cpp
 create mode 100644 src/models/qwen2moe.cpp
 create mode 100644 src/models/qwen2vl.cpp
 create mode 100644 src/models/qwen3.cpp
 create mode 100644 src/models/qwen3moe.cpp
 create mode 100644 src/models/qwen3vl-moe.cpp
 create mode 100644 src/models/qwen3vl.cpp
 create mode 100644 src/models/refact.cpp
 create mode 100644 src/models/rwkv6-base.cpp
 create mode 100644 src/models/rwkv6.cpp
 create mode 100644 src/models/rwkv6qwen2.cpp
 create mode 100644 src/models/rwkv7-base.cpp
 create mode 100644 src/models/rwkv7.cpp
 create mode 100644 src/models/seed-oss.cpp
 create mode 100644 src/models/smallthinker.cpp
 create mode 100644 src/models/smollm3.cpp
 create mode 100644 src/models/stablelm.cpp
 create mode 100644 src/models/starcoder.cpp
 create mode 100644 src/models/starcoder2.cpp
 create mode 100644 src/models/t5-dec.cpp
 create mode 100644 src/models/t5-enc.cpp
 create mode 100644 src/models/wavtokenizer-dec.cpp
 create mode 100644 src/models/xverse.cpp

diff --git a/src/CMakeLists.txt b/src/CMakeLists.txt
index 18cfc76564d..832b58e315d 100644
--- a/src/CMakeLists.txt
+++ b/src/CMakeLists.txt
@@ -35,6 +35,100 @@ add_library(llama
             unicode-data.cpp
             unicode.cpp
             unicode.h
+            models/apertus.cpp
+            models/arcee.cpp
+            models/arctic.cpp
+            models/arwkv7.cpp
+            models/baichuan.cpp
+            models/bailingmoe.cpp
+            models/bailingmoe2.cpp
+            models/bert.cpp
+            models/bitnet.cpp
+            models/bloom.cpp
+            models/chameleon.cpp
+            models/chatglm.cpp
+            models/codeshell.cpp
+            models/cogvlm.cpp
+            models/cohere2-iswa.cpp
+            models/command-r.cpp
+            models/dbrx.cpp
+            models/deci.cpp
+            models/deepseek.cpp
+            models/deepseek2.cpp
+            models/dots1.cpp
+            models/dream.cpp
+            models/ernie4-5-moe.cpp
+            models/ernie4-5.cpp
+            models/exaone.cpp
+            models/exaone4.cpp
+            models/falcon-h1.cpp
+            models/falcon.cpp
+            models/gemma-embedding.cpp
+            models/gemma.cpp
+            models/gemma2-iswa.cpp
+            models/gemma3-iswa.cpp
+            models/gemma3n-iswa.cpp
+            models/glm4-moe.cpp
+            models/glm4.cpp
+            models/gpt2.cpp
+            models/gptneox.cpp
+            models/granite-hybrid.cpp
+            models/granite.cpp
+            models/grok.cpp
+            models/grovemoe.cpp
+            models/hunyuan-dense.cpp
+            models/hunyuan-moe.cpp
+            models/internlm2.cpp
+            models/jais.cpp
+            models/jamba.cpp
+            models/lfm2.cpp
+            models/llada-moe.cpp
+            models/llada.cpp
+            models/llama-iswa.cpp
+            models/llama.cpp
+            models/mamba.cpp
+            models/minicpm3.cpp
+            models/minimax-m2.cpp
+            models/mpt.cpp
+            models/nemotron-h.cpp
+            models/nemotron.cpp
+            models/neo-bert.cpp
+            models/olmo.cpp
+            models/olmo2.cpp
+            models/olmoe.cpp
+            models/openai-moe-iswa.cpp
+            models/openelm.cpp
+            models/orion.cpp
+            models/phi2.cpp
+            models/phi3.cpp
+            models/plamo.cpp
+            models/plamo2.cpp
+            models/plm.cpp
+            models/qwen.cpp
+            models/qwen2.cpp
+            models/qwen2moe.cpp
+            models/qwen2vl.cpp
+            models/qwen3.cpp
+            models/qwen3vl.cpp
+            models/qwen3vl-moe.cpp
+            models/qwen3moe.cpp
+            models/refact.cpp
+            models/rwkv6-base.cpp
+            models/rwkv6.cpp
+            models/rwkv6qwen2.cpp
+            models/rwkv7-base.cpp
+            models/rwkv7.cpp
+            models/seed-oss.cpp
+            models/smallthinker.cpp
+            models/smollm3.cpp
+            models/stablelm.cpp
+            models/starcoder.cpp
+            models/starcoder2.cpp
+            models/t5-dec.cpp
+            models/t5-enc.cpp
+            models/wavtokenizer-dec.cpp
+            models/xverse.cpp
+            models/graph-context-mamba.cpp
             )
 
 target_include_directories(llama PRIVATE .)
diff --git a/src/llama-model.cpp b/src/llama-model.cpp
index db536525752..04239181c77 100644
--- a/src/llama-model.cpp
+++ b/src/llama-model.cpp
@@ -13,6 +13,8 @@
 
 #include "ggml-cpp.h"
 
+#include "models/models.h"
+
 #include <algorithm>
 #include <cassert>
 #include <cfloat>
@@ -6724,13569 +6726,6 @@ ggml_tensor * llama_model::get_rope_factors(const llama_cparams & cparams, int i
     return layers[il].rope_short;
 }
 
-struct llm_build_llama : public llm_graph_context {
-    llm_build_llama(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        const float kq_scale = hparams.f_attention_scale == 0.0f ? 1.0f/sqrtf(float(n_embd_head)) : hparams.f_attention_scale;
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                // rope freq factors for llama3; may return nullptr for llama2 and other models
-                ggml_tensor * rope_factors = model.get_rope_factors(cparams, il);
-
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-                if (model.layers[il].bq) {
-                    Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
-                    cb(Qcur, "Qcur", il);
-                }
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-                if (model.layers[il].bk) {
-                    Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
-                    cb(Kcur, "Kcur", il);
-                }
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-                if (model.layers[il].bv) {
-                    Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
-                    cb(Vcur, "Vcur", il);
-                }
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, rope_factors,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, rope_factors,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                if (hparams.use_kq_norm) {
-                    // Llama4TextL2Norm
-                    Qcur = ggml_rms_norm(ctx0, Qcur, hparams.f_norm_rms_eps);
-                    Kcur = ggml_rms_norm(ctx0, Kcur, hparams.f_norm_rms_eps);
-                    cb(Qcur, "Qcur_normed", il);
-                    cb(Kcur, "Kcur_normed", il);
-                }
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, kq_scale, il);
-                cb(cur, "attn_out", il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed-forward network (non-MoE)
-            if (model.layers[il].ffn_gate_inp == nullptr) {
-
-                cur = build_norm(ffn_inp,
-                        model.layers[il].ffn_norm, NULL,
-                        LLM_NORM_RMS, il);
-                cb(cur, "ffn_norm", il);
-
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up,   model.layers[il].ffn_up_b,   NULL,
-                        model.layers[il].ffn_gate, model.layers[il].ffn_gate_b, NULL,
-                        model.layers[il].ffn_down, model.layers[il].ffn_down_b, NULL,
-                        NULL,
-                        LLM_FFN_SILU, LLM_FFN_PAR, il);
-                cb(cur, "ffn_out", il);
-            } else {
-                // MoE branch
-                cur = build_norm(ffn_inp,
-                        model.layers[il].ffn_norm, NULL,
-                        LLM_NORM_RMS, il);
-                cb(cur, "ffn_norm", il);
-
-                cur = build_moe_ffn(cur,
-                        model.layers[il].ffn_gate_inp,
-                        model.layers[il].ffn_up_exps,
-                        model.layers[il].ffn_gate_exps,
-                        model.layers[il].ffn_down_exps,
-                        nullptr,
-                        n_expert, n_expert_used,
-                        LLM_FFN_SILU, true,
-                        false, 0.0,
-                        LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
-                        il);
-                cb(cur, "ffn_moe_out", il);
-            }
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-            cb(cur, "ffn_out", il);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_llama_iswa : public llm_graph_context {
-    llm_build_llama_iswa(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        // temperature tuning
-        ggml_tensor * inp_attn_scale = nullptr;
-        inp_attn_scale = build_inp_attn_scale();
-
-        auto * inp_attn = build_attn_inp_kv_iswa();
-
-        const float kq_scale = hparams.f_attention_scale == 0.0f ? 1.0f/sqrtf(float(n_embd_head)) : hparams.f_attention_scale;
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            const bool use_rope = hparams.n_no_rope_layer_step > 0 &&
-                                  (il + 1) % hparams.n_no_rope_layer_step != 0;
-
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                // rope freq factors for llama3; may return nullptr for llama2 and other models
-                ggml_tensor * rope_factors = model.get_rope_factors(cparams, il);
-
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-                if (model.layers[il].bq) {
-                    Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
-                    cb(Qcur, "Qcur", il);
-                }
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-                if (model.layers[il].bk) {
-                    Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
-                    cb(Kcur, "Kcur", il);
-                }
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-                if (model.layers[il].bv) {
-                    Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
-                    cb(Vcur, "Vcur", il);
-                }
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                if (use_rope) {
-                    Qcur = ggml_rope_ext(
-                            ctx0, Qcur, inp_pos, rope_factors,
-                            n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                            ext_factor, attn_factor, beta_fast, beta_slow
-                            );
-
-                    Kcur = ggml_rope_ext(
-                            ctx0, Kcur, inp_pos, rope_factors,
-                            n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                            ext_factor, attn_factor, beta_fast, beta_slow
-                            );
-                } else if (inp_attn_scale) {
-                    Qcur = ggml_mul(ctx0, Qcur, inp_attn_scale);
-                }
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                if (use_rope && hparams.use_kq_norm) {
-                    // Llama4TextL2Norm
-                    Qcur = ggml_rms_norm(ctx0, Qcur, hparams.f_norm_rms_eps);
-                    Kcur = ggml_rms_norm(ctx0, Kcur, hparams.f_norm_rms_eps);
-                    cb(Qcur, "Qcur_normed", il);
-                    cb(Kcur, "Kcur_normed", il);
-                }
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, kq_scale, il);
-                cb(cur, "attn_out", il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed-forward network (non-MoE)
-            if (model.layers[il].ffn_gate_inp == nullptr) {
-                cur = build_norm(ffn_inp,
-                        model.layers[il].ffn_norm, NULL,
-                        LLM_NORM_RMS, il);
-                cb(cur, "ffn_norm", il);
-
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up,   model.layers[il].ffn_up_b,   NULL,
-                        model.layers[il].ffn_gate, model.layers[il].ffn_gate_b, NULL,
-                        model.layers[il].ffn_down, model.layers[il].ffn_down_b, NULL,
-                        NULL,
-                        LLM_FFN_SILU, LLM_FFN_PAR, il);
-                cb(cur, "ffn_out", il);
-            } else {
-                ggml_tensor * ffn_inp_normed = build_norm(ffn_inp,
-                        model.layers[il].ffn_norm, NULL,
-                        LLM_NORM_RMS, il);
-                cb(cur, "ffn_norm", il);
-
-                ggml_tensor * moe_out = build_moe_ffn(ffn_inp_normed,
-                        model.layers[il].ffn_gate_inp,
-                        model.layers[il].ffn_up_exps,
-                        model.layers[il].ffn_gate_exps,
-                        model.layers[il].ffn_down_exps,
-                        nullptr,
-                        n_expert, n_expert_used,
-                        LLM_FFN_SILU, false,
-                        false, 0.0,
-                        LLAMA_EXPERT_GATING_FUNC_TYPE_SIGMOID,
-                        il);
-
-                // Shared experts
-                ggml_tensor * shexp_out = build_ffn(ffn_inp_normed,
-                    model.layers[il].ffn_up_shexp,   NULL, NULL,
-                    model.layers[il].ffn_gate_shexp, NULL, NULL,
-                    model.layers[il].ffn_down_shexp, NULL, NULL,
-                    NULL,
-                    LLM_FFN_SILU, LLM_FFN_PAR, il);
-                cb(shexp_out, "ffn_moe_shexp", il);
-
-                cur = ggml_add(ctx0, moe_out, shexp_out);
-                cb(cur, "ffn_moe_out_merged", il);
-            }
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-            cb(cur, "ffn_out", il);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_deci : public llm_graph_context {
-    llm_build_deci(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        const float kq_scale = hparams.f_attention_scale == 0.0f ? 1.0f/sqrtf(float(n_embd_head)) : hparams.f_attention_scale;
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-            const int64_t n_head_kv = hparams.n_head_kv(il);
-            const int64_t n_head    = hparams.n_head(il);
-            const int64_t n_ff      = hparams.n_ff(il);
-
-            if (n_head == 0) {
-                // attention-free layer of Llama-3_1-Nemotron-51B
-                cur = inpL;
-            } else {
-                // norm
-                cur = build_norm(inpL,
-                        model.layers[il].attn_norm, NULL,
-                        LLM_NORM_RMS, il);
-                cb(cur, "attn_norm", il);
-            }
-
-            if (n_head > 0 && n_head_kv == 0) {
-                // "linear attention" of Llama-3_1-Nemotron-51B
-                cur = build_lora_mm(model.layers[il].wo, cur);
-                cb(cur, "wo", il);
-            } else if (n_head > 0) {
-                // self-attention
-                // rope freq factors for llama3; may return nullptr for llama2 and other models
-                ggml_tensor * rope_factors = model.get_rope_factors(cparams, il);
-
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-                if (model.layers[il].bq) {
-                    Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
-                    cb(Qcur, "Qcur", il);
-                }
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-                if (model.layers[il].bk) {
-                    Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
-                    cb(Kcur, "Kcur", il);
-                }
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-                if (model.layers[il].bv) {
-                    Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
-                    cb(Vcur, "Vcur", il);
-                }
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, rope_factors,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, rope_factors,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, kq_scale, il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            // FFN-free layer of Llama-3_1-Nemotron-Ultra-253B
-            if (n_ff == 0) {
-                continue;
-            }
-
-            // modified to support attention-free layer of Llama-3_1-Nemotron-51B
-            ggml_tensor * ffn_inp = cur;
-            if (n_head > 0) {
-                ffn_inp = ggml_add(ctx0, cur, inpSA);
-                cb(ffn_inp, "ffn_inp", il);
-            }
-
-            // feed-forward network
-            if (model.layers[il].ffn_gate_inp == nullptr) {
-                cur = build_norm(ffn_inp,
-                        model.layers[il].ffn_norm, NULL,
-                        LLM_NORM_RMS, il);
-                cb(cur, "ffn_norm", il);
-
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up,   model.layers[il].ffn_up_b,   NULL,
-                        model.layers[il].ffn_gate, model.layers[il].ffn_gate_b, NULL,
-                        model.layers[il].ffn_down, model.layers[il].ffn_down_b, NULL,
-                        NULL,
-                        LLM_FFN_SILU, LLM_FFN_PAR, il);
-                cb(cur, "ffn_out", il);
-            }
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-            cb(cur, "ffn_out", il);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_baichuan : public llm_graph_context {
-    llm_build_baichuan(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = model.type == LLM_TYPE_7B ? build_inp_pos() : nullptr;
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                switch (model.type) {
-                    case LLM_TYPE_7B:
-                        Qcur = ggml_rope_ext(
-                                ctx0, Qcur, inp_pos, nullptr,
-                                n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                                ext_factor, attn_factor, beta_fast, beta_slow
-                                );
-                        Kcur = ggml_rope_ext(
-                                ctx0, Kcur, inp_pos, nullptr,
-                                n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                                ext_factor, attn_factor, beta_fast, beta_slow
-                                );
-                        break;
-                    case LLM_TYPE_13B:
-                        break;
-                    default:
-                        GGML_ABORT("fatal error");
-                }
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, NULL,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed-forward network
-            {
-                cur = build_norm(ffn_inp,
-                        model.layers[il].ffn_norm, NULL,
-                        LLM_NORM_RMS, il);
-                cb(cur, "ffn_norm", il);
-
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up,   NULL, NULL,
-                        model.layers[il].ffn_gate, NULL, NULL,
-                        model.layers[il].ffn_down, NULL, NULL,
-                        NULL,
-                        LLM_FFN_SILU, LLM_FFN_PAR, il);
-                cb(cur, "ffn_out", il);
-            }
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_xverse : public llm_graph_context {
-    llm_build_xverse(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, NULL,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed-forward network
-            {
-                cur = build_norm(ffn_inp,
-                        model.layers[il].ffn_norm, NULL,
-                        LLM_NORM_RMS, il);
-                cb(cur, "ffn_norm", il);
-
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up,   NULL, NULL,
-                        model.layers[il].ffn_gate, NULL, NULL,
-                        model.layers[il].ffn_down, NULL, NULL,
-                        NULL,
-                        LLM_FFN_SILU, LLM_FFN_PAR, il);
-                cb(cur, "ffn_out", il);
-            }
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur, model.output_norm, NULL, LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_falcon : public llm_graph_context {
-    llm_build_falcon(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-        const int64_t n_embd_gqa  = hparams.n_embd_v_gqa();
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * attn_norm;
-
-            attn_norm = build_norm(inpL,
-                    model.layers[il].attn_norm,
-                    model.layers[il].attn_norm_b,
-                    LLM_NORM, il);
-            cb(attn_norm, "attn_norm", il);
-
-            // self-attention
-            {
-                if (model.layers[il].attn_norm_2) {
-                    // Falcon-40B
-                    cur = build_norm(inpL,
-                            model.layers[il].attn_norm_2,
-                            model.layers[il].attn_norm_2_b,
-                            LLM_NORM, il);
-                    cb(cur, "attn_norm_2", il);
-                } else {
-                    cur = attn_norm;
-                }
-
-                cur = build_lora_mm(model.layers[il].wqkv, cur);
-                cb(cur, "wqkv", il);
-
-                ggml_tensor * Qcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head,    n_tokens, n_embd_head*sizeof(float), cur->nb[1], 0*sizeof(float)*(n_embd));
-                ggml_tensor * Kcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd));
-                ggml_tensor * Vcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd + n_embd_gqa));
-
-                // using mode = 2 for neox mode
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, NULL,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur       = ggml_get_rows(ctx0,       cur, inp_out_ids);
-                inpL      = ggml_get_rows(ctx0,      inpL, inp_out_ids);
-                attn_norm = ggml_get_rows(ctx0, attn_norm, inp_out_ids);
-            }
-
-            ggml_tensor * ffn_inp = cur;
-
-            // feed forward
-            {
-                cur = build_ffn(attn_norm, // !! use the attn norm, not the result
-                        model.layers[il].ffn_up,   NULL, NULL,
-                        NULL,                      NULL, NULL,
-                        model.layers[il].ffn_down, NULL, NULL,
-                        NULL,
-                        LLM_FFN_GELU, LLM_FFN_SEQ, il);
-                cb(cur, "ffn_out", il);
-            }
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-            cur = ggml_add(ctx0, cur, inpL);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        // norm
-        cur = build_norm(cur,
-                model.output_norm,
-                model.output_norm_b,
-                LLM_NORM, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_grok : public llm_graph_context {
-    llm_build_grok(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-
-            // self-attention
-            {
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-                if (model.layers[il].bq) {
-                    Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
-                    cb(Qcur, "Qcur", il);
-                }
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-                if (model.layers[il].bk) {
-                    Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
-                    cb(Kcur, "Kcur", il);
-                }
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-                if (model.layers[il].bv) {
-                    Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
-                    cb(Vcur, "Vcur", il);
-                }
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f, il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            cur = build_norm(cur,
-                    model.layers[il].attn_out_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_out_norm", il);
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed-forward network
-            cur = build_norm(ffn_inp,
-                    model.layers[il].ffn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-
-            // MoE branch
-            ggml_tensor * moe_out = build_moe_ffn(cur,
-                    model.layers[il].ffn_gate_inp,
-                    model.layers[il].ffn_up_exps,
-                    model.layers[il].ffn_gate_exps,
-                    model.layers[il].ffn_down_exps,
-                    nullptr,
-                    n_expert, n_expert_used,
-                    LLM_FFN_GELU, true,
-                    false, 0.0,
-                    LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
-                    il);
-            cb(moe_out, "ffn_moe_out", il);
-
-            if (model.layers[il].ffn_up) {
-                ggml_tensor * ffn_out = build_ffn(cur,
-                        model.layers[il].ffn_up,   NULL, NULL,
-                        model.layers[il].ffn_gate, NULL, NULL,
-                        model.layers[il].ffn_down, NULL, NULL,
-                        NULL,
-                        LLM_FFN_GELU, LLM_FFN_PAR, il);
-                cb(ffn_out, "ffn_out", il);
-
-                cur = ggml_scale(ctx0, ggml_add(ctx0, ffn_out, moe_out), std::sqrt(2) / 2);
-                cb(cur, "ffn_out", il);
-            } else {
-                cur = moe_out;
-            }
-
-            cur = build_norm(cur,
-                    model.layers[il].ffn_post_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "ffn_post_norm", il);
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-            cb(cur, "ffn_out", il);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        cur = ggml_scale(ctx0, cur, hparams.f_logit_scale);
-
-        // final logit soft-capping
-        if (hparams.f_final_logit_softcapping) {
-            cur = ggml_scale(ctx0, cur, 1.0f / hparams.f_final_logit_softcapping);
-            cur = ggml_tanh(ctx0, cur);
-            cur = ggml_scale(ctx0, cur, hparams.f_final_logit_softcapping);
-        }
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_dbrx : public llm_graph_context {
-    llm_build_dbrx(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-        const int64_t n_embd_gqa  = hparams.n_embd_v_gqa();
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                ggml_tensor * Qcur = nullptr;
-                ggml_tensor * Kcur = nullptr;
-                ggml_tensor * Vcur = nullptr;
-
-                cur = build_lora_mm(model.layers[il].wqkv, cur);
-                cb(cur, "wqkv", il);
-
-                cur = ggml_clamp(ctx0, cur, -hparams.f_clamp_kqv, hparams.f_clamp_kqv);
-                cb(cur, "wqkv_clamped", il);
-
-                Qcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head,    n_tokens, n_embd_head*sizeof(float), cur->nb[1], 0*sizeof(float)*(n_embd));
-                Kcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd));
-                Vcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd + n_embd_gqa));
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, NULL,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed-forward network
-            // MoE branch
-            cur = build_norm(ffn_inp,
-                    model.layers[il].attn_out_norm, NULL,
-                    LLM_NORM, il);
-            cb(cur, "attn_out_norm", il);
-
-            cur = build_moe_ffn(cur,
-                    model.layers[il].ffn_gate_inp,
-                    model.layers[il].ffn_up_exps,
-                    model.layers[il].ffn_gate_exps,
-                    model.layers[il].ffn_down_exps,
-                    nullptr,
-                    n_expert, n_expert_used,
-                    LLM_FFN_SILU, true,
-                    false, 0.0,
-                    LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
-                    il);
-            cb(cur, "ffn_moe_out", il);
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-            cb(cur, "ffn_out", il);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_starcoder : public llm_graph_context {
-    llm_build_starcoder(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-        const int64_t n_embd_gqa  = hparams.n_embd_v_gqa();
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        ggml_tensor * pos = ggml_get_rows(ctx0, model.pos_embd, inp_pos);
-        cb(pos, "pos_embd", -1);
-
-        inpL = ggml_add(ctx0, inpL, pos);
-        cb(inpL, "inpL", -1);
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm,
-                    model.layers[il].attn_norm_b,
-                    LLM_NORM, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                cur = build_lora_mm(model.layers[il].wqkv, cur);
-                cb(cur, "wqkv", il);
-
-                cur = ggml_add(ctx0, cur, model.layers[il].bqkv);
-                cb(cur, "bqkv", il);
-
-                ggml_tensor * Qcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head,    n_tokens, n_embd_head*sizeof(float), cur->nb[1], 0*sizeof(float)*(n_embd));
-                ggml_tensor * Kcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd));
-                ggml_tensor * Vcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd + n_embd_gqa));
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur  = ggml_get_rows(ctx0,  cur, inp_out_ids);
-                inpL = ggml_get_rows(ctx0, inpL, inp_out_ids);
-            }
-
-            // add the input
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpL);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // FF
-            {
-                cur = build_norm(ffn_inp,
-                        model.layers[il].ffn_norm,
-                        model.layers[il].ffn_norm_b,
-                        LLM_NORM, il);
-                cb(cur, "ffn_norm", il);
-
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up,   model.layers[il].ffn_up_b,   NULL,
-                        NULL,                      NULL,                        NULL,
-                        model.layers[il].ffn_down, model.layers[il].ffn_down_b, NULL,
-                        NULL,
-                        LLM_FFN_GELU, LLM_FFN_SEQ, il);
-                cb(cur, "ffn_out", il);
-            }
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = build_norm(inpL,
-                model.output_norm,
-                model.output_norm_b,
-                LLM_NORM, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_refact : public llm_graph_context {
-    llm_build_refact(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, NULL,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed-forward network
-            {
-                cur = build_norm(ffn_inp,
-                        model.layers[il].ffn_norm, NULL,
-                        LLM_NORM_RMS, il);
-                cb(cur, "ffn_norm", il);
-
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up,   NULL, NULL,
-                        model.layers[il].ffn_gate, NULL, NULL,
-                        model.layers[il].ffn_down, NULL, NULL,
-                        NULL,
-                        LLM_FFN_SILU, LLM_FFN_PAR, il);
-                cb(cur, "ffn_out", il);
-            }
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_bert : public llm_graph_context {
-    llm_build_bert(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-        const int64_t n_embd_gqa  = hparams.n_embd_v_gqa();
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-        ggml_tensor * inp_pos = nullptr;
-
-        if (model.arch != LLM_ARCH_JINA_BERT_V2) {
-            inp_pos = build_inp_pos();
-        }
-
-        // construct input embeddings (token, type, position)
-        inpL = build_inp_embd(model.tok_embd);
-
-        // token types are hardcoded to zero ("Sentence A")
-        if (model.type_embd) {
-            ggml_tensor * type_row0 = ggml_view_1d(ctx0, model.type_embd, n_embd, 0);
-            inpL = ggml_add(ctx0, inpL, type_row0);
-        }
-        if (model.arch == LLM_ARCH_BERT) {
-            inpL = ggml_add(ctx0, ggml_get_rows(ctx0, model.pos_embd, inp_pos), inpL);
-        }
-        cb(inpL, "inp_embd", -1);
-
-        // embed layer norm
-        inpL = build_norm(inpL, model.tok_norm, model.tok_norm_b, LLM_NORM, -1);
-        cb(inpL, "inp_norm", -1);
-
-        auto * inp_attn = build_attn_inp_no_cache();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * cur = inpL;
-
-            {
-                ggml_tensor * Qcur;
-                ggml_tensor * Kcur;
-                ggml_tensor * Vcur;
-
-                // self-attention
-                if (model.layers[il].wqkv) {
-                    cur = build_lora_mm(model.layers[il].wqkv, cur);
-                    cb(cur, "wqkv", il);
-
-                    if (model.layers[il].bqkv) {
-                        cur = ggml_add(ctx0, cur, model.layers[il].bqkv);
-                        cb(cur, "bqkv", il);
-                    }
-
-                    Qcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head,    n_tokens, n_embd_head*sizeof(float), cur->nb[1], 0*sizeof(float)*(n_embd));
-                    Kcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd));
-                    Vcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd + n_embd_gqa));
-                } else {
-                    Qcur = ggml_add(ctx0, build_lora_mm(model.layers[il].wq, cur), model.layers[il].bq);
-                    Kcur = ggml_add(ctx0, build_lora_mm(model.layers[il].wk, cur), model.layers[il].bk);
-                    Vcur = ggml_add(ctx0, build_lora_mm(model.layers[il].wv, cur), model.layers[il].bv);
-
-                    Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                    Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                    Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-                }
-
-                if (model.layers[il].attn_q_norm) {
-                    Qcur = ggml_reshape_2d(ctx0, Qcur, n_embd_head*n_head, n_tokens);
-
-                    Qcur = build_norm(Qcur,
-                            model.layers[il].attn_q_norm,
-                            model.layers[il].attn_q_norm_b,
-                            LLM_NORM, il);
-
-                    Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                }
-
-                if (model.layers[il].attn_k_norm) {
-                    Kcur = ggml_reshape_2d(ctx0, Kcur, n_embd_head*n_head_kv, n_tokens);
-
-                    Kcur = build_norm(Kcur,
-                            model.layers[il].attn_k_norm,
-                            model.layers[il].attn_k_norm_b,
-                            LLM_NORM, il);
-
-                    Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                }
-
-                // RoPE
-                if (model.arch == LLM_ARCH_NOMIC_BERT || model.arch == LLM_ARCH_NOMIC_BERT_MOE || model.arch == LLM_ARCH_JINA_BERT_V3) {
-                    Qcur = ggml_rope_ext(
-                            ctx0, Qcur, inp_pos, nullptr,
-                            n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                            ext_factor, attn_factor, beta_fast, beta_slow
-                            );
-
-                    Kcur = ggml_rope_ext(
-                            ctx0, Kcur, inp_pos, nullptr,
-                            n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                            ext_factor, attn_factor, beta_fast, beta_slow
-                            );
-                }
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-                cb(cur, "kqv_out", il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur  = ggml_get_rows(ctx0,  cur, inp_out_ids);
-                inpL = ggml_get_rows(ctx0, inpL, inp_out_ids);
-            }
-
-            // re-add the layer input
-            cur = ggml_add(ctx0, cur, inpL);
-
-            // attention layer norm
-            cur = build_norm(cur, model.layers[il].attn_out_norm, model.layers[il].attn_out_norm_b, LLM_NORM, il);
-
-            if (model.layers[il].attn_norm_2 != nullptr) {
-                cur = ggml_add(ctx0, cur, inpL); // re-add the layer input
-                cur = build_norm(cur, model.layers[il].attn_norm_2, model.layers[il].attn_norm_2_b, LLM_NORM, il);
-            }
-
-            ggml_tensor * ffn_inp = cur;
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed-forward network
-            if (hparams.moe_every_n_layers > 0 && il % hparams.moe_every_n_layers == 1) {
-                // MoE branch
-                cur = build_moe_ffn(cur,
-                        model.layers[il].ffn_gate_inp,
-                        model.layers[il].ffn_up_exps,
-                        nullptr,
-                        model.layers[il].ffn_down_exps,
-                        nullptr,
-                        hparams.n_expert,
-                        hparams.n_expert_used,
-                        LLM_FFN_GELU,
-                        false, false,
-                        0.0f,
-                        LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX, il);
-                cb(cur, "ffn_moe_out", il);
-            } else if (model.arch == LLM_ARCH_BERT || model.arch == LLM_ARCH_NOMIC_BERT_MOE || model.arch == LLM_ARCH_JINA_BERT_V3) {
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up,   model.layers[il].ffn_up_b,   NULL,
-                        NULL,                      NULL,                        NULL,
-                        model.layers[il].ffn_down, model.layers[il].ffn_down_b, NULL,
-                        NULL,
-                        LLM_FFN_GELU, LLM_FFN_SEQ, il);
-                cb(cur, "ffn_out", il);
-            } else if (model.arch == LLM_ARCH_JINA_BERT_V2) {
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up,   NULL,                        NULL,
-                        model.layers[il].ffn_gate, NULL,                        NULL,
-                        model.layers[il].ffn_down, model.layers[il].ffn_down_b, NULL,
-                        NULL,
-                        model.layers[il].ffn_gate ? LLM_FFN_GELU : LLM_FFN_GEGLU, LLM_FFN_PAR, il);
-                cb(cur, "ffn_out", il);
-            } else {
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up,   NULL, NULL,
-                        model.layers[il].ffn_gate, NULL, NULL,
-                        model.layers[il].ffn_down, NULL, NULL,
-                        NULL,
-                        LLM_FFN_SILU, LLM_FFN_PAR, il);
-                cb(cur, "ffn_out", il);
-            }
-
-            // attentions bypass the intermediate layer
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            // output layer norm
-            cur = build_norm(cur, model.layers[il].layer_out_norm, model.layers[il].layer_out_norm_b, LLM_NORM, il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cb(cur, "result_embd", -1);
-        res->t_embd = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_neo_bert : public llm_graph_context {
-    llm_build_neo_bert(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-        const int64_t n_embd_gqa  = hparams.n_embd_v_gqa();
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        // construct input embeddings (token, type, position)
-        inpL = build_inp_embd(model.tok_embd);
-        cb(inpL, "inp_embd", -1);
-
-        auto * inp_attn = build_attn_inp_no_cache();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * cur = inpL;
-
-            // pre-norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-
-            {
-                ggml_tensor * Qcur;
-                ggml_tensor * Kcur;
-                ggml_tensor * Vcur;
-
-                // self-attention
-                cur = build_lora_mm(model.layers[il].wqkv, cur);
-                cb(cur, "wqkv", il);
-
-                Qcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head,    n_tokens, n_embd_head*sizeof(float), cur->nb[1], 0*sizeof(float)*(n_embd));
-                Kcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd));
-                Vcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd + n_embd_gqa));
-
-                // RoPE
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, nullptr,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-                cb(cur, "kqv_out", il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur  = ggml_get_rows(ctx0,  cur, inp_out_ids);
-                inpL = ggml_get_rows(ctx0, inpL, inp_out_ids);
-            }
-
-            // re-add the layer input
-            cur = ggml_add(ctx0, cur, inpL);
-
-            ggml_tensor * ffn_inp = cur;
-            cb(ffn_inp, "ffn_inp", il);
-
-            // pre-norm
-            cur = build_norm(ffn_inp,
-                    model.layers[il].ffn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-
-            // feed-forward network
-            cur = build_ffn(cur,
-                    model.layers[il].ffn_up,
-                    NULL, NULL, NULL, NULL, NULL,
-                    model.layers[il].ffn_down,
-                    NULL, NULL, NULL,
-                    LLM_FFN_SWIGLU, LLM_FFN_SEQ, il);
-
-            // attentions bypass the intermediate layer
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm_enc, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_embd", -1);
-        res->t_embd = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_bloom : public llm_graph_context {
-    llm_build_bloom(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-        const int64_t n_embd_gqa  = hparams.n_embd_v_gqa();
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        inpL = build_norm(inpL,
-                model.tok_norm,
-                model.tok_norm_b,
-                LLM_NORM, -1);
-        cb(inpL, "inp_norm", -1);
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm,
-                    model.layers[il].attn_norm_b,
-                    LLM_NORM, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                cur = build_lora_mm(model.layers[il].wqkv, cur);
-                cb(cur, "wqkv", il);
-
-                cur = ggml_add(ctx0, cur, model.layers[il].bqkv);
-                cb(cur, "bqkv", il);
-
-                ggml_tensor * Qcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head,    n_tokens, n_embd_head*sizeof(float), cur->nb[1], 0*sizeof(float)*(n_embd));
-                ggml_tensor * Kcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd));
-                ggml_tensor * Vcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd + n_embd_gqa));
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur  = ggml_get_rows(ctx0,  cur, inp_out_ids);
-                inpL = ggml_get_rows(ctx0, inpL, inp_out_ids);
-            }
-
-            // Add the input
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpL);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // FF
-            {
-                cur = build_norm(ffn_inp,
-                        model.layers[il].ffn_norm,
-                        model.layers[il].ffn_norm_b,
-                        LLM_NORM, il);
-                cb(cur, "ffn_norm", il);
-
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up,   model.layers[il].ffn_up_b,   NULL,
-                        NULL,                      NULL,                        NULL,
-                        model.layers[il].ffn_down, model.layers[il].ffn_down_b, NULL,
-                        NULL,
-                        LLM_FFN_GELU, LLM_FFN_SEQ, il);
-                cb(cur, "ffn_out", il);
-            }
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = build_norm(inpL,
-                model.output_norm,
-                model.output_norm_b,
-                LLM_NORM, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_mpt : public llm_graph_context {
-    llm_build_mpt(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-        const int64_t n_embd_gqa  = hparams.n_embd_v_gqa();
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-
-        ggml_tensor * cur;
-        ggml_tensor * pos;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        if (model.pos_embd) {
-            // inp_pos - contains the positions
-            ggml_tensor * inp_pos = build_inp_pos();
-            pos = ggml_get_rows(ctx0, model.pos_embd, inp_pos);
-            cb(pos, "pos_embd", -1);
-
-            inpL = ggml_add(ctx0, inpL, pos);
-            cb(inpL, "inpL", -1);
-        }
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * attn_norm;
-
-            attn_norm = build_norm(inpL,
-                    model.layers[il].attn_norm,
-                    model.layers[il].attn_norm_b,
-                    LLM_NORM, il);
-            cb(attn_norm, "attn_norm", il);
-
-            // self-attention
-            {
-                cur = attn_norm;
-
-                cur = build_lora_mm(model.layers[il].wqkv, cur);
-                cb(cur, "wqkv", il);
-
-                if (model.layers[il].bqkv){
-                    cur = ggml_add(ctx0, cur, model.layers[il].bqkv);
-                    cb(cur, "bqkv", il);
-                }
-
-                if (hparams.f_clamp_kqv > 0.0f) {
-                    cur = ggml_clamp(ctx0, cur, -hparams.f_clamp_kqv, hparams.f_clamp_kqv);
-                    cb(cur, "wqkv_clamped", il);
-                }
-
-                ggml_tensor * Qcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head,    n_tokens, n_embd_head*sizeof(float), cur->nb[1], 0*sizeof(float)*(n_embd));
-                ggml_tensor * Kcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd));
-                ggml_tensor * Vcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd + n_embd_gqa));
-
-                // Q/K Layernorm
-                if (model.layers[il].attn_q_norm) {
-                    Qcur = ggml_reshape_2d(ctx0, Qcur, n_embd_head*n_head,    n_tokens);
-                    Kcur = ggml_reshape_2d(ctx0, Kcur, n_embd_head*n_head_kv, n_tokens);
-
-                    Qcur = build_norm(Qcur,
-                            model.layers[il].attn_q_norm,
-                            model.layers[il].attn_q_norm_b,
-                            LLM_NORM, il);
-
-                    Kcur = build_norm(Kcur,
-                            model.layers[il].attn_k_norm,
-                            model.layers[il].attn_k_norm_b,
-                            LLM_NORM, il);
-
-                    Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                    Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                }
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur  = ggml_get_rows(ctx0,  cur, inp_out_ids);
-                inpL = ggml_get_rows(ctx0, inpL, inp_out_ids);
-            }
-
-            // Add the input
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpL);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed forward
-            {
-                cur = build_norm(ffn_inp,
-                        model.layers[il].ffn_norm,
-                        model.layers[il].ffn_norm_b,
-                        LLM_NORM, il);
-                cb(cur, "ffn_norm", il);
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up,   model.layers[il].ffn_up_b,   NULL,
-                        NULL,                      NULL,                        NULL,
-                        model.layers[il].ffn_down, model.layers[il].ffn_down_b, NULL,
-                        model.layers[il].ffn_act,
-                        LLM_FFN_GELU, LLM_FFN_SEQ, il);
-                cb(cur, "ffn_out", il);
-            }
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm,
-                model.output_norm_b,
-                LLM_NORM, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_stablelm : public llm_graph_context {
-    llm_build_stablelm(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm,
-                    model.layers[il].attn_norm_b,
-                    LLM_NORM, il);
-            cb(cur, "attn_norm", il);
-
-            ggml_tensor * inpSA = cur;
-
-            // self-attention
-            {
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-                if (model.layers[il].bq) {
-                    Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
-                    cb(Qcur, "Qcur", il);
-                }
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-                if (model.layers[il].bk) {
-                    Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
-                    cb(Kcur, "Kcur", il);
-                }
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-                if (model.layers[il].bv) {
-                    Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
-                    cb(Vcur, "Vcur", il);
-                }
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                if (model.layers[il].attn_q_norm) {
-                    Qcur = build_norm(Qcur,
-                            model.layers[il].attn_q_norm,
-                            NULL,
-                            LLM_NORM, il);
-                    cb(Qcur, "Qcur", il);
-                }
-
-                if (model.layers[il].attn_k_norm) {
-                    Kcur = build_norm(Kcur,
-                            model.layers[il].attn_k_norm,
-                            NULL,
-                            LLM_NORM, il);
-                    cb(Kcur, "Kcur", il);
-                }
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, NULL,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpL  = ggml_get_rows(ctx0,  inpL, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpL);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed-forward network
-            {
-                if (model.layers[il].ffn_norm) {
-                    cur = build_norm(ffn_inp,
-                            model.layers[il].ffn_norm,
-                            model.layers[il].ffn_norm_b,
-                            LLM_NORM, il);
-                    cb(cur, "ffn_norm", il);
-                } else {
-                    // parallel residual
-                    cur = inpSA;
-                }
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up,   NULL, NULL,
-                        model.layers[il].ffn_gate, NULL, NULL,
-                        model.layers[il].ffn_down, NULL, NULL,
-                        NULL,
-                        LLM_FFN_SILU, LLM_FFN_PAR, il);
-                cb(cur, "ffn_out", il);
-            }
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm,
-                model.output_norm_b,
-                LLM_NORM, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_qwen : public llm_graph_context {
-    llm_build_qwen(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                cur = build_lora_mm(model.layers[il].wqkv, cur);
-                cb(cur, "wqkv", il);
-
-                cur = ggml_add(ctx0, cur, model.layers[il].bqkv);
-                cb(cur, "bqkv", il);
-
-                ggml_tensor * Qcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head,    n_tokens, n_embd_head*sizeof(float), cur->nb[1], 0*sizeof(float)*(n_embd));
-                ggml_tensor * Kcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd));
-                ggml_tensor * Vcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 2*sizeof(float)*(n_embd));
-
-                // using mode = 2 for neox mode
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, NULL,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed-forward forward
-            {
-                cur = build_norm(ffn_inp,
-                        model.layers[il].ffn_norm, NULL,
-                        LLM_NORM_RMS, il);
-                cb(cur, "ffn_norm", il);
-
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up,   NULL, NULL,
-                        model.layers[il].ffn_gate, NULL, NULL,
-                        model.layers[il].ffn_down, NULL, NULL,
-                        NULL,
-                        LLM_FFN_SILU, LLM_FFN_PAR, il);
-                cb(cur, "ffn_out", il);
-            }
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_qwen2 : public llm_graph_context {
-    llm_build_qwen2(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
-                cb(Qcur, "Qcur", il);
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
-                cb(Kcur, "Kcur", il);
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
-                cb(Vcur, "Vcur", il);
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed-forward network
-            cur = build_norm(ffn_inp,
-                    model.layers[il].ffn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-
-            cur = build_ffn(cur,
-                    model.layers[il].ffn_up,   NULL, NULL,
-                    model.layers[il].ffn_gate, NULL, NULL,
-                    model.layers[il].ffn_down, NULL, NULL,
-                    NULL,
-                    LLM_FFN_SILU, LLM_FFN_PAR, il);
-            cb(cur, "ffn_out", il);
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        if (model.output_b != nullptr) {
-            cur = ggml_add(ctx0, cur, model.output_b);
-        }
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_dream : public llm_graph_context {
-    llm_build_dream(const llama_model & model, const llm_graph_params & params) :
-        llm_graph_context(params) {
-        //copied from qwen2
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_no_cache();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            // norm
-            cur = build_norm(inpL, model.layers[il].attn_norm, NULL, LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                Qcur               = ggml_add(ctx0, Qcur, model.layers[il].bq);
-                cb(Qcur, "Qcur", il);
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                Kcur               = ggml_add(ctx0, Kcur, model.layers[il].bk);
-                cb(Kcur, "Kcur", il);
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                Vcur               = ggml_add(ctx0, Vcur, model.layers[il].bv);
-                cb(Vcur, "Vcur", il);
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head, n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = ggml_rope_ext(ctx0, Qcur, inp_pos, nullptr, n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                                     ext_factor, attn_factor, beta_fast, beta_slow);
-
-                Kcur = ggml_rope_ext(ctx0, Kcur, inp_pos, nullptr, n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                                     ext_factor, attn_factor, beta_fast, beta_slow);
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f / sqrtf(float(n_embd_head)), il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0, cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed-forward network
-            cur = build_norm(ffn_inp, model.layers[il].ffn_norm, NULL, LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-
-            cur = build_ffn(cur, model.layers[il].ffn_up, NULL, NULL, model.layers[il].ffn_gate, NULL, NULL,
-                            model.layers[il].ffn_down, NULL, NULL, NULL, LLM_FFN_SILU, LLM_FFN_PAR, il);
-            cb(cur, "ffn_out", il);
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur, model.output_norm, NULL, LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_llada : public llm_graph_context {
-    llm_build_llada(const llama_model & model, const llm_graph_params & params) :
-        llm_graph_context(params) {
-        // LLaDA is similar to LLaMA but uses non-causal attention for diffusion
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        // Non-causal attention for diffusion
-        auto * inp_attn = build_attn_inp_no_cache();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            // norm
-            cur = build_norm(inpL, model.layers[il].attn_norm, NULL, LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                // compute separate Q, K, V projections without bias, matching LLaDALlamaBlock
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head, n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = ggml_rope_ext(ctx0, Qcur, inp_pos, nullptr, n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                                     ext_factor, attn_factor, beta_fast, beta_slow);
-
-                Kcur = ggml_rope_ext(ctx0, Kcur, inp_pos, nullptr, n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                                     ext_factor, attn_factor, beta_fast, beta_slow);
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, NULL,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f / sqrtf(float(n_embd_head)), il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0, cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed-forward network
-            cur = build_norm(ffn_inp, model.layers[il].ffn_norm, NULL, LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-
-            cur = build_ffn(cur, model.layers[il].ffn_up, NULL, NULL, model.layers[il].ffn_gate, NULL, NULL,
-                            model.layers[il].ffn_down, NULL, NULL, NULL, LLM_FFN_SILU, LLM_FFN_PAR, il);
-            cb(cur, "ffn_out", il);
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur, model.output_norm, NULL, LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_qwen2vl : public llm_graph_context {
-    llm_build_qwen2vl(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        int sections[4];
-        std::copy(std::begin(hparams.rope_sections), std::begin(hparams.rope_sections) + 4, sections);
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
-                cb(Qcur, "Qcur", il);
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
-                cb(Kcur, "Kcur", il);
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
-                cb(Vcur, "Vcur", il);
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = ggml_rope_multi(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, sections, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_multi(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, sections, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed-forward network
-            cur = build_norm(ffn_inp,
-                    model.layers[il].ffn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-
-            cur = build_ffn(cur,
-                    model.layers[il].ffn_up,   NULL, NULL,
-                    model.layers[il].ffn_gate, NULL, NULL,
-                    model.layers[il].ffn_down, NULL, NULL,
-                    NULL,
-                    LLM_FFN_SILU, LLM_FFN_PAR, il);
-            cb(cur, "ffn_out", il);
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_qwen2moe : public llm_graph_context {
-    llm_build_qwen2moe(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self_attention
-            {
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-                if (model.layers[il].bq) {
-                    Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
-                    cb(Qcur, "Qcur", il);
-                }
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-                if (model.layers[il].bk) {
-                    Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
-                    cb(Kcur, "Kcur", il);
-                }
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-                if (model.layers[il].bv) {
-                    Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
-                    cb(Vcur, "Vcur", il);
-                }
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // MoE branch
-            cur = build_norm(ffn_inp,
-                    model.layers[il].ffn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-
-            ggml_tensor * moe_out =
-                build_moe_ffn(cur,
-                        model.layers[il].ffn_gate_inp,
-                        model.layers[il].ffn_up_exps,
-                        model.layers[il].ffn_gate_exps,
-                        model.layers[il].ffn_down_exps,
-                        nullptr,
-                        n_expert, n_expert_used,
-                        LLM_FFN_SILU, false,
-                        false, 0.0,
-                        LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
-                        il);
-            cb(moe_out, "ffn_moe_out", il);
-
-            // FFN shared expert
-            {
-                ggml_tensor * cur_gate_inp = build_lora_mm(model.layers[il].ffn_gate_inp_shexp, cur);
-                cb(cur_gate_inp, "ffn_shexp_gate_inp", il);
-
-                // sigmoid
-                ggml_tensor * cur_gate = ggml_div(ctx0, ggml_silu(ctx0, cur_gate_inp), cur_gate_inp);
-                cb(cur_gate, "ffn_shexp_gate", il);
-
-                ggml_tensor * cur_ffn = build_ffn(cur,
-                        model.layers[il].ffn_up_shexp,   NULL, NULL,
-                        model.layers[il].ffn_gate_shexp, NULL, NULL,
-                        model.layers[il].ffn_down_shexp, NULL, NULL,
-                        NULL,
-                        LLM_FFN_SILU, LLM_FFN_PAR, il);
-                cb(cur_ffn, "ffn_shexp", il);
-
-                ggml_tensor * ffn_shexp_out = ggml_mul(ctx0, cur_ffn, cur_gate);
-                cb(ffn_shexp_out, "ffn_shexp_out", il);
-
-                moe_out = ggml_add(ctx0, moe_out, ffn_shexp_out);
-                cb(moe_out, "ffn_out", il);
-
-                cur = moe_out;
-            }
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_qwen3 : public llm_graph_context {
-    llm_build_qwen3(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL, LLM_NORM_RMS, il);
-                cb(Qcur, "Qcur_normed", il);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, NULL, LLM_NORM_RMS, il);
-                cb(Kcur, "Kcur_normed", il);
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed-forward network
-            cur = build_norm(ffn_inp,
-                    model.layers[il].ffn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-
-            cur = build_ffn(cur,
-                    model.layers[il].ffn_up,   NULL, NULL,
-                    model.layers[il].ffn_gate, NULL, NULL,
-                    model.layers[il].ffn_down, NULL, NULL,
-                    NULL,
-                    LLM_FFN_SILU, LLM_FFN_PAR, il);
-            cb(cur, "ffn_out", il);
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_qwen3moe : public llm_graph_context {
-    llm_build_qwen3moe(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self_attention
-            {
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL, LLM_NORM_RMS, il);
-                cb(Qcur, "Qcur_normed", il);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, NULL, LLM_NORM_RMS, il);
-                cb(Kcur, "Kcur_normed", il);
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // MoE branch
-            cur = build_norm(ffn_inp,
-                    model.layers[il].ffn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-
-            ggml_tensor * moe_out =
-                build_moe_ffn(cur,
-                        model.layers[il].ffn_gate_inp,
-                        model.layers[il].ffn_up_exps,
-                        model.layers[il].ffn_gate_exps,
-                        model.layers[il].ffn_down_exps,
-                        nullptr,
-                        n_expert, n_expert_used,
-                        LLM_FFN_SILU, true,
-                        false, 0.0,
-                        LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
-                        il);
-            cb(moe_out, "ffn_moe_out", il);
-            cur = moe_out;
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_qwen3vl : public llm_graph_context {
-    llm_build_qwen3vl(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-
-        const int64_t n_embd_full = hparams.n_embd; // main embd + deepstack embds
-        const size_t n_deepstack_layers = hparams.n_deepstack_layers;
-        const int64_t n_embd = n_embd_full / (n_deepstack_layers + 1);
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        int sections[4];
-        std::copy(std::begin(hparams.rope_sections), std::begin(hparams.rope_sections) + 4, sections);
-
-        std::vector<ggml_tensor *> deepstack_features(n_deepstack_layers, nullptr);
-
-        if (ubatch.embd) {
-            // Image input: split main embd and deepstack embds
-            ggml_tensor * inpL_main = ggml_view_2d(ctx0, inpL, n_embd, n_tokens, inpL->nb[1], 0);
-            for (size_t i = 0; i < n_deepstack_layers; i++) {
-                deepstack_features[i] = ggml_view_2d(ctx0, inpL, n_embd, n_tokens, inpL->nb[1], (i + 1) * n_embd * sizeof(float));
-            }
-            inpL = inpL_main;
-        }
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL, LLM_NORM_RMS, il);
-                cb(Qcur, "Qcur_normed", il);
-
-                Qcur = ggml_rope_multi(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, sections, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, NULL, LLM_NORM_RMS, il);
-                cb(Kcur, "Kcur_normed", il);
-
-                Kcur = ggml_rope_multi(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, sections, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed-forward network
-            cur = build_norm(ffn_inp,
-                    model.layers[il].ffn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-
-            cur = build_ffn(cur,
-                    model.layers[il].ffn_up,   NULL, NULL,
-                    model.layers[il].ffn_gate, NULL, NULL,
-                    model.layers[il].ffn_down, NULL, NULL,
-                    NULL,
-                    LLM_FFN_SILU, LLM_FFN_PAR, il);
-            cb(cur, "ffn_out", il);
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            if (ubatch.embd && (size_t)il < n_deepstack_layers) {
-                cur = ggml_add(ctx0, cur, deepstack_features[il]);
-                cb(cur, "deepstack_out", il);
-            }
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_qwen3vlmoe : public llm_graph_context {
-    llm_build_qwen3vlmoe(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_full = hparams.n_embd; // main embd + deepstack embds
-        const size_t n_deepstack_layers = hparams.n_deepstack_layers;
-        const int64_t n_embd = n_embd_full / (n_deepstack_layers + 1);
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        int sections[4];
-        std::copy(std::begin(hparams.rope_sections), std::begin(hparams.rope_sections) + 4, sections);
-
-        std::vector<ggml_tensor *> deepstack_features(n_deepstack_layers, nullptr);
-
-        if (ubatch.embd) {
-            // Image input: split main embd and deepstack embds
-            ggml_tensor * inpL_main = ggml_view_2d(ctx0, inpL, n_embd, n_tokens, inpL->nb[1], 0);
-            for (size_t i = 0; i < n_deepstack_layers; i++) {
-                deepstack_features[i] = ggml_view_2d(ctx0, inpL, n_embd, n_tokens, inpL->nb[1], (i + 1) * n_embd * sizeof(float));
-            }
-            inpL = inpL_main;
-        }
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self_attention
-            {
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL, LLM_NORM_RMS, il);
-                cb(Qcur, "Qcur_normed", il);
-
-                Qcur = ggml_rope_multi(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, sections, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, NULL, LLM_NORM_RMS, il);
-                cb(Kcur, "Kcur_normed", il);
-
-                Kcur = ggml_rope_multi(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, sections, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // MoE branch
-            cur = build_norm(ffn_inp,
-                    model.layers[il].ffn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-
-            ggml_tensor * moe_out =
-                build_moe_ffn(cur,
-                        model.layers[il].ffn_gate_inp,
-                        model.layers[il].ffn_up_exps,
-                        model.layers[il].ffn_gate_exps,
-                        model.layers[il].ffn_down_exps,
-                        nullptr,
-                        n_expert, n_expert_used,
-                        LLM_FFN_SILU, true,
-                        false, 0.0,
-                        LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
-                        il);
-            cb(moe_out, "ffn_moe_out", il);
-            cur = moe_out;
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            if (ubatch.embd && (size_t)il < n_deepstack_layers) {
-                cur = ggml_add(ctx0, cur, deepstack_features[il]);
-                cb(cur, "deepstack_out", il);
-            }
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_phi2 : public llm_graph_context {
-    llm_build_phi2(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-        const int64_t n_embd_gqa  = hparams.n_embd_v_gqa();
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-
-        ggml_tensor * cur;
-        ggml_tensor * attn_norm_output;
-        ggml_tensor * ffn_output;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            attn_norm_output = build_norm(inpL,
-                    model.layers[il].attn_norm,
-                    model.layers[il].attn_norm_b,
-                    LLM_NORM, il);
-            cb(attn_norm_output, "attn_norm", il);
-
-            // self-attention
-            {
-                ggml_tensor * Qcur = nullptr;
-                ggml_tensor * Kcur = nullptr;
-                ggml_tensor * Vcur = nullptr;
-
-                if (model.layers[il].wqkv) {
-                    cur = build_lora_mm(model.layers[il].wqkv, attn_norm_output);
-                    cb(cur, "wqkv", il);
-
-                    cur = ggml_add(ctx0, cur, model.layers[il].bqkv);
-                    cb(cur, "bqkv", il);
-
-                    Qcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head,    n_tokens, n_embd_head*sizeof(float), cur->nb[1], 0*sizeof(float)*(n_embd));
-                    Kcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd));
-                    Vcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd + n_embd_gqa));
-                } else {
-                    Qcur = ggml_add(ctx0, build_lora_mm(model.layers[il].wq, attn_norm_output), model.layers[il].bq);
-                    Kcur = ggml_add(ctx0, build_lora_mm(model.layers[il].wk, attn_norm_output), model.layers[il].bk);
-                    Vcur = ggml_add(ctx0, build_lora_mm(model.layers[il].wv, attn_norm_output), model.layers[il].bv);
-
-                    Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                    Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                    Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-                }
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                // with phi2, we scale the Q to avoid precision issues
-                // ref: https://github.com/ml-explore/mlx-examples/blob/08e862336ade809bc37d1035f94b359e7d1a5152/phi2/phi2.py#L64-L66
-                Qcur = ggml_scale(ctx0, Qcur, 1.0f/sqrtf(float(n_embd_head)));
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f, il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur              = ggml_get_rows(ctx0,              cur, inp_out_ids);
-                inpL             = ggml_get_rows(ctx0,             inpL, inp_out_ids);
-                attn_norm_output = ggml_get_rows(ctx0, attn_norm_output, inp_out_ids);
-            }
-
-            // FF
-            {
-                ffn_output = build_ffn(attn_norm_output,
-                        model.layers[il].ffn_up,   model.layers[il].ffn_up_b,   NULL,
-                        NULL,                      NULL,                        NULL,
-                        model.layers[il].ffn_down, model.layers[il].ffn_down_b, NULL,
-                        NULL,
-                        LLM_FFN_GELU, LLM_FFN_SEQ, il);
-                cb(ffn_output, "ffn_out", il);
-            }
-
-            cur = ggml_add(ctx0, cur, ffn_output);
-            cur = ggml_add(ctx0, cur, inpL);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = build_norm(inpL,
-                model.output_norm,
-                model.output_norm_b,
-                LLM_NORM, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        cur = build_lora_mm(model.output, cur);
-        cb(cur, "result_output_no_bias", -1);
-
-        cur = ggml_add(ctx0, cur, model.output_b);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-template<bool iswa>
-struct llm_build_phi3 : public llm_graph_context {
-    llm_build_phi3(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-        const int64_t n_embd_gqa = hparams.n_embd_v_gqa();
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        using inp_attn_type = std::conditional_t<iswa, llm_graph_input_attn_kv_iswa, llm_graph_input_attn_kv>;
-        inp_attn_type * inp_attn = nullptr;
-
-        if constexpr (iswa) {
-            inp_attn = build_attn_inp_kv_iswa();
-        } else {
-            inp_attn = build_attn_inp_kv();
-        }
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            auto * residual = inpL;
-
-            // self-attention
-            {
-                // rope freq factors for 128k context
-                ggml_tensor * rope_factors = model.get_rope_factors(cparams, il);
-
-                ggml_tensor* attn_norm_output = build_norm(inpL,
-                        model.layers[il].attn_norm,
-                        model.layers[il].attn_norm_b,
-                        LLM_NORM_RMS, il);
-                cb(attn_norm_output, "attn_norm", il);
-
-                ggml_tensor * Qcur = nullptr;
-                ggml_tensor * Kcur = nullptr;
-                ggml_tensor * Vcur = nullptr;
-
-                if (model.layers[il].wqkv) {
-                    cur = build_lora_mm(model.layers[il].wqkv, attn_norm_output);
-                    cb(cur, "wqkv", il);
-
-                    Qcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head,    n_tokens, n_embd_head * sizeof(float), cur->nb[1], 0 * sizeof(float) * (n_embd));
-                    Kcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head * sizeof(float), cur->nb[1], 1 * sizeof(float) * (n_embd));
-                    Vcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head * sizeof(float), cur->nb[1], 1 * sizeof(float) * (n_embd + n_embd_gqa));
-                } else {
-                    Qcur = ggml_add(ctx0, build_lora_mm(model.layers[il].wq, attn_norm_output), model.layers[il].bq);
-                    Kcur = ggml_add(ctx0, build_lora_mm(model.layers[il].wk, attn_norm_output), model.layers[il].bk);
-                    Vcur = ggml_add(ctx0, build_lora_mm(model.layers[il].wv, attn_norm_output), model.layers[il].bv);
-
-                    Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                    Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                    Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-                }
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, rope_factors,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, rope_factors,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                Qcur = ggml_scale(ctx0, Qcur, 1.0f / sqrtf(float(n_embd_head)));
-                cb(Qcur, "Qcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f, il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur      = ggml_get_rows(ctx0, cur,      inp_out_ids);
-                residual = ggml_get_rows(ctx0, residual, inp_out_ids);
-            }
-
-            cur = ggml_add(ctx0, cur, residual);
-            residual = cur;
-
-            cur = build_norm(cur,
-                    model.layers[il].ffn_norm, model.layers[il].ffn_norm_b,
-                    LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-
-            // feed-forward network
-            if (model.layers[il].ffn_gate_inp == nullptr) {
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up,   NULL, NULL,
-                        NULL,                      NULL, NULL,
-                        model.layers[il].ffn_down, NULL, NULL,
-                        NULL,
-                        LLM_FFN_SWIGLU, LLM_FFN_SEQ, il);
-                cb(cur, "ffn_out", il);
-            } else {
-                // MoE branch
-                cur = build_moe_ffn(cur,
-                        model.layers[il].ffn_gate_inp,
-                        model.layers[il].ffn_up_exps,
-                        model.layers[il].ffn_gate_exps,
-                        model.layers[il].ffn_down_exps,
-                        nullptr,
-                        n_expert, n_expert_used,
-                        LLM_FFN_SILU, true,
-                        false, 0.0,
-                        LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
-                        il);
-                cb(cur, "ffn_moe_out", il);
-            }
-
-            cur = ggml_add(ctx0, residual, cur);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = build_norm(inpL,
-                model.output_norm,
-                model.output_norm_b,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        cur = build_lora_mm(model.output, cur);
-
-        if (model.output_b != nullptr) {
-            cb(cur, "result_output_no_bias", -1);
-            cur = ggml_add(ctx0, cur, model.output_b);
-        }
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_plamo : public llm_graph_context {
-    llm_build_plamo(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            ggml_tensor * sa_inp = cur;
-
-            // self-attention
-            {
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_embd_head, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_embd_head, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, NULL,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur    = ggml_get_rows(ctx0,    cur, inp_out_ids);
-                sa_inp = ggml_get_rows(ctx0, sa_inp, inp_out_ids);
-                inpL   = ggml_get_rows(ctx0,   inpL, inp_out_ids);
-            }
-
-            ggml_tensor * sa_out = cur;
-
-            cur = sa_inp;
-
-            // feed-forward network
-            {
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up,   NULL, NULL,
-                        model.layers[il].ffn_gate, NULL, NULL,
-                        model.layers[il].ffn_down, NULL, NULL,
-                        NULL,
-                        LLM_FFN_SILU, LLM_FFN_PAR, il);
-                cb(cur, "ffn_out", il);
-            }
-
-            cur = ggml_add(ctx0, cur, sa_out);
-            cur = ggml_add(ctx0, cur, inpL);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_gpt2 : public llm_graph_context {
-    llm_build_gpt2(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-        const int64_t n_embd_gqa  = hparams.n_embd_v_gqa();
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-
-        ggml_tensor * cur;
-        ggml_tensor * pos;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        pos = ggml_get_rows(ctx0, model.pos_embd, inp_pos);
-        cb(pos, "pos_embd", -1);
-
-        inpL = ggml_add(ctx0, inpL, pos);
-        cb(inpL, "inpL", -1);
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm,
-                    model.layers[il].attn_norm_b,
-                    LLM_NORM, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                cur = build_lora_mm(model.layers[il].wqkv, cur);
-                cb(cur, "wqkv", il);
-
-                cur = ggml_add(ctx0, cur, model.layers[il].bqkv);
-                cb(cur, "bqkv", il);
-
-                ggml_tensor * Qcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head,    n_tokens, n_embd_head*sizeof(float), cur->nb[1], 0*sizeof(float)*(n_embd));
-                ggml_tensor * Kcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd));
-                ggml_tensor * Vcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd + n_embd_gqa));
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur  = ggml_get_rows(ctx0,  cur, inp_out_ids);
-                inpL = ggml_get_rows(ctx0, inpL, inp_out_ids);
-            }
-
-            // add the input
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpL);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // FF
-            {
-                cur = build_norm(ffn_inp,
-                        model.layers[il].ffn_norm,
-                        model.layers[il].ffn_norm_b,
-                        LLM_NORM, il);
-                cb(cur, "ffn_norm", il);
-
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up,   model.layers[il].ffn_up_b,   NULL,
-                        NULL,                      NULL,                        NULL,
-                        model.layers[il].ffn_down, model.layers[il].ffn_down_b, NULL,
-                        NULL,
-                        LLM_FFN_GELU, LLM_FFN_SEQ, il);
-                cb(cur, "ffn_out", il);
-            }
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = build_norm(inpL,
-                model.output_norm,
-                model.output_norm_b,
-                LLM_NORM, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_codeshell : public llm_graph_context {
-    llm_build_codeshell(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-        const int64_t n_embd_gqa  = hparams.n_embd_v_gqa();
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm,
-                    model.layers[il].attn_norm_b,
-                    LLM_NORM, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                cur = build_lora_mm(model.layers[il].wqkv, cur);
-                cb(cur, "wqkv", il);
-
-                cur = ggml_add(ctx0, cur, model.layers[il].bqkv);
-                cb(cur, "bqkv", il);
-
-                ggml_tensor * Qcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head,    n_tokens, n_embd_head*sizeof(float), cur->nb[1], 0*sizeof(float)*(n_embd));
-                ggml_tensor * Kcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd));
-                ggml_tensor * Vcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd + n_embd_gqa));
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur  = ggml_get_rows(ctx0,  cur, inp_out_ids);
-                inpL = ggml_get_rows(ctx0, inpL, inp_out_ids);
-            }
-
-            // add the input
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpL);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // FF
-            {
-                cur = build_norm(ffn_inp,
-                        model.layers[il].ffn_norm,
-                        model.layers[il].ffn_norm_b,
-                        LLM_NORM, il);
-                cb(cur, "ffn_norm", il);
-
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up,   model.layers[il].ffn_up_b,   NULL,
-                        NULL,                      NULL,                        NULL,
-                        model.layers[il].ffn_down, model.layers[il].ffn_down_b, NULL,
-                        NULL,
-                        LLM_FFN_GELU, LLM_FFN_SEQ, il);
-                cb(cur, "ffn_out", il);
-            }
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = build_norm(inpL,
-                model.output_norm,
-                model.output_norm_b,
-                LLM_NORM, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_orion : public llm_graph_context {
-    llm_build_orion(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, model.layers[il].attn_norm_b,
-                    LLM_NORM, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-                // if (model.layers[il].bq) {
-                //     Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
-                //     cb(Qcur, "Qcur", il);
-                // }
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-                // if (model.layers[il].bk) {
-                //     Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
-                //     cb(Kcur, "Kcur", il);
-                // }
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-                // if (model.layers[il].bv) {
-                //     Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
-                //     cb(Vcur, "Vcur", il);
-                // }
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, NULL,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed-forward network
-            cur = build_norm(ffn_inp,
-                    model.layers[il].ffn_norm, model.layers[il].ffn_norm_b,
-                    LLM_NORM, il);
-            cb(cur, "ffn_norm", il);
-
-            cur = build_ffn(cur,
-                    model.layers[il].ffn_up,   NULL, NULL,
-                    model.layers[il].ffn_gate, NULL, NULL,
-                    model.layers[il].ffn_down, NULL, NULL,
-                    NULL,
-                    LLM_FFN_SILU, LLM_FFN_PAR, il);
-            cb(cur, "ffn_out", il);
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, model.output_norm_b,
-                LLM_NORM, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_internlm2 : public llm_graph_context {
-    llm_build_internlm2(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-                if (model.layers[il].bq) {
-                    Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
-                    cb(Qcur, "Qcur", il);
-                }
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-                if (model.layers[il].bk) {
-                    Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
-                    cb(Kcur, "Kcur", il);
-                }
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-                if (model.layers[il].bv) {
-                    Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
-                    cb(Vcur, "Vcur", il);
-                }
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed-forward network
-            cur = build_norm(ffn_inp,
-                    model.layers[il].ffn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-
-            cur = build_ffn(cur,
-                    model.layers[il].ffn_up,   NULL, NULL,
-                    model.layers[il].ffn_gate, NULL, NULL,
-                    model.layers[il].ffn_down, NULL, NULL,
-                    NULL,
-                    LLM_FFN_SILU, LLM_FFN_PAR, il);
-            cb(cur, "ffn_out", il);
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_minicpm3 : public llm_graph_context {
-    llm_build_minicpm3(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        //TODO: if the model varies, these parameters need to be read from the model
-        const int64_t n_embd_base = 256;
-        const float scale_embd  = 12.0f;
-        const float scale_depth = 1.4f;
-        const float kq_scale = 1.0f / sqrtf(float(hparams.n_embd_head_k));
-
-        const uint32_t n_embd_head_qk_rope = hparams.n_rot;
-        const uint32_t n_embd_head_qk_nope = hparams.n_embd_head_k - hparams.n_rot;
-        const uint32_t kv_lora_rank = hparams.n_lora_kv;
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // scale the input embeddings
-        inpL = ggml_scale(ctx0, inpL, scale_embd);
-        cb(inpL, "inp_scaled", -1);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            ggml_tensor * rope_factors = model.get_rope_factors(cparams, il);
-
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self_attention
-            {
-                ggml_tensor * q = NULL;
-                // {n_embd, q_lora_rank} * {n_embd, n_tokens} -> {q_lora_rank, n_tokens}
-                q = ggml_mul_mat(ctx0, model.layers[il].wq_a, cur);
-                cb(q, "q", il);
-
-                q = build_norm(q,
-                        model.layers[il].attn_q_a_norm, NULL,
-                        LLM_NORM_RMS, il);
-                cb(q, "q", il);
-
-                // {q_lora_rank, n_head * hparams.n_embd_head_k} * {q_lora_rank, n_tokens} -> {n_head * hparams.n_embd_head_k, n_tokens}
-                q = ggml_mul_mat(ctx0, model.layers[il].wq_b, q);
-                cb(q, "q", il);
-
-                // split into {n_head * n_embd_head_qk_nope, n_tokens}
-                ggml_tensor * q_nope = ggml_view_3d(ctx0, q, n_embd_head_qk_nope, n_head, n_tokens,
-                        ggml_row_size(q->type, hparams.n_embd_head_k),
-                        ggml_row_size(q->type, hparams.n_embd_head_k * n_head),
-                        0);
-                cb(q_nope, "q_nope", il);
-
-                // and {n_head * n_embd_head_qk_rope, n_tokens}
-                ggml_tensor * q_pe = ggml_view_3d(ctx0, q, n_embd_head_qk_rope, n_head, n_tokens,
-                        ggml_row_size(q->type, hparams.n_embd_head_k),
-                        ggml_row_size(q->type, hparams.n_embd_head_k * n_head),
-                        ggml_row_size(q->type, n_embd_head_qk_nope));
-                cb(q_pe, "q_pe", il);
-
-                // {n_embd, kv_lora_rank + n_embd_head_qk_rope} * {n_embd, n_tokens} -> {kv_lora_rank + n_embd_head_qk_rope, n_tokens}
-                ggml_tensor * kv_pe_compresseed = ggml_mul_mat(ctx0, model.layers[il].wkv_a_mqa, cur);
-                cb(kv_pe_compresseed, "kv_pe_compresseed", il);
-
-                // split into {kv_lora_rank, n_tokens}
-                ggml_tensor * kv_compressed = ggml_view_2d(ctx0, kv_pe_compresseed, kv_lora_rank, n_tokens,
-                        kv_pe_compresseed->nb[1],
-                        0);
-                cb(kv_compressed, "kv_compressed", il);
-
-                // and {n_embd_head_qk_rope, n_tokens}
-                ggml_tensor * k_pe = ggml_view_3d(ctx0, kv_pe_compresseed, n_embd_head_qk_rope, 1, n_tokens,
-                        kv_pe_compresseed->nb[1],
-                        kv_pe_compresseed->nb[1],
-                        ggml_row_size(kv_pe_compresseed->type, kv_lora_rank));
-                cb(k_pe, "k_pe", il);
-
-                kv_compressed = build_norm(kv_compressed,
-                        model.layers[il].attn_kv_a_norm, NULL,
-                        LLM_NORM_RMS, il);
-                cb(kv_compressed, "kv_compressed", il);
-
-                // {kv_lora_rank, n_head * (n_embd_head_qk_nope + n_embd_head_v)} * {kv_lora_rank, n_tokens} -> {n_head * (n_embd_head_qk_nope + n_embd_head_v), n_tokens}
-                ggml_tensor * kv = ggml_mul_mat(ctx0, model.layers[il].wkv_b, kv_compressed);
-                cb(kv, "kv", il);
-
-                // split into {n_head * n_embd_head_qk_nope, n_tokens}
-                ggml_tensor * k_nope = ggml_view_3d(ctx0, kv, n_embd_head_qk_nope, n_head, n_tokens,
-                        ggml_row_size(kv->type, n_embd_head_qk_nope + hparams.n_embd_head_v),
-                        ggml_row_size(kv->type, n_head * (n_embd_head_qk_nope + hparams.n_embd_head_v)),
-                        0);
-                cb(k_nope, "k_nope", il);
-
-                // and {n_head * n_embd_head_v, n_tokens}
-                ggml_tensor * v_states = ggml_view_3d(ctx0, kv, hparams.n_embd_head_v, n_head, n_tokens,
-                        ggml_row_size(kv->type, (n_embd_head_qk_nope + hparams.n_embd_head_v)),
-                        ggml_row_size(kv->type, (n_embd_head_qk_nope + hparams.n_embd_head_v)*n_head),
-                        ggml_row_size(kv->type, (n_embd_head_qk_nope)));
-                cb(v_states, "v_states", il);
-
-                v_states = ggml_cont(ctx0, v_states);
-                cb(v_states, "v_states", il);
-
-                q_pe = ggml_rope_ext(
-                        ctx0, q_pe, inp_pos, rope_factors,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-                cb(q_pe, "q_pe", il);
-
-                // shared RoPE key
-                k_pe = ggml_rope_ext(
-                        ctx0, k_pe, inp_pos, rope_factors,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-                cb(k_pe, "k_pe", il);
-
-                ggml_tensor * q_states = ggml_concat(ctx0, q_nope, q_pe, 0);
-                cb(q_states, "q_states", il);
-
-                ggml_tensor * k_states = ggml_concat(ctx0, k_nope, ggml_repeat(ctx0, k_pe, q_pe), 0);
-                cb(k_states, "k_states", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, NULL,
-                        q_states, k_states, v_states, nullptr, nullptr, nullptr, kq_scale, il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            // scale_res - scale the hidden states for residual connection
-            const float scale_res = scale_depth/sqrtf(float(n_layer)); // TODO: is this correct?
-            cur = ggml_scale(ctx0, cur, scale_res);
-            cb(cur, "hidden_scaled", il);
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed-forward network
-            {
-                cur = build_norm(ffn_inp,
-                        model.layers[il].ffn_norm, NULL,
-                        LLM_NORM_RMS, il);
-                cb(cur, "ffn_norm", il);
-
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up,   NULL, NULL,
-                        model.layers[il].ffn_gate, NULL, NULL,
-                        model.layers[il].ffn_down, NULL, NULL,
-                        NULL,
-                        LLM_FFN_SILU, LLM_FFN_PAR, il);
-                cb(cur, "ffn_out", il);
-            }
-
-            // scale the hidden states for residual connection
-            cur = ggml_scale(ctx0, cur, scale_res);
-            cb(cur, "hidden_scaled_ffn", il);
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head scaling
-        const float scale_lmhead = float(n_embd_base)/float(n_embd);
-        cur = ggml_scale(ctx0, cur, scale_lmhead);
-        cb(cur, "lmhead_scaling", -1);
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_gemma : public llm_graph_context {
-    llm_build_gemma(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        inpL = ggml_scale(ctx0, inpL, sqrtf(n_embd));
-        cb(inpL, "inp_scaled", -1);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow);
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow);
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                Qcur = ggml_scale(ctx0, Qcur, 1.0f / sqrtf(float(n_embd_head)));
-                cb(Qcur, "Qcur_scaled", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, NULL,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f, il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur  = ggml_get_rows(ctx0,  cur, inp_out_ids);
-                inpL = ggml_get_rows(ctx0, inpL, inp_out_ids);
-            }
-
-            ggml_tensor * sa_out = ggml_add(ctx0, cur, inpL);
-            cb(sa_out, "sa_out", il);
-
-            cur = build_norm(sa_out,
-                    model.layers[il].ffn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-
-            // feed-forward network
-            {
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up,   NULL, NULL,
-                        model.layers[il].ffn_gate, NULL, NULL,
-                        model.layers[il].ffn_down, NULL, NULL,
-                        NULL,
-                        LLM_FFN_GELU, LLM_FFN_PAR, il);
-                cb(cur, "ffn_out", il);
-            }
-
-            cur = ggml_add(ctx0, cur, sa_out);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_gemma2_iswa : public llm_graph_context {
-    llm_build_gemma2_iswa(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_k;
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        inpL = ggml_scale(ctx0, inpL, sqrtf(n_embd));
-        cb(inpL, "inp_scaled", -1);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv_iswa();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow);
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow);
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                Qcur = ggml_scale(ctx0, Qcur, hparams.f_attention_scale);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, NULL,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f, il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur  = ggml_get_rows(ctx0,  cur, inp_out_ids);
-                inpL = ggml_get_rows(ctx0, inpL, inp_out_ids);
-            }
-
-            cur = build_norm(cur,
-                    model.layers[il].attn_post_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_post_norm", il);
-
-            ggml_tensor * sa_out = ggml_add(ctx0, cur, inpL);
-            cb(sa_out, "sa_out", il);
-
-            cur = build_norm(sa_out,
-                    model.layers[il].ffn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-
-            // feed-forward network
-            {
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up,   NULL, NULL,
-                        model.layers[il].ffn_gate, NULL, NULL,
-                        model.layers[il].ffn_down, NULL, NULL,
-                        NULL,
-                        LLM_FFN_GELU, LLM_FFN_PAR, il);
-                cb(cur, "ffn_out", il);
-            }
-
-            cur = build_norm(cur,
-                    model.layers[il].ffn_post_norm, NULL,
-                    LLM_NORM_RMS, -1);
-            cb(cur, "ffn_post_norm", -1);
-
-            cur = ggml_add(ctx0, cur, sa_out);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        // final logit soft-capping
-        cur = ggml_scale(ctx0, cur, 1.0f / hparams.f_final_logit_softcapping);
-        cur = ggml_tanh(ctx0, cur);
-        cur = ggml_scale(ctx0, cur, hparams.f_final_logit_softcapping);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_gemma3_iswa : public llm_graph_context {
-    llm_build_gemma3_iswa(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_k;
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // important: do not normalize weights for raw embeddings input (i.e. encoded image emdeddings)
-        if (ubatch.token) {
-            inpL = ggml_scale(ctx0, inpL, sqrtf(n_embd));
-            cb(inpL, "inp_scaled", -1);
-        }
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        // TODO: is causal == true correct? might need some changes
-        auto * inp_attn = build_attn_inp_kv_iswa();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            const float freq_base_l  = model.get_rope_freq_base (cparams, il);
-            const float freq_scale_l = model.get_rope_freq_scale(cparams, il);
-
-            // norm
-            cur = build_norm(inpL, model.layers[il].attn_norm, NULL, LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL, LLM_NORM_RMS, il);
-                cb(Qcur, "Qcur_normed", il);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base_l, freq_scale_l,
-                        ext_factor, attn_factor, beta_fast, beta_slow);
-
-                Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, NULL, LLM_NORM_RMS, il);
-                cb(Kcur, "Kcur_normed", il);
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base_l, freq_scale_l,
-                        ext_factor, attn_factor, beta_fast, beta_slow);
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                // ref: https://github.com/google/gemma_pytorch/blob/014acb7ac4563a5f77c76d7ff98f31b568c16508/gemma/model.py#L315
-                Qcur = ggml_scale(ctx0, Qcur, hparams.f_attention_scale);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, NULL,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f, il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur  = ggml_get_rows(ctx0,  cur, inp_out_ids);
-                inpL = ggml_get_rows(ctx0, inpL, inp_out_ids);
-            }
-
-            cur = build_norm(cur,
-                    model.layers[il].attn_post_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_post_norm", il);
-
-            ggml_tensor * sa_out = ggml_add(ctx0, cur, inpL);
-            cb(sa_out, "sa_out", il);
-
-            cur = build_norm(sa_out,
-                    model.layers[il].ffn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-
-            // feed-forward network
-            {
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up,   NULL, NULL,
-                        model.layers[il].ffn_gate, NULL, NULL,
-                        model.layers[il].ffn_down, NULL, NULL,
-                        NULL,
-                        LLM_FFN_GELU, LLM_FFN_PAR, il);
-                cb(cur, "ffn_out", il);
-            }
-
-            cur = build_norm(cur,
-                    model.layers[il].ffn_post_norm, NULL,
-                    LLM_NORM_RMS, -1);
-            cb(cur, "ffn_post_norm", -1);
-
-            cur = ggml_add(ctx0, cur, sa_out);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_gemma3n_iswa : public llm_graph_context {
-    const llama_model & model;
-
-    const int64_t n_embd_head;
-    const int64_t n_embd_altup;
-    const int64_t n_altup;
-    const int     i_altup_act;
-    const int     n_layer_sparsity = 10; // number of layers using activation sparsity
-    const float   f_sparsity_std_mul = 1.6448533535003662f; // std_multiplier = normal_dist.icdf(0.95)
-
-    llm_build_gemma3n_iswa(const llama_model & model, const llm_graph_params & params)
-            : llm_graph_context(params),
-              model(model),
-              n_embd_head(model.hparams.n_embd_head_k),
-              n_embd_altup(model.hparams.n_embd_altup),
-              n_altup(model.hparams.n_altup),
-              i_altup_act(model.hparams.i_altup_act) {
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // important: do not normalize weights for raw embeddings input (i.e. encoded image emdeddings)
-        if (ubatch.token) {
-            inpL = ggml_scale(ctx0, inpL, sqrtf(n_embd));
-            cb(inpL, "inp_scaled", -1);
-        }
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        // TODO: is causal == true correct? might need some changes
-        auto * inp_attn = build_attn_inp_kv_iswa();
-
-        // inp_per_layer shape: [n_embd_altup, n_tokens, n_layer]
-        ggml_tensor * inp_per_layer = project_per_layer_inputs(inpL, get_per_layer_inputs());
-
-        // inpL now has only 1 altup, project it to the rest of the altups
-        // these "added" altups will be concat to the last dim of inpL
-        {
-            ggml_tensor * target_magnitude = calc_magnitude(inpL);
-            ggml_tensor * inp_repeated = ggml_repeat_4d(ctx0, inpL, n_embd, n_tokens, n_altup - 1, 1);
-            ggml_tensor * altup_added = ggml_mul_mat(ctx0, model.altup_proj, inp_repeated); // shape: [n_embd, n_tokens, n_altup - 1]
-            ggml_tensor * new_magnitude = calc_magnitude(altup_added);
-            altup_added = ggml_div(ctx0,
-                                ggml_mul(ctx0, altup_added, target_magnitude),
-                                new_magnitude);
-            inpL = ggml_concat(ctx0, inpL, altup_added, 2); // shape: [n_embd, n_tokens, n_altup]
-            cb(inpL, "inp_stacked", -1);
-        }
-
-        // inpL now has shape:          [n_embd,       n_tokens, n_altup]
-        // inp_per_layer now has shape: [n_embd_altup, n_tokens, n_layer]
-
-        for (int il = 0; il < n_layer; ++il) {
-            // this block is made to be closely resemble Gemma3p5DecoderLayer on python code
-            const float freq_base_l  = model.get_rope_freq_base (cparams, il);
-            const float freq_scale_l = model.get_rope_freq_scale(cparams, il);
-
-            ggml_tensor * cur = inpL; // [n_embd, n_tokens, n_altup]
-            ggml_tensor * predictions = altup_predict(cur, il); // [n_embd, n_tokens, n_altup]
-
-            // predicted value will go through self-attention and laurel
-            ggml_tensor * active_prediction = view_2d_slice(predictions, i_altup_act); // [n_embd, n_tokens]
-            cur = active_prediction;
-            cb(cur, "active_prediction", il);
-
-            // norm
-            cur = build_norm(cur, model.layers[il].attn_norm, NULL, LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // laurel
-            ggml_tensor * laurel_out = laurel(cur, il); // [n_embd, n_tokens]
-
-            // self-attention
-            if (hparams.has_kv(il)) {
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL, LLM_NORM_RMS, il);
-                Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, NULL, LLM_NORM_RMS, il);
-                Vcur = ggml_rms_norm(ctx0, Vcur, hparams.f_norm_rms_eps);
-
-                cb(Qcur, "Qcur_normed", il);
-                cb(Kcur, "Kcur_normed", il);
-                cb(Vcur, "Vcur_normed", il);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base_l, freq_scale_l,
-                        ext_factor, attn_factor, beta_fast, beta_slow);
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base_l, freq_scale_l,
-                        ext_factor, attn_factor, beta_fast, beta_slow);
-
-                cb(Qcur, "Qcur_pos", il);
-                cb(Kcur, "Kcur_pos", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, NULL,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, hparams.f_attention_scale, il);
-            } else {
-                // reuse KV cache of earlier layers
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head, n_tokens);
-
-                Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL, LLM_NORM_RMS, il);
-                cb(Qcur, "Qcur_normed", il);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base_l, freq_scale_l,
-                        ext_factor, attn_factor, beta_fast, beta_slow);
-                cb(Qcur, "Qcur_pos", il);
-
-                cur = build_attn(inp_attn,
-                    model.layers[il].wo, NULL,
-                    Qcur, nullptr, nullptr, nullptr, nullptr, nullptr, hparams.f_attention_scale, il);
-            }
-
-            cur = build_norm(cur,
-                    model.layers[il].attn_post_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_post_norm", il);
-
-            cur = ggml_add(ctx0, cur, active_prediction); // [n_embd, n_tokens]
-            cb(cur, "attn_gated", il);
-
-            ggml_tensor * attn_laurel = ggml_scale(ctx0,
-                                            ggml_add(ctx0, cur, laurel_out),
-                                            1.0f / sqrtf(2.0f)); // [n_embd, n_tokens]
-            cb(attn_laurel, "attn_laurel", il);
-
-            cur = build_norm(attn_laurel,
-                    model.layers[il].ffn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-
-            // feed-forward network
-            {
-                ggml_tensor * up_proj   = build_lora_mm(model.layers[il].ffn_up,   cur);
-                ggml_tensor * gate_proj = build_lora_mm(model.layers[il].ffn_gate, cur);
-
-                if (il < n_layer_sparsity) {
-                    // apply activation sparsity
-                    gate_proj = gaussian_topk(gate_proj);
-                }
-                gate_proj = ggml_gelu(ctx0, gate_proj);
-
-                cur = ggml_mul(ctx0, up_proj, gate_proj);
-                cur = build_lora_mm(model.layers[il].ffn_down, cur);
-                cb(cur, "ffn_out", il);
-            }
-
-            cur = build_norm(cur,
-                    model.layers[il].ffn_post_norm, NULL,
-                    LLM_NORM_RMS, -1);
-            cb(cur, "ffn_post_norm", il);
-
-            ggml_tensor * attn_ffw_laurel_gated = ggml_add(ctx0, cur, attn_laurel); // [n_embd, n_tokens]
-            cb(attn_ffw_laurel_gated, "attn_ffw_laurel_gated", il);
-
-            ggml_tensor * corrected = altup_correct(predictions, attn_ffw_laurel_gated, il); // [n_embd, n_tokens, n_altup]
-
-            ggml_tensor * first_prediction; // [n_embd, n_tokens]
-            {
-                first_prediction = view_2d_slice(corrected, i_altup_act); // [n_embd, n_tokens]
-                first_prediction = ggml_mul(ctx0, first_prediction, model.layers[il].altup_correct_scale);
-                first_prediction = build_lora_mm(model.layers[il].per_layer_inp_gate, first_prediction);
-                first_prediction = ggml_gelu(ctx0, first_prediction); // [n_embd_altup, n_tokens]
-                cb(first_prediction, "first_prediction_gated", il);
-                ggml_tensor * inp_this_layer = view_2d_slice(inp_per_layer, il); // [n_embd_altup, n_tokens]
-                first_prediction = ggml_mul(ctx0, first_prediction, inp_this_layer); // [n_embd_altup, n_tokens]
-                cb(first_prediction, "first_prediction_scaled", il);
-
-                first_prediction = build_lora_mm(model.layers[il].per_layer_proj, first_prediction); // [n_embd, n_tokens]
-                first_prediction = build_norm(first_prediction,
-                        model.layers[il].per_layer_post_norm, NULL,
-                        LLM_NORM_RMS, il);
-                cb(first_prediction, "first_prediction_out", il);
-            }
-
-            // equivalent to python code: corrected_predictions[1:] += first_prediction
-            {
-                ggml_tensor * slice_first = view_2d_slice(corrected, 0);
-                ggml_tensor * slice_rest  = ggml_view_3d(ctx0, corrected, n_embd, n_tokens, n_altup - 1,
-                                                    ggml_row_size(corrected->type, n_embd),
-                                                    ggml_row_size(corrected->type, n_embd*n_tokens),
-                                                    n_embd*n_tokens*ggml_element_size(corrected));
-                ggml_tensor * tmp = ggml_add(ctx0, slice_rest, first_prediction); // [n_embd, n_tokens, n_altup - 1]
-                corrected = ggml_concat(ctx0, slice_first, tmp, 2); // [n_embd, n_tokens, n_altup]
-            }
-
-            cur = corrected; // [n_embd, n_tokens, n_altup]
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL; // [n_embd, n_tokens, n_altup]
-
-        // cur now has multiple altup(s), we want to merge them back to 1 altup
-        {
-            ggml_tensor * target_magnitude = calc_magnitude(view_2d_slice(cur, i_altup_act)); // [n_embd, n_tokens]
-            // do a view to skip the first slice (active altup)
-            ggml_tensor * alt_slice = ggml_view_3d(ctx0, cur, n_embd, n_tokens, n_altup - 1,
-                                                    ggml_row_size(cur->type, n_embd),
-                                                    ggml_row_size(cur->type, n_embd*n_tokens),
-                                                    n_embd*n_tokens*ggml_element_size(cur));
-            ggml_tensor * altup_unembd = ggml_mul_mat(ctx0, model.altup_unembd_proj, alt_slice); // shape: [n_embd, n_tokens, n_altup - 1]
-            ggml_tensor * new_magnitude = calc_magnitude(altup_unembd);
-            altup_unembd = ggml_div(ctx0,
-                                ggml_mul(ctx0, altup_unembd, target_magnitude),
-                                new_magnitude);
-            cb(altup_unembd, "altup_unembd", -1);
-
-            // equivalent to torch.mean(hidden_states, dim=0)
-            cur = view_2d_slice(cur, 0); // [n_embd, n_tokens]
-            for (int i = 0; i < n_altup - 1; ++i) {
-                cur = ggml_add(ctx0, cur, view_2d_slice(altup_unembd, i));
-            }
-            cur = ggml_scale(ctx0, cur, 1.0f / float(n_altup)); // [n_embd, n_tokens]
-            cb(cur, "unembd_merged", -1);
-        }
-
-        // cur now has shape: [n_embd, n_tokens]
-
-        // TODO: move this to right after the last KV layer
-        {
-            // skip computing output for unused tokens
-            ggml_tensor * inp_out_ids = build_inp_out_ids();
-            cur  = ggml_get_rows(ctx0,  cur, inp_out_ids);
-        }
-
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        cur = build_lora_mm(model.output, cur);
-
-        {
-            // final logit soft-capping
-            cur = ggml_scale(ctx0, cur, 1.0f / hparams.f_final_logit_softcapping);
-            cur = ggml_tanh(ctx0, cur);
-            cur = ggml_scale(ctx0, cur, hparams.f_final_logit_softcapping);
-        }
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-
-    ggml_tensor * calc_magnitude(ggml_tensor * x) {
-        return ggml_sqrt(ctx0, ggml_sum_rows(ctx0, ggml_sqr(ctx0, x)));
-    }
-
-    // get 2D slice view from a 3D tensor, the idx corresponds to the 3rd dim
-    ggml_tensor * view_2d_slice(ggml_tensor * x, int idx) {
-        GGML_ASSERT(idx < (int)x->ne[2]);
-        return ggml_view_2d(ctx0, x, x->ne[0], x->ne[1],
-                            ggml_row_size(x->type, x->ne[0]),
-                            idx * x->ne[0] * x->ne[1] * ggml_element_size(x));
-    }
-
-    // equivalent to get_per_layer_inputs() in python code
-    // output shape: [n_embd_altup, n_layer, n_tokens]
-    ggml_tensor * get_per_layer_inputs() {
-        auto inp = std::make_unique<llm_graph_input_embd>();
-        ggml_tensor * inp_per_layer;
-        if (ubatch.token) {
-            inp->tokens = ggml_new_tensor_1d(ctx0, GGML_TYPE_I32, ubatch.n_tokens);
-            ggml_set_input(inp->tokens);
-            res->t_tokens = inp->tokens;
-            inp_per_layer = ggml_get_rows(ctx0, model.tok_embd_per_layer, inp->tokens);
-            inp_per_layer = ggml_reshape_3d(ctx0, inp_per_layer, n_embd_altup, n_layer, n_tokens);
-            inp_per_layer = ggml_scale(ctx0, inp_per_layer, sqrtf((float)n_embd_altup));
-            cb(inp_per_layer, "inp_per_layer_selected", -1);
-        } else {
-            GGML_ABORT("TODO: support embd input");
-        }
-        res->add_input(std::move(inp));
-        return inp_per_layer;
-    }
-
-    // equivalent to project_per_layer_inputs() in python code
-    // this calculates the per-layer inputs, so the final tensor shape will have n_layer as the last dim
-    // output shape: [n_embd_altup, n_tokens, n_layer]
-    ggml_tensor * project_per_layer_inputs(ggml_tensor * inputs_embeds, ggml_tensor * inp_per_layer) {
-        const float per_layer_projection_scale = 1.0f / sqrtf((float)n_embd);
-        const float per_layer_input_scale      = 1.0f / sqrtf(2.0f);
-
-        ggml_tensor * per_layer_proj = ggml_mul_mat(ctx0, model.per_layer_model_proj, inputs_embeds);
-        per_layer_proj = ggml_scale(ctx0, per_layer_proj, per_layer_projection_scale);
-        per_layer_proj = ggml_reshape_3d(ctx0, per_layer_proj, n_embd_altup, n_layer, n_tokens);
-        per_layer_proj = build_norm(per_layer_proj,
-                                    model.per_layer_proj_norm, NULL,
-                                    LLM_NORM_RMS, -1); // [n_embd_altup, n_layer, n_tokens]
-        cb(per_layer_proj, "per_layer_proj", -1);
-
-        inp_per_layer = ggml_add(ctx0, inp_per_layer, per_layer_proj);
-        inp_per_layer = ggml_scale(ctx0, inp_per_layer, per_layer_input_scale);
-        cb(inp_per_layer, "inp_per_layer", -1);
-
-        // permute to shape: [n_embd_altup, n_tokens, n_layer]
-        inp_per_layer = ggml_cont(ctx0, ggml_permute(ctx0, inp_per_layer, 0, 2, 1, 3));
-        return inp_per_layer;
-    }
-
-    // input cur shape: [n_altup, n_tokens]
-    // output    shape: [n_altup, n_tokens]
-    ggml_tensor * laurel(ggml_tensor * cur, int il) {
-        ggml_tensor * tmp = cur;
-        tmp = build_lora_mm(model.layers[il].laurel_l, tmp);
-        tmp = build_lora_mm(model.layers[il].laurel_r, tmp);
-        tmp = build_norm(tmp, model.layers[il].laurel_post_norm, NULL, LLM_NORM_RMS, il);
-        tmp = ggml_add(ctx0, tmp, cur);
-        cb(tmp, "laurel_out", il);
-        return tmp;
-    }
-
-    // input x shape: [n_embd, n_tokens]
-    // output  shape: [n_embd, n_tokens]
-    ggml_tensor * gaussian_topk(ggml_tensor * x) {
-        ggml_tensor * mean = ggml_mean(ctx0, x);
-        ggml_tensor * std  = ggml_sqrt(ctx0, ggml_scale(ctx0,
-            ggml_sum_rows(ctx0, ggml_sqr(ctx0, ggml_sub(ctx0, x, mean))),
-            1.0f / (float)(x->ne[0] - 1)
-        ));
-        ggml_tensor * cutoff_x = ggml_add(ctx0, mean, ggml_scale(ctx0, std, f_sparsity_std_mul));
-        return ggml_relu(ctx0, ggml_sub(ctx0, x, cutoff_x));
-    }
-
-    //
-    // altup functions
-    //
-
-    // equivalent to compute_router_modalities() in python code
-    // input x shape: [n_embd,  n_tokens]
-    // output  shape: [n_altup, n_tokens]
-    ggml_tensor * altup_compute_router_modalities(ggml_tensor * x, int il) {
-        ggml_tensor * router_inputs = build_norm(x,
-            model.layers[il].altup_router_norm, NULL,
-            LLM_NORM_RMS, il);
-
-        // router_input_scale
-        router_inputs = ggml_scale(ctx0, router_inputs, 1.0f / (float)n_embd);
-
-        ggml_tensor * output = ggml_mul_mat(ctx0, model.layers[il].altup_router, router_inputs);
-        return ggml_tanh(ctx0, output); // [n_altup, n_tokens]
-    }
-
-    // input cur shape: [n_embd, n_tokens, n_altup]
-    // output    shape: [n_embd, n_tokens, n_altup]
-    ggml_tensor * altup_predict(ggml_tensor * cur, int il) {
-        ggml_tensor * activated = view_2d_slice(cur, i_altup_act); // [n_embd, n_tokens]
-        ggml_tensor * modalities = altup_compute_router_modalities(activated, il); // [n_altup, n_tokens]
-        cb(modalities, "modalities", il);
-
-        ggml_tensor * all_coefs = build_lora_mm(model.layers[il].altup_predict_coef, modalities);
-        cb(all_coefs, "all_coefs", il);
-        // first dim now having n_altup^2 elements, we reshape it to 2D (so we end up with 3D tensor)
-        all_coefs = ggml_reshape_3d(ctx0, all_coefs, n_altup, n_altup, n_tokens);
-
-        // permute to [n_altup, n_embd, n_tokens]
-        ggml_tensor * cur_permuted = ggml_cont(ctx0, ggml_permute(ctx0, cur, 1, 2, 0, 3));
-        ggml_tensor * predictions = ggml_mul_mat(ctx0, cur_permuted, all_coefs); // [n_altup, n_embd, n_tokens]
-
-        // final shape must be the same as cur: [n_embd, n_tokens, n_altup]
-        predictions = ggml_cont(ctx0, ggml_permute(ctx0, predictions, 0, 2, 1, 3));
-        predictions = ggml_add(ctx0, predictions, cur);
-        cb(predictions, "predictions", il);
-
-        return predictions;
-    }
-
-    // input predictions       shape: [n_embd, n_tokens, n_altup]
-    // input activated         shape: [n_embd, n_tokens]
-    // output                  shape: [n_embd, n_tokens, n_altup]
-    ggml_tensor * altup_correct(ggml_tensor * predictions, ggml_tensor * activated, int il) {
-        ggml_tensor * modalities = altup_compute_router_modalities(activated, il); // [n_altup, n_tokens]
-        cb(modalities, "modalities", il);
-
-        ggml_tensor * active_prediction = view_2d_slice(predictions, i_altup_act);
-        ggml_tensor * innovation = ggml_sub(ctx0, activated, active_prediction); // [n_embd, n_tokens]
-        cb(innovation, "innovation", il);
-
-        ggml_tensor * all_coefs = build_lora_mm(model.layers[il].altup_correct_coef, modalities); // [n_altup, n_tokens]
-        all_coefs = ggml_scale_bias(ctx0, all_coefs, 1.0f, 1.0f); // + 1.0
-        cb(all_coefs, "all_coefs", il);
-        all_coefs = ggml_transpose(ctx0, all_coefs); // [n_tokens, n_altup]
-        all_coefs = ggml_cont_3d(ctx0, all_coefs, 1, n_tokens, n_altup); // [1, n_tokens, n_altup]
-
-        innovation = ggml_repeat_4d(ctx0, innovation, n_embd, n_tokens, n_altup, 1);
-        ggml_tensor * corrected = ggml_mul(ctx0, innovation, all_coefs); // [n_embd, n_tokens, n_altup]
-        corrected = ggml_add(ctx0, corrected, predictions); // [n_embd, n_tokens, n_altup]
-        cb(corrected, "corrected", il);
-
-        return corrected;
-    }
-};
-
-struct llm_build_gemma_embedding : public llm_graph_context {
-    llm_build_gemma_embedding(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_k;
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // important: do not normalize weights for raw embeddings input (i.e. encoded image emdeddings)
-        if (ubatch.token) {
-            inpL = ggml_scale(ctx0, inpL, sqrtf(n_embd));
-            cb(inpL, "inp_scaled", -1);
-        }
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_no_cache();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            const float freq_base_l  = model.get_rope_freq_base (cparams, il);
-            const float freq_scale_l = model.get_rope_freq_scale(cparams, il);
-
-            // norm
-            cur = build_norm(inpL, model.layers[il].attn_norm, NULL, LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL, LLM_NORM_RMS, il);
-                cb(Qcur, "Qcur_normed", il);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base_l, freq_scale_l,
-                        ext_factor, attn_factor, beta_fast, beta_slow);
-
-                Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, NULL, LLM_NORM_RMS, il);
-                cb(Kcur, "Kcur_normed", il);
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base_l, freq_scale_l,
-                        ext_factor, attn_factor, beta_fast, beta_slow);
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                // ref: https://github.com/google/gemma_pytorch/blob/014acb7ac4563a5f77c76d7ff98f31b568c16508/gemma/model.py#L315
-                Qcur = ggml_scale(ctx0, Qcur, hparams.f_attention_scale);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, NULL,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f, il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur  = ggml_get_rows(ctx0,  cur, inp_out_ids);
-                inpL = ggml_get_rows(ctx0, inpL, inp_out_ids);
-            }
-
-            cur = build_norm(cur,
-                    model.layers[il].attn_post_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_post_norm", il);
-
-            ggml_tensor * sa_out = ggml_add(ctx0, cur, inpL);
-            cb(sa_out, "sa_out", il);
-
-            cur = build_norm(sa_out,
-                    model.layers[il].ffn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-
-            // feed-forward network
-            {
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up,   NULL, NULL,
-                        model.layers[il].ffn_gate, NULL, NULL,
-                        model.layers[il].ffn_down, NULL, NULL,
-                        NULL,
-                        LLM_FFN_GELU, LLM_FFN_PAR, il);
-                cb(cur, "ffn_out", il);
-            }
-
-            cur = build_norm(cur,
-                    model.layers[il].ffn_post_norm, NULL,
-                    LLM_NORM_RMS, -1);
-            cb(cur, "ffn_post_norm", -1);
-
-            cur = ggml_add(ctx0, cur, sa_out);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-// TODO: move up next to build_starcoder
-struct llm_build_starcoder2 : public llm_graph_context {
-    llm_build_starcoder2(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, model.layers[il].attn_norm_b,
-                    LLM_NORM, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-                if (model.layers[il].bq) {
-                    Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
-                    cb(Qcur, "Qcur", il);
-                }
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-                if (model.layers[il].bk) {
-                    Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
-                    cb(Kcur, "Kcur", il);
-                }
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-                if (model.layers[il].bv) {
-                    Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
-                    cb(Vcur, "Vcur", il);
-                }
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed-forward network
-
-            cur = build_norm(ffn_inp,
-                    model.layers[il].ffn_norm, model.layers[il].ffn_norm_b,
-                    LLM_NORM, il);
-            cb(cur, "ffn_norm", il);
-
-            cur = build_ffn(cur,
-                    model.layers[il].ffn_up,   model.layers[il].ffn_up_b,   NULL,
-                    NULL,                      NULL,                        NULL,
-                    model.layers[il].ffn_down, model.layers[il].ffn_down_b, NULL,
-                    NULL,
-                    LLM_FFN_GELU, LLM_FFN_SEQ, il);
-            cb(cur, "ffn_out", il);
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, model.output_norm_b,
-                LLM_NORM, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_graph_context_mamba : public llm_graph_context {
-    llm_graph_context_mamba(const llm_graph_params & params) : llm_graph_context(params) {}
-
-    ggml_tensor * build_mamba_layer(
-        llm_graph_input_rs * inp,
-               ggml_tensor * cur,
-         const llama_model & model,
-        const llama_ubatch & ubatch,
-                       int   il) {
-
-        const auto * mctx_cur = inp->mctx;
-
-        const auto kv_head = mctx_cur->get_head();
-
-        const auto & layer = model.layers[il];
-
-        const int64_t d_conv  = hparams.ssm_d_conv;
-        const int64_t d_inner = hparams.ssm_d_inner;
-        const int64_t d_state = hparams.ssm_d_state;
-        const int64_t dt_rank = hparams.ssm_dt_rank;
-        const int64_t n_head  = d_inner;
-        const int64_t head_dim = 1;
-        const int64_t n_seqs  = ubatch.n_seqs;
-        // Some variants of Mamba arch (e.g. FalconMamba do apply layer norm on B and Dt layers)
-        const bool ssm_dt_b_c_rms = hparams.ssm_dt_b_c_rms;
-
-        const int64_t n_seq_tokens = ubatch.n_seq_tokens;
-
-        GGML_ASSERT(n_seqs != 0);
-        GGML_ASSERT(ubatch.equal_seqs());
-        GGML_ASSERT(ubatch.n_tokens == n_seq_tokens * n_seqs);
-
-        ggml_tensor * conv_states_all = mctx_cur->get_r_l(il);
-        ggml_tensor * ssm_states_all  = mctx_cur->get_s_l(il);
-
-        ggml_tensor * conv = build_rs(inp, conv_states_all, hparams.n_embd_r(), n_seqs);
-        conv = ggml_reshape_3d(ctx0, conv, d_conv - 1, d_inner, n_seqs);
-
-        // {n_embd, n_tokens} => {n_embd, n_seq_tokens, n_seqs}
-        cur = ggml_reshape_3d(ctx0, cur, cur->ne[0], n_seq_tokens, n_seqs);
-
-        // {n_embd, 2*d_inner} @ {n_embd, n_seq_tokens, n_seqs} => {2*d_inner, n_seq_tokens, n_seqs}
-        ggml_tensor * xz = build_lora_mm(layer.ssm_in, cur);
-        // split the above in two
-        // => {d_inner, n_seq_tokens, n_seqs}
-        ggml_tensor * x = ggml_view_3d(ctx0, xz, d_inner, xz->ne[1], xz->ne[2], xz->nb[1], xz->nb[2], 0);
-        ggml_tensor * z = ggml_view_3d(ctx0, xz, d_inner, xz->ne[1], xz->ne[2], xz->nb[1], xz->nb[2], d_inner*ggml_element_size(xz));
-
-        // conv
-        {
-            // => {d_conv - 1 + n_seq_tokens, d_inner, n_seqs}
-            ggml_tensor * conv_x = ggml_concat(ctx0, conv, ggml_transpose(ctx0, x), 0);
-
-            // copy last (d_conv - 1) columns back into the state cache
-            ggml_tensor * last_conv = ggml_view_3d(ctx0, conv_x, d_conv - 1, d_inner, n_seqs, conv_x->nb[1], conv_x->nb[2], n_seq_tokens*(conv_x->nb[0]));
-
-            ggml_build_forward_expand(gf,
-                ggml_cpy(ctx0, last_conv,
-                    ggml_view_1d(ctx0, conv_states_all,
-                        (d_conv - 1)*(d_inner)*(n_seqs),
-                        kv_head*(d_conv - 1)*(d_inner)*ggml_element_size(conv_states_all))));
-
-            // 1D convolution
-            // The equivalent is to make a self-overlapping view of conv_x
-            // over d_conv columns at each stride in the 3rd dimension,
-            // then element-wise multiply that with the conv1d weight,
-            // then sum the elements of each row,
-            // (the last two steps are a dot product over rows (also doable with mul_mat))
-            // then permute away the ne[0] dimension,
-            // and then you're left with the resulting x tensor.
-            // For simultaneous sequences, all sequences need to have the same length.
-            x = ggml_ssm_conv(ctx0, conv_x, layer.ssm_conv1d);
-
-            // bias
-            x = ggml_add(ctx0, x, layer.ssm_conv1d_b);
-
-            x = ggml_silu(ctx0, x);
-        }
-
-        // ssm
-        {
-            // {d_inner, dt_rank + 2*d_state} @ {d_inner, n_seq_tokens, n_seqs} => {dt_rank + 2*d_state, n_seq_tokens, n_seqs}
-            ggml_tensor * x_db = build_lora_mm(layer.ssm_x, x);
-            // split
-            ggml_tensor * dt = ggml_view_3d(ctx0, x_db, dt_rank, n_seq_tokens, n_seqs, x_db->nb[1], x_db->nb[2], 0);
-            ggml_tensor * B  = ggml_view_4d(ctx0, x_db, d_state, /* n_group */ 1, n_seq_tokens, n_seqs, d_state*x_db->nb[0], x_db->nb[1], x_db->nb[2], ggml_element_size(x_db)*dt_rank);
-            ggml_tensor * C  = ggml_view_4d(ctx0, x_db, d_state, /* n_group */ 1, n_seq_tokens, n_seqs, d_state*x_db->nb[0], x_db->nb[1], x_db->nb[2], ggml_element_size(x_db)*(dt_rank+d_state));
-
-            // Some Mamba variants (e.g. FalconMamba, Jamba) apply RMS norm in B, C & Dt layers
-            if (ssm_dt_b_c_rms || (layer.ssm_dt_norm && layer.ssm_b_norm && layer.ssm_c_norm)) {
-                dt = build_norm(dt, layer.ssm_dt_norm, NULL, LLM_NORM_RMS, il);
-                B  = build_norm(B,  layer.ssm_b_norm,  NULL, LLM_NORM_RMS, il);
-                C  = build_norm(C,  layer.ssm_c_norm,  NULL, LLM_NORM_RMS, il);
-            }
-
-            // {dt_rank, d_inner} @ {dt_rank, n_seq_tokens, n_seqs} => {d_inner, n_seq_tokens, n_seqs}
-            dt = build_lora_mm(layer.ssm_dt, dt);
-            dt = ggml_add(ctx0, dt, layer.ssm_dt_b);
-
-            cur = x;
-            x = ggml_reshape_4d(ctx0, x, head_dim, n_head, n_seq_tokens, n_seqs);
-
-            ggml_tensor * A = layer.ssm_a;
-
-            // use the states and the indices provided by build_recurrent_state
-            // (this is necessary in order to properly use the states before they are overwritten,
-            //  while avoiding to make unnecessary copies of the states)
-            auto get_ssm_rows = [&](ggml_context * ctx, ggml_tensor * states, ggml_tensor * ids) {
-                ggml_tensor * ssm = ggml_reshape_4d(ctx, states, d_state, head_dim, n_head, mctx_cur->get_size());
-
-                // Custom operator to optimize the parallel associative scan
-                // as described in the Annex D of the Mamba paper.
-                // => {d_inner, n_seq_tokens, n_seqs} and {d_state, d_inner, n_seqs}
-                return ggml_ssm_scan(ctx, ssm, x, dt, A, B, C, ids);
-            };
-
-            ggml_tensor * y_ssm = build_rs(inp, ssm_states_all, hparams.n_embd_s(), ubatch.n_seqs, get_ssm_rows);
-
-            // store last states
-            ggml_build_forward_expand(gf,
-                ggml_cpy(ctx0,
-                    ggml_view_1d(ctx0, y_ssm, d_state*d_inner*n_seqs, x->nb[3]*x->ne[3]),
-                    ggml_view_1d(ctx0, ssm_states_all, d_state*d_inner*n_seqs, kv_head*d_state*d_inner*ggml_element_size(ssm_states_all))));
-
-            ggml_tensor * y = ggml_view_3d(ctx0, y_ssm, d_inner, n_seq_tokens, n_seqs, x->nb[2], x->nb[3], 0);
-
-            // TODO: skip computing output earlier for unused tokens
-
-            y = ggml_add(ctx0, y, ggml_mul(ctx0, cur, layer.ssm_d));
-            y = ggml_swiglu_split(ctx0, ggml_cont(ctx0, z), y);
-
-            // {d_inner, n_embd} @ {d_inner, n_seq_tokens, n_seqs} => {n_embd, n_seq_tokens, n_seqs}
-            cur = build_lora_mm(layer.ssm_out, y);
-        }
-
-        // {n_embd, n_seq_tokens, n_seqs} => {n_embd, n_tokens}
-        cur = ggml_reshape_2d(ctx0, cur, cur->ne[0], n_seq_tokens * n_seqs);
-
-        return cur;
-    }
-
-    ggml_tensor * build_mamba2_layer(
-        llm_graph_input_rs * inp,
-               ggml_tensor * cur,
-         const llama_model & model,
-        const llama_ubatch & ubatch,
-                       int   il) const {
-
-        const auto * mctx_cur = inp->mctx;
-
-        const auto kv_head = mctx_cur->get_head();
-
-        const int64_t d_conv  = hparams.ssm_d_conv;
-        const int64_t d_inner = hparams.ssm_d_inner;
-        const int64_t d_state = hparams.ssm_d_state;
-        const int64_t n_head  = hparams.ssm_dt_rank;
-        const int64_t head_dim = d_inner / n_head;
-        const int64_t n_group = hparams.ssm_n_group;
-        const int64_t n_seqs  = ubatch.n_seqs;
-
-        const int64_t n_seq_tokens = ubatch.n_seq_tokens;
-
-        GGML_ASSERT(n_seqs != 0);
-        GGML_ASSERT(ubatch.equal_seqs());
-        GGML_ASSERT(ubatch.n_tokens == n_seq_tokens * n_seqs);
-
-        ggml_tensor * conv_states_all = mctx_cur->get_r_l(il);
-        ggml_tensor * ssm_states_all  = mctx_cur->get_s_l(il);
-
-        ggml_tensor * conv = build_rs(inp, conv_states_all, hparams.n_embd_r(), n_seqs);
-        conv = ggml_reshape_3d(ctx0, conv, d_conv - 1, d_inner + 2*n_group*d_state, n_seqs);
-
-        // {n_embd, n_tokens} => {n_embd, n_seq_tokens, n_seqs}
-        cur = ggml_reshape_3d(ctx0, cur, cur->ne[0], n_seq_tokens, n_seqs);
-
-        // d_in_proj = 2 * self.d_inner + 2 * self.ngroups * self.d_state + self.nheads
-
-        // {n_embd, d_in_proj} @ {n_embd, n_seq_tokens, n_seqs} => {d_in_proj, n_seq_tokens, n_seqs}
-        ggml_tensor * zxBCdt = build_lora_mm(model.layers[il].ssm_in, cur);
-
-        // split the above in three
-        ggml_tensor * z = ggml_view_4d(ctx0, zxBCdt, head_dim, n_head, n_seq_tokens, n_seqs, head_dim*zxBCdt->nb[0], zxBCdt->nb[1], zxBCdt->nb[2], 0);
-        ggml_tensor * xBC = ggml_view_3d(ctx0, zxBCdt, d_inner + 2*n_group*d_state, n_seq_tokens, n_seqs, zxBCdt->nb[1], zxBCdt->nb[2], d_inner*ggml_element_size(zxBCdt));
-        ggml_tensor * dt = ggml_view_3d(ctx0, zxBCdt, n_head, n_seq_tokens, n_seqs, zxBCdt->nb[1], zxBCdt->nb[2], (2*d_inner + 2*n_group*d_state)*ggml_element_size(zxBCdt));
-
-        // conv
-        {
-            // => {d_conv - 1 + n_seq_tokens, d_inner + 2*n_group*d_state, n_seqs}
-            ggml_tensor * conv_x = ggml_concat(ctx0, conv, ggml_transpose(ctx0, xBC), 0);
-
-            // copy last (d_conv - 1) columns back into the state cache
-            ggml_tensor * last_conv = ggml_view_3d(ctx0, conv_x, d_conv - 1, d_inner + 2*n_group*d_state, n_seqs, conv_x->nb[1], conv_x->nb[2], n_seq_tokens*(conv_x->nb[0]));
-
-            ggml_build_forward_expand(gf,
-                ggml_cpy(ctx0, last_conv,
-                    ggml_view_1d(ctx0, conv_states_all,
-                        (d_conv - 1)*(d_inner + 2*n_group*d_state)*(n_seqs),
-                        kv_head*(d_conv - 1)*(d_inner + 2*n_group*d_state)*ggml_element_size(conv_states_all))));
-
-            // 1D convolution
-            // The equivalent is to make a self-overlapping view of conv_x
-            // over d_conv columns at each stride in the 3rd dimension,
-            // then element-wise multiply that with the conv1d weight,
-            // then sum the elements of each row,
-            // (the last two steps are a dot product over rows (also doable with mul_mat))
-            // then permute away the ne[0] dimension,
-            // and then you're left with the resulting x tensor.
-            // For simultaneous sequences, all sequences need to have the same length.
-            xBC = ggml_ssm_conv(ctx0, conv_x, model.layers[il].ssm_conv1d);
-
-            // bias
-            xBC = ggml_add(ctx0, xBC, model.layers[il].ssm_conv1d_b);
-
-            xBC = ggml_silu(ctx0, xBC);
-        }
-
-        // ssm
-        {
-            // These correspond to V K Q in SSM/attention duality
-            ggml_tensor * x = ggml_view_4d(ctx0, xBC, head_dim, n_head, n_seq_tokens, n_seqs, head_dim*xBC->nb[0], xBC->nb[1], xBC->nb[2], 0);
-            ggml_tensor * B = ggml_view_4d(ctx0, xBC, d_state, n_group, n_seq_tokens, n_seqs, d_state*xBC->nb[0], xBC->nb[1], xBC->nb[2], d_inner*ggml_element_size(xBC));
-            ggml_tensor * C = ggml_view_4d(ctx0, xBC, d_state, n_group, n_seq_tokens, n_seqs, d_state*xBC->nb[0], xBC->nb[1], xBC->nb[2], (d_inner + n_group*d_state)*ggml_element_size(xBC));
-
-            // {n_head, n_seq_tokens, n_seqs}
-            dt = ggml_add(ctx0, ggml_cont(ctx0, dt), model.layers[il].ssm_dt_b);
-
-            ggml_tensor * A = model.layers[il].ssm_a;
-
-            // use the states and the indices provided by build_recurrent_state
-            // (this is necessary in order to properly use the states before they are overwritten,
-            //  while avoiding to make unnecessary copies of the states)
-            auto get_ssm_rows = [&](ggml_context * ctx, ggml_tensor * states, ggml_tensor * ids) {
-                ggml_tensor * ssm = ggml_reshape_4d(ctx, states, d_state, head_dim, n_head, mctx_cur->get_size());
-
-                // TODO: use semistructured matrices to implement state-space duality
-                // => {d_inner, n_seq_tokens, n_seqs} and {d_state, d_inner, n_seqs}
-                return ggml_ssm_scan(ctx, ssm, x, dt, A, B, C, ids);
-            };
-
-            ggml_tensor * y_ssm = build_rs(inp, ssm_states_all, hparams.n_embd_s(), ubatch.n_seqs, get_ssm_rows);
-
-            // store last states
-            ggml_build_forward_expand(gf,
-                ggml_cpy(ctx0,
-                    ggml_view_1d(ctx0, y_ssm, d_state*d_inner*n_seqs, ggml_nelements(x)*x->nb[0]),
-                    ggml_view_1d(ctx0, ssm_states_all, d_state*d_inner*n_seqs, kv_head*d_state*d_inner*ggml_element_size(ssm_states_all))));
-
-            ggml_tensor * y = ggml_view_4d(ctx0, y_ssm, head_dim, n_head, n_seq_tokens, n_seqs, x->nb[1], n_head*x->nb[1], n_seq_tokens*n_head*x->nb[1], 0);
-
-            // TODO: skip computing output earlier for unused tokens
-
-            y = ggml_add(ctx0, y, ggml_mul(ctx0, x, model.layers[il].ssm_d));
-            cb(y, "mamba2_y_add_d", il);
-            y = ggml_swiglu_split(ctx0, ggml_cont(ctx0, z), y);
-
-            // grouped RMS norm
-            if (model.layers[il].ssm_norm) {
-                y = ggml_reshape_4d(ctx0, y, d_inner / n_group, n_group, n_seq_tokens, n_seqs);
-                y = build_norm(y, model.layers[il].ssm_norm, NULL, LLM_NORM_RMS, il);
-            }
-
-            y = ggml_reshape_3d(ctx0, y, d_inner, n_seq_tokens, n_seqs);
-
-            // {d_inner, n_embd} @ {d_inner, n_seq_tokens, n_seqs} => {n_embd, n_seq_tokens, n_seqs}
-            cur = build_lora_mm(model.layers[il].ssm_out, y);
-        }
-
-        // {n_embd, n_seq_tokens, n_seqs} => {n_embd, n_tokens}
-        cur = ggml_reshape_2d(ctx0, cur, cur->ne[0], n_seq_tokens * n_seqs);
-        cb(cur, "mamba_out", il);
-
-        return cur;
-    }
-};
-
-struct llm_build_mamba : public llm_graph_context_mamba {
-    llm_build_mamba(const llama_model & model, const llm_graph_params & params) : llm_graph_context_mamba(params) {
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        // {n_embd, n_tokens}
-        inpL = build_inp_embd(model.tok_embd);
-
-        auto * rs_inp = build_rs_inp();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            if (model.arch == LLM_ARCH_MAMBA2) {
-                cur = build_mamba2_layer(rs_inp, cur, model, ubatch, il);
-            } else {
-                cur = build_mamba_layer(rs_inp, cur, model, ubatch, il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur  = ggml_get_rows(ctx0,  cur, inp_out_ids);
-                inpL = ggml_get_rows(ctx0, inpL, inp_out_ids);
-            }
-
-            // residual
-            cur = ggml_add(ctx0, cur, inpL);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        // final rmsnorm
-        cur = build_norm(inpL, model.output_norm, NULL, LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-
-};
-
-struct llm_build_jamba : public llm_graph_context_mamba {
-    llm_build_jamba(const llama_model & model, const llm_graph_params & params) : llm_graph_context_mamba(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        // {n_embd, n_tokens}
-        inpL = build_inp_embd(model.tok_embd);
-
-        auto * inp_hybrid = build_inp_mem_hybrid();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            const int64_t n_head_kv = hparams.n_head_kv(il);
-
-            cur = build_norm(inpL, model.layers[il].attn_norm, NULL, LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            if (n_head_kv == 0) {
-                cur = build_mamba_layer(inp_hybrid->get_recr(), cur, model, ubatch, il);
-            } else {
-                // Attention
-
-                struct ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                struct ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                struct ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                // No RoPE :)
-                cur = build_attn(inp_hybrid->get_attn(),
-                        model.layers[il].wo, NULL,
-                        Qcur, Kcur, Vcur, NULL, NULL, NULL, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur  = ggml_get_rows(ctx0,  cur, inp_out_ids);
-                inpL = ggml_get_rows(ctx0, inpL, inp_out_ids);
-            }
-
-            // residual
-            struct ggml_tensor * ffn_inp = ggml_add(ctx0, inpL, cur);
-            cb(cur, "ffn_inp", il);
-
-            cur = build_norm(ffn_inp, model.layers[il].ffn_norm, NULL, LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-
-            // feed-forward network
-            if (model.layers[il].ffn_gate_inp == nullptr) {
-                // FFN
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up,   NULL, NULL,
-                        model.layers[il].ffn_gate, NULL, NULL,
-                        model.layers[il].ffn_down, NULL, NULL,
-                        NULL,
-                        LLM_FFN_SILU, LLM_FFN_PAR, il);
-                cb(cur, "ffn_out", il);
-            } else {
-                // MoE branch
-                cur = build_moe_ffn(cur,
-                        model.layers[il].ffn_gate_inp,
-                        model.layers[il].ffn_up_exps,
-                        model.layers[il].ffn_gate_exps,
-                        model.layers[il].ffn_down_exps,
-                        nullptr,
-                        n_expert, n_expert_used,
-                        LLM_FFN_SILU, false,
-                        false, 0.0,
-                        LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
-                        il);
-                cb(cur, "ffn_moe_out", il);
-            }
-
-            // residual
-            cur = ggml_add(ctx0, ffn_inp, cur);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        // final rmsnorm
-        cur = build_norm(inpL, model.output_norm, NULL, LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_command_r : public llm_graph_context {
-    llm_build_command_r(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-
-        const float f_logit_scale = hparams.f_logit_scale;
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM, il);
-            cb(cur, "attn_norm", il);
-
-            ggml_tensor * ffn_inp = cur;
-
-            // self-attention
-            {
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-                if (model.layers[il].bq) {
-                    Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
-                    cb(Qcur, "Qcur", il);
-                }
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-                if (model.layers[il].bk) {
-                    Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
-                    cb(Kcur, "Kcur", il);
-                }
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-                if (model.layers[il].bv) {
-                    Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
-                    cb(Vcur, "Vcur", il);
-                }
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                if (model.layers[il].attn_q_norm) {
-                    Qcur = build_norm(Qcur,
-                            model.layers[il].attn_q_norm,
-                            NULL,
-                            LLM_NORM, il);
-                    cb(Qcur, "Qcur", il);
-                }
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                if (model.layers[il].attn_k_norm) {
-                    Kcur = build_norm(Kcur,
-                            model.layers[il].attn_k_norm,
-                            NULL,
-                            LLM_NORM, il);
-                    cb(Kcur, "Kcur", il);
-                }
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur     = ggml_get_rows(ctx0,     cur, inp_out_ids);
-                inpL    = ggml_get_rows(ctx0,    inpL, inp_out_ids);
-                ffn_inp = ggml_get_rows(ctx0, ffn_inp, inp_out_ids);
-            }
-
-            ggml_tensor * attn_out = cur;
-
-            // feed-forward network
-            {
-                cur = build_ffn(ffn_inp,
-                        model.layers[il].ffn_up,   NULL, NULL,
-                        model.layers[il].ffn_gate, NULL, NULL,
-                        model.layers[il].ffn_down, NULL, NULL,
-                        NULL,
-                        LLM_FFN_SILU, LLM_FFN_PAR, il);
-                cb(cur, "ffn_out", il);
-            }
-
-            // add together residual + FFN + self-attention
-            cur = ggml_add(ctx0, cur, inpL);
-            cur = ggml_add(ctx0, cur, attn_out);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        if (f_logit_scale) {
-            cur = ggml_scale(ctx0, cur, f_logit_scale);
-        }
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_cohere2_iswa : public llm_graph_context {
-    llm_build_cohere2_iswa(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-
-        const float f_logit_scale = hparams.f_logit_scale;
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv_iswa();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            const bool is_swa = hparams.is_swa(il);
-
-            // norm
-            cur = build_norm(inpL, model.layers[il].attn_norm, NULL, LLM_NORM, il);
-            cb(cur, "attn_norm", il);
-            ggml_tensor * ffn_inp = cur;
-
-            // self-attention
-            {
-                // rope freq factors for 128k context
-                ggml_tensor * rope_factors = model.get_rope_factors(cparams, il);
-
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-                if (model.layers[il].bq) {
-                    Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
-                    cb(Qcur, "Qcur", il);
-                }
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-                if (model.layers[il].bk) {
-                    Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
-                    cb(Kcur, "Kcur", il);
-                }
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-                if (model.layers[il].bv) {
-                    Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
-                    cb(Vcur, "Vcur", il);
-                }
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                if (is_swa) {
-                    Qcur = ggml_rope_ext(
-                            ctx0, Qcur, inp_pos, rope_factors,
-                            n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                            ext_factor, attn_factor, beta_fast, beta_slow
-                            );
-
-                    Kcur = ggml_rope_ext(
-                            ctx0, Kcur, inp_pos, rope_factors,
-                            n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                            ext_factor, attn_factor, beta_fast, beta_slow
-                            );
-                }
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur     = ggml_get_rows(ctx0, cur, inp_out_ids);
-                inpL    = ggml_get_rows(ctx0, inpL, inp_out_ids);
-                ffn_inp = ggml_get_rows(ctx0, ffn_inp, inp_out_ids);
-            }
-
-            ggml_tensor * attn_out = cur;
-
-            // feed-forward network
-            {
-                cur = build_ffn(ffn_inp, model.layers[il].ffn_up, NULL, NULL, model.layers[il].ffn_gate,
-                        NULL, NULL, model.layers[il].ffn_down, NULL, NULL, NULL, LLM_FFN_SILU, LLM_FFN_PAR,
-                        il);
-                cb(cur, "ffn_out", il);
-            }
-
-            // add together residual + FFN + self-attention
-            cur = ggml_add(ctx0, cur, inpL);
-            cur = ggml_add(ctx0, cur, attn_out);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur, model.output_norm, NULL, LLM_NORM, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        if (f_logit_scale) {
-            cur = ggml_scale(ctx0, cur, f_logit_scale);
-        }
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-// ref: https://allenai.org/olmo
-// based on the original build_llama() function, changes:
-//   * non-parametric layer norm
-//   * clamp qkv
-//   * removed bias
-//   * removed MoE
-struct llm_build_olmo : public llm_graph_context {
-    llm_build_olmo(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            // norm
-            cur = build_norm(inpL,
-                    NULL, NULL,
-                    LLM_NORM, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-                if (hparams.f_clamp_kqv > 0.0f) {
-                    Qcur = ggml_clamp(ctx0, Qcur, -hparams.f_clamp_kqv, hparams.f_clamp_kqv);
-                    cb(Qcur, "Qcur", il);
-                }
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-                if (hparams.f_clamp_kqv > 0.0f) {
-                    Kcur = ggml_clamp(ctx0, Kcur, -hparams.f_clamp_kqv, hparams.f_clamp_kqv);
-                    cb(Kcur, "Kcur", il);
-                }
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-                if (hparams.f_clamp_kqv > 0.0f) {
-                    Vcur = ggml_clamp(ctx0, Vcur, -hparams.f_clamp_kqv, hparams.f_clamp_kqv);
-                    cb(Vcur, "Vcur", il);
-                }
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, nullptr,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed-forward network
-            cur = build_norm(ffn_inp,
-                    NULL, NULL,
-                    LLM_NORM, il);
-            cb(cur, "ffn_norm", il);
-
-            cur = build_ffn(cur,
-                    model.layers[il].ffn_up,   NULL, NULL,
-                    model.layers[il].ffn_gate, NULL, NULL,
-                    model.layers[il].ffn_down, NULL, NULL,
-                    NULL,
-                    LLM_FFN_SILU, LLM_FFN_PAR, il);
-            cb(cur, "ffn_out", il);
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-            cb(cur, "ffn_out", il);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                NULL, NULL,
-                LLM_NORM, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-template <bool iswa>
-struct llm_build_olmo2 : public llm_graph_context {
-    llm_build_olmo2(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        using inp_attn_type = std::conditional_t<iswa, llm_graph_input_attn_kv_iswa, llm_graph_input_attn_kv>;
-        inp_attn_type * inp_attn = nullptr;
-
-        if constexpr (iswa) {
-            inp_attn = build_attn_inp_kv_iswa();
-        } else {
-            inp_attn = build_attn_inp_kv();
-        }
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            cur = inpL;
-
-            // self_attention
-            {
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-
-                Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL,
-                        LLM_NORM_RMS, il);
-                cb(Qcur, "Qcur_normed", il);
-
-                Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, NULL,
-                        LLM_NORM_RMS, il);
-                cb(Kcur, "Kcur_normed", il);
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                const bool is_swa = hparams.is_swa(il);
-
-                if (is_swa) {
-                    // For sliding window layers, Olmo3 use regular rope with no yarn rope scaling.
-                    // This is achieved here by setting freq_scale and attn_factor to 1.
-                    // We also set ext_factor to 0 to avoid a few unnecessary computations.
-                    Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, 1.0,
-                        0.0, 1.0, beta_fast, beta_slow
-                        );
-
-                    Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, 1.0,
-                        0.0, 1.0, beta_fast, beta_slow
-                        );
-                } else {
-                    Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                    Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-                }
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, NULL,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            cur = build_norm(cur,
-                    model.layers[il].attn_post_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_post_norm", il);
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed-forward network
-            cur = build_ffn(ffn_inp,
-                    model.layers[il].ffn_up,   NULL, NULL,
-                    model.layers[il].ffn_gate, NULL, NULL,
-                    model.layers[il].ffn_down, NULL, NULL,
-                    NULL,
-                    LLM_FFN_SILU, LLM_FFN_PAR, il);
-            cb(cur, "ffn_out", il);
-
-            cur = build_norm(cur,
-                    model.layers[il].ffn_post_norm, NULL,
-                    LLM_NORM_RMS, -1);
-            cb(cur, "ffn_post_norm", -1);
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-            cb(cur, "ffn_out", il);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-// based on the build_qwen2moe() function, changes:
-//   * removed shared experts
-//   * removed bias
-//   * added q, k norm
-struct llm_build_olmoe : public llm_graph_context {
-    llm_build_olmoe(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self_attention
-            {
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-
-                Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL,
-                        LLM_NORM_RMS, il);
-                cb(Qcur, "Qcur_normed", il);
-
-                Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, NULL,
-                        LLM_NORM_RMS, il);
-                cb(Kcur, "Kcur_normed", il);
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, NULL,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // MoE branch
-            cur = build_norm(ffn_inp,
-                    model.layers[il].ffn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-
-            cur = build_moe_ffn(cur,
-                    model.layers[il].ffn_gate_inp,
-                    model.layers[il].ffn_up_exps,
-                    model.layers[il].ffn_gate_exps,
-                    model.layers[il].ffn_down_exps,
-                    nullptr,
-                    n_expert, n_expert_used,
-                    LLM_FFN_SILU, false,
-                    false, 0.0,
-                    LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
-                    il);
-            cb(cur, "ffn_moe_out", il);
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_llada_moe : public llm_graph_context {
-    llm_build_llada_moe(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_no_cache();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self_attention
-            {
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head, n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL, LLM_NORM_RMS, il);
-                cb(Qcur, "Qcur_normed", il);
-
-                Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, NULL, LLM_NORM_RMS, il);
-                cb(Kcur, "Kcur_normed", il);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, NULL,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // MoE branch
-            cur = build_norm(ffn_inp,
-                    model.layers[il].ffn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-
-            cur = build_moe_ffn(cur,
-                    model.layers[il].ffn_gate_inp,
-                    model.layers[il].ffn_up_exps,
-                    model.layers[il].ffn_gate_exps,
-                    model.layers[il].ffn_down_exps,
-                    nullptr,
-                    n_expert, n_expert_used,
-                    LLM_FFN_SILU, false,
-                    false, 0.0,
-                    LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
-                    il);
-            cb(cur, "ffn_moe_out", il);
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_openelm : public llm_graph_context {
-    llm_build_openelm(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            const int64_t n_head    = hparams.n_head(il);
-            const int64_t n_head_kv = hparams.n_head_kv(il);
-            const int64_t n_head_qkv = 2*n_head_kv + n_head;
-
-            cur = inpL;
-            ggml_tensor * residual = cur;
-
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                cur = build_lora_mm(model.layers[il].wqkv, cur);
-                cb(cur, "wqkv", il);
-
-                cur = ggml_reshape_3d(ctx0, cur, n_embd_head_k, n_head_qkv, n_tokens);
-
-                ggml_tensor * Qcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head,    n_tokens, cur->nb[1], cur->nb[2], 0);
-                cb(Qcur, "Qcur", il);
-
-                ggml_tensor * Kcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, cur->nb[1], cur->nb[2], cur->nb[1]*n_head);
-                cb(Kcur, "Kcur", il);
-
-                ggml_tensor * Vcur = ggml_cont(ctx0, ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, cur->nb[1], cur->nb[2], cur->nb[1]*(n_head+n_head_kv)));
-                cb(Vcur, "Vcur", il);
-
-                Qcur = build_norm(Qcur,
-                        model.layers[il].attn_q_norm, NULL,
-                        LLM_NORM_RMS, il);
-                cb(Qcur, "Qcur", il);
-
-                Kcur = build_norm(Kcur,
-                        model.layers[il].attn_k_norm, NULL,
-                        LLM_NORM_RMS, il);
-                cb(Kcur, "Kcur", il);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, NULL,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, NULL,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Qcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, NULL,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                residual = ggml_get_rows(ctx0, residual, inp_out_ids);
-                cur      = ggml_get_rows(ctx0, cur,      inp_out_ids);
-            }
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, residual, cur);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed-forward network
-            {
-                cur = build_norm(ffn_inp,
-                        model.layers[il].ffn_norm, NULL,
-                        LLM_NORM_RMS, il);
-                cb(cur, "ffn_norm", il);
-
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up,   NULL, NULL,
-                        model.layers[il].ffn_gate, NULL, NULL,
-                        model.layers[il].ffn_down, NULL, NULL,
-                        NULL,
-                        LLM_FFN_SILU, LLM_FFN_PAR, il);
-                cb(cur, "ffn_out", il);
-            }
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        // norm
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_gptneox : public llm_graph_context {
-    llm_build_gptneox(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-        const int64_t n_embd_gqa  = hparams.n_embd_v_gqa();
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm,
-                    model.layers[il].attn_norm_b,
-                    LLM_NORM, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                cur = build_lora_mm(model.layers[il].wqkv, cur);
-                cb(cur, "wqkv", il);
-
-                cur = ggml_add(ctx0, cur, model.layers[il].bqkv);
-                cb(cur, "bqkv", il);
-
-                ggml_tensor * Qcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head,    n_tokens, n_embd_head*sizeof(float), cur->nb[1], 0*sizeof(float)*(n_embd));
-                ggml_tensor * Kcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd));
-                ggml_tensor * Vcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd + n_embd_gqa));
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur  = ggml_get_rows(ctx0,  cur, inp_out_ids);
-                inpL = ggml_get_rows(ctx0, inpL, inp_out_ids);
-            }
-
-            // ffn
-            if (hparams.use_par_res) {
-                // attention and ffn are computed in parallel
-                // x = x + attn(ln1(x)) + ffn(ln2(x))
-
-                ggml_tensor * attn_out = cur;
-
-                cur = build_norm(inpL,
-                        model.layers[il].ffn_norm,
-                        model.layers[il].ffn_norm_b,
-                        LLM_NORM, il);
-                cb(cur, "ffn_norm", il);
-
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up,   model.layers[il].ffn_up_b,   NULL,
-                        NULL,                      NULL,                        NULL,
-                        model.layers[il].ffn_down, model.layers[il].ffn_down_b, NULL,
-                        NULL,
-                        LLM_FFN_GELU, LLM_FFN_SEQ, il);
-                cb(cur, "ffn_out", il);
-
-                cur = ggml_add(ctx0, cur, inpL);
-                cb(cur, "ffn_out", il);
-
-                cur = ggml_add(ctx0, cur, attn_out);
-
-                cur = build_cvec(cur, il);
-                cb(cur, "l_out", il);
-
-                // input for next layer
-                inpL = cur;
-            } else {
-                // attention and ffn are computed sequentially
-                // x = x + attn(ln1(x))
-                // x = x + ffn(ln2(x))
-
-                ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpL);
-                cb(ffn_inp, "ffn_inp", il);
-
-                cur = build_norm(ffn_inp,
-                        model.layers[il].ffn_norm,
-                        model.layers[il].ffn_norm_b,
-                        LLM_NORM, il);
-                cb(cur, "ffn_norm", il);
-
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up,   model.layers[il].ffn_up_b,   NULL,
-                        NULL,                      NULL,                        NULL,
-                        model.layers[il].ffn_down, model.layers[il].ffn_down_b, NULL,
-                        NULL,
-                        LLM_FFN_GELU, LLM_FFN_SEQ, il);
-                cb(cur, "ffn_out", il);
-
-                cur = ggml_add(ctx0, cur, ffn_inp);
-
-                cur = build_cvec(cur, il);
-                cb(cur, "l_out", il);
-
-                // input for next layer
-                inpL = cur;
-            }
-        }
-
-        cur = build_norm(inpL,
-                model.output_norm,
-                model.output_norm_b,
-                LLM_NORM, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_arctic : public llm_graph_context {
-    llm_build_arctic(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, NULL,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed-forward network
-            cur = build_norm(ffn_inp,
-                    model.layers[il].ffn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-
-            cur = build_ffn(cur,
-                    model.layers[il].ffn_up,   NULL, NULL,
-                    model.layers[il].ffn_gate, NULL, NULL,
-                    model.layers[il].ffn_down, NULL, NULL,
-                    NULL,
-                    LLM_FFN_SILU, LLM_FFN_PAR, il);
-            cb(cur, "ffn_out", il);
-
-            ggml_tensor * ffn_out = ggml_add(ctx0, cur, ffn_inp);
-            cb(ffn_out, "ffn_out", il);
-
-            // MoE
-            cur = build_norm(inpSA,
-                    model.layers[il].ffn_norm_exps, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm_exps", il);
-
-            cur = build_moe_ffn(cur,
-                    model.layers[il].ffn_gate_inp,
-                    model.layers[il].ffn_up_exps,
-                    model.layers[il].ffn_gate_exps,
-                    model.layers[il].ffn_down_exps,
-                    nullptr,
-                    n_expert, n_expert_used,
-                    LLM_FFN_SILU, true,
-                    false, 0.0,
-                    LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
-                    il);
-            cb(cur, "ffn_moe_out", il);
-
-            cur = ggml_add(ctx0, cur, ffn_out);
-            cb(cur, "ffn_out", il);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_deepseek : public llm_graph_context {
-    llm_build_deepseek(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        const float kq_scale = hparams.f_attention_scale == 0.0f ? 1.0f/sqrtf(float(n_embd_head)) : hparams.f_attention_scale;
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                // rope freq factors for llama3; may return nullptr for llama2 and other models
-                ggml_tensor * rope_factors = model.get_rope_factors(cparams, il);
-
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-                if (model.layers[il].bq) {
-                    Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
-                    cb(Qcur, "Qcur", il);
-                }
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-                if (model.layers[il].bk) {
-                    Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
-                    cb(Kcur, "Kcur", il);
-                }
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-                if (model.layers[il].bv) {
-                    Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
-                    cb(Vcur, "Vcur", il);
-                }
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, rope_factors,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, rope_factors,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, kq_scale, il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            cur = build_norm(ffn_inp,
-                    model.layers[il].ffn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-
-            if ((uint32_t) il < hparams.n_layer_dense_lead) {
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up,   NULL, NULL,
-                        model.layers[il].ffn_gate, NULL, NULL,
-                        model.layers[il].ffn_down, NULL, NULL,
-                        NULL,
-                        LLM_FFN_SILU, LLM_FFN_PAR, il);
-                cb(cur, "ffn_out", il);
-            } else {
-                // MoE branch
-                ggml_tensor * moe_out =
-                    build_moe_ffn(cur,
-                            model.layers[il].ffn_gate_inp,
-                            model.layers[il].ffn_up_exps,
-                            model.layers[il].ffn_gate_exps,
-                            model.layers[il].ffn_down_exps,
-                            nullptr,
-                            n_expert, n_expert_used,
-                            LLM_FFN_SILU, false,
-                            false, hparams.expert_weights_scale,
-                            LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
-                            il);
-                cb(moe_out, "ffn_moe_out", il);
-
-                // FFN shared expert
-                {
-                    ggml_tensor * ffn_shexp = build_ffn(cur,
-                            model.layers[il].ffn_up_shexp,   NULL, NULL,
-                            model.layers[il].ffn_gate_shexp, NULL, NULL,
-                            model.layers[il].ffn_down_shexp, NULL, NULL,
-                            NULL,
-                            LLM_FFN_SILU, LLM_FFN_PAR, il);
-                    cb(ffn_shexp, "ffn_shexp", il);
-
-                    cur = ggml_add(ctx0, moe_out, ffn_shexp);
-                    cb(cur, "ffn_out", il);
-                }
-            }
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_deepseek2 : public llm_graph_context {
-    llm_build_deepseek2(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        bool is_lite = (hparams.n_layer == 27);
-
-        const bool is_mla = (hparams.n_embd_head_k_mla != 0 && hparams.n_embd_head_v_mla != 0);
-
-        // note: these are the actual head sizes you get when treating as MHA or after "decompression" using wv_b for MLA
-        const int64_t n_embd_head_k = is_mla ? hparams.n_embd_head_k_mla : hparams.n_embd_head_k;
-        const int64_t n_embd_head_v = is_mla ? hparams.n_embd_head_v_mla : hparams.n_embd_head_v;
-
-        const int64_t n_embd_head_qk_rope = hparams.n_rot;
-        const int64_t n_embd_head_qk_nope = n_embd_head_k - n_embd_head_qk_rope;
-
-        const uint32_t kv_lora_rank = hparams.n_lora_kv;
-
-        // We have to pre-scale kq_scale and attn_factor to make the YaRN RoPE work correctly.
-        // See https://github.com/ggerganov/llama.cpp/discussions/7416 for detailed explanation.
-        const float mscale = attn_factor * (1.0f + hparams.rope_yarn_log_mul * logf(1.0f / freq_scale));
-        const float kq_scale = 1.0f*mscale*mscale/sqrtf(float(n_embd_head_k));
-        const float attn_factor = 1.0f / (1.0f + 0.1f * logf(1.0f / freq_scale));
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        // {n_embd, n_tokens}
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self_attention
-            {
-                ggml_tensor * q = NULL;
-                if (!is_lite) {
-                    q = ggml_mul_mat(ctx0, model.layers[il].wq_a, cur);
-                    cb(q, "q", il);
-
-                    q = build_norm(q,
-                            model.layers[il].attn_q_a_norm, nullptr,
-                            LLM_NORM_RMS, il);
-                    cb(q, "q", il);
-
-                    q = ggml_mul_mat(ctx0, model.layers[il].wq_b, q);
-                    cb(q, "q", il);
-                } else {
-                    q = ggml_mul_mat(ctx0, model.layers[il].wq, cur);
-                    cb(q, "q", il);
-                }
-
-                // split into {n_embd_head_qk_nope, n_head, n_tokens}
-                ggml_tensor * q_nope = ggml_view_3d(ctx0, q,
-                        n_embd_head_qk_nope, n_head, n_tokens,
-                        ggml_row_size(q->type, n_embd_head_k),
-                        ggml_row_size(q->type, n_embd_head_k) * n_head,
-                        0);
-                cb(q_nope, "q_nope", il);
-
-                // and {n_embd_head_qk_rope, n_head, n_tokens}
-                ggml_tensor * q_pe = ggml_view_3d(ctx0, q,
-                        n_embd_head_qk_rope, n_head, n_tokens,
-                        ggml_row_size(q->type, n_embd_head_k),
-                        ggml_row_size(q->type, n_embd_head_k) * n_head,
-                        ggml_row_size(q->type, n_embd_head_qk_nope));
-                cb(q_pe, "q_pe", il);
-
-                ggml_tensor * kv_cmpr_pe = ggml_mul_mat(ctx0, model.layers[il].wkv_a_mqa, cur);
-                cb(kv_cmpr_pe, "kv_cmpr_pe", il);
-
-                // split into {kv_lora_rank, n_tokens}
-                ggml_tensor * kv_cmpr = ggml_view_2d(ctx0, kv_cmpr_pe,
-                        kv_lora_rank, n_tokens,
-                        ggml_row_size(kv_cmpr_pe->type, kv_lora_rank + n_embd_head_qk_rope),
-                        0);
-                cb(kv_cmpr, "kv_cmpr", il);
-
-                // and {n_embd_head_qk_rope, 1, n_tokens}
-                ggml_tensor * k_pe = ggml_view_3d(ctx0, kv_cmpr_pe,
-                        n_embd_head_qk_rope, 1, n_tokens,
-                        ggml_row_size(kv_cmpr_pe->type, kv_lora_rank + n_embd_head_qk_rope),
-                        ggml_row_size(kv_cmpr_pe->type, kv_lora_rank + n_embd_head_qk_rope),
-                        ggml_row_size(kv_cmpr_pe->type, kv_lora_rank));
-                cb(k_pe, "k_pe", il);
-
-                q_pe = ggml_rope_ext(ctx0, q_pe, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                );
-                cb(q_pe, "q_pe", il);
-
-                k_pe = ggml_rope_ext(ctx0, k_pe, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                );
-                cb(k_pe, "k_pe", il);
-
-                kv_cmpr = build_norm(kv_cmpr,
-                        model.layers[il].attn_kv_a_norm, nullptr,
-                        LLM_NORM_RMS, il);
-                cb(kv_cmpr, "kv_cmpr", il);
-
-                if (is_mla) {
-                    // {n_embd_head_qk_nope, n_tokens, n_head}
-                    q_nope = ggml_permute(ctx0, q_nope, 0, 2, 1, 3);
-                    cb(q_nope, "q_nope_perm", il);
-
-                    // {n_embd_head_qk_nope, kv_lora_rank, n_head} x {n_embd_head_qk_nope, n_tokens, n_head}
-                    ggml_tensor * q_nope_absorbed = ggml_mul_mat(ctx0, model.layers[il].wk_b, q_nope);
-                    cb(q_nope_absorbed, "q_nope_absorbed", il);
-
-                    // {kv_lora_rank, n_head, n_tokens}
-                    q_nope_absorbed = ggml_permute(ctx0, q_nope_absorbed, 0, 2, 1, 3);
-                    cb(q_nope_absorbed, "q_nope_absorbed_perm", il);
-
-                    // {n_embd_head_qk_rope + kv_lora_rank, n_head, n_tokens}
-                    // note: rope must go first for in-place context shifting in build_rope_shift()
-                    ggml_tensor * Qcur = ggml_concat(ctx0, q_pe, q_nope_absorbed, 0);
-                    cb(Qcur, "Qcur", il);
-
-                    kv_cmpr = ggml_reshape_3d(ctx0, kv_cmpr, kv_lora_rank, 1, n_tokens);
-                    cb(kv_cmpr, "kv_cmpr_reshape", il);
-
-                    // {n_embd_head_qk_rope + kv_lora_rank, 1, n_tokens}
-                    ggml_tensor * Kcur = ggml_concat(ctx0, k_pe, kv_cmpr, 0);
-                    cb(Kcur, "Kcur", il);
-
-                    // {kv_lora_rank, 1, n_tokens}
-                    ggml_tensor * Vcur = kv_cmpr;
-                    cb(Vcur, "Vcur", il);
-
-                    // note: MLA with the absorption optimzation converts into MQA (ie: GQA with 1 group)
-                    cur = build_attn(inp_attn,
-                            model.layers[il].wo, NULL,
-                            Qcur, Kcur, Vcur, nullptr, nullptr, model.layers[il].wv_b, kq_scale, il);
-                } else {
-                    ggml_tensor * kv = ggml_mul_mat(ctx0, model.layers[il].wkv_b, kv_cmpr);
-                    cb(kv, "kv", il);
-
-                    // split into {n_embd_head_qk_nope, n_head, n_tokens}
-                    ggml_tensor * k_nope = ggml_view_3d(ctx0, kv,
-                            n_embd_head_qk_nope, n_head, n_tokens,
-                            ggml_row_size(kv->type, n_embd_head_qk_nope + n_embd_head_v),
-                            ggml_row_size(kv->type, n_embd_head_qk_nope + n_embd_head_v) * n_head,
-                            0);
-                    cb(k_nope, "k_nope_view", il);
-
-                    // and {n_embd_head_v, n_head, n_tokens}
-                    ggml_tensor * Vcur = ggml_view_3d(ctx0, kv,
-                            n_embd_head_v, n_head, n_tokens,
-                            ggml_row_size(kv->type, n_embd_head_qk_nope + n_embd_head_v),
-                            ggml_row_size(kv->type, n_embd_head_qk_nope + n_embd_head_v) * n_head,
-                            ggml_row_size(kv->type, n_embd_head_qk_nope));
-                    cb(Vcur, "Vcur_view", il);
-
-                    Vcur = ggml_cont(ctx0, Vcur);
-                    cb(Vcur, "Vcur_cont", il);
-
-                    // note: rope must go first for in-place context shifting in build_rope_shift()
-                    ggml_tensor * Qcur = ggml_concat(ctx0, q_pe, q_nope, 0);
-                    cb(Qcur, "Qcur", il);
-
-                    ggml_tensor * Kcur = ggml_concat(ctx0, ggml_repeat(ctx0, k_pe, q_pe), k_nope, 0);
-                    cb(Kcur, "Kcur", il);
-
-                    // note: MLA without the absorption optimization converts into MHA (ie: GQA with full n_head groups)
-                    cur = build_attn(inp_attn,
-                            model.layers[il].wo, NULL,
-                            Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, kq_scale, il);
-                }
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            cur = build_norm(ffn_inp,
-                    model.layers[il].ffn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-
-            if ((uint32_t) il < hparams.n_layer_dense_lead) {
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up,   NULL, NULL,
-                        model.layers[il].ffn_gate, NULL, NULL,
-                        model.layers[il].ffn_down, NULL, NULL,
-                        NULL,
-                        LLM_FFN_SILU, LLM_FFN_PAR, il);
-                cb(cur, "ffn_out", il);
-            } else {
-                // MoE branch
-                ggml_tensor * moe_out =
-                    build_moe_ffn(cur,
-                            model.layers[il].ffn_gate_inp,
-                            model.layers[il].ffn_up_exps,
-                            model.layers[il].ffn_gate_exps,
-                            model.layers[il].ffn_down_exps,
-                            model.layers[il].ffn_exp_probs_b,
-                            n_expert, n_expert_used,
-                            LLM_FFN_SILU, hparams.expert_weights_norm,
-                            true, hparams.expert_weights_scale,
-                            (llama_expert_gating_func_type) hparams.expert_gating_func,
-                            il);
-                cb(moe_out, "ffn_moe_out", il);
-
-                // FFN shared expert
-                {
-                    ggml_tensor * ffn_shexp = build_ffn(cur,
-                            model.layers[il].ffn_up_shexp,   NULL, NULL,
-                            model.layers[il].ffn_gate_shexp, NULL, NULL,
-                            model.layers[il].ffn_down_shexp, NULL, NULL,
-                            NULL,
-                            LLM_FFN_SILU, LLM_FFN_PAR, il);
-                    cb(ffn_shexp, "ffn_shexp", il);
-
-                    cur = ggml_add(ctx0, moe_out, ffn_shexp);
-                    cb(cur, "ffn_out", il);
-                }
-            }
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = ggml_mul_mat(ctx0, model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_bitnet : public llm_graph_context {
-    llm_build_bitnet(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                if (model.layers[il].wq_scale) {
-                    Qcur = ggml_mul(ctx0, Qcur, model.layers[il].wq_scale);
-                }
-                cb(Qcur, "Qcur", il);
-                if (model.layers[il].bq) {
-                    Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
-                    cb(Qcur, "Qcur", il);
-                }
-
-                // B1.K
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                if (model.layers[il].wk_scale) {
-                    Kcur = ggml_mul(ctx0, Kcur, model.layers[il].wk_scale);
-                }
-                cb(Kcur, "Kcur", il);
-                if (model.layers[il].bk) {
-                    Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
-                    cb(Kcur, "Kcur", il);
-                }
-
-                // B1.V
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                if (model.layers[il].wv_scale) {
-                    Vcur = ggml_mul(ctx0, Vcur, model.layers[il].wv_scale);
-                }
-                cb(Vcur, "Vcur", il);
-                if (model.layers[il].bv) {
-                    Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
-                    cb(Vcur, "Vcur", il);
-                }
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        NULL, NULL,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-
-                cur = build_norm(cur,
-                        model.layers[il].attn_sub_norm, NULL,
-                        LLM_NORM_RMS, il);
-                cb(cur, "attn_sub_norm", il);
-
-                cur = build_lora_mm(model.layers[il].wo, cur);
-                if (model.layers[il].wo_scale) {
-                    cur = ggml_mul(ctx0, cur, model.layers[il].wo_scale);
-                }
-                if (model.layers[il].bo) {
-                    cur = ggml_add(ctx0, cur, model.layers[il].bo);
-                }
-                cb(cur, "attn_o_out", il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed-forward forward
-            cur = build_norm(ffn_inp,
-                    model.layers[il].ffn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-
-            cur = build_ffn(cur,
-                    model.layers[il].ffn_up,   NULL, model.layers[il].ffn_up_scale,
-                    model.layers[il].ffn_gate, NULL, model.layers[il].ffn_gate_scale,
-                    NULL,                      NULL, NULL,
-                    NULL,
-                    LLM_FFN_SILU, LLM_FFN_PAR, il);
-            cb(cur, "ffn_sub_out", il);
-
-            cur = build_norm(cur,
-                    model.layers[il].ffn_sub_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "ffn_sub_norm", il);
-
-            cur = build_lora_mm(model.layers[il].ffn_down, cur);
-            if (model.layers[il].ffn_down_scale) {
-                cur = ggml_mul(ctx0, cur, model.layers[il].ffn_down_scale);
-            }
-            cb(cur, "ffn_down", il);
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        // FIXME: do not use model.tok_embd directly, duplicate as model.output
-        cur = build_lora_mm(model.tok_embd, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_t5_enc : public llm_graph_context {
-    llm_build_t5_enc(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        ggml_tensor * pos_bucket_enc = build_inp_pos_bucket_enc();
-
-        auto * inp_attn = build_attn_inp_no_cache();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm_enc, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq_enc, cur);
-                cb(Qcur, "Qcur", il);
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk_enc, cur);
-                cb(Kcur, "Kcur", il);
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv_enc, cur);
-                cb(Vcur, "Vcur", il);
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                ggml_tensor * attn_rel_b = model.layers[il].attn_rel_b_enc ? model.layers[il].attn_rel_b_enc : model.layers[0].attn_rel_b_enc;
-                ggml_tensor * kq_b = build_pos_bias(pos_bucket_enc, attn_rel_b);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo_enc, nullptr,
-                        Qcur, Kcur, Vcur, kq_b, nullptr, nullptr, 1.0f, il);
-                cb(cur, "kqv_out", il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed-forward network
-            {
-                cur = build_norm(ffn_inp,
-                        model.layers[il].ffn_norm_enc, NULL,
-                        LLM_NORM_RMS, il);
-                cb(cur, "ffn_norm", il);
-
-                // T5 uses relu, flan-T5 uses gelu-gated
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up_enc,   NULL, NULL,
-                        model.layers[il].ffn_gate_enc, NULL, NULL,
-                        model.layers[il].ffn_down_enc, NULL, NULL,
-                        NULL,
-                        model.layers[il].ffn_gate_enc ? LLM_FFN_GELU : LLM_FFN_RELU,
-                        model.layers[il].ffn_gate_enc ? LLM_FFN_PAR  : LLM_FFN_SEQ,
-                        il);
-                cb(cur, "ffn_out", il);
-            }
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-            cb(cur, "ffn_out", il);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-        cb(cur, "result_embd", -1);
-
-        cur = build_norm(cur,
-                model.output_norm_enc, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_t5_dec : public llm_graph_context {
-    llm_build_t5_dec(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-        //const int64_t n_embd_gqa  = hparams.n_embd_v_gqa();
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        ggml_tensor * embd_enc       = build_inp_cross_embd();
-        ggml_tensor * pos_bucket_dec = build_inp_pos_bucket_dec();
-
-        const int64_t n_outputs_enc = embd_enc->ne[1];
-
-        auto * inp_attn_self  = build_attn_inp_kv();
-        auto * inp_attn_cross = build_attn_inp_cross();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        const int64_t dec_n_layer = hparams.dec_n_layer;
-
-        for (int il = 0; il < dec_n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                ggml_tensor * attn_rel_b = model.layers[il].attn_rel_b ? model.layers[il].attn_rel_b : model.layers[0].attn_rel_b;
-                ggml_tensor * kq_b = build_pos_bias(pos_bucket_dec, attn_rel_b);
-
-                cur = build_attn(inp_attn_self,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, kq_b, nullptr, nullptr, 1.0f, il);
-                cb(cur, "kqv_out", il);
-            }
-
-            cur = ggml_add(ctx0, cur, inpSA);
-            cb(cur, "cross_inp", il);
-
-            ggml_tensor * inpCA = cur;
-
-            // norm
-            cur = build_norm(cur,
-                    model.layers[il].attn_norm_cross, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm_cross", il);
-
-            // cross-attention
-            {
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq_cross, cur);
-                cb(Qcur, "Qcur", il);
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk_cross, embd_enc);
-                cb(Kcur, "Kcur", il);
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv_cross, embd_enc);
-                cb(Vcur, "Vcur", il);
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_outputs_enc);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_outputs_enc);
-
-                cur = build_attn(inp_attn_cross,
-                        model.layers[il].wo_cross, nullptr,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f, il);
-                cb(cur, "kqv_out", il);
-
-                //ggml_tensor * q =                 ggml_permute(ctx0, Qcur, 0, 2, 1, 3);
-                //ggml_tensor * k = ggml_cont(ctx0, ggml_permute(ctx0, Kcur, 0, 2, 1, 3));
-
-                //ggml_tensor * kq = ggml_mul_mat(ctx0, k, q);
-                //cb(kq, "kq", il);
-
-                //kq = ggml_soft_max_ext(ctx0, kq, KQ_mask_cross, 1.0f, hparams.f_max_alibi_bias);
-                //cb(kq, "kq_soft_max_ext", il);
-
-                //ggml_tensor * v = ggml_cont(ctx0, ggml_transpose(ctx0, ggml_reshape_2d(ctx0, Vcur, n_embd_gqa, n_outputs_enc)));
-                //cb(v, "v", il);
-
-                //ggml_tensor * kqv = ggml_mul_mat(ctx0, ggml_reshape_3d(ctx0, v, n_outputs_enc, n_embd_head, n_head_kv), kq);
-                //cb(kqv, "kqv", il);
-
-                //ggml_tensor * kqv_merged = ggml_permute(ctx0, kqv, 0, 2, 1, 3);
-                //cb(kqv_merged, "kqv_merged", il);
-
-                //cur = ggml_cont_2d(ctx0, kqv_merged, n_embd_gqa, n_tokens);
-                //cb(cur, "kqv_merged_cont", il);
-
-                //ggml_build_forward_expand(gf, cur);
-
-                //cur = build_lora_mm(model.layers[il].wo_cross, cur);
-                //cb(cur, "kqv_out", il);
-            }
-
-            if (il == dec_n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpCA = ggml_get_rows(ctx0, inpCA, inp_out_ids);
-            }
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpCA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed-forward network
-            {
-                cur = build_norm(ffn_inp,
-                        model.layers[il].ffn_norm, NULL,
-                        LLM_NORM_RMS, il);
-                cb(cur, "ffn_norm", il);
-
-                // T5 uses relu, flan-T5 uses gelu-gated
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up,   NULL, NULL,
-                        model.layers[il].ffn_gate, NULL, NULL,
-                        model.layers[il].ffn_down, NULL, NULL,
-                        NULL,
-                        model.layers[il].ffn_gate ? LLM_FFN_GELU : LLM_FFN_RELU,
-                        model.layers[il].ffn_gate ? LLM_FFN_PAR : LLM_FFN_SEQ,
-                        il);
-                cb(cur, "ffn_out", il);
-            }
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-            cb(cur, "ffn_out", il);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-        cb(cur, "result_embd", -1);
-
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_jais : public llm_graph_context {
-    llm_build_jais(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-        const int64_t n_embd_gqa  = hparams.n_embd_v_gqa();
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm,
-                    model.layers[il].attn_norm_b,
-                    LLM_NORM, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                cur = build_lora_mm(model.layers[il].wqkv, cur);
-                cb(cur, "wqkv", il);
-
-                cur = ggml_add(ctx0, cur, model.layers[il].bqkv);
-                cb(cur, "bqkv", il);
-
-                ggml_tensor * Qcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head,    n_tokens, n_embd_head*sizeof(float), cur->nb[1], 0*cur->nb[0]*(n_embd));
-                ggml_tensor * Kcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*cur->nb[0]*(n_embd));
-                ggml_tensor * Vcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*cur->nb[0]*(n_embd + n_embd_gqa));
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/float(n_embd_head), il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur  = ggml_get_rows(ctx0,  cur, inp_out_ids);
-                inpL = ggml_get_rows(ctx0, inpL, inp_out_ids);
-            }
-
-            // add the input
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpL);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // FF
-            {
-                cur = build_norm(ffn_inp,
-                        model.layers[il].ffn_norm,
-                        model.layers[il].ffn_norm_b,
-                        LLM_NORM, il);
-                cb(cur, "ffn_norm", il);
-
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up,   model.layers[il].ffn_up_b,   NULL,
-                        model.layers[il].ffn_gate, model.layers[il].ffn_gate_b, NULL,
-                        model.layers[il].ffn_down, model.layers[il].ffn_down_b, NULL,
-                        NULL,
-                        LLM_FFN_SILU, LLM_FFN_PAR, il);
-                cb(cur, "ffn_out", il);
-            }
-
-            inpL = ggml_add(ctx0, cur, ffn_inp);
-            cb(inpL, "l_out", il);
-        }
-
-        cur = build_norm(inpL,
-                model.output_norm,
-                model.output_norm_b,
-                LLM_NORM, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_chatglm : public llm_graph_context {
-    llm_build_chatglm(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-        const int64_t n_embd_gqa  = hparams.n_embd_v_gqa();
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm,
-                    NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                ggml_tensor * Qcur = nullptr;
-                ggml_tensor * Kcur = nullptr;
-                ggml_tensor * Vcur = nullptr;
-
-                if (model.layers[il].wqkv == nullptr) {
-                    Qcur = build_lora_mm(model.layers[il].wq, cur);
-                    if (model.layers[il].bq) {
-                        Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
-                    }
-                    Kcur = build_lora_mm(model.layers[il].wk, cur);
-                    if (model.layers[il].bk) {
-                        Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
-                    }
-                    Vcur = build_lora_mm(model.layers[il].wv, cur);
-                    if (model.layers[il].bv) {
-                        Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
-                    }
-                    Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                    Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                    Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-                } else {
-                    cur = build_lora_mm(model.layers[il].wqkv, cur);
-                    cb(cur, "wqkv", il);
-                    if (model.layers[il].bqkv) {
-                        cur = ggml_add(ctx0, cur, model.layers[il].bqkv);
-                        cb(cur, "bqkv", il);
-                    }
-                    Qcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head,    n_tokens, n_embd_head*sizeof(float), cur->nb[1], 0*sizeof(float)*(n_embd));
-                    Kcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd));
-                    Vcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd + n_embd_gqa));
-                }
-
-                //printf("freq_base: %f freq_scale: %f ext_factor: %f attn_factor: %f\n", freq_base, freq_scale, ext_factor, attn_factor);
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, NULL,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            // Add the input
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // FF
-            {
-                cur = build_norm(ffn_inp,
-                        model.layers[il].ffn_norm,
-                        NULL,
-                        LLM_NORM_RMS, il);
-                cb(cur, "ffn_norm", il);
-
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up,   NULL, NULL,
-                        NULL,                      NULL, NULL,
-                        model.layers[il].ffn_down, NULL, NULL,
-                        NULL,
-                        LLM_FFN_SWIGLU, LLM_FFN_SEQ, il);
-                cb(cur, "ffn_out", il);
-
-            }
-
-            inpL = ggml_add(ctx0, cur, ffn_inp);
-            cb(inpL, "l_out", il);
-        }
-
-        cur = build_norm(inpL,
-                model.output_norm,
-                NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_glm4 : public llm_graph_context {
-    llm_build_glm4(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-        const int64_t n_embd_gqa  = hparams.n_embd_v_gqa();
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            // Pre-attention norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm,
-                    NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                ggml_tensor * Qcur = nullptr;
-                ggml_tensor * Kcur = nullptr;
-                ggml_tensor * Vcur = nullptr;
-
-                if (model.layers[il].wqkv == nullptr) {
-                    Qcur = build_lora_mm(model.layers[il].wq, cur);
-                    if (model.layers[il].bq) {
-                        Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
-                    }
-                    Kcur = build_lora_mm(model.layers[il].wk, cur);
-                    if (model.layers[il].bk) {
-                        Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
-                    }
-                    Vcur = build_lora_mm(model.layers[il].wv, cur);
-                    if (model.layers[il].bv) {
-                        Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
-                    }
-                    Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                    Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                    Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-                } else {
-                    cur = build_lora_mm(model.layers[il].wqkv, cur);
-                    cb(cur, "wqkv", il);
-                    if (model.layers[il].bqkv) {
-                        cur = ggml_add(ctx0, cur, model.layers[il].bqkv);
-                        cb(cur, "bqkv", il);
-                    }
-                    Qcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head,    n_tokens, n_embd_head*sizeof(float), cur->nb[1], 0*sizeof(float)*(n_embd));
-                    Kcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd));
-                    Vcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd + n_embd_gqa));
-                }
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, NULL,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            // Post-attention norm (new!)
-            cur = build_norm(cur,
-                    model.layers[il].attn_post_norm,
-                    NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "post_attn_norm", il);
-
-            // Add the input (residual connection after post-attention norm)
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // FF
-            {
-                // Pre-MLP norm
-                cur = build_norm(ffn_inp,
-                        model.layers[il].ffn_norm,
-                        NULL,
-                        LLM_NORM_RMS, il);
-                cb(cur, "ffn_norm", il);
-
-                // MLP
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up,   NULL, NULL,
-                        NULL,                      NULL, NULL,
-                        model.layers[il].ffn_down, NULL, NULL,
-                        NULL,
-                        LLM_FFN_SWIGLU, LLM_FFN_SEQ, il);
-                cb(cur, "ffn_out", il);
-
-                // Post-MLP norm
-                cur = build_norm(cur,
-                        model.layers[il].ffn_post_norm,
-                        NULL,
-                        LLM_NORM_RMS, il);
-                cb(cur, "post_mlp_norm", il);
-            }
-
-            // Add residual connection after post-MLP norm
-            inpL = ggml_add(ctx0, cur, ffn_inp);
-            cb(inpL, "l_out", il);
-        }
-
-        // Final norm
-        cur = build_norm(inpL,
-                model.output_norm,
-                NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // Output projection
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_glm4_moe : public llm_graph_context {
-    llm_build_glm4_moe(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        // Only process up to last layer (skip final NextN layer)
-        // Final layer tensors are loaded but not processed in forward pass
-        const int n_transformer_layers = n_layer - hparams.nextn_predict_layers;
-        for (int il = 0; il < n_transformer_layers; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            // Pre-attention norm
-            cur = build_norm(inpL, model.layers[il].attn_norm, NULL, LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                if (model.layers[il].bq) {
-                    Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
-                }
-                cb(Qcur, "Qcur", il);
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                if (model.layers[il].bk) {
-                    Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
-                }
-                cb(Kcur, "Kcur", il);
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                if (model.layers[il].bv) {
-                    Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
-                }
-                cb(Vcur, "Vcur", il);
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head, n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                // Apply Q/K norm if available (GLM-4.5 355B variant)
-                if (model.layers[il].attn_q_norm) {
-                    Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL, LLM_NORM_RMS, il);
-                    cb(Qcur, "Qcur_normed", il);
-                }
-                if (model.layers[il].attn_k_norm) {
-                    Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, NULL, LLM_NORM_RMS, il);
-                    cb(Kcur, "Kcur_normed", il);
-                }
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, NULL,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-
-            if (il == n_transformer_layers - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0, cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // Post-attention norm
-            cur = build_norm(ffn_inp, model.layers[il].attn_post_norm, NULL, LLM_NORM_RMS, il);
-            cb(cur, "post_attn_norm", il);
-
-            // Check if this is a dense layer (n_layer_dense_lead=1, so layer 0 is dense)
-            if (static_cast<uint32_t>(il) < hparams.n_layer_dense_lead) {
-                // Dense FFN layer
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up,   NULL, NULL,
-                        model.layers[il].ffn_gate, NULL, NULL,
-                        model.layers[il].ffn_down, NULL, NULL,
-                        NULL,
-                        LLM_FFN_SILU, LLM_FFN_PAR, il);
-                cb(cur, "ffn_out", il);
-            } else {
-                // Process routed experts using existing MoE infrastructure
-                ggml_tensor * routed_out = build_moe_ffn(cur,
-                        model.layers[il].ffn_gate_inp,
-                        model.layers[il].ffn_up_exps,
-                        model.layers[il].ffn_gate_exps,
-                        model.layers[il].ffn_down_exps,
-                        model.layers[il].ffn_exp_probs_b,
-                        n_expert, n_expert_used,
-                        LLM_FFN_SILU, hparams.expert_weights_norm,
-                        true, hparams.expert_weights_scale,
-                        (llama_expert_gating_func_type) hparams.expert_gating_func,
-                        il);
-                cb(routed_out, "ffn_moe_out", il);
-
-                // Process shared expert on original input
-                ggml_tensor * shared_out = build_ffn(cur,
-                        model.layers[il].ffn_up_shexp,   NULL, NULL,
-                        model.layers[il].ffn_gate_shexp, NULL, NULL,
-                        model.layers[il].ffn_down_shexp, NULL, NULL,
-                        NULL,
-                        LLM_FFN_SILU, LLM_FFN_PAR, il);
-                cb(shared_out, "ffn_shexp_out", il);
-
-                // Final output: routed_output + shared_output
-                cur = ggml_add(ctx0, routed_out, shared_out);
-                cb(cur, "ffn_out", il);
-            }
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-        cur = build_norm(cur, model.output_norm, NULL, LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_nemotron : public llm_graph_context {
-    llm_build_nemotron(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        //GGML_ASSERT(n_embd_head == hparams.n_rot);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm,
-                    model.layers[il].attn_norm_b,
-                    LLM_NORM, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-                if (model.layers[il].bq) {
-                    Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
-                    cb(Qcur, "Qcur", il);
-                }
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-                if (model.layers[il].bk) {
-                    Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
-                    cb(Kcur, "Kcur", il);
-                }
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-                if (model.layers[il].bv) {
-                    Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
-                    cb(Vcur, "Vcur", il);
-                }
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed-forward network
-            cur = build_norm(ffn_inp,
-                    model.layers[il].ffn_norm,
-                    model.layers[il].ffn_norm_b,
-                    LLM_NORM, il);
-            cb(cur, "ffn_norm", il);
-
-            cur = build_ffn(cur,
-                    model.layers[il].ffn_up,   model.layers[il].ffn_up_b,   NULL,
-                    NULL,                      NULL,                        NULL,
-                    model.layers[il].ffn_down, model.layers[il].ffn_down_b, NULL,
-                    NULL,
-                    LLM_FFN_RELU_SQR, LLM_FFN_SEQ, il);
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-            cb(cur, "ffn_out", il);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, model.output_norm_b,
-                LLM_NORM, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_nemotron_h : public llm_graph_context_mamba {
-    llm_build_nemotron_h(
-            const llama_model      & model,
-            const llm_graph_params & params) :
-        llm_graph_context_mamba(params) {
-
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-        ggml_build_forward_expand(gf, inpL);
-
-        auto * inp = build_inp_mem_hybrid();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            struct ggml_tensor * inpSA = inpL;
-
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            if (hparams.is_recurrent(il)) {
-                // ssm layer //
-                cur = build_mamba2_layer(inp->get_recr(), cur, model, ubatch, il);
-            } else if (hparams.n_ff(il) == 0) {
-                // attention layer //
-                cur = build_attention_layer(cur, inp->get_attn(), model, n_embd_head, il);
-            } else {
-                cur = build_ffn_layer(cur, model, il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            // add residual
-            cur = ggml_add(ctx0, cur, inpSA);
-            cb(cur, "nemotron_h_block_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-
-    ggml_tensor * build_attention_layer(
-              ggml_tensor             * cur,
-              llm_graph_input_attn_kv * inp_attn,
-        const llama_model             & model,
-        const int64_t                   n_embd_head,
-        const int                       il) {
-
-        // compute Q and K and (optionally) RoPE them
-        ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-        cb(Qcur, "Qcur", il);
-        if (model.layers[il].bq) {
-            Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
-            cb(Qcur, "Qcur", il);
-        }
-
-        ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-        cb(Kcur, "Kcur", il);
-        if (model.layers[il].bk) {
-            Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
-            cb(Kcur, "Kcur", il);
-        }
-
-        ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-        cb(Vcur, "Vcur", il);
-        if (model.layers[il].bv) {
-            Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
-            cb(Vcur, "Vcur", il);
-        }
-
-        Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, hparams.n_head(il),    n_tokens);
-        Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, hparams.n_head_kv(il), n_tokens);
-        Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, hparams.n_head_kv(il), n_tokens);
-
-        cb(Qcur, "Qcur", il);
-        cb(Kcur, "Kcur", il);
-        cb(Vcur, "Vcur", il);
-
-        const float kq_scale = hparams.f_attention_scale == 0.0f ? 1.0f/sqrtf(float(n_embd_head)) : hparams.f_attention_scale;
-        cur = build_attn(inp_attn,
-                model.layers[il].wo, model.layers[il].bo,
-                Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, kq_scale, il);
-                cb(cur, "attn_out", il);
-        return cur;
-    }
-
-    ggml_tensor * build_ffn_layer(
-              ggml_tensor * cur,
-        const llama_model & model,
-        const int           il) {
-
-        cur = build_ffn(cur,
-                model.layers[il].ffn_up,   model.layers[il].ffn_up_b,   NULL,
-                NULL,                      NULL,                        NULL,
-                model.layers[il].ffn_down, model.layers[il].ffn_down_b, NULL,
-                NULL,
-                LLM_FFN_RELU_SQR, LLM_FFN_PAR, il);
-        cb(cur, "ffn_out", il);
-
-        cur = build_cvec(cur, il);
-        cb(cur, "l_out", il);
-
-        return cur;
-    }
-};
-
-struct llm_build_exaone : public llm_graph_context {
-    llm_build_exaone(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                // rope freq factors for llama3; may return nullptr for llama2 and other models
-                ggml_tensor * rope_factors = model.get_rope_factors(cparams, il);
-
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-                if (model.layers[il].bq) {
-                    Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
-                    cb(Qcur, "Qcur", il);
-                }
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-                if (model.layers[il].bk) {
-                    Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
-                    cb(Kcur, "Kcur", il);
-                }
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-                if (model.layers[il].bv) {
-                    Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
-                    cb(Vcur, "Vcur", il);
-                }
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, rope_factors,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, rope_factors,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed-forward network
-            cur = build_norm(ffn_inp,
-                    model.layers[il].ffn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-
-            cur = build_ffn(cur,
-                    model.layers[il].ffn_up,   NULL, NULL,
-                    model.layers[il].ffn_gate, NULL, NULL,
-                    model.layers[il].ffn_down, NULL, NULL,
-                    NULL,
-                    LLM_FFN_SILU, LLM_FFN_PAR, il);
-            cb(cur, "ffn_out", il);
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-            cb(cur, "ffn_out", il);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-template <bool iswa>
-struct llm_build_exaone4 : public llm_graph_context {
-    llm_build_exaone4(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_k;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_v);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        using inp_attn_type = std::conditional_t<iswa, llm_graph_input_attn_kv_iswa, llm_graph_input_attn_kv>;
-        inp_attn_type * inp_attn = nullptr;
-
-        if constexpr (iswa) {
-            inp_attn = build_attn_inp_kv_iswa();
-        } else {
-            inp_attn = build_attn_inp_kv();
-        }
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            // use RoPE for SWA layers or non-SWA models
-            const bool use_rope = hparams.is_swa(il) || hparams.swa_type == LLAMA_SWA_TYPE_NONE;
-
-            cur = inpL;
-
-            // self-attention
-            {
-                ggml_tensor * rope_factors = model.get_rope_factors(cparams, il);
-
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL, LLM_NORM_RMS, il);
-                Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, NULL, LLM_NORM_RMS, il);
-                cb(Qcur, "Qcur_normed", il);
-                cb(Kcur, "Kcur_normed", il);
-
-                if (use_rope) {
-                    Qcur = ggml_rope_ext(
-                            ctx0, Qcur, inp_pos, rope_factors,
-                            n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                            ext_factor, attn_factor, beta_fast, beta_slow
-                            );
-
-                    Kcur = ggml_rope_ext(
-                            ctx0, Kcur, inp_pos, rope_factors,
-                            n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                            ext_factor, attn_factor, beta_fast, beta_slow
-                            );
-                }
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, NULL,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-                cb(cur, "attn_out", il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            cur = build_norm(cur,
-                    model.layers[il].attn_post_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_post_norm", il);
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed-forward network
-            cur = build_ffn(ffn_inp,
-                    model.layers[il].ffn_up,   NULL, NULL,
-                    model.layers[il].ffn_gate, NULL, NULL,
-                    model.layers[il].ffn_down, NULL, NULL,
-                    NULL,
-                    LLM_FFN_SILU, LLM_FFN_PAR, il);
-            cb(cur, "ffn_out", il);
-
-            cur = build_norm(cur,
-                    model.layers[il].ffn_post_norm, NULL,
-                    LLM_NORM_RMS, -1);
-            cb(cur, "ffn_post_norm", -1);
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_rwkv6_base : public llm_graph_context {
-    const llama_model & model;
-
-    llm_build_rwkv6_base(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params), model(model) {
-    }
-
-    ggml_tensor * build_rwkv6_channel_mix(
-            const llama_layer * layer,
-            ggml_tensor * cur,
-            ggml_tensor * x_prev,
-            llm_arch arch) const {
-        ggml_tensor * sx = ggml_sub(ctx0, x_prev, cur);
-        switch (arch) {
-            case LLM_ARCH_RWKV6:
-                {
-                    ggml_tensor * xk = ggml_add(ctx0, ggml_mul(ctx0, sx, layer->channel_mix_lerp_k), cur);
-                    ggml_tensor * xr = ggml_add(ctx0, ggml_mul(ctx0, sx, layer->channel_mix_lerp_r), cur);
-
-                    ggml_tensor * r = ggml_sigmoid(ctx0, build_lora_mm(layer->channel_mix_receptance, xr));
-                    ggml_tensor * k = ggml_sqr(
-                            ctx0,
-                            ggml_relu(
-                                ctx0,
-                                build_lora_mm(layer->channel_mix_key, xk)
-                                )
-                            );
-                    cur = ggml_mul(ctx0, r, build_lora_mm(layer->channel_mix_value, k));
-                } break;
-            default:
-                GGML_ABORT("fatal error");
-        }
-
-        return cur;
-    }
-
-    ggml_tensor * build_rwkv6_time_mix(
-            llm_graph_input_rs * inp,
-            ggml_tensor * cur,
-            ggml_tensor * x_prev,
-            const llama_ubatch & ubatch,
-            int   il) const {
-        const auto * mctx_cur = static_cast<const llama_memory_recurrent_context *>(mctx);
-
-        const auto n_tokens = ubatch.n_tokens;
-        const auto n_seqs = ubatch.n_seqs;
-        const auto n_seq_tokens = ubatch.n_seq_tokens;
-        const auto n_embd = hparams.n_embd;
-        const auto head_size = hparams.wkv_head_size;
-        const auto n_head = n_embd / head_size;
-        const auto n_head_kv = hparams.n_head_kv(il);
-
-        const auto kv_head = mctx_cur->get_head();
-
-        const auto & layer = model.layers[il];
-
-        bool is_qrwkv = layer.time_mix_first == nullptr;
-
-        ggml_tensor * sx = ggml_sub(ctx0, x_prev, cur);
-
-        sx  = ggml_reshape_2d(ctx0, sx,  n_embd, n_tokens);
-        cur = ggml_reshape_2d(ctx0, cur, n_embd, n_tokens);
-
-        ggml_tensor * xxx = ggml_add(ctx0, ggml_mul(ctx0, sx, layer.time_mix_lerp_x), cur);
-
-        xxx = ggml_reshape_4d(
-                ctx0,
-                ggml_tanh(
-                    ctx0,
-                    ggml_mul_mat(ctx0, layer.time_mix_w1, xxx)
-                    ),
-                layer.time_mix_w1->ne[1] / 5, 1, 5, n_tokens
-                );
-
-        xxx = ggml_cont(ctx0, ggml_permute(ctx0, xxx, 0, 1, 3, 2));
-
-        xxx = ggml_mul_mat(
-                ctx0,
-                ggml_reshape_4d(
-                    ctx0,
-                    layer.time_mix_w2,
-                    layer.time_mix_w2->ne[0], layer.time_mix_w2->ne[1], 1, 5
-                    ),
-                xxx
-                );
-
-        ggml_tensor *xw, *xk, *xv, *xr, *xg;
-        if (layer.time_mix_lerp_fused) {
-            // fusing these weights makes some performance improvement
-            sx  = ggml_reshape_3d(ctx0, sx,  n_embd, 1, n_tokens);
-            cur = ggml_reshape_3d(ctx0, cur, n_embd, 1, n_tokens);
-            xxx = ggml_add(ctx0, ggml_mul(ctx0, ggml_add(ctx0, xxx, layer.time_mix_lerp_fused), sx), cur);
-            xw = ggml_view_2d(ctx0, xxx, n_embd, n_tokens, xxx->nb[1], 0);
-            xk = ggml_view_2d(ctx0, xxx, n_embd, n_tokens, xxx->nb[1], n_embd * n_tokens * sizeof(float));
-            xv = ggml_view_2d(ctx0, xxx, n_embd, n_tokens, xxx->nb[1], n_embd * n_tokens * 2 * sizeof(float));
-            xr = ggml_view_2d(ctx0, xxx, n_embd, n_tokens, xxx->nb[1], n_embd * n_tokens * 3 * sizeof(float));
-            xg = ggml_view_2d(ctx0, xxx, n_embd, n_tokens, xxx->nb[1], n_embd * n_tokens * 4 * sizeof(float));
-        } else {
-            // for backward compatibility
-            xw = ggml_view_2d(ctx0, xxx, n_embd, n_tokens, xxx->nb[1], 0);
-            xk = ggml_view_2d(ctx0, xxx, n_embd, n_tokens, xxx->nb[1], n_embd * n_tokens * sizeof(float));
-            xv = ggml_view_2d(ctx0, xxx, n_embd, n_tokens, xxx->nb[1], n_embd * n_tokens * 2 * sizeof(float));
-            xr = ggml_view_2d(ctx0, xxx, n_embd, n_tokens, xxx->nb[1], n_embd * n_tokens * 3 * sizeof(float));
-            xg = ggml_view_2d(ctx0, xxx, n_embd, n_tokens, xxx->nb[1], n_embd * n_tokens * 4 * sizeof(float));
-
-            xw = ggml_add(ctx0, ggml_mul(ctx0, ggml_add(ctx0, xw, layer.time_mix_lerp_w), sx), cur);
-            xk = ggml_add(ctx0, ggml_mul(ctx0, ggml_add(ctx0, xk, layer.time_mix_lerp_k), sx), cur);
-            xv = ggml_add(ctx0, ggml_mul(ctx0, ggml_add(ctx0, xv, layer.time_mix_lerp_v), sx), cur);
-            xr = ggml_add(ctx0, ggml_mul(ctx0, ggml_add(ctx0, xr, layer.time_mix_lerp_r), sx), cur);
-            xg = ggml_add(ctx0, ggml_mul(ctx0, ggml_add(ctx0, xg, layer.time_mix_lerp_g), sx), cur);
-        }
-
-        ggml_tensor * r = build_lora_mm(layer.time_mix_receptance, xr);
-        ggml_tensor * k = build_lora_mm(layer.time_mix_key,        xk);
-        ggml_tensor * v = build_lora_mm(layer.time_mix_value,      xv);
-        if (layer.time_mix_receptance_b) {
-            r = ggml_add(ctx0, r, layer.time_mix_receptance_b);
-        }
-        if (layer.time_mix_key_b) {
-            k = ggml_add(ctx0, k, layer.time_mix_key_b);
-        }
-        if (layer.time_mix_value_b) {
-            v = ggml_add(ctx0, v, layer.time_mix_value_b);
-        }
-
-        ggml_tensor * g = build_lora_mm(layer.time_mix_gate, xg);
-        if (is_qrwkv) {
-            g = ggml_sigmoid(ctx0, g);
-        } else {
-            g = ggml_silu(ctx0, g);
-        }
-
-        if (n_head_kv != 0 && n_head_kv != n_head) {
-            GGML_ASSERT(n_head % n_head_kv == 0);
-            k = ggml_reshape_4d(ctx0, k, head_size, 1, n_head_kv, n_tokens);
-            v = ggml_reshape_4d(ctx0, v, head_size, 1, n_head_kv, n_tokens);
-            ggml_tensor * tmp = ggml_new_tensor_4d(ctx0, GGML_TYPE_F32, head_size, n_head / n_head_kv, n_head_kv, n_tokens);
-            k = ggml_repeat(ctx0, k, tmp);
-            v = ggml_repeat(ctx0, v, tmp);
-        }
-
-        k = ggml_reshape_3d(ctx0, k, head_size, n_head, n_tokens);
-        v = ggml_reshape_3d(ctx0, v, head_size, n_head, n_tokens);
-        r = ggml_reshape_3d(ctx0, r, head_size, n_head, n_tokens);
-
-        ggml_tensor * w = ggml_mul_mat(
-                ctx0,
-                layer.time_mix_decay_w2,
-                ggml_tanh(
-                    ctx0,
-                    ggml_mul_mat(ctx0, layer.time_mix_decay_w1, xw)
-                    )
-                );
-
-        w = ggml_add(ctx0, w, layer.time_mix_decay);
-        w = ggml_exp(ctx0, ggml_neg(ctx0, ggml_exp(ctx0, w)));
-        w = ggml_reshape_3d(ctx0, w, head_size, n_head, n_tokens);
-
-        if (is_qrwkv) {
-            // k = k * (1 - w)
-            k = ggml_sub(ctx0, k, ggml_mul(ctx0, k, w));
-        }
-
-        ggml_tensor * wkv_state = build_rs(
-                inp, mctx_cur->get_s_l(il),
-                hparams.n_embd_s(), n_seqs);
-
-        ggml_tensor * wkv_output;
-        if (is_qrwkv) {
-            wkv_output = ggml_gated_linear_attn(ctx0, k, v, r, w, wkv_state, pow(head_size, -0.5f));
-        } else {
-            wkv_output = ggml_rwkv_wkv6(ctx0, k, v, r, layer.time_mix_first, w, wkv_state);
-        }
-        cur = ggml_view_1d(ctx0, wkv_output, n_embd * n_tokens, 0);
-        wkv_state = ggml_view_1d(ctx0, wkv_output, n_embd * head_size * n_seqs, n_embd * n_tokens * sizeof(float));
-
-        ggml_build_forward_expand(
-                gf,
-                ggml_cpy(
-                    ctx0,
-                    wkv_state,
-                    ggml_view_1d(
-                        ctx0,
-                        mctx_cur->get_s_l(il),
-                        hparams.n_embd_s() * n_seqs,
-                        hparams.n_embd_s() * kv_head * ggml_element_size(mctx_cur->get_s_l(il))
-                        )
-                    )
-                );
-
-        if (!is_qrwkv) {
-            // group norm with head_count groups
-            cur = ggml_reshape_3d(ctx0, cur, n_embd / n_head, n_head, n_tokens);
-            cur = ggml_norm(ctx0, cur, 64e-5f);
-
-            // Convert back to regular vectors.
-            cur = ggml_reshape_2d(ctx0, cur, n_embd, n_tokens);
-            cur = ggml_add(ctx0, ggml_mul(ctx0, cur, layer.time_mix_ln), layer.time_mix_ln_b);
-        } else {
-            cur = ggml_reshape_2d(ctx0, cur, n_embd, n_tokens);
-        }
-
-        cur = ggml_mul(ctx0, cur, g);
-        cur = build_lora_mm(layer.time_mix_output, cur);
-
-        return ggml_reshape_3d(ctx0, cur, n_embd, n_seq_tokens, n_seqs);
-    }
-};
-
-struct llm_build_rwkv6 : public llm_build_rwkv6_base {
-    llm_build_rwkv6(const llama_model & model, const llm_graph_params & params) : llm_build_rwkv6_base(model, params) {
-        GGML_ASSERT(hparams.token_shift_count == 2);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-        inpL = build_norm(inpL, model.tok_norm, model.tok_norm_b, LLM_NORM, -1);
-
-        auto * rs_inp = build_rs_inp();
-
-        const auto n_embd = hparams.n_embd;
-        const auto n_seq_tokens = ubatch.n_seq_tokens;
-        const auto n_seqs = ubatch.n_seqs;
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            const llama_layer * layer = &model.layers[il];
-            inpL = ggml_reshape_3d(ctx0, inpL, n_embd, n_seq_tokens, n_seqs);
-
-            ggml_tensor * token_shift = build_rwkv_token_shift_load(rs_inp, ubatch, il);
-
-            ggml_tensor * att_shift = ggml_view_3d(ctx0, token_shift, n_embd, 1, n_seqs, token_shift->nb[1], token_shift->nb[2], 0);
-            ggml_tensor * ffn_shift = ggml_view_3d(ctx0, token_shift, n_embd, 1, n_seqs, token_shift->nb[1], token_shift->nb[2], n_embd * ggml_element_size(token_shift));
-
-            ggml_tensor * att_norm = build_norm(inpL, layer->attn_norm, layer->attn_norm_b, LLM_NORM, il);
-            cb(att_norm, "attn_norm", il);
-
-            ggml_tensor * x_prev = ggml_concat(
-                    ctx0,
-                    att_shift,
-                    ggml_view_3d(ctx0, att_norm, n_embd, n_seq_tokens - 1, n_seqs, att_norm->nb[1], att_norm->nb[2], 0),
-                    1
-                    );
-
-            cur = build_rwkv6_time_mix(rs_inp, att_norm, x_prev, ubatch, il);
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpL);
-            cb(ffn_inp, "ffn_inp", il);
-
-            ggml_tensor * ffn_norm = build_norm(ffn_inp, layer->attn_norm_2, layer->attn_norm_2_b, LLM_NORM, il);
-            cb(ffn_norm, "ffn_norm", il);
-
-            x_prev = ggml_concat(
-                    ctx0,
-                    ffn_shift,
-                    ggml_view_3d(ctx0, ffn_norm, n_embd, n_seq_tokens - 1, n_seqs, ffn_norm->nb[1], ffn_norm->nb[2], 0),
-                    1
-                    );
-
-            token_shift = ggml_concat(ctx0,
-                    ggml_view_3d(ctx0, att_norm, n_embd, 1, n_seqs, att_norm->nb[1], att_norm->nb[2], (n_seq_tokens-1)*n_embd*ggml_element_size(att_norm)),
-                    ggml_view_3d(ctx0, ffn_norm, n_embd, 1, n_seqs, ffn_norm->nb[1], ffn_norm->nb[2], (n_seq_tokens-1)*n_embd*ggml_element_size(ffn_norm)),
-                    1
-                    );
-            ggml_build_forward_expand(gf, build_rwkv_token_shift_store(token_shift, ubatch, il));
-
-            ffn_inp  = ggml_reshape_2d(ctx0, ffn_inp,  n_embd, n_tokens);
-            ffn_norm = ggml_reshape_2d(ctx0, ffn_norm, n_embd, n_tokens);
-            x_prev   = ggml_reshape_2d(ctx0, x_prev,   n_embd, n_tokens);
-            cur      = ggml_reshape_2d(ctx0, cur,      n_embd, n_tokens);
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                ffn_inp  = ggml_get_rows(ctx0, ffn_inp,  inp_out_ids);
-                ffn_norm = ggml_get_rows(ctx0, ffn_norm, inp_out_ids);
-                x_prev   = ggml_get_rows(ctx0, x_prev,   inp_out_ids);
-                cur      = ggml_get_rows(ctx0, cur,      inp_out_ids);
-            }
-
-            cur = build_rwkv6_channel_mix(layer, ffn_norm, x_prev, LLM_ARCH_RWKV6);
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            if (hparams.rescale_every_n_layers != 0 && (il + 1) % hparams.rescale_every_n_layers == 0) {
-                cur = ggml_scale(ctx0, cur, 0.5F);
-            }
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-        cur = build_norm(cur, model.output_norm, model.output_norm_b, LLM_NORM, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-// ref: https://huggingface.co/recursal/QRWKV6-32B-Instruct-Preview-v0.1/blob/main/modeling_rwkv6qwen2.py
-struct llm_build_rwkv6qwen2 : public llm_build_rwkv6_base {
-    llm_build_rwkv6qwen2(const llama_model & model, const llm_graph_params & params) : llm_build_rwkv6_base(model, params) {
-        GGML_ASSERT(n_embd == hparams.n_embd_r());
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        auto * rs_inp = build_rs_inp();
-
-        const auto n_embd = hparams.n_embd;
-        const auto n_seq_tokens = ubatch.n_seq_tokens;
-        const auto n_seqs = ubatch.n_seqs;
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            const llama_layer * layer = &model.layers[il];
-            inpL = ggml_reshape_3d(ctx0, inpL, n_embd, n_seq_tokens, n_seqs);
-
-            ggml_tensor * token_shift = build_rwkv_token_shift_load(rs_inp, ubatch, il);
-
-            ggml_tensor * att_norm = build_norm(inpL, layer->attn_norm, layer->attn_norm_b, LLM_NORM_RMS, il);
-            cb(att_norm, "attn_norm", il);
-
-            ggml_tensor * x_prev = ggml_concat(
-                    ctx0,
-                    token_shift,
-                    ggml_view_3d(ctx0, att_norm, n_embd, n_seq_tokens - 1, n_seqs, att_norm->nb[1], att_norm->nb[2], 0),
-                    1
-                    );
-
-            cur = build_rwkv6_time_mix(rs_inp, att_norm, x_prev, ubatch, il);
-
-            token_shift = ggml_view_3d(ctx0, att_norm, n_embd, 1, n_seqs, att_norm->nb[1], att_norm->nb[2], (n_seq_tokens-1)*n_embd*ggml_element_size(att_norm));
-            ggml_build_forward_expand(gf, build_rwkv_token_shift_store(token_shift, ubatch, il));
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpL);
-            cb(ffn_inp, "ffn_inp", il);
-
-            cur     = ggml_reshape_2d(ctx0, cur,     n_embd, n_tokens);
-            ffn_inp = ggml_reshape_2d(ctx0, ffn_inp, n_embd, n_tokens);
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur     = ggml_get_rows(ctx0, cur,     inp_out_ids);
-                ffn_inp = ggml_get_rows(ctx0, ffn_inp, inp_out_ids);
-            }
-
-            // feed-forward network
-            cur = build_norm(ffn_inp,
-                    model.layers[il].ffn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-
-            cur = build_ffn(cur,
-                    model.layers[il].ffn_up,   NULL, NULL,
-                    model.layers[il].ffn_gate, NULL, NULL,
-                    model.layers[il].ffn_down, NULL, NULL,
-                    NULL,
-                    LLM_FFN_SILU, LLM_FFN_PAR, il);
-            cb(cur, "ffn_out", il);
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-        cur = build_norm(cur, model.output_norm, model.output_norm_b, LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_rwkv7_base : public llm_graph_context {
-    const llama_model & model;
-
-    llm_build_rwkv7_base(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params), model(model) {
-    }
-
-    ggml_tensor * build_rwkv7_channel_mix(
-            const llama_layer * layer,
-            ggml_tensor * cur,
-            ggml_tensor * x_prev,
-            llm_arch arch) const {
-        ggml_tensor * sx = ggml_sub(ctx0, x_prev, cur);
-        switch (arch) {
-            case LLM_ARCH_RWKV7:
-                {
-                    ggml_tensor * xk = ggml_add(ctx0, ggml_mul(ctx0, sx, layer->channel_mix_lerp_k), cur);
-
-                    ggml_tensor * k = ggml_sqr(
-                        ctx0,
-                        ggml_relu(
-                            ctx0,
-                            build_lora_mm(layer->channel_mix_key, xk)
-                        )
-                    );
-
-                    cur = build_lora_mm(layer->channel_mix_value, k);
-                } break;
-            default:
-                GGML_ABORT("fatal error");
-        }
-
-        return cur;
-    }
-
-    ggml_tensor * build_rwkv7_time_mix(
-            llm_graph_input_rs * inp,
-            ggml_tensor * cur,
-            ggml_tensor * x_prev,
-            ggml_tensor *& first_layer_value,
-            const llama_ubatch & ubatch,
-            int   il) const {
-        const auto * mctx_cur = static_cast<const llama_memory_recurrent_context *>(mctx);
-
-        const auto n_tokens = ubatch.n_tokens;
-        const auto n_seqs = ubatch.n_seqs;
-        const auto n_embd = hparams.n_embd;
-        const auto head_size = hparams.wkv_head_size;
-        const auto head_count = n_embd / head_size;
-        const auto n_seq_tokens = ubatch.n_seq_tokens;
-
-        const auto kv_head = mctx_cur->get_head();
-
-        const auto & layer = model.layers[il];
-
-        bool has_gating = layer.time_mix_g1 && layer.time_mix_g2;
-
-        ggml_tensor * sx = ggml_sub(ctx0, x_prev, cur);
-        ggml_tensor * dummy = ggml_new_tensor_4d(ctx0, GGML_TYPE_F32, n_embd, n_seq_tokens, n_seqs, has_gating ? 6 : 5);
-        sx = ggml_repeat(ctx0, sx, dummy);
-
-        ggml_tensor * xxx = ggml_add(ctx0, ggml_mul(ctx0, sx, layer.time_mix_lerp_fused), cur);
-
-        ggml_tensor * xr = ggml_view_2d(ctx0, xxx, n_embd, n_tokens, xxx->nb[1], 0);
-        ggml_tensor * xw = ggml_view_2d(ctx0, xxx, n_embd, n_tokens, xxx->nb[1], n_embd * n_tokens * sizeof(float));
-        ggml_tensor * xk = ggml_view_2d(ctx0, xxx, n_embd, n_tokens, xxx->nb[1], n_embd * n_tokens * 2 * sizeof(float));
-        ggml_tensor * xv = ggml_view_2d(ctx0, xxx, n_embd, n_tokens, xxx->nb[1], n_embd * n_tokens * 3 * sizeof(float));
-        ggml_tensor * xa = ggml_view_2d(ctx0, xxx, n_embd, n_tokens, xxx->nb[1], n_embd * n_tokens * 4 * sizeof(float));
-        ggml_tensor * xg = has_gating ? ggml_view_2d(ctx0, xxx, n_embd, n_tokens, xxx->nb[1], n_embd * n_tokens * 5 * sizeof(float)) : nullptr;
-
-        ggml_tensor * r = build_lora_mm(layer.time_mix_receptance, xr);
-        ggml_tensor * w = ggml_add(
-            ctx0,
-            ggml_mul_mat(ctx0, layer.time_mix_w2, ggml_tanh(ctx0, ggml_mul_mat(ctx0, layer.time_mix_w1, xw))),
-            layer.time_mix_w0
-        );
-        w = ggml_exp(ctx0, ggml_scale(ctx0, ggml_sigmoid(ctx0, w), -0.606531));
-
-        ggml_tensor * k = build_lora_mm(layer.time_mix_key, xk);
-        ggml_tensor * v = build_lora_mm(layer.time_mix_value, xv);
-        if (first_layer_value == nullptr) {
-            first_layer_value = v;
-        } else {
-            // Add the first layer value as a residual connection.
-            v = ggml_add(ctx0, v,
-                ggml_mul(ctx0,
-                    ggml_sub(ctx0, first_layer_value, v),
-                    ggml_sigmoid(ctx0, ggml_add(ctx0,
-                            ggml_mul_mat(ctx0, layer.time_mix_v2, ggml_mul_mat(ctx0, layer.time_mix_v1, xv)),
-                            layer.time_mix_v0
-                        )
-                    )
-                )
-            );
-        }
-
-        ggml_tensor * g = nullptr;
-        if (layer.time_mix_g1 && layer.time_mix_g2) {
-            g = ggml_mul_mat(ctx0, layer.time_mix_g2, ggml_sigmoid(ctx0, ggml_mul_mat(ctx0, layer.time_mix_g1, xg)));
-        }
-
-        ggml_tensor * a = ggml_sigmoid(ctx0,
-            ggml_add(
-                ctx0,
-                ggml_mul_mat(ctx0, layer.time_mix_a2, ggml_mul_mat(ctx0, layer.time_mix_a1, xa)),
-                layer.time_mix_a0
-            )
-        );
-
-        ggml_tensor * kk = ggml_reshape_3d(ctx0, ggml_mul(ctx0, k, layer.time_mix_k_k), head_size, head_count, n_tokens);
-        kk = ggml_l2_norm(ctx0, kk, 1e-12);
-
-        ggml_tensor * ka = ggml_mul(ctx0, k, layer.time_mix_k_a);
-        k = ggml_add(ctx0, k, ggml_sub(ctx0, ggml_mul(ctx0, a, ka), ka));
-
-        r = ggml_reshape_3d(ctx0, r, head_size, head_count, n_tokens);
-        w = ggml_reshape_3d(ctx0, w, head_size, head_count, n_tokens);
-        k = ggml_reshape_3d(ctx0, k, head_size, head_count, n_tokens);
-        v = ggml_reshape_3d(ctx0, v, head_size, head_count, n_tokens);
-        a = ggml_reshape_3d(ctx0, a, head_size, head_count, n_tokens);
-
-        ggml_tensor * wkv_state = build_rs(
-                inp, mctx_cur->get_s_l(il),
-                hparams.n_embd_s(), n_seqs);
-
-        ggml_tensor * wkv_output = ggml_rwkv_wkv7(ctx0, r, w, k, v, ggml_neg(ctx0, kk), ggml_mul(ctx0, kk, a), wkv_state);
-        cur = ggml_view_1d(ctx0, wkv_output, n_embd * n_tokens, 0);
-        wkv_state = ggml_view_1d(ctx0, wkv_output, n_embd * head_size * n_seqs, n_embd * n_tokens * sizeof(float));
-
-        ggml_build_forward_expand(
-                gf,
-                ggml_cpy(
-                    ctx0,
-                    wkv_state,
-                    ggml_view_1d(
-                        ctx0,
-                        mctx_cur->get_s_l(il),
-                        hparams.n_embd_s() * n_seqs,
-                        hparams.n_embd_s() * kv_head * ggml_element_size(mctx_cur->get_s_l(il))
-                        )
-                    )
-                );
-
-        if (layer.time_mix_ln && layer.time_mix_ln_b) {
-            // group norm with head_count groups
-            cur = ggml_reshape_3d(ctx0, cur, n_embd / head_count, head_count, n_tokens);
-            cur = ggml_norm(ctx0, cur, 64e-5f);
-
-            // Convert back to regular vectors.
-            cur = ggml_reshape_2d(ctx0, cur, n_embd, n_tokens);
-            cur = ggml_add(ctx0, ggml_mul(ctx0, cur, layer.time_mix_ln), layer.time_mix_ln_b);
-        } else {
-            cur = ggml_reshape_2d(ctx0, cur, n_embd, n_tokens);
-        }
-
-        ggml_tensor * rk = ggml_sum_rows(ctx0,
-                ggml_mul(ctx0, ggml_mul(ctx0, k, r), ggml_reshape_2d(ctx0, layer.time_mix_r_k, head_size, head_count)));
-        cur = ggml_add(ctx0, cur, ggml_reshape_2d(ctx0, ggml_mul(ctx0, v, rk), n_embd, n_tokens));
-
-        if (has_gating) {
-            cur = ggml_mul(ctx0, cur, g);
-        }
-        cur = build_lora_mm(layer.time_mix_output, cur);
-
-        return ggml_reshape_3d(ctx0, cur, n_embd, n_seq_tokens, n_seqs);
-    }
-};
-
-struct llm_build_rwkv7 : public llm_build_rwkv7_base {
-    llm_build_rwkv7(const llama_model & model, const llm_graph_params & params) : llm_build_rwkv7_base(model, params) {
-        GGML_ASSERT(hparams.token_shift_count == 2);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-        ggml_tensor * v_first = nullptr;
-
-        inpL = build_inp_embd(model.tok_embd);
-        inpL = build_norm(inpL, model.tok_norm, model.tok_norm_b, LLM_NORM, -1);
-
-        auto * rs_inp = build_rs_inp();
-
-        const auto n_embd = hparams.n_embd;
-        const auto n_seq_tokens = ubatch.n_seq_tokens;
-        const auto n_seqs = ubatch.n_seqs;
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            const llama_layer * layer = &model.layers[il];
-            inpL = ggml_reshape_3d(ctx0, inpL, n_embd, n_seq_tokens, n_seqs);
-
-            ggml_tensor * token_shift = build_rwkv_token_shift_load(rs_inp, ubatch, il);
-
-            ggml_tensor * att_shift = ggml_view_3d(ctx0, token_shift, n_embd, 1, n_seqs, token_shift->nb[1], token_shift->nb[2], 0);
-            ggml_tensor * ffn_shift = ggml_view_3d(ctx0, token_shift, n_embd, 1, n_seqs, token_shift->nb[1], token_shift->nb[2], n_embd * ggml_element_size(token_shift));
-
-            ggml_tensor * att_norm = build_norm(inpL, layer->attn_norm, layer->attn_norm_b, LLM_NORM, il);
-            cb(att_norm, "attn_norm", il);
-
-            ggml_tensor * x_prev = ggml_concat(
-                    ctx0,
-                    att_shift,
-                    ggml_view_3d(ctx0, att_norm, n_embd, n_seq_tokens - 1, n_seqs, att_norm->nb[1], att_norm->nb[2], 0),
-                    1
-                    );
-
-            cur = build_rwkv7_time_mix(rs_inp, att_norm, x_prev, v_first, ubatch, il);
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpL);
-            cb(ffn_inp, "ffn_inp", il);
-
-            ggml_tensor * ffn_norm = build_norm(ffn_inp, layer->attn_norm_2, layer->attn_norm_2_b, LLM_NORM, il);
-            cb(ffn_norm, "ffn_norm", il);
-
-            x_prev = ggml_concat(
-                    ctx0,
-                    ffn_shift,
-                    ggml_view_3d(ctx0, ffn_norm, n_embd, n_seq_tokens - 1, n_seqs, ffn_norm->nb[1], ffn_norm->nb[2], 0),
-                    1
-                    );
-
-            token_shift = ggml_concat(ctx0,
-                    ggml_view_3d(ctx0, att_norm, n_embd, 1, n_seqs, att_norm->nb[1], att_norm->nb[2], (n_seq_tokens-1)*n_embd*ggml_element_size(att_norm)),
-                    ggml_view_3d(ctx0, ffn_norm, n_embd, 1, n_seqs, ffn_norm->nb[1], ffn_norm->nb[2], (n_seq_tokens-1)*n_embd*ggml_element_size(ffn_norm)),
-                    1
-                    );
-            ggml_build_forward_expand(gf, build_rwkv_token_shift_store(token_shift, ubatch, il));
-
-            ffn_inp  = ggml_reshape_2d(ctx0, ffn_inp,  n_embd, n_tokens);
-            ffn_norm = ggml_reshape_2d(ctx0, ffn_norm, n_embd, n_tokens);
-            x_prev   = ggml_reshape_2d(ctx0, x_prev,   n_embd, n_tokens);
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                ffn_inp  = ggml_get_rows(ctx0, ffn_inp,  inp_out_ids);
-                ffn_norm = ggml_get_rows(ctx0, ffn_norm, inp_out_ids);
-                x_prev   = ggml_get_rows(ctx0, x_prev,   inp_out_ids);
-            }
-
-            cur = build_rwkv7_channel_mix(layer, ffn_norm, x_prev, LLM_ARCH_RWKV7);
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-        cur = build_norm(cur, model.output_norm, model.output_norm_b, LLM_NORM, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-
-struct llm_build_arwkv7 : public llm_build_rwkv7_base {
-    llm_build_arwkv7(const llama_model & model, const llm_graph_params & params) : llm_build_rwkv7_base(model, params) {
-        GGML_ASSERT(n_embd == hparams.n_embd_r());
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-        ggml_tensor * v_first = nullptr;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        auto * rs_inp = build_rs_inp();
-
-        const auto n_embd = hparams.n_embd;
-        const auto n_seq_tokens = ubatch.n_seq_tokens;
-        const auto n_seqs = ubatch.n_seqs;
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            const llama_layer * layer = &model.layers[il];
-            inpL = ggml_reshape_3d(ctx0, inpL, n_embd, n_seq_tokens, n_seqs);
-
-            ggml_tensor * token_shift = build_rwkv_token_shift_load(rs_inp, ubatch, il);
-
-            ggml_tensor * att_norm = build_norm(inpL, layer->attn_norm, layer->attn_norm_b, LLM_NORM_RMS, il);
-            cb(att_norm, "attn_norm", il);
-
-            ggml_tensor * x_prev = ggml_concat(
-                    ctx0,
-                    token_shift,
-                    ggml_view_3d(ctx0, att_norm, n_embd, n_seq_tokens - 1, n_seqs, att_norm->nb[1], att_norm->nb[2], 0),
-                    1
-                    );
-
-            cur = build_rwkv7_time_mix(rs_inp, att_norm, x_prev, v_first, ubatch, il);
-
-            token_shift = ggml_view_3d(ctx0, att_norm, n_embd, 1, n_seqs, att_norm->nb[1], att_norm->nb[2], (n_seq_tokens-1)*n_embd*ggml_element_size(att_norm));
-            ggml_build_forward_expand(gf, build_rwkv_token_shift_store(token_shift, ubatch, il));
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpL);
-            cb(ffn_inp, "ffn_inp", il);
-
-            cur     = ggml_reshape_2d(ctx0, cur,     n_embd, n_tokens);
-            ffn_inp = ggml_reshape_2d(ctx0, ffn_inp, n_embd, n_tokens);
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur     = ggml_get_rows(ctx0, cur,     inp_out_ids);
-                ffn_inp = ggml_get_rows(ctx0, ffn_inp, inp_out_ids);
-            }
-
-            // feed-forward network
-            cur = build_norm(ffn_inp,
-                    model.layers[il].ffn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-
-            cur = build_ffn(cur,
-                    model.layers[il].ffn_up,   NULL, NULL,
-                    model.layers[il].ffn_gate, NULL, NULL,
-                    model.layers[il].ffn_down, NULL, NULL,
-                    NULL,
-                    LLM_FFN_SILU, LLM_FFN_PAR, il);
-            cb(cur, "ffn_out", il);
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-        cur = build_norm(cur, model.output_norm, model.output_norm_b, LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_granite : public llm_graph_context {
-    llm_build_granite(
-        const llama_model & model,
-        const llm_graph_params & params)
-        : llm_graph_context(params) {
-
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - built only if rope enabled
-        ggml_tensor * inp_pos = nullptr;
-        if (hparams.rope_finetuned) {
-            inp_pos = build_inp_pos();
-        }
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            cur = build_attention_layer(
-                cur, inp_pos, inp_attn,
-                model, n_embd_head, il);
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            // ffn
-            cur = build_layer_ffn(cur, inpSA, model, il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        // For Granite architectures - scale logits
-        cur = ggml_scale(ctx0, cur, 1.0f / hparams.f_logit_scale);
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-
-    ggml_tensor * build_attention_layer(
-              ggml_tensor             * cur,
-              ggml_tensor             * inp_pos,
-              llm_graph_input_attn_kv * inp_attn,
-        const llama_model             & model,
-        const int64_t                 n_embd_head,
-        const int                     il) {
-
-        // compute Q and K and (optionally) RoPE them
-        ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-        cb(Qcur, "Qcur", il);
-        if (model.layers[il].bq) {
-            Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
-            cb(Qcur, "Qcur", il);
-        }
-
-        ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-        cb(Kcur, "Kcur", il);
-        if (model.layers[il].bk) {
-            Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
-            cb(Kcur, "Kcur", il);
-        }
-
-        ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-        cb(Vcur, "Vcur", il);
-        if (model.layers[il].bv) {
-            Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
-            cb(Vcur, "Vcur", il);
-        }
-
-        Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, hparams.n_head(il),    n_tokens);
-        Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, hparams.n_head_kv(il), n_tokens);
-        Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, hparams.n_head_kv(il), n_tokens);
-
-        const bool use_rope = hparams.rope_finetuned;
-        if (use_rope) {
-            ggml_tensor * rope_factors = model.get_rope_factors(cparams, il);
-            Qcur = ggml_rope_ext(
-                    ctx0, Qcur, inp_pos, rope_factors,
-                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                    ext_factor, attn_factor, beta_fast, beta_slow
-                    );
-
-            Kcur = ggml_rope_ext(
-                    ctx0, Kcur, inp_pos, rope_factors,
-                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                    ext_factor, attn_factor, beta_fast, beta_slow
-                    );
-        }
-
-        cb(Qcur, "Qcur", il);
-        cb(Kcur, "Kcur", il);
-        cb(Vcur, "Vcur", il);
-
-        const float kq_scale = hparams.f_attention_scale == 0.0f ? 1.0f/sqrtf(float(n_embd_head)) : hparams.f_attention_scale;
-        cur = build_attn(inp_attn,
-                model.layers[il].wo, model.layers[il].bo,
-                Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, kq_scale, il);
-                cb(cur, "attn_out", il);
-        return cur;
-    }
-
-    ggml_tensor * build_layer_ffn(
-              ggml_tensor       * cur,
-              ggml_tensor       * inpSA,
-        const llama_model       & model,
-        const int                 il) {
-
-        // For Granite architectures - scale residual
-        if (hparams.f_residual_scale) {
-            cur = ggml_scale(ctx0, cur, hparams.f_residual_scale);
-        }
-        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-        cb(ffn_inp, "ffn_inp", il);
-
-        // feed-forward network (non-MoE)
-        if (model.layers[il].ffn_gate_inp == nullptr) {
-
-            cur = build_norm(ffn_inp,
-                    model.layers[il].ffn_norm, NULL,
-                    LLM_NORM_RMS, il);
-                    cb(cur, "ffn_norm", il);
-
-            cur = build_ffn(cur,
-                    model.layers[il].ffn_up,   model.layers[il].ffn_up_b,   NULL,
-                    model.layers[il].ffn_gate, model.layers[il].ffn_gate_b, NULL,
-                    model.layers[il].ffn_down, model.layers[il].ffn_down_b, NULL,
-                    NULL,
-                    LLM_FFN_SILU, LLM_FFN_PAR, il);
-                    cb(cur, "ffn_out", il);
-
-        } else {
-            // MoE branch
-            cur = build_norm(ffn_inp,
-                    model.layers[il].ffn_norm, NULL,
-                    LLM_NORM_RMS, il);
-                    cb(cur, "ffn_norm", il);
-
-            ggml_tensor * moe_out = build_moe_ffn(cur,
-                    model.layers[il].ffn_gate_inp,
-                    model.layers[il].ffn_up_exps,
-                    model.layers[il].ffn_gate_exps,
-                    model.layers[il].ffn_down_exps,
-                    nullptr,
-                    n_expert, n_expert_used,
-                    LLM_FFN_SILU, true,
-                    false, 0.0,
-                    LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
-                    il);
-            cb(moe_out, "ffn_moe_out", il);
-
-            // For Granite MoE Shared
-            if (hparams.n_ff_shexp > 0) {
-                ggml_tensor * ffn_shexp = build_ffn(cur,
-                    model.layers[il].ffn_up_shexp,   NULL, NULL,
-                    model.layers[il].ffn_gate_shexp, NULL, NULL,
-                    model.layers[il].ffn_down_shexp, NULL, NULL,
-                    NULL,
-                    LLM_FFN_SILU, LLM_FFN_PAR, il);
-                cb(ffn_shexp, "ffn_shexp", il);
-
-                cur = ggml_add(ctx0, moe_out, ffn_shexp);
-                cb(cur, "ffn_out", il);
-            } else {
-                cur = moe_out;
-            }
-        }
-
-        // For Granite architectures - scale residual
-        if (hparams.f_residual_scale) {
-            cur = ggml_scale(ctx0, cur, hparams.f_residual_scale);
-        }
-        cur = ggml_add(ctx0, cur, ffn_inp);
-        cb(cur, "ffn_out", il);
-
-        cur = build_cvec(cur, il);
-        cb(cur, "l_out", il);
-
-        return cur;
-    }
-};
-
-struct llm_build_granite_hybrid : public llm_graph_context_mamba {
-    llm_build_granite_hybrid(
-                 const llama_model & model,
-            const llm_graph_params & params) :
-        llm_graph_context_mamba(params) {
-
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        auto * inp = build_inp_mem_hybrid();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        // Positional embeddings populated if rope enabled
-        ggml_tensor * inp_pos = nullptr;
-        if (hparams.rope_finetuned) {
-            inp_pos = build_inp_pos();
-        }
-
-        for (int il = 0; il < n_layer; ++il) {
-            struct ggml_tensor * inpSA = inpL;
-
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            if (hparams.is_recurrent(il)) {
-                // ssm layer //
-                cur = build_mamba2_layer(inp->get_recr(), cur, model, ubatch, il);
-            } else {
-                // attention layer //
-                cur = build_attention_layer(
-                    cur, inp_pos, inp->get_attn(), model,
-                    n_embd_head, il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            // ffn
-            cur = build_layer_ffn(cur, inpSA, model, il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        // For Granite architectures - scale logits
-        if (hparams.f_logit_scale) {
-            cur = ggml_scale(ctx0, cur, 1.0f / hparams.f_logit_scale);
-        }
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-
-    ggml_tensor * build_attention_layer(
-              ggml_tensor             * cur,
-              ggml_tensor             * inp_pos,
-              llm_graph_input_attn_kv * inp_attn,
-        const llama_model             & model,
-        const int64_t                 n_embd_head,
-        const int                     il) {
-
-        // compute Q and K and (optionally) RoPE them
-        ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-        cb(Qcur, "Qcur", il);
-        if (model.layers[il].bq) {
-            Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
-            cb(Qcur, "Qcur", il);
-        }
-
-        ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-        cb(Kcur, "Kcur", il);
-        if (model.layers[il].bk) {
-            Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
-            cb(Kcur, "Kcur", il);
-        }
-
-        ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-        cb(Vcur, "Vcur", il);
-        if (model.layers[il].bv) {
-            Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
-            cb(Vcur, "Vcur", il);
-        }
-
-        Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, hparams.n_head(il),    n_tokens);
-        Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, hparams.n_head_kv(il), n_tokens);
-        Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, hparams.n_head_kv(il), n_tokens);
-
-        const bool use_rope = hparams.rope_finetuned;
-        if (use_rope) {
-            ggml_tensor * rope_factors = model.get_rope_factors(cparams, il);
-            Qcur = ggml_rope_ext(
-                    ctx0, Qcur, inp_pos, rope_factors,
-                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                    ext_factor, attn_factor, beta_fast, beta_slow
-                    );
-
-            Kcur = ggml_rope_ext(
-                    ctx0, Kcur, inp_pos, rope_factors,
-                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                    ext_factor, attn_factor, beta_fast, beta_slow
-                    );
-        }
-
-        cb(Qcur, "Qcur", il);
-        cb(Kcur, "Kcur", il);
-        cb(Vcur, "Vcur", il);
-
-        const float kq_scale = hparams.f_attention_scale == 0.0f ? 1.0f/sqrtf(float(n_embd_head)) : hparams.f_attention_scale;
-        cur = build_attn(inp_attn,
-                model.layers[il].wo, model.layers[il].bo,
-                Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, kq_scale, il);
-                cb(cur, "attn_out", il);
-        return cur;
-    }
-
-    ggml_tensor * build_layer_ffn(
-              ggml_tensor * cur,
-              ggml_tensor * inpSA,
-        const llama_model & model,
-        const int           il) {
-
-        // For Granite architectures - scale residual
-        if (hparams.f_residual_scale) {
-            cur = ggml_scale(ctx0, cur, hparams.f_residual_scale);
-        }
-        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-        cb(ffn_inp, "ffn_inp", il);
-
-        // feed-forward network (non-MoE)
-        if (model.layers[il].ffn_gate_inp == nullptr) {
-
-            cur = build_norm(ffn_inp,
-                    model.layers[il].ffn_norm, NULL,
-                    LLM_NORM_RMS, il);
-                    cb(cur, "ffn_norm", il);
-
-            cur = build_ffn(cur,
-                    model.layers[il].ffn_up,   model.layers[il].ffn_up_b,   NULL,
-                    model.layers[il].ffn_gate, model.layers[il].ffn_gate_b, NULL,
-                    model.layers[il].ffn_down, model.layers[il].ffn_down_b, NULL,
-                    NULL,
-                    LLM_FFN_SILU, LLM_FFN_PAR, il);
-                    cb(cur, "ffn_out", il);
-
-        } else {
-            // MoE branch
-            cur = build_norm(ffn_inp,
-                    model.layers[il].ffn_norm, NULL,
-                    LLM_NORM_RMS, il);
-                    cb(cur, "ffn_norm", il);
-
-            ggml_tensor * moe_out = build_moe_ffn(cur,
-                    model.layers[il].ffn_gate_inp,
-                    model.layers[il].ffn_up_exps,
-                    model.layers[il].ffn_gate_exps,
-                    model.layers[il].ffn_down_exps,
-                    nullptr,
-                    n_expert, n_expert_used,
-                    LLM_FFN_SILU, true,
-                    false, 0.0,
-                    LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
-                    il);
-            cb(moe_out, "ffn_moe_out", il);
-
-            // For Granite MoE Shared
-            if (hparams.n_ff_shexp > 0) {
-                ggml_tensor * ffn_shexp = build_ffn(cur,
-                    model.layers[il].ffn_up_shexp,   NULL, NULL,
-                    model.layers[il].ffn_gate_shexp, NULL, NULL,
-                    model.layers[il].ffn_down_shexp, NULL, NULL,
-                    NULL,
-                    LLM_FFN_SILU, LLM_FFN_PAR, il);
-                cb(ffn_shexp, "ffn_shexp", il);
-
-                cur = ggml_add(ctx0, moe_out, ffn_shexp);
-                cb(cur, "ffn_out", il);
-            } else {
-                cur = moe_out;
-            }
-        }
-
-        // For Granite architectures - scale residual
-        if (hparams.f_residual_scale) {
-            cur = ggml_scale(ctx0, cur, hparams.f_residual_scale);
-        }
-        cur = ggml_add(ctx0, cur, ffn_inp);
-        cb(cur, "ffn_out", il);
-
-        cur = build_cvec(cur, il);
-        cb(cur, "l_out", il);
-
-        return cur;
-    }
-};
-
-// ref: https://github.com/facebookresearch/chameleon
-// based on the original build_llama() function, changes:
-//   * qk-norm
-//   * swin-norm
-//   * removed bias
-//   * removed MoE
-struct llm_build_chameleon : public llm_graph_context {
-    llm_build_chameleon(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            // norm
-            if (hparams.swin_norm) {
-                cur = inpL;
-            } else {
-                cur = build_norm(inpL,
-                        model.layers[il].attn_norm, NULL,
-                        LLM_NORM_RMS, il);
-                cb(cur, "attn_norm", il);
-            }
-
-            // self-attention
-            {
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-
-                if (model.layers[il].attn_q_norm) {
-                    Qcur = ggml_view_3d(ctx0, Qcur, n_embd_head, n_head, n_tokens,
-                            ggml_element_size(Qcur) * n_embd_head,
-                            ggml_element_size(Qcur) * n_embd_head * n_head,
-                            0);
-                    cb(Qcur, "Qcur", il);
-
-                    Qcur = build_norm(Qcur,
-                            model.layers[il].attn_q_norm,
-                            model.layers[il].attn_q_norm_b,
-                            LLM_NORM, il);
-                    cb(Qcur, "Qcur", il);
-                }
-
-                if (model.layers[il].attn_k_norm) {
-                    Kcur = ggml_view_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens,
-                            ggml_element_size(Kcur) * n_embd_head,
-                            ggml_element_size(Kcur) * n_embd_head * n_head_kv,
-                            0);
-                    cb(Kcur, "Kcur", il);
-
-                    Kcur = build_norm(Kcur,
-                            model.layers[il].attn_k_norm,
-                            model.layers[il].attn_k_norm_b,
-                            LLM_NORM, il);
-                    cb(Kcur, "Kcur", il);
-                }
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, nullptr,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            if (hparams.swin_norm) {
-                cur = build_norm(cur,
-                        model.layers[il].attn_norm, NULL,
-                        LLM_NORM_RMS, il);
-            }
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed-forward network
-            if (!hparams.swin_norm) {
-                cur = build_norm(ffn_inp,
-                        model.layers[il].ffn_norm, NULL,
-                        LLM_NORM_RMS, il);
-                cb(cur, "ffn_norm", il);
-            }
-
-            cur = build_ffn(cur,
-                    model.layers[il].ffn_up,   NULL, NULL,
-                    model.layers[il].ffn_gate, NULL, NULL,
-                    model.layers[il].ffn_down, NULL, NULL,
-                    NULL,
-                    LLM_FFN_SILU, LLM_FFN_PAR, il);
-            cb(cur, "ffn_out", il);
-
-            if (hparams.swin_norm) {
-                cur = build_norm(cur,
-                        model.layers[il].ffn_norm, NULL,
-                        LLM_NORM_RMS, il);
-                cb(cur, "ffn_norm", il);
-            }
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-            cb(cur, "ffn_out", il);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-        cb(cur, "result_output_with_img_logits", -1);
-
-        // TODO: this suppresses the output of image tokens, which is required to enable text-only outputs.
-        // Needs to be removed once image outputs are supported.
-        int img_token_end_idx = 8196;
-        int img_token_start_idx = 4;
-        int num_img_tokens = img_token_end_idx - img_token_start_idx;
-        // creates 1d tensor of size num_img_tokens and values -FLT_MAX,
-        // which ensures that text token values are always at least larger than image token values
-        ggml_tensor * img_logits = ggml_new_tensor_1d(ctx0, GGML_TYPE_F32, num_img_tokens);
-        img_logits = ggml_clamp(ctx0, img_logits, -FLT_MAX, -FLT_MAX);
-        cb(img_logits, "img_logits", -1);
-
-        cur = ggml_set_1d(ctx0, cur, img_logits, ggml_element_size(cur) * img_token_start_idx);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_wavtokenizer_dec : public llm_graph_context {
-    llm_build_wavtokenizer_dec(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        cur = ggml_cont(ctx0, ggml_transpose(ctx0, inpL));
-
-        cur = ggml_conv_1d_ph(ctx0, model.conv1d, cur, 1, 1);
-        cur = ggml_add(ctx0, cur, model.conv1d_b);
-
-        // posnet
-        for (uint32_t il = 0; il < hparams.posnet.n_layer; ++il) {
-            const auto & layer = model.layers[il].posnet;
-
-            inpL = cur;
-
-            switch (il) {
-                case 0:
-                case 1:
-                case 3:
-                case 4:
-                    {
-                        cur = build_norm(cur,
-                                layer.norm1,
-                                layer.norm1_b,
-                                LLM_NORM_GROUP, 0);
-
-                        cur = ggml_mul(ctx0, ggml_sigmoid(ctx0, cur), cur);
-
-                        cur = ggml_conv_1d_ph(ctx0, layer.conv1, cur, 1, 1);
-                        cur = ggml_add(ctx0, cur, layer.conv1_b);
-
-                        cur = build_norm(cur,
-                                layer.norm2,
-                                layer.norm2_b,
-                                LLM_NORM_GROUP, 0);
-
-                        cur = ggml_mul(ctx0, ggml_sigmoid(ctx0, cur), cur);
-
-                        cur = ggml_conv_1d_ph(ctx0, layer.conv2, cur, 1, 1);
-                        cur = ggml_add(ctx0, cur, layer.conv2_b);
-
-                        cur = ggml_add(ctx0, cur, inpL);
-                    } break;
-                case 2:
-                    {
-                        cur = build_norm(cur,
-                                layer.attn_norm,
-                                layer.attn_norm_b,
-                                LLM_NORM_GROUP, 0);
-
-                        ggml_tensor * q;
-                        ggml_tensor * k;
-                        ggml_tensor * v;
-
-                        q = ggml_conv_1d_ph(ctx0, layer.attn_q, cur, 1, 1);
-                        k = ggml_conv_1d_ph(ctx0, layer.attn_k, cur, 1, 1);
-                        v = ggml_conv_1d_ph(ctx0, layer.attn_v, cur, 1, 1);
-
-                        q = ggml_add(ctx0, q, layer.attn_q_b);
-                        k = ggml_add(ctx0, k, layer.attn_k_b);
-                        v = ggml_add(ctx0, v, layer.attn_v_b);
-
-                        q = ggml_cont(ctx0, ggml_transpose(ctx0, q));
-                        k = ggml_cont(ctx0, ggml_transpose(ctx0, k));
-
-                        ggml_tensor * kq = ggml_mul_mat(ctx0, k, q);
-
-                        kq = ggml_soft_max_ext(ctx0, kq, nullptr, 1.0f/sqrtf(float(hparams.posnet.n_embd)), 0.0f);
-
-                        cur = ggml_mul_mat(ctx0, kq, v);
-
-                        cur = ggml_conv_1d_ph(ctx0, layer.attn_o, cur, 1, 1);
-                        cur = ggml_add(ctx0, cur, layer.attn_o_b);
-
-                        cur = ggml_add(ctx0, cur, inpL);
-                    } break;
-                case 5:
-                    {
-                        cur = build_norm(cur,
-                                layer.norm,
-                                layer.norm_b,
-                                LLM_NORM_GROUP, 0);
-                    } break;
-                default: GGML_ABORT("unknown posnet layer");
-            };
-        }
-
-        cur = ggml_cont(ctx0, ggml_transpose(ctx0, cur));
-
-        cur = build_norm(cur,
-                model.tok_norm,
-                model.tok_norm_b,
-                LLM_NORM, -1);
-
-        cur = ggml_cont(ctx0, ggml_transpose(ctx0, cur));
-
-        inpL = cur;
-
-        // convnext
-        for (uint32_t il = 0; il < hparams.convnext.n_layer; ++il) {
-            const auto & layer = model.layers[il].convnext;
-
-            cur = inpL;
-
-            cur = ggml_conv_1d_dw_ph(ctx0, layer.dw, cur, 1, 1);
-            cur = ggml_add(ctx0, cur, layer.dw_b);
-
-            cur = ggml_cont(ctx0, ggml_transpose(ctx0, cur));
-
-            cur = build_norm(cur,
-                    layer.norm,
-                    layer.norm_b,
-                    LLM_NORM, -1);
-
-            cur = build_ffn(cur,
-                    layer.pw1, layer.pw1_b, NULL,
-                    NULL,      NULL,        NULL,
-                    layer.pw2, layer.pw2_b, NULL,
-                    NULL,
-                    LLM_FFN_GELU, LLM_FFN_SEQ, il);
-
-            cur = ggml_mul(ctx0, cur, layer.gamma);
-
-            cur = ggml_cont(ctx0, ggml_transpose(ctx0, cur));
-
-            inpL = ggml_add(ctx0, cur, inpL);
-        }
-
-        cur = inpL;
-
-        cur = ggml_cont(ctx0, ggml_transpose(ctx0, cur));
-
-        cur = build_norm(cur,
-                model.output_norm,
-                model.output_norm_b,
-                LLM_NORM, -1);
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        cur = ggml_add(ctx0, cur, model.output_b);
-
-        cb(cur, "result_embd", -1);
-        res->t_embd = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_plm : public llm_graph_context {
-    llm_build_plm(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const float kq_scale = 1.0f/sqrtf(float(hparams.n_embd_head_k));
-
-        const uint32_t n_embd_head_qk_rope = hparams.n_rot;
-        const uint32_t n_embd_head_qk_nope = hparams.n_embd_head_k - hparams.n_rot;
-        const uint32_t kv_lora_rank = hparams.n_lora_kv;
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        // {n_embd, n_tokens}
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self_attention
-            {
-                ggml_tensor * q = NULL;
-                q = ggml_mul_mat(ctx0, model.layers[il].wq, cur);
-                cb(q, "q", il);
-
-                // split into {n_head * n_embd_head_qk_nope, n_tokens}
-                ggml_tensor * q_nope = ggml_view_3d(ctx0, q, n_embd_head_qk_nope, n_head, n_tokens,
-                        ggml_row_size(q->type, hparams.n_embd_head_k),
-                        ggml_row_size(q->type, hparams.n_embd_head_k * n_head),
-                        0);
-                cb(q_nope, "q_nope", il);
-
-                // and {n_head * n_embd_head_qk_rope, n_tokens}
-                ggml_tensor * q_pe = ggml_view_3d(ctx0, q, n_embd_head_qk_rope, n_head, n_tokens,
-                        ggml_row_size(q->type, hparams.n_embd_head_k),
-                        ggml_row_size(q->type, hparams.n_embd_head_k * n_head),
-                        ggml_row_size(q->type, n_embd_head_qk_nope));
-                cb(q_pe, "q_pe", il);
-
-                // {n_embd, kv_lora_rank + n_embd_head_qk_rope} * {n_embd, n_tokens} -> {kv_lora_rank + n_embd_head_qk_rope, n_tokens}
-                ggml_tensor * kv_pe_compresseed = ggml_mul_mat(ctx0, model.layers[il].wkv_a_mqa, cur);
-                cb(kv_pe_compresseed, "kv_pe_compresseed", il);
-
-                // split into {kv_lora_rank, n_tokens}
-                ggml_tensor * kv_compressed = ggml_view_2d(ctx0, kv_pe_compresseed, kv_lora_rank, n_tokens,
-                        kv_pe_compresseed->nb[1],
-                        0);
-                cb(kv_compressed, "kv_compressed", il);
-
-                // and {n_embd_head_qk_rope, n_tokens}
-                ggml_tensor * k_pe = ggml_view_3d(ctx0, kv_pe_compresseed, n_embd_head_qk_rope, 1, n_tokens,
-                        kv_pe_compresseed->nb[1],
-                        kv_pe_compresseed->nb[1],
-                        ggml_row_size(kv_pe_compresseed->type, kv_lora_rank));
-                cb(k_pe, "k_pe", il);
-
-                kv_compressed = build_norm(kv_compressed,
-                        model.layers[il].attn_kv_a_norm, NULL,
-                        LLM_NORM_RMS, il);
-                cb(kv_compressed, "kv_compressed", il);
-
-                // {kv_lora_rank, n_head * (n_embd_head_qk_nope + n_embd_head_v)} * {kv_lora_rank, n_tokens} -> {n_head * (n_embd_head_qk_nope + n_embd_head_v), n_tokens}
-                ggml_tensor * kv = ggml_mul_mat(ctx0, model.layers[il].wkv_b, kv_compressed);
-                cb(kv, "kv", il);
-
-                // split into {n_head * n_embd_head_qk_nope, n_tokens}
-                ggml_tensor * k_nope = ggml_view_3d(ctx0, kv, n_embd_head_qk_nope, n_head, n_tokens,
-                        ggml_row_size(kv->type, n_embd_head_qk_nope + hparams.n_embd_head_v),
-                        ggml_row_size(kv->type, n_head * (n_embd_head_qk_nope + hparams.n_embd_head_v)),
-                        0);
-                cb(k_nope, "k_nope", il);
-
-                // and {n_head * n_embd_head_v, n_tokens}
-                ggml_tensor * v_states = ggml_view_3d(ctx0, kv, hparams.n_embd_head_v, n_head, n_tokens,
-                        ggml_row_size(kv->type, (n_embd_head_qk_nope + hparams.n_embd_head_v)),
-                        ggml_row_size(kv->type, (n_embd_head_qk_nope + hparams.n_embd_head_v)*n_head),
-                        ggml_row_size(kv->type, (n_embd_head_qk_nope)));
-                cb(v_states, "v_states", il);
-
-                v_states = ggml_cont(ctx0, v_states);
-                cb(v_states, "v_states", il);
-
-                v_states = ggml_view_2d(ctx0, v_states, hparams.n_embd_head_v * n_head, n_tokens,
-                        ggml_row_size(kv->type, hparams.n_embd_head_v * n_head),
-                        0);
-                cb(v_states, "v_states", il);
-
-                q_pe = ggml_rope_ext(
-                        ctx0, q_pe, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-                cb(q_pe, "q_pe", il);
-
-                // shared RoPE key
-                k_pe = ggml_rope_ext(
-                        ctx0, k_pe, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-                cb(k_pe, "k_pe", il);
-
-                ggml_tensor * q_states = ggml_concat(ctx0, q_nope, q_pe, 0);
-                cb(q_states, "q_states", il);
-
-                ggml_tensor * k_states = ggml_concat(ctx0, k_nope, ggml_repeat(ctx0, k_pe, q_pe), 0);
-                cb(k_states, "k_states", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, NULL,
-                        q_states, k_states, v_states, nullptr, nullptr, nullptr, kq_scale, il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            cur = build_norm(ffn_inp,
-                    model.layers[il].ffn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-
-            cur = build_ffn(cur,
-                    model.layers[il].ffn_up,   NULL, NULL,
-                    NULL, NULL, NULL,
-                    model.layers[il].ffn_down, NULL, NULL,
-                    NULL,
-                    LLM_FFN_RELU_SQR, LLM_FFN_SEQ, il);
-            cb(cur, "ffn_out", il);
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_bailingmoe : public llm_graph_context {
-    llm_build_bailingmoe(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                // rope freq factors for llama3; may return nullptr for llama2 and other models
-                ggml_tensor * rope_factors = model.get_rope_factors(cparams, il);
-
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-                if (model.layers[il].bq) {
-                    Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
-                    cb(Qcur, "Qcur", il);
-                }
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-                if (model.layers[il].bk) {
-                    Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
-                    cb(Kcur, "Kcur", il);
-                }
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-                if (model.layers[il].bv) {
-                    Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
-                    cb(Vcur, "Vcur", il);
-                }
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_rot, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_rot, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_rot, n_head_kv, n_tokens);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, rope_factors,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, rope_factors,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_rot)), il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            cur = build_norm(ffn_inp,
-                    model.layers[il].ffn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-
-            ggml_tensor * moe_out =
-                build_moe_ffn(cur,
-                        model.layers[il].ffn_gate_inp,
-                        model.layers[il].ffn_up_exps,
-                        model.layers[il].ffn_gate_exps,
-                        model.layers[il].ffn_down_exps,
-                        nullptr,
-                        n_expert, n_expert_used,
-                        LLM_FFN_SILU, hparams.expert_weights_norm,
-                        false, hparams.expert_weights_scale,
-                        LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
-                        il);
-            cb(moe_out, "ffn_moe_out", il);
-
-            // FFN shared expert
-            {
-                ggml_tensor * ffn_shexp = build_ffn(cur,
-                        model.layers[il].ffn_up_shexp,   NULL, NULL,
-                        model.layers[il].ffn_gate_shexp, NULL, NULL,
-                        model.layers[il].ffn_down_shexp, NULL, NULL,
-                        NULL,
-                        LLM_FFN_SILU, LLM_FFN_PAR, il);
-                cb(ffn_shexp, "ffn_shexp", il);
-
-                cur = ggml_add(ctx0, moe_out, ffn_shexp);
-                cb(cur, "ffn_out", il);
-            }
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_bailingmoe2 : public llm_graph_context {
-    llm_build_bailingmoe2(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-        const int64_t n_embd_gqa  = hparams.n_embd_v_gqa();
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        const int n_transformer_layers = n_layer - hparams.nextn_predict_layers;
-        for (int il = 0; il < n_transformer_layers; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self_attention
-            {
-                cur = build_lora_mm(model.layers[il].wqkv, cur);
-                cb(cur, "wqkv", il);
-
-                ggml_tensor * Qcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head,    n_tokens, n_embd_head*sizeof(float), cur->nb[1], 0*sizeof(float)*(n_embd));
-                ggml_tensor * Kcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd));
-                ggml_tensor * Vcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd + n_embd_gqa));
-
-                Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL, LLM_NORM_RMS, il);
-                cb(Qcur, "Qcur_normed", il);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, NULL, LLM_NORM_RMS, il);
-                cb(Kcur, "Kcur_normed", il);
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-
-            if (il == n_transformer_layers - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            ggml_tensor * sa_out = ggml_add(ctx0, cur, inpSA);
-            cb(sa_out, "sa_out", il);
-
-            // MoE branch
-            cur = build_norm(sa_out,
-                    model.layers[il].ffn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-
-            if (static_cast<uint32_t>(il) < hparams.n_layer_dense_lead) {
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up,   NULL, NULL,
-                        model.layers[il].ffn_gate, NULL, NULL,
-                        model.layers[il].ffn_down, NULL, NULL,
-                        NULL,
-                        LLM_FFN_SILU, LLM_FFN_PAR, il);
-                cb(cur, "ffn_out", il);
-            } else {
-                ggml_tensor * moe_out =
-                    build_moe_ffn(cur,
-                            model.layers[il].ffn_gate_inp,
-                            model.layers[il].ffn_up_exps,
-                            model.layers[il].ffn_gate_exps,
-                            model.layers[il].ffn_down_exps,
-                            model.layers[il].ffn_exp_probs_b,
-                            n_expert, n_expert_used,
-                            LLM_FFN_SILU, hparams.expert_weights_norm,
-                            true, hparams.expert_weights_scale,
-                            (llama_expert_gating_func_type) hparams.expert_gating_func,
-                            il);
-                cb(moe_out, "ffn_moe_out", il);
-
-                {
-                    ggml_tensor * ffn_shexp = build_ffn(cur,
-                            model.layers[il].ffn_up_shexp,   NULL, NULL,
-                            model.layers[il].ffn_gate_shexp, NULL, NULL,
-                            model.layers[il].ffn_down_shexp, NULL, NULL,
-                            NULL,
-                            LLM_FFN_SILU, LLM_FFN_PAR, il);
-                    cb(ffn_shexp, "ffn_shexp", il);
-
-                    cur = ggml_add(ctx0, moe_out, ffn_shexp);
-                    cb(cur, "ffn_out", il);
-                }
-            }
-
-            cur = ggml_add(ctx0, cur, sa_out);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_dots1 : public llm_graph_context {
-    llm_build_dots1(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self_attention
-            {
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL, LLM_NORM_RMS, il);
-                cb(Qcur, "Qcur_normed", il);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, NULL, LLM_NORM_RMS, il);
-                cb(Kcur, "Kcur_normed", il);
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // MoE branch
-            cur = build_norm(ffn_inp,
-                    model.layers[il].ffn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-
-            if ((uint32_t) il < hparams.n_layer_dense_lead) {
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up,   NULL, NULL,
-                        model.layers[il].ffn_gate, NULL, NULL,
-                        model.layers[il].ffn_down, NULL, NULL,
-                        NULL,
-                        LLM_FFN_SILU, LLM_FFN_PAR, il);
-                cb(cur, "ffn_out", il);
-            } else {
-                ggml_tensor * moe_out =
-                    build_moe_ffn(cur,
-                            model.layers[il].ffn_gate_inp,
-                            model.layers[il].ffn_up_exps,
-                            model.layers[il].ffn_gate_exps,
-                            model.layers[il].ffn_down_exps,
-                            model.layers[il].ffn_exp_probs_b,
-                            n_expert, n_expert_used,
-                            LLM_FFN_SILU, hparams.expert_weights_norm,
-                            true, hparams.expert_weights_scale,
-                            (llama_expert_gating_func_type) hparams.expert_gating_func,
-                            il);
-                cb(moe_out, "ffn_moe_out", il);
-
-                {
-                    ggml_tensor * ffn_shexp = build_ffn(cur,
-                            model.layers[il].ffn_up_shexp,   NULL, NULL,
-                            model.layers[il].ffn_gate_shexp, NULL, NULL,
-                            model.layers[il].ffn_down_shexp, NULL, NULL,
-                            NULL,
-                            LLM_FFN_SILU, LLM_FFN_PAR, il);
-                    cb(ffn_shexp, "ffn_shexp", il);
-
-                    cur = ggml_add(ctx0, moe_out, ffn_shexp);
-                    cb(cur, "ffn_out", il);
-                }
-            }
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_ernie4_5 : public llm_graph_context {
-    llm_build_ernie4_5(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            // norm
-            {
-                cur = build_norm(inpL,
-                        model.layers[il].attn_norm, NULL,
-                        LLM_NORM_RMS, il);
-                cb(cur, "attn_norm", il);
-            }
-
-            // self-attention
-            {
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-                if (model.layers[il].bq) {
-                    Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
-                    cb(Qcur, "Qcur", il);
-                }
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-                if (model.layers[il].bk) {
-                    Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
-                    cb(Kcur, "Kcur", il);
-                }
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-                if (model.layers[il].bv) {
-                    Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
-                    cb(Vcur, "Vcur", il);
-                }
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, NULL,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-
-            if (il == n_layer - 1) {
-                // skip computing output for unused tokens
-                ggml_tensor * inp_out_ids = build_inp_out_ids();
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed-forward network
-            {
-                cur = build_norm(ffn_inp,
-                        model.layers[il].ffn_norm, NULL,
-                        LLM_NORM_RMS, il);
-                cb(cur, "ffn_norm", il);
-
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up,   NULL, NULL,
-                        model.layers[il].ffn_gate, NULL, NULL,
-                        model.layers[il].ffn_down, NULL, NULL,
-                        NULL,
-                        LLM_FFN_SILU, LLM_FFN_PAR, il);
-                cb(cur, "ffn_out", il);
-            }
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_ernie4_5_moe : public llm_graph_context {
-    llm_build_ernie4_5_moe(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        GGML_ASSERT(hparams.n_moe_layer_step > 0 && "Ernie 4.5 MoE requires n_moe_layer_step > 0");
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-            // norm
-            {
-                cur = build_norm(inpL,
-                        model.layers[il].attn_norm, NULL,
-                        LLM_NORM_RMS, il);
-                cb(cur, "attn_norm", il);
-            }
-
-            // self-attention
-            {
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-                if (model.layers[il].bq) {
-                    Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
-                    cb(Qcur, "Qcur", il);
-                }
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-                if (model.layers[il].bk) {
-                    Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
-                    cb(Kcur, "Kcur", il);
-                }
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-                if (model.layers[il].bv) {
-                    Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
-                    cb(Vcur, "Vcur", il);
-                }
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, NULL,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-                cb(cur, "attn_out", il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed-forward network
-            bool is_moe_layer = static_cast<uint32_t>(il) >= hparams.n_layer_dense_lead && (il + 1) % hparams.n_moe_layer_step == 0;
-
-            if (!is_moe_layer) {
-                cur = build_norm(ffn_inp,
-                        model.layers[il].ffn_norm, NULL,
-                        LLM_NORM_RMS, il);
-                cb(cur, "ffn_norm", il);
-
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up,   NULL, NULL,
-                        model.layers[il].ffn_gate, NULL, NULL,
-                        model.layers[il].ffn_down, NULL, NULL,
-                        NULL,
-                        LLM_FFN_SILU, LLM_FFN_PAR, il);
-                cb(cur, "ffn_out", il);
-            } else {
-                // MoE branch
-                cur = build_norm(ffn_inp,
-                        model.layers[il].ffn_norm, NULL,
-                        LLM_NORM_RMS, il);
-                cb(cur, "ffn_norm", il);
-
-                ggml_tensor * moe_out = build_moe_ffn(cur,
-                        model.layers[il].ffn_gate_inp,
-                        model.layers[il].ffn_up_exps,
-                        model.layers[il].ffn_gate_exps,
-                        model.layers[il].ffn_down_exps,
-                        model.layers[il].ffn_exp_probs_b,
-                        n_expert, n_expert_used,
-                        LLM_FFN_SILU, true,
-                        false, 0.0,
-                        LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
-                        il);
-                cb(moe_out, "ffn_moe_out", il);
-
-                // Shared expert (if present)
-                if (hparams.n_ff_shexp > 0) {
-                    ggml_tensor * ffn_shexp = build_ffn(cur,
-                        model.layers[il].ffn_up_shexp,   NULL, NULL,
-                        model.layers[il].ffn_gate_shexp, NULL, NULL,
-                        model.layers[il].ffn_down_shexp, NULL, NULL,
-                        NULL,
-                        LLM_FFN_SILU, LLM_FFN_PAR, il);
-                    cb(ffn_shexp, "ffn_shexp", il);
-
-                    cur = ggml_add(ctx0, moe_out, ffn_shexp);
-                } else {
-                    cur = moe_out;
-                }
-                cb(cur, "ffn_out", il);
-            }
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-            cb(cur, "ffn_out", il);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_falcon_h1 : public llm_graph_context_mamba {
-    llm_build_falcon_h1(const llama_model & model, const llm_graph_params & params) : llm_graph_context_mamba(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        // Build the inputs in the recurrent & kv cache
-        auto * inp = build_inp_mem_hybrid();
-
-        const float kq_scale = hparams.f_attention_scale == 0.0f ? 1.0f/sqrtf(float(n_embd_head)) : hparams.f_attention_scale;
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-            cb(Qcur, "Qcur", il);
-
-            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-            cb(Kcur, "Kcur", il);
-
-            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-            cb(Vcur, "Vcur", il);
-
-            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-
-            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-            Qcur = ggml_rope_ext(
-                    ctx0, Qcur, inp_pos, nullptr,
-                    n_rot, hparams.rope_type, n_ctx_orig, freq_base, freq_scale,
-                    ext_factor, attn_factor, beta_fast, beta_slow);
-
-            Kcur = ggml_rope_ext(
-                    ctx0, Kcur, inp_pos, nullptr,
-                    n_rot, hparams.rope_type, n_ctx_orig, freq_base, freq_scale,
-                    ext_factor, attn_factor, beta_fast, beta_slow
-                    );
-
-            cb(Qcur, "Qcur-post-rope", il);
-            cb(Kcur, "Kcur-post-rope", il);
-            cb(Vcur, "Vcur-post-rope", il);
-
-            ggml_tensor * attn_out = build_attn(inp->get_attn(),
-                    model.layers[il].wo, NULL,
-                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, kq_scale, il);
-            cb(attn_out, "attn_out", il);
-
-            cur = build_norm(inpL,
-                model.layers[il].attn_norm, NULL,
-                LLM_NORM_RMS, il);
-            // Mamba2 layer
-            cb(cur, "ssm_in", il);
-
-            ggml_tensor * ssm_out = build_mamba2_layer(inp->get_recr(), cur, model, ubatch, il);
-            cb(ssm_out, "ssm_out", il);
-
-            // // Aggregation
-            cur = ggml_add(ctx0, attn_out, ssm_out);
-            inpSA = ggml_add(ctx0, cur, inpSA);
-            cb(cur, "layer_out", il);
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            ggml_tensor * ffn_inp = inpSA;
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed-forward network
-            cur = build_norm(ffn_inp,
-                    model.layers[il].ffn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-
-            cur = build_ffn(cur,
-                    model.layers[il].ffn_up,   model.layers[il].ffn_up_b, NULL,
-                    model.layers[il].ffn_gate, model.layers[il].ffn_gate_b, NULL,
-                    model.layers[il].ffn_down, model.layers[il].ffn_down_b, NULL,
-                    NULL,
-                    LLM_FFN_SILU, LLM_FFN_PAR, il);
-            cb(cur, "ffn_out", il);
-
-            cur = ggml_add(ctx0, cur, inpSA);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_plamo2 : public llm_graph_context_mamba {
-    llm_build_plamo2(const llama_model & model, const llm_graph_params & params) : llm_graph_context_mamba(params) {
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        // {n_embd, n_tokens}
-        inpL = build_inp_embd(model.tok_embd);
-        cb(inpL, "embedding_output", -1);
-
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_hybrid = build_inp_mem_hybrid();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * residual = inpL;
-
-            // ggml_graph_add_node(gf, model.layers[il].attn_norm);
-            // cb(model.layers[il].attn_norm, "attn_norm", il);
-
-            // pre_mixer_norm
-            cur = build_norm(inpL, model.layers[il].attn_norm, NULL, LLM_NORM_RMS, il);
-
-            // check if this layer is Mamba or Attention
-            bool is_mamba_layer = hparams.is_recurrent(il);
-
-            if (is_mamba_layer) {
-                // PLaMo-2 Mamba layer
-                cur = build_plamo2_mamba_layer(inp_hybrid->get_recr(), cur, model, ubatch, il);
-            } else {
-                // PLaMo-2 Attention layer
-                cur = build_plamo2_attn_layer(inp_hybrid->get_attn(), inp_pos, cur, model, il);
-            }
-
-            // post_mixer_norm
-            cur = build_norm(cur, model.layers[il].attn_post_norm, NULL, LLM_NORM_RMS, il);
-            cb(cur, "attn_post_norm", il);
-
-            // residual connection
-            cur = ggml_add(ctx0, cur, residual);
-            cb(cur, "attn_residual", il);
-            residual = cur;
-
-            // pre-ffn norm
-            cur = build_norm(cur, model.layers[il].ffn_norm, NULL, LLM_NORM_RMS, il);
-            cb(cur, "ffn_pre_norm", il);
-
-            // feed-forward network
-            cur = build_ffn(cur,
-                    model.layers[il].ffn_up,   NULL, NULL,
-                    NULL,                      NULL, NULL,
-                    model.layers[il].ffn_down, NULL, NULL,
-                    NULL,
-                    LLM_FFN_SWIGLU, LLM_FFN_SEQ, il);
-            cb(cur, "ffn_out", il);
-
-            // post ffn norm
-            cur = build_norm(cur, model.layers[il].ffn_post_norm, NULL, LLM_NORM_RMS, il);
-            cb(cur, "ffn_post_norm", il);
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur  = ggml_get_rows(ctx0,  cur, inp_out_ids);
-                residual = ggml_get_rows(ctx0, residual, inp_out_ids);
-            }
-
-            // residual connection
-            cur = ggml_add(ctx0, cur, residual);
-            cb(cur, "ffn_residual", il);
-
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        // final norm
-        cur = build_norm(cur, model.output_norm, NULL, LLM_NORM_RMS, -1);
-        cb(cur, "result_norm", -1);
-
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-        cb(cur, "result_output", -1);
-
-        // Explicitly mark as output tensor to ensure proper backend assignment
-        ggml_set_output(cur);
-
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-
-private:
-    ggml_tensor * build_plamo2_attn_layer(
-            llm_graph_input_attn_kv * inp,
-            ggml_tensor * inp_pos,
-            ggml_tensor * cur,
-            const llama_model & model,
-            int il) {
-
-        // self-attention
-        {
-            // PLaMo-2 uses combined QKV tensor
-            ggml_tensor * qkv = build_lora_mm(model.layers[il].wqkv, cur);
-            cb(qkv, "wqkv", il);
-
-            // split QKV tensor into Q, K, V
-            const int64_t n_embd_head_q = hparams.n_embd_head_k;
-            const int64_t n_embd_head_k = hparams.n_embd_head_k;
-            const int64_t n_embd_head_v = hparams.n_embd_head_v;
-            int32_t n_head = hparams.n_head(il);
-            int32_t n_head_kv = hparams.n_head_kv(il);
-
-            const int64_t q_offset = 0;
-            const int64_t k_offset = n_embd_head_q * n_head;
-            const int64_t v_offset = k_offset + n_embd_head_k * n_head_kv;
-
-            ggml_tensor * Qcur = ggml_view_3d(ctx0, qkv, n_embd_head_q, n_head,    n_tokens, n_embd_head_q * sizeof(float), qkv->nb[1], q_offset * ggml_element_size(qkv));
-            ggml_tensor * Kcur = ggml_view_3d(ctx0, qkv, n_embd_head_k, n_head_kv, n_tokens, n_embd_head_k * sizeof(float), qkv->nb[1], k_offset * ggml_element_size(qkv));
-            ggml_tensor * Vcur = ggml_view_3d(ctx0, qkv, n_embd_head_v, n_head_kv, n_tokens, n_embd_head_v * sizeof(float), qkv->nb[1], v_offset * ggml_element_size(qkv));
-
-            cb(Qcur, "Qcur", il);
-            cb(Kcur, "Kcur", il);
-            cb(Vcur, "Vcur", il);
-
-            Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL, LLM_NORM_RMS, il);
-            cb(Qcur, "Qcur_normed", il);
-
-            Qcur = ggml_rope_ext(
-                    ctx0, Qcur, inp_pos, nullptr,
-                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                    ext_factor, attn_factor, beta_fast, beta_slow
-                    );
-
-            Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, NULL, LLM_NORM_RMS, il);
-            cb(Kcur, "Kcur_normed", il);
-
-            Kcur = ggml_rope_ext(
-                    ctx0, Kcur, inp_pos, nullptr,
-                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                    ext_factor, attn_factor, beta_fast, beta_slow
-                    );
-
-            cur = build_attn(inp,
-                    model.layers[il].wo, NULL,
-                    Qcur, Kcur, Vcur, NULL, NULL, NULL, 1.0f/sqrtf(float(n_embd_head_v)), il);
-        }
-
-        cb(cur, "attn_out", il);
-
-        return cur;
-    }
-
-    ggml_tensor * build_plamo2_mamba_layer(
-         llm_graph_input_rs * inp,
-               ggml_tensor * cur,
-         const llama_model & model,
-        const llama_ubatch & ubatch,
-                       int   il) {
-
-        const auto * mctx_cur = inp->mctx;
-
-        const auto kv_head = mctx_cur->get_head();
-
-        const int64_t d_conv   = hparams.ssm_d_conv;
-        const int64_t d_inner  = hparams.ssm_d_inner;
-        const int64_t d_state  = hparams.ssm_d_state;
-        const int64_t n_heads  = hparams.ssm_dt_rank;
-        const int64_t head_dim = d_inner / n_heads;
-        const int64_t n_group  = hparams.ssm_n_group;
-        const int64_t n_seqs   = ubatch.n_seqs;
-
-        const int64_t n_seq_tokens = ubatch.n_seq_tokens;
-
-        GGML_ASSERT(n_seqs != 0);
-        GGML_ASSERT(ubatch.equal_seqs());
-        GGML_ASSERT(ubatch.n_tokens == n_seq_tokens * n_seqs);
-
-        ggml_tensor * conv_states_all = mctx_cur->get_r_l(il);
-        ggml_tensor * ssm_states_all  = mctx_cur->get_s_l(il);
-
-        ggml_tensor * conv = build_rs(inp, conv_states_all, hparams.n_embd_r(), n_seqs);
-        conv = ggml_reshape_3d(ctx0, conv, d_conv - 1, d_inner + 2*n_group*d_state, n_seqs);
-
-        // {n_embd, n_tokens} => {n_embd, n_seq_tokens, n_seqs}
-        cur = ggml_reshape_3d(ctx0, cur, cur->ne[0], n_seq_tokens, n_seqs);
-
-        // in_proj: {n_embd, 2*d_inner} @ {n_embd, n_seq_tokens, n_seqs} => {2*d_inner, n_seq_tokens, n_seqs}
-        ggml_tensor * zx = build_lora_mm(model.layers[il].ssm_in, cur);
-        cb(zx, "mamba_in_proj", il);
-        // {8192, 5, 1, 1} -> {8192, 1, 5, 1}
-        zx = ggml_permute(ctx0, zx, 0, 2, 1, 3);
-        zx = ggml_cont_4d(ctx0, zx, head_dim * 2, n_heads, n_seq_tokens, n_seqs);
-        cb(zx, "mamba_in_proj_out", il);
-
-        // split into z and x
-        // => {head_dim * n_heads, n_seq_tokens, n_seqs}
-        ggml_tensor * x = ggml_view_4d(ctx0, zx, head_dim, n_heads, n_seq_tokens, n_seqs, zx->nb[1], zx->nb[2], zx->nb[3], head_dim*ggml_element_size(zx));
-        x = ggml_cont_3d(ctx0, x, head_dim * n_heads, n_seq_tokens, n_seqs);
-        // x = ggml_permute(ctx0, x, 0, 2, 1, 3);
-        cb(x, "mamba_x_split", il);
-
-        ggml_tensor * z = ggml_view_4d(ctx0, zx, head_dim, n_heads, n_seq_tokens, n_seqs, zx->nb[1], zx->nb[2], zx->nb[3], 0);
-        cb(z, "mamba_z_split", il);
-
-        // conv1d
-        {
-            // => {d_conv - 1 + n_seq_tokens, d_inner, n_seqs}
-            ggml_tensor * conv_x = ggml_concat(ctx0, conv, ggml_transpose(ctx0, x), 0);
-            cb(conv_x, "mamba_conv1d_input", il);
-
-            // copy last (d_conv - 1) columns back into the state cache
-            ggml_tensor * last_conv = ggml_view_3d(ctx0, conv_x, d_conv - 1, d_inner, n_seqs,
-                    conv_x->nb[1], conv_x->nb[2], n_seq_tokens*(conv_x->nb[0]));
-
-            ggml_build_forward_expand(gf,
-                ggml_cpy(ctx0, last_conv,
-                    ggml_view_1d(ctx0, conv_states_all,
-                        (d_conv - 1)*(d_inner + 2*n_group*d_state)*(n_seqs),
-                        kv_head*(d_conv - 1)*(d_inner + 2*n_group*d_state)*ggml_element_size(conv_states_all))));
-            cb(conv_states_all, "mamba_conv1d_state", il);
-
-            // 1D convolution
-            x = ggml_ssm_conv(ctx0, conv_x, model.layers[il].ssm_conv1d);
-            cb(x, "mamba_conv1d", il);
-
-            x = ggml_silu(ctx0, x);
-            cb(x, "mamba_conv1d_silu", il);
-        }
-
-        // SSM
-        {
-            // bcdt_proj: {d_inner, dt_rank + 2*d_state} @ {d_inner, n_seq_tokens, n_seqs} => {dt_rank + 2*d_state, n_seq_tokens, n_seqs}
-            ggml_tensor * x_bcdt = build_lora_mm(model.layers[il].ssm_x, x);
-            cb(x_bcdt, "mamba_bcdt_proj", il);
-
-            // split into dt, B, C
-            const int64_t dt_dim = std::max(64, int(hparams.n_embd / 16));
-            ggml_tensor * B = ggml_view_3d(ctx0, x_bcdt, d_state, n_seq_tokens, n_seqs, x_bcdt->nb[1], x_bcdt->nb[2], 0);
-            ggml_tensor * C  = ggml_view_3d(ctx0, x_bcdt, d_state, n_seq_tokens, n_seqs, x_bcdt->nb[1], x_bcdt->nb[2], ggml_element_size(x_bcdt)*d_state);
-            ggml_tensor * dt  = ggml_view_3d(ctx0, x_bcdt, dt_dim, n_seq_tokens, n_seqs, x_bcdt->nb[1], x_bcdt->nb[2], ggml_element_size(x_bcdt)*(2*d_state));
-            cb(B, "mamba_B_raw", il);
-            cb(C, "mamba_C_raw", il);
-            cb(dt, "mamba_dt_raw", il);
-
-            // Apply RMS norm to dt, B, C (PLaMo-2 specific)
-            B = build_norm(B, model.layers[il].ssm_b_norm, NULL, LLM_NORM_RMS, il);
-            C = build_norm(C, model.layers[il].ssm_c_norm, NULL, LLM_NORM_RMS, il);
-            dt = build_norm(dt, model.layers[il].ssm_dt_norm, NULL, LLM_NORM_RMS, il);
-            cb(B, "mamba_B_normed", il);
-            cb(C, "mamba_C_normed", il);
-            cb(dt, "mamba_dt_normed", il);
-
-            // dt_proj: {dt_rank, d_inner} @ {dt_rank, n_seq_tokens, n_seqs} => {d_inner, n_seq_tokens, n_seqs}
-            dt = build_lora_mm(model.layers[il].ssm_dt, dt);
-            dt = ggml_add(ctx0, dt, model.layers[il].ssm_dt_b);
-            cb(dt, "mamba_dt_proj", il);
-
-            ggml_tensor * A = ggml_reshape_2d(ctx0, model.layers[il].ssm_a, 1, n_heads);
-            cb(A, "mamba_A", il);
-
-            x = ggml_view_4d(ctx0, x, head_dim, n_heads, n_seq_tokens, n_seqs, head_dim * ggml_element_size(x), head_dim * n_heads * ggml_element_size(x), head_dim * n_heads * n_seq_tokens * ggml_element_size(x), 0);
-            B = ggml_view_4d(ctx0, B, d_state, 1, n_seq_tokens, n_seqs, d_state * B->nb[0], B->nb[1], B->nb[2], 0);
-            C = ggml_view_4d(ctx0, C, d_state, 1, n_seq_tokens, n_seqs, d_state * C->nb[0], C->nb[1], C->nb[2], 0);
-
-            // use the states and the indices provided by build_recurrent_state
-            // (this is necessary in order to properly use the states before they are overwritten,
-            //  while avoiding to make unnecessary copies of the states)
-            auto get_ssm_rows = [&](ggml_context * ctx, ggml_tensor * states, ggml_tensor * ids) {
-                ggml_tensor * ssm = ggml_reshape_4d(ctx, states, d_state, head_dim, n_heads, mctx_cur->get_size());
-
-                // Custom operator to optimize the parallel associative scan
-                // as described in the Annex D of the Mamba paper.
-                // => {d_inner, n_seq_tokens, n_seqs} and {d_state, d_inner, n_seqs}
-                return ggml_ssm_scan(ctx, ssm, x, dt, A, B, C, ids);
-            };
-
-            ggml_tensor * y_ssm = build_rs(inp, ssm_states_all, hparams.n_embd_s(), ubatch.n_seqs, get_ssm_rows);
-            cb(y_ssm, "mamba_ssm_scan", il);
-
-            // store last states
-            ggml_build_forward_expand(gf,
-                ggml_cpy(ctx0,
-                    ggml_view_1d(ctx0, y_ssm, n_heads*head_dim*d_state*n_seqs, n_heads*head_dim*n_seq_tokens*n_seqs*ggml_element_size(y_ssm)),
-                    ggml_view_1d(ctx0, ssm_states_all, n_heads*head_dim*d_state*n_seqs, kv_head*n_seqs*n_heads*head_dim*d_state*ggml_element_size(ssm_states_all))));
-            cb(ssm_states_all, "mamba_ssm_states", il);
-
-            ggml_tensor * y = ggml_view_4d(ctx0, y_ssm, head_dim, n_heads, n_seq_tokens, n_seqs, head_dim * ggml_element_size(x), head_dim * n_heads * ggml_element_size(x), head_dim * n_heads * n_seq_tokens * ggml_element_size(x), 0);
-            cb(y, "mamba_y_view", il);
-
-            // Add D parameter and apply gating with z
-            // {d_inner, n_seq_tokens, n_seqs} * {d_inner} => {d_inner, n_seq_tokens, n_seqs}
-            ggml_tensor * D = ggml_reshape_2d(ctx0, model.layers[il].ssm_d, 1, n_heads);
-            y = ggml_add(ctx0, y, ggml_mul(ctx0, x, D));
-            cb(y, "mamba_y_add_d", il);
-
-            y = ggml_swiglu_split(ctx0, ggml_cont(ctx0, z), y);
-            cb(y, "mamba_y_swiglu_z", il);
-
-            // out_proj: {d_inner, n_embd} @ {d_inner, n_seq_tokens, n_seqs} => {n_embd, n_seq_tokens, n_seqs}
-            y = ggml_view_3d(ctx0, y, head_dim * n_heads, n_seq_tokens, n_seqs, y->nb[2], y->nb[3], 0);
-            cur = build_lora_mm(model.layers[il].ssm_out, y);
-            cb(cur, "mamba_out_proj", il);
-        }
-
-        // {n_embd, n_seq_tokens, n_seqs} => {n_embd, n_tokens}
-        cur = ggml_reshape_2d(ctx0, cur, cur->ne[0], n_seq_tokens * n_seqs);
-        cb(cur, "mamba_out", il);
-
-        return cur;
-    }
-};
-
-struct llm_build_arcee : public llm_graph_context {
-    llm_build_arcee(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        const float kq_scale = hparams.f_attention_scale == 0.0f ? 1.0f/sqrtf(float(n_embd_head)) : hparams.f_attention_scale;
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                // rope freq factors for llama3; may return nullptr for llama2 and other models
-                ggml_tensor * rope_factors = model.get_rope_factors(cparams, il);
-
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-                if (model.layers[il].bq) {
-                    Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
-                    cb(Qcur, "Qcur", il);
-                }
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-                if (model.layers[il].bk) {
-                    Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
-                    cb(Kcur, "Kcur", il);
-                }
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-                if (model.layers[il].bv) {
-                    Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
-                    cb(Vcur, "Vcur", il);
-                }
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, rope_factors,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, rope_factors,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, kq_scale, il);
-                cb(cur, "attn_out", il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed-forward network
-            // ARCEE uses relu^2 instead of silu
-            cur = build_norm(ffn_inp,
-                    model.layers[il].ffn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-
-            cur = build_ffn(cur,
-                    model.layers[il].ffn_up,   NULL, NULL,
-                    NULL,                      NULL, NULL,
-                    model.layers[il].ffn_down, NULL, NULL,
-                    NULL,
-                    LLM_FFN_RELU_SQR, LLM_FFN_SEQ, il);
-            cb(cur, "ffn_out", il);
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-            cb(cur, "ffn_out", il);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_hunyuan_moe : public llm_graph_context {
-    llm_build_hunyuan_moe(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        const float kq_scale = 1.0f / sqrtf(float(n_embd_head));
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                // rope freq factors for llama3; may return nullptr for llama2 and other models
-                ggml_tensor * rope_factors = model.get_rope_factors(cparams, il);
-
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-                if (model.layers[il].bq) {
-                    Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
-                    cb(Qcur, "Qcur", il);
-                }
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-                if (model.layers[il].bk) {
-                    Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
-                    cb(Kcur, "Kcur", il);
-                }
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-                if (model.layers[il].bv) {
-                    Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
-                    cb(Vcur, "Vcur", il);
-                }
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, rope_factors,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, rope_factors,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = build_norm(Kcur,
-                        model.layers[il].attn_k_norm, nullptr,
-                        LLM_NORM_RMS, il);
-                cb(Kcur, "Kcur_norm", il);
-
-                Qcur = build_norm(Qcur,
-                        model.layers[il].attn_q_norm, nullptr,
-                        LLM_NORM_RMS, il);
-                cb(Qcur, "Qcur_norm", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, kq_scale, il);
-                cb(cur, "attn_out", il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            cur = build_norm(ffn_inp,
-                model.layers[il].ffn_norm, NULL,
-                LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-
-            // feed-forward network (non-MoE)
-            ggml_tensor * cur_mlp = build_ffn(cur,
-                    model.layers[il].ffn_up_shexp,   NULL, NULL,
-                    model.layers[il].ffn_gate_shexp, NULL, NULL,
-                    model.layers[il].ffn_down_shexp, NULL, NULL,
-                    NULL,
-                    LLM_FFN_SILU, LLM_FFN_PAR, il);
-            cb(cur_mlp, "ffn_mlp", il);
-
-            // MoE branch
-            ggml_tensor * cur_moe = build_moe_ffn(cur,
-                    model.layers[il].ffn_gate_inp,
-                    model.layers[il].ffn_up_exps,
-                    model.layers[il].ffn_gate_exps,
-                    model.layers[il].ffn_down_exps,
-                    nullptr,
-                    n_expert, n_expert_used,
-                    LLM_FFN_SILU,
-                    true, // norm_topk_prob
-                    false,
-                    0.0,
-                    LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
-                    il);
-            cb(cur_moe, "ffn_moe_out", il);
-
-            ggml_tensor * ffn_out = ggml_add(ctx0, cur_moe, cur_mlp);
-            cb(ffn_out, "ffn_out", il);
-
-            cur = ggml_add(ctx0, ffn_out, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_hunyuan_dense : public llm_graph_context {
-    llm_build_hunyuan_dense(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        const float kq_scale = 1.0f / sqrtf(float(n_embd_head));
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-            // self-attention
-            {
-                // rope freq factors for llama3; may return nullptr for llama2 and other models
-                ggml_tensor * rope_factors = model.get_rope_factors(cparams, il);
-
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-                if (model.layers[il].bq) {
-                    Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
-                    cb(Qcur, "Qcur", il);
-                }
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-                if (model.layers[il].bk) {
-                    Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
-                    cb(Kcur, "Kcur", il);
-                }
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-                if (model.layers[il].bv) {
-                    Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
-                    cb(Vcur, "Vcur", il);
-                }
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = ggml_rope_ext(
-                         ctx0, Qcur, inp_pos, rope_factors,
-                         n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                         ext_factor, attn_factor, beta_fast, beta_slow
-                         );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                Kcur = ggml_rope_ext(
-                         ctx0, Kcur, inp_pos, rope_factors,
-                         n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                         ext_factor, attn_factor, beta_fast, beta_slow
-                         );
-
-                Kcur = build_norm(Kcur,
-                         model.layers[il].attn_k_norm, nullptr,
-                         LLM_NORM_RMS, il);
-                cb(Kcur, "Kcur_norm", il);
-
-                Qcur = build_norm(Qcur,
-                         model.layers[il].attn_q_norm, nullptr,
-                         LLM_NORM_RMS, il);
-                cb(Qcur, "Qcur_norm", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, kq_scale, il);
-                cb(cur, "attn_out", il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            cur = build_norm(ffn_inp,
-                    model.layers[il].ffn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-            // feed-forward network (non-MoE)
-            ggml_tensor * cur_mlp = build_ffn(cur,
-                        model.layers[il].ffn_up,   NULL, NULL,
-                        model.layers[il].ffn_gate, NULL, NULL,
-                        model.layers[il].ffn_down, NULL, NULL,
-                        NULL,
-                        LLM_FFN_SILU, LLM_FFN_PAR, il);
-            cb(cur_mlp, "ffn_out", il);
-
-            cur = ggml_add(ctx0, cur_mlp, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_smollm3 : public llm_graph_context {
-    llm_build_smollm3(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        const float kq_scale = hparams.f_attention_scale == 0.0f ? 1.0f/sqrtf(float(n_embd_head)) : hparams.f_attention_scale;
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            const bool use_rope = (il + 1) % hparams.n_no_rope_layer_step != 0;
-
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-                if (model.layers[il].bq) {
-                    Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
-                    cb(Qcur, "Qcur", il);
-                }
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-                if (model.layers[il].bk) {
-                    Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
-                    cb(Kcur, "Kcur", il);
-                }
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-                if (model.layers[il].bv) {
-                    Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
-                    cb(Vcur, "Vcur", il);
-                }
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                if (use_rope) {
-                    Qcur = ggml_rope_ext(
-                            ctx0, Qcur, inp_pos, nullptr,
-                            n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                            ext_factor, attn_factor, beta_fast, beta_slow
-                            );
-
-                    Kcur = ggml_rope_ext(
-                            ctx0, Kcur, inp_pos, nullptr,
-                            n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                            ext_factor, attn_factor, beta_fast, beta_slow
-                            );
-                }
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, kq_scale, il);
-                cb(cur, "attn_out", il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed-forward network
-            {
-                cur = build_norm(ffn_inp,
-                        model.layers[il].ffn_norm, NULL,
-                        LLM_NORM_RMS, il);
-                cb(cur, "ffn_norm", il);
-
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up,   model.layers[il].ffn_up_b,   NULL,
-                        model.layers[il].ffn_gate, model.layers[il].ffn_gate_b, NULL,
-                        model.layers[il].ffn_down, model.layers[il].ffn_down_b, NULL,
-                        NULL,
-                        LLM_FFN_SILU, LLM_FFN_PAR, il);
-                cb(cur, "ffn_out", il);
-            }
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-            cb(cur, "ffn_out", il);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_openai_moe_iswa : public llm_graph_context {
-    llm_build_openai_moe_iswa(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv_iswa();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, nullptr,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-                if (model.layers[il].bq) {
-                    Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
-                    cb(Qcur, "Qcur", il);
-                }
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-                if (model.layers[il].bk) {
-                    Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
-                    cb(Kcur, "Kcur", il);
-                }
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-                if (model.layers[il].bv) {
-                    Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
-                    cb(Vcur, "Vcur", il);
-                }
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_rot, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_rot, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_rot, n_head_kv, n_tokens);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, model.layers[il].attn_sinks, nullptr, 1.0f/sqrtf(float(n_rot)), il);
-
-                cb(cur, "attn_out", il);
-            }
-
-            if (il == n_layer - 1) {
-                // skip computing output for unused tokens
-                ggml_tensor * inp_out_ids = build_inp_out_ids();
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            cur = ffn_inp;
-            cur = build_norm(cur,
-                    model.layers[il].attn_post_norm, nullptr,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_post_norm", il);
-
-            // MoE branch
-            cur = build_moe_ffn(cur,
-                    model.layers[il].ffn_gate_inp,  model.layers[il].ffn_gate_inp_b,
-                    model.layers[il].ffn_up_exps,   model.layers[il].ffn_up_exps_b,
-                    model.layers[il].ffn_gate_exps, model.layers[il].ffn_gate_exps_b,
-                    model.layers[il].ffn_down_exps, model.layers[il].ffn_down_exps_b,
-                    nullptr,
-                    n_expert, n_expert_used,
-                    LLM_FFN_SWIGLU_OAI_MOE, false,
-                    false, 0.0,
-                    LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX_WEIGHT,
-                    il);
-            cb(cur, "ffn_moe_out", il);
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_lfm2 : public llm_graph_context {
-    const llama_model & model;
-
-    llm_build_lfm2(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params), model(model) {
-
-        ggml_tensor * cur = build_inp_embd(model.tok_embd);
-        cb(cur, "model.embed_tokens", -1);
-
-        ggml_tensor * inp_pos     = build_inp_pos();
-        auto        * inp_hybrid  = build_inp_mem_hybrid();
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            const bool is_moe_layer = il >= static_cast<int>(hparams.n_layer_dense_lead);
-
-            auto * prev_cur = cur;
-            cur = build_norm(cur, model.layers[il].attn_norm, NULL, LLM_NORM_RMS, il);
-            cb(cur, "model.layers.{}.operator_norm", il);
-
-            cur = hparams.is_recurrent(il) ?
-                build_shortconv_block(cur, inp_hybrid->get_recr(), il) :
-                build_attn_block(cur, inp_pos, inp_hybrid->get_attn(), il) ;
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur      = ggml_get_rows(ctx0,      cur, inp_out_ids);
-                prev_cur = ggml_get_rows(ctx0, prev_cur, inp_out_ids);
-            }
-
-            cur = ggml_add(ctx0, prev_cur, cur);
-
-            auto * ffn_norm_out = build_norm(cur, model.layers[il].ffn_norm, NULL, LLM_NORM_RMS, il);
-            cb(ffn_norm_out, "model.layers.{}.ffn_norm", il);
-
-            ggml_tensor * ffn_out = is_moe_layer ?
-                build_moe_feed_forward(ffn_norm_out, il) :
-                build_dense_feed_forward(ffn_norm_out, il);
-            cb(ffn_norm_out, "model.layers.{}.ffn_out", il);
-
-            cur = ggml_add(ctx0, cur, ffn_out);
-        }
-
-        cur = build_norm(cur, model.tok_norm, NULL, LLM_NORM_RMS, -1);
-        cb(cur, "model.embedding_norm", -1);
-        res->t_embd = cur;
-
-        cur = build_lora_mm(model.output, cur);
-        cb(cur, "lm_head", -1);
-
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-
-    ggml_tensor * build_moe_feed_forward(ggml_tensor * cur,
-                                         int           il) const {
-        return build_moe_ffn(cur,
-                    model.layers[il].ffn_gate_inp,
-                    model.layers[il].ffn_up_exps,
-                    model.layers[il].ffn_gate_exps,
-                    model.layers[il].ffn_down_exps,
-                    model.layers[il].ffn_exp_probs_b,
-                    n_expert, n_expert_used,
-                    LLM_FFN_SILU, true,
-                    false, 0.0,
-                    static_cast<llama_expert_gating_func_type>(hparams.expert_gating_func),
-                    il);
-    }
-
-    ggml_tensor * build_dense_feed_forward(ggml_tensor * cur,
-                                           int           il) const {
-        GGML_ASSERT(!model.layers[il].ffn_up_b);
-        GGML_ASSERT(!model.layers[il].ffn_gate_b);
-        GGML_ASSERT(!model.layers[il].ffn_down_b);
-        return build_ffn(cur,
-                model.layers[il].ffn_up,   NULL, NULL,
-                model.layers[il].ffn_gate, NULL, NULL,
-                model.layers[il].ffn_down, NULL, NULL,
-                NULL,
-                LLM_FFN_SILU, LLM_FFN_PAR, il);
-    }
-
-    ggml_tensor * build_attn_block(ggml_tensor             * cur,
-                                   ggml_tensor             * inp_pos,
-                                   llm_graph_input_attn_kv * inp_attn,
-                                   int                     il) const {
-        GGML_ASSERT(hparams.n_embd_v_gqa(il) == hparams.n_embd_k_gqa(il));
-        auto const n_embd_head = hparams.n_embd_head_v;
-        auto const n_head_kv = hparams.n_head_kv(il);
-
-        auto * q = build_lora_mm(model.layers[il].wq, cur);
-        cb(q, "model.layers.{}.self_attn.q_proj", il);
-        auto * k = build_lora_mm(model.layers[il].wk, cur);
-        cb(k, "model.layers.{}.self_attn.k_proj", il);
-        auto * v = build_lora_mm(model.layers[il].wv, cur);
-        cb(v, "model.layers.{}.self_attn.v_proj", il);
-
-        q = ggml_reshape_3d(ctx0, q, n_embd_head, n_head,    n_tokens);
-        k = ggml_reshape_3d(ctx0, k, n_embd_head, n_head_kv, n_tokens);
-        v = ggml_reshape_3d(ctx0, v, n_embd_head, n_head_kv, n_tokens);
-
-        // qk norm
-        q = build_norm(q, model.layers[il].attn_q_norm, NULL, LLM_NORM_RMS, il);
-        cb(q, "model.layers.{}.self_attn.q_layernorm", il);
-        k = build_norm(k, model.layers[il].attn_k_norm, NULL, LLM_NORM_RMS, il);
-        cb(k, "model.layers.{}.self_attn.k_layernorm", il);
-
-        // RoPE
-        q = ggml_rope_ext(
-                ctx0, q, inp_pos, nullptr,
-                n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                ext_factor, attn_factor, beta_fast, beta_slow
-                );
-        k = ggml_rope_ext(
-                ctx0, k, inp_pos, nullptr,
-                n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                ext_factor, attn_factor, beta_fast, beta_slow
-                );
-
-        cur = build_attn(inp_attn, model.layers[il].wo, NULL,
-                q, k, v, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-
-        cb(cur, "model.layers.{}.self_attn.out_proj", il);
-
-        return cur;
-    }
-
-    ggml_tensor * build_shortconv_block(ggml_tensor        * cur,
-                                        llm_graph_input_rs * inp_recr,
-                                        int                il) {
-        const auto *   mctx_cur     = static_cast<const llama_memory_hybrid_context *>(mctx)->get_recr();
-        const uint32_t kv_head      = mctx_cur->get_head();
-        const int64_t  n_seq_tokens = ubatch.n_seq_tokens;
-        const int64_t  n_seqs       = ubatch.n_seqs;
-        GGML_ASSERT(n_seqs != 0);
-        GGML_ASSERT(ubatch.equal_seqs());
-        GGML_ASSERT(ubatch.n_tokens == n_seq_tokens * n_seqs);
-
-        GGML_ASSERT(hparams.n_shortconv_l_cache > 1);
-        const uint32_t d_conv = hparams.n_shortconv_l_cache - 1;
-
-        // {n_embd, n_tokens} => {n_embd, n_seq_tokens, n_seqs}
-        cur = ggml_reshape_3d(ctx0, cur, cur->ne[0], n_seq_tokens, n_seqs);
-
-        auto * bcx = build_lora_mm(model.layers[il].shortconv.in_proj, cur);
-        cb(bcx, "model.layers.{}.conv.in_proj", il);
-
-        constexpr auto n_chunks = 3;
-        GGML_ASSERT(bcx->ne[0] % n_chunks == 0);
-        auto const chunk_size = bcx->ne[0] / n_chunks;
-        auto * b = ggml_view_3d(ctx0, bcx, chunk_size, bcx->ne[1], bcx->ne[2], bcx->nb[1], bcx->nb[2], 0*chunk_size*ggml_element_size(bcx));
-        auto * c = ggml_view_3d(ctx0, bcx, chunk_size, bcx->ne[1], bcx->ne[2], bcx->nb[1], bcx->nb[2], 1*chunk_size*ggml_element_size(bcx));
-        auto * x = ggml_view_3d(ctx0, bcx, chunk_size, bcx->ne[1], bcx->ne[2], bcx->nb[1], bcx->nb[2], 2*chunk_size*ggml_element_size(bcx));
-
-        auto * bx = ggml_transpose(ctx0, ggml_mul(ctx0, b, x));
-
-        // read conv state
-        auto * conv_state = mctx_cur->get_r_l(il);
-        auto * conv_rs    = build_rs(inp_recr, conv_state, hparams.n_embd_r(), n_seqs);
-        auto * conv       = ggml_reshape_3d(ctx0, conv_rs, d_conv, hparams.n_embd, n_seqs);
-
-        bx = ggml_concat(ctx0, conv, bx, 0);
-        GGML_ASSERT(bx->ne[0] > conv->ne[0]);
-
-        // last d_conv columns is a new conv state
-        auto * new_conv = ggml_view_3d(ctx0, bx, conv->ne[0], bx->ne[1], bx->ne[2], bx->nb[1], bx->nb[2], (bx->ne[0] - conv->ne[0])*ggml_element_size(bx));
-        GGML_ASSERT(ggml_are_same_shape(conv, new_conv));
-
-        // write new conv conv state
-        ggml_build_forward_expand(
-                gf,
-                ggml_cpy(
-                    ctx0,
-                    new_conv,
-                    ggml_view_1d(
-                        ctx0,
-                        conv_state,
-                        ggml_nelements(new_conv),
-                        kv_head*d_conv*n_embd*ggml_element_size(new_conv)
-                        )
-                    )
-                );
-
-        auto * conv_kernel = model.layers[il].shortconv.conv;
-        auto * conv_out = ggml_ssm_conv(ctx0, bx, conv_kernel);
-        cb(conv_out, "model.layers.{}.conv.conv", il);
-
-        auto * y = ggml_mul(ctx0, c, conv_out);
-        y = build_lora_mm(model.layers[il].shortconv.out_proj, y);
-        cb(y, "model.layers.{}.conv.out_proj", il);
-        // {n_embd, n_seq_tokens, n_seqs} => {n_embd, n_tokens}
-        y = ggml_reshape_2d(ctx0, y, y->ne[0], n_seq_tokens * n_seqs);
-
-        return y;
-    }
-};
-
-struct llm_build_seed_oss : public llm_graph_context {
-    llm_build_seed_oss(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        const float kq_scale = hparams.f_attention_scale == 0.0f ? 1.0f/sqrtf(float(n_embd_head)) : hparams.f_attention_scale;
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-                if (model.layers[il].bq) {
-                    Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
-                    cb(Qcur, "Qcur", il);
-                }
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-                if (model.layers[il].bk) {
-                    Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
-                    cb(Kcur, "Kcur", il);
-                }
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-                if (model.layers[il].bv) {
-                    Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
-                    cb(Vcur, "Vcur", il);
-                }
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, kq_scale, il);
-                cb(cur, "attn_out", il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed-forward network
-            cur = build_norm(ffn_inp,
-                    model.layers[il].attn_post_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_post_norm", il);
-
-            cur = build_ffn(cur,
-                    model.layers[il].ffn_up,   NULL, NULL,
-                    model.layers[il].ffn_gate, NULL, NULL,
-                    model.layers[il].ffn_down, NULL, NULL,
-                    NULL,
-                    LLM_FFN_SILU, LLM_FFN_PAR, il);
-            cb(cur, "ffn_out", il);
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-            cb(cur, "ffn_out", il);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-template <bool iswa>
-struct llm_build_smallthinker : public llm_graph_context{
-    llm_build_smallthinker(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params){
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        using inp_attn_type = std::conditional_t<iswa, llm_graph_input_attn_kv_iswa, llm_graph_input_attn_kv>;
-        inp_attn_type * inp_attn = nullptr;
-
-        if constexpr (iswa) {
-            inp_attn = build_attn_inp_kv_iswa();
-        } else {
-            inp_attn = build_attn_inp_kv();
-        }
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA  = inpL;
-            ggml_tensor * probs  = nullptr;
-
-            probs = build_lora_mm(model.layers[il].ffn_gate_inp, inpL);  // [n_expert, n_tokens]
-            cb(probs, "ffn_moe_logits", il);
-
-            // norm
-            cur = build_norm(inpL,model.layers[il].attn_norm, NULL, LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self_attention
-            {
-                // compute Q and K and RoPE them
-                struct ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-
-                struct ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-
-                struct ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head, n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                if (hparams.n_no_rope_layer_step == n_layer || il % hparams.n_no_rope_layer_step != 0) {
-                    Qcur = ggml_rope_ext(ctx0, Qcur, inp_pos, nullptr, n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                                     ext_factor, attn_factor, beta_fast, beta_slow);
-
-                    Kcur = ggml_rope_ext(ctx0, Kcur, inp_pos, nullptr, n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                                     ext_factor, attn_factor, beta_fast, beta_slow);
-                }
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f / sqrtf(float(n_embd_head)), il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur = ggml_get_rows(ctx0, cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-                probs = ggml_get_rows(ctx0, probs, inp_out_ids);
-            }
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // MoE branch
-            cur = build_norm(ffn_inp, model.layers[il].ffn_norm, NULL, LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-
-            ggml_tensor * ffn_out =
-                build_moe_ffn(cur,
-                        nullptr,
-                        model.layers[il].ffn_up_exps,
-                        model.layers[il].ffn_gate_exps,
-                        model.layers[il].ffn_down_exps,
-                        nullptr,
-                        n_expert, n_expert_used,
-                        LLM_FFN_RELU, true,
-                        false, 0.0,
-                        static_cast<llama_expert_gating_func_type>(hparams.expert_gating_func),
-                        il, probs);
-
-            cb(ffn_out, "ffn_out", il);
-            cur = ffn_out;
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur, model.output_norm, NULL, LLM_NORM_RMS, -1);
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_grovemoe : public llm_graph_context {
-    llm_build_grovemoe(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-        const int64_t n_chunk_expert = n_expert / hparams.n_group_experts;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self_attention
-            {
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL, LLM_NORM_RMS, il);
-                cb(Qcur, "Qcur_normed", il);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, NULL, LLM_NORM_RMS, il);
-                cb(Kcur, "Kcur_normed", il);
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // MoE branch
-            cur = build_norm(ffn_inp,
-                    model.layers[il].ffn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-
-            ggml_tensor * probs = build_lora_mm(model.layers[il].ffn_gate_inp, cur); // [n_expert, n_tokens]
-            cb(probs, "ffn_moe_logits", il);
-
-            ggml_tensor * moe_out =
-                build_moe_ffn(cur,
-                        nullptr,
-                        model.layers[il].ffn_up_exps,
-                        model.layers[il].ffn_gate_exps,
-                        model.layers[il].ffn_down_exps,
-                        nullptr,
-                        n_expert, n_expert_used,
-                        LLM_FFN_SILU, true,
-                        false, 0.0,
-                        LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
-                        il, probs);
-            cb(moe_out, "ffn_moe_out", il);
-            cur = moe_out;
-
-            // TODO: Only do the expert selection and weights once
-            moe_out =
-                build_moe_ffn(cur,
-                        nullptr,
-                        model.layers[il].ffn_up_chexps,
-                        model.layers[il].ffn_gate_chexps,
-                        model.layers[il].ffn_down_chexps,
-                        nullptr,
-                        n_chunk_expert, n_expert_used > n_chunk_expert ? n_chunk_expert : n_expert_used,
-                        LLM_FFN_SILU, true,
-                        false, 0.0,
-                        LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
-                        il, probs);
-            cb(moe_out, "ffn_adj_moe_out", il);
-
-            cur = ggml_add(ctx0, cur, ggml_scale(ctx0, moe_out, hparams.expert_group_scale));
-            cb(cur, "ffn_final_moe_out", il);
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_apertus : public llm_graph_context {
-    llm_build_apertus(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        ggml_tensor * inp_pos = build_inp_pos();
-        auto * inp_attn = build_attn_inp_kv();
-
-        const float kq_scale = hparams.f_attention_scale == 0.0f ? 1.0f / sqrtf(float(n_embd_head)) : hparams.f_attention_scale;
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, nullptr,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                ggml_tensor * rope_factors = model.get_rope_factors(cparams, il);
-
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL, LLM_NORM_RMS, il);
-                cb(Qcur, "Qcur_normed", il);
-
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, NULL, LLM_NORM_RMS, il);
-                cb(Kcur, "Kcur_normed", il);
-
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, rope_factors,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, rope_factors,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur_pos", il);
-                cb(Kcur, "Kcur_pos", il);
-                cb(Vcur, "Vcur_pos", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, kq_scale, il);
-                cb(cur, "attn_out", il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed-forward network with xIELU activation
-            {
-                cur = build_norm(ffn_inp,
-                        model.layers[il].ffn_norm, nullptr,
-                        LLM_NORM_RMS, il);
-                cb(cur, "ffn_norm", il);
-
-                // Up projection
-                ggml_tensor * up = build_lora_mm(model.layers[il].ffn_up, cur);
-                cb(up, "ffn_up", il);
-
-                float alpha_n_val = hparams.xielu_alpha_n[il];
-                float alpha_p_val = hparams.xielu_alpha_p[il];
-                float beta_val = hparams.xielu_beta[il];
-                float eps_val = hparams.xielu_eps[il];
-
-                // Apply xIELU activation
-                ggml_tensor * activated = ggml_xielu(ctx0, up, alpha_n_val, alpha_p_val, beta_val, eps_val);
-                cb(activated, "ffn_xielu", il);
-
-                // Down projection
-                cur = build_lora_mm(model.layers[il].ffn_down, activated);
-                cb(cur, "ffn_down", il);
-            }
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-            cb(cur, "ffn_out", il);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, nullptr,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_minimax_m2 : public llm_graph_context {
-    llm_build_minimax_m2(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        // GGML_ASSERT(n_embd_head == hparams.n_rot); this is wrong in case of minimax, head_dim = 128, n_rot = 64
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        ggml_tensor * inp_pos = build_inp_pos();
-        auto inp_attn = build_attn_inp_kv();
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            cur = inpL;
-
-            // self_attention
-            {
-                cur = build_norm(inpL, model.layers[il].attn_norm, NULL, LLM_NORM_RMS, il);
-                cb(cur, "attn_norm", il);
-
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-
-                Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL,
-                        LLM_NORM_RMS, il);
-                cb(Qcur, "Qcur_normed", il);
-
-                Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, NULL,
-                        LLM_NORM_RMS, il);
-                cb(Kcur, "Kcur_normed", il);
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = ggml_rope_ext(
-                    ctx0, Qcur, inp_pos, nullptr,
-                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                    ext_factor, attn_factor, beta_fast, beta_slow
-                    );
-
-                Kcur = ggml_rope_ext(
-                    ctx0, Kcur, inp_pos, nullptr,
-                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                    ext_factor, attn_factor, beta_fast, beta_slow
-                    );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, NULL,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // MoE branch
-            cur = build_norm(ffn_inp,
-                    model.layers[il].ffn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-
-            cur = build_moe_ffn(cur,
-                    model.layers[il].ffn_gate_inp,
-                    model.layers[il].ffn_up_exps,
-                    model.layers[il].ffn_gate_exps,
-                    model.layers[il].ffn_down_exps,
-                    model.layers[il].ffn_exp_probs_b,
-                    n_expert, n_expert_used,
-                    LLM_FFN_SILU, true,
-                    false, 0.0,
-                    (llama_expert_gating_func_type) hparams.expert_gating_func,
-                    il);
-            cb(cur, "ffn_moe_out", il);
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
-    }
-};
-
-struct llm_build_cogvlm : public llm_graph_context {
-    llm_build_cogvlm(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-        float kq_scale = 1.0f / sqrtf(float(n_embd_head));
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
-
-        ggml_tensor * inpL, * cur;
-        inpL = build_inp_embd(model.tok_embd);
-
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        // check ubatch to see if we have input tokens (text)
-        // or an input embedding vector (image)
-        bool is_text;
-        if (ubatch.token) {
-            is_text = true;
-        } else {
-            is_text = false;
-        }
-
-        for (int il = 0; il < n_layer; ++il) {
-            // get either the text or image weight tensors
-            ggml_tensor * wqkv, * wo;
-            ggml_tensor * ffn_gate, * ffn_down, * ffn_up;
-
-            if (is_text) {
-                wqkv = model.layers[il].wqkv;
-                wo = model.layers[il].wo;
-                ffn_gate = model.layers[il].ffn_gate;
-                ffn_down = model.layers[il].ffn_down;
-                ffn_up = model.layers[il].ffn_up;
-            } else {
-                wqkv = model.layers[il].visexp_attn_wqkv;
-                wo = model.layers[il].visexp_attn_wo;
-                ffn_gate = model.layers[il].visexp_ffn_gate;
-                ffn_down = model.layers[il].visexp_ffn_down;
-                ffn_up = model.layers[il].visexp_ffn_up;
-            }
-
-            ggml_tensor * inpSA = inpL;
-            cur = build_norm(inpSA, model.layers[il].attn_norm, NULL, LLM_NORM_RMS, il);
-
-            // build self attention
-            {
-                ggml_tensor * qkv = build_lora_mm(wqkv, cur);
-
-                // split qkv into Q, K, V along the first dimension
-                ggml_tensor * Qcur = ggml_view_3d(ctx0, qkv, n_embd_head, n_head, n_tokens, n_embd_head * sizeof(float),
-                    qkv->nb[1], 0);
-                ggml_tensor * Kcur = ggml_view_3d(ctx0, qkv, n_embd_head, n_head_kv, n_tokens, n_embd_head * sizeof(float),
-                    qkv->nb[1], n_embd * ggml_element_size(qkv));
-                ggml_tensor * Vcur = ggml_view_3d(ctx0, qkv, n_embd_head, n_head_kv, n_tokens, n_embd_head * sizeof(float),
-                    qkv->nb[1], 2 * n_embd * ggml_element_size(qkv));
-
-                Qcur = ggml_rope(ctx0, Qcur, inp_pos, n_embd_head, rope_type);
-                Kcur = ggml_rope(ctx0, Kcur, inp_pos, n_embd_head, rope_type);
-
-                cur = build_attn(inp_attn, wo, nullptr, Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, kq_scale, il);
-                cb(cur, "attn_out", il);
-            }
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            cur = build_norm(ffn_inp, model.layers[il].ffn_norm, NULL, LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-
-            cur = build_ffn(cur,
-                    ffn_up,   NULL, NULL,
-                    ffn_gate, NULL, NULL,
-                    ffn_down, NULL, NULL,
-                    NULL,
-                    LLM_FFN_SILU, LLM_FFN_PAR, il);
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-            cb(cur, "ffn_out", il);
-
-            inpL = cur;
-        }
-
-        cur = inpL;
-
-        cur = build_norm(cur, model.output_norm, NULL, LLM_NORM_RMS, -1);
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        cur = build_lora_mm(model.output, cur);
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-        ggml_build_forward_expand(gf, cur);
-
-    }
-};
-
 llama_memory_i * llama_model::create_memory(const llama_memory_params & params, const llama_cparams & cparams) const {
     llama_memory_i * res;
 
diff --git a/src/models/apertus.cpp b/src/models/apertus.cpp
new file mode 100644
index 00000000000..9af19c1bfe8
--- /dev/null
+++ b/src/models/apertus.cpp
@@ -0,0 +1,125 @@
+#include "models.h"
+
+
+
+llm_build_apertus::llm_build_apertus(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+    const int64_t n_embd_head = hparams.n_embd_head_v;
+
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+    GGML_ASSERT(n_embd_head == hparams.n_rot);
+
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+
+    inpL = build_inp_embd(model.tok_embd);
+
+    ggml_tensor * inp_pos  = build_inp_pos();
+    auto *        inp_attn = build_attn_inp_kv();
+
+    const float kq_scale =
+        hparams.f_attention_scale == 0.0f ? 1.0f / sqrtf(float(n_embd_head)) : hparams.f_attention_scale;
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * inpSA = inpL;
+
+        cur = build_norm(inpL, model.layers[il].attn_norm, nullptr, LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
+
+        // self-attention
+        {
+            ggml_tensor * rope_factors = model.get_rope_factors(cparams, il);
+
+            // compute Q and K and RoPE them
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            cb(Qcur, "Qcur", il);
+
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            cb(Kcur, "Kcur", il);
+
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            cb(Vcur, "Vcur", il);
+
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head, n_tokens);
+            Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL, LLM_NORM_RMS, il);
+            cb(Qcur, "Qcur_normed", il);
+
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, NULL, LLM_NORM_RMS, il);
+            cb(Kcur, "Kcur_normed", il);
+
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+            Qcur = ggml_rope_ext(ctx0, Qcur, inp_pos, rope_factors, n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                                 ext_factor, attn_factor, beta_fast, beta_slow);
+
+            Kcur = ggml_rope_ext(ctx0, Kcur, inp_pos, rope_factors, n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                                 ext_factor, attn_factor, beta_fast, beta_slow);
+
+            cb(Qcur, "Qcur_pos", il);
+            cb(Kcur, "Kcur_pos", il);
+            cb(Vcur, "Vcur_pos", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, model.layers[il].bo,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, kq_scale, il);
+            cb(cur, "attn_out", il);
+        }
+
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0, cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+        }
+
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+        cb(ffn_inp, "ffn_inp", il);
+
+        // feed-forward network with xIELU activation
+        {
+            cur = build_norm(ffn_inp, model.layers[il].ffn_norm, nullptr, LLM_NORM_RMS, il);
+            cb(cur, "ffn_norm", il);
+
+            // Up projection
+            ggml_tensor * up = build_lora_mm(model.layers[il].ffn_up, cur);
+            cb(up, "ffn_up", il);
+
+            float alpha_n_val = hparams.xielu_alpha_n[il];
+            float alpha_p_val = hparams.xielu_alpha_p[il];
+            float beta_val    = hparams.xielu_beta[il];
+            float eps_val     = hparams.xielu_eps[il];
+
+            // Apply xIELU activation
+            ggml_tensor * activated = ggml_xielu(ctx0, up, alpha_n_val, alpha_p_val, beta_val, eps_val);
+            cb(activated, "ffn_xielu", il);
+
+            // Down projection
+            cur = build_lora_mm(model.layers[il].ffn_down, activated);
+            cb(cur, "ffn_down", il);
+        }
+
+        cur = ggml_add(ctx0, cur, ffn_inp);
+        cb(cur, "ffn_out", il);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+
+    cur = inpL;
+
+    cur = build_norm(cur, model.output_norm, nullptr, LLM_NORM_RMS, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
+
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/arcee.cpp b/src/models/arcee.cpp
new file mode 100644
index 00000000000..aa6167dba1e
--- /dev/null
+++ b/src/models/arcee.cpp
@@ -0,0 +1,135 @@
+#include "models.h"
+
+
+llm_build_arcee::llm_build_arcee(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+    const int64_t n_embd_head = hparams.n_embd_head_v;
+
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+    GGML_ASSERT(n_embd_head == hparams.n_rot);
+
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+
+    inpL = build_inp_embd(model.tok_embd);
+
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
+
+    auto * inp_attn = build_attn_inp_kv();
+
+    const float kq_scale = hparams.f_attention_scale == 0.0f ? 1.0f/sqrtf(float(n_embd_head)) : hparams.f_attention_scale;
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * inpSA = inpL;
+
+        // norm
+        cur = build_norm(inpL,
+                model.layers[il].attn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
+
+        // self-attention
+        {
+            // rope freq factors for llama3; may return nullptr for llama2 and other models
+            ggml_tensor * rope_factors = model.get_rope_factors(cparams, il);
+
+            // compute Q and K and RoPE them
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            cb(Qcur, "Qcur", il);
+            if (model.layers[il].bq) {
+                Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
+                cb(Qcur, "Qcur", il);
+            }
+
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            cb(Kcur, "Kcur", il);
+            if (model.layers[il].bk) {
+                Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
+                cb(Kcur, "Kcur", il);
+            }
+
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            cb(Vcur, "Vcur", il);
+            if (model.layers[il].bv) {
+                Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
+                cb(Vcur, "Vcur", il);
+            }
+
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+            Qcur = ggml_rope_ext(
+                    ctx0, Qcur, inp_pos, rope_factors,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            Kcur = ggml_rope_ext(
+                    ctx0, Kcur, inp_pos, rope_factors,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, model.layers[il].bo,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, kq_scale, il);
+            cb(cur, "attn_out", il);
+        }
+
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+        }
+
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+        cb(ffn_inp, "ffn_inp", il);
+
+        // feed-forward network
+        // ARCEE uses relu^2 instead of silu
+        cur = build_norm(ffn_inp,
+                model.layers[il].ffn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "ffn_norm", il);
+
+        cur = build_ffn(cur,
+                model.layers[il].ffn_up,   NULL, NULL,
+                NULL,                      NULL, NULL,
+                model.layers[il].ffn_down, NULL, NULL,
+                NULL,
+                LLM_FFN_RELU_SQR, LLM_FFN_SEQ, il);
+        cb(cur, "ffn_out", il);
+
+        cur = ggml_add(ctx0, cur, ffn_inp);
+        cb(cur, "ffn_out", il);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+
+    cur = inpL;
+
+    cur = build_norm(cur,
+            model.output_norm, NULL,
+            LLM_NORM_RMS, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
+
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/arctic.cpp b/src/models/arctic.cpp
new file mode 100644
index 00000000000..e8f028a723e
--- /dev/null
+++ b/src/models/arctic.cpp
@@ -0,0 +1,138 @@
+#include "models.h"
+
+
+llm_build_arctic::llm_build_arctic(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+    const int64_t n_embd_head = hparams.n_embd_head_v;
+
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+    GGML_ASSERT(n_embd_head == hparams.n_rot);
+
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+
+    inpL = build_inp_embd(model.tok_embd);
+
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
+
+    auto * inp_attn = build_attn_inp_kv();
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * inpSA = inpL;
+
+        // norm
+        cur = build_norm(inpL,
+                model.layers[il].attn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
+
+        // self-attention
+        {
+            // compute Q and K and RoPE them
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            cb(Qcur, "Qcur", il);
+
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            cb(Kcur, "Kcur", il);
+
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            cb(Vcur, "Vcur", il);
+
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+            Qcur = ggml_rope_ext(
+                    ctx0, Qcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            Kcur = ggml_rope_ext(
+                    ctx0, Kcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, NULL,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+        }
+
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+        }
+
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+        cb(ffn_inp, "ffn_inp", il);
+
+        // feed-forward network
+        cur = build_norm(ffn_inp,
+                model.layers[il].ffn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "ffn_norm", il);
+
+        cur = build_ffn(cur,
+                model.layers[il].ffn_up,   NULL, NULL,
+                model.layers[il].ffn_gate, NULL, NULL,
+                model.layers[il].ffn_down, NULL, NULL,
+                NULL,
+                LLM_FFN_SILU, LLM_FFN_PAR, il);
+        cb(cur, "ffn_out", il);
+
+        ggml_tensor * ffn_out = ggml_add(ctx0, cur, ffn_inp);
+        cb(ffn_out, "ffn_out", il);
+
+        // MoE
+        cur = build_norm(inpSA,
+                model.layers[il].ffn_norm_exps, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "ffn_norm_exps", il);
+
+        cur = build_moe_ffn(cur,
+                model.layers[il].ffn_gate_inp,
+                model.layers[il].ffn_up_exps,
+                model.layers[il].ffn_gate_exps,
+                model.layers[il].ffn_down_exps,
+                nullptr,
+                n_expert, n_expert_used,
+                LLM_FFN_SILU, true,
+                false, 0.0,
+                LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
+                il);
+        cb(cur, "ffn_moe_out", il);
+
+        cur = ggml_add(ctx0, cur, ffn_out);
+        cb(cur, "ffn_out", il);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+
+    cur = inpL;
+
+    cur = build_norm(cur,
+            model.output_norm, NULL,
+            LLM_NORM_RMS, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
+
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/arwkv7.cpp b/src/models/arwkv7.cpp
new file mode 100644
index 00000000000..107a3bef8da
--- /dev/null
+++ b/src/models/arwkv7.cpp
@@ -0,0 +1,86 @@
+#include "models.h"
+
+
+llm_build_arwkv7::llm_build_arwkv7(const llama_model & model, const llm_graph_params & params) : llm_build_rwkv7_base(model, params) {
+    GGML_ASSERT(n_embd == hparams.n_embd_r());
+
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+    ggml_tensor * v_first = nullptr;
+
+    inpL = build_inp_embd(model.tok_embd);
+
+    auto * rs_inp = build_rs_inp();
+
+    const auto n_embd = hparams.n_embd;
+    const auto n_seq_tokens = ubatch.n_seq_tokens;
+    const auto n_seqs = ubatch.n_seqs;
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        const llama_layer * layer = &model.layers[il];
+        inpL = ggml_reshape_3d(ctx0, inpL, n_embd, n_seq_tokens, n_seqs);
+
+        ggml_tensor * token_shift = build_rwkv_token_shift_load(rs_inp, ubatch, il);
+
+        ggml_tensor * att_norm = build_norm(inpL, layer->attn_norm, layer->attn_norm_b, LLM_NORM_RMS, il);
+        cb(att_norm, "attn_norm", il);
+
+        ggml_tensor * x_prev = ggml_concat(
+                ctx0,
+                token_shift,
+                ggml_view_3d(ctx0, att_norm, n_embd, n_seq_tokens - 1, n_seqs, att_norm->nb[1], att_norm->nb[2], 0),
+                1
+                );
+
+        cur = build_rwkv7_time_mix(rs_inp, att_norm, x_prev, v_first, ubatch, il);
+
+        token_shift = ggml_view_3d(ctx0, att_norm, n_embd, 1, n_seqs, att_norm->nb[1], att_norm->nb[2], (n_seq_tokens-1)*n_embd*ggml_element_size(att_norm));
+        ggml_build_forward_expand(gf, build_rwkv_token_shift_store(token_shift, ubatch, il));
+
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpL);
+        cb(ffn_inp, "ffn_inp", il);
+
+        cur     = ggml_reshape_2d(ctx0, cur,     n_embd, n_tokens);
+        ffn_inp = ggml_reshape_2d(ctx0, ffn_inp, n_embd, n_tokens);
+
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur     = ggml_get_rows(ctx0, cur,     inp_out_ids);
+            ffn_inp = ggml_get_rows(ctx0, ffn_inp, inp_out_ids);
+        }
+        // feed-forward network
+        cur = build_norm(ffn_inp,
+                model.layers[il].ffn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "ffn_norm", il);
+
+        cur = build_ffn(cur,
+                model.layers[il].ffn_up,   NULL, NULL,
+                model.layers[il].ffn_gate, NULL, NULL,
+                model.layers[il].ffn_down, NULL, NULL,
+                NULL,
+                LLM_FFN_SILU, LLM_FFN_PAR, il);
+        cb(cur, "ffn_out", il);
+
+        cur = ggml_add(ctx0, cur, ffn_inp);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+    cur = inpL;
+    cur = build_norm(cur, model.output_norm, model.output_norm_b, LLM_NORM_RMS, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    cur = build_lora_mm(model.output, cur);
+
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/baichuan.cpp b/src/models/baichuan.cpp
new file mode 100644
index 00000000000..c04b0c98b0b
--- /dev/null
+++ b/src/models/baichuan.cpp
@@ -0,0 +1,122 @@
+#include "models.h"
+
+
+llm_build_baichuan::llm_build_baichuan(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+    const int64_t n_embd_head = hparams.n_embd_head_v;
+
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+    GGML_ASSERT(n_embd_head == hparams.n_rot);
+
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+
+    inpL = build_inp_embd(model.tok_embd);
+
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = model.type == LLM_TYPE_7B ? build_inp_pos() : nullptr;
+
+    auto * inp_attn = build_attn_inp_kv();
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * inpSA = inpL;
+
+        cur = build_norm(inpL,
+                model.layers[il].attn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
+
+        // self-attention
+        {
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            cb(Qcur, "Qcur", il);
+
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            cb(Kcur, "Kcur", il);
+
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            cb(Vcur, "Vcur", il);
+
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+            switch (model.type) {
+                case LLM_TYPE_7B:
+                    Qcur = ggml_rope_ext(
+                            ctx0, Qcur, inp_pos, nullptr,
+                            n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                            ext_factor, attn_factor, beta_fast, beta_slow
+                            );
+                    Kcur = ggml_rope_ext(
+                            ctx0, Kcur, inp_pos, nullptr,
+                            n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                            ext_factor, attn_factor, beta_fast, beta_slow
+                            );
+                    break;
+                case LLM_TYPE_13B:
+                    break;
+                default:
+                    GGML_ABORT("fatal error");
+            }
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, NULL,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+        }
+
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+        }
+
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+        cb(ffn_inp, "ffn_inp", il);
+
+        // feed-forward network
+        {
+            cur = build_norm(ffn_inp,
+                    model.layers[il].ffn_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "ffn_norm", il);
+
+            cur = build_ffn(cur,
+                    model.layers[il].ffn_up,   NULL, NULL,
+                    model.layers[il].ffn_gate, NULL, NULL,
+                    model.layers[il].ffn_down, NULL, NULL,
+                    NULL,
+                    LLM_FFN_SILU, LLM_FFN_PAR, il);
+            cb(cur, "ffn_out", il);
+        }
+
+        cur = ggml_add(ctx0, cur, ffn_inp);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+
+    cur = inpL;
+
+    cur = build_norm(cur,
+            model.output_norm, NULL,
+            LLM_NORM_RMS, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
+
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/bailingmoe.cpp b/src/models/bailingmoe.cpp
new file mode 100644
index 00000000000..ed56b9c4713
--- /dev/null
+++ b/src/models/bailingmoe.cpp
@@ -0,0 +1,144 @@
+#include "models.h"
+
+
+llm_build_bailingmoe::llm_build_bailingmoe(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+
+    inpL = build_inp_embd(model.tok_embd);
+
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
+
+    auto * inp_attn = build_attn_inp_kv();
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * inpSA = inpL;
+
+        // norm
+        cur = build_norm(inpL,
+                model.layers[il].attn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
+
+        // self-attention
+        {
+            // rope freq factors for llama3; may return nullptr for llama2 and other models
+            ggml_tensor * rope_factors = model.get_rope_factors(cparams, il);
+
+            // compute Q and K and RoPE them
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            cb(Qcur, "Qcur", il);
+            if (model.layers[il].bq) {
+                Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
+                cb(Qcur, "Qcur", il);
+            }
+
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            cb(Kcur, "Kcur", il);
+            if (model.layers[il].bk) {
+                Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
+                cb(Kcur, "Kcur", il);
+            }
+
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            cb(Vcur, "Vcur", il);
+            if (model.layers[il].bv) {
+                Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
+                cb(Vcur, "Vcur", il);
+            }
+
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_rot, n_head,    n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_rot, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_rot, n_head_kv, n_tokens);
+
+            Qcur = ggml_rope_ext(
+                    ctx0, Qcur, inp_pos, rope_factors,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            Kcur = ggml_rope_ext(
+                    ctx0, Kcur, inp_pos, rope_factors,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, model.layers[il].bo,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_rot)), il);
+        }
+
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+        }
+
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+        cb(ffn_inp, "ffn_inp", il);
+
+        cur = build_norm(ffn_inp,
+                model.layers[il].ffn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "ffn_norm", il);
+
+        ggml_tensor * moe_out =
+            build_moe_ffn(cur,
+                    model.layers[il].ffn_gate_inp,
+                    model.layers[il].ffn_up_exps,
+                    model.layers[il].ffn_gate_exps,
+                    model.layers[il].ffn_down_exps,
+                    nullptr,
+                    n_expert, n_expert_used,
+                    LLM_FFN_SILU, hparams.expert_weights_norm,
+                    false, hparams.expert_weights_scale,
+                    LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
+                    il);
+        cb(moe_out, "ffn_moe_out", il);
+
+        // FFN shared expert
+        {
+            ggml_tensor * ffn_shexp = build_ffn(cur,
+                    model.layers[il].ffn_up_shexp,   NULL, NULL,
+                    model.layers[il].ffn_gate_shexp, NULL, NULL,
+                    model.layers[il].ffn_down_shexp, NULL, NULL,
+                    NULL,
+                    LLM_FFN_SILU, LLM_FFN_PAR, il);
+            cb(ffn_shexp, "ffn_shexp", il);
+
+            cur = ggml_add(ctx0, moe_out, ffn_shexp);
+            cb(cur, "ffn_out", il);
+        }
+
+        cur = ggml_add(ctx0, cur, ffn_inp);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+
+    cur = inpL;
+
+    cur = build_norm(cur,
+            model.output_norm, NULL,
+            LLM_NORM_RMS, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
+
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/bailingmoe2.cpp b/src/models/bailingmoe2.cpp
new file mode 100644
index 00000000000..fbf7b210c42
--- /dev/null
+++ b/src/models/bailingmoe2.cpp
@@ -0,0 +1,135 @@
+#include "models.h"
+
+
+
+llm_build_bailingmoe2::llm_build_bailingmoe2(const llama_model & model, const llm_graph_params & params) :
+    llm_graph_context(params) {
+    const int64_t n_embd_head = hparams.n_embd_head_v;
+    const int64_t n_embd_gqa  = hparams.n_embd_v_gqa();
+
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+
+    inpL = build_inp_embd(model.tok_embd);
+
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
+
+    auto * inp_attn = build_attn_inp_kv();
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    const int n_transformer_layers = n_layer - hparams.nextn_predict_layers;
+    for (int il = 0; il < n_transformer_layers; ++il) {
+        ggml_tensor * inpSA = inpL;
+
+        // norm
+        cur = build_norm(inpL, model.layers[il].attn_norm, NULL, LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
+
+        // self_attention
+        {
+            cur = build_lora_mm(model.layers[il].wqkv, cur);
+            cb(cur, "wqkv", il);
+
+            ggml_tensor * Qcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head, n_tokens, n_embd_head * sizeof(float),
+                                              cur->nb[1], 0 * sizeof(float) * (n_embd));
+            ggml_tensor * Kcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head * sizeof(float),
+                                              cur->nb[1], 1 * sizeof(float) * (n_embd));
+            ggml_tensor * Vcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head * sizeof(float),
+                                              cur->nb[1], 1 * sizeof(float) * (n_embd + n_embd_gqa));
+
+            Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL, LLM_NORM_RMS, il);
+            cb(Qcur, "Qcur_normed", il);
+
+            Qcur = ggml_rope_ext(ctx0, Qcur, inp_pos, nullptr, n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                                 ext_factor, attn_factor, beta_fast, beta_slow);
+
+            Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, NULL, LLM_NORM_RMS, il);
+            cb(Kcur, "Kcur_normed", il);
+
+            Kcur = ggml_rope_ext(ctx0, Kcur, inp_pos, nullptr, n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                                 ext_factor, attn_factor, beta_fast, beta_slow);
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, model.layers[il].bo,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f / sqrtf(float(n_embd_head)), il);
+        }
+
+        if (il == n_transformer_layers - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0, cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+        }
+
+        ggml_tensor * sa_out = ggml_add(ctx0, cur, inpSA);
+        cb(sa_out, "sa_out", il);
+
+        // MoE branch
+        cur = build_norm(sa_out, model.layers[il].ffn_norm, NULL, LLM_NORM_RMS, il);
+        cb(cur, "ffn_norm", il);
+
+        if (static_cast<uint32_t>(il) < hparams.n_layer_dense_lead) {
+            cur = build_ffn(cur,
+                    model.layers[il].ffn_up, NULL, NULL,
+                    model.layers[il].ffn_gate, NULL, NULL,
+                    model.layers[il].ffn_down, NULL, NULL,
+                    NULL, LLM_FFN_SILU, LLM_FFN_PAR, il);
+            cb(cur, "ffn_out", il);
+        } else {
+            ggml_tensor * moe_out = build_moe_ffn(cur,
+                model.layers[il].ffn_gate_inp,
+                model.layers[il].ffn_up_exps,
+                model.layers[il].ffn_gate_exps,
+                model.layers[il].ffn_down_exps,
+                model.layers[il].ffn_exp_probs_b,
+                n_expert, n_expert_used,
+                LLM_FFN_SILU, hparams.expert_weights_norm,
+                true, hparams.expert_weights_scale,
+                (llama_expert_gating_func_type) hparams.expert_gating_func,
+                il);
+            cb(moe_out, "ffn_moe_out", il);
+
+            {
+                ggml_tensor * ffn_shexp =
+                    build_ffn(cur,
+                        model.layers[il].ffn_up_shexp, NULL, NULL,
+                        model.layers[il].ffn_gate_shexp, NULL, NULL,
+                        model.layers[il].ffn_down_shexp, NULL, NULL,
+                        NULL, LLM_FFN_SILU, LLM_FFN_PAR, il);
+                cb(ffn_shexp, "ffn_shexp", il);
+
+                cur = ggml_add(ctx0, moe_out, ffn_shexp);
+                cb(cur, "ffn_out", il);
+            }
+        }
+
+        cur = ggml_add(ctx0, cur, sa_out);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+
+    cur = inpL;
+
+    cur = build_norm(cur, model.output_norm, NULL, LLM_NORM_RMS, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
+
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/bert.cpp b/src/models/bert.cpp
new file mode 100644
index 00000000000..3274fa3b99d
--- /dev/null
+++ b/src/models/bert.cpp
@@ -0,0 +1,176 @@
+#include "models.h"
+
+
+
+llm_build_bert::llm_build_bert(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+    const int64_t n_embd_head = hparams.n_embd_head_v;
+    const int64_t n_embd_gqa  = hparams.n_embd_v_gqa();
+
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+    ggml_tensor * inp_pos = nullptr;
+
+    if (model.arch != LLM_ARCH_JINA_BERT_V2) {
+        inp_pos = build_inp_pos();
+    }
+
+    // construct input embeddings (token, type, position)
+    inpL = build_inp_embd(model.tok_embd);
+
+    // token types are hardcoded to zero ("Sentence A")
+    if (model.type_embd) {
+        ggml_tensor * type_row0 = ggml_view_1d(ctx0, model.type_embd, n_embd, 0);
+        inpL                    = ggml_add(ctx0, inpL, type_row0);
+    }
+    if (model.arch == LLM_ARCH_BERT) {
+        inpL = ggml_add(ctx0, ggml_get_rows(ctx0, model.pos_embd, inp_pos), inpL);
+    }
+    cb(inpL, "inp_embd", -1);
+
+    // embed layer norm
+    inpL = build_norm(inpL, model.tok_norm, model.tok_norm_b, LLM_NORM, -1);
+    cb(inpL, "inp_norm", -1);
+
+    auto * inp_attn = build_attn_inp_no_cache();
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * cur = inpL;
+
+        {
+            ggml_tensor * Qcur;
+            ggml_tensor * Kcur;
+            ggml_tensor * Vcur;
+
+            // self-attention
+            if (model.layers[il].wqkv) {
+                cur = build_lora_mm(model.layers[il].wqkv, cur);
+                cb(cur, "wqkv", il);
+
+                if (model.layers[il].bqkv) {
+                    cur = ggml_add(ctx0, cur, model.layers[il].bqkv);
+                    cb(cur, "bqkv", il);
+                }
+
+                Qcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head, n_tokens, n_embd_head * sizeof(float), cur->nb[1],
+                                    0 * sizeof(float) * (n_embd));
+                Kcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head * sizeof(float),
+                                    cur->nb[1], 1 * sizeof(float) * (n_embd));
+                Vcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head * sizeof(float),
+                                    cur->nb[1], 1 * sizeof(float) * (n_embd + n_embd_gqa));
+            } else {
+                Qcur = ggml_add(ctx0, build_lora_mm(model.layers[il].wq, cur), model.layers[il].bq);
+                Kcur = ggml_add(ctx0, build_lora_mm(model.layers[il].wk, cur), model.layers[il].bk);
+                Vcur = ggml_add(ctx0, build_lora_mm(model.layers[il].wv, cur), model.layers[il].bv);
+
+                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head, n_tokens);
+                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+            }
+
+            if (model.layers[il].attn_q_norm) {
+                Qcur = ggml_reshape_2d(ctx0, Qcur, n_embd_head * n_head, n_tokens);
+
+                Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, model.layers[il].attn_q_norm_b, LLM_NORM, il);
+
+                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head, n_tokens);
+            }
+
+            if (model.layers[il].attn_k_norm) {
+                Kcur = ggml_reshape_2d(ctx0, Kcur, n_embd_head * n_head_kv, n_tokens);
+
+                Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, model.layers[il].attn_k_norm_b, LLM_NORM, il);
+
+                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            }
+
+            // RoPE
+            if (model.arch == LLM_ARCH_NOMIC_BERT || model.arch == LLM_ARCH_NOMIC_BERT_MOE ||
+                model.arch == LLM_ARCH_JINA_BERT_V3) {
+                Qcur = ggml_rope_ext(ctx0, Qcur, inp_pos, nullptr, n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                                     ext_factor, attn_factor, beta_fast, beta_slow);
+
+                Kcur = ggml_rope_ext(ctx0, Kcur, inp_pos, nullptr, n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                                     ext_factor, attn_factor, beta_fast, beta_slow);
+            }
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, model.layers[il].bo,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f / sqrtf(float(n_embd_head)), il);
+            cb(cur, "kqv_out", il);
+        }
+
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur  = ggml_get_rows(ctx0, cur, inp_out_ids);
+            inpL = ggml_get_rows(ctx0, inpL, inp_out_ids);
+        }
+
+        // re-add the layer input
+        cur = ggml_add(ctx0, cur, inpL);
+
+        // attention layer norm
+        cur = build_norm(cur, model.layers[il].attn_out_norm, model.layers[il].attn_out_norm_b, LLM_NORM, il);
+
+        if (model.layers[il].attn_norm_2 != nullptr) {
+            cur = ggml_add(ctx0, cur, inpL);  // re-add the layer input
+            cur = build_norm(cur, model.layers[il].attn_norm_2, model.layers[il].attn_norm_2_b, LLM_NORM, il);
+        }
+
+        ggml_tensor * ffn_inp = cur;
+        cb(ffn_inp, "ffn_inp", il);
+
+        // feed-forward network
+        if (hparams.moe_every_n_layers > 0 && il % hparams.moe_every_n_layers == 1) {
+            // MoE branch
+            cur = build_moe_ffn(cur, model.layers[il].ffn_gate_inp, model.layers[il].ffn_up_exps, nullptr,
+                                model.layers[il].ffn_down_exps, nullptr, hparams.n_expert, hparams.n_expert_used,
+                                LLM_FFN_GELU, false, false, 0.0f, LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX, il);
+            cb(cur, "ffn_moe_out", il);
+        } else if (model.arch == LLM_ARCH_BERT || model.arch == LLM_ARCH_NOMIC_BERT_MOE ||
+                   model.arch == LLM_ARCH_JINA_BERT_V3) {
+            cur = build_ffn(cur,
+                    model.layers[il].ffn_up, model.layers[il].ffn_up_b, NULL,
+                    NULL, NULL, NULL,
+                    model.layers[il].ffn_down, model.layers[il].ffn_down_b, NULL, NULL,
+                    LLM_FFN_GELU, LLM_FFN_SEQ, il);
+            cb(cur, "ffn_out", il);
+        } else if (model.arch == LLM_ARCH_JINA_BERT_V2) {
+            cur = build_ffn(cur,
+                    model.layers[il].ffn_up, NULL, NULL,
+                    model.layers[il].ffn_gate, NULL, NULL,
+                    model.layers[il].ffn_down, model.layers[il].ffn_down_b, NULL, NULL,
+                    model.layers[il].ffn_gate ? LLM_FFN_GELU : LLM_FFN_GEGLU, LLM_FFN_PAR, il);
+            cb(cur, "ffn_out", il);
+        } else {
+            cur = build_ffn(cur,
+                model.layers[il].ffn_up, NULL, NULL,
+                model.layers[il].ffn_gate, NULL, NULL,
+                model.layers[il].ffn_down, NULL, NULL,
+                NULL, LLM_FFN_SILU, LLM_FFN_PAR, il);
+            cb(cur, "ffn_out", il);
+        }
+
+        // attentions bypass the intermediate layer
+        cur = ggml_add(ctx0, cur, ffn_inp);
+
+        // output layer norm
+        cur = build_norm(cur, model.layers[il].layer_out_norm, model.layers[il].layer_out_norm_b, LLM_NORM, il);
+
+        // input for next layer
+        inpL = cur;
+    }
+
+    cur = inpL;
+
+    cb(cur, "result_embd", -1);
+    res->t_embd = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/bitnet.cpp b/src/models/bitnet.cpp
new file mode 100644
index 00000000000..331a3f11197
--- /dev/null
+++ b/src/models/bitnet.cpp
@@ -0,0 +1,160 @@
+#include "models.h"
+
+
+llm_build_bitnet::llm_build_bitnet(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+    const int64_t n_embd_head = hparams.n_embd_head_v;
+
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+
+    inpL = build_inp_embd(model.tok_embd);
+
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
+
+    auto * inp_attn = build_attn_inp_kv();
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * inpSA = inpL;
+
+        cur = build_norm(inpL,
+                model.layers[il].attn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
+
+        // self-attention
+        {
+            // compute Q and K and RoPE them
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            if (model.layers[il].wq_scale) {
+                Qcur = ggml_mul(ctx0, Qcur, model.layers[il].wq_scale);
+            }
+            cb(Qcur, "Qcur", il);
+            if (model.layers[il].bq) {
+                Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
+                cb(Qcur, "Qcur", il);
+            }
+
+            // B1.K
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            if (model.layers[il].wk_scale) {
+                Kcur = ggml_mul(ctx0, Kcur, model.layers[il].wk_scale);
+            }
+            cb(Kcur, "Kcur", il);
+            if (model.layers[il].bk) {
+                Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
+                cb(Kcur, "Kcur", il);
+            }
+
+            // B1.V
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            if (model.layers[il].wv_scale) {
+                Vcur = ggml_mul(ctx0, Vcur, model.layers[il].wv_scale);
+            }
+            cb(Vcur, "Vcur", il);
+            if (model.layers[il].bv) {
+                Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
+                cb(Vcur, "Vcur", il);
+            }
+
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+            Qcur = ggml_rope_ext(
+                    ctx0, Qcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            Kcur = ggml_rope_ext(
+                    ctx0, Kcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    NULL, NULL,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+
+            cur = build_norm(cur,
+                    model.layers[il].attn_sub_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "attn_sub_norm", il);
+
+            cur = build_lora_mm(model.layers[il].wo, cur);
+            if (model.layers[il].wo_scale) {
+                cur = ggml_mul(ctx0, cur, model.layers[il].wo_scale);
+            }
+            if (model.layers[il].bo) {
+                cur = ggml_add(ctx0, cur, model.layers[il].bo);
+            }
+            cb(cur, "attn_out", il);
+        }
+
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+        }
+
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+        cb(ffn_inp, "ffn_inp", il);
+
+        // feed-forward forward
+        cur = build_norm(ffn_inp,
+                model.layers[il].ffn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "ffn_norm", il);
+
+        cur = build_ffn(cur,
+                model.layers[il].ffn_up,   NULL, model.layers[il].ffn_up_scale,
+                model.layers[il].ffn_gate, NULL, model.layers[il].ffn_gate_scale,
+                NULL,                      NULL, NULL,
+                NULL,
+                LLM_FFN_SILU, LLM_FFN_PAR, il);
+        cb(cur, "ffn_sub_out", il);
+
+        cur = build_norm(cur,
+                model.layers[il].ffn_sub_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "ffn_sub_norm", il);
+
+        cur = build_lora_mm(model.layers[il].ffn_down, cur);
+        if (model.layers[il].ffn_down_scale) {
+            cur = ggml_mul(ctx0, cur, model.layers[il].ffn_down_scale);
+        }
+        cb(cur, "ffn_down", il);
+
+        cur = ggml_add(ctx0, cur, ffn_inp);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+
+    cur = inpL;
+
+    cur = build_norm(cur,
+            model.output_norm, NULL,
+            LLM_NORM_RMS, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    // lm_head
+    // FIXME: do not use model.tok_embd directly, duplicate as model.output
+    cur = build_lora_mm(model.tok_embd, cur);
+
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/bloom.cpp b/src/models/bloom.cpp
new file mode 100644
index 00000000000..2c552d1d15e
--- /dev/null
+++ b/src/models/bloom.cpp
@@ -0,0 +1,101 @@
+#include "models.h"
+
+llm_build_bloom::llm_build_bloom(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+    const int64_t n_embd_head = hparams.n_embd_head_v;
+    const int64_t n_embd_gqa  = hparams.n_embd_v_gqa();
+
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+
+    inpL = build_inp_embd(model.tok_embd);
+
+    auto * inp_attn = build_attn_inp_kv();
+
+    inpL = build_norm(inpL,
+            model.tok_norm,
+            model.tok_norm_b,
+            LLM_NORM, -1);
+    cb(inpL, "inp_norm", -1);
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        cur = build_norm(inpL,
+                model.layers[il].attn_norm,
+                model.layers[il].attn_norm_b,
+                LLM_NORM, il);
+        cb(cur, "attn_norm", il);
+
+        // self-attention
+        {
+            cur = build_lora_mm(model.layers[il].wqkv, cur);
+            cb(cur, "wqkv", il);
+
+            cur = ggml_add(ctx0, cur, model.layers[il].bqkv);
+            cb(cur, "bqkv", il);
+
+            ggml_tensor * Qcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head,    n_tokens, n_embd_head*sizeof(float), cur->nb[1], 0*sizeof(float)*(n_embd));
+            ggml_tensor * Kcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd));
+            ggml_tensor * Vcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd + n_embd_gqa));
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, model.layers[il].bo,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+        }
+
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur  = ggml_get_rows(ctx0,  cur, inp_out_ids);
+            inpL = ggml_get_rows(ctx0, inpL, inp_out_ids);
+        }
+
+        // Add the input
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpL);
+        cb(ffn_inp, "ffn_inp", il);
+
+        // FF
+        {
+            cur = build_norm(ffn_inp,
+                    model.layers[il].ffn_norm,
+                    model.layers[il].ffn_norm_b,
+                    LLM_NORM, il);
+            cb(cur, "ffn_norm", il);
+
+            cur = build_ffn(cur,
+                    model.layers[il].ffn_up,   model.layers[il].ffn_up_b,   NULL,
+                    NULL,                      NULL,                        NULL,
+                    model.layers[il].ffn_down, model.layers[il].ffn_down_b, NULL,
+                    NULL,
+                    LLM_FFN_GELU, LLM_FFN_SEQ, il);
+            cb(cur, "ffn_out", il);
+        }
+
+        cur = ggml_add(ctx0, cur, ffn_inp);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+
+    cur = build_norm(inpL,
+            model.output_norm,
+            model.output_norm_b,
+            LLM_NORM, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    cur = build_lora_mm(model.output, cur);
+
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/chameleon.cpp b/src/models/chameleon.cpp
new file mode 100644
index 00000000000..184511aed4c
--- /dev/null
+++ b/src/models/chameleon.cpp
@@ -0,0 +1,178 @@
+#include "models.h"
+
+#include <float.h>
+
+llm_build_chameleon::llm_build_chameleon(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+    const int64_t n_embd_head = hparams.n_embd_head_v;
+
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+    GGML_ASSERT(n_embd_head == hparams.n_rot);
+
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+
+    inpL = build_inp_embd(model.tok_embd);
+
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
+
+    auto * inp_attn = build_attn_inp_kv();
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * inpSA = inpL;
+
+        // norm
+        if (hparams.swin_norm) {
+            cur = inpL;
+        } else {
+            cur = build_norm(inpL,
+                    model.layers[il].attn_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "attn_norm", il);
+        }
+
+        // self-attention
+        {
+            // compute Q and K and RoPE them
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            cb(Qcur, "Qcur", il);
+
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            cb(Kcur, "Kcur", il);
+
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            cb(Vcur, "Vcur", il);
+
+            if (model.layers[il].attn_q_norm) {
+                Qcur = ggml_view_3d(ctx0, Qcur, n_embd_head, n_head, n_tokens,
+                        ggml_element_size(Qcur) * n_embd_head,
+                        ggml_element_size(Qcur) * n_embd_head * n_head,
+                        0);
+                cb(Qcur, "Qcur", il);
+
+                Qcur = build_norm(Qcur,
+                        model.layers[il].attn_q_norm,
+                        model.layers[il].attn_q_norm_b,
+                        LLM_NORM, il);
+                cb(Qcur, "Qcur", il);
+            }
+
+            if (model.layers[il].attn_k_norm) {
+                Kcur = ggml_view_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens,
+                        ggml_element_size(Kcur) * n_embd_head,
+                        ggml_element_size(Kcur) * n_embd_head * n_head_kv,
+                        0);
+                cb(Kcur, "Kcur", il);
+
+                Kcur = build_norm(Kcur,
+                        model.layers[il].attn_k_norm,
+                        model.layers[il].attn_k_norm_b,
+                        LLM_NORM, il);
+                cb(Kcur, "Kcur", il);
+            }
+
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+            Qcur = ggml_rope_ext(
+                    ctx0, Qcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            Kcur = ggml_rope_ext(
+                    ctx0, Kcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, nullptr,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+        }
+
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+        }
+
+        if (hparams.swin_norm) {
+            cur = build_norm(cur,
+                    model.layers[il].attn_norm, NULL,
+                    LLM_NORM_RMS, il);
+        }
+
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+        cb(ffn_inp, "ffn_inp", il);
+
+        // feed-forward network
+        if (!hparams.swin_norm) {
+            cur = build_norm(ffn_inp,
+                    model.layers[il].ffn_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "ffn_norm", il);
+        }
+
+        cur = build_ffn(cur,
+                model.layers[il].ffn_up,   NULL, NULL,
+                model.layers[il].ffn_gate, NULL, NULL,
+                model.layers[il].ffn_down, NULL, NULL,
+                NULL,
+                LLM_FFN_SILU, LLM_FFN_PAR, il);
+        cb(cur, "ffn_out", il);
+
+        if (hparams.swin_norm) {
+            cur = build_norm(cur,
+                    model.layers[il].ffn_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "ffn_norm", il);
+        }
+
+        cur = ggml_add(ctx0, cur, ffn_inp);
+        cb(cur, "ffn_out", il);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+
+    cur = inpL;
+
+    cur = build_norm(cur,
+            model.output_norm, NULL,
+            LLM_NORM_RMS, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
+    cb(cur, "result_output_with_img_logits", -1);
+
+    // TODO: this suppresses the output of image tokens, which is required to enable text-only outputs.
+    // Needs to be removed once image outputs are supported.
+    int img_token_end_idx = 8196;
+    int img_token_start_idx = 4;
+    int num_img_tokens = img_token_end_idx - img_token_start_idx;
+    // creates 1d tensor of size num_img_tokens and values -FLT_MAX,
+    // which ensures that text token values are always at least larger than image token values
+    ggml_tensor * img_logits = ggml_new_tensor_1d(ctx0, GGML_TYPE_F32, num_img_tokens);
+    img_logits = ggml_clamp(ctx0, img_logits, -FLT_MAX, -FLT_MAX);
+    cb(img_logits, "img_logits", -1);
+
+    cur = ggml_set_1d(ctx0, cur, img_logits, ggml_element_size(cur) * img_token_start_idx);
+
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/chatglm.cpp b/src/models/chatglm.cpp
new file mode 100644
index 00000000000..2685d4fbcbe
--- /dev/null
+++ b/src/models/chatglm.cpp
@@ -0,0 +1,132 @@
+#include "models.h"
+
+
+llm_build_chatglm::llm_build_chatglm(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+    const int64_t n_embd_head = hparams.n_embd_head_v;
+    const int64_t n_embd_gqa  = hparams.n_embd_v_gqa();
+
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+
+    inpL = build_inp_embd(model.tok_embd);
+
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
+
+    auto * inp_attn = build_attn_inp_kv();
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * inpSA = inpL;
+
+        cur = build_norm(inpL,
+                model.layers[il].attn_norm,
+                NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
+
+        // self-attention
+        {
+            ggml_tensor * Qcur = nullptr;
+            ggml_tensor * Kcur = nullptr;
+            ggml_tensor * Vcur = nullptr;
+
+            if (model.layers[il].wqkv == nullptr) {
+                Qcur = build_lora_mm(model.layers[il].wq, cur);
+                if (model.layers[il].bq) {
+                    Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
+                }
+                Kcur = build_lora_mm(model.layers[il].wk, cur);
+                if (model.layers[il].bk) {
+                    Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
+                }
+                Vcur = build_lora_mm(model.layers[il].wv, cur);
+                if (model.layers[il].bv) {
+                    Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
+                }
+                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+            } else {
+                cur = build_lora_mm(model.layers[il].wqkv, cur);
+                cb(cur, "wqkv", il);
+                if (model.layers[il].bqkv) {
+                    cur = ggml_add(ctx0, cur, model.layers[il].bqkv);
+                    cb(cur, "bqkv", il);
+                }
+                Qcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head,    n_tokens, n_embd_head*sizeof(float), cur->nb[1], 0*sizeof(float)*(n_embd));
+                Kcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd));
+                Vcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd + n_embd_gqa));
+            }
+
+            //printf("freq_base: %f freq_scale: %f ext_factor: %f attn_factor: %f\n", freq_base, freq_scale, ext_factor, attn_factor);
+            Qcur = ggml_rope_ext(
+                    ctx0, Qcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            Kcur = ggml_rope_ext(
+                    ctx0, Kcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, NULL,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+        }
+
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+        }
+
+        // Add the input
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+        cb(ffn_inp, "ffn_inp", il);
+
+        // FF
+        {
+            cur = build_norm(ffn_inp,
+                    model.layers[il].ffn_norm,
+                    NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "ffn_norm", il);
+
+            cur = build_ffn(cur,
+                    model.layers[il].ffn_up,   NULL, NULL,
+                    NULL,                      NULL, NULL,
+                    model.layers[il].ffn_down, NULL, NULL,
+                    NULL,
+                    LLM_FFN_SWIGLU, LLM_FFN_SEQ, il);
+            cb(cur, "ffn_out", il);
+
+        }
+
+        inpL = ggml_add(ctx0, cur, ffn_inp);
+        cb(inpL, "l_out", il);
+    }
+
+    cur = build_norm(inpL,
+            model.output_norm,
+            NULL,
+            LLM_NORM_RMS, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    cur = build_lora_mm(model.output, cur);
+
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/codeshell.cpp b/src/models/codeshell.cpp
new file mode 100644
index 00000000000..0b3bdbff529
--- /dev/null
+++ b/src/models/codeshell.cpp
@@ -0,0 +1,111 @@
+#include "models.h"
+
+llm_build_codeshell::llm_build_codeshell(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+    const int64_t n_embd_head = hparams.n_embd_head_v;
+    const int64_t n_embd_gqa  = hparams.n_embd_v_gqa();
+
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+    GGML_ASSERT(n_embd_head == hparams.n_rot);
+
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+
+    inpL = build_inp_embd(model.tok_embd);
+
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
+
+    auto * inp_attn = build_attn_inp_kv();
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        cur = build_norm(inpL,
+                model.layers[il].attn_norm,
+                model.layers[il].attn_norm_b,
+                LLM_NORM, il);
+        cb(cur, "attn_norm", il);
+
+        // self-attention
+        {
+            cur = build_lora_mm(model.layers[il].wqkv, cur);
+            cb(cur, "wqkv", il);
+
+            cur = ggml_add(ctx0, cur, model.layers[il].bqkv);
+            cb(cur, "bqkv", il);
+
+            ggml_tensor * Qcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head,    n_tokens, n_embd_head*sizeof(float), cur->nb[1], 0*sizeof(float)*(n_embd));
+            ggml_tensor * Kcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd));
+            ggml_tensor * Vcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd + n_embd_gqa));
+
+            Qcur = ggml_rope_ext(
+                    ctx0, Qcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            Kcur = ggml_rope_ext(
+                    ctx0, Kcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, model.layers[il].bo,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+        }
+
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur  = ggml_get_rows(ctx0,  cur, inp_out_ids);
+            inpL = ggml_get_rows(ctx0, inpL, inp_out_ids);
+        }
+
+        // add the input
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpL);
+        cb(ffn_inp, "ffn_inp", il);
+
+        // FF
+        {
+            cur = build_norm(ffn_inp,
+                    model.layers[il].ffn_norm,
+                    model.layers[il].ffn_norm_b,
+                    LLM_NORM, il);
+            cb(cur, "ffn_norm", il);
+
+            cur = build_ffn(cur,
+                    model.layers[il].ffn_up,   model.layers[il].ffn_up_b,   NULL,
+                    NULL,                      NULL,                        NULL,
+                    model.layers[il].ffn_down, model.layers[il].ffn_down_b, NULL,
+                    NULL,
+                    LLM_FFN_GELU, LLM_FFN_SEQ, il);
+            cb(cur, "ffn_out", il);
+        }
+
+        cur = ggml_add(ctx0, cur, ffn_inp);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+
+    cur = build_norm(inpL,
+            model.output_norm,
+            model.output_norm_b,
+            LLM_NORM, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    cur = build_lora_mm(model.output, cur);
+
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/cogvlm.cpp b/src/models/cogvlm.cpp
new file mode 100644
index 00000000000..edf0d1424ce
--- /dev/null
+++ b/src/models/cogvlm.cpp
@@ -0,0 +1,100 @@
+#include "models.h"
+
+llm_build_cogvlm::llm_build_cogvlm(const llama_model & model, const llm_graph_params & params) :
+    llm_graph_context(params) {
+    const int64_t n_embd_head = hparams.n_embd_head_v;
+    float         kq_scale    = 1.0f / sqrtf(float(n_embd_head));
+
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+    GGML_ASSERT(n_embd_head == hparams.n_rot);
+
+    ggml_tensor *inpL, *cur;
+    inpL = build_inp_embd(model.tok_embd);
+
+    ggml_tensor * inp_pos = build_inp_pos();
+
+    auto * inp_attn = build_attn_inp_kv();
+
+    // check ubatch to see if we have input tokens (text)
+    // or an input embedding vector (image)
+    bool is_text;
+    if (ubatch.token) {
+        is_text = true;
+    } else {
+        is_text = false;
+    }
+
+    for (int il = 0; il < n_layer; ++il) {
+        // get either the text or image weight tensors
+        ggml_tensor *wqkv, *wo;
+        ggml_tensor *ffn_gate, *ffn_down, *ffn_up;
+
+        if (is_text) {
+            wqkv     = model.layers[il].wqkv;
+            wo       = model.layers[il].wo;
+            ffn_gate = model.layers[il].ffn_gate;
+            ffn_down = model.layers[il].ffn_down;
+            ffn_up   = model.layers[il].ffn_up;
+        } else {
+            wqkv     = model.layers[il].visexp_attn_wqkv;
+            wo       = model.layers[il].visexp_attn_wo;
+            ffn_gate = model.layers[il].visexp_ffn_gate;
+            ffn_down = model.layers[il].visexp_ffn_down;
+            ffn_up   = model.layers[il].visexp_ffn_up;
+        }
+
+        ggml_tensor * inpSA = inpL;
+        cur                 = build_norm(inpSA, model.layers[il].attn_norm, NULL, LLM_NORM_RMS, il);
+
+        // build self attention
+        {
+            ggml_tensor * qkv = build_lora_mm(wqkv, cur);
+
+            // split qkv into Q, K, V along the first dimension
+            ggml_tensor * Qcur =
+                ggml_view_3d(ctx0, qkv, n_embd_head, n_head, n_tokens, n_embd_head * sizeof(float), qkv->nb[1], 0);
+            ggml_tensor * Kcur = ggml_view_3d(ctx0, qkv, n_embd_head, n_head_kv, n_tokens, n_embd_head * sizeof(float),
+                                              qkv->nb[1], n_embd * ggml_element_size(qkv));
+            ggml_tensor * Vcur = ggml_view_3d(ctx0, qkv, n_embd_head, n_head_kv, n_tokens, n_embd_head * sizeof(float),
+                                              qkv->nb[1], 2 * n_embd * ggml_element_size(qkv));
+
+            Qcur = ggml_rope(ctx0, Qcur, inp_pos, n_embd_head, rope_type);
+            Kcur = ggml_rope(ctx0, Kcur, inp_pos, n_embd_head, rope_type);
+
+            cur = build_attn(inp_attn,
+                wo, nullptr,
+                Qcur, Kcur, Vcur,
+                nullptr, nullptr, nullptr,
+                kq_scale, il);
+            cb(cur, "attn_out", il);
+        }
+
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+        cb(ffn_inp, "ffn_inp", il);
+
+        cur = build_norm(ffn_inp, model.layers[il].ffn_norm, NULL, LLM_NORM_RMS, il);
+        cb(cur, "ffn_norm", il);
+
+        cur = build_ffn(cur,
+                ffn_up, NULL, NULL,
+                ffn_gate, NULL, NULL,
+                ffn_down, NULL, NULL,
+                NULL, LLM_FFN_SILU, LLM_FFN_PAR, il);
+
+        cur = ggml_add(ctx0, cur, ffn_inp);
+        cb(cur, "ffn_out", il);
+
+        inpL = cur;
+    }
+
+    cur = inpL;
+
+    cur = build_norm(cur, model.output_norm, NULL, LLM_NORM_RMS, -1);
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    cur = build_lora_mm(model.output, cur);
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+    ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/cohere2-iswa.cpp b/src/models/cohere2-iswa.cpp
new file mode 100644
index 00000000000..b18aa8c4e6c
--- /dev/null
+++ b/src/models/cohere2-iswa.cpp
@@ -0,0 +1,131 @@
+#include "models.h"
+
+llm_build_cohere2_iswa::llm_build_cohere2_iswa(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+    const int64_t n_embd_head = hparams.n_embd_head_v;
+
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+
+    const float f_logit_scale = hparams.f_logit_scale;
+
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+
+    inpL = build_inp_embd(model.tok_embd);
+
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
+
+    auto * inp_attn = build_attn_inp_kv_iswa();
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        const bool is_swa = hparams.is_swa(il);
+
+        // norm
+        cur = build_norm(inpL, model.layers[il].attn_norm, NULL, LLM_NORM, il);
+        cb(cur, "attn_norm", il);
+        ggml_tensor * ffn_inp = cur;
+
+        // self-attention
+        {
+            // rope freq factors for 128k context
+            ggml_tensor * rope_factors = model.get_rope_factors(cparams, il);
+
+            // compute Q and K and RoPE them
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            cb(Qcur, "Qcur", il);
+            if (model.layers[il].bq) {
+                Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
+                cb(Qcur, "Qcur", il);
+            }
+
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            cb(Kcur, "Kcur", il);
+            if (model.layers[il].bk) {
+                Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
+                cb(Kcur, "Kcur", il);
+            }
+
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            cb(Vcur, "Vcur", il);
+            if (model.layers[il].bv) {
+                Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
+                cb(Vcur, "Vcur", il);
+            }
+
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+            if (is_swa) {
+                Qcur = ggml_rope_ext(
+                        ctx0, Qcur, inp_pos, rope_factors,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+                Kcur = ggml_rope_ext(
+                        ctx0, Kcur, inp_pos, rope_factors,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+            }
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, model.layers[il].bo,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+        }
+
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur     = ggml_get_rows(ctx0, cur, inp_out_ids);
+            inpL    = ggml_get_rows(ctx0, inpL, inp_out_ids);
+            ffn_inp = ggml_get_rows(ctx0, ffn_inp, inp_out_ids);
+        }
+
+        ggml_tensor * attn_out = cur;
+
+        // feed-forward network
+        {
+            cur = build_ffn(ffn_inp,
+                    model.layers[il].ffn_up, NULL, NULL,
+                    model.layers[il].ffn_gate, NULL, NULL,
+                    model.layers[il].ffn_down, NULL, NULL,
+                    NULL, LLM_FFN_SILU, LLM_FFN_PAR, il);
+            cb(cur, "ffn_out", il);
+        }
+
+        // add together residual + FFN + self-attention
+        cur = ggml_add(ctx0, cur, inpL);
+        cur = ggml_add(ctx0, cur, attn_out);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+
+    cur = inpL;
+
+    cur = build_norm(cur, model.output_norm, NULL, LLM_NORM, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
+
+    if (f_logit_scale) {
+        cur = ggml_scale(ctx0, cur, f_logit_scale);
+    }
+
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/command-r.cpp b/src/models/command-r.cpp
new file mode 100644
index 00000000000..4d3b643b444
--- /dev/null
+++ b/src/models/command-r.cpp
@@ -0,0 +1,122 @@
+#include "models.h"
+
+
+
+llm_build_command_r::llm_build_command_r(const llama_model & model, const llm_graph_params & params) :
+    llm_graph_context(params) {
+    const int64_t n_embd_head = hparams.n_embd_head_v;
+
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+
+    const float f_logit_scale = hparams.f_logit_scale;
+
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+
+    inpL = build_inp_embd(model.tok_embd);
+
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
+
+    auto * inp_attn = build_attn_inp_kv();
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        // norm
+        cur = build_norm(inpL, model.layers[il].attn_norm, NULL, LLM_NORM, il);
+        cb(cur, "attn_norm", il);
+
+        ggml_tensor * ffn_inp = cur;
+
+        // self-attention
+        {
+            // compute Q and K and RoPE them
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            cb(Qcur, "Qcur", il);
+            if (model.layers[il].bq) {
+                Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
+                cb(Qcur, "Qcur", il);
+            }
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            cb(Kcur, "Kcur", il);
+            if (model.layers[il].bk) {
+                Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
+                cb(Kcur, "Kcur", il);
+            }
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            cb(Vcur, "Vcur", il);
+            if (model.layers[il].bv) {
+                Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
+                cb(Vcur, "Vcur", il);
+            }
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head, n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+            if (model.layers[il].attn_q_norm) {
+                Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL, LLM_NORM, il);
+                cb(Qcur, "Qcur", il);
+            }
+            Qcur = ggml_rope_ext(ctx0, Qcur, inp_pos, nullptr, n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                                 ext_factor, attn_factor, beta_fast, beta_slow);
+
+            if (model.layers[il].attn_k_norm) {
+                Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, NULL, LLM_NORM, il);
+                cb(Kcur, "Kcur", il);
+            }
+            Kcur = ggml_rope_ext(ctx0, Kcur, inp_pos, nullptr, n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                                 ext_factor, attn_factor, beta_fast, beta_slow);
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, model.layers[il].bo,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f / sqrtf(float(n_embd_head)), il);
+        }
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur     = ggml_get_rows(ctx0, cur, inp_out_ids);
+            inpL    = ggml_get_rows(ctx0, inpL, inp_out_ids);
+            ffn_inp = ggml_get_rows(ctx0, ffn_inp, inp_out_ids);
+        }
+        ggml_tensor * attn_out = cur;
+
+        // feed-forward network
+        {
+            cur = build_ffn(ffn_inp,
+                    model.layers[il].ffn_up, NULL, NULL,
+                    model.layers[il].ffn_gate, NULL, NULL,
+                    model.layers[il].ffn_down, NULL, NULL,
+                    NULL, LLM_FFN_SILU, LLM_FFN_PAR, il);
+            cb(cur, "ffn_out", il);
+        }
+        // add together residual + FFN + self-attention
+        cur = ggml_add(ctx0, cur, inpL);
+        cur = ggml_add(ctx0, cur, attn_out);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+    cur = inpL;
+
+    cur = build_norm(cur, model.output_norm, NULL, LLM_NORM, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
+
+    if (f_logit_scale) {
+        cur = ggml_scale(ctx0, cur, f_logit_scale);
+    }
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/dbrx.cpp b/src/models/dbrx.cpp
new file mode 100644
index 00000000000..6d2a0ebf1b7
--- /dev/null
+++ b/src/models/dbrx.cpp
@@ -0,0 +1,123 @@
+#include "models.h"
+
+
+llm_build_dbrx::llm_build_dbrx(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+    const int64_t n_embd_head = hparams.n_embd_head_v;
+    const int64_t n_embd_gqa  = hparams.n_embd_v_gqa();
+
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+    GGML_ASSERT(n_embd_head == hparams.n_rot);
+
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+
+    inpL = build_inp_embd(model.tok_embd);
+
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
+
+    auto * inp_attn = build_attn_inp_kv();
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * inpSA = inpL;
+
+        // norm
+        cur = build_norm(inpL,
+                model.layers[il].attn_norm, NULL,
+                LLM_NORM, il);
+        cb(cur, "attn_norm", il);
+
+        // self-attention
+        {
+            ggml_tensor * Qcur = nullptr;
+            ggml_tensor * Kcur = nullptr;
+            ggml_tensor * Vcur = nullptr;
+
+            cur = build_lora_mm(model.layers[il].wqkv, cur);
+            cb(cur, "wqkv", il);
+
+            cur = ggml_clamp(ctx0, cur, -hparams.f_clamp_kqv, hparams.f_clamp_kqv);
+            cb(cur, "wqkv_clamped", il);
+
+            Qcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head,    n_tokens, n_embd_head*sizeof(float), cur->nb[1], 0*sizeof(float)*(n_embd));
+            Kcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd));
+            Vcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd + n_embd_gqa));
+
+            Qcur = ggml_rope_ext(
+                    ctx0, Qcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            Kcur = ggml_rope_ext(
+                    ctx0, Kcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, NULL,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+        }
+
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+        }
+
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+        cb(ffn_inp, "ffn_inp", il);
+
+        // feed-forward network
+        // MoE branch
+        cur = build_norm(ffn_inp,
+                model.layers[il].attn_out_norm, NULL,
+                LLM_NORM, il);
+        cb(cur, "attn_out_norm", il);
+
+        cur = build_moe_ffn(cur,
+                model.layers[il].ffn_gate_inp,
+                model.layers[il].ffn_up_exps,
+                model.layers[il].ffn_gate_exps,
+                model.layers[il].ffn_down_exps,
+                nullptr,
+                n_expert, n_expert_used,
+                LLM_FFN_SILU, true,
+                false, 0.0,
+                LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
+                il);
+        cb(cur, "ffn_moe_out", il);
+
+        cur = ggml_add(ctx0, cur, ffn_inp);
+        cb(cur, "ffn_out", il);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+
+    cur = inpL;
+
+    cur = build_norm(cur,
+            model.output_norm, NULL,
+            LLM_NORM, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
+
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/deci.cpp b/src/models/deci.cpp
new file mode 100644
index 00000000000..7410a3a46d9
--- /dev/null
+++ b/src/models/deci.cpp
@@ -0,0 +1,135 @@
+#include "models.h"
+
+
+
+llm_build_deci::llm_build_deci(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+    const int64_t n_embd_head = hparams.n_embd_head_v;
+
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+    GGML_ASSERT(n_embd_head == hparams.n_rot);
+
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+
+    inpL = build_inp_embd(model.tok_embd);
+
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
+
+    auto * inp_attn = build_attn_inp_kv();
+
+    const float kq_scale =
+        hparams.f_attention_scale == 0.0f ? 1.0f / sqrtf(float(n_embd_head)) : hparams.f_attention_scale;
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * inpSA     = inpL;
+        const int64_t n_head_kv = hparams.n_head_kv(il);
+        const int64_t n_head    = hparams.n_head(il);
+        const int64_t n_ff      = hparams.n_ff(il);
+
+        if (n_head == 0) {
+            // attention-free layer of Llama-3_1-Nemotron-51B
+            cur = inpL;
+        } else {
+            // norm
+            cur = build_norm(inpL, model.layers[il].attn_norm, NULL, LLM_NORM_RMS, il);
+            cb(cur, "attn_norm", il);
+        }
+        if (n_head > 0 && n_head_kv == 0) {
+            // "linear attention" of Llama-3_1-Nemotron-51B
+            cur = build_lora_mm(model.layers[il].wo, cur);
+            cb(cur, "wo", il);
+        } else if (n_head > 0) {
+            // self-attention
+            // rope freq factors for llama3; may return nullptr for llama2 and other models
+            ggml_tensor * rope_factors = model.get_rope_factors(cparams, il);
+
+            // compute Q and K and RoPE them
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            cb(Qcur, "Qcur", il);
+            if (model.layers[il].bq) {
+                Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
+                cb(Qcur, "Qcur", il);
+            }
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            cb(Kcur, "Kcur", il);
+            if (model.layers[il].bk) {
+                Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
+                cb(Kcur, "Kcur", il);
+            }
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            cb(Vcur, "Vcur", il);
+            if (model.layers[il].bv) {
+                Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
+                cb(Vcur, "Vcur", il);
+            }
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head, n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+            Qcur = ggml_rope_ext(ctx0, Qcur, inp_pos, rope_factors, n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                                 ext_factor, attn_factor, beta_fast, beta_slow);
+
+            Kcur = ggml_rope_ext(ctx0, Kcur, inp_pos, rope_factors, n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                                 ext_factor, attn_factor, beta_fast, beta_slow);
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, model.layers[il].bo,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, kq_scale, il);
+        }
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0, cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+        }
+        // FFN-free layer of Llama-3_1-Nemotron-Ultra-253B
+        if (n_ff == 0) {
+            continue;
+        }
+        // modified to support attention-free layer of Llama-3_1-Nemotron-51B
+        ggml_tensor * ffn_inp = cur;
+        if (n_head > 0) {
+            ffn_inp = ggml_add(ctx0, cur, inpSA);
+            cb(ffn_inp, "ffn_inp", il);
+        }
+        // feed-forward network
+        if (model.layers[il].ffn_gate_inp == nullptr) {
+            cur = build_norm(ffn_inp, model.layers[il].ffn_norm, NULL, LLM_NORM_RMS, il);
+            cb(cur, "ffn_norm", il);
+
+            cur = build_ffn(cur,
+                model.layers[il].ffn_up, model.layers[il].ffn_up_b, NULL,
+                model.layers[il].ffn_gate, model.layers[il].ffn_gate_b, NULL,
+                model.layers[il].ffn_down, model.layers[il].ffn_down_b, NULL,
+                NULL, LLM_FFN_SILU, LLM_FFN_PAR, il);
+            cb(cur, "ffn_out", il);
+        }
+        cur = ggml_add(ctx0, cur, ffn_inp);
+        cb(cur, "ffn_out", il);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+    cur = inpL;
+
+    cur = build_norm(cur, model.output_norm, NULL, LLM_NORM_RMS, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
+
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/deepseek.cpp b/src/models/deepseek.cpp
new file mode 100644
index 00000000000..17866c0d88e
--- /dev/null
+++ b/src/models/deepseek.cpp
@@ -0,0 +1,144 @@
+#include "models.h"
+
+
+
+llm_build_deepseek::llm_build_deepseek(const llama_model & model, const llm_graph_params & params) :
+    llm_graph_context(params) {
+    const int64_t n_embd_head = hparams.n_embd_head_v;
+
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+    GGML_ASSERT(n_embd_head == hparams.n_rot);
+
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+
+    inpL = build_inp_embd(model.tok_embd);
+
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
+
+    auto * inp_attn = build_attn_inp_kv();
+
+    const float kq_scale =
+        hparams.f_attention_scale == 0.0f ? 1.0f / sqrtf(float(n_embd_head)) : hparams.f_attention_scale;
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * inpSA = inpL;
+
+        // norm
+        cur = build_norm(inpL, model.layers[il].attn_norm, NULL, LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
+
+        // self-attention
+        {
+            // rope freq factors for llama3; may return nullptr for llama2 and other models
+            ggml_tensor * rope_factors = model.get_rope_factors(cparams, il);
+
+            // compute Q and K and RoPE them
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            cb(Qcur, "Qcur", il);
+            if (model.layers[il].bq) {
+                Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
+                cb(Qcur, "Qcur", il);
+            }
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            cb(Kcur, "Kcur", il);
+            if (model.layers[il].bk) {
+                Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
+                cb(Kcur, "Kcur", il);
+            }
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            cb(Vcur, "Vcur", il);
+            if (model.layers[il].bv) {
+                Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
+                cb(Vcur, "Vcur", il);
+            }
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head, n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+            Qcur = ggml_rope_ext(ctx0, Qcur, inp_pos, rope_factors, n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                                 ext_factor, attn_factor, beta_fast, beta_slow);
+
+            Kcur = ggml_rope_ext(ctx0, Kcur, inp_pos, rope_factors, n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                                 ext_factor, attn_factor, beta_fast, beta_slow);
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, model.layers[il].bo,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, kq_scale, il);
+        }
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0, cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+        }
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+        cb(ffn_inp, "ffn_inp", il);
+
+        cur = build_norm(ffn_inp, model.layers[il].ffn_norm, NULL, LLM_NORM_RMS, il);
+        cb(cur, "ffn_norm", il);
+
+        if ((uint32_t) il < hparams.n_layer_dense_lead) {
+            cur = build_ffn(cur,
+                    model.layers[il].ffn_up, NULL, NULL,
+                    model.layers[il].ffn_gate, NULL, NULL,
+                    model.layers[il].ffn_down, NULL, NULL,
+                    NULL, LLM_FFN_SILU, LLM_FFN_PAR, il);
+            cb(cur, "ffn_out", il);
+        } else {
+            // MoE branch
+            ggml_tensor * moe_out = build_moe_ffn(cur,
+                model.layers[il].ffn_gate_inp,
+                model.layers[il].ffn_up_exps,
+                model.layers[il].ffn_gate_exps,
+                model.layers[il].ffn_down_exps,
+                nullptr,
+                n_expert, n_expert_used,
+                LLM_FFN_SILU, false,
+                false, hparams.expert_weights_scale,
+                LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
+                il);
+            cb(moe_out, "ffn_moe_out", il);
+
+            // FFN shared expert
+            {
+                ggml_tensor * ffn_shexp =
+                    build_ffn(cur,
+                        model.layers[il].ffn_up_shexp, NULL, NULL,
+                        model.layers[il].ffn_gate_shexp, NULL, NULL,
+                        model.layers[il].ffn_down_shexp, NULL, NULL,
+                        NULL, LLM_FFN_SILU, LLM_FFN_PAR, il);
+                cb(ffn_shexp, "ffn_shexp", il);
+
+                cur = ggml_add(ctx0, moe_out, ffn_shexp);
+                cb(cur, "ffn_out", il);
+            }
+        }
+        cur = ggml_add(ctx0, cur, ffn_inp);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+    cur = inpL;
+
+    cur = build_norm(cur, model.output_norm, NULL, LLM_NORM_RMS, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
+
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/deepseek2.cpp b/src/models/deepseek2.cpp
new file mode 100644
index 00000000000..68f72f72bb6
--- /dev/null
+++ b/src/models/deepseek2.cpp
@@ -0,0 +1,236 @@
+#include "models.h"
+
+
+
+llm_build_deepseek2::llm_build_deepseek2(const llama_model & model, const llm_graph_params & params) :
+    llm_graph_context(params) {
+    bool is_lite = (hparams.n_layer == 27);
+
+    const bool is_mla = (hparams.n_embd_head_k_mla != 0 && hparams.n_embd_head_v_mla != 0);
+
+    // note: these are the actual head sizes you get when treating as MHA or after "decompression" using wv_b for MLA
+    const int64_t n_embd_head_k = is_mla ? hparams.n_embd_head_k_mla : hparams.n_embd_head_k;
+    const int64_t n_embd_head_v = is_mla ? hparams.n_embd_head_v_mla : hparams.n_embd_head_v;
+
+    const int64_t n_embd_head_qk_rope = hparams.n_rot;
+    const int64_t n_embd_head_qk_nope = n_embd_head_k - n_embd_head_qk_rope;
+
+    const uint32_t kv_lora_rank = hparams.n_lora_kv;
+
+    // We have to pre-scale kq_scale and attn_factor to make the YaRN RoPE work correctly.
+    // See https://github.com/ggerganov/llama.cpp/discussions/7416 for detailed explanation.
+    const float mscale      = attn_factor * (1.0f + hparams.rope_yarn_log_mul * logf(1.0f / freq_scale));
+    const float kq_scale    = 1.0f * mscale * mscale / sqrtf(float(n_embd_head_k));
+    const float attn_factor = 1.0f / (1.0f + 0.1f * logf(1.0f / freq_scale));
+
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+
+    // {n_embd, n_tokens}
+    inpL = build_inp_embd(model.tok_embd);
+
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
+
+    auto * inp_attn = build_attn_inp_kv();
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * inpSA = inpL;
+
+        // norm
+        cur = build_norm(inpL, model.layers[il].attn_norm, NULL, LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
+
+        // self_attention
+        {
+            ggml_tensor * q = NULL;
+            if (!is_lite) {
+                q = ggml_mul_mat(ctx0, model.layers[il].wq_a, cur);
+                cb(q, "q", il);
+
+                q = build_norm(q, model.layers[il].attn_q_a_norm, nullptr, LLM_NORM_RMS, il);
+                cb(q, "q", il);
+
+                q = ggml_mul_mat(ctx0, model.layers[il].wq_b, q);
+                cb(q, "q", il);
+            } else {
+                q = ggml_mul_mat(ctx0, model.layers[il].wq, cur);
+                cb(q, "q", il);
+            }
+            // split into {n_embd_head_qk_nope, n_head, n_tokens}
+            ggml_tensor * q_nope =
+                ggml_view_3d(ctx0, q, n_embd_head_qk_nope, n_head, n_tokens, ggml_row_size(q->type, n_embd_head_k),
+                             ggml_row_size(q->type, n_embd_head_k) * n_head, 0);
+            cb(q_nope, "q_nope", il);
+
+            // and {n_embd_head_qk_rope, n_head, n_tokens}
+            ggml_tensor * q_pe = ggml_view_3d(
+                ctx0, q, n_embd_head_qk_rope, n_head, n_tokens, ggml_row_size(q->type, n_embd_head_k),
+                ggml_row_size(q->type, n_embd_head_k) * n_head, ggml_row_size(q->type, n_embd_head_qk_nope));
+            cb(q_pe, "q_pe", il);
+
+            ggml_tensor * kv_cmpr_pe = ggml_mul_mat(ctx0, model.layers[il].wkv_a_mqa, cur);
+            cb(kv_cmpr_pe, "kv_cmpr_pe", il);
+
+            // split into {kv_lora_rank, n_tokens}
+            ggml_tensor * kv_cmpr =
+                ggml_view_2d(ctx0, kv_cmpr_pe, kv_lora_rank, n_tokens,
+                             ggml_row_size(kv_cmpr_pe->type, kv_lora_rank + n_embd_head_qk_rope), 0);
+            cb(kv_cmpr, "kv_cmpr", il);
+
+            // and {n_embd_head_qk_rope, 1, n_tokens}
+            ggml_tensor * k_pe = ggml_view_3d(ctx0, kv_cmpr_pe, n_embd_head_qk_rope, 1, n_tokens,
+                                              ggml_row_size(kv_cmpr_pe->type, kv_lora_rank + n_embd_head_qk_rope),
+                                              ggml_row_size(kv_cmpr_pe->type, kv_lora_rank + n_embd_head_qk_rope),
+                                              ggml_row_size(kv_cmpr_pe->type, kv_lora_rank));
+            cb(k_pe, "k_pe", il);
+
+            q_pe = ggml_rope_ext(ctx0, q_pe, inp_pos, nullptr, n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                                 ext_factor, attn_factor, beta_fast, beta_slow);
+            cb(q_pe, "q_pe", il);
+
+            k_pe = ggml_rope_ext(ctx0, k_pe, inp_pos, nullptr, n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                                 ext_factor, attn_factor, beta_fast, beta_slow);
+            cb(k_pe, "k_pe", il);
+
+            kv_cmpr = build_norm(kv_cmpr, model.layers[il].attn_kv_a_norm, nullptr, LLM_NORM_RMS, il);
+            cb(kv_cmpr, "kv_cmpr", il);
+
+            if (is_mla) {
+                // {n_embd_head_qk_nope, n_tokens, n_head}
+                q_nope = ggml_permute(ctx0, q_nope, 0, 2, 1, 3);
+                cb(q_nope, "q_nope_perm", il);
+
+                // {n_embd_head_qk_nope, kv_lora_rank, n_head} x {n_embd_head_qk_nope, n_tokens, n_head}
+                ggml_tensor * q_nope_absorbed = ggml_mul_mat(ctx0, model.layers[il].wk_b, q_nope);
+                cb(q_nope_absorbed, "q_nope_absorbed", il);
+
+                // {kv_lora_rank, n_head, n_tokens}
+                q_nope_absorbed = ggml_permute(ctx0, q_nope_absorbed, 0, 2, 1, 3);
+                cb(q_nope_absorbed, "q_nope_absorbed_perm", il);
+
+                // {n_embd_head_qk_rope + kv_lora_rank, n_head, n_tokens}
+                // note: rope must go first for in-place context shifting in build_rope_shift()
+                ggml_tensor * Qcur = ggml_concat(ctx0, q_pe, q_nope_absorbed, 0);
+                cb(Qcur, "Qcur", il);
+
+                kv_cmpr = ggml_reshape_3d(ctx0, kv_cmpr, kv_lora_rank, 1, n_tokens);
+                cb(kv_cmpr, "kv_cmpr_reshape", il);
+
+                // {n_embd_head_qk_rope + kv_lora_rank, 1, n_tokens}
+                ggml_tensor * Kcur = ggml_concat(ctx0, k_pe, kv_cmpr, 0);
+                cb(Kcur, "Kcur", il);
+
+                // {kv_lora_rank, 1, n_tokens}
+                ggml_tensor * Vcur = kv_cmpr;
+                cb(Vcur, "Vcur", il);
+
+                // note: MLA with the absorption optimzation converts into MQA (ie: GQA with 1 group)
+                cur = build_attn(inp_attn,
+                        model.layers[il].wo, NULL,
+                        Qcur, Kcur, Vcur, nullptr, nullptr, model.layers[il].wv_b, kq_scale, il);
+            } else {
+                ggml_tensor * kv = ggml_mul_mat(ctx0, model.layers[il].wkv_b, kv_cmpr);
+                cb(kv, "kv", il);
+
+                // split into {n_embd_head_qk_nope, n_head, n_tokens}
+                ggml_tensor * k_nope =
+                    ggml_view_3d(ctx0, kv, n_embd_head_qk_nope, n_head, n_tokens,
+                                 ggml_row_size(kv->type, n_embd_head_qk_nope + n_embd_head_v),
+                                 ggml_row_size(kv->type, n_embd_head_qk_nope + n_embd_head_v) * n_head, 0);
+                cb(k_nope, "k_nope_view", il);
+
+                // and {n_embd_head_v, n_head, n_tokens}
+                ggml_tensor * Vcur = ggml_view_3d(ctx0, kv, n_embd_head_v, n_head, n_tokens,
+                                                  ggml_row_size(kv->type, n_embd_head_qk_nope + n_embd_head_v),
+                                                  ggml_row_size(kv->type, n_embd_head_qk_nope + n_embd_head_v) * n_head,
+                                                  ggml_row_size(kv->type, n_embd_head_qk_nope));
+                cb(Vcur, "Vcur_view", il);
+
+                Vcur = ggml_cont(ctx0, Vcur);
+                cb(Vcur, "Vcur_cont", il);
+
+                // note: rope must go first for in-place context shifting in build_rope_shift()
+                ggml_tensor * Qcur = ggml_concat(ctx0, q_pe, q_nope, 0);
+                cb(Qcur, "Qcur", il);
+
+                ggml_tensor * Kcur = ggml_concat(ctx0, ggml_repeat(ctx0, k_pe, q_pe), k_nope, 0);
+                cb(Kcur, "Kcur", il);
+
+                // note: MLA without the absorption optimization converts into MHA (ie: GQA with full n_head groups)
+                cur = build_attn(inp_attn,
+                            model.layers[il].wo, NULL,
+                            Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, kq_scale, il);
+            }
+        }
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0, cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+        }
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+        cb(ffn_inp, "ffn_inp", il);
+
+        cur = build_norm(ffn_inp, model.layers[il].ffn_norm, NULL, LLM_NORM_RMS, il);
+        cb(cur, "ffn_norm", il);
+
+        if ((uint32_t) il < hparams.n_layer_dense_lead) {
+            cur = build_ffn(cur,
+                model.layers[il].ffn_up, NULL, NULL,
+                model.layers[il].ffn_gate, NULL, NULL,
+                model.layers[il].ffn_down, NULL, NULL,
+                NULL, LLM_FFN_SILU, LLM_FFN_PAR, il);
+            cb(cur, "ffn_out", il);
+        } else {
+            // MoE branch
+            ggml_tensor * moe_out = build_moe_ffn(cur,
+                model.layers[il].ffn_gate_inp,
+                model.layers[il].ffn_up_exps,
+                model.layers[il].ffn_gate_exps,
+                model.layers[il].ffn_down_exps,
+                model.layers[il].ffn_exp_probs_b,
+                n_expert, n_expert_used,
+                LLM_FFN_SILU, hparams.expert_weights_norm,
+                true, hparams.expert_weights_scale,
+                (llama_expert_gating_func_type) hparams.expert_gating_func,
+                il);
+            cb(moe_out, "ffn_moe_out", il);
+
+            // FFN shared expert
+            {
+                ggml_tensor * ffn_shexp =
+                    build_ffn(cur,
+                        model.layers[il].ffn_up_shexp, NULL, NULL,
+                        model.layers[il].ffn_gate_shexp, NULL, NULL,
+                        model.layers[il].ffn_down_shexp, NULL, NULL,
+                        NULL, LLM_FFN_SILU, LLM_FFN_PAR, il);
+                cb(ffn_shexp, "ffn_shexp", il);
+
+                cur = ggml_add(ctx0, moe_out, ffn_shexp);
+                cb(cur, "ffn_out", il);
+            }
+        }
+        cur = ggml_add(ctx0, cur, ffn_inp);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+    cur = inpL;
+
+    cur = build_norm(cur, model.output_norm, NULL, LLM_NORM_RMS, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    // lm_head
+    cur = ggml_mul_mat(ctx0, model.output, cur);
+
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/dots1.cpp b/src/models/dots1.cpp
new file mode 100644
index 00000000000..09c36f82fe2
--- /dev/null
+++ b/src/models/dots1.cpp
@@ -0,0 +1,134 @@
+#include "models.h"
+
+
+
+llm_build_dots1::llm_build_dots1(const llama_model & model, const llm_graph_params & params) :
+    llm_graph_context(params) {
+    const int64_t n_embd_head = hparams.n_embd_head_v;
+
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+    GGML_ASSERT(n_embd_head == hparams.n_rot);
+
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+
+    inpL = build_inp_embd(model.tok_embd);
+
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
+
+    auto * inp_attn = build_attn_inp_kv();
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * inpSA = inpL;
+
+        // norm
+        cur = build_norm(inpL, model.layers[il].attn_norm, NULL, LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
+
+        // self_attention
+        {
+            // compute Q and K and RoPE them
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            cb(Qcur, "Qcur", il);
+
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            cb(Kcur, "Kcur", il);
+
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            cb(Vcur, "Vcur", il);
+
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head, n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+            Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL, LLM_NORM_RMS, il);
+            cb(Qcur, "Qcur_normed", il);
+
+            Qcur = ggml_rope_ext(ctx0, Qcur, inp_pos, nullptr, n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                                 ext_factor, attn_factor, beta_fast, beta_slow);
+
+            Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, NULL, LLM_NORM_RMS, il);
+            cb(Kcur, "Kcur_normed", il);
+
+            Kcur = ggml_rope_ext(ctx0, Kcur, inp_pos, nullptr, n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                                 ext_factor, attn_factor, beta_fast, beta_slow);
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, model.layers[il].bo,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f / sqrtf(float(n_embd_head)), il);
+        }
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0, cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+        }
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+        cb(ffn_inp, "ffn_inp", il);
+
+        // MoE branch
+        cur = build_norm(ffn_inp, model.layers[il].ffn_norm, NULL, LLM_NORM_RMS, il);
+        cb(cur, "ffn_norm", il);
+
+        if ((uint32_t) il < hparams.n_layer_dense_lead) {
+            cur = build_ffn(cur,
+                    model.layers[il].ffn_up, NULL, NULL,
+                    model.layers[il].ffn_gate, NULL, NULL,
+                    model.layers[il].ffn_down, NULL, NULL,
+                    NULL, LLM_FFN_SILU, LLM_FFN_PAR, il);
+            cb(cur, "ffn_out", il);
+        } else {
+            ggml_tensor * moe_out = build_moe_ffn(cur,
+                model.layers[il].ffn_gate_inp,
+                model.layers[il].ffn_up_exps,
+                model.layers[il].ffn_gate_exps,
+                model.layers[il].ffn_down_exps,
+                model.layers[il].ffn_exp_probs_b,
+                n_expert, n_expert_used,
+                LLM_FFN_SILU, hparams.expert_weights_norm,
+                true, hparams.expert_weights_scale,
+                (llama_expert_gating_func_type) hparams.expert_gating_func,
+                il);
+            cb(moe_out, "ffn_moe_out", il);
+
+            {
+                ggml_tensor * ffn_shexp =
+                    build_ffn(cur,
+                        model.layers[il].ffn_up_shexp, NULL, NULL,
+                        model.layers[il].ffn_gate_shexp, NULL, NULL,
+                        model.layers[il].ffn_down_shexp, NULL, NULL,
+                        NULL, LLM_FFN_SILU, LLM_FFN_PAR, il);
+                cb(ffn_shexp, "ffn_shexp", il);
+
+                cur = ggml_add(ctx0, moe_out, ffn_shexp);
+                cb(cur, "ffn_out", il);
+            }
+        }
+        cur = ggml_add(ctx0, cur, ffn_inp);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+    cur = inpL;
+
+    cur = build_norm(cur, model.output_norm, NULL, LLM_NORM_RMS, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
+
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/dream.cpp b/src/models/dream.cpp
new file mode 100644
index 00000000000..2aafbae1397
--- /dev/null
+++ b/src/models/dream.cpp
@@ -0,0 +1,105 @@
+#include "models.h"
+
+
+
+llm_build_dream::llm_build_dream(const llama_model & model, const llm_graph_params & params) :
+    llm_graph_context(params) {
+    //copied from qwen2
+    const int64_t n_embd_head = hparams.n_embd_head_v;
+
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+    GGML_ASSERT(n_embd_head == hparams.n_rot);
+
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+
+    inpL = build_inp_embd(model.tok_embd);
+
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
+
+    auto * inp_attn = build_attn_inp_no_cache();
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * inpSA = inpL;
+
+        // norm
+        cur = build_norm(inpL, model.layers[il].attn_norm, NULL, LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
+
+        // self-attention
+        {
+            // compute Q and K and RoPE them
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            Qcur               = ggml_add(ctx0, Qcur, model.layers[il].bq);
+            cb(Qcur, "Qcur", il);
+
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            Kcur               = ggml_add(ctx0, Kcur, model.layers[il].bk);
+            cb(Kcur, "Kcur", il);
+
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            Vcur               = ggml_add(ctx0, Vcur, model.layers[il].bv);
+            cb(Vcur, "Vcur", il);
+
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head, n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+            Qcur = ggml_rope_ext(ctx0, Qcur, inp_pos, nullptr, n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                                 ext_factor, attn_factor, beta_fast, beta_slow);
+
+            Kcur = ggml_rope_ext(ctx0, Kcur, inp_pos, nullptr, n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                                 ext_factor, attn_factor, beta_fast, beta_slow);
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, model.layers[il].bo,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f / sqrtf(float(n_embd_head)), il);
+        }
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0, cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+        }
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+        cb(ffn_inp, "ffn_inp", il);
+
+        // feed-forward network
+        cur = build_norm(ffn_inp, model.layers[il].ffn_norm, NULL, LLM_NORM_RMS, il);
+        cb(cur, "ffn_norm", il);
+
+        cur = build_ffn(cur,
+            model.layers[il].ffn_up, NULL, NULL,
+            model.layers[il].ffn_gate, NULL, NULL,
+            model.layers[il].ffn_down, NULL, NULL,
+            NULL, LLM_FFN_SILU, LLM_FFN_PAR, il);
+        cb(cur, "ffn_out", il);
+
+        cur = ggml_add(ctx0, cur, ffn_inp);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+    cur = inpL;
+
+    cur = build_norm(cur, model.output_norm, NULL, LLM_NORM_RMS, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
+
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/ernie4-5-moe.cpp b/src/models/ernie4-5-moe.cpp
new file mode 100644
index 00000000000..0d96d14e6fd
--- /dev/null
+++ b/src/models/ernie4-5-moe.cpp
@@ -0,0 +1,150 @@
+#include "models.h"
+
+
+
+llm_build_ernie4_5_moe::llm_build_ernie4_5_moe(const llama_model & model, const llm_graph_params & params) :
+    llm_graph_context(params) {
+    const int64_t n_embd_head = hparams.n_embd_head_v;
+
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+    GGML_ASSERT(n_embd_head == hparams.n_rot);
+
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+
+    inpL = build_inp_embd(model.tok_embd);
+
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
+
+    auto * inp_attn = build_attn_inp_kv();
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    GGML_ASSERT(hparams.n_moe_layer_step > 0 && "Ernie 4.5 MoE requires n_moe_layer_step > 0");
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * inpSA = inpL;
+        // norm
+        {
+            cur = build_norm(inpL, model.layers[il].attn_norm, NULL, LLM_NORM_RMS, il);
+            cb(cur, "attn_norm", il);
+        }
+        // self-attention
+        {
+            // compute Q and K and RoPE them
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            cb(Qcur, "Qcur", il);
+            if (model.layers[il].bq) {
+                Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
+                cb(Qcur, "Qcur", il);
+            }
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            cb(Kcur, "Kcur", il);
+            if (model.layers[il].bk) {
+                Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
+                cb(Kcur, "Kcur", il);
+            }
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            cb(Vcur, "Vcur", il);
+            if (model.layers[il].bv) {
+                Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
+                cb(Vcur, "Vcur", il);
+            }
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head, n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+            Qcur = ggml_rope_ext(ctx0, Qcur, inp_pos, nullptr, n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                                 ext_factor, attn_factor, beta_fast, beta_slow);
+
+            Kcur = ggml_rope_ext(ctx0, Kcur, inp_pos, nullptr, n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                                 ext_factor, attn_factor, beta_fast, beta_slow);
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, NULL,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f / sqrtf(float(n_embd_head)), il);
+            cb(cur, "attn_out", il);
+        }
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0, cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+        }
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+        cb(ffn_inp, "ffn_inp", il);
+
+        // feed-forward network
+        bool is_moe_layer =
+            static_cast<uint32_t>(il) >= hparams.n_layer_dense_lead && (il + 1) % hparams.n_moe_layer_step == 0;
+
+        if (!is_moe_layer) {
+            cur = build_norm(ffn_inp, model.layers[il].ffn_norm, NULL, LLM_NORM_RMS, il);
+            cb(cur, "ffn_norm", il);
+
+            cur = build_ffn(cur,
+                    model.layers[il].ffn_up, NULL, NULL,
+                    model.layers[il].ffn_gate, NULL, NULL,
+                    model.layers[il].ffn_down, NULL, NULL,
+                    NULL, LLM_FFN_SILU, LLM_FFN_PAR, il);
+            cb(cur, "ffn_out", il);
+        } else {
+            // MoE branch
+            cur = build_norm(ffn_inp, model.layers[il].ffn_norm, NULL, LLM_NORM_RMS, il);
+            cb(cur, "ffn_norm", il);
+
+            ggml_tensor * moe_out = build_moe_ffn(cur,
+                                        model.layers[il].ffn_gate_inp,
+                                        model.layers[il].ffn_up_exps,
+                                        model.layers[il].ffn_gate_exps,
+                                        model.layers[il].ffn_down_exps,
+                                        model.layers[il].ffn_exp_probs_b,
+                                        n_expert, n_expert_used,
+                                        LLM_FFN_SILU, true,
+                                        false, 0.0,
+                                        LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
+                                        il);
+            cb(moe_out, "ffn_moe_out", il);
+
+            // Shared expert (if present)
+            if (hparams.n_ff_shexp > 0) {
+                ggml_tensor * ffn_shexp =
+                    build_ffn(cur,
+                        model.layers[il].ffn_up_shexp, NULL, NULL,
+                        model.layers[il].ffn_gate_shexp, NULL, NULL,
+                        model.layers[il].ffn_down_shexp, NULL, NULL,
+                        NULL, LLM_FFN_SILU, LLM_FFN_PAR, il);
+                cb(ffn_shexp, "ffn_shexp", il);
+
+                cur = ggml_add(ctx0, moe_out, ffn_shexp);
+            } else {
+                cur = moe_out;
+            }
+            cb(cur, "ffn_out", il);
+        }
+        cur = ggml_add(ctx0, cur, ffn_inp);
+        cb(cur, "ffn_out", il);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+    cur = inpL;
+
+    cur = build_norm(cur, model.output_norm, NULL, LLM_NORM_RMS, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
+
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/ernie4-5.cpp b/src/models/ernie4-5.cpp
new file mode 100644
index 00000000000..99962af111f
--- /dev/null
+++ b/src/models/ernie4-5.cpp
@@ -0,0 +1,111 @@
+#include "models.h"
+
+
+
+llm_build_ernie4_5::llm_build_ernie4_5(const llama_model & model, const llm_graph_params & params) :
+    llm_graph_context(params) {
+    const int64_t n_embd_head = hparams.n_embd_head_v;
+
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+    GGML_ASSERT(n_embd_head == hparams.n_rot);
+
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+
+    inpL = build_inp_embd(model.tok_embd);
+
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
+
+    auto * inp_attn = build_attn_inp_kv();
+
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * inpSA = inpL;
+
+        // norm
+        {
+            cur = build_norm(inpL, model.layers[il].attn_norm, NULL, LLM_NORM_RMS, il);
+            cb(cur, "attn_norm", il);
+        }
+        // self-attention
+        {
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            cb(Qcur, "Qcur", il);
+            if (model.layers[il].bq) {
+                Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
+                cb(Qcur, "Qcur", il);
+            }
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            cb(Kcur, "Kcur", il);
+            if (model.layers[il].bk) {
+                Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
+                cb(Kcur, "Kcur", il);
+            }
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            cb(Vcur, "Vcur", il);
+            if (model.layers[il].bv) {
+                Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
+                cb(Vcur, "Vcur", il);
+            }
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head, n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+            Qcur = ggml_rope_ext(ctx0, Qcur, inp_pos, nullptr, n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                                 ext_factor, attn_factor, beta_fast, beta_slow);
+
+            Kcur = ggml_rope_ext(ctx0, Kcur, inp_pos, nullptr, n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                                 ext_factor, attn_factor, beta_fast, beta_slow);
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, NULL,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f / sqrtf(float(n_embd_head)), il);
+        }
+        if (il == n_layer - 1) {
+            // skip computing output for unused tokens
+            ggml_tensor * inp_out_ids = build_inp_out_ids();
+            cur                       = ggml_get_rows(ctx0, cur, inp_out_ids);
+            inpSA                     = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+        }
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+        cb(ffn_inp, "ffn_inp", il);
+
+        // feed-forward network
+        {
+            cur = build_norm(ffn_inp, model.layers[il].ffn_norm, NULL, LLM_NORM_RMS, il);
+            cb(cur, "ffn_norm", il);
+
+            cur = build_ffn(cur,
+                    model.layers[il].ffn_up, NULL, NULL,
+                    model.layers[il].ffn_gate, NULL, NULL,
+                    model.layers[il].ffn_down, NULL, NULL,
+                    NULL, LLM_FFN_SILU, LLM_FFN_PAR, il);
+            cb(cur, "ffn_out", il);
+        }
+        cur = ggml_add(ctx0, cur, ffn_inp);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+    cur = inpL;
+
+    cur = build_norm(cur, model.output_norm, NULL, LLM_NORM_RMS, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
+
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/exaone.cpp b/src/models/exaone.cpp
new file mode 100644
index 00000000000..62602b284de
--- /dev/null
+++ b/src/models/exaone.cpp
@@ -0,0 +1,114 @@
+#include "models.h"
+
+
+
+llm_build_exaone::llm_build_exaone(const llama_model & model, const llm_graph_params & params) :
+    llm_graph_context(params) {
+    const int64_t n_embd_head = hparams.n_embd_head_v;
+
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+    GGML_ASSERT(n_embd_head == hparams.n_rot);
+
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+
+    inpL = build_inp_embd(model.tok_embd);
+
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
+
+    auto * inp_attn = build_attn_inp_kv();
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * inpSA = inpL;
+
+        // norm
+        cur = build_norm(inpL, model.layers[il].attn_norm, NULL, LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
+
+        // self-attention
+        {
+            // rope freq factors for llama3; may return nullptr for llama2 and other models
+            ggml_tensor * rope_factors = model.get_rope_factors(cparams, il);
+
+            // compute Q and K and RoPE them
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            cb(Qcur, "Qcur", il);
+            if (model.layers[il].bq) {
+                Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
+                cb(Qcur, "Qcur", il);
+            }
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            cb(Kcur, "Kcur", il);
+            if (model.layers[il].bk) {
+                Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
+                cb(Kcur, "Kcur", il);
+            }
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            cb(Vcur, "Vcur", il);
+            if (model.layers[il].bv) {
+                Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
+                cb(Vcur, "Vcur", il);
+            }
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head, n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+            Qcur = ggml_rope_ext(ctx0, Qcur, inp_pos, rope_factors, n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                                 ext_factor, attn_factor, beta_fast, beta_slow);
+
+            Kcur = ggml_rope_ext(ctx0, Kcur, inp_pos, rope_factors, n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                                 ext_factor, attn_factor, beta_fast, beta_slow);
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, model.layers[il].bo,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f / sqrtf(float(n_embd_head)), il);
+        }
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0, cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+        }
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+        cb(ffn_inp, "ffn_inp", il);
+
+        // feed-forward network
+        cur = build_norm(ffn_inp, model.layers[il].ffn_norm, NULL, LLM_NORM_RMS, il);
+        cb(cur, "ffn_norm", il);
+
+        cur = build_ffn(cur,
+                model.layers[il].ffn_up, NULL, NULL,
+                model.layers[il].ffn_gate, NULL, NULL,
+                model.layers[il].ffn_down, NULL, NULL,
+                NULL, LLM_FFN_SILU, LLM_FFN_PAR, il);
+        cb(cur, "ffn_out", il);
+
+        cur = ggml_add(ctx0, cur, ffn_inp);
+        cb(cur, "ffn_out", il);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+    cur = inpL;
+
+    cur = build_norm(cur, model.output_norm, NULL, LLM_NORM_RMS, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
+
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/exaone4.cpp b/src/models/exaone4.cpp
new file mode 100644
index 00000000000..8b7e3dc06e5
--- /dev/null
+++ b/src/models/exaone4.cpp
@@ -0,0 +1,123 @@
+#include "models.h"
+
+
+template <bool iswa>
+llm_build_exaone4<iswa>::llm_build_exaone4(const llama_model & model, const llm_graph_params & params) :
+    llm_graph_context(params) {
+    const int64_t n_embd_head = hparams.n_embd_head_k;
+
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_v);
+    GGML_ASSERT(n_embd_head == hparams.n_rot);
+
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+
+    inpL = build_inp_embd(model.tok_embd);
+
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
+
+    using inp_attn_type      = std::conditional_t<iswa, llm_graph_input_attn_kv_iswa, llm_graph_input_attn_kv>;
+    inp_attn_type * inp_attn = nullptr;
+
+    if constexpr (iswa) {
+        inp_attn = build_attn_inp_kv_iswa();
+    } else {
+        inp_attn = build_attn_inp_kv();
+    }
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * inpSA = inpL;
+
+        // use RoPE for SWA layers or non-SWA models
+        const bool use_rope = hparams.is_swa(il) || hparams.swa_type == LLAMA_SWA_TYPE_NONE;
+
+        cur = inpL;
+
+        // self-attention
+        {
+            ggml_tensor * rope_factors = model.get_rope_factors(cparams, il);
+
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            cb(Qcur, "Qcur", il);
+
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            cb(Kcur, "Kcur", il);
+
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            cb(Vcur, "Vcur", il);
+
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head, n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+            Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL, LLM_NORM_RMS, il);
+            Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, NULL, LLM_NORM_RMS, il);
+            cb(Qcur, "Qcur_normed", il);
+            cb(Kcur, "Kcur_normed", il);
+
+            if (use_rope) {
+                Qcur = ggml_rope_ext(ctx0, Qcur, inp_pos, rope_factors, n_rot, rope_type, n_ctx_orig, freq_base,
+                                     freq_scale, ext_factor, attn_factor, beta_fast, beta_slow);
+
+                Kcur = ggml_rope_ext(ctx0, Kcur, inp_pos, rope_factors, n_rot, rope_type, n_ctx_orig, freq_base,
+                                     freq_scale, ext_factor, attn_factor, beta_fast, beta_slow);
+            }
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, NULL,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f / sqrtf(float(n_embd_head)), il);
+            cb(cur, "attn_out", il);
+        }
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0, cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+        }
+        cur = build_norm(cur, model.layers[il].attn_post_norm, NULL, LLM_NORM_RMS, il);
+        cb(cur, "attn_post_norm", il);
+
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+        cb(ffn_inp, "ffn_inp", il);
+
+        // feed-forward network
+        cur = build_ffn(ffn_inp,
+                model.layers[il].ffn_up, NULL, NULL,
+                model.layers[il].ffn_gate, NULL, NULL,
+                model.layers[il].ffn_down, NULL, NULL, NULL,
+                LLM_FFN_SILU, LLM_FFN_PAR, il);
+        cb(cur, "ffn_out", il);
+
+        cur = build_norm(cur, model.layers[il].ffn_post_norm, NULL, LLM_NORM_RMS, -1);
+        cb(cur, "ffn_post_norm", -1);
+
+        cur = ggml_add(ctx0, cur, ffn_inp);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+    cur = inpL;
+
+    cur = build_norm(cur, model.output_norm, NULL, LLM_NORM_RMS, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
+
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}
+
+// Explicit template instantiations
+template struct llm_build_exaone4<false>;
+template struct llm_build_exaone4<true>;
diff --git a/src/models/falcon-h1.cpp b/src/models/falcon-h1.cpp
new file mode 100644
index 00000000000..b641a094079
--- /dev/null
+++ b/src/models/falcon-h1.cpp
@@ -0,0 +1,113 @@
+#include "models.h"
+
+
+
+llm_build_falcon_h1::llm_build_falcon_h1(const llama_model & model, const llm_graph_params & params) :
+    llm_graph_context_mamba(params) {
+    const int64_t n_embd_head = hparams.n_embd_head_v;
+
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+
+    inpL = build_inp_embd(model.tok_embd);
+
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
+
+    // Build the inputs in the recurrent & kv cache
+    auto * inp = build_inp_mem_hybrid();
+
+    const float kq_scale =
+        hparams.f_attention_scale == 0.0f ? 1.0f / sqrtf(float(n_embd_head)) : hparams.f_attention_scale;
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * inpSA = inpL;
+
+        cur = build_norm(inpL, model.layers[il].attn_norm, NULL, LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
+
+        // self-attention
+        ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+        cb(Qcur, "Qcur", il);
+
+        ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+        cb(Kcur, "Kcur", il);
+
+        ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+        cb(Vcur, "Vcur", il);
+
+        Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head, n_tokens);
+        Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+
+        Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+        Qcur = ggml_rope_ext(ctx0, Qcur, inp_pos, nullptr, n_rot, hparams.rope_type, n_ctx_orig, freq_base, freq_scale,
+                             ext_factor, attn_factor, beta_fast, beta_slow);
+
+        Kcur = ggml_rope_ext(ctx0, Kcur, inp_pos, nullptr, n_rot, hparams.rope_type, n_ctx_orig, freq_base, freq_scale,
+                             ext_factor, attn_factor, beta_fast, beta_slow);
+
+        cb(Qcur, "Qcur-post-rope", il);
+        cb(Kcur, "Kcur-post-rope", il);
+        cb(Vcur, "Vcur-post-rope", il);
+
+        ggml_tensor * attn_out = build_attn(inp->get_attn(),
+                                    model.layers[il].wo, NULL,
+                                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, kq_scale, il);
+        cb(attn_out, "attn_out", il);
+
+        cur = build_norm(inpL, model.layers[il].attn_norm, NULL, LLM_NORM_RMS, il);
+        // Mamba2 layer
+        cb(cur, "ssm_in", il);
+
+        ggml_tensor * ssm_out = build_mamba2_layer(inp->get_recr(), cur, model, ubatch, il);
+        cb(ssm_out, "ssm_out", il);
+
+        // // Aggregation
+        cur   = ggml_add(ctx0, attn_out, ssm_out);
+        inpSA = ggml_add(ctx0, cur, inpSA);
+        cb(cur, "layer_out", il);
+
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0, cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+        }
+        ggml_tensor * ffn_inp = inpSA;
+        cb(ffn_inp, "ffn_inp", il);
+
+        // feed-forward network
+        cur = build_norm(ffn_inp, model.layers[il].ffn_norm, NULL, LLM_NORM_RMS, il);
+        cb(cur, "ffn_norm", il);
+
+        cur = build_ffn(cur,
+                model.layers[il].ffn_up, model.layers[il].ffn_up_b, NULL,
+                model.layers[il].ffn_gate, model.layers[il].ffn_gate_b, NULL,
+                model.layers[il].ffn_down, model.layers[il].ffn_down_b, NULL,
+                NULL, LLM_FFN_SILU, LLM_FFN_PAR, il);
+        cb(cur, "ffn_out", il);
+
+        cur = ggml_add(ctx0, cur, inpSA);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+    cur = inpL;
+
+    cur = build_norm(cur, model.output_norm, NULL, LLM_NORM_RMS, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
+
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/falcon.cpp b/src/models/falcon.cpp
new file mode 100644
index 00000000000..db1ccdb5008
--- /dev/null
+++ b/src/models/falcon.cpp
@@ -0,0 +1,120 @@
+#include "models.h"
+
+
+llm_build_falcon::llm_build_falcon(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+    const int64_t n_embd_head = hparams.n_embd_head_v;
+    const int64_t n_embd_gqa  = hparams.n_embd_v_gqa();
+
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+    GGML_ASSERT(n_embd_head == hparams.n_rot);
+
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+
+    inpL = build_inp_embd(model.tok_embd);
+
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
+
+    auto * inp_attn = build_attn_inp_kv();
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * attn_norm;
+
+        attn_norm = build_norm(inpL,
+                model.layers[il].attn_norm,
+                model.layers[il].attn_norm_b,
+                LLM_NORM, il);
+        cb(attn_norm, "attn_norm", il);
+
+        // self-attention
+        {
+            if (model.layers[il].attn_norm_2) {
+                // Falcon-40B
+                cur = build_norm(inpL,
+                        model.layers[il].attn_norm_2,
+                        model.layers[il].attn_norm_2_b,
+                        LLM_NORM, il);
+                cb(cur, "attn_norm_2", il);
+            } else {
+                cur = attn_norm;
+            }
+
+            cur = build_lora_mm(model.layers[il].wqkv, cur);
+            cb(cur, "wqkv", il);
+
+            ggml_tensor * Qcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head,    n_tokens, n_embd_head*sizeof(float), cur->nb[1], 0*sizeof(float)*(n_embd));
+            ggml_tensor * Kcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd));
+            ggml_tensor * Vcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd + n_embd_gqa));
+
+            // using mode = 2 for neox mode
+            Qcur = ggml_rope_ext(
+                    ctx0, Qcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            Kcur = ggml_rope_ext(
+                    ctx0, Kcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, NULL,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+        }
+
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur       = ggml_get_rows(ctx0,       cur, inp_out_ids);
+            inpL      = ggml_get_rows(ctx0,      inpL, inp_out_ids);
+            attn_norm = ggml_get_rows(ctx0, attn_norm, inp_out_ids);
+        }
+
+        ggml_tensor * ffn_inp = cur;
+
+        // feed forward
+        {
+            cur = build_ffn(attn_norm, // !! use the attn norm, not the result
+                    model.layers[il].ffn_up,   NULL, NULL,
+                    NULL,                      NULL, NULL,
+                    model.layers[il].ffn_down, NULL, NULL,
+                    NULL,
+                    LLM_FFN_GELU, LLM_FFN_SEQ, il);
+            cb(cur, "ffn_out", il);
+        }
+
+        cur = ggml_add(ctx0, cur, ffn_inp);
+        cur = ggml_add(ctx0, cur, inpL);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+
+    cur = inpL;
+
+    // norm
+    cur = build_norm(cur,
+            model.output_norm,
+            model.output_norm_b,
+            LLM_NORM, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    cur = build_lora_mm(model.output, cur);
+
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/gemma-embedding.cpp b/src/models/gemma-embedding.cpp
new file mode 100644
index 00000000000..90a98f7abf0
--- /dev/null
+++ b/src/models/gemma-embedding.cpp
@@ -0,0 +1,120 @@
+#include "models.h"
+
+
+
+llm_build_gemma_embedding::llm_build_gemma_embedding(const llama_model & model, const llm_graph_params & params) :
+    llm_graph_context(params) {
+    const int64_t n_embd_head = hparams.n_embd_head_k;
+
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+
+    inpL = build_inp_embd(model.tok_embd);
+
+    // important: do not normalize weights for raw embeddings input (i.e. encoded image emdeddings)
+    if (ubatch.token) {
+        inpL = ggml_scale(ctx0, inpL, sqrtf(n_embd));
+        cb(inpL, "inp_scaled", -1);
+    }
+
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
+
+    auto * inp_attn = build_attn_inp_no_cache();
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        const float freq_base_l  = model.get_rope_freq_base(cparams, il);
+        const float freq_scale_l = model.get_rope_freq_scale(cparams, il);
+
+        // norm
+        cur = build_norm(inpL, model.layers[il].attn_norm, NULL, LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
+
+        // self-attention
+        {
+            // compute Q and K and RoPE them
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            cb(Qcur, "Qcur", il);
+
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            cb(Kcur, "Kcur", il);
+
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            cb(Vcur, "Vcur", il);
+
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head, n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+            Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL, LLM_NORM_RMS, il);
+            cb(Qcur, "Qcur_normed", il);
+
+            Qcur = ggml_rope_ext(ctx0, Qcur, inp_pos, nullptr, n_rot, rope_type, n_ctx_orig, freq_base_l, freq_scale_l,
+                                 ext_factor, attn_factor, beta_fast, beta_slow);
+
+            Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, NULL, LLM_NORM_RMS, il);
+            cb(Kcur, "Kcur_normed", il);
+
+            Kcur = ggml_rope_ext(ctx0, Kcur, inp_pos, nullptr, n_rot, rope_type, n_ctx_orig, freq_base_l, freq_scale_l,
+                                 ext_factor, attn_factor, beta_fast, beta_slow);
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            // ref: https://github.com/google/gemma_pytorch/blob/014acb7ac4563a5f77c76d7ff98f31b568c16508/gemma/model.py#L315
+            Qcur = ggml_scale(ctx0, Qcur, hparams.f_attention_scale);
+
+            cur =
+                build_attn(inp_attn,
+                    model.layers[il].wo, NULL,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f, il);
+        }
+
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur  = ggml_get_rows(ctx0, cur, inp_out_ids);
+            inpL = ggml_get_rows(ctx0, inpL, inp_out_ids);
+        }
+
+        cur = build_norm(cur, model.layers[il].attn_post_norm, NULL, LLM_NORM_RMS, il);
+        cb(cur, "attn_post_norm", il);
+
+        ggml_tensor * sa_out = ggml_add(ctx0, cur, inpL);
+        cb(sa_out, "sa_out", il);
+
+        cur = build_norm(sa_out, model.layers[il].ffn_norm, NULL, LLM_NORM_RMS, il);
+        cb(cur, "ffn_norm", il);
+
+        // feed-forward network
+        {
+            cur = build_ffn(cur,
+                model.layers[il].ffn_up, NULL, NULL,
+                model.layers[il].ffn_gate, NULL, NULL,
+                model.layers[il].ffn_down, NULL, NULL,
+                NULL, LLM_FFN_GELU, LLM_FFN_PAR, il);
+            cb(cur, "ffn_out", il);
+        }
+
+        cur = build_norm(cur, model.layers[il].ffn_post_norm, NULL, LLM_NORM_RMS, -1);
+        cb(cur, "ffn_post_norm", -1);
+
+        cur = ggml_add(ctx0, cur, sa_out);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+
+    cur = inpL;
+
+    cur = build_norm(cur, model.output_norm, NULL, LLM_NORM_RMS, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/gemma.cpp b/src/models/gemma.cpp
new file mode 100644
index 00000000000..4893d9af4b8
--- /dev/null
+++ b/src/models/gemma.cpp
@@ -0,0 +1,112 @@
+#include "models.h"
+
+
+llm_build_gemma::llm_build_gemma(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+    const int64_t n_embd_head = hparams.n_embd_head_v;
+
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+
+    inpL = build_inp_embd(model.tok_embd);
+
+    inpL = ggml_scale(ctx0, inpL, sqrtf(n_embd));
+    cb(inpL, "inp_scaled", -1);
+
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
+
+    auto * inp_attn = build_attn_inp_kv();
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        // norm
+        cur = build_norm(inpL,
+                model.layers[il].attn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
+
+        // self-attention
+        {
+            // compute Q and K and RoPE them
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            cb(Qcur, "Qcur", il);
+
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            cb(Kcur, "Kcur", il);
+
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            cb(Vcur, "Vcur", il);
+
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+            Qcur = ggml_rope_ext(
+                    ctx0, Qcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow);
+
+            Kcur = ggml_rope_ext(
+                    ctx0, Kcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow);
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            Qcur = ggml_scale(ctx0, Qcur, 1.0f / sqrtf(float(n_embd_head)));
+            cb(Qcur, "Qcur_scaled", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, NULL,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f, il);
+        }
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur  = ggml_get_rows(ctx0,  cur, inp_out_ids);
+            inpL = ggml_get_rows(ctx0, inpL, inp_out_ids);
+        }
+        ggml_tensor * sa_out = ggml_add(ctx0, cur, inpL);
+        cb(sa_out, "sa_out", il);
+
+        cur = build_norm(sa_out,
+                model.layers[il].ffn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "ffn_norm", il);
+
+        // feed-forward network
+        {
+            cur = build_ffn(cur,
+                    model.layers[il].ffn_up,   NULL, NULL,
+                    model.layers[il].ffn_gate, NULL, NULL,
+                    model.layers[il].ffn_down, NULL, NULL,
+                    NULL,
+                    LLM_FFN_GELU, LLM_FFN_PAR, il);
+            cb(cur, "ffn_out", il);
+        }
+        cur = ggml_add(ctx0, cur, sa_out);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+    cur = inpL;
+
+    cur = build_norm(cur,
+            model.output_norm, NULL,
+            LLM_NORM_RMS, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
+
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/gemma2-iswa.cpp b/src/models/gemma2-iswa.cpp
new file mode 100644
index 00000000000..1f2b597c65e
--- /dev/null
+++ b/src/models/gemma2-iswa.cpp
@@ -0,0 +1,125 @@
+#include "models.h"
+
+llm_build_gemma2_iswa::llm_build_gemma2_iswa(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+        const int64_t n_embd_head = hparams.n_embd_head_k;
+
+        ggml_tensor * cur;
+        ggml_tensor * inpL;
+
+        inpL = build_inp_embd(model.tok_embd);
+
+        inpL = ggml_scale(ctx0, inpL, sqrtf(n_embd));
+        cb(inpL, "inp_scaled", -1);
+
+        // inp_pos - contains the positions
+        ggml_tensor * inp_pos = build_inp_pos();
+
+        auto * inp_attn = build_attn_inp_kv_iswa();
+
+        ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+        for (int il = 0; il < n_layer; ++il) {
+            // norm
+            cur = build_norm(inpL,
+                    model.layers[il].attn_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "attn_norm", il);
+
+            // self-attention
+            {
+                // compute Q and K and RoPE them
+                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+                cb(Qcur, "Qcur", il);
+
+                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+                cb(Kcur, "Kcur", il);
+
+                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+                cb(Vcur, "Vcur", il);
+
+                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+                Qcur = ggml_rope_ext(
+                        ctx0, Qcur, inp_pos, nullptr,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow);
+
+                Kcur = ggml_rope_ext(
+                        ctx0, Kcur, inp_pos, nullptr,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow);
+
+                cb(Qcur, "Qcur", il);
+                cb(Kcur, "Kcur", il);
+                cb(Vcur, "Vcur", il);
+
+                Qcur = ggml_scale(ctx0, Qcur, hparams.f_attention_scale);
+
+                cur = build_attn(inp_attn,
+                        model.layers[il].wo, NULL,
+                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f, il);
+            }
+            if (il == n_layer - 1 && inp_out_ids) {
+                cur  = ggml_get_rows(ctx0,  cur, inp_out_ids);
+                inpL = ggml_get_rows(ctx0, inpL, inp_out_ids);
+            }
+            cur = build_norm(cur,
+                    model.layers[il].attn_post_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "attn_post_norm", il);
+
+            ggml_tensor * sa_out = ggml_add(ctx0, cur, inpL);
+            cb(sa_out, "sa_out", il);
+
+            cur = build_norm(sa_out,
+                    model.layers[il].ffn_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "ffn_norm", il);
+
+            // feed-forward network
+            {
+                cur = build_ffn(cur,
+                        model.layers[il].ffn_up,   NULL, NULL,
+                        model.layers[il].ffn_gate, NULL, NULL,
+                        model.layers[il].ffn_down, NULL, NULL,
+                        NULL,
+                        LLM_FFN_GELU, LLM_FFN_PAR, il);
+                cb(cur, "ffn_out", il);
+            }
+            cur = build_norm(cur,
+                    model.layers[il].ffn_post_norm, NULL,
+                    LLM_NORM_RMS, -1);
+            cb(cur, "ffn_post_norm", -1);
+
+            cur = ggml_add(ctx0, cur, sa_out);
+
+            cur = build_cvec(cur, il);
+            cb(cur, "l_out", il);
+
+            // input for next layer
+            inpL = cur;
+        }
+        cur = inpL;
+
+        cur = build_norm(cur,
+                model.output_norm, NULL,
+                LLM_NORM_RMS, -1);
+
+        cb(cur, "result_norm", -1);
+        res->t_embd = cur;
+
+        // lm_head
+        cur = build_lora_mm(model.output, cur);
+
+        // final logit soft-capping
+        cur = ggml_scale(ctx0, cur, 1.0f / hparams.f_final_logit_softcapping);
+        cur = ggml_tanh(ctx0, cur);
+        cur = ggml_scale(ctx0, cur, hparams.f_final_logit_softcapping);
+
+        cb(cur, "result_output", -1);
+        res->t_logits = cur;
+
+        ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/gemma3-iswa.cpp b/src/models/gemma3-iswa.cpp
new file mode 100644
index 00000000000..84badc38f17
--- /dev/null
+++ b/src/models/gemma3-iswa.cpp
@@ -0,0 +1,131 @@
+#include "models.h"
+
+llm_build_gemma3_iswa::llm_build_gemma3_iswa(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+        const int64_t n_embd_head = hparams.n_embd_head_k;
+
+        ggml_tensor * cur;
+        ggml_tensor * inpL;
+
+        inpL = build_inp_embd(model.tok_embd);
+
+        // important: do not normalize weights for raw embeddings input (i.e. encoded image emdeddings)
+        if (ubatch.token) {
+            inpL = ggml_scale(ctx0, inpL, sqrtf(n_embd));
+            cb(inpL, "inp_scaled", -1);
+        }
+        // inp_pos - contains the positions
+        ggml_tensor * inp_pos = build_inp_pos();
+
+        // TODO: is causal == true correct? might need some changes
+        auto * inp_attn = build_attn_inp_kv_iswa();
+
+        ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+        for (int il = 0; il < n_layer; ++il) {
+            const float freq_base_l  = model.get_rope_freq_base (cparams, il);
+            const float freq_scale_l = model.get_rope_freq_scale(cparams, il);
+
+            // norm
+            cur = build_norm(inpL, model.layers[il].attn_norm, NULL, LLM_NORM_RMS, il);
+            cb(cur, "attn_norm", il);
+
+            // self-attention
+            {
+                // compute Q and K and RoPE them
+                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+                cb(Qcur, "Qcur", il);
+
+                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+                cb(Kcur, "Kcur", il);
+
+                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+                cb(Vcur, "Vcur", il);
+
+                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+                Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL, LLM_NORM_RMS, il);
+                cb(Qcur, "Qcur_normed", il);
+
+                Qcur = ggml_rope_ext(
+                        ctx0, Qcur, inp_pos, nullptr,
+                        n_rot, rope_type, n_ctx_orig, freq_base_l, freq_scale_l,
+                        ext_factor, attn_factor, beta_fast, beta_slow);
+
+                Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, NULL, LLM_NORM_RMS, il);
+                cb(Kcur, "Kcur_normed", il);
+
+                Kcur = ggml_rope_ext(
+                        ctx0, Kcur, inp_pos, nullptr,
+                        n_rot, rope_type, n_ctx_orig, freq_base_l, freq_scale_l,
+                        ext_factor, attn_factor, beta_fast, beta_slow);
+
+                cb(Qcur, "Qcur", il);
+                cb(Kcur, "Kcur", il);
+                cb(Vcur, "Vcur", il);
+
+                // ref: https://github.com/google/gemma_pytorch/blob/014acb7ac4563a5f77c76d7ff98f31b568c16508/gemma/model.py#L315
+                Qcur = ggml_scale(ctx0, Qcur, hparams.f_attention_scale);
+
+                cur = build_attn(inp_attn,
+                        model.layers[il].wo, NULL,
+                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f, il);
+            }
+            if (il == n_layer - 1 && inp_out_ids) {
+                cur  = ggml_get_rows(ctx0,  cur, inp_out_ids);
+                inpL = ggml_get_rows(ctx0, inpL, inp_out_ids);
+            }
+            cur = build_norm(cur,
+                    model.layers[il].attn_post_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "attn_post_norm", il);
+
+            ggml_tensor * sa_out = ggml_add(ctx0, cur, inpL);
+            cb(sa_out, "sa_out", il);
+
+            cur = build_norm(sa_out,
+                    model.layers[il].ffn_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "ffn_norm", il);
+
+            // feed-forward network
+            {
+                cur = build_ffn(cur,
+                        model.layers[il].ffn_up,   NULL, NULL,
+                        model.layers[il].ffn_gate, NULL, NULL,
+                        model.layers[il].ffn_down, NULL, NULL,
+                        NULL,
+                        LLM_FFN_GELU, LLM_FFN_PAR, il);
+                cb(cur, "ffn_out", il);
+            }
+            cur = build_norm(cur,
+                    model.layers[il].ffn_post_norm, NULL,
+                    LLM_NORM_RMS, -1);
+            cb(cur, "ffn_post_norm", -1);
+
+            cur = ggml_add(ctx0, cur, sa_out);
+
+            cur = build_cvec(cur, il);
+            cb(cur, "l_out", il);
+
+            // input for next layer
+            inpL = cur;
+        }
+        cur = inpL;
+
+        cur = build_norm(cur,
+                model.output_norm, NULL,
+                LLM_NORM_RMS, -1);
+
+        cb(cur, "result_norm", -1);
+        res->t_embd = cur;
+
+        // lm_head
+        cur = build_lora_mm(model.output, cur);
+
+        cb(cur, "result_output", -1);
+        res->t_logits = cur;
+
+        ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/gemma3n-iswa.cpp b/src/models/gemma3n-iswa.cpp
new file mode 100644
index 00000000000..a0bdd6a15a1
--- /dev/null
+++ b/src/models/gemma3n-iswa.cpp
@@ -0,0 +1,377 @@
+#include "models.h"
+
+
+
+llm_build_gemma3n_iswa::llm_build_gemma3n_iswa(const llama_model & model, const llm_graph_params & params) :
+    llm_graph_context(params),
+    model(model),
+    n_embd_head(model.hparams.n_embd_head_k),
+    n_embd_altup(model.hparams.n_embd_altup),
+    n_altup(model.hparams.n_altup),
+    i_altup_act(model.hparams.i_altup_act) {
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+
+    inpL = build_inp_embd(model.tok_embd);
+
+    // important: do not normalize weights for raw embeddings input (i.e. encoded image emdeddings)
+    if (ubatch.token) {
+        inpL = ggml_scale(ctx0, inpL, sqrtf(n_embd));
+        cb(inpL, "inp_scaled", -1);
+    }
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
+
+    // TODO: is causal == true correct? might need some changes
+    auto * inp_attn = build_attn_inp_kv_iswa();
+
+    // inp_per_layer shape: [n_embd_altup, n_tokens, n_layer]
+    ggml_tensor * inp_per_layer = project_per_layer_inputs(inpL, get_per_layer_inputs());
+
+    // inpL now has only 1 altup, project it to the rest of the altups
+    // these "added" altups will be concat to the last dim of inpL
+    {
+        ggml_tensor * target_magnitude = calc_magnitude(inpL);
+        ggml_tensor * inp_repeated     = ggml_repeat_4d(ctx0, inpL, n_embd, n_tokens, n_altup - 1, 1);
+        ggml_tensor * altup_added =
+            ggml_mul_mat(ctx0, model.altup_proj, inp_repeated);  // shape: [n_embd, n_tokens, n_altup - 1]
+        ggml_tensor * new_magnitude = calc_magnitude(altup_added);
+        altup_added                 = ggml_div(ctx0, ggml_mul(ctx0, altup_added, target_magnitude), new_magnitude);
+        inpL                        = ggml_concat(ctx0, inpL, altup_added, 2);  // shape: [n_embd, n_tokens, n_altup]
+        cb(inpL, "inp_stacked", -1);
+    }
+    // inpL now has shape:          [n_embd,       n_tokens, n_altup]
+    // inp_per_layer now has shape: [n_embd_altup, n_tokens, n_layer]
+
+    for (int il = 0; il < n_layer; ++il) {
+        // this block is made to be closely resemble Gemma3p5DecoderLayer on python code
+        const float freq_base_l  = model.get_rope_freq_base(cparams, il);
+        const float freq_scale_l = model.get_rope_freq_scale(cparams, il);
+
+        ggml_tensor * cur         = inpL;                    // [n_embd, n_tokens, n_altup]
+        ggml_tensor * predictions = altup_predict(cur, il);  // [n_embd, n_tokens, n_altup]
+
+        // predicted value will go through self-attention and laurel
+        ggml_tensor * active_prediction = view_2d_slice(predictions, i_altup_act);  // [n_embd, n_tokens]
+        cur                             = active_prediction;
+        cb(cur, "active_prediction", il);
+
+        // norm
+        cur = build_norm(cur, model.layers[il].attn_norm, NULL, LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
+
+        // laurel
+        ggml_tensor * laurel_out = laurel(cur, il);  // [n_embd, n_tokens]
+
+        // self-attention
+        if (hparams.has_kv(il)) {
+            // compute Q and K and RoPE them
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            cb(Qcur, "Qcur", il);
+
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            cb(Kcur, "Kcur", il);
+
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            cb(Vcur, "Vcur", il);
+
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head, n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+            Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL, LLM_NORM_RMS, il);
+            Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, NULL, LLM_NORM_RMS, il);
+            Vcur = ggml_rms_norm(ctx0, Vcur, hparams.f_norm_rms_eps);
+
+            cb(Qcur, "Qcur_normed", il);
+            cb(Kcur, "Kcur_normed", il);
+            cb(Vcur, "Vcur_normed", il);
+
+            Qcur = ggml_rope_ext(ctx0, Qcur, inp_pos, nullptr, n_rot, rope_type, n_ctx_orig, freq_base_l, freq_scale_l,
+                                 ext_factor, attn_factor, beta_fast, beta_slow);
+
+            Kcur = ggml_rope_ext(ctx0, Kcur, inp_pos, nullptr, n_rot, rope_type, n_ctx_orig, freq_base_l, freq_scale_l,
+                                 ext_factor, attn_factor, beta_fast, beta_slow);
+
+            cb(Qcur, "Qcur_pos", il);
+            cb(Kcur, "Kcur_pos", il);
+
+            cur = build_attn(inp_attn, model.layers[il].wo,
+                    NULL, Qcur, Kcur, Vcur, nullptr, nullptr, nullptr,
+                    hparams.f_attention_scale, il);
+        } else {
+            // reuse KV cache of earlier layers
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            cb(Qcur, "Qcur", il);
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head, n_tokens);
+
+            Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL, LLM_NORM_RMS, il);
+            cb(Qcur, "Qcur_normed", il);
+
+            Qcur = ggml_rope_ext(ctx0, Qcur, inp_pos, nullptr, n_rot, rope_type, n_ctx_orig, freq_base_l, freq_scale_l,
+                                 ext_factor, attn_factor, beta_fast, beta_slow);
+            cb(Qcur, "Qcur_pos", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, NULL,
+                    Qcur, nullptr, nullptr, nullptr, nullptr, nullptr, hparams.f_attention_scale, il);
+        }
+        cur = build_norm(cur, model.layers[il].attn_post_norm, NULL, LLM_NORM_RMS, il);
+        cb(cur, "attn_post_norm", il);
+
+        cur = ggml_add(ctx0, cur, active_prediction);  // [n_embd, n_tokens]
+        cb(cur, "attn_gated", il);
+
+        ggml_tensor * attn_laurel = ggml_scale(ctx0, ggml_add(ctx0, cur, laurel_out),
+                                               1.0f / sqrtf(2.0f));  // [n_embd, n_tokens]
+        cb(attn_laurel, "attn_laurel", il);
+
+        cur = build_norm(attn_laurel, model.layers[il].ffn_norm, NULL, LLM_NORM_RMS, il);
+        cb(cur, "ffn_norm", il);
+
+        // feed-forward network
+        {
+            ggml_tensor * up_proj   = build_lora_mm(model.layers[il].ffn_up, cur);
+            ggml_tensor * gate_proj = build_lora_mm(model.layers[il].ffn_gate, cur);
+
+            if (il < n_layer_sparsity) {
+                // apply activation sparsity
+                gate_proj = gaussian_topk(gate_proj);
+            }
+            gate_proj = ggml_gelu(ctx0, gate_proj);
+
+            cur = ggml_mul(ctx0, up_proj, gate_proj);
+            cur = build_lora_mm(model.layers[il].ffn_down, cur);
+            cb(cur, "ffn_out", il);
+        }
+        cur = build_norm(cur, model.layers[il].ffn_post_norm, NULL, LLM_NORM_RMS, -1);
+        cb(cur, "ffn_post_norm", il);
+
+        ggml_tensor * attn_ffw_laurel_gated = ggml_add(ctx0, cur, attn_laurel);  // [n_embd, n_tokens]
+        cb(attn_ffw_laurel_gated, "attn_ffw_laurel_gated", il);
+
+        ggml_tensor * corrected = altup_correct(predictions, attn_ffw_laurel_gated, il);  // [n_embd, n_tokens, n_altup]
+
+        ggml_tensor * first_prediction;                                                   // [n_embd, n_tokens]
+        {
+            first_prediction = view_2d_slice(corrected, i_altup_act);                     // [n_embd, n_tokens]
+            first_prediction = ggml_mul(ctx0, first_prediction, model.layers[il].altup_correct_scale);
+            first_prediction = build_lora_mm(model.layers[il].per_layer_inp_gate, first_prediction);
+            first_prediction = ggml_gelu(ctx0, first_prediction);                 // [n_embd_altup, n_tokens]
+            cb(first_prediction, "first_prediction_gated", il);
+            ggml_tensor * inp_this_layer = view_2d_slice(inp_per_layer, il);      // [n_embd_altup, n_tokens]
+            first_prediction = ggml_mul(ctx0, first_prediction, inp_this_layer);  // [n_embd_altup, n_tokens]
+            cb(first_prediction, "first_prediction_scaled", il);
+
+            first_prediction = build_lora_mm(model.layers[il].per_layer_proj, first_prediction);  // [n_embd, n_tokens]
+            first_prediction =
+                build_norm(first_prediction, model.layers[il].per_layer_post_norm, NULL, LLM_NORM_RMS, il);
+            cb(first_prediction, "first_prediction_out", il);
+        }
+        // equivalent to python code: corrected_predictions[1:] += first_prediction
+        {
+            ggml_tensor * slice_first = view_2d_slice(corrected, 0);
+            ggml_tensor * slice_rest  = ggml_view_3d(
+                ctx0, corrected, n_embd, n_tokens, n_altup - 1, ggml_row_size(corrected->type, n_embd),
+                ggml_row_size(corrected->type, n_embd * n_tokens), n_embd * n_tokens * ggml_element_size(corrected));
+            ggml_tensor * tmp = ggml_add(ctx0, slice_rest, first_prediction);  // [n_embd, n_tokens, n_altup - 1]
+            corrected         = ggml_concat(ctx0, slice_first, tmp, 2);        // [n_embd, n_tokens, n_altup]
+        }
+        cur = corrected;                                                       // [n_embd, n_tokens, n_altup]
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+    cur = inpL;  // [n_embd, n_tokens, n_altup]
+
+    // cur now has multiple altup(s), we want to merge them back to 1 altup
+    {
+        ggml_tensor * target_magnitude = calc_magnitude(view_2d_slice(cur, i_altup_act));  // [n_embd, n_tokens]
+        // do a view to skip the first slice (active altup)
+        ggml_tensor * alt_slice =
+            ggml_view_3d(ctx0, cur, n_embd, n_tokens, n_altup - 1, ggml_row_size(cur->type, n_embd),
+                         ggml_row_size(cur->type, n_embd * n_tokens), n_embd * n_tokens * ggml_element_size(cur));
+        ggml_tensor * altup_unembd =
+            ggml_mul_mat(ctx0, model.altup_unembd_proj, alt_slice);  // shape: [n_embd, n_tokens, n_altup - 1]
+        ggml_tensor * new_magnitude = calc_magnitude(altup_unembd);
+        altup_unembd                = ggml_div(ctx0, ggml_mul(ctx0, altup_unembd, target_magnitude), new_magnitude);
+        cb(altup_unembd, "altup_unembd", -1);
+
+        // equivalent to torch.mean(hidden_states, dim=0)
+        cur = view_2d_slice(cur, 0);  // [n_embd, n_tokens]
+        for (int i = 0; i < n_altup - 1; ++i) {
+            cur = ggml_add(ctx0, cur, view_2d_slice(altup_unembd, i));
+        }
+        cur = ggml_scale(ctx0, cur, 1.0f / float(n_altup));  // [n_embd, n_tokens]
+        cb(cur, "unembd_merged", -1);
+    }
+    // cur now has shape: [n_embd, n_tokens]
+
+    // TODO: move this to right after the last KV layer
+    {
+        // skip computing output for unused tokens
+        ggml_tensor * inp_out_ids = build_inp_out_ids();
+        cur                       = ggml_get_rows(ctx0, cur, inp_out_ids);
+    }
+    cur = build_norm(cur, model.output_norm, NULL, LLM_NORM_RMS, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    cur = build_lora_mm(model.output, cur);
+
+    {
+        // final logit soft-capping
+        cur = ggml_scale(ctx0, cur, 1.0f / hparams.f_final_logit_softcapping);
+        cur = ggml_tanh(ctx0, cur);
+        cur = ggml_scale(ctx0, cur, hparams.f_final_logit_softcapping);
+    }
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}
+
+ggml_tensor * llm_build_gemma3n_iswa::calc_magnitude(ggml_tensor * x) {
+    return ggml_sqrt(ctx0, ggml_sum_rows(ctx0, ggml_sqr(ctx0, x)));
+}
+
+// get 2D slice view from a 3D tensor, the idx corresponds to the 3rd dim
+ggml_tensor * llm_build_gemma3n_iswa::view_2d_slice(ggml_tensor * x, int idx) {
+    GGML_ASSERT(idx < (int) x->ne[2]);
+    return ggml_view_2d(ctx0, x, x->ne[0], x->ne[1], ggml_row_size(x->type, x->ne[0]),
+                        idx * x->ne[0] * x->ne[1] * ggml_element_size(x));
+}
+
+// equivalent to get_per_layer_inputs() in python code
+// output shape: [n_embd_altup, n_layer, n_tokens]
+ggml_tensor * llm_build_gemma3n_iswa::get_per_layer_inputs() {
+    auto          inp = std::make_unique<llm_graph_input_embd>();
+    ggml_tensor * inp_per_layer;
+    if (ubatch.token) {
+        inp->tokens = ggml_new_tensor_1d(ctx0, GGML_TYPE_I32, ubatch.n_tokens);
+        ggml_set_input(inp->tokens);
+        res->t_tokens = inp->tokens;
+        inp_per_layer = ggml_get_rows(ctx0, model.tok_embd_per_layer, inp->tokens);
+        inp_per_layer = ggml_reshape_3d(ctx0, inp_per_layer, n_embd_altup, n_layer, n_tokens);
+        inp_per_layer = ggml_scale(ctx0, inp_per_layer, sqrtf((float) n_embd_altup));
+        cb(inp_per_layer, "inp_per_layer_selected", -1);
+    } else {
+        GGML_ABORT("TODO: support embd input");
+    }
+    res->add_input(std::move(inp));
+    return inp_per_layer;
+}
+
+// equivalent to project_per_layer_inputs() in python code
+// this calculates the per-layer inputs, so the final tensor shape will have n_layer as the last dim
+// output shape: [n_embd_altup, n_tokens, n_layer]
+ggml_tensor * llm_build_gemma3n_iswa::project_per_layer_inputs(ggml_tensor * inputs_embeds, ggml_tensor * inp_per_layer) {
+    const float per_layer_projection_scale = 1.0f / sqrtf((float) n_embd);
+    const float per_layer_input_scale      = 1.0f / sqrtf(2.0f);
+
+    ggml_tensor * per_layer_proj = ggml_mul_mat(ctx0, model.per_layer_model_proj, inputs_embeds);
+    per_layer_proj               = ggml_scale(ctx0, per_layer_proj, per_layer_projection_scale);
+    per_layer_proj               = ggml_reshape_3d(ctx0, per_layer_proj, n_embd_altup, n_layer, n_tokens);
+    per_layer_proj               = build_norm(per_layer_proj, model.per_layer_proj_norm, NULL, LLM_NORM_RMS,
+                                              -1);  // [n_embd_altup, n_layer, n_tokens]
+    cb(per_layer_proj, "per_layer_proj", -1);
+
+    inp_per_layer = ggml_add(ctx0, inp_per_layer, per_layer_proj);
+    inp_per_layer = ggml_scale(ctx0, inp_per_layer, per_layer_input_scale);
+    cb(inp_per_layer, "inp_per_layer", -1);
+
+    // permute to shape: [n_embd_altup, n_tokens, n_layer]
+    inp_per_layer = ggml_cont(ctx0, ggml_permute(ctx0, inp_per_layer, 0, 2, 1, 3));
+    return inp_per_layer;
+}
+
+// input cur shape: [n_altup, n_tokens]
+// output    shape: [n_altup, n_tokens]
+ggml_tensor * llm_build_gemma3n_iswa::laurel(ggml_tensor * cur, int il) {
+    ggml_tensor * tmp = cur;
+    tmp               = build_lora_mm(model.layers[il].laurel_l, tmp);
+    tmp               = build_lora_mm(model.layers[il].laurel_r, tmp);
+    tmp               = build_norm(tmp, model.layers[il].laurel_post_norm, NULL, LLM_NORM_RMS, il);
+    tmp               = ggml_add(ctx0, tmp, cur);
+    cb(tmp, "laurel_out", il);
+    return tmp;
+}
+
+// input x shape: [n_embd, n_tokens]
+// output  shape: [n_embd, n_tokens]
+ggml_tensor * llm_build_gemma3n_iswa::gaussian_topk(ggml_tensor * x) {
+    ggml_tensor * mean = ggml_mean(ctx0, x);
+    ggml_tensor * std  = ggml_sqrt(ctx0, ggml_scale(ctx0, ggml_sum_rows(ctx0, ggml_sqr(ctx0, ggml_sub(ctx0, x, mean))),
+                                                    1.0f / (float) (x->ne[0] - 1)));
+    ggml_tensor * cutoff_x = ggml_add(ctx0, mean, ggml_scale(ctx0, std, f_sparsity_std_mul));
+    return ggml_relu(ctx0, ggml_sub(ctx0, x, cutoff_x));
+}
+
+//
+// altup functions
+//
+
+// equivalent to compute_router_modalities() in python code
+// input x shape: [n_embd,  n_tokens]
+// output  shape: [n_altup, n_tokens]
+ggml_tensor * llm_build_gemma3n_iswa::altup_compute_router_modalities(ggml_tensor * x, int il) {
+    ggml_tensor * router_inputs = build_norm(x, model.layers[il].altup_router_norm, NULL, LLM_NORM_RMS, il);
+
+    // router_input_scale
+    router_inputs = ggml_scale(ctx0, router_inputs, 1.0f / (float) n_embd);
+
+    ggml_tensor * output = ggml_mul_mat(ctx0, model.layers[il].altup_router, router_inputs);
+    return ggml_tanh(ctx0, output);  // [n_altup, n_tokens]
+}
+
+// input cur shape: [n_embd, n_tokens, n_altup]
+// output    shape: [n_embd, n_tokens, n_altup]
+ggml_tensor * llm_build_gemma3n_iswa::altup_predict(ggml_tensor * cur, int il) {
+    ggml_tensor * activated  = view_2d_slice(cur, i_altup_act);                 // [n_embd, n_tokens]
+    ggml_tensor * modalities = altup_compute_router_modalities(activated, il);  // [n_altup, n_tokens]
+    cb(modalities, "modalities", il);
+
+    ggml_tensor * all_coefs = build_lora_mm(model.layers[il].altup_predict_coef, modalities);
+    cb(all_coefs, "all_coefs", il);
+    // first dim now having n_altup^2 elements, we reshape it to 2D (so we end up with 3D tensor)
+    all_coefs = ggml_reshape_3d(ctx0, all_coefs, n_altup, n_altup, n_tokens);
+
+    // permute to [n_altup, n_embd, n_tokens]
+    ggml_tensor * cur_permuted = ggml_cont(ctx0, ggml_permute(ctx0, cur, 1, 2, 0, 3));
+    ggml_tensor * predictions  = ggml_mul_mat(ctx0, cur_permuted, all_coefs);  // [n_altup, n_embd, n_tokens]
+
+    // final shape must be the same as cur: [n_embd, n_tokens, n_altup]
+    predictions = ggml_cont(ctx0, ggml_permute(ctx0, predictions, 0, 2, 1, 3));
+    predictions = ggml_add(ctx0, predictions, cur);
+    cb(predictions, "predictions", il);
+
+    return predictions;
+}
+
+// input predictions       shape: [n_embd, n_tokens, n_altup]
+// input activated         shape: [n_embd, n_tokens]
+// output                  shape: [n_embd, n_tokens, n_altup]
+ggml_tensor * llm_build_gemma3n_iswa::altup_correct(ggml_tensor * predictions, ggml_tensor * activated, int il) {
+    ggml_tensor * modalities = altup_compute_router_modalities(activated, il);  // [n_altup, n_tokens]
+    cb(modalities, "modalities", il);
+
+    ggml_tensor * active_prediction = view_2d_slice(predictions, i_altup_act);
+    ggml_tensor * innovation        = ggml_sub(ctx0, activated, active_prediction);  // [n_embd, n_tokens]
+    cb(innovation, "innovation", il);
+
+    ggml_tensor * all_coefs = build_lora_mm(model.layers[il].altup_correct_coef, modalities);  // [n_altup, n_tokens]
+    all_coefs               = ggml_scale_bias(ctx0, all_coefs, 1.0f, 1.0f);                    // + 1.0
+    cb(all_coefs, "all_coefs", il);
+    all_coefs = ggml_transpose(ctx0, all_coefs);                                               // [n_tokens, n_altup]
+    all_coefs = ggml_cont_3d(ctx0, all_coefs, 1, n_tokens, n_altup);                           // [1, n_tokens, n_altup]
+
+    innovation              = ggml_repeat_4d(ctx0, innovation, n_embd, n_tokens, n_altup, 1);
+    ggml_tensor * corrected = ggml_mul(ctx0, innovation, all_coefs);   // [n_embd, n_tokens, n_altup]
+    corrected               = ggml_add(ctx0, corrected, predictions);  // [n_embd, n_tokens, n_altup]
+    cb(corrected, "corrected", il);
+
+    return corrected;
+}
diff --git a/src/models/glm4-moe.cpp b/src/models/glm4-moe.cpp
new file mode 100644
index 00000000000..036625dc34e
--- /dev/null
+++ b/src/models/glm4-moe.cpp
@@ -0,0 +1,153 @@
+#include "models.h"
+
+llm_build_glm4_moe::llm_build_glm4_moe(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+        const int64_t n_embd_head = hparams.n_embd_head_v;
+
+        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+
+        ggml_tensor * cur;
+        ggml_tensor * inpL;
+
+        inpL = build_inp_embd(model.tok_embd);
+
+        // inp_pos - contains the positions
+        ggml_tensor * inp_pos = build_inp_pos();
+
+        auto * inp_attn = build_attn_inp_kv();
+
+        ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+        // Only process up to last layer (skip final NextN layer)
+        // Final layer tensors are loaded but not processed in forward pass
+        const int n_transformer_layers = n_layer - hparams.nextn_predict_layers;
+        for (int il = 0; il < n_transformer_layers; ++il) {
+            ggml_tensor * inpSA = inpL;
+
+            // Pre-attention norm
+            cur = build_norm(inpL, model.layers[il].attn_norm, NULL, LLM_NORM_RMS, il);
+            cb(cur, "attn_norm", il);
+
+            // self-attention
+            {
+                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+                if (model.layers[il].bq) {
+                    Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
+                }
+                cb(Qcur, "Qcur", il);
+
+                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+                if (model.layers[il].bk) {
+                    Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
+                }
+                cb(Kcur, "Kcur", il);
+
+                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+                if (model.layers[il].bv) {
+                    Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
+                }
+                cb(Vcur, "Vcur", il);
+
+                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head, n_tokens);
+                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+                // Apply Q/K norm if available (GLM-4.5 355B variant)
+                if (model.layers[il].attn_q_norm) {
+                    Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL, LLM_NORM_RMS, il);
+                    cb(Qcur, "Qcur_normed", il);
+                }
+                if (model.layers[il].attn_k_norm) {
+                    Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, NULL, LLM_NORM_RMS, il);
+                    cb(Kcur, "Kcur_normed", il);
+                }
+                Qcur = ggml_rope_ext(
+                        ctx0, Qcur, inp_pos, nullptr,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+                Kcur = ggml_rope_ext(
+                        ctx0, Kcur, inp_pos, nullptr,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+                cb(Qcur, "Qcur", il);
+                cb(Kcur, "Kcur", il);
+                cb(Vcur, "Vcur", il);
+
+                cur = build_attn(inp_attn,
+                        model.layers[il].wo, NULL,
+                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+            }
+            if (il == n_transformer_layers - 1 && inp_out_ids) {
+                cur   = ggml_get_rows(ctx0, cur, inp_out_ids);
+                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+            }
+            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+            cb(ffn_inp, "ffn_inp", il);
+
+            // Post-attention norm
+            cur = build_norm(ffn_inp, model.layers[il].attn_post_norm, NULL, LLM_NORM_RMS, il);
+            cb(cur, "post_attn_norm", il);
+
+            // Check if this is a dense layer (n_layer_dense_lead=1, so layer 0 is dense)
+            if (static_cast<uint32_t>(il) < hparams.n_layer_dense_lead) {
+                // Dense FFN layer
+                cur = build_ffn(cur,
+                        model.layers[il].ffn_up,   NULL, NULL,
+                        model.layers[il].ffn_gate, NULL, NULL,
+                        model.layers[il].ffn_down, NULL, NULL,
+                        NULL,
+                        LLM_FFN_SILU, LLM_FFN_PAR, il);
+                cb(cur, "ffn_out", il);
+            } else {
+                // Process routed experts using existing MoE infrastructure
+                ggml_tensor * routed_out = build_moe_ffn(cur,
+                        model.layers[il].ffn_gate_inp,
+                        model.layers[il].ffn_up_exps,
+                        model.layers[il].ffn_gate_exps,
+                        model.layers[il].ffn_down_exps,
+                        model.layers[il].ffn_exp_probs_b,
+                        n_expert, n_expert_used,
+                        LLM_FFN_SILU, hparams.expert_weights_norm,
+                        true, hparams.expert_weights_scale,
+                        (llama_expert_gating_func_type) hparams.expert_gating_func,
+                        il);
+                cb(routed_out, "ffn_moe_out", il);
+
+                // Process shared expert on original input
+                ggml_tensor * shared_out = build_ffn(cur,
+                        model.layers[il].ffn_up_shexp,   NULL, NULL,
+                        model.layers[il].ffn_gate_shexp, NULL, NULL,
+                        model.layers[il].ffn_down_shexp, NULL, NULL,
+                        NULL,
+                        LLM_FFN_SILU, LLM_FFN_PAR, il);
+                cb(shared_out, "ffn_shexp_out", il);
+
+                // Final output: routed_output + shared_output
+                cur = ggml_add(ctx0, routed_out, shared_out);
+                cb(cur, "ffn_out", il);
+            }
+            cur = ggml_add(ctx0, cur, ffn_inp);
+
+            cur = build_cvec(cur, il);
+            cb(cur, "l_out", il);
+
+            // input for next layer
+            inpL = cur;
+        }
+        cur = inpL;
+        cur = build_norm(cur, model.output_norm, NULL, LLM_NORM_RMS, -1);
+
+        cb(cur, "result_norm", -1);
+        res->t_embd = cur;
+
+        // lm_head
+        cur = build_lora_mm(model.output, cur);
+
+        cb(cur, "result_output", -1);
+        res->t_logits = cur;
+
+        ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/glm4.cpp b/src/models/glm4.cpp
new file mode 100644
index 00000000000..f789b282488
--- /dev/null
+++ b/src/models/glm4.cpp
@@ -0,0 +1,127 @@
+#include "models.h"
+
+
+
+llm_build_glm4::llm_build_glm4(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+    const int64_t n_embd_head = hparams.n_embd_head_v;
+    const int64_t n_embd_gqa  = hparams.n_embd_v_gqa();
+
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+
+    inpL = build_inp_embd(model.tok_embd);
+
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
+
+    auto * inp_attn = build_attn_inp_kv();
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * inpSA = inpL;
+
+        // Pre-attention norm
+        cur = build_norm(inpL, model.layers[il].attn_norm, NULL, LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
+
+        // self-attention
+        {
+            ggml_tensor * Qcur = nullptr;
+            ggml_tensor * Kcur = nullptr;
+            ggml_tensor * Vcur = nullptr;
+
+            if (model.layers[il].wqkv == nullptr) {
+                Qcur = build_lora_mm(model.layers[il].wq, cur);
+                if (model.layers[il].bq) {
+                    Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
+                }
+                Kcur = build_lora_mm(model.layers[il].wk, cur);
+                if (model.layers[il].bk) {
+                    Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
+                }
+                Vcur = build_lora_mm(model.layers[il].wv, cur);
+                if (model.layers[il].bv) {
+                    Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
+                }
+                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head, n_tokens);
+                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+            } else {
+                cur = build_lora_mm(model.layers[il].wqkv, cur);
+                cb(cur, "wqkv", il);
+                if (model.layers[il].bqkv) {
+                    cur = ggml_add(ctx0, cur, model.layers[il].bqkv);
+                    cb(cur, "bqkv", il);
+                }
+                Qcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head, n_tokens, n_embd_head * sizeof(float), cur->nb[1],
+                                    0 * sizeof(float) * (n_embd));
+                Kcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head * sizeof(float),
+                                    cur->nb[1], 1 * sizeof(float) * (n_embd));
+                Vcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head * sizeof(float),
+                                    cur->nb[1], 1 * sizeof(float) * (n_embd + n_embd_gqa));
+            }
+            Qcur = ggml_rope_ext(ctx0, Qcur, inp_pos, nullptr, n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                                 ext_factor, attn_factor, beta_fast, beta_slow);
+
+            Kcur = ggml_rope_ext(ctx0, Kcur, inp_pos, nullptr, n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                                 ext_factor, attn_factor, beta_fast, beta_slow);
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, NULL,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f / sqrtf(float(n_embd_head)), il);
+        }
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0, cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+        }
+        // Post-attention norm (new!)
+        cur = build_norm(cur, model.layers[il].attn_post_norm, NULL, LLM_NORM_RMS, il);
+        cb(cur, "post_attn_norm", il);
+
+        // Add the input (residual connection after post-attention norm)
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+        cb(ffn_inp, "ffn_inp", il);
+
+        // FF
+        {
+            // Pre-MLP norm
+            cur = build_norm(ffn_inp, model.layers[il].ffn_norm, NULL, LLM_NORM_RMS, il);
+            cb(cur, "ffn_norm", il);
+
+            // MLP
+            cur = build_ffn(cur,
+                    model.layers[il].ffn_up, NULL, NULL,
+                    NULL, NULL, NULL,
+                    model.layers[il].ffn_down, NULL, NULL,
+                    NULL, LLM_FFN_SWIGLU, LLM_FFN_SEQ, il);
+            cb(cur, "ffn_out", il);
+
+            // Post-MLP norm
+            cur = build_norm(cur, model.layers[il].ffn_post_norm, NULL, LLM_NORM_RMS, il);
+            cb(cur, "post_mlp_norm", il);
+        }
+        // Add residual connection after post-MLP norm
+        inpL = ggml_add(ctx0, cur, ffn_inp);
+        cb(inpL, "l_out", il);
+    }
+    // Final norm
+    cur = build_norm(inpL, model.output_norm, NULL, LLM_NORM_RMS, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    // Output projection
+    cur = build_lora_mm(model.output, cur);
+
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/gpt2.cpp b/src/models/gpt2.cpp
new file mode 100644
index 00000000000..60761c8e765
--- /dev/null
+++ b/src/models/gpt2.cpp
@@ -0,0 +1,105 @@
+#include "models.h"
+
+llm_build_gpt2::llm_build_gpt2(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+    const int64_t n_embd_head = hparams.n_embd_head_v;
+    const int64_t n_embd_gqa  = hparams.n_embd_v_gqa();
+
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+
+    ggml_tensor * cur;
+    ggml_tensor * pos;
+    ggml_tensor * inpL;
+
+    inpL = build_inp_embd(model.tok_embd);
+
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
+
+    auto * inp_attn = build_attn_inp_kv();
+
+    pos = ggml_get_rows(ctx0, model.pos_embd, inp_pos);
+    cb(pos, "pos_embd", -1);
+
+    inpL = ggml_add(ctx0, inpL, pos);
+    cb(inpL, "inpL", -1);
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        cur = build_norm(inpL,
+                model.layers[il].attn_norm,
+                model.layers[il].attn_norm_b,
+                LLM_NORM, il);
+        cb(cur, "attn_norm", il);
+
+        // self-attention
+        {
+            cur = build_lora_mm(model.layers[il].wqkv, cur);
+            cb(cur, "wqkv", il);
+
+            cur = ggml_add(ctx0, cur, model.layers[il].bqkv);
+            cb(cur, "bqkv", il);
+
+            ggml_tensor * Qcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head,    n_tokens, n_embd_head*sizeof(float), cur->nb[1], 0*sizeof(float)*(n_embd));
+            ggml_tensor * Kcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd));
+            ggml_tensor * Vcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd + n_embd_gqa));
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, model.layers[il].bo,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+        }
+
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur  = ggml_get_rows(ctx0,  cur, inp_out_ids);
+            inpL = ggml_get_rows(ctx0, inpL, inp_out_ids);
+        }
+
+        // add the input
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpL);
+        cb(ffn_inp, "ffn_inp", il);
+
+        // FF
+        {
+            cur = build_norm(ffn_inp,
+                    model.layers[il].ffn_norm,
+                    model.layers[il].ffn_norm_b,
+                    LLM_NORM, il);
+            cb(cur, "ffn_norm", il);
+
+            cur = build_ffn(cur,
+                    model.layers[il].ffn_up,   model.layers[il].ffn_up_b,   NULL,
+                    NULL,                      NULL,                        NULL,
+                    model.layers[il].ffn_down, model.layers[il].ffn_down_b, NULL,
+                    NULL,
+                    LLM_FFN_GELU, LLM_FFN_SEQ, il);
+            cb(cur, "ffn_out", il);
+        }
+
+        cur = ggml_add(ctx0, cur, ffn_inp);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+
+    cur = build_norm(inpL,
+            model.output_norm,
+            model.output_norm_b,
+            LLM_NORM, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    cur = build_lora_mm(model.output, cur);
+
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/gptneox.cpp b/src/models/gptneox.cpp
new file mode 100644
index 00000000000..2151b14e939
--- /dev/null
+++ b/src/models/gptneox.cpp
@@ -0,0 +1,144 @@
+#include "models.h"
+
+
+llm_build_gptneox::llm_build_gptneox(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+    const int64_t n_embd_head = hparams.n_embd_head_v;
+    const int64_t n_embd_gqa  = hparams.n_embd_v_gqa();
+
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+
+    inpL = build_inp_embd(model.tok_embd);
+
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
+
+    auto * inp_attn = build_attn_inp_kv();
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        cur = build_norm(inpL,
+                model.layers[il].attn_norm,
+                model.layers[il].attn_norm_b,
+                LLM_NORM, il);
+        cb(cur, "attn_norm", il);
+
+        // self-attention
+        {
+            cur = build_lora_mm(model.layers[il].wqkv, cur);
+            cb(cur, "wqkv", il);
+
+            cur = ggml_add(ctx0, cur, model.layers[il].bqkv);
+            cb(cur, "bqkv", il);
+
+            ggml_tensor * Qcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head,    n_tokens, n_embd_head*sizeof(float), cur->nb[1], 0*sizeof(float)*(n_embd));
+            ggml_tensor * Kcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd));
+            ggml_tensor * Vcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd + n_embd_gqa));
+
+            Qcur = ggml_rope_ext(
+                    ctx0, Qcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            Kcur = ggml_rope_ext(
+                    ctx0, Kcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, model.layers[il].bo,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+        }
+
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur  = ggml_get_rows(ctx0,  cur, inp_out_ids);
+            inpL = ggml_get_rows(ctx0, inpL, inp_out_ids);
+        }
+
+        // ffn
+        if (hparams.use_par_res) {
+            // attention and ffn are computed in parallel
+            // x = x + attn(ln1(x)) + ffn(ln2(x))
+
+            ggml_tensor * attn_out = cur;
+
+            cur = build_norm(inpL,
+                    model.layers[il].ffn_norm,
+                    model.layers[il].ffn_norm_b,
+                    LLM_NORM, il);
+            cb(cur, "ffn_norm", il);
+
+            cur = build_ffn(cur,
+                    model.layers[il].ffn_up,   model.layers[il].ffn_up_b,   NULL,
+                    NULL,                      NULL,                        NULL,
+                    model.layers[il].ffn_down, model.layers[il].ffn_down_b, NULL,
+                    NULL,
+                    LLM_FFN_GELU, LLM_FFN_SEQ, il);
+            cb(cur, "ffn_out", il);
+
+            cur = ggml_add(ctx0, cur, inpL);
+            cb(cur, "ffn_out", il);
+
+            cur = ggml_add(ctx0, cur, attn_out);
+
+            cur = build_cvec(cur, il);
+            cb(cur, "l_out", il);
+
+            // input for next layer
+            inpL = cur;
+        } else {
+            // attention and ffn are computed sequentially
+            // x = x + attn(ln1(x))
+            // x = x + ffn(ln2(x))
+
+            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpL);
+            cb(ffn_inp, "ffn_inp", il);
+
+            cur = build_norm(ffn_inp,
+                    model.layers[il].ffn_norm,
+                    model.layers[il].ffn_norm_b,
+                    LLM_NORM, il);
+            cb(cur, "ffn_norm", il);
+
+            cur = build_ffn(cur,
+                    model.layers[il].ffn_up,   model.layers[il].ffn_up_b,   NULL,
+                    NULL,                      NULL,                        NULL,
+                    model.layers[il].ffn_down, model.layers[il].ffn_down_b, NULL,
+                    NULL,
+                    LLM_FFN_GELU, LLM_FFN_SEQ, il);
+            cb(cur, "ffn_out", il);
+
+            cur = ggml_add(ctx0, cur, ffn_inp);
+
+            cur = build_cvec(cur, il);
+            cb(cur, "l_out", il);
+
+            // input for next layer
+            inpL = cur;
+        }
+    }
+
+    cur = build_norm(inpL,
+            model.output_norm,
+            model.output_norm_b,
+            LLM_NORM, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    cur = build_lora_mm(model.output, cur);
+
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/granite-hybrid.cpp b/src/models/granite-hybrid.cpp
new file mode 100644
index 00000000000..f6ca4c17a21
--- /dev/null
+++ b/src/models/granite-hybrid.cpp
@@ -0,0 +1,196 @@
+#include "models.h"
+
+
+llm_build_granite_hybrid::llm_build_granite_hybrid(const llama_model & model, const llm_graph_params & params) :
+    llm_graph_context_mamba(params) {
+    const int64_t n_embd_head = hparams.n_embd_head_v;
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+
+    inpL = build_inp_embd(model.tok_embd);
+
+    auto * inp = build_inp_mem_hybrid();
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    // Positional embeddings populated if rope enabled
+    ggml_tensor * inp_pos = nullptr;
+    if (hparams.rope_finetuned) {
+        inp_pos = build_inp_pos();
+    }
+
+    for (int il = 0; il < n_layer; ++il) {
+        struct ggml_tensor * inpSA = inpL;
+
+        // norm
+        cur = build_norm(inpL, model.layers[il].attn_norm, NULL, LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
+
+        if (hparams.is_recurrent(il)) {
+            // ssm layer //
+            cur = build_mamba2_layer(inp->get_recr(), cur, model, ubatch, il);
+        } else {
+            // attention layer //
+            cur = build_attention_layer(cur, inp_pos, inp->get_attn(), model, n_embd_head, il);
+        }
+
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0, cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+        }
+
+        // ffn
+        cur = build_layer_ffn(cur, inpSA, model, il);
+
+        // input for next layer
+        inpL = cur;
+    }
+
+    cur = inpL;
+
+    cur = build_norm(cur, model.output_norm, NULL, LLM_NORM_RMS, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
+
+    // For Granite architectures - scale logits
+    if (hparams.f_logit_scale) {
+        cur = ggml_scale(ctx0, cur, 1.0f / hparams.f_logit_scale);
+    }
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}
+
+ggml_tensor * llm_build_granite_hybrid::build_attention_layer(ggml_tensor *             cur,
+                                                              ggml_tensor *             inp_pos,
+                                                              llm_graph_input_attn_kv * inp_attn,
+                                                              const llama_model &       model,
+                                                              const int64_t             n_embd_head,
+                                                              const int                 il) {
+    // compute Q and K and (optionally) RoPE them
+    ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+    cb(Qcur, "Qcur", il);
+    if (model.layers[il].bq) {
+        Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
+        cb(Qcur, "Qcur", il);
+    }
+
+    ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+    cb(Kcur, "Kcur", il);
+    if (model.layers[il].bk) {
+        Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
+        cb(Kcur, "Kcur", il);
+    }
+
+    ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+    cb(Vcur, "Vcur", il);
+    if (model.layers[il].bv) {
+        Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
+        cb(Vcur, "Vcur", il);
+    }
+
+    Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, hparams.n_head(il), n_tokens);
+    Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, hparams.n_head_kv(il), n_tokens);
+    Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, hparams.n_head_kv(il), n_tokens);
+
+    const bool use_rope = hparams.rope_finetuned;
+    if (use_rope) {
+        ggml_tensor * rope_factors = model.get_rope_factors(cparams, il);
+        Qcur = ggml_rope_ext(ctx0, Qcur, inp_pos, rope_factors, n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                             ext_factor, attn_factor, beta_fast, beta_slow);
+
+        Kcur = ggml_rope_ext(ctx0, Kcur, inp_pos, rope_factors, n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                             ext_factor, attn_factor, beta_fast, beta_slow);
+    }
+
+    cb(Qcur, "Qcur", il);
+    cb(Kcur, "Kcur", il);
+    cb(Vcur, "Vcur", il);
+
+    const float kq_scale =
+        hparams.f_attention_scale == 0.0f ? 1.0f / sqrtf(float(n_embd_head)) : hparams.f_attention_scale;
+    cur = build_attn(inp_attn,
+            model.layers[il].wo, model.layers[il].bo,
+            Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, kq_scale, il);
+    cb(cur, "attn_out", il);
+    return cur;
+}
+
+ggml_tensor * llm_build_granite_hybrid::build_layer_ffn(ggml_tensor *       cur,
+                                                        ggml_tensor *       inpSA,
+                                                        const llama_model & model,
+                                                        const int           il) {
+    // For Granite architectures - scale residual
+    if (hparams.f_residual_scale) {
+        cur = ggml_scale(ctx0, cur, hparams.f_residual_scale);
+    }
+    ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+    cb(ffn_inp, "ffn_inp", il);
+
+    // feed-forward network (non-MoE)
+    if (model.layers[il].ffn_gate_inp == nullptr) {
+        cur = build_norm(ffn_inp, model.layers[il].ffn_norm, NULL, LLM_NORM_RMS, il);
+        cb(cur, "ffn_norm", il);
+
+        cur = build_ffn(cur,
+                model.layers[il].ffn_up, model.layers[il].ffn_up_b, NULL,
+                model.layers[il].ffn_gate, model.layers[il].ffn_gate_b, NULL,
+                model.layers[il].ffn_down, model.layers[il].ffn_down_b, NULL,
+                NULL, LLM_FFN_SILU, LLM_FFN_PAR, il);
+        cb(cur, "ffn_out", il);
+
+    } else {
+        // MoE branch
+        cur = build_norm(ffn_inp, model.layers[il].ffn_norm, NULL, LLM_NORM_RMS, il);
+        cb(cur, "ffn_norm", il);
+
+        ggml_tensor * moe_out =
+            build_moe_ffn(cur,
+                model.layers[il].ffn_gate_inp,
+                model.layers[il].ffn_up_exps,
+                model.layers[il].ffn_gate_exps,
+                model.layers[il].ffn_down_exps,
+                nullptr,
+                n_expert, n_expert_used,
+                LLM_FFN_SILU, true,
+                false, 0.0,
+                LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
+                il);
+        cb(moe_out, "ffn_moe_out", il);
+
+        // For Granite MoE Shared
+        if (hparams.n_ff_shexp > 0) {
+            ggml_tensor * ffn_shexp =
+                build_ffn(cur,
+                    model.layers[il].ffn_up_shexp, NULL, NULL,
+                    model.layers[il].ffn_gate_shexp, NULL, NULL,
+                    model.layers[il].ffn_down_shexp, NULL, NULL,
+                    NULL, LLM_FFN_SILU, LLM_FFN_PAR, il);
+            cb(ffn_shexp, "ffn_shexp", il);
+
+            cur = ggml_add(ctx0, moe_out, ffn_shexp);
+            cb(cur, "ffn_out", il);
+        } else {
+            cur = moe_out;
+        }
+    }
+
+    // For Granite architectures - scale residual
+    if (hparams.f_residual_scale) {
+        cur = ggml_scale(ctx0, cur, hparams.f_residual_scale);
+    }
+    cur = ggml_add(ctx0, cur, ffn_inp);
+    cb(cur, "ffn_out", il);
+
+    cur = build_cvec(cur, il);
+    cb(cur, "l_out", il);
+
+    return cur;
+}
diff --git a/src/models/granite.cpp b/src/models/granite.cpp
new file mode 100644
index 00000000000..18748e9c26c
--- /dev/null
+++ b/src/models/granite.cpp
@@ -0,0 +1,211 @@
+#include "models.h"
+
+
+llm_build_granite::llm_build_granite(
+    const llama_model & model,
+    const llm_graph_params & params)
+    : llm_graph_context(params) {
+
+    const int64_t n_embd_head = hparams.n_embd_head_v;
+
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+    GGML_ASSERT(n_embd_head == hparams.n_rot);
+
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+
+    inpL = build_inp_embd(model.tok_embd);
+
+    // inp_pos - built only if rope enabled
+    ggml_tensor * inp_pos = nullptr;
+    if (hparams.rope_finetuned) {
+        inp_pos = build_inp_pos();
+    }
+    auto * inp_attn = build_attn_inp_kv();
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * inpSA = inpL;
+
+        // norm
+        cur = build_norm(inpL,
+                model.layers[il].attn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
+
+        // self-attention
+        cur = build_attention_layer(
+            cur, inp_pos, inp_attn,
+            model, n_embd_head, il);
+
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+        }
+        // ffn
+        cur = build_layer_ffn(cur, inpSA, model, il);
+
+        // input for next layer
+        inpL = cur;
+    }
+    cur = inpL;
+
+    cur = build_norm(cur,
+            model.output_norm, NULL,
+            LLM_NORM_RMS, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
+
+    // For Granite architectures - scale logits
+    cur = ggml_scale(ctx0, cur, 1.0f / hparams.f_logit_scale);
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}
+
+ggml_tensor * llm_build_granite::build_attention_layer(
+          ggml_tensor             * cur,
+          ggml_tensor             * inp_pos,
+          llm_graph_input_attn_kv * inp_attn,
+    const llama_model             & model,
+    const int64_t                 n_embd_head,
+    const int                     il) {
+
+    // compute Q and K and (optionally) RoPE them
+    ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+    cb(Qcur, "Qcur", il);
+    if (model.layers[il].bq) {
+        Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
+        cb(Qcur, "Qcur", il);
+    }
+
+    ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+    cb(Kcur, "Kcur", il);
+    if (model.layers[il].bk) {
+        Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
+        cb(Kcur, "Kcur", il);
+    }
+
+    ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+    cb(Vcur, "Vcur", il);
+    if (model.layers[il].bv) {
+        Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
+        cb(Vcur, "Vcur", il);
+    }
+
+    Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, hparams.n_head(il),    n_tokens);
+    Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, hparams.n_head_kv(il), n_tokens);
+    Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, hparams.n_head_kv(il), n_tokens);
+
+    const bool use_rope = hparams.rope_finetuned;
+    if (use_rope) {
+        ggml_tensor * rope_factors = model.get_rope_factors(cparams, il);
+        Qcur = ggml_rope_ext(
+                ctx0, Qcur, inp_pos, rope_factors,
+                n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                ext_factor, attn_factor, beta_fast, beta_slow
+                );
+
+        Kcur = ggml_rope_ext(
+                ctx0, Kcur, inp_pos, rope_factors,
+                n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                ext_factor, attn_factor, beta_fast, beta_slow
+                );
+    }
+
+    cb(Qcur, "Qcur", il);
+    cb(Kcur, "Kcur", il);
+    cb(Vcur, "Vcur", il);
+
+    const float kq_scale = hparams.f_attention_scale == 0.0f ? 1.0f/sqrtf(float(n_embd_head)) : hparams.f_attention_scale;
+    cur = build_attn(inp_attn,
+            model.layers[il].wo, model.layers[il].bo,
+            Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, kq_scale, il);
+            cb(cur, "attn_out", il);
+    return cur;
+}
+
+ggml_tensor * llm_build_granite::build_layer_ffn(
+          ggml_tensor       * cur,
+          ggml_tensor       * inpSA,
+    const llama_model       & model,
+    const int                 il) {
+
+    // For Granite architectures - scale residual
+    if (hparams.f_residual_scale) {
+        cur = ggml_scale(ctx0, cur, hparams.f_residual_scale);
+    }
+    ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+    cb(ffn_inp, "ffn_inp", il);
+
+    // feed-forward network (non-MoE)
+    if (model.layers[il].ffn_gate_inp == nullptr) {
+
+        cur = build_norm(ffn_inp,
+                model.layers[il].ffn_norm, NULL,
+                LLM_NORM_RMS, il);
+                cb(cur, "ffn_norm", il);
+
+        cur = build_ffn(cur,
+                model.layers[il].ffn_up,   model.layers[il].ffn_up_b,   NULL,
+                model.layers[il].ffn_gate, model.layers[il].ffn_gate_b, NULL,
+                model.layers[il].ffn_down, model.layers[il].ffn_down_b, NULL,
+                NULL,
+                LLM_FFN_SILU, LLM_FFN_PAR, il);
+                cb(cur, "ffn_out", il);
+
+    } else {
+        // MoE branch
+        cur = build_norm(ffn_inp,
+                model.layers[il].ffn_norm, NULL,
+                LLM_NORM_RMS, il);
+                cb(cur, "ffn_norm", il);
+
+        ggml_tensor * moe_out = build_moe_ffn(cur,
+                model.layers[il].ffn_gate_inp,
+                model.layers[il].ffn_up_exps,
+                model.layers[il].ffn_gate_exps,
+                model.layers[il].ffn_down_exps,
+                nullptr,
+                n_expert, n_expert_used,
+                LLM_FFN_SILU, true,
+                false, 0.0,
+                LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
+                il);
+        cb(moe_out, "ffn_moe_out", il);
+
+        // For Granite MoE Shared
+        if (hparams.n_ff_shexp > 0) {
+            ggml_tensor * ffn_shexp = build_ffn(cur,
+                model.layers[il].ffn_up_shexp,   NULL, NULL,
+                model.layers[il].ffn_gate_shexp, NULL, NULL,
+                model.layers[il].ffn_down_shexp, NULL, NULL,
+                NULL,
+                LLM_FFN_SILU, LLM_FFN_PAR, il);
+            cb(ffn_shexp, "ffn_shexp", il);
+
+            cur = ggml_add(ctx0, moe_out, ffn_shexp);
+            cb(cur, "ffn_out", il);
+        } else {
+            cur = moe_out;
+        }
+    }
+
+    // For Granite architectures - scale residual
+    if (hparams.f_residual_scale) {
+        cur = ggml_scale(ctx0, cur, hparams.f_residual_scale);
+    }
+    cur = ggml_add(ctx0, cur, ffn_inp);
+    cb(cur, "ffn_out", il);
+
+    cur = build_cvec(cur, il);
+    cb(cur, "l_out", il);
+
+    return cur;
+}
diff --git a/src/models/graph-context-mamba.cpp b/src/models/graph-context-mamba.cpp
new file mode 100644
index 00000000000..b9a363b32b6
--- /dev/null
+++ b/src/models/graph-context-mamba.cpp
@@ -0,0 +1,283 @@
+#include "models.h"
+
+llm_graph_context_mamba::llm_graph_context_mamba(const llm_graph_params & params) : llm_graph_context(params) {}
+
+ggml_tensor * llm_graph_context_mamba::build_mamba_layer(llm_graph_input_rs * inp,
+                                                         ggml_tensor *        cur,
+                                                         const llama_model &  model,
+                                                         const llama_ubatch & ubatch,
+                                                         int                  il) {
+    const auto * mctx_cur = inp->mctx;
+
+    const auto kv_head = mctx_cur->get_head();
+
+    const auto & layer = model.layers[il];
+
+    const int64_t d_conv         = hparams.ssm_d_conv;
+    const int64_t d_inner        = hparams.ssm_d_inner;
+    const int64_t d_state        = hparams.ssm_d_state;
+    const int64_t dt_rank        = hparams.ssm_dt_rank;
+    const int64_t n_head         = d_inner;
+    const int64_t head_dim       = 1;
+    const int64_t n_seqs         = ubatch.n_seqs;
+    // Some variants of Mamba arch (e.g. FalconMamba do apply layer norm on B and Dt layers)
+    const bool    ssm_dt_b_c_rms = hparams.ssm_dt_b_c_rms;
+
+    const int64_t n_seq_tokens = ubatch.n_seq_tokens;
+
+    GGML_ASSERT(n_seqs != 0);
+    GGML_ASSERT(ubatch.equal_seqs());
+    GGML_ASSERT(ubatch.n_tokens == n_seq_tokens * n_seqs);
+
+    ggml_tensor * conv_states_all = mctx_cur->get_r_l(il);
+    ggml_tensor * ssm_states_all  = mctx_cur->get_s_l(il);
+
+    ggml_tensor * conv = build_rs(inp, conv_states_all, hparams.n_embd_r(), n_seqs);
+    conv               = ggml_reshape_3d(ctx0, conv, d_conv - 1, d_inner, n_seqs);
+
+    // {n_embd, n_tokens} => {n_embd, n_seq_tokens, n_seqs}
+    cur = ggml_reshape_3d(ctx0, cur, cur->ne[0], n_seq_tokens, n_seqs);
+
+    // {n_embd, 2*d_inner} @ {n_embd, n_seq_tokens, n_seqs} => {2*d_inner, n_seq_tokens, n_seqs}
+    ggml_tensor * xz = build_lora_mm(layer.ssm_in, cur);
+    // split the above in two
+    // => {d_inner, n_seq_tokens, n_seqs}
+    ggml_tensor * x  = ggml_view_3d(ctx0, xz, d_inner, xz->ne[1], xz->ne[2], xz->nb[1], xz->nb[2], 0);
+    ggml_tensor * z =
+        ggml_view_3d(ctx0, xz, d_inner, xz->ne[1], xz->ne[2], xz->nb[1], xz->nb[2], d_inner * ggml_element_size(xz));
+
+    // conv
+    {
+        // => {d_conv - 1 + n_seq_tokens, d_inner, n_seqs}
+        ggml_tensor * conv_x = ggml_concat(ctx0, conv, ggml_transpose(ctx0, x), 0);
+
+        // copy last (d_conv - 1) columns back into the state cache
+        ggml_tensor * last_conv = ggml_view_3d(ctx0, conv_x, d_conv - 1, d_inner, n_seqs, conv_x->nb[1], conv_x->nb[2],
+                                               n_seq_tokens * (conv_x->nb[0]));
+
+        ggml_build_forward_expand(
+            gf, ggml_cpy(ctx0, last_conv,
+                         ggml_view_1d(ctx0, conv_states_all, (d_conv - 1) * (d_inner) * (n_seqs),
+                                      kv_head * (d_conv - 1) * (d_inner) *ggml_element_size(conv_states_all))));
+
+        // 1D convolution
+        // The equivalent is to make a self-overlapping view of conv_x
+        // over d_conv columns at each stride in the 3rd dimension,
+        // then element-wise multiply that with the conv1d weight,
+        // then sum the elements of each row,
+        // (the last two steps are a dot product over rows (also doable with mul_mat))
+        // then permute away the ne[0] dimension,
+        // and then you're left with the resulting x tensor.
+        // For simultaneous sequences, all sequences need to have the same length.
+        x = ggml_ssm_conv(ctx0, conv_x, layer.ssm_conv1d);
+
+        // bias
+        x = ggml_add(ctx0, x, layer.ssm_conv1d_b);
+
+        x = ggml_silu(ctx0, x);
+    }
+
+    // ssm
+    {
+        // {d_inner, dt_rank + 2*d_state} @ {d_inner, n_seq_tokens, n_seqs} => {dt_rank + 2*d_state, n_seq_tokens, n_seqs}
+        ggml_tensor * x_db = build_lora_mm(layer.ssm_x, x);
+        // split
+        ggml_tensor * dt   = ggml_view_3d(ctx0, x_db, dt_rank, n_seq_tokens, n_seqs, x_db->nb[1], x_db->nb[2], 0);
+        ggml_tensor * B =
+            ggml_view_4d(ctx0, x_db, d_state, /* n_group */ 1, n_seq_tokens, n_seqs, d_state * x_db->nb[0], x_db->nb[1],
+                         x_db->nb[2], ggml_element_size(x_db) * dt_rank);
+        ggml_tensor * C =
+            ggml_view_4d(ctx0, x_db, d_state, /* n_group */ 1, n_seq_tokens, n_seqs, d_state * x_db->nb[0], x_db->nb[1],
+                         x_db->nb[2], ggml_element_size(x_db) * (dt_rank + d_state));
+
+        // Some Mamba variants (e.g. FalconMamba, Jamba) apply RMS norm in B, C & Dt layers
+        if (ssm_dt_b_c_rms || (layer.ssm_dt_norm && layer.ssm_b_norm && layer.ssm_c_norm)) {
+            dt = build_norm(dt, layer.ssm_dt_norm, NULL, LLM_NORM_RMS, il);
+            B  = build_norm(B, layer.ssm_b_norm, NULL, LLM_NORM_RMS, il);
+            C  = build_norm(C, layer.ssm_c_norm, NULL, LLM_NORM_RMS, il);
+        }
+
+        // {dt_rank, d_inner} @ {dt_rank, n_seq_tokens, n_seqs} => {d_inner, n_seq_tokens, n_seqs}
+        dt = build_lora_mm(layer.ssm_dt, dt);
+        dt = ggml_add(ctx0, dt, layer.ssm_dt_b);
+
+        cur = x;
+        x   = ggml_reshape_4d(ctx0, x, head_dim, n_head, n_seq_tokens, n_seqs);
+
+        ggml_tensor * A = layer.ssm_a;
+
+        // use the states and the indices provided by build_recurrent_state
+        // (this is necessary in order to properly use the states before they are overwritten,
+        //  while avoiding to make unnecessary copies of the states)
+        auto get_ssm_rows = [&](ggml_context * ctx, ggml_tensor * states, ggml_tensor * ids) {
+            ggml_tensor * ssm = ggml_reshape_4d(ctx, states, d_state, head_dim, n_head, mctx_cur->get_size());
+
+            // Custom operator to optimize the parallel associative scan
+            // as described in the Annex D of the Mamba paper.
+            // => {d_inner, n_seq_tokens, n_seqs} and {d_state, d_inner, n_seqs}
+            return ggml_ssm_scan(ctx, ssm, x, dt, A, B, C, ids);
+        };
+
+        ggml_tensor * y_ssm = build_rs(inp, ssm_states_all, hparams.n_embd_s(), ubatch.n_seqs, get_ssm_rows);
+
+        // store last states
+        ggml_build_forward_expand(
+            gf, ggml_cpy(ctx0, ggml_view_1d(ctx0, y_ssm, d_state * d_inner * n_seqs, x->nb[3] * x->ne[3]),
+                         ggml_view_1d(ctx0, ssm_states_all, d_state * d_inner * n_seqs,
+                                      kv_head * d_state * d_inner * ggml_element_size(ssm_states_all))));
+
+        ggml_tensor * y = ggml_view_3d(ctx0, y_ssm, d_inner, n_seq_tokens, n_seqs, x->nb[2], x->nb[3], 0);
+
+        // TODO: skip computing output earlier for unused tokens
+
+        y = ggml_add(ctx0, y, ggml_mul(ctx0, cur, layer.ssm_d));
+        y = ggml_swiglu_split(ctx0, ggml_cont(ctx0, z), y);
+
+        // {d_inner, n_embd} @ {d_inner, n_seq_tokens, n_seqs} => {n_embd, n_seq_tokens, n_seqs}
+        cur = build_lora_mm(layer.ssm_out, y);
+    }
+
+    // {n_embd, n_seq_tokens, n_seqs} => {n_embd, n_tokens}
+    cur = ggml_reshape_2d(ctx0, cur, cur->ne[0], n_seq_tokens * n_seqs);
+
+    return cur;
+}
+
+ggml_tensor * llm_graph_context_mamba::build_mamba2_layer(llm_graph_input_rs * inp,
+                                                          ggml_tensor *        cur,
+                                                          const llama_model &  model,
+                                                          const llama_ubatch & ubatch,
+                                                          int                  il) const {
+    const auto * mctx_cur = inp->mctx;
+
+    const auto kv_head = mctx_cur->get_head();
+
+    const int64_t d_conv   = hparams.ssm_d_conv;
+    const int64_t d_inner  = hparams.ssm_d_inner;
+    const int64_t d_state  = hparams.ssm_d_state;
+    const int64_t n_head   = hparams.ssm_dt_rank;
+    const int64_t head_dim = d_inner / n_head;
+    const int64_t n_group  = hparams.ssm_n_group;
+    const int64_t n_seqs   = ubatch.n_seqs;
+
+    const int64_t n_seq_tokens = ubatch.n_seq_tokens;
+
+    GGML_ASSERT(n_seqs != 0);
+    GGML_ASSERT(ubatch.equal_seqs());
+    GGML_ASSERT(ubatch.n_tokens == n_seq_tokens * n_seqs);
+
+    ggml_tensor * conv_states_all = mctx_cur->get_r_l(il);
+    ggml_tensor * ssm_states_all  = mctx_cur->get_s_l(il);
+
+    ggml_tensor * conv = build_rs(inp, conv_states_all, hparams.n_embd_r(), n_seqs);
+    conv               = ggml_reshape_3d(ctx0, conv, d_conv - 1, d_inner + 2 * n_group * d_state, n_seqs);
+
+    // {n_embd, n_tokens} => {n_embd, n_seq_tokens, n_seqs}
+    cur = ggml_reshape_3d(ctx0, cur, cur->ne[0], n_seq_tokens, n_seqs);
+
+    // d_in_proj = 2 * self.d_inner + 2 * self.ngroups * self.d_state + self.nheads
+
+    // {n_embd, d_in_proj} @ {n_embd, n_seq_tokens, n_seqs} => {d_in_proj, n_seq_tokens, n_seqs}
+    ggml_tensor * zxBCdt = build_lora_mm(model.layers[il].ssm_in, cur);
+
+    // split the above in three
+    ggml_tensor * z   = ggml_view_4d(ctx0, zxBCdt, head_dim, n_head, n_seq_tokens, n_seqs, head_dim * zxBCdt->nb[0],
+                                     zxBCdt->nb[1], zxBCdt->nb[2], 0);
+    ggml_tensor * xBC = ggml_view_3d(ctx0, zxBCdt, d_inner + 2 * n_group * d_state, n_seq_tokens, n_seqs, zxBCdt->nb[1],
+                                     zxBCdt->nb[2], d_inner * ggml_element_size(zxBCdt));
+    ggml_tensor * dt  = ggml_view_3d(ctx0, zxBCdt, n_head, n_seq_tokens, n_seqs, zxBCdt->nb[1], zxBCdt->nb[2],
+                                     (2 * d_inner + 2 * n_group * d_state) * ggml_element_size(zxBCdt));
+
+    // conv
+    {
+        // => {d_conv - 1 + n_seq_tokens, d_inner + 2*n_group*d_state, n_seqs}
+        ggml_tensor * conv_x = ggml_concat(ctx0, conv, ggml_transpose(ctx0, xBC), 0);
+
+        // copy last (d_conv - 1) columns back into the state cache
+        ggml_tensor * last_conv = ggml_view_3d(ctx0, conv_x, d_conv - 1, d_inner + 2 * n_group * d_state, n_seqs,
+                                               conv_x->nb[1], conv_x->nb[2], n_seq_tokens * (conv_x->nb[0]));
+
+        ggml_build_forward_expand(gf, ggml_cpy(ctx0, last_conv,
+                                               ggml_view_1d(ctx0, conv_states_all,
+                                                            (d_conv - 1) * (d_inner + 2 * n_group * d_state) * (n_seqs),
+                                                            kv_head * (d_conv - 1) * (d_inner + 2 * n_group * d_state) *
+                                                                ggml_element_size(conv_states_all))));
+
+        // 1D convolution
+        // The equivalent is to make a self-overlapping view of conv_x
+        // over d_conv columns at each stride in the 3rd dimension,
+        // then element-wise multiply that with the conv1d weight,
+        // then sum the elements of each row,
+        // (the last two steps are a dot product over rows (also doable with mul_mat))
+        // then permute away the ne[0] dimension,
+        // and then you're left with the resulting x tensor.
+        // For simultaneous sequences, all sequences need to have the same length.
+        xBC = ggml_ssm_conv(ctx0, conv_x, model.layers[il].ssm_conv1d);
+
+        // bias
+        xBC = ggml_add(ctx0, xBC, model.layers[il].ssm_conv1d_b);
+
+        xBC = ggml_silu(ctx0, xBC);
+    }
+
+    // ssm
+    {
+        // These correspond to V K Q in SSM/attention duality
+        ggml_tensor * x = ggml_view_4d(ctx0, xBC, head_dim, n_head, n_seq_tokens, n_seqs, head_dim * xBC->nb[0],
+                                       xBC->nb[1], xBC->nb[2], 0);
+        ggml_tensor * B = ggml_view_4d(ctx0, xBC, d_state, n_group, n_seq_tokens, n_seqs, d_state * xBC->nb[0],
+                                       xBC->nb[1], xBC->nb[2], d_inner * ggml_element_size(xBC));
+        ggml_tensor * C = ggml_view_4d(ctx0, xBC, d_state, n_group, n_seq_tokens, n_seqs, d_state * xBC->nb[0],
+                                       xBC->nb[1], xBC->nb[2], (d_inner + n_group * d_state) * ggml_element_size(xBC));
+
+        // {n_head, n_seq_tokens, n_seqs}
+        dt = ggml_add(ctx0, ggml_cont(ctx0, dt), model.layers[il].ssm_dt_b);
+
+        ggml_tensor * A = model.layers[il].ssm_a;
+
+        // use the states and the indices provided by build_recurrent_state
+        // (this is necessary in order to properly use the states before they are overwritten,
+        //  while avoiding to make unnecessary copies of the states)
+        auto get_ssm_rows = [&](ggml_context * ctx, ggml_tensor * states, ggml_tensor * ids) {
+            ggml_tensor * ssm = ggml_reshape_4d(ctx, states, d_state, head_dim, n_head, mctx_cur->get_size());
+
+            // TODO: use semistructured matrices to implement state-space duality
+            // => {d_inner, n_seq_tokens, n_seqs} and {d_state, d_inner, n_seqs}
+            return ggml_ssm_scan(ctx, ssm, x, dt, A, B, C, ids);
+        };
+
+        ggml_tensor * y_ssm = build_rs(inp, ssm_states_all, hparams.n_embd_s(), ubatch.n_seqs, get_ssm_rows);
+
+        // store last states
+        ggml_build_forward_expand(
+            gf, ggml_cpy(ctx0, ggml_view_1d(ctx0, y_ssm, d_state * d_inner * n_seqs, ggml_nelements(x) * x->nb[0]),
+                         ggml_view_1d(ctx0, ssm_states_all, d_state * d_inner * n_seqs,
+                                      kv_head * d_state * d_inner * ggml_element_size(ssm_states_all))));
+
+        ggml_tensor * y = ggml_view_4d(ctx0, y_ssm, head_dim, n_head, n_seq_tokens, n_seqs, x->nb[1], n_head * x->nb[1],
+                                       n_seq_tokens * n_head * x->nb[1], 0);
+
+        // TODO: skip computing output earlier for unused tokens
+
+        y = ggml_add(ctx0, y, ggml_mul(ctx0, x, model.layers[il].ssm_d));
+        cb(y, "mamba2_y_add_d", il);
+        y = ggml_swiglu_split(ctx0, ggml_cont(ctx0, z), y);
+
+        // grouped RMS norm
+        if (model.layers[il].ssm_norm) {
+            y = ggml_reshape_4d(ctx0, y, d_inner / n_group, n_group, n_seq_tokens, n_seqs);
+            y = build_norm(y, model.layers[il].ssm_norm, NULL, LLM_NORM_RMS, il);
+        }
+
+        y = ggml_reshape_3d(ctx0, y, d_inner, n_seq_tokens, n_seqs);
+
+        // {d_inner, n_embd} @ {d_inner, n_seq_tokens, n_seqs} => {n_embd, n_seq_tokens, n_seqs}
+        cur = build_lora_mm(model.layers[il].ssm_out, y);
+    }
+
+    // {n_embd, n_seq_tokens, n_seqs} => {n_embd, n_tokens}
+    cur = ggml_reshape_2d(ctx0, cur, cur->ne[0], n_seq_tokens * n_seqs);
+    cb(cur, "mamba_out", il);
+
+    return cur;
+}
diff --git a/src/models/grok.cpp b/src/models/grok.cpp
new file mode 100644
index 00000000000..6781a0e924a
--- /dev/null
+++ b/src/models/grok.cpp
@@ -0,0 +1,160 @@
+#include "models.h"
+
+llm_build_grok::llm_build_grok(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+        const int64_t n_embd_head = hparams.n_embd_head_v;
+
+        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+        GGML_ASSERT(n_embd_head == hparams.n_rot);
+
+        ggml_tensor * cur;
+        ggml_tensor * inpL;
+
+        inpL = build_inp_embd(model.tok_embd);
+
+        // inp_pos - contains the positions
+        ggml_tensor * inp_pos = build_inp_pos();
+
+        auto * inp_attn = build_attn_inp_kv();
+
+        ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+        for (int il = 0; il < n_layer; ++il) {
+            ggml_tensor * inpSA = inpL;
+
+            // norm
+            cur = build_norm(inpL,
+                    model.layers[il].attn_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "attn_norm", il);
+
+
+            // self-attention
+            {
+                // compute Q and K and RoPE them
+                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+                cb(Qcur, "Qcur", il);
+                if (model.layers[il].bq) {
+                    Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
+                    cb(Qcur, "Qcur", il);
+                }
+                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+                cb(Kcur, "Kcur", il);
+                if (model.layers[il].bk) {
+                    Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
+                    cb(Kcur, "Kcur", il);
+                }
+                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+                cb(Vcur, "Vcur", il);
+                if (model.layers[il].bv) {
+                    Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
+                    cb(Vcur, "Vcur", il);
+                }
+                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+                Qcur = ggml_rope_ext(
+                        ctx0, Qcur, inp_pos, nullptr,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+                Kcur = ggml_rope_ext(
+                        ctx0, Kcur, inp_pos, nullptr,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+                cb(Qcur, "Qcur", il);
+                cb(Kcur, "Kcur", il);
+                cb(Vcur, "Vcur", il);
+
+                cur = build_attn(inp_attn,
+                        model.layers[il].wo, model.layers[il].bo,
+                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f, il);
+            }
+            if (il == n_layer - 1 && inp_out_ids) {
+                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+            }
+            cur = build_norm(cur,
+                    model.layers[il].attn_out_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "attn_out_norm", il);
+
+            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+            cb(ffn_inp, "ffn_inp", il);
+
+            // feed-forward network
+            cur = build_norm(ffn_inp,
+                    model.layers[il].ffn_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "ffn_norm", il);
+
+            // MoE branch
+            ggml_tensor * moe_out = build_moe_ffn(cur,
+                    model.layers[il].ffn_gate_inp,
+                    model.layers[il].ffn_up_exps,
+                    model.layers[il].ffn_gate_exps,
+                    model.layers[il].ffn_down_exps,
+                    nullptr,
+                    n_expert, n_expert_used,
+                    LLM_FFN_GELU, true,
+                    false, 0.0,
+                    LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
+                    il);
+            cb(moe_out, "ffn_moe_out", il);
+
+            if (model.layers[il].ffn_up) {
+                ggml_tensor * ffn_out = build_ffn(cur,
+                        model.layers[il].ffn_up,   NULL, NULL,
+                        model.layers[il].ffn_gate, NULL, NULL,
+                        model.layers[il].ffn_down, NULL, NULL,
+                        NULL,
+                        LLM_FFN_GELU, LLM_FFN_PAR, il);
+                cb(ffn_out, "ffn_out", il);
+
+                cur = ggml_scale(ctx0, ggml_add(ctx0, ffn_out, moe_out), std::sqrt(2) / 2);
+                cb(cur, "ffn_out", il);
+            } else {
+                cur = moe_out;
+            }
+            cur = build_norm(cur,
+                    model.layers[il].ffn_post_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "ffn_post_norm", il);
+
+            cur = ggml_add(ctx0, cur, ffn_inp);
+            cb(cur, "ffn_out", il);
+
+            cur = build_cvec(cur, il);
+            cb(cur, "l_out", il);
+
+            // input for next layer
+            inpL = cur;
+        }
+        cur = inpL;
+
+        cur = build_norm(cur,
+                model.output_norm, NULL,
+                LLM_NORM_RMS, -1);
+
+        cb(cur, "result_norm", -1);
+        res->t_embd = cur;
+
+        // lm_head
+        cur = build_lora_mm(model.output, cur);
+
+        cur = ggml_scale(ctx0, cur, hparams.f_logit_scale);
+
+        // final logit soft-capping
+        if (hparams.f_final_logit_softcapping) {
+            cur = ggml_scale(ctx0, cur, 1.0f / hparams.f_final_logit_softcapping);
+            cur = ggml_tanh(ctx0, cur);
+            cur = ggml_scale(ctx0, cur, hparams.f_final_logit_softcapping);
+        }
+        cb(cur, "result_output", -1);
+        res->t_logits = cur;
+
+        ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/grovemoe.cpp b/src/models/grovemoe.cpp
new file mode 100644
index 00000000000..56b6db9a3d0
--- /dev/null
+++ b/src/models/grovemoe.cpp
@@ -0,0 +1,141 @@
+#include "models.h"
+
+
+
+llm_build_grovemoe::llm_build_grovemoe(const llama_model & model, const llm_graph_params & params) :
+    llm_graph_context(params) {
+    const int64_t n_embd_head    = hparams.n_embd_head_v;
+    const int64_t n_chunk_expert = n_expert / hparams.n_group_experts;
+
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+    GGML_ASSERT(n_embd_head == hparams.n_rot);
+
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+
+    inpL = build_inp_embd(model.tok_embd);
+
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
+
+    auto * inp_attn = build_attn_inp_kv();
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * inpSA = inpL;
+
+        // norm
+        cur = build_norm(inpL, model.layers[il].attn_norm, NULL, LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
+
+        // self_attention
+        {
+            // compute Q and K and RoPE them
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            cb(Qcur, "Qcur", il);
+
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            cb(Kcur, "Kcur", il);
+
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            cb(Vcur, "Vcur", il);
+
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head, n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+            Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL, LLM_NORM_RMS, il);
+            cb(Qcur, "Qcur_normed", il);
+
+            Qcur = ggml_rope_ext(ctx0, Qcur, inp_pos, nullptr, n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                                 ext_factor, attn_factor, beta_fast, beta_slow);
+
+            Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, NULL, LLM_NORM_RMS, il);
+            cb(Kcur, "Kcur_normed", il);
+
+            Kcur = ggml_rope_ext(ctx0, Kcur, inp_pos, nullptr, n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                                 ext_factor, attn_factor, beta_fast, beta_slow);
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, model.layers[il].bo,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f / sqrtf(float(n_embd_head)), il);
+        }
+
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0, cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+        }
+
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+        cb(ffn_inp, "ffn_inp", il);
+
+        // MoE branch
+        cur = build_norm(ffn_inp, model.layers[il].ffn_norm, NULL, LLM_NORM_RMS, il);
+        cb(cur, "ffn_norm", il);
+
+        ggml_tensor * probs = build_lora_mm(model.layers[il].ffn_gate_inp, cur);  // [n_expert, n_tokens]
+        cb(probs, "ffn_moe_logits", il);
+
+        ggml_tensor * moe_out =
+            build_moe_ffn(cur,
+                nullptr,
+                model.layers[il].ffn_up_exps,
+                model.layers[il].ffn_gate_exps,
+                model.layers[il].ffn_down_exps,
+                nullptr,
+                n_expert, n_expert_used,
+                LLM_FFN_SILU, true,
+                false, 0.0,
+                LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
+                il,
+                probs);
+        cb(moe_out, "ffn_moe_out", il);
+        cur = moe_out;
+
+        // TODO: Only do the expert selection and weights once
+        moe_out = build_moe_ffn(cur,
+                    nullptr,
+                    model.layers[il].ffn_up_chexps,
+                    model.layers[il].ffn_gate_chexps,
+                    model.layers[il].ffn_down_chexps,
+                    nullptr,
+                    n_chunk_expert, n_expert_used > n_chunk_expert ? n_chunk_expert : n_expert_used,
+                    LLM_FFN_SILU, true,
+                    false, 0.0,
+                    LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
+                    il,
+                    probs);
+        cb(moe_out, "ffn_adj_moe_out", il);
+
+        cur = ggml_add(ctx0, cur, ggml_scale(ctx0, moe_out, hparams.expert_group_scale));
+        cb(cur, "ffn_final_moe_out", il);
+
+        cur = ggml_add(ctx0, cur, ffn_inp);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+
+    cur = inpL;
+
+    cur = build_norm(cur, model.output_norm, NULL, LLM_NORM_RMS, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
+
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/hunyuan-dense.cpp b/src/models/hunyuan-dense.cpp
new file mode 100644
index 00000000000..cb30a6a33aa
--- /dev/null
+++ b/src/models/hunyuan-dense.cpp
@@ -0,0 +1,132 @@
+#include "models.h"
+
+llm_build_hunyuan_dense::llm_build_hunyuan_dense(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+        const int64_t n_embd_head = hparams.n_embd_head_v;
+
+        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+        GGML_ASSERT(n_embd_head == hparams.n_rot);
+
+        ggml_tensor * cur;
+        ggml_tensor * inpL;
+
+        inpL = build_inp_embd(model.tok_embd);
+
+        // inp_pos - contains the positions
+        ggml_tensor * inp_pos = build_inp_pos();
+
+        auto * inp_attn = build_attn_inp_kv();
+
+        const float kq_scale = 1.0f / sqrtf(float(n_embd_head));
+
+        ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+        for (int il = 0; il < n_layer; ++il) {
+            ggml_tensor * inpSA = inpL;
+
+            // norm
+            cur = build_norm(inpL,
+                    model.layers[il].attn_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "attn_norm", il);
+            // self-attention
+            {
+                // rope freq factors for llama3; may return nullptr for llama2 and other models
+                ggml_tensor * rope_factors = model.get_rope_factors(cparams, il);
+
+                // compute Q and K and RoPE them
+                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+                cb(Qcur, "Qcur", il);
+                if (model.layers[il].bq) {
+                    Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
+                    cb(Qcur, "Qcur", il);
+                }
+                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+                cb(Kcur, "Kcur", il);
+                if (model.layers[il].bk) {
+                    Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
+                    cb(Kcur, "Kcur", il);
+                }
+                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+                cb(Vcur, "Vcur", il);
+                if (model.layers[il].bv) {
+                    Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
+                    cb(Vcur, "Vcur", il);
+                }
+                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+                Qcur = ggml_rope_ext(
+                         ctx0, Qcur, inp_pos, rope_factors,
+                         n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                         ext_factor, attn_factor, beta_fast, beta_slow
+                         );
+
+                cb(Qcur, "Qcur", il);
+                cb(Kcur, "Kcur", il);
+                cb(Vcur, "Vcur", il);
+
+                Kcur = ggml_rope_ext(
+                         ctx0, Kcur, inp_pos, rope_factors,
+                         n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                         ext_factor, attn_factor, beta_fast, beta_slow
+                         );
+
+                Kcur = build_norm(Kcur,
+                         model.layers[il].attn_k_norm, nullptr,
+                         LLM_NORM_RMS, il);
+                cb(Kcur, "Kcur_norm", il);
+
+                Qcur = build_norm(Qcur,
+                         model.layers[il].attn_q_norm, nullptr,
+                         LLM_NORM_RMS, il);
+                cb(Qcur, "Qcur_norm", il);
+
+                cur = build_attn(inp_attn,
+                        model.layers[il].wo, model.layers[il].bo,
+                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, kq_scale, il);
+                cb(cur, "attn_out", il);
+            }
+            if (il == n_layer - 1 && inp_out_ids) {
+                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+            }
+            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+            cb(ffn_inp, "ffn_inp", il);
+
+            cur = build_norm(ffn_inp,
+                    model.layers[il].ffn_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "ffn_norm", il);
+            // feed-forward network (non-MoE)
+            ggml_tensor * cur_mlp = build_ffn(cur,
+                        model.layers[il].ffn_up,   NULL, NULL,
+                        model.layers[il].ffn_gate, NULL, NULL,
+                        model.layers[il].ffn_down, NULL, NULL,
+                        NULL,
+                        LLM_FFN_SILU, LLM_FFN_PAR, il);
+            cb(cur_mlp, "ffn_out", il);
+
+            cur = ggml_add(ctx0, cur_mlp, ffn_inp);
+
+            cur = build_cvec(cur, il);
+            cb(cur, "l_out", il);
+
+            // input for next layer
+            inpL = cur;
+        }
+        cur = inpL;
+
+        cur = build_norm(cur,
+                model.output_norm, NULL,
+                LLM_NORM_RMS, -1);
+
+        cb(cur, "result_norm", -1);
+        res->t_embd = cur;
+        // lm_head
+        cur = build_lora_mm(model.output, cur);
+        cb(cur, "result_output", -1);
+        res->t_logits = cur;
+
+        ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/hunyuan-moe.cpp b/src/models/hunyuan-moe.cpp
new file mode 100644
index 00000000000..a9940b04af9
--- /dev/null
+++ b/src/models/hunyuan-moe.cpp
@@ -0,0 +1,154 @@
+#include "models.h"
+
+llm_build_hunyuan_moe::llm_build_hunyuan_moe(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+        const int64_t n_embd_head = hparams.n_embd_head_v;
+
+        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+        GGML_ASSERT(n_embd_head == hparams.n_rot);
+
+        ggml_tensor * cur;
+        ggml_tensor * inpL;
+
+        inpL = build_inp_embd(model.tok_embd);
+
+        // inp_pos - contains the positions
+        ggml_tensor * inp_pos = build_inp_pos();
+
+        auto * inp_attn = build_attn_inp_kv();
+
+        const float kq_scale = 1.0f / sqrtf(float(n_embd_head));
+
+        ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+        for (int il = 0; il < n_layer; ++il) {
+            ggml_tensor * inpSA = inpL;
+
+            // norm
+            cur = build_norm(inpL,
+                    model.layers[il].attn_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "attn_norm", il);
+
+            // self-attention
+            {
+                // rope freq factors for llama3; may return nullptr for llama2 and other models
+                ggml_tensor * rope_factors = model.get_rope_factors(cparams, il);
+
+                // compute Q and K and RoPE them
+                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+                cb(Qcur, "Qcur", il);
+                if (model.layers[il].bq) {
+                    Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
+                    cb(Qcur, "Qcur", il);
+                }
+                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+                cb(Kcur, "Kcur", il);
+                if (model.layers[il].bk) {
+                    Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
+                    cb(Kcur, "Kcur", il);
+                }
+                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+                cb(Vcur, "Vcur", il);
+                if (model.layers[il].bv) {
+                    Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
+                    cb(Vcur, "Vcur", il);
+                }
+                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+                Qcur = ggml_rope_ext(
+                        ctx0, Qcur, inp_pos, rope_factors,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+                cb(Qcur, "Qcur", il);
+                cb(Kcur, "Kcur", il);
+                cb(Vcur, "Vcur", il);
+
+                Kcur = ggml_rope_ext(
+                        ctx0, Kcur, inp_pos, rope_factors,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+                Kcur = build_norm(Kcur,
+                        model.layers[il].attn_k_norm, nullptr,
+                        LLM_NORM_RMS, il);
+                cb(Kcur, "Kcur_norm", il);
+
+                Qcur = build_norm(Qcur,
+                        model.layers[il].attn_q_norm, nullptr,
+                        LLM_NORM_RMS, il);
+                cb(Qcur, "Qcur_norm", il);
+
+                cur = build_attn(inp_attn,
+                        model.layers[il].wo, model.layers[il].bo,
+                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, kq_scale, il);
+                cb(cur, "attn_out", il);
+            }
+            if (il == n_layer - 1 && inp_out_ids) {
+                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+            }
+            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+            cb(ffn_inp, "ffn_inp", il);
+
+            cur = build_norm(ffn_inp,
+                model.layers[il].ffn_norm, NULL,
+                LLM_NORM_RMS, il);
+            cb(cur, "ffn_norm", il);
+
+            // feed-forward network (non-MoE)
+            ggml_tensor * cur_mlp = build_ffn(cur,
+                    model.layers[il].ffn_up_shexp,   NULL, NULL,
+                    model.layers[il].ffn_gate_shexp, NULL, NULL,
+                    model.layers[il].ffn_down_shexp, NULL, NULL,
+                    NULL,
+                    LLM_FFN_SILU, LLM_FFN_PAR, il);
+            cb(cur_mlp, "ffn_mlp", il);
+
+            // MoE branch
+            ggml_tensor * cur_moe = build_moe_ffn(cur,
+                    model.layers[il].ffn_gate_inp,
+                    model.layers[il].ffn_up_exps,
+                    model.layers[il].ffn_gate_exps,
+                    model.layers[il].ffn_down_exps,
+                    nullptr,
+                    n_expert, n_expert_used,
+                    LLM_FFN_SILU,
+                    true, // norm_topk_prob
+                    false,
+                    0.0,
+                    LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
+                    il);
+            cb(cur_moe, "ffn_moe_out", il);
+
+            ggml_tensor * ffn_out = ggml_add(ctx0, cur_moe, cur_mlp);
+            cb(ffn_out, "ffn_out", il);
+
+            cur = ggml_add(ctx0, ffn_out, ffn_inp);
+
+            cur = build_cvec(cur, il);
+            cb(cur, "l_out", il);
+
+            // input for next layer
+            inpL = cur;
+        }
+        cur = inpL;
+
+        cur = build_norm(cur,
+                model.output_norm, NULL,
+                LLM_NORM_RMS, -1);
+
+        cb(cur, "result_norm", -1);
+        res->t_embd = cur;
+
+        // lm_head
+        cur = build_lora_mm(model.output, cur);
+        cb(cur, "result_output", -1);
+        res->t_logits = cur;
+
+        ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/internlm2.cpp b/src/models/internlm2.cpp
new file mode 100644
index 00000000000..e97c82198df
--- /dev/null
+++ b/src/models/internlm2.cpp
@@ -0,0 +1,121 @@
+#include "models.h"
+
+
+llm_build_internlm2::llm_build_internlm2(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+        const int64_t n_embd_head = hparams.n_embd_head_v;
+
+        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+        GGML_ASSERT(n_embd_head == hparams.n_rot);
+
+        ggml_tensor * cur;
+        ggml_tensor * inpL;
+
+        inpL = build_inp_embd(model.tok_embd);
+
+        // inp_pos - contains the positions
+        ggml_tensor * inp_pos = build_inp_pos();
+
+        auto * inp_attn = build_attn_inp_kv();
+
+        ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+        for (int il = 0; il < n_layer; ++il) {
+            ggml_tensor * inpSA = inpL;
+
+            // norm
+            cur = build_norm(inpL,
+                    model.layers[il].attn_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "attn_norm", il);
+
+            // self-attention
+            {
+                // compute Q and K and RoPE them
+                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+                cb(Qcur, "Qcur", il);
+                if (model.layers[il].bq) {
+                    Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
+                    cb(Qcur, "Qcur", il);
+                }
+                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+                cb(Kcur, "Kcur", il);
+                if (model.layers[il].bk) {
+                    Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
+                    cb(Kcur, "Kcur", il);
+                }
+                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+                cb(Vcur, "Vcur", il);
+                if (model.layers[il].bv) {
+                    Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
+                    cb(Vcur, "Vcur", il);
+                }
+                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+                Qcur = ggml_rope_ext(
+                        ctx0, Qcur, inp_pos, nullptr,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+                Kcur = ggml_rope_ext(
+                        ctx0, Kcur, inp_pos, nullptr,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+                cb(Qcur, "Qcur", il);
+                cb(Kcur, "Kcur", il);
+                cb(Vcur, "Vcur", il);
+
+                cur = build_attn(inp_attn,
+                        model.layers[il].wo, model.layers[il].bo,
+                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+            }
+            if (il == n_layer - 1 && inp_out_ids) {
+                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+            }
+            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+            cb(ffn_inp, "ffn_inp", il);
+
+            // feed-forward network
+            cur = build_norm(ffn_inp,
+                    model.layers[il].ffn_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "ffn_norm", il);
+
+            cur = build_ffn(cur,
+                    model.layers[il].ffn_up,   NULL, NULL,
+                    model.layers[il].ffn_gate, NULL, NULL,
+                    model.layers[il].ffn_down, NULL, NULL,
+                    NULL,
+                    LLM_FFN_SILU, LLM_FFN_PAR, il);
+            cb(cur, "ffn_out", il);
+
+            cur = ggml_add(ctx0, cur, ffn_inp);
+
+            cur = build_cvec(cur, il);
+            cb(cur, "l_out", il);
+
+            // input for next layer
+            inpL = cur;
+        }
+        cur = inpL;
+
+        cur = build_norm(cur,
+                model.output_norm, NULL,
+                LLM_NORM_RMS, -1);
+
+        cb(cur, "result_norm", -1);
+        res->t_embd = cur;
+
+        // lm_head
+        cur = build_lora_mm(model.output, cur);
+
+        cb(cur, "result_output", -1);
+        res->t_logits = cur;
+
+        ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/jais.cpp b/src/models/jais.cpp
new file mode 100644
index 00000000000..a1c43065bbc
--- /dev/null
+++ b/src/models/jais.cpp
@@ -0,0 +1,86 @@
+#include "models.h"
+
+llm_build_jais::llm_build_jais(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+        const int64_t n_embd_head = hparams.n_embd_head_v;
+        const int64_t n_embd_gqa  = hparams.n_embd_v_gqa();
+
+        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+
+        ggml_tensor * cur;
+        ggml_tensor * inpL;
+
+        inpL = build_inp_embd(model.tok_embd);
+
+        auto * inp_attn = build_attn_inp_kv();
+
+        ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+        for (int il = 0; il < n_layer; ++il) {
+            cur = build_norm(inpL,
+                    model.layers[il].attn_norm,
+                    model.layers[il].attn_norm_b,
+                    LLM_NORM, il);
+            cb(cur, "attn_norm", il);
+
+            // self-attention
+            {
+                cur = build_lora_mm(model.layers[il].wqkv, cur);
+                cb(cur, "wqkv", il);
+
+                cur = ggml_add(ctx0, cur, model.layers[il].bqkv);
+                cb(cur, "bqkv", il);
+
+                ggml_tensor * Qcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head,    n_tokens, n_embd_head*sizeof(float), cur->nb[1], 0*cur->nb[0]*(n_embd));
+                ggml_tensor * Kcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*cur->nb[0]*(n_embd));
+                ggml_tensor * Vcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*cur->nb[0]*(n_embd + n_embd_gqa));
+
+                cb(Qcur, "Qcur", il);
+                cb(Kcur, "Kcur", il);
+                cb(Vcur, "Vcur", il);
+
+                cur = build_attn(inp_attn,
+                        model.layers[il].wo, model.layers[il].bo,
+                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/float(n_embd_head), il);
+            }
+            if (il == n_layer - 1 && inp_out_ids) {
+                cur  = ggml_get_rows(ctx0,  cur, inp_out_ids);
+                inpL = ggml_get_rows(ctx0, inpL, inp_out_ids);
+            }
+            // add the input
+            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpL);
+            cb(ffn_inp, "ffn_inp", il);
+
+            // FF
+            {
+                cur = build_norm(ffn_inp,
+                        model.layers[il].ffn_norm,
+                        model.layers[il].ffn_norm_b,
+                        LLM_NORM, il);
+                cb(cur, "ffn_norm", il);
+
+                cur = build_ffn(cur,
+                        model.layers[il].ffn_up,   model.layers[il].ffn_up_b,   NULL,
+                        model.layers[il].ffn_gate, model.layers[il].ffn_gate_b, NULL,
+                        model.layers[il].ffn_down, model.layers[il].ffn_down_b, NULL,
+                        NULL,
+                        LLM_FFN_SILU, LLM_FFN_PAR, il);
+                cb(cur, "ffn_out", il);
+            }
+            inpL = ggml_add(ctx0, cur, ffn_inp);
+            cb(inpL, "l_out", il);
+        }
+        cur = build_norm(inpL,
+                model.output_norm,
+                model.output_norm_b,
+                LLM_NORM, -1);
+
+        cb(cur, "result_norm", -1);
+        res->t_embd = cur;
+
+        cur = build_lora_mm(model.output, cur);
+
+        cb(cur, "result_output", -1);
+        res->t_logits = cur;
+
+        ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/jamba.cpp b/src/models/jamba.cpp
new file mode 100644
index 00000000000..0c8c1361d4e
--- /dev/null
+++ b/src/models/jamba.cpp
@@ -0,0 +1,107 @@
+#include "models.h"
+
+
+llm_build_jamba::llm_build_jamba(const llama_model & model, const llm_graph_params & params) : llm_graph_context_mamba(params) {
+        const int64_t n_embd_head = hparams.n_embd_head_v;
+
+        ggml_tensor * cur;
+        ggml_tensor * inpL;
+
+        // {n_embd, n_tokens}
+        inpL = build_inp_embd(model.tok_embd);
+
+        auto * inp_hybrid = build_inp_mem_hybrid();
+
+        ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+        for (int il = 0; il < n_layer; ++il) {
+            const int64_t n_head_kv = hparams.n_head_kv(il);
+
+            cur = build_norm(inpL, model.layers[il].attn_norm, NULL, LLM_NORM_RMS, il);
+            cb(cur, "attn_norm", il);
+
+            if (n_head_kv == 0) {
+                cur = build_mamba_layer(inp_hybrid->get_recr(), cur, model, ubatch, il);
+            } else {
+                // Attention
+
+                struct ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+                struct ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+                struct ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+
+                cb(Qcur, "Qcur", il);
+                cb(Kcur, "Kcur", il);
+                cb(Vcur, "Vcur", il);
+
+                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+                cb(Qcur, "Qcur", il);
+                cb(Kcur, "Kcur", il);
+                cb(Vcur, "Vcur", il);
+
+                // No RoPE :)
+                cur = build_attn(inp_hybrid->get_attn(),
+                        model.layers[il].wo, NULL,
+                        Qcur, Kcur, Vcur, NULL, NULL, NULL, 1.0f/sqrtf(float(n_embd_head)), il);
+            }
+            if (il == n_layer - 1 && inp_out_ids) {
+                cur  = ggml_get_rows(ctx0,  cur, inp_out_ids);
+                inpL = ggml_get_rows(ctx0, inpL, inp_out_ids);
+            }
+            // residual
+            struct ggml_tensor * ffn_inp = ggml_add(ctx0, inpL, cur);
+            cb(cur, "ffn_inp", il);
+
+            cur = build_norm(ffn_inp, model.layers[il].ffn_norm, NULL, LLM_NORM_RMS, il);
+            cb(cur, "ffn_norm", il);
+
+            // feed-forward network
+            if (model.layers[il].ffn_gate_inp == nullptr) {
+                // FFN
+                cur = build_ffn(cur,
+                        model.layers[il].ffn_up,   NULL, NULL,
+                        model.layers[il].ffn_gate, NULL, NULL,
+                        model.layers[il].ffn_down, NULL, NULL,
+                        NULL,
+                        LLM_FFN_SILU, LLM_FFN_PAR, il);
+                cb(cur, "ffn_out", il);
+            } else {
+                // MoE branch
+                cur = build_moe_ffn(cur,
+                        model.layers[il].ffn_gate_inp,
+                        model.layers[il].ffn_up_exps,
+                        model.layers[il].ffn_gate_exps,
+                        model.layers[il].ffn_down_exps,
+                        nullptr,
+                        n_expert, n_expert_used,
+                        LLM_FFN_SILU, false,
+                        false, 0.0,
+                        LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
+                        il);
+                cb(cur, "ffn_moe_out", il);
+            }
+            // residual
+            cur = ggml_add(ctx0, ffn_inp, cur);
+
+            cur = build_cvec(cur, il);
+            cb(cur, "l_out", il);
+
+            // input for next layer
+            inpL = cur;
+        }
+        // final rmsnorm
+        cur = build_norm(inpL, model.output_norm, NULL, LLM_NORM_RMS, -1);
+
+        cb(cur, "result_norm", -1);
+        res->t_embd = cur;
+
+        // lm_head
+        cur = build_lora_mm(model.output, cur);
+
+        cb(cur, "result_output", -1);
+        res->t_logits = cur;
+
+        ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/lfm2.cpp b/src/models/lfm2.cpp
new file mode 100644
index 00000000000..ca06bacd7bc
--- /dev/null
+++ b/src/models/lfm2.cpp
@@ -0,0 +1,173 @@
+#include "models.h"
+
+#include "../llama-memory-hybrid.h"
+
+
+llm_build_lfm2::llm_build_lfm2(const llama_model & model, const llm_graph_params & params) :
+    llm_graph_context(params),
+    model(model) {
+    ggml_tensor * cur = build_inp_embd(model.tok_embd);
+    cb(cur, "model.embed_tokens", -1);
+
+    ggml_tensor * inp_pos     = build_inp_pos();
+    auto *        inp_hybrid  = build_inp_mem_hybrid();
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        const bool is_moe_layer = il >= static_cast<int>(hparams.n_layer_dense_lead);
+
+        auto * prev_cur = cur;
+        cur             = build_norm(cur, model.layers[il].attn_norm, NULL, LLM_NORM_RMS, il);
+        cb(cur, "model.layers.{}.operator_norm", il);
+
+        cur = hparams.is_recurrent(il) ? build_shortconv_block(cur, inp_hybrid->get_recr(), il) :
+                                         build_attn_block(cur, inp_pos, inp_hybrid->get_attn(), il);
+
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur      = ggml_get_rows(ctx0, cur, inp_out_ids);
+            prev_cur = ggml_get_rows(ctx0, prev_cur, inp_out_ids);
+        }
+
+        cur = ggml_add(ctx0, prev_cur, cur);
+
+        auto * ffn_norm_out = build_norm(cur, model.layers[il].ffn_norm, NULL, LLM_NORM_RMS, il);
+        cb(ffn_norm_out, "model.layers.{}.ffn_norm", il);
+
+        ggml_tensor * ffn_out =
+            is_moe_layer ? build_moe_feed_forward(ffn_norm_out, il) : build_dense_feed_forward(ffn_norm_out, il);
+        cb(ffn_norm_out, "model.layers.{}.ffn_out", il);
+
+        cur = ggml_add(ctx0, cur, ffn_out);
+    }
+
+    cur = build_norm(cur, model.tok_norm, NULL, LLM_NORM_RMS, -1);
+    cb(cur, "model.embedding_norm", -1);
+    res->t_embd = cur;
+
+    cur = build_lora_mm(model.output, cur);
+    cb(cur, "lm_head", -1);
+
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}
+
+ggml_tensor * llm_build_lfm2::build_moe_feed_forward(ggml_tensor * cur, int il) const {
+    return build_moe_ffn(cur,
+                        model.layers[il].ffn_gate_inp, model.layers[il].ffn_up_exps,
+                        model.layers[il].ffn_gate_exps, model.layers[il].ffn_down_exps,
+                        model.layers[il].ffn_exp_probs_b, n_expert, n_expert_used, LLM_FFN_SILU, true, false, 0.0,
+                        static_cast<llama_expert_gating_func_type>(hparams.expert_gating_func), il);
+}
+
+ggml_tensor * llm_build_lfm2::build_dense_feed_forward(ggml_tensor * cur, int il) const {
+    GGML_ASSERT(!model.layers[il].ffn_up_b);
+    GGML_ASSERT(!model.layers[il].ffn_gate_b);
+    GGML_ASSERT(!model.layers[il].ffn_down_b);
+    return build_ffn(cur,
+        model.layers[il].ffn_up, NULL, NULL,
+        model.layers[il].ffn_gate, NULL, NULL,
+        model.layers[il].ffn_down, NULL, NULL,
+        NULL, LLM_FFN_SILU, LLM_FFN_PAR, il);
+}
+
+ggml_tensor * llm_build_lfm2::build_attn_block(ggml_tensor *             cur,
+                                               ggml_tensor *             inp_pos,
+                                               llm_graph_input_attn_kv * inp_attn,
+                                               int                       il) const {
+    GGML_ASSERT(hparams.n_embd_v_gqa(il) == hparams.n_embd_k_gqa(il));
+    const auto n_embd_head = hparams.n_embd_head_v;
+    const auto n_head_kv   = hparams.n_head_kv(il);
+
+    auto * q = build_lora_mm(model.layers[il].wq, cur);
+    cb(q, "model.layers.{}.self_attn.q_proj", il);
+    auto * k = build_lora_mm(model.layers[il].wk, cur);
+    cb(k, "model.layers.{}.self_attn.k_proj", il);
+    auto * v = build_lora_mm(model.layers[il].wv, cur);
+    cb(v, "model.layers.{}.self_attn.v_proj", il);
+
+    q = ggml_reshape_3d(ctx0, q, n_embd_head, n_head, n_tokens);
+    k = ggml_reshape_3d(ctx0, k, n_embd_head, n_head_kv, n_tokens);
+    v = ggml_reshape_3d(ctx0, v, n_embd_head, n_head_kv, n_tokens);
+
+    // qk norm
+    q = build_norm(q, model.layers[il].attn_q_norm, NULL, LLM_NORM_RMS, il);
+    cb(q, "model.layers.{}.self_attn.q_layernorm", il);
+    k = build_norm(k, model.layers[il].attn_k_norm, NULL, LLM_NORM_RMS, il);
+    cb(k, "model.layers.{}.self_attn.k_layernorm", il);
+
+    // RoPE
+    q = ggml_rope_ext(ctx0, q, inp_pos, nullptr, n_rot, rope_type, n_ctx_orig, freq_base, freq_scale, ext_factor,
+                      attn_factor, beta_fast, beta_slow);
+    k = ggml_rope_ext(ctx0, k, inp_pos, nullptr, n_rot, rope_type, n_ctx_orig, freq_base, freq_scale, ext_factor,
+                      attn_factor, beta_fast, beta_slow);
+
+    cur = build_attn(inp_attn,
+            model.layers[il].wo, NULL,
+            q, k, v, nullptr, nullptr, nullptr, 1.0f / sqrtf(float(n_embd_head)), il);
+
+    cb(cur, "model.layers.{}.self_attn.out_proj", il);
+
+    return cur;
+}
+
+ggml_tensor * llm_build_lfm2::build_shortconv_block(ggml_tensor * cur, llm_graph_input_rs * inp_recr, int il) {
+    const auto *   mctx_cur     = static_cast<const llama_memory_hybrid_context *>(mctx)->get_recr();
+    const uint32_t kv_head      = mctx_cur->get_head();
+    const int64_t  n_seq_tokens = ubatch.n_seq_tokens;
+    const int64_t  n_seqs       = ubatch.n_seqs;
+    GGML_ASSERT(n_seqs != 0);
+    GGML_ASSERT(ubatch.equal_seqs());
+    GGML_ASSERT(ubatch.n_tokens == n_seq_tokens * n_seqs);
+
+    GGML_ASSERT(hparams.n_shortconv_l_cache > 1);
+    const uint32_t d_conv = hparams.n_shortconv_l_cache - 1;
+
+    // {n_embd, n_tokens} => {n_embd, n_seq_tokens, n_seqs}
+    cur = ggml_reshape_3d(ctx0, cur, cur->ne[0], n_seq_tokens, n_seqs);
+
+    auto * bcx = build_lora_mm(model.layers[il].shortconv.in_proj, cur);
+    cb(bcx, "model.layers.{}.conv.in_proj", il);
+
+    constexpr auto n_chunks = 3;
+    GGML_ASSERT(bcx->ne[0] % n_chunks == 0);
+    const auto chunk_size = bcx->ne[0] / n_chunks;
+    auto *     b          = ggml_view_3d(ctx0, bcx, chunk_size, bcx->ne[1], bcx->ne[2], bcx->nb[1], bcx->nb[2],
+                                         0 * chunk_size * ggml_element_size(bcx));
+    auto *     c          = ggml_view_3d(ctx0, bcx, chunk_size, bcx->ne[1], bcx->ne[2], bcx->nb[1], bcx->nb[2],
+                                         1 * chunk_size * ggml_element_size(bcx));
+    auto *     x          = ggml_view_3d(ctx0, bcx, chunk_size, bcx->ne[1], bcx->ne[2], bcx->nb[1], bcx->nb[2],
+                                         2 * chunk_size * ggml_element_size(bcx));
+
+    auto * bx = ggml_transpose(ctx0, ggml_mul(ctx0, b, x));
+
+    // read conv state
+    auto * conv_state = mctx_cur->get_r_l(il);
+    auto * conv_rs    = build_rs(inp_recr, conv_state, hparams.n_embd_r(), n_seqs);
+    auto * conv       = ggml_reshape_3d(ctx0, conv_rs, d_conv, hparams.n_embd, n_seqs);
+
+    bx = ggml_concat(ctx0, conv, bx, 0);
+    GGML_ASSERT(bx->ne[0] > conv->ne[0]);
+
+    // last d_conv columns is a new conv state
+    auto * new_conv = ggml_view_3d(ctx0, bx, conv->ne[0], bx->ne[1], bx->ne[2], bx->nb[1], bx->nb[2],
+                                   (bx->ne[0] - conv->ne[0]) * ggml_element_size(bx));
+    GGML_ASSERT(ggml_are_same_shape(conv, new_conv));
+
+    // write new conv conv state
+    ggml_build_forward_expand(gf, ggml_cpy(ctx0, new_conv,
+                                           ggml_view_1d(ctx0, conv_state, ggml_nelements(new_conv),
+                                                        kv_head * d_conv * n_embd * ggml_element_size(new_conv))));
+
+    auto * conv_kernel = model.layers[il].shortconv.conv;
+    auto * conv_out    = ggml_ssm_conv(ctx0, bx, conv_kernel);
+    cb(conv_out, "model.layers.{}.conv.conv", il);
+
+    auto * y = ggml_mul(ctx0, c, conv_out);
+    y        = build_lora_mm(model.layers[il].shortconv.out_proj, y);
+    cb(y, "model.layers.{}.conv.out_proj", il);
+    // {n_embd, n_seq_tokens, n_seqs} => {n_embd, n_tokens}
+    y = ggml_reshape_2d(ctx0, y, y->ne[0], n_seq_tokens * n_seqs);
+
+    return y;
+}
diff --git a/src/models/llada-moe.cpp b/src/models/llada-moe.cpp
new file mode 100644
index 00000000000..2dcef4caccc
--- /dev/null
+++ b/src/models/llada-moe.cpp
@@ -0,0 +1,123 @@
+#include "models.h"
+
+llm_build_llada_moe::llm_build_llada_moe(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+        const int64_t n_embd_head = hparams.n_embd_head_v;
+
+        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+        GGML_ASSERT(n_embd_head == hparams.n_rot);
+
+        ggml_tensor * cur;
+        ggml_tensor * inpL;
+
+        inpL = build_inp_embd(model.tok_embd);
+
+        // inp_pos - contains the positions
+        ggml_tensor * inp_pos = build_inp_pos();
+
+        auto * inp_attn = build_attn_inp_no_cache();
+
+        ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+        for (int il = 0; il < n_layer; ++il) {
+            ggml_tensor * inpSA = inpL;
+
+            // norm
+            cur = build_norm(inpL,
+                    model.layers[il].attn_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "attn_norm", il);
+
+            // self_attention
+            {
+                // compute Q and K and RoPE them
+                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+                cb(Qcur, "Qcur", il);
+
+                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+                cb(Kcur, "Kcur", il);
+
+                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+                cb(Vcur, "Vcur", il);
+
+                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head, n_tokens);
+                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+                Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL, LLM_NORM_RMS, il);
+                cb(Qcur, "Qcur_normed", il);
+
+                Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, NULL, LLM_NORM_RMS, il);
+                cb(Kcur, "Kcur_normed", il);
+
+                Qcur = ggml_rope_ext(
+                        ctx0, Qcur, inp_pos, nullptr,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+                Kcur = ggml_rope_ext(
+                        ctx0, Kcur, inp_pos, nullptr,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+                cb(Qcur, "Qcur", il);
+                cb(Kcur, "Kcur", il);
+                cb(Vcur, "Vcur", il);
+
+                cur = build_attn(inp_attn,
+                        model.layers[il].wo, NULL,
+                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+            }
+            if (il == n_layer - 1 && inp_out_ids) {
+                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+            }
+            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+            cb(ffn_inp, "ffn_inp", il);
+
+            // MoE branch
+            cur = build_norm(ffn_inp,
+                    model.layers[il].ffn_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "ffn_norm", il);
+
+            cur = build_moe_ffn(cur,
+                    model.layers[il].ffn_gate_inp,
+                    model.layers[il].ffn_up_exps,
+                    model.layers[il].ffn_gate_exps,
+                    model.layers[il].ffn_down_exps,
+                    nullptr,
+                    n_expert, n_expert_used,
+                    LLM_FFN_SILU, false,
+                    false, 0.0,
+                    LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
+                    il);
+            cb(cur, "ffn_moe_out", il);
+
+            cur = ggml_add(ctx0, cur, ffn_inp);
+
+            cur = build_cvec(cur, il);
+            cb(cur, "l_out", il);
+
+            // input for next layer
+            inpL = cur;
+        }
+        cur = inpL;
+
+        cur = build_norm(cur,
+                model.output_norm, NULL,
+                LLM_NORM_RMS, -1);
+
+        cb(cur, "result_norm", -1);
+        res->t_embd = cur;
+
+        // lm_head
+        cur = build_lora_mm(model.output, cur);
+
+        cb(cur, "result_output", -1);
+        res->t_logits = cur;
+
+        ggml_build_forward_expand(gf, cur);
+}
+
diff --git a/src/models/llada.cpp b/src/models/llada.cpp
new file mode 100644
index 00000000000..b10b89b1f62
--- /dev/null
+++ b/src/models/llada.cpp
@@ -0,0 +1,101 @@
+#include "models.h"
+
+
+llm_build_llada::llm_build_llada(const llama_model & model, const llm_graph_params & params) :
+        llm_graph_context(params) {
+        // LLaDA is similar to LLaMA but uses non-causal attention for diffusion
+        const int64_t n_embd_head = hparams.n_embd_head_v;
+
+        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+        GGML_ASSERT(n_embd_head == hparams.n_rot);
+
+        ggml_tensor * cur;
+        ggml_tensor * inpL;
+
+        inpL = build_inp_embd(model.tok_embd);
+
+        // inp_pos - contains the positions
+        ggml_tensor * inp_pos = build_inp_pos();
+
+        // Non-causal attention for diffusion
+        auto * inp_attn = build_attn_inp_no_cache();
+
+        ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+        for (int il = 0; il < n_layer; ++il) {
+            ggml_tensor * inpSA = inpL;
+
+            // norm
+            cur = build_norm(inpL, model.layers[il].attn_norm, NULL, LLM_NORM_RMS, il);
+            cb(cur, "attn_norm", il);
+
+            // self-attention
+            {
+                // compute separate Q, K, V projections without bias, matching LLaDALlamaBlock
+                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+
+                cb(Qcur, "Qcur", il);
+                cb(Kcur, "Kcur", il);
+                cb(Vcur, "Vcur", il);
+
+                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head, n_tokens);
+                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+                Qcur = ggml_rope_ext(ctx0, Qcur, inp_pos, nullptr, n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                                     ext_factor, attn_factor, beta_fast, beta_slow);
+
+                Kcur = ggml_rope_ext(ctx0, Kcur, inp_pos, nullptr, n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                                     ext_factor, attn_factor, beta_fast, beta_slow);
+
+                cb(Qcur, "Qcur", il);
+                cb(Kcur, "Kcur", il);
+                cb(Vcur, "Vcur", il);
+
+                cur = build_attn(inp_attn,
+                        model.layers[il].wo, NULL,
+                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f / sqrtf(float(n_embd_head)), il);
+            }
+            if (il == n_layer - 1 && inp_out_ids) {
+                cur   = ggml_get_rows(ctx0, cur, inp_out_ids);
+                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+            }
+            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+            cb(ffn_inp, "ffn_inp", il);
+
+            // feed-forward network
+            cur = build_norm(ffn_inp, model.layers[il].ffn_norm, NULL, LLM_NORM_RMS, il);
+            cb(cur, "ffn_norm", il);
+
+            cur = build_ffn(cur,
+                    model.layers[il].ffn_up, NULL, NULL,
+                    model.layers[il].ffn_gate, NULL, NULL,
+                    model.layers[il].ffn_down, NULL, NULL,
+                    NULL, LLM_FFN_SILU, LLM_FFN_PAR, il);
+            cb(cur, "ffn_out", il);
+
+            cur = ggml_add(ctx0, cur, ffn_inp);
+
+            cur = build_cvec(cur, il);
+            cb(cur, "l_out", il);
+
+            // input for next layer
+            inpL = cur;
+        }
+        cur = inpL;
+
+        cur = build_norm(cur, model.output_norm, NULL, LLM_NORM_RMS, -1);
+
+        cb(cur, "result_norm", -1);
+        res->t_embd = cur;
+
+        // lm_head
+        cur = build_lora_mm(model.output, cur);
+
+        cb(cur, "result_output", -1);
+        res->t_logits = cur;
+
+        ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/llama-iswa.cpp b/src/models/llama-iswa.cpp
new file mode 100644
index 00000000000..03f80616821
--- /dev/null
+++ b/src/models/llama-iswa.cpp
@@ -0,0 +1,174 @@
+#include "models.h"
+
+llm_build_llama_iswa::llm_build_llama_iswa(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+    const int64_t n_embd_head = hparams.n_embd_head_v;
+
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+    GGML_ASSERT(n_embd_head == hparams.n_rot);
+
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+
+    inpL = build_inp_embd(model.tok_embd);
+
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
+
+    // temperature tuning
+    ggml_tensor * inp_attn_scale = nullptr;
+    inp_attn_scale = build_inp_attn_scale();
+
+    auto * inp_attn = build_attn_inp_kv_iswa();
+
+    const float kq_scale = hparams.f_attention_scale == 0.0f ? 1.0f/sqrtf(float(n_embd_head)) : hparams.f_attention_scale;
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * inpSA = inpL;
+
+        const bool use_rope = hparams.n_no_rope_layer_step > 0 &&
+                              (il + 1) % hparams.n_no_rope_layer_step != 0;
+
+        // norm
+        cur = build_norm(inpL,
+                model.layers[il].attn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
+
+        // self-attention
+        {
+            // rope freq factors for llama3; may return nullptr for llama2 and other models
+            ggml_tensor * rope_factors = model.get_rope_factors(cparams, il);
+
+            // compute Q and K and RoPE them
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            cb(Qcur, "Qcur", il);
+            if (model.layers[il].bq) {
+                Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
+                cb(Qcur, "Qcur", il);
+            }
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            cb(Kcur, "Kcur", il);
+            if (model.layers[il].bk) {
+                Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
+                cb(Kcur, "Kcur", il);
+            }
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            cb(Vcur, "Vcur", il);
+            if (model.layers[il].bv) {
+                Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
+                cb(Vcur, "Vcur", il);
+            }
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+            if (use_rope) {
+                Qcur = ggml_rope_ext(
+                        ctx0, Qcur, inp_pos, rope_factors,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+                Kcur = ggml_rope_ext(
+                        ctx0, Kcur, inp_pos, rope_factors,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+            } else if (inp_attn_scale) {
+                Qcur = ggml_mul(ctx0, Qcur, inp_attn_scale);
+            }
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            if (use_rope && hparams.use_kq_norm) {
+                // Llama4TextL2Norm
+                Qcur = ggml_rms_norm(ctx0, Qcur, hparams.f_norm_rms_eps);
+                Kcur = ggml_rms_norm(ctx0, Kcur, hparams.f_norm_rms_eps);
+                cb(Qcur, "Qcur_normed", il);
+                cb(Kcur, "Kcur_normed", il);
+            }
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, model.layers[il].bo,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, kq_scale, il);
+            cb(cur, "attn_out", il);
+        }
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+        }
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+        cb(ffn_inp, "ffn_inp", il);
+
+        // feed-forward network (non-MoE)
+        if (model.layers[il].ffn_gate_inp == nullptr) {
+            cur = build_norm(ffn_inp,
+                    model.layers[il].ffn_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "ffn_norm", il);
+
+            cur = build_ffn(cur,
+                    model.layers[il].ffn_up,   model.layers[il].ffn_up_b,   NULL,
+                    model.layers[il].ffn_gate, model.layers[il].ffn_gate_b, NULL,
+                    model.layers[il].ffn_down, model.layers[il].ffn_down_b, NULL,
+                    NULL,
+                    LLM_FFN_SILU, LLM_FFN_PAR, il);
+            cb(cur, "ffn_out", il);
+        } else {
+            ggml_tensor * ffn_inp_normed = build_norm(ffn_inp,
+                    model.layers[il].ffn_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "ffn_norm", il);
+
+            ggml_tensor * moe_out = build_moe_ffn(ffn_inp_normed,
+                    model.layers[il].ffn_gate_inp,
+                    model.layers[il].ffn_up_exps,
+                    model.layers[il].ffn_gate_exps,
+                    model.layers[il].ffn_down_exps,
+                    nullptr,
+                    n_expert, n_expert_used,
+                    LLM_FFN_SILU, false,
+                    false, 0.0,
+                    LLAMA_EXPERT_GATING_FUNC_TYPE_SIGMOID,
+                    il);
+
+            // Shared experts
+            ggml_tensor * shexp_out = build_ffn(ffn_inp_normed,
+                model.layers[il].ffn_up_shexp,   NULL, NULL,
+                model.layers[il].ffn_gate_shexp, NULL, NULL,
+                model.layers[il].ffn_down_shexp, NULL, NULL,
+                NULL,
+                LLM_FFN_SILU, LLM_FFN_PAR, il);
+            cb(shexp_out, "ffn_moe_shexp", il);
+
+            cur = ggml_add(ctx0, moe_out, shexp_out);
+            cb(cur, "ffn_moe_out_merged", il);
+        }
+        cur = ggml_add(ctx0, cur, ffn_inp);
+        cb(cur, "ffn_out", il);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+    cur = inpL;
+
+    cur = build_norm(cur,
+            model.output_norm, NULL,
+            LLM_NORM_RMS, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
+
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/llama.cpp b/src/models/llama.cpp
new file mode 100644
index 00000000000..289028959f9
--- /dev/null
+++ b/src/models/llama.cpp
@@ -0,0 +1,156 @@
+#include "models.h"
+
+
+llm_build_llama::llm_build_llama(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+        const int64_t n_embd_head = hparams.n_embd_head_v;
+
+        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+        GGML_ASSERT(n_embd_head == hparams.n_rot);
+
+        ggml_tensor * cur;
+        ggml_tensor * inpL;
+
+        inpL = build_inp_embd(model.tok_embd);
+
+        // inp_pos - contains the positions
+        ggml_tensor * inp_pos = build_inp_pos();
+
+        auto * inp_attn = build_attn_inp_kv();
+
+        const float kq_scale = hparams.f_attention_scale == 0.0f ? 1.0f/sqrtf(float(n_embd_head)) : hparams.f_attention_scale;
+
+        ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+        for (int il = 0; il < n_layer; ++il) {
+            ggml_tensor * inpSA = inpL;
+
+            // norm
+            cur = build_norm(inpL,
+                    model.layers[il].attn_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "attn_norm", il);
+
+            // self-attention
+            {
+                // rope freq factors for llama3; may return nullptr for llama2 and other models
+                ggml_tensor * rope_factors = model.get_rope_factors(cparams, il);
+
+                // compute Q and K and RoPE them
+                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+                cb(Qcur, "Qcur", il);
+                if (model.layers[il].bq) {
+                    Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
+                    cb(Qcur, "Qcur", il);
+                }
+                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+                cb(Kcur, "Kcur", il);
+                if (model.layers[il].bk) {
+                    Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
+                    cb(Kcur, "Kcur", il);
+                }
+                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+                cb(Vcur, "Vcur", il);
+                if (model.layers[il].bv) {
+                    Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
+                    cb(Vcur, "Vcur", il);
+                }
+                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+                Qcur = ggml_rope_ext(
+                        ctx0, Qcur, inp_pos, rope_factors,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+                Kcur = ggml_rope_ext(
+                        ctx0, Kcur, inp_pos, rope_factors,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+                cb(Qcur, "Qcur", il);
+                cb(Kcur, "Kcur", il);
+                cb(Vcur, "Vcur", il);
+
+                if (hparams.use_kq_norm) {
+                    // Llama4TextL2Norm
+                    Qcur = ggml_rms_norm(ctx0, Qcur, hparams.f_norm_rms_eps);
+                    Kcur = ggml_rms_norm(ctx0, Kcur, hparams.f_norm_rms_eps);
+                    cb(Qcur, "Qcur_normed", il);
+                    cb(Kcur, "Kcur_normed", il);
+                }
+                cur = build_attn(inp_attn,
+                        model.layers[il].wo, model.layers[il].bo,
+                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, kq_scale, il);
+                cb(cur, "attn_out", il);
+            }
+            if (il == n_layer - 1 && inp_out_ids) {
+                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+            }
+            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+            cb(ffn_inp, "ffn_inp", il);
+
+            // feed-forward network (non-MoE)
+            if (model.layers[il].ffn_gate_inp == nullptr) {
+
+                cur = build_norm(ffn_inp,
+                        model.layers[il].ffn_norm, NULL,
+                        LLM_NORM_RMS, il);
+                cb(cur, "ffn_norm", il);
+
+                cur = build_ffn(cur,
+                        model.layers[il].ffn_up,   model.layers[il].ffn_up_b,   NULL,
+                        model.layers[il].ffn_gate, model.layers[il].ffn_gate_b, NULL,
+                        model.layers[il].ffn_down, model.layers[il].ffn_down_b, NULL,
+                        NULL,
+                        LLM_FFN_SILU, LLM_FFN_PAR, il);
+                cb(cur, "ffn_out", il);
+            } else {
+                // MoE branch
+                cur = build_norm(ffn_inp,
+                        model.layers[il].ffn_norm, NULL,
+                        LLM_NORM_RMS, il);
+                cb(cur, "ffn_norm", il);
+
+                cur = build_moe_ffn(cur,
+                        model.layers[il].ffn_gate_inp,
+                        model.layers[il].ffn_up_exps,
+                        model.layers[il].ffn_gate_exps,
+                        model.layers[il].ffn_down_exps,
+                        nullptr,
+                        n_expert, n_expert_used,
+                        LLM_FFN_SILU, true,
+                        false, 0.0,
+                        LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
+                        il);
+                cb(cur, "ffn_moe_out", il);
+            }
+            cur = ggml_add(ctx0, cur, ffn_inp);
+            cb(cur, "ffn_out", il);
+
+            cur = build_cvec(cur, il);
+            cb(cur, "l_out", il);
+
+            // input for next layer
+            inpL = cur;
+        }
+        cur = inpL;
+
+        cur = build_norm(cur,
+                model.output_norm, NULL,
+                LLM_NORM_RMS, -1);
+
+        cb(cur, "result_norm", -1);
+        res->t_embd = cur;
+
+        // lm_head
+        cur = build_lora_mm(model.output, cur);
+
+        cb(cur, "result_output", -1);
+        res->t_logits = cur;
+
+        ggml_build_forward_expand(gf, cur);
+    }
diff --git a/src/models/mamba.cpp b/src/models/mamba.cpp
new file mode 100644
index 00000000000..46819613c2d
--- /dev/null
+++ b/src/models/mamba.cpp
@@ -0,0 +1,55 @@
+#include "models.h"
+
+
+llm_build_mamba::llm_build_mamba(const llama_model & model, const llm_graph_params & params) : llm_graph_context_mamba(params) {
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+
+    // {n_embd, n_tokens}
+    inpL = build_inp_embd(model.tok_embd);
+
+    auto * rs_inp = build_rs_inp();
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        // norm
+        cur = build_norm(inpL, model.layers[il].attn_norm, NULL, LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
+
+        if (model.arch == LLM_ARCH_MAMBA2) {
+            cur = build_mamba2_layer(rs_inp, cur, model, ubatch, il);
+        } else {
+            cur = build_mamba_layer(rs_inp, cur, model, ubatch, il);
+        }
+
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur  = ggml_get_rows(ctx0, cur, inp_out_ids);
+            inpL = ggml_get_rows(ctx0, inpL, inp_out_ids);
+        }
+
+        // residual
+        cur = ggml_add(ctx0, cur, inpL);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+
+    // final rmsnorm
+    cur = build_norm(inpL, model.output_norm, NULL, LLM_NORM_RMS, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
+
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}
+
diff --git a/src/models/minicpm3.cpp b/src/models/minicpm3.cpp
new file mode 100644
index 00000000000..02ce21ce653
--- /dev/null
+++ b/src/models/minicpm3.cpp
@@ -0,0 +1,200 @@
+#include "models.h"
+
+
+llm_build_minicpm3::llm_build_minicpm3(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+        //TODO: if the model varies, these parameters need to be read from the model
+        const int64_t n_embd_base = 256;
+        const float scale_embd  = 12.0f;
+        const float scale_depth = 1.4f;
+        const float kq_scale = 1.0f / sqrtf(float(hparams.n_embd_head_k));
+
+        const uint32_t n_embd_head_qk_rope = hparams.n_rot;
+        const uint32_t n_embd_head_qk_nope = hparams.n_embd_head_k - hparams.n_rot;
+        const uint32_t kv_lora_rank = hparams.n_lora_kv;
+
+        ggml_tensor * cur;
+        ggml_tensor * inpL;
+
+        inpL = build_inp_embd(model.tok_embd);
+
+        // scale the input embeddings
+        inpL = ggml_scale(ctx0, inpL, scale_embd);
+        cb(inpL, "inp_scaled", -1);
+
+        // inp_pos - contains the positions
+        ggml_tensor * inp_pos = build_inp_pos();
+
+        auto * inp_attn = build_attn_inp_kv();
+
+        ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+        for (int il = 0; il < n_layer; ++il) {
+            ggml_tensor * inpSA = inpL;
+
+            ggml_tensor * rope_factors = model.get_rope_factors(cparams, il);
+
+            // norm
+            cur = build_norm(inpL,
+                    model.layers[il].attn_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "attn_norm", il);
+
+            // self_attention
+            {
+                ggml_tensor * q = NULL;
+                // {n_embd, q_lora_rank} * {n_embd, n_tokens} -> {q_lora_rank, n_tokens}
+                q = ggml_mul_mat(ctx0, model.layers[il].wq_a, cur);
+                cb(q, "q", il);
+
+                q = build_norm(q,
+                        model.layers[il].attn_q_a_norm, NULL,
+                        LLM_NORM_RMS, il);
+                cb(q, "q", il);
+
+                // {q_lora_rank, n_head * hparams.n_embd_head_k} * {q_lora_rank, n_tokens} -> {n_head * hparams.n_embd_head_k, n_tokens}
+                q = ggml_mul_mat(ctx0, model.layers[il].wq_b, q);
+                cb(q, "q", il);
+
+                // split into {n_head * n_embd_head_qk_nope, n_tokens}
+                ggml_tensor * q_nope = ggml_view_3d(ctx0, q, n_embd_head_qk_nope, n_head, n_tokens,
+                        ggml_row_size(q->type, hparams.n_embd_head_k),
+                        ggml_row_size(q->type, hparams.n_embd_head_k * n_head),
+                        0);
+                cb(q_nope, "q_nope", il);
+
+                // and {n_head * n_embd_head_qk_rope, n_tokens}
+                ggml_tensor * q_pe = ggml_view_3d(ctx0, q, n_embd_head_qk_rope, n_head, n_tokens,
+                        ggml_row_size(q->type, hparams.n_embd_head_k),
+                        ggml_row_size(q->type, hparams.n_embd_head_k * n_head),
+                        ggml_row_size(q->type, n_embd_head_qk_nope));
+                cb(q_pe, "q_pe", il);
+
+                // {n_embd, kv_lora_rank + n_embd_head_qk_rope} * {n_embd, n_tokens} -> {kv_lora_rank + n_embd_head_qk_rope, n_tokens}
+                ggml_tensor * kv_pe_compresseed = ggml_mul_mat(ctx0, model.layers[il].wkv_a_mqa, cur);
+                cb(kv_pe_compresseed, "kv_pe_compresseed", il);
+
+                // split into {kv_lora_rank, n_tokens}
+                ggml_tensor * kv_compressed = ggml_view_2d(ctx0, kv_pe_compresseed, kv_lora_rank, n_tokens,
+                        kv_pe_compresseed->nb[1],
+                        0);
+                cb(kv_compressed, "kv_compressed", il);
+
+                // and {n_embd_head_qk_rope, n_tokens}
+                ggml_tensor * k_pe = ggml_view_3d(ctx0, kv_pe_compresseed, n_embd_head_qk_rope, 1, n_tokens,
+                        kv_pe_compresseed->nb[1],
+                        kv_pe_compresseed->nb[1],
+                        ggml_row_size(kv_pe_compresseed->type, kv_lora_rank));
+                cb(k_pe, "k_pe", il);
+
+                kv_compressed = build_norm(kv_compressed,
+                        model.layers[il].attn_kv_a_norm, NULL,
+                        LLM_NORM_RMS, il);
+                cb(kv_compressed, "kv_compressed", il);
+
+                // {kv_lora_rank, n_head * (n_embd_head_qk_nope + n_embd_head_v)} * {kv_lora_rank, n_tokens} -> {n_head * (n_embd_head_qk_nope + n_embd_head_v), n_tokens}
+                ggml_tensor * kv = ggml_mul_mat(ctx0, model.layers[il].wkv_b, kv_compressed);
+                cb(kv, "kv", il);
+
+                // split into {n_head * n_embd_head_qk_nope, n_tokens}
+                ggml_tensor * k_nope = ggml_view_3d(ctx0, kv, n_embd_head_qk_nope, n_head, n_tokens,
+                        ggml_row_size(kv->type, n_embd_head_qk_nope + hparams.n_embd_head_v),
+                        ggml_row_size(kv->type, n_head * (n_embd_head_qk_nope + hparams.n_embd_head_v)),
+                        0);
+                cb(k_nope, "k_nope", il);
+
+                // and {n_head * n_embd_head_v, n_tokens}
+                ggml_tensor * v_states = ggml_view_3d(ctx0, kv, hparams.n_embd_head_v, n_head, n_tokens,
+                        ggml_row_size(kv->type, (n_embd_head_qk_nope + hparams.n_embd_head_v)),
+                        ggml_row_size(kv->type, (n_embd_head_qk_nope + hparams.n_embd_head_v)*n_head),
+                        ggml_row_size(kv->type, (n_embd_head_qk_nope)));
+                cb(v_states, "v_states", il);
+
+                v_states = ggml_cont(ctx0, v_states);
+                cb(v_states, "v_states", il);
+
+                q_pe = ggml_rope_ext(
+                        ctx0, q_pe, inp_pos, rope_factors,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+                cb(q_pe, "q_pe", il);
+
+                // shared RoPE key
+                k_pe = ggml_rope_ext(
+                        ctx0, k_pe, inp_pos, rope_factors,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+                cb(k_pe, "k_pe", il);
+
+                ggml_tensor * q_states = ggml_concat(ctx0, q_nope, q_pe, 0);
+                cb(q_states, "q_states", il);
+
+                ggml_tensor * k_states = ggml_concat(ctx0, k_nope, ggml_repeat(ctx0, k_pe, q_pe), 0);
+                cb(k_states, "k_states", il);
+
+                cur = build_attn(inp_attn,
+                        model.layers[il].wo, NULL,
+                        q_states, k_states, v_states, nullptr, nullptr, nullptr, kq_scale, il);
+            }
+            if (il == n_layer - 1 && inp_out_ids) {
+                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+            }
+            // scale_res - scale the hidden states for residual connection
+            const float scale_res = scale_depth/sqrtf(float(n_layer)); // TODO: is this correct?
+            cur = ggml_scale(ctx0, cur, scale_res);
+            cb(cur, "hidden_scaled", il);
+
+            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+            cb(ffn_inp, "ffn_inp", il);
+
+            // feed-forward network
+            {
+                cur = build_norm(ffn_inp,
+                        model.layers[il].ffn_norm, NULL,
+                        LLM_NORM_RMS, il);
+                cb(cur, "ffn_norm", il);
+
+                cur = build_ffn(cur,
+                        model.layers[il].ffn_up,   NULL, NULL,
+                        model.layers[il].ffn_gate, NULL, NULL,
+                        model.layers[il].ffn_down, NULL, NULL,
+                        NULL,
+                        LLM_FFN_SILU, LLM_FFN_PAR, il);
+                cb(cur, "ffn_out", il);
+            }
+            // scale the hidden states for residual connection
+            cur = ggml_scale(ctx0, cur, scale_res);
+            cb(cur, "hidden_scaled_ffn", il);
+
+            cur = ggml_add(ctx0, cur, ffn_inp);
+
+            cur = build_cvec(cur, il);
+            cb(cur, "l_out", il);
+
+            // input for next layer
+            inpL = cur;
+        }
+        cur = inpL;
+
+        cur = build_norm(cur,
+                model.output_norm, NULL,
+                LLM_NORM_RMS, -1);
+
+        cb(cur, "result_norm", -1);
+        res->t_embd = cur;
+
+        // lm_head scaling
+        const float scale_lmhead = float(n_embd_base)/float(n_embd);
+        cur = ggml_scale(ctx0, cur, scale_lmhead);
+        cb(cur, "lmhead_scaling", -1);
+
+        // lm_head
+        cur = build_lora_mm(model.output, cur);
+
+        cb(cur, "result_output", -1);
+        res->t_logits = cur;
+
+        ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/minimax-m2.cpp b/src/models/minimax-m2.cpp
new file mode 100644
index 00000000000..f7001badf75
--- /dev/null
+++ b/src/models/minimax-m2.cpp
@@ -0,0 +1,124 @@
+
+#include "models.h"
+
+llm_build_minimax_m2::llm_build_minimax_m2(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+    const int64_t n_embd_head = hparams.n_embd_head_v;
+
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+    // GGML_ASSERT(n_embd_head == hparams.n_rot); this is wrong in case of minimax, head_dim = 128, n_rot = 64
+
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+
+    inpL = build_inp_embd(model.tok_embd);
+
+    ggml_tensor * inp_pos = build_inp_pos();
+    auto inp_attn = build_attn_inp_kv();
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * inpSA = inpL;
+
+        cur = inpL;
+
+        // self_attention
+        {
+            cur = build_norm(inpL, model.layers[il].attn_norm, NULL, LLM_NORM_RMS, il);
+            cb(cur, "attn_norm", il);
+
+            // compute Q and K and RoPE them
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            cb(Qcur, "Qcur", il);
+
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            cb(Kcur, "Kcur", il);
+
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            cb(Vcur, "Vcur", il);
+
+            Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(Qcur, "Qcur_normed", il);
+
+            Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(Kcur, "Kcur_normed", il);
+
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+            Qcur = ggml_rope_ext(
+                ctx0, Qcur, inp_pos, nullptr,
+                n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                ext_factor, attn_factor, beta_fast, beta_slow
+                );
+
+            Kcur = ggml_rope_ext(
+                ctx0, Kcur, inp_pos, nullptr,
+                n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                ext_factor, attn_factor, beta_fast, beta_slow
+                );
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, NULL,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+        }
+
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+        }
+
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+        cb(ffn_inp, "ffn_inp", il);
+
+        // MoE branch
+        cur = build_norm(ffn_inp,
+                model.layers[il].ffn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "ffn_norm", il);
+
+        cur = build_moe_ffn(cur,
+                model.layers[il].ffn_gate_inp,
+                model.layers[il].ffn_up_exps,
+                model.layers[il].ffn_gate_exps,
+                model.layers[il].ffn_down_exps,
+                model.layers[il].ffn_exp_probs_b,
+                n_expert, n_expert_used,
+                LLM_FFN_SILU, true,
+                false, 0.0,
+                (llama_expert_gating_func_type) hparams.expert_gating_func,
+                il);
+        cb(cur, "ffn_moe_out", il);
+
+        cur = ggml_add(ctx0, cur, ffn_inp);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+
+    cur = inpL;
+
+    cur = build_norm(cur,
+            model.output_norm, NULL,
+            LLM_NORM_RMS, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
+
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/models.h b/src/models/models.h
new file mode 100644
index 00000000000..af203343a4d
--- /dev/null
+++ b/src/models/models.h
@@ -0,0 +1,477 @@
+#pragma once
+
+#include "../llama-model.h"
+#include "../llama-graph.h"
+#include "../llama-memory-recurrent.h"
+
+#include <cmath>
+
+struct llm_graph_context_mamba : public llm_graph_context {
+    llm_graph_context_mamba(const llm_graph_params & params);
+
+    virtual ~llm_graph_context_mamba() = default;
+
+    ggml_tensor * build_mamba_layer(llm_graph_input_rs * inp, ggml_tensor * cur, const llama_model & model, const llama_ubatch & ubatch, int il);
+    ggml_tensor * build_mamba2_layer(llm_graph_input_rs * inp, ggml_tensor * cur, const llama_model & model, const llama_ubatch & ubatch, int il) const;
+
+};
+
+// Base class for RWKV-related models
+struct llm_build_rwkv6_base : public llm_graph_context {
+    const llama_model & model;
+
+    llm_build_rwkv6_base(const llama_model & model, const llm_graph_params & params);
+
+    virtual ~llm_build_rwkv6_base() = default;
+
+    ggml_tensor * build_rwkv6_channel_mix(const llama_layer * layer,
+                                          ggml_tensor *       cur,
+                                          ggml_tensor *       x_prev,
+                                          llm_arch            arch) const;
+
+    ggml_tensor * build_rwkv6_time_mix(llm_graph_input_rs * inp,
+                                       ggml_tensor *        cur,
+                                       ggml_tensor *        x_prev,
+                                       const llama_ubatch & ubatch,
+                                       int                  il) const;
+};
+
+// Base class for RWKV7-related models
+struct llm_build_rwkv7_base : public llm_graph_context {
+    const llama_model & model;
+
+    llm_build_rwkv7_base(const llama_model & model, const llm_graph_params & params);
+
+    virtual ~llm_build_rwkv7_base() = default;
+
+    // RWKV7-specific graph building methods
+    ggml_tensor * build_rwkv7_channel_mix(const llama_layer * layer,
+                                          ggml_tensor *       cur,
+                                          ggml_tensor *       x_prev,
+                                          llm_arch            arch) const;
+    ggml_tensor * build_rwkv7_time_mix(llm_graph_input_rs * inp,
+                                       ggml_tensor *        cur,
+                                       ggml_tensor *        x_prev,
+                                       ggml_tensor *&       first_layer_value,
+                                       const llama_ubatch & ubatch,
+                                       int                  il) const;
+};
+
+struct llm_build_apertus : public llm_graph_context {
+    llm_build_apertus(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_arcee : public llm_graph_context {
+    llm_build_arcee(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_arctic : public llm_graph_context {
+    llm_build_arctic(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_arwkv7 : public llm_build_rwkv7_base {
+    llm_build_arwkv7(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_baichuan : public llm_graph_context {
+    llm_build_baichuan(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_bailingmoe2 : public llm_graph_context {
+    llm_build_bailingmoe2(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_bailingmoe : public llm_graph_context {
+    llm_build_bailingmoe(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_bert : public llm_graph_context {
+    llm_build_bert(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_bitnet : public llm_graph_context {
+    llm_build_bitnet(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_bloom : public llm_graph_context {
+    llm_build_bloom(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_chameleon : public llm_graph_context {
+    llm_build_chameleon(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_chatglm : public llm_graph_context {
+    llm_build_chatglm(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_codeshell : public llm_graph_context {
+    llm_build_codeshell(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_cogvlm : public llm_graph_context {
+    llm_build_cogvlm(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_cohere2_iswa : public llm_graph_context {
+    llm_build_cohere2_iswa(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_command_r : public llm_graph_context {
+    llm_build_command_r(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_dbrx : public llm_graph_context {
+    llm_build_dbrx(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_deci : public llm_graph_context {
+    llm_build_deci(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_deepseek2 : public llm_graph_context {
+    llm_build_deepseek2(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_deepseek : public llm_graph_context {
+    llm_build_deepseek(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_dots1 : public llm_graph_context {
+    llm_build_dots1(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_dream : public llm_graph_context {
+    llm_build_dream(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_ernie4_5 : public llm_graph_context {
+    llm_build_ernie4_5(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_ernie4_5_moe : public llm_graph_context {
+    llm_build_ernie4_5_moe(const llama_model & model, const llm_graph_params & params);
+};
+
+template <bool iswa>
+struct llm_build_exaone4 : public llm_graph_context {
+    llm_build_exaone4(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_exaone : public llm_graph_context {
+    llm_build_exaone(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_falcon : public llm_graph_context {
+    llm_build_falcon(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_falcon_h1 : public llm_graph_context_mamba {
+    llm_build_falcon_h1(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_gemma2_iswa : public llm_graph_context {
+    llm_build_gemma2_iswa(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_gemma3_iswa : public llm_graph_context {
+    llm_build_gemma3_iswa(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_gemma3n_iswa : public llm_graph_context {
+    const llama_model & model;
+
+    const int64_t n_embd_head;
+    const int64_t n_embd_altup;
+    const int64_t n_altup;
+    const int     i_altup_act;
+    const int     n_layer_sparsity = 10; // number of layers using activation sparsity
+    const float   f_sparsity_std_mul = 1.6448533535003662f; // std_multiplier = normal_dist.icdf(0.95)
+
+    llm_build_gemma3n_iswa(const llama_model & model, const llm_graph_params & params);
+    ggml_tensor * calc_magnitude(ggml_tensor * x);
+    ggml_tensor * view_2d_slice(ggml_tensor * x, int idx);
+    ggml_tensor * get_per_layer_inputs();
+    ggml_tensor * project_per_layer_inputs(ggml_tensor * inputs_embeds, ggml_tensor * inp_per_layer);
+    ggml_tensor * gaussian_topk(ggml_tensor * x);
+    ggml_tensor * altup_compute_router_modalities(ggml_tensor * x, int il);
+    ggml_tensor * altup_predict(ggml_tensor * cur, int il);
+    ggml_tensor * laurel(ggml_tensor * cur, int il);
+    ggml_tensor * altup_correct(ggml_tensor * predictions, ggml_tensor * activated, int il);
+};
+
+struct llm_build_gemma_embedding : public llm_graph_context {
+    llm_build_gemma_embedding(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_gemma : public llm_graph_context {
+    llm_build_gemma(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_glm4 : public llm_graph_context {
+    llm_build_glm4(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_glm4_moe : public llm_graph_context {
+    llm_build_glm4_moe(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_gpt2 : public llm_graph_context {
+    llm_build_gpt2(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_gptneox : public llm_graph_context {
+    llm_build_gptneox(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_granite : public llm_graph_context {
+    llm_build_granite(const llama_model & model, const llm_graph_params & params);
+
+private:
+    ggml_tensor * build_attention_layer(
+              ggml_tensor             * cur,
+              ggml_tensor             * inp_pos,
+              llm_graph_input_attn_kv * inp_attn,
+        const llama_model             & model,
+        const int64_t                 n_embd_head,
+        const int                     il);
+
+    ggml_tensor * build_layer_ffn(
+              ggml_tensor       * cur,
+              ggml_tensor       * inpSA,
+        const llama_model       & model,
+        const int                 il);
+};
+
+struct llm_build_granite_hybrid : public llm_graph_context_mamba {
+    llm_build_granite_hybrid(const llama_model & model, const llm_graph_params & params);
+    ggml_tensor * build_layer_ffn(ggml_tensor * cur, ggml_tensor * inpSA, const llama_model & model, const int il);
+    ggml_tensor * build_attention_layer(ggml_tensor * cur, ggml_tensor * inp_pos, llm_graph_input_attn_kv * inp_attn,
+        const llama_model & model,const int64_t n_embd_head, const int il);
+};
+
+struct llm_build_grok : public llm_graph_context {
+    llm_build_grok(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_grovemoe : public llm_graph_context {
+    llm_build_grovemoe(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_hunyuan_dense : public llm_graph_context {
+    llm_build_hunyuan_dense(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_hunyuan_moe : public llm_graph_context {
+    llm_build_hunyuan_moe(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_internlm2 : public llm_graph_context {
+    llm_build_internlm2(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_jais : public llm_graph_context {
+    llm_build_jais(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_jamba : public llm_graph_context_mamba {
+    llm_build_jamba(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_lfm2 : public llm_graph_context {
+    const llama_model & model;
+
+    llm_build_lfm2(const llama_model & model, const llm_graph_params & params);
+    ggml_tensor * build_moe_feed_forward(ggml_tensor * cur, int il) const;
+    ggml_tensor * build_dense_feed_forward(ggml_tensor * cur, int il) const;
+    ggml_tensor * build_attn_block(ggml_tensor * cur, ggml_tensor * inp_pos, llm_graph_input_attn_kv * inp_attn, int il) const;
+    ggml_tensor * build_shortconv_block(ggml_tensor * cur, llm_graph_input_rs * inp_recr, int il);
+
+};
+
+struct llm_build_llada : public llm_graph_context {
+    llm_build_llada(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_llada_moe : public llm_graph_context {
+    llm_build_llada_moe(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_llama : public llm_graph_context {
+    llm_build_llama(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_llama_iswa : public llm_graph_context {
+    llm_build_llama_iswa(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_mamba : public llm_graph_context_mamba {
+    llm_build_mamba(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_minicpm3 : public llm_graph_context {
+    llm_build_minicpm3(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_minimax_m2 : public llm_graph_context {
+    llm_build_minimax_m2(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_mpt : public llm_graph_context {
+    llm_build_mpt(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_nemotron : public llm_graph_context {
+    llm_build_nemotron(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_nemotron_h : public llm_graph_context_mamba {
+    llm_build_nemotron_h(const llama_model & model, const llm_graph_params & params);
+    ggml_tensor * build_ffn_layer(ggml_tensor * cur, const llama_model & model, const int il);
+    ggml_tensor * build_attention_layer(ggml_tensor * cur, llm_graph_input_attn_kv * inp_attn,
+        const llama_model & model, const int64_t n_embd_head, const int il);
+};
+
+struct llm_build_neo_bert : public llm_graph_context {
+    llm_build_neo_bert(const llama_model & model, const llm_graph_params & params);
+};
+
+template <bool iswa>
+struct llm_build_olmo2 : public llm_graph_context {
+    llm_build_olmo2(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_olmoe : public llm_graph_context {
+    llm_build_olmoe(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_olmo : public llm_graph_context {
+    llm_build_olmo(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_openai_moe_iswa : public llm_graph_context {
+    llm_build_openai_moe_iswa(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_openelm : public llm_graph_context {
+    llm_build_openelm(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_orion : public llm_graph_context {
+    llm_build_orion(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_phi2 : public llm_graph_context {
+    llm_build_phi2(const llama_model & model, const llm_graph_params & params);
+};
+
+template<bool iswa>
+struct llm_build_phi3 : public llm_graph_context {
+    llm_build_phi3(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_plamo2 : public llm_graph_context_mamba {
+    llm_build_plamo2(const llama_model & model, const llm_graph_params & params);
+    private:
+        ggml_tensor * build_plamo2_mamba_layer(llm_graph_input_rs * inp, ggml_tensor * cur, const llama_model & model, const llama_ubatch & ubatch, int il);
+        ggml_tensor * build_plamo2_attn_layer(llm_graph_input_attn_kv * inp, ggml_tensor * inp_pos, ggml_tensor * cur,
+                                                const llama_model & model, int il);
+};
+
+struct llm_build_plamo : public llm_graph_context {
+    llm_build_plamo(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_plm : public llm_graph_context {
+    llm_build_plm(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_qwen2 : public llm_graph_context {
+    llm_build_qwen2(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_qwen2moe : public llm_graph_context {
+    llm_build_qwen2moe(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_qwen2vl : public llm_graph_context {
+    llm_build_qwen2vl(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_qwen3 : public llm_graph_context {
+    llm_build_qwen3(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_qwen3moe : public llm_graph_context {
+    llm_build_qwen3moe(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_qwen3vl : public llm_graph_context {
+    llm_build_qwen3vl(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_qwen3vlmoe : public llm_graph_context {
+    llm_build_qwen3vlmoe(const llama_model & model, const llm_graph_params & params);
+};
+
+
+struct llm_build_qwen : public llm_graph_context {
+    llm_build_qwen(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_refact : public llm_graph_context {
+    llm_build_refact(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_rwkv6 : public llm_build_rwkv6_base {
+    llm_build_rwkv6(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_rwkv6qwen2 : public llm_build_rwkv6_base {
+    llm_build_rwkv6qwen2(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_rwkv7 : public llm_build_rwkv7_base {
+    llm_build_rwkv7(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_seed_oss : public llm_graph_context {
+    llm_build_seed_oss(const llama_model & model, const llm_graph_params & params);
+};
+
+template <bool iswa>
+struct llm_build_smallthinker : public llm_graph_context {
+    llm_build_smallthinker(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_smollm3 : public llm_graph_context {
+    llm_build_smollm3(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_stablelm : public llm_graph_context {
+    llm_build_stablelm(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_starcoder2 : public llm_graph_context {
+    llm_build_starcoder2(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_starcoder : public llm_graph_context {
+    llm_build_starcoder(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_t5_dec : public llm_graph_context {
+    llm_build_t5_dec(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_t5_enc : public llm_graph_context {
+    llm_build_t5_enc(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_wavtokenizer_dec : public llm_graph_context {
+    llm_build_wavtokenizer_dec(const llama_model & model, const llm_graph_params & params);
+};
+
+struct llm_build_xverse : public llm_graph_context {
+    llm_build_xverse(const llama_model & model, const llm_graph_params & params);
+};
diff --git a/src/models/mpt.cpp b/src/models/mpt.cpp
new file mode 100644
index 00000000000..2328e027a74
--- /dev/null
+++ b/src/models/mpt.cpp
@@ -0,0 +1,126 @@
+#include "models.h"
+
+
+
+llm_build_mpt::llm_build_mpt(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+    const int64_t n_embd_head = hparams.n_embd_head_v;
+    const int64_t n_embd_gqa  = hparams.n_embd_v_gqa();
+
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+
+    ggml_tensor * cur;
+    ggml_tensor * pos;
+    ggml_tensor * inpL;
+
+    inpL = build_inp_embd(model.tok_embd);
+
+    auto * inp_attn = build_attn_inp_kv();
+
+    if (model.pos_embd) {
+        // inp_pos - contains the positions
+        ggml_tensor * inp_pos = build_inp_pos();
+        pos                   = ggml_get_rows(ctx0, model.pos_embd, inp_pos);
+        cb(pos, "pos_embd", -1);
+
+        inpL = ggml_add(ctx0, inpL, pos);
+        cb(inpL, "inpL", -1);
+    }
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * attn_norm;
+
+        attn_norm = build_norm(inpL, model.layers[il].attn_norm, model.layers[il].attn_norm_b, LLM_NORM, il);
+        cb(attn_norm, "attn_norm", il);
+
+        // self-attention
+        {
+            cur = attn_norm;
+
+            cur = build_lora_mm(model.layers[il].wqkv, cur);
+            cb(cur, "wqkv", il);
+
+            if (model.layers[il].bqkv) {
+                cur = ggml_add(ctx0, cur, model.layers[il].bqkv);
+                cb(cur, "bqkv", il);
+            }
+
+            if (hparams.f_clamp_kqv > 0.0f) {
+                cur = ggml_clamp(ctx0, cur, -hparams.f_clamp_kqv, hparams.f_clamp_kqv);
+                cb(cur, "wqkv_clamped", il);
+            }
+
+            ggml_tensor * Qcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head, n_tokens, n_embd_head * sizeof(float),
+                                              cur->nb[1], 0 * sizeof(float) * (n_embd));
+            ggml_tensor * Kcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head * sizeof(float),
+                                              cur->nb[1], 1 * sizeof(float) * (n_embd));
+            ggml_tensor * Vcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head * sizeof(float),
+                                              cur->nb[1], 1 * sizeof(float) * (n_embd + n_embd_gqa));
+
+            // Q/K Layernorm
+            if (model.layers[il].attn_q_norm) {
+                Qcur = ggml_reshape_2d(ctx0, Qcur, n_embd_head * n_head, n_tokens);
+                Kcur = ggml_reshape_2d(ctx0, Kcur, n_embd_head * n_head_kv, n_tokens);
+
+                Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, model.layers[il].attn_q_norm_b, LLM_NORM, il);
+
+                Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, model.layers[il].attn_k_norm_b, LLM_NORM, il);
+
+                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head, n_tokens);
+                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            }
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, model.layers[il].bo,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f / sqrtf(float(n_embd_head)), il);
+        }
+
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur  = ggml_get_rows(ctx0, cur, inp_out_ids);
+            inpL = ggml_get_rows(ctx0, inpL, inp_out_ids);
+        }
+
+        // Add the input
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpL);
+        cb(ffn_inp, "ffn_inp", il);
+
+        // feed forward
+        {
+            cur = build_norm(ffn_inp, model.layers[il].ffn_norm, model.layers[il].ffn_norm_b, LLM_NORM, il);
+            cb(cur, "ffn_norm", il);
+            cur = build_ffn(cur,
+                model.layers[il].ffn_up, model.layers[il].ffn_up_b, NULL,
+                NULL, NULL, NULL,
+                model.layers[il].ffn_down, model.layers[il].ffn_down_b, NULL,
+                model.layers[il].ffn_act, LLM_FFN_GELU, LLM_FFN_SEQ, il);
+            cb(cur, "ffn_out", il);
+        }
+
+        cur = ggml_add(ctx0, cur, ffn_inp);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+
+    cur = inpL;
+
+    cur = build_norm(cur, model.output_norm, model.output_norm_b, LLM_NORM, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    cur = build_lora_mm(model.output, cur);
+
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/nemotron-h.cpp b/src/models/nemotron-h.cpp
new file mode 100644
index 00000000000..54143488887
--- /dev/null
+++ b/src/models/nemotron-h.cpp
@@ -0,0 +1,121 @@
+#include "models.h"
+
+
+
+llm_build_nemotron_h::llm_build_nemotron_h(const llama_model & model, const llm_graph_params & params) :
+    llm_graph_context_mamba(params) {
+    const int64_t n_embd_head = hparams.n_embd_head_v;
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+
+    inpL = build_inp_embd(model.tok_embd);
+    ggml_build_forward_expand(gf, inpL);
+
+    auto * inp = build_inp_mem_hybrid();
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        struct ggml_tensor * inpSA = inpL;
+
+        // norm
+        cur = build_norm(inpL, model.layers[il].attn_norm, NULL, LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
+
+        if (hparams.is_recurrent(il)) {
+            // ssm layer //
+            cur = build_mamba2_layer(inp->get_recr(), cur, model, ubatch, il);
+        } else if (hparams.n_ff(il) == 0) {
+            // attention layer //
+            cur = build_attention_layer(cur, inp->get_attn(), model, n_embd_head, il);
+        } else {
+            cur = build_ffn_layer(cur, model, il);
+        }
+
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0, cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+        }
+
+        // add residual
+        cur = ggml_add(ctx0, cur, inpSA);
+        cb(cur, "nemotron_h_block_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+
+    cur = inpL;
+
+    cur = build_norm(cur, model.output_norm, NULL, LLM_NORM_RMS, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}
+
+ggml_tensor * llm_build_nemotron_h::build_attention_layer(ggml_tensor *             cur,
+                                                          llm_graph_input_attn_kv * inp_attn,
+                                                          const llama_model &       model,
+                                                          const int64_t             n_embd_head,
+                                                          const int                 il) {
+    // compute Q and K and (optionally) RoPE them
+    ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+    cb(Qcur, "Qcur", il);
+    if (model.layers[il].bq) {
+        Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
+        cb(Qcur, "Qcur", il);
+    }
+
+    ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+    cb(Kcur, "Kcur", il);
+    if (model.layers[il].bk) {
+        Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
+        cb(Kcur, "Kcur", il);
+    }
+
+    ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+    cb(Vcur, "Vcur", il);
+    if (model.layers[il].bv) {
+        Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
+        cb(Vcur, "Vcur", il);
+    }
+
+    Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, hparams.n_head(il), n_tokens);
+    Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, hparams.n_head_kv(il), n_tokens);
+    Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, hparams.n_head_kv(il), n_tokens);
+
+    cb(Qcur, "Qcur", il);
+    cb(Kcur, "Kcur", il);
+    cb(Vcur, "Vcur", il);
+
+    const float kq_scale =
+        hparams.f_attention_scale == 0.0f ? 1.0f / sqrtf(float(n_embd_head)) : hparams.f_attention_scale;
+    cur = build_attn(inp_attn,
+            model.layers[il].wo, model.layers[il].bo,
+            Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, kq_scale, il);
+    cb(cur, "attn_out", il);
+    return cur;
+}
+
+ggml_tensor * llm_build_nemotron_h::build_ffn_layer(ggml_tensor * cur, const llama_model & model, const int il) {
+    cur = build_ffn(cur,
+            model.layers[il].ffn_up, model.layers[il].ffn_up_b, NULL,
+            NULL, NULL, NULL,
+            model.layers[il].ffn_down, model.layers[il].ffn_down_b, NULL,
+            NULL, LLM_FFN_RELU_SQR, LLM_FFN_PAR, il);
+    cb(cur, "ffn_out", il);
+
+    cur = build_cvec(cur, il);
+    cb(cur, "l_out", il);
+
+    return cur;
+}
diff --git a/src/models/nemotron.cpp b/src/models/nemotron.cpp
new file mode 100644
index 00000000000..781aa719393
--- /dev/null
+++ b/src/models/nemotron.cpp
@@ -0,0 +1,122 @@
+#include "models.h"
+
+llm_build_nemotron::llm_build_nemotron(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+        const int64_t n_embd_head = hparams.n_embd_head_v;
+
+        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+        //GGML_ASSERT(n_embd_head == hparams.n_rot);
+
+        ggml_tensor * cur;
+        ggml_tensor * inpL;
+
+        inpL = build_inp_embd(model.tok_embd);
+
+        // inp_pos - contains the positions
+        ggml_tensor * inp_pos = build_inp_pos();
+
+        auto * inp_attn = build_attn_inp_kv();
+
+        ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+        for (int il = 0; il < n_layer; ++il) {
+            ggml_tensor * inpSA = inpL;
+
+            // norm
+            cur = build_norm(inpL,
+                    model.layers[il].attn_norm,
+                    model.layers[il].attn_norm_b,
+                    LLM_NORM, il);
+            cb(cur, "attn_norm", il);
+
+            // self-attention
+            {
+                // compute Q and K and RoPE them
+                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+                cb(Qcur, "Qcur", il);
+                if (model.layers[il].bq) {
+                    Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
+                    cb(Qcur, "Qcur", il);
+                }
+                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+                cb(Kcur, "Kcur", il);
+                if (model.layers[il].bk) {
+                    Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
+                    cb(Kcur, "Kcur", il);
+                }
+                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+                cb(Vcur, "Vcur", il);
+                if (model.layers[il].bv) {
+                    Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
+                    cb(Vcur, "Vcur", il);
+                }
+                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+                Qcur = ggml_rope_ext(
+                        ctx0, Qcur, inp_pos, nullptr,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+                Kcur = ggml_rope_ext(
+                        ctx0, Kcur, inp_pos, nullptr,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+                cb(Qcur, "Qcur", il);
+                cb(Kcur, "Kcur", il);
+                cb(Vcur, "Vcur", il);
+
+                cur = build_attn(inp_attn,
+                        model.layers[il].wo, model.layers[il].bo,
+                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+            }
+            if (il == n_layer - 1 && inp_out_ids) {
+                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+            }
+            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+            cb(ffn_inp, "ffn_inp", il);
+
+            // feed-forward network
+            cur = build_norm(ffn_inp,
+                    model.layers[il].ffn_norm,
+                    model.layers[il].ffn_norm_b,
+                    LLM_NORM, il);
+            cb(cur, "ffn_norm", il);
+
+            cur = build_ffn(cur,
+                    model.layers[il].ffn_up,   model.layers[il].ffn_up_b,   NULL,
+                    NULL,                      NULL,                        NULL,
+                    model.layers[il].ffn_down, model.layers[il].ffn_down_b, NULL,
+                    NULL,
+                    LLM_FFN_RELU_SQR, LLM_FFN_SEQ, il);
+
+            cur = ggml_add(ctx0, cur, ffn_inp);
+            cb(cur, "ffn_out", il);
+
+            cur = build_cvec(cur, il);
+            cb(cur, "l_out", il);
+
+            // input for next layer
+            inpL = cur;
+        }
+        cur = inpL;
+
+        cur = build_norm(cur,
+                model.output_norm, model.output_norm_b,
+                LLM_NORM, -1);
+
+        cb(cur, "result_norm", -1);
+        res->t_embd = cur;
+
+        // lm_head
+        cur = build_lora_mm(model.output, cur);
+
+        cb(cur, "result_output", -1);
+        res->t_logits = cur;
+
+        ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/neo-bert.cpp b/src/models/neo-bert.cpp
new file mode 100644
index 00000000000..b05c79025bb
--- /dev/null
+++ b/src/models/neo-bert.cpp
@@ -0,0 +1,104 @@
+#include "models.h"
+
+llm_build_neo_bert::llm_build_neo_bert(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+        const int64_t n_embd_head = hparams.n_embd_head_v;
+        const int64_t n_embd_gqa  = hparams.n_embd_v_gqa();
+
+        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+
+        ggml_tensor * cur;
+        ggml_tensor * inpL;
+        ggml_tensor * inp_pos = build_inp_pos();
+
+        // construct input embeddings (token, type, position)
+        inpL = build_inp_embd(model.tok_embd);
+        cb(inpL, "inp_embd", -1);
+
+        auto * inp_attn = build_attn_inp_no_cache();
+
+        ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+        for (int il = 0; il < n_layer; ++il) {
+            ggml_tensor * cur = inpL;
+
+            // pre-norm
+            cur = build_norm(inpL,
+                    model.layers[il].attn_norm, NULL,
+                    LLM_NORM_RMS, il);
+
+            {
+                ggml_tensor * Qcur;
+                ggml_tensor * Kcur;
+                ggml_tensor * Vcur;
+
+                // self-attention
+                cur = build_lora_mm(model.layers[il].wqkv, cur);
+                cb(cur, "wqkv", il);
+
+                Qcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head,    n_tokens, n_embd_head*sizeof(float), cur->nb[1], 0*sizeof(float)*(n_embd));
+                Kcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd));
+                Vcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd + n_embd_gqa));
+
+                // RoPE
+                Qcur = ggml_rope_ext(
+                        ctx0, Qcur, inp_pos, nullptr,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+                Kcur = ggml_rope_ext(
+                        ctx0, Kcur, inp_pos, nullptr,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+                cb(Qcur, "Qcur", il);
+                cb(Kcur, "Kcur", il);
+                cb(Vcur, "Vcur", il);
+
+                cur = build_attn(inp_attn,
+                        model.layers[il].wo, nullptr,
+                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+                cb(cur, "kqv_out", il);
+            }
+            if (il == n_layer - 1 && inp_out_ids) {
+                cur  = ggml_get_rows(ctx0,  cur, inp_out_ids);
+                inpL = ggml_get_rows(ctx0, inpL, inp_out_ids);
+            }
+            // re-add the layer input
+            cur = ggml_add(ctx0, cur, inpL);
+
+            ggml_tensor * ffn_inp = cur;
+            cb(ffn_inp, "ffn_inp", il);
+
+            // pre-norm
+            cur = build_norm(ffn_inp,
+                    model.layers[il].ffn_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "ffn_norm", il);
+
+            // feed-forward network
+            cur = build_ffn(cur,
+                    model.layers[il].ffn_up,
+                    NULL, NULL, NULL, NULL, NULL,
+                    model.layers[il].ffn_down,
+                    NULL, NULL, NULL,
+                    LLM_FFN_SWIGLU, LLM_FFN_SEQ, il);
+
+            // attentions bypass the intermediate layer
+            cur = ggml_add(ctx0, cur, ffn_inp);
+
+            // input for next layer
+            inpL = cur;
+        }
+        cur = inpL;
+
+        cur = build_norm(cur,
+                model.output_norm_enc, NULL,
+                LLM_NORM_RMS, -1);
+
+        cb(cur, "result_embd", -1);
+        res->t_embd = cur;
+
+        ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/olmo.cpp b/src/models/olmo.cpp
new file mode 100644
index 00000000000..e15d716536d
--- /dev/null
+++ b/src/models/olmo.cpp
@@ -0,0 +1,121 @@
+#include "models.h"
+
+llm_build_olmo::llm_build_olmo(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+        const int64_t n_embd_head = hparams.n_embd_head_v;
+
+        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+        GGML_ASSERT(n_embd_head == hparams.n_rot);
+
+        ggml_tensor * cur;
+        ggml_tensor * inpL;
+
+        inpL = build_inp_embd(model.tok_embd);
+
+        // inp_pos - contains the positions
+        ggml_tensor * inp_pos = build_inp_pos();
+
+        auto * inp_attn = build_attn_inp_kv();
+
+        ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+        for (int il = 0; il < n_layer; ++il) {
+            ggml_tensor * inpSA = inpL;
+
+            // norm
+            cur = build_norm(inpL,
+                    NULL, NULL,
+                    LLM_NORM, il);
+            cb(cur, "attn_norm", il);
+
+            // self-attention
+            {
+                // compute Q and K and RoPE them
+                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+                cb(Qcur, "Qcur", il);
+                if (hparams.f_clamp_kqv > 0.0f) {
+                    Qcur = ggml_clamp(ctx0, Qcur, -hparams.f_clamp_kqv, hparams.f_clamp_kqv);
+                    cb(Qcur, "Qcur", il);
+                }
+                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+                cb(Kcur, "Kcur", il);
+                if (hparams.f_clamp_kqv > 0.0f) {
+                    Kcur = ggml_clamp(ctx0, Kcur, -hparams.f_clamp_kqv, hparams.f_clamp_kqv);
+                    cb(Kcur, "Kcur", il);
+                }
+                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+                cb(Vcur, "Vcur", il);
+                if (hparams.f_clamp_kqv > 0.0f) {
+                    Vcur = ggml_clamp(ctx0, Vcur, -hparams.f_clamp_kqv, hparams.f_clamp_kqv);
+                    cb(Vcur, "Vcur", il);
+                }
+                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+                Qcur = ggml_rope_ext(
+                        ctx0, Qcur, inp_pos, nullptr,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+                Kcur = ggml_rope_ext(
+                        ctx0, Kcur, inp_pos, nullptr,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+                cb(Qcur, "Qcur", il);
+                cb(Kcur, "Kcur", il);
+                cb(Vcur, "Vcur", il);
+
+                cur = build_attn(inp_attn,
+                        model.layers[il].wo, nullptr,
+                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+            }
+            if (il == n_layer - 1 && inp_out_ids) {
+                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+            }
+            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+            cb(ffn_inp, "ffn_inp", il);
+
+            // feed-forward network
+            cur = build_norm(ffn_inp,
+                    NULL, NULL,
+                    LLM_NORM, il);
+            cb(cur, "ffn_norm", il);
+
+            cur = build_ffn(cur,
+                    model.layers[il].ffn_up,   NULL, NULL,
+                    model.layers[il].ffn_gate, NULL, NULL,
+                    model.layers[il].ffn_down, NULL, NULL,
+                    NULL,
+                    LLM_FFN_SILU, LLM_FFN_PAR, il);
+            cb(cur, "ffn_out", il);
+
+            cur = ggml_add(ctx0, cur, ffn_inp);
+            cb(cur, "ffn_out", il);
+
+            cur = build_cvec(cur, il);
+            cb(cur, "l_out", il);
+
+            // input for next layer
+            inpL = cur;
+        }
+        cur = inpL;
+
+        cur = build_norm(cur,
+                NULL, NULL,
+                LLM_NORM, -1);
+
+        cb(cur, "result_norm", -1);
+        res->t_embd = cur;
+
+        // lm_head
+        cur = build_lora_mm(model.output, cur);
+
+        cb(cur, "result_output", -1);
+        res->t_logits = cur;
+
+        ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/olmo2.cpp b/src/models/olmo2.cpp
new file mode 100644
index 00000000000..b05a3f9b4b0
--- /dev/null
+++ b/src/models/olmo2.cpp
@@ -0,0 +1,151 @@
+#include "models.h"
+
+
+template <bool iswa>
+llm_build_olmo2<iswa>::llm_build_olmo2(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+        const int64_t n_embd_head = hparams.n_embd_head_v;
+
+        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+        GGML_ASSERT(n_embd_head == hparams.n_rot);
+
+        ggml_tensor * cur;
+        ggml_tensor * inpL;
+
+        inpL = build_inp_embd(model.tok_embd);
+
+        // inp_pos - contains the positions
+        ggml_tensor * inp_pos = build_inp_pos();
+
+        using inp_attn_type = std::conditional_t<iswa, llm_graph_input_attn_kv_iswa, llm_graph_input_attn_kv>;
+        inp_attn_type * inp_attn = nullptr;
+
+        if constexpr (iswa) {
+            inp_attn = build_attn_inp_kv_iswa();
+        } else {
+            inp_attn = build_attn_inp_kv();
+        }
+        ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+        for (int il = 0; il < n_layer; ++il) {
+            ggml_tensor * inpSA = inpL;
+
+            cur = inpL;
+
+            // self_attention
+            {
+                // compute Q and K and RoPE them
+                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+                cb(Qcur, "Qcur", il);
+
+                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+                cb(Kcur, "Kcur", il);
+
+                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+                cb(Vcur, "Vcur", il);
+
+                Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL,
+                        LLM_NORM_RMS, il);
+                cb(Qcur, "Qcur_normed", il);
+
+                Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, NULL,
+                        LLM_NORM_RMS, il);
+                cb(Kcur, "Kcur_normed", il);
+
+                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+                const bool is_swa = hparams.is_swa(il);
+
+                if (is_swa) {
+                    // For sliding window layers, Olmo3 use regular rope with no yarn rope scaling.
+                    // This is achieved here by setting freq_scale and attn_factor to 1.
+                    // We also set ext_factor to 0 to avoid a few unnecessary computations.
+                    Qcur = ggml_rope_ext(
+                        ctx0, Qcur, inp_pos, nullptr,
+                        n_rot, rope_type, n_ctx_orig, freq_base, 1.0,
+                        0.0, 1.0, beta_fast, beta_slow
+                        );
+
+                    Kcur = ggml_rope_ext(
+                        ctx0, Kcur, inp_pos, nullptr,
+                        n_rot, rope_type, n_ctx_orig, freq_base, 1.0,
+                        0.0, 1.0, beta_fast, beta_slow
+                        );
+                } else {
+                    Qcur = ggml_rope_ext(
+                        ctx0, Qcur, inp_pos, nullptr,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+                    Kcur = ggml_rope_ext(
+                        ctx0, Kcur, inp_pos, nullptr,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+                }
+                cb(Qcur, "Qcur", il);
+                cb(Kcur, "Kcur", il);
+                cb(Vcur, "Vcur", il);
+
+                cur = build_attn(inp_attn,
+                        model.layers[il].wo, NULL,
+                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+            }
+            if (il == n_layer - 1 && inp_out_ids) {
+                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+            }
+            cur = build_norm(cur,
+                    model.layers[il].attn_post_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "attn_post_norm", il);
+
+            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+            cb(ffn_inp, "ffn_inp", il);
+
+            // feed-forward network
+            cur = build_ffn(ffn_inp,
+                    model.layers[il].ffn_up,   NULL, NULL,
+                    model.layers[il].ffn_gate, NULL, NULL,
+                    model.layers[il].ffn_down, NULL, NULL,
+                    NULL,
+                    LLM_FFN_SILU, LLM_FFN_PAR, il);
+            cb(cur, "ffn_out", il);
+
+            cur = build_norm(cur,
+                    model.layers[il].ffn_post_norm, NULL,
+                    LLM_NORM_RMS, -1);
+            cb(cur, "ffn_post_norm", -1);
+
+            cur = ggml_add(ctx0, cur, ffn_inp);
+            cb(cur, "ffn_out", il);
+
+            cur = build_cvec(cur, il);
+            cb(cur, "l_out", il);
+
+            // input for next layer
+            inpL = cur;
+        }
+        cur = inpL;
+
+        cur = build_norm(cur,
+                model.output_norm, NULL,
+                LLM_NORM_RMS, -1);
+
+        cb(cur, "result_norm", -1);
+        res->t_embd = cur;
+
+        // lm_head
+        cur = build_lora_mm(model.output, cur);
+
+        cb(cur, "result_output", -1);
+        res->t_logits = cur;
+
+        ggml_build_forward_expand(gf, cur);
+    }
+
+// Explicit template instantiations
+template struct llm_build_olmo2<false>;
+template struct llm_build_olmo2<true>;
diff --git a/src/models/olmoe.cpp b/src/models/olmoe.cpp
new file mode 100644
index 00000000000..49f51f9724c
--- /dev/null
+++ b/src/models/olmoe.cpp
@@ -0,0 +1,124 @@
+#include "models.h"
+
+llm_build_olmoe::llm_build_olmoe(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+        const int64_t n_embd_head = hparams.n_embd_head_v;
+
+        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+        GGML_ASSERT(n_embd_head == hparams.n_rot);
+
+        ggml_tensor * cur;
+        ggml_tensor * inpL;
+
+        inpL = build_inp_embd(model.tok_embd);
+
+        // inp_pos - contains the positions
+        ggml_tensor * inp_pos = build_inp_pos();
+
+        auto * inp_attn = build_attn_inp_kv();
+
+        ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+        for (int il = 0; il < n_layer; ++il) {
+            ggml_tensor * inpSA = inpL;
+
+            // norm
+            cur = build_norm(inpL,
+                    model.layers[il].attn_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "attn_norm", il);
+
+            // self_attention
+            {
+                // compute Q and K and RoPE them
+                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+                cb(Qcur, "Qcur", il);
+
+                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+                cb(Kcur, "Kcur", il);
+
+                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+                cb(Vcur, "Vcur", il);
+
+                Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL,
+                        LLM_NORM_RMS, il);
+                cb(Qcur, "Qcur_normed", il);
+
+                Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, NULL,
+                        LLM_NORM_RMS, il);
+                cb(Kcur, "Kcur_normed", il);
+
+                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+                Qcur = ggml_rope_ext(
+                        ctx0, Qcur, inp_pos, nullptr,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+                Kcur = ggml_rope_ext(
+                        ctx0, Kcur, inp_pos, nullptr,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+                cb(Qcur, "Qcur", il);
+                cb(Kcur, "Kcur", il);
+                cb(Vcur, "Vcur", il);
+
+                cur = build_attn(inp_attn,
+                        model.layers[il].wo, NULL,
+                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+            }
+            if (il == n_layer - 1 && inp_out_ids) {
+                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+            }
+            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+            cb(ffn_inp, "ffn_inp", il);
+
+            // MoE branch
+            cur = build_norm(ffn_inp,
+                    model.layers[il].ffn_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "ffn_norm", il);
+
+            cur = build_moe_ffn(cur,
+                    model.layers[il].ffn_gate_inp,
+                    model.layers[il].ffn_up_exps,
+                    model.layers[il].ffn_gate_exps,
+                    model.layers[il].ffn_down_exps,
+                    nullptr,
+                    n_expert, n_expert_used,
+                    LLM_FFN_SILU, false,
+                    false, 0.0,
+                    LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
+                    il);
+            cb(cur, "ffn_moe_out", il);
+
+            cur = ggml_add(ctx0, cur, ffn_inp);
+
+            cur = build_cvec(cur, il);
+            cb(cur, "l_out", il);
+
+            // input for next layer
+            inpL = cur;
+        }
+        cur = inpL;
+
+        cur = build_norm(cur,
+                model.output_norm, NULL,
+                LLM_NORM_RMS, -1);
+
+        cb(cur, "result_norm", -1);
+        res->t_embd = cur;
+
+        // lm_head
+        cur = build_lora_mm(model.output, cur);
+
+        cb(cur, "result_output", -1);
+        res->t_logits = cur;
+
+        ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/openai-moe-iswa.cpp b/src/models/openai-moe-iswa.cpp
new file mode 100644
index 00000000000..14e55eeb7a9
--- /dev/null
+++ b/src/models/openai-moe-iswa.cpp
@@ -0,0 +1,123 @@
+#include "models.h"
+
+llm_build_openai_moe_iswa::llm_build_openai_moe_iswa(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+        ggml_tensor * cur;
+        ggml_tensor * inpL;
+
+        inpL = build_inp_embd(model.tok_embd);
+
+        // inp_pos - contains the positions
+        ggml_tensor * inp_pos = build_inp_pos();
+
+        auto * inp_attn = build_attn_inp_kv_iswa();
+
+        for (int il = 0; il < n_layer; ++il) {
+            ggml_tensor * inpSA = inpL;
+
+            // norm
+            cur = build_norm(inpL,
+                    model.layers[il].attn_norm, nullptr,
+                    LLM_NORM_RMS, il);
+            cb(cur, "attn_norm", il);
+
+            // self-attention
+            {
+                // compute Q and K and RoPE them
+                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+                cb(Qcur, "Qcur", il);
+                if (model.layers[il].bq) {
+                    Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
+                    cb(Qcur, "Qcur", il);
+                }
+                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+                cb(Kcur, "Kcur", il);
+                if (model.layers[il].bk) {
+                    Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
+                    cb(Kcur, "Kcur", il);
+                }
+                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+                cb(Vcur, "Vcur", il);
+                if (model.layers[il].bv) {
+                    Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
+                    cb(Vcur, "Vcur", il);
+                }
+                Qcur = ggml_reshape_3d(ctx0, Qcur, n_rot, n_head,    n_tokens);
+                Kcur = ggml_reshape_3d(ctx0, Kcur, n_rot, n_head_kv, n_tokens);
+                Vcur = ggml_reshape_3d(ctx0, Vcur, n_rot, n_head_kv, n_tokens);
+
+                Qcur = ggml_rope_ext(
+                        ctx0, Qcur, inp_pos, nullptr,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+                Kcur = ggml_rope_ext(
+                        ctx0, Kcur, inp_pos, nullptr,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+                cb(Qcur, "Qcur", il);
+                cb(Kcur, "Kcur", il);
+                cb(Vcur, "Vcur", il);
+
+                cur = build_attn(inp_attn,
+                        model.layers[il].wo, model.layers[il].bo,
+                        Qcur, Kcur, Vcur, nullptr, model.layers[il].attn_sinks, nullptr, 1.0f/sqrtf(float(n_rot)), il);
+
+                cb(cur, "attn_out", il);
+            }
+            if (il == n_layer - 1) {
+                // skip computing output for unused tokens
+                ggml_tensor * inp_out_ids = build_inp_out_ids();
+                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+            }
+            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+            cb(ffn_inp, "ffn_inp", il);
+
+            cur = ffn_inp;
+            cur = build_norm(cur,
+                    model.layers[il].attn_post_norm, nullptr,
+                    LLM_NORM_RMS, il);
+            cb(cur, "attn_post_norm", il);
+
+            // MoE branch
+            cur = build_moe_ffn(cur,
+                    model.layers[il].ffn_gate_inp,  model.layers[il].ffn_gate_inp_b,
+                    model.layers[il].ffn_up_exps,   model.layers[il].ffn_up_exps_b,
+                    model.layers[il].ffn_gate_exps, model.layers[il].ffn_gate_exps_b,
+                    model.layers[il].ffn_down_exps, model.layers[il].ffn_down_exps_b,
+                    nullptr,
+                    n_expert, n_expert_used,
+                    LLM_FFN_SWIGLU_OAI_MOE, false,
+                    false, 0.0,
+                    LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX_WEIGHT,
+                    il);
+            cb(cur, "ffn_moe_out", il);
+
+            cur = ggml_add(ctx0, cur, ffn_inp);
+
+            cur = build_cvec(cur, il);
+            cb(cur, "l_out", il);
+
+            // input for next layer
+            inpL = cur;
+        }
+        cur = inpL;
+
+        cur = build_norm(cur,
+                model.output_norm, NULL,
+                LLM_NORM_RMS, -1);
+
+        cb(cur, "result_norm", -1);
+        res->t_embd = cur;
+
+        // lm_head
+        cur = build_lora_mm(model.output, cur);
+
+        cb(cur, "result_output", -1);
+        res->t_logits = cur;
+
+        ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/openelm.cpp b/src/models/openelm.cpp
new file mode 100644
index 00000000000..a16a459f3fa
--- /dev/null
+++ b/src/models/openelm.cpp
@@ -0,0 +1,124 @@
+#include "models.h"
+
+llm_build_openelm::llm_build_openelm(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+        const int64_t n_embd_head = hparams.n_embd_head_v;
+
+        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+
+        ggml_tensor * cur;
+        ggml_tensor * inpL;
+        inpL = build_inp_embd(model.tok_embd);
+
+        // inp_pos - contains the positions
+        ggml_tensor * inp_pos = build_inp_pos();
+
+        auto * inp_attn = build_attn_inp_kv();
+
+        ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+        for (int il = 0; il < n_layer; ++il) {
+            const int64_t n_head    = hparams.n_head(il);
+            const int64_t n_head_kv = hparams.n_head_kv(il);
+            const int64_t n_head_qkv = 2*n_head_kv + n_head;
+
+            cur = inpL;
+            ggml_tensor * residual = cur;
+
+            // norm
+            cur = build_norm(inpL,
+                    model.layers[il].attn_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "attn_norm", il);
+
+            // self-attention
+            {
+                cur = build_lora_mm(model.layers[il].wqkv, cur);
+                cb(cur, "wqkv", il);
+
+                cur = ggml_reshape_3d(ctx0, cur, n_embd_head_k, n_head_qkv, n_tokens);
+
+                ggml_tensor * Qcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head,    n_tokens, cur->nb[1], cur->nb[2], 0);
+                cb(Qcur, "Qcur", il);
+
+                ggml_tensor * Kcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, cur->nb[1], cur->nb[2], cur->nb[1]*n_head);
+                cb(Kcur, "Kcur", il);
+
+                ggml_tensor * Vcur = ggml_cont(ctx0, ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, cur->nb[1], cur->nb[2], cur->nb[1]*(n_head+n_head_kv)));
+                cb(Vcur, "Vcur", il);
+
+                Qcur = build_norm(Qcur,
+                        model.layers[il].attn_q_norm, NULL,
+                        LLM_NORM_RMS, il);
+                cb(Qcur, "Qcur", il);
+
+                Kcur = build_norm(Kcur,
+                        model.layers[il].attn_k_norm, NULL,
+                        LLM_NORM_RMS, il);
+                cb(Kcur, "Kcur", il);
+
+                Qcur = ggml_rope_ext(
+                        ctx0, Qcur, inp_pos, NULL,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+                Kcur = ggml_rope_ext(
+                        ctx0, Kcur, inp_pos, NULL,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+                cb(Qcur, "Qcur", il);
+                cb(Kcur, "Kcur", il);
+                cb(Qcur, "Vcur", il);
+
+                cur = build_attn(inp_attn,
+                        model.layers[il].wo, NULL,
+                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+            }
+            if (il == n_layer - 1 && inp_out_ids) {
+                residual = ggml_get_rows(ctx0, residual, inp_out_ids);
+                cur      = ggml_get_rows(ctx0, cur,      inp_out_ids);
+            }
+            ggml_tensor * ffn_inp = ggml_add(ctx0, residual, cur);
+            cb(ffn_inp, "ffn_inp", il);
+
+            // feed-forward network
+            {
+                cur = build_norm(ffn_inp,
+                        model.layers[il].ffn_norm, NULL,
+                        LLM_NORM_RMS, il);
+                cb(cur, "ffn_norm", il);
+
+                cur = build_ffn(cur,
+                        model.layers[il].ffn_up,   NULL, NULL,
+                        model.layers[il].ffn_gate, NULL, NULL,
+                        model.layers[il].ffn_down, NULL, NULL,
+                        NULL,
+                        LLM_FFN_SILU, LLM_FFN_PAR, il);
+                cb(cur, "ffn_out", il);
+            }
+            cur = ggml_add(ctx0, cur, ffn_inp);
+
+            cur = build_cvec(cur, il);
+            cb(cur, "l_out", il);
+
+            inpL = cur;
+        }
+        cur = inpL;
+
+        // norm
+        cur = build_norm(cur,
+                model.output_norm, NULL,
+                LLM_NORM_RMS, -1);
+
+        cb(cur, "result_norm", -1);
+        res->t_embd = cur;
+
+        cur = build_lora_mm(model.output, cur);
+
+        cb(cur, "result_output", -1);
+        res->t_logits = cur;
+
+        ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/orion.cpp b/src/models/orion.cpp
new file mode 100644
index 00000000000..8c20c003ce0
--- /dev/null
+++ b/src/models/orion.cpp
@@ -0,0 +1,123 @@
+#include "models.h"
+
+llm_build_orion::llm_build_orion(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+        const int64_t n_embd_head = hparams.n_embd_head_v;
+
+        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+        GGML_ASSERT(n_embd_head == hparams.n_rot);
+
+        ggml_tensor * cur;
+        ggml_tensor * inpL;
+
+        inpL = build_inp_embd(model.tok_embd);
+
+        // inp_pos - contains the positions
+        ggml_tensor * inp_pos = build_inp_pos();
+
+        auto * inp_attn = build_attn_inp_kv();
+
+        ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+        for (int il = 0; il < n_layer; ++il) {
+            ggml_tensor * inpSA = inpL;
+
+            // norm
+            cur = build_norm(inpL,
+                    model.layers[il].attn_norm, model.layers[il].attn_norm_b,
+                    LLM_NORM, il);
+            cb(cur, "attn_norm", il);
+
+            // self-attention
+            {
+                // compute Q and K and RoPE them
+                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+                cb(Qcur, "Qcur", il);
+                // if (model.layers[il].bq) {
+                //     Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
+                //     cb(Qcur, "Qcur", il);
+                // }
+
+                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+                cb(Kcur, "Kcur", il);
+                // if (model.layers[il].bk) {
+                //     Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
+                //     cb(Kcur, "Kcur", il);
+                // }
+
+                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+                cb(Vcur, "Vcur", il);
+                // if (model.layers[il].bv) {
+                //     Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
+                //     cb(Vcur, "Vcur", il);
+                // }
+
+                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+                Qcur = ggml_rope_ext(
+                        ctx0, Qcur, inp_pos, nullptr,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+                Kcur = ggml_rope_ext(
+                        ctx0, Kcur, inp_pos, nullptr,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+                cb(Qcur, "Qcur", il);
+                cb(Kcur, "Kcur", il);
+                cb(Vcur, "Vcur", il);
+
+                cur = build_attn(inp_attn,
+                        model.layers[il].wo, NULL,
+                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+            }
+            if (il == n_layer - 1 && inp_out_ids) {
+                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+            }
+            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+            cb(ffn_inp, "ffn_inp", il);
+
+            // feed-forward network
+            cur = build_norm(ffn_inp,
+                    model.layers[il].ffn_norm, model.layers[il].ffn_norm_b,
+                    LLM_NORM, il);
+            cb(cur, "ffn_norm", il);
+
+            cur = build_ffn(cur,
+                    model.layers[il].ffn_up,   NULL, NULL,
+                    model.layers[il].ffn_gate, NULL, NULL,
+                    model.layers[il].ffn_down, NULL, NULL,
+                    NULL,
+                    LLM_FFN_SILU, LLM_FFN_PAR, il);
+            cb(cur, "ffn_out", il);
+
+            cur = ggml_add(ctx0, cur, ffn_inp);
+
+            cur = build_cvec(cur, il);
+            cb(cur, "l_out", il);
+
+            // input for next layer
+            inpL = cur;
+        }
+        cur = inpL;
+
+        cur = build_norm(cur,
+                model.output_norm, model.output_norm_b,
+                LLM_NORM, -1);
+
+        cb(cur, "result_norm", -1);
+        res->t_embd = cur;
+
+        // lm_head
+        cur = build_lora_mm(model.output, cur);
+
+        cb(cur, "result_output", -1);
+        res->t_logits = cur;
+
+        ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/phi2.cpp b/src/models/phi2.cpp
new file mode 100644
index 00000000000..22dbf610767
--- /dev/null
+++ b/src/models/phi2.cpp
@@ -0,0 +1,121 @@
+#include "models.h"
+
+
+llm_build_phi2::llm_build_phi2(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+    const int64_t n_embd_head = hparams.n_embd_head_v;
+    const int64_t n_embd_gqa  = hparams.n_embd_v_gqa();
+
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+
+    ggml_tensor * cur;
+    ggml_tensor * attn_norm_output;
+    ggml_tensor * ffn_output;
+    ggml_tensor * inpL;
+
+    inpL = build_inp_embd(model.tok_embd);
+
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
+
+    auto * inp_attn = build_attn_inp_kv();
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        attn_norm_output = build_norm(inpL,
+                model.layers[il].attn_norm,
+                model.layers[il].attn_norm_b,
+                LLM_NORM, il);
+        cb(attn_norm_output, "attn_norm", il);
+
+        // self-attention
+        {
+            ggml_tensor * Qcur = nullptr;
+            ggml_tensor * Kcur = nullptr;
+            ggml_tensor * Vcur = nullptr;
+
+            if (model.layers[il].wqkv) {
+                cur = build_lora_mm(model.layers[il].wqkv, attn_norm_output);
+                cb(cur, "wqkv", il);
+
+                cur = ggml_add(ctx0, cur, model.layers[il].bqkv);
+                cb(cur, "bqkv", il);
+
+                Qcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head,    n_tokens, n_embd_head*sizeof(float), cur->nb[1], 0*sizeof(float)*(n_embd));
+                Kcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd));
+                Vcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd + n_embd_gqa));
+            } else {
+                Qcur = ggml_add(ctx0, build_lora_mm(model.layers[il].wq, attn_norm_output), model.layers[il].bq);
+                Kcur = ggml_add(ctx0, build_lora_mm(model.layers[il].wk, attn_norm_output), model.layers[il].bk);
+                Vcur = ggml_add(ctx0, build_lora_mm(model.layers[il].wv, attn_norm_output), model.layers[il].bv);
+
+                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+            }
+            Qcur = ggml_rope_ext(
+                    ctx0, Qcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            Kcur = ggml_rope_ext(
+                    ctx0, Kcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            // with phi2, we scale the Q to avoid precision issues
+            // ref: https://github.com/ml-explore/mlx-examples/blob/08e862336ade809bc37d1035f94b359e7d1a5152/phi2/phi2.py#L64-L66
+            Qcur = ggml_scale(ctx0, Qcur, 1.0f/sqrtf(float(n_embd_head)));
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, model.layers[il].bo,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f, il);
+        }
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur              = ggml_get_rows(ctx0,              cur, inp_out_ids);
+            inpL             = ggml_get_rows(ctx0,             inpL, inp_out_ids);
+            attn_norm_output = ggml_get_rows(ctx0, attn_norm_output, inp_out_ids);
+        }
+        // FF
+        {
+            ffn_output = build_ffn(attn_norm_output,
+                    model.layers[il].ffn_up,   model.layers[il].ffn_up_b,   NULL,
+                    NULL,                      NULL,                        NULL,
+                    model.layers[il].ffn_down, model.layers[il].ffn_down_b, NULL,
+                    NULL,
+                    LLM_FFN_GELU, LLM_FFN_SEQ, il);
+            cb(ffn_output, "ffn_out", il);
+        }
+        cur = ggml_add(ctx0, cur, ffn_output);
+        cur = ggml_add(ctx0, cur, inpL);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+    cur = build_norm(inpL,
+            model.output_norm,
+            model.output_norm_b,
+            LLM_NORM, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    cur = build_lora_mm(model.output, cur);
+    cb(cur, "result_output_no_bias", -1);
+
+    cur = ggml_add(ctx0, cur, model.output_b);
+
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/phi3.cpp b/src/models/phi3.cpp
new file mode 100644
index 00000000000..63907e3d4ed
--- /dev/null
+++ b/src/models/phi3.cpp
@@ -0,0 +1,153 @@
+#include "models.h"
+
+
+template<bool iswa>
+llm_build_phi3<iswa>::llm_build_phi3(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+        const int64_t n_embd_head = hparams.n_embd_head_v;
+        const int64_t n_embd_gqa = hparams.n_embd_v_gqa();
+
+        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+
+        ggml_tensor * cur;
+        ggml_tensor * inpL;
+
+        inpL = build_inp_embd(model.tok_embd);
+
+        // inp_pos - contains the positions
+        ggml_tensor * inp_pos = build_inp_pos();
+
+        using inp_attn_type = std::conditional_t<iswa, llm_graph_input_attn_kv_iswa, llm_graph_input_attn_kv>;
+        inp_attn_type * inp_attn = nullptr;
+
+        if constexpr (iswa) {
+            inp_attn = build_attn_inp_kv_iswa();
+        } else {
+            inp_attn = build_attn_inp_kv();
+        }
+        ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+        for (int il = 0; il < n_layer; ++il) {
+            auto * residual = inpL;
+
+            // self-attention
+            {
+                // rope freq factors for 128k context
+                ggml_tensor * rope_factors = model.get_rope_factors(cparams, il);
+
+                ggml_tensor* attn_norm_output = build_norm(inpL,
+                        model.layers[il].attn_norm,
+                        model.layers[il].attn_norm_b,
+                        LLM_NORM_RMS, il);
+                cb(attn_norm_output, "attn_norm", il);
+
+                ggml_tensor * Qcur = nullptr;
+                ggml_tensor * Kcur = nullptr;
+                ggml_tensor * Vcur = nullptr;
+
+                if (model.layers[il].wqkv) {
+                    cur = build_lora_mm(model.layers[il].wqkv, attn_norm_output);
+                    cb(cur, "wqkv", il);
+
+                    Qcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head,    n_tokens, n_embd_head * sizeof(float), cur->nb[1], 0 * sizeof(float) * (n_embd));
+                    Kcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head * sizeof(float), cur->nb[1], 1 * sizeof(float) * (n_embd));
+                    Vcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head * sizeof(float), cur->nb[1], 1 * sizeof(float) * (n_embd + n_embd_gqa));
+                    }
+                    else {
+                    Qcur = ggml_add(ctx0, build_lora_mm(model.layers[il].wq, attn_norm_output), model.layers[il].bq);
+                    Kcur = ggml_add(ctx0, build_lora_mm(model.layers[il].wk, attn_norm_output), model.layers[il].bk);
+                    Vcur = ggml_add(ctx0, build_lora_mm(model.layers[il].wv, attn_norm_output), model.layers[il].bv);
+
+                    Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+                    Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+                    Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+                }
+                Qcur = ggml_rope_ext(
+                        ctx0, Qcur, inp_pos, rope_factors,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+                Kcur = ggml_rope_ext(
+                        ctx0, Kcur, inp_pos, rope_factors,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+                cb(Qcur, "Qcur", il);
+                cb(Kcur, "Kcur", il);
+                cb(Vcur, "Vcur", il);
+
+                Qcur = ggml_scale(ctx0, Qcur, 1.0f / sqrtf(float(n_embd_head)));
+                cb(Qcur, "Qcur", il);
+
+                cur = build_attn(inp_attn,
+                        model.layers[il].wo, model.layers[il].bo,
+                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f, il);
+            }
+            if (il == n_layer - 1 && inp_out_ids) {
+                cur      = ggml_get_rows(ctx0, cur,      inp_out_ids);
+                residual = ggml_get_rows(ctx0, residual, inp_out_ids);
+            }
+            cur = ggml_add(ctx0, cur, residual);
+            residual = cur;
+
+            cur = build_norm(cur,
+                    model.layers[il].ffn_norm, model.layers[il].ffn_norm_b,
+                    LLM_NORM_RMS, il);
+            cb(cur, "ffn_norm", il);
+
+            // feed-forward network
+            if (model.layers[il].ffn_gate_inp == nullptr) {
+                cur = build_ffn(cur,
+                        model.layers[il].ffn_up,   NULL, NULL,
+                        NULL,                      NULL, NULL,
+                        model.layers[il].ffn_down, NULL, NULL,
+                        NULL,
+                        LLM_FFN_SWIGLU, LLM_FFN_SEQ, il);
+                cb(cur, "ffn_out", il);
+            } else {
+                // MoE branch
+                cur = build_moe_ffn(cur,
+                        model.layers[il].ffn_gate_inp,
+                        model.layers[il].ffn_up_exps,
+                        model.layers[il].ffn_gate_exps,
+                        model.layers[il].ffn_down_exps,
+                        nullptr,
+                        n_expert, n_expert_used,
+                        LLM_FFN_SILU, true,
+                        false, 0.0,
+                        LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
+                        il);
+                cb(cur, "ffn_moe_out", il);
+            }
+            cur = ggml_add(ctx0, residual, cur);
+
+            cur = build_cvec(cur, il);
+            cb(cur, "l_out", il);
+
+            // input for next layer
+            inpL = cur;
+        }
+        cur = build_norm(inpL,
+                model.output_norm,
+                model.output_norm_b,
+                LLM_NORM_RMS, -1);
+
+        cb(cur, "result_norm", -1);
+        res->t_embd = cur;
+
+        cur = build_lora_mm(model.output, cur);
+
+        if (model.output_b != nullptr) {
+            cb(cur, "result_output_no_bias", -1);
+            cur = ggml_add(ctx0, cur, model.output_b);
+        }
+        cb(cur, "result_output", -1);
+        res->t_logits = cur;
+
+        ggml_build_forward_expand(gf, cur);
+    }
+
+// Explicit template instantiations
+template struct llm_build_phi3<false>;
+template struct llm_build_phi3<true>;
diff --git a/src/models/plamo.cpp b/src/models/plamo.cpp
new file mode 100644
index 00000000000..73b4473fcab
--- /dev/null
+++ b/src/models/plamo.cpp
@@ -0,0 +1,110 @@
+#include "models.h"
+
+llm_build_plamo::llm_build_plamo(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+        const int64_t n_embd_head = hparams.n_embd_head_v;
+
+        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+        GGML_ASSERT(n_embd_head == hparams.n_rot);
+
+        ggml_tensor * cur;
+        ggml_tensor * inpL;
+
+        inpL = build_inp_embd(model.tok_embd);
+
+        // inp_pos - contains the positions
+        ggml_tensor * inp_pos = build_inp_pos();
+
+        auto * inp_attn = build_attn_inp_kv();
+
+        ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+        for (int il = 0; il < n_layer; ++il) {
+            // norm
+            cur = build_norm(inpL,
+                    model.layers[il].attn_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "attn_norm", il);
+
+            ggml_tensor * sa_inp = cur;
+
+            // self-attention
+            {
+                // compute Q and K and RoPE them
+                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+                cb(Qcur, "Qcur", il);
+
+                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+                cb(Kcur, "Kcur", il);
+
+                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+                cb(Vcur, "Vcur", il);
+
+                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+                Qcur = ggml_rope_ext(
+                        ctx0, Qcur, inp_pos, nullptr,
+                        n_embd_head, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+                Kcur = ggml_rope_ext(
+                        ctx0, Kcur, inp_pos, nullptr,
+                        n_embd_head, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+                cb(Qcur, "Qcur", il);
+                cb(Kcur, "Kcur", il);
+                cb(Vcur, "Vcur", il);
+
+                cur = build_attn(inp_attn,
+                        model.layers[il].wo, NULL,
+                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+            }
+            if (il == n_layer - 1 && inp_out_ids) {
+                cur    = ggml_get_rows(ctx0,    cur, inp_out_ids);
+                sa_inp = ggml_get_rows(ctx0, sa_inp, inp_out_ids);
+                inpL   = ggml_get_rows(ctx0,   inpL, inp_out_ids);
+            }
+            ggml_tensor * sa_out = cur;
+
+            cur = sa_inp;
+
+            // feed-forward network
+            {
+                cur = build_ffn(cur,
+                        model.layers[il].ffn_up,   NULL, NULL,
+                        model.layers[il].ffn_gate, NULL, NULL,
+                        model.layers[il].ffn_down, NULL, NULL,
+                        NULL,
+                        LLM_FFN_SILU, LLM_FFN_PAR, il);
+                cb(cur, "ffn_out", il);
+            }
+            cur = ggml_add(ctx0, cur, sa_out);
+            cur = ggml_add(ctx0, cur, inpL);
+
+            cur = build_cvec(cur, il);
+            cb(cur, "l_out", il);
+
+            // input for next layer
+            inpL = cur;
+        }
+        cur = inpL;
+
+        cur = build_norm(cur,
+                model.output_norm, NULL,
+                LLM_NORM_RMS, -1);
+
+        cb(cur, "result_norm", -1);
+        res->t_embd = cur;
+
+        // lm_head
+        cur = build_lora_mm(model.output, cur);
+
+        cb(cur, "result_output", -1);
+        res->t_logits = cur;
+
+        ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/plamo2.cpp b/src/models/plamo2.cpp
new file mode 100644
index 00000000000..31115a08f95
--- /dev/null
+++ b/src/models/plamo2.cpp
@@ -0,0 +1,316 @@
+#include "models.h"
+
+llm_build_plamo2::llm_build_plamo2(const llama_model & model, const llm_graph_params & params) :
+    llm_graph_context_mamba(params) {
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+
+    // {n_embd, n_tokens}
+    inpL = build_inp_embd(model.tok_embd);
+    cb(inpL, "embedding_output", -1);
+
+    ggml_tensor * inp_pos = build_inp_pos();
+
+    auto * inp_hybrid = build_inp_mem_hybrid();
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * residual = inpL;
+
+        // ggml_graph_add_node(gf, model.layers[il].attn_norm);
+        // cb(model.layers[il].attn_norm, "attn_norm", il);
+
+        // pre_mixer_norm
+        cur = build_norm(inpL, model.layers[il].attn_norm, NULL, LLM_NORM_RMS, il);
+
+        // check if this layer is Mamba or Attention
+        bool is_mamba_layer = hparams.is_recurrent(il);
+
+        if (is_mamba_layer) {
+            // PLaMo-2 Mamba layer
+            cur = build_plamo2_mamba_layer(inp_hybrid->get_recr(), cur, model, ubatch, il);
+        } else {
+            // PLaMo-2 Attention layer
+            cur = build_plamo2_attn_layer(inp_hybrid->get_attn(), inp_pos, cur, model, il);
+        }
+
+        // post_mixer_norm
+        cur = build_norm(cur, model.layers[il].attn_post_norm, NULL, LLM_NORM_RMS, il);
+        cb(cur, "attn_post_norm", il);
+
+        // residual connection
+        cur = ggml_add(ctx0, cur, residual);
+        cb(cur, "attn_residual", il);
+        residual = cur;
+
+        // pre-ffn norm
+        cur = build_norm(cur, model.layers[il].ffn_norm, NULL, LLM_NORM_RMS, il);
+        cb(cur, "ffn_pre_norm", il);
+
+        // feed-forward network
+        cur = build_ffn(cur,
+                model.layers[il].ffn_up, NULL, NULL,
+                NULL, NULL, NULL,
+                model.layers[il].ffn_down, NULL, NULL,
+                NULL, LLM_FFN_SWIGLU, LLM_FFN_SEQ, il);
+        cb(cur, "ffn_out", il);
+
+        // post ffn norm
+        cur = build_norm(cur, model.layers[il].ffn_post_norm, NULL, LLM_NORM_RMS, il);
+        cb(cur, "ffn_post_norm", il);
+
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur      = ggml_get_rows(ctx0, cur, inp_out_ids);
+            residual = ggml_get_rows(ctx0, residual, inp_out_ids);
+        }
+
+        // residual connection
+        cur = ggml_add(ctx0, cur, residual);
+        cb(cur, "ffn_residual", il);
+
+        inpL = cur;
+    }
+
+    cur = inpL;
+
+    // final norm
+    cur = build_norm(cur, model.output_norm, NULL, LLM_NORM_RMS, -1);
+    cb(cur, "result_norm", -1);
+
+    res->t_embd = cur;
+
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
+    cb(cur, "result_output", -1);
+
+    // Explicitly mark as output tensor to ensure proper backend assignment
+    ggml_set_output(cur);
+
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}
+
+ggml_tensor * llm_build_plamo2::build_plamo2_attn_layer(llm_graph_input_attn_kv * inp,
+                                                        ggml_tensor *             inp_pos,
+                                                        ggml_tensor *             cur,
+                                                        const llama_model &       model,
+                                                        int                       il) {
+    // self-attention
+    {
+        // PLaMo-2 uses combined QKV tensor
+        ggml_tensor * qkv = build_lora_mm(model.layers[il].wqkv, cur);
+        cb(qkv, "wqkv", il);
+
+        // split QKV tensor into Q, K, V
+        const int64_t n_embd_head_q = hparams.n_embd_head_k;
+        const int64_t n_embd_head_k = hparams.n_embd_head_k;
+        const int64_t n_embd_head_v = hparams.n_embd_head_v;
+        int32_t       n_head        = hparams.n_head(il);
+        int32_t       n_head_kv     = hparams.n_head_kv(il);
+
+        const int64_t q_offset = 0;
+        const int64_t k_offset = n_embd_head_q * n_head;
+        const int64_t v_offset = k_offset + n_embd_head_k * n_head_kv;
+
+        ggml_tensor * Qcur = ggml_view_3d(ctx0, qkv, n_embd_head_q, n_head, n_tokens, n_embd_head_q * sizeof(float),
+                                          qkv->nb[1], q_offset * ggml_element_size(qkv));
+        ggml_tensor * Kcur = ggml_view_3d(ctx0, qkv, n_embd_head_k, n_head_kv, n_tokens, n_embd_head_k * sizeof(float),
+                                          qkv->nb[1], k_offset * ggml_element_size(qkv));
+        ggml_tensor * Vcur = ggml_view_3d(ctx0, qkv, n_embd_head_v, n_head_kv, n_tokens, n_embd_head_v * sizeof(float),
+                                          qkv->nb[1], v_offset * ggml_element_size(qkv));
+
+        cb(Qcur, "Qcur", il);
+        cb(Kcur, "Kcur", il);
+        cb(Vcur, "Vcur", il);
+
+        Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL, LLM_NORM_RMS, il);
+        cb(Qcur, "Qcur_normed", il);
+
+        Qcur = ggml_rope_ext(ctx0, Qcur, inp_pos, nullptr, n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                             ext_factor, attn_factor, beta_fast, beta_slow);
+
+        Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, NULL, LLM_NORM_RMS, il);
+        cb(Kcur, "Kcur_normed", il);
+
+        Kcur = ggml_rope_ext(ctx0, Kcur, inp_pos, nullptr, n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                             ext_factor, attn_factor, beta_fast, beta_slow);
+
+        cur = build_attn(inp,
+            model.layers[il].wo, NULL,
+            Qcur, Kcur, Vcur, NULL, NULL, NULL, 1.0f / sqrtf(float(n_embd_head_v)), il);
+    }
+
+    cb(cur, "attn_out", il);
+
+    return cur;
+}
+
+ggml_tensor * llm_build_plamo2::build_plamo2_mamba_layer(llm_graph_input_rs * inp,
+                                                         ggml_tensor *        cur,
+                                                         const llama_model &  model,
+                                                         const llama_ubatch & ubatch,
+                                                         int                  il) {
+    const auto * mctx_cur = inp->mctx;
+
+    const auto kv_head = mctx_cur->get_head();
+
+    const int64_t d_conv   = hparams.ssm_d_conv;
+    const int64_t d_inner  = hparams.ssm_d_inner;
+    const int64_t d_state  = hparams.ssm_d_state;
+    const int64_t n_heads  = hparams.ssm_dt_rank;
+    const int64_t head_dim = d_inner / n_heads;
+    const int64_t n_group  = hparams.ssm_n_group;
+    const int64_t n_seqs   = ubatch.n_seqs;
+
+    const int64_t n_seq_tokens = ubatch.n_seq_tokens;
+
+    GGML_ASSERT(n_seqs != 0);
+    GGML_ASSERT(ubatch.equal_seqs());
+    GGML_ASSERT(ubatch.n_tokens == n_seq_tokens * n_seqs);
+
+    ggml_tensor * conv_states_all = mctx_cur->get_r_l(il);
+    ggml_tensor * ssm_states_all  = mctx_cur->get_s_l(il);
+
+    ggml_tensor * conv = build_rs(inp, conv_states_all, hparams.n_embd_r(), n_seqs);
+    conv               = ggml_reshape_3d(ctx0, conv, d_conv - 1, d_inner + 2 * n_group * d_state, n_seqs);
+
+    // {n_embd, n_tokens} => {n_embd, n_seq_tokens, n_seqs}
+    cur = ggml_reshape_3d(ctx0, cur, cur->ne[0], n_seq_tokens, n_seqs);
+
+    // in_proj: {n_embd, 2*d_inner} @ {n_embd, n_seq_tokens, n_seqs} => {2*d_inner, n_seq_tokens, n_seqs}
+    ggml_tensor * zx = build_lora_mm(model.layers[il].ssm_in, cur);
+    cb(zx, "mamba_in_proj", il);
+    // {8192, 5, 1, 1} -> {8192, 1, 5, 1}
+    zx = ggml_permute(ctx0, zx, 0, 2, 1, 3);
+    zx = ggml_cont_4d(ctx0, zx, head_dim * 2, n_heads, n_seq_tokens, n_seqs);
+    cb(zx, "mamba_in_proj_out", il);
+
+    // split into z and x
+    // => {head_dim * n_heads, n_seq_tokens, n_seqs}
+    ggml_tensor * x = ggml_view_4d(ctx0, zx, head_dim, n_heads, n_seq_tokens, n_seqs, zx->nb[1], zx->nb[2], zx->nb[3],
+                                   head_dim * ggml_element_size(zx));
+    x               = ggml_cont_3d(ctx0, x, head_dim * n_heads, n_seq_tokens, n_seqs);
+    // x = ggml_permute(ctx0, x, 0, 2, 1, 3);
+    cb(x, "mamba_x_split", il);
+
+    ggml_tensor * z =
+        ggml_view_4d(ctx0, zx, head_dim, n_heads, n_seq_tokens, n_seqs, zx->nb[1], zx->nb[2], zx->nb[3], 0);
+    cb(z, "mamba_z_split", il);
+
+    // conv1d
+    {
+        // => {d_conv - 1 + n_seq_tokens, d_inner, n_seqs}
+        ggml_tensor * conv_x = ggml_concat(ctx0, conv, ggml_transpose(ctx0, x), 0);
+        cb(conv_x, "mamba_conv1d_input", il);
+
+        // copy last (d_conv - 1) columns back into the state cache
+        ggml_tensor * last_conv = ggml_view_3d(ctx0, conv_x, d_conv - 1, d_inner, n_seqs, conv_x->nb[1], conv_x->nb[2],
+                                               n_seq_tokens * (conv_x->nb[0]));
+
+        ggml_build_forward_expand(gf, ggml_cpy(ctx0, last_conv,
+                                               ggml_view_1d(ctx0, conv_states_all,
+                                                            (d_conv - 1) * (d_inner + 2 * n_group * d_state) * (n_seqs),
+                                                            kv_head * (d_conv - 1) * (d_inner + 2 * n_group * d_state) *
+                                                                ggml_element_size(conv_states_all))));
+        cb(conv_states_all, "mamba_conv1d_state", il);
+
+        // 1D convolution
+        x = ggml_ssm_conv(ctx0, conv_x, model.layers[il].ssm_conv1d);
+        cb(x, "mamba_conv1d", il);
+
+        x = ggml_silu(ctx0, x);
+        cb(x, "mamba_conv1d_silu", il);
+    }
+
+    // SSM
+    {
+        // bcdt_proj: {d_inner, dt_rank + 2*d_state} @ {d_inner, n_seq_tokens, n_seqs} => {dt_rank + 2*d_state, n_seq_tokens, n_seqs}
+        ggml_tensor * x_bcdt = build_lora_mm(model.layers[il].ssm_x, x);
+        cb(x_bcdt, "mamba_bcdt_proj", il);
+
+        // split into dt, B, C
+        const int64_t dt_dim = std::max(64, int(hparams.n_embd / 16));
+        ggml_tensor * B  = ggml_view_3d(ctx0, x_bcdt, d_state, n_seq_tokens, n_seqs, x_bcdt->nb[1], x_bcdt->nb[2], 0);
+        ggml_tensor * C  = ggml_view_3d(ctx0, x_bcdt, d_state, n_seq_tokens, n_seqs, x_bcdt->nb[1], x_bcdt->nb[2],
+                                        ggml_element_size(x_bcdt) * d_state);
+        ggml_tensor * dt = ggml_view_3d(ctx0, x_bcdt, dt_dim, n_seq_tokens, n_seqs, x_bcdt->nb[1], x_bcdt->nb[2],
+                                        ggml_element_size(x_bcdt) * (2 * d_state));
+        cb(B, "mamba_B_raw", il);
+        cb(C, "mamba_C_raw", il);
+        cb(dt, "mamba_dt_raw", il);
+
+        // Apply RMS norm to dt, B, C (PLaMo-2 specific)
+        B  = build_norm(B, model.layers[il].ssm_b_norm, NULL, LLM_NORM_RMS, il);
+        C  = build_norm(C, model.layers[il].ssm_c_norm, NULL, LLM_NORM_RMS, il);
+        dt = build_norm(dt, model.layers[il].ssm_dt_norm, NULL, LLM_NORM_RMS, il);
+        cb(B, "mamba_B_normed", il);
+        cb(C, "mamba_C_normed", il);
+        cb(dt, "mamba_dt_normed", il);
+
+        // dt_proj: {dt_rank, d_inner} @ {dt_rank, n_seq_tokens, n_seqs} => {d_inner, n_seq_tokens, n_seqs}
+        dt = build_lora_mm(model.layers[il].ssm_dt, dt);
+        dt = ggml_add(ctx0, dt, model.layers[il].ssm_dt_b);
+        cb(dt, "mamba_dt_proj", il);
+
+        ggml_tensor * A = ggml_reshape_2d(ctx0, model.layers[il].ssm_a, 1, n_heads);
+        cb(A, "mamba_A", il);
+
+        x = ggml_view_4d(ctx0, x, head_dim, n_heads, n_seq_tokens, n_seqs, head_dim * ggml_element_size(x),
+                         head_dim * n_heads * ggml_element_size(x),
+                         head_dim * n_heads * n_seq_tokens * ggml_element_size(x), 0);
+        B = ggml_view_4d(ctx0, B, d_state, 1, n_seq_tokens, n_seqs, d_state * B->nb[0], B->nb[1], B->nb[2], 0);
+        C = ggml_view_4d(ctx0, C, d_state, 1, n_seq_tokens, n_seqs, d_state * C->nb[0], C->nb[1], C->nb[2], 0);
+
+        // use the states and the indices provided by build_recurrent_state
+        // (this is necessary in order to properly use the states before they are overwritten,
+        //  while avoiding to make unnecessary copies of the states)
+        auto get_ssm_rows = [&](ggml_context * ctx, ggml_tensor * states, ggml_tensor * ids) {
+            ggml_tensor * ssm = ggml_reshape_4d(ctx, states, d_state, head_dim, n_heads, mctx_cur->get_size());
+
+            // Custom operator to optimize the parallel associative scan
+            // as described in the Annex D of the Mamba paper.
+            // => {d_inner, n_seq_tokens, n_seqs} and {d_state, d_inner, n_seqs}
+            return ggml_ssm_scan(ctx, ssm, x, dt, A, B, C, ids);
+        };
+
+        ggml_tensor * y_ssm = build_rs(inp, ssm_states_all, hparams.n_embd_s(), ubatch.n_seqs, get_ssm_rows);
+        cb(y_ssm, "mamba_ssm_scan", il);
+
+        // store last states
+        ggml_build_forward_expand(
+            gf, ggml_cpy(
+                    ctx0,
+                    ggml_view_1d(ctx0, y_ssm, n_heads * head_dim * d_state * n_seqs,
+                                 n_heads * head_dim * n_seq_tokens * n_seqs * ggml_element_size(y_ssm)),
+                    ggml_view_1d(ctx0, ssm_states_all, n_heads * head_dim * d_state * n_seqs,
+                                 kv_head * n_seqs * n_heads * head_dim * d_state * ggml_element_size(ssm_states_all))));
+        cb(ssm_states_all, "mamba_ssm_states", il);
+
+        ggml_tensor * y = ggml_view_4d(ctx0, y_ssm, head_dim, n_heads, n_seq_tokens, n_seqs,
+                                       head_dim * ggml_element_size(x), head_dim * n_heads * ggml_element_size(x),
+                                       head_dim * n_heads * n_seq_tokens * ggml_element_size(x), 0);
+        cb(y, "mamba_y_view", il);
+
+        // Add D parameter and apply gating with z
+        // {d_inner, n_seq_tokens, n_seqs} * {d_inner} => {d_inner, n_seq_tokens, n_seqs}
+        ggml_tensor * D = ggml_reshape_2d(ctx0, model.layers[il].ssm_d, 1, n_heads);
+        y               = ggml_add(ctx0, y, ggml_mul(ctx0, x, D));
+        cb(y, "mamba_y_add_d", il);
+
+        y = ggml_swiglu_split(ctx0, ggml_cont(ctx0, z), y);
+        cb(y, "mamba_y_swiglu_z", il);
+
+        // out_proj: {d_inner, n_embd} @ {d_inner, n_seq_tokens, n_seqs} => {n_embd, n_seq_tokens, n_seqs}
+        y   = ggml_view_3d(ctx0, y, head_dim * n_heads, n_seq_tokens, n_seqs, y->nb[2], y->nb[3], 0);
+        cur = build_lora_mm(model.layers[il].ssm_out, y);
+        cb(cur, "mamba_out_proj", il);
+    }
+
+    // {n_embd, n_seq_tokens, n_seqs} => {n_embd, n_tokens}
+    cur = ggml_reshape_2d(ctx0, cur, cur->ne[0], n_seq_tokens * n_seqs);
+    cb(cur, "mamba_out", il);
+
+    return cur;
+}
diff --git a/src/models/plm.cpp b/src/models/plm.cpp
new file mode 100644
index 00000000000..ddd52162b23
--- /dev/null
+++ b/src/models/plm.cpp
@@ -0,0 +1,168 @@
+#include "models.h"
+
+llm_build_plm::llm_build_plm(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+        const float kq_scale = 1.0f/sqrtf(float(hparams.n_embd_head_k));
+
+        const uint32_t n_embd_head_qk_rope = hparams.n_rot;
+        const uint32_t n_embd_head_qk_nope = hparams.n_embd_head_k - hparams.n_rot;
+        const uint32_t kv_lora_rank = hparams.n_lora_kv;
+
+        ggml_tensor * cur;
+        ggml_tensor * inpL;
+
+        // {n_embd, n_tokens}
+        inpL = build_inp_embd(model.tok_embd);
+
+        // inp_pos - contains the positions
+        ggml_tensor * inp_pos = build_inp_pos();
+
+        auto * inp_attn = build_attn_inp_kv();
+
+        ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+        for (int il = 0; il < n_layer; ++il) {
+            ggml_tensor * inpSA = inpL;
+
+            // norm
+            cur = build_norm(inpL,
+                    model.layers[il].attn_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "attn_norm", il);
+
+            // self_attention
+            {
+                ggml_tensor * q = NULL;
+                q = ggml_mul_mat(ctx0, model.layers[il].wq, cur);
+                cb(q, "q", il);
+
+                // split into {n_head * n_embd_head_qk_nope, n_tokens}
+                ggml_tensor * q_nope = ggml_view_3d(ctx0, q, n_embd_head_qk_nope, n_head, n_tokens,
+                        ggml_row_size(q->type, hparams.n_embd_head_k),
+                        ggml_row_size(q->type, hparams.n_embd_head_k * n_head),
+                        0);
+                cb(q_nope, "q_nope", il);
+
+                // and {n_head * n_embd_head_qk_rope, n_tokens}
+                ggml_tensor * q_pe = ggml_view_3d(ctx0, q, n_embd_head_qk_rope, n_head, n_tokens,
+                        ggml_row_size(q->type, hparams.n_embd_head_k),
+                        ggml_row_size(q->type, hparams.n_embd_head_k * n_head),
+                        ggml_row_size(q->type, n_embd_head_qk_nope));
+                cb(q_pe, "q_pe", il);
+
+                // {n_embd, kv_lora_rank + n_embd_head_qk_rope} * {n_embd, n_tokens} -> {kv_lora_rank + n_embd_head_qk_rope, n_tokens}
+                ggml_tensor * kv_pe_compresseed = ggml_mul_mat(ctx0, model.layers[il].wkv_a_mqa, cur);
+                cb(kv_pe_compresseed, "kv_pe_compresseed", il);
+
+                // split into {kv_lora_rank, n_tokens}
+                ggml_tensor * kv_compressed = ggml_view_2d(ctx0, kv_pe_compresseed, kv_lora_rank, n_tokens,
+                        kv_pe_compresseed->nb[1],
+                        0);
+                cb(kv_compressed, "kv_compressed", il);
+
+                // and {n_embd_head_qk_rope, n_tokens}
+                ggml_tensor * k_pe = ggml_view_3d(ctx0, kv_pe_compresseed, n_embd_head_qk_rope, 1, n_tokens,
+                        kv_pe_compresseed->nb[1],
+                        kv_pe_compresseed->nb[1],
+                        ggml_row_size(kv_pe_compresseed->type, kv_lora_rank));
+                cb(k_pe, "k_pe", il);
+
+                kv_compressed = build_norm(kv_compressed,
+                        model.layers[il].attn_kv_a_norm, NULL,
+                        LLM_NORM_RMS, il);
+                cb(kv_compressed, "kv_compressed", il);
+
+                // {kv_lora_rank, n_head * (n_embd_head_qk_nope + n_embd_head_v)} * {kv_lora_rank, n_tokens} -> {n_head * (n_embd_head_qk_nope + n_embd_head_v), n_tokens}
+                ggml_tensor * kv = ggml_mul_mat(ctx0, model.layers[il].wkv_b, kv_compressed);
+                cb(kv, "kv", il);
+
+                // split into {n_head * n_embd_head_qk_nope, n_tokens}
+                ggml_tensor * k_nope = ggml_view_3d(ctx0, kv, n_embd_head_qk_nope, n_head, n_tokens,
+                        ggml_row_size(kv->type, n_embd_head_qk_nope + hparams.n_embd_head_v),
+                        ggml_row_size(kv->type, n_head * (n_embd_head_qk_nope + hparams.n_embd_head_v)),
+                        0);
+                cb(k_nope, "k_nope", il);
+
+                // and {n_head * n_embd_head_v, n_tokens}
+                ggml_tensor * v_states = ggml_view_3d(ctx0, kv, hparams.n_embd_head_v, n_head, n_tokens,
+                        ggml_row_size(kv->type, (n_embd_head_qk_nope + hparams.n_embd_head_v)),
+                        ggml_row_size(kv->type, (n_embd_head_qk_nope + hparams.n_embd_head_v)*n_head),
+                        ggml_row_size(kv->type, (n_embd_head_qk_nope)));
+                cb(v_states, "v_states", il);
+
+                v_states = ggml_cont(ctx0, v_states);
+                cb(v_states, "v_states", il);
+
+                v_states = ggml_view_2d(ctx0, v_states, hparams.n_embd_head_v * n_head, n_tokens,
+                        ggml_row_size(kv->type, hparams.n_embd_head_v * n_head),
+                        0);
+                cb(v_states, "v_states", il);
+
+                q_pe = ggml_rope_ext(
+                        ctx0, q_pe, inp_pos, nullptr,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+                cb(q_pe, "q_pe", il);
+
+                // shared RoPE key
+                k_pe = ggml_rope_ext(
+                        ctx0, k_pe, inp_pos, nullptr,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+                cb(k_pe, "k_pe", il);
+
+                ggml_tensor * q_states = ggml_concat(ctx0, q_nope, q_pe, 0);
+                cb(q_states, "q_states", il);
+
+                ggml_tensor * k_states = ggml_concat(ctx0, k_nope, ggml_repeat(ctx0, k_pe, q_pe), 0);
+                cb(k_states, "k_states", il);
+
+                cur = build_attn(inp_attn,
+                        model.layers[il].wo, NULL,
+                        q_states, k_states, v_states, nullptr, nullptr, nullptr, kq_scale, il);
+            }
+            if (il == n_layer - 1 && inp_out_ids) {
+                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+            }
+            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+            cb(ffn_inp, "ffn_inp", il);
+
+            cur = build_norm(ffn_inp,
+                    model.layers[il].ffn_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "ffn_norm", il);
+
+            cur = build_ffn(cur,
+                    model.layers[il].ffn_up,   NULL, NULL,
+                    NULL, NULL, NULL,
+                    model.layers[il].ffn_down, NULL, NULL,
+                    NULL,
+                    LLM_FFN_RELU_SQR, LLM_FFN_SEQ, il);
+            cb(cur, "ffn_out", il);
+
+            cur = ggml_add(ctx0, cur, ffn_inp);
+
+            cur = build_cvec(cur, il);
+            cb(cur, "l_out", il);
+
+            // input for next layer
+            inpL = cur;
+        }
+        cur = inpL;
+
+        cur = build_norm(cur,
+                model.output_norm, NULL,
+                LLM_NORM_RMS, -1);
+
+        cb(cur, "result_norm", -1);
+        res->t_embd = cur;
+
+        cur = build_lora_mm(model.output, cur);
+
+        cb(cur, "result_output", -1);
+        res->t_logits = cur;
+
+        ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/qwen.cpp b/src/models/qwen.cpp
new file mode 100644
index 00000000000..31fd9b73763
--- /dev/null
+++ b/src/models/qwen.cpp
@@ -0,0 +1,108 @@
+#include "models.h"
+
+
+llm_build_qwen::llm_build_qwen(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+    const int64_t n_embd_head = hparams.n_embd_head_v;
+
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+
+    inpL = build_inp_embd(model.tok_embd);
+
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
+
+    auto * inp_attn = build_attn_inp_kv();
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * inpSA = inpL;
+
+        cur = build_norm(inpL,
+                model.layers[il].attn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
+
+        // self-attention
+        {
+            cur = build_lora_mm(model.layers[il].wqkv, cur);
+            cb(cur, "wqkv", il);
+
+            cur = ggml_add(ctx0, cur, model.layers[il].bqkv);
+            cb(cur, "bqkv", il);
+
+            ggml_tensor * Qcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head,    n_tokens, n_embd_head*sizeof(float), cur->nb[1], 0*sizeof(float)*(n_embd));
+            ggml_tensor * Kcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd));
+            ggml_tensor * Vcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 2*sizeof(float)*(n_embd));
+
+            // using mode = 2 for neox mode
+            Qcur = ggml_rope_ext(
+                    ctx0, Qcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            Kcur = ggml_rope_ext(
+                    ctx0, Kcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, NULL,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+        }
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+        }
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+        cb(ffn_inp, "ffn_inp", il);
+
+        // feed-forward forward
+        {
+            cur = build_norm(ffn_inp,
+                    model.layers[il].ffn_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "ffn_norm", il);
+
+            cur = build_ffn(cur,
+                    model.layers[il].ffn_up,   NULL, NULL,
+                    model.layers[il].ffn_gate, NULL, NULL,
+                    model.layers[il].ffn_down, NULL, NULL,
+                    NULL,
+                    LLM_FFN_SILU, LLM_FFN_PAR, il);
+            cb(cur, "ffn_out", il);
+        }
+        cur = ggml_add(ctx0, cur, ffn_inp);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+    cur = inpL;
+
+    cur = build_norm(cur,
+            model.output_norm, NULL,
+            LLM_NORM_RMS, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
+
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/qwen2.cpp b/src/models/qwen2.cpp
new file mode 100644
index 00000000000..885cb46894d
--- /dev/null
+++ b/src/models/qwen2.cpp
@@ -0,0 +1,118 @@
+#include "models.h"
+
+
+llm_build_qwen2::llm_build_qwen2(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+        const int64_t n_embd_head = hparams.n_embd_head_v;
+
+        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+        GGML_ASSERT(n_embd_head == hparams.n_rot);
+
+        ggml_tensor * cur;
+        ggml_tensor * inpL;
+
+        inpL = build_inp_embd(model.tok_embd);
+
+        // inp_pos - contains the positions
+        ggml_tensor * inp_pos = build_inp_pos();
+
+        auto * inp_attn = build_attn_inp_kv();
+
+        ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+        for (int il = 0; il < n_layer; ++il) {
+            ggml_tensor * inpSA = inpL;
+
+            // norm
+            cur = build_norm(inpL,
+                    model.layers[il].attn_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "attn_norm", il);
+
+            // self-attention
+            {
+                // compute Q and K and RoPE them
+                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+                Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
+                cb(Qcur, "Qcur", il);
+
+                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+                Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
+                cb(Kcur, "Kcur", il);
+
+                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+                Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
+                cb(Vcur, "Vcur", il);
+
+                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+                Qcur = ggml_rope_ext(
+                        ctx0, Qcur, inp_pos, nullptr,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+                Kcur = ggml_rope_ext(
+                        ctx0, Kcur, inp_pos, nullptr,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+                cb(Qcur, "Qcur", il);
+                cb(Kcur, "Kcur", il);
+                cb(Vcur, "Vcur", il);
+
+                cur = build_attn(inp_attn,
+                        model.layers[il].wo, model.layers[il].bo,
+                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+            }
+            if (il == n_layer - 1 && inp_out_ids) {
+                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+            }
+            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+            cb(ffn_inp, "ffn_inp", il);
+
+            // feed-forward network
+            cur = build_norm(ffn_inp,
+                    model.layers[il].ffn_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "ffn_norm", il);
+
+            cur = build_ffn(cur,
+                    model.layers[il].ffn_up,   NULL, NULL,
+                    model.layers[il].ffn_gate, NULL, NULL,
+                    model.layers[il].ffn_down, NULL, NULL,
+                    NULL,
+                    LLM_FFN_SILU, LLM_FFN_PAR, il);
+            cb(cur, "ffn_out", il);
+
+            cur = ggml_add(ctx0, cur, ffn_inp);
+
+            cur = build_cvec(cur, il);
+            cb(cur, "l_out", il);
+
+            // input for next layer
+            inpL = cur;
+        }
+        cur = inpL;
+
+        cur = build_norm(cur,
+                model.output_norm, NULL,
+                LLM_NORM_RMS, -1);
+
+        cb(cur, "result_norm", -1);
+        res->t_embd = cur;
+
+        // lm_head
+        cur = build_lora_mm(model.output, cur);
+
+        if (model.output_b != nullptr) {
+            cur = ggml_add(ctx0, cur, model.output_b);
+        }
+        cb(cur, "result_output", -1);
+        res->t_logits = cur;
+
+        ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/qwen2moe.cpp b/src/models/qwen2moe.cpp
new file mode 100644
index 00000000000..40623ea66f2
--- /dev/null
+++ b/src/models/qwen2moe.cpp
@@ -0,0 +1,151 @@
+#include "models.h"
+
+llm_build_qwen2moe::llm_build_qwen2moe(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+        const int64_t n_embd_head = hparams.n_embd_head_v;
+
+        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+        GGML_ASSERT(n_embd_head == hparams.n_rot);
+
+        ggml_tensor * cur;
+        ggml_tensor * inpL;
+
+        inpL = build_inp_embd(model.tok_embd);
+
+        // inp_pos - contains the positions
+        ggml_tensor * inp_pos = build_inp_pos();
+
+        auto * inp_attn = build_attn_inp_kv();
+
+        ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+        for (int il = 0; il < n_layer; ++il) {
+            ggml_tensor * inpSA = inpL;
+
+            // norm
+            cur = build_norm(inpL,
+                    model.layers[il].attn_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "attn_norm", il);
+
+            // self_attention
+            {
+                // compute Q and K and RoPE them
+                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+                cb(Qcur, "Qcur", il);
+                if (model.layers[il].bq) {
+                    Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
+                    cb(Qcur, "Qcur", il);
+                }
+                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+                cb(Kcur, "Kcur", il);
+                if (model.layers[il].bk) {
+                    Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
+                    cb(Kcur, "Kcur", il);
+                }
+                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+                cb(Vcur, "Vcur", il);
+                if (model.layers[il].bv) {
+                    Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
+                    cb(Vcur, "Vcur", il);
+                }
+                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+                Qcur = ggml_rope_ext(
+                        ctx0, Qcur, inp_pos, nullptr,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+                Kcur = ggml_rope_ext(
+                        ctx0, Kcur, inp_pos, nullptr,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+                cb(Qcur, "Qcur", il);
+                cb(Kcur, "Kcur", il);
+                cb(Vcur, "Vcur", il);
+
+                cur = build_attn(inp_attn,
+                        model.layers[il].wo, model.layers[il].bo,
+                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+            }
+            if (il == n_layer - 1 && inp_out_ids) {
+                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+            }
+            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+            cb(ffn_inp, "ffn_inp", il);
+
+            // MoE branch
+            cur = build_norm(ffn_inp,
+                    model.layers[il].ffn_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "ffn_norm", il);
+
+            ggml_tensor * moe_out =
+                build_moe_ffn(cur,
+                        model.layers[il].ffn_gate_inp,
+                        model.layers[il].ffn_up_exps,
+                        model.layers[il].ffn_gate_exps,
+                        model.layers[il].ffn_down_exps,
+                        nullptr,
+                        n_expert, n_expert_used,
+                        LLM_FFN_SILU, false,
+                        false, 0.0,
+                        LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
+                        il);
+            cb(moe_out, "ffn_moe_out", il);
+
+            // FFN shared expert
+            {
+                ggml_tensor * cur_gate_inp = build_lora_mm(model.layers[il].ffn_gate_inp_shexp, cur);
+                cb(cur_gate_inp, "ffn_shexp_gate_inp", il);
+
+                // sigmoid
+                ggml_tensor * cur_gate = ggml_div(ctx0, ggml_silu(ctx0, cur_gate_inp), cur_gate_inp);
+                cb(cur_gate, "ffn_shexp_gate", il);
+
+                ggml_tensor * cur_ffn = build_ffn(cur,
+                        model.layers[il].ffn_up_shexp,   NULL, NULL,
+                        model.layers[il].ffn_gate_shexp, NULL, NULL,
+                        model.layers[il].ffn_down_shexp, NULL, NULL,
+                        NULL,
+                        LLM_FFN_SILU, LLM_FFN_PAR, il);
+                cb(cur_ffn, "ffn_shexp", il);
+
+                ggml_tensor * ffn_shexp_out = ggml_mul(ctx0, cur_ffn, cur_gate);
+                cb(ffn_shexp_out, "ffn_shexp_out", il);
+
+                moe_out = ggml_add(ctx0, moe_out, ffn_shexp_out);
+                cb(moe_out, "ffn_out", il);
+
+                cur = moe_out;
+            }
+            cur = ggml_add(ctx0, cur, ffn_inp);
+
+            cur = build_cvec(cur, il);
+            cb(cur, "l_out", il);
+
+            // input for next layer
+            inpL = cur;
+        }
+        cur = inpL;
+
+        cur = build_norm(cur,
+                model.output_norm, NULL,
+                LLM_NORM_RMS, -1);
+
+        cb(cur, "result_norm", -1);
+        res->t_embd = cur;
+
+        // lm_head
+        cur = build_lora_mm(model.output, cur);
+
+        cb(cur, "result_output", -1);
+        res->t_logits = cur;
+
+        ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/qwen2vl.cpp b/src/models/qwen2vl.cpp
new file mode 100644
index 00000000000..addc37f9a8f
--- /dev/null
+++ b/src/models/qwen2vl.cpp
@@ -0,0 +1,117 @@
+#include "models.h"
+
+llm_build_qwen2vl::llm_build_qwen2vl(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+        const int64_t n_embd_head = hparams.n_embd_head_v;
+
+        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+        GGML_ASSERT(n_embd_head == hparams.n_rot);
+
+        ggml_tensor * cur;
+        ggml_tensor * inpL;
+
+        inpL = build_inp_embd(model.tok_embd);
+
+        // inp_pos - contains the positions
+        ggml_tensor * inp_pos = build_inp_pos();
+
+        auto * inp_attn = build_attn_inp_kv();
+
+        int sections[4];
+        std::copy(std::begin(hparams.rope_sections), std::begin(hparams.rope_sections) + 4, sections);
+
+        ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+        for (int il = 0; il < n_layer; ++il) {
+            ggml_tensor * inpSA = inpL;
+
+            // norm
+            cur = build_norm(inpL,
+                    model.layers[il].attn_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "attn_norm", il);
+
+            // self-attention
+            {
+                // compute Q and K and RoPE them
+                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+                Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
+                cb(Qcur, "Qcur", il);
+
+                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+                Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
+                cb(Kcur, "Kcur", il);
+
+                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+                Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
+                cb(Vcur, "Vcur", il);
+
+                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+                Qcur = ggml_rope_multi(
+                        ctx0, Qcur, inp_pos, nullptr,
+                        n_rot, sections, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+                Kcur = ggml_rope_multi(
+                        ctx0, Kcur, inp_pos, nullptr,
+                        n_rot, sections, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+                cb(Qcur, "Qcur", il);
+                cb(Kcur, "Kcur", il);
+                cb(Vcur, "Vcur", il);
+
+                cur = build_attn(inp_attn,
+                        model.layers[il].wo, model.layers[il].bo,
+                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+            }
+            if (il == n_layer - 1 && inp_out_ids) {
+                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+            }
+            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+            cb(ffn_inp, "ffn_inp", il);
+
+            // feed-forward network
+            cur = build_norm(ffn_inp,
+                    model.layers[il].ffn_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "ffn_norm", il);
+
+            cur = build_ffn(cur,
+                    model.layers[il].ffn_up,   NULL, NULL,
+                    model.layers[il].ffn_gate, NULL, NULL,
+                    model.layers[il].ffn_down, NULL, NULL,
+                    NULL,
+                    LLM_FFN_SILU, LLM_FFN_PAR, il);
+            cb(cur, "ffn_out", il);
+
+            cur = ggml_add(ctx0, cur, ffn_inp);
+
+            cur = build_cvec(cur, il);
+            cb(cur, "l_out", il);
+
+            // input for next layer
+            inpL = cur;
+        }
+        cur = inpL;
+
+        cur = build_norm(cur,
+                model.output_norm, NULL,
+                LLM_NORM_RMS, -1);
+
+        cb(cur, "result_norm", -1);
+        res->t_embd = cur;
+
+        // lm_head
+        cur = build_lora_mm(model.output, cur);
+
+        cb(cur, "result_output", -1);
+        res->t_logits = cur;
+
+        ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/qwen3.cpp b/src/models/qwen3.cpp
new file mode 100644
index 00000000000..782d32107a3
--- /dev/null
+++ b/src/models/qwen3.cpp
@@ -0,0 +1,117 @@
+#include "models.h"
+
+llm_build_qwen3::llm_build_qwen3(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+        const int64_t n_embd_head = hparams.n_embd_head_v;
+
+        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+        GGML_ASSERT(n_embd_head == hparams.n_rot);
+
+        ggml_tensor * cur;
+        ggml_tensor * inpL;
+
+        inpL = build_inp_embd(model.tok_embd);
+
+        // inp_pos - contains the positions
+        ggml_tensor * inp_pos = build_inp_pos();
+
+        auto * inp_attn = build_attn_inp_kv();
+
+        ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+        for (int il = 0; il < n_layer; ++il) {
+            ggml_tensor * inpSA = inpL;
+
+            // norm
+            cur = build_norm(inpL,
+                    model.layers[il].attn_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "attn_norm", il);
+
+            // self-attention
+            {
+                // compute Q and K and RoPE them
+                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+                cb(Qcur, "Qcur", il);
+
+                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+                cb(Kcur, "Kcur", il);
+
+                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+                cb(Vcur, "Vcur", il);
+
+                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+                Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL, LLM_NORM_RMS, il);
+                cb(Qcur, "Qcur_normed", il);
+
+                Qcur = ggml_rope_ext(
+                        ctx0, Qcur, inp_pos, nullptr,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+                Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, NULL, LLM_NORM_RMS, il);
+                cb(Kcur, "Kcur_normed", il);
+
+                Kcur = ggml_rope_ext(
+                        ctx0, Kcur, inp_pos, nullptr,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+                cb(Qcur, "Qcur", il);
+                cb(Kcur, "Kcur", il);
+                cb(Vcur, "Vcur", il);
+
+                cur = build_attn(inp_attn,
+                        model.layers[il].wo, model.layers[il].bo,
+                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+            }
+            if (il == n_layer - 1 && inp_out_ids) {
+                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+            }
+            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+            cb(ffn_inp, "ffn_inp", il);
+
+            // feed-forward network
+            cur = build_norm(ffn_inp,
+                    model.layers[il].ffn_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "ffn_norm", il);
+
+            cur = build_ffn(cur,
+                    model.layers[il].ffn_up,   NULL, NULL,
+                    model.layers[il].ffn_gate, NULL, NULL,
+                    model.layers[il].ffn_down, NULL, NULL,
+                    NULL,
+                    LLM_FFN_SILU, LLM_FFN_PAR, il);
+            cb(cur, "ffn_out", il);
+
+            cur = ggml_add(ctx0, cur, ffn_inp);
+
+            cur = build_cvec(cur, il);
+            cb(cur, "l_out", il);
+
+            // input for next layer
+            inpL = cur;
+        }
+        cur = inpL;
+
+        cur = build_norm(cur,
+                model.output_norm, NULL,
+                LLM_NORM_RMS, -1);
+
+        cb(cur, "result_norm", -1);
+        res->t_embd = cur;
+
+        // lm_head
+        cur = build_lora_mm(model.output, cur);
+
+        cb(cur, "result_output", -1);
+        res->t_logits = cur;
+
+        ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/qwen3moe.cpp b/src/models/qwen3moe.cpp
new file mode 100644
index 00000000000..f5087cdb06a
--- /dev/null
+++ b/src/models/qwen3moe.cpp
@@ -0,0 +1,124 @@
+#include "models.h"
+
+llm_build_qwen3moe::llm_build_qwen3moe(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+        const int64_t n_embd_head = hparams.n_embd_head_v;
+
+        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+        GGML_ASSERT(n_embd_head == hparams.n_rot);
+
+        ggml_tensor * cur;
+        ggml_tensor * inpL;
+
+        inpL = build_inp_embd(model.tok_embd);
+
+        // inp_pos - contains the positions
+        ggml_tensor * inp_pos = build_inp_pos();
+
+        auto * inp_attn = build_attn_inp_kv();
+
+        ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+        for (int il = 0; il < n_layer; ++il) {
+            ggml_tensor * inpSA = inpL;
+
+            // norm
+            cur = build_norm(inpL,
+                    model.layers[il].attn_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "attn_norm", il);
+
+            // self_attention
+            {
+                // compute Q and K and RoPE them
+                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+                cb(Qcur, "Qcur", il);
+
+                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+                cb(Kcur, "Kcur", il);
+
+                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+                cb(Vcur, "Vcur", il);
+
+                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+                Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL, LLM_NORM_RMS, il);
+                cb(Qcur, "Qcur_normed", il);
+
+                Qcur = ggml_rope_ext(
+                        ctx0, Qcur, inp_pos, nullptr,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+                Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, NULL, LLM_NORM_RMS, il);
+                cb(Kcur, "Kcur_normed", il);
+
+                Kcur = ggml_rope_ext(
+                        ctx0, Kcur, inp_pos, nullptr,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+                cb(Qcur, "Qcur", il);
+                cb(Kcur, "Kcur", il);
+                cb(Vcur, "Vcur", il);
+
+                cur = build_attn(inp_attn,
+                        model.layers[il].wo, model.layers[il].bo,
+                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+            }
+            if (il == n_layer - 1 && inp_out_ids) {
+                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+            }
+            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+            cb(ffn_inp, "ffn_inp", il);
+
+            // MoE branch
+            cur = build_norm(ffn_inp,
+                    model.layers[il].ffn_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "ffn_norm", il);
+
+            ggml_tensor * moe_out =
+                build_moe_ffn(cur,
+                        model.layers[il].ffn_gate_inp,
+                        model.layers[il].ffn_up_exps,
+                        model.layers[il].ffn_gate_exps,
+                        model.layers[il].ffn_down_exps,
+                        nullptr,
+                        n_expert, n_expert_used,
+                        LLM_FFN_SILU, true,
+                        false, 0.0,
+                        LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
+                        il);
+            cb(moe_out, "ffn_moe_out", il);
+            cur = moe_out;
+
+            cur = ggml_add(ctx0, cur, ffn_inp);
+
+            cur = build_cvec(cur, il);
+            cb(cur, "l_out", il);
+
+            // input for next layer
+            inpL = cur;
+        }
+        cur = inpL;
+
+        cur = build_norm(cur,
+                model.output_norm, NULL,
+                LLM_NORM_RMS, -1);
+
+        cb(cur, "result_norm", -1);
+        res->t_embd = cur;
+
+        // lm_head
+        cur = build_lora_mm(model.output, cur);
+
+        cb(cur, "result_output", -1);
+        res->t_logits = cur;
+
+        ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/qwen3vl-moe.cpp b/src/models/qwen3vl-moe.cpp
new file mode 100644
index 00000000000..c48643c0cd1
--- /dev/null
+++ b/src/models/qwen3vl-moe.cpp
@@ -0,0 +1,150 @@
+#include "models.h"
+
+llm_build_qwen3vlmoe::llm_build_qwen3vlmoe(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+    const int64_t n_embd_full = hparams.n_embd; // main embd + deepstack embds
+    const size_t n_deepstack_layers = hparams.n_deepstack_layers;
+    const int64_t n_embd = n_embd_full / (n_deepstack_layers + 1);
+    const int64_t n_embd_head = hparams.n_embd_head_v;
+
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+    GGML_ASSERT(n_embd_head == hparams.n_rot);
+
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+
+    inpL = build_inp_embd(model.tok_embd);
+
+    int sections[4];
+    std::copy(std::begin(hparams.rope_sections), std::begin(hparams.rope_sections) + 4, sections);
+
+    std::vector<ggml_tensor *> deepstack_features(n_deepstack_layers, nullptr);
+
+    if (ubatch.embd) {
+        // Image input: split main embd and deepstack embds
+        ggml_tensor * inpL_main = ggml_view_2d(ctx0, inpL, n_embd, n_tokens, inpL->nb[1], 0);
+        for (size_t i = 0; i < n_deepstack_layers; i++) {
+            deepstack_features[i] = ggml_view_2d(ctx0, inpL, n_embd, n_tokens, inpL->nb[1], (i + 1) * n_embd * sizeof(float));
+        }
+        inpL = inpL_main;
+    }
+
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
+
+    auto * inp_attn = build_attn_inp_kv();
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * inpSA = inpL;
+
+        // norm
+        cur = build_norm(inpL,
+                model.layers[il].attn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
+
+        // self_attention
+        {
+            // compute Q and K and RoPE them
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            cb(Qcur, "Qcur", il);
+
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            cb(Kcur, "Kcur", il);
+
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            cb(Vcur, "Vcur", il);
+
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+            Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL, LLM_NORM_RMS, il);
+            cb(Qcur, "Qcur_normed", il);
+
+            Qcur = ggml_rope_multi(
+                    ctx0, Qcur, inp_pos, nullptr,
+                    n_rot, sections, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, NULL, LLM_NORM_RMS, il);
+            cb(Kcur, "Kcur_normed", il);
+
+            Kcur = ggml_rope_multi(
+                    ctx0, Kcur, inp_pos, nullptr,
+                    n_rot, sections, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, model.layers[il].bo,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+        }
+
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+        }
+
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+        cb(ffn_inp, "ffn_inp", il);
+
+        // MoE branch
+        cur = build_norm(ffn_inp,
+                model.layers[il].ffn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "ffn_norm", il);
+
+        ggml_tensor * moe_out =
+            build_moe_ffn(cur,
+                    model.layers[il].ffn_gate_inp,
+                    model.layers[il].ffn_up_exps,
+                    model.layers[il].ffn_gate_exps,
+                    model.layers[il].ffn_down_exps,
+                    nullptr,
+                    n_expert, n_expert_used,
+                    LLM_FFN_SILU, true,
+                    false, 0.0,
+                    LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
+                    il);
+        cb(moe_out, "ffn_moe_out", il);
+        cur = moe_out;
+
+        cur = ggml_add(ctx0, cur, ffn_inp);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        if (ubatch.embd && (size_t)il < n_deepstack_layers) {
+            cur = ggml_add(ctx0, cur, deepstack_features[il]);
+            cb(cur, "deepstack_out", il);
+        }
+
+        // input for next layer
+        inpL = cur;
+    }
+
+    cur = inpL;
+
+    cur = build_norm(cur,
+            model.output_norm, NULL,
+            LLM_NORM_RMS, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
+
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}
+
diff --git a/src/models/qwen3vl.cpp b/src/models/qwen3vl.cpp
new file mode 100644
index 00000000000..10b36c1f65e
--- /dev/null
+++ b/src/models/qwen3vl.cpp
@@ -0,0 +1,144 @@
+#include "models.h"
+
+llm_build_qwen3vl::llm_build_qwen3vl(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+
+    const int64_t n_embd_full = hparams.n_embd; // main embd + deepstack embds
+    const size_t n_deepstack_layers = hparams.n_deepstack_layers;
+    const int64_t n_embd = n_embd_full / (n_deepstack_layers + 1);
+    const int64_t n_embd_head = hparams.n_embd_head_v;
+
+
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+    GGML_ASSERT(n_embd_head == hparams.n_rot);
+
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+
+    inpL = build_inp_embd(model.tok_embd);
+
+    int sections[4];
+    std::copy(std::begin(hparams.rope_sections), std::begin(hparams.rope_sections) + 4, sections);
+
+    std::vector<ggml_tensor *> deepstack_features(n_deepstack_layers, nullptr);
+
+    if (ubatch.embd) {
+        // Image input: split main embd and deepstack embds
+        ggml_tensor * inpL_main = ggml_view_2d(ctx0, inpL, n_embd, n_tokens, inpL->nb[1], 0);
+        for (size_t i = 0; i < n_deepstack_layers; i++) {
+            deepstack_features[i] = ggml_view_2d(ctx0, inpL, n_embd, n_tokens, inpL->nb[1], (i + 1) * n_embd * sizeof(float));
+        }
+        inpL = inpL_main;
+    }
+
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
+
+    auto * inp_attn = build_attn_inp_kv();
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * inpSA = inpL;
+
+        // norm
+        cur = build_norm(inpL,
+                model.layers[il].attn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
+
+        // self-attention
+        {
+            // compute Q and K and RoPE them
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            cb(Qcur, "Qcur", il);
+
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            cb(Kcur, "Kcur", il);
+
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            cb(Vcur, "Vcur", il);
+
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+            Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL, LLM_NORM_RMS, il);
+            cb(Qcur, "Qcur_normed", il);
+
+            Qcur = ggml_rope_multi(
+                    ctx0, Qcur, inp_pos, nullptr,
+                    n_rot, sections, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, NULL, LLM_NORM_RMS, il);
+            cb(Kcur, "Kcur_normed", il);
+
+            Kcur = ggml_rope_multi(
+                    ctx0, Kcur, inp_pos, nullptr,
+                    n_rot, sections, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, model.layers[il].bo,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+        }
+
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+        }
+
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+        cb(ffn_inp, "ffn_inp", il);
+
+        // feed-forward network
+        cur = build_norm(ffn_inp,
+                model.layers[il].ffn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "ffn_norm", il);
+
+        cur = build_ffn(cur,
+                model.layers[il].ffn_up,   NULL, NULL,
+                model.layers[il].ffn_gate, NULL, NULL,
+                model.layers[il].ffn_down, NULL, NULL,
+                NULL,
+                LLM_FFN_SILU, LLM_FFN_PAR, il);
+        cb(cur, "ffn_out", il);
+
+        cur = ggml_add(ctx0, cur, ffn_inp);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        if (ubatch.embd && (size_t)il < n_deepstack_layers) {
+            cur = ggml_add(ctx0, cur, deepstack_features[il]);
+            cb(cur, "deepstack_out", il);
+        }
+
+        // input for next layer
+        inpL = cur;
+    }
+
+    cur = inpL;
+
+    cur = build_norm(cur,
+            model.output_norm, NULL,
+            LLM_NORM_RMS, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
+
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/refact.cpp b/src/models/refact.cpp
new file mode 100644
index 00000000000..951844f6408
--- /dev/null
+++ b/src/models/refact.cpp
@@ -0,0 +1,94 @@
+#include "models.h"
+
+llm_build_refact::llm_build_refact(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+        const int64_t n_embd_head = hparams.n_embd_head_v;
+
+        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+
+        ggml_tensor * cur;
+        ggml_tensor * inpL;
+
+        inpL = build_inp_embd(model.tok_embd);
+
+        auto * inp_attn = build_attn_inp_kv();
+
+        ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+        for (int il = 0; il < n_layer; ++il) {
+            ggml_tensor * inpSA = inpL;
+
+            cur = build_norm(inpL,
+                    model.layers[il].attn_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "attn_norm", il);
+
+            // self-attention
+            {
+                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+                cb(Qcur, "Qcur", il);
+
+                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+                cb(Kcur, "Kcur", il);
+
+                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+                cb(Vcur, "Vcur", il);
+
+                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+                cb(Qcur, "Qcur", il);
+                cb(Kcur, "Kcur", il);
+                cb(Vcur, "Vcur", il);
+
+                cur = build_attn(inp_attn,
+                        model.layers[il].wo, NULL,
+                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+            }
+            if (il == n_layer - 1 && inp_out_ids) {
+                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+            }
+            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+            cb(ffn_inp, "ffn_inp", il);
+
+            // feed-forward network
+            {
+                cur = build_norm(ffn_inp,
+                        model.layers[il].ffn_norm, NULL,
+                        LLM_NORM_RMS, il);
+                cb(cur, "ffn_norm", il);
+
+                cur = build_ffn(cur,
+                        model.layers[il].ffn_up,   NULL, NULL,
+                        model.layers[il].ffn_gate, NULL, NULL,
+                        model.layers[il].ffn_down, NULL, NULL,
+                        NULL,
+                        LLM_FFN_SILU, LLM_FFN_PAR, il);
+                cb(cur, "ffn_out", il);
+            }
+            cur = ggml_add(ctx0, cur, ffn_inp);
+
+            cur = build_cvec(cur, il);
+            cb(cur, "l_out", il);
+
+            // input for next layer
+            inpL = cur;
+        }
+        cur = inpL;
+
+        cur = build_norm(cur,
+                model.output_norm, NULL,
+                LLM_NORM_RMS, -1);
+
+        cb(cur, "result_norm", -1);
+        res->t_embd = cur;
+
+        // lm_head
+        cur = build_lora_mm(model.output, cur);
+
+        cb(cur, "result_output", -1);
+        res->t_logits = cur;
+
+        ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/rwkv6-base.cpp b/src/models/rwkv6-base.cpp
new file mode 100644
index 00000000000..7beed2daffb
--- /dev/null
+++ b/src/models/rwkv6-base.cpp
@@ -0,0 +1,162 @@
+#include "models.h"
+
+llm_build_rwkv6_base::llm_build_rwkv6_base(const llama_model & model, const llm_graph_params & params) :
+    llm_graph_context(params),
+    model(model) {}
+
+ggml_tensor * llm_build_rwkv6_base::build_rwkv6_channel_mix(const llama_layer * layer,
+                                                            ggml_tensor *       cur,
+                                                            ggml_tensor *       x_prev,
+                                                            llm_arch            arch) const {
+    ggml_tensor * sx = ggml_sub(ctx0, x_prev, cur);
+    switch (arch) {
+        case LLM_ARCH_RWKV6:
+            {
+                ggml_tensor * xk = ggml_add(ctx0, ggml_mul(ctx0, sx, layer->channel_mix_lerp_k), cur);
+                ggml_tensor * xr = ggml_add(ctx0, ggml_mul(ctx0, sx, layer->channel_mix_lerp_r), cur);
+
+                ggml_tensor * r = ggml_sigmoid(ctx0, build_lora_mm(layer->channel_mix_receptance, xr));
+                ggml_tensor * k = ggml_sqr(ctx0, ggml_relu(ctx0, build_lora_mm(layer->channel_mix_key, xk)));
+                cur             = ggml_mul(ctx0, r, build_lora_mm(layer->channel_mix_value, k));
+            }
+            break;
+        default:
+            GGML_ABORT("fatal error");
+    }
+    return cur;
+}
+
+ggml_tensor * llm_build_rwkv6_base::build_rwkv6_time_mix(llm_graph_input_rs * inp,
+                                                         ggml_tensor *        cur,
+                                                         ggml_tensor *        x_prev,
+                                                         const llama_ubatch & ubatch,
+                                                         int                  il) const {
+    const auto * mctx_cur = static_cast<const llama_memory_recurrent_context *>(mctx);
+
+    const auto n_tokens     = ubatch.n_tokens;
+    const auto n_seqs       = ubatch.n_seqs;
+    const auto n_seq_tokens = ubatch.n_seq_tokens;
+    const auto n_embd       = hparams.n_embd;
+    const auto head_size    = hparams.wkv_head_size;
+    const auto n_head       = n_embd / head_size;
+    const auto n_head_kv    = hparams.n_head_kv(il);
+
+    const auto kv_head = mctx_cur->get_head();
+
+    const auto & layer = model.layers[il];
+
+    bool is_qrwkv = layer.time_mix_first == nullptr;
+
+    ggml_tensor * sx = ggml_sub(ctx0, x_prev, cur);
+
+    sx  = ggml_reshape_2d(ctx0, sx, n_embd, n_tokens);
+    cur = ggml_reshape_2d(ctx0, cur, n_embd, n_tokens);
+
+    ggml_tensor * xxx = ggml_add(ctx0, ggml_mul(ctx0, sx, layer.time_mix_lerp_x), cur);
+
+    xxx = ggml_reshape_4d(ctx0, ggml_tanh(ctx0, ggml_mul_mat(ctx0, layer.time_mix_w1, xxx)),
+                          layer.time_mix_w1->ne[1] / 5, 1, 5, n_tokens);
+
+    xxx = ggml_cont(ctx0, ggml_permute(ctx0, xxx, 0, 1, 3, 2));
+
+    xxx = ggml_mul_mat(
+        ctx0, ggml_reshape_4d(ctx0, layer.time_mix_w2, layer.time_mix_w2->ne[0], layer.time_mix_w2->ne[1], 1, 5), xxx);
+
+    ggml_tensor *xw, *xk, *xv, *xr, *xg;
+    if (layer.time_mix_lerp_fused) {
+        // fusing these weights makes some performance improvement
+        sx  = ggml_reshape_3d(ctx0, sx, n_embd, 1, n_tokens);
+        cur = ggml_reshape_3d(ctx0, cur, n_embd, 1, n_tokens);
+        xxx = ggml_add(ctx0, ggml_mul(ctx0, ggml_add(ctx0, xxx, layer.time_mix_lerp_fused), sx), cur);
+        xw  = ggml_view_2d(ctx0, xxx, n_embd, n_tokens, xxx->nb[1], 0);
+        xk  = ggml_view_2d(ctx0, xxx, n_embd, n_tokens, xxx->nb[1], n_embd * n_tokens * sizeof(float));
+        xv  = ggml_view_2d(ctx0, xxx, n_embd, n_tokens, xxx->nb[1], n_embd * n_tokens * 2 * sizeof(float));
+        xr  = ggml_view_2d(ctx0, xxx, n_embd, n_tokens, xxx->nb[1], n_embd * n_tokens * 3 * sizeof(float));
+        xg  = ggml_view_2d(ctx0, xxx, n_embd, n_tokens, xxx->nb[1], n_embd * n_tokens * 4 * sizeof(float));
+    } else {
+        // for backward compatibility
+        xw = ggml_view_2d(ctx0, xxx, n_embd, n_tokens, xxx->nb[1], 0);
+        xk = ggml_view_2d(ctx0, xxx, n_embd, n_tokens, xxx->nb[1], n_embd * n_tokens * sizeof(float));
+        xv = ggml_view_2d(ctx0, xxx, n_embd, n_tokens, xxx->nb[1], n_embd * n_tokens * 2 * sizeof(float));
+        xr = ggml_view_2d(ctx0, xxx, n_embd, n_tokens, xxx->nb[1], n_embd * n_tokens * 3 * sizeof(float));
+        xg = ggml_view_2d(ctx0, xxx, n_embd, n_tokens, xxx->nb[1], n_embd * n_tokens * 4 * sizeof(float));
+
+        xw = ggml_add(ctx0, ggml_mul(ctx0, ggml_add(ctx0, xw, layer.time_mix_lerp_w), sx), cur);
+        xk = ggml_add(ctx0, ggml_mul(ctx0, ggml_add(ctx0, xk, layer.time_mix_lerp_k), sx), cur);
+        xv = ggml_add(ctx0, ggml_mul(ctx0, ggml_add(ctx0, xv, layer.time_mix_lerp_v), sx), cur);
+        xr = ggml_add(ctx0, ggml_mul(ctx0, ggml_add(ctx0, xr, layer.time_mix_lerp_r), sx), cur);
+        xg = ggml_add(ctx0, ggml_mul(ctx0, ggml_add(ctx0, xg, layer.time_mix_lerp_g), sx), cur);
+    }
+    ggml_tensor * r = build_lora_mm(layer.time_mix_receptance, xr);
+    ggml_tensor * k = build_lora_mm(layer.time_mix_key, xk);
+    ggml_tensor * v = build_lora_mm(layer.time_mix_value, xv);
+    if (layer.time_mix_receptance_b) {
+        r = ggml_add(ctx0, r, layer.time_mix_receptance_b);
+    }
+    if (layer.time_mix_key_b) {
+        k = ggml_add(ctx0, k, layer.time_mix_key_b);
+    }
+    if (layer.time_mix_value_b) {
+        v = ggml_add(ctx0, v, layer.time_mix_value_b);
+    }
+    ggml_tensor * g = build_lora_mm(layer.time_mix_gate, xg);
+    if (is_qrwkv) {
+        g = ggml_sigmoid(ctx0, g);
+    } else {
+        g = ggml_silu(ctx0, g);
+    }
+    if (n_head_kv != 0 && n_head_kv != n_head) {
+        GGML_ASSERT(n_head % n_head_kv == 0);
+        k                 = ggml_reshape_4d(ctx0, k, head_size, 1, n_head_kv, n_tokens);
+        v                 = ggml_reshape_4d(ctx0, v, head_size, 1, n_head_kv, n_tokens);
+        ggml_tensor * tmp = ggml_new_tensor_4d(ctx0, GGML_TYPE_F32, head_size, n_head / n_head_kv, n_head_kv, n_tokens);
+        k                 = ggml_repeat(ctx0, k, tmp);
+        v                 = ggml_repeat(ctx0, v, tmp);
+    }
+    k = ggml_reshape_3d(ctx0, k, head_size, n_head, n_tokens);
+    v = ggml_reshape_3d(ctx0, v, head_size, n_head, n_tokens);
+    r = ggml_reshape_3d(ctx0, r, head_size, n_head, n_tokens);
+
+    ggml_tensor * w =
+        ggml_mul_mat(ctx0, layer.time_mix_decay_w2, ggml_tanh(ctx0, ggml_mul_mat(ctx0, layer.time_mix_decay_w1, xw)));
+
+    w = ggml_add(ctx0, w, layer.time_mix_decay);
+    w = ggml_exp(ctx0, ggml_neg(ctx0, ggml_exp(ctx0, w)));
+    w = ggml_reshape_3d(ctx0, w, head_size, n_head, n_tokens);
+
+    if (is_qrwkv) {
+        // k = k * (1 - w)
+        k = ggml_sub(ctx0, k, ggml_mul(ctx0, k, w));
+    }
+    ggml_tensor * wkv_state = build_rs(inp, mctx_cur->get_s_l(il), hparams.n_embd_s(), n_seqs);
+
+    ggml_tensor * wkv_output;
+    if (is_qrwkv) {
+        wkv_output = ggml_gated_linear_attn(ctx0, k, v, r, w, wkv_state, pow(head_size, -0.5f));
+    } else {
+        wkv_output = ggml_rwkv_wkv6(ctx0, k, v, r, layer.time_mix_first, w, wkv_state);
+    }
+    cur       = ggml_view_1d(ctx0, wkv_output, n_embd * n_tokens, 0);
+    wkv_state = ggml_view_1d(ctx0, wkv_output, n_embd * head_size * n_seqs, n_embd * n_tokens * sizeof(float));
+
+    ggml_build_forward_expand(
+        gf, ggml_cpy(ctx0, wkv_state,
+                     ggml_view_1d(ctx0, mctx_cur->get_s_l(il), hparams.n_embd_s() * n_seqs,
+                                  hparams.n_embd_s() * kv_head * ggml_element_size(mctx_cur->get_s_l(il)))));
+
+    if (!is_qrwkv) {
+        // group norm with head_count groups
+        cur = ggml_reshape_3d(ctx0, cur, n_embd / n_head, n_head, n_tokens);
+        cur = ggml_norm(ctx0, cur, 64e-5f);
+
+        // Convert back to regular vectors.
+        cur = ggml_reshape_2d(ctx0, cur, n_embd, n_tokens);
+        cur = ggml_add(ctx0, ggml_mul(ctx0, cur, layer.time_mix_ln), layer.time_mix_ln_b);
+    } else {
+        cur = ggml_reshape_2d(ctx0, cur, n_embd, n_tokens);
+    }
+    cur = ggml_mul(ctx0, cur, g);
+    cur = build_lora_mm(layer.time_mix_output, cur);
+
+    return ggml_reshape_3d(ctx0, cur, n_embd, n_seq_tokens, n_seqs);
+}
diff --git a/src/models/rwkv6.cpp b/src/models/rwkv6.cpp
new file mode 100644
index 00000000000..15453fbf50f
--- /dev/null
+++ b/src/models/rwkv6.cpp
@@ -0,0 +1,94 @@
+#include "models.h"
+
+llm_build_rwkv6::llm_build_rwkv6(const llama_model & model, const llm_graph_params & params) :
+    llm_build_rwkv6_base(model, params) {
+    GGML_ASSERT(hparams.token_shift_count == 2);
+
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+
+    inpL = build_inp_embd(model.tok_embd);
+    inpL = build_norm(inpL, model.tok_norm, model.tok_norm_b, LLM_NORM, -1);
+
+    auto * rs_inp = build_rs_inp();
+
+    const auto n_embd       = hparams.n_embd;
+    const auto n_seq_tokens = ubatch.n_seq_tokens;
+    const auto n_seqs       = ubatch.n_seqs;
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        const llama_layer * layer = &model.layers[il];
+        inpL                      = ggml_reshape_3d(ctx0, inpL, n_embd, n_seq_tokens, n_seqs);
+
+        ggml_tensor * token_shift = build_rwkv_token_shift_load(rs_inp, ubatch, il);
+
+        ggml_tensor * att_shift =
+            ggml_view_3d(ctx0, token_shift, n_embd, 1, n_seqs, token_shift->nb[1], token_shift->nb[2], 0);
+        ggml_tensor * ffn_shift = ggml_view_3d(ctx0, token_shift, n_embd, 1, n_seqs, token_shift->nb[1],
+                                               token_shift->nb[2], n_embd * ggml_element_size(token_shift));
+
+        ggml_tensor * att_norm = build_norm(inpL, layer->attn_norm, layer->attn_norm_b, LLM_NORM, il);
+        cb(att_norm, "attn_norm", il);
+
+        ggml_tensor * x_prev = ggml_concat(
+            ctx0, att_shift,
+            ggml_view_3d(ctx0, att_norm, n_embd, n_seq_tokens - 1, n_seqs, att_norm->nb[1], att_norm->nb[2], 0), 1);
+
+        cur = build_rwkv6_time_mix(rs_inp, att_norm, x_prev, ubatch, il);
+
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpL);
+        cb(ffn_inp, "ffn_inp", il);
+
+        ggml_tensor * ffn_norm = build_norm(ffn_inp, layer->attn_norm_2, layer->attn_norm_2_b, LLM_NORM, il);
+        cb(ffn_norm, "ffn_norm", il);
+
+        x_prev = ggml_concat(
+            ctx0, ffn_shift,
+            ggml_view_3d(ctx0, ffn_norm, n_embd, n_seq_tokens - 1, n_seqs, ffn_norm->nb[1], ffn_norm->nb[2], 0), 1);
+
+        token_shift = ggml_concat(ctx0,
+                                  ggml_view_3d(ctx0, att_norm, n_embd, 1, n_seqs, att_norm->nb[1], att_norm->nb[2],
+                                               (n_seq_tokens - 1) * n_embd * ggml_element_size(att_norm)),
+                                  ggml_view_3d(ctx0, ffn_norm, n_embd, 1, n_seqs, ffn_norm->nb[1], ffn_norm->nb[2],
+                                               (n_seq_tokens - 1) * n_embd * ggml_element_size(ffn_norm)),
+                                  1);
+        ggml_build_forward_expand(gf, build_rwkv_token_shift_store(token_shift, ubatch, il));
+
+        ffn_inp  = ggml_reshape_2d(ctx0, ffn_inp, n_embd, n_tokens);
+        ffn_norm = ggml_reshape_2d(ctx0, ffn_norm, n_embd, n_tokens);
+        x_prev   = ggml_reshape_2d(ctx0, x_prev, n_embd, n_tokens);
+        cur      = ggml_reshape_2d(ctx0, cur, n_embd, n_tokens);
+
+        if (il == n_layer - 1 && inp_out_ids) {
+            ffn_inp  = ggml_get_rows(ctx0, ffn_inp, inp_out_ids);
+            ffn_norm = ggml_get_rows(ctx0, ffn_norm, inp_out_ids);
+            x_prev   = ggml_get_rows(ctx0, x_prev, inp_out_ids);
+            cur      = ggml_get_rows(ctx0, cur, inp_out_ids);
+        }
+        cur = build_rwkv6_channel_mix(layer, ffn_norm, x_prev, LLM_ARCH_RWKV6);
+        cur = ggml_add(ctx0, cur, ffn_inp);
+
+        if (hparams.rescale_every_n_layers != 0 && (il + 1) % hparams.rescale_every_n_layers == 0) {
+            cur = ggml_scale(ctx0, cur, 0.5F);
+        }
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+    cur = inpL;
+    cur = build_norm(cur, model.output_norm, model.output_norm_b, LLM_NORM, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    cur = build_lora_mm(model.output, cur);
+
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/rwkv6qwen2.cpp b/src/models/rwkv6qwen2.cpp
new file mode 100644
index 00000000000..e84e5973820
--- /dev/null
+++ b/src/models/rwkv6qwen2.cpp
@@ -0,0 +1,86 @@
+#include "models.h"
+
+llm_build_rwkv6qwen2::llm_build_rwkv6qwen2(const llama_model & model, const llm_graph_params & params) : llm_build_rwkv6_base(model, params) {
+    GGML_ASSERT(n_embd == hparams.n_embd_r());
+
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+
+    inpL = build_inp_embd(model.tok_embd);
+
+    auto * rs_inp = build_rs_inp();
+
+    const auto n_embd = hparams.n_embd;
+    const auto n_seq_tokens = ubatch.n_seq_tokens;
+    const auto n_seqs = ubatch.n_seqs;
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        const llama_layer * layer = &model.layers[il];
+        inpL = ggml_reshape_3d(ctx0, inpL, n_embd, n_seq_tokens, n_seqs);
+
+        ggml_tensor * token_shift = build_rwkv_token_shift_load(rs_inp, ubatch, il);
+
+        ggml_tensor * att_norm = build_norm(inpL, layer->attn_norm, layer->attn_norm_b, LLM_NORM_RMS, il);
+        cb(att_norm, "attn_norm", il);
+
+        ggml_tensor * x_prev = ggml_concat(
+                ctx0,
+                token_shift,
+                ggml_view_3d(ctx0, att_norm, n_embd, n_seq_tokens - 1, n_seqs, att_norm->nb[1], att_norm->nb[2], 0),
+                1
+                );
+
+        cur = build_rwkv6_time_mix(rs_inp, att_norm, x_prev, ubatch, il);
+
+        token_shift = ggml_view_3d(ctx0, att_norm, n_embd, 1, n_seqs, att_norm->nb[1], att_norm->nb[2], (n_seq_tokens-1)*n_embd*ggml_element_size(att_norm));
+        ggml_build_forward_expand(gf, build_rwkv_token_shift_store(token_shift, ubatch, il));
+
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpL);
+        cb(ffn_inp, "ffn_inp", il);
+
+        cur     = ggml_reshape_2d(ctx0, cur,     n_embd, n_tokens);
+        ffn_inp = ggml_reshape_2d(ctx0, ffn_inp, n_embd, n_tokens);
+
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur     = ggml_get_rows(ctx0, cur,     inp_out_ids);
+            ffn_inp = ggml_get_rows(ctx0, ffn_inp, inp_out_ids);
+        }
+
+        // feed-forward network
+        cur = build_norm(ffn_inp,
+                model.layers[il].ffn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "ffn_norm", il);
+
+        cur = build_ffn(cur,
+                model.layers[il].ffn_up,   NULL, NULL,
+                model.layers[il].ffn_gate, NULL, NULL,
+                model.layers[il].ffn_down, NULL, NULL,
+                NULL,
+                LLM_FFN_SILU, LLM_FFN_PAR, il);
+        cb(cur, "ffn_out", il);
+
+        cur = ggml_add(ctx0, cur, ffn_inp);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+
+    cur = inpL;
+    cur = build_norm(cur, model.output_norm, model.output_norm_b, LLM_NORM_RMS, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    cur = build_lora_mm(model.output, cur);
+
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/rwkv7-base.cpp b/src/models/rwkv7-base.cpp
new file mode 100644
index 00000000000..cda44653849
--- /dev/null
+++ b/src/models/rwkv7-base.cpp
@@ -0,0 +1,135 @@
+#include "models.h"
+
+llm_build_rwkv7_base::llm_build_rwkv7_base(const llama_model & model, const llm_graph_params & params) :
+    llm_graph_context(params),
+    model(model) {}
+
+ggml_tensor * llm_build_rwkv7_base::build_rwkv7_channel_mix(const llama_layer * layer,
+                                                            ggml_tensor *       cur,
+                                                            ggml_tensor *       x_prev,
+                                                            llm_arch            arch) const {
+    ggml_tensor * sx = ggml_sub(ctx0, x_prev, cur);
+    switch (arch) {
+        case LLM_ARCH_RWKV7:
+            {
+                ggml_tensor * xk = ggml_add(ctx0, ggml_mul(ctx0, sx, layer->channel_mix_lerp_k), cur);
+
+                ggml_tensor * k = ggml_sqr(ctx0, ggml_relu(ctx0, build_lora_mm(layer->channel_mix_key, xk)));
+
+                cur = build_lora_mm(layer->channel_mix_value, k);
+            }
+            break;
+        default:
+            GGML_ABORT("fatal error");
+    }
+    return cur;
+}
+
+ggml_tensor * llm_build_rwkv7_base::build_rwkv7_time_mix(llm_graph_input_rs * inp,
+                                                         ggml_tensor *        cur,
+                                                         ggml_tensor *        x_prev,
+                                                         ggml_tensor *&       first_layer_value,
+                                                         const llama_ubatch & ubatch,
+                                                         int                  il) const {
+    const auto * mctx_cur = static_cast<const llama_memory_recurrent_context *>(mctx);
+
+    const auto n_tokens     = ubatch.n_tokens;
+    const auto n_seqs       = ubatch.n_seqs;
+    const auto n_embd       = hparams.n_embd;
+    const auto head_size    = hparams.wkv_head_size;
+    const auto head_count   = n_embd / head_size;
+    const auto n_seq_tokens = ubatch.n_seq_tokens;
+
+    const auto kv_head = mctx_cur->get_head();
+
+    const auto & layer = model.layers[il];
+
+    bool has_gating = layer.time_mix_g1 && layer.time_mix_g2;
+
+    ggml_tensor * sx    = ggml_sub(ctx0, x_prev, cur);
+    ggml_tensor * dummy = ggml_new_tensor_4d(ctx0, GGML_TYPE_F32, n_embd, n_seq_tokens, n_seqs, has_gating ? 6 : 5);
+    sx                  = ggml_repeat(ctx0, sx, dummy);
+
+    ggml_tensor * xxx = ggml_add(ctx0, ggml_mul(ctx0, sx, layer.time_mix_lerp_fused), cur);
+
+    ggml_tensor * xr = ggml_view_2d(ctx0, xxx, n_embd, n_tokens, xxx->nb[1], 0);
+    ggml_tensor * xw = ggml_view_2d(ctx0, xxx, n_embd, n_tokens, xxx->nb[1], n_embd * n_tokens * sizeof(float));
+    ggml_tensor * xk = ggml_view_2d(ctx0, xxx, n_embd, n_tokens, xxx->nb[1], n_embd * n_tokens * 2 * sizeof(float));
+    ggml_tensor * xv = ggml_view_2d(ctx0, xxx, n_embd, n_tokens, xxx->nb[1], n_embd * n_tokens * 3 * sizeof(float));
+    ggml_tensor * xa = ggml_view_2d(ctx0, xxx, n_embd, n_tokens, xxx->nb[1], n_embd * n_tokens * 4 * sizeof(float));
+    ggml_tensor * xg =
+        has_gating ? ggml_view_2d(ctx0, xxx, n_embd, n_tokens, xxx->nb[1], n_embd * n_tokens * 5 * sizeof(float)) :
+                     nullptr;
+
+    ggml_tensor * r = build_lora_mm(layer.time_mix_receptance, xr);
+    ggml_tensor * w = ggml_add(
+        ctx0, ggml_mul_mat(ctx0, layer.time_mix_w2, ggml_tanh(ctx0, ggml_mul_mat(ctx0, layer.time_mix_w1, xw))),
+        layer.time_mix_w0);
+    w = ggml_exp(ctx0, ggml_scale(ctx0, ggml_sigmoid(ctx0, w), -0.606531));
+
+    ggml_tensor * k = build_lora_mm(layer.time_mix_key, xk);
+    ggml_tensor * v = build_lora_mm(layer.time_mix_value, xv);
+    if (first_layer_value == nullptr) {
+        first_layer_value = v;
+    } else {
+        // Add the first layer value as a residual connection.
+        v = ggml_add(ctx0, v,
+                     ggml_mul(ctx0, ggml_sub(ctx0, first_layer_value, v),
+                              ggml_sigmoid(ctx0, ggml_add(ctx0,
+                                                          ggml_mul_mat(ctx0, layer.time_mix_v2,
+                                                                       ggml_mul_mat(ctx0, layer.time_mix_v1, xv)),
+                                                          layer.time_mix_v0))));
+    }
+    ggml_tensor * g = nullptr;
+    if (layer.time_mix_g1 && layer.time_mix_g2) {
+        g = ggml_mul_mat(ctx0, layer.time_mix_g2, ggml_sigmoid(ctx0, ggml_mul_mat(ctx0, layer.time_mix_g1, xg)));
+    }
+    ggml_tensor * a = ggml_sigmoid(
+        ctx0, ggml_add(ctx0, ggml_mul_mat(ctx0, layer.time_mix_a2, ggml_mul_mat(ctx0, layer.time_mix_a1, xa)),
+                       layer.time_mix_a0));
+
+    ggml_tensor * kk = ggml_reshape_3d(ctx0, ggml_mul(ctx0, k, layer.time_mix_k_k), head_size, head_count, n_tokens);
+    kk               = ggml_l2_norm(ctx0, kk, 1e-12);
+
+    ggml_tensor * ka = ggml_mul(ctx0, k, layer.time_mix_k_a);
+    k                = ggml_add(ctx0, k, ggml_sub(ctx0, ggml_mul(ctx0, a, ka), ka));
+
+    r = ggml_reshape_3d(ctx0, r, head_size, head_count, n_tokens);
+    w = ggml_reshape_3d(ctx0, w, head_size, head_count, n_tokens);
+    k = ggml_reshape_3d(ctx0, k, head_size, head_count, n_tokens);
+    v = ggml_reshape_3d(ctx0, v, head_size, head_count, n_tokens);
+    a = ggml_reshape_3d(ctx0, a, head_size, head_count, n_tokens);
+
+    ggml_tensor * wkv_state = build_rs(inp, mctx_cur->get_s_l(il), hparams.n_embd_s(), n_seqs);
+
+    ggml_tensor * wkv_output = ggml_rwkv_wkv7(ctx0, r, w, k, v, ggml_neg(ctx0, kk), ggml_mul(ctx0, kk, a), wkv_state);
+    cur                      = ggml_view_1d(ctx0, wkv_output, n_embd * n_tokens, 0);
+    wkv_state = ggml_view_1d(ctx0, wkv_output, n_embd * head_size * n_seqs, n_embd * n_tokens * sizeof(float));
+
+    ggml_build_forward_expand(
+        gf, ggml_cpy(ctx0, wkv_state,
+                     ggml_view_1d(ctx0, mctx_cur->get_s_l(il), hparams.n_embd_s() * n_seqs,
+                                  hparams.n_embd_s() * kv_head * ggml_element_size(mctx_cur->get_s_l(il)))));
+
+    if (layer.time_mix_ln && layer.time_mix_ln_b) {
+        // group norm with head_count groups
+        cur = ggml_reshape_3d(ctx0, cur, n_embd / head_count, head_count, n_tokens);
+        cur = ggml_norm(ctx0, cur, 64e-5f);
+
+        // Convert back to regular vectors.
+        cur = ggml_reshape_2d(ctx0, cur, n_embd, n_tokens);
+        cur = ggml_add(ctx0, ggml_mul(ctx0, cur, layer.time_mix_ln), layer.time_mix_ln_b);
+    } else {
+        cur = ggml_reshape_2d(ctx0, cur, n_embd, n_tokens);
+    }
+    ggml_tensor * rk = ggml_sum_rows(
+        ctx0, ggml_mul(ctx0, ggml_mul(ctx0, k, r), ggml_reshape_2d(ctx0, layer.time_mix_r_k, head_size, head_count)));
+    cur = ggml_add(ctx0, cur, ggml_reshape_2d(ctx0, ggml_mul(ctx0, v, rk), n_embd, n_tokens));
+
+    if (has_gating) {
+        cur = ggml_mul(ctx0, cur, g);
+    }
+    cur = build_lora_mm(layer.time_mix_output, cur);
+
+    return ggml_reshape_3d(ctx0, cur, n_embd, n_seq_tokens, n_seqs);
+}
diff --git a/src/models/rwkv7.cpp b/src/models/rwkv7.cpp
new file mode 100644
index 00000000000..5caf6553dfe
--- /dev/null
+++ b/src/models/rwkv7.cpp
@@ -0,0 +1,90 @@
+#include "models.h"
+
+llm_build_rwkv7::llm_build_rwkv7(const llama_model & model, const llm_graph_params & params) :
+    llm_build_rwkv7_base(model, params) {
+    GGML_ASSERT(hparams.token_shift_count == 2);
+
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+    ggml_tensor * v_first = nullptr;
+
+    inpL = build_inp_embd(model.tok_embd);
+    inpL = build_norm(inpL, model.tok_norm, model.tok_norm_b, LLM_NORM, -1);
+
+    auto * rs_inp = build_rs_inp();
+
+    const auto n_embd       = hparams.n_embd;
+    const auto n_seq_tokens = ubatch.n_seq_tokens;
+    const auto n_seqs       = ubatch.n_seqs;
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        const llama_layer * layer = &model.layers[il];
+        inpL                      = ggml_reshape_3d(ctx0, inpL, n_embd, n_seq_tokens, n_seqs);
+
+        ggml_tensor * token_shift = build_rwkv_token_shift_load(rs_inp, ubatch, il);
+
+        ggml_tensor * att_shift =
+            ggml_view_3d(ctx0, token_shift, n_embd, 1, n_seqs, token_shift->nb[1], token_shift->nb[2], 0);
+        ggml_tensor * ffn_shift = ggml_view_3d(ctx0, token_shift, n_embd, 1, n_seqs, token_shift->nb[1],
+                                               token_shift->nb[2], n_embd * ggml_element_size(token_shift));
+
+        ggml_tensor * att_norm = build_norm(inpL, layer->attn_norm, layer->attn_norm_b, LLM_NORM, il);
+        cb(att_norm, "attn_norm", il);
+
+        ggml_tensor * x_prev = ggml_concat(
+            ctx0, att_shift,
+            ggml_view_3d(ctx0, att_norm, n_embd, n_seq_tokens - 1, n_seqs, att_norm->nb[1], att_norm->nb[2], 0), 1);
+
+        cur = build_rwkv7_time_mix(rs_inp, att_norm, x_prev, v_first, ubatch, il);
+
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpL);
+        cb(ffn_inp, "ffn_inp", il);
+
+        ggml_tensor * ffn_norm = build_norm(ffn_inp, layer->attn_norm_2, layer->attn_norm_2_b, LLM_NORM, il);
+        cb(ffn_norm, "ffn_norm", il);
+
+        x_prev = ggml_concat(
+            ctx0, ffn_shift,
+            ggml_view_3d(ctx0, ffn_norm, n_embd, n_seq_tokens - 1, n_seqs, ffn_norm->nb[1], ffn_norm->nb[2], 0), 1);
+
+        token_shift = ggml_concat(ctx0,
+                                  ggml_view_3d(ctx0, att_norm, n_embd, 1, n_seqs, att_norm->nb[1], att_norm->nb[2],
+                                               (n_seq_tokens - 1) * n_embd * ggml_element_size(att_norm)),
+                                  ggml_view_3d(ctx0, ffn_norm, n_embd, 1, n_seqs, ffn_norm->nb[1], ffn_norm->nb[2],
+                                               (n_seq_tokens - 1) * n_embd * ggml_element_size(ffn_norm)),
+                                  1);
+        ggml_build_forward_expand(gf, build_rwkv_token_shift_store(token_shift, ubatch, il));
+
+        ffn_inp  = ggml_reshape_2d(ctx0, ffn_inp, n_embd, n_tokens);
+        ffn_norm = ggml_reshape_2d(ctx0, ffn_norm, n_embd, n_tokens);
+        x_prev   = ggml_reshape_2d(ctx0, x_prev, n_embd, n_tokens);
+
+        if (il == n_layer - 1 && inp_out_ids) {
+            ffn_inp  = ggml_get_rows(ctx0, ffn_inp, inp_out_ids);
+            ffn_norm = ggml_get_rows(ctx0, ffn_norm, inp_out_ids);
+            x_prev   = ggml_get_rows(ctx0, x_prev, inp_out_ids);
+        }
+        cur = build_rwkv7_channel_mix(layer, ffn_norm, x_prev, LLM_ARCH_RWKV7);
+        cur = ggml_add(ctx0, cur, ffn_inp);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+    cur = inpL;
+    cur = build_norm(cur, model.output_norm, model.output_norm_b, LLM_NORM, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    cur = build_lora_mm(model.output, cur);
+
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/seed-oss.cpp b/src/models/seed-oss.cpp
new file mode 100644
index 00000000000..94ce1633629
--- /dev/null
+++ b/src/models/seed-oss.cpp
@@ -0,0 +1,124 @@
+#include "models.h"
+
+llm_build_seed_oss::llm_build_seed_oss(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+        const int64_t n_embd_head = hparams.n_embd_head_v;
+
+        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+        GGML_ASSERT(n_embd_head == hparams.n_rot);
+
+        ggml_tensor * cur;
+        ggml_tensor * inpL;
+
+        inpL = build_inp_embd(model.tok_embd);
+
+        // inp_pos - contains the positions
+        ggml_tensor * inp_pos = build_inp_pos();
+
+        auto * inp_attn = build_attn_inp_kv();
+
+        const float kq_scale = hparams.f_attention_scale == 0.0f ? 1.0f/sqrtf(float(n_embd_head)) : hparams.f_attention_scale;
+
+        ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+        for (int il = 0; il < n_layer; ++il) {
+            ggml_tensor * inpSA = inpL;
+
+            // norm
+            cur = build_norm(inpL,
+                    model.layers[il].attn_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "attn_norm", il);
+
+            // self-attention
+            {
+                // compute Q and K and RoPE them
+                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+                cb(Qcur, "Qcur", il);
+                if (model.layers[il].bq) {
+                    Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
+                    cb(Qcur, "Qcur", il);
+                }
+                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+                cb(Kcur, "Kcur", il);
+                if (model.layers[il].bk) {
+                    Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
+                    cb(Kcur, "Kcur", il);
+                }
+                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+                cb(Vcur, "Vcur", il);
+                if (model.layers[il].bv) {
+                    Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
+                    cb(Vcur, "Vcur", il);
+                }
+                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+                Qcur = ggml_rope_ext(
+                        ctx0, Qcur, inp_pos, nullptr,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+                Kcur = ggml_rope_ext(
+                        ctx0, Kcur, inp_pos, nullptr,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+                cb(Qcur, "Qcur", il);
+                cb(Kcur, "Kcur", il);
+                cb(Vcur, "Vcur", il);
+
+                cur = build_attn(inp_attn,
+                        model.layers[il].wo, model.layers[il].bo,
+                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, kq_scale, il);
+                cb(cur, "attn_out", il);
+            }
+            if (il == n_layer - 1 && inp_out_ids) {
+                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+            }
+            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+            cb(ffn_inp, "ffn_inp", il);
+
+            // feed-forward network
+            cur = build_norm(ffn_inp,
+                    model.layers[il].attn_post_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "attn_post_norm", il);
+
+            cur = build_ffn(cur,
+                    model.layers[il].ffn_up,   NULL, NULL,
+                    model.layers[il].ffn_gate, NULL, NULL,
+                    model.layers[il].ffn_down, NULL, NULL,
+                    NULL,
+                    LLM_FFN_SILU, LLM_FFN_PAR, il);
+            cb(cur, "ffn_out", il);
+
+            cur = ggml_add(ctx0, cur, ffn_inp);
+            cb(cur, "ffn_out", il);
+
+            cur = build_cvec(cur, il);
+            cb(cur, "l_out", il);
+
+            // input for next layer
+            inpL = cur;
+        }
+        cur = inpL;
+
+        cur = build_norm(cur,
+                model.output_norm, NULL,
+                LLM_NORM_RMS, -1);
+
+        cb(cur, "result_norm", -1);
+        res->t_embd = cur;
+
+        // lm_head
+        cur = build_lora_mm(model.output, cur);
+
+        cb(cur, "result_output", -1);
+        res->t_logits = cur;
+
+        ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/smallthinker.cpp b/src/models/smallthinker.cpp
new file mode 100644
index 00000000000..2fcd87a8a0e
--- /dev/null
+++ b/src/models/smallthinker.cpp
@@ -0,0 +1,120 @@
+#include "models.h"
+
+template <bool iswa>
+llm_build_smallthinker<iswa>::llm_build_smallthinker(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params){
+        const int64_t n_embd_head = hparams.n_embd_head_v;
+
+        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+        GGML_ASSERT(n_embd_head == hparams.n_rot);
+
+        ggml_tensor * cur;
+        ggml_tensor * inpL;
+
+        inpL = build_inp_embd(model.tok_embd);
+
+        // inp_pos - contains the positions
+        ggml_tensor * inp_pos = build_inp_pos();
+
+        using inp_attn_type = std::conditional_t<iswa, llm_graph_input_attn_kv_iswa, llm_graph_input_attn_kv>;
+        inp_attn_type * inp_attn = nullptr;
+
+        if constexpr (iswa) {
+            inp_attn = build_attn_inp_kv_iswa();
+        } else {
+            inp_attn = build_attn_inp_kv();
+        }
+        ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+        for (int il = 0; il < n_layer; ++il) {
+            ggml_tensor * inpSA  = inpL;
+            ggml_tensor * probs  = nullptr;
+
+            probs = build_lora_mm(model.layers[il].ffn_gate_inp, inpL);  // [n_expert, n_tokens]
+            cb(probs, "ffn_moe_logits", il);
+
+            // norm
+            cur = build_norm(inpL,model.layers[il].attn_norm, NULL, LLM_NORM_RMS, il);
+            cb(cur, "attn_norm", il);
+
+            // self_attention
+            {
+                // compute Q and K and RoPE them
+                struct ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+                cb(Qcur, "Qcur", il);
+
+                struct ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+                cb(Kcur, "Kcur", il);
+
+                struct ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+                cb(Vcur, "Vcur", il);
+
+                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head, n_tokens);
+                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+                if (hparams.n_no_rope_layer_step == n_layer || il % hparams.n_no_rope_layer_step != 0) {
+                    Qcur = ggml_rope_ext(ctx0, Qcur, inp_pos, nullptr, n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                                     ext_factor, attn_factor, beta_fast, beta_slow);
+
+                    Kcur = ggml_rope_ext(ctx0, Kcur, inp_pos, nullptr, n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                                     ext_factor, attn_factor, beta_fast, beta_slow);
+                }
+                cb(Qcur, "Qcur", il);
+                cb(Kcur, "Kcur", il);
+
+                cur = build_attn(inp_attn,
+                        model.layers[il].wo, model.layers[il].bo,
+                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f / sqrtf(float(n_embd_head)), il);
+            }
+            if (il == n_layer - 1 && inp_out_ids) {
+                cur = ggml_get_rows(ctx0, cur, inp_out_ids);
+                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+                probs = ggml_get_rows(ctx0, probs, inp_out_ids);
+            }
+            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+            cb(ffn_inp, "ffn_inp", il);
+
+            // MoE branch
+            cur = build_norm(ffn_inp, model.layers[il].ffn_norm, NULL, LLM_NORM_RMS, il);
+            cb(cur, "ffn_norm", il);
+
+            ggml_tensor * ffn_out =
+                build_moe_ffn(cur,
+                        nullptr,
+                        model.layers[il].ffn_up_exps,
+                        model.layers[il].ffn_gate_exps,
+                        model.layers[il].ffn_down_exps,
+                        nullptr,
+                        n_expert, n_expert_used,
+                        LLM_FFN_RELU, true,
+                        false, 0.0,
+                        static_cast<llama_expert_gating_func_type>(hparams.expert_gating_func),
+                        il, probs);
+
+            cb(ffn_out, "ffn_out", il);
+            cur = ffn_out;
+
+            cur = ggml_add(ctx0, cur, ffn_inp);
+            cur = build_cvec(cur, il);
+            cb(cur, "l_out", il);
+
+            // input for next layer
+            inpL = cur;
+        }
+        cur = inpL;
+
+        cur = build_norm(cur, model.output_norm, NULL, LLM_NORM_RMS, -1);
+        cb(cur, "result_norm", -1);
+        res->t_embd = cur;
+
+        // lm_head
+        cur = build_lora_mm(model.output, cur);
+        cb(cur, "result_output", -1);
+        res->t_logits = cur;
+
+        ggml_build_forward_expand(gf, cur);
+    }
+
+// Explicit template instantiations
+template struct llm_build_smallthinker<false>;
+template struct llm_build_smallthinker<true>;
diff --git a/src/models/smollm3.cpp b/src/models/smollm3.cpp
new file mode 100644
index 00000000000..830aa35415e
--- /dev/null
+++ b/src/models/smollm3.cpp
@@ -0,0 +1,128 @@
+#include "models.h"
+
+llm_build_smollm3::llm_build_smollm3(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+        const int64_t n_embd_head = hparams.n_embd_head_v;
+
+        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+        GGML_ASSERT(n_embd_head == hparams.n_rot);
+
+        ggml_tensor * cur;
+        ggml_tensor * inpL;
+
+        inpL = build_inp_embd(model.tok_embd);
+
+        // inp_pos - contains the positions
+        ggml_tensor * inp_pos = build_inp_pos();
+
+        auto * inp_attn = build_attn_inp_kv();
+
+        const float kq_scale = hparams.f_attention_scale == 0.0f ? 1.0f/sqrtf(float(n_embd_head)) : hparams.f_attention_scale;
+
+        ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+        for (int il = 0; il < n_layer; ++il) {
+            ggml_tensor * inpSA = inpL;
+
+            const bool use_rope = (il + 1) % hparams.n_no_rope_layer_step != 0;
+
+            // norm
+            cur = build_norm(inpL,
+                    model.layers[il].attn_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "attn_norm", il);
+
+            // self-attention
+            {
+                // compute Q and K and RoPE them
+                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+                cb(Qcur, "Qcur", il);
+                if (model.layers[il].bq) {
+                    Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
+                    cb(Qcur, "Qcur", il);
+                }
+                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+                cb(Kcur, "Kcur", il);
+                if (model.layers[il].bk) {
+                    Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
+                    cb(Kcur, "Kcur", il);
+                }
+                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+                cb(Vcur, "Vcur", il);
+                if (model.layers[il].bv) {
+                    Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
+                    cb(Vcur, "Vcur", il);
+                }
+                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+                if (use_rope) {
+                    Qcur = ggml_rope_ext(
+                            ctx0, Qcur, inp_pos, nullptr,
+                            n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                            ext_factor, attn_factor, beta_fast, beta_slow
+                            );
+
+                    Kcur = ggml_rope_ext(
+                            ctx0, Kcur, inp_pos, nullptr,
+                            n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                            ext_factor, attn_factor, beta_fast, beta_slow
+                            );
+                }
+                cb(Qcur, "Qcur", il);
+                cb(Kcur, "Kcur", il);
+                cb(Vcur, "Vcur", il);
+
+                cur = build_attn(inp_attn,
+                        model.layers[il].wo, model.layers[il].bo,
+                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, kq_scale, il);
+                cb(cur, "attn_out", il);
+            }
+            if (il == n_layer - 1 && inp_out_ids) {
+                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+            }
+            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+            cb(ffn_inp, "ffn_inp", il);
+
+            // feed-forward network
+            {
+                cur = build_norm(ffn_inp,
+                        model.layers[il].ffn_norm, NULL,
+                        LLM_NORM_RMS, il);
+                cb(cur, "ffn_norm", il);
+
+                cur = build_ffn(cur,
+                        model.layers[il].ffn_up,   model.layers[il].ffn_up_b,   NULL,
+                        model.layers[il].ffn_gate, model.layers[il].ffn_gate_b, NULL,
+                        model.layers[il].ffn_down, model.layers[il].ffn_down_b, NULL,
+                        NULL,
+                        LLM_FFN_SILU, LLM_FFN_PAR, il);
+                cb(cur, "ffn_out", il);
+            }
+            cur = ggml_add(ctx0, cur, ffn_inp);
+            cb(cur, "ffn_out", il);
+
+            cur = build_cvec(cur, il);
+            cb(cur, "l_out", il);
+
+            // input for next layer
+            inpL = cur;
+        }
+        cur = inpL;
+
+        cur = build_norm(cur,
+                model.output_norm, NULL,
+                LLM_NORM_RMS, -1);
+
+        cb(cur, "result_norm", -1);
+        res->t_embd = cur;
+
+        // lm_head
+        cur = build_lora_mm(model.output, cur);
+
+        cb(cur, "result_output", -1);
+        res->t_logits = cur;
+
+        ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/stablelm.cpp b/src/models/stablelm.cpp
new file mode 100644
index 00000000000..bed1915c006
--- /dev/null
+++ b/src/models/stablelm.cpp
@@ -0,0 +1,146 @@
+#include "models.h"
+
+llm_build_stablelm::llm_build_stablelm(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+    const int64_t n_embd_head = hparams.n_embd_head_v;
+
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+
+    inpL = build_inp_embd(model.tok_embd);
+
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
+
+    auto * inp_attn = build_attn_inp_kv();
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        // norm
+        cur = build_norm(inpL,
+                model.layers[il].attn_norm,
+                model.layers[il].attn_norm_b,
+                LLM_NORM, il);
+        cb(cur, "attn_norm", il);
+
+        ggml_tensor * inpSA = cur;
+
+        // self-attention
+        {
+            // compute Q and K and RoPE them
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            cb(Qcur, "Qcur", il);
+            if (model.layers[il].bq) {
+                Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
+                cb(Qcur, "Qcur", il);
+            }
+
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            cb(Kcur, "Kcur", il);
+            if (model.layers[il].bk) {
+                Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
+                cb(Kcur, "Kcur", il);
+            }
+
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            cb(Vcur, "Vcur", il);
+            if (model.layers[il].bv) {
+                Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
+                cb(Vcur, "Vcur", il);
+            }
+
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+            if (model.layers[il].attn_q_norm) {
+                Qcur = build_norm(Qcur,
+                        model.layers[il].attn_q_norm,
+                        NULL,
+                        LLM_NORM, il);
+                cb(Qcur, "Qcur", il);
+            }
+            if (model.layers[il].attn_k_norm) {
+                Kcur = build_norm(Kcur,
+                        model.layers[il].attn_k_norm,
+                        NULL,
+                        LLM_NORM, il);
+                cb(Kcur, "Kcur", il);
+            }
+
+            Qcur = ggml_rope_ext(
+                    ctx0, Qcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            Kcur = ggml_rope_ext(
+                    ctx0, Kcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, NULL,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+        }
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+            inpL  = ggml_get_rows(ctx0,  inpL, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+        }
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpL);
+        cb(ffn_inp, "ffn_inp", il);
+
+        // feed-forward network
+        {
+            if (model.layers[il].ffn_norm) {
+                cur = build_norm(ffn_inp,
+                        model.layers[il].ffn_norm,
+                        model.layers[il].ffn_norm_b,
+                        LLM_NORM, il);
+                cb(cur, "ffn_norm", il);
+            } else {
+                // parallel residual
+                cur = inpSA;
+            }
+            cur = build_ffn(cur,
+                    model.layers[il].ffn_up,   NULL, NULL,
+                    model.layers[il].ffn_gate, NULL, NULL,
+                    model.layers[il].ffn_down, NULL, NULL,
+                    NULL,
+                    LLM_FFN_SILU, LLM_FFN_PAR, il);
+            cb(cur, "ffn_out", il);
+        }
+        cur = ggml_add(ctx0, cur, ffn_inp);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+    cur = inpL;
+
+    cur = build_norm(cur,
+            model.output_norm,
+            model.output_norm_b,
+            LLM_NORM, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
+
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/starcoder.cpp b/src/models/starcoder.cpp
new file mode 100644
index 00000000000..0b9e58982aa
--- /dev/null
+++ b/src/models/starcoder.cpp
@@ -0,0 +1,100 @@
+#include "models.h"
+
+llm_build_starcoder::llm_build_starcoder(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+        const int64_t n_embd_head = hparams.n_embd_head_v;
+        const int64_t n_embd_gqa  = hparams.n_embd_v_gqa();
+
+        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+
+        ggml_tensor * cur;
+        ggml_tensor * inpL;
+
+        inpL = build_inp_embd(model.tok_embd);
+
+        // inp_pos - contains the positions
+        ggml_tensor * inp_pos = build_inp_pos();
+
+        auto * inp_attn = build_attn_inp_kv();
+
+        ggml_tensor * pos = ggml_get_rows(ctx0, model.pos_embd, inp_pos);
+        cb(pos, "pos_embd", -1);
+
+        inpL = ggml_add(ctx0, inpL, pos);
+        cb(inpL, "inpL", -1);
+
+        ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+        for (int il = 0; il < n_layer; ++il) {
+            cur = build_norm(inpL,
+                    model.layers[il].attn_norm,
+                    model.layers[il].attn_norm_b,
+                    LLM_NORM, il);
+            cb(cur, "attn_norm", il);
+
+            // self-attention
+            {
+                cur = build_lora_mm(model.layers[il].wqkv, cur);
+                cb(cur, "wqkv", il);
+
+                cur = ggml_add(ctx0, cur, model.layers[il].bqkv);
+                cb(cur, "bqkv", il);
+
+                ggml_tensor * Qcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head,    n_tokens, n_embd_head*sizeof(float), cur->nb[1], 0*sizeof(float)*(n_embd));
+                ggml_tensor * Kcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd));
+                ggml_tensor * Vcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd + n_embd_gqa));
+
+                cb(Qcur, "Qcur", il);
+                cb(Kcur, "Kcur", il);
+                cb(Vcur, "Vcur", il);
+
+                cur = build_attn(inp_attn,
+                        model.layers[il].wo, model.layers[il].bo,
+                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+            }
+            if (il == n_layer - 1 && inp_out_ids) {
+                cur  = ggml_get_rows(ctx0,  cur, inp_out_ids);
+                inpL = ggml_get_rows(ctx0, inpL, inp_out_ids);
+            }
+            // add the input
+            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpL);
+            cb(ffn_inp, "ffn_inp", il);
+
+            // FF
+            {
+                cur = build_norm(ffn_inp,
+                        model.layers[il].ffn_norm,
+                        model.layers[il].ffn_norm_b,
+                        LLM_NORM, il);
+                cb(cur, "ffn_norm", il);
+
+                cur = build_ffn(cur,
+                        model.layers[il].ffn_up,   model.layers[il].ffn_up_b,   NULL,
+                        NULL,                      NULL,                        NULL,
+                        model.layers[il].ffn_down, model.layers[il].ffn_down_b, NULL,
+                        NULL,
+                        LLM_FFN_GELU, LLM_FFN_SEQ, il);
+                cb(cur, "ffn_out", il);
+            }
+            cur = ggml_add(ctx0, cur, ffn_inp);
+
+            cur = build_cvec(cur, il);
+            cb(cur, "l_out", il);
+
+            // input for next layer
+            inpL = cur;
+        }
+        cur = build_norm(inpL,
+                model.output_norm,
+                model.output_norm_b,
+                LLM_NORM, -1);
+
+        cb(cur, "result_norm", -1);
+        res->t_embd = cur;
+
+        cur = build_lora_mm(model.output, cur);
+
+        cb(cur, "result_output", -1);
+        res->t_logits = cur;
+
+        ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/starcoder2.cpp b/src/models/starcoder2.cpp
new file mode 100644
index 00000000000..67c26149e3b
--- /dev/null
+++ b/src/models/starcoder2.cpp
@@ -0,0 +1,121 @@
+#include "models.h"
+
+llm_build_starcoder2::llm_build_starcoder2(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+        const int64_t n_embd_head = hparams.n_embd_head_v;
+
+        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+        GGML_ASSERT(n_embd_head == hparams.n_rot);
+
+        ggml_tensor * cur;
+        ggml_tensor * inpL;
+
+        inpL = build_inp_embd(model.tok_embd);
+
+        // inp_pos - contains the positions
+        ggml_tensor * inp_pos = build_inp_pos();
+
+        auto * inp_attn = build_attn_inp_kv();
+
+        ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+        for (int il = 0; il < n_layer; ++il) {
+            ggml_tensor * inpSA = inpL;
+
+            // norm
+            cur = build_norm(inpL,
+                    model.layers[il].attn_norm, model.layers[il].attn_norm_b,
+                    LLM_NORM, il);
+            cb(cur, "attn_norm", il);
+
+            // self-attention
+            {
+                // compute Q and K and RoPE them
+                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+                cb(Qcur, "Qcur", il);
+                if (model.layers[il].bq) {
+                    Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
+                    cb(Qcur, "Qcur", il);
+                }
+                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+                cb(Kcur, "Kcur", il);
+                if (model.layers[il].bk) {
+                    Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
+                    cb(Kcur, "Kcur", il);
+                }
+                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+                cb(Vcur, "Vcur", il);
+                if (model.layers[il].bv) {
+                    Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
+                    cb(Vcur, "Vcur", il);
+                }
+                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+                Qcur = ggml_rope_ext(
+                        ctx0, Qcur, inp_pos, nullptr,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+                Kcur = ggml_rope_ext(
+                        ctx0, Kcur, inp_pos, nullptr,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+                cb(Qcur, "Qcur", il);
+                cb(Kcur, "Kcur", il);
+                cb(Vcur, "Vcur", il);
+
+                cur = build_attn(inp_attn,
+                        model.layers[il].wo, model.layers[il].bo,
+                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+            }
+            if (il == n_layer - 1 && inp_out_ids) {
+                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+            }
+            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+            cb(ffn_inp, "ffn_inp", il);
+
+            // feed-forward network
+
+            cur = build_norm(ffn_inp,
+                    model.layers[il].ffn_norm, model.layers[il].ffn_norm_b,
+                    LLM_NORM, il);
+            cb(cur, "ffn_norm", il);
+
+            cur = build_ffn(cur,
+                    model.layers[il].ffn_up,   model.layers[il].ffn_up_b,   NULL,
+                    NULL,                      NULL,                        NULL,
+                    model.layers[il].ffn_down, model.layers[il].ffn_down_b, NULL,
+                    NULL,
+                    LLM_FFN_GELU, LLM_FFN_SEQ, il);
+            cb(cur, "ffn_out", il);
+
+            cur = ggml_add(ctx0, cur, ffn_inp);
+
+            cur = build_cvec(cur, il);
+            cb(cur, "l_out", il);
+
+            // input for next layer
+            inpL = cur;
+        }
+        cur = inpL;
+
+        cur = build_norm(cur,
+                model.output_norm, model.output_norm_b,
+                LLM_NORM, -1);
+
+        cb(cur, "result_norm", -1);
+        res->t_embd = cur;
+
+        // lm_head
+        cur = build_lora_mm(model.output, cur);
+
+        cb(cur, "result_output", -1);
+        res->t_logits = cur;
+
+        ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/t5-dec.cpp b/src/models/t5-dec.cpp
new file mode 100644
index 00000000000..c1974e78215
--- /dev/null
+++ b/src/models/t5-dec.cpp
@@ -0,0 +1,166 @@
+#include "models.h"
+
+llm_build_t5_dec::llm_build_t5_dec(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+        const int64_t n_embd_head = hparams.n_embd_head_v;
+        //const int64_t n_embd_gqa  = hparams.n_embd_v_gqa();
+
+        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+
+        ggml_tensor * cur;
+        ggml_tensor * inpL;
+
+        inpL = build_inp_embd(model.tok_embd);
+
+        ggml_tensor * embd_enc       = build_inp_cross_embd();
+        ggml_tensor * pos_bucket_dec = build_inp_pos_bucket_dec();
+
+        const int64_t n_outputs_enc = embd_enc->ne[1];
+
+        auto * inp_attn_self  = build_attn_inp_kv();
+        auto * inp_attn_cross = build_attn_inp_cross();
+
+        ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+        const int64_t dec_n_layer = hparams.dec_n_layer;
+
+        for (int il = 0; il < dec_n_layer; ++il) {
+            ggml_tensor * inpSA = inpL;
+
+            // norm
+            cur = build_norm(inpL,
+                    model.layers[il].attn_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "attn_norm", il);
+
+            // self-attention
+            {
+                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+                cb(Qcur, "Qcur", il);
+
+                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+                cb(Kcur, "Kcur", il);
+
+                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+                cb(Vcur, "Vcur", il);
+
+                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+                ggml_tensor * attn_rel_b = model.layers[il].attn_rel_b ? model.layers[il].attn_rel_b : model.layers[0].attn_rel_b;
+                ggml_tensor * kq_b = build_pos_bias(pos_bucket_dec, attn_rel_b);
+
+                cur = build_attn(inp_attn_self,
+                        model.layers[il].wo, model.layers[il].bo,
+                        Qcur, Kcur, Vcur, kq_b, nullptr, nullptr, 1.0f, il);
+                cb(cur, "kqv_out", il);
+            }
+            cur = ggml_add(ctx0, cur, inpSA);
+            cb(cur, "cross_inp", il);
+
+            ggml_tensor * inpCA = cur;
+
+            // norm
+            cur = build_norm(cur,
+                    model.layers[il].attn_norm_cross, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "attn_norm_cross", il);
+
+            // cross-attention
+            {
+                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq_cross, cur);
+                cb(Qcur, "Qcur", il);
+
+                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk_cross, embd_enc);
+                cb(Kcur, "Kcur", il);
+
+                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv_cross, embd_enc);
+                cb(Vcur, "Vcur", il);
+
+                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_outputs_enc);
+                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_outputs_enc);
+
+                cur = build_attn(inp_attn_cross,
+                        model.layers[il].wo_cross, nullptr,
+                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f, il);
+                cb(cur, "kqv_out", il);
+
+                //ggml_tensor * q =                 ggml_permute(ctx0, Qcur, 0, 2, 1, 3);
+                //ggml_tensor * k = ggml_cont(ctx0, ggml_permute(ctx0, Kcur, 0, 2, 1, 3));
+
+                //ggml_tensor * kq = ggml_mul_mat(ctx0, k, q);
+                //cb(kq, "kq", il);
+
+                //kq = ggml_soft_max_ext(ctx0, kq, KQ_mask_cross, 1.0f, hparams.f_max_alibi_bias);
+                //cb(kq, "kq_soft_max_ext", il);
+
+                //ggml_tensor * v = ggml_cont(ctx0, ggml_transpose(ctx0, ggml_reshape_2d(ctx0, Vcur, n_embd_gqa, n_outputs_enc)));
+                //cb(v, "v", il);
+
+                //ggml_tensor * kqv = ggml_mul_mat(ctx0, ggml_reshape_3d(ctx0, v, n_outputs_enc, n_embd_head, n_head_kv), kq);
+                //cb(kqv, "kqv", il);
+
+                //ggml_tensor * kqv_merged = ggml_permute(ctx0, kqv, 0, 2, 1, 3);
+                //cb(kqv_merged, "kqv_merged", il);
+
+                //cur = ggml_cont_2d(ctx0, kqv_merged, n_embd_gqa, n_tokens);
+                //cb(cur, "kqv_merged_cont", il);
+
+                //ggml_build_forward_expand(gf, cur);
+
+                //cur = build_lora_mm(model.layers[il].wo_cross, cur);
+                //cb(cur, "kqv_out", il);
+            }
+            if (il == dec_n_layer - 1 && inp_out_ids) {
+                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+                inpCA = ggml_get_rows(ctx0, inpCA, inp_out_ids);
+            }
+            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpCA);
+            cb(ffn_inp, "ffn_inp", il);
+
+            // feed-forward network
+            {
+                cur = build_norm(ffn_inp,
+                        model.layers[il].ffn_norm, NULL,
+                        LLM_NORM_RMS, il);
+                cb(cur, "ffn_norm", il);
+
+                // T5 uses relu, flan-T5 uses gelu-gated
+                cur = build_ffn(cur,
+                        model.layers[il].ffn_up,   NULL, NULL,
+                        model.layers[il].ffn_gate, NULL, NULL,
+                        model.layers[il].ffn_down, NULL, NULL,
+                        NULL,
+                        model.layers[il].ffn_gate ? LLM_FFN_GELU : LLM_FFN_RELU,
+                        model.layers[il].ffn_gate ? LLM_FFN_PAR : LLM_FFN_SEQ,
+                        il);
+                cb(cur, "ffn_out", il);
+            }
+            cur = ggml_add(ctx0, cur, ffn_inp);
+            cb(cur, "ffn_out", il);
+
+            cur = build_cvec(cur, il);
+            cb(cur, "l_out", il);
+
+            // input for next layer
+            inpL = cur;
+        }
+        cur = inpL;
+        cb(cur, "result_embd", -1);
+
+        cur = build_norm(cur,
+                model.output_norm, NULL,
+                LLM_NORM_RMS, -1);
+
+        cb(cur, "result_norm", -1);
+        res->t_embd = cur;
+
+        // lm_head
+        cur = build_lora_mm(model.output, cur);
+
+        cb(cur, "result_output", -1);
+        res->t_logits = cur;
+
+        ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/t5-enc.cpp b/src/models/t5-enc.cpp
new file mode 100644
index 00000000000..6b29355d20f
--- /dev/null
+++ b/src/models/t5-enc.cpp
@@ -0,0 +1,96 @@
+#include "models.h"
+
+llm_build_t5_enc::llm_build_t5_enc(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+        const int64_t n_embd_head = hparams.n_embd_head_v;
+
+        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+
+        ggml_tensor * cur;
+        ggml_tensor * inpL;
+
+        inpL = build_inp_embd(model.tok_embd);
+
+        ggml_tensor * pos_bucket_enc = build_inp_pos_bucket_enc();
+
+        auto * inp_attn = build_attn_inp_no_cache();
+
+        ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+        for (int il = 0; il < n_layer; ++il) {
+            ggml_tensor * inpSA = inpL;
+
+            // norm
+            cur = build_norm(inpL,
+                    model.layers[il].attn_norm_enc, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "attn_norm", il);
+
+            // self-attention
+            {
+                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq_enc, cur);
+                cb(Qcur, "Qcur", il);
+
+                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk_enc, cur);
+                cb(Kcur, "Kcur", il);
+
+                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv_enc, cur);
+                cb(Vcur, "Vcur", il);
+
+                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+                ggml_tensor * attn_rel_b = model.layers[il].attn_rel_b_enc ? model.layers[il].attn_rel_b_enc : model.layers[0].attn_rel_b_enc;
+                ggml_tensor * kq_b = build_pos_bias(pos_bucket_enc, attn_rel_b);
+
+                cur = build_attn(inp_attn,
+                        model.layers[il].wo_enc, nullptr,
+                        Qcur, Kcur, Vcur, kq_b, nullptr, nullptr, 1.0f, il);
+                cb(cur, "kqv_out", il);
+            }
+            if (il == n_layer - 1 && inp_out_ids) {
+                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+            }
+            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+            cb(ffn_inp, "ffn_inp", il);
+
+            // feed-forward network
+            {
+                cur = build_norm(ffn_inp,
+                        model.layers[il].ffn_norm_enc, NULL,
+                        LLM_NORM_RMS, il);
+                cb(cur, "ffn_norm", il);
+
+                // T5 uses relu, flan-T5 uses gelu-gated
+                cur = build_ffn(cur,
+                        model.layers[il].ffn_up_enc,   NULL, NULL,
+                        model.layers[il].ffn_gate_enc, NULL, NULL,
+                        model.layers[il].ffn_down_enc, NULL, NULL,
+                        NULL,
+                        model.layers[il].ffn_gate_enc ? LLM_FFN_GELU : LLM_FFN_RELU,
+                        model.layers[il].ffn_gate_enc ? LLM_FFN_PAR  : LLM_FFN_SEQ,
+                        il);
+                cb(cur, "ffn_out", il);
+            }
+            cur = ggml_add(ctx0, cur, ffn_inp);
+            cb(cur, "ffn_out", il);
+
+            cur = build_cvec(cur, il);
+            cb(cur, "l_out", il);
+
+            // input for next layer
+            inpL = cur;
+        }
+        cur = inpL;
+        cb(cur, "result_embd", -1);
+
+        cur = build_norm(cur,
+                model.output_norm_enc, NULL,
+                LLM_NORM_RMS, -1);
+
+        cb(cur, "result_norm", -1);
+        res->t_embd = cur;
+
+        ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/wavtokenizer-dec.cpp b/src/models/wavtokenizer-dec.cpp
new file mode 100644
index 00000000000..81a3c5cd628
--- /dev/null
+++ b/src/models/wavtokenizer-dec.cpp
@@ -0,0 +1,149 @@
+#include "models.h"
+
+llm_build_wavtokenizer_dec::llm_build_wavtokenizer_dec(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+        ggml_tensor * cur;
+        ggml_tensor * inpL;
+
+        inpL = build_inp_embd(model.tok_embd);
+
+        cur = ggml_cont(ctx0, ggml_transpose(ctx0, inpL));
+
+        cur = ggml_conv_1d_ph(ctx0, model.conv1d, cur, 1, 1);
+        cur = ggml_add(ctx0, cur, model.conv1d_b);
+
+        // posnet
+        for (uint32_t il = 0; il < hparams.posnet.n_layer; ++il) {
+            const auto & layer = model.layers[il].posnet;
+
+            inpL = cur;
+
+            switch (il) {
+                case 0:
+                case 1:
+                case 3:
+                case 4:
+                    {
+                        cur = build_norm(cur,
+                                layer.norm1,
+                                layer.norm1_b,
+                                LLM_NORM_GROUP, 0);
+
+                        cur = ggml_mul(ctx0, ggml_sigmoid(ctx0, cur), cur);
+
+                        cur = ggml_conv_1d_ph(ctx0, layer.conv1, cur, 1, 1);
+                        cur = ggml_add(ctx0, cur, layer.conv1_b);
+
+                        cur = build_norm(cur,
+                                layer.norm2,
+                                layer.norm2_b,
+                                LLM_NORM_GROUP, 0);
+
+                        cur = ggml_mul(ctx0, ggml_sigmoid(ctx0, cur), cur);
+
+                        cur = ggml_conv_1d_ph(ctx0, layer.conv2, cur, 1, 1);
+                        cur = ggml_add(ctx0, cur, layer.conv2_b);
+
+                        cur = ggml_add(ctx0, cur, inpL);
+                    } break;
+                case 2:
+                    {
+                        cur = build_norm(cur,
+                                layer.attn_norm,
+                                layer.attn_norm_b,
+                                LLM_NORM_GROUP, 0);
+
+                        ggml_tensor * q;
+                        ggml_tensor * k;
+                        ggml_tensor * v;
+
+                        q = ggml_conv_1d_ph(ctx0, layer.attn_q, cur, 1, 1);
+                        k = ggml_conv_1d_ph(ctx0, layer.attn_k, cur, 1, 1);
+                        v = ggml_conv_1d_ph(ctx0, layer.attn_v, cur, 1, 1);
+
+                        q = ggml_add(ctx0, q, layer.attn_q_b);
+                        k = ggml_add(ctx0, k, layer.attn_k_b);
+                        v = ggml_add(ctx0, v, layer.attn_v_b);
+
+                        q = ggml_cont(ctx0, ggml_transpose(ctx0, q));
+                        k = ggml_cont(ctx0, ggml_transpose(ctx0, k));
+
+                        ggml_tensor * kq = ggml_mul_mat(ctx0, k, q);
+
+                        kq = ggml_soft_max_ext(ctx0, kq, nullptr, 1.0f/sqrtf(float(hparams.posnet.n_embd)), 0.0f);
+
+                        cur = ggml_mul_mat(ctx0, kq, v);
+
+                        cur = ggml_conv_1d_ph(ctx0, layer.attn_o, cur, 1, 1);
+                        cur = ggml_add(ctx0, cur, layer.attn_o_b);
+
+                        cur = ggml_add(ctx0, cur, inpL);
+                    } break;
+                case 5:
+                    {
+                        cur = build_norm(cur,
+                                layer.norm,
+                                layer.norm_b,
+                                LLM_NORM_GROUP, 0);
+                    } break;
+                default: GGML_ABORT("unknown posnet layer");
+            };
+        }
+        cur = ggml_cont(ctx0, ggml_transpose(ctx0, cur));
+
+        cur = build_norm(cur,
+                model.tok_norm,
+                model.tok_norm_b,
+                LLM_NORM, -1);
+
+        cur = ggml_cont(ctx0, ggml_transpose(ctx0, cur));
+
+        inpL = cur;
+
+        // convnext
+        for (uint32_t il = 0; il < hparams.convnext.n_layer; ++il) {
+            const auto & layer = model.layers[il].convnext;
+
+            cur = inpL;
+
+            cur = ggml_conv_1d_dw_ph(ctx0, layer.dw, cur, 1, 1);
+            cur = ggml_add(ctx0, cur, layer.dw_b);
+
+            cur = ggml_cont(ctx0, ggml_transpose(ctx0, cur));
+
+            cur = build_norm(cur,
+                    layer.norm,
+                    layer.norm_b,
+                    LLM_NORM, -1);
+
+            cur = build_ffn(cur,
+                    layer.pw1, layer.pw1_b, NULL,
+                    NULL,      NULL,        NULL,
+                    layer.pw2, layer.pw2_b, NULL,
+                    NULL,
+                    LLM_FFN_GELU, LLM_FFN_SEQ, il);
+
+            cur = ggml_mul(ctx0, cur, layer.gamma);
+
+            cur = ggml_cont(ctx0, ggml_transpose(ctx0, cur));
+
+            inpL = ggml_add(ctx0, cur, inpL);
+        }
+        cur = inpL;
+
+        cur = ggml_cont(ctx0, ggml_transpose(ctx0, cur));
+
+        cur = build_norm(cur,
+                model.output_norm,
+                model.output_norm_b,
+                LLM_NORM, -1);
+
+        // lm_head
+        cur = build_lora_mm(model.output, cur);
+
+        cur = ggml_add(ctx0, cur, model.output_b);
+
+        cb(cur, "result_embd", -1);
+        res->t_embd = cur;
+
+        ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/xverse.cpp b/src/models/xverse.cpp
new file mode 100644
index 00000000000..95e2eafef3d
--- /dev/null
+++ b/src/models/xverse.cpp
@@ -0,0 +1,108 @@
+#include "models.h"
+
+llm_build_xverse::llm_build_xverse(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+        const int64_t n_embd_head = hparams.n_embd_head_v;
+
+        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+        GGML_ASSERT(n_embd_head == hparams.n_rot);
+
+        ggml_tensor * cur;
+        ggml_tensor * inpL;
+
+        inpL = build_inp_embd(model.tok_embd);
+
+        // inp_pos - contains the positions
+        ggml_tensor * inp_pos = build_inp_pos();
+
+        auto * inp_attn = build_attn_inp_kv();
+
+        ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+        for (int il = 0; il < n_layer; ++il) {
+            ggml_tensor * inpSA = inpL;
+
+            cur = build_norm(inpL,
+                    model.layers[il].attn_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "attn_norm", il);
+
+            // self-attention
+            {
+                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+                cb(Qcur, "Qcur", il);
+
+                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+                cb(Kcur, "Kcur", il);
+
+                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+                cb(Vcur, "Vcur", il);
+
+                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+                Qcur = ggml_rope_ext(
+                        ctx0, Qcur, inp_pos, nullptr,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+                Kcur = ggml_rope_ext(
+                        ctx0, Kcur, inp_pos, nullptr,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+                cb(Qcur, "Qcur", il);
+                cb(Kcur, "Kcur", il);
+                cb(Vcur, "Vcur", il);
+
+                cur = build_attn(inp_attn,
+                        model.layers[il].wo, NULL,
+                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+            }
+            if (il == n_layer - 1 && inp_out_ids) {
+                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+            }
+            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+            cb(ffn_inp, "ffn_inp", il);
+
+            // feed-forward network
+            {
+                cur = build_norm(ffn_inp,
+                        model.layers[il].ffn_norm, NULL,
+                        LLM_NORM_RMS, il);
+                cb(cur, "ffn_norm", il);
+
+                cur = build_ffn(cur,
+                        model.layers[il].ffn_up,   NULL, NULL,
+                        model.layers[il].ffn_gate, NULL, NULL,
+                        model.layers[il].ffn_down, NULL, NULL,
+                        NULL,
+                        LLM_FFN_SILU, LLM_FFN_PAR, il);
+                cb(cur, "ffn_out", il);
+            }
+            cur = ggml_add(ctx0, cur, ffn_inp);
+
+            cur = build_cvec(cur, il);
+            cb(cur, "l_out", il);
+
+            // input for next layer
+            inpL = cur;
+        }
+        cur = inpL;
+
+        cur = build_norm(cur, model.output_norm, NULL, LLM_NORM_RMS, -1);
+
+        cb(cur, "result_norm", -1);
+        res->t_embd = cur;
+
+        // lm_head
+        cur = build_lora_mm(model.output, cur);
+
+        cb(cur, "result_output", -1);
+        res->t_logits = cur;
+
+        ggml_build_forward_expand(gf, cur);
+}

From d3dc9dd898be805c23a408cc36daed5b3bf29221 Mon Sep 17 00:00:00 2001
From: Oliver Simons <osimons@nvidia.com>
Date: Sat, 1 Nov 2025 06:13:26 +0100
Subject: [PATCH 042/185] CUDA: Remove unneded bias/gate dims in fused mmvq
 (#16858)
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

* CUDA: Remove unneded bias/gate dims in fused mmvq

Pointed out
[here](https://github.com/ggml-org/llama.cpp/pull/16847#discussion_r2476798989)
that only a single value is needed per target col per thread

* Apply suggestions from code review

Co-authored-by: Johannes Gäßler <johannesg@5d6.de>

* Fix "Error 991-D: extra braces are nonstandard" during compilation

---------

Co-authored-by: Johannes Gäßler <johannesg@5d6.de>
---
 ggml/src/ggml-cuda/mmvq.cu | 14 ++++++++------
 1 file changed, 8 insertions(+), 6 deletions(-)

diff --git a/ggml/src/ggml-cuda/mmvq.cu b/ggml/src/ggml-cuda/mmvq.cu
index 07645ad9e71..d671551c171 100644
--- a/ggml/src/ggml-cuda/mmvq.cu
+++ b/ggml/src/ggml-cuda/mmvq.cu
@@ -190,8 +190,8 @@ static __global__ void mul_mat_vec_q(
 
     const uint32_t channel_bias = ids ? channel_x : channel_dst;
 
-    float x_biases[ncols_dst][rows_per_cuda_block]    = { { 0.0f } };
-    float gate_biases[ncols_dst][rows_per_cuda_block] = { { 0.0f } };
+    float x_biases[ncols_dst]    = { 0.0f };
+    float gate_biases[ncols_dst] = { 0.0f };
     if constexpr (has_fusion) {
         if (use_bias) {
             x_bias = x_bias + sample_dst*stride_sample_dst + channel_bias*stride_channel_dst + row0;
@@ -199,8 +199,9 @@ static __global__ void mul_mat_vec_q(
             // 2. load only on threads that won't die after partial sum calculation
             if (threadIdx.x < rows_per_cuda_block && threadIdx.y == 0 &&
                 (rows_per_cuda_block == 1 || uint32_t(row0 + threadIdx.x) < stride_col_dst)) {
+#pragma unroll
                 for (int j = 0; j < ncols_dst; ++j) {
-                    x_biases[j][threadIdx.x] = x_bias[j * stride_col_dst + threadIdx.x];
+                    x_biases[j] = x_bias[j * stride_col_dst + threadIdx.x];
                 }
             }
         }
@@ -208,8 +209,9 @@ static __global__ void mul_mat_vec_q(
             gate_bias = gate_bias + sample_dst*stride_sample_dst + channel_bias*stride_channel_dst + row0;
             if (threadIdx.x < rows_per_cuda_block && threadIdx.y == 0 &&
                 (rows_per_cuda_block == 1 || uint32_t(row0 + threadIdx.x) < stride_col_dst)) {
+#pragma unroll
                 for (int j = 0; j < ncols_dst; ++j) {
-                    gate_biases[j][threadIdx.x] = gate_bias[j * stride_col_dst + threadIdx.x];
+                    gate_biases[j] = gate_bias[j * stride_col_dst + threadIdx.x];
                 }
             }
         }
@@ -299,12 +301,12 @@ static __global__ void mul_mat_vec_q(
             float result = tmp[j][threadIdx.x];
             if constexpr (has_fusion) {
                 if (use_bias) {
-                    result += x_biases[j][threadIdx.x];
+                    result += x_biases[j];
                 }
                 if (use_gate) {
                     float gate_value = tmp_gate[j][threadIdx.x];
                     if (use_gate_bias) {
-                        gate_value += gate_biases[j][threadIdx.x];
+                        gate_value += gate_biases[j];
                     }
                     switch (active_glu) {
                         case GGML_GLU_OP_SWIGLU:

From 2e76e013600cb0d51ccf158571ca1d0502952a07 Mon Sep 17 00:00:00 2001
From: Jeff Bolz <jbolz@nvidia.com>
Date: Sat, 1 Nov 2025 00:45:28 -0500
Subject: [PATCH 043/185] vulkan: fuse mul_mat+add and mul_mat_id+add_id
 (#16868)
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

* vulkan: fuse mul_mat+add and mul_mat_id+add_id

The fusion is only applied for the mat-vec mul paths.

* Apply suggestions from code review

Co-authored-by: Sigbjørn Skjæret <sigbjorn.skjaeret@scala.com>

* fix 32b build

---------

Co-authored-by: Sigbjørn Skjæret <sigbjorn.skjaeret@scala.com>
---
 ggml/src/ggml-vulkan/ggml-vulkan.cpp          | 515 +++++++++++++-----
 .../vulkan-shaders/mul_mat_vec_base.glsl      |  34 +-
 .../vulkan-shaders/mul_mat_vec_nc.comp        |   6 +
 .../vulkan-shaders/mul_mat_vec_p021.comp      |   6 +
 4 files changed, 437 insertions(+), 124 deletions(-)

diff --git a/ggml/src/ggml-vulkan/ggml-vulkan.cpp b/ggml/src/ggml-vulkan/ggml-vulkan.cpp
index c3e5a9eccc3..6a46d0889bd 100644
--- a/ggml/src/ggml-vulkan/ggml-vulkan.cpp
+++ b/ggml/src/ggml-vulkan/ggml-vulkan.cpp
@@ -797,9 +797,18 @@ struct vk_mat_mat_push_constants {
     uint32_t padded_N;
 };
 struct vk_mat_vec_push_constants {
-    uint32_t ncols; uint32_t stride_a; uint32_t stride_b; uint32_t stride_d;
-    uint32_t batch_stride_a; uint32_t batch_stride_b; uint32_t batch_stride_d;
-    uint32_t ne02; uint32_t ne12; uint32_t broadcast2; uint32_t broadcast3;
+    uint32_t ncols;
+    uint32_t stride_a;
+    uint32_t stride_b;
+    uint32_t stride_d;
+    uint32_t batch_stride_a;
+    uint32_t batch_stride_b;
+    uint32_t batch_stride_d;
+    uint32_t enable_bias;
+    uint32_t ne02;
+    uint32_t ne12;
+    uint32_t broadcast2;
+    uint32_t broadcast3;
 };
 
 struct vk_mat_mat_id_push_constants {
@@ -810,9 +819,16 @@ struct vk_mat_mat_id_push_constants {
     uint32_t padded_N;
 };
 struct vk_mat_vec_id_push_constants {
-    uint32_t ncols; uint32_t stride_a; uint32_t stride_b; uint32_t stride_d;
-    uint32_t batch_stride_a; uint32_t batch_stride_b; uint32_t batch_stride_d;
-    uint32_t nei0; uint32_t ne11;
+    uint32_t ncols;
+    uint32_t stride_a;
+    uint32_t stride_b;
+    uint32_t stride_d;
+    uint32_t batch_stride_a;
+    uint32_t batch_stride_b;
+    uint32_t batch_stride_d;
+    uint32_t enable_bias;
+    uint32_t nei0;
+    uint32_t ne11;
 };
 
 struct vk_flash_attn_push_constants {
@@ -3347,92 +3363,92 @@ static void ggml_vk_load_shaders(vk_device& device) {
                                               SHADER_REDUCTION_MODE_SHMEM;
 
         for (uint32_t i = 0; i < mul_mat_vec_max_cols; ++i) {
-            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f32_f32[w][GGML_TYPE_F32 ][i], "mul_mat_vec_f32_f32_f32",  arr_dmmv_f32_f32_f32_len[reduc],  arr_dmmv_f32_f32_f32_data[reduc],  "main", 3, sizeof(vk_mat_vec_push_constants), {2, 1, 1}, {wg_size_subgroup, 2, i+1}, 1, false, use_subgroups, force_subgroup_size);
-            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f32_f32[w][GGML_TYPE_F16 ][i], "mul_mat_vec_f16_f32_f32",  arr_dmmv_f16_f32_f32_len[reduc],  arr_dmmv_f16_f32_f32_data[reduc],  "main", 3, sizeof(vk_mat_vec_push_constants), {2, 1, 1}, {wg_size_subgroup, 2, i+1}, 1, false, use_subgroups, force_subgroup_size);
-            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f32_f32[w][GGML_TYPE_BF16][i], "mul_mat_vec_bf16_f32_f32", arr_dmmv_bf16_f32_f32_len[reduc], arr_dmmv_bf16_f32_f32_data[reduc], "main", 3, sizeof(vk_mat_vec_push_constants), {2, 1, 1}, {wg_size_subgroup, 2, i+1}, 1, false, use_subgroups, force_subgroup_size);
-            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f32_f32[w][GGML_TYPE_Q4_0][i], "mul_mat_vec_q4_0_f32_f32", arr_dmmv_q4_0_f32_f32_len[reduc], arr_dmmv_q4_0_f32_f32_data[reduc], "main", 3, sizeof(vk_mat_vec_push_constants), {2*rm_stdq, 1, 1}, {wg_size_subgroup, 2*rm_stdq, i+1}, 1, true, use_subgroups, force_subgroup_size);
-            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f32_f32[w][GGML_TYPE_Q4_1][i], "mul_mat_vec_q4_1_f32_f32", arr_dmmv_q4_1_f32_f32_len[reduc], arr_dmmv_q4_1_f32_f32_data[reduc], "main", 3, sizeof(vk_mat_vec_push_constants), {2*rm_stdq, 1, 1}, {wg_size_subgroup, 2*rm_stdq, i+1}, 1, true, use_subgroups, force_subgroup_size);
-            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f32_f32[w][GGML_TYPE_Q5_0][i], "mul_mat_vec_q5_0_f32_f32", arr_dmmv_q5_0_f32_f32_len[reduc], arr_dmmv_q5_0_f32_f32_data[reduc], "main", 3, sizeof(vk_mat_vec_push_constants), {2*rm_stdq, 1, 1}, {wg_size_subgroup, 2*rm_stdq, i+1}, 1, true, use_subgroups, force_subgroup_size);
-            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f32_f32[w][GGML_TYPE_Q5_1][i], "mul_mat_vec_q5_1_f32_f32", arr_dmmv_q5_1_f32_f32_len[reduc], arr_dmmv_q5_1_f32_f32_data[reduc], "main", 3, sizeof(vk_mat_vec_push_constants), {2*rm_stdq, 1, 1}, {wg_size_subgroup, 2*rm_stdq, i+1}, 1, true, use_subgroups, force_subgroup_size);
-            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f32_f32[w][GGML_TYPE_Q8_0][i], "mul_mat_vec_q8_0_f32_f32", arr_dmmv_q8_0_f32_f32_len[reduc], arr_dmmv_q8_0_f32_f32_data[reduc], "main", 3, sizeof(vk_mat_vec_push_constants), {1*rm_stdq, 1, 1}, {wg_size_subgroup, 1*rm_stdq, i+1}, 1, true, use_subgroups, force_subgroup_size);
-            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f32_f32[w][GGML_TYPE_Q2_K][i], "mul_mat_vec_q2_k_f32_f32", arr_dmmv_q2_k_f32_f32_len[reduc16], arr_dmmv_q2_k_f32_f32_data[reduc16], "main", 3, sizeof(vk_mat_vec_push_constants), {rm_kq, 1, 1}, {wg_size_subgroup16, rm_kq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
-            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f32_f32[w][GGML_TYPE_Q3_K][i], "mul_mat_vec_q3_k_f32_f32", arr_dmmv_q3_k_f32_f32_len[reduc16], arr_dmmv_q3_k_f32_f32_data[reduc16], "main", 3, sizeof(vk_mat_vec_push_constants), {rm_kq, 1, 1}, {wg_size_subgroup16, rm_kq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
-            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f32_f32[w][GGML_TYPE_Q4_K][i], "mul_mat_vec_q4_k_f32_f32", arr_dmmv_q4_k_f32_f32_len[reduc16], arr_dmmv_q4_k_f32_f32_data[reduc16], "main", 3, sizeof(vk_mat_vec_push_constants), {rm_kq, 1, 1}, {wg_size_subgroup16, rm_kq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
-            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f32_f32[w][GGML_TYPE_Q5_K][i], "mul_mat_vec_q5_k_f32_f32", arr_dmmv_q5_k_f32_f32_len[reduc16], arr_dmmv_q5_k_f32_f32_data[reduc16], "main", 3, sizeof(vk_mat_vec_push_constants), {rm_kq, 1, 1}, {wg_size_subgroup16, rm_kq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
-            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f32_f32[w][GGML_TYPE_Q6_K][i], "mul_mat_vec_q6_k_f32_f32", arr_dmmv_q6_k_f32_f32_len[reduc16], arr_dmmv_q6_k_f32_f32_data[reduc16], "main", 3, sizeof(vk_mat_vec_push_constants), {rm_kq, 1, 1}, {wg_size_subgroup16, rm_kq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
-            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f32_f32[w][GGML_TYPE_IQ1_S][i],   "mul_mat_vec_iq1_s_f32_f32",   arr_dmmv_iq1_s_f32_f32_len[reduc16],   arr_dmmv_iq1_s_f32_f32_data[reduc16],   "main", 3, sizeof(vk_mat_vec_push_constants), {rm_iq, 1, 1}, {wg_size_subgroup16, rm_iq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
-            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f32_f32[w][GGML_TYPE_IQ1_M][i],   "mul_mat_vec_iq1_m_f32_f32",   arr_dmmv_iq1_m_f32_f32_len[reduc16],   arr_dmmv_iq1_m_f32_f32_data[reduc16],   "main", 3, sizeof(vk_mat_vec_push_constants), {rm_iq, 1, 1}, {wg_size_subgroup16, rm_iq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
-            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f32_f32[w][GGML_TYPE_IQ2_XXS][i], "mul_mat_vec_iq2_xxs_f32_f32", arr_dmmv_iq2_xxs_f32_f32_len[reduc16], arr_dmmv_iq2_xxs_f32_f32_data[reduc16], "main", 3, sizeof(vk_mat_vec_push_constants), {rm_iq, 1, 1}, {wg_size_subgroup16, rm_iq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
-            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f32_f32[w][GGML_TYPE_IQ2_XS][i],  "mul_mat_vec_iq2_xs_f32_f32",  arr_dmmv_iq2_xs_f32_f32_len[reduc16],  arr_dmmv_iq2_xs_f32_f32_data[reduc16],  "main", 3, sizeof(vk_mat_vec_push_constants), {rm_iq, 1, 1}, {wg_size_subgroup16, rm_iq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
-            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f32_f32[w][GGML_TYPE_IQ2_S][i],   "mul_mat_vec_iq2_s_f32_f32",   arr_dmmv_iq2_s_f32_f32_len[reduc16],   arr_dmmv_iq2_s_f32_f32_data[reduc16],   "main", 3, sizeof(vk_mat_vec_push_constants), {rm_iq, 1, 1}, {wg_size_subgroup16, rm_iq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
-            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f32_f32[w][GGML_TYPE_IQ3_XXS][i], "mul_mat_vec_iq3_xxs_f32_f32", arr_dmmv_iq3_xxs_f32_f32_len[reduc16], arr_dmmv_iq3_xxs_f32_f32_data[reduc16], "main", 3, sizeof(vk_mat_vec_push_constants), {rm_iq, 1, 1}, {wg_size_subgroup16, rm_iq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
-            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f32_f32[w][GGML_TYPE_IQ3_S][i],   "mul_mat_vec_iq3_s_f32_f32",   arr_dmmv_iq3_s_f32_f32_len[reduc16],   arr_dmmv_iq3_s_f32_f32_data[reduc16],   "main", 3, sizeof(vk_mat_vec_push_constants), {rm_iq, 1, 1}, {wg_size_subgroup16, rm_iq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
-            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f32_f32[w][GGML_TYPE_IQ4_XS][i],  "mul_mat_vec_iq4_xs_f32_f32",  arr_dmmv_iq4_xs_f32_f32_len[reduc16],  arr_dmmv_iq4_xs_f32_f32_data[reduc16],  "main", 3, sizeof(vk_mat_vec_push_constants), {rm_iq, 1, 1}, {wg_size_subgroup16, rm_iq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
-            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f32_f32[w][GGML_TYPE_IQ4_NL][i],  "mul_mat_vec_iq4_nl_f32_f32",  arr_dmmv_iq4_nl_f32_f32_len[reduc16],  arr_dmmv_iq4_nl_f32_f32_data[reduc16],  "main", 3, sizeof(vk_mat_vec_push_constants), {rm_iq, 1, 1}, {wg_size_subgroup16, rm_iq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
-            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f32_f32[w][GGML_TYPE_MXFP4][i],   "mul_mat_vec_mxfp4_f32_f32",   arr_dmmv_mxfp4_f32_f32_len[reduc16],   arr_dmmv_mxfp4_f32_f32_data[reduc16],   "main", 3, sizeof(vk_mat_vec_push_constants), {rm_iq, 1, 1}, {wg_size_subgroup16, rm_iq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
-
-            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f16_f32[w][GGML_TYPE_F32 ][i], "mul_mat_vec_f32_f16_f32",  arr_dmmv_f32_f16_f32_len[reduc],  arr_dmmv_f32_f16_f32_data[reduc],  "main", 3, sizeof(vk_mat_vec_push_constants), {2, 1, 1}, {wg_size_subgroup, 2, i+1}, 1, false, use_subgroups, force_subgroup_size);
-            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f16_f32[w][GGML_TYPE_F16 ][i], "mul_mat_vec_f16_f16_f32",  arr_dmmv_f16_f16_f32_len[reduc],  arr_dmmv_f16_f16_f32_data[reduc],  "main", 3, sizeof(vk_mat_vec_push_constants), {2, 1, 1}, {wg_size_subgroup, 2, i+1}, 1, false, use_subgroups, force_subgroup_size);
-            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f16_f32[w][GGML_TYPE_BF16][i], "mul_mat_vec_bf16_f16_f32", arr_dmmv_bf16_f16_f32_len[reduc], arr_dmmv_bf16_f16_f32_data[reduc], "main", 3, sizeof(vk_mat_vec_push_constants), {2, 1, 1}, {wg_size_subgroup, 2, i+1}, 1, false, use_subgroups, force_subgroup_size);
-            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f16_f32[w][GGML_TYPE_Q4_0][i], "mul_mat_vec_q4_0_f16_f32", arr_dmmv_q4_0_f16_f32_len[reduc], arr_dmmv_q4_0_f16_f32_data[reduc], "main", 3, sizeof(vk_mat_vec_push_constants), {2*rm_stdq, 1, 1}, {wg_size_subgroup, 2*rm_stdq, i+1}, 1, true, use_subgroups, force_subgroup_size);
-            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f16_f32[w][GGML_TYPE_Q4_1][i], "mul_mat_vec_q4_1_f16_f32", arr_dmmv_q4_1_f16_f32_len[reduc], arr_dmmv_q4_1_f16_f32_data[reduc], "main", 3, sizeof(vk_mat_vec_push_constants), {2*rm_stdq, 1, 1}, {wg_size_subgroup, 2*rm_stdq, i+1}, 1, true, use_subgroups, force_subgroup_size);
-            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f16_f32[w][GGML_TYPE_Q5_0][i], "mul_mat_vec_q5_0_f16_f32", arr_dmmv_q5_0_f16_f32_len[reduc], arr_dmmv_q5_0_f16_f32_data[reduc], "main", 3, sizeof(vk_mat_vec_push_constants), {2*rm_stdq, 1, 1}, {wg_size_subgroup, 2*rm_stdq, i+1}, 1, true, use_subgroups, force_subgroup_size);
-            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f16_f32[w][GGML_TYPE_Q5_1][i], "mul_mat_vec_q5_1_f16_f32", arr_dmmv_q5_1_f16_f32_len[reduc], arr_dmmv_q5_1_f16_f32_data[reduc], "main", 3, sizeof(vk_mat_vec_push_constants), {2*rm_stdq, 1, 1}, {wg_size_subgroup, 2*rm_stdq, i+1}, 1, true, use_subgroups, force_subgroup_size);
-            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f16_f32[w][GGML_TYPE_Q8_0][i], "mul_mat_vec_q8_0_f16_f32", arr_dmmv_q8_0_f16_f32_len[reduc], arr_dmmv_q8_0_f16_f32_data[reduc], "main", 3, sizeof(vk_mat_vec_push_constants), {1*rm_stdq, 1, 1}, {wg_size_subgroup, 1*rm_stdq, i+1}, 1, true, use_subgroups, force_subgroup_size);
-            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f16_f32[w][GGML_TYPE_Q2_K][i], "mul_mat_vec_q2_k_f16_f32", arr_dmmv_q2_k_f16_f32_len[reduc16], arr_dmmv_q2_k_f16_f32_data[reduc16], "main", 3, sizeof(vk_mat_vec_push_constants), {rm_kq, 1, 1}, {wg_size_subgroup16, rm_kq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
-            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f16_f32[w][GGML_TYPE_Q3_K][i], "mul_mat_vec_q3_k_f16_f32", arr_dmmv_q3_k_f16_f32_len[reduc16], arr_dmmv_q3_k_f16_f32_data[reduc16], "main", 3, sizeof(vk_mat_vec_push_constants), {rm_kq, 1, 1}, {wg_size_subgroup16, rm_kq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
-            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f16_f32[w][GGML_TYPE_Q4_K][i], "mul_mat_vec_q4_k_f16_f32", arr_dmmv_q4_k_f16_f32_len[reduc16], arr_dmmv_q4_k_f16_f32_data[reduc16], "main", 3, sizeof(vk_mat_vec_push_constants), {rm_kq, 1, 1}, {wg_size_subgroup16, rm_kq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
-            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f16_f32[w][GGML_TYPE_Q5_K][i], "mul_mat_vec_q5_k_f16_f32", arr_dmmv_q5_k_f16_f32_len[reduc16], arr_dmmv_q5_k_f16_f32_data[reduc16], "main", 3, sizeof(vk_mat_vec_push_constants), {rm_kq, 1, 1}, {wg_size_subgroup16, rm_kq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
-            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f16_f32[w][GGML_TYPE_Q6_K][i], "mul_mat_vec_q6_k_f16_f32", arr_dmmv_q6_k_f16_f32_len[reduc16], arr_dmmv_q6_k_f16_f32_data[reduc16], "main", 3, sizeof(vk_mat_vec_push_constants), {rm_kq, 1, 1}, {wg_size_subgroup16, rm_kq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
-            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f16_f32[w][GGML_TYPE_IQ1_S][i],   "mul_mat_vec_iq1_s_f16_f32",   arr_dmmv_iq1_s_f16_f32_len[reduc16],   arr_dmmv_iq1_s_f16_f32_data[reduc16],   "main", 3, sizeof(vk_mat_vec_push_constants), {rm_iq, 1, 1}, {wg_size_subgroup16, rm_iq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
-            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f16_f32[w][GGML_TYPE_IQ1_M][i],   "mul_mat_vec_iq1_m_f16_f32",   arr_dmmv_iq1_m_f16_f32_len[reduc16],   arr_dmmv_iq1_m_f16_f32_data[reduc16],   "main", 3, sizeof(vk_mat_vec_push_constants), {rm_iq, 1, 1}, {wg_size_subgroup16, rm_iq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
-            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f16_f32[w][GGML_TYPE_IQ2_XXS][i], "mul_mat_vec_iq2_xxs_f16_f32", arr_dmmv_iq2_xxs_f16_f32_len[reduc16], arr_dmmv_iq2_xxs_f16_f32_data[reduc16], "main", 3, sizeof(vk_mat_vec_push_constants), {rm_iq, 1, 1}, {wg_size_subgroup16, rm_iq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
-            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f16_f32[w][GGML_TYPE_IQ2_XS][i],  "mul_mat_vec_iq2_xs_f16_f32",  arr_dmmv_iq2_xs_f16_f32_len[reduc16],  arr_dmmv_iq2_xs_f16_f32_data[reduc16],  "main", 3, sizeof(vk_mat_vec_push_constants), {rm_iq, 1, 1}, {wg_size_subgroup16, rm_iq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
-            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f16_f32[w][GGML_TYPE_IQ2_S][i],   "mul_mat_vec_iq2_s_f16_f32",   arr_dmmv_iq2_s_f16_f32_len[reduc16],   arr_dmmv_iq2_s_f16_f32_data[reduc16],   "main", 3, sizeof(vk_mat_vec_push_constants), {rm_iq, 1, 1}, {wg_size_subgroup16, rm_iq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
-            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f16_f32[w][GGML_TYPE_IQ3_XXS][i], "mul_mat_vec_iq3_xxs_f16_f32", arr_dmmv_iq3_xxs_f16_f32_len[reduc16], arr_dmmv_iq3_xxs_f16_f32_data[reduc16], "main", 3, sizeof(vk_mat_vec_push_constants), {rm_iq, 1, 1}, {wg_size_subgroup16, rm_iq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
-            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f16_f32[w][GGML_TYPE_IQ3_S][i],   "mul_mat_vec_iq3_s_f16_f32",   arr_dmmv_iq3_s_f16_f32_len[reduc16],   arr_dmmv_iq3_s_f16_f32_data[reduc16],   "main", 3, sizeof(vk_mat_vec_push_constants), {rm_iq, 1, 1}, {wg_size_subgroup16, rm_iq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
-            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f16_f32[w][GGML_TYPE_IQ4_XS][i],  "mul_mat_vec_iq4_xs_f16_f32",  arr_dmmv_iq4_xs_f16_f32_len[reduc16],  arr_dmmv_iq4_xs_f16_f32_data[reduc16],  "main", 3, sizeof(vk_mat_vec_push_constants), {rm_iq, 1, 1}, {wg_size_subgroup16, rm_iq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
-            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f16_f32[w][GGML_TYPE_IQ4_NL][i],  "mul_mat_vec_iq4_nl_f16_f32",  arr_dmmv_iq4_nl_f16_f32_len[reduc16],  arr_dmmv_iq4_nl_f16_f32_data[reduc16],  "main", 3, sizeof(vk_mat_vec_push_constants), {rm_iq, 1, 1}, {wg_size_subgroup16, rm_iq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
-            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f16_f32[w][GGML_TYPE_MXFP4][i],   "mul_mat_vec_mxfp4_f16_f32",   arr_dmmv_mxfp4_f16_f32_len[reduc16],   arr_dmmv_mxfp4_f16_f32_data[reduc16],   "main", 3, sizeof(vk_mat_vec_push_constants), {rm_iq, 1, 1}, {wg_size_subgroup16, rm_iq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
+            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f32_f32[w][GGML_TYPE_F32 ][i], "mul_mat_vec_f32_f32_f32",  arr_dmmv_f32_f32_f32_len[reduc],  arr_dmmv_f32_f32_f32_data[reduc],  "main", 4, sizeof(vk_mat_vec_push_constants), {2, 1, 1}, {wg_size_subgroup, 2, i+1}, 1, false, use_subgroups, force_subgroup_size);
+            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f32_f32[w][GGML_TYPE_F16 ][i], "mul_mat_vec_f16_f32_f32",  arr_dmmv_f16_f32_f32_len[reduc],  arr_dmmv_f16_f32_f32_data[reduc],  "main", 4, sizeof(vk_mat_vec_push_constants), {2, 1, 1}, {wg_size_subgroup, 2, i+1}, 1, false, use_subgroups, force_subgroup_size);
+            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f32_f32[w][GGML_TYPE_BF16][i], "mul_mat_vec_bf16_f32_f32", arr_dmmv_bf16_f32_f32_len[reduc], arr_dmmv_bf16_f32_f32_data[reduc], "main", 4, sizeof(vk_mat_vec_push_constants), {2, 1, 1}, {wg_size_subgroup, 2, i+1}, 1, false, use_subgroups, force_subgroup_size);
+            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f32_f32[w][GGML_TYPE_Q4_0][i], "mul_mat_vec_q4_0_f32_f32", arr_dmmv_q4_0_f32_f32_len[reduc], arr_dmmv_q4_0_f32_f32_data[reduc], "main", 4, sizeof(vk_mat_vec_push_constants), {2*rm_stdq, 1, 1}, {wg_size_subgroup, 2*rm_stdq, i+1}, 1, true, use_subgroups, force_subgroup_size);
+            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f32_f32[w][GGML_TYPE_Q4_1][i], "mul_mat_vec_q4_1_f32_f32", arr_dmmv_q4_1_f32_f32_len[reduc], arr_dmmv_q4_1_f32_f32_data[reduc], "main", 4, sizeof(vk_mat_vec_push_constants), {2*rm_stdq, 1, 1}, {wg_size_subgroup, 2*rm_stdq, i+1}, 1, true, use_subgroups, force_subgroup_size);
+            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f32_f32[w][GGML_TYPE_Q5_0][i], "mul_mat_vec_q5_0_f32_f32", arr_dmmv_q5_0_f32_f32_len[reduc], arr_dmmv_q5_0_f32_f32_data[reduc], "main", 4, sizeof(vk_mat_vec_push_constants), {2*rm_stdq, 1, 1}, {wg_size_subgroup, 2*rm_stdq, i+1}, 1, true, use_subgroups, force_subgroup_size);
+            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f32_f32[w][GGML_TYPE_Q5_1][i], "mul_mat_vec_q5_1_f32_f32", arr_dmmv_q5_1_f32_f32_len[reduc], arr_dmmv_q5_1_f32_f32_data[reduc], "main", 4, sizeof(vk_mat_vec_push_constants), {2*rm_stdq, 1, 1}, {wg_size_subgroup, 2*rm_stdq, i+1}, 1, true, use_subgroups, force_subgroup_size);
+            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f32_f32[w][GGML_TYPE_Q8_0][i], "mul_mat_vec_q8_0_f32_f32", arr_dmmv_q8_0_f32_f32_len[reduc], arr_dmmv_q8_0_f32_f32_data[reduc], "main", 4, sizeof(vk_mat_vec_push_constants), {1*rm_stdq, 1, 1}, {wg_size_subgroup, 1*rm_stdq, i+1}, 1, true, use_subgroups, force_subgroup_size);
+            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f32_f32[w][GGML_TYPE_Q2_K][i], "mul_mat_vec_q2_k_f32_f32", arr_dmmv_q2_k_f32_f32_len[reduc16], arr_dmmv_q2_k_f32_f32_data[reduc16], "main", 4, sizeof(vk_mat_vec_push_constants), {rm_kq, 1, 1}, {wg_size_subgroup16, rm_kq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
+            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f32_f32[w][GGML_TYPE_Q3_K][i], "mul_mat_vec_q3_k_f32_f32", arr_dmmv_q3_k_f32_f32_len[reduc16], arr_dmmv_q3_k_f32_f32_data[reduc16], "main", 4, sizeof(vk_mat_vec_push_constants), {rm_kq, 1, 1}, {wg_size_subgroup16, rm_kq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
+            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f32_f32[w][GGML_TYPE_Q4_K][i], "mul_mat_vec_q4_k_f32_f32", arr_dmmv_q4_k_f32_f32_len[reduc16], arr_dmmv_q4_k_f32_f32_data[reduc16], "main", 4, sizeof(vk_mat_vec_push_constants), {rm_kq, 1, 1}, {wg_size_subgroup16, rm_kq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
+            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f32_f32[w][GGML_TYPE_Q5_K][i], "mul_mat_vec_q5_k_f32_f32", arr_dmmv_q5_k_f32_f32_len[reduc16], arr_dmmv_q5_k_f32_f32_data[reduc16], "main", 4, sizeof(vk_mat_vec_push_constants), {rm_kq, 1, 1}, {wg_size_subgroup16, rm_kq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
+            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f32_f32[w][GGML_TYPE_Q6_K][i], "mul_mat_vec_q6_k_f32_f32", arr_dmmv_q6_k_f32_f32_len[reduc16], arr_dmmv_q6_k_f32_f32_data[reduc16], "main", 4, sizeof(vk_mat_vec_push_constants), {rm_kq, 1, 1}, {wg_size_subgroup16, rm_kq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
+            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f32_f32[w][GGML_TYPE_IQ1_S][i],   "mul_mat_vec_iq1_s_f32_f32",   arr_dmmv_iq1_s_f32_f32_len[reduc16],   arr_dmmv_iq1_s_f32_f32_data[reduc16],   "main", 4, sizeof(vk_mat_vec_push_constants), {rm_iq, 1, 1}, {wg_size_subgroup16, rm_iq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
+            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f32_f32[w][GGML_TYPE_IQ1_M][i],   "mul_mat_vec_iq1_m_f32_f32",   arr_dmmv_iq1_m_f32_f32_len[reduc16],   arr_dmmv_iq1_m_f32_f32_data[reduc16],   "main", 4, sizeof(vk_mat_vec_push_constants), {rm_iq, 1, 1}, {wg_size_subgroup16, rm_iq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
+            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f32_f32[w][GGML_TYPE_IQ2_XXS][i], "mul_mat_vec_iq2_xxs_f32_f32", arr_dmmv_iq2_xxs_f32_f32_len[reduc16], arr_dmmv_iq2_xxs_f32_f32_data[reduc16], "main", 4, sizeof(vk_mat_vec_push_constants), {rm_iq, 1, 1}, {wg_size_subgroup16, rm_iq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
+            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f32_f32[w][GGML_TYPE_IQ2_XS][i],  "mul_mat_vec_iq2_xs_f32_f32",  arr_dmmv_iq2_xs_f32_f32_len[reduc16],  arr_dmmv_iq2_xs_f32_f32_data[reduc16],  "main", 4, sizeof(vk_mat_vec_push_constants), {rm_iq, 1, 1}, {wg_size_subgroup16, rm_iq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
+            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f32_f32[w][GGML_TYPE_IQ2_S][i],   "mul_mat_vec_iq2_s_f32_f32",   arr_dmmv_iq2_s_f32_f32_len[reduc16],   arr_dmmv_iq2_s_f32_f32_data[reduc16],   "main", 4, sizeof(vk_mat_vec_push_constants), {rm_iq, 1, 1}, {wg_size_subgroup16, rm_iq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
+            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f32_f32[w][GGML_TYPE_IQ3_XXS][i], "mul_mat_vec_iq3_xxs_f32_f32", arr_dmmv_iq3_xxs_f32_f32_len[reduc16], arr_dmmv_iq3_xxs_f32_f32_data[reduc16], "main", 4, sizeof(vk_mat_vec_push_constants), {rm_iq, 1, 1}, {wg_size_subgroup16, rm_iq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
+            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f32_f32[w][GGML_TYPE_IQ3_S][i],   "mul_mat_vec_iq3_s_f32_f32",   arr_dmmv_iq3_s_f32_f32_len[reduc16],   arr_dmmv_iq3_s_f32_f32_data[reduc16],   "main", 4, sizeof(vk_mat_vec_push_constants), {rm_iq, 1, 1}, {wg_size_subgroup16, rm_iq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
+            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f32_f32[w][GGML_TYPE_IQ4_XS][i],  "mul_mat_vec_iq4_xs_f32_f32",  arr_dmmv_iq4_xs_f32_f32_len[reduc16],  arr_dmmv_iq4_xs_f32_f32_data[reduc16],  "main", 4, sizeof(vk_mat_vec_push_constants), {rm_iq, 1, 1}, {wg_size_subgroup16, rm_iq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
+            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f32_f32[w][GGML_TYPE_IQ4_NL][i],  "mul_mat_vec_iq4_nl_f32_f32",  arr_dmmv_iq4_nl_f32_f32_len[reduc16],  arr_dmmv_iq4_nl_f32_f32_data[reduc16],  "main", 4, sizeof(vk_mat_vec_push_constants), {rm_iq, 1, 1}, {wg_size_subgroup16, rm_iq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
+            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f32_f32[w][GGML_TYPE_MXFP4][i],   "mul_mat_vec_mxfp4_f32_f32",   arr_dmmv_mxfp4_f32_f32_len[reduc16],   arr_dmmv_mxfp4_f32_f32_data[reduc16],   "main", 4, sizeof(vk_mat_vec_push_constants), {rm_iq, 1, 1}, {wg_size_subgroup16, rm_iq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
+
+            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f16_f32[w][GGML_TYPE_F32 ][i], "mul_mat_vec_f32_f16_f32",  arr_dmmv_f32_f16_f32_len[reduc],  arr_dmmv_f32_f16_f32_data[reduc],  "main", 4, sizeof(vk_mat_vec_push_constants), {2, 1, 1}, {wg_size_subgroup, 2, i+1}, 1, false, use_subgroups, force_subgroup_size);
+            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f16_f32[w][GGML_TYPE_F16 ][i], "mul_mat_vec_f16_f16_f32",  arr_dmmv_f16_f16_f32_len[reduc],  arr_dmmv_f16_f16_f32_data[reduc],  "main", 4, sizeof(vk_mat_vec_push_constants), {2, 1, 1}, {wg_size_subgroup, 2, i+1}, 1, false, use_subgroups, force_subgroup_size);
+            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f16_f32[w][GGML_TYPE_BF16][i], "mul_mat_vec_bf16_f16_f32", arr_dmmv_bf16_f16_f32_len[reduc], arr_dmmv_bf16_f16_f32_data[reduc], "main", 4, sizeof(vk_mat_vec_push_constants), {2, 1, 1}, {wg_size_subgroup, 2, i+1}, 1, false, use_subgroups, force_subgroup_size);
+            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f16_f32[w][GGML_TYPE_Q4_0][i], "mul_mat_vec_q4_0_f16_f32", arr_dmmv_q4_0_f16_f32_len[reduc], arr_dmmv_q4_0_f16_f32_data[reduc], "main", 4, sizeof(vk_mat_vec_push_constants), {2*rm_stdq, 1, 1}, {wg_size_subgroup, 2*rm_stdq, i+1}, 1, true, use_subgroups, force_subgroup_size);
+            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f16_f32[w][GGML_TYPE_Q4_1][i], "mul_mat_vec_q4_1_f16_f32", arr_dmmv_q4_1_f16_f32_len[reduc], arr_dmmv_q4_1_f16_f32_data[reduc], "main", 4, sizeof(vk_mat_vec_push_constants), {2*rm_stdq, 1, 1}, {wg_size_subgroup, 2*rm_stdq, i+1}, 1, true, use_subgroups, force_subgroup_size);
+            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f16_f32[w][GGML_TYPE_Q5_0][i], "mul_mat_vec_q5_0_f16_f32", arr_dmmv_q5_0_f16_f32_len[reduc], arr_dmmv_q5_0_f16_f32_data[reduc], "main", 4, sizeof(vk_mat_vec_push_constants), {2*rm_stdq, 1, 1}, {wg_size_subgroup, 2*rm_stdq, i+1}, 1, true, use_subgroups, force_subgroup_size);
+            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f16_f32[w][GGML_TYPE_Q5_1][i], "mul_mat_vec_q5_1_f16_f32", arr_dmmv_q5_1_f16_f32_len[reduc], arr_dmmv_q5_1_f16_f32_data[reduc], "main", 4, sizeof(vk_mat_vec_push_constants), {2*rm_stdq, 1, 1}, {wg_size_subgroup, 2*rm_stdq, i+1}, 1, true, use_subgroups, force_subgroup_size);
+            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f16_f32[w][GGML_TYPE_Q8_0][i], "mul_mat_vec_q8_0_f16_f32", arr_dmmv_q8_0_f16_f32_len[reduc], arr_dmmv_q8_0_f16_f32_data[reduc], "main", 4, sizeof(vk_mat_vec_push_constants), {1*rm_stdq, 1, 1}, {wg_size_subgroup, 1*rm_stdq, i+1}, 1, true, use_subgroups, force_subgroup_size);
+            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f16_f32[w][GGML_TYPE_Q2_K][i], "mul_mat_vec_q2_k_f16_f32", arr_dmmv_q2_k_f16_f32_len[reduc16], arr_dmmv_q2_k_f16_f32_data[reduc16], "main", 4, sizeof(vk_mat_vec_push_constants), {rm_kq, 1, 1}, {wg_size_subgroup16, rm_kq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
+            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f16_f32[w][GGML_TYPE_Q3_K][i], "mul_mat_vec_q3_k_f16_f32", arr_dmmv_q3_k_f16_f32_len[reduc16], arr_dmmv_q3_k_f16_f32_data[reduc16], "main", 4, sizeof(vk_mat_vec_push_constants), {rm_kq, 1, 1}, {wg_size_subgroup16, rm_kq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
+            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f16_f32[w][GGML_TYPE_Q4_K][i], "mul_mat_vec_q4_k_f16_f32", arr_dmmv_q4_k_f16_f32_len[reduc16], arr_dmmv_q4_k_f16_f32_data[reduc16], "main", 4, sizeof(vk_mat_vec_push_constants), {rm_kq, 1, 1}, {wg_size_subgroup16, rm_kq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
+            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f16_f32[w][GGML_TYPE_Q5_K][i], "mul_mat_vec_q5_k_f16_f32", arr_dmmv_q5_k_f16_f32_len[reduc16], arr_dmmv_q5_k_f16_f32_data[reduc16], "main", 4, sizeof(vk_mat_vec_push_constants), {rm_kq, 1, 1}, {wg_size_subgroup16, rm_kq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
+            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f16_f32[w][GGML_TYPE_Q6_K][i], "mul_mat_vec_q6_k_f16_f32", arr_dmmv_q6_k_f16_f32_len[reduc16], arr_dmmv_q6_k_f16_f32_data[reduc16], "main", 4, sizeof(vk_mat_vec_push_constants), {rm_kq, 1, 1}, {wg_size_subgroup16, rm_kq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
+            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f16_f32[w][GGML_TYPE_IQ1_S][i],   "mul_mat_vec_iq1_s_f16_f32",   arr_dmmv_iq1_s_f16_f32_len[reduc16],   arr_dmmv_iq1_s_f16_f32_data[reduc16],   "main", 4, sizeof(vk_mat_vec_push_constants), {rm_iq, 1, 1}, {wg_size_subgroup16, rm_iq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
+            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f16_f32[w][GGML_TYPE_IQ1_M][i],   "mul_mat_vec_iq1_m_f16_f32",   arr_dmmv_iq1_m_f16_f32_len[reduc16],   arr_dmmv_iq1_m_f16_f32_data[reduc16],   "main", 4, sizeof(vk_mat_vec_push_constants), {rm_iq, 1, 1}, {wg_size_subgroup16, rm_iq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
+            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f16_f32[w][GGML_TYPE_IQ2_XXS][i], "mul_mat_vec_iq2_xxs_f16_f32", arr_dmmv_iq2_xxs_f16_f32_len[reduc16], arr_dmmv_iq2_xxs_f16_f32_data[reduc16], "main", 4, sizeof(vk_mat_vec_push_constants), {rm_iq, 1, 1}, {wg_size_subgroup16, rm_iq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
+            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f16_f32[w][GGML_TYPE_IQ2_XS][i],  "mul_mat_vec_iq2_xs_f16_f32",  arr_dmmv_iq2_xs_f16_f32_len[reduc16],  arr_dmmv_iq2_xs_f16_f32_data[reduc16],  "main", 4, sizeof(vk_mat_vec_push_constants), {rm_iq, 1, 1}, {wg_size_subgroup16, rm_iq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
+            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f16_f32[w][GGML_TYPE_IQ2_S][i],   "mul_mat_vec_iq2_s_f16_f32",   arr_dmmv_iq2_s_f16_f32_len[reduc16],   arr_dmmv_iq2_s_f16_f32_data[reduc16],   "main", 4, sizeof(vk_mat_vec_push_constants), {rm_iq, 1, 1}, {wg_size_subgroup16, rm_iq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
+            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f16_f32[w][GGML_TYPE_IQ3_XXS][i], "mul_mat_vec_iq3_xxs_f16_f32", arr_dmmv_iq3_xxs_f16_f32_len[reduc16], arr_dmmv_iq3_xxs_f16_f32_data[reduc16], "main", 4, sizeof(vk_mat_vec_push_constants), {rm_iq, 1, 1}, {wg_size_subgroup16, rm_iq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
+            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f16_f32[w][GGML_TYPE_IQ3_S][i],   "mul_mat_vec_iq3_s_f16_f32",   arr_dmmv_iq3_s_f16_f32_len[reduc16],   arr_dmmv_iq3_s_f16_f32_data[reduc16],   "main", 4, sizeof(vk_mat_vec_push_constants), {rm_iq, 1, 1}, {wg_size_subgroup16, rm_iq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
+            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f16_f32[w][GGML_TYPE_IQ4_XS][i],  "mul_mat_vec_iq4_xs_f16_f32",  arr_dmmv_iq4_xs_f16_f32_len[reduc16],  arr_dmmv_iq4_xs_f16_f32_data[reduc16],  "main", 4, sizeof(vk_mat_vec_push_constants), {rm_iq, 1, 1}, {wg_size_subgroup16, rm_iq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
+            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f16_f32[w][GGML_TYPE_IQ4_NL][i],  "mul_mat_vec_iq4_nl_f16_f32",  arr_dmmv_iq4_nl_f16_f32_len[reduc16],  arr_dmmv_iq4_nl_f16_f32_data[reduc16],  "main", 4, sizeof(vk_mat_vec_push_constants), {rm_iq, 1, 1}, {wg_size_subgroup16, rm_iq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
+            ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_f16_f32[w][GGML_TYPE_MXFP4][i],   "mul_mat_vec_mxfp4_f16_f32",   arr_dmmv_mxfp4_f16_f32_len[reduc16],   arr_dmmv_mxfp4_f16_f32_data[reduc16],   "main", 4, sizeof(vk_mat_vec_push_constants), {rm_iq, 1, 1}, {wg_size_subgroup16, rm_iq, i+1}, 1, true, use_subgroups16, force_subgroup_size16);
 
 #if defined(GGML_VULKAN_INTEGER_DOT_GLSLC_SUPPORT)
             if (device->integer_dot_product) {
                 const uint32_t subgroup_size_int = (device->vendor_id == VK_VENDOR_ID_INTEL && device->subgroup_size_control) ? device->subgroup_min_size : device->subgroup_size;
                 const uint32_t wg_size_subgroup_int = (w == DMMV_WG_SIZE_SUBGROUP) ? subgroup_size_int : (subgroup_size_int * 4);
 
-                ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_q8_1_f32[w][GGML_TYPE_Q4_0][i], "mul_mat_vec_q4_0_q8_1_f32", arr_dmmv_q4_0_q8_1_f32_len[reduc], arr_dmmv_q4_0_q8_1_f32_data[reduc], "main", 3, sizeof(vk_mat_vec_push_constants), {2*rm_stdq, 1, 1}, {wg_size_subgroup_int, 2*rm_stdq, i+1}, 1, true, use_subgroups, subgroup_size_int);
-                ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_q8_1_f32[w][GGML_TYPE_Q4_1][i], "mul_mat_vec_q4_1_q8_1_f32", arr_dmmv_q4_1_q8_1_f32_len[reduc], arr_dmmv_q4_1_q8_1_f32_data[reduc], "main", 3, sizeof(vk_mat_vec_push_constants), {2*rm_stdq, 1, 1}, {wg_size_subgroup_int, 2*rm_stdq, i+1}, 1, true, use_subgroups, subgroup_size_int);
-                ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_q8_1_f32[w][GGML_TYPE_Q5_0][i], "mul_mat_vec_q5_0_q8_1_f32", arr_dmmv_q5_0_q8_1_f32_len[reduc], arr_dmmv_q5_0_q8_1_f32_data[reduc], "main", 3, sizeof(vk_mat_vec_push_constants), {2*rm_stdq, 1, 1}, {wg_size_subgroup_int, 2*rm_stdq, i+1}, 1, true, use_subgroups, subgroup_size_int);
-                ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_q8_1_f32[w][GGML_TYPE_Q5_1][i], "mul_mat_vec_q5_1_q8_1_f32", arr_dmmv_q5_1_q8_1_f32_len[reduc], arr_dmmv_q5_1_q8_1_f32_data[reduc], "main", 3, sizeof(vk_mat_vec_push_constants), {2*rm_stdq, 1, 1}, {wg_size_subgroup_int, 2*rm_stdq, i+1}, 1, true, use_subgroups, subgroup_size_int);
-                ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_q8_1_f32[w][GGML_TYPE_Q8_0][i], "mul_mat_vec_q8_0_q8_1_f32", arr_dmmv_q8_0_q8_1_f32_len[reduc], arr_dmmv_q8_0_q8_1_f32_data[reduc], "main", 3, sizeof(vk_mat_vec_push_constants), {1*rm_stdq, 1, 1}, {wg_size_subgroup_int, 1*rm_stdq, i+1}, 1, true, use_subgroups, subgroup_size_int);
+                ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_q8_1_f32[w][GGML_TYPE_Q4_0][i], "mul_mat_vec_q4_0_q8_1_f32", arr_dmmv_q4_0_q8_1_f32_len[reduc], arr_dmmv_q4_0_q8_1_f32_data[reduc], "main", 4, sizeof(vk_mat_vec_push_constants), {2*rm_stdq, 1, 1}, {wg_size_subgroup_int, 2*rm_stdq, i+1}, 1, true, use_subgroups, subgroup_size_int);
+                ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_q8_1_f32[w][GGML_TYPE_Q4_1][i], "mul_mat_vec_q4_1_q8_1_f32", arr_dmmv_q4_1_q8_1_f32_len[reduc], arr_dmmv_q4_1_q8_1_f32_data[reduc], "main", 4, sizeof(vk_mat_vec_push_constants), {2*rm_stdq, 1, 1}, {wg_size_subgroup_int, 2*rm_stdq, i+1}, 1, true, use_subgroups, subgroup_size_int);
+                ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_q8_1_f32[w][GGML_TYPE_Q5_0][i], "mul_mat_vec_q5_0_q8_1_f32", arr_dmmv_q5_0_q8_1_f32_len[reduc], arr_dmmv_q5_0_q8_1_f32_data[reduc], "main", 4, sizeof(vk_mat_vec_push_constants), {2*rm_stdq, 1, 1}, {wg_size_subgroup_int, 2*rm_stdq, i+1}, 1, true, use_subgroups, subgroup_size_int);
+                ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_q8_1_f32[w][GGML_TYPE_Q5_1][i], "mul_mat_vec_q5_1_q8_1_f32", arr_dmmv_q5_1_q8_1_f32_len[reduc], arr_dmmv_q5_1_q8_1_f32_data[reduc], "main", 4, sizeof(vk_mat_vec_push_constants), {2*rm_stdq, 1, 1}, {wg_size_subgroup_int, 2*rm_stdq, i+1}, 1, true, use_subgroups, subgroup_size_int);
+                ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_q8_1_f32[w][GGML_TYPE_Q8_0][i], "mul_mat_vec_q8_0_q8_1_f32", arr_dmmv_q8_0_q8_1_f32_len[reduc], arr_dmmv_q8_0_q8_1_f32_data[reduc], "main", 4, sizeof(vk_mat_vec_push_constants), {1*rm_stdq, 1, 1}, {wg_size_subgroup_int, 1*rm_stdq, i+1}, 1, true, use_subgroups, subgroup_size_int);
             }
 #endif // GGML_VULKAN_INTEGER_DOT_GLSLC_SUPPORT
         }
     }
 
-    ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_id_f32[GGML_TYPE_F32 ], "mul_mat_vec_id_f32_f32",  mul_mat_vec_id_f32_f32_len,  mul_mat_vec_id_f32_f32_data,  "main", 4, sizeof(vk_mat_vec_id_push_constants), {2, 1, 1}, {device->subgroup_size, 2}, 1);
-    ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_id_f32[GGML_TYPE_F16 ], "mul_mat_vec_id_f16_f32",  mul_mat_vec_id_f16_f32_len,  mul_mat_vec_id_f16_f32_data,  "main", 4, sizeof(vk_mat_vec_id_push_constants), {2, 1, 1}, {device->subgroup_size, 2}, 1);
-    ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_id_f32[GGML_TYPE_BF16], "mul_mat_vec_id_bf16_f32", mul_mat_vec_id_bf16_f32_len, mul_mat_vec_id_bf16_f32_data, "main", 4, sizeof(vk_mat_vec_id_push_constants), {2, 1, 1}, {device->subgroup_size, 2}, 1);
-    ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_id_f32[GGML_TYPE_Q4_0], "mul_mat_vec_id_q4_0_f32", mul_mat_vec_id_q4_0_f32_len, mul_mat_vec_id_q4_0_f32_data, "main", 4, sizeof(vk_mat_vec_id_push_constants), {2*rm_stdq, 1, 1}, {device->subgroup_size, 2*rm_stdq}, 1, true);
-    ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_id_f32[GGML_TYPE_Q4_1], "mul_mat_vec_id_q4_1_f32", mul_mat_vec_id_q4_1_f32_len, mul_mat_vec_id_q4_1_f32_data, "main", 4, sizeof(vk_mat_vec_id_push_constants), {2*rm_stdq, 1, 1}, {device->subgroup_size, 2*rm_stdq}, 1, true);
-    ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_id_f32[GGML_TYPE_Q5_0], "mul_mat_vec_id_q5_0_f32", mul_mat_vec_id_q5_0_f32_len, mul_mat_vec_id_q5_0_f32_data, "main", 4, sizeof(vk_mat_vec_id_push_constants), {2*rm_stdq, 1, 1}, {device->subgroup_size, 2*rm_stdq}, 1, true);
-    ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_id_f32[GGML_TYPE_Q5_1], "mul_mat_vec_id_q5_1_f32", mul_mat_vec_id_q5_1_f32_len, mul_mat_vec_id_q5_1_f32_data, "main", 4, sizeof(vk_mat_vec_id_push_constants), {2*rm_stdq, 1, 1}, {device->subgroup_size, 2*rm_stdq}, 1, true);
-    ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_id_f32[GGML_TYPE_Q8_0], "mul_mat_vec_id_q8_0_f32", mul_mat_vec_id_q8_0_f32_len, mul_mat_vec_id_q8_0_f32_data, "main", 4, sizeof(vk_mat_vec_id_push_constants), {1*rm_stdq, 1, 1}, {device->subgroup_size, 1*rm_stdq}, 1, true);
-    ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_id_f32[GGML_TYPE_Q2_K], "mul_mat_vec_id_q2_k_f32", mul_mat_vec_id_q2_k_f32_len, mul_mat_vec_id_q2_k_f32_data, "main", 4, sizeof(vk_mat_vec_id_push_constants), {rm_kq, 1, 1}, {subgroup_size_16, rm_kq}, 1, true);
-    ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_id_f32[GGML_TYPE_Q3_K], "mul_mat_vec_id_q3_k_f32", mul_mat_vec_id_q3_k_f32_len, mul_mat_vec_id_q3_k_f32_data, "main", 4, sizeof(vk_mat_vec_id_push_constants), {rm_kq, 1, 1}, {subgroup_size_16, rm_kq}, 1, true);
-    ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_id_f32[GGML_TYPE_Q4_K], "mul_mat_vec_id_q4_k_f32", mul_mat_vec_id_q4_k_f32_len, mul_mat_vec_id_q4_k_f32_data, "main", 4, sizeof(vk_mat_vec_id_push_constants), {rm_kq, 1, 1}, {subgroup_size_16, rm_kq}, 1, true);
-    ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_id_f32[GGML_TYPE_Q5_K], "mul_mat_vec_id_q5_k_f32", mul_mat_vec_id_q5_k_f32_len, mul_mat_vec_id_q5_k_f32_data, "main", 4, sizeof(vk_mat_vec_id_push_constants), {rm_kq, 1, 1}, {subgroup_size_16, rm_kq}, 1, true);
-    ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_id_f32[GGML_TYPE_Q6_K], "mul_mat_vec_id_q6_k_f32", mul_mat_vec_id_q6_k_f32_len, mul_mat_vec_id_q6_k_f32_data, "main", 4, sizeof(vk_mat_vec_id_push_constants), {rm_kq, 1, 1}, {subgroup_size_16, rm_kq}, 1, true);
-    ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_id_f32[GGML_TYPE_IQ1_S],   "mul_mat_vec_id_iq1_s_f32",   mul_mat_vec_id_iq1_s_f32_len,   mul_mat_vec_id_iq1_s_f32_data,   "main", 4, sizeof(vk_mat_vec_id_push_constants), {rm_iq, 1, 1}, {subgroup_size_16, rm_iq}, 1, true);
-    ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_id_f32[GGML_TYPE_IQ1_M],   "mul_mat_vec_id_iq1_m_f32",   mul_mat_vec_id_iq1_m_f32_len,   mul_mat_vec_id_iq1_m_f32_data,   "main", 4, sizeof(vk_mat_vec_id_push_constants), {rm_iq, 1, 1}, {subgroup_size_16, rm_iq}, 1, true);
-    ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_id_f32[GGML_TYPE_IQ2_XXS], "mul_mat_vec_id_iq2_xxs_f32", mul_mat_vec_id_iq2_xxs_f32_len, mul_mat_vec_id_iq2_xxs_f32_data, "main", 4, sizeof(vk_mat_vec_id_push_constants), {rm_iq, 1, 1}, {subgroup_size_16, rm_iq}, 1, true);
-    ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_id_f32[GGML_TYPE_IQ2_XS],  "mul_mat_vec_id_iq2_xs_f32",  mul_mat_vec_id_iq2_xs_f32_len,  mul_mat_vec_id_iq2_xs_f32_data,  "main", 4, sizeof(vk_mat_vec_id_push_constants), {rm_iq, 1, 1}, {subgroup_size_16, rm_iq}, 1, true);
-    ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_id_f32[GGML_TYPE_IQ2_S],   "mul_mat_vec_id_iq2_s_f32",   mul_mat_vec_id_iq2_s_f32_len,   mul_mat_vec_id_iq2_s_f32_data,   "main", 4, sizeof(vk_mat_vec_id_push_constants), {rm_iq, 1, 1}, {subgroup_size_16, rm_iq}, 1, true);
-    ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_id_f32[GGML_TYPE_IQ3_XXS], "mul_mat_vec_id_iq3_xxs_f32", mul_mat_vec_id_iq3_xxs_f32_len, mul_mat_vec_id_iq3_xxs_f32_data, "main", 4, sizeof(vk_mat_vec_id_push_constants), {rm_iq, 1, 1}, {subgroup_size_16, rm_iq}, 1, true);
-    ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_id_f32[GGML_TYPE_IQ3_S],   "mul_mat_vec_id_iq3_s_f32",   mul_mat_vec_id_iq3_s_f32_len,   mul_mat_vec_id_iq3_s_f32_data,   "main", 4, sizeof(vk_mat_vec_id_push_constants), {rm_iq, 1, 1}, {subgroup_size_16, rm_iq}, 1, true);
-    ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_id_f32[GGML_TYPE_IQ4_XS],  "mul_mat_vec_id_iq4_xs_f32",  mul_mat_vec_id_iq4_xs_f32_len,  mul_mat_vec_id_iq4_xs_f32_data,  "main", 4, sizeof(vk_mat_vec_id_push_constants), {rm_iq, 1, 1}, {subgroup_size_16, rm_iq}, 1, true);
-    ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_id_f32[GGML_TYPE_IQ4_NL],  "mul_mat_vec_id_iq4_nl_f32",  mul_mat_vec_id_iq4_nl_f32_len,  mul_mat_vec_id_iq4_nl_f32_data,  "main", 4, sizeof(vk_mat_vec_id_push_constants), {rm_iq, 1, 1}, {subgroup_size_16, rm_iq}, 1, true);
-    ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_id_f32[GGML_TYPE_MXFP4],   "mul_mat_vec_id_mxfp4_f32",   mul_mat_vec_id_mxfp4_f32_len,   mul_mat_vec_id_mxfp4_f32_data,   "main", 4, sizeof(vk_mat_vec_id_push_constants), {rm_iq, 1, 1}, {subgroup_size_16, rm_iq}, 1, true);
+    ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_id_f32[GGML_TYPE_F32 ], "mul_mat_vec_id_f32_f32",  mul_mat_vec_id_f32_f32_len,  mul_mat_vec_id_f32_f32_data,  "main", 5, sizeof(vk_mat_vec_id_push_constants), {2, 1, 1}, {device->subgroup_size, 2}, 1);
+    ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_id_f32[GGML_TYPE_F16 ], "mul_mat_vec_id_f16_f32",  mul_mat_vec_id_f16_f32_len,  mul_mat_vec_id_f16_f32_data,  "main", 5, sizeof(vk_mat_vec_id_push_constants), {2, 1, 1}, {device->subgroup_size, 2}, 1);
+    ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_id_f32[GGML_TYPE_BF16], "mul_mat_vec_id_bf16_f32", mul_mat_vec_id_bf16_f32_len, mul_mat_vec_id_bf16_f32_data, "main", 5, sizeof(vk_mat_vec_id_push_constants), {2, 1, 1}, {device->subgroup_size, 2}, 1);
+    ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_id_f32[GGML_TYPE_Q4_0], "mul_mat_vec_id_q4_0_f32", mul_mat_vec_id_q4_0_f32_len, mul_mat_vec_id_q4_0_f32_data, "main", 5, sizeof(vk_mat_vec_id_push_constants), {2*rm_stdq, 1, 1}, {device->subgroup_size, 2*rm_stdq}, 1, true);
+    ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_id_f32[GGML_TYPE_Q4_1], "mul_mat_vec_id_q4_1_f32", mul_mat_vec_id_q4_1_f32_len, mul_mat_vec_id_q4_1_f32_data, "main", 5, sizeof(vk_mat_vec_id_push_constants), {2*rm_stdq, 1, 1}, {device->subgroup_size, 2*rm_stdq}, 1, true);
+    ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_id_f32[GGML_TYPE_Q5_0], "mul_mat_vec_id_q5_0_f32", mul_mat_vec_id_q5_0_f32_len, mul_mat_vec_id_q5_0_f32_data, "main", 5, sizeof(vk_mat_vec_id_push_constants), {2*rm_stdq, 1, 1}, {device->subgroup_size, 2*rm_stdq}, 1, true);
+    ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_id_f32[GGML_TYPE_Q5_1], "mul_mat_vec_id_q5_1_f32", mul_mat_vec_id_q5_1_f32_len, mul_mat_vec_id_q5_1_f32_data, "main", 5, sizeof(vk_mat_vec_id_push_constants), {2*rm_stdq, 1, 1}, {device->subgroup_size, 2*rm_stdq}, 1, true);
+    ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_id_f32[GGML_TYPE_Q8_0], "mul_mat_vec_id_q8_0_f32", mul_mat_vec_id_q8_0_f32_len, mul_mat_vec_id_q8_0_f32_data, "main", 5, sizeof(vk_mat_vec_id_push_constants), {1*rm_stdq, 1, 1}, {device->subgroup_size, 1*rm_stdq}, 1, true);
+    ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_id_f32[GGML_TYPE_Q2_K], "mul_mat_vec_id_q2_k_f32", mul_mat_vec_id_q2_k_f32_len, mul_mat_vec_id_q2_k_f32_data, "main", 5, sizeof(vk_mat_vec_id_push_constants), {rm_kq, 1, 1}, {subgroup_size_16, rm_kq}, 1, true);
+    ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_id_f32[GGML_TYPE_Q3_K], "mul_mat_vec_id_q3_k_f32", mul_mat_vec_id_q3_k_f32_len, mul_mat_vec_id_q3_k_f32_data, "main", 5, sizeof(vk_mat_vec_id_push_constants), {rm_kq, 1, 1}, {subgroup_size_16, rm_kq}, 1, true);
+    ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_id_f32[GGML_TYPE_Q4_K], "mul_mat_vec_id_q4_k_f32", mul_mat_vec_id_q4_k_f32_len, mul_mat_vec_id_q4_k_f32_data, "main", 5, sizeof(vk_mat_vec_id_push_constants), {rm_kq, 1, 1}, {subgroup_size_16, rm_kq}, 1, true);
+    ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_id_f32[GGML_TYPE_Q5_K], "mul_mat_vec_id_q5_k_f32", mul_mat_vec_id_q5_k_f32_len, mul_mat_vec_id_q5_k_f32_data, "main", 5, sizeof(vk_mat_vec_id_push_constants), {rm_kq, 1, 1}, {subgroup_size_16, rm_kq}, 1, true);
+    ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_id_f32[GGML_TYPE_Q6_K], "mul_mat_vec_id_q6_k_f32", mul_mat_vec_id_q6_k_f32_len, mul_mat_vec_id_q6_k_f32_data, "main", 5, sizeof(vk_mat_vec_id_push_constants), {rm_kq, 1, 1}, {subgroup_size_16, rm_kq}, 1, true);
+    ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_id_f32[GGML_TYPE_IQ1_S],   "mul_mat_vec_id_iq1_s_f32",   mul_mat_vec_id_iq1_s_f32_len,   mul_mat_vec_id_iq1_s_f32_data,   "main", 5, sizeof(vk_mat_vec_id_push_constants), {rm_iq, 1, 1}, {subgroup_size_16, rm_iq}, 1, true);
+    ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_id_f32[GGML_TYPE_IQ1_M],   "mul_mat_vec_id_iq1_m_f32",   mul_mat_vec_id_iq1_m_f32_len,   mul_mat_vec_id_iq1_m_f32_data,   "main", 5, sizeof(vk_mat_vec_id_push_constants), {rm_iq, 1, 1}, {subgroup_size_16, rm_iq}, 1, true);
+    ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_id_f32[GGML_TYPE_IQ2_XXS], "mul_mat_vec_id_iq2_xxs_f32", mul_mat_vec_id_iq2_xxs_f32_len, mul_mat_vec_id_iq2_xxs_f32_data, "main", 5, sizeof(vk_mat_vec_id_push_constants), {rm_iq, 1, 1}, {subgroup_size_16, rm_iq}, 1, true);
+    ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_id_f32[GGML_TYPE_IQ2_XS],  "mul_mat_vec_id_iq2_xs_f32",  mul_mat_vec_id_iq2_xs_f32_len,  mul_mat_vec_id_iq2_xs_f32_data,  "main", 5, sizeof(vk_mat_vec_id_push_constants), {rm_iq, 1, 1}, {subgroup_size_16, rm_iq}, 1, true);
+    ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_id_f32[GGML_TYPE_IQ2_S],   "mul_mat_vec_id_iq2_s_f32",   mul_mat_vec_id_iq2_s_f32_len,   mul_mat_vec_id_iq2_s_f32_data,   "main", 5, sizeof(vk_mat_vec_id_push_constants), {rm_iq, 1, 1}, {subgroup_size_16, rm_iq}, 1, true);
+    ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_id_f32[GGML_TYPE_IQ3_XXS], "mul_mat_vec_id_iq3_xxs_f32", mul_mat_vec_id_iq3_xxs_f32_len, mul_mat_vec_id_iq3_xxs_f32_data, "main", 5, sizeof(vk_mat_vec_id_push_constants), {rm_iq, 1, 1}, {subgroup_size_16, rm_iq}, 1, true);
+    ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_id_f32[GGML_TYPE_IQ3_S],   "mul_mat_vec_id_iq3_s_f32",   mul_mat_vec_id_iq3_s_f32_len,   mul_mat_vec_id_iq3_s_f32_data,   "main", 5, sizeof(vk_mat_vec_id_push_constants), {rm_iq, 1, 1}, {subgroup_size_16, rm_iq}, 1, true);
+    ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_id_f32[GGML_TYPE_IQ4_XS],  "mul_mat_vec_id_iq4_xs_f32",  mul_mat_vec_id_iq4_xs_f32_len,  mul_mat_vec_id_iq4_xs_f32_data,  "main", 5, sizeof(vk_mat_vec_id_push_constants), {rm_iq, 1, 1}, {subgroup_size_16, rm_iq}, 1, true);
+    ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_id_f32[GGML_TYPE_IQ4_NL],  "mul_mat_vec_id_iq4_nl_f32",  mul_mat_vec_id_iq4_nl_f32_len,  mul_mat_vec_id_iq4_nl_f32_data,  "main", 5, sizeof(vk_mat_vec_id_push_constants), {rm_iq, 1, 1}, {subgroup_size_16, rm_iq}, 1, true);
+    ggml_vk_create_pipeline(device, device->pipeline_dequant_mul_mat_vec_id_f32[GGML_TYPE_MXFP4],   "mul_mat_vec_id_mxfp4_f32",   mul_mat_vec_id_mxfp4_f32_len,   mul_mat_vec_id_mxfp4_f32_data,   "main", 5, sizeof(vk_mat_vec_id_push_constants), {rm_iq, 1, 1}, {subgroup_size_16, rm_iq}, 1, true);
 
     // dequant shaders
     ggml_vk_create_pipeline(device, device->pipeline_dequant[GGML_TYPE_F32 ], "f32_to_f16",   dequant_f32_len,  dequant_f32_data,  "main", 2, 5 * sizeof(uint32_t), {256 * 16, 1, 1}, {}, 1);
@@ -3519,12 +3535,12 @@ static void ggml_vk_load_shaders(vk_device& device) {
 
     for (uint32_t i = 0; i < p021_max_gqa_ratio; ++i) {
         if (device->subgroup_arithmetic && device->subgroup_require_full_support) {
-            ggml_vk_create_pipeline2(device, device->pipeline_mul_mat_vec_p021_f16_f32[i], "mul_mat_vec_p021_f16_f32"+std::to_string(i+1), mul_mat_vec_p021_f16_f32_subgroup_add_len, mul_mat_vec_p021_f16_f32_subgroup_add_data, "main", 3, 6 * sizeof(uint32_t), {1, 1, 1}, {device->subgroup_size, i + 1}, 1, true, true);
+            ggml_vk_create_pipeline2(device, device->pipeline_mul_mat_vec_p021_f16_f32[i], "mul_mat_vec_p021_f16_f32"+std::to_string(i+1), mul_mat_vec_p021_f16_f32_subgroup_add_len, mul_mat_vec_p021_f16_f32_subgroup_add_data, "main", 4, 7 * sizeof(uint32_t), {1, 1, 1}, {device->subgroup_size, i + 1}, 1, true, true);
         } else {
-            ggml_vk_create_pipeline2(device, device->pipeline_mul_mat_vec_p021_f16_f32[i], "mul_mat_vec_p021_f16_f32"+std::to_string(i+1), mul_mat_vec_p021_f16_f32_len,              mul_mat_vec_p021_f16_f32_data,              "main", 3, 6 * sizeof(uint32_t), {1, 1, 1}, {device->subgroup_size, i + 1}, 1, true);
+            ggml_vk_create_pipeline2(device, device->pipeline_mul_mat_vec_p021_f16_f32[i], "mul_mat_vec_p021_f16_f32"+std::to_string(i+1), mul_mat_vec_p021_f16_f32_len,              mul_mat_vec_p021_f16_f32_data,              "main", 4, 7 * sizeof(uint32_t), {1, 1, 1}, {device->subgroup_size, i + 1}, 1, true);
         }
     }
-    ggml_vk_create_pipeline(device, device->pipeline_mul_mat_vec_nc_f16_f32, "mul_mat_vec_nc_f16_f32", mul_mat_vec_nc_f16_f32_len, mul_mat_vec_nc_f16_f32_data, "main", 3, 12 * sizeof(uint32_t), {1, 1, 1}, {}, 1);
+    ggml_vk_create_pipeline(device, device->pipeline_mul_mat_vec_nc_f16_f32, "mul_mat_vec_nc_f16_f32", mul_mat_vec_nc_f16_f32_len, mul_mat_vec_nc_f16_f32_data, "main", 4, 13 * sizeof(uint32_t), {1, 1, 1}, {}, 1);
 
     ggml_vk_create_pipeline(device, device->pipeline_norm_f32, "norm_f32", norm_f32_len, norm_f32_data, "main", 2, sizeof(vk_op_push_constants), {1, 1, 1}, {}, 1);
     ggml_vk_create_pipeline(device, device->pipeline_group_norm_f32, "group_norm_f32", group_norm_f32_len, group_norm_f32_data, "main", 2, sizeof(vk_op_push_constants), {1, 1, 1}, {}, 1);
@@ -6501,7 +6517,11 @@ static bool ggml_vk_should_use_mmvq(const vk_device& device, uint32_t m, uint32_
     GGML_UNUSED(k);
 }
 
-static void ggml_vk_mul_mat_vec_q_f16(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, ggml_tensor * dst, bool dryrun = false) {
+static void ggml_vk_mul_mat_vec_q_f16(ggml_backend_vk_context * ctx, vk_context& subctx, const struct ggml_cgraph * cgraph, int node_idx, bool dryrun = false) {
+    ggml_tensor * dst = cgraph->nodes[node_idx];
+    const ggml_tensor * src0 = dst->src[0];
+    const ggml_tensor * src1 = dst->src[1];
+
     VK_LOG_DEBUG("ggml_vk_mul_mat_vec_q_f16((" << src0 << ", name=" << src0->name << ", type=" << src0->type << ", ne0=" << src0->ne[0] << ", ne1=" << src0->ne[1] << ", ne2=" << src0->ne[2] << ", ne3=" << src0->ne[3] << ", nb0=" << src0->nb[0] << ", nb1=" << src0->nb[1] << ", nb2=" << src0->nb[2] << ", nb3=" << src0->nb[3];
     std::cerr << "), (" << src1 << ", name=" << src1->name << ", type=" << src1->type << ", ne0=" << src1->ne[0] << ", ne1=" << src1->ne[1] << ", ne2=" << src1->ne[2] << ", ne3=" << src1->ne[3] << ", nb0=" << src1->nb[0] << ", nb1=" << src1->nb[1] << ", nb2=" << src1->nb[2] << ", nb3=" << src1->nb[3];
     std::cerr << "), (" << dst << ", name=" << dst->name << ", type=" << dst->type << ", ne0=" << dst->ne[0] << ", ne1=" << dst->ne[1] << ", ne2=" << dst->ne[2] << ", ne3=" << dst->ne[3] << ", nb0=" << dst->nb[0] << ", nb1=" << dst->nb[1] << ", nb2=" << dst->nb[2] << ", nb3=" << dst->nb[3];
@@ -6532,7 +6552,6 @@ static void ggml_vk_mul_mat_vec_q_f16(ggml_backend_vk_context * ctx, vk_context&
     GGML_ASSERT(ne11 == 1 || ne12 * ne13 == 1);
     bool batch_n = ne11 > 1;
 
-    ggml_backend_vk_buffer_context * dst_buf_ctx = (ggml_backend_vk_buffer_context *)dst->buffer->context;
     ggml_backend_vk_buffer_context * src0_buf_ctx = (ggml_backend_vk_buffer_context *)src0->buffer->context;
     ggml_backend_vk_buffer_context * src1_buf_ctx = (ggml_backend_vk_buffer_context *)src1->buffer->context;
 
@@ -6634,8 +6653,20 @@ static void ggml_vk_mul_mat_vec_q_f16(ggml_backend_vk_context * ctx, vk_context&
         return;
     }
 
-    vk_buffer d_D = dst_buf_ctx->dev_buffer;
-    const uint64_t d_buf_offset = vk_tensor_offset(dst) + dst->view_offs;
+    vk_buffer d_D;
+    uint64_t d_buf_offset = 0;
+
+    if (ctx->num_additional_fused_ops > 0) {
+        const ggml_tensor * add = cgraph->nodes[node_idx + 1];
+        ggml_backend_vk_buffer_context * dst_buf_ctx = (ggml_backend_vk_buffer_context *)add->buffer->context;
+        d_D = dst_buf_ctx->dev_buffer;
+        d_buf_offset = vk_tensor_offset(add) + add->view_offs;
+    } else {
+        ggml_backend_vk_buffer_context * dst_buf_ctx = (ggml_backend_vk_buffer_context *)dst->buffer->context;
+        d_D = dst_buf_ctx->dev_buffer;
+        d_buf_offset = vk_tensor_offset(dst) + dst->view_offs;
+    }
+
     GGML_ASSERT(d_D != nullptr);
     vk_buffer d_X;
     uint64_t x_buf_offset = 0;
@@ -6730,14 +6761,43 @@ static void ggml_vk_mul_mat_vec_q_f16(ggml_backend_vk_context * ctx, vk_context&
         y_sz_total = CEIL_DIV(y_sz_total, 144) * 144;
     }
 
+    uint32_t enable_bias = ctx->num_additional_fused_ops > 0;
+
+    vk_buffer d_B = d_D;
+    size_t b_buf_offset = 0;
+    uint64_t b_sz = 0;
+
+    if (enable_bias) {
+        const ggml_tensor * add = cgraph->nodes[node_idx + 1];
+        const ggml_tensor * bias = add->src[0] == dst ? add->src[1] : add->src[0];
+
+        bool b_uma = false;
+        if (ctx->device->uma) {
+            ggml_vk_host_get(ctx->device, bias->data, d_B, b_buf_offset);
+            b_uma = d_B != nullptr;
+        }
+        if(!b_uma) {
+            ggml_backend_vk_buffer_context * bias_buf_ctx = (ggml_backend_vk_buffer_context *)bias->buffer->context;
+            d_B = bias_buf_ctx->dev_buffer;
+            b_buf_offset = vk_tensor_offset(bias) + bias->view_offs;
+            GGML_ASSERT(d_B != nullptr);
+            b_sz = ggml_nbytes(bias);
+        }
+    }
+
     // compute
     const vk_mat_vec_push_constants pc = {
         (uint32_t)ne00, (uint32_t)ne10, (uint32_t)ne10, (uint32_t)ne01,
-        stride_batch_x, stride_batch_y, stride_batch_d,
+        stride_batch_x, stride_batch_y, stride_batch_d, enable_bias,
         (uint32_t)ne02, (uint32_t)ne12, (uint32_t)r2, (uint32_t)r3,
     };
     ggml_vk_dispatch_pipeline(ctx, subctx, dmmv,
-                              { vk_subbuffer{ d_X, x_buf_offset, x_sz * ne02 * ne03 }, vk_subbuffer{ d_Y, y_buf_offset, y_sz_total }, vk_subbuffer{ d_D, d_buf_offset, d_sz * ne22 * ne23} },
+                              {
+                                vk_subbuffer{ d_X, x_buf_offset, x_sz * ne02 * ne03 },
+                                vk_subbuffer{ d_Y, y_buf_offset, y_sz_total },
+                                vk_subbuffer{ d_D, d_buf_offset, d_sz * ne22 * ne23},
+                                vk_subbuffer{ d_B, b_buf_offset, b_sz },
+                              },
                               pc, { groups_x, (uint32_t)(ne12 * ne13), groups_z });
 
     if (x_non_contig) {
@@ -6748,7 +6808,10 @@ static void ggml_vk_mul_mat_vec_q_f16(ggml_backend_vk_context * ctx, vk_context&
     }
 }
 
-static void ggml_vk_mul_mat_vec_p021_f16_f32(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, ggml_tensor * dst, bool dryrun = false) {
+static void ggml_vk_mul_mat_vec_p021_f16_f32(ggml_backend_vk_context * ctx, vk_context& subctx, const struct ggml_cgraph * cgraph, int node_idx, bool dryrun = false) {
+    ggml_tensor * dst = cgraph->nodes[node_idx];
+    const ggml_tensor * src0 = dst->src[0];
+    const ggml_tensor * src1 = dst->src[1];
     VK_LOG_DEBUG("ggml_vk_mul_mat_p021_f16_f32(" << src0 << ", name=" << src0->name << ", type=" << src0->type << ", ne0=" << src0->ne[0] << ", ne1=" << src0->ne[1] << ", ne2=" << src0->ne[2] << ", ne3=" << src0->ne[3] << ", nb0=" << src0->nb[0] << ", nb1=" << src0->nb[1] << ", nb2=" << src0->nb[2] << ", nb3=" << src0->nb[3];
     std::cerr << "), (" << src1 << ", name=" << src1->name << ", type=" << src1->type << ", ne0=" << src1->ne[0] << ", ne1=" << src1->ne[1] << ", ne2=" << src1->ne[2] << ", ne3=" << src1->ne[3] << ", nb0=" << src1->nb[0] << ", nb1=" << src1->nb[1] << ", nb2=" << src1->nb[2] << ", nb3=" << src1->nb[3];
     std::cerr << "), (" << dst << ", name=" << dst->name << ", type=" << dst->type << ", ne0=" << dst->ne[0] << ", ne1=" << dst->ne[1] << ", ne2=" << dst->ne[2] << ", ne3=" << dst->ne[3] << ", nb0=" << dst->nb[0] << ", nb1=" << dst->nb[1] << ", nb2=" << dst->nb[2] << ", nb3=" << dst->nb[3];
@@ -6771,7 +6834,6 @@ static void ggml_vk_mul_mat_vec_p021_f16_f32(ggml_backend_vk_context * ctx, vk_c
 
     GGML_ASSERT(ne11 == 1);
 
-    ggml_backend_vk_buffer_context * dst_buf_ctx = (ggml_backend_vk_buffer_context *)dst->buffer->context;
     ggml_backend_vk_buffer_context * src0_buf_ctx = (ggml_backend_vk_buffer_context *)src0->buffer->context;
     ggml_backend_vk_buffer_context * src1_buf_ctx = (ggml_backend_vk_buffer_context *)src1->buffer->context;
 
@@ -6805,8 +6867,19 @@ static void ggml_vk_mul_mat_vec_p021_f16_f32(ggml_backend_vk_context * ctx, vk_c
         return;
     }
 
-    vk_buffer d_D = dst_buf_ctx->dev_buffer;
-    const uint64_t d_buf_offset = vk_tensor_offset(dst) + dst->view_offs;
+    vk_buffer d_D;
+    uint64_t d_buf_offset = 0;
+
+    if (ctx->num_additional_fused_ops > 0) {
+        const ggml_tensor * add = cgraph->nodes[node_idx + 1];
+        ggml_backend_vk_buffer_context * dst_buf_ctx = (ggml_backend_vk_buffer_context *)add->buffer->context;
+        d_D = dst_buf_ctx->dev_buffer;
+        d_buf_offset = vk_tensor_offset(add) + add->view_offs;
+    } else {
+        ggml_backend_vk_buffer_context * dst_buf_ctx = (ggml_backend_vk_buffer_context *)dst->buffer->context;
+        d_D = dst_buf_ctx->dev_buffer;
+        d_buf_offset = vk_tensor_offset(dst) + dst->view_offs;
+    }
     GGML_ASSERT(d_D != nullptr);
     vk_buffer d_Qx = src0_buf_ctx->dev_buffer;
     const uint64_t qx_buf_offset = vk_tensor_offset(src0) + src0->view_offs;
@@ -6823,8 +6896,32 @@ static void ggml_vk_mul_mat_vec_p021_f16_f32(ggml_backend_vk_context * ctx, vk_c
     const uint64_t d_buffer_offset = (d_buf_offset / ctx->device->properties.limits.minStorageBufferOffsetAlignment) * ctx->device->properties.limits.minStorageBufferOffsetAlignment;
     const uint64_t d_shader_offset = d_buf_offset - d_buffer_offset;
 
+    uint32_t enable_bias = ctx->num_additional_fused_ops > 0;
+
+    vk_buffer d_B = d_D;
+    size_t b_buf_offset = 0;
+    uint64_t b_sz = 0;
+
+    if (enable_bias) {
+        const ggml_tensor * add = cgraph->nodes[node_idx + 1];
+        const ggml_tensor * bias = add->src[0] == dst ? add->src[1] : add->src[0];
+
+        bool b_uma = false;
+        if (ctx->device->uma) {
+            ggml_vk_host_get(ctx->device, bias->data, d_B, b_buf_offset);
+            b_uma = d_B != nullptr;
+        }
+        if(!b_uma) {
+            ggml_backend_vk_buffer_context * bias_buf_ctx = (ggml_backend_vk_buffer_context *)bias->buffer->context;
+            d_B = bias_buf_ctx->dev_buffer;
+            b_buf_offset = vk_tensor_offset(bias) + bias->view_offs;
+            GGML_ASSERT(d_B != nullptr);
+            b_sz = ggml_nbytes(bias);
+        }
+    }
+
     // compute
-    const std::array<uint32_t, 6> pc = { (uint32_t)ne00, (uint32_t)ne01, (uint32_t)ne02, (uint32_t)ne12, (uint32_t)(qy_shader_offset / ggml_type_size(src1->type)), (uint32_t)(d_shader_offset / ggml_type_size(dst->type)) };
+    const std::array<uint32_t, 7> pc = { (uint32_t)ne00, (uint32_t)ne01, (uint32_t)ne02, (uint32_t)ne12, (uint32_t)(qy_shader_offset / ggml_type_size(src1->type)), (uint32_t)(d_shader_offset / ggml_type_size(dst->type)), enable_bias };
 
     uint32_t workgroups_z = (uint32_t)ne12;
     // When gqa_ratio > 1, each invocation does multiple rows and we can launch fewer workgroups
@@ -6832,10 +6929,19 @@ static void ggml_vk_mul_mat_vec_p021_f16_f32(ggml_backend_vk_context * ctx, vk_c
         workgroups_z /= gqa_ratio;
     }
 
-    ggml_vk_dispatch_pipeline(ctx, subctx, ctx->device->pipeline_mul_mat_vec_p021_f16_f32[gqa_ratio - 1], { vk_subbuffer{ d_Qx, qx_buf_offset, qx_sz }, vk_subbuffer{ d_Qy, qy_buffer_offset, qy_sz + qy_shader_offset }, vk_subbuffer{ d_D, d_buffer_offset, d_sz + d_shader_offset } }, pc, { 1, (uint32_t)ne01, workgroups_z });
+    ggml_vk_dispatch_pipeline(ctx, subctx, ctx->device->pipeline_mul_mat_vec_p021_f16_f32[gqa_ratio - 1],
+        {
+            vk_subbuffer{ d_Qx, qx_buf_offset, qx_sz },
+            vk_subbuffer{ d_Qy, qy_buffer_offset, qy_sz + qy_shader_offset },
+            vk_subbuffer{ d_D, d_buffer_offset, d_sz + d_shader_offset },
+            vk_subbuffer{ d_B, b_buf_offset, b_sz },
+        }, pc, { 1, (uint32_t)ne01, workgroups_z });
 }
 
-static void ggml_vk_mul_mat_vec_nc_f16_f32(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, ggml_tensor * dst, bool dryrun = false) {
+static void ggml_vk_mul_mat_vec_nc_f16_f32(ggml_backend_vk_context * ctx, vk_context& subctx, const struct ggml_cgraph * cgraph, int node_idx, bool dryrun = false) {
+    ggml_tensor * dst = cgraph->nodes[node_idx];
+    const ggml_tensor * src0 = dst->src[0];
+    const ggml_tensor * src1 = dst->src[1];
     VK_LOG_DEBUG("ggml_vk_mul_mat_nc_f16_f32((" << src0 << ", name=" << src0->name << ", type=" << src0->type << ", ne0=" << src0->ne[0] << ", ne1=" << src0->ne[1] << ", ne2=" << src0->ne[2] << ", ne3=" << src0->ne[3] << ", nb0=" << src0->nb[0] << ", nb1=" << src0->nb[1] << ", nb2=" << src0->nb[2] << ", nb3=" << src0->nb[3];
     std::cerr << "), (" << src1 << ", name=" << src1->name << ", type=" << src1->type << ", ne0=" << src1->ne[0] << ", ne1=" << src1->ne[1] << ", ne2=" << src1->ne[2] << ", ne3=" << src1->ne[3] << ", nb0=" << src1->nb[0] << ", nb1=" << src1->nb[1] << ", nb2=" << src1->nb[2] << ", nb3=" << src1->nb[3];
     std::cerr << "), (" << dst << ", name=" << dst->name << ", type=" << dst->type << ", ne0=" << dst->ne[0] << ", ne1=" << dst->ne[1] << ", ne2=" << dst->ne[2] << ", ne3=" << dst->ne[3] << ", nb0=" << dst->nb[0] << ", nb1=" << dst->nb[1] << ", nb2=" << dst->nb[2] << ", nb3=" << dst->nb[3];
@@ -6868,7 +6974,6 @@ static void ggml_vk_mul_mat_vec_nc_f16_f32(ggml_backend_vk_context * ctx, vk_con
     GGML_ASSERT(ne11 == 1);
     GGML_ASSERT(src0->ne[3] == src1->ne[3]); // checked in supports_op
 
-    ggml_backend_vk_buffer_context * dst_buf_ctx = (ggml_backend_vk_buffer_context *)dst->buffer->context;
     ggml_backend_vk_buffer_context * src0_buf_ctx = (ggml_backend_vk_buffer_context *)src0->buffer->context;
     ggml_backend_vk_buffer_context * src1_buf_ctx = (ggml_backend_vk_buffer_context *)src1->buffer->context;
 
@@ -6898,8 +7003,20 @@ static void ggml_vk_mul_mat_vec_nc_f16_f32(ggml_backend_vk_context * ctx, vk_con
         return;
     }
 
-    vk_buffer d_D = dst_buf_ctx->dev_buffer;
-    const uint64_t d_buf_offset = vk_tensor_offset(dst) + dst->view_offs;
+    vk_buffer d_D;
+    uint64_t d_buf_offset = 0;
+
+    if (ctx->num_additional_fused_ops > 0) {
+        const ggml_tensor * add = cgraph->nodes[node_idx + 1];
+        ggml_backend_vk_buffer_context * dst_buf_ctx = (ggml_backend_vk_buffer_context *)add->buffer->context;
+        d_D = dst_buf_ctx->dev_buffer;
+        d_buf_offset = vk_tensor_offset(add) + add->view_offs;
+    } else {
+        ggml_backend_vk_buffer_context * dst_buf_ctx = (ggml_backend_vk_buffer_context *)dst->buffer->context;
+        d_D = dst_buf_ctx->dev_buffer;
+        d_buf_offset = vk_tensor_offset(dst) + dst->view_offs;
+    }
+
     GGML_ASSERT(d_D != nullptr);
     vk_buffer d_Qx = src0_buf_ctx->dev_buffer;
     const uint64_t qx_buf_offset = vk_tensor_offset(src0) + src0->view_offs;
@@ -6916,13 +7033,45 @@ static void ggml_vk_mul_mat_vec_nc_f16_f32(ggml_backend_vk_context * ctx, vk_con
     const uint64_t d_buffer_offset = (d_buf_offset / ctx->device->properties.limits.minStorageBufferOffsetAlignment) * ctx->device->properties.limits.minStorageBufferOffsetAlignment;
     const uint64_t d_shader_offset = d_buf_offset - d_buffer_offset;
 
+    uint32_t enable_bias = ctx->num_additional_fused_ops > 0;
+
+    vk_buffer d_B = d_D;
+    size_t b_buf_offset = 0;
+    uint64_t b_sz = 0;
+
+    if (enable_bias) {
+        const ggml_tensor * add = cgraph->nodes[node_idx + 1];
+        const ggml_tensor * bias = add->src[0] == dst ? add->src[1] : add->src[0];
+
+        bool b_uma = false;
+        if (ctx->device->uma) {
+            ggml_vk_host_get(ctx->device, bias->data, d_B, b_buf_offset);
+            b_uma = d_B != nullptr;
+        }
+        if(!b_uma) {
+            ggml_backend_vk_buffer_context * bias_buf_ctx = (ggml_backend_vk_buffer_context *)bias->buffer->context;
+            d_B = bias_buf_ctx->dev_buffer;
+            b_buf_offset = vk_tensor_offset(bias) + bias->view_offs;
+            GGML_ASSERT(d_B != nullptr);
+            b_sz = ggml_nbytes(bias);
+        }
+    }
+
     // compute
-    const std::array<uint32_t, 12> pc = { (uint32_t)ne00, (uint32_t)ne01, row_stride_x, channel_stride_x, channel_stride_y, (uint32_t)(ne12 / ne02), (uint32_t)ne12, (uint32_t)(qy_shader_offset / ggml_type_size(src1->type)), (uint32_t)(d_shader_offset / ggml_type_size(dst->type)), nb03, nb13, nb23 };
+    const std::array<uint32_t, 13> pc = { (uint32_t)ne00, (uint32_t)ne01, row_stride_x, channel_stride_x, channel_stride_y, (uint32_t)(ne12 / ne02), (uint32_t)ne12, (uint32_t)(qy_shader_offset / ggml_type_size(src1->type)), (uint32_t)(d_shader_offset / ggml_type_size(dst->type)), nb03, nb13, nb23, enable_bias };
     ggml_vk_dispatch_pipeline(ctx, subctx, ctx->device->pipeline_mul_mat_vec_nc_f16_f32,
-        { vk_subbuffer{ d_Qx, qx_buf_offset, qx_sz }, vk_subbuffer{ d_Qy, qy_buffer_offset, qy_sz + qy_shader_offset }, vk_subbuffer{ d_D, d_buffer_offset, d_sz + d_shader_offset } }, pc, { (uint32_t)ne03, (uint32_t)ne01, (uint32_t)ne12 });
+        {
+            vk_subbuffer{ d_Qx, qx_buf_offset, qx_sz },
+            vk_subbuffer{ d_Qy, qy_buffer_offset, qy_sz + qy_shader_offset },
+            vk_subbuffer{ d_D, d_buffer_offset, d_sz + d_shader_offset },
+            vk_subbuffer{ d_B, b_buf_offset, b_sz },
+        }, pc, { (uint32_t)ne03, (uint32_t)ne01, (uint32_t)ne12 });
 }
 
-static void ggml_vk_mul_mat(ggml_backend_vk_context * ctx, vk_context& subctx, ggml_tensor * src0, ggml_tensor * src1, ggml_tensor * dst, bool dryrun = false) {
+static void ggml_vk_mul_mat(ggml_backend_vk_context * ctx, vk_context& subctx, const struct ggml_cgraph * cgraph, int node_idx, bool dryrun = false) {
+    ggml_tensor * dst = cgraph->nodes[node_idx];
+    ggml_tensor * src0 = dst->src[0];
+    ggml_tensor * src1 = dst->src[1];
     VK_LOG_DEBUG("ggml_vk_mul_mat(" << src0 << ", " << src1 << ", " << dst << ")");
 
     // Handle huge A matrix by splitting the M dimensions. This works well for convolution use cases
@@ -6961,15 +7110,15 @@ static void ggml_vk_mul_mat(ggml_backend_vk_context * ctx, vk_context& subctx, g
         src1->nb[1] <= src1->nb[3] &&
         src0->ne[3] == 1 &&
         src1->ne[3] == 1) {
-        ggml_vk_mul_mat_vec_p021_f16_f32(ctx, subctx, src0, src1, dst, dryrun);
+        ggml_vk_mul_mat_vec_p021_f16_f32(ctx, subctx, cgraph, node_idx, dryrun);
     } else if (src0->type == GGML_TYPE_F16 && !ggml_is_contiguous(src0) && !ggml_is_transposed(src1) && dst->ne[1] == 1 &&
                !ggml_is_permuted(src0) && !ggml_is_permuted(src1)) {
-        ggml_vk_mul_mat_vec_nc_f16_f32(ctx, subctx, src0, src1, dst, dryrun);
+        ggml_vk_mul_mat_vec_nc_f16_f32(ctx, subctx, cgraph, node_idx, dryrun);
     // mul_mat_vec supports batching ne12*ne13 when ne11==1, or treating ne11 as the batch size (up to four)
     // when ne12 and ne13 are one.
     } else if ((dst->ne[1] == 1 || (dst->ne[1] <= mul_mat_vec_max_cols && src1->ne[2] * src1->ne[3] == 1)) &&
                (src0->type == GGML_TYPE_F32 || src0->type == GGML_TYPE_F16 || src0->type == GGML_TYPE_BF16 || ggml_is_quantized(src0->type))) {
-        ggml_vk_mul_mat_vec_q_f16(ctx, subctx, src0, src1, dst, dryrun);
+        ggml_vk_mul_mat_vec_q_f16(ctx, subctx, cgraph, node_idx, dryrun);
     } else {
         ggml_vk_mul_mat_q_f16(ctx, subctx, src0, src1, dst, false, dryrun);
     }
@@ -7249,7 +7398,11 @@ static void ggml_vk_mul_mat_id_q_f16(ggml_backend_vk_context * ctx, vk_context&
     }
 }
 
-static void ggml_vk_mul_mat_vec_id_q_f16(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, const ggml_tensor * ids, ggml_tensor * dst, bool dryrun = false) {
+static void ggml_vk_mul_mat_vec_id_q_f16(ggml_backend_vk_context * ctx, vk_context& subctx, const struct ggml_cgraph * cgraph, int node_idx, bool dryrun = false) {
+    ggml_tensor * dst = cgraph->nodes[node_idx];
+    ggml_tensor * src0 = dst->src[0];
+    ggml_tensor * src1 = dst->src[1];
+    ggml_tensor * ids = dst->src[2];
     VK_LOG_DEBUG("ggml_vk_mul_mat_vec_id_q_f16((" << src0 << ", name=" << src0->name << ", type=" << src0->type << ", ne0=" << src0->ne[0] << ", ne1=" << src0->ne[1] << ", ne2=" << src0->ne[2] << ", ne3=" << src0->ne[3] << ", nb0=" << src0->nb[0] << ", nb1=" << src0->nb[1] << ", nb2=" << src0->nb[2] << ", nb3=" << src0->nb[3];
     std::cerr << "), (" << src1 << ", name=" << src1->name << ", type=" << src1->type << ", ne0=" << src1->ne[0] << ", ne1=" << src1->ne[1] << ", ne2=" << src1->ne[2] << ", ne3=" << src1->ne[3] << ", nb0=" << src1->nb[0] << ", nb1=" << src1->nb[1] << ", nb2=" << src1->nb[2] << ", nb3=" << src1->nb[3];
     std::cerr << "), (" << ids << ", name=" << ids->name << ", type=" << ids->type << ", ne0=" << ids->ne[0] << ", ne1=" << ids->ne[1] << ", ne2=" << ids->ne[2] << ", ne3=" << ids->ne[3] << ", nb0=" << ids->nb[0] << ", nb1=" << ids->nb[1] << ", nb2=" << ids->nb[2] << ", nb3=" << ids->nb[3];
@@ -7281,7 +7434,6 @@ static void ggml_vk_mul_mat_vec_id_q_f16(ggml_backend_vk_context * ctx, vk_conte
     const uint64_t ne22 = dst->ne[2];
     const uint64_t ne23 = dst->ne[3];
 
-    ggml_backend_vk_buffer_context * dst_buf_ctx = (ggml_backend_vk_buffer_context *)dst->buffer->context;
     ggml_backend_vk_buffer_context * src0_buf_ctx = (ggml_backend_vk_buffer_context *)src0->buffer->context;
     ggml_backend_vk_buffer_context * src1_buf_ctx = (ggml_backend_vk_buffer_context *)src1->buffer->context;
     ggml_backend_vk_buffer_context * ids_buf_ctx = (ggml_backend_vk_buffer_context *)ids->buffer->context;
@@ -7369,8 +7521,20 @@ static void ggml_vk_mul_mat_vec_id_q_f16(ggml_backend_vk_context * ctx, vk_conte
         return;
     }
 
-    vk_buffer d_D = dst_buf_ctx->dev_buffer;
-    const uint64_t d_buf_offset = vk_tensor_offset(dst) + dst->view_offs;
+    vk_buffer d_D;
+    uint64_t d_buf_offset = 0;
+
+    if (ctx->num_additional_fused_ops > 0) {
+        const ggml_tensor * add = cgraph->nodes[node_idx + 1];
+        ggml_backend_vk_buffer_context * dst_buf_ctx = (ggml_backend_vk_buffer_context *)add->buffer->context;
+        d_D = dst_buf_ctx->dev_buffer;
+        d_buf_offset = vk_tensor_offset(add) + add->view_offs;
+    } else {
+        ggml_backend_vk_buffer_context * dst_buf_ctx = (ggml_backend_vk_buffer_context *)dst->buffer->context;
+        d_D = dst_buf_ctx->dev_buffer;
+        d_buf_offset = vk_tensor_offset(dst) + dst->view_offs;
+    }
+
     GGML_ASSERT(d_D != nullptr);
     vk_buffer d_X;
     uint64_t x_buf_offset = 0;
@@ -7445,15 +7609,46 @@ static void ggml_vk_mul_mat_vec_id_q_f16(ggml_backend_vk_context * ctx, vk_conte
         groups_x = CEIL_DIV(groups_x, groups_z);
     }
 
+    uint32_t enable_bias = ctx->num_additional_fused_ops > 0;
+
+    vk_buffer d_B = d_D;
+    size_t b_buf_offset = 0;
+    uint64_t b_sz = 0;
+
+    if (enable_bias) {
+        const ggml_tensor * bias = cgraph->nodes[node_idx + 1]->src[1];
+
+        bool b_uma = false;
+        if (ctx->device->uma) {
+            ggml_vk_host_get(ctx->device, bias->data, d_B, b_buf_offset);
+            b_uma = d_B != nullptr;
+        }
+        if(!b_uma) {
+            ggml_backend_vk_buffer_context * bias_buf_ctx = (ggml_backend_vk_buffer_context *)bias->buffer->context;
+            d_B = bias_buf_ctx->dev_buffer;
+            b_buf_offset = vk_tensor_offset(bias) + bias->view_offs;
+            GGML_ASSERT(d_B != nullptr);
+            b_sz = ggml_nbytes(bias);
+        }
+    }
+
     // compute
     const vk_mat_vec_id_push_constants pc = {
         (uint32_t)ne00, (uint32_t)ne10, (uint32_t)ne10, (uint32_t)ne01,
         (uint32_t)x_ne, stride_batch_y, (uint32_t)(ne20*ne21),
+
+        enable_bias,
+
         (uint32_t)nei0, (uint32_t)ne11,
     };
     ggml_vk_dispatch_pipeline(ctx, subctx, dmmv,
-        { vk_subbuffer{ d_X, x_buf_offset, x_sz * ne02 * ne03 },
-        vk_subbuffer{ d_Y, y_buf_offset, y_sz * ne12 * ne13 }, vk_subbuffer{ d_D, d_buf_offset, d_sz * ne22 * ne23}, vk_subbuffer{ d_ids, ids_buf_offset, ids_sz } },
+        {
+            vk_subbuffer{ d_X, x_buf_offset, x_sz * ne02 * ne03 },
+            vk_subbuffer{ d_Y, y_buf_offset, y_sz * ne12 * ne13 },
+            vk_subbuffer{ d_D, d_buf_offset, d_sz * ne22 * ne23},
+            vk_subbuffer{ d_B, b_buf_offset, b_sz },
+            vk_subbuffer{ d_ids, ids_buf_offset, ids_sz },
+        },
         pc, { groups_x, (uint32_t)nei0, groups_z });
 
     if (x_non_contig) {
@@ -7464,10 +7659,21 @@ static void ggml_vk_mul_mat_vec_id_q_f16(ggml_backend_vk_context * ctx, vk_conte
     }
 }
 
-static void ggml_vk_mul_mat_id(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, const ggml_tensor * src2, ggml_tensor * dst, bool dryrun = false) {
+static bool ggml_vk_use_mul_mat_vec_id(const struct ggml_cgraph * cgraph, int node_idx) {
+    ggml_tensor * dst = cgraph->nodes[node_idx];
+    ggml_tensor * src0 = dst->src[0];
+    ggml_tensor * src2 = dst->src[2];
+    return src2->ne[1] == 1 && (src0->type == GGML_TYPE_F32 || src0->type == GGML_TYPE_F16 || ggml_is_quantized(src0->type));
+}
+
+static void ggml_vk_mul_mat_id(ggml_backend_vk_context * ctx, vk_context& subctx, const struct ggml_cgraph * cgraph, int node_idx, bool dryrun = false) {
+    ggml_tensor * dst = cgraph->nodes[node_idx];
+    ggml_tensor * src0 = dst->src[0];
+    ggml_tensor * src1 = dst->src[1];
+    ggml_tensor * src2 = dst->src[2];
     VK_LOG_DEBUG("ggml_vk_mul_mat_id(" << src0 << ", " << src1 << ", " << src2 << ", " << dst << ")");
-    if (src2->ne[1] == 1 && (src0->type == GGML_TYPE_F32 || src0->type == GGML_TYPE_F16 || ggml_is_quantized(src0->type))) {
-        ggml_vk_mul_mat_vec_id_q_f16(ctx, subctx, src0, src1, src2, dst, dryrun);
+    if (ggml_vk_use_mul_mat_vec_id(cgraph, node_idx)) {
+        ggml_vk_mul_mat_vec_id_q_f16(ctx, subctx, cgraph, node_idx, dryrun);
     } else {
         ggml_vk_mul_mat_id_q_f16(ctx, subctx, src0, src1, src2, dst, dryrun);
     }
@@ -8433,7 +8639,7 @@ static bool ggml_vk_op_supports_incontiguous(ggml_op op) {
     }
 }
 
-static uint32_t get_misalign_bytes(ggml_backend_vk_context * ctx, const ggml_tensor * t)
+static uint32_t get_misalign_bytes(const ggml_backend_vk_context * ctx, const ggml_tensor * t)
 {
     return ((vk_tensor_offset(t) + t->view_offs) & (ctx->device->properties.limits.minStorageBufferOffsetAlignment - 1));;
 }
@@ -11793,11 +11999,11 @@ static bool ggml_vk_build_graph(ggml_backend_vk_context * ctx, ggml_cgraph * cgr
 
         break;
     case GGML_OP_MUL_MAT:
-        ggml_vk_mul_mat(ctx, compute_ctx, src0, src1, node, dryrun);
+        ggml_vk_mul_mat(ctx, compute_ctx, cgraph, node_idx, dryrun);
 
         break;
     case GGML_OP_MUL_MAT_ID:
-        ggml_vk_mul_mat_id(ctx, compute_ctx, src0, src1, src2, node, dryrun);
+        ggml_vk_mul_mat_id(ctx, compute_ctx, cgraph, node_idx, dryrun);
 
         break;
 
@@ -12474,7 +12680,7 @@ static bool ggml_vk_is_empty(ggml_tensor * node) {
     return ggml_is_empty(node) || node->op == GGML_OP_NONE || node->op == GGML_OP_RESHAPE || node->op == GGML_OP_TRANSPOSE || node->op == GGML_OP_VIEW || node->op == GGML_OP_PERMUTE;
 }
 
-static bool ggml_vk_can_fuse(const struct ggml_cgraph * cgraph, int node_idx, std::initializer_list<enum ggml_op> ops) {
+static bool ggml_vk_can_fuse(const ggml_backend_vk_context * ctx, const struct ggml_cgraph * cgraph, int node_idx, std::initializer_list<enum ggml_op> ops) {
     if (!ggml_can_fuse(cgraph, node_idx, ops)) {
         return false;
     }
@@ -12502,6 +12708,61 @@ static bool ggml_vk_can_fuse(const struct ggml_cgraph * cgraph, int node_idx, st
             return false;
         }
     }
+    if (ops.size() == 2 && ops.begin()[0] == GGML_OP_MUL_MAT && ops.begin()[1] == GGML_OP_ADD) {
+        // additional constraints specific to this fusion
+        const ggml_tensor *mul = cgraph->nodes[node_idx];
+        const ggml_tensor *add = cgraph->nodes[node_idx + 1];
+        const ggml_tensor *bias = add->src[0] == mul ? add->src[1] : add->src[0];
+
+        // mat-vec only
+        if (ggml_nrows(mul) != 1) {
+            return false;
+        }
+        // shaders assume the types match
+        if (mul->type != bias->type) {
+            return false;
+        }
+        // shaders reuse the D shape for bias
+        if (!ggml_are_same_shape(mul, bias) ||
+            !ggml_are_same_stride(mul, bias)) {
+            return false;
+        }
+        // unaligned bias isn't handled
+        if (get_misalign_bytes(ctx, bias) != 0) {
+            return false;
+        }
+    }
+    if (ops.size() == 2 && ops.begin()[0] == GGML_OP_MUL_MAT_ID && ops.begin()[1] == GGML_OP_ADD_ID) {
+        // additional constraints specific to this fusion
+        const ggml_tensor *mul = cgraph->nodes[node_idx];
+        const ggml_tensor *add = cgraph->nodes[node_idx + 1];
+        const ggml_tensor *bias = add->src[1];
+
+        if (mul != add->src[0]) {
+            return false;
+        }
+        // mat-vec only
+        if (!ggml_vk_use_mul_mat_vec_id(cgraph, node_idx)) {
+            return false;
+        }
+        // shaders assume the types match
+        if (mul->type != bias->type) {
+            return false;
+        }
+        // shaders assume the bias is contiguous
+        if (!ggml_is_contiguous(bias)) {
+            return false;
+        }
+        // the ID tensor must be the same for mul_mat_id and add_id
+        if (mul->src[2] != add->src[2]) {
+            return false;
+        }
+        // unaligned bias isn't handled
+        if (get_misalign_bytes(ctx, bias) != 0) {
+            return false;
+        }
+    }
+
     return true;
 }
 
@@ -12670,7 +12931,11 @@ static ggml_status ggml_backend_vk_graph_compute(ggml_backend_t backend, ggml_cg
             uint32_t num_adds = ggml_vk_fuse_multi_add(ctx, cgraph, i);
             if (num_adds) {
                 ctx->num_additional_fused_ops = num_adds - 1;
-            } else if (ggml_vk_can_fuse(cgraph, i, { GGML_OP_RMS_NORM, GGML_OP_MUL })) {
+            } else if (ggml_vk_can_fuse(ctx, cgraph, i, { GGML_OP_RMS_NORM, GGML_OP_MUL })) {
+                ctx->num_additional_fused_ops = 1;
+            } else if (ggml_vk_can_fuse(ctx, cgraph, i, { GGML_OP_MUL_MAT, GGML_OP_ADD })) {
+                ctx->num_additional_fused_ops = 1;
+            } else if (ggml_vk_can_fuse(ctx, cgraph, i, { GGML_OP_MUL_MAT_ID, GGML_OP_ADD_ID })) {
                 ctx->num_additional_fused_ops = 1;
             } else if (ggml_can_fuse_subgraph(cgraph, i, { GGML_OP_ROPE, GGML_OP_VIEW, GGML_OP_SET_ROWS }, { i + 2 }) &&
                        ggml_check_edges(cgraph, i, rope_view_set_rows_edges) &&
@@ -12783,7 +13048,11 @@ static ggml_status ggml_backend_vk_graph_compute(ggml_backend_t backend, ggml_cg
             uint32_t num_adds = ggml_vk_fuse_multi_add(ctx, cgraph, i);
             if (num_adds) {
                 ctx->num_additional_fused_ops = num_adds - 1;
-            } else if (ggml_vk_can_fuse(cgraph, i, { GGML_OP_RMS_NORM, GGML_OP_MUL })) {
+            } else if (ggml_vk_can_fuse(ctx, cgraph, i, { GGML_OP_RMS_NORM, GGML_OP_MUL })) {
+                ctx->num_additional_fused_ops = 1;
+            } else if (ggml_vk_can_fuse(ctx, cgraph, i, { GGML_OP_MUL_MAT, GGML_OP_ADD })) {
+                ctx->num_additional_fused_ops = 1;
+            } else if (ggml_vk_can_fuse(ctx, cgraph, i, { GGML_OP_MUL_MAT_ID, GGML_OP_ADD_ID })) {
                 ctx->num_additional_fused_ops = 1;
             } else if (ggml_can_fuse_subgraph(cgraph, i, { GGML_OP_ROPE, GGML_OP_VIEW, GGML_OP_SET_ROWS }, { i + 2 }) &&
                        ggml_check_edges(cgraph, i, rope_view_set_rows_edges) &&
@@ -13005,7 +13274,9 @@ static void ggml_vk_graph_optimize(ggml_backend_t backend, struct ggml_cgraph *
             for (int c = first_unused; c < j; ++c) {
                 if (!used[c] &&
                     is_src_of(graph->nodes[j], graph->nodes[c]) &&
-                    !(j == c+1 && c == current_set.back() && graph->nodes[c]->op == GGML_OP_RMS_NORM && graph->nodes[j]->op == GGML_OP_MUL)) {
+                    !(j == c+1 && c == current_set.back() && graph->nodes[c]->op == GGML_OP_RMS_NORM && graph->nodes[j]->op == GGML_OP_MUL) &&
+                    !(j == c+1 && c == current_set.back() && graph->nodes[c]->op == GGML_OP_MUL_MAT && graph->nodes[j]->op == GGML_OP_ADD) &&
+                    !(j == c+1 && c == current_set.back() && graph->nodes[c]->op == GGML_OP_MUL_MAT_ID && graph->nodes[j]->op == GGML_OP_ADD_ID)) {
                     ok = false;
                     break;
                 }
diff --git a/ggml/src/ggml-vulkan/vulkan-shaders/mul_mat_vec_base.glsl b/ggml/src/ggml-vulkan/vulkan-shaders/mul_mat_vec_base.glsl
index 450dee04087..bbb4d1206b7 100644
--- a/ggml/src/ggml-vulkan/vulkan-shaders/mul_mat_vec_base.glsl
+++ b/ggml/src/ggml-vulkan/vulkan-shaders/mul_mat_vec_base.glsl
@@ -28,8 +28,11 @@ layout (binding = 1) readonly buffer BV4 {B_TYPE_VEC4 data_b_v4[];};
 #endif
 
 layout (binding = 2) writeonly buffer D {D_TYPE data_d[];};
+
+layout (binding = 3) readonly buffer Bias {D_TYPE data_bias[];};
+
 #ifdef MUL_MAT_ID
-layout (binding = 3) readonly buffer IDS {int data_ids[];};
+layout (binding = 4) readonly buffer IDS {int data_ids[];};
 #endif
 
 #include "dequant_funcs.glsl"
@@ -45,6 +48,8 @@ layout (push_constant) uniform parameter
     uint batch_stride_b;
     uint batch_stride_d;
 
+    uint enable_bias;
+
 #ifdef MUL_MAT_ID
     uint nei0;
     uint ne11;
@@ -56,6 +61,10 @@ layout (push_constant) uniform parameter
 #endif
 } p;
 
+#ifdef MUL_MAT_ID
+uint expert_id;
+#endif
+
 void get_offsets(out uint a_offset, out uint b_offset, out uint d_offset) {
 #ifdef MUL_MAT_ID
     const uint expert_idx = gl_GlobalInvocationID.y;
@@ -75,7 +84,7 @@ void get_offsets(out uint a_offset, out uint b_offset, out uint d_offset) {
         batch_idx_a = i03 * p.ne02 + i02;
     }
 #else
-    const uint expert_id = data_ids[expert_idx];
+    expert_id = data_ids[expert_idx];
 #endif
 
     a_offset =
@@ -113,6 +122,13 @@ void reduce_result(inout FLOAT_TYPE temp[NUM_COLS][NUM_ROWS], const in uint32_t
     if (tid == 0) {
         [[unroll]] for (uint j = 0; j < NUM_COLS; ++j) {
             [[unroll]] for (uint n = 0; n < num_rows; ++n) {
+                if (p.enable_bias != 0) {
+#ifdef MUL_MAT_ID
+                    temp[j][n] += FLOAT_TYPE(data_bias[expert_id*p.stride_d + first_row + n]);
+#else
+                    temp[j][n] += FLOAT_TYPE(data_bias[j*p.batch_stride_d + d_offset + first_row + n]);
+#endif
+                }
                 data_d[j*p.batch_stride_d + d_offset + first_row + n] = D_TYPE(temp[j][n]);
             }
         }
@@ -148,6 +164,13 @@ void reduce_result(FLOAT_TYPE temp[NUM_COLS][NUM_ROWS], const in uint32_t d_offs
                 [[unroll]] for (uint s = 0; s < gl_NumSubgroups; ++s) {
                     temp[j][n] += tmpsh[j][n][s];
                 }
+                if (p.enable_bias != 0) {
+#ifdef MUL_MAT_ID
+                    temp[j][n] += FLOAT_TYPE(data_bias[expert_id*p.stride_d + first_row + n]);
+#else
+                    temp[j][n] += FLOAT_TYPE(data_bias[j*p.batch_stride_d + d_offset + first_row + n]);
+#endif
+                }
                 data_d[j*p.batch_stride_d + d_offset + first_row + n] = D_TYPE(temp[j][n]);
             }
         }
@@ -173,6 +196,13 @@ void reduce_result(FLOAT_TYPE temp[NUM_COLS][NUM_ROWS], const in uint32_t d_offs
     if (tid == 0) {
         [[unroll]] for (uint j = 0; j < NUM_COLS; ++j) {
             [[unroll]] for (uint n = 0; n < num_rows; ++n) {
+                if (p.enable_bias != 0) {
+#ifdef MUL_MAT_ID
+                    tmpsh[j][n][0] += FLOAT_TYPE(data_bias[expert_id*p.stride_d + first_row + n]);
+#else
+                    tmpsh[j][n][0] += FLOAT_TYPE(data_bias[j*p.batch_stride_d + d_offset + first_row + n]);
+#endif
+                }
                 data_d[j*p.batch_stride_d + d_offset + first_row + n] = D_TYPE(tmpsh[j][n][0]);
             }
         }
diff --git a/ggml/src/ggml-vulkan/vulkan-shaders/mul_mat_vec_nc.comp b/ggml/src/ggml-vulkan/vulkan-shaders/mul_mat_vec_nc.comp
index 638878d94ce..3f4584c984c 100644
--- a/ggml/src/ggml-vulkan/vulkan-shaders/mul_mat_vec_nc.comp
+++ b/ggml/src/ggml-vulkan/vulkan-shaders/mul_mat_vec_nc.comp
@@ -15,6 +15,8 @@ layout (binding = 2) writeonly buffer D {D_TYPE dst[];};
 layout (binding = 0) readonly buffer AV4 {A_TYPE_VEC4 data_a_v4[];};
 layout (binding = 1) readonly buffer BV4 {B_TYPE_VEC4 data_b_v4[];};
 
+layout (binding = 3) readonly buffer Bias {D_TYPE data_bias[];};
+
 layout (push_constant) uniform parameter
 {
     uint ncols_x;
@@ -29,6 +31,7 @@ layout (push_constant) uniform parameter
     uint nb03;
     uint nb13;
     uint nb23;
+    uint enable_bias;
 } p;
 
 shared FLOAT_TYPE tmp[BLOCK_SIZE];
@@ -117,6 +120,9 @@ void main() {
     }
 
     if (tid == 0) {
+        if (p.enable_bias != 0) {
+            tmp[0] += FLOAT_TYPE(data_bias[idst]);
+        }
         dst[idst] = tmp[0];
     }
 }
diff --git a/ggml/src/ggml-vulkan/vulkan-shaders/mul_mat_vec_p021.comp b/ggml/src/ggml-vulkan/vulkan-shaders/mul_mat_vec_p021.comp
index 7aa070eebdf..d51424d4175 100644
--- a/ggml/src/ggml-vulkan/vulkan-shaders/mul_mat_vec_p021.comp
+++ b/ggml/src/ggml-vulkan/vulkan-shaders/mul_mat_vec_p021.comp
@@ -17,6 +17,8 @@ layout (binding = 2) writeonly buffer D {D_TYPE dst[];};
 layout (binding = 0) readonly buffer AV4 {A_TYPE_VEC4 data_a_v4[];};
 layout (binding = 1) readonly buffer BV4 {B_TYPE_VEC4 data_b_v4[];};
 
+layout (binding = 3) readonly buffer Bias {D_TYPE data_bias[];};
+
 layout(constant_id = 0) const int BLOCK_SIZE = 32;
 // gqa_ratio is in the range [1,8]
 layout(constant_id = 1) const uint gqa_ratio = 1;
@@ -29,6 +31,7 @@ layout (push_constant) uniform parameter
     uint nchannels_y;
     uint b_offset;
     uint d_offset;
+    uint enable_bias;
 } p;
 
 #if !USE_SUBGROUP_ADD
@@ -148,6 +151,9 @@ void main() {
         [[unroll]] for (uint c = 0; c < gqa_ratio; ++c) {
             // dst is not transposed and not permuted
             const uint idst = (channel + c)*nrows_dst + row_dst;
+            if (p.enable_bias != 0) {
+                temp[c] += FLOAT_TYPE(data_bias[idst]);
+            }
             dst[idst] = temp[c];
         }
     }

From 5d8bb900bc7daa84bfa7bb1d25ab7e32394919f3 Mon Sep 17 00:00:00 2001
From: Jeff Bolz <jbolz@nvidia.com>
Date: Sat, 1 Nov 2025 00:52:14 -0500
Subject: [PATCH 044/185] vulkan: Fix multi_add invalid descriptor usage
 (#16899)

---
 ggml/src/ggml-vulkan/ggml-vulkan.cpp          |   2 -
 .../ggml-vulkan/vulkan-shaders/multi_add.comp | 104 ++++++++++++++++--
 2 files changed, 94 insertions(+), 12 deletions(-)

diff --git a/ggml/src/ggml-vulkan/ggml-vulkan.cpp b/ggml/src/ggml-vulkan/ggml-vulkan.cpp
index 6a46d0889bd..8d1a85c9693 100644
--- a/ggml/src/ggml-vulkan/ggml-vulkan.cpp
+++ b/ggml/src/ggml-vulkan/ggml-vulkan.cpp
@@ -4274,8 +4274,6 @@ static vk_device ggml_vk_get_device(size_t idx) {
 
         device->multi_add = vk12_props.shaderRoundingModeRTEFloat16 &&
                             device->properties.limits.maxPushConstantsSize >= sizeof(vk_op_multi_add_push_constants) &&
-                            vk12_features.runtimeDescriptorArray &&
-                            device->vendor_id != VK_VENDOR_ID_INTEL &&
                             getenv("GGML_VK_DISABLE_MULTI_ADD") == nullptr;
 
         device->shader_int64 = device_features2.features.shaderInt64;
diff --git a/ggml/src/ggml-vulkan/vulkan-shaders/multi_add.comp b/ggml/src/ggml-vulkan/vulkan-shaders/multi_add.comp
index 1e8f694a724..10cf5202a4a 100644
--- a/ggml/src/ggml-vulkan/vulkan-shaders/multi_add.comp
+++ b/ggml/src/ggml-vulkan/vulkan-shaders/multi_add.comp
@@ -23,16 +23,100 @@ layout (push_constant) uniform parameter2
     uint rms_partials;
 } p;
 
-// Workaround for MoltenVK Bug, see https://github.com/ggml-org/llama.cpp/issues/15498
-// layout (binding = 0) readonly buffer A {A_TYPE data_a[];} a[];
-// layout (binding = 0) writeonly buffer D {D_TYPE data_d[];} d[];
-layout (binding = 0) buffer A {A_TYPE data_a[];} a[];
-layout (binding = 0) buffer D {D_TYPE data_d[];} d[];
-
-layout (binding = 0, std430) buffer PartialBuf {float partial_sums[];} partials[];
+// No readonly/writeonly decorations. Workaround for MoltenVK Bug, see https://github.com/ggml-org/llama.cpp/issues/15498
+layout (binding = 0)  buffer A0 {A_TYPE data_a[];} a0;
+layout (binding = 1)  buffer A1 {A_TYPE data_a[];} a1;
+layout (binding = 2)  buffer A2 {A_TYPE data_a[];} a2;
+layout (binding = 3)  buffer A3 {A_TYPE data_a[];} a3;
+layout (binding = 4)  buffer A4 {A_TYPE data_a[];} a4;
+layout (binding = 5)  buffer A5 {A_TYPE data_a[];} a5;
+layout (binding = 6)  buffer A6 {A_TYPE data_a[];} a6;
+layout (binding = 7)  buffer A7 {A_TYPE data_a[];} a7;
+layout (binding = 8)  buffer A8 {A_TYPE data_a[];} a8;
+layout (binding = 9)  buffer A9 {A_TYPE data_a[];} a9;
+layout (binding = 10) buffer A10 {A_TYPE data_a[];} a10;
+layout (binding = 11) buffer A11 {A_TYPE data_a[];} a11;
+layout (binding = 0)  buffer D0 {D_TYPE data_d[];} d0;
+layout (binding = 1)  buffer D1 {D_TYPE data_d[];} d1;
+layout (binding = 2)  buffer D2 {D_TYPE data_d[];} d2;
+layout (binding = 3)  buffer D3 {D_TYPE data_d[];} d3;
+layout (binding = 4)  buffer D4 {D_TYPE data_d[];} d4;
+layout (binding = 5)  buffer D5 {D_TYPE data_d[];} d5;
+layout (binding = 6)  buffer D6 {D_TYPE data_d[];} d6;
+layout (binding = 7)  buffer D7 {D_TYPE data_d[];} d7;
+layout (binding = 8)  buffer D8 {D_TYPE data_d[];} d8;
+layout (binding = 9)  buffer D9 {D_TYPE data_d[];} d9;
+layout (binding = 10) buffer D10 {D_TYPE data_d[];} d10;
+layout (binding = 11) buffer D11 {D_TYPE data_d[];} d11;
+layout (binding = 0, std430)  buffer PartialBuf0 {float partial_sums[];} partials0;
+layout (binding = 1, std430)  buffer PartialBuf1 {float partial_sums[];} partials1;
+layout (binding = 2, std430)  buffer PartialBuf2 {float partial_sums[];} partials2;
+layout (binding = 3, std430)  buffer PartialBuf3 {float partial_sums[];} partials3;
+layout (binding = 4, std430)  buffer PartialBuf4 {float partial_sums[];} partials4;
+layout (binding = 5, std430)  buffer PartialBuf5 {float partial_sums[];} partials5;
+layout (binding = 6, std430)  buffer PartialBuf6 {float partial_sums[];} partials6;
+layout (binding = 7, std430)  buffer PartialBuf7 {float partial_sums[];} partials7;
+layout (binding = 8, std430)  buffer PartialBuf8 {float partial_sums[];} partials8;
+layout (binding = 9, std430)  buffer PartialBuf9 {float partial_sums[];} partials9;
+layout (binding = 10, std430) buffer PartialBuf10 {float partial_sums[];} partials10;
+layout (binding = 11, std430) buffer PartialBuf11 {float partial_sums[];} partials11;
 
 layout(constant_id = 0) const uint num_srcs = 2;
 
+FLOAT_TYPE load_a(uint b, uint i) {
+    switch (b) {
+    case 0:  return FLOAT_TYPE(a0.data_a[i]);
+    case 1:  return FLOAT_TYPE(a1.data_a[i]);
+    case 2:  return FLOAT_TYPE(a2.data_a[i]);
+    case 3:  return FLOAT_TYPE(a3.data_a[i]);
+    case 4:  return FLOAT_TYPE(a4.data_a[i]);
+    case 5:  return FLOAT_TYPE(a5.data_a[i]);
+    case 6:  return FLOAT_TYPE(a6.data_a[i]);
+    case 7:  return FLOAT_TYPE(a7.data_a[i]);
+    case 8:  return FLOAT_TYPE(a8.data_a[i]);
+    case 9:  return FLOAT_TYPE(a9.data_a[i]);
+    case 10: return FLOAT_TYPE(a10.data_a[i]);
+    case 11: return FLOAT_TYPE(a11.data_a[i]);
+    default: return FLOAT_TYPE(0);
+    }
+}
+
+void store_d(uint b, uint i, FLOAT_TYPE v) {
+    switch (b) {
+    case 0:  d0.data_d[i] = D_TYPE(v); break;
+    case 1:  d1.data_d[i] = D_TYPE(v); break;
+    case 2:  d2.data_d[i] = D_TYPE(v); break;
+    case 3:  d3.data_d[i] = D_TYPE(v); break;
+    case 4:  d4.data_d[i] = D_TYPE(v); break;
+    case 5:  d5.data_d[i] = D_TYPE(v); break;
+    case 6:  d6.data_d[i] = D_TYPE(v); break;
+    case 7:  d7.data_d[i] = D_TYPE(v); break;
+    case 8:  d8.data_d[i] = D_TYPE(v); break;
+    case 9:  d9.data_d[i] = D_TYPE(v); break;
+    case 10: d10.data_d[i] = D_TYPE(v); break;
+    case 11: d11.data_d[i] = D_TYPE(v); break;
+    default: break;
+    }
+}
+
+void store_partial(uint b, uint i, float v) {
+    switch (b) {
+    case 0:  partials0.partial_sums[i] = v; break;
+    case 1:  partials1.partial_sums[i] = v; break;
+    case 2:  partials2.partial_sums[i] = v; break;
+    case 3:  partials3.partial_sums[i] = v; break;
+    case 4:  partials4.partial_sums[i] = v; break;
+    case 5:  partials5.partial_sums[i] = v; break;
+    case 6:  partials6.partial_sums[i] = v; break;
+    case 7:  partials7.partial_sums[i] = v; break;
+    case 8:  partials8.partial_sums[i] = v; break;
+    case 9:  partials9.partial_sums[i] = v; break;
+    case 10: partials10.partial_sums[i] = v; break;
+    case 11: partials11.partial_sums[i] = v; break;
+    default: break;
+    }
+}
+
 uint src_idx(uint s, uint i00, uint i01, uint i02, uint i03) {
     return i03*p.nb[s][3] + i02*p.nb[s][2] + i01*p.nb[s][1] + i00*p.nb[s][0];
 }
@@ -78,10 +162,10 @@ void main() {
 
         FLOAT_TYPE sum = FLOAT_TYPE(0);
         [[unroll]] for (uint s = 0; s < num_srcs; ++s) {
-            sum += FLOAT_TYPE(a[s].data_a[src_idx(s, i00, i01, i02, i03)]);
+            sum += load_a(s, src_idx(s, i00, i01, i02, i03));
         }
         sum_sq += sum*sum;
-        d[num_srcs].data_d[dst_idx(i00, i01, i02, i03)] = D_TYPE(sum);
+        store_d(num_srcs, dst_idx(i00, i01, i02, i03), sum);
 
         idx += num_threads;
     }
@@ -104,7 +188,7 @@ void main() {
         }
 
         if (gl_SubgroupID == 0 && gl_SubgroupInvocationID == 0) {
-            partials[num_srcs + 1].partial_sums[orig_idx / (num_iter * num_threads)] = sum_sq;
+            store_partial(num_srcs + 1, orig_idx / (num_iter * num_threads), sum_sq);
         }
     }
 #endif

From 74fef4129fa58f6277c243777a4894371479dbad Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sigbj=C3=B8rn=20Skj=C3=A6ret?= <sigbjorn.skjaeret@scala.com>
Date: Sat, 1 Nov 2025 08:55:25 +0100
Subject: [PATCH 045/185] codeowners : update after refactor (#16905)

---
 CODEOWNERS | 1 +
 1 file changed, 1 insertion(+)

diff --git a/CODEOWNERS b/CODEOWNERS
index bacc86cbbd6..908d13a35b9 100644
--- a/CODEOWNERS
+++ b/CODEOWNERS
@@ -89,6 +89,7 @@
 /src/llama-model-loader.*               @slaren
 /src/llama-model.*                      @CISC
 /src/llama-vocab.*                      @CISC
+/src/models/                            @CISC
 /tests/                                 @ggerganov
 /tests/test-backend-ops.cpp             @slaren
 /tests/test-thread-safety.cpp           @slaren

From 961660b8c395afb8903f61ace69396a158ea0cb4 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sigbj=C3=B8rn=20Skj=C3=A6ret?= <sigbjorn.skjaeret@scala.com>
Date: Sat, 1 Nov 2025 11:01:42 +0100
Subject: [PATCH 046/185] common : allow --system-prompt-file for diffusion-cli
 (#16903)

---
 common/arg.cpp | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/common/arg.cpp b/common/arg.cpp
index e8941cda41c..d8f9bbd2430 100644
--- a/common/arg.cpp
+++ b/common/arg.cpp
@@ -2030,7 +2030,7 @@ common_params_context common_params_parser_init(common_params & params, llama_ex
                 params.system_prompt.pop_back();
             }
         }
-    ).set_examples({LLAMA_EXAMPLE_MAIN}));
+    ).set_examples({LLAMA_EXAMPLE_MAIN, LLAMA_EXAMPLE_DIFFUSION}));
     add_opt(common_arg(
         {"--in-file"}, "FNAME",
         "an input file (repeat to specify multiple files)",

From 1ae74882f8f6755e44dff8f23f3abdc5b53ab7c1 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Jarom=C3=ADr=20Hrad=C3=ADlek?= <jhradilek@gmail.com>
Date: Sat, 1 Nov 2025 15:02:57 +0100
Subject: [PATCH 047/185] webui: recognize AsciiDoc files as valid text files
 (#16850)

* webui: recognize AsciiDoc files as valid text files

* webui: add an updated static webui build

* webui: add the updated dependency list

* webui: re-add an updated static webui build

This also reverts commit 742dbb837939c176a813868c268d28ebd3fafb7c.
---
 tools/server/public/index.html.gz             | Bin 859993 -> 860046 bytes
 .../src/lib/constants/supported-file-types.ts |   4 ++++
 tools/server/webui/src/lib/enums/files.ts     |   3 +++
 3 files changed, 7 insertions(+)

diff --git a/tools/server/public/index.html.gz b/tools/server/public/index.html.gz
index 026b53b28632fb82031333a4ef411444cdabddb2..29579e08c251298048f842eafac774166f23d516 100644
GIT binary patch
delta 794871
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diff --git a/tools/server/webui/src/lib/constants/supported-file-types.ts b/tools/server/webui/src/lib/constants/supported-file-types.ts
index f6c5d2dc18f..1258c3a059c 100644
--- a/tools/server/webui/src/lib/constants/supported-file-types.ts
+++ b/tools/server/webui/src/lib/constants/supported-file-types.ts
@@ -69,6 +69,10 @@ export const TEXT_FILE_TYPES = {
 		extensions: [FileExtensionText.MD],
 		mimeTypes: [MimeTypeText.MARKDOWN]
 	},
+	[FileTypeText.ASCIIDOC]: {
+		extensions: [FileExtensionText.ADOC],
+		mimeTypes: [MimeTypeText.ASCIIDOC]
+	},
 	[FileTypeText.JAVASCRIPT]: {
 		extensions: [FileExtensionText.JS],
 		mimeTypes: [MimeTypeText.JAVASCRIPT, MimeTypeText.JAVASCRIPT_APP]
diff --git a/tools/server/webui/src/lib/enums/files.ts b/tools/server/webui/src/lib/enums/files.ts
index 19b79d32de3..3f725da2273 100644
--- a/tools/server/webui/src/lib/enums/files.ts
+++ b/tools/server/webui/src/lib/enums/files.ts
@@ -33,6 +33,7 @@ export enum FileTypePdf {
 export enum FileTypeText {
 	PLAIN_TEXT = 'plainText',
 	MARKDOWN = 'markdown',
+	ASCIIDOC = 'asciidoc',
 	JAVASCRIPT = 'javascript',
 	TYPESCRIPT = 'typescript',
 	JSX = 'jsx',
@@ -86,6 +87,7 @@ export enum FileExtensionPdf {
 export enum FileExtensionText {
 	TXT = '.txt',
 	MD = '.md',
+	ADOC = '.adoc',
 	JS = '.js',
 	TS = '.ts',
 	JSX = '.jsx',
@@ -147,6 +149,7 @@ export enum MimeTypeImage {
 export enum MimeTypeText {
 	PLAIN = 'text/plain',
 	MARKDOWN = 'text/markdown',
+	ASCIIDOC = 'text/asciidoc',
 	JAVASCRIPT = 'text/javascript',
 	JAVASCRIPT_APP = 'application/javascript',
 	TYPESCRIPT = 'text/typescript',

From d8b860a219c2415faac8cc0e50b48b4aa11e3b64 Mon Sep 17 00:00:00 2001
From: Aleksander Grygier <aleksander.grygier@gmail.com>
Date: Sat, 1 Nov 2025 15:35:57 +0100
Subject: [PATCH 048/185] Add a setting to display message generation
 statistics (#16901)

* feat: Add setting to display message generation statistics

* chore: build static webui output
---
 tools/server/public/index.html.gz             | Bin 860046 -> 861835 bytes
 .../ChatMessages/ChatMessageAssistant.svelte  |  73 ++++++++++++++----
 .../ChatSettings/ChatSettingsDialog.svelte    |   5 ++
 .../src/lib/constants/settings-config.ts      |   3 +
 4 files changed, 67 insertions(+), 14 deletions(-)

diff --git a/tools/server/public/index.html.gz b/tools/server/public/index.html.gz
index 29579e08c251298048f842eafac774166f23d516..a81bae04d1983d992a4b46da93153d1cfa63c704 100644
GIT binary patch
delta 856927
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diff --git a/tools/server/webui/src/lib/components/app/chat/ChatMessages/ChatMessageAssistant.svelte b/tools/server/webui/src/lib/components/app/chat/ChatMessages/ChatMessageAssistant.svelte
index e878e7bf8a2..41774c6f874 100644
--- a/tools/server/webui/src/lib/components/app/chat/ChatMessages/ChatMessageAssistant.svelte
+++ b/tools/server/webui/src/lib/components/app/chat/ChatMessages/ChatMessageAssistant.svelte
@@ -3,7 +3,16 @@
 	import { useProcessingState } from '$lib/hooks/use-processing-state.svelte';
 	import { isLoading } from '$lib/stores/chat.svelte';
 	import { fade } from 'svelte/transition';
-	import { Check, Copy, Package, X } from '@lucide/svelte';
+	import {
+		Check,
+		Copy,
+		Package,
+		X,
+		Gauge,
+		Clock,
+		WholeWord,
+		ChartNoAxesColumn
+	} from '@lucide/svelte';
 	import { Button } from '$lib/components/ui/button';
 	import { Checkbox } from '$lib/components/ui/checkbox';
 	import { INPUT_CLASSES } from '$lib/constants/input-classes';
@@ -160,22 +169,58 @@
 		</div>
 	{/if}
 
-	{#if displayedModel()}
-		<span class="mt-6 mb-4 inline-flex items-center gap-1 text-xs text-muted-foreground">
-			<Package class="h-3.5 w-3.5" />
+	<div class="info my-6 grid gap-4">
+		{#if displayedModel()}
+			<span class="inline-flex items-center gap-2 text-xs text-muted-foreground">
+				<span class="inline-flex items-center gap-1">
+					<Package class="h-3.5 w-3.5" />
 
-			<span>Model used:</span>
+					<span>Model used:</span>
+				</span>
 
-			<button
-				class="inline-flex cursor-pointer items-center gap-1 rounded-sm bg-muted-foreground/15 px-1.5 py-0.75"
-				onclick={handleCopyModel}
-			>
-				{displayedModel()}
+				<button
+					class="inline-flex cursor-pointer items-center gap-1 rounded-sm bg-muted-foreground/15 px-1.5 py-0.75"
+					onclick={handleCopyModel}
+				>
+					{displayedModel()}
 
-				<Copy class="ml-1 h-3 w-3 " />
-			</button>
-		</span>
-	{/if}
+					<Copy class="ml-1 h-3 w-3 " />
+				</button>
+			</span>
+		{/if}
+
+		{#if currentConfig.showMessageStats && message.timings && message.timings.predicted_n && message.timings.predicted_ms}
+			{@const tokensPerSecond = (message.timings.predicted_n / message.timings.predicted_ms) * 1000}
+			<span class="inline-flex items-center gap-2 text-xs text-muted-foreground">
+				<span class="inline-flex items-center gap-1">
+					<ChartNoAxesColumn class="h-3.5 w-3.5" />
+
+					<span>Statistics:</span>
+				</span>
+
+				<div class="inline-flex flex-wrap items-center gap-2 text-xs text-muted-foreground">
+					<span
+						class="inline-flex items-center gap-1 rounded-sm bg-muted-foreground/15 px-1.5 py-0.75"
+					>
+						<Gauge class="h-3 w-3" />
+						{tokensPerSecond.toFixed(2)} tokens/s
+					</span>
+					<span
+						class="inline-flex items-center gap-1 rounded-sm bg-muted-foreground/15 px-1.5 py-0.75"
+					>
+						<WholeWord class="h-3 w-3" />
+						{message.timings.predicted_n} tokens
+					</span>
+					<span
+						class="inline-flex items-center gap-1 rounded-sm bg-muted-foreground/15 px-1.5 py-0.75"
+					>
+						<Clock class="h-3 w-3" />
+						{(message.timings.predicted_ms / 1000).toFixed(2)}s
+					</span>
+				</div>
+			</span>
+		{/if}
+	</div>
 
 	{#if message.timestamp && !isEditing}
 		<ChatMessageActions
diff --git a/tools/server/webui/src/lib/components/app/chat/ChatSettings/ChatSettingsDialog.svelte b/tools/server/webui/src/lib/components/app/chat/ChatSettings/ChatSettingsDialog.svelte
index 20e4d3b3324..e4672b787ee 100644
--- a/tools/server/webui/src/lib/components/app/chat/ChatSettings/ChatSettingsDialog.svelte
+++ b/tools/server/webui/src/lib/components/app/chat/ChatSettings/ChatSettingsDialog.svelte
@@ -52,6 +52,11 @@
 						{ value: 'dark', label: 'Dark', icon: Moon }
 					]
 				},
+				{
+					key: 'showMessageStats',
+					label: 'Show message generation statistics',
+					type: 'checkbox'
+				},
 				{
 					key: 'showTokensPerSecond',
 					label: 'Show tokens per second',
diff --git a/tools/server/webui/src/lib/constants/settings-config.ts b/tools/server/webui/src/lib/constants/settings-config.ts
index 512dcc96997..c25f380846c 100644
--- a/tools/server/webui/src/lib/constants/settings-config.ts
+++ b/tools/server/webui/src/lib/constants/settings-config.ts
@@ -8,6 +8,7 @@ export const SETTING_CONFIG_DEFAULT: Record<string, string | number | boolean> =
 	showThoughtInProgress: false,
 	disableReasoningFormat: false,
 	keepStatsVisible: false,
+	showMessageStats: true,
 	askForTitleConfirmation: false,
 	pasteLongTextToFileLen: 2500,
 	pdfAsImage: false,
@@ -82,6 +83,8 @@ export const SETTING_CONFIG_INFO: Record<string, string> = {
 	disableReasoningFormat:
 		'Show raw LLM output without backend parsing and frontend Markdown rendering to inspect streaming across different models.',
 	keepStatsVisible: 'Keep processing statistics visible after generation finishes.',
+	showMessageStats:
+		'Display generation statistics (tokens/second, token count, duration) below each assistant message.',
 	askForTitleConfirmation:
 		'Ask for confirmation before automatically changing conversation title when editing the first message.',
 	pdfAsImage: 'Parse PDF as image instead of text (requires vision-capable model).',

From cf659bbb8ef9eb048e5153a27cf787fd83c05560 Mon Sep 17 00:00:00 2001
From: Xuan-Son Nguyen <son@huggingface.co>
Date: Sat, 1 Nov 2025 15:51:36 +0100
Subject: [PATCH 049/185] mtmd: refactor preprocessing + support max/min pixels
 (#16878)

* mtmd: refactor preprocessing + support max/min pixels

* fix mlp type

* implement mix/max pixels

* improve hparams

* better image preproc for qwen

* fix

* fix out of bound composite

* fix (2)

* fix token calculation

* get_merge_kernel_size()

* fix llama4 and lfm2

* gonna fix them all

* use simple resize for qwen

* qwen: increase min tokens

* no resize if dst size == src size

* restore to initial min/max tokens value for qwen
---
 tools/mtmd/clip-impl.h |   2 +-
 tools/mtmd/clip.cpp    | 760 +++++++++++++++++++++++------------------
 2 files changed, 431 insertions(+), 331 deletions(-)

diff --git a/tools/mtmd/clip-impl.h b/tools/mtmd/clip-impl.h
index 311a4c9086a..c7e9498349c 100644
--- a/tools/mtmd/clip-impl.h
+++ b/tools/mtmd/clip-impl.h
@@ -154,8 +154,8 @@ enum projector_type {
     PROJECTOR_TYPE_LFM2,
     PROJECTOR_TYPE_KIMIVL,
     PROJECTOR_TYPE_LIGHTONOCR,
-    PROJECTOR_TYPE_UNKNOWN,
     PROJECTOR_TYPE_COGVLM,
+    PROJECTOR_TYPE_UNKNOWN,
 };
 
 static std::map<projector_type, std::string> PROJECTOR_TYPE_NAMES = {
diff --git a/tools/mtmd/clip.cpp b/tools/mtmd/clip.cpp
index b312fda637f..dcfdb49600b 100644
--- a/tools/mtmd/clip.cpp
+++ b/tools/mtmd/clip.cpp
@@ -171,8 +171,10 @@ struct clip_hparams {
     int32_t n_head;
     int32_t n_layer;
     // idefics3
-    int32_t preproc_image_size = 0; // aka max_dimension
-    int32_t proj_scale_factor = 0;
+    int32_t image_longest_edge = 0;
+    int32_t image_min_pixels = 0;
+    int32_t image_max_pixels = 0;
+    int32_t n_merge = 0; // number of patch merges **per-side**
 
     float image_mean[3];
     float image_std[3];
@@ -194,7 +196,6 @@ struct clip_hparams {
     std::unordered_set<int32_t> vision_feature_layer;
     int32_t attn_window_size = 0;
     int32_t n_wa_pattern = 0;
-    int32_t spatial_merge_size = 0;
 
     // audio
     int32_t n_mel_bins = 0; // whisper preprocessor
@@ -204,6 +205,21 @@ struct clip_hparams {
     bool has_llava_projector = false;
     int minicpmv_version = 0;
     int32_t minicpmv_query_num = 0;         // MiniCPM-V query number
+
+    void set_limit_image_tokens(int n_tokens_min, int n_tokens_max) {
+        const int cur_merge = n_merge == 0 ? 1 : n_merge;
+        const int patch_area = patch_size * patch_size * cur_merge * cur_merge;
+        image_min_pixels = n_tokens_min * patch_area;
+        image_max_pixels = n_tokens_max * patch_area;
+        warmup_image_size = static_cast<int>(std::sqrt(image_max_pixels));
+    }
+
+    void set_warmup_n_tokens(int n_tokens) {
+        int n_tok_per_side = static_cast<int>(std::sqrt(n_tokens));
+        GGML_ASSERT(n_tok_per_side * n_tok_per_side == n_tokens && "n_tokens must be n*n");
+        const int cur_merge = n_merge == 0 ? 1 : n_merge;
+        warmup_image_size = n_tok_per_side * patch_size * cur_merge;
+    }
 };
 
 struct clip_layer {
@@ -532,7 +548,7 @@ struct clip_graph {
             const int batch_size = 1;
             GGML_ASSERT(n_patches_x == n_patches_y);
             const int patches_per_image = n_patches_x;
-            const int kernel_size = hparams.proj_scale_factor;
+            const int kernel_size = hparams.n_merge;
 
             cur = ggml_transpose(ctx0, cur);
             cur = ggml_cont_4d(ctx0, cur, patches_per_image, patches_per_image, n_embd, batch_size);
@@ -554,13 +570,13 @@ struct clip_graph {
         } else if (ctx->proj_type() == PROJECTOR_TYPE_IDEFICS3) {
             // pixel_shuffle
             // https://github.com/huggingface/transformers/blob/0a950e0bbe1ed58d5401a6b547af19f15f0c195e/src/transformers/models/idefics3/modeling_idefics3.py#L578
-            const int scale_factor = model.hparams.proj_scale_factor;
+            const int scale_factor = model.hparams.n_merge;
             cur = build_patch_merge_permute(cur, scale_factor);
             cur = ggml_mul_mat(ctx0, model.projection, cur);
 
         } else if (ctx->proj_type() == PROJECTOR_TYPE_LFM2) {
             // pixel unshuffle block
-            const int scale_factor = model.hparams.proj_scale_factor;
+            const int scale_factor = model.hparams.n_merge;
             cur = build_patch_merge_permute(cur, scale_factor);
 
             // projection
@@ -584,7 +600,7 @@ struct clip_graph {
     }
 
     ggml_cgraph * build_pixtral() {
-        const int n_merge = hparams.spatial_merge_size;
+        const int n_merge = hparams.n_merge;
 
         // 2D input positions
         ggml_tensor * pos_h = ggml_new_tensor_1d(ctx0, GGML_TYPE_I32, n_patches);
@@ -610,7 +626,7 @@ struct clip_graph {
         // mistral small 3.1 patch merger
         // ref: https://github.com/huggingface/transformers/blob/7a3e208892c06a5e278144eaf38c8599a42f53e7/src/transformers/models/mistral3/modeling_mistral3.py#L67
         if (model.mm_patch_merger_w) {
-            GGML_ASSERT(hparams.spatial_merge_size > 0);
+            GGML_ASSERT(hparams.n_merge > 0);
 
             cur = ggml_mul(ctx0, ggml_rms_norm(ctx0, cur, eps), model.mm_input_norm_w);
 
@@ -926,7 +942,7 @@ struct clip_graph {
 
         // deepstack features (stack along the feature dimension), [n_embd * len(deepstack_layers), n_patches_x * n_patches_y, batch_size]
         ggml_tensor * deepstack_features = nullptr;
-        const int merge_factor = hparams.spatial_merge_size > 0 ? hparams.spatial_merge_size * hparams.spatial_merge_size : 4; // default 2x2=4 for qwen3vl
+        const int merge_factor = hparams.n_merge > 0 ? hparams.n_merge * hparams.n_merge : 4; // default 2x2=4 for qwen3vl
 
         // loop over layers
         for (int il = 0; il < n_layer; il++) {
@@ -1149,7 +1165,7 @@ struct clip_graph {
 
         // pixel shuffle
         {
-            const int scale_factor = model.hparams.proj_scale_factor;
+            const int scale_factor = model.hparams.n_merge;
             const int bsz    = 1; // batch size, always 1 for now since we don't support batching
             const int height = n_patches_y;
             const int width  = n_patches_x;
@@ -1239,7 +1255,7 @@ struct clip_graph {
         // based on Llama4VisionPixelShuffleMLP
         // https://github.com/huggingface/transformers/blob/2932f318a20d9e54cc7aea052e040164d85de7d6/src/transformers/models/llama4/modeling_llama4.py#L1151
         {
-            const int scale_factor = model.hparams.proj_scale_factor;
+            const int scale_factor = model.hparams.n_merge;
             const int bsz = 1; // batch size, always 1 for now since we don't support batching
             GGML_ASSERT(scale_factor > 0);
             GGML_ASSERT(n_patches_x == n_patches_y); // llama4 only supports square images
@@ -1311,7 +1327,7 @@ struct clip_graph {
 
         {
             // patch_merger
-            const int scale_factor = model.hparams.proj_scale_factor;
+            const int scale_factor = model.hparams.n_merge;
             cur = build_patch_merge_permute(cur, scale_factor);
 
             // projection norm
@@ -2577,7 +2593,6 @@ struct clip_model_loader {
 
             if (is_vision) {
                 get_u32(KEY_IMAGE_SIZE, hparams.image_size);
-                get_u32(KEY_PREPROC_IMAGE_SIZE, hparams.preproc_image_size, false);
                 get_u32(KEY_PATCH_SIZE, hparams.patch_size);
                 get_u32(KEY_IMAGE_CROP_RESOLUTION, hparams.image_crop_resolution, false);
                 get_i32(KEY_MINICPMV_VERSION, hparams.minicpmv_version, false); // legacy
@@ -2686,65 +2701,68 @@ struct clip_model_loader {
                             hparams.minicpmv_version = 2; // default to 2 if not set
                         }
                     } break;
+                case PROJECTOR_TYPE_INTERNVL:
+                    {
+                        get_u32(KEY_PROJ_SCALE_FACTOR, hparams.n_merge, false);
+                    } break;
                 case PROJECTOR_TYPE_IDEFICS3:
+                    {
+                        get_u32(KEY_PROJ_SCALE_FACTOR, hparams.n_merge, false);
+                        get_u32(KEY_PREPROC_IMAGE_SIZE, hparams.image_longest_edge, false);
+                    } break;
                 case PROJECTOR_TYPE_LFM2:
-                case PROJECTOR_TYPE_INTERNVL:
                     {
-                        get_u32(KEY_PROJ_SCALE_FACTOR, hparams.proj_scale_factor, false);
+                        get_u32(KEY_PROJ_SCALE_FACTOR, hparams.n_merge, false);
+                        // ref: https://huggingface.co/LiquidAI/LFM2-VL-3B/blob/main/preprocessor_config.json
+                        hparams.set_limit_image_tokens(64, 256);
                     } break;
                 case PROJECTOR_TYPE_PIXTRAL:
                 case PROJECTOR_TYPE_LIGHTONOCR:
                     {
+                        // ref: https://huggingface.co/mistral-community/pixtral-12b/blob/main/preprocessor_config.json
+                        // TODO: verify the image_min_tokens
                         hparams.rope_theta = 10000.0f;
-                        hparams.warmup_image_size = hparams.patch_size * 8;
-                        // Mistral Small 2506 needs 1024x1024 image size cap to prevent OOM
-                        // ref: https://github.com/ggml-org/llama.cpp/issues/14310
-                        hparams.image_size = 1024;
-                        get_u32(KEY_SPATIAL_MERGE_SIZE, hparams.spatial_merge_size, false);
+                        get_u32(KEY_SPATIAL_MERGE_SIZE, hparams.n_merge, false);
+                        hparams.set_limit_image_tokens(8, 1024);
+                        hparams.set_warmup_n_tokens(256); // avoid OOM on warmup
                     } break;
                 case PROJECTOR_TYPE_KIMIVL:
                     {
                         hparams.rope_theta = 10000.0f;
-                        hparams.warmup_image_size = hparams.patch_size * 8;
-                        get_u32(KEY_PROJ_SCALE_FACTOR, hparams.proj_scale_factor, false);
+                        get_u32(KEY_PROJ_SCALE_FACTOR, hparams.n_merge, false);
+                        // TODO: check kimivl preprocessor for exact values
+                        hparams.set_limit_image_tokens(8, 1024);
+                        hparams.set_warmup_n_tokens(256); // avoid OOM on warmup
                     } break;
                 case PROJECTOR_TYPE_GEMMA3:
                     {
                         // default value (used by all model sizes in gemma 3 family)
                         // number of patches for each **side** is reduced by a factor of 4
-                        hparams.proj_scale_factor = 4;
+                        hparams.n_merge = 4;
                         // test model (tinygemma3) has a different value, we optionally read it
-                        get_u32(KEY_PROJ_SCALE_FACTOR, hparams.proj_scale_factor, false);
+                        get_u32(KEY_PROJ_SCALE_FACTOR, hparams.n_merge, false);
                     } break;
                 case PROJECTOR_TYPE_QWEN2VL:
-                    {
-                        // max image size = sqrt(max_pixels) = 3584
-                        // ref: https://huggingface.co/Qwen/Qwen2-VL-7B-Instruct/blob/main/preprocessor_config.json
-                        // however, the model use unreasonable memory past 1024 size, we force it to 1024 otherwise it's unusable
-                        // ref: https://huggingface.co/Qwen/Qwen2-VL-2B-Instruct/discussions/10
-                        hparams.image_size = 1024;
-                        hparams.warmup_image_size = hparams.patch_size * 8;
-                    } break;
                 case PROJECTOR_TYPE_QWEN25VL:
-                    {
-                        // max image size = sqrt(max_pixels)
-                        // https://huggingface.co/Qwen/Qwen2.5-VL-7B-Instruct/blob/main/preprocessor_config.json
-                        // however, the model use unreasonable memory past 1024 size, we force it to 1024 otherwise it's unusable
-                        // ref: https://huggingface.co/Qwen/Qwen2-VL-2B-Instruct/discussions/10
-                        hparams.image_size = 1024;
-                        hparams.warmup_image_size = hparams.patch_size * 8;
-                        get_u32(KEY_WIN_ATTN_PATTERN, hparams.n_wa_pattern);
-                    } break;
                 case PROJECTOR_TYPE_QWEN3VL:
                     {
-                        hparams.image_size = 1024; // still need this?
-                        hparams.warmup_image_size = hparams.patch_size * 8;
-                        get_u32(KEY_SPATIAL_MERGE_SIZE, hparams.spatial_merge_size, false);
+                        hparams.n_merge = 2; // default value for Qwen 2 and 2.5
+                        get_u32(KEY_SPATIAL_MERGE_SIZE, hparams.n_merge, false);
+                        get_u32(KEY_WIN_ATTN_PATTERN, hparams.n_wa_pattern, model.proj_type == PROJECTOR_TYPE_QWEN25VL); // only 2.5 requires it
+                        // ref: https://huggingface.co/Qwen/Qwen2.5-VL-7B-Instruct/blob/main/preprocessor_config.json
+                        // the actual max limit is 12845056/14/14/2/2/4 = 4096 tokens
+                        // but we set a lower value to avoid OOM
+                        // TODO: make it configurable by user
+                        // TODO (2): bbox coordinates become inaccurate with small number of tokens,
+                        //           therefore we need to increase the min_tokens
+                        //           see: https://github.com/ggml-org/llama.cpp/issues/16842#issuecomment-3475144858
+                        hparams.set_limit_image_tokens(8, 2048);
+                        hparams.set_warmup_n_tokens(256); // avoid OOM on warmup
                     } break;
                 case PROJECTOR_TYPE_LLAMA4:
                     {
                         hparams.rope_theta = 10000.0f;
-                        get_u32(KEY_PROJ_SCALE_FACTOR, hparams.proj_scale_factor);
+                        get_u32(KEY_PROJ_SCALE_FACTOR, hparams.n_merge, false);
                         set_llava_uhd_res_candidates(model, 3);
                     } break;
                 case PROJECTOR_TYPE_ULTRAVOX:
@@ -2777,10 +2795,13 @@ struct clip_model_loader {
                 LOG_INF("%s: patch_size:         %d\n", __func__, hparams.patch_size);
                 LOG_INF("%s: has_llava_proj:     %d\n", __func__, hparams.has_llava_projector);
                 LOG_INF("%s: minicpmv_version:   %d\n", __func__, hparams.minicpmv_version);
-                LOG_INF("%s: proj_scale_factor:  %d\n", __func__, hparams.proj_scale_factor);
+                LOG_INF("%s: n_merge:            %d\n", __func__, hparams.n_merge);
                 LOG_INF("%s: n_wa_pattern:       %d\n", __func__, hparams.n_wa_pattern);
-                if (hparams.spatial_merge_size > 0) {
-                    LOG_INF("%s: spatial_merge_size: %d\n", __func__, hparams.spatial_merge_size);
+                if (hparams.image_min_pixels > 0) {
+                    LOG_INF("%s: image_min_pixels:   %d\n", __func__, hparams.image_min_pixels);
+                }
+                if (hparams.image_max_pixels > 0) {
+                    LOG_INF("%s: image_max_pixels:   %d\n", __func__, hparams.image_max_pixels);
                 }
             } else if (is_audio) {
                 LOG_INF("\n--- audio hparams ---\n");
@@ -3181,9 +3202,11 @@ struct clip_model_loader {
         if (ctx_clip.model.modality == CLIP_MODALITY_VISION) {
             img->nx = hparams.warmup_image_size;
             img->ny = hparams.warmup_image_size;
+            LOG_INF("%s: warmup with image size = %d x %d\n", __func__, img->nx, img->ny);
         } else {
             img->nx = hparams.warmup_audio_size;
             img->ny = hparams.n_mel_bins;
+            LOG_INF("%s: warmup with audio size = %d\n", __func__, img->nx);
         }
         batch.entries.push_back(std::move(img));
 
@@ -3399,9 +3422,169 @@ static void normalize_image_u8_to_f32(const clip_image_u8 & src, clip_image_f32
 
 // set of tools to manupulate images
 // in the future, we can have HW acceleration by allowing this struct to access 3rd party lib like imagick or opencv
-struct image_manipulation {
+struct img_tool {
+    enum resize_algo {
+        RESIZE_ALGO_BILINEAR,
+        RESIZE_ALGO_BICUBIC,
+        // RESIZE_ALGO_LANCZOS, // TODO
+    };
+
+    static void resize(
+            const clip_image_u8 & src,
+            clip_image_u8 & dst,
+            const clip_image_size & target_resolution,
+            resize_algo algo,
+            bool add_padding = true, // TODO: define the behavior for add_padding = false
+            std::array<uint8_t, 3> pad_color = {0, 0, 0}) {
+        dst.nx = target_resolution.width;
+        dst.ny = target_resolution.height;
+        dst.buf.resize(3 * dst.nx * dst.ny);
+
+        if (dst.nx == src.nx && dst.ny == src.ny) {
+            // no resize needed, simple copy
+            dst.buf = src.buf;
+            return;
+        }
+
+        if (!add_padding) {
+            // direct resize
+            switch (algo) {
+                case RESIZE_ALGO_BILINEAR:
+                    resize_bilinear(src, dst, target_resolution.width, target_resolution.height);
+                    break;
+                case RESIZE_ALGO_BICUBIC:
+                    resize_bicubic(src, dst, target_resolution.width, target_resolution.height);
+                    break;
+                default:
+                    throw std::runtime_error("Unsupported resize algorithm");
+            }
+        } else {
+            // resize with padding
+            clip_image_u8 resized_image;
+            float scale_w = static_cast<float>(target_resolution.width) / src.nx;
+            float scale_h = static_cast<float>(target_resolution.height) / src.ny;
+            float scale = std::min(scale_w, scale_h);
+            int new_width  = std::min(static_cast<int>(std::ceil(src.nx * scale)), target_resolution.width);
+            int new_height = std::min(static_cast<int>(std::ceil(src.ny * scale)), target_resolution.height);
+
+            switch (algo) {
+                case RESIZE_ALGO_BILINEAR:
+                    resize_bilinear(src, resized_image, new_width, new_height);
+                    break;
+                case RESIZE_ALGO_BICUBIC:
+                    resize_bicubic(src, resized_image, new_width, new_height);
+                    break;
+                default:
+                    throw std::runtime_error("Unsupported resize algorithm");
+            }
+
+            // fill dst with pad_color
+            fill(dst, pad_color);
+
+            int offset_x = (target_resolution.width  - new_width)  / 2;
+            int offset_y = (target_resolution.height - new_height) / 2;
+
+            composite(dst, resized_image, offset_x, offset_y);
+        }
+    }
+
+    static void crop(const clip_image_u8 & image, clip_image_u8 & dst, int x, int y, int w, int h) {
+        dst.nx = w;
+        dst.ny = h;
+        dst.buf.resize(3 * w * h);
+
+        for (int i = 0; i < h; ++i) {
+            for (int j = 0; j < w; ++j) {
+                int src_idx = 3 * ((y + i)*image.nx + (x + j));
+                int dst_idx = 3 * (i*w + j);
+                dst.buf[dst_idx]     = image.buf[src_idx];
+                dst.buf[dst_idx + 1] = image.buf[src_idx + 1];
+                dst.buf[dst_idx + 2] = image.buf[src_idx + 2];
+            }
+        }
+    }
+
+    // calculate the size of the **resized** image, while preserving the aspect ratio
+    // the calculated size will be aligned to the nearest multiple of align_size
+    // if H or W size is larger than longest_edge, it will be resized to longest_edge
+    static clip_image_size calc_size_preserved_ratio(const clip_image_size & inp_size, const int align_size, const int longest_edge) {
+        GGML_ASSERT(align_size > 0);
+        if (inp_size.width <= 0 || inp_size.height <= 0 || longest_edge <= 0) {
+            return {0, 0};
+        }
+
+        float scale = std::min(static_cast<float>(longest_edge) / inp_size.width,
+                               static_cast<float>(longest_edge) / inp_size.height);
+
+        float target_width_f  = static_cast<float>(inp_size.width)  * scale;
+        float target_height_f = static_cast<float>(inp_size.height) * scale;
+
+        auto ceil_by_factor = [f = align_size](float x) { return static_cast<int>(std::ceil(x / static_cast<float>(f))) * f; };
+        int aligned_width  = ceil_by_factor(target_width_f);
+        int aligned_height = ceil_by_factor(target_height_f);
+
+        return {aligned_width, aligned_height};
+    }
+
+    // calculate the size of the **resized** image, while preserving the aspect ratio
+    // the calculated size will have min_pixels <= W*H <= max_pixels
+    // this is referred as "smart_resize" in transformers code
+    static clip_image_size calc_size_preserved_ratio(const clip_image_size & inp_size, const int align_size, const int min_pixels, const int max_pixels) {
+        GGML_ASSERT(align_size > 0);
+        const int width  = inp_size.width;
+        const int height = inp_size.height;
+
+        auto ceil_by_factor  = [f = align_size](float x) { return static_cast<int>(std::ceil(x / static_cast<float>(f))) * f; };
+        auto floor_by_factor = [f = align_size](float x) { return static_cast<int>(std::floor(x / static_cast<float>(f))) * f; };
+
+        // always align up first
+        int h_bar = std::max(align_size, ceil_by_factor(height));
+        int w_bar = std::max(align_size, ceil_by_factor(width));
+
+        if (h_bar * w_bar > max_pixels) {
+            const auto beta = std::sqrt(static_cast<float>(height * width) / max_pixels);
+            h_bar = std::max(align_size, floor_by_factor(height / beta));
+            w_bar = std::max(align_size, floor_by_factor(width  / beta));
+        } else if (h_bar * w_bar < min_pixels) {
+            const auto beta = std::sqrt(static_cast<float>(min_pixels) / (height * width));
+            h_bar = ceil_by_factor(height * beta);
+            w_bar = ceil_by_factor(width * beta);
+        }
+
+        return {w_bar, h_bar};
+    }
+
+    // draw src image into dst image at offset (offset_x, offset_y)
+    static void composite(clip_image_u8 & dst, const clip_image_u8 & src, int offset_x, int offset_y) {
+        for (int y = 0; y < src.ny; ++y) {
+            for (int x = 0; x < src.nx; ++x) {
+                int dx = x + offset_x;
+                int dy = y + offset_y;
+                // skip pixels that would be out of bounds in the destination
+                if (dx < 0 || dy < 0 || dx >= dst.nx || dy >= dst.ny) {
+                    continue;
+                }
+                size_t dst_idx = 3 * (static_cast<size_t>(dy) * dst.nx + static_cast<size_t>(dx));
+                size_t src_idx = 3 * (static_cast<size_t>(y) * src.nx + static_cast<size_t>(x));
+                dst.buf[dst_idx + 0] = src.buf[src_idx + 0];
+                dst.buf[dst_idx + 1] = src.buf[src_idx + 1];
+                dst.buf[dst_idx + 2] = src.buf[src_idx + 2];
+            }
+        }
+    }
+
+    // fill the image with a solid color
+    static void fill(clip_image_u8 & img, const std::array<uint8_t, 3> & color) {
+        for (size_t i = 0; i < img.buf.size(); i += 3) {
+            img.buf[i]     = color[0];
+            img.buf[i + 1] = color[1];
+            img.buf[i + 2] = color[2];
+        }
+    }
+
+private:
     // Bilinear resize function
-    static void bilinear_resize(const clip_image_u8& src, clip_image_u8& dst, int target_width, int target_height) {
+    static void resize_bilinear(const clip_image_u8 & src, clip_image_u8 & dst, int target_width, int target_height) {
         dst.nx = target_width;
         dst.ny = target_height;
         dst.buf.resize(3 * target_width * target_height);
@@ -3437,7 +3620,7 @@ struct image_manipulation {
 
     // Bicubic resize function
     // part of image will be cropped if the aspect ratio is different
-    static bool bicubic_resize(const clip_image_u8 & img, clip_image_u8 & dst, int target_width, int target_height) {
+    static bool resize_bicubic(const clip_image_u8 & img, clip_image_u8 & dst, int target_width, int target_height) {
         const int nx = img.nx;
         const int ny = img.ny;
 
@@ -3500,93 +3683,6 @@ struct image_manipulation {
         return true;
     }
 
-    // llava-1.6 type of resize_and_pad
-    // if the ratio is not 1:1, padding with pad_color will be applied
-    // pad_color is single channel, default is 0 (black)
-    static void resize_and_pad_image(const clip_image_u8 & image, clip_image_u8 & dst, const clip_image_size & target_resolution, std::array<uint8_t, 3> pad_color = {0, 0, 0}) {
-        int target_width  = target_resolution.width;
-        int target_height = target_resolution.height;
-
-        float scale_w = static_cast<float>(target_width) / image.nx;
-        float scale_h = static_cast<float>(target_height) / image.ny;
-
-        int new_width, new_height;
-
-        if (scale_w < scale_h) {
-            new_width  = target_width;
-            new_height = std::min(static_cast<int>(std::ceil(image.ny * scale_w)), target_height);
-        } else {
-            new_height = target_height;
-            new_width  = std::min(static_cast<int>(std::ceil(image.nx * scale_h)), target_width);
-        }
-
-        clip_image_u8 resized_image;
-        bicubic_resize(image, resized_image, new_width, new_height);
-
-        clip_image_u8 padded_image;
-        padded_image.nx = target_width;
-        padded_image.ny = target_height;
-        padded_image.buf.resize(3 * target_width * target_height);
-
-        // Fill the padded image with the fill color
-        for (size_t i = 0; i < padded_image.buf.size(); i += 3) {
-            padded_image.buf[i]     = pad_color[0];
-            padded_image.buf[i + 1] = pad_color[1];
-            padded_image.buf[i + 2] = pad_color[2];
-        }
-
-        // Calculate padding offsets
-        int pad_x = (target_width  - new_width)  / 2;
-        int pad_y = (target_height - new_height) / 2;
-
-        // Copy the resized image into the center of the padded buffer
-        for (int y = 0; y < new_height; ++y) {
-            for (int x = 0; x < new_width; ++x) {
-                for (int c = 0; c < 3; ++c) {
-                    padded_image.buf[3 * ((y + pad_y) * target_width + (x + pad_x)) + c] = resized_image.buf[3 * (y * new_width + x) + c];
-                }
-            }
-        }
-        dst = std::move(padded_image);
-    }
-
-    static void crop_image(const clip_image_u8 & image, clip_image_u8 & dst, int x, int y, int w, int h) {
-        dst.nx = w;
-        dst.ny = h;
-        dst.buf.resize(3 * w * h);
-
-        for (int i = 0; i < h; ++i) {
-            for (int j = 0; j < w; ++j) {
-                int src_idx = 3 * ((y + i)*image.nx + (x + j));
-                int dst_idx = 3 * (i*w + j);
-                dst.buf[dst_idx]     = image.buf[src_idx];
-                dst.buf[dst_idx + 1] = image.buf[src_idx + 1];
-                dst.buf[dst_idx + 2] = image.buf[src_idx + 2];
-            }
-        }
-    }
-
-    // calculate the size of the **resized** image, while preserving the aspect ratio
-    // the calculated size will be aligned to the nearest multiple of align_size
-    // if H or W size is larger than max_dimension, it will be resized to max_dimension
-    static clip_image_size calc_size_preserved_ratio(const clip_image_size & inp_size, const int align_size, const int max_dimension) {
-        if (inp_size.width <= 0 || inp_size.height <= 0 || align_size <= 0 || max_dimension <= 0) {
-            return {0, 0};
-        }
-
-        float scale = std::min(static_cast<float>(max_dimension) / inp_size.width,
-                               static_cast<float>(max_dimension) / inp_size.height);
-
-        float target_width_f  = static_cast<float>(inp_size.width)  * scale;
-        float target_height_f = static_cast<float>(inp_size.height) * scale;
-
-        int aligned_width  = CLIP_ALIGN((int)target_width_f,  align_size);
-        int aligned_height = CLIP_ALIGN((int)target_height_f, align_size);
-
-        return {aligned_width, aligned_height};
-    }
-
-private:
     static inline int clip(int x, int lower, int upper) {
         return std::max(lower, std::min(x, upper));
     }
@@ -3735,10 +3831,11 @@ struct llava_uhd {
 
     static std::vector<clip_image_u8_ptr> slice_image(const clip_image_u8 * img, const slice_instructions & inst) {
         std::vector<clip_image_u8_ptr> output;
+        img_tool::resize_algo interpolation = img_tool::RESIZE_ALGO_BILINEAR; // TODO: make it configurable
 
         // resize to overview size
         clip_image_u8_ptr resized_img(clip_image_u8_init());
-        image_manipulation::resize_and_pad_image(*img, *resized_img, inst.overview_size);
+        img_tool::resize(*img, *resized_img, inst.overview_size, interpolation);
         output.push_back(std::move(resized_img));
         if (inst.slices.empty()) {
             // no slices, just return the resized image
@@ -3748,9 +3845,11 @@ struct llava_uhd {
         // resize to refined size
         clip_image_u8_ptr refined_img(clip_image_u8_init());
         if (inst.padding_refined) {
-            image_manipulation::resize_and_pad_image(*img, *refined_img, inst.refined_size);
+            img_tool::resize(*img, *refined_img, inst.refined_size, interpolation);
         } else {
-            image_manipulation::bilinear_resize(*img, *refined_img, inst.refined_size.width, inst.refined_size.height);
+            // only algo bicubic preserves the ratio; old models rely on this behavior
+            // TODO: do we need to support other algos here?
+            img_tool::resize(*img, *refined_img, inst.refined_size, img_tool::RESIZE_ALGO_BICUBIC, false);
         }
 
         // create slices
@@ -3761,7 +3860,7 @@ struct llava_uhd {
             int h = slice.size.height;
 
             clip_image_u8_ptr img_slice(clip_image_u8_init());
-            image_manipulation::crop_image(*refined_img, *img_slice, x, y, w, h);
+            img_tool::crop(*refined_img, *img_slice, x, y, w, h);
             output.push_back(std::move(img_slice));
         }
 
@@ -3896,208 +3995,211 @@ struct llava_uhd {
 // res_imgs memory is being allocated here, previous allocations will be freed if found
 bool clip_image_preprocess(struct clip_ctx * ctx, const clip_image_u8 * img, struct clip_image_f32_batch * res_imgs) {
     clip_image_size original_size{img->nx, img->ny};
-    bool pad_to_square = true;
     auto & params = ctx->model.hparams;
-    // The model config actually contains all we need to decide on how to preprocess, here we automatically switch to the new llava-1.6 preprocessing
-    if (params.mm_patch_merge_type == PATCH_MERGE_SPATIAL_UNPAD) {
-        pad_to_square = false;
-    }
 
-    if (clip_is_minicpmv(ctx)) {
-        auto const inst = llava_uhd::get_slice_instructions(ctx, original_size);
-        std::vector<clip_image_u8_ptr> imgs = llava_uhd::slice_image(img, inst);
+    switch (ctx->proj_type()) {
+        case PROJECTOR_TYPE_MINICPMV:
+            {
+                auto const inst = llava_uhd::get_slice_instructions(ctx, original_size);
+                std::vector<clip_image_u8_ptr> imgs = llava_uhd::slice_image(img, inst);
+
+                for (size_t i = 0; i < imgs.size(); ++i) {
+                    // clip_image_save_to_bmp(*imgs[i], "slice_" + std::to_string(i) + ".bmp");
+                    clip_image_f32_ptr res(clip_image_f32_init());
+                    normalize_image_u8_to_f32(*imgs[i], *res, params.image_mean, params.image_std);
+                    res_imgs->entries.push_back(std::move(res));
+                }
 
-        for (size_t i = 0; i < imgs.size(); ++i) {
-            // clip_image_save_to_bmp(*imgs[i], "slice_" + std::to_string(i) + ".bmp");
-            clip_image_f32_ptr res(clip_image_f32_init());
-            normalize_image_u8_to_f32(*imgs[i], *res, params.image_mean, params.image_std);
-            res_imgs->entries.push_back(std::move(res));
-        }
+                res_imgs->grid_x = inst.grid_size.width;
+                res_imgs->grid_y = inst.grid_size.height;
+            } break;
 
-        res_imgs->grid_x = inst.grid_size.width;
-        res_imgs->grid_y = inst.grid_size.height;
-        return true;
+        case PROJECTOR_TYPE_QWEN2VL:
+        case PROJECTOR_TYPE_QWEN25VL:
+        case PROJECTOR_TYPE_QWEN3VL:
+            {
+                // step 1: make a blank canvas which aligns to the grid
+                clip_image_u8 resized;
+                const clip_image_size new_size = img_tool::calc_size_preserved_ratio(
+                    original_size,
+                    params.patch_size * 2,
+                    params.image_min_pixels,
+                    params.image_max_pixels);
+                img_tool::resize(*img, resized, new_size, img_tool::RESIZE_ALGO_BILINEAR, false);
+                // clip_image_save_to_bmp(resized, "preproc.bmp");
+                clip_image_f32_ptr img_f32(clip_image_f32_init());
+                // clip_image_f32_ptr res(clip_image_f32_init());
+                normalize_image_u8_to_f32(resized, *img_f32, params.image_mean, params.image_std);
+                // res_imgs->data[0] = *res;
+                res_imgs->entries.push_back(std::move(img_f32));
+            } break;
 
-    } else if (ctx->proj_type() == PROJECTOR_TYPE_QWEN2VL || ctx->proj_type() == PROJECTOR_TYPE_QWEN25VL || ctx->proj_type() == PROJECTOR_TYPE_QWEN3VL) {
-        clip_image_u8 resized;
-        auto patch_size = params.patch_size * 2;
-        auto new_size = image_manipulation::calc_size_preserved_ratio(original_size, patch_size, params.image_size);
-        image_manipulation::bicubic_resize(*img, resized, new_size.width, new_size.height);
-
-        clip_image_f32_ptr img_f32(clip_image_f32_init());
-        // clip_image_f32_ptr res(clip_image_f32_init());
-        normalize_image_u8_to_f32(resized, *img_f32, params.image_mean, params.image_std);
-        // res_imgs->data[0] = *res;
-        res_imgs->entries.push_back(std::move(img_f32));
-        return true;
-    } else if (ctx->proj_type() == PROJECTOR_TYPE_IDEFICS3) {
-        // The refined size has two steps:
-        // 1. Resize w/ aspect-ratio preserving such that the longer side is
-        //      the preprocessor longest size
-        // 2. Resize w/out preserving aspect ratio such that both sides are
-        //      multiples of image_size (always rounding up)
-        //
-        // CITE: https://github.com/huggingface/transformers/blob/main/src/transformers/models/idefics3/image_processing_idefics3.py#L737
-        const clip_image_size refined_size = image_manipulation::calc_size_preserved_ratio(
-            original_size, params.image_size, params.preproc_image_size);
-        // LOG_INF("%s: original size: %d x %d, refined size: %d x %d\n",
-        //         __func__, original_size.width, original_size.height,
-        //         refined_size.width, refined_size.height);
-
-        llava_uhd::slice_instructions instructions;
-        instructions.overview_size = clip_image_size{params.image_size, params.image_size};
-        instructions.refined_size = refined_size;
-        instructions.grid_size = clip_image_size{
-            static_cast<int>(std::ceil(static_cast<float>(refined_size.width) / params.image_size)),
-            static_cast<int>(std::ceil(static_cast<float>(refined_size.height) / params.image_size)),
-        };
-        for (int y = 0; y < refined_size.height; y += params.image_size) {
-            for (int x = 0; x < refined_size.width; x += params.image_size) {
-                // LOG_INF("%s: adding slice at x=%d, y=%d\n", __func__, x, y);
-                instructions.slices.push_back(llava_uhd::slice_coordinates{
-                    /* x    */x,
-                    /* y    */y,
-                    /* size */clip_image_size{
-                        std::min(params.image_size, refined_size.width - x),
-                        std::min(params.image_size, refined_size.height - y)
+        case PROJECTOR_TYPE_IDEFICS3:
+            {
+                // The refined size has two steps:
+                // 1. Resize w/ aspect-ratio preserving such that the longer side is
+                //      the preprocessor longest size
+                // 2. Resize w/out preserving aspect ratio such that both sides are
+                //      multiples of image_size (always rounding up)
+                //
+                // CITE: https://github.com/huggingface/transformers/blob/main/src/transformers/models/idefics3/image_processing_idefics3.py#L737
+                const clip_image_size refined_size = img_tool::calc_size_preserved_ratio(
+                    original_size, params.image_size, params.image_longest_edge);
+                // LOG_INF("%s: original size: %d x %d, refined size: %d x %d\n",
+                //         __func__, original_size.width, original_size.height,
+                //         refined_size.width, refined_size.height);
+
+                llava_uhd::slice_instructions instructions;
+                instructions.overview_size = clip_image_size{params.image_size, params.image_size};
+                instructions.refined_size = refined_size;
+                instructions.grid_size = clip_image_size{
+                    static_cast<int>(std::ceil(static_cast<float>(refined_size.width) / params.image_size)),
+                    static_cast<int>(std::ceil(static_cast<float>(refined_size.height) / params.image_size)),
+                };
+                for (int y = 0; y < refined_size.height; y += params.image_size) {
+                    for (int x = 0; x < refined_size.width; x += params.image_size) {
+                        // LOG_INF("%s: adding slice at x=%d, y=%d\n", __func__, x, y);
+                        instructions.slices.push_back(llava_uhd::slice_coordinates{
+                            /* x    */x,
+                            /* y    */y,
+                            /* size */clip_image_size{
+                                std::min(params.image_size, refined_size.width - x),
+                                std::min(params.image_size, refined_size.height - y)
+                            }
+                        });
                     }
-                });
-            }
-        }
-        auto imgs = llava_uhd::slice_image(img, instructions);
-
-        // cast and normalize to f32
-        for (size_t i = 0; i < imgs.size(); ++i) {
-            // clip_image_save_to_bmp(*imgs[i], "slice_" + std::to_string(i) + ".bmp");
-            clip_image_f32_ptr res(clip_image_f32_init());
-            normalize_image_u8_to_f32(*imgs[i], *res, params.image_mean, params.image_std);
-            res_imgs->entries.push_back(std::move(res));
-        }
-
-        res_imgs->grid_x = instructions.grid_size.width;
-        res_imgs->grid_y = instructions.grid_size.height;
-        return true;
-    } else if (ctx->proj_type() == PROJECTOR_TYPE_GLM_EDGE
-            || ctx->proj_type() == PROJECTOR_TYPE_GEMMA3
-            || ctx->proj_type() == PROJECTOR_TYPE_INTERNVL // TODO @ngxson : support dynamic resolution
-    ) {
-        clip_image_u8 resized_image;
-        int sz = params.image_size;
-        image_manipulation::resize_and_pad_image(*img, resized_image, {sz, sz});
-        clip_image_f32_ptr img_f32(clip_image_f32_init());
-        //clip_image_save_to_bmp(resized_image, "resized.bmp");
-        normalize_image_u8_to_f32(resized_image, *img_f32, params.image_mean, params.image_std);
-        res_imgs->entries.push_back(std::move(img_f32));
-        return true;
-
-    } else if (ctx->proj_type() == PROJECTOR_TYPE_PIXTRAL
-            || ctx->proj_type() == PROJECTOR_TYPE_LIGHTONOCR
-    ) {
-        clip_image_u8 resized_image;
-        auto new_size = image_manipulation::calc_size_preserved_ratio(original_size, params.patch_size, params.image_size);
-        image_manipulation::bilinear_resize(*img, resized_image, new_size.width, new_size.height);
-        clip_image_f32_ptr img_f32(clip_image_f32_init());
-        normalize_image_u8_to_f32(resized_image, *img_f32, params.image_mean, params.image_std);
-        res_imgs->entries.push_back(std::move(img_f32));
-        return true;
-
-    } else if (ctx->proj_type() == PROJECTOR_TYPE_LLAMA4) {
-        GGML_ASSERT(!params.image_res_candidates.empty());
-        auto const inst = llava_uhd::get_slice_instructions(ctx, original_size);
-        std::vector<clip_image_u8_ptr> imgs = llava_uhd::slice_image(img, inst);
-
-        for (size_t i = 0; i < imgs.size(); ++i) {
-            clip_image_f32_ptr res(clip_image_f32_init());
-            normalize_image_u8_to_f32(*imgs[i], *res, params.image_mean, params.image_std);
-            res_imgs->entries.push_back(std::move(res));
-        }
-
-        res_imgs->grid_x = inst.grid_size.width;
-        res_imgs->grid_y = inst.grid_size.height;
-        return true;
-
-    } else if ( ctx->proj_type() == PROJECTOR_TYPE_LFM2
-             || ctx->proj_type() == PROJECTOR_TYPE_KIMIVL
-    ) {
-        GGML_ASSERT(params.proj_scale_factor);
+                }
+                auto imgs = llava_uhd::slice_image(img, instructions);
+
+                // cast and normalize to f32
+                for (size_t i = 0; i < imgs.size(); ++i) {
+                    // clip_image_save_to_bmp(*imgs[i], "slice_" + std::to_string(i) + ".bmp");
+                    clip_image_f32_ptr res(clip_image_f32_init());
+                    normalize_image_u8_to_f32(*imgs[i], *res, params.image_mean, params.image_std);
+                    res_imgs->entries.push_back(std::move(res));
+                }
 
-        // smart resize
-        const int width = img->nx;
-        const int height = img->ny;
-        const int total_factor = params.patch_size * params.proj_scale_factor;
-        constexpr int min_image_tokens = 64;
-        constexpr int max_image_tokens = 1024;
-        const float min_pixels = min_image_tokens * total_factor * total_factor;
-        const float max_pixels = max_image_tokens * total_factor * total_factor;
+                res_imgs->grid_x = instructions.grid_size.width;
+                res_imgs->grid_y = instructions.grid_size.height;
+            } break;
 
-        auto round_by_factor = [f = total_factor](float x) { return static_cast<int>(std::nearbyintf(x / static_cast<float>(f))) * f; };
-        auto ceil_by_factor  = [f = total_factor](float x) { return static_cast<int>(std::ceil(x / static_cast<float>(f))) * f; };
-        auto floor_by_factor = [f = total_factor](float x) { return static_cast<int>(std::floor(x / static_cast<float>(f))) * f; };
+        case PROJECTOR_TYPE_GLM_EDGE:
+        case PROJECTOR_TYPE_GEMMA3:
+        case PROJECTOR_TYPE_INTERNVL: // TODO @ngxson : support dynamic resolution
+            {
+                clip_image_u8 resized_image;
+                int sz = params.image_size;
+                img_tool::resize(*img, resized_image, {sz, sz}, img_tool::RESIZE_ALGO_BILINEAR);
+                clip_image_f32_ptr img_f32(clip_image_f32_init());
+                //clip_image_save_to_bmp(resized_image, "resized.bmp");
+                normalize_image_u8_to_f32(resized_image, *img_f32, params.image_mean, params.image_std);
+                res_imgs->entries.push_back(std::move(img_f32));
+            } break;
 
-        int h_bar = std::max(total_factor, round_by_factor(height));
-        int w_bar = std::max(total_factor, round_by_factor(width));
+        case PROJECTOR_TYPE_PIXTRAL:
+        case PROJECTOR_TYPE_LIGHTONOCR:
+            {
+                GGML_ASSERT(params.image_min_pixels && params.image_max_pixels);
+                clip_image_u8 resized_image;
+                // the original pixtral model doesn't have n_merge
+                const int cur_merge = params.n_merge == 0 ? 1 : params.n_merge;
+                const clip_image_size target_size = img_tool::calc_size_preserved_ratio(
+                    original_size,
+                    params.patch_size * cur_merge,
+                    params.image_min_pixels,
+                    params.image_max_pixels);
+                img_tool::resize(*img, resized_image, target_size, img_tool::RESIZE_ALGO_BILINEAR);
+                clip_image_f32_ptr img_f32(clip_image_f32_init());
+                normalize_image_u8_to_f32(resized_image, *img_f32, params.image_mean, params.image_std);
+                res_imgs->entries.push_back(std::move(img_f32));
+            } break;
 
-        if (h_bar * w_bar > max_pixels) {
-            const auto beta = std::sqrt((height * width) / max_pixels);
-            h_bar = std::max(total_factor, floor_by_factor(height / beta));
-            w_bar = std::max(total_factor, floor_by_factor(width / beta));
-        } else if (h_bar * w_bar < min_pixels) {
-            const auto beta = std::sqrt(min_pixels / (height * width));
-            h_bar = ceil_by_factor(height * beta);
-            w_bar = ceil_by_factor(width * beta);
-        }
+        case PROJECTOR_TYPE_LLAMA4:
+            {
+                GGML_ASSERT(!params.image_res_candidates.empty());
+                auto const inst = llava_uhd::get_slice_instructions(ctx, original_size);
+                std::vector<clip_image_u8_ptr> imgs = llava_uhd::slice_image(img, inst);
+
+                for (size_t i = 0; i < imgs.size(); ++i) {
+                    clip_image_f32_ptr res(clip_image_f32_init());
+                    normalize_image_u8_to_f32(*imgs[i], *res, params.image_mean, params.image_std);
+                    res_imgs->entries.push_back(std::move(res));
+                }
 
-        const std::array<uint8_t, 3> pad_color = {122, 116, 104};
+                res_imgs->grid_x = inst.grid_size.width;
+                res_imgs->grid_y = inst.grid_size.height;
+            } break;
 
-        clip_image_u8 resized_img;
-        image_manipulation::resize_and_pad_image(*img, resized_img, clip_image_size{w_bar, h_bar}, pad_color);
-        clip_image_f32_ptr res(clip_image_f32_init());
-        normalize_image_u8_to_f32(resized_img, *res, params.image_mean, params.image_std);
-        res_imgs->entries.push_back(std::move(res));
-        return true;
-    }
+        case PROJECTOR_TYPE_LFM2:
+        case PROJECTOR_TYPE_KIMIVL:
+            {
+                GGML_ASSERT(params.image_min_pixels && params.image_max_pixels);
+                const clip_image_size target_size = img_tool::calc_size_preserved_ratio(
+                    original_size,
+                    params.patch_size * params.n_merge,
+                    params.image_min_pixels,
+                    params.image_max_pixels);
+                const std::array<uint8_t, 3> pad_color = {122, 116, 104};
+
+                clip_image_u8 resized_img;
+                img_tool::resize(*img, resized_img, target_size, img_tool::RESIZE_ALGO_BILINEAR, true, pad_color);
+                clip_image_f32_ptr res(clip_image_f32_init());
+                normalize_image_u8_to_f32(resized_img, *res, params.image_mean, params.image_std);
+                res_imgs->entries.push_back(std::move(res));
+            } break;
 
-    // the logic below is to pad the shorter side to the longer side with a background color: rgb(122, 116, 104)
-    // see https://github.com/haotian-liu/LLaVA/blob/e854a2bf85118c504f6f16bf5c3c7c92f8fa8c6b/llava/conversation.py#L113-L156
+        case PROJECTOR_TYPE_MLP:
+        case PROJECTOR_TYPE_MLP_NORM:
+        case PROJECTOR_TYPE_LDP:
+        case PROJECTOR_TYPE_LDPV2:
+        case PROJECTOR_TYPE_COGVLM: // TODO @ngxson : is this correct for cogvlm?
+            {
+                // TODO @ngxson : refactor the code below to avoid duplicated logic
 
-    clip_image_u8_ptr temp(clip_image_u8_init()); // we will keep the input image data here temporarily
+                // the logic below is to pad the shorter side to the longer side with a background color: rgb(122, 116, 104)
+                // see https://github.com/haotian-liu/LLaVA/blob/e854a2bf85118c504f6f16bf5c3c7c92f8fa8c6b/llava/conversation.py#L113-L156
 
-    if (pad_to_square) {
-        // for llava-1.5, we resize image to a square, and pad the shorter side with a background color
-        // see https://github.com/haotian-liu/LLaVA/blob/e854a2bf85118c504f6f16bf5c3c7c92f8fa8c6b/llava/conversation.py#L113-L156
-        const int longer_side = std::max(img->nx, img->ny);
-        temp->nx = longer_side;
-        temp->ny = longer_side;
-        temp->buf.resize(3 * longer_side * longer_side);
+                clip_image_u8_ptr temp(clip_image_u8_init()); // we will keep the input image data here temporarily
 
-        // background color in RGB from LLaVA (this is the mean rgb color * 255)
-        const std::array<uint8_t, 3> pad_color = {122, 116, 104};
+                // The model config actually contains all we need to decide on how to preprocess, here we automatically switch to the new llava-1.6 preprocessing
+                if (params.image_res_candidates.empty()) { // pad_to_square
+                    // for llava-1.5, we resize image to a square, and pad the shorter side with a background color
+                    // see https://github.com/haotian-liu/LLaVA/blob/e854a2bf85118c504f6f16bf5c3c7c92f8fa8c6b/llava/conversation.py#L113-L156
+                    const int longer_side = std::max(img->nx, img->ny);
+                    temp->nx = longer_side;
+                    temp->ny = longer_side;
+                    temp->buf.resize(3 * longer_side * longer_side);
 
-        // resize the image to the target_size
-        image_manipulation::resize_and_pad_image(*img, *temp, clip_image_size{params.image_size, params.image_size}, pad_color);
+                    // background color in RGB from LLaVA (this is the mean rgb color * 255)
+                    const std::array<uint8_t, 3> pad_color = {122, 116, 104};
 
-        clip_image_f32_ptr res(clip_image_f32_init());
-        normalize_image_u8_to_f32(*temp, *res, params.image_mean, params.image_std);
-        res_imgs->entries.push_back(std::move(res));
-        return true;
+                    // resize the image to the target_size
+                    img_tool::resize(*img, *temp, clip_image_size{params.image_size, params.image_size}, img_tool::RESIZE_ALGO_BILINEAR, true, pad_color);
 
-    } else if (!params.image_res_candidates.empty()) {
-        // "spatial_unpad" with "anyres" processing for llava-1.6
-        auto const inst = llava_uhd::get_slice_instructions(ctx, original_size);
-        std::vector<clip_image_u8_ptr> imgs = llava_uhd::slice_image(img, inst);
+                    clip_image_f32_ptr res(clip_image_f32_init());
+                    normalize_image_u8_to_f32(*temp, *res, params.image_mean, params.image_std);
+                    res_imgs->entries.push_back(std::move(res));
 
-        for (size_t i = 0; i < imgs.size(); ++i) {
-            // clip_image_save_to_bmp(*imgs[i], "slice_" + std::to_string(i) + ".bmp");
-            clip_image_f32_ptr res(clip_image_f32_init());
-            normalize_image_u8_to_f32(*imgs[i], *res, params.image_mean, params.image_std);
-            res_imgs->entries.push_back(std::move(res));
-        }
+                } else {
+                    // "spatial_unpad" with "anyres" processing for llava-1.6
+                    auto const inst = llava_uhd::get_slice_instructions(ctx, original_size);
+                    std::vector<clip_image_u8_ptr> imgs = llava_uhd::slice_image(img, inst);
+
+                    for (size_t i = 0; i < imgs.size(); ++i) {
+                        // clip_image_save_to_bmp(*imgs[i], "slice_" + std::to_string(i) + ".bmp");
+                        clip_image_f32_ptr res(clip_image_f32_init());
+                        normalize_image_u8_to_f32(*imgs[i], *res, params.image_mean, params.image_std);
+                        res_imgs->entries.push_back(std::move(res));
+                    }
+                }
+            } break;
 
-        return true;
-    } else {
-        GGML_ABORT("Unknown image preprocessing type");
+        default:
+            LOG_ERR("%s: unsupported projector type %d\n", __func__, ctx->proj_type());
+            return false;
     }
 
+    return true;
 }
 
 ggml_tensor * clip_get_newline_tensor(const struct clip_ctx * ctx) {
@@ -4145,7 +4247,7 @@ int clip_n_output_tokens_x(const struct clip_ctx * ctx, struct clip_image_f32 *
     const auto & params = ctx->model.hparams;
     const int n_total = clip_n_output_tokens(ctx, img);
     if (ctx->proj_type() == PROJECTOR_TYPE_QWEN2VL || ctx->proj_type() == PROJECTOR_TYPE_QWEN25VL || ctx->proj_type() == PROJECTOR_TYPE_QWEN3VL) {
-        return img->nx / (params.patch_size * 2) + (int)(img->nx % params.patch_size > 0);
+        return img->nx / (params.patch_size * 2);
     }
     return n_total;
 }
@@ -4153,7 +4255,7 @@ int clip_n_output_tokens_x(const struct clip_ctx * ctx, struct clip_image_f32 *
 int clip_n_output_tokens_y(const struct clip_ctx * ctx, struct clip_image_f32 * img) {
     const auto & params = ctx->model.hparams;
     if (ctx->proj_type() == PROJECTOR_TYPE_QWEN2VL || ctx->proj_type() == PROJECTOR_TYPE_QWEN25VL || ctx->proj_type() == PROJECTOR_TYPE_QWEN3VL) {
-        return img->ny / (params.patch_size * 2) + (int)(img->ny % params.patch_size > 0);
+        return img->ny / (params.patch_size * 2);
     }
     return 1;
 }
@@ -4211,9 +4313,8 @@ int clip_n_output_tokens(const struct clip_ctx * ctx, struct clip_image_f32 * im
         case PROJECTOR_TYPE_QWEN3VL:
             {
                 // dynamic size (2 conv, so double patch size)
-                int patch_size = params.patch_size * 2;
-                int x_patch = img->nx / patch_size + (int)(img->nx % patch_size > 0);
-                int y_patch = img->ny / patch_size + (int)(img->ny % patch_size > 0);
+                int x_patch = img->nx / (params.patch_size * 2);
+                int y_patch = img->ny / (params.patch_size * 2);
                 n_patches = x_patch * y_patch;
             } break;
         case PROJECTOR_TYPE_GEMMA3:
@@ -4222,15 +4323,14 @@ int clip_n_output_tokens(const struct clip_ctx * ctx, struct clip_image_f32 * im
         case PROJECTOR_TYPE_LLAMA4:
             {
                 // both X and Y are downscaled by the scale factor
-                int scale_factor = ctx->model.hparams.proj_scale_factor;
+                int scale_factor = ctx->model.hparams.n_merge;
                 n_patches /= (scale_factor * scale_factor);
             } break;
         case PROJECTOR_TYPE_LFM2:
         case PROJECTOR_TYPE_KIMIVL:
             {
                 // dynamic size
-                int scale_factor = ctx->model.hparams.proj_scale_factor;
-                int out_patch_size = params.patch_size * scale_factor;
+                int out_patch_size = params.patch_size * ctx->model.hparams.n_merge;
                 int x_patch = CLIP_ALIGN(img->nx, out_patch_size) / out_patch_size;
                 int y_patch = CLIP_ALIGN(img->ny, out_patch_size) / out_patch_size;
                 n_patches = x_patch * y_patch;
@@ -4239,7 +4339,7 @@ int clip_n_output_tokens(const struct clip_ctx * ctx, struct clip_image_f32 * im
         case PROJECTOR_TYPE_LIGHTONOCR:
             {
                 // dynamic size
-                int n_merge = params.spatial_merge_size;
+                int n_merge = ctx->model.hparams.n_merge;
                 int n_patches_x = img->nx / patch_size / (n_merge > 0 ? n_merge : 1);
                 int n_patches_y = img->ny / patch_size / (n_merge > 0 ? n_merge : 1);
                 if (ctx->model.token_embd_img_break) {

From dd5e8cab512c7752392b6e51a6f118f348fb3f16 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Adrien=20Gallou=C3=ABt?= <angt@huggingface.co>
Date: Sat, 1 Nov 2025 16:52:17 +0100
Subject: [PATCH 050/185] vendor : update cpp-httplib to 0.27.0 (#16846)
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

Signed-off-by: Adrien Gallouët <angt@huggingface.co>
---
 vendor/cpp-httplib/httplib.h | 268 +++++++++++++++++++++++++++--------
 1 file changed, 211 insertions(+), 57 deletions(-)

diff --git a/vendor/cpp-httplib/httplib.h b/vendor/cpp-httplib/httplib.h
index db55d07e253..b76a17d07ac 100644
--- a/vendor/cpp-httplib/httplib.h
+++ b/vendor/cpp-httplib/httplib.h
@@ -8,8 +8,8 @@
 #ifndef CPPHTTPLIB_HTTPLIB_H
 #define CPPHTTPLIB_HTTPLIB_H
 
-#define CPPHTTPLIB_VERSION "0.26.0"
-#define CPPHTTPLIB_VERSION_NUM "0x001A00"
+#define CPPHTTPLIB_VERSION "0.27.0"
+#define CPPHTTPLIB_VERSION_NUM "0x001B00"
 
 /*
  * Platform compatibility check
@@ -1052,6 +1052,9 @@ class RegexMatcher final : public MatcherBase {
 
 ssize_t write_headers(Stream &strm, const Headers &headers);
 
+std::string make_host_and_port_string(const std::string &host, int port,
+                                      bool is_ssl);
+
 } // namespace detail
 
 class Server {
@@ -1129,6 +1132,8 @@ class Server {
   Server &
   set_header_writer(std::function<ssize_t(Stream &, Headers &)> const &writer);
 
+  Server &set_trusted_proxies(const std::vector<std::string> &proxies);
+
   Server &set_keep_alive_max_count(size_t count);
   Server &set_keep_alive_timeout(time_t sec);
 
@@ -1167,6 +1172,9 @@ class Server {
                        const std::function<void(Request &)> &setup_request);
 
   std::atomic<socket_t> svr_sock_{INVALID_SOCKET};
+
+  std::vector<std::string> trusted_proxies_;
+
   size_t keep_alive_max_count_ = CPPHTTPLIB_KEEPALIVE_MAX_COUNT;
   time_t keep_alive_timeout_sec_ = CPPHTTPLIB_KEEPALIVE_TIMEOUT_SECOND;
   time_t read_timeout_sec_ = CPPHTTPLIB_SERVER_READ_TIMEOUT_SECOND;
@@ -1719,8 +1727,6 @@ class ClientImpl {
       const std::string &boundary, const UploadFormDataItems &items,
       const FormDataProviderItems &provider_items) const;
 
-  std::string adjust_host_string(const std::string &host) const;
-
   virtual bool
   process_socket(const Socket &socket,
                  std::chrono::time_point<std::chrono::steady_clock> start_time,
@@ -1953,14 +1959,17 @@ class SSLServer : public Server {
   void update_certs(X509 *cert, EVP_PKEY *private_key,
                     X509_STORE *client_ca_cert_store = nullptr);
 
+  int ssl_last_error() const { return last_ssl_error_; }
+
 private:
   bool process_and_close_socket(socket_t sock) override;
 
+  STACK_OF(X509_NAME) * extract_ca_names_from_x509_store(X509_STORE *store);
+
   SSL_CTX *ctx_;
   std::mutex ctx_mutex_;
-#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
+
   int last_ssl_error_ = 0;
-#endif
 };
 
 class SSLClient final : public ClientImpl {
@@ -4596,13 +4605,35 @@ inline bool zstd_decompressor::decompress(const char *data, size_t data_length,
 }
 #endif
 
+inline bool is_prohibited_header_name(const std::string &name) {
+  using udl::operator""_t;
+
+  switch (str2tag(name)) {
+  case "REMOTE_ADDR"_t:
+  case "REMOTE_PORT"_t:
+  case "LOCAL_ADDR"_t:
+  case "LOCAL_PORT"_t: return true;
+  default: return false;
+  }
+}
+
 inline bool has_header(const Headers &headers, const std::string &key) {
+  if (is_prohibited_header_name(key)) { return false; }
   return headers.find(key) != headers.end();
 }
 
 inline const char *get_header_value(const Headers &headers,
                                     const std::string &key, const char *def,
                                     size_t id) {
+  if (is_prohibited_header_name(key)) {
+#ifndef CPPHTTPLIB_NO_EXCEPTIONS
+    std::string msg = "Prohibited header name '" + key + "' is specified.";
+    throw std::invalid_argument(msg);
+#else
+    return "";
+#endif
+  }
+
   auto rng = headers.equal_range(key);
   auto it = rng.first;
   std::advance(it, static_cast<ssize_t>(id));
@@ -7261,6 +7292,30 @@ inline bool RegexMatcher::match(Request &request) const {
   return std::regex_match(request.path, request.matches, regex_);
 }
 
+inline std::string make_host_and_port_string(const std::string &host, int port,
+                                             bool is_ssl) {
+  std::string result;
+
+  // Enclose IPv6 address in brackets (but not if already enclosed)
+  if (host.find(':') == std::string::npos ||
+      (!host.empty() && host[0] == '[')) {
+    // IPv4, hostname, or already bracketed IPv6
+    result = host;
+  } else {
+    // IPv6 address without brackets
+    result = "[" + host + "]";
+  }
+
+  // Append port if not default
+  if ((!is_ssl && port == 80) || (is_ssl && port == 443)) {
+    ; // do nothing
+  } else {
+    result += ":" + std::to_string(port);
+  }
+
+  return result;
+}
+
 } // namespace detail
 
 // HTTP server implementation
@@ -7473,6 +7528,12 @@ inline Server &Server::set_header_writer(
   return *this;
 }
 
+inline Server &
+Server::set_trusted_proxies(const std::vector<std::string> &proxies) {
+  trusted_proxies_ = proxies;
+  return *this;
+}
+
 inline Server &Server::set_keep_alive_max_count(size_t count) {
   keep_alive_max_count_ = count;
   return *this;
@@ -8261,6 +8322,40 @@ inline bool Server::dispatch_request_for_content_reader(
   return false;
 }
 
+inline std::string
+get_client_ip(const std::string &x_forwarded_for,
+              const std::vector<std::string> &trusted_proxies) {
+  // X-Forwarded-For is a comma-separated list per RFC 7239
+  std::vector<std::string> ip_list;
+  detail::split(x_forwarded_for.data(),
+                x_forwarded_for.data() + x_forwarded_for.size(), ',',
+                [&](const char *b, const char *e) {
+                  auto r = detail::trim(b, e, 0, static_cast<size_t>(e - b));
+                  ip_list.emplace_back(std::string(b + r.first, b + r.second));
+                });
+
+  for (size_t i = 0; i < ip_list.size(); ++i) {
+    auto ip = ip_list[i];
+
+    auto is_trusted_proxy =
+        std::any_of(trusted_proxies.begin(), trusted_proxies.end(),
+                    [&](const std::string &proxy) { return ip == proxy; });
+
+    if (is_trusted_proxy) {
+      if (i == 0) {
+        // If the trusted proxy is the first IP, there's no preceding client IP
+        return ip;
+      } else {
+        // Return the IP immediately before the trusted proxy
+        return ip_list[i - 1];
+      }
+    }
+  }
+
+  // If no trusted proxy is found, return the first IP in the list
+  return ip_list.front();
+}
+
 inline bool
 Server::process_request(Stream &strm, const std::string &remote_addr,
                         int remote_port, const std::string &local_addr,
@@ -8324,15 +8419,16 @@ Server::process_request(Stream &strm, const std::string &remote_addr,
     connection_closed = true;
   }
 
-  req.remote_addr = remote_addr;
+  if (!trusted_proxies_.empty() && req.has_header("X-Forwarded-For")) {
+    auto x_forwarded_for = req.get_header_value("X-Forwarded-For");
+    req.remote_addr = get_client_ip(x_forwarded_for, trusted_proxies_);
+  } else {
+    req.remote_addr = remote_addr;
+  }
   req.remote_port = remote_port;
-  req.set_header("REMOTE_ADDR", req.remote_addr);
-  req.set_header("REMOTE_PORT", std::to_string(req.remote_port));
 
   req.local_addr = local_addr;
   req.local_port = local_port;
-  req.set_header("LOCAL_ADDR", req.local_addr);
-  req.set_header("LOCAL_PORT", std::to_string(req.local_port));
 
   if (req.has_header("Accept")) {
     const auto &accept_header = req.get_header_value("Accept");
@@ -8522,7 +8618,7 @@ inline ClientImpl::ClientImpl(const std::string &host, int port,
                               const std::string &client_cert_path,
                               const std::string &client_key_path)
     : host_(detail::escape_abstract_namespace_unix_domain(host)), port_(port),
-      host_and_port_(adjust_host_string(host_) + ":" + std::to_string(port)),
+      host_and_port_(detail::make_host_and_port_string(host_, port, is_ssl())),
       client_cert_path_(client_cert_path), client_key_path_(client_key_path) {}
 
 inline ClientImpl::~ClientImpl() {
@@ -8703,8 +8799,9 @@ inline bool ClientImpl::send_(Request &req, Response &res, Error &error) {
   {
     std::lock_guard<std::mutex> guard(socket_mutex_);
 
-    // Set this to false immediately - if it ever gets set to true by the end of
-    // the request, we know another thread instructed us to close the socket.
+    // Set this to false immediately - if it ever gets set to true by the end
+    // of the request, we know another thread instructed us to close the
+    // socket.
     socket_should_be_closed_when_request_is_done_ = false;
 
     auto is_alive = false;
@@ -8720,10 +8817,10 @@ inline bool ClientImpl::send_(Request &req, Response &res, Error &error) {
 #endif
 
       if (!is_alive) {
-        // Attempt to avoid sigpipe by shutting down non-gracefully if it seems
-        // like the other side has already closed the connection Also, there
-        // cannot be any requests in flight from other threads since we locked
-        // request_mutex_, so safe to close everything immediately
+        // Attempt to avoid sigpipe by shutting down non-gracefully if it
+        // seems like the other side has already closed the connection Also,
+        // there cannot be any requests in flight from other threads since we
+        // locked request_mutex_, so safe to close everything immediately
         const bool shutdown_gracefully = false;
         shutdown_ssl(socket_, shutdown_gracefully);
         shutdown_socket(socket_);
@@ -9027,7 +9124,8 @@ inline bool ClientImpl::create_redirect_client(
   }
 }
 
-// New method for robust client setup (based on basic_manual_redirect.cpp logic)
+// New method for robust client setup (based on basic_manual_redirect.cpp
+// logic)
 template <typename ClientType>
 inline void ClientImpl::setup_redirect_client(ClientType &client) {
   // Copy basic settings first
@@ -9131,18 +9229,8 @@ inline bool ClientImpl::write_request(Stream &strm, Request &req,
     // curl behavior)
     if (address_family_ == AF_UNIX) {
       req.set_header("Host", "localhost");
-    } else if (is_ssl()) {
-      if (port_ == 443) {
-        req.set_header("Host", host_);
-      } else {
-        req.set_header("Host", host_and_port_);
-      }
     } else {
-      if (port_ == 80) {
-        req.set_header("Host", host_);
-      } else {
-        req.set_header("Host", host_and_port_);
-      }
+      req.set_header("Host", host_and_port_);
     }
   }
 
@@ -9409,12 +9497,6 @@ inline Result ClientImpl::send_with_content_provider(
 #endif
 }
 
-inline std::string
-ClientImpl::adjust_host_string(const std::string &host) const {
-  if (host.find(':') != std::string::npos) { return "[" + host + "]"; }
-  return host;
-}
-
 inline void ClientImpl::output_log(const Request &req,
                                    const Response &res) const {
   if (logger_) {
@@ -9538,8 +9620,8 @@ inline ContentProviderWithoutLength ClientImpl::get_multipart_content_provider(
     const FormDataProviderItems &provider_items) const {
   size_t cur_item = 0;
   size_t cur_start = 0;
-  // cur_item and cur_start are copied to within the std::function and maintain
-  // state between successive calls
+  // cur_item and cur_start are copied to within the std::function and
+  // maintain state between successive calls
   return [&, cur_item, cur_start](size_t offset,
                                   DataSink &sink) mutable -> bool {
     if (!offset && !items.empty()) {
@@ -10251,8 +10333,8 @@ inline void ClientImpl::stop() {
   // If there is anything ongoing right now, the ONLY thread-safe thing we can
   // do is to shutdown_socket, so that threads using this socket suddenly
   // discover they can't read/write any more and error out. Everything else
-  // (closing the socket, shutting ssl down) is unsafe because these actions are
-  // not thread-safe.
+  // (closing the socket, shutting ssl down) is unsafe because these actions
+  // are not thread-safe.
   if (socket_requests_in_flight_ > 0) {
     shutdown_socket(socket_);
 
@@ -10705,6 +10787,19 @@ inline SSLServer::SSLServer(const char *cert_path, const char *private_key_path,
       SSL_CTX_load_verify_locations(ctx_, client_ca_cert_file_path,
                                     client_ca_cert_dir_path);
 
+      // Set client CA list to be sent to clients during TLS handshake
+      if (client_ca_cert_file_path) {
+        auto ca_list = SSL_load_client_CA_file(client_ca_cert_file_path);
+        if (ca_list != nullptr) {
+          SSL_CTX_set_client_CA_list(ctx_, ca_list);
+        } else {
+          // Failed to load client CA list, but we continue since
+          // SSL_CTX_load_verify_locations already succeeded and
+          // certificate verification will still work
+          last_ssl_error_ = static_cast<int>(ERR_get_error());
+        }
+      }
+
       SSL_CTX_set_verify(
           ctx_, SSL_VERIFY_PEER | SSL_VERIFY_FAIL_IF_NO_PEER_CERT, nullptr);
     }
@@ -10729,6 +10824,15 @@ inline SSLServer::SSLServer(X509 *cert, EVP_PKEY *private_key,
     } else if (client_ca_cert_store) {
       SSL_CTX_set_cert_store(ctx_, client_ca_cert_store);
 
+      // Extract CA names from the store and set them as the client CA list
+      auto ca_list = extract_ca_names_from_x509_store(client_ca_cert_store);
+      if (ca_list) {
+        SSL_CTX_set_client_CA_list(ctx_, ca_list);
+      } else {
+        // Failed to extract CA names, record the error
+        last_ssl_error_ = static_cast<int>(ERR_get_error());
+      }
+
       SSL_CTX_set_verify(
           ctx_, SSL_VERIFY_PEER | SSL_VERIFY_FAIL_IF_NO_PEER_CERT, nullptr);
     }
@@ -10809,6 +10913,44 @@ inline bool SSLServer::process_and_close_socket(socket_t sock) {
   return ret;
 }
 
+inline STACK_OF(X509_NAME) * SSLServer::extract_ca_names_from_x509_store(
+                                 X509_STORE *store) {
+  if (!store) { return nullptr; }
+
+  auto ca_list = sk_X509_NAME_new_null();
+  if (!ca_list) { return nullptr; }
+
+  // Get all objects from the store
+  auto objs = X509_STORE_get0_objects(store);
+  if (!objs) {
+    sk_X509_NAME_free(ca_list);
+    return nullptr;
+  }
+
+  // Iterate through objects and extract certificate subject names
+  for (int i = 0; i < sk_X509_OBJECT_num(objs); i++) {
+    auto obj = sk_X509_OBJECT_value(objs, i);
+    if (X509_OBJECT_get_type(obj) == X509_LU_X509) {
+      auto cert = X509_OBJECT_get0_X509(obj);
+      if (cert) {
+        auto subject = X509_get_subject_name(cert);
+        if (subject) {
+          auto name_dup = X509_NAME_dup(subject);
+          if (name_dup) { sk_X509_NAME_push(ca_list, name_dup); }
+        }
+      }
+    }
+  }
+
+  // If no names were extracted, free the list and return nullptr
+  if (sk_X509_NAME_num(ca_list) == 0) {
+    sk_X509_NAME_free(ca_list);
+    return nullptr;
+  }
+
+  return ca_list;
+}
+
 // SSL HTTP client implementation
 inline SSLClient::SSLClient(const std::string &host)
     : SSLClient(host, 443, std::string(), std::string()) {}
@@ -10889,7 +11031,8 @@ inline void SSLClient::set_ca_cert_store(X509_STORE *ca_cert_store) {
   if (ca_cert_store) {
     if (ctx_) {
       if (SSL_CTX_get_cert_store(ctx_) != ca_cert_store) {
-        // Free memory allocated for old cert and use new store `ca_cert_store`
+        // Free memory allocated for old cert and use new store
+        // `ca_cert_store`
         SSL_CTX_set_cert_store(ctx_, ca_cert_store);
         ca_cert_store_ = ca_cert_store;
       }
@@ -10911,10 +11054,15 @@ inline long SSLClient::get_openssl_verify_result() const {
 inline SSL_CTX *SSLClient::ssl_context() const { return ctx_; }
 
 inline bool SSLClient::create_and_connect_socket(Socket &socket, Error &error) {
-  return is_valid() && ClientImpl::create_and_connect_socket(socket, error);
+  if (!is_valid()) {
+    error = Error::SSLConnection;
+    return false;
+  }
+  return ClientImpl::create_and_connect_socket(socket, error);
 }
 
-// Assumes that socket_mutex_ is locked and that there are no requests in flight
+// Assumes that socket_mutex_ is locked and that there are no requests in
+// flight
 inline bool SSLClient::connect_with_proxy(
     Socket &socket,
     std::chrono::time_point<std::chrono::steady_clock> start_time,
@@ -11128,6 +11276,11 @@ inline bool SSLClient::initialize_ssl(Socket &socket, Error &error) {
     return true;
   }
 
+  if (ctx_ == nullptr) {
+    error = Error::SSLConnection;
+    last_openssl_error_ = ERR_get_error();
+  }
+
   shutdown_socket(socket);
   close_socket(socket);
   return false;
@@ -11221,21 +11374,22 @@ SSLClient::verify_host_with_subject_alt_name(X509 *server_cert) const {
 
     for (decltype(count) i = 0; i < count && !dsn_matched; i++) {
       auto val = sk_GENERAL_NAME_value(alt_names, i);
-      if (val->type == type) {
-        auto name =
-            reinterpret_cast<const char *>(ASN1_STRING_get0_data(val->d.ia5));
-        auto name_len = static_cast<size_t>(ASN1_STRING_length(val->d.ia5));
-
-        switch (type) {
-        case GEN_DNS: dsn_matched = check_host_name(name, name_len); break;
-
-        case GEN_IPADD:
-          if (!memcmp(&addr6, name, addr_len) ||
-              !memcmp(&addr, name, addr_len)) {
-            ip_matched = true;
-          }
-          break;
+      if (!val || val->type != type) { continue; }
+
+      auto name =
+          reinterpret_cast<const char *>(ASN1_STRING_get0_data(val->d.ia5));
+      if (name == nullptr) { continue; }
+
+      auto name_len = static_cast<size_t>(ASN1_STRING_length(val->d.ia5));
+
+      switch (type) {
+      case GEN_DNS: dsn_matched = check_host_name(name, name_len); break;
+
+      case GEN_IPADD:
+        if (!memcmp(&addr6, name, addr_len) || !memcmp(&addr, name, addr_len)) {
+          ip_matched = true;
         }
+        break;
       }
     }
 

From e4a71599e5846110159955dec0008eb4aa24222b Mon Sep 17 00:00:00 2001
From: Pascal <admin@serveurperso.com>
Date: Sat, 1 Nov 2025 17:14:54 +0100
Subject: [PATCH 051/185] webui: add HTML/JS preview support to MarkdownContent
 with sandboxed iframe (#16757)

* webui: add HTML/JS preview support to MarkdownContent with sandboxed iframe dialog

Extended MarkdownContent to flag previewable code languages,
add a preview button alongside copy controls, manage preview
dialog state, and share styling for the new button group

Introduced CodePreviewDialog.svelte, a sandboxed iframe modal
for rendering HTML/JS previews with consistent dialog controls

* webui: fullscreen HTML preview dialog using bits-ui

* Update tools/server/webui/src/lib/components/app/misc/CodePreviewDialog.svelte

Co-authored-by: Aleksander Grygier <aleksander.grygier@gmail.com>

* Update tools/server/webui/src/lib/components/app/misc/MarkdownContent.svelte

Co-authored-by: Aleksander Grygier <aleksander.grygier@gmail.com>

* webui: pedantic style tweak for CodePreviewDialog close button

* webui: remove overengineered preview language logic

* chore: update webui static build

---------

Co-authored-by: Aleksander Grygier <aleksander.grygier@gmail.com>
---
 tools/server/public/index.html.gz             | Bin 861835 -> 861777 bytes
 .../app/misc/CodePreviewDialog.svelte         |  93 +++++++++
 .../app/misc/MarkdownContent.svelte           | 180 +++++++++++++-----
 3 files changed, 230 insertions(+), 43 deletions(-)
 create mode 100644 tools/server/webui/src/lib/components/app/misc/CodePreviewDialog.svelte

diff --git a/tools/server/public/index.html.gz b/tools/server/public/index.html.gz
index a81bae04d1983d992a4b46da93153d1cfa63c704..501fa455a24169b1c00bb2ebe056c3719b4ce1e8 100644
GIT binary patch
delta 822429
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diff --git a/tools/server/webui/src/lib/components/app/misc/CodePreviewDialog.svelte b/tools/server/webui/src/lib/components/app/misc/CodePreviewDialog.svelte
new file mode 100644
index 00000000000..702519f9ff9
--- /dev/null
+++ b/tools/server/webui/src/lib/components/app/misc/CodePreviewDialog.svelte
@@ -0,0 +1,93 @@
+<script lang="ts">
+	import { Dialog as DialogPrimitive } from 'bits-ui';
+	import XIcon from '@lucide/svelte/icons/x';
+
+	interface Props {
+		open: boolean;
+		code: string;
+		language: string;
+		onOpenChange?: (open: boolean) => void;
+	}
+
+	let { open = $bindable(), code, language, onOpenChange }: Props = $props();
+
+	let iframeRef = $state<HTMLIFrameElement | null>(null);
+
+	$effect(() => {
+		if (!iframeRef) return;
+
+		if (open) {
+			iframeRef.srcdoc = code;
+		} else {
+			iframeRef.srcdoc = '';
+		}
+	});
+
+	function handleOpenChange(nextOpen: boolean) {
+		open = nextOpen;
+		onOpenChange?.(nextOpen);
+	}
+</script>
+
+<DialogPrimitive.Root {open} onOpenChange={handleOpenChange}>
+	<DialogPrimitive.Portal>
+		<DialogPrimitive.Overlay class="code-preview-overlay" />
+
+		<DialogPrimitive.Content class="code-preview-content">
+			<iframe
+				bind:this={iframeRef}
+				title="Preview {language}"
+				sandbox="allow-scripts"
+				class="code-preview-iframe"
+			></iframe>
+
+			<DialogPrimitive.Close
+				class="code-preview-close absolute top-4 right-4 border-none bg-transparent text-white opacity-70 mix-blend-difference transition-opacity hover:opacity-100 focus-visible:ring-0 focus-visible:ring-offset-0 focus-visible:outline-none disabled:pointer-events-none [&_svg]:pointer-events-none [&_svg]:shrink-0 [&_svg:not([class*='size-'])]:size-8"
+				aria-label="Close preview"
+			>
+				<XIcon />
+				<span class="sr-only">Close preview</span>
+			</DialogPrimitive.Close>
+		</DialogPrimitive.Content>
+	</DialogPrimitive.Portal>
+</DialogPrimitive.Root>
+
+<style lang="postcss">
+	:global(.code-preview-overlay) {
+		position: fixed;
+		inset: 0;
+		background-color: transparent;
+		z-index: 100000;
+	}
+
+	:global(.code-preview-content) {
+		position: fixed;
+		inset: 0;
+		top: 0 !important;
+		left: 0 !important;
+		width: 100dvw;
+		height: 100dvh;
+		margin: 0;
+		padding: 0;
+		border: none;
+		border-radius: 0;
+		background-color: transparent;
+		box-shadow: none;
+		display: block;
+		overflow: hidden;
+		transform: none !important;
+		z-index: 100001;
+	}
+
+	:global(.code-preview-iframe) {
+		display: block;
+		width: 100dvw;
+		height: 100dvh;
+		border: 0;
+	}
+
+	:global(.code-preview-close) {
+		position: absolute;
+		z-index: 100002;
+	}
+</style>
diff --git a/tools/server/webui/src/lib/components/app/misc/MarkdownContent.svelte b/tools/server/webui/src/lib/components/app/misc/MarkdownContent.svelte
index 1f4caa9003b..1c069db58d8 100644
--- a/tools/server/webui/src/lib/components/app/misc/MarkdownContent.svelte
+++ b/tools/server/webui/src/lib/components/app/misc/MarkdownContent.svelte
@@ -15,6 +15,7 @@
 	import githubLightCss from 'highlight.js/styles/github.css?inline';
 	import { mode } from 'mode-watcher';
 	import { remarkLiteralHtml } from '$lib/markdown/literal-html';
+	import CodePreviewDialog from './CodePreviewDialog.svelte';
 
 	interface Props {
 		content: string;
@@ -25,6 +26,9 @@
 
 	let containerRef = $state<HTMLDivElement>();
 	let processedHtml = $state('');
+	let previewDialogOpen = $state(false);
+	let previewCode = $state('');
+	let previewLanguage = $state('text');
 
 	function loadHighlightTheme(isDark: boolean) {
 		if (!browser) return;
@@ -117,7 +121,6 @@
 
 			const rawCode = codeElement.textContent || '';
 			const codeId = `code-${Date.now()}-${index}`;
-
 			codeElement.setAttribute('data-code-id', codeId);
 			codeElement.setAttribute('data-raw-code', rawCode);
 
@@ -138,11 +141,30 @@
 			copyButton.setAttribute('type', 'button');
 
 			copyButton.innerHTML = `
-				<svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-copy-icon lucide-copy"><rect width="14" height="14" x="8" y="8" rx="2" ry="2"/><path d="M4 16c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h10c1.1 0 2 .9 2 2"/></svg>
-			`;
+                                <svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-copy-icon lucide-copy"><rect width="14" height="14" x="8" y="8" rx="2" ry="2"/><path d="M4 16c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h10c1.1 0 2 .9 2 2"/></svg>
+                        `;
+
+			const actions = document.createElement('div');
+			actions.className = 'code-block-actions';
+
+			actions.appendChild(copyButton);
+
+			if (language.toLowerCase() === 'html') {
+				const previewButton = document.createElement('button');
+				previewButton.className = 'preview-code-btn';
+				previewButton.setAttribute('data-code-id', codeId);
+				previewButton.setAttribute('title', 'Preview code');
+				previewButton.setAttribute('type', 'button');
+
+				previewButton.innerHTML = `
+                                        <svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" class="lucide lucide-eye lucide-eye-icon"><path d="M2.062 12.345a1 1 0 0 1 0-.69C3.5 7.73 7.36 5 12 5s8.5 2.73 9.938 6.655a1 1 0 0 1 0 .69C20.5 16.27 16.64 19 12 19s-8.5-2.73-9.938-6.655"/><circle cx="12" cy="12" r="3"/></svg>
+                                `;
+
+				actions.appendChild(previewButton);
+			}
 
 			header.appendChild(languageLabel);
-			header.appendChild(copyButton);
+			header.appendChild(actions);
 			wrapper.appendChild(header);
 
 			const clonedPre = pre.cloneNode(true) as HTMLElement;
@@ -180,49 +202,105 @@
 		}
 	}
 
-	function setupCopyButtons() {
-		if (!containerRef) return;
+	function getCodeInfoFromTarget(target: HTMLElement) {
+		const wrapper = target.closest('.code-block-wrapper');
 
-		const copyButtons = containerRef.querySelectorAll('.copy-code-btn');
+		if (!wrapper) {
+			console.error('No wrapper found');
+			return null;
+		}
 
-		for (const button of copyButtons) {
-			button.addEventListener('click', async (e) => {
-				e.preventDefault();
-				e.stopPropagation();
+		const codeElement = wrapper.querySelector<HTMLElement>('code[data-code-id]');
 
-				const target = e.currentTarget as HTMLButtonElement;
-				const codeId = target.getAttribute('data-code-id');
+		if (!codeElement) {
+			console.error('No code element found in wrapper');
+			return null;
+		}
 
-				if (!codeId) {
-					console.error('No code ID found on button');
-					return;
-				}
+		const rawCode = codeElement.getAttribute('data-raw-code');
 
-				// Find the code element within the same wrapper
-				const wrapper = target.closest('.code-block-wrapper');
-				if (!wrapper) {
-					console.error('No wrapper found');
-					return;
-				}
+		if (rawCode === null) {
+			console.error('No raw code found');
+			return null;
+		}
 
-				const codeElement = wrapper.querySelector('code[data-code-id]');
-				if (!codeElement) {
-					console.error('No code element found in wrapper');
-					return;
-				}
+		const languageLabel = wrapper.querySelector<HTMLElement>('.code-language');
+		const language = languageLabel?.textContent?.trim() || 'text';
 
-				const rawCode = codeElement.getAttribute('data-raw-code');
-				if (!rawCode) {
-					console.error('No raw code found');
-					return;
-				}
+		return { rawCode, language };
+	}
 
-				try {
-					await copyCodeToClipboard(rawCode);
-				} catch (error) {
-					console.error('Failed to copy code:', error);
-				}
-			});
+	async function handleCopyClick(event: Event) {
+		event.preventDefault();
+		event.stopPropagation();
+
+		const target = event.currentTarget as HTMLButtonElement | null;
+
+		if (!target) {
+			return;
+		}
+
+		const info = getCodeInfoFromTarget(target);
+
+		if (!info) {
+			return;
+		}
+
+		try {
+			await copyCodeToClipboard(info.rawCode);
+		} catch (error) {
+			console.error('Failed to copy code:', error);
+		}
+	}
+
+	function handlePreviewClick(event: Event) {
+		event.preventDefault();
+		event.stopPropagation();
+
+		const target = event.currentTarget as HTMLButtonElement | null;
+
+		if (!target) {
+			return;
+		}
+
+		const info = getCodeInfoFromTarget(target);
+
+		if (!info) {
+			return;
+		}
+
+		previewCode = info.rawCode;
+		previewLanguage = info.language;
+		previewDialogOpen = true;
+	}
+
+	function setupCodeBlockActions() {
+		if (!containerRef) return;
+
+		const wrappers = containerRef.querySelectorAll<HTMLElement>('.code-block-wrapper');
+
+		for (const wrapper of wrappers) {
+			const copyButton = wrapper.querySelector<HTMLButtonElement>('.copy-code-btn');
+			const previewButton = wrapper.querySelector<HTMLButtonElement>('.preview-code-btn');
+
+			if (copyButton && copyButton.dataset.listenerBound !== 'true') {
+				copyButton.dataset.listenerBound = 'true';
+				copyButton.addEventListener('click', handleCopyClick);
+			}
+
+			if (previewButton && previewButton.dataset.listenerBound !== 'true') {
+				previewButton.dataset.listenerBound = 'true';
+				previewButton.addEventListener('click', handlePreviewClick);
+			}
+		}
+	}
+
+	function handlePreviewDialogOpenChange(open: boolean) {
+		previewDialogOpen = open;
+
+		if (!open) {
+			previewCode = '';
+			previewLanguage = 'text';
 		}
 	}
 
@@ -243,7 +321,7 @@
 
 	$effect(() => {
 		if (containerRef && processedHtml) {
-			setupCopyButtons();
+			setupCodeBlockActions();
 		}
 	});
 </script>
@@ -253,6 +331,13 @@
 	{@html processedHtml}
 </div>
 
+<CodePreviewDialog
+	open={previewDialogOpen}
+	code={previewCode}
+	language={previewLanguage}
+	onOpenChange={handlePreviewDialogOpenChange}
+/>
+
 <style>
 	/* Base typography styles */
 	div :global(p:not(:last-child)) {
@@ -472,7 +557,14 @@
 		letter-spacing: 0.05em;
 	}
 
-	div :global(.copy-code-btn) {
+	div :global(.code-block-actions) {
+		display: flex;
+		align-items: center;
+		gap: 0.5rem;
+	}
+
+	div :global(.copy-code-btn),
+	div :global(.preview-code-btn) {
 		display: flex;
 		align-items: center;
 		justify-content: center;
@@ -483,11 +575,13 @@
 		transition: all 0.2s ease;
 	}
 
-	div :global(.copy-code-btn:hover) {
+	div :global(.copy-code-btn:hover),
+	div :global(.preview-code-btn:hover) {
 		transform: scale(1.05);
 	}
 
-	div :global(.copy-code-btn:active) {
+	div :global(.copy-code-btn:active),
+	div :global(.preview-code-btn:active) {
 		transform: scale(0.95);
 	}
 

From 2f68ce7cfd20e9e7098514bf730e5389b7bba908 Mon Sep 17 00:00:00 2001
From: Pascal <admin@serveurperso.com>
Date: Sat, 1 Nov 2025 19:49:51 +0100
Subject: [PATCH 052/185] webui: auto-refresh /props on inference start to
 resync model metadata (#16784)

* webui: auto-refresh /props on inference start to resync model metadata

- Add no-cache headers to /props and /slots
- Throttle slot checks to 30s
- Prevent concurrent fetches with promise guard
- Trigger refresh from chat streaming for legacy and ModelSelector
- Show dynamic serverWarning when using cached data

* fix: restore proper legacy behavior in webui by using unified /props refresh

Updated assistant message bubbles to show each message's stored model when available,
falling back to the current server model only when the per-message value is missing

When the model selector is disabled, now fetches /props and prioritizes that model name
over chunk metadata, then persists it with the streamed message so legacy mode properly
reflects the backend configuration

* fix: detect first valid SSE chunk and refresh server props once

* fix: removed the slots availability throttle constant and state

* webui: purge ai-generated cruft

* chore: update webui static build
---
 tools/server/public/index.html.gz             | Bin 861777 -> 862214 bytes
 .../ChatMessages/ChatMessageAssistant.svelte  |   4 +-
 tools/server/webui/src/lib/services/chat.ts   |  20 +-
 .../webui/src/lib/stores/chat.svelte.ts       |  54 +++++-
 .../webui/src/lib/stores/server.svelte.ts     | 174 +++++++++++-------
 tools/server/webui/src/lib/types/api.d.ts     |   1 +
 .../server/webui/src/lib/types/settings.d.ts  |   1 +
 7 files changed, 182 insertions(+), 72 deletions(-)

diff --git a/tools/server/public/index.html.gz b/tools/server/public/index.html.gz
index 501fa455a24169b1c00bb2ebe056c3719b4ce1e8..b71690cc81e29b13069e5b548016b91ba074014e 100644
GIT binary patch
delta 821147
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diff --git a/tools/server/webui/src/lib/components/app/chat/ChatMessages/ChatMessageAssistant.svelte b/tools/server/webui/src/lib/components/app/chat/ChatMessages/ChatMessageAssistant.svelte
index 41774c6f874..d8f5630fd14 100644
--- a/tools/server/webui/src/lib/components/app/chat/ChatMessages/ChatMessageAssistant.svelte
+++ b/tools/server/webui/src/lib/components/app/chat/ChatMessages/ChatMessageAssistant.svelte
@@ -85,8 +85,8 @@
 	let displayedModel = $derived((): string | null => {
 		if (!currentConfig.showModelInfo) return null;
 
-		if (currentConfig.modelSelectorEnabled) {
-			return message.model ?? null;
+		if (message.model) {
+			return message.model;
 		}
 
 		return serverModel;
diff --git a/tools/server/webui/src/lib/services/chat.ts b/tools/server/webui/src/lib/services/chat.ts
index df03b10251a..414e060764d 100644
--- a/tools/server/webui/src/lib/services/chat.ts
+++ b/tools/server/webui/src/lib/services/chat.ts
@@ -54,6 +54,7 @@ export class ChatService {
 			onError,
 			onReasoningChunk,
 			onModel,
+			onFirstValidChunk,
 			// Generation parameters
 			temperature,
 			max_tokens,
@@ -201,6 +202,7 @@ export class ChatService {
 					onError,
 					onReasoningChunk,
 					onModel,
+					onFirstValidChunk,
 					conversationId,
 					abortController.signal
 				);
@@ -267,6 +269,7 @@ export class ChatService {
 		onError?: (error: Error) => void,
 		onReasoningChunk?: (chunk: string) => void,
 		onModel?: (model: string) => void,
+		onFirstValidChunk?: () => void,
 		conversationId?: string,
 		abortSignal?: AbortSignal
 	): Promise<void> {
@@ -283,6 +286,7 @@ export class ChatService {
 		let lastTimings: ChatMessageTimings | undefined;
 		let streamFinished = false;
 		let modelEmitted = false;
+		let firstValidChunkEmitted = false;
 
 		try {
 			let chunk = '';
@@ -311,10 +315,12 @@ export class ChatService {
 						try {
 							const parsed: ApiChatCompletionStreamChunk = JSON.parse(data);
 
-							const chunkModel = this.extractModelName(parsed);
-							if (chunkModel && !modelEmitted) {
-								modelEmitted = true;
-								onModel?.(chunkModel);
+							if (!firstValidChunkEmitted && parsed.object === 'chat.completion.chunk') {
+								firstValidChunkEmitted = true;
+
+								if (!abortSignal?.aborted) {
+									onFirstValidChunk?.();
+								}
 							}
 
 							const content = parsed.choices[0]?.delta?.content;
@@ -322,6 +328,12 @@ export class ChatService {
 							const timings = parsed.timings;
 							const promptProgress = parsed.prompt_progress;
 
+							const chunkModel = this.extractModelName(parsed);
+							if (chunkModel && !modelEmitted) {
+								modelEmitted = true;
+								onModel?.(chunkModel);
+							}
+
 							if (timings || promptProgress) {
 								this.updateProcessingState(timings, promptProgress, conversationId);
 								if (timings) {
diff --git a/tools/server/webui/src/lib/stores/chat.svelte.ts b/tools/server/webui/src/lib/stores/chat.svelte.ts
index a2e74a2e107..3f97a89183d 100644
--- a/tools/server/webui/src/lib/stores/chat.svelte.ts
+++ b/tools/server/webui/src/lib/stores/chat.svelte.ts
@@ -1,6 +1,7 @@
 import { DatabaseStore } from '$lib/stores/database';
 import { chatService, slotsService } from '$lib/services';
 import { config } from '$lib/stores/settings.svelte';
+import { serverStore } from '$lib/stores/server.svelte';
 import { normalizeModelName } from '$lib/utils/model-names';
 import { filterByLeafNodeId, findLeafNode, findDescendantMessages } from '$lib/utils/branching';
 import { browser } from '$app/environment';
@@ -362,9 +363,41 @@ class ChatStore {
 
 		let resolvedModel: string | null = null;
 		let modelPersisted = false;
+		const currentConfig = config();
+		const preferServerPropsModel = !currentConfig.modelSelectorEnabled;
+		let serverPropsRefreshed = false;
+		let updateModelFromServerProps: ((persistImmediately?: boolean) => void) | null = null;
+
+		const refreshServerPropsOnce = () => {
+			if (serverPropsRefreshed) {
+				return;
+			}
+
+			serverPropsRefreshed = true;
+
+			const hasExistingProps = serverStore.serverProps !== null;
 
-		const recordModel = (modelName: string, persistImmediately = true): void => {
-			const normalizedModel = normalizeModelName(modelName);
+			serverStore
+				.fetchServerProps({ silent: hasExistingProps })
+				.then(() => {
+					updateModelFromServerProps?.(true);
+				})
+				.catch((error) => {
+					console.warn('Failed to refresh server props after streaming started:', error);
+				});
+		};
+
+		const recordModel = (modelName: string | null | undefined, persistImmediately = true): void => {
+			const serverModelName = serverStore.modelName;
+			const preferredModelSource = preferServerPropsModel
+				? (serverModelName ?? modelName ?? null)
+				: (modelName ?? serverModelName ?? null);
+
+			if (!preferredModelSource) {
+				return;
+			}
+
+			const normalizedModel = normalizeModelName(preferredModelSource);
 
 			if (!normalizedModel || normalizedModel === resolvedModel) {
 				return;
@@ -388,6 +421,20 @@ class ChatStore {
 			}
 		};
 
+		if (preferServerPropsModel) {
+			updateModelFromServerProps = (persistImmediately = true) => {
+				const currentServerModel = serverStore.modelName;
+
+				if (!currentServerModel) {
+					return;
+				}
+
+				recordModel(currentServerModel, persistImmediately);
+			};
+
+			updateModelFromServerProps(false);
+		}
+
 		slotsService.startStreaming();
 		slotsService.setActiveConversation(assistantMessage.convId);
 
@@ -396,6 +443,9 @@ class ChatStore {
 			{
 				...this.getApiOptions(),
 
+				onFirstValidChunk: () => {
+					refreshServerPropsOnce();
+				},
 				onChunk: (chunk: string) => {
 					streamedContent += chunk;
 					this.setConversationStreaming(
diff --git a/tools/server/webui/src/lib/stores/server.svelte.ts b/tools/server/webui/src/lib/stores/server.svelte.ts
index 1fd4afb0402..c7056cc120e 100644
--- a/tools/server/webui/src/lib/stores/server.svelte.ts
+++ b/tools/server/webui/src/lib/stores/server.svelte.ts
@@ -52,6 +52,7 @@ class ServerStore {
 	private _error = $state<string | null>(null);
 	private _serverWarning = $state<string | null>(null);
 	private _slotsEndpointAvailable = $state<boolean | null>(null);
+	private fetchServerPropsPromise: Promise<void> | null = null;
 
 	private readCachedServerProps(): ApiLlamaCppServerProps | null {
 		if (!browser) return null;
@@ -171,73 +172,65 @@ class ServerStore {
 	/**
 	 * Fetches server properties from the server
 	 */
-	async fetchServerProps(): Promise<void> {
-		this._loading = true;
-		this._error = null;
-		this._serverWarning = null;
+	async fetchServerProps(options: { silent?: boolean } = {}): Promise<void> {
+		const { silent = false } = options;
+		const isSilent = silent && this._serverProps !== null;
 
-		try {
-			console.log('Fetching server properties...');
-			const props = await ChatService.getServerProps();
-			this._serverProps = props;
-			this.persistServerProps(props);
-			console.log('Server properties loaded:', props);
-
-			// Check slots endpoint availability after server props are loaded
-			await this.checkSlotsEndpointAvailability();
-		} catch (error) {
-			const hadCachedProps = this._serverProps !== null;
-			let errorMessage = 'Failed to connect to server';
-			let isOfflineLikeError = false;
-			let isServerSideError = false;
-
-			if (error instanceof Error) {
-				// Handle specific error types with user-friendly messages
-				if (error.name === 'TypeError' && error.message.includes('fetch')) {
-					errorMessage = 'Server is not running or unreachable';
-					isOfflineLikeError = true;
-				} else if (error.message.includes('ECONNREFUSED')) {
-					errorMessage = 'Connection refused - server may be offline';
-					isOfflineLikeError = true;
-				} else if (error.message.includes('ENOTFOUND')) {
-					errorMessage = 'Server not found - check server address';
-					isOfflineLikeError = true;
-				} else if (error.message.includes('ETIMEDOUT')) {
-					errorMessage = 'Request timed out - the server took too long to respond';
-					isOfflineLikeError = true;
-				} else if (error.message.includes('503')) {
-					errorMessage = 'Server temporarily unavailable - try again shortly';
-					isServerSideError = true;
-				} else if (error.message.includes('500')) {
-					errorMessage = 'Server error - check server logs';
-					isServerSideError = true;
-				} else if (error.message.includes('404')) {
-					errorMessage = 'Server endpoint not found';
-				} else if (error.message.includes('403') || error.message.includes('401')) {
-					errorMessage = 'Access denied';
+		if (this.fetchServerPropsPromise) {
+			return this.fetchServerPropsPromise;
+		}
+
+		if (!isSilent) {
+			this._loading = true;
+			this._error = null;
+			this._serverWarning = null;
+		}
+
+		const hadProps = this._serverProps !== null;
+
+		const fetchPromise = (async () => {
+			try {
+				const props = await ChatService.getServerProps();
+				this._serverProps = props;
+				this.persistServerProps(props);
+				this._error = null;
+				this._serverWarning = null;
+				await this.checkSlotsEndpointAvailability();
+			} catch (error) {
+				if (isSilent && hadProps) {
+					console.warn('Silent server props refresh failed, keeping cached data:', error);
+					return;
+				}
+
+				this.handleFetchServerPropsError(error, hadProps);
+			} finally {
+				if (!isSilent) {
+					this._loading = false;
 				}
+
+				this.fetchServerPropsPromise = null;
 			}
+		})();
+
+		this.fetchServerPropsPromise = fetchPromise;
+
+		await fetchPromise;
+	}
 
-			let cachedProps: ApiLlamaCppServerProps | null = null;
+	/**
+	 * Handles fetch failures by attempting to recover cached server props and
+	 * updating the user-facing error or warning state appropriately.
+	 */
+	private handleFetchServerPropsError(error: unknown, hadProps: boolean): void {
+		const { errorMessage, isOfflineLikeError, isServerSideError } = this.normalizeFetchError(error);
 
-			if (!hadCachedProps) {
-				cachedProps = this.readCachedServerProps();
-				if (cachedProps) {
-					this._serverProps = cachedProps;
-					this._error = null;
+		let cachedProps: ApiLlamaCppServerProps | null = null;
 
-					if (isOfflineLikeError || isServerSideError) {
-						this._serverWarning = errorMessage;
-					}
+		if (!hadProps) {
+			cachedProps = this.readCachedServerProps();
 
-					console.warn(
-						'Failed to refresh server properties, using cached values from localStorage:',
-						errorMessage
-					);
-				} else {
-					this._error = errorMessage;
-				}
-			} else {
+			if (cachedProps) {
+				this._serverProps = cachedProps;
 				this._error = null;
 
 				if (isOfflineLikeError || isServerSideError) {
@@ -245,14 +238,66 @@ class ServerStore {
 				}
 
 				console.warn(
-					'Failed to refresh server properties, continuing with cached values:',
+					'Failed to refresh server properties, using cached values from localStorage:',
 					errorMessage
 				);
+			} else {
+				this._error = errorMessage;
+			}
+		} else {
+			this._error = null;
+
+			if (isOfflineLikeError || isServerSideError) {
+				this._serverWarning = errorMessage;
 			}
-			console.error('Error fetching server properties:', error);
-		} finally {
-			this._loading = false;
+
+			console.warn(
+				'Failed to refresh server properties, continuing with cached values:',
+				errorMessage
+			);
 		}
+
+		console.error('Error fetching server properties:', error);
+	}
+
+	private normalizeFetchError(error: unknown): {
+		errorMessage: string;
+		isOfflineLikeError: boolean;
+		isServerSideError: boolean;
+	} {
+		let errorMessage = 'Failed to connect to server';
+		let isOfflineLikeError = false;
+		let isServerSideError = false;
+
+		if (error instanceof Error) {
+			const message = error.message || '';
+
+			if (error.name === 'TypeError' && message.includes('fetch')) {
+				errorMessage = 'Server is not running or unreachable';
+				isOfflineLikeError = true;
+			} else if (message.includes('ECONNREFUSED')) {
+				errorMessage = 'Connection refused - server may be offline';
+				isOfflineLikeError = true;
+			} else if (message.includes('ENOTFOUND')) {
+				errorMessage = 'Server not found - check server address';
+				isOfflineLikeError = true;
+			} else if (message.includes('ETIMEDOUT')) {
+				errorMessage = 'Request timed out - the server took too long to respond';
+				isOfflineLikeError = true;
+			} else if (message.includes('503')) {
+				errorMessage = 'Server temporarily unavailable - try again shortly';
+				isServerSideError = true;
+			} else if (message.includes('500')) {
+				errorMessage = 'Server error - check server logs';
+				isServerSideError = true;
+			} else if (message.includes('404')) {
+				errorMessage = 'Server endpoint not found';
+			} else if (message.includes('403') || message.includes('401')) {
+				errorMessage = 'Access denied';
+			}
+		}
+
+		return { errorMessage, isOfflineLikeError, isServerSideError };
 	}
 
 	/**
@@ -264,6 +309,7 @@ class ServerStore {
 		this._serverWarning = null;
 		this._loading = false;
 		this._slotsEndpointAvailable = null;
+		this.fetchServerPropsPromise = null;
 		this.persistServerProps(null);
 	}
 }
diff --git a/tools/server/webui/src/lib/types/api.d.ts b/tools/server/webui/src/lib/types/api.d.ts
index 6d76ab1f68e..6ebc43db0e3 100644
--- a/tools/server/webui/src/lib/types/api.d.ts
+++ b/tools/server/webui/src/lib/types/api.d.ts
@@ -186,6 +186,7 @@ export interface ApiChatCompletionRequest {
 }
 
 export interface ApiChatCompletionStreamChunk {
+	object?: string;
 	model?: string;
 	choices: Array<{
 		model?: string;
diff --git a/tools/server/webui/src/lib/types/settings.d.ts b/tools/server/webui/src/lib/types/settings.d.ts
index 659fb0c7d1c..946ef015e92 100644
--- a/tools/server/webui/src/lib/types/settings.d.ts
+++ b/tools/server/webui/src/lib/types/settings.d.ts
@@ -42,6 +42,7 @@ export interface SettingsChatServiceOptions {
 	onChunk?: (chunk: string) => void;
 	onReasoningChunk?: (chunk: string) => void;
 	onModel?: (model: string) => void;
+	onFirstValidChunk?: () => void;
 	onComplete?: (response: string, reasoningContent?: string, timings?: ChatMessageTimings) => void;
 	onError?: (error: Error) => void;
 }

From 7fd205a8e8832ead273f62c5fd81d2b8aa910535 Mon Sep 17 00:00:00 2001
From: Georgi Gerganov <ggerganov@gmail.com>
Date: Sun, 2 Nov 2025 00:15:31 +0200
Subject: [PATCH 053/185] scripts : add script to bench models (#16894)

---
 scripts/bench-models.sh               | 74 +++++++++++++++++++++++++++
 tools/batched-bench/batched-bench.cpp |  2 -
 2 files changed, 74 insertions(+), 2 deletions(-)
 create mode 100644 scripts/bench-models.sh

diff --git a/scripts/bench-models.sh b/scripts/bench-models.sh
new file mode 100644
index 00000000000..744b0de359c
--- /dev/null
+++ b/scripts/bench-models.sh
@@ -0,0 +1,74 @@
+#!/usr/bin/env bash
+
+RESULTS="bench-models-results.txt"
+: > "$RESULTS"
+
+ARGS_BB="-c 270336 -npp 512,4096,8192 -npl 1,2,4,8,16,32 -ntg 32"
+ARGS_B="-d 0,4096,8192,16384,32768 -p 2048 -n 32"
+
+QUICK=0
+while (( "$#" )); do
+  case "$1" in
+    --quick) QUICK=1; shift ;;
+    *) shift ;;
+  esac
+done
+
+if (( QUICK )); then
+  ARGS_BB="-c 20480 -npp 512,4096 -npl 1,2,4 -ntg 32"
+  ARGS_B="-d 0 -p 2048 -n 32"
+fi
+
+run_model() {
+  local HFR=$1
+  local HFF=$2
+
+  printf "## ${HFR}\n" | tee -a "$RESULTS"
+  printf "\n" | tee -a "$RESULTS"
+  printf "Model: https://huggingface.co/${HFR}\n" | tee -a "$RESULTS"
+  printf "\n" | tee -a "$RESULTS"
+
+  printf -- "- \`llama-batched-bench\`\n" | tee -a "$RESULTS"
+  printf "\n" | tee -a "$RESULTS"
+
+  ./bin/llama-batched-bench \
+    -hfr "${HFR}" -hff "${HFF}" \
+    -m "${HFF}" -fa 1 -ub 2048 --no-mmap \
+    ${ARGS_BB} | tee -a "$RESULTS"
+
+  printf "\n" | tee -a "$RESULTS"
+
+  printf -- "- \`llama-bench\`\n" | tee -a "$RESULTS"
+  printf "\n" | tee -a "$RESULTS"
+
+  ./bin/llama-bench \
+    -m "${HFF}" -fa 1 -ub 2048 -mmp 0 \
+    ${ARGS_B} | tee -a "$RESULTS"
+
+  printf "\n" | tee -a "$RESULTS"
+
+  printf "\n"
+}
+
+run_model "ggml-org/gpt-oss-20b-GGUF"                       "gpt-oss-20b-mxfp4.gguf"
+run_model "ggml-org/gpt-oss-120b-GGUF"                      "gpt-oss-120b-mxfp4-00001-of-00003.gguf"
+run_model "ggml-org/Qwen3-Coder-30B-A3B-Instruct-Q8_0-GGUF" "qwen3-coder-30b-a3b-instruct-q8_0.gguf"
+run_model "ggml-org/Qwen2.5-Coder-7B-Q8_0-GGUF"             "qwen2.5-coder-7b-q8_0.gguf"
+run_model "ggml-org/gemma-3-4b-it-qat-GGUF"                 "gemma-3-4b-it-qat-Q4_0.gguf"
+
+if [[ -f models-extra.txt ]]; then
+    while read -r HFR HFF; do
+        [[ -z "$HFR" ]] && continue
+        run_model "$HFR" "$HFF"
+    done < models-extra.txt
+fi
+
+printf "\n=====================================\n"
+printf "\n"
+
+cat "$RESULTS"
+
+printf "\n"
+printf "Done! Results are written to $RESULTS\n"
+printf "\n"
+
diff --git a/tools/batched-bench/batched-bench.cpp b/tools/batched-bench/batched-bench.cpp
index fcfcd80771c..f1ab27cd54d 100644
--- a/tools/batched-bench/batched-bench.cpp
+++ b/tools/batched-bench/batched-bench.cpp
@@ -221,7 +221,5 @@ int main(int argc, char ** argv) {
 
     llama_backend_free();
 
-    LOG("\n\n");
-
     return 0;
 }

From d38d9f0877a5872daa3c5f06fb9a86376bf15d50 Mon Sep 17 00:00:00 2001
From: Aaron Teo <aaron.teo1@ibm.com>
Date: Sun, 2 Nov 2025 08:48:23 +0800
Subject: [PATCH 054/185] ggml: add s390x cpu-feats (#16774)

---
 .github/workflows/release.yml             |  4 +-
 ggml/src/CMakeLists.txt                   |  9 ++--
 ggml/src/ggml-cpu/CMakeLists.txt          | 13 ++++--
 ggml/src/ggml-cpu/arch/s390/cpu-feats.cpp | 50 +++++++++++++++++++++++
 4 files changed, 68 insertions(+), 8 deletions(-)
 create mode 100644 ggml/src/ggml-cpu/arch/s390/cpu-feats.cpp

diff --git a/.github/workflows/release.yml b/.github/workflows/release.yml
index cab3ba9e68e..e72caa423ba 100644
--- a/.github/workflows/release.yml
+++ b/.github/workflows/release.yml
@@ -134,8 +134,8 @@ jobs:
         include:
           - build: 'x64'
             os: ubuntu-22.04
-          - build: 's390x-z15' # z15 because our CI runners are on z15
-            os: ubuntu-22.04-s390x
+          - build: 's390x'
+            os: ubuntu-24.04-s390x
           # GGML_BACKEND_DL and GGML_CPU_ALL_VARIANTS are not currently supported on arm
           # - build: 'arm64'
           #   os: ubuntu-22.04-arm
diff --git a/ggml/src/CMakeLists.txt b/ggml/src/CMakeLists.txt
index ba281b8e6d1..f30e4ac9020 100644
--- a/ggml/src/CMakeLists.txt
+++ b/ggml/src/CMakeLists.txt
@@ -308,6 +308,10 @@ function(ggml_add_cpu_backend_variant tag_name)
             set(GGML_INTERNAL_${feat} ON)
         endforeach()
     elseif (GGML_SYSTEM_ARCH STREQUAL "s390x")
+        foreach (feat VXE2 NNPA)
+            set(GGML_INTERNAL_${feat} OFF)
+        endforeach()
+
         foreach (feat ${ARGN})
             set(GGML_INTERNAL_${feat} ON)
         endforeach()
@@ -377,9 +381,8 @@ if (GGML_CPU_ALL_VARIANTS)
         endif()
     elseif (GGML_SYSTEM_ARCH STREQUAL "s390x")
         if (CMAKE_SYSTEM_NAME MATCHES "Linux")
-            ggml_add_cpu_backend_variant(s390x_z15  Z15 VXE)
-            # ggml_add_cpu_backend_variant(s390x_z16  Z16 VXE)
-            # ggml_add_cpu_backend_variant(s390x_z17  Z17 VXE)
+            ggml_add_cpu_backend_variant(z15    Z15 VXE2)
+            ggml_add_cpu_backend_variant(z16    Z16 VXE2 NNPA)
         else()
             message(FATAL_ERROR "Unsupported s390x target OS: ${CMAKE_SYSTEM_NAME}")
         endif()
diff --git a/ggml/src/ggml-cpu/CMakeLists.txt b/ggml/src/ggml-cpu/CMakeLists.txt
index 34323afa076..23ec8bb08a7 100644
--- a/ggml/src/ggml-cpu/CMakeLists.txt
+++ b/ggml/src/ggml-cpu/CMakeLists.txt
@@ -504,11 +504,18 @@ function(ggml_add_cpu_backend_variant_impl tag_name)
             endforeach()
         endif()
 
-        if (GGML_VXE OR GGML_INTERNAL_VXE)
-            message(STATUS "VX/VXE/VXE2 enabled")
+        if (GGML_VXE OR GGML_INTERNAL_VXE2)
+            message(STATUS "VXE2 enabled")
             list(APPEND ARCH_FLAGS -mvx -mzvector)
-            list(APPEND ARCH_DEFINITIONS GGML_VXE)
+            list(APPEND ARCH_DEFINITIONS GGML_USE_VXE2)
         endif()
+
+        if (GGML_INTERNAL_NNPA)
+            message(STATUS "NNPA enabled")
+            list(APPEND ARCH_DEFINITIONS GGML_USE_NNPA)
+        endif()
+
+        ggml_add_cpu_backend_features(${GGML_CPU_NAME} s390 ${ARCH_DEFINITIONS})
     elseif (CMAKE_SYSTEM_PROCESSOR MATCHES "wasm")
         message(STATUS "Wasm detected")
         list (APPEND GGML_CPU_SOURCES ggml-cpu/arch/wasm/quants.c)
diff --git a/ggml/src/ggml-cpu/arch/s390/cpu-feats.cpp b/ggml/src/ggml-cpu/arch/s390/cpu-feats.cpp
new file mode 100644
index 00000000000..5f4405a7f30
--- /dev/null
+++ b/ggml/src/ggml-cpu/arch/s390/cpu-feats.cpp
@@ -0,0 +1,50 @@
+#include "ggml-backend-impl.h"
+
+#if defined(__s390x__)
+#include <sys/auxv.h>
+
+// find hwcap bits in asm/elf.h
+#ifndef HWCAP_VXRS_EXT2
+#define HWCAP_VXRS_EXT2 (1 << 15)
+#endif
+
+#ifndef HWCAP_NNPA
+#define HWCAP_NNPA (1 << 20)
+#endif
+
+struct s390x_features {
+    bool has_vxe2 = false;
+    bool has_nnpa = false;
+
+    s390x_features() {
+        uint32_t hwcap = getauxval(AT_HWCAP);
+        // NOTE: use hwcap2 with DFLT for z17 and later
+        // uint32_t hwcap2 = getauxval(AT_HWCAP2);
+
+        has_vxe2 = !!(hwcap & HWCAP_VXRS_EXT2);
+        has_nnpa = !!(hwcap & HWCAP_NNPA);
+    }
+};
+
+static int ggml_backend_cpu_s390x_score() {
+    int score = 1;
+    s390x_features sf;
+
+// IBM z15 / LinuxONE 3
+#ifdef GGML_USE_VXE2
+    if (!sf.has_vxe2) { return 0; }
+    score += 1 << 1;
+#endif
+
+// IBM z16 / LinuxONE 4 and z17 / LinuxONE 5
+#ifdef GGML_USE_NNPA
+    if (!sf.has_nnpa) { return 0; }
+    score += 1 << 2;
+#endif
+
+    return score;
+}
+
+GGML_BACKEND_DL_SCORE_IMPL(ggml_backend_cpu_s390x_score)
+
+#endif  // __s390x__

From a864132ba546b6385922226480ee4e392aaa065c Mon Sep 17 00:00:00 2001
From: Aaron Teo <aaron.teo1@ibm.com>
Date: Sun, 2 Nov 2025 08:48:46 +0800
Subject: [PATCH 055/185] devops: fix failing s390x docker build (#16918)

---
 .devops/s390x.Dockerfile | 5 ++++-
 docs/docker.md           | 6 +++---
 2 files changed, 7 insertions(+), 4 deletions(-)

diff --git a/.devops/s390x.Dockerfile b/.devops/s390x.Dockerfile
index 3df1a2b0def..b7c9457680b 100644
--- a/.devops/s390x.Dockerfile
+++ b/.devops/s390x.Dockerfile
@@ -24,8 +24,9 @@ RUN --mount=type=cache,target=/root/.ccache \
         -DCMAKE_C_COMPILER_LAUNCHER=ccache \
         -DCMAKE_CXX_COMPILER_LAUNCHER=ccache \
         -DLLAMA_BUILD_TESTS=OFF \
-        -DGGML_BACKEND_DL=OFF \
         -DGGML_NATIVE=OFF \
+        -DGGML_BACKEND_DL=ON \
+        -DGGML_CPU_ALL_VARIANTS=ON \
         -DGGML_BLAS=ON \
         -DGGML_BLAS_VENDOR=OpenBLAS && \
     cmake --build build --config Release -j $(nproc) && \
@@ -103,6 +104,7 @@ FROM base AS light
 WORKDIR /llama.cpp/bin
 
 # Copy llama.cpp binaries and libraries
+COPY --from=collector /llama.cpp/bin/*.so /llama.cpp/bin
 COPY --from=collector /llama.cpp/bin/llama-cli /llama.cpp/bin
 
 ENTRYPOINT [ "/llama.cpp/bin/llama-cli" ]
@@ -116,6 +118,7 @@ ENV LLAMA_ARG_HOST=0.0.0.0
 WORKDIR /llama.cpp/bin
 
 # Copy llama.cpp binaries and libraries
+COPY --from=collector /llama.cpp/bin/*.so /llama.cpp/bin
 COPY --from=collector /llama.cpp/bin/llama-server /llama.cpp/bin
 
 EXPOSE 8080
diff --git a/docs/docker.md b/docs/docker.md
index bfabf2425a7..98502a0c505 100644
--- a/docs/docker.md
+++ b/docs/docker.md
@@ -7,9 +7,9 @@
 ## Images
 We have three Docker images available for this project:
 
-1. `ghcr.io/ggml-org/llama.cpp:full`: This image includes both the main executable file and the tools to convert LLaMA models into ggml and convert into 4-bit quantization. (platforms: `linux/amd64`, `linux/arm64`)
-2. `ghcr.io/ggml-org/llama.cpp:light`: This image only includes the main executable file. (platforms: `linux/amd64`, `linux/arm64`)
-3. `ghcr.io/ggml-org/llama.cpp:server`: This image only includes the server executable file. (platforms: `linux/amd64`, `linux/arm64`)
+1. `ghcr.io/ggml-org/llama.cpp:full`: This image includes both the main executable file and the tools to convert LLaMA models into ggml and convert into 4-bit quantization. (platforms: `linux/amd64`, `linux/arm64`, `linux/s390x`)
+2. `ghcr.io/ggml-org/llama.cpp:light`: This image only includes the main executable file. (platforms: `linux/amd64`, `linux/arm64`, `linux/s390x`)
+3. `ghcr.io/ggml-org/llama.cpp:server`: This image only includes the server executable file. (platforms: `linux/amd64`, `linux/arm64`, `linux/s390x`)
 
 Additionally, there the following images, similar to the above:
 

From 7db35a7958a943be1693879f42d166f152613979 Mon Sep 17 00:00:00 2001
From: mnehete32 <33429707+mnehete32@users.noreply.github.com>
Date: Sun, 2 Nov 2025 08:42:57 +0530
Subject: [PATCH 056/185] CUDA: add FLOOR, CEIL, ROUND, TRUNC unary ops
 (#16917)

---
 ggml/src/ggml-cuda/ggml-cuda.cu | 16 ++++++++++++++++
 ggml/src/ggml-cuda/unary.cu     | 32 ++++++++++++++++++++++++++++++++
 ggml/src/ggml-cuda/unary.cuh    |  8 ++++++++
 3 files changed, 56 insertions(+)

diff --git a/ggml/src/ggml-cuda/ggml-cuda.cu b/ggml/src/ggml-cuda/ggml-cuda.cu
index 61a8f1df87d..5667ec0c4d7 100644
--- a/ggml/src/ggml-cuda/ggml-cuda.cu
+++ b/ggml/src/ggml-cuda/ggml-cuda.cu
@@ -2499,6 +2499,18 @@ static bool ggml_cuda_compute_forward(ggml_backend_cuda_context & ctx, struct gg
                 case GGML_UNARY_OP_XIELU:
                     ggml_cuda_op_xielu(ctx, dst);
                     break;
+                case GGML_UNARY_OP_FLOOR:
+                    ggml_cuda_op_floor(ctx, dst);
+                    break;
+                case GGML_UNARY_OP_CEIL:
+                    ggml_cuda_op_ceil(ctx, dst);
+                    break;
+                case GGML_UNARY_OP_ROUND:
+                    ggml_cuda_op_round(ctx, dst);
+                    break;
+                case GGML_UNARY_OP_TRUNC:
+                    ggml_cuda_op_trunc(ctx, dst);
+                    break;
                 default:
                     return false;
             }
@@ -3769,6 +3781,10 @@ static bool ggml_backend_cuda_device_supports_op(ggml_backend_dev_t dev, const g
                 case GGML_UNARY_OP_TANH:
                 case GGML_UNARY_OP_EXP:
                 case GGML_UNARY_OP_ELU:
+                case GGML_UNARY_OP_FLOOR:
+                case GGML_UNARY_OP_CEIL:
+                case GGML_UNARY_OP_ROUND:
+                case GGML_UNARY_OP_TRUNC:
                     return ggml_is_contiguous(op->src[0]);
                 default:
                     return false;
diff --git a/ggml/src/ggml-cuda/unary.cu b/ggml/src/ggml-cuda/unary.cu
index 5f0d3a6726a..c1dc6ddbf8f 100644
--- a/ggml/src/ggml-cuda/unary.cu
+++ b/ggml/src/ggml-cuda/unary.cu
@@ -85,6 +85,22 @@ static __device__ __forceinline__ float op_elu(float x) {
     return (x > 0.f) ? x : expm1f(x);
 }
 
+static __device__ __forceinline__ float op_floor(float x) {
+    return floorf(x);
+}
+
+static __device__ __forceinline__ float op_ceil(float x) {
+    return ceilf(x);
+}
+
+static __device__ __forceinline__ float op_round(float x) {
+    return round(x);
+}
+
+static __device__ __forceinline__ float op_trunc(float x) {
+    return trunc(x);
+}
+
 template <float (*op)(float), typename T>
 static __global__ void unary_op_kernel(const T * x, T * dst, const int k) {
     const int i = blockDim.x*blockIdx.x + threadIdx.x;
@@ -201,6 +217,22 @@ void ggml_cuda_op_log(ggml_backend_cuda_context & ctx, ggml_tensor * dst) {
 void ggml_cuda_op_elu(ggml_backend_cuda_context & ctx, ggml_tensor * dst) {
     ggml_cuda_op_unary<op_elu>(ctx, dst);
 }
+
+void ggml_cuda_op_floor(ggml_backend_cuda_context & ctx, ggml_tensor * dst) {
+    ggml_cuda_op_unary<op_floor>(ctx, dst);
+}
+
+void ggml_cuda_op_ceil(ggml_backend_cuda_context & ctx, ggml_tensor * dst) {
+    ggml_cuda_op_unary<op_ceil>(ctx, dst);
+}
+
+void ggml_cuda_op_round(ggml_backend_cuda_context & ctx, ggml_tensor * dst) {
+    ggml_cuda_op_unary<op_round>(ctx, dst);
+}
+
+void ggml_cuda_op_trunc(ggml_backend_cuda_context & ctx, ggml_tensor * dst) {
+    ggml_cuda_op_unary<op_trunc>(ctx, dst);
+}
 /* gated ops */
 
 template <float (*op)(float), typename T>
diff --git a/ggml/src/ggml-cuda/unary.cuh b/ggml/src/ggml-cuda/unary.cuh
index 6c738cefecf..2800c75ba3f 100644
--- a/ggml/src/ggml-cuda/unary.cuh
+++ b/ggml/src/ggml-cuda/unary.cuh
@@ -63,6 +63,14 @@ void ggml_cuda_op_log(ggml_backend_cuda_context & ctx, ggml_tensor * dst);
 
 void ggml_cuda_op_elu(ggml_backend_cuda_context & ctx, ggml_tensor * dst);
 
+void ggml_cuda_op_floor(ggml_backend_cuda_context & ctx, ggml_tensor * dst);
+
+void ggml_cuda_op_ceil(ggml_backend_cuda_context & ctx, ggml_tensor * dst);
+
+void ggml_cuda_op_round(ggml_backend_cuda_context & ctx, ggml_tensor * dst);
+
+void ggml_cuda_op_trunc(ggml_backend_cuda_context & ctx, ggml_tensor * dst);
+
 void ggml_cuda_op_reglu(ggml_backend_cuda_context & ctx, ggml_tensor * dst);
 
 void ggml_cuda_op_geglu(ggml_backend_cuda_context & ctx, ggml_tensor * dst);

From 76af40aaaad78c42faecd8016a88362c788b84b0 Mon Sep 17 00:00:00 2001
From: Adrian Lundberg <47256989+alundb@users.noreply.github.com>
Date: Sun, 2 Nov 2025 10:28:37 +0100
Subject: [PATCH 057/185] docs: remove llama_sampler_accept reference in
 sampling sample usage (#16920)

commit 5fb5e24811cb01d48b482c15a974bfbd9f433e1d (llama : minor
sampling refactor (2) (#9386)) moved the llama_sampler_accept call
into llama_sampler_sample, but the sampling sample usage in llama.h
was forgotten to be updated accordingly.
---
 include/llama.h | 2 --
 1 file changed, 2 deletions(-)

diff --git a/include/llama.h b/include/llama.h
index 08e2ffa34c9..05baa43da08 100644
--- a/include/llama.h
+++ b/include/llama.h
@@ -1111,8 +1111,6 @@ extern "C" {
     //        // sample from the logits of the last token in the batch
     //        const llama_token id = llama_sampler_sample(smpl, ctx, -1);
     //
-    //        // accepting the token updates the internal state of certain samplers (e.g. grammar, repetition, etc.)
-    //        llama_sampler_accept(smpl, id);
     //        ...
     //    }
     //

From 87c9efc3b297b8a498716b1db3d061842e6fc85b Mon Sep 17 00:00:00 2001
From: Aldehir Rojas <hello@alde.dev>
Date: Sun, 2 Nov 2025 08:56:28 -0600
Subject: [PATCH 058/185] common : move gpt-oss reasoning processing to init
 params (#16937)

---
 common/chat.cpp | 19 +++++++++++++++++--
 1 file changed, 17 insertions(+), 2 deletions(-)

diff --git a/common/chat.cpp b/common/chat.cpp
index 63583fb2248..938872e82ee 100644
--- a/common/chat.cpp
+++ b/common/chat.cpp
@@ -313,7 +313,6 @@ json common_chat_msgs_to_json_oaicompat(const std::vector<common_chat_msg> & msg
         }
         if (!msg.reasoning_content.empty()) {
             jmsg["reasoning_content"] = msg.reasoning_content;
-            jmsg["thinking"] = msg.reasoning_content; // gpt-oss
         }
         if (!msg.tool_name.empty()) {
             jmsg["name"] = msg.tool_name;
@@ -1810,7 +1809,23 @@ static void common_chat_parse_deepseek_v3_1(common_chat_msg_parser & builder) {
 
 static common_chat_params common_chat_params_init_gpt_oss(const common_chat_template & tmpl, const struct templates_params & inputs) {
     common_chat_params data;
-    auto prompt = apply(tmpl, inputs);
+
+    // Copy reasoning to the "thinking" field as expected by the gpt-oss template
+    auto adjusted_messages = json::array();
+    for (const auto & msg : inputs.messages) {
+        auto has_reasoning_content = msg.contains("reasoning_content") && msg.at("reasoning_content").is_string();
+        auto has_tool_calls = msg.contains("tool_calls") && msg.at("tool_calls").is_array();
+
+        if (has_reasoning_content && has_tool_calls) {
+            auto adjusted_message = msg;
+            adjusted_message["thinking"] = msg.at("reasoning_content");
+            adjusted_messages.push_back(adjusted_message);
+        } else {
+            adjusted_messages.push_back(msg);
+        }
+    }
+
+    auto prompt = apply(tmpl, inputs, /* messages_override= */ adjusted_messages);
 
     // Check if we need to replace the return token with end token during
     // inference and without generation prompt. For more details see:

From cd5e3b57541ecc52421130742f4d89acbcf77cd4 Mon Sep 17 00:00:00 2001
From: Georgi Gerganov <ggerganov@gmail.com>
Date: Sun, 2 Nov 2025 18:14:04 +0200
Subject: [PATCH 059/185] server : support unified cache across slots (#16736)

* server : support unified context across slots

* cont : fix speculative decoding initialization

* context : fix n_ctx_per_seq computation

* server : purge slots one by one

* tests : add unified cache server tests

* llama : update per-seq context computation

* test-thread-safety : handle tiny training context of the input model

* server : fix server_tokens clear()

* server : use 4 slots + unified KV by default

* llama : add note about context size queries

* cont : update todos [no ci]

* context : do not cap the size of the context

* tests : adjust parameters to be CI friendlier

* context : add warning
---
 include/llama.h                               |  5 +-
 src/llama-context.cpp                         | 37 +++++---
 src/llama-context.h                           | 10 +--
 src/llama-cparams.h                           |  1 +
 src/llama-model.cpp                           | 14 +--
 tests/test-thread-safety.cpp                  |  9 +-
 tools/server/server.cpp                       | 86 ++++++++++++++++---
 .../server/tests/unit/test_chat_completion.py |  8 +-
 tools/server/tests/unit/test_completion.py    | 31 +++++++
 tools/server/tests/unit/test_infill.py        |  4 +-
 tools/server/tests/utils.py                   |  3 +
 tools/server/utils.hpp                        |  3 +-
 12 files changed, 163 insertions(+), 48 deletions(-)

diff --git a/include/llama.h b/include/llama.h
index 05baa43da08..98bed9d6150 100644
--- a/include/llama.h
+++ b/include/llama.h
@@ -461,7 +461,10 @@ extern "C" {
     LLAMA_API bool llama_supports_gpu_offload(void);
     LLAMA_API bool llama_supports_rpc        (void);
 
+    // NOTE: After creating a llama_context, it is recommended to query the actual values using these functions
+    //       In some cases the requested values via llama_context_params may differ from the actual values used by the context
     LLAMA_API uint32_t llama_n_ctx      (const struct llama_context * ctx);
+    LLAMA_API uint32_t llama_n_ctx_seq  (const struct llama_context * ctx);
     LLAMA_API uint32_t llama_n_batch    (const struct llama_context * ctx);
     LLAMA_API uint32_t llama_n_ubatch   (const struct llama_context * ctx);
     LLAMA_API uint32_t llama_n_seq_max  (const struct llama_context * ctx);
@@ -585,7 +588,7 @@ extern "C" {
     LLAMA_API int32_t llama_adapter_meta_val_str_by_index(const struct llama_adapter_lora * adapter, int32_t i, char * buf, size_t buf_size);
 
     // Manually free a LoRA adapter
-    // Note: loaded adapters will be free when the associated model is deleted
+    // NOTE: loaded adapters will be free when the associated model is deleted
     LLAMA_API void llama_adapter_lora_free(struct llama_adapter_lora * adapter);
 
     // Get the invocation tokens if the current lora is an alora
diff --git a/src/llama-context.cpp b/src/llama-context.cpp
index f6192a36e0e..2b39366271f 100644
--- a/src/llama-context.cpp
+++ b/src/llama-context.cpp
@@ -112,11 +112,24 @@ llama_context::llama_context(
         }
     }
 
-    const uint32_t n_ctx_per_seq = cparams.n_ctx / cparams.n_seq_max;
+    if (cparams.kv_unified) {
+        cparams.n_ctx_seq = cparams.n_ctx;
+    } else {
+        cparams.n_ctx_seq = cparams.n_ctx / cparams.n_seq_max;
+
+        if (cparams.n_ctx_seq == 0) {
+            throw std::runtime_error("n_ctx_seq == 0");
+        }
+
+        if (cparams.n_ctx != cparams.n_ctx_seq * cparams.n_seq_max) {
+            cparams.n_ctx =  cparams.n_ctx_seq * cparams.n_seq_max;
+            LLAMA_LOG_WARN("%s: n_ctx is not divisible by n_seq_max - rounding down to %u\n", __func__, cparams.n_ctx);
+        }
+    }
 
     LLAMA_LOG_INFO("%s: n_seq_max     = %u\n",   __func__, cparams.n_seq_max);
     LLAMA_LOG_INFO("%s: n_ctx         = %u\n",   __func__, cparams.n_ctx);
-    LLAMA_LOG_INFO("%s: n_ctx_per_seq = %u\n",   __func__, n_ctx_per_seq);
+    LLAMA_LOG_INFO("%s: n_ctx_seq     = %u\n",   __func__, cparams.n_ctx_seq);
     LLAMA_LOG_INFO("%s: n_batch       = %u\n",   __func__, cparams.n_batch);
     LLAMA_LOG_INFO("%s: n_ubatch      = %u\n",   __func__, cparams.n_ubatch);
     LLAMA_LOG_INFO("%s: causal_attn   = %d\n",   __func__, cparams.causal_attn);
@@ -125,14 +138,14 @@ llama_context::llama_context(
     LLAMA_LOG_INFO("%s: freq_base     = %.1f\n", __func__, cparams.rope_freq_base);
     LLAMA_LOG_INFO("%s: freq_scale    = %g\n",   __func__, cparams.rope_freq_scale);
 
-    if (n_ctx_per_seq < hparams.n_ctx_train) {
-        LLAMA_LOG_WARN("%s: n_ctx_per_seq (%u) < n_ctx_train (%u) -- the full capacity of the model will not be utilized\n",
-                __func__, n_ctx_per_seq, hparams.n_ctx_train);
+    if (cparams.n_ctx_seq < hparams.n_ctx_train) {
+        LLAMA_LOG_WARN("%s: n_ctx_seq (%u) < n_ctx_train (%u) -- the full capacity of the model will not be utilized\n",
+                __func__, cparams.n_ctx_seq, hparams.n_ctx_train);
     }
 
-    if (n_ctx_per_seq > hparams.n_ctx_train) {
-        LLAMA_LOG_WARN("%s: n_ctx_per_seq (%u) > n_ctx_train (%u) -- possible training context overflow\n",
-                __func__, n_ctx_per_seq, hparams.n_ctx_train);
+    if (cparams.n_ctx_seq > hparams.n_ctx_train) {
+        LLAMA_LOG_WARN("%s: n_ctx_seq (%u) > n_ctx_train (%u) -- possible training context overflow\n",
+                __func__, cparams.n_ctx_seq, hparams.n_ctx_train);
     }
 
     if (!hparams.vocab_only) {
@@ -453,8 +466,8 @@ uint32_t llama_context::n_ctx() const {
     return cparams.n_ctx;
 }
 
-uint32_t llama_context::n_ctx_per_seq() const {
-    return cparams.n_ctx / cparams.n_seq_max;
+uint32_t llama_context::n_ctx_seq() const {
+    return cparams.n_ctx_seq;
 }
 
 uint32_t llama_context::n_batch() const {
@@ -2383,6 +2396,10 @@ uint32_t llama_n_ctx(const llama_context * ctx) {
     return ctx->n_ctx();
 }
 
+uint32_t llama_n_ctx_seq(const llama_context * ctx) {
+    return ctx->n_ctx_seq();
+}
+
 uint32_t llama_n_batch(const llama_context * ctx) {
     return ctx->n_batch();
 }
diff --git a/src/llama-context.h b/src/llama-context.h
index ed6d82cb396..20cbd789554 100644
--- a/src/llama-context.h
+++ b/src/llama-context.h
@@ -43,11 +43,11 @@ struct llama_context {
 
     ggml_backend_sched_t get_sched() const;
 
-    uint32_t n_ctx()         const;
-    uint32_t n_ctx_per_seq() const;
-    uint32_t n_batch()       const;
-    uint32_t n_ubatch()      const;
-    uint32_t n_seq_max()     const;
+    uint32_t n_ctx()     const;
+    uint32_t n_ctx_seq() const;
+    uint32_t n_batch()   const;
+    uint32_t n_ubatch()  const;
+    uint32_t n_seq_max() const;
 
     uint32_t n_threads()       const;
     uint32_t n_threads_batch() const;
diff --git a/src/llama-cparams.h b/src/llama-cparams.h
index eae7b839f48..fcef8fa9760 100644
--- a/src/llama-cparams.h
+++ b/src/llama-cparams.h
@@ -8,6 +8,7 @@
 
 struct llama_cparams {
     uint32_t n_ctx;           // context size used during inference
+    uint32_t n_ctx_seq;       // context for a single sequence
     uint32_t n_batch;
     uint32_t n_ubatch;
     uint32_t n_seq_max;
diff --git a/src/llama-model.cpp b/src/llama-model.cpp
index 04239181c77..896725466ce 100644
--- a/src/llama-model.cpp
+++ b/src/llama-model.cpp
@@ -6712,14 +6712,14 @@ float llama_model::get_rope_freq_scale(const llama_cparams & cparams, int il) co
 }
 
 ggml_tensor * llama_model::get_rope_factors(const llama_cparams & cparams, int il) const {
-    const uint32_t n_ctx_per_seq = cparams.n_ctx / cparams.n_seq_max;
+    const uint32_t n_ctx_seq = cparams.n_ctx_seq;
 
     // choose long/short freq factors based on the context size
     if (layers[il].rope_freqs != nullptr) {
         return layers[il].rope_freqs;
     }
 
-    if (n_ctx_per_seq > hparams.n_ctx_orig_yarn) {
+    if (n_ctx_seq > hparams.n_ctx_orig_yarn) {
         return layers[il].rope_long;
     }
 
@@ -6795,12 +6795,6 @@ llama_memory_i * llama_model::create_memory(const llama_memory_params & params,
                         /* filter_attn       */ std::move(filter_attn),
                         /* filter_recr       */ std::move(filter_recr));
                 } else {
-                    uint32_t n_ctx_per_stream = cparams.n_ctx;
-
-                    if (!cparams.kv_unified) {
-                        n_ctx_per_stream = (cparams.n_ctx + cparams.n_seq_max - 1)/cparams.n_seq_max;
-                    }
-
                     llama_memory_i::layer_reuse_cb reuse = nullptr;
 
                     if (arch == LLM_ARCH_GEMMA3N) {
@@ -6824,7 +6818,7 @@ llama_memory_i * llama_model::create_memory(const llama_memory_params & params,
                                 cparams.offload_kqv,
                                 params.swa_full,
                                 cparams.kv_unified,
-                                n_ctx_per_stream,
+                                cparams.n_ctx_seq,
                                 cparams.n_seq_max,
                                 cparams.n_ubatch,
                                 1,
@@ -6840,7 +6834,7 @@ llama_memory_i * llama_model::create_memory(const llama_memory_params & params,
                                 !cparams.flash_attn,
                                 cparams.offload_kqv,
                                 cparams.kv_unified,
-                                n_ctx_per_stream,
+                                cparams.n_ctx_seq,
                                 cparams.n_seq_max,
                                 1,
                                 hparams.n_swa,
diff --git a/tests/test-thread-safety.cpp b/tests/test-thread-safety.cpp
index e5158fb5062..bcb86c35e66 100644
--- a/tests/test-thread-safety.cpp
+++ b/tests/test-thread-safety.cpp
@@ -131,7 +131,14 @@ int main(int argc, char ** argv) {
                     }
 
                     batch = llama_batch_get_one(&token, 1);
-                    if (llama_decode(ctx.get(), batch)) {
+
+                    int ret = llama_decode(ctx.get(), batch);
+                    if (ret == 1 && i > 0) {
+                        LOG_INF("Context full, stopping generation.\n");
+                        break;
+                    }
+
+                    if (ret != 0) {
                         LOG_ERR("Model %d/%d, Context %d/%d: failed to decode\n", m + 1, num_models, c + 1, num_contexts);
                         failed.store(true);
                         return;
diff --git a/tools/server/server.cpp b/tools/server/server.cpp
index 92d30664e41..aa498158520 100644
--- a/tools/server/server.cpp
+++ b/tools/server/server.cpp
@@ -2407,7 +2407,7 @@ struct server_context {
 
             params_dft.devices      = params_base.speculative.devices;
             params_dft.model        = params_base.speculative.model;
-            params_dft.n_ctx        = params_base.speculative.n_ctx == 0 ? params_base.n_ctx / params_base.n_parallel : params_base.speculative.n_ctx;
+            params_dft.n_ctx        = params_base.speculative.n_ctx == 0 ? llama_n_ctx_seq(ctx) : params_base.speculative.n_ctx;
             params_dft.n_gpu_layers = params_base.speculative.n_gpu_layers;
             params_dft.n_parallel   = 1;
             params_dft.cache_type_k = params_base.speculative.cache_type_k;
@@ -2495,10 +2495,16 @@ struct server_context {
     }
 
     void init() {
-        const int32_t n_ctx_slot = n_ctx / params_base.n_parallel;
-
         SRV_INF("initializing slots, n_slots = %d\n", params_base.n_parallel);
 
+        const int n_ctx_train = llama_model_n_ctx_train(model);
+
+        int n_ctx_slot = llama_n_ctx_seq(ctx);
+        if (n_ctx_slot > n_ctx_train) {
+            SRV_WRN("the slot context (%d) exceeds the training context of the model (%d) - capping\n", n_ctx_slot, n_ctx_train);
+            n_ctx_slot = n_ctx_train;
+        }
+
         for (int i = 0; i < params_base.n_parallel; i++) {
             server_slot slot;
 
@@ -2527,7 +2533,7 @@ struct server_context {
                 }
             }
 
-            SLT_INF(slot, "new slot n_ctx_slot = %d\n", slot.n_ctx);
+            SLT_INF(slot, "new slot, n_ctx = %d\n", slot.n_ctx);
 
             slot.callback_on_release = [this](int) {
                 queue_tasks.pop_deferred_task();
@@ -2699,6 +2705,39 @@ struct server_context {
         return ret;
     }
 
+    // return true if at least one slot has been purged
+    // TODO: improve logic
+    //       - smarter decision which slot to purge (LRU or longest prompt?)
+    //       - move slot to level 2 cache instead of removing?
+    //       - instead of purging, try to store and resume later?
+    bool try_purge_idle_slots() {
+        bool res = false;
+
+        if (!params_base.kv_unified) {
+            return res;
+        }
+
+        for (auto & slot : slots) {
+            if (slot.is_processing()) {
+                continue;
+            }
+
+            if (slot.prompt.n_tokens() > 0) {
+                SRV_WRN("purging slot %d with %zu tokens\n", slot.id, slot.prompt.tokens.size());
+
+                llama_memory_seq_rm(llama_get_memory(ctx), slot.id, -1, -1);
+                slot.prompt.tokens.clear();
+
+                res = true;
+
+                // purge slots one by one
+                break;
+            }
+        }
+
+        return res;
+    }
+
     bool launch_slot_with_task(server_slot & slot, server_task && task) {
         slot.reset();
 
@@ -3635,9 +3674,10 @@ struct server_context {
         int32_t n_batch  = llama_n_batch(ctx);
         int32_t n_ubatch = llama_n_ubatch(ctx);
 
-        // next, batch any pending prompts without exceeding n_batch
-        float alora_scale = -1.0f;
+        float  alora_scale       = -1.0f;
         size_t alora_disabled_id = 0;
+
+        // next, batch any pending prompts without exceeding n_batch
         if (params_base.cont_batching || batch.n_tokens == 0) {
             for (auto & slot : slots) {
                 // check if we can batch this slot with the previous one
@@ -3914,8 +3954,11 @@ struct server_context {
 
                     // truncate any tokens that are beyond n_past for this slot
                     const llama_pos p0 = slot.prompt.tokens.pos_next();
+
+                    SLT_INF(slot, "n_tokens = %d, memory_seq_rm [%d, end)\n", slot.prompt.n_tokens(), p0);
+
                     if (!llama_memory_seq_rm(llama_get_memory(ctx), slot.id, p0, -1)) {
-                        SLT_WRN(slot, "failed to truncate tokens with position >= %d\n", p0);
+                        SLT_WRN(slot, "failed to truncate tokens with position >= %d - clearing the memory\n", p0);
                         llama_memory_seq_rm(llama_get_memory(ctx), slot.id, -1, -1);
 
                         // there is no common part left
@@ -3924,8 +3967,6 @@ struct server_context {
                         slot.prompt.tokens.clear();
                     }
 
-                    SLT_INF(slot, "n_tokens = %d, memory_seq_rm [%d, end)\n", slot.prompt.n_tokens(), p0);
-
                     // check if we should process the image
                     if (slot.prompt.n_tokens() < slot.task->n_tokens() && input_tokens[slot.prompt.n_tokens()] == LLAMA_TOKEN_NULL) {
                         // process the image
@@ -4126,6 +4167,8 @@ struct server_context {
                     std::string err;
 
                     if (n_batch == 1 && ret == 1) {
+                        // TODO: try to terminate only the largest active slot/sequence and continue with the rest
+                        //       need to remove the tokens from the current batch too
                         err = "Context size has been exceeded.";
                     }
 
@@ -4141,17 +4184,23 @@ struct server_context {
                     // TODO: handle ret == 2 (abort) when we start aborting
 
                     if (!err.empty()) {
-                        SRV_ERR("%s, i = %d, n_batch = %d, ret = %d\n", err.c_str(), i, n_batch, ret);
+                        SRV_ERR("%s i = %d, n_batch = %d, ret = %d\n", err.c_str(), i, n_batch, ret);
+
                         for (auto & slot : slots) {
-                            send_error(slot, err);
-                            slot.release();
+                            if (slot.is_processing()) {
+                                send_error(slot, err);
+                                slot.release();
+                            }
                         }
+
                         break;
                     }
                 }
 
                 // retry with half the batch size to try to find a free slot in the KV cache
-                n_batch /= 2;
+                if (!try_purge_idle_slots()) {
+                    n_batch /= 2;
+                }
 
                 SRV_WRN("failed to find free space in the KV cache, retrying with smaller batch size, i = %d, n_batch = %d, ret = %d\n", i, n_batch, ret);
 
@@ -4391,6 +4440,15 @@ int main(int argc, char ** argv) {
         return 1;
     }
 
+    // TODO: should we have a separate n_parallel parameter for the server?
+    //       https://github.com/ggml-org/llama.cpp/pull/16736#discussion_r2483763177
+    if (params.n_parallel == 1 && params.kv_unified == false) {
+        LOG_WRN("%s: setting n_parallel = 4 and kv_unified = true\n", __func__);
+
+        params.n_parallel = 4;
+        params.kv_unified = true;
+    }
+
     common_init();
 
     // struct that contains llama context and inference
@@ -4944,7 +5002,7 @@ int main(int argc, char ** argv) {
                 // Everything else, including multimodal completions.
                 inputs = tokenize_input_prompts(ctx_server.vocab, ctx_server.mctx, prompt, true, true);
             }
-            const size_t n_ctx_slot = ctx_server.n_ctx / ctx_server.params_base.n_parallel;
+            const size_t n_ctx_slot = ctx_server.slots.front().n_ctx;
             tasks.reserve(inputs.size());
             for (size_t i = 0; i < inputs.size(); i++) {
                 auto n_prompt_tokens = inputs[i].size();
diff --git a/tools/server/tests/unit/test_chat_completion.py b/tools/server/tests/unit/test_chat_completion.py
index d56d3d5f178..392e0efecdb 100644
--- a/tools/server/tests/unit/test_chat_completion.py
+++ b/tools/server/tests/unit/test_chat_completion.py
@@ -433,21 +433,21 @@ def test_context_size_exceeded_stream():
 @pytest.mark.parametrize(
     "n_batch,batch_count,reuse_cache",
     [
-        (64, 15, False),
+        (64, 3, False),
         (64, 1, True),
     ]
 )
-def test_return_progresssss(n_batch, batch_count, reuse_cache):
+def test_return_progress(n_batch, batch_count, reuse_cache):
     global server
     server.n_batch = n_batch
-    server.n_ctx = 2048
+    server.n_ctx = 256
     server.n_slots = 1
     server.start()
     def make_cmpl_request():
         return server.make_stream_request("POST", "/chat/completions", data={
             "max_tokens": 10,
             "messages": [
-                {"role": "user", "content": "This is a test" * 100},
+                {"role": "user", "content": "This is a test" * 10},
             ],
             "stream": True,
             "return_progress": True,
diff --git a/tools/server/tests/unit/test_completion.py b/tools/server/tests/unit/test_completion.py
index 00ba78cf67c..3c0ce98973f 100644
--- a/tools/server/tests/unit/test_completion.py
+++ b/tools/server/tests/unit/test_completion.py
@@ -368,6 +368,37 @@ def check_slots_status():
         # assert match_regex(re_content, res.body["content"])
 
 
+@pytest.mark.parametrize(
+    "n_ctx,n_slots,n_predict_vals,expected_success",
+    [
+        (256, 4, [80, 40, 80, 80], [True,  True,  True,  True]),
+        (256, 4, [70, 70, 70, 70], [False, False, False, False]),
+        (256, 4, [90, 90, 40, 90], [False, False, True,  False]),
+        (256, 4, [90, 90, 40, 75], [True,  True,  True,  True]),
+    ],
+)
+def test_completion_unified(n_ctx, n_slots, n_predict_vals, expected_success):
+    global server
+    server.n_slots = n_slots
+    server.kv_unified = True
+    server.n_ctx = n_ctx
+    server.start()
+    prompt = "A"
+    tasks = []
+    for n_predict in n_predict_vals:
+        tasks.append((server.make_request, ("POST", "/completion", {"prompt": prompt, "n_predict": n_predict})))
+    results = parallel_function_calls(tasks)
+    for res, n_predict, expect_ok in zip(results, n_predict_vals, expected_success):
+        if expect_ok:
+            assert res.status_code == 200
+            assert "content" in res.body
+            if "timings" in res.body:
+                assert res.body["timings"]["predicted_n"] == n_predict
+        else:
+            assert res.status_code == 500
+            assert "content" not in res.body
+
+
 @pytest.mark.parametrize(
     "prompt,n_predict,response_fields",
     [
diff --git a/tools/server/tests/unit/test_infill.py b/tools/server/tests/unit/test_infill.py
index 73dacdae812..cd1a391b4ad 100644
--- a/tools/server/tests/unit/test_infill.py
+++ b/tools/server/tests/unit/test_infill.py
@@ -18,7 +18,7 @@ def test_infill_without_input_extra():
         "input_suffix": "}\n",
     })
     assert res.status_code == 200
-    assert match_regex("(Ann|small|shiny|Daddy)+", res.body["content"])
+    assert match_regex("(Ann|small|shiny|Daddy|Jimmy)+", res.body["content"])
 
 
 def test_infill_with_input_extra():
@@ -34,7 +34,7 @@ def test_infill_with_input_extra():
         "input_suffix": "}\n",
     })
     assert res.status_code == 200
-    assert match_regex("(Dad|excited|park)+", res.body["content"])
+    assert match_regex("(Dad|excited|park|Jimmy)+", res.body["content"])
 
 
 @pytest.mark.parametrize("input_extra", [
diff --git a/tools/server/tests/utils.py b/tools/server/tests/utils.py
index 4ba3d43c330..da703c4c51a 100644
--- a/tools/server/tests/utils.py
+++ b/tools/server/tests/utils.py
@@ -78,6 +78,7 @@ class ServerProcess:
     server_embeddings: bool | None = False
     server_reranking: bool | None = False
     server_metrics: bool | None = False
+    kv_unified: bool | None = False
     server_slots: bool | None = False
     pooling: str | None = None
     draft: int | None = None
@@ -159,6 +160,8 @@ def start(self, timeout_seconds: int | None = DEFAULT_HTTP_TIMEOUT) -> None:
             server_args.append("--reranking")
         if self.server_metrics:
             server_args.append("--metrics")
+        if self.kv_unified:
+            server_args.append("--kv-unified")
         if self.server_slots:
             server_args.append("--slots")
         else:
diff --git a/tools/server/utils.hpp b/tools/server/utils.hpp
index b6198edfc48..2bce2f4a47a 100644
--- a/tools/server/utils.hpp
+++ b/tools/server/utils.hpp
@@ -1212,7 +1212,7 @@ struct server_tokens {
             for (auto it = tokens.map_idx_to_media.begin(); it != tokens.map_idx_to_media.end(); ) {
                 auto * chunk = tokens.map_idx_to_media[it->first].get();
                 mtmd::input_chunk_ptr new_chunk(mtmd_input_chunk_copy(chunk));
-                map_idx_to_media[start_idx+it->first] = std::move(new_chunk);
+                map_idx_to_media[start_idx + it->first] = std::move(new_chunk);
             }
         }
     }
@@ -1244,6 +1244,7 @@ struct server_tokens {
     }
 
     void clear() {
+        map_idx_to_media.clear();
         tokens.clear();
     }
 

From 2f966b8ed87514e74bb96592217226cb6a6974dd Mon Sep 17 00:00:00 2001
From: Georgi Gerganov <ggerganov@gmail.com>
Date: Sun, 2 Nov 2025 22:21:48 +0200
Subject: [PATCH 060/185] clip : use FA (#16837)

* clip : use FA

* cont : add warning about unsupported ops

* implement "auto" mode for clip flash attn

* clip : print more detailed op support info during warmup

* cont : remove obsolete comment [no ci]

* improve debugging message

* trailing space

* metal : remove stray return

---------

Co-authored-by: Xuan Son Nguyen <son@huggingface.co>
---
 ggml/src/ggml-metal/ggml-metal-device.m |   1 +
 ggml/src/ggml-metal/ggml-metal.metal    |   8 +
 tests/test-backend-ops.cpp              |   4 +-
 tools/mtmd/clip.cpp                     | 197 +++++++++++++++++++-----
 tools/mtmd/clip.h                       |   8 +
 tools/mtmd/mtmd-cli.cpp                 |   1 +
 tools/mtmd/mtmd.cpp                     |  16 +-
 tools/mtmd/mtmd.h                       |   1 +
 tools/server/server.cpp                 |   1 +
 9 files changed, 194 insertions(+), 43 deletions(-)

diff --git a/ggml/src/ggml-metal/ggml-metal-device.m b/ggml/src/ggml-metal/ggml-metal-device.m
index 360fbe19f0f..0cadd19a30f 100644
--- a/ggml/src/ggml-metal/ggml-metal-device.m
+++ b/ggml/src/ggml-metal/ggml-metal-device.m
@@ -707,6 +707,7 @@ bool ggml_metal_device_supports_op(ggml_metal_device_t dev, const struct ggml_te
             if (op->src[0]->ne[0] != 32 &&
                 op->src[0]->ne[0] != 40 &&
                 op->src[0]->ne[0] != 64 &&
+                op->src[0]->ne[0] != 72 &&
                 op->src[0]->ne[0] != 80 &&
                 op->src[0]->ne[0] != 96 &&
                 op->src[0]->ne[0] != 112 &&
diff --git a/ggml/src/ggml-metal/ggml-metal.metal b/ggml/src/ggml-metal/ggml-metal.metal
index fa839a1df6e..424c400f24b 100644
--- a/ggml/src/ggml-metal/ggml-metal.metal
+++ b/ggml/src/ggml-metal/ggml-metal.metal
@@ -5362,6 +5362,7 @@ typedef decltype(kernel_flash_attn_ext<FA_TYPES, half4x4, 1, dequantize_f16, hal
 template [[host_name("kernel_flash_attn_ext_f32_dk32_dv32"  )]]  kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES_F32, float4x4,   1, dequantize_f32,  float4x4,   1, dequantize_f32,  32,  32>;
 template [[host_name("kernel_flash_attn_ext_f32_dk40_dv40"  )]]  kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES_F32, float4x4,   1, dequantize_f32,  float4x4,   1, dequantize_f32,  40,  40>;
 template [[host_name("kernel_flash_attn_ext_f32_dk64_dv64"  )]]  kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES_F32, float4x4,   1, dequantize_f32,  float4x4,   1, dequantize_f32,  64,  64>;
+template [[host_name("kernel_flash_attn_ext_f32_dk72_dv72"  )]]  kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES_F32, float4x4,   1, dequantize_f32,  float4x4,   1, dequantize_f32,  72,  72>;
 template [[host_name("kernel_flash_attn_ext_f32_dk80_dv80"  )]]  kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES_F32, float4x4,   1, dequantize_f32,  float4x4,   1, dequantize_f32,  80,  80>;
 template [[host_name("kernel_flash_attn_ext_f32_dk96_dv96"  )]]  kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES_F32, float4x4,   1, dequantize_f32,  float4x4,   1, dequantize_f32,  96,  96>;
 template [[host_name("kernel_flash_attn_ext_f32_dk112_dv112")]]  kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES_F32, float4x4,   1, dequantize_f32,  float4x4,   1, dequantize_f32,  112, 112>;
@@ -5374,6 +5375,7 @@ template [[host_name("kernel_flash_attn_ext_f32_dk576_dv512")]]  kernel flash_at
 template [[host_name("kernel_flash_attn_ext_f16_dk32_dv32"  )]]  kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    half4x4,    1, dequantize_f16,  half4x4,    1, dequantize_f16,  32,  32>;
 template [[host_name("kernel_flash_attn_ext_f16_dk40_dv40"  )]]  kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    half4x4,    1, dequantize_f16,  half4x4,    1, dequantize_f16,  40,  40>;
 template [[host_name("kernel_flash_attn_ext_f16_dk64_dv64"  )]]  kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    half4x4,    1, dequantize_f16,  half4x4,    1, dequantize_f16,  64,  64>;
+template [[host_name("kernel_flash_attn_ext_f16_dk72_dv72"  )]]  kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    half4x4,    1, dequantize_f16,  half4x4,    1, dequantize_f16,  72,  72>;
 template [[host_name("kernel_flash_attn_ext_f16_dk80_dv80"  )]]  kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    half4x4,    1, dequantize_f16,  half4x4,    1, dequantize_f16,  80,  80>;
 template [[host_name("kernel_flash_attn_ext_f16_dk96_dv96"  )]]  kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    half4x4,    1, dequantize_f16,  half4x4,    1, dequantize_f16,  96,  96>;
 template [[host_name("kernel_flash_attn_ext_f16_dk112_dv112")]]  kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    half4x4,    1, dequantize_f16,  half4x4,    1, dequantize_f16,  112, 112>;
@@ -5387,6 +5389,7 @@ template [[host_name("kernel_flash_attn_ext_f16_dk576_dv512")]]  kernel flash_at
 template [[host_name("kernel_flash_attn_ext_bf16_dk32_dv32"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES_BF, bfloat4x4,  1, dequantize_bf16, bfloat4x4,  1, dequantize_bf16, 32,  32>;
 template [[host_name("kernel_flash_attn_ext_bf16_dk40_dv40"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES_BF, bfloat4x4,  1, dequantize_bf16, bfloat4x4,  1, dequantize_bf16, 40,  40>;
 template [[host_name("kernel_flash_attn_ext_bf16_dk64_dv64"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES_BF, bfloat4x4,  1, dequantize_bf16, bfloat4x4,  1, dequantize_bf16, 64,  64>;
+template [[host_name("kernel_flash_attn_ext_bf16_dk72_dv72"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES_BF, bfloat4x4,  1, dequantize_bf16, bfloat4x4,  1, dequantize_bf16, 72,  72>;
 template [[host_name("kernel_flash_attn_ext_bf16_dk80_dv80"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES_BF, bfloat4x4,  1, dequantize_bf16, bfloat4x4,  1, dequantize_bf16, 80,  80>;
 template [[host_name("kernel_flash_attn_ext_bf16_dk96_dv96"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES_BF, bfloat4x4,  1, dequantize_bf16, bfloat4x4,  1, dequantize_bf16, 96,  96>;
 template [[host_name("kernel_flash_attn_ext_bf16_dk112_dv112")]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES_BF, bfloat4x4,  1, dequantize_bf16, bfloat4x4,  1, dequantize_bf16, 112, 112>;
@@ -5400,6 +5403,7 @@ template [[host_name("kernel_flash_attn_ext_bf16_dk576_dv512")]] kernel flash_at
 template [[host_name("kernel_flash_attn_ext_q4_0_dk32_dv32"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q4_0, 2, dequantize_q4_0, block_q4_0, 2, dequantize_q4_0, 32,  32>;
 template [[host_name("kernel_flash_attn_ext_q4_0_dk40_dv40"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q4_0, 2, dequantize_q4_0, block_q4_0, 2, dequantize_q4_0, 40,  40>;
 template [[host_name("kernel_flash_attn_ext_q4_0_dk64_dv64"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q4_0, 2, dequantize_q4_0, block_q4_0, 2, dequantize_q4_0, 64,  64>;
+template [[host_name("kernel_flash_attn_ext_q4_0_dk72_dv72"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q4_0, 2, dequantize_q4_0, block_q4_0, 2, dequantize_q4_0, 72,  72>;
 template [[host_name("kernel_flash_attn_ext_q4_0_dk80_dv80"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q4_0, 2, dequantize_q4_0, block_q4_0, 2, dequantize_q4_0, 80,  80>;
 template [[host_name("kernel_flash_attn_ext_q4_0_dk96_dv96"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q4_0, 2, dequantize_q4_0, block_q4_0, 2, dequantize_q4_0, 96,  96>;
 template [[host_name("kernel_flash_attn_ext_q4_0_dk112_dv112")]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q4_0, 2, dequantize_q4_0, block_q4_0, 2, dequantize_q4_0, 112, 112>;
@@ -5412,6 +5416,7 @@ template [[host_name("kernel_flash_attn_ext_q4_0_dk576_dv512")]] kernel flash_at
 template [[host_name("kernel_flash_attn_ext_q4_1_dk32_dv32"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q4_1, 2, dequantize_q4_1, block_q4_1, 2, dequantize_q4_1, 32,  32>;
 template [[host_name("kernel_flash_attn_ext_q4_1_dk40_dv40"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q4_1, 2, dequantize_q4_1, block_q4_1, 2, dequantize_q4_1, 40,  40>;
 template [[host_name("kernel_flash_attn_ext_q4_1_dk64_dv64"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q4_1, 2, dequantize_q4_1, block_q4_1, 2, dequantize_q4_1, 64,  64>;
+template [[host_name("kernel_flash_attn_ext_q4_1_dk72_dv72"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q4_1, 2, dequantize_q4_1, block_q4_1, 2, dequantize_q4_1, 72,  72>;
 template [[host_name("kernel_flash_attn_ext_q4_1_dk80_dv80"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q4_1, 2, dequantize_q4_1, block_q4_1, 2, dequantize_q4_1, 80,  80>;
 template [[host_name("kernel_flash_attn_ext_q4_1_dk96_dv96"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q4_1, 2, dequantize_q4_1, block_q4_1, 2, dequantize_q4_1, 96,  96>;
 template [[host_name("kernel_flash_attn_ext_q4_1_dk112_dv112")]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q4_1, 2, dequantize_q4_1, block_q4_1, 2, dequantize_q4_1, 112, 112>;
@@ -5424,6 +5429,7 @@ template [[host_name("kernel_flash_attn_ext_q4_1_dk576_dv512")]] kernel flash_at
 template [[host_name("kernel_flash_attn_ext_q5_0_dk32_dv32"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q5_0, 2, dequantize_q5_0, block_q5_0, 2, dequantize_q5_0, 32,  32>;
 template [[host_name("kernel_flash_attn_ext_q5_0_dk40_dv40"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q5_0, 2, dequantize_q5_0, block_q5_0, 2, dequantize_q5_0, 40,  40>;
 template [[host_name("kernel_flash_attn_ext_q5_0_dk64_dv64"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q5_0, 2, dequantize_q5_0, block_q5_0, 2, dequantize_q5_0, 64,  64>;
+template [[host_name("kernel_flash_attn_ext_q5_0_dk72_dv72"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q5_0, 2, dequantize_q5_0, block_q5_0, 2, dequantize_q5_0, 72,  72>;
 template [[host_name("kernel_flash_attn_ext_q5_0_dk80_dv80"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q5_0, 2, dequantize_q5_0, block_q5_0, 2, dequantize_q5_0, 80,  80>;
 template [[host_name("kernel_flash_attn_ext_q5_0_dk96_dv96"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q5_0, 2, dequantize_q5_0, block_q5_0, 2, dequantize_q5_0, 96,  96>;
 template [[host_name("kernel_flash_attn_ext_q5_0_dk112_dv112")]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q5_0, 2, dequantize_q5_0, block_q5_0, 2, dequantize_q5_0, 112, 112>;
@@ -5436,6 +5442,7 @@ template [[host_name("kernel_flash_attn_ext_q5_0_dk576_dv512")]] kernel flash_at
 template [[host_name("kernel_flash_attn_ext_q5_1_dk32_dv32"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q5_1, 2, dequantize_q5_1, block_q5_1, 2, dequantize_q5_1, 32,  32>;
 template [[host_name("kernel_flash_attn_ext_q5_1_dk40_dv40"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q5_1, 2, dequantize_q5_1, block_q5_1, 2, dequantize_q5_1, 40,  40>;
 template [[host_name("kernel_flash_attn_ext_q5_1_dk64_dv64"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q5_1, 2, dequantize_q5_1, block_q5_1, 2, dequantize_q5_1, 64,  64>;
+template [[host_name("kernel_flash_attn_ext_q5_1_dk72_dv72"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q5_1, 2, dequantize_q5_1, block_q5_1, 2, dequantize_q5_1, 72,  72>;
 template [[host_name("kernel_flash_attn_ext_q5_1_dk80_dv80"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q5_1, 2, dequantize_q5_1, block_q5_1, 2, dequantize_q5_1, 80,  80>;
 template [[host_name("kernel_flash_attn_ext_q5_1_dk96_dv96"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q5_1, 2, dequantize_q5_1, block_q5_1, 2, dequantize_q5_1, 96,  96>;
 template [[host_name("kernel_flash_attn_ext_q5_1_dk112_dv112")]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q5_1, 2, dequantize_q5_1, block_q5_1, 2, dequantize_q5_1, 112, 112>;
@@ -5448,6 +5455,7 @@ template [[host_name("kernel_flash_attn_ext_q5_1_dk576_dv512")]] kernel flash_at
 template [[host_name("kernel_flash_attn_ext_q8_0_dk32_dv32"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q8_0, 2, dequantize_q8_0, block_q8_0, 2, dequantize_q8_0, 32,  32>;
 template [[host_name("kernel_flash_attn_ext_q8_0_dk40_dv40"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q8_0, 2, dequantize_q8_0, block_q8_0, 2, dequantize_q8_0, 40,  40>;
 template [[host_name("kernel_flash_attn_ext_q8_0_dk64_dv64"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q8_0, 2, dequantize_q8_0, block_q8_0, 2, dequantize_q8_0, 64,  64>;
+template [[host_name("kernel_flash_attn_ext_q8_0_dk72_dv72"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q8_0, 2, dequantize_q8_0, block_q8_0, 2, dequantize_q8_0, 72,  72>;
 template [[host_name("kernel_flash_attn_ext_q8_0_dk80_dv80"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q8_0, 2, dequantize_q8_0, block_q8_0, 2, dequantize_q8_0, 80,  80>;
 template [[host_name("kernel_flash_attn_ext_q8_0_dk96_dv96"  )]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q8_0, 2, dequantize_q8_0, block_q8_0, 2, dequantize_q8_0, 96,  96>;
 template [[host_name("kernel_flash_attn_ext_q8_0_dk112_dv112")]] kernel flash_attn_ext_t kernel_flash_attn_ext<FA_TYPES,    block_q8_0, 2, dequantize_q8_0, block_q8_0, 2, dequantize_q8_0, 112, 112>;
diff --git a/tests/test-backend-ops.cpp b/tests/test-backend-ops.cpp
index 04fa1b62d3b..2886bd37d68 100644
--- a/tests/test-backend-ops.cpp
+++ b/tests/test-backend-ops.cpp
@@ -7225,8 +7225,8 @@ static std::vector<std::unique_ptr<test_case>> make_test_cases_eval() {
         test_cases.emplace_back(new test_pad_ext(GGML_TYPE_F32, {11, 22, 33, 44}, 1, 2, 3, 4, 5, 6, 7, 8, v));
     }
 
-    for (int hsk : { 40, 64, 80, 96, 128, 192, 256, 576 }) {
-        for (int hsv : { 40, 64, 80, 96, 128, 192, 256, 512 }) {
+    for (int hsk : { 40, 64, 72, 80, 96, 128, 192, 256, 576 }) {
+        for (int hsv : { 40, 64, 72, 80, 96, 128, 192, 256, 512 }) {
             if (hsk != 192 && hsk != 576 && hsk != hsv) continue;
             if (hsk == 192 && (hsv != 128 && hsv != 192)) continue;
             if (hsk == 576 && hsv != 512) continue; // DeepSeek MLA
diff --git a/tools/mtmd/clip.cpp b/tools/mtmd/clip.cpp
index dcfdb49600b..a7e1799e93d 100644
--- a/tools/mtmd/clip.cpp
+++ b/tools/mtmd/clip.cpp
@@ -6,7 +6,6 @@
 #include "clip-impl.h"
 #include "ggml.h"
 #include "ggml-cpp.h"
-#include "ggml-cpu.h"
 #include "ggml-alloc.h"
 #include "ggml-backend.h"
 #include "gguf.h"
@@ -17,17 +16,15 @@
 #include <cstring>
 #include <fstream>
 #include <map>
-#include <regex>
 #include <stdexcept>
 #include <unordered_set>
 #include <vector>
-#include <sstream>
 #include <cinttypes>
 #include <limits>
 #include <array>
-#include <numeric>
 #include <functional>
 
+// TODO: allow to pass callback from user code
 struct clip_logger_state g_logger_state = {GGML_LOG_LEVEL_CONT, clip_log_callback_default, NULL};
 
 enum ffn_op_type {
@@ -426,12 +423,14 @@ struct clip_ctx {
 
     int max_nodes = 8192;
     ggml_backend_sched_ptr sched;
+    clip_flash_attn_type flash_attn_type = CLIP_FLASH_ATTN_TYPE_AUTO;
 
     // for debugging
     bool debug_graph = false;
     std::vector<ggml_tensor *> debug_print_tensors;
 
     clip_ctx(clip_context_params & ctx_params) {
+        flash_attn_type = ctx_params.flash_attn_type;
         debug_graph = std::getenv("MTMD_DEBUG_GRAPH") != nullptr;
         backend_cpu = ggml_backend_init_by_type(GGML_BACKEND_DEVICE_TYPE_CPU, nullptr);
         if (!backend_cpu) {
@@ -2260,17 +2259,25 @@ struct clip_graph {
         ggml_tensor * k = ggml_permute(ctx0, k_cur, 0, 2, 1, 3);
         //cb(k, "k", il);
 
-        ggml_tensor * v = ggml_permute(ctx0, v_cur, 1, 2, 0, 3);
-        v = ggml_cont(ctx0, v);
-        //cb(k, "v", il);
-
         ggml_tensor * cur;
 
-        // TODO @ngxson : support flash attention
-        {
+        if (ctx->flash_attn_type == CLIP_FLASH_ATTN_TYPE_ENABLED) {
+            ggml_tensor * v = ggml_permute(ctx0, v_cur, 0, 2, 1, 3);
+
+            k = ggml_cast(ctx0, k, GGML_TYPE_F16);
+            v = ggml_cast(ctx0, v, GGML_TYPE_F16);
+
+            cur = ggml_flash_attn_ext(ctx0, q, k, v, kq_mask, kq_scale, 0.0f, 0.0f);
+            ggml_flash_attn_ext_set_prec(cur, GGML_PREC_F32);
+
+            cur = ggml_reshape_2d(ctx0, cur, cur->ne[0]*cur->ne[1], cur->ne[2]*cur->ne[3]);
+
+        } else {
+            ggml_tensor * v = ggml_permute(ctx0, v_cur, 1, 2, 0, 3);
+            v = ggml_cont(ctx0, v);
+
             const auto n_tokens = q->ne[1];
             const auto n_head   = q->ne[2];
-            // const auto n_kv     = k->ne[1]; // for flash attention
 
             ggml_tensor * kq = ggml_mul_mat(ctx0, k, q);
             // F32 may not needed for vision encoders?
@@ -3192,7 +3199,87 @@ struct clip_model_loader {
         }
     }
 
-    void alloc_compute_meta(clip_ctx & ctx_clip) {
+    struct support_info_op {
+        ggml_tensor * op;
+
+        // true if the op runs on the accelerated ctx_clip.backend
+        bool is_accel = true;
+    };
+
+    struct support_info_graph {
+        // whether the clip_ctx.backend supports flash attention
+        bool fattn = true;
+        ggml_tensor * fattn_op = nullptr; // for debugging
+
+        std::vector<support_info_op> ops;
+    };
+
+    static void warmup(clip_ctx & ctx_clip) {
+        support_info_graph info;
+
+        if (ctx_clip.flash_attn_type == CLIP_FLASH_ATTN_TYPE_AUTO) {
+            // try to enable flash attention to see if it's supported
+            ctx_clip.flash_attn_type = CLIP_FLASH_ATTN_TYPE_ENABLED;
+            info = alloc_compute_meta(ctx_clip);
+            if (!info.fattn && info.fattn_op) {
+                auto op = info.fattn_op;
+                LOG_WRN("%s: *****************************************************************\n", __func__);
+                LOG_WRN("%s: WARNING: flash attention not supported by %s, memory usage will increase\n", __func__, ggml_backend_name(ctx_clip.backend));
+                LOG_WRN("%s: op params: \n", __func__);
+                static auto print_shape = [](const char * fn, const char * name, ggml_tensor * t) {
+                    LOG_WRN("%s:   %s: type = %s, ne = [%d %d %d %d], nb = [%d %d %d %d]\n", fn,
+                            name, ggml_type_name(t->type),
+                            t->ne[0], t->ne[1], t->ne[2], t->ne[3],
+                            t->nb[0], t->nb[1], t->nb[2], t->nb[3]);
+                };
+                print_shape(__func__, " dst", op);
+                print_shape(__func__, "src0", op->src[0]);
+                print_shape(__func__, "src1", op->src[1]);
+                print_shape(__func__, "src2", op->src[2]);
+                LOG_WRN("%s: please report this on github as an issue\n", __func__);
+                LOG_WRN("%s: *****************************************************************\n", __func__);
+                ctx_clip.flash_attn_type = CLIP_FLASH_ATTN_TYPE_DISABLED;
+                alloc_compute_meta(ctx_clip);
+            }
+        } else {
+            info = alloc_compute_meta(ctx_clip);
+            if (!info.fattn && ctx_clip.flash_attn_type == CLIP_FLASH_ATTN_TYPE_ENABLED) {
+                LOG_WRN("%s: flash attention is not supported by the current backend; falling back to CPU (performance will be degraded)\n", __func__);
+            }
+        }
+
+        LOG_INF("%s: flash attention is %s\n", __func__,
+            (ctx_clip.flash_attn_type == CLIP_FLASH_ATTN_TYPE_ENABLED) ? "enabled" : "disabled");
+
+        // print ops that are not supported by the GPU backend (if there is one)
+        if (ctx_clip.backend && ctx_clip.backend != ctx_clip.backend_cpu) {
+            std::vector<support_info_op> unsupported_ops;
+            for (const auto & op : info.ops) {
+                if (!op.is_accel) {
+                    unsupported_ops.push_back(op);
+                }
+            }
+            if (!unsupported_ops.empty()) {
+                LOG_WRN("%s: *****************************************************************\n", __func__);
+                LOG_WRN("%s: WARNING: the CLIP graph uses unsupported operators by the backend\n", __func__);
+                LOG_WRN("%s:          the performance will be suboptimal                      \n", __func__);
+                LOG_WRN("%s:          list of unsupported ops (backend=%s):\n", __func__, ggml_backend_name(ctx_clip.backend));
+                for (const auto & op : unsupported_ops) {
+                    LOG_WRN("%s: %16s: type = %s, ne = [%d %d %d %d]\n", __func__,
+                            ggml_op_name(op.op->op),
+                            ggml_type_name(op.op->type),
+                            op.op->ne[0], op.op->ne[1], op.op->ne[2], op.op->ne[3]);
+                }
+                LOG_WRN("%s: flash attention is %s\n", __func__,
+                    (ctx_clip.flash_attn_type == CLIP_FLASH_ATTN_TYPE_ENABLED) ? "enabled" : "disabled");
+                LOG_WRN("%s: please report this on github as an issue\n", __func__);
+                LOG_WRN("%s: ref: https://github.com/ggml-org/llama.cpp/pull/16837#issuecomment-3461676118\n", __func__);
+                LOG_WRN("%s: *****************************************************************\n", __func__);
+            }
+        }
+    }
+
+    static support_info_graph alloc_compute_meta(clip_ctx & ctx_clip) {
         const auto & hparams = ctx_clip.model.hparams;
         ctx_clip.buf_compute_meta.resize(ctx_clip.max_nodes * ggml_tensor_overhead() + ggml_graph_overhead());
 
@@ -3223,57 +3310,95 @@ struct clip_model_loader {
                         size / 1024.0 / 1024.0);
             }
         }
+
+        const int n_splits = ggml_backend_sched_get_n_splits(ctx_clip.sched.get());
+        const int n_nodes  = ggml_graph_n_nodes(gf);
+
+        LOG_INF("%s: graph splits = %d, nodes = %d\n", __func__,  n_splits, n_nodes);
+
+        support_info_graph res {
+            /*.fattn    = */ true,
+            /*.fattn_op = */ nullptr,
+            /*.ops      = */ {},
+        };
+
+        // check op support
+        for (int i = 0; i < ggml_graph_n_nodes(gf); i++) {
+            ggml_tensor * node = ggml_graph_node(gf, i);
+            res.ops.push_back({node, true});
+            if (!ggml_backend_supports_op(ctx_clip.backend, node)) {
+                res.ops.back().is_accel = false;
+                if (node->op == GGML_OP_FLASH_ATTN_EXT) {
+                    res.fattn    = false;
+                    res.fattn_op = node;
+                }
+            }
+        }
+
+        return res;
     }
 
-    void get_bool(const std::string & key, bool & output, bool required = true) {
+    void get_bool(const std::string & key, bool & output, bool required = true) const {
         const int i = gguf_find_key(ctx_gguf.get(), key.c_str());
         if (i < 0) {
-            if (required) throw std::runtime_error("Key not found: " + key);
+            if (required) {
+                throw std::runtime_error("Key not found: " + key);
+            }
             return;
         }
         output = gguf_get_val_bool(ctx_gguf.get(), i);
     }
 
-    void get_i32(const std::string & key, int & output, bool required = true) {
+    void get_i32(const std::string & key, int & output, bool required = true) const {
         const int i = gguf_find_key(ctx_gguf.get(), key.c_str());
         if (i < 0) {
-            if (required) throw std::runtime_error("Key not found: " + key);
+            if (required) {
+                throw std::runtime_error("Key not found: " + key);
+            }
             return;
         }
         output = gguf_get_val_i32(ctx_gguf.get(), i);
     }
 
-    void get_u32(const std::string & key, int & output, bool required = true) {
+    void get_u32(const std::string & key, int & output, bool required = true) const {
         const int i = gguf_find_key(ctx_gguf.get(), key.c_str());
         if (i < 0) {
-            if (required) throw std::runtime_error("Key not found: " + key);
+            if (required) {
+                throw std::runtime_error("Key not found: " + key);
+            }
             return;
         }
         output = gguf_get_val_u32(ctx_gguf.get(), i);
     }
 
-    void get_f32(const std::string & key, float & output, bool required = true) {
+    void get_f32(const std::string & key, float & output, bool required = true) const {
         const int i = gguf_find_key(ctx_gguf.get(), key.c_str());
         if (i < 0) {
-            if (required) throw std::runtime_error("Key not found: " + key);
+            if (required) {
+                throw std::runtime_error("Key not found: " + key);
+            }
             return;
         }
         output = gguf_get_val_f32(ctx_gguf.get(), i);
     }
 
-    void get_string(const std::string & key, std::string & output, bool required = true) {
+    void get_string(const std::string & key, std::string & output, bool required = true) const {
         const int i = gguf_find_key(ctx_gguf.get(), key.c_str());
         if (i < 0) {
-            if (required) throw std::runtime_error("Key not found: " + key);
+            if (required) {
+                throw std::runtime_error("Key not found: " + key);
+            }
             return;
         }
         output = std::string(gguf_get_val_str(ctx_gguf.get(), i));
     }
 
-    void get_arr_int(const std::string & key, std::vector<int> & output, bool required = true) {
+    void get_arr_int(const std::string & key, std::vector<int> & output, bool required = true) const {
         const int i = gguf_find_key(ctx_gguf.get(), key.c_str());
         if (i < 0) {
-            if (required) throw std::runtime_error("Key not found: " + key);
+            if (required) {
+                throw std::runtime_error("Key not found: " + key);
+            }
             return;
         }
         int n = gguf_get_arr_n(ctx_gguf.get(), i);
@@ -3284,7 +3409,7 @@ struct clip_model_loader {
         }
     }
 
-    void set_llava_uhd_res_candidates(clip_model & model, const int max_patches_per_side) {
+    static void set_llava_uhd_res_candidates(clip_model & model, const int max_patches_per_side) {
         auto & hparams = model.hparams;
         for (int x = 1; x <= max_patches_per_side; x++) {
             for (int y = 1; y <= max_patches_per_side; y++) {
@@ -3312,24 +3437,22 @@ struct clip_init_result clip_init(const char * fname, struct clip_context_params
             ctx_vision = new clip_ctx(ctx_params);
             loader.load_hparams(ctx_vision->model, CLIP_MODALITY_VISION);
             loader.load_tensors(*ctx_vision);
-            loader.alloc_compute_meta(*ctx_vision);
+            loader.warmup(*ctx_vision);
         }
 
         if (loader.has_audio) {
             ctx_audio = new clip_ctx(ctx_params);
             loader.load_hparams(ctx_audio->model, CLIP_MODALITY_AUDIO);
             loader.load_tensors(*ctx_audio);
-            loader.alloc_compute_meta(*ctx_audio);
+            loader.warmup(*ctx_audio);
         }
 
     } catch (const std::exception & e) {
         LOG_ERR("%s: failed to load model '%s': %s\n", __func__, fname, e.what());
-        if (ctx_vision) {
-            delete ctx_vision;
-        }
-        if (ctx_audio) {
-            delete ctx_audio;
-        }
+
+        delete ctx_vision;
+        delete ctx_audio;
+
         return {nullptr, nullptr};
     }
 
@@ -3367,10 +3490,10 @@ void clip_image_size_free(struct clip_image_size * load_image_size) {
     }
     delete load_image_size;
 }
-void clip_image_u8_free(struct clip_image_u8  * img) { if (img) delete img; }
-void clip_image_f32_free(struct clip_image_f32 * img) { if (img) delete img; }
-void clip_image_u8_batch_free(struct clip_image_u8_batch * batch) { if (batch) delete batch; }
-void clip_image_f32_batch_free(struct clip_image_f32_batch * batch) { if (batch) delete batch; }
+void clip_image_u8_free(struct clip_image_u8  * img) { delete img; }
+void clip_image_f32_free(struct clip_image_f32 * img) { delete img; }
+void clip_image_u8_batch_free(struct clip_image_u8_batch * batch) { delete batch; }
+void clip_image_f32_batch_free(struct clip_image_f32_batch * batch) { delete batch; }
 
 size_t clip_image_f32_batch_n_images(const struct clip_image_f32_batch * batch) {
     return batch->entries.size();
diff --git a/tools/mtmd/clip.h b/tools/mtmd/clip.h
index 3387cdbd369..6384e2adaf7 100644
--- a/tools/mtmd/clip.h
+++ b/tools/mtmd/clip.h
@@ -1,6 +1,7 @@
 #pragma once
 
 #include "ggml.h"
+
 #include <stddef.h>
 #include <stdint.h>
 
@@ -22,9 +23,16 @@ enum clip_modality {
     CLIP_MODALITY_AUDIO,
 };
 
+enum clip_flash_attn_type {
+    CLIP_FLASH_ATTN_TYPE_AUTO     = -1,
+    CLIP_FLASH_ATTN_TYPE_DISABLED = 0,
+    CLIP_FLASH_ATTN_TYPE_ENABLED  = 1,
+};
+
 struct clip_context_params {
     bool use_gpu;
     enum ggml_log_level verbosity;
+    enum clip_flash_attn_type flash_attn_type;
 };
 
 struct clip_init_result {
diff --git a/tools/mtmd/mtmd-cli.cpp b/tools/mtmd/mtmd-cli.cpp
index fd1fb6581b1..17aea1472b3 100644
--- a/tools/mtmd/mtmd-cli.cpp
+++ b/tools/mtmd/mtmd-cli.cpp
@@ -136,6 +136,7 @@ struct mtmd_cli_context {
         mparams.print_timings = true;
         mparams.n_threads = params.cpuparams.n_threads;
         mparams.verbosity = params.verbosity > 0 ? GGML_LOG_LEVEL_DEBUG : GGML_LOG_LEVEL_INFO;
+        mparams.flash_attn_type = params.flash_attn_type;
         ctx_vision.reset(mtmd_init_from_file(clip_path, model, mparams));
         if (!ctx_vision.get()) {
             LOG_ERR("Failed to load vision model from %s\n", clip_path);
diff --git a/tools/mtmd/mtmd.cpp b/tools/mtmd/mtmd.cpp
index 196641dd95e..297eef437ab 100644
--- a/tools/mtmd/mtmd.cpp
+++ b/tools/mtmd/mtmd.cpp
@@ -19,7 +19,6 @@
 #include <cstdio>
 #include <cstdlib>
 #include <cstring>
-#include <limits>
 #include <vector>
 
 // represents raw image data, layout is RGBRGBRGB...
@@ -92,6 +91,15 @@ const char * mtmd_default_marker() {
     return "<__media__>";
 }
 
+static clip_flash_attn_type mtmd_get_clip_flash_attn_type(enum llama_flash_attn_type flash_attn_type) {
+    switch (flash_attn_type) {
+        case LLAMA_FLASH_ATTN_TYPE_AUTO:     return CLIP_FLASH_ATTN_TYPE_AUTO;
+        case LLAMA_FLASH_ATTN_TYPE_DISABLED: return CLIP_FLASH_ATTN_TYPE_DISABLED;
+        case LLAMA_FLASH_ATTN_TYPE_ENABLED:  return CLIP_FLASH_ATTN_TYPE_ENABLED;
+    }
+    return CLIP_FLASH_ATTN_TYPE_AUTO;
+}
+
 mtmd_context_params mtmd_context_params_default() {
     mtmd_context_params params;
     params.use_gpu = true;
@@ -100,6 +108,7 @@ mtmd_context_params mtmd_context_params_default() {
     params.verbosity = GGML_LOG_LEVEL_INFO;
     params.image_marker = MTMD_DEFAULT_IMAGE_MARKER;
     params.media_marker = mtmd_default_marker();
+    params.flash_attn_type = LLAMA_FLASH_ATTN_TYPE_AUTO;
     return params;
 }
 
@@ -164,6 +173,7 @@ struct mtmd_context {
         clip_context_params ctx_clip_params;
         ctx_clip_params.use_gpu   = ctx_params.use_gpu;
         ctx_clip_params.verbosity = ctx_params.verbosity;
+        ctx_clip_params.flash_attn_type = mtmd_get_clip_flash_attn_type(ctx_params.flash_attn_type);
         auto res = clip_init(mmproj_fname, ctx_clip_params);
         ctx_v = res.ctx_v;
         ctx_a = res.ctx_a;
@@ -378,9 +388,7 @@ mtmd_context * mtmd_init_from_file(const char * mmproj_fname,
 }
 
 void mtmd_free(mtmd_context * ctx) {
-    if (ctx) {
-        delete ctx;
-    }
+    delete ctx;
 }
 
 struct mtmd_tokenizer {
diff --git a/tools/mtmd/mtmd.h b/tools/mtmd/mtmd.h
index 0b5d2ba0c76..4ae1925bcdf 100644
--- a/tools/mtmd/mtmd.h
+++ b/tools/mtmd/mtmd.h
@@ -82,6 +82,7 @@ struct mtmd_context_params {
     enum ggml_log_level verbosity;
     const char * image_marker; // deprecated, use media_marker instead
     const char * media_marker;
+    enum llama_flash_attn_type flash_attn_type;
 };
 
 MTMD_API const char * mtmd_default_marker(void);
diff --git a/tools/server/server.cpp b/tools/server/server.cpp
index aa498158520..a9bef35189b 100644
--- a/tools/server/server.cpp
+++ b/tools/server/server.cpp
@@ -2456,6 +2456,7 @@ struct server_context {
             mparams.print_timings = false;
             mparams.n_threads     = params_base.cpuparams.n_threads;
             mparams.verbosity     = params_base.verbosity > 0 ? GGML_LOG_LEVEL_DEBUG : GGML_LOG_LEVEL_INFO;
+            mparams.flash_attn_type = params_base.flash_attn_type;
             mctx = mtmd_init_from_file(mmproj_path.c_str(), model, mparams);
             if (mctx == nullptr) {
                 SRV_ERR("failed to load multimodal model, '%s'\n", mmproj_path.c_str());

From 6b9a52422bac0f50dd8f1f8386744fa3ce9783bf Mon Sep 17 00:00:00 2001
From: Zhiyong Wang <85110830+ravenouse@users.noreply.github.com>
Date: Sun, 2 Nov 2025 13:08:04 -0800
Subject: [PATCH 061/185] model: add Janus Pro for image understanding (#16906)
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

* Add support for Janus Pro

* Update gguf-py/gguf/tensor_mapping.py

Co-authored-by: Sigbjørn Skjæret <sigbjorn.skjaeret@scala.com>

* Update gguf-py/gguf/tensor_mapping.py

Co-authored-by: Sigbjørn Skjæret <sigbjorn.skjaeret@scala.com>

* Address reviewer suggestions

Co-authored-by: Sigbjørn Skjæret <sigbjorn.skjaeret@scala.com>

* Add JANUS_PRO constant

* Update clip model handling

Co-authored-by: Xuan-Son Nguyen <son@huggingface.co>

* Update tools/mtmd/clip.cpp

Co-authored-by: Xuan-Son Nguyen <thichthat@gmail.com>

* Refactor JANUS_PRO handling in clip.cpp

Co-authored-by: Xuan-Son Nguyen <son@huggingface.co>

* Update tools/mtmd/clip.cpp

Co-authored-by: Sigbjørn Skjæret <sigbjorn.skjaeret@scala.com>

* em whitespace

---------

Co-authored-by: Sigbjørn Skjæret <sigbjorn.skjaeret@scala.com>
Co-authored-by: Xuan-Son Nguyen <son@huggingface.co>
Co-authored-by: Xuan-Son Nguyen <thichthat@gmail.com>
---
 convert_hf_to_gguf.py          | 107 +++++++++++++++++++++++++++++++++
 gguf-py/gguf/constants.py      |   1 +
 gguf-py/gguf/tensor_mapping.py |   2 +
 tools/mtmd/clip-impl.h         |   2 +
 tools/mtmd/clip.cpp            |  36 ++++++++++-
 5 files changed, 147 insertions(+), 1 deletion(-)

diff --git a/convert_hf_to_gguf.py b/convert_hf_to_gguf.py
index f186c2167d7..c6f5ba6a04c 100755
--- a/convert_hf_to_gguf.py
+++ b/convert_hf_to_gguf.py
@@ -9802,6 +9802,113 @@ def modify_tensors(self, data_torch: Tensor, name: str, bid: int | None) -> Iter
 
         return [(self.map_tensor_name(name), data_torch)]
 
+
+@ModelBase.register("JanusForConditionalGeneration")
+class JanusProModel(LlamaModel):
+    model_arch = gguf.MODEL_ARCH.LLAMA  # reuse Llama arch
+
+    def modify_tensors(self, data_torch: Tensor, name: str, bid: int | None) -> Iterable[tuple[str, Tensor]]:
+        # Skip vision, aligner, and generation tensors
+        skip_prefixes = (
+            'model.vision_model.',
+            'model.aligner.',
+            'model.vqmodel.',
+            'model.generation_embeddings.',
+            'model.generation_aligner.',
+            'model.generation_head.',
+        )
+        if name.startswith(skip_prefixes):
+            return []
+
+        if name.startswith('model.language_model.'):
+            name = name.replace('model.language_model.', 'model.')
+        elif name.startswith('language_model.'):
+            name = name.replace('language_model.', '')
+
+        return super().modify_tensors(data_torch, name, bid)
+
+
+@ModelBase.register("JanusForConditionalGeneration")
+class JanusProVisionModel(MmprojModel):
+    def __init__(self, *args, **kwargs):
+        super().__init__(*args, **kwargs)
+        assert self.hparams_vision is not None
+        if "intermediate_size" not in self.hparams_vision:
+            mlp_ratio = self.hparams_vision.get("mlp_ratio")
+            hidden_size = self.hparams_vision.get("hidden_size")
+            if mlp_ratio is not None and hidden_size is not None:
+                self.hparams_vision["intermediate_size"] = int(round(hidden_size * mlp_ratio))
+
+    def set_gguf_parameters(self):
+        super().set_gguf_parameters()
+        assert self.hparams_vision is not None
+
+        self.gguf_writer.add_clip_projector_type(gguf.VisionProjectorType.JANUS_PRO)
+
+        self.gguf_writer.add_vision_attention_layernorm_eps(self.hparams_vision.get("layer_norm_eps", 1e-6))
+
+        hidden_act = str(self.hparams_vision.get("hidden_act", "")).lower()
+        if hidden_act == "gelu":
+            self.gguf_writer.add_vision_use_gelu(True)
+        elif hidden_act == "silu":
+            self.gguf_writer.add_vision_use_silu(True)
+
+    def _map_aligner_tensor(self, data_torch: Tensor, name: str) -> Iterable[tuple[str, Tensor]]:
+        """Map aligner tensors to projector format"""
+        suffix = ".bias" if name.endswith(".bias") else ".weight"
+
+        if name.startswith("model.aligner."):
+            local_name = name[len("model.aligner."):]
+        elif name.startswith("aligner."):
+            local_name = name[len("aligner."):]
+        else:
+            raise ValueError(f"Unsupported Janus aligner prefix: {name}")
+
+        if local_name.startswith("fc1."):
+            mm_index = 0
+        elif local_name.startswith("hidden_layers."):
+            parts = local_name.split(".", 2)
+            if len(parts) < 3:
+                raise ValueError(f"Unexpected Janus aligner tensor name: {name}")
+            mm_index = int(parts[1]) + 1
+        else:
+            raise ValueError(f"Unsupported Janus aligner tensor: {name}")
+
+        tensor_name = self.format_tensor_name(gguf.MODEL_TENSOR.V_MMPROJ, mm_index, suffix=suffix)
+        return [(tensor_name, data_torch)]
+
+    def modify_tensors(self, data_torch: Tensor, name: str, bid: int | None) -> Iterable[tuple[str, Tensor]]:
+        del bid  # unused
+
+        # Skip language model tensors as they will be handled by `JanusProModel`
+        if name.startswith(('model.language_model.', 'language_model.')):
+            return []
+
+        # Skip generation-related components
+        skip_generation_prefixes = (
+            'model.vqmodel.',
+            'vqmodel.',
+            'model.generation_embeddings.',
+            'generation_embeddings.',
+            'model.generation_aligner.',
+            'generation_aligner.',
+            'model.generation_head.',
+            'generation_head.',
+        )
+        if name.startswith(skip_generation_prefixes):
+            return []
+
+        # Handle aligner tensors
+        if name.startswith(('model.aligner.', 'aligner.')):
+            return list(self._map_aligner_tensor(data_torch, name))
+
+        # Handle vision tensors
+        if name.startswith(('model.vision_model.', 'vision_model.')):
+            return [(self.map_tensor_name(name), data_torch)]
+
+        return []
+
+
 ###### CONVERSION LOGIC ######
 
 
diff --git a/gguf-py/gguf/constants.py b/gguf-py/gguf/constants.py
index 0d5afa01edf..77e3b0650ff 100644
--- a/gguf-py/gguf/constants.py
+++ b/gguf-py/gguf/constants.py
@@ -3186,6 +3186,7 @@ class VisionProjectorType:
     KIMIVL = "kimivl"
     LIGHTONOCR = "lightonocr"
     COGVLM = "cogvlm"
+    JANUS_PRO = "janus_pro"
 
 
 # Items here are (block size, type size)
diff --git a/gguf-py/gguf/tensor_mapping.py b/gguf-py/gguf/tensor_mapping.py
index cef5acec758..92940668761 100644
--- a/gguf-py/gguf/tensor_mapping.py
+++ b/gguf-py/gguf/tensor_mapping.py
@@ -1183,6 +1183,7 @@ class TensorNameMap:
             "model.mm_projector.mlp.mlp.{bid}",
             "vision_model.vision_adapter.mlp.fc{bid}", # llama 4
             "mlp1.{bid}", # InternVL
+            "model.aligner.fc1.hidden_layers.{bid}", # Janus Pro
         ),
 
         MODEL_TENSOR.V_MMPROJ_PEG: (
@@ -1291,6 +1292,7 @@ class TensorNameMap:
             "model.vision_tower.encoder.layer.{bid}.attention.projection_layer", # Intern-S1
             "vpm.encoder.layers.{bid}.self_attn.out_proj",
             "model.vision_model.encoder.layers.{bid}.self_attn.out_proj", # SmolVLM
+            "model.vision_model.encoder.layers.{bid}.self_attn.projection_layer", # Janus Pro
             "vision_model.model.layers.{bid}.self_attn.o_proj", # llama4
             "vision_tower.transformer.layers.{bid}.attention.o_proj", # pixtral-hf
             "vision_encoder.transformer.layers.{bid}.attention.wo", # pixtral
diff --git a/tools/mtmd/clip-impl.h b/tools/mtmd/clip-impl.h
index c7e9498349c..722b1a4948d 100644
--- a/tools/mtmd/clip-impl.h
+++ b/tools/mtmd/clip-impl.h
@@ -155,6 +155,7 @@ enum projector_type {
     PROJECTOR_TYPE_KIMIVL,
     PROJECTOR_TYPE_LIGHTONOCR,
     PROJECTOR_TYPE_COGVLM,
+    PROJECTOR_TYPE_JANUS_PRO,
     PROJECTOR_TYPE_UNKNOWN,
 };
 
@@ -180,6 +181,7 @@ static std::map<projector_type, std::string> PROJECTOR_TYPE_NAMES = {
     { PROJECTOR_TYPE_KIMIVL,    "kimivl"},
     { PROJECTOR_TYPE_LIGHTONOCR,"lightonocr"},
     { PROJECTOR_TYPE_COGVLM,    "cogvlm"},
+    { PROJECTOR_TYPE_JANUS_PRO, "janus_pro"},
 };
 
 static projector_type clip_projector_type_from_string(const std::string & str) {
diff --git a/tools/mtmd/clip.cpp b/tools/mtmd/clip.cpp
index a7e1799e93d..0784e69fcdf 100644
--- a/tools/mtmd/clip.cpp
+++ b/tools/mtmd/clip.cpp
@@ -588,6 +588,15 @@ struct clip_graph {
             cur = ggml_gelu(ctx0, cur);
             cur = ggml_mul_mat(ctx0, model.mm_2_w, cur);
             cur = ggml_add(ctx0, cur, model.mm_2_b);
+
+        } else if (ctx->proj_type() == PROJECTOR_TYPE_JANUS_PRO) {
+            cur = build_ffn(cur,
+                model.mm_0_w, model.mm_0_b,
+                nullptr, nullptr,
+                model.mm_1_w, model.mm_1_b,
+                hparams.ffn_op,
+                -1);
+
         } else {
             GGML_ABORT("SigLIP: Unsupported projector type");
         }
@@ -1729,7 +1738,6 @@ struct clip_graph {
 
         return gf;
     }
-
     // whisper encoder with custom projector
     ggml_cgraph * build_whisper_enc() {
         const int n_frames = img.nx;
@@ -2457,6 +2465,10 @@ static ggml_cgraph * clip_image_build_graph(clip_ctx * ctx, const clip_image_f32
             {
                 res = graph.build_kimivl();
             } break;
+        case PROJECTOR_TYPE_JANUS_PRO:
+            {
+                res = graph.build_siglip();
+            } break;
         case PROJECTOR_TYPE_COGVLM:
             {
                 res = graph.build_cogvlm();
@@ -3158,6 +3170,13 @@ struct clip_model_loader {
                     model.mm_boi            = get_tensor(TN_TOK_BOI);
                     model.mm_eoi            = get_tensor(TN_TOK_EOI);
                 } break;
+            case PROJECTOR_TYPE_JANUS_PRO:
+                {
+                    model.mm_0_w = get_tensor(string_format(TN_LLAVA_PROJ, 0, "weight"));
+                    model.mm_0_b = get_tensor(string_format(TN_LLAVA_PROJ, 0, "bias"));
+                    model.mm_1_w = get_tensor(string_format(TN_LLAVA_PROJ, 1, "weight"));
+                    model.mm_1_b = get_tensor(string_format(TN_LLAVA_PROJ, 1, "bias"));
+                } break;
             default:
                 GGML_ASSERT(false && "unknown projector type");
         }
@@ -4219,6 +4238,18 @@ bool clip_image_preprocess(struct clip_ctx * ctx, const clip_image_u8 * img, str
                 res_imgs->entries.push_back(std::move(img_f32));
             } break;
 
+        case PROJECTOR_TYPE_JANUS_PRO:
+            {
+                // Janus Pro preprocessing: pad to square with gray(127), resize to 384x384
+                const std::array<uint8_t, 3> pad_color = {127, 127, 127};
+                clip_image_u8 resized_image;
+                int sz = params.image_size;
+                img_tool::resize(*img, resized_image, {sz, sz}, img_tool::RESIZE_ALGO_BILINEAR, true, pad_color);
+                clip_image_f32_ptr img_f32(clip_image_f32_init());
+                normalize_image_u8_to_f32(resized_image, *img_f32, params.image_mean, params.image_std);
+                res_imgs->entries.push_back(std::move(img_f32));
+            } break;
+
         case PROJECTOR_TYPE_PIXTRAL:
         case PROJECTOR_TYPE_LIGHTONOCR:
             {
@@ -4395,6 +4426,7 @@ int clip_n_output_tokens(const struct clip_ctx * ctx, struct clip_image_f32 * im
     switch (proj) {
         case PROJECTOR_TYPE_MLP:
         case PROJECTOR_TYPE_MLP_NORM:
+        case PROJECTOR_TYPE_JANUS_PRO:
             {
                 // do nothing
             } break;
@@ -4905,6 +4937,7 @@ bool clip_image_batch_encode(clip_ctx * ctx, const int n_threads, const clip_ima
         case PROJECTOR_TYPE_ULTRAVOX:
         case PROJECTOR_TYPE_LFM2:
         case PROJECTOR_TYPE_VOXTRAL:
+        case PROJECTOR_TYPE_JANUS_PRO:
         case PROJECTOR_TYPE_COGVLM:
             {
                 // do nothing
@@ -4993,6 +5026,7 @@ int clip_n_mmproj_embd(const struct clip_ctx * ctx) {
             return ctx->model.mm_model_mlp_3_w->ne[1];
         case PROJECTOR_TYPE_QWEN2VL:
         case PROJECTOR_TYPE_QWEN25VL:
+        case PROJECTOR_TYPE_JANUS_PRO:
             return ctx->model.mm_1_b->ne[0];
         case PROJECTOR_TYPE_QWEN3VL:
             // main path + deepstack paths

From dd5286805004db1f9ac3176a1cbbfe373bdda0f8 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sigbj=C3=B8rn=20Skj=C3=A6ret?= <sigbjorn.skjaeret@scala.com>
Date: Sun, 2 Nov 2025 23:11:21 +0100
Subject: [PATCH 062/185] ci : disable failing riscv cross build (#16952)

---
 .github/workflows/build-linux-cross.yml | 74 ++++++++++++-------------
 1 file changed, 37 insertions(+), 37 deletions(-)

diff --git a/.github/workflows/build-linux-cross.yml b/.github/workflows/build-linux-cross.yml
index 937306f7afa..36201281f00 100644
--- a/.github/workflows/build-linux-cross.yml
+++ b/.github/workflows/build-linux-cross.yml
@@ -4,49 +4,49 @@ on:
   workflow_call:
 
 jobs:
-  ubuntu-24-riscv64-cpu-cross:
-    runs-on: ubuntu-24.04
+  # ubuntu-24-riscv64-cpu-cross:
+  #   runs-on: ubuntu-24.04
 
-    steps:
-      - uses: actions/checkout@v4
-      - name: Setup Riscv
-        run: |
-          sudo dpkg --add-architecture riscv64
+  #   steps:
+  #     - uses: actions/checkout@v4
+  #     - name: Setup Riscv
+  #       run: |
+  #         sudo dpkg --add-architecture riscv64
 
-          # Add arch-specific repositories for non-amd64 architectures
-          cat << EOF | sudo tee /etc/apt/sources.list.d/riscv64-ports.list
-          deb [arch=riscv64] http://ports.ubuntu.com/ubuntu-ports/ noble main universe
-          deb [arch=riscv64] http://ports.ubuntu.com/ubuntu-ports/ noble-updates main universe
-          deb [arch=riscv64] http://ports.ubuntu.com/ubuntu-ports/ noble-security main universe
-          deb [arch=riscv64] http://ports.ubuntu.com/ubuntu-ports/ noble-backports main universe
-          EOF
+  #         # Add arch-specific repositories for non-amd64 architectures
+  #         cat << EOF | sudo tee /etc/apt/sources.list.d/riscv64-ports.list
+  #         deb [arch=riscv64] http://ports.ubuntu.com/ubuntu-ports/ noble main universe
+  #         deb [arch=riscv64] http://ports.ubuntu.com/ubuntu-ports/ noble-updates main universe
+  #         deb [arch=riscv64] http://ports.ubuntu.com/ubuntu-ports/ noble-security main universe
+  #         deb [arch=riscv64] http://ports.ubuntu.com/ubuntu-ports/ noble-backports main universe
+  #         EOF
 
-          sudo apt-get update || true    ;# Prevent failure due to missing URLs.
+  #         sudo apt-get update || true    ;# Prevent failure due to missing URLs.
 
-          sudo apt-get install -y --no-install-recommends \
-                  build-essential \
-                  gcc-14-riscv64-linux-gnu \
-                  g++-14-riscv64-linux-gnu
+  #         sudo apt-get install -y --no-install-recommends \
+  #                 build-essential \
+  #                 gcc-14-riscv64-linux-gnu \
+  #                 g++-14-riscv64-linux-gnu
 
-      - name: Build
-        run: |
-          cmake -B build -DLLAMA_CURL=OFF \
-                         -DCMAKE_BUILD_TYPE=Release \
-                         -DGGML_OPENMP=OFF \
-                         -DLLAMA_BUILD_EXAMPLES=ON \
-                         -DLLAMA_BUILD_TOOLS=ON \
-                         -DLLAMA_BUILD_TESTS=OFF \
-                         -DCMAKE_SYSTEM_NAME=Linux \
-                         -DCMAKE_SYSTEM_PROCESSOR=riscv64 \
-                         -DCMAKE_C_COMPILER=riscv64-linux-gnu-gcc-14 \
-                         -DCMAKE_CXX_COMPILER=riscv64-linux-gnu-g++-14 \
-                         -DCMAKE_POSITION_INDEPENDENT_CODE=ON \
-                         -DCMAKE_FIND_ROOT_PATH=/usr/lib/riscv64-linux-gnu \
-                         -DCMAKE_FIND_ROOT_PATH_MODE_PROGRAM=NEVER \
-                         -DCMAKE_FIND_ROOT_PATH_MODE_LIBRARY=ONLY \
-                         -DCMAKE_FIND_ROOT_PATH_MODE_INCLUDE=BOTH
+  #     - name: Build
+  #       run: |
+  #         cmake -B build -DLLAMA_CURL=OFF \
+  #                        -DCMAKE_BUILD_TYPE=Release \
+  #                        -DGGML_OPENMP=OFF \
+  #                        -DLLAMA_BUILD_EXAMPLES=ON \
+  #                        -DLLAMA_BUILD_TOOLS=ON \
+  #                        -DLLAMA_BUILD_TESTS=OFF \
+  #                        -DCMAKE_SYSTEM_NAME=Linux \
+  #                        -DCMAKE_SYSTEM_PROCESSOR=riscv64 \
+  #                        -DCMAKE_C_COMPILER=riscv64-linux-gnu-gcc-14 \
+  #                        -DCMAKE_CXX_COMPILER=riscv64-linux-gnu-g++-14 \
+  #                        -DCMAKE_POSITION_INDEPENDENT_CODE=ON \
+  #                        -DCMAKE_FIND_ROOT_PATH=/usr/lib/riscv64-linux-gnu \
+  #                        -DCMAKE_FIND_ROOT_PATH_MODE_PROGRAM=NEVER \
+  #                        -DCMAKE_FIND_ROOT_PATH_MODE_LIBRARY=ONLY \
+  #                        -DCMAKE_FIND_ROOT_PATH_MODE_INCLUDE=BOTH
 
-          cmake --build build --config Release -j $(nproc)
+  #         cmake --build build --config Release -j $(nproc)
 
   # ubuntu-24-riscv64-vulkan-cross:
   #   runs-on: ubuntu-24.04

From a2054e3a8ff0da3978a4acc18c349ff58554d336 Mon Sep 17 00:00:00 2001
From: Shagun Bera <141054835+notV3NOM@users.noreply.github.com>
Date: Mon, 3 Nov 2025 04:40:30 +0530
Subject: [PATCH 063/185] test-backend-ops : fix segfault in moe-expert-reduce
 test in support mode and coverage (#16936)

* tests: fix segfault in moe-expert-reduce test in support mode and --show-coverage

* tests: init gf and filter out fusion tests for support mode

* tests: filter out fusion cases before calling eval_support

* tests: filter out fusion cases from show_test_coverage as well, fix lint
---
 tests/test-backend-ops.cpp | 19 +++++++++++++++++++
 1 file changed, 19 insertions(+)

diff --git a/tests/test-backend-ops.cpp b/tests/test-backend-ops.cpp
index 2886bd37d68..967a53c63d8 100644
--- a/tests/test-backend-ops.cpp
+++ b/tests/test-backend-ops.cpp
@@ -1454,6 +1454,8 @@ struct test_case {
         ggml_context_ptr ctx(ggml_init(params)); // smart ptr
         GGML_ASSERT(ctx);
 
+        gf = ggml_new_graph_custom(ctx.get(), graph_nodes, false);
+
         ggml_tensor * out = build_graph(ctx.get());
         current_op_name   = op_desc(out);
 
@@ -7569,6 +7571,15 @@ static bool test_backend(ggml_backend_t backend, test_mode mode, const char * op
     if (mode == MODE_SUPPORT) {
         auto test_cases = make_test_cases_eval();
         filter_test_cases(test_cases, params_filter);
+
+        // Filter out fusion cases
+        test_cases.erase(
+            std::remove_if(test_cases.begin(), test_cases.end(), [](const std::unique_ptr<test_case> & tc) {
+                return tc->run_whole_graph();
+            }),
+            test_cases.end()
+        );
+
         for (auto & test : test_cases) {
             test->eval_support(backend, op_names_filter, output_printer);
         }
@@ -7619,6 +7630,14 @@ static void show_test_coverage() {
         all_ops.insert(ggml_glu_op_name((enum ggml_glu_op)i));
     }
     auto test_cases = make_test_cases_eval();
+    // Filter out fusion cases
+    test_cases.erase(
+        std::remove_if(test_cases.begin(), test_cases.end(), [](const std::unique_ptr<test_case> & tc) {
+            return tc->run_whole_graph();
+        }),
+        test_cases.end()
+    );
+
     std::set<std::string> tested_ops;
 
     ggml_init_params params = {

From bcfa87622ae46be6345a8e3dfdbdc5ba5414042b Mon Sep 17 00:00:00 2001
From: Sascha Rogmann <59577610+srogmann@users.noreply.github.com>
Date: Mon, 3 Nov 2025 00:41:08 +0100
Subject: [PATCH 064/185] feat(webui): improve LaTeX rendering with currency
 detection (#16508)

* webui : Revised LaTeX formula recognition

* webui : Further examples containg amounts

* webui : vitest for maskInlineLaTeX

* webui: Moved preprocessLaTeX to lib/utils

* webui: LaTeX in table-cells

* chore: update webui build output (use theirs)

* webui: backslash in LaTeX-preprocessing

* chore: update webui build output

* webui: look-behind backslash-check

* chore: update webui build output

* Apply suggestions from code review

Code maintenance (variable names, code formatting, string handling)

Co-authored-by: Aleksander Grygier <aleksander.grygier@gmail.com>

* webui: Moved constants to lib/constants.

* webui: package woff2 inside base64 data

* webui: LaTeX-line-break in display formula

* chore: update webui build output

* webui: Bugfix (font embedding)

* webui: Bugfix (font embedding)

* webui: vite embeds assets

* webui: don't suppress 404 (fonts)

* refactor: KaTeX integration with SCSS

Moves KaTeX styling to SCSS for better customization and font embedding.

This change includes:
- Adding `sass` as a dev dependency.
- Introducing a custom SCSS file to override KaTeX variables and disable TTF/WOFF fonts, relying solely on WOFF2 for embedding.
- Adjusting the Vite configuration to resolve `katex-fonts` alias and inject SCSS variables.

* fix: LaTeX processing within blockquotes

* webui: update webui build output

---------

Co-authored-by: Aleksander Grygier <aleksander.grygier@gmail.com>
---
 tools/server/public/index.html.gz             | Bin 862214 -> 1127221 bytes
 tools/server/webui/package-lock.json          | 361 ++++++++++++++++++
 tools/server/webui/package.json               |   1 +
 .../app/misc/MarkdownContent.svelte           |  15 +-
 .../src/lib/constants/latex-protection.ts     |  35 ++
 .../src/lib/utils/latex-protection.test.ts    | 355 +++++++++++++++++
 .../webui/src/lib/utils/latex-protection.ts   | 267 +++++++++++++
 .../src/stories/fixtures/math-formulas.ts     |  65 ++++
 .../server/webui/src/styles/katex-custom.scss |  13 +
 tools/server/webui/svelte.config.js           |   3 +
 tools/server/webui/vite.config.ts             |  31 +-
 11 files changed, 1131 insertions(+), 15 deletions(-)
 create mode 100644 tools/server/webui/src/lib/constants/latex-protection.ts
 create mode 100644 tools/server/webui/src/lib/utils/latex-protection.test.ts
 create mode 100644 tools/server/webui/src/lib/utils/latex-protection.ts
 create mode 100644 tools/server/webui/src/styles/katex-custom.scss

diff --git a/tools/server/public/index.html.gz b/tools/server/public/index.html.gz
index b71690cc81e29b13069e5b548016b91ba074014e..6a570b65e2ce104f2f3d13c420058e58a5acb46b 100644
GIT binary patch
delta 1115050
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diff --git a/tools/server/webui/package-lock.json b/tools/server/webui/package-lock.json
index f86b9282c9b..8fab38f6f14 100644
--- a/tools/server/webui/package-lock.json
+++ b/tools/server/webui/package-lock.json
@@ -59,6 +59,7 @@
 				"prettier-plugin-tailwindcss": "^0.6.11",
 				"rehype-katex": "^7.0.1",
 				"remark-math": "^6.0.0",
+				"sass": "^1.93.3",
 				"storybook": "^9.0.17",
 				"svelte": "^5.0.0",
 				"svelte-check": "^4.0.0",
@@ -1176,6 +1177,330 @@
 				"node": ">= 8"
 			}
 		},
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+			"dev": true,
+			"hasInstallScript": true,
+			"license": "MIT",
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+			},
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+			},
+			"funding": {
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+				"url": "https://opencollective.com/parcel"
+			},
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+				"@parcel/watcher-darwin-arm64": "2.5.1",
+				"@parcel/watcher-darwin-x64": "2.5.1",
+				"@parcel/watcher-freebsd-x64": "2.5.1",
+				"@parcel/watcher-linux-arm-glibc": "2.5.1",
+				"@parcel/watcher-linux-arm-musl": "2.5.1",
+				"@parcel/watcher-linux-arm64-glibc": "2.5.1",
+				"@parcel/watcher-linux-arm64-musl": "2.5.1",
+				"@parcel/watcher-linux-x64-glibc": "2.5.1",
+				"@parcel/watcher-linux-x64-musl": "2.5.1",
+				"@parcel/watcher-win32-arm64": "2.5.1",
+				"@parcel/watcher-win32-ia32": "2.5.1",
+				"@parcel/watcher-win32-x64": "2.5.1"
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+				"url": "https://opencollective.com/parcel"
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+				"url": "https://opencollective.com/parcel"
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+			"optional": true,
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+			],
+			"engines": {
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+			},
+			"funding": {
+				"type": "opencollective",
+				"url": "https://opencollective.com/parcel"
+			}
+		},
+		"node_modules/@parcel/watcher/node_modules/detect-libc": {
+			"version": "1.0.3",
+			"resolved": "https://registry.npmjs.org/detect-libc/-/detect-libc-1.0.3.tgz",
+			"integrity": "sha512-pGjwhsmsp4kL2RTz08wcOlGN83otlqHeD/Z5T8GXZB+/YcpQ/dgo+lbU8ZsGxV0HIvqqxo9l7mqYwyYMD9bKDg==",
+			"dev": true,
+			"license": "Apache-2.0",
+			"optional": true,
+			"bin": {
+				"detect-libc": "bin/detect-libc.js"
+			},
+			"engines": {
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 		"node_modules/@playwright/test": {
 			"version": "1.54.1",
 			"resolved": "https://registry.npmjs.org/@playwright/test/-/test-1.54.1.tgz",
@@ -4697,6 +5022,13 @@
 				"node": ">= 4"
 			}
 		},
+		"node_modules/immutable": {
+			"version": "5.1.4",
+			"resolved": "https://registry.npmjs.org/immutable/-/immutable-5.1.4.tgz",
+			"integrity": "sha512-p6u1bG3YSnINT5RQmx/yRZBpenIl30kVxkTLDyHLIMk0gict704Q9n+thfDI7lTRm9vXdDYutVzXhzcThxTnXA==",
+			"dev": true,
+			"license": "MIT"
+		},
 		"node_modules/import-fresh": {
 			"version": "3.3.1",
 			"resolved": "https://registry.npmjs.org/import-fresh/-/import-fresh-3.3.1.tgz",
@@ -6462,6 +6794,14 @@
 				"tslib": "^2.0.3"
 			}
 		},
+		"node_modules/node-addon-api": {
+			"version": "7.1.1",
+			"resolved": "https://registry.npmjs.org/node-addon-api/-/node-addon-api-7.1.1.tgz",
+			"integrity": "sha512-5m3bsyrjFWE1xf7nz7YXdN4udnVtXK6/Yfgn5qnahL6bCkf2yKt4k3nuTKAtT4r3IG8JNR2ncsIMdZuAzJjHQQ==",
+			"dev": true,
+			"license": "MIT",
+			"optional": true
+		},
 		"node_modules/object-inspect": {
 			"version": "1.13.4",
 			"resolved": "https://registry.npmjs.org/object-inspect/-/object-inspect-1.13.4.tgz",
@@ -7484,6 +7824,27 @@
 			"dev": true,
 			"license": "MIT"
 		},
+		"node_modules/sass": {
+			"version": "1.93.3",
+			"resolved": "https://registry.npmjs.org/sass/-/sass-1.93.3.tgz",
+			"integrity": "sha512-elOcIZRTM76dvxNAjqYrucTSI0teAF/L2Lv0s6f6b7FOwcwIuA357bIE871580AjHJuSvLIRUosgV+lIWx6Rgg==",
+			"dev": true,
+			"license": "MIT",
+			"dependencies": {
+				"chokidar": "^4.0.0",
+				"immutable": "^5.0.2",
+				"source-map-js": ">=0.6.2 <2.0.0"
+			},
+			"bin": {
+				"sass": "sass.js"
+			},
+			"engines": {
+				"node": ">=14.0.0"
+			},
+			"optionalDependencies": {
+				"@parcel/watcher": "^2.4.1"
+			}
+		},
 		"node_modules/scheduler": {
 			"version": "0.26.0",
 			"resolved": "https://registry.npmjs.org/scheduler/-/scheduler-0.26.0.tgz",
diff --git a/tools/server/webui/package.json b/tools/server/webui/package.json
index 376f6901526..92c7457bd31 100644
--- a/tools/server/webui/package.json
+++ b/tools/server/webui/package.json
@@ -61,6 +61,7 @@
 		"prettier-plugin-tailwindcss": "^0.6.11",
 		"rehype-katex": "^7.0.1",
 		"remark-math": "^6.0.0",
+		"sass": "^1.93.3",
 		"storybook": "^9.0.17",
 		"svelte": "^5.0.0",
 		"svelte-check": "^4.0.0",
diff --git a/tools/server/webui/src/lib/components/app/misc/MarkdownContent.svelte b/tools/server/webui/src/lib/components/app/misc/MarkdownContent.svelte
index 1c069db58d8..7e83d30f132 100644
--- a/tools/server/webui/src/lib/components/app/misc/MarkdownContent.svelte
+++ b/tools/server/webui/src/lib/components/app/misc/MarkdownContent.svelte
@@ -8,8 +8,9 @@
 	import rehypeKatex from 'rehype-katex';
 	import rehypeStringify from 'rehype-stringify';
 	import { copyCodeToClipboard } from '$lib/utils/copy';
+	import { preprocessLaTeX } from '$lib/utils/latex-protection';
 	import { browser } from '$app/environment';
-	import 'katex/dist/katex.min.css';
+	import '$styles/katex-custom.scss';
 
 	import githubDarkCss from 'highlight.js/styles/github-dark.css?inline';
 	import githubLightCss from 'highlight.js/styles/github.css?inline';
@@ -176,19 +177,9 @@
 		return mutated ? tempDiv.innerHTML : html;
 	}
 
-	function normalizeMathDelimiters(text: string): string {
-		return text
-			.replace(/(^|[^\\])\\\[((?:\\.|[\s\S])*?)\\\]/g, (_, prefix: string, content: string) => {
-				return `${prefix}$$${content}$$`;
-			})
-			.replace(/(^|[^\\])\\\(((?:\\.|[\s\S])*?)\\\)/g, (_, prefix: string, content: string) => {
-				return `${prefix}$${content}$`;
-			});
-	}
-
 	async function processMarkdown(text: string): Promise<string> {
 		try {
-			const normalized = normalizeMathDelimiters(text);
+			let normalized = preprocessLaTeX(text);
 			const result = await processor().process(normalized);
 			const html = String(result);
 			const enhancedLinks = enhanceLinks(html);
diff --git a/tools/server/webui/src/lib/constants/latex-protection.ts b/tools/server/webui/src/lib/constants/latex-protection.ts
new file mode 100644
index 00000000000..27c88e7252a
--- /dev/null
+++ b/tools/server/webui/src/lib/constants/latex-protection.ts
@@ -0,0 +1,35 @@
+/**
+ * Matches common Markdown code blocks to exclude them from further processing (e.g. LaTeX).
+ * - Fenced: ```...```
+ * - Inline: `...` (does NOT support nested backticks or multi-backtick syntax)
+ *
+ * Note: This pattern does not handle advanced cases like:
+ *       `` `code with `backticks` `` or \\``...\\``
+ */
+export const CODE_BLOCK_REGEXP = /(```[\s\S]*?```|`[^`\n]+`)/g;
+
+/**
+ * Matches LaTeX math delimiters \(...\) and \[...\] only when not preceded by a backslash (i.e., not escaped),
+ * while also capturing code blocks (```, `...`) so they can be skipped during processing.
+ *
+ * Uses negative lookbehind `(?<!\\)` to avoid matching \\( or \\[.
+ * Using the look‑behind pattern `(?<!\\)` we skip matches
+ * that are preceded by a backslash, e.g.
+ * `Definitions\\(also called macros)` (title of chapter 20 in The TeXbook)
+ * or `\\[4pt]` (LaTeX line-break).
+ *
+ * group 1: code-block
+ * group 2: square-bracket
+ * group 3: round-bracket
+ */
+export const LATEX_MATH_AND_CODE_PATTERN =
+	/(```[\S\s]*?```|`.*?`)|(?<!\\)\\\[([\S\s]*?[^\\])\\]|(?<!\\)\\\((.*?)\\\)/g;
+
+/** Regex to capture the content of a $$...\\\\...$$ block (display-formula with line-break) */
+export const LATEX_LINEBREAK_REGEXP = /\$\$([\s\S]*?\\\\[\s\S]*?)\$\$/;
+
+/** map from mchem-regexp to replacement */
+export const MHCHEM_PATTERN_MAP: readonly [RegExp, string][] = [
+	[/(\s)\$\\ce{/g, '$1$\\\\ce{'],
+	[/(\s)\$\\pu{/g, '$1$\\\\pu{']
+] as const;
diff --git a/tools/server/webui/src/lib/utils/latex-protection.test.ts b/tools/server/webui/src/lib/utils/latex-protection.test.ts
new file mode 100644
index 00000000000..2354f8fa0ec
--- /dev/null
+++ b/tools/server/webui/src/lib/utils/latex-protection.test.ts
@@ -0,0 +1,355 @@
+/* eslint-disable no-irregular-whitespace */
+import { describe, it, expect, test } from 'vitest';
+import { maskInlineLaTeX, preprocessLaTeX } from './latex-protection';
+
+describe('maskInlineLaTeX', () => {
+	it('should protect LaTeX $x + y$ but not money $3.99', () => {
+		const latexExpressions: string[] = [];
+		const input = 'I have $10, $3.99 and $x + y$ and $100x$. The amount is $2,000.';
+		const output = maskInlineLaTeX(input, latexExpressions);
+
+		expect(output).toBe('I have $10, $3.99 and <<LATEX_0>> and <<LATEX_1>>. The amount is $2,000.');
+		expect(latexExpressions).toEqual(['$x + y$', '$100x$']);
+	});
+
+	it('should ignore money like $5 and $12.99', () => {
+		const latexExpressions: string[] = [];
+		const input = 'Prices are $12.99 and $5. Tax?';
+		const output = maskInlineLaTeX(input, latexExpressions);
+
+		expect(output).toBe('Prices are $12.99 and $5. Tax?');
+		expect(latexExpressions).toEqual([]);
+	});
+
+	it('should protect inline math $a^2 + b^2$ even after text', () => {
+		const latexExpressions: string[] = [];
+		const input = 'Pythagorean: $a^2 + b^2 = c^2$.';
+		const output = maskInlineLaTeX(input, latexExpressions);
+
+		expect(output).toBe('Pythagorean: <<LATEX_0>>.');
+		expect(latexExpressions).toEqual(['$a^2 + b^2 = c^2$']);
+	});
+
+	it('should not protect math that has letter after closing $ (e.g. units)', () => {
+		const latexExpressions: string[] = [];
+		const input = 'The cost is $99 and change.';
+		const output = maskInlineLaTeX(input, latexExpressions);
+
+		expect(output).toBe('The cost is $99 and change.');
+		expect(latexExpressions).toEqual([]);
+	});
+
+	it('should allow $x$ followed by punctuation', () => {
+		const latexExpressions: string[] = [];
+		const input = 'We know $x$, right?';
+		const output = maskInlineLaTeX(input, latexExpressions);
+
+		expect(output).toBe('We know <<LATEX_0>>, right?');
+		expect(latexExpressions).toEqual(['$x$']);
+	});
+
+	it('should work across multiple lines', () => {
+		const latexExpressions: string[] = [];
+		const input = `Emma buys cupcakes for $3 each.\nHow much is $x + y$?`;
+		const output = maskInlineLaTeX(input, latexExpressions);
+
+		expect(output).toBe(`Emma buys cupcakes for $3 each.\nHow much is <<LATEX_0>>?`);
+		expect(latexExpressions).toEqual(['$x + y$']);
+	});
+
+	it('should not protect $100 but protect $matrix$', () => {
+		const latexExpressions: string[] = [];
+		const input = '$100 and $\\mathrm{GL}_2(\\mathbb{F}_7)$ are different.';
+		const output = maskInlineLaTeX(input, latexExpressions);
+
+		expect(output).toBe('$100 and <<LATEX_0>> are different.');
+		expect(latexExpressions).toEqual(['$\\mathrm{GL}_2(\\mathbb{F}_7)$']);
+	});
+
+	it('should skip if $ is followed by digit and alphanumeric after close (money)', () => {
+		const latexExpressions: string[] = [];
+		const input = 'I paid $5 quickly.';
+		const output = maskInlineLaTeX(input, latexExpressions);
+
+		expect(output).toBe('I paid $5 quickly.');
+		expect(latexExpressions).toEqual([]);
+	});
+
+	it('should protect LaTeX even with special chars inside', () => {
+		const latexExpressions: string[] = [];
+		const input = 'Consider $\\alpha_1 + \\beta_2$ now.';
+		const output = maskInlineLaTeX(input, latexExpressions);
+
+		expect(output).toBe('Consider <<LATEX_0>> now.');
+		expect(latexExpressions).toEqual(['$\\alpha_1 + \\beta_2$']);
+	});
+
+	it('short text', () => {
+		const latexExpressions: string[] = ['$0$'];
+		const input = '$a$\n$a$ and $b$';
+		const output = maskInlineLaTeX(input, latexExpressions);
+
+		expect(output).toBe('<<LATEX_1>>\n<<LATEX_2>> and <<LATEX_3>>');
+		expect(latexExpressions).toEqual(['$0$', '$a$', '$a$', '$b$']);
+	});
+
+	it('empty text', () => {
+		const latexExpressions: string[] = [];
+		const input = '$\n$$\n';
+		const output = maskInlineLaTeX(input, latexExpressions);
+
+		expect(output).toBe('$\n$$\n');
+		expect(latexExpressions).toEqual([]);
+	});
+
+	it('LaTeX-spacer preceded by backslash', () => {
+		const latexExpressions: string[] = [];
+		const input = `\\[
+\\boxed{
+\\begin{aligned}
+N_{\\text{att}}^{\\text{(MHA)}} &=
+h \\bigl[\\, d_{\\text{model}}\\;d_{k} + d_{\\text{model}}\\;d_{v}\\, \\bigr]   && (\\text{Q,K,V の重み})\\\\
+&\\quad+ h(d_{k}+d_{k}+d_{v})                                          && (\\text{バイアス Q,K,V）}\\\\[4pt]
+&\\quad+ (h d_{v})\\, d_{\\text{model}}                                 && (\\text{出力射影 }W^{O})\\\\
+&\\quad+ d_{\\text{model}}                                            && (\\text{バイアス }b^{O})
+\\end{aligned}}
+\\]`;
+		const output = maskInlineLaTeX(input, latexExpressions);
+
+		expect(output).toBe(input);
+		expect(latexExpressions).toEqual([]);
+	});
+});
+
+describe('preprocessLaTeX', () => {
+	test('converts inline \\( ... \\) to $...$', () => {
+		const input =
+			'\\( \\mathrm{GL}_2(\\mathbb{F}_7) \\): Group of invertible matrices with entries in \\(\\mathbb{F}_7\\).';
+		const output = preprocessLaTeX(input);
+		expect(output).toBe(
+			'$ \\mathrm{GL}_2(\\mathbb{F}_7) $: Group of invertible matrices with entries in $\\mathbb{F}_7$.'
+		);
+	});
+
+	test("don't inline \\\\( ... \\) to $...$", () => {
+		const input =
+			'Chapter 20 of The TeXbook, in source "Definitions\\\\(also called Macros)", containst the formula \\((x_1,\\ldots,x_n)\\).';
+		const output = preprocessLaTeX(input);
+		expect(output).toBe(
+			'Chapter 20 of The TeXbook, in source "Definitions\\\\(also called Macros)", containst the formula $(x_1,\\ldots,x_n)$.'
+		);
+	});
+
+	test('preserves display math \\[ ... \\] and protects adjacent text', () => {
+		const input = `Some kernel of \\(\\mathrm{SL}_2(\\mathbb{F}_7)\\):
+  \\[
+  \\left\\{ \\begin{pmatrix} 1 & 0 \\\\ 0 & 1 \\end{pmatrix}, \\begin{pmatrix} -1 & 0 \\\\ 0 & -1 \\end{pmatrix} \\right\\} = \\{\\pm I\\}
+  \\]`;
+		const output = preprocessLaTeX(input);
+
+		expect(output).toBe(`Some kernel of $\\mathrm{SL}_2(\\mathbb{F}_7)$:
+  $$
+  \\left\\{ \\begin{pmatrix} 1 & 0 \\\\ 0 & 1 \\end{pmatrix}, \\begin{pmatrix} -1 & 0 \\\\ 0 & -1 \\end{pmatrix} \\right\\} = \\{\\pm I\\}
+  $$`);
+	});
+
+	test('handles standalone display math equation', () => {
+		const input = `Algebra:
+\\[
+x = \\frac{-b \\pm \\sqrt{\\,b^{2}-4ac\\,}}{2a}
+\\]`;
+		const output = preprocessLaTeX(input);
+
+		expect(output).toBe(`Algebra:
+$$
+x = \\frac{-b \\pm \\sqrt{\\,b^{2}-4ac\\,}}{2a}
+$$`);
+	});
+
+	test('does not interpret currency values as LaTeX', () => {
+		const input = 'I have $10, $3.99 and $x + y$ and $100x$. The amount is $2,000.';
+		const output = preprocessLaTeX(input);
+
+		expect(output).toBe('I have \\$10, \\$3.99 and $x + y$ and $100x$. The amount is \\$2,000.');
+	});
+
+	test('ignores dollar signs followed by digits (money), but keeps valid math $x + y$', () => {
+		const input = 'I have $10, $3.99 and $x + y$ and $100x$. The amount is $2,000.';
+		const output = preprocessLaTeX(input);
+
+		expect(output).toBe('I have \\$10, \\$3.99 and $x + y$ and $100x$. The amount is \\$2,000.');
+	});
+
+	test('handles real-world word problems with amounts and no math delimiters', () => {
+		const input =
+			'Emma buys 2 cupcakes for $3 each and 1 cookie for $1.50. How much money does she spend in total?';
+		const output = preprocessLaTeX(input);
+
+		expect(output).toBe(
+			'Emma buys 2 cupcakes for \\$3 each and 1 cookie for \\$1.50. How much money does she spend in total?'
+		);
+	});
+
+	test('handles decimal amounts in word problem correctly', () => {
+		const input =
+			'Maria has $20. She buys a notebook for $4.75 and a pack of pencils for $3.25. How much change does she receive?';
+		const output = preprocessLaTeX(input);
+
+		expect(output).toBe(
+			'Maria has \\$20. She buys a notebook for \\$4.75 and a pack of pencils for \\$3.25. How much change does she receive?'
+		);
+	});
+
+	test('preserves display math with surrounding non-ASCII text', () => {
+		const input = `1 kg の質量は
+  \\[
+  E = (1\\ \\text{kg}) \\times (3.0 \\times 10^8\\ \\text{m/s})^2 \\approx 9.0 \\times 10^{16}\\ \\text{J}
+  \\]
+  というエネルギーに相当します。これは約 21 百万トンの TNT が爆発したときのエネルギーに匹敵します。`;
+		const output = preprocessLaTeX(input);
+
+		expect(output).toBe(
+			`1 kg の質量は
+  $$
+  E = (1\\ \\text{kg}) \\times (3.0 \\times 10^8\\ \\text{m/s})^2 \\approx 9.0 \\times 10^{16}\\ \\text{J}
+  $$
+  というエネルギーに相当します。これは約 21 百万トンの TNT が爆発したときのエネルギーに匹敵します。`
+		);
+	});
+
+	test('LaTeX-spacer preceded by backslash', () => {
+		const input = `\\[
+\\boxed{
+\\begin{aligned}
+N_{\\text{att}}^{\\text{(MHA)}} &=
+h \\bigl[\\, d_{\\text{model}}\\;d_{k} + d_{\\text{model}}\\;d_{v}\\, \\bigr]   && (\\text{Q,K,V の重み})\\\\
+&\\quad+ h(d_{k}+d_{k}+d_{v})                                          && (\\text{バイアス Q,K,V）}\\\\[4pt]
+&\\quad+ (h d_{v})\\, d_{\\text{model}}                                 && (\\text{出力射影 }W^{O})\\\\
+&\\quad+ d_{\\text{model}}                                            && (\\text{バイアス }b^{O})
+\\end{aligned}}
+\\]`;
+		const output = preprocessLaTeX(input);
+		expect(output).toBe(
+			`$$
+\\boxed{
+\\begin{aligned}
+N_{\\text{att}}^{\\text{(MHA)}} &=
+h \\bigl[\\, d_{\\text{model}}\\;d_{k} + d_{\\text{model}}\\;d_{v}\\, \\bigr]   && (\\text{Q,K,V の重み})\\\\
+&\\quad+ h(d_{k}+d_{k}+d_{v})                                          && (\\text{バイアス Q,K,V）}\\\\[4pt]
+&\\quad+ (h d_{v})\\, d_{\\text{model}}                                 && (\\text{出力射影 }W^{O})\\\\
+&\\quad+ d_{\\text{model}}                                            && (\\text{バイアス }b^{O})
+\\end{aligned}}
+$$`
+		);
+	});
+
+	test('converts \\[ ... \\] even when preceded by text without space', () => {
+		const input = 'Some line ...\nAlgebra: \\[x = \\frac{-b \\pm \\sqrt{\\,b^{2}-4ac\\,}}{2a}\\]';
+		const output = preprocessLaTeX(input);
+
+		expect(output).toBe(
+			'Some line ...\nAlgebra: \n$$x = \\frac{-b \\pm \\sqrt{\\,b^{2}-4ac\\,}}{2a}$$\n'
+		);
+	});
+
+	test('converts \\[ ... \\] in table-cells', () => {
+		const input = `| ID | Expression |\n| #1 | \\[
+			x = \\frac{-b \\pm \\sqrt{\\,b^{2}-4ac\\,}}{2a}
+\\] |`;
+		const output = preprocessLaTeX(input);
+
+		expect(output).toBe(
+			'| ID | Expression |\n| #1 | $x = \\frac{-b \\pm \\sqrt{\\,b^{2}-4ac\\,}}{2a}$ |'
+		);
+	});
+
+	test('escapes isolated $ before digits ($5 → \\$5), but not valid math', () => {
+		const input = 'This costs $5 and this is math $x^2$. $100 is money.';
+		const output = preprocessLaTeX(input);
+
+		expect(output).toBe('This costs \\$5 and this is math $x^2$. \\$100 is money.');
+		// Note: Since $x^2$ is detected as valid LaTeX, it's preserved.
+		// $5 becomes \$5 only *after* real math is masked — but here it's correct because the masking logic avoids treating $5 as math.
+	});
+
+	test('display with LaTeX-line-breaks', () => {
+		const input = String.raw`- Algebraic topology, Homotopy Groups of $\mathbb{S}^3$:
+$$\pi_n(\mathbb{S}^3) = \begin{cases}
+\mathbb{Z} & n = 3 \\
+0 & n > 3, n \neq 4 \\
+\mathbb{Z}_2 & n = 4 \\
+\end{cases}$$`;
+		const output = preprocessLaTeX(input);
+		// If the formula contains '\\' the $$-delimiters should be in their own line.
+		expect(output).toBe(`- Algebraic topology, Homotopy Groups of $\\mathbb{S}^3$:
+$$\n\\pi_n(\\mathbb{S}^3) = \\begin{cases}
+\\mathbb{Z} & n = 3 \\\\
+0 & n > 3, n \\neq 4 \\\\
+\\mathbb{Z}_2 & n = 4 \\\\
+\\end{cases}\n$$`);
+	});
+
+	test('handles mhchem notation safely if present', () => {
+		const input = 'Chemical reaction: \\( \\ce{H2O} \\) and $\\ce{CO2}$';
+		const output = preprocessLaTeX(input);
+
+		expect(output).toBe('Chemical reaction: $ \\ce{H2O} $ and $\\ce{CO2}$');
+	});
+
+	test('preserves code blocks', () => {
+		const input = 'Inline code: `sum $total` and block:\n```\ndollar $amount\n```\nEnd.';
+		const output = preprocessLaTeX(input);
+
+		expect(output).toBe(input); // Code blocks prevent misinterpretation
+	});
+
+	test('escape backslash in mchem ce', () => {
+		const input = 'mchem ce:\n$\\ce{2H2(g) + O2(g) -> 2H2O(l)}$';
+		const output = preprocessLaTeX(input);
+
+		// mhchem-escape would insert a backslash here.
+		expect(output).toBe('mchem ce:\n$\\ce{2H2(g) + O2(g) -> 2H2O(l)}$');
+	});
+
+	test('escape backslash in mchem pu', () => {
+		const input = 'mchem pu:\n$\\pu{-572 kJ mol^{-1}}$';
+		const output = preprocessLaTeX(input);
+
+		// mhchem-escape would insert a backslash here.
+		expect(output).toBe('mchem pu:\n$\\pu{-572 kJ mol^{-1}}$');
+	});
+
+	test('LaTeX in blockquotes with display math', () => {
+		const input =
+			'> **Definition (limit):**  \n>  \\[\n>  \\lim_{x\\to a} f(x) = L\n>  \\]\n>  means that as \\(x\\) gets close to \\(a\\).';
+		const output = preprocessLaTeX(input);
+
+		// Blockquote markers should be preserved, LaTeX should be converted
+		expect(output).toContain('> **Definition (limit):**');
+		expect(output).toContain('$$');
+		expect(output).toContain('$x$');
+		expect(output).not.toContain('\\[');
+		expect(output).not.toContain('\\]');
+		expect(output).not.toContain('\\(');
+		expect(output).not.toContain('\\)');
+	});
+
+	test('LaTeX in blockquotes with inline math', () => {
+		const input =
+			"> The derivative \\(f'(x)\\) at point \\(x=a\\) measures slope.\n> Formula: \\(f'(a)=\\lim_{h\\to 0}\\frac{f(a+h)-f(a)}{h}\\)";
+		const output = preprocessLaTeX(input);
+
+		// Blockquote markers should be preserved, inline LaTeX converted to $...$
+		expect(output).toContain("> The derivative $f'(x)$ at point $x=a$ measures slope.");
+		expect(output).toContain("> Formula: $f'(a)=\\lim_{h\\to 0}\\frac{f(a+h)-f(a)}{h}$");
+	});
+
+	test('Mixed content with blockquotes and regular text', () => {
+		const input =
+			'Regular text with \\(x^2\\).\n\n> Quote with \\(y^2\\).\n\nMore text with \\(z^2\\).';
+		const output = preprocessLaTeX(input);
+
+		// All LaTeX should be converted, blockquote markers preserved
+		expect(output).toBe('Regular text with $x^2$.\n\n> Quote with $y^2$.\n\nMore text with $z^2$.');
+	});
+});
diff --git a/tools/server/webui/src/lib/utils/latex-protection.ts b/tools/server/webui/src/lib/utils/latex-protection.ts
new file mode 100644
index 00000000000..7f5cf2cddfa
--- /dev/null
+++ b/tools/server/webui/src/lib/utils/latex-protection.ts
@@ -0,0 +1,267 @@
+import {
+	CODE_BLOCK_REGEXP,
+	LATEX_MATH_AND_CODE_PATTERN,
+	LATEX_LINEBREAK_REGEXP,
+	MHCHEM_PATTERN_MAP
+} from '$lib/constants/latex-protection';
+
+/**
+ * Replaces inline LaTeX expressions enclosed in `$...$` with placeholders, avoiding dollar signs
+ * that appear to be part of monetary values or identifiers.
+ *
+ * This function processes the input line by line and skips `$` sequences that are likely
+ * part of money amounts (e.g., `$5`, `$100.99`) or code-like tokens (e.g., `var$`, `$var`).
+ * Valid LaTeX inline math is replaced with a placeholder like `<<LATEX_0>>`, and the
+ * actual LaTeX content is stored in the provided `latexExpressions` array.
+ *
+ * @param content - The input text potentially containing LaTeX expressions.
+ * @param latexExpressions - An array used to collect extracted LaTeX expressions.
+ * @returns The processed string with LaTeX replaced by placeholders.
+ */
+export function maskInlineLaTeX(content: string, latexExpressions: string[]): string {
+	if (!content.includes('$')) {
+		return content;
+	}
+	return content
+		.split('\n')
+		.map((line) => {
+			if (line.indexOf('$') == -1) {
+				return line;
+			}
+
+			let processedLine = '';
+			let currentPosition = 0;
+
+			while (currentPosition < line.length) {
+				const openDollarIndex = line.indexOf('$', currentPosition);
+
+				if (openDollarIndex == -1) {
+					processedLine += line.slice(currentPosition);
+					break;
+				}
+
+				// Is there a next $-sign?
+				const closeDollarIndex = line.indexOf('$', openDollarIndex + 1);
+
+				if (closeDollarIndex == -1) {
+					processedLine += line.slice(currentPosition);
+					break;
+				}
+
+				const charBeforeOpen = openDollarIndex > 0 ? line[openDollarIndex - 1] : '';
+				const charAfterOpen = line[openDollarIndex + 1];
+				const charBeforeClose =
+					openDollarIndex + 1 < closeDollarIndex ? line[closeDollarIndex - 1] : '';
+				const charAfterClose = closeDollarIndex + 1 < line.length ? line[closeDollarIndex + 1] : '';
+
+				let shouldSkipAsNonLatex = false;
+
+				if (closeDollarIndex == currentPosition + 1) {
+					// No content
+					shouldSkipAsNonLatex = true;
+				}
+
+				if (/[A-Za-z0-9_$-]/.test(charBeforeOpen)) {
+					// Character, digit, $, _ or - before first '$', no TeX.
+					shouldSkipAsNonLatex = true;
+				}
+
+				if (
+					/[0-9]/.test(charAfterOpen) &&
+					(/[A-Za-z0-9_$-]/.test(charAfterClose) || ' ' == charBeforeClose)
+				) {
+					// First $ seems to belong to an amount.
+					shouldSkipAsNonLatex = true;
+				}
+
+				if (shouldSkipAsNonLatex) {
+					processedLine += line.slice(currentPosition, openDollarIndex + 1);
+					currentPosition = openDollarIndex + 1;
+
+					continue;
+				}
+
+				// Treat as LaTeX
+				processedLine += line.slice(currentPosition, openDollarIndex);
+				const latexContent = line.slice(openDollarIndex, closeDollarIndex + 1);
+				latexExpressions.push(latexContent);
+				processedLine += `<<LATEX_${latexExpressions.length - 1}>>`;
+				currentPosition = closeDollarIndex + 1;
+			}
+
+			return processedLine;
+		})
+		.join('\n');
+}
+
+function escapeBrackets(text: string): string {
+	return text.replace(
+		LATEX_MATH_AND_CODE_PATTERN,
+		(
+			match: string,
+			codeBlock: string | undefined,
+			squareBracket: string | undefined,
+			roundBracket: string | undefined
+		): string => {
+			if (codeBlock != null) {
+				return codeBlock;
+			} else if (squareBracket != null) {
+				return `$$${squareBracket}$$`;
+			} else if (roundBracket != null) {
+				return `$${roundBracket}$`;
+			}
+
+			return match;
+		}
+	);
+}
+
+// Escape $\\ce{...} → $\\ce{...} but with proper handling
+function escapeMhchem(text: string): string {
+	return MHCHEM_PATTERN_MAP.reduce((result, [pattern, replacement]) => {
+		return result.replace(pattern, replacement);
+	}, text);
+}
+
+const doEscapeMhchem = false;
+
+/**
+ * Preprocesses markdown content to safely handle LaTeX math expressions while protecting
+ * against false positives (e.g., dollar amounts like $5.99) and ensuring proper rendering.
+ *
+ * This function:
+ * - Protects code blocks (```) and inline code (`...`)
+ * - Safeguards block and inline LaTeX: \(...\), \[...\], $$...$$, and selective $...$
+ * - Escapes standalone dollar signs before numbers (e.g., $5 → \$5) to prevent misinterpretation
+ * - Restores protected LaTeX and code blocks after processing
+ * - Converts \(...\) → $...$ and \[...\] → $$...$$ for compatibility with math renderers
+ * - Applies additional escaping for brackets and mhchem syntax if needed
+ *
+ * @param content - The raw text (e.g., markdown) that may contain LaTeX or code blocks.
+ * @returns The preprocessed string with properly escaped and normalized LaTeX.
+ *
+ * @example
+ * preprocessLaTeX("Price: $10. The equation is \\(x^2\\).")
+ * // → "Price: $10. The equation is $x^2$."
+ */
+export function preprocessLaTeX(content: string): string {
+	// See also:
+	// https://github.com/danny-avila/LibreChat/blob/main/client/src/utils/latex.ts
+
+	// Step 0: Temporarily remove blockquote markers (>) to process LaTeX correctly
+	// Store the structure so we can restore it later
+	const blockquoteMarkers: Map<number, string> = new Map();
+	const lines = content.split('\n');
+	const processedLines = lines.map((line, index) => {
+		const match = line.match(/^(>\s*)/);
+		if (match) {
+			blockquoteMarkers.set(index, match[1]);
+			return line.slice(match[1].length);
+		}
+		return line;
+	});
+	content = processedLines.join('\n');
+
+	// Step 1: Protect code blocks
+	const codeBlocks: string[] = [];
+
+	content = content.replace(CODE_BLOCK_REGEXP, (match) => {
+		codeBlocks.push(match);
+
+		return `<<CODE_BLOCK_${codeBlocks.length - 1}>>`;
+	});
+
+	// Step 2: Protect existing LaTeX expressions
+	const latexExpressions: string[] = [];
+
+	// Match \S...\[...\] and protect them and insert a line-break.
+	content = content.replace(/([\S].*?)\\\[([\s\S]*?)\\\](.*)/g, (match, group1, group2, group3) => {
+		// Check if there are characters following the formula (display-formula in a table-cell?)
+		if (group1.endsWith('\\')) {
+			return match; // Backslash before \[, do nothing.
+		}
+		const hasSuffix = /\S/.test(group3);
+		let optBreak;
+
+		if (hasSuffix) {
+			latexExpressions.push(`\\(${group2.trim()}\\)`); // Convert into inline.
+			optBreak = '';
+		} else {
+			latexExpressions.push(`\\[${group2}\\]`);
+			optBreak = '\n';
+		}
+
+		return `${group1}${optBreak}<<LATEX_${latexExpressions.length - 1}>>${optBreak}${group3}`;
+	});
+
+	// Match \(...\), \[...\], $$...$$ and protect them
+	content = content.replace(
+		/(\$\$[\s\S]*?\$\$|(?<!\\)\\\[[\s\S]*?\\\]|(?<!\\)\\\(.*?\\\))/g,
+		(match) => {
+			latexExpressions.push(match);
+
+			return `<<LATEX_${latexExpressions.length - 1}>>`;
+		}
+	);
+
+	// Protect inline $...$ but NOT if it looks like money (e.g., $10, $3.99)
+	content = maskInlineLaTeX(content, latexExpressions);
+
+	// Step 3: Escape standalone $ before digits (currency like $5 → \$5)
+	// (Now that inline math is protected, this will only escape dollars not already protected)
+	content = content.replace(/\$(?=\d)/g, '\\$');
+
+	// Step 4: Restore protected LaTeX expressions (they are valid)
+	content = content.replace(/<<LATEX_(\d+)>>/g, (_, index) => {
+		let expr = latexExpressions[parseInt(index)];
+		const match = expr.match(LATEX_LINEBREAK_REGEXP);
+		if (match) {
+			// Katex: The $$-delimiters should be in their own line
+			// if there are \\-line-breaks.
+			const formula = match[1];
+			const prefix = formula.startsWith('\n') ? '' : '\n';
+			const suffix = formula.endsWith('\n') ? '' : '\n';
+			expr = '$$' + prefix + formula + suffix + '$$';
+		}
+		return expr;
+	});
+
+	// Step 5: Restore code blocks
+	content = content.replace(/<<CODE_BLOCK_(\d+)>>/g, (_, index) => {
+		return codeBlocks[parseInt(index)];
+	});
+
+	// Step 6: Apply additional escaping functions (brackets and mhchem)
+	content = escapeBrackets(content);
+
+	if (doEscapeMhchem && (content.includes('\\ce{') || content.includes('\\pu{'))) {
+		content = escapeMhchem(content);
+	}
+
+	// Final pass: Convert \(...\) → $...$, \[...\] → $$...$$
+	content = content
+		// Using the look‑behind pattern `(?<!\\)` we skip matches
+		// that are preceded by a backslash, e.g.
+		// `Definitions\\(also called macros)` (title of chapter 20 in The TeXbook).
+		.replace(/(?<!\\)\\\((.+?)\\\)/g, '$$$1$') // inline
+		.replace(
+			// Using the look‑behind pattern `(?<!\\)` we skip matches
+			// that are preceded by a backslash, e.g. `\\[4pt]`.
+			/(?<!\\)\\\[([\s\S]*?)\\\]/g, // display, see also PR #16599
+			(_, prefix: string, content: string) => {
+				return `${prefix}$$${content}$$`;
+			}
+		);
+
+	// Step 7: Restore blockquote markers
+	if (blockquoteMarkers.size > 0) {
+		const finalLines = content.split('\n');
+		const restoredLines = finalLines.map((line, index) => {
+			const marker = blockquoteMarkers.get(index);
+			return marker ? marker + line : line;
+		});
+		content = restoredLines.join('\n');
+	}
+
+	return content;
+}
diff --git a/tools/server/webui/src/stories/fixtures/math-formulas.ts b/tools/server/webui/src/stories/fixtures/math-formulas.ts
index a4e9ab0ed88..1355256b20c 100644
--- a/tools/server/webui/src/stories/fixtures/math-formulas.ts
+++ b/tools/server/webui/src/stories/fixtures/math-formulas.ts
@@ -1,3 +1,4 @@
+/* eslint-disable no-irregular-whitespace */
 // Math Formulas Content
 export const MATH_FORMULAS_MD = String.raw`
 # Mathematical Formulas and Expressions
@@ -150,6 +151,70 @@ $$\lim_{x \to 0} \frac{\sin x}{x} = 1$$
 
 $$\lim_{n \to \infty} \left(1 + \frac{x}{n}\right)^n = e^x$$
 
+## Further Bracket Styles and Amounts
+
+-  \( \mathrm{GL}_2(\mathbb{F}_7) \): Group of invertible matrices with entries in \(\mathbb{F}_7\).
+- Some kernel of \(\mathrm{SL}_2(\mathbb{F}_7)\):
+  \[
+  \left\{ \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}, \begin{pmatrix} -1 & 0 \\ 0 & -1 \end{pmatrix} \right\} = \{\pm I\}
+  \]
+- Algebra:
+\[
+x = \frac{-b \pm \sqrt{\,b^{2}-4ac\,}}{2a}
+\]
+- $100 and $12.99 are amounts, not LaTeX.
+- I have $10, $3.99 and $x + y$ and $100x$. The amount is $2,000.
+- Emma buys 2 cupcakes for $3 each and 1 cookie for $1.50. How much money does she spend in total?
+- Maria has $20. She buys a notebook for $4.75 and a pack of pencils for $3.25. How much change does she receive?
+- 1 kg の質量は
+  \[
+  E = (1\ \text{kg}) \times (3.0 \times 10^8\ \text{m/s})^2 \approx 9.0 \times 10^{16}\ \text{J}
+  \]
+  というエネルギーに相当します。これは約 21 百万トンの TNT が爆発したときのエネルギーに匹敵します。
+- Algebra: \[
+x = \frac{-b \pm \sqrt{\,b^{2}-4ac\,}}{2a}
+\]
+- Algebraic topology, Homotopy Groups of $\mathbb{S}^3$:
+$$\pi_n(\mathbb{S}^3) = \begin{cases}
+\mathbb{Z} & n = 3 \\
+0 & n > 3, n \neq 4 \\
+\mathbb{Z}_2 & n = 4 \\
+\end{cases}$$
+- Spacer preceded by backslash:
+\[
+\boxed{
+\begin{aligned}
+N_{\text{att}}^{\text{(MHA)}} &=
+h \bigl[\, d_{\text{model}}\;d_{k} + d_{\text{model}}\;d_{v}\, \bigr]   && (\text{Q,K,V の重み})\\
+&\quad+ h(d_{k}+d_{k}+d_{v})                                          && (\text{バイアス Q,K,V）}\\[4pt]
+&\quad+ (h d_{v})\, d_{\text{model}}                                 && (\text{出力射影 }W^{O})\\
+&\quad+ d_{\text{model}}                                            && (\text{バイアス }b^{O})
+\end{aligned}}
+\]
+
+## Formulas in a Table
+
+| Area | Expression | Comment |
+|------|------------|---------|
+| **Algebra** | \[
+x = \frac{-b \pm \sqrt{\,b^{2}-4ac\,}}{2a}
+\] | Quadratic formula |
+| | \[
+(a+b)^{n} = \sum_{k=0}^{n}\binom{n}{k}\,a^{\,n-k}\,b^{\,k}
+\] | Binomial theorem |
+| | \(\displaystyle \prod_{k=1}^{n}k = n! \) | Factorial definition |
+| **Geometry** | \( \mathbf{a}\cdot \mathbf{b} = \|\mathbf{a}\|\,\|\mathbf{b}\|\,\cos\theta \) | Dot product & angle |
+
+## No math (but chemical)
+
+Balanced chemical reaction with states:
+
+\[
+\ce{2H2(g) + O2(g) -> 2H2O(l)}
+\]
+
+The standard enthalpy change for the reaction is: $\Delta H^\circ = \pu{-572 kJ mol^{-1}}$.
+
 ---
 
 *This document showcases various mathematical notation and formulas that can be rendered in markdown using LaTeX syntax.*
diff --git a/tools/server/webui/src/styles/katex-custom.scss b/tools/server/webui/src/styles/katex-custom.scss
new file mode 100644
index 00000000000..9c8b96ed52f
--- /dev/null
+++ b/tools/server/webui/src/styles/katex-custom.scss
@@ -0,0 +1,13 @@
+// Override KaTeX SCSS variables to disable ttf and woff fonts
+// Only use woff2 format which is embedded in the bundle
+$use-woff2: true;
+$use-woff: false;
+$use-ttf: false;
+
+// Use Vite alias for font folder
+$font-folder: 'katex-fonts';
+
+// Import KaTeX SCSS with overridden variables
+// Note: @import is deprecated but required because KaTeX uses @import internally
+// The deprecation warnings are from KaTeX's code and cannot be avoided
+@import 'katex/src/styles/katex.scss';
diff --git a/tools/server/webui/svelte.config.js b/tools/server/webui/svelte.config.js
index f25494236bd..947499363b8 100644
--- a/tools/server/webui/svelte.config.js
+++ b/tools/server/webui/svelte.config.js
@@ -22,6 +22,9 @@ const config = {
 		}),
 		output: {
 			bundleStrategy: 'inline'
+		},
+		alias: {
+			$styles: 'src/styles'
 		}
 	},
 
diff --git a/tools/server/webui/vite.config.ts b/tools/server/webui/vite.config.ts
index b077e232ab0..11ff665d8b2 100644
--- a/tools/server/webui/vite.config.ts
+++ b/tools/server/webui/vite.config.ts
@@ -18,6 +18,15 @@ const GUIDE_FOR_FRONTEND = `
 
 const MAX_BUNDLE_SIZE = 2 * 1024 * 1024;
 
+/**
+ * the maximum size of an embedded asset in bytes,
+ * e.g. maximum size of embedded font (see node_modules/katex/dist/fonts/*.woff2)
+ */
+const MAX_ASSET_SIZE = 32000;
+
+/** public/index.html.gz minified flag */
+const ENABLE_JS_MINIFICATION = true;
+
 function llamaCppBuildPlugin() {
 	return {
 		name: 'llamacpp:build',
@@ -75,12 +84,28 @@ function llamaCppBuildPlugin() {
 }
 
 export default defineConfig({
+	resolve: {
+		alias: {
+			'katex-fonts': resolve('node_modules/katex/dist/fonts')
+		}
+	},
 	build: {
-		chunkSizeWarningLimit: 3072
+		assetsInlineLimit: MAX_ASSET_SIZE,
+		chunkSizeWarningLimit: 3072,
+		minify: ENABLE_JS_MINIFICATION
+	},
+	css: {
+		preprocessorOptions: {
+			scss: {
+				additionalData: `
+					$use-woff2: true;
+					$use-woff: false;
+					$use-ttf: false;
+				`
+			}
+		}
 	},
-
 	plugins: [tailwindcss(), sveltekit(), devtoolsJson(), llamaCppBuildPlugin()],
-
 	test: {
 		projects: [
 			{

From 7e994168b1ccc12337ba8de939c4fd466107c1fb Mon Sep 17 00:00:00 2001
From: shani-f <s0556787439@gmail.com>
Date: Mon, 3 Nov 2025 03:35:33 +0200
Subject: [PATCH 065/185] =?UTF-8?q?SYCL:=20optimized=20repeat=5Fback=20ker?=
 =?UTF-8?q?nel=20(3=C3=97=20fewer=20asm=20instructions,=202=C3=97=20faster?=
 =?UTF-8?q?)Feature/sycl=20repeat=20back=20opt=20(#16869)?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

* SYCL repeat_back v1 — add core op + switch case

* Implement repeat_back SYCL operation and minor fixes

* SYCL: optimize repeat_back kernel

* Remove Hebrew comment from repeat_back.cpp

* Remove comments for code clarity

Removed comments to clean up the code.

* Fix formatting in ggml-sycl.cpp

* Formatted lambda according to legacy style. No logic changes

* Remove blank line in repeat_back.cpp

Remove unnecessary blank line before assigning acc to dst_dd.
---
 ggml/src/ggml-sycl/repeat_back.cpp | 70 +++++++++++++++++++-----------
 1 file changed, 45 insertions(+), 25 deletions(-)

diff --git a/ggml/src/ggml-sycl/repeat_back.cpp b/ggml/src/ggml-sycl/repeat_back.cpp
index abcd4cee72a..845b48468c1 100644
--- a/ggml/src/ggml-sycl/repeat_back.cpp
+++ b/ggml/src/ggml-sycl/repeat_back.cpp
@@ -2,26 +2,43 @@
 
 #include "common.hpp"
 
-void ggml_sycl_op_repeat_back(ggml_backend_sycl_context & ctx, ggml_tensor * dst) {
+#define GGML_ASSERT_TENSOR_FITS_INT(t) \
+    GGML_ASSERT((t)->ne[0] < INT_MAX && (t)->ne[1] < INT_MAX && (t)->ne[2] < INT_MAX && (t)->ne[3] < INT_MAX)
 
+void ggml_sycl_op_repeat_back(ggml_backend_sycl_context & ctx, ggml_tensor * dst) {
     GGML_ASSERT(dst->src[0]->type == GGML_TYPE_F32);
     GGML_ASSERT(dst->type == GGML_TYPE_F32);
 
     const float * src0_dd = (const float *) dst->src[0]->data;
     float *       dst_dd  = (float *) dst->data;
 
-    const int64_t ne0 = dst->ne[0], ne1 = dst->ne[1], ne2 = dst->ne[2], ne3 = dst->ne[3];
-    const int64_t ne00 = dst->src[0]->ne[0], ne01 = dst->src[0]->ne[1], ne02 = dst->src[0]->ne[2],
-                  ne03 = dst->src[0]->ne[3];
+    GGML_ASSERT_TENSOR_FITS_INT(dst);
+    GGML_ASSERT_TENSOR_FITS_INT(dst->src[0]);
+
+    const int ne0 = dst->ne[0], ne1 = dst->ne[1], ne2 = dst->ne[2], ne3 = dst->ne[3];
+    const int ne00 = dst->src[0]->ne[0], ne01 = dst->src[0]->ne[1], ne02 = dst->src[0]->ne[2],
+              ne03 = dst->src[0]->ne[3];
+
+    const int nr0 = ne00 / ne0;
+    const int nr1 = ne01 / ne1;
+    const int nr2 = ne02 / ne2;
+    const int nr3 = ne03 / ne3;
 
-    const int nr0 = (int) (ne00 / ne0);
-    const int nr1 = (int) (ne01 / ne1);
-    const int nr2 = (int) (ne02 / ne2);
-    const int nr3 = (int) (ne03 / ne3);
+    const int nb0 = dst->src[0]->nb[0];
+    const int nb1 = dst->src[0]->nb[1];
+    const int nb2 = dst->src[0]->nb[2];
+    const int nb3 = dst->src[0]->nb[3];
 
-    const size_t total      = ne0 * ne1 * ne2 * ne3;
-    const int    BLOCK_SIZE = 256;
-    const int    num_blocks = (total + BLOCK_SIZE - 1) / BLOCK_SIZE;
+    const char * base = (const char *) src0_dd;
+
+    const size_t  total      = (size_t) ne0 * ne1 * ne2 * ne3;
+    constexpr int BLOCK_SIZE = 256;
+    const int     num_blocks = (total + BLOCK_SIZE - 1) / BLOCK_SIZE;
+
+    const float inv_ne0      = 1.0f / ne0;
+    const float inv_ne_01    = 1.0f / (ne0 * ne1);
+    const float inv_ne_012   = 1.0f / (ne0 * ne1 * ne2);
+    const int   repeat_count = nr0 * nr1 * nr2 * nr3;
 
     queue_ptr stream = ctx.stream();
 
@@ -33,24 +50,27 @@ void ggml_sycl_op_repeat_back(ggml_backend_sycl_context & ctx, ggml_tensor * dst
                 return;
             }
 
-            const int i0 = i % ne0;
-            const int i1 = (i / ne0) % ne1;
-            const int i2 = (i / (ne0 * ne1)) % ne2;
-            const int i3 = i / (ne0 * ne1 * ne2);
+            const int i3 = (int) (i * inv_ne_012);
+            const int i2 = (int) (i * inv_ne_01) - i3 * ne2;
+            const int i1 = (int) (i * inv_ne0) - (int) (i * inv_ne_01) * ne1;
+            const int i0 = i - (int) (i * inv_ne0) * ne0;
 
+            int   j0 = 0, j1 = 0, j2 = 0, j3 = 0;
             float acc = 0.0f;
 
-            for (int j3 = 0; j3 < nr3; ++j3) {
-                for (int j2 = 0; j2 < nr2; ++j2) {
-                    for (int j1 = 0; j1 < nr1; ++j1) {
-                        for (int j0 = 0; j0 < nr0; ++j0) {
-                            acc += src0_dd[(i0 + j0 * ne0) + (i1 + j1 * ne1) * ne00 + (i2 + j2 * ne2) * ne00 * ne01 +
-                                           (i3 + j3 * ne3) * ne00 * ne01 * ne02];
-                        }
-                    }
-                }
-            }
+            for (int j = 0; j < repeat_count; ++j) {
+                const float * ptr = (const float *) (base + (i0 + j0 * ne0) * nb0 + (i1 + j1 * ne1) * nb1 +
+                    (i2 + j2 * ne2) * nb2 + (i3 + j3 * ne3) * nb3);
+                acc += *ptr;
 
+                int carry = (++j0 >= nr0);
+                j0 -= carry * nr0;
+                carry = (carry && (++j1 >= nr1));
+                j1 -= carry * nr1;
+                carry = (carry && (++j2 >= nr2));
+                j2 -= carry * nr2;
+                j3 += carry;
+            }
             dst_dd[i] = acc;
         });
 }

From ee3a5a10adf9e83722d1914dddc56a0623ececaf Mon Sep 17 00:00:00 2001
From: Olivier Chafik <olivier.chafik@gmail.com>
Date: Mon, 3 Nov 2025 05:33:56 +0000
Subject: [PATCH 066/185] sync: minja (glm 4.6 & minmax m2 templates) (#16949)

* sync: minja

* Sync https://github.com/ochafik/minja/pull/7 (MinMax M2)
---
 vendor/minja/chat-template.hpp | 11 +++++++++--
 vendor/minja/minja.hpp         | 12 +++++-------
 2 files changed, 14 insertions(+), 9 deletions(-)

diff --git a/vendor/minja/chat-template.hpp b/vendor/minja/chat-template.hpp
index d5295b335b4..f080aa92f10 100644
--- a/vendor/minja/chat-template.hpp
+++ b/vendor/minja/chat-template.hpp
@@ -192,18 +192,25 @@ class chat_template {
             };
         };
         const json dummy_args_obj {{"argument_needle", "print('Hello, World!')"}};
+        const auto contains_arg_needle = [&](const std::string & out_str) {
+            return contains(out_str, "<parameter=argument_needle>")
+                || contains(out_str, "\"argument_needle\":")
+                || contains(out_str, "'argument_needle':")
+                || contains(out_str, ">argument_needle<")
+                || contains(out_str, "<parameter name=\"argument_needle\">");
+        };
 
         // Note: the arguments are rendered in both cases, but may be double-escaped, which we don't want.
         out = try_raw_render(json::array({
             dummy_user_msg,
             make_tool_calls_msg(json::array({make_tool_call("ipython", dummy_args_obj.dump())})),
         }), {}, false);
-        auto tool_call_renders_str_arguments = contains(out, "<parameter=argument_needle>") || contains(out, "\"argument_needle\":") || contains(out, "'argument_needle':");
+        auto tool_call_renders_str_arguments = contains_arg_needle(out);
         out = try_raw_render(json::array({
             dummy_user_msg,
             make_tool_calls_msg(json::array({make_tool_call("ipython", dummy_args_obj)})),
         }), {}, false);
-        auto tool_call_renders_obj_arguments = contains(out, "<parameter=argument_needle>") || contains(out, "\"argument_needle\":") || contains(out, "'argument_needle':");
+        auto tool_call_renders_obj_arguments = contains_arg_needle(out);
 
         caps_.supports_tool_calls = tool_call_renders_str_arguments || tool_call_renders_obj_arguments;
         caps_.requires_object_arguments = !tool_call_renders_str_arguments && tool_call_renders_obj_arguments;
diff --git a/vendor/minja/minja.hpp b/vendor/minja/minja.hpp
index 57b138add6a..873ece8c180 100644
--- a/vendor/minja/minja.hpp
+++ b/vendor/minja/minja.hpp
@@ -2205,7 +2205,7 @@ class Parser {
 
       auto value = parseValue();
 
-      while (it != end && consumeSpaces() && peekSymbols({ "[", "." })) {
+      while (it != end && consumeSpaces() && peekSymbols({ "[", ".", "(" })) {
         if (!consumeToken("[").empty()) {
           std::shared_ptr<Expression> index;
           auto slice_loc = get_location();
@@ -2250,15 +2250,13 @@ class Parser {
               auto key = std::make_shared<LiteralExpr>(identifier->location, Value(identifier->get_name()));
               value = std::make_shared<SubscriptExpr>(identifier->location, std::move(value), std::move(key));
             }
+        } else if (peekSymbols({ "(" })) {
+          auto callParams = parseCallArgs();
+          value = std::make_shared<CallExpr>(get_location(), std::move(value), std::move(callParams));
         }
         consumeSpaces();
       }
 
-      if (peekSymbols({ "(" })) {
-        auto location = get_location();
-        auto callParams = parseCallArgs();
-        value = std::make_shared<CallExpr>(location, std::move(value), std::move(callParams));
-      }
       return value;
     }
 
@@ -2738,7 +2736,7 @@ inline std::shared_ptr<Context> Context::builtins() {
   globals.set("raise_exception", simple_function("raise_exception", { "message" }, [](const std::shared_ptr<Context> &, Value & args) -> Value {
     throw std::runtime_error(args.at("message").get<std::string>());
   }));
-  globals.set("tojson", simple_function("tojson", { "value", "indent" }, [](const std::shared_ptr<Context> &, Value & args) {
+  globals.set("tojson", simple_function("tojson", { "value", "indent", "ensure_ascii" }, [](const std::shared_ptr<Context> &, Value & args) {
     return Value(args.at("value").dump(args.get<int64_t>("indent", -1), /* to_json= */ true));
   }));
   globals.set("items", simple_function("items", { "object" }, [](const std::shared_ptr<Context> &, Value & args) {

From fcfce040e816c542f374ad51461b3561d73c4bc9 Mon Sep 17 00:00:00 2001
From: Jinyang He <hejinyang@loongson.cn>
Date: Mon, 3 Nov 2025 14:40:02 +0800
Subject: [PATCH 067/185] ggml : LoongArch fixes (#16958)

* Fix test-quantize-fns f16 and q4_0 failed when use LSX

* Fix LoongArch set float intrinsic when use LSX/LASX
---
 ggml/src/ggml-cpu/arch/loongarch/quants.c |  9 ++--
 ggml/src/ggml-cpu/ggml-cpu-impl.h         |  4 +-
 ggml/src/ggml-cpu/simd-mappings.h         | 50 +++++++++++------------
 3 files changed, 32 insertions(+), 31 deletions(-)

diff --git a/ggml/src/ggml-cpu/arch/loongarch/quants.c b/ggml/src/ggml-cpu/arch/loongarch/quants.c
index 22fc7607fa9..f531e916b9e 100644
--- a/ggml/src/ggml-cpu/arch/loongarch/quants.c
+++ b/ggml/src/ggml-cpu/arch/loongarch/quants.c
@@ -700,7 +700,8 @@ void ggml_vec_dot_q4_0_q8_0(int n, float * GGML_RESTRICT s, size_t bs, const voi
     for (; ib + 1 < nb; ib += 2) {
 
         // Compute combined scale for the block 0 and 1
-        const __m128 d_0_1 = (__m128)__lsx_vreplgr2vr_w( GGML_CPU_FP16_TO_FP32(x[ib].d) * GGML_CPU_FP16_TO_FP32(y[ib].d) );
+        const float ft0 = GGML_CPU_FP16_TO_FP32(x[ib].d) * GGML_CPU_FP16_TO_FP32(y[ib].d);
+        const __m128 d_0_1 = (__m128)(v4f32){ft0, ft0, ft0, ft0};
 
         const __m128i tmp_0_1 = __lsx_vld((const __m128i *)x[ib].qs, 0);
 
@@ -714,11 +715,9 @@ void ggml_vec_dot_q4_0_q8_0(int n, float * GGML_RESTRICT s, size_t bs, const voi
         bx_1 = __lsx_vsub_b(bx_1, off);
         const __m128i i32_1 = mul_sum_i8_pairs(bx_1, by_1);
 
-        //_mm_prefetch(&x[ib] + 2 * sizeof(block_q4_0), _MM_HINT_T0);
-        //_mm_prefetch(&y[ib] + 2 * sizeof(block_q8_0), _MM_HINT_T0);
-
         // Compute combined scale for the block 2 and 3
-        const __m128 d_2_3 = (__m128)__lsx_vreplgr2vr_w( GGML_CPU_FP16_TO_FP32(x[ib + 1].d) * GGML_CPU_FP16_TO_FP32(y[ib + 1].d) );
+        const float ft1 = GGML_CPU_FP16_TO_FP32(x[ib + 1].d) * GGML_CPU_FP16_TO_FP32(y[ib + 1].d);
+        const __m128 d_2_3 = (__m128)(v4f32){ft1, ft1, ft1, ft1};
 
         const __m128i tmp_2_3 = __lsx_vld((const __m128i *)x[ib + 1].qs, 0);
 
diff --git a/ggml/src/ggml-cpu/ggml-cpu-impl.h b/ggml/src/ggml-cpu/ggml-cpu-impl.h
index 713bf85e5a8..7597377cc27 100644
--- a/ggml/src/ggml-cpu/ggml-cpu-impl.h
+++ b/ggml/src/ggml-cpu/ggml-cpu-impl.h
@@ -500,13 +500,15 @@ inline static int32x4_t ggml_vec_dot(int32x4_t acc, int8x16_t a, int8x16_t b) {
 
 #endif
 
-#if defined(__loongarch_asx)
+#if defined(__loongarch_sx)
 /* float type data load instructions */
 static __m128 __lsx_vreplfr2vr_s(const float val) {
     v4f32 res = {val, val, val, val};
     return (__m128)res;
 }
+#endif
 
+#if defined(__loongarch_asx)
 static __m256 __lasx_xvreplfr2vr_s(const float val) {
     v8f32 res = {val, val, val, val, val, val, val, val};
     return (__m256)res;
diff --git a/ggml/src/ggml-cpu/simd-mappings.h b/ggml/src/ggml-cpu/simd-mappings.h
index 8daec6637b0..74c74d1a284 100644
--- a/ggml/src/ggml-cpu/simd-mappings.h
+++ b/ggml/src/ggml-cpu/simd-mappings.h
@@ -956,7 +956,7 @@ do {                                                              \
 
 #define GGML_F32Cx8          __m256
 #define GGML_F32Cx8_ZERO    (__m256)__lasx_xvldi(0)
-#define GGML_F32Cx8_SET1(x) (__m256)__lasx_xvreplgr2vr_w((x))
+#define GGML_F32Cx8_SET1(x) (__m256)__lasx_xvreplfr2vr_s((x))
 
 static inline __m256 __lasx_f32cx8_load(const ggml_fp16_t * x) {
     __m256i a;
@@ -999,34 +999,34 @@ static inline void __lasx_f32cx8_store(ggml_fp16_t * x, __m256 y) {
 
 #define GGML_F32x4         __m128
 #define GGML_F32x4_ZERO    (__m128)__lsx_vldi(0)
-#define GGML_F32x4_SET1(x) (__m128)__lsx_vinsgr2vr_w(__lsx_vldi(0),(x), 0)
+#define GGML_F32x4_SET1(x) (__m128)__lsx_vreplfr2vr_s((x))
 #define GGML_F32x4_LOAD(x) (__m128)__lsx_vld((x), 0)
 #define GGML_F32x4_STORE(x, y)   __lsx_vst(y, x, 0)
 #define GGML_F32x4_FMA(a, b, c) __lsx_vfmadd_s(b, c, a)
 #define GGML_F32x4_ADD     __lsx_vfadd_s
 #define GGML_F32x4_MUL     __lsx_vfmul_s
-#define GGML_F32x4_REDUCE(res, x)                                                     \
-{                                                                                     \
-    int offset = GGML_F32_ARR >> 1;                                                   \
-    for (int i = 0; i < offset; ++i) {                                                \
-        x[i] = __lsx_vfadd_s(x[i], x[offset + i]);                                    \
-    }                                                                                 \
-    offset >>= 1;                                                                     \
-    for (int i = 0; i < offset; ++i) {                                                \
-        x[i] = __lsx_vfadd_s(x[i], x[offset + i]);                                    \
-    }                                                                                 \
-    offset >>= 1;                                                                     \
-    for (int i = 0; i < offset; ++i) {                                                \
-        x[i] = __lsx_vfadd_s(x[i], x[offset + i]);                                    \
-    }                                                                                 \
-    __m128i tmp     = __lsx_vsrli_d((__m128i) x[0], 32);                              \
-    tmp             = (__m128i) __lsx_vfadd_s((__m128) tmp, x[0]);                    \
-    tmp             = __lsx_vpickev_w(__lsx_vldi(0), tmp);                            \
-    const __m128 t0 = (__m128)__lsx_vshuf4i_w(tmp, 0x88);                                     \
-    tmp             = __lsx_vsrli_d((__m128i) t0, 32);                                \
-    tmp             = (__m128i) __lsx_vfadd_s((__m128) tmp, t0);                      \
-    tmp             = __lsx_vpickev_w(__lsx_vldi(0), tmp);                            \
-    res             = (ggml_float) __lsx_vpickve2gr_w(__lsx_vshuf4i_w(tmp, 0x88), 0); \
+
+#define GGML_F32x4_REDUCE(res, x)                               \
+{                                                               \
+    int offset = GGML_F32_ARR >> 1;                             \
+    for (int i = 0; i < offset; ++i) {                          \
+        x[i] = __lsx_vfadd_s(x[i], x[offset+i]);                \
+    }                                                           \
+    offset >>= 1;                                               \
+    for (int i = 0; i < offset; ++i) {                          \
+        x[i] = __lsx_vfadd_s(x[i], x[offset+i]);                \
+    }                                                           \
+    offset >>= 1;                                               \
+    for (int i = 0; i < offset; ++i) {                          \
+        x[i] = __lsx_vfadd_s(x[i], x[offset+i]);                \
+    }                                                           \
+    __m128i t0 = __lsx_vpickev_w((__m128i)x[0], (__m128i)x[0]); \
+    __m128i t1 = __lsx_vpickod_w((__m128i)x[0], (__m128i)x[0]); \
+    __m128 t2 = __lsx_vfadd_s((__m128)t0, (__m128)t1);          \
+    __m128i t3 = __lsx_vpickev_w((__m128i)t2, (__m128i)t2);     \
+    __m128i t4 = __lsx_vpickod_w((__m128i)t2, (__m128i)t2);     \
+    __m128 t5 = __lsx_vfadd_s((__m128)t3, (__m128)t4);          \
+    res = (ggml_float) ((v4f32)t5)[0];                          \
 }
 
 #define GGML_F32_VEC        GGML_F32x4
@@ -1068,7 +1068,7 @@ static inline void __lsx_f16x4_store(ggml_fp16_t * x, __m128 y) {
 
 #define GGML_F32Cx4             __m128
 #define GGML_F32Cx4_ZERO        (__m128)__lsx_vldi(0)
-#define GGML_F32Cx4_SET1(x)     (__m128)__lsx_vinsgr2vr_w(__lsx_vldi(0),(x), 0)
+#define GGML_F32Cx4_SET1(x)     (__m128)__lsx_vreplfr2vr_s((x))
 #define GGML_F32Cx4_LOAD(x)     (__m128)__lsx_f16x4_load(x)
 #define GGML_F32Cx4_STORE(x, y) __lsx_f16x4_store(x, y)
 #define GGML_F32Cx4_FMA         GGML_F32x4_FMA

From bf7b0c9725ed0c406c5debaea022ec7258430634 Mon Sep 17 00:00:00 2001
From: Xuan-Son Nguyen <son@huggingface.co>
Date: Mon, 3 Nov 2025 10:25:55 +0100
Subject: [PATCH 068/185] mtmd: pad mask for qwen2.5vl (#16954)

* mtmd: pad mask for qwen2.5vl

* improve
---
 tools/mtmd/clip.cpp | 9 +++++++++
 1 file changed, 9 insertions(+)

diff --git a/tools/mtmd/clip.cpp b/tools/mtmd/clip.cpp
index 0784e69fcdf..60516d582a5 100644
--- a/tools/mtmd/clip.cpp
+++ b/tools/mtmd/clip.cpp
@@ -761,6 +761,15 @@ struct clip_graph {
             ggml_set_name(window_mask, "window_mask");
             ggml_set_input(window_mask);
 
+            // if flash attn is used, we need to pad the mask and cast to f16
+            if (ctx->flash_attn_type == CLIP_FLASH_ATTN_TYPE_ENABLED) {
+                int n_pad = GGML_PAD(window_mask->ne[1], GGML_KQ_MASK_PAD) - window_mask->ne[1];
+                if (n_pad > 0) {
+                    window_mask = ggml_pad(ctx0, window_mask, 0, n_pad, 0, 0);
+                }
+                window_mask = ggml_cast(ctx0, window_mask, GGML_TYPE_F16);
+            }
+
             // inpL shape: [n_embd, n_patches_x * n_patches_y, batch_size]
             GGML_ASSERT(batch_size == 1);
             inpL = ggml_reshape_2d(ctx0, inpL, n_embd * 4, n_patches_x * n_patches_y * batch_size / 4);

From 070ff4d5356083d60b807bb34d36b31c3653a29e Mon Sep 17 00:00:00 2001
From: Xuan-Son Nguyen <son@huggingface.co>
Date: Mon, 3 Nov 2025 11:11:18 +0100
Subject: [PATCH 069/185] mtmd: add --image-min/max-tokens (#16921)

---
 common/arg.cpp          | 14 ++++++++++++++
 common/common.h         |  2 ++
 tools/mtmd/clip.cpp     | 43 ++++++++++++++++++++++++++++++++---------
 tools/mtmd/clip.h       |  2 ++
 tools/mtmd/mtmd-cli.cpp | 12 +++++++-----
 tools/mtmd/mtmd.cpp     | 12 +++++++++---
 tools/mtmd/mtmd.h       |  4 ++++
 tools/server/server.cpp | 12 +++++++-----
 8 files changed, 79 insertions(+), 22 deletions(-)

diff --git a/common/arg.cpp b/common/arg.cpp
index d8f9bbd2430..4316917d745 100644
--- a/common/arg.cpp
+++ b/common/arg.cpp
@@ -2768,6 +2768,20 @@ common_params_context common_params_parser_init(common_params & params, llama_ex
             params.image.emplace_back(value);
         }
     ).set_examples({LLAMA_EXAMPLE_MTMD}));
+    add_opt(common_arg(
+        {"--image-min-tokens"}, "N",
+        "minimum number of tokens each image can take, only used by vision models with dynamic resolution (default: read from model)",
+        [](common_params & params, int value) {
+            params.image_min_tokens = value;
+        }
+    ).set_examples(mmproj_examples).set_env("LLAMA_ARG_IMAGE_MIN_TOKENS"));
+    add_opt(common_arg(
+        {"--image-max-tokens"}, "N",
+        "maximum number of tokens each image can take, only used by vision models with dynamic resolution (default: read from model)",
+        [](common_params & params, int value) {
+            params.image_max_tokens = value;
+        }
+    ).set_examples(mmproj_examples).set_env("LLAMA_ARG_IMAGE_MAX_TOKENS"));
     if (llama_supports_rpc()) {
         add_opt(common_arg(
             {"--rpc"}, "SERVERS",
diff --git a/common/common.h b/common/common.h
index a8cb630ea58..78c568a7bc6 100644
--- a/common/common.h
+++ b/common/common.h
@@ -406,6 +406,8 @@ struct common_params {
     bool mmproj_use_gpu = true;     // use GPU for multimodal model
     bool no_mmproj = false;         // explicitly disable multimodal model
     std::vector<std::string> image; // path to image file(s)
+    int image_min_tokens = -1;
+    int image_max_tokens = -1;
 
     // finetune
     struct lr_opt lr;
diff --git a/tools/mtmd/clip.cpp b/tools/mtmd/clip.cpp
index 60516d582a5..99775cb3e35 100644
--- a/tools/mtmd/clip.cpp
+++ b/tools/mtmd/clip.cpp
@@ -169,8 +169,8 @@ struct clip_hparams {
     int32_t n_layer;
     // idefics3
     int32_t image_longest_edge = 0;
-    int32_t image_min_pixels = 0;
-    int32_t image_max_pixels = 0;
+    int32_t image_min_pixels = -1;
+    int32_t image_max_pixels = -1;
     int32_t n_merge = 0; // number of patch merges **per-side**
 
     float image_mean[3];
@@ -203,11 +203,15 @@ struct clip_hparams {
     int minicpmv_version = 0;
     int32_t minicpmv_query_num = 0;         // MiniCPM-V query number
 
+    // custom value provided by user, can be undefined if not set
+    int32_t custom_image_min_tokens = -1;
+    int32_t custom_image_max_tokens = -1;
+
     void set_limit_image_tokens(int n_tokens_min, int n_tokens_max) {
         const int cur_merge = n_merge == 0 ? 1 : n_merge;
         const int patch_area = patch_size * patch_size * cur_merge * cur_merge;
-        image_min_pixels = n_tokens_min * patch_area;
-        image_max_pixels = n_tokens_max * patch_area;
+        image_min_pixels = (custom_image_min_tokens > 0 ? custom_image_min_tokens : n_tokens_min) * patch_area;
+        image_max_pixels = (custom_image_max_tokens > 0 ? custom_image_max_tokens : n_tokens_max) * patch_area;
         warmup_image_size = static_cast<int>(std::sqrt(image_max_pixels));
     }
 
@@ -216,6 +220,7 @@ struct clip_hparams {
         GGML_ASSERT(n_tok_per_side * n_tok_per_side == n_tokens && "n_tokens must be n*n");
         const int cur_merge = n_merge == 0 ? 1 : n_merge;
         warmup_image_size = n_tok_per_side * patch_size * cur_merge;
+        // TODO: support warmup size for custom token numbers
     }
 };
 
@@ -459,6 +464,13 @@ struct clip_ctx {
             LOG_INF("%s: CLIP using CPU backend\n", __func__);
         }
 
+        if (ctx_params.image_min_tokens > 0) {
+            model.hparams.custom_image_min_tokens = ctx_params.image_min_tokens;
+        }
+        if (ctx_params.image_max_tokens > 0) {
+            model.hparams.custom_image_max_tokens = ctx_params.image_max_tokens;
+        }
+
         backend_ptrs.push_back(backend_cpu);
         backend_buft.push_back(ggml_backend_get_default_buffer_type(backend_cpu));
 
@@ -2786,6 +2798,12 @@ struct clip_model_loader {
                         //           see: https://github.com/ggml-org/llama.cpp/issues/16842#issuecomment-3475144858
                         hparams.set_limit_image_tokens(8, 2048);
                         hparams.set_warmup_n_tokens(256); // avoid OOM on warmup
+                        const int warn_min_pixels = 1024 * hparams.n_merge * hparams.n_merge * hparams.patch_size * hparams.patch_size;
+                        if (hparams.image_min_pixels < warn_min_pixels) {
+                            LOG_WRN("%s: Qwen-VL models require at minimum 1024 image tokens to function correctly on grounding tasks\n", __func__);
+                            LOG_WRN("%s: if you encounter problems with accuracy, try adding --image-min-tokens 1024\n", __func__);
+                            LOG_WRN("%s: more info: https://github.com/ggml-org/llama.cpp/issues/16842\n\n", __func__);
+                        }
                     } break;
                 case PROJECTOR_TYPE_LLAMA4:
                     {
@@ -2810,6 +2828,13 @@ struct clip_model_loader {
                     break;
             }
 
+            // sanity check
+            {
+                if (hparams.image_max_pixels < hparams.image_min_pixels) {
+                    throw std::runtime_error(string_format("%s: image_max_pixels (%d) is less than image_min_pixels (%d)\n", __func__, hparams.image_max_pixels, hparams.image_min_pixels));
+                }
+            }
+
             LOG_INF("%s: projector:          %s\n", __func__, proj_type.c_str());
             LOG_INF("%s: n_embd:             %d\n", __func__, hparams.n_embd);
             LOG_INF("%s: n_head:             %d\n", __func__, hparams.n_head);
@@ -2826,10 +2851,10 @@ struct clip_model_loader {
                 LOG_INF("%s: n_merge:            %d\n", __func__, hparams.n_merge);
                 LOG_INF("%s: n_wa_pattern:       %d\n", __func__, hparams.n_wa_pattern);
                 if (hparams.image_min_pixels > 0) {
-                    LOG_INF("%s: image_min_pixels:   %d\n", __func__, hparams.image_min_pixels);
+                    LOG_INF("%s: image_min_pixels:   %d%s\n", __func__, hparams.image_min_pixels, hparams.custom_image_min_tokens > 0 ? " (custom value)" : "");
                 }
                 if (hparams.image_max_pixels > 0) {
-                    LOG_INF("%s: image_max_pixels:   %d\n", __func__, hparams.image_max_pixels);
+                    LOG_INF("%s: image_max_pixels:   %d%s\n", __func__, hparams.image_max_pixels, hparams.custom_image_max_tokens > 0 ? " (custom value)" : "");
                 }
             } else if (is_audio) {
                 LOG_INF("\n--- audio hparams ---\n");
@@ -4169,7 +4194,7 @@ bool clip_image_preprocess(struct clip_ctx * ctx, const clip_image_u8 * img, str
         case PROJECTOR_TYPE_QWEN25VL:
         case PROJECTOR_TYPE_QWEN3VL:
             {
-                // step 1: make a blank canvas which aligns to the grid
+                GGML_ASSERT(params.image_min_pixels > 0 && params.image_max_pixels > 0);
                 clip_image_u8 resized;
                 const clip_image_size new_size = img_tool::calc_size_preserved_ratio(
                     original_size,
@@ -4262,7 +4287,7 @@ bool clip_image_preprocess(struct clip_ctx * ctx, const clip_image_u8 * img, str
         case PROJECTOR_TYPE_PIXTRAL:
         case PROJECTOR_TYPE_LIGHTONOCR:
             {
-                GGML_ASSERT(params.image_min_pixels && params.image_max_pixels);
+                GGML_ASSERT(params.image_min_pixels > 0 && params.image_max_pixels > 0);
                 clip_image_u8 resized_image;
                 // the original pixtral model doesn't have n_merge
                 const int cur_merge = params.n_merge == 0 ? 1 : params.n_merge;
@@ -4296,7 +4321,7 @@ bool clip_image_preprocess(struct clip_ctx * ctx, const clip_image_u8 * img, str
         case PROJECTOR_TYPE_LFM2:
         case PROJECTOR_TYPE_KIMIVL:
             {
-                GGML_ASSERT(params.image_min_pixels && params.image_max_pixels);
+                GGML_ASSERT(params.image_min_pixels > 0 && params.image_max_pixels > 0);
                 const clip_image_size target_size = img_tool::calc_size_preserved_ratio(
                     original_size,
                     params.patch_size * params.n_merge,
diff --git a/tools/mtmd/clip.h b/tools/mtmd/clip.h
index 6384e2adaf7..3e4c985f117 100644
--- a/tools/mtmd/clip.h
+++ b/tools/mtmd/clip.h
@@ -33,6 +33,8 @@ struct clip_context_params {
     bool use_gpu;
     enum ggml_log_level verbosity;
     enum clip_flash_attn_type flash_attn_type;
+    int image_min_tokens;
+    int image_max_tokens;
 };
 
 struct clip_init_result {
diff --git a/tools/mtmd/mtmd-cli.cpp b/tools/mtmd/mtmd-cli.cpp
index 17aea1472b3..3e19e95958a 100644
--- a/tools/mtmd/mtmd-cli.cpp
+++ b/tools/mtmd/mtmd-cli.cpp
@@ -132,11 +132,13 @@ struct mtmd_cli_context {
     void init_vision_context(common_params & params) {
         const char * clip_path = params.mmproj.path.c_str();
         mtmd_context_params mparams = mtmd_context_params_default();
-        mparams.use_gpu = params.mmproj_use_gpu;
-        mparams.print_timings = true;
-        mparams.n_threads = params.cpuparams.n_threads;
-        mparams.verbosity = params.verbosity > 0 ? GGML_LOG_LEVEL_DEBUG : GGML_LOG_LEVEL_INFO;
-        mparams.flash_attn_type = params.flash_attn_type;
+        mparams.use_gpu          = params.mmproj_use_gpu;
+        mparams.print_timings    = true;
+        mparams.n_threads        = params.cpuparams.n_threads;
+        mparams.verbosity        = params.verbosity > 0 ? GGML_LOG_LEVEL_DEBUG : GGML_LOG_LEVEL_INFO;
+        mparams.flash_attn_type  = params.flash_attn_type;
+        mparams.image_min_tokens = params.image_min_tokens;
+        mparams.image_max_tokens = params.image_max_tokens;
         ctx_vision.reset(mtmd_init_from_file(clip_path, model, mparams));
         if (!ctx_vision.get()) {
             LOG_ERR("Failed to load vision model from %s\n", clip_path);
diff --git a/tools/mtmd/mtmd.cpp b/tools/mtmd/mtmd.cpp
index 297eef437ab..325f7ff995e 100644
--- a/tools/mtmd/mtmd.cpp
+++ b/tools/mtmd/mtmd.cpp
@@ -109,6 +109,8 @@ mtmd_context_params mtmd_context_params_default() {
     params.image_marker = MTMD_DEFAULT_IMAGE_MARKER;
     params.media_marker = mtmd_default_marker();
     params.flash_attn_type = LLAMA_FLASH_ATTN_TYPE_AUTO;
+    params.image_min_tokens = -1;
+    params.image_max_tokens = -1;
     return params;
 }
 
@@ -171,9 +173,13 @@ struct mtmd_context {
         }
 
         clip_context_params ctx_clip_params;
-        ctx_clip_params.use_gpu   = ctx_params.use_gpu;
-        ctx_clip_params.verbosity = ctx_params.verbosity;
-        ctx_clip_params.flash_attn_type = mtmd_get_clip_flash_attn_type(ctx_params.flash_attn_type);
+        ctx_clip_params.use_gpu          = ctx_params.use_gpu;
+        ctx_clip_params.verbosity        = ctx_params.verbosity;
+        ctx_clip_params.flash_attn_type  = mtmd_get_clip_flash_attn_type(ctx_params.flash_attn_type);
+        // custom image token limits
+        ctx_clip_params.image_min_tokens = ctx_params.image_min_tokens;
+        ctx_clip_params.image_max_tokens = ctx_params.image_max_tokens;
+
         auto res = clip_init(mmproj_fname, ctx_clip_params);
         ctx_v = res.ctx_v;
         ctx_a = res.ctx_a;
diff --git a/tools/mtmd/mtmd.h b/tools/mtmd/mtmd.h
index 4ae1925bcdf..775fba6215c 100644
--- a/tools/mtmd/mtmd.h
+++ b/tools/mtmd/mtmd.h
@@ -83,6 +83,10 @@ struct mtmd_context_params {
     const char * image_marker; // deprecated, use media_marker instead
     const char * media_marker;
     enum llama_flash_attn_type flash_attn_type;
+
+    // limit number of image tokens, only for vision models with dynamic resolution
+    int image_min_tokens; // minimum number of tokens for image input (default: read from metadata)
+    int image_max_tokens; // maximum number of tokens for image input (default: read from metadata)
 };
 
 MTMD_API const char * mtmd_default_marker(void);
diff --git a/tools/server/server.cpp b/tools/server/server.cpp
index a9bef35189b..a8d7773c968 100644
--- a/tools/server/server.cpp
+++ b/tools/server/server.cpp
@@ -2452,11 +2452,13 @@ struct server_context {
         std::string & mmproj_path = params_base.mmproj.path;
         if (!mmproj_path.empty()) {
             mtmd_context_params mparams = mtmd_context_params_default();
-            mparams.use_gpu       = params_base.mmproj_use_gpu;
-            mparams.print_timings = false;
-            mparams.n_threads     = params_base.cpuparams.n_threads;
-            mparams.verbosity     = params_base.verbosity > 0 ? GGML_LOG_LEVEL_DEBUG : GGML_LOG_LEVEL_INFO;
-            mparams.flash_attn_type = params_base.flash_attn_type;
+            mparams.use_gpu          = params_base.mmproj_use_gpu;
+            mparams.print_timings    = false;
+            mparams.n_threads        = params_base.cpuparams.n_threads;
+            mparams.verbosity        = params_base.verbosity > 0 ? GGML_LOG_LEVEL_DEBUG : GGML_LOG_LEVEL_INFO;
+            mparams.flash_attn_type  = params_base.flash_attn_type;
+            mparams.image_min_tokens = params_base.image_min_tokens;
+            mparams.image_max_tokens = params_base.image_max_tokens;
             mctx = mtmd_init_from_file(mmproj_path.c_str(), model, mparams);
             if (mctx == nullptr) {
                 SRV_ERR("failed to load multimodal model, '%s'\n", mmproj_path.c_str());

From 622cd010ff4a65bef67edbf2f9bf4707c01f98f7 Mon Sep 17 00:00:00 2001
From: theo77186 <theo77186@users.noreply.github.com>
Date: Mon, 3 Nov 2025 14:29:11 +0100
Subject: [PATCH 070/185] ggml: CUDA: add head size 72 for flash-attn (#16962)

---
 ggml/src/ggml-cuda/fattn-tile.cu              |  4 +++
 ggml/src/ggml-cuda/fattn-tile.cuh             | 31 +++++++++++++++++--
 ggml/src/ggml-cuda/fattn.cu                   |  5 +--
 .../fattn-tile-instance-dkq72-dv72.cu         |  5 +++
 .../template-instances/generate_cu_files.py   |  4 ++-
 5 files changed, 44 insertions(+), 5 deletions(-)
 create mode 100644 ggml/src/ggml-cuda/template-instances/fattn-tile-instance-dkq72-dv72.cu

diff --git a/ggml/src/ggml-cuda/fattn-tile.cu b/ggml/src/ggml-cuda/fattn-tile.cu
index 3a5806d9091..3fcb09b7a2b 100644
--- a/ggml/src/ggml-cuda/fattn-tile.cu
+++ b/ggml/src/ggml-cuda/fattn-tile.cu
@@ -14,6 +14,10 @@ void ggml_cuda_flash_attn_ext_tile(ggml_backend_cuda_context & ctx, ggml_tensor
             GGML_ASSERT(V->ne[0] == K->ne[0]);
             ggml_cuda_flash_attn_ext_tile_case< 64,  64>(ctx, dst);
         } break;
+        case  72: {
+            GGML_ASSERT(V->ne[0] == K->ne[0]);
+            ggml_cuda_flash_attn_ext_tile_case< 72,  72>(ctx, dst);
+        } break;
         case  80: {
             GGML_ASSERT(V->ne[0] == K->ne[0]);
             ggml_cuda_flash_attn_ext_tile_case< 80,  80>(ctx, dst);
diff --git a/ggml/src/ggml-cuda/fattn-tile.cuh b/ggml/src/ggml-cuda/fattn-tile.cuh
index 2b60b3bb135..c358aa1e87e 100644
--- a/ggml/src/ggml-cuda/fattn-tile.cuh
+++ b/ggml/src/ggml-cuda/fattn-tile.cuh
@@ -6,7 +6,7 @@
 // nbatch_K == number of K columns to load in parallel for KQ calculation
 
 // TODO optimize kernel parameters for FP16 NVIDIA (P100)
-// TODO optimize kernel parameters for head sizes 40, 80, 96, 112
+// TODO optimize kernel parameters for head sizes 40, 72, 80, 96, 112
 
 // The ROCm compiler cannot handle templating in __launch_bounds__.
 // As a workaround, define a macro to package the kernel parameters as uint32_t:
@@ -32,6 +32,12 @@ static constexpr __host__ __device__ uint32_t ggml_cuda_fattn_tile_get_config_nv
     GGML_CUDA_FATTN_TILE_CONFIG_CASE( 64,  64, 16, 256, 2,  64,  64)
     GGML_CUDA_FATTN_TILE_CONFIG_CASE( 64,  64, 32, 256, 2,  64,  64)
 
+    GGML_CUDA_FATTN_TILE_CONFIG_CASE( 72,  72,  2,  64, 2,  64,  72)
+    GGML_CUDA_FATTN_TILE_CONFIG_CASE( 72,  72,  4, 128, 2,  64,  72)
+    GGML_CUDA_FATTN_TILE_CONFIG_CASE( 72,  72,  8, 256, 2,  64,  72)
+    GGML_CUDA_FATTN_TILE_CONFIG_CASE( 72,  72, 16, 256, 2,  64,  72)
+    GGML_CUDA_FATTN_TILE_CONFIG_CASE( 72,  72, 32, 256, 2,  64,  72)
+
     GGML_CUDA_FATTN_TILE_CONFIG_CASE( 80,  80,  2,  64, 2,  64,  40)
     GGML_CUDA_FATTN_TILE_CONFIG_CASE( 80,  80,  4, 128, 2,  64,  40)
     GGML_CUDA_FATTN_TILE_CONFIG_CASE( 80,  80,  8, 256, 2,  64,  40)
@@ -80,6 +86,12 @@ static constexpr __host__ __device__ uint32_t ggml_cuda_fattn_tile_get_config_nv
     GGML_CUDA_FATTN_TILE_CONFIG_CASE( 64,  64, 16, 128, 3,  64,  64)
     GGML_CUDA_FATTN_TILE_CONFIG_CASE( 64,  64, 32, 256, 2,  64,  64)
 
+    GGML_CUDA_FATTN_TILE_CONFIG_CASE( 72,  72,  2,  64, 2,  32,  72)
+    GGML_CUDA_FATTN_TILE_CONFIG_CASE( 72,  72,  4, 128, 2,  32,  72)
+    GGML_CUDA_FATTN_TILE_CONFIG_CASE( 72,  72,  8, 256, 2,  32,  72)
+    GGML_CUDA_FATTN_TILE_CONFIG_CASE( 72,  72, 16, 256, 2,  32,  72)
+    GGML_CUDA_FATTN_TILE_CONFIG_CASE( 72,  72, 32, 256, 2,  32,  72)
+
     GGML_CUDA_FATTN_TILE_CONFIG_CASE( 80,  80,  2,  64, 2,  32,  40)
     GGML_CUDA_FATTN_TILE_CONFIG_CASE( 80,  80,  4, 128, 2,  32,  40)
     GGML_CUDA_FATTN_TILE_CONFIG_CASE( 80,  80,  8, 256, 2,  32,  40)
@@ -130,6 +142,13 @@ static constexpr __host__ __device__ uint32_t ggml_cuda_fattn_tile_get_config_am
     GGML_CUDA_FATTN_TILE_CONFIG_CASE( 64,  64, 32, 256, 2,  64,  64)
     GGML_CUDA_FATTN_TILE_CONFIG_CASE( 64,  64, 64, 256, 2,  64,  64)
 
+    GGML_CUDA_FATTN_TILE_CONFIG_CASE( 72,  72,  2,  64, 2,  32,  72)
+    GGML_CUDA_FATTN_TILE_CONFIG_CASE( 72,  72,  4, 128, 2,  32,  72)
+    GGML_CUDA_FATTN_TILE_CONFIG_CASE( 72,  72,  8, 256, 2,  32,  72)
+    GGML_CUDA_FATTN_TILE_CONFIG_CASE( 72,  72, 16, 256, 2,  32,  72)
+    GGML_CUDA_FATTN_TILE_CONFIG_CASE( 72,  72, 32, 256, 2,  32,  72)
+    GGML_CUDA_FATTN_TILE_CONFIG_CASE( 72,  72, 64, 256, 2,  32,  72)
+
     GGML_CUDA_FATTN_TILE_CONFIG_CASE( 80,  80,  2,  64, 2,  32,  40)
     GGML_CUDA_FATTN_TILE_CONFIG_CASE( 80,  80,  4, 128, 2,  32,  40)
     GGML_CUDA_FATTN_TILE_CONFIG_CASE( 80,  80,  8, 256, 2,  32,  40)
@@ -185,6 +204,13 @@ static constexpr __host__ __device__ uint32_t ggml_cuda_fattn_tile_get_config_am
     GGML_CUDA_FATTN_TILE_CONFIG_CASE( 64,  64, 32, 128, 4,  64,  64)
     GGML_CUDA_FATTN_TILE_CONFIG_CASE( 64,  64, 64, 128, 5,  64,  64)
 
+    GGML_CUDA_FATTN_TILE_CONFIG_CASE( 72,  72,  2,  64, 2,  32,  72)
+    GGML_CUDA_FATTN_TILE_CONFIG_CASE( 72,  72,  4, 128, 2,  32,  72)
+    GGML_CUDA_FATTN_TILE_CONFIG_CASE( 72,  72,  8, 256, 2,  32,  72)
+    GGML_CUDA_FATTN_TILE_CONFIG_CASE( 72,  72, 16, 256, 2,  32,  72)
+    GGML_CUDA_FATTN_TILE_CONFIG_CASE( 72,  72, 32, 256, 2,  32,  72)
+    GGML_CUDA_FATTN_TILE_CONFIG_CASE( 72,  72, 64, 256, 2,  32,  72)
+
     GGML_CUDA_FATTN_TILE_CONFIG_CASE( 80,  80,  2,  64, 2,  32,  40)
     GGML_CUDA_FATTN_TILE_CONFIG_CASE( 80,  80,  4, 128, 2,  32,  40)
     GGML_CUDA_FATTN_TILE_CONFIG_CASE( 80,  80,  8, 256, 2,  32,  40)
@@ -723,7 +749,7 @@ static __global__ void flash_attn_tile(
 
     if (
 #ifdef GGML_USE_WMMA_FATTN
-            (ncols2 != 1 && DV != 40 && DV != 512) ||
+            (ncols2 != 1 && DV != 40 && DV != 72 && DV != 512) ||
 #endif // GGML_USE_WMMA_FATTN
             (use_logit_softcap && !(DV == 128 || DV == 256))
     ) {
@@ -1198,6 +1224,7 @@ void ggml_cuda_flash_attn_ext_tile(ggml_backend_cuda_context & ctx, ggml_tensor
 
 extern DECL_FATTN_TILE_CASE( 40,  40);
 extern DECL_FATTN_TILE_CASE( 64,  64);
+extern DECL_FATTN_TILE_CASE( 72,  72);
 extern DECL_FATTN_TILE_CASE( 80,  80);
 extern DECL_FATTN_TILE_CASE( 96,  96);
 extern DECL_FATTN_TILE_CASE(112, 112);
diff --git a/ggml/src/ggml-cuda/fattn.cu b/ggml/src/ggml-cuda/fattn.cu
index 7dee032c291..82405991cea 100644
--- a/ggml/src/ggml-cuda/fattn.cu
+++ b/ggml/src/ggml-cuda/fattn.cu
@@ -223,6 +223,7 @@ static best_fattn_kernel ggml_cuda_get_best_fattn_kernel(const int device, const
     switch (K->ne[0]) {
         case  40:
         case  64:
+        case  72:
         case  80:
         case  96:
         case 128:
@@ -275,7 +276,7 @@ static best_fattn_kernel ggml_cuda_get_best_fattn_kernel(const int device, const
     const bool can_use_vector_kernel = Q->ne[0] <= 256 && Q->ne[0] % 64 == 0 && K->ne[1] % FATTN_KQ_STRIDE == 0;
 
     // If Turing tensor cores available, use them:
-    if (turing_mma_available(cc) && K->ne[1] % FATTN_KQ_STRIDE == 0 && Q->ne[0] != 40) {
+    if (turing_mma_available(cc) && K->ne[1] % FATTN_KQ_STRIDE == 0 && Q->ne[0] != 40 && Q->ne[0] != 72) {
         if (can_use_vector_kernel) {
             if (!ggml_is_quantized(K->type) && !ggml_is_quantized(V->type)) {
                 if (cc >= GGML_CUDA_CC_ADA_LOVELACE && Q->ne[1] == 1 && Q->ne[3] == 1 && !(gqa_ratio > 4 && K->ne[1] >= 8192)) {
@@ -301,7 +302,7 @@ static best_fattn_kernel ggml_cuda_get_best_fattn_kernel(const int device, const
     }
 
     // Use the WMMA kernel if possible:
-    if (ggml_cuda_should_use_wmma_fattn(cc) && K->ne[1] % FATTN_KQ_STRIDE == 0 && Q->ne[0] != 40 && Q->ne[0] != 576) {
+    if (ggml_cuda_should_use_wmma_fattn(cc) && K->ne[1] % FATTN_KQ_STRIDE == 0 && Q->ne[0] != 40 && Q->ne[0] != 72 && Q->ne[0] != 576) {
         if (can_use_vector_kernel && Q->ne[1] <= 2) {
             return BEST_FATTN_KERNEL_VEC;
         }
diff --git a/ggml/src/ggml-cuda/template-instances/fattn-tile-instance-dkq72-dv72.cu b/ggml/src/ggml-cuda/template-instances/fattn-tile-instance-dkq72-dv72.cu
new file mode 100644
index 00000000000..8f9d5315f2a
--- /dev/null
+++ b/ggml/src/ggml-cuda/template-instances/fattn-tile-instance-dkq72-dv72.cu
@@ -0,0 +1,5 @@
+// This file has been autogenerated by generate_cu_files.py, do not edit manually.
+
+#include "../fattn-tile.cuh"
+
+DECL_FATTN_TILE_CASE(72, 72);
diff --git a/ggml/src/ggml-cuda/template-instances/generate_cu_files.py b/ggml/src/ggml-cuda/template-instances/generate_cu_files.py
index 81a986f38ca..a5602da02bb 100755
--- a/ggml/src/ggml-cuda/template-instances/generate_cu_files.py
+++ b/ggml/src/ggml-cuda/template-instances/generate_cu_files.py
@@ -3,7 +3,7 @@
 from glob import glob
 import os
 
-HEAD_SIZES_KQ = [40, 64, 80, 96, 112, 128, 256, 576]
+HEAD_SIZES_KQ = [40, 64, 72, 80, 96, 112, 128, 256, 576]
 
 TYPES_KV = ["GGML_TYPE_F16", "GGML_TYPE_Q4_0", "GGML_TYPE_Q4_1", "GGML_TYPE_Q5_0", "GGML_TYPE_Q5_1", "GGML_TYPE_Q8_0"]
 
@@ -81,6 +81,8 @@ def get_short_name(long_quant_name):
             for head_size_kq in HEAD_SIZES_KQ:
                 if head_size_kq == 40:
                     continue
+                if head_size_kq == 72:
+                    continue
                 if head_size_kq != 576 and ncols2 == 16:
                     continue
                 if head_size_kq == 576 and ncols2 != 16:

From 48bd26501b08a3f0bff1249db47f313641f7bebb Mon Sep 17 00:00:00 2001
From: Georgi Gerganov <ggerganov@gmail.com>
Date: Mon, 3 Nov 2025 15:38:23 +0200
Subject: [PATCH 071/185] server : add props.model_alias (#16943)

* server : add props.model_alias

* webui : npm run format
---
 tools/server/public/index.html.gz             | Bin 1127221 -> 1127227 bytes
 tools/server/server.cpp                       |   1 +
 .../webui/src/lib/stores/server.svelte.ts     |   3 +++
 3 files changed, 4 insertions(+)

diff --git a/tools/server/public/index.html.gz b/tools/server/public/index.html.gz
index 6a570b65e2ce104f2f3d13c420058e58a5acb46b..b5314f4807b0739d0485936a27f0e5b9c21ac251 100644
GIT binary patch
delta 780926
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diff --git a/tools/server/server.cpp b/tools/server/server.cpp
index a8d7773c968..ec7dc1a130f 100644
--- a/tools/server/server.cpp
+++ b/tools/server/server.cpp
@@ -4910,6 +4910,7 @@ int main(int argc, char ** argv) {
         json data = {
             { "default_generation_settings", default_generation_settings_for_props },
             { "total_slots",                 ctx_server.params_base.n_parallel },
+            { "model_alias",                 ctx_server.params_base.model_alias },
             { "model_path",                  ctx_server.params_base.model.path },
             { "modalities",                  json {
                 {"vision", ctx_server.oai_parser_opt.allow_image},
diff --git a/tools/server/webui/src/lib/stores/server.svelte.ts b/tools/server/webui/src/lib/stores/server.svelte.ts
index c7056cc120e..e95c0bcea2f 100644
--- a/tools/server/webui/src/lib/stores/server.svelte.ts
+++ b/tools/server/webui/src/lib/stores/server.svelte.ts
@@ -99,6 +99,9 @@ class ServerStore {
 	}
 
 	get modelName(): string | null {
+		if (this._serverProps?.model_alias) {
+			return this._serverProps.model_alias;
+		}
 		if (!this._serverProps?.model_path) return null;
 		return this._serverProps.model_path.split(/(\\|\/)/).pop() || null;
 	}

From ed8aa63320393512bdcfe4b05b5ae01ba91888e1 Mon Sep 17 00:00:00 2001
From: Daniel Bevenius <daniel.bevenius@gmail.com>
Date: Mon, 3 Nov 2025 18:01:59 +0100
Subject: [PATCH 072/185] model-conversion : pass config to from_pretrained
 (#16963)

This commit modifies the script `run-org-model.py` to ensure that the
model configuration is explicitly passed to the `from_pretrained` method
when loading the model. It also removes a duplicate configuration
loading which was a mistake.

The motivation for this change is that enables the config object to be
modified and then passed to the model loading function, which can be
useful when testing new models.
---
 .../model-conversion/scripts/causal/run-org-model.py     | 9 ++++-----
 1 file changed, 4 insertions(+), 5 deletions(-)

diff --git a/examples/model-conversion/scripts/causal/run-org-model.py b/examples/model-conversion/scripts/causal/run-org-model.py
index 7fb55e9af1f..85529c612f5 100755
--- a/examples/model-conversion/scripts/causal/run-org-model.py
+++ b/examples/model-conversion/scripts/causal/run-org-model.py
@@ -138,6 +138,9 @@ def fn(_m, input, output):
         "Model path must be specified either via --model-path argument or MODEL_PATH environment variable"
     )
 
+
+print("Loading model and tokenizer using AutoTokenizer:", model_path)
+tokenizer = AutoTokenizer.from_pretrained(model_path, trust_remote_code=True)
 config = AutoConfig.from_pretrained(model_path, trust_remote_code=True)
 
 print("Model type:       ", config.model_type)
@@ -147,10 +150,6 @@ def fn(_m, input, output):
 print("BOS token id:     ", config.bos_token_id)
 print("EOS token id:     ", config.eos_token_id)
 
-print("Loading model and tokenizer using AutoTokenizer:", model_path)
-tokenizer = AutoTokenizer.from_pretrained(model_path, trust_remote_code=True)
-config = AutoConfig.from_pretrained(model_path, trust_remote_code=True)
-
 if unreleased_model_name:
     model_name_lower = unreleased_model_name.lower()
     unreleased_module_path = (
@@ -171,7 +170,7 @@ def fn(_m, input, output):
         exit(1)
 else:
     model = AutoModelForCausalLM.from_pretrained(
-        model_path, device_map="auto", offload_folder="offload", trust_remote_code=True
+        model_path, device_map="auto", offload_folder="offload", trust_remote_code=True, config=config
     )
 
 for name, module in model.named_modules():

From e7da30b584dc1f2ee0414c4a1298ce64eef97e8d Mon Sep 17 00:00:00 2001
From: Aleksander Grygier <aleksander.grygier@gmail.com>
Date: Mon, 3 Nov 2025 18:53:26 +0100
Subject: [PATCH 073/185] fix: Viewing multiple PDF attachments (#16974)

---
 tools/server/public/index.html.gz             | Bin 1127227 -> 1127240 bytes
 .../ChatAttachmentPreviewDialog.svelte        |   9 +++++++++
 2 files changed, 9 insertions(+)

diff --git a/tools/server/public/index.html.gz b/tools/server/public/index.html.gz
index b5314f4807b0739d0485936a27f0e5b9c21ac251..a796c255c18579093dd7a63e150a4fe9d0cdb327 100644
GIT binary patch
delta 756068
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zf_9+&ULou~8SQ)cU!9%p{^LW1zl2Neetc4yB&c4PSOD>P+k8L0QQfEsajh^F{^mEo
z`BGo}-_JiU;0?GOy&o@szW?Cx@E^ZNZ2TF_h!T7QXD*64D9*B1{O`lNxFV0wmXGk`
j;oaf*1O9k;_i#2mfApJ&cj@Bu=r{ilIoGI^=_@h-IW}q&

diff --git a/tools/server/webui/src/lib/components/app/chat/ChatAttachments/ChatAttachmentPreviewDialog.svelte b/tools/server/webui/src/lib/components/app/chat/ChatAttachments/ChatAttachmentPreviewDialog.svelte
index c28cb1c1089..3c1ee7fc5d9 100644
--- a/tools/server/webui/src/lib/components/app/chat/ChatAttachments/ChatAttachmentPreviewDialog.svelte
+++ b/tools/server/webui/src/lib/components/app/chat/ChatAttachments/ChatAttachmentPreviewDialog.svelte
@@ -134,6 +134,15 @@
 		}
 	}
 
+	$effect(() => {
+		if (open) {
+			pdfImages = [];
+			pdfImagesLoading = false;
+			pdfImagesError = null;
+			pdfViewMode = 'pages';
+		}
+	});
+
 	$effect(() => {
 		if (open && isPdf && pdfViewMode === 'pages') {
 			loadPdfImages();

From c5023daf607c578d6344c628eb7da18ac3d92d32 Mon Sep 17 00:00:00 2001
From: lhez <lih@qti.qualcomm.com>
Date: Mon, 3 Nov 2025 11:47:57 -0800
Subject: [PATCH 074/185] opencl: support imrope (#16914)

* opencl: support imrope

* opencl: fix whitespace
---
 ggml/src/ggml-opencl/ggml-opencl.cpp |  6 +++
 ggml/src/ggml-opencl/kernels/rope.cl | 74 +++++++++++++++++++---------
 2 files changed, 56 insertions(+), 24 deletions(-)

diff --git a/ggml/src/ggml-opencl/ggml-opencl.cpp b/ggml/src/ggml-opencl/ggml-opencl.cpp
index 93a3600b63f..3dc4d035509 100644
--- a/ggml/src/ggml-opencl/ggml-opencl.cpp
+++ b/ggml/src/ggml-opencl/ggml-opencl.cpp
@@ -8399,6 +8399,7 @@ static void ggml_cl_rope(ggml_backend_t backend, const ggml_tensor * src0, const
     const bool is_neox = mode & 2;
     const bool is_mrope = mode & GGML_ROPE_TYPE_MROPE;
     const bool is_vision = mode == GGML_ROPE_TYPE_VISION;
+    const int  is_imrope = mode == GGML_ROPE_TYPE_IMROPE;
 
     if (is_mrope) {
         GGML_ASSERT(sections[0] > 0 || sections[1] > 0 || sections[2] > 0);
@@ -8489,9 +8490,14 @@ static void ggml_cl_rope(ggml_backend_t backend, const ggml_tensor * src0, const
     CL_CHECK(clSetKernelArg(kernel, 30, sizeof(float),    &attn_factor));
     CL_CHECK(clSetKernelArg(kernel, 31, sizeof(float),    &beta_fast));
     CL_CHECK(clSetKernelArg(kernel, 32, sizeof(float),    &beta_slow));
+    // both mrope and vision kernels have sections
     if (is_mrope || is_vision) {
         CL_CHECK(clSetKernelArg(kernel, 33, sizeof(int32_t)*4, &sections));
     }
+    // only mrope has is_imrope
+    if (is_mrope && !is_vision) {
+        CL_CHECK(clSetKernelArg(kernel, 34, sizeof(int), &is_imrope));
+    }
 
     size_t global_work_size[] = {(size_t)ne01*nth, (size_t)ne02, (size_t)ne03};
     size_t local_work_size[] = {(size_t)nth, 1, 1};
diff --git a/ggml/src/ggml-opencl/kernels/rope.cl b/ggml/src/ggml-opencl/kernels/rope.cl
index 0247730c036..82f4cd87407 100644
--- a/ggml/src/ggml-opencl/kernels/rope.cl
+++ b/ggml/src/ggml-opencl/kernels/rope.cl
@@ -392,7 +392,8 @@ kernel void kernel_rope_multi_f32(
         float attn_factor,
         float beta_fast,
         float beta_slow,
-        int4 sections
+        int4 sections,
+        int  is_imrope
 ) {
     src0 = (global void*)((global char*)src0 + offset0);
     src1 = (global int*)((global char*)src1 + offset1);
@@ -419,17 +420,29 @@ kernel void kernel_rope_multi_f32(
             const int sector = (i0 / 2) % sect_dims;
             float theta_base = 0.0f;
 
-            if (sector < sections.s0) {
-                theta_base = pos[i2];
-            }
-            else if (sector >= sections.s0 && sector < sec_w) {
-                theta_base = pos[i2 + ne2 * 1];
-            }
-            else if (sector >= sec_w && sector < sec_w + sections.s2) {
-                theta_base = pos[i2 + ne2 * 2];
-            }
-            else if (sector >= sec_w + sections.s2) {
-                theta_base = pos[i2 + ne2 * 3];
+            if (is_imrope) {
+                if (sector % 3 == 1 && sector < 3 * sections.s1) { // h
+                    theta_base = (float) pos[i2 + ne02 * 1];
+                } else if (sector % 3 == 2 && sector < 3 * sections.s2) { // w
+                    theta_base = (float) pos[i2 + ne02 * 2];
+                } else if (sector % 3 == 0 && sector < 3 * sections.s0) { // t
+                    theta_base = (float) pos[i2 + ne02 * 0];
+                } else { // e
+                    theta_base = (float) pos[i2 + ne02 * 3];
+                }
+            } else {
+                if (sector < sections.s0) {
+                    theta_base = pos[i2];
+                }
+                else if (sector >= sections.s0 && sector < sec_w) {
+                    theta_base = pos[i2 + ne2 * 1];
+                }
+                else if (sector >= sec_w && sector < sec_w + sections.s2) {
+                    theta_base = pos[i2 + ne2 * 2];
+                }
+                else if (sector >= sec_w + sections.s2) {
+                    theta_base = pos[i2 + ne2 * 3];
+                }
             }
 
             const float theta = theta_base * pow(freq_base, inv_ndims*i0);
@@ -490,7 +503,8 @@ kernel void kernel_rope_multi_f16(
         float attn_factor,
         float beta_fast,
         float beta_slow,
-        int4 sections
+        int4 sections,
+        int  is_imrope
 ) {
     src0 = (global void*)((global char*)src0 + offset0);
     src1 = (global int*)((global char*)src1 + offset1);
@@ -517,17 +531,29 @@ kernel void kernel_rope_multi_f16(
             const int sector = (i0 / 2) % sect_dims;
             float theta_base = 0.0f;
 
-            if (sector < sections.s0) {
-                theta_base = pos[i2];
-            }
-            else if (sector >= sections.s0 && sector < sec_w) {
-                theta_base = pos[i2 + ne2 * 1];
-            }
-            else if (sector >= sec_w && sector < sec_w + sections.s2) {
-                theta_base = pos[i2 + ne2 * 2];
-            }
-            else if (sector >= sec_w + sections.s2) {
-                theta_base = pos[i2 + ne2 * 3];
+            if (is_imrope) {
+                if (sector % 3 == 1 && sector < 3 * sections.s1) { // h
+                    theta_base = (float) pos[i2 + ne02 * 1];
+                } else if (sector % 3 == 2 && sector < 3 * sections.s2) { // w
+                    theta_base = (float) pos[i2 + ne02 * 2];
+                } else if (sector % 3 == 0 && sector < 3 * sections.s0) { // t
+                    theta_base = (float) pos[i2 + ne02 * 0];
+                } else { // e
+                    theta_base = (float) pos[i2 + ne02 * 3];
+                }
+            } else {
+                if (sector < sections.s0) {
+                    theta_base = pos[i2];
+                }
+                else if (sector >= sections.s0 && sector < sec_w) {
+                    theta_base = pos[i2 + ne2 * 1];
+                }
+                else if (sector >= sec_w && sector < sec_w + sections.s2) {
+                    theta_base = pos[i2 + ne2 * 2];
+                }
+                else if (sector >= sec_w + sections.s2) {
+                    theta_base = pos[i2 + ne2 * 3];
+                }
             }
 
             const float theta = theta_base * pow(freq_base, inv_ndims*i0);

From 2759ccdb4adc8568add4316780d5e675519b0775 Mon Sep 17 00:00:00 2001
From: Aman Gupta <amangupta052@gmail.com>
Date: Tue, 4 Nov 2025 10:53:48 +0800
Subject: [PATCH 075/185] CUDA: avoid mul + bias fusion when doing fusion
 (#16935)

---
 ggml/src/ggml-cuda/ggml-cuda.cu | 17 +++++++++++++++++
 1 file changed, 17 insertions(+)

diff --git a/ggml/src/ggml-cuda/ggml-cuda.cu b/ggml/src/ggml-cuda/ggml-cuda.cu
index 5667ec0c4d7..415a7e962d7 100644
--- a/ggml/src/ggml-cuda/ggml-cuda.cu
+++ b/ggml/src/ggml-cuda/ggml-cuda.cu
@@ -2115,6 +2115,14 @@ static bool ggml_cuda_should_fuse_mul_mat_vec_f(const ggml_tensor * tensor) {
     const int cc      = ggml_cuda_info().devices[ggml_cuda_get_device()].cc;
     use_mul_mat_vec_f = use_mul_mat_vec_f && ggml_cuda_should_use_mmvf(src0->type, cc, src0->ne, is_mul_mat_id ? src1->ne[2] : src1->ne[1]);
 
+    const bool split = ggml_backend_buft_is_cuda_split(src0->buffer->buft) ||
+                       ggml_backend_buft_is_cuda_split(src1->buffer->buft);
+
+    //TODO: add support for fusion for split buffers
+    if (split) {
+        return false;
+    }
+
     //we only support fusion for ncols_dst = 1
     if (tensor->op == GGML_OP_MUL_MAT && dst->ne[1] != 1) {
         return false;
@@ -2154,6 +2162,15 @@ static bool ggml_cuda_should_fuse_mul_mat_vec_q(const ggml_tensor * tensor) {
         return false;
     }
 
+
+    const bool split = ggml_backend_buft_is_cuda_split(src0->buffer->buft) ||
+                       ggml_backend_buft_is_cuda_split(src1->buffer->buft);
+
+    //TODO: add support for fusion for split buffers
+    if (split) {
+        return false;
+    }
+
     return use_mul_mat_vec_q;
 }
 

From 1f5accb8d0056e6099cd5b772b1cb787dd590a13 Mon Sep 17 00:00:00 2001
From: Noah <99681487+NoahOksuz@users.noreply.github.com>
Date: Tue, 4 Nov 2025 05:04:59 +0000
Subject: [PATCH 076/185] Fix garbled output with REPACK at high thread counts
 (#16956)

* Fix garbled output with REPACK at high thread counts

Fixed a race condition in the REPACK matrix multiplication code that caused garbled output when using 26+ threads (model-dependent threshold). The issue occurred because with high thread counts, the code forced chunk count to equal thread count, creating many small chunks. After aligning these chunks to NB_COLS boundaries, adjacent chunks could overlap, causing data corruption and race conditions. The fix enforces minimum chunk sizes based on NB_COLS and caps maximum chunk count to prevent creating too many tiny chunks, ensuring proper alignment without overlaps.

* Update ggml/src/ggml-cpu/repack.cpp

Co-authored-by: Georgi Gerganov <ggerganov@gmail.com>

* Update ggml/src/ggml-cpu/repack.cpp

Co-authored-by: Georgi Gerganov <ggerganov@gmail.com>

---------

Co-authored-by: Georgi Gerganov <ggerganov@gmail.com>
---
 ggml/src/ggml-cpu/repack.cpp | 25 +++++++++++++++++++++++++
 1 file changed, 25 insertions(+)

diff --git a/ggml/src/ggml-cpu/repack.cpp b/ggml/src/ggml-cpu/repack.cpp
index 8da1e0e9245..8421c84ce09 100644
--- a/ggml/src/ggml-cpu/repack.cpp
+++ b/ggml/src/ggml-cpu/repack.cpp
@@ -1678,10 +1678,24 @@ template <typename BLOC_TYPE, int64_t INTER_SIZE, int64_t NB_COLS, ggml_type PAR
         int64_t chunk_size = (nr + nth_scaled - 1) / nth_scaled;
         int64_t nchunk     = (nr + chunk_size - 1) / chunk_size;
 
+        // Ensure minimum chunk size to avoid alignment issues with high thread counts
+        // Minimum chunk size should be at least NB_COLS to prevent overlapping chunks after alignment
+        const int64_t min_chunk_size = NB_COLS;
+        if (nchunk > 0 && (nr / nchunk) < min_chunk_size && nr >= min_chunk_size) {
+            nchunk = (nr + min_chunk_size - 1) / min_chunk_size;
+        }
+
         if (nth == 1 || nchunk < nth || disable_chunking) {
             nchunk = nth;
         }
 
+        // Ensure nchunk doesn't exceed the number of rows divided by minimum chunk size
+        // This prevents creating too many tiny chunks that could overlap after alignment
+        const int64_t max_nchunk = (nr + min_chunk_size - 1) / min_chunk_size;
+        if (nchunk > max_nchunk) {
+            nchunk = max_nchunk;
+        }
+
         if (ith == 0) {
             // Every thread starts at ith, so the first unprocessed chunk is nth.  This save a bit of coordination right at the start.
             ggml_threadpool_chunk_set(params->threadpool, nth);
@@ -1695,8 +1709,15 @@ template <typename BLOC_TYPE, int64_t INTER_SIZE, int64_t NB_COLS, ggml_type PAR
         while (current_chunk < nchunk) {
             int64_t src0_start = (current_chunk * ne01) / nchunk;
             int64_t src0_end   = ((current_chunk + 1) * ne01) / nchunk;
+
+            // Align boundaries to NB_COLS - round up to ensure all data is included
+            // The chunk size limiting above ensures chunks are large enough to prevent overlaps
             src0_start = (src0_start % NB_COLS) ? src0_start + NB_COLS - (src0_start % NB_COLS) : src0_start;
             src0_end   = (src0_end   % NB_COLS) ? src0_end   + NB_COLS - (src0_end   % NB_COLS) : src0_end;
+            if (src0_end > ne01) {
+                src0_end = ne01;
+            }
+
             if (src0_start >= src0_end) {
                 break;
             }
@@ -1808,8 +1829,12 @@ template <typename BLOC_TYPE, int64_t INTER_SIZE, int64_t NB_COLS, ggml_type PAR
             int64_t src0_cur_start = (ith * ne01) / nth;
             int64_t src0_cur_end   = ((ith + 1) * ne01) / nth;
 
+            // Align boundaries to NB_COLS - round up to ensure all data is included
             src0_cur_start = (src0_cur_start % NB_COLS) ? src0_cur_start + NB_COLS - (src0_cur_start % NB_COLS) : src0_cur_start;
             src0_cur_end   = (src0_cur_end   % NB_COLS) ? src0_cur_end   + NB_COLS - (src0_cur_end   % NB_COLS) : src0_cur_end;
+            if (src0_cur_end > ne01) {
+                src0_cur_end = ne01;
+            }
 
             if (src0_cur_start >= src0_cur_end) {
                 return;

From b164259bbaa579e1d82b2bc18be133947ac71290 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sigbj=C3=B8rn=20Skj=C3=A6ret?= <sigbjorn.skjaeret@scala.com>
Date: Tue, 4 Nov 2025 12:29:15 +0100
Subject: [PATCH 077/185] chore : fix models indent after refactor (#16992)

---
 src/models/gemma2-iswa.cpp      | 226 ++++++++++----------
 src/models/gemma3-iswa.cpp      | 232 ++++++++++-----------
 src/models/glm4-moe.cpp         | 278 ++++++++++++-------------
 src/models/grok.cpp             | 267 ++++++++++++------------
 src/models/hunyuan-dense.cpp    | 226 ++++++++++----------
 src/models/hunyuan-moe.cpp      | 270 ++++++++++++------------
 src/models/internlm2.cpp        | 195 +++++++++---------
 src/models/jais.cpp             | 140 ++++++-------
 src/models/jamba.cpp            | 195 +++++++++---------
 src/models/llada-moe.cpp        | 227 ++++++++++----------
 src/models/llada.cpp            | 144 +++++++------
 src/models/llama.cpp            | 257 ++++++++++++-----------
 src/models/minicpm3.cpp         | 355 ++++++++++++++++----------------
 src/models/nemotron.cpp         | 198 +++++++++---------
 src/models/neo-bert.cpp         | 194 ++++++++---------
 src/models/olmo.cpp             | 196 +++++++++---------
 src/models/olmo2.cpp            | 245 +++++++++++-----------
 src/models/olmoe.cpp            | 214 +++++++++----------
 src/models/openai-moe-iswa.cpp  | 212 +++++++++----------
 src/models/openelm.cpp          | 210 +++++++++----------
 src/models/orion.cpp            | 226 ++++++++++----------
 src/models/phi3.cpp             | 257 ++++++++++++-----------
 src/models/plamo.cpp            | 200 +++++++++---------
 src/models/plm.cpp              | 308 +++++++++++++--------------
 src/models/qwen2.cpp            | 217 ++++++++++---------
 src/models/qwen2moe.cpp         | 254 +++++++++++------------
 src/models/qwen2vl.cpp          | 214 +++++++++----------
 src/models/qwen3.cpp            | 214 +++++++++----------
 src/models/qwen3moe.cpp         | 230 ++++++++++-----------
 src/models/refact.cpp           | 152 +++++++-------
 src/models/seed-oss.cpp         | 200 +++++++++---------
 src/models/smallthinker.cpp     | 184 ++++++++---------
 src/models/smollm3.cpp          | 200 +++++++++---------
 src/models/starcoder.cpp        | 162 +++++++--------
 src/models/starcoder2.cpp       | 186 ++++++++---------
 src/models/t5-dec.cpp           | 270 ++++++++++++------------
 src/models/t5-enc.cpp           | 154 +++++++-------
 src/models/wavtokenizer-dec.cpp | 212 +++++++++----------
 src/models/xverse.cpp           | 178 ++++++++--------
 39 files changed, 4244 insertions(+), 4255 deletions(-)

diff --git a/src/models/gemma2-iswa.cpp b/src/models/gemma2-iswa.cpp
index 1f2b597c65e..9cc59a53ee5 100644
--- a/src/models/gemma2-iswa.cpp
+++ b/src/models/gemma2-iswa.cpp
@@ -1,125 +1,125 @@
 #include "models.h"
 
 llm_build_gemma2_iswa::llm_build_gemma2_iswa(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_k;
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        inpL = ggml_scale(ctx0, inpL, sqrtf(n_embd));
-        cb(inpL, "inp_scaled", -1);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv_iswa();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow);
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow);
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                Qcur = ggml_scale(ctx0, Qcur, hparams.f_attention_scale);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, NULL,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f, il);
-            }
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur  = ggml_get_rows(ctx0,  cur, inp_out_ids);
-                inpL = ggml_get_rows(ctx0, inpL, inp_out_ids);
-            }
-            cur = build_norm(cur,
-                    model.layers[il].attn_post_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_post_norm", il);
-
-            ggml_tensor * sa_out = ggml_add(ctx0, cur, inpL);
-            cb(sa_out, "sa_out", il);
-
-            cur = build_norm(sa_out,
-                    model.layers[il].ffn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-
-            // feed-forward network
-            {
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up,   NULL, NULL,
-                        model.layers[il].ffn_gate, NULL, NULL,
-                        model.layers[il].ffn_down, NULL, NULL,
-                        NULL,
-                        LLM_FFN_GELU, LLM_FFN_PAR, il);
-                cb(cur, "ffn_out", il);
-            }
-            cur = build_norm(cur,
-                    model.layers[il].ffn_post_norm, NULL,
-                    LLM_NORM_RMS, -1);
-            cb(cur, "ffn_post_norm", -1);
-
-            cur = ggml_add(ctx0, cur, sa_out);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-        cur = inpL;
+    const int64_t n_embd_head = hparams.n_embd_head_k;
+
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+
+    inpL = build_inp_embd(model.tok_embd);
+
+    inpL = ggml_scale(ctx0, inpL, sqrtf(n_embd));
+    cb(inpL, "inp_scaled", -1);
+
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
+
+    auto * inp_attn = build_attn_inp_kv_iswa();
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        // norm
+        cur = build_norm(inpL,
+                model.layers[il].attn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
+
+        // self-attention
+        {
+            // compute Q and K and RoPE them
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            cb(Qcur, "Qcur", il);
+
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            cb(Kcur, "Kcur", il);
+
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            cb(Vcur, "Vcur", il);
+
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
 
+            Qcur = ggml_rope_ext(
+                    ctx0, Qcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow);
+
+            Kcur = ggml_rope_ext(
+                    ctx0, Kcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow);
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            Qcur = ggml_scale(ctx0, Qcur, hparams.f_attention_scale);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, NULL,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f, il);
+        }
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur  = ggml_get_rows(ctx0,  cur, inp_out_ids);
+            inpL = ggml_get_rows(ctx0, inpL, inp_out_ids);
+        }
         cur = build_norm(cur,
-                model.output_norm, NULL,
+                model.layers[il].attn_post_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "attn_post_norm", il);
+
+        ggml_tensor * sa_out = ggml_add(ctx0, cur, inpL);
+        cb(sa_out, "sa_out", il);
+
+        cur = build_norm(sa_out,
+                model.layers[il].ffn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "ffn_norm", il);
+
+        // feed-forward network
+        {
+            cur = build_ffn(cur,
+                    model.layers[il].ffn_up,   NULL, NULL,
+                    model.layers[il].ffn_gate, NULL, NULL,
+                    model.layers[il].ffn_down, NULL, NULL,
+                    NULL,
+                    LLM_FFN_GELU, LLM_FFN_PAR, il);
+            cb(cur, "ffn_out", il);
+        }
+        cur = build_norm(cur,
+                model.layers[il].ffn_post_norm, NULL,
                 LLM_NORM_RMS, -1);
+        cb(cur, "ffn_post_norm", -1);
+
+        cur = ggml_add(ctx0, cur, sa_out);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+    cur = inpL;
+
+    cur = build_norm(cur,
+            model.output_norm, NULL,
+            LLM_NORM_RMS, -1);
 
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
 
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
 
-        // final logit soft-capping
-        cur = ggml_scale(ctx0, cur, 1.0f / hparams.f_final_logit_softcapping);
-        cur = ggml_tanh(ctx0, cur);
-        cur = ggml_scale(ctx0, cur, hparams.f_final_logit_softcapping);
+    // final logit soft-capping
+    cur = ggml_scale(ctx0, cur, 1.0f / hparams.f_final_logit_softcapping);
+    cur = ggml_tanh(ctx0, cur);
+    cur = ggml_scale(ctx0, cur, hparams.f_final_logit_softcapping);
 
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
 
-        ggml_build_forward_expand(gf, cur);
+    ggml_build_forward_expand(gf, cur);
 }
diff --git a/src/models/gemma3-iswa.cpp b/src/models/gemma3-iswa.cpp
index 84badc38f17..839ff6d3d93 100644
--- a/src/models/gemma3-iswa.cpp
+++ b/src/models/gemma3-iswa.cpp
@@ -1,131 +1,131 @@
 #include "models.h"
 
 llm_build_gemma3_iswa::llm_build_gemma3_iswa(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_k;
+    const int64_t n_embd_head = hparams.n_embd_head_k;
 
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
 
-        inpL = build_inp_embd(model.tok_embd);
+    inpL = build_inp_embd(model.tok_embd);
 
-        // important: do not normalize weights for raw embeddings input (i.e. encoded image emdeddings)
-        if (ubatch.token) {
-            inpL = ggml_scale(ctx0, inpL, sqrtf(n_embd));
-            cb(inpL, "inp_scaled", -1);
+    // important: do not normalize weights for raw embeddings input (i.e. encoded image emdeddings)
+    if (ubatch.token) {
+        inpL = ggml_scale(ctx0, inpL, sqrtf(n_embd));
+        cb(inpL, "inp_scaled", -1);
+    }
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
+
+    // TODO: is causal == true correct? might need some changes
+    auto * inp_attn = build_attn_inp_kv_iswa();
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        const float freq_base_l  = model.get_rope_freq_base (cparams, il);
+        const float freq_scale_l = model.get_rope_freq_scale(cparams, il);
+
+        // norm
+        cur = build_norm(inpL, model.layers[il].attn_norm, NULL, LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
+
+        // self-attention
+        {
+            // compute Q and K and RoPE them
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            cb(Qcur, "Qcur", il);
+
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            cb(Kcur, "Kcur", il);
+
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            cb(Vcur, "Vcur", il);
+
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+            Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL, LLM_NORM_RMS, il);
+            cb(Qcur, "Qcur_normed", il);
+
+            Qcur = ggml_rope_ext(
+                    ctx0, Qcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base_l, freq_scale_l,
+                    ext_factor, attn_factor, beta_fast, beta_slow);
+
+            Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, NULL, LLM_NORM_RMS, il);
+            cb(Kcur, "Kcur_normed", il);
+
+            Kcur = ggml_rope_ext(
+                    ctx0, Kcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base_l, freq_scale_l,
+                    ext_factor, attn_factor, beta_fast, beta_slow);
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            // ref: https://github.com/google/gemma_pytorch/blob/014acb7ac4563a5f77c76d7ff98f31b568c16508/gemma/model.py#L315
+            Qcur = ggml_scale(ctx0, Qcur, hparams.f_attention_scale);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, NULL,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f, il);
         }
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        // TODO: is causal == true correct? might need some changes
-        auto * inp_attn = build_attn_inp_kv_iswa();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            const float freq_base_l  = model.get_rope_freq_base (cparams, il);
-            const float freq_scale_l = model.get_rope_freq_scale(cparams, il);
-
-            // norm
-            cur = build_norm(inpL, model.layers[il].attn_norm, NULL, LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL, LLM_NORM_RMS, il);
-                cb(Qcur, "Qcur_normed", il);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base_l, freq_scale_l,
-                        ext_factor, attn_factor, beta_fast, beta_slow);
-
-                Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, NULL, LLM_NORM_RMS, il);
-                cb(Kcur, "Kcur_normed", il);
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base_l, freq_scale_l,
-                        ext_factor, attn_factor, beta_fast, beta_slow);
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                // ref: https://github.com/google/gemma_pytorch/blob/014acb7ac4563a5f77c76d7ff98f31b568c16508/gemma/model.py#L315
-                Qcur = ggml_scale(ctx0, Qcur, hparams.f_attention_scale);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, NULL,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f, il);
-            }
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur  = ggml_get_rows(ctx0,  cur, inp_out_ids);
-                inpL = ggml_get_rows(ctx0, inpL, inp_out_ids);
-            }
-            cur = build_norm(cur,
-                    model.layers[il].attn_post_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_post_norm", il);
-
-            ggml_tensor * sa_out = ggml_add(ctx0, cur, inpL);
-            cb(sa_out, "sa_out", il);
-
-            cur = build_norm(sa_out,
-                    model.layers[il].ffn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-
-            // feed-forward network
-            {
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up,   NULL, NULL,
-                        model.layers[il].ffn_gate, NULL, NULL,
-                        model.layers[il].ffn_down, NULL, NULL,
-                        NULL,
-                        LLM_FFN_GELU, LLM_FFN_PAR, il);
-                cb(cur, "ffn_out", il);
-            }
-            cur = build_norm(cur,
-                    model.layers[il].ffn_post_norm, NULL,
-                    LLM_NORM_RMS, -1);
-            cb(cur, "ffn_post_norm", -1);
-
-            cur = ggml_add(ctx0, cur, sa_out);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur  = ggml_get_rows(ctx0,  cur, inp_out_ids);
+            inpL = ggml_get_rows(ctx0, inpL, inp_out_ids);
         }
-        cur = inpL;
-
         cur = build_norm(cur,
-                model.output_norm, NULL,
+                model.layers[il].attn_post_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "attn_post_norm", il);
+
+        ggml_tensor * sa_out = ggml_add(ctx0, cur, inpL);
+        cb(sa_out, "sa_out", il);
+
+        cur = build_norm(sa_out,
+                model.layers[il].ffn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "ffn_norm", il);
+
+        // feed-forward network
+        {
+            cur = build_ffn(cur,
+                    model.layers[il].ffn_up,   NULL, NULL,
+                    model.layers[il].ffn_gate, NULL, NULL,
+                    model.layers[il].ffn_down, NULL, NULL,
+                    NULL,
+                    LLM_FFN_GELU, LLM_FFN_PAR, il);
+            cb(cur, "ffn_out", il);
+        }
+        cur = build_norm(cur,
+                model.layers[il].ffn_post_norm, NULL,
                 LLM_NORM_RMS, -1);
+        cb(cur, "ffn_post_norm", -1);
+
+        cur = ggml_add(ctx0, cur, sa_out);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+    cur = inpL;
+
+    cur = build_norm(cur,
+            model.output_norm, NULL,
+            LLM_NORM_RMS, -1);
 
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
 
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
 
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
 
-        ggml_build_forward_expand(gf, cur);
+    ggml_build_forward_expand(gf, cur);
 }
diff --git a/src/models/glm4-moe.cpp b/src/models/glm4-moe.cpp
index 036625dc34e..33ee7070463 100644
--- a/src/models/glm4-moe.cpp
+++ b/src/models/glm4-moe.cpp
@@ -1,153 +1,153 @@
 #include "models.h"
 
 llm_build_glm4_moe::llm_build_glm4_moe(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        // Only process up to last layer (skip final NextN layer)
-        // Final layer tensors are loaded but not processed in forward pass
-        const int n_transformer_layers = n_layer - hparams.nextn_predict_layers;
-        for (int il = 0; il < n_transformer_layers; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            // Pre-attention norm
-            cur = build_norm(inpL, model.layers[il].attn_norm, NULL, LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                if (model.layers[il].bq) {
-                    Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
-                }
-                cb(Qcur, "Qcur", il);
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                if (model.layers[il].bk) {
-                    Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
-                }
-                cb(Kcur, "Kcur", il);
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                if (model.layers[il].bv) {
-                    Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
-                }
-                cb(Vcur, "Vcur", il);
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head, n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                // Apply Q/K norm if available (GLM-4.5 355B variant)
-                if (model.layers[il].attn_q_norm) {
-                    Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL, LLM_NORM_RMS, il);
-                    cb(Qcur, "Qcur_normed", il);
-                }
-                if (model.layers[il].attn_k_norm) {
-                    Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, NULL, LLM_NORM_RMS, il);
-                    cb(Kcur, "Kcur_normed", il);
-                }
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, NULL,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+    const int64_t n_embd_head = hparams.n_embd_head_v;
+
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+
+    inpL = build_inp_embd(model.tok_embd);
+
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
+
+    auto * inp_attn = build_attn_inp_kv();
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    // Only process up to last layer (skip final NextN layer)
+    // Final layer tensors are loaded but not processed in forward pass
+    const int n_transformer_layers = n_layer - hparams.nextn_predict_layers;
+    for (int il = 0; il < n_transformer_layers; ++il) {
+        ggml_tensor * inpSA = inpL;
+
+        // Pre-attention norm
+        cur = build_norm(inpL, model.layers[il].attn_norm, NULL, LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
+
+        // self-attention
+        {
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            if (model.layers[il].bq) {
+                Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
             }
-            if (il == n_transformer_layers - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0, cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+            cb(Qcur, "Qcur", il);
+
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            if (model.layers[il].bk) {
+                Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
             }
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // Post-attention norm
-            cur = build_norm(ffn_inp, model.layers[il].attn_post_norm, NULL, LLM_NORM_RMS, il);
-            cb(cur, "post_attn_norm", il);
-
-            // Check if this is a dense layer (n_layer_dense_lead=1, so layer 0 is dense)
-            if (static_cast<uint32_t>(il) < hparams.n_layer_dense_lead) {
-                // Dense FFN layer
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up,   NULL, NULL,
-                        model.layers[il].ffn_gate, NULL, NULL,
-                        model.layers[il].ffn_down, NULL, NULL,
-                        NULL,
-                        LLM_FFN_SILU, LLM_FFN_PAR, il);
-                cb(cur, "ffn_out", il);
-            } else {
-                // Process routed experts using existing MoE infrastructure
-                ggml_tensor * routed_out = build_moe_ffn(cur,
-                        model.layers[il].ffn_gate_inp,
-                        model.layers[il].ffn_up_exps,
-                        model.layers[il].ffn_gate_exps,
-                        model.layers[il].ffn_down_exps,
-                        model.layers[il].ffn_exp_probs_b,
-                        n_expert, n_expert_used,
-                        LLM_FFN_SILU, hparams.expert_weights_norm,
-                        true, hparams.expert_weights_scale,
-                        (llama_expert_gating_func_type) hparams.expert_gating_func,
-                        il);
-                cb(routed_out, "ffn_moe_out", il);
-
-                // Process shared expert on original input
-                ggml_tensor * shared_out = build_ffn(cur,
-                        model.layers[il].ffn_up_shexp,   NULL, NULL,
-                        model.layers[il].ffn_gate_shexp, NULL, NULL,
-                        model.layers[il].ffn_down_shexp, NULL, NULL,
-                        NULL,
-                        LLM_FFN_SILU, LLM_FFN_PAR, il);
-                cb(shared_out, "ffn_shexp_out", il);
-
-                // Final output: routed_output + shared_output
-                cur = ggml_add(ctx0, routed_out, shared_out);
-                cb(cur, "ffn_out", il);
+            cb(Kcur, "Kcur", il);
+
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            if (model.layers[il].bv) {
+                Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
             }
-            cur = ggml_add(ctx0, cur, ffn_inp);
+            cb(Vcur, "Vcur", il);
 
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head, n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
 
-            // input for next layer
-            inpL = cur;
+            // Apply Q/K norm if available (GLM-4.5 355B variant)
+            if (model.layers[il].attn_q_norm) {
+                Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL, LLM_NORM_RMS, il);
+                cb(Qcur, "Qcur_normed", il);
+            }
+            if (model.layers[il].attn_k_norm) {
+                Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, NULL, LLM_NORM_RMS, il);
+                cb(Kcur, "Kcur_normed", il);
+            }
+            Qcur = ggml_rope_ext(
+                    ctx0, Qcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            Kcur = ggml_rope_ext(
+                    ctx0, Kcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, NULL,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
         }
-        cur = inpL;
-        cur = build_norm(cur, model.output_norm, NULL, LLM_NORM_RMS, -1);
+        if (il == n_transformer_layers - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0, cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+        }
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+        cb(ffn_inp, "ffn_inp", il);
+
+        // Post-attention norm
+        cur = build_norm(ffn_inp, model.layers[il].attn_post_norm, NULL, LLM_NORM_RMS, il);
+        cb(cur, "post_attn_norm", il);
+
+        // Check if this is a dense layer (n_layer_dense_lead=1, so layer 0 is dense)
+        if (static_cast<uint32_t>(il) < hparams.n_layer_dense_lead) {
+            // Dense FFN layer
+            cur = build_ffn(cur,
+                    model.layers[il].ffn_up,   NULL, NULL,
+                    model.layers[il].ffn_gate, NULL, NULL,
+                    model.layers[il].ffn_down, NULL, NULL,
+                    NULL,
+                    LLM_FFN_SILU, LLM_FFN_PAR, il);
+            cb(cur, "ffn_out", il);
+        } else {
+            // Process routed experts using existing MoE infrastructure
+            ggml_tensor * routed_out = build_moe_ffn(cur,
+                    model.layers[il].ffn_gate_inp,
+                    model.layers[il].ffn_up_exps,
+                    model.layers[il].ffn_gate_exps,
+                    model.layers[il].ffn_down_exps,
+                    model.layers[il].ffn_exp_probs_b,
+                    n_expert, n_expert_used,
+                    LLM_FFN_SILU, hparams.expert_weights_norm,
+                    true, hparams.expert_weights_scale,
+                    (llama_expert_gating_func_type) hparams.expert_gating_func,
+                    il);
+            cb(routed_out, "ffn_moe_out", il);
+
+            // Process shared expert on original input
+            ggml_tensor * shared_out = build_ffn(cur,
+                    model.layers[il].ffn_up_shexp,   NULL, NULL,
+                    model.layers[il].ffn_gate_shexp, NULL, NULL,
+                    model.layers[il].ffn_down_shexp, NULL, NULL,
+                    NULL,
+                    LLM_FFN_SILU, LLM_FFN_PAR, il);
+            cb(shared_out, "ffn_shexp_out", il);
+
+            // Final output: routed_output + shared_output
+            cur = ggml_add(ctx0, routed_out, shared_out);
+            cb(cur, "ffn_out", il);
+        }
+        cur = ggml_add(ctx0, cur, ffn_inp);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+    cur = inpL;
+    cur = build_norm(cur, model.output_norm, NULL, LLM_NORM_RMS, -1);
 
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
 
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
 
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
 
-        ggml_build_forward_expand(gf, cur);
+    ggml_build_forward_expand(gf, cur);
 }
diff --git a/src/models/grok.cpp b/src/models/grok.cpp
index 6781a0e924a..3c54dfee636 100644
--- a/src/models/grok.cpp
+++ b/src/models/grok.cpp
@@ -1,160 +1,159 @@
 #include "models.h"
 
 llm_build_grok::llm_build_grok(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
+    const int64_t n_embd_head = hparams.n_embd_head_v;
 
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+    GGML_ASSERT(n_embd_head == hparams.n_rot);
 
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
 
-        inpL = build_inp_embd(model.tok_embd);
+    inpL = build_inp_embd(model.tok_embd);
 
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
 
-        auto * inp_attn = build_attn_inp_kv();
+    auto * inp_attn = build_attn_inp_kv();
 
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
 
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * inpSA = inpL;
 
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-
-            // self-attention
-            {
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-                if (model.layers[il].bq) {
-                    Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
-                    cb(Qcur, "Qcur", il);
-                }
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-                if (model.layers[il].bk) {
-                    Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
-                    cb(Kcur, "Kcur", il);
-                }
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-                if (model.layers[il].bv) {
-                    Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
-                    cb(Vcur, "Vcur", il);
-                }
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
+        // norm
+        cur = build_norm(inpL,
+                model.layers[il].attn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
 
+        // self-attention
+        {
+            // compute Q and K and RoPE them
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            cb(Qcur, "Qcur", il);
+            if (model.layers[il].bq) {
+                Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
                 cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f, il);
             }
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            cb(Kcur, "Kcur", il);
+            if (model.layers[il].bk) {
+                Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
+                cb(Kcur, "Kcur", il);
             }
-            cur = build_norm(cur,
-                    model.layers[il].attn_out_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_out_norm", il);
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed-forward network
-            cur = build_norm(ffn_inp,
-                    model.layers[il].ffn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-
-            // MoE branch
-            ggml_tensor * moe_out = build_moe_ffn(cur,
-                    model.layers[il].ffn_gate_inp,
-                    model.layers[il].ffn_up_exps,
-                    model.layers[il].ffn_gate_exps,
-                    model.layers[il].ffn_down_exps,
-                    nullptr,
-                    n_expert, n_expert_used,
-                    LLM_FFN_GELU, true,
-                    false, 0.0,
-                    LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
-                    il);
-            cb(moe_out, "ffn_moe_out", il);
-
-            if (model.layers[il].ffn_up) {
-                ggml_tensor * ffn_out = build_ffn(cur,
-                        model.layers[il].ffn_up,   NULL, NULL,
-                        model.layers[il].ffn_gate, NULL, NULL,
-                        model.layers[il].ffn_down, NULL, NULL,
-                        NULL,
-                        LLM_FFN_GELU, LLM_FFN_PAR, il);
-                cb(ffn_out, "ffn_out", il);
-
-                cur = ggml_scale(ctx0, ggml_add(ctx0, ffn_out, moe_out), std::sqrt(2) / 2);
-                cb(cur, "ffn_out", il);
-            } else {
-                cur = moe_out;
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            cb(Vcur, "Vcur", il);
+            if (model.layers[il].bv) {
+                Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
+                cb(Vcur, "Vcur", il);
             }
-            cur = build_norm(cur,
-                    model.layers[il].ffn_post_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "ffn_post_norm", il);
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+            Qcur = ggml_rope_ext(
+                    ctx0, Qcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            Kcur = ggml_rope_ext(
+                    ctx0, Kcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, model.layers[il].bo,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f, il);
+        }
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+        }
+        cur = build_norm(cur,
+                model.layers[il].attn_out_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "attn_out_norm", il);
+
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+        cb(ffn_inp, "ffn_inp", il);
+
+        // feed-forward network
+        cur = build_norm(ffn_inp,
+                model.layers[il].ffn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "ffn_norm", il);
+
+        // MoE branch
+        ggml_tensor * moe_out = build_moe_ffn(cur,
+                model.layers[il].ffn_gate_inp,
+                model.layers[il].ffn_up_exps,
+                model.layers[il].ffn_gate_exps,
+                model.layers[il].ffn_down_exps,
+                nullptr,
+                n_expert, n_expert_used,
+                LLM_FFN_GELU, true,
+                false, 0.0,
+                LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
+                il);
+        cb(moe_out, "ffn_moe_out", il);
+
+        if (model.layers[il].ffn_up) {
+            ggml_tensor * ffn_out = build_ffn(cur,
+                    model.layers[il].ffn_up,   NULL, NULL,
+                    model.layers[il].ffn_gate, NULL, NULL,
+                    model.layers[il].ffn_down, NULL, NULL,
+                    NULL,
+                    LLM_FFN_GELU, LLM_FFN_PAR, il);
+            cb(ffn_out, "ffn_out", il);
+
+            cur = ggml_scale(ctx0, ggml_add(ctx0, ffn_out, moe_out), std::sqrt(2) / 2);
             cb(cur, "ffn_out", il);
+        } else {
+            cur = moe_out;
+        }
+        cur = build_norm(cur,
+                model.layers[il].ffn_post_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "ffn_post_norm", il);
 
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
+        cur = ggml_add(ctx0, cur, ffn_inp);
+        cb(cur, "ffn_out", il);
 
-            // input for next layer
-            inpL = cur;
-        }
-        cur = inpL;
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
 
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
+        // input for next layer
+        inpL = cur;
+    }
+    cur = inpL;
 
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
+    cur = build_norm(cur,
+            model.output_norm, NULL,
+            LLM_NORM_RMS, -1);
 
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
 
-        cur = ggml_scale(ctx0, cur, hparams.f_logit_scale);
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
 
-        // final logit soft-capping
-        if (hparams.f_final_logit_softcapping) {
-            cur = ggml_scale(ctx0, cur, 1.0f / hparams.f_final_logit_softcapping);
-            cur = ggml_tanh(ctx0, cur);
-            cur = ggml_scale(ctx0, cur, hparams.f_final_logit_softcapping);
-        }
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
+    cur = ggml_scale(ctx0, cur, hparams.f_logit_scale);
+
+    // final logit soft-capping
+    if (hparams.f_final_logit_softcapping) {
+        cur = ggml_scale(ctx0, cur, 1.0f / hparams.f_final_logit_softcapping);
+        cur = ggml_tanh(ctx0, cur);
+        cur = ggml_scale(ctx0, cur, hparams.f_final_logit_softcapping);
+    }
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
 
-        ggml_build_forward_expand(gf, cur);
+    ggml_build_forward_expand(gf, cur);
 }
diff --git a/src/models/hunyuan-dense.cpp b/src/models/hunyuan-dense.cpp
index cb30a6a33aa..7d5dcc7828b 100644
--- a/src/models/hunyuan-dense.cpp
+++ b/src/models/hunyuan-dense.cpp
@@ -1,132 +1,132 @@
 #include "models.h"
 
 llm_build_hunyuan_dense::llm_build_hunyuan_dense(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
+    const int64_t n_embd_head = hparams.n_embd_head_v;
 
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+    GGML_ASSERT(n_embd_head == hparams.n_rot);
 
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
 
-        inpL = build_inp_embd(model.tok_embd);
+    inpL = build_inp_embd(model.tok_embd);
 
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
 
-        auto * inp_attn = build_attn_inp_kv();
+    auto * inp_attn = build_attn_inp_kv();
 
-        const float kq_scale = 1.0f / sqrtf(float(n_embd_head));
+    const float kq_scale = 1.0f / sqrtf(float(n_embd_head));
 
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
 
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * inpSA = inpL;
 
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-            // self-attention
-            {
-                // rope freq factors for llama3; may return nullptr for llama2 and other models
-                ggml_tensor * rope_factors = model.get_rope_factors(cparams, il);
-
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-                if (model.layers[il].bq) {
-                    Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
-                    cb(Qcur, "Qcur", il);
-                }
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-                if (model.layers[il].bk) {
-                    Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
-                    cb(Kcur, "Kcur", il);
-                }
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-                if (model.layers[il].bv) {
-                    Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
-                    cb(Vcur, "Vcur", il);
-                }
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = ggml_rope_ext(
-                         ctx0, Qcur, inp_pos, rope_factors,
-                         n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                         ext_factor, attn_factor, beta_fast, beta_slow
-                         );
+        // norm
+        cur = build_norm(inpL,
+                model.layers[il].attn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
+        // self-attention
+        {
+            // rope freq factors for llama3; may return nullptr for llama2 and other models
+            ggml_tensor * rope_factors = model.get_rope_factors(cparams, il);
 
+            // compute Q and K and RoPE them
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            cb(Qcur, "Qcur", il);
+            if (model.layers[il].bq) {
+                Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
                 cb(Qcur, "Qcur", il);
+            }
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            cb(Kcur, "Kcur", il);
+            if (model.layers[il].bk) {
+                Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
                 cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                Kcur = ggml_rope_ext(
-                         ctx0, Kcur, inp_pos, rope_factors,
-                         n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                         ext_factor, attn_factor, beta_fast, beta_slow
-                         );
-
-                Kcur = build_norm(Kcur,
-                         model.layers[il].attn_k_norm, nullptr,
-                         LLM_NORM_RMS, il);
-                cb(Kcur, "Kcur_norm", il);
-
-                Qcur = build_norm(Qcur,
-                         model.layers[il].attn_q_norm, nullptr,
-                         LLM_NORM_RMS, il);
-                cb(Qcur, "Qcur_norm", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, kq_scale, il);
-                cb(cur, "attn_out", il);
             }
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            cb(Vcur, "Vcur", il);
+            if (model.layers[il].bv) {
+                Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
+                cb(Vcur, "Vcur", il);
             }
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            cur = build_norm(ffn_inp,
-                    model.layers[il].ffn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-            // feed-forward network (non-MoE)
-            ggml_tensor * cur_mlp = build_ffn(cur,
-                        model.layers[il].ffn_up,   NULL, NULL,
-                        model.layers[il].ffn_gate, NULL, NULL,
-                        model.layers[il].ffn_down, NULL, NULL,
-                        NULL,
-                        LLM_FFN_SILU, LLM_FFN_PAR, il);
-            cb(cur_mlp, "ffn_out", il);
-
-            cur = ggml_add(ctx0, cur_mlp, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+            Qcur = ggml_rope_ext(
+                        ctx0, Qcur, inp_pos, rope_factors,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            Kcur = ggml_rope_ext(
+                        ctx0, Kcur, inp_pos, rope_factors,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+            Kcur = build_norm(Kcur,
+                        model.layers[il].attn_k_norm, nullptr,
+                        LLM_NORM_RMS, il);
+            cb(Kcur, "Kcur_norm", il);
+
+            Qcur = build_norm(Qcur,
+                        model.layers[il].attn_q_norm, nullptr,
+                        LLM_NORM_RMS, il);
+            cb(Qcur, "Qcur_norm", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, model.layers[il].bo,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, kq_scale, il);
+            cb(cur, "attn_out", il);
         }
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+        }
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+        cb(ffn_inp, "ffn_inp", il);
+
+        cur = build_norm(ffn_inp,
+                model.layers[il].ffn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "ffn_norm", il);
+        // feed-forward network (non-MoE)
+        ggml_tensor * cur_mlp = build_ffn(cur,
+                    model.layers[il].ffn_up,   NULL, NULL,
+                    model.layers[il].ffn_gate, NULL, NULL,
+                    model.layers[il].ffn_down, NULL, NULL,
+                    NULL,
+                    LLM_FFN_SILU, LLM_FFN_PAR, il);
+        cb(cur_mlp, "ffn_out", il);
+
+        cur = ggml_add(ctx0, cur_mlp, ffn_inp);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+    cur = inpL;
+
+    cur = build_norm(cur,
+            model.output_norm, NULL,
+            LLM_NORM_RMS, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
 }
diff --git a/src/models/hunyuan-moe.cpp b/src/models/hunyuan-moe.cpp
index a9940b04af9..77e39de5b8b 100644
--- a/src/models/hunyuan-moe.cpp
+++ b/src/models/hunyuan-moe.cpp
@@ -1,154 +1,154 @@
 #include "models.h"
 
 llm_build_hunyuan_moe::llm_build_hunyuan_moe(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
+    const int64_t n_embd_head = hparams.n_embd_head_v;
 
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+    GGML_ASSERT(n_embd_head == hparams.n_rot);
 
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
 
-        inpL = build_inp_embd(model.tok_embd);
+    inpL = build_inp_embd(model.tok_embd);
 
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
 
-        auto * inp_attn = build_attn_inp_kv();
+    auto * inp_attn = build_attn_inp_kv();
 
-        const float kq_scale = 1.0f / sqrtf(float(n_embd_head));
+    const float kq_scale = 1.0f / sqrtf(float(n_embd_head));
 
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
 
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                // rope freq factors for llama3; may return nullptr for llama2 and other models
-                ggml_tensor * rope_factors = model.get_rope_factors(cparams, il);
-
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-                if (model.layers[il].bq) {
-                    Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
-                    cb(Qcur, "Qcur", il);
-                }
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-                if (model.layers[il].bk) {
-                    Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
-                    cb(Kcur, "Kcur", il);
-                }
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-                if (model.layers[il].bv) {
-                    Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
-                    cb(Vcur, "Vcur", il);
-                }
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, rope_factors,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * inpSA = inpL;
 
+        // norm
+        cur = build_norm(inpL,
+                model.layers[il].attn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
+
+        // self-attention
+        {
+            // rope freq factors for llama3; may return nullptr for llama2 and other models
+            ggml_tensor * rope_factors = model.get_rope_factors(cparams, il);
+
+            // compute Q and K and RoPE them
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            cb(Qcur, "Qcur", il);
+            if (model.layers[il].bq) {
+                Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
                 cb(Qcur, "Qcur", il);
+            }
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            cb(Kcur, "Kcur", il);
+            if (model.layers[il].bk) {
+                Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
                 cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, rope_factors,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = build_norm(Kcur,
-                        model.layers[il].attn_k_norm, nullptr,
-                        LLM_NORM_RMS, il);
-                cb(Kcur, "Kcur_norm", il);
-
-                Qcur = build_norm(Qcur,
-                        model.layers[il].attn_q_norm, nullptr,
-                        LLM_NORM_RMS, il);
-                cb(Qcur, "Qcur_norm", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, kq_scale, il);
-                cb(cur, "attn_out", il);
             }
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            cb(Vcur, "Vcur", il);
+            if (model.layers[il].bv) {
+                Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
+                cb(Vcur, "Vcur", il);
             }
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            cur = build_norm(ffn_inp,
-                model.layers[il].ffn_norm, NULL,
-                LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-
-            // feed-forward network (non-MoE)
-            ggml_tensor * cur_mlp = build_ffn(cur,
-                    model.layers[il].ffn_up_shexp,   NULL, NULL,
-                    model.layers[il].ffn_gate_shexp, NULL, NULL,
-                    model.layers[il].ffn_down_shexp, NULL, NULL,
-                    NULL,
-                    LLM_FFN_SILU, LLM_FFN_PAR, il);
-            cb(cur_mlp, "ffn_mlp", il);
-
-            // MoE branch
-            ggml_tensor * cur_moe = build_moe_ffn(cur,
-                    model.layers[il].ffn_gate_inp,
-                    model.layers[il].ffn_up_exps,
-                    model.layers[il].ffn_gate_exps,
-                    model.layers[il].ffn_down_exps,
-                    nullptr,
-                    n_expert, n_expert_used,
-                    LLM_FFN_SILU,
-                    true, // norm_topk_prob
-                    false,
-                    0.0,
-                    LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
-                    il);
-            cb(cur_moe, "ffn_moe_out", il);
-
-            ggml_tensor * ffn_out = ggml_add(ctx0, cur_moe, cur_mlp);
-            cb(ffn_out, "ffn_out", il);
-
-            cur = ggml_add(ctx0, ffn_out, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-        cur = inpL;
-
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+            Qcur = ggml_rope_ext(
+                    ctx0, Qcur, inp_pos, rope_factors,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            Kcur = ggml_rope_ext(
+                    ctx0, Kcur, inp_pos, rope_factors,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            Kcur = build_norm(Kcur,
+                    model.layers[il].attn_k_norm, nullptr,
+                    LLM_NORM_RMS, il);
+            cb(Kcur, "Kcur_norm", il);
 
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
+            Qcur = build_norm(Qcur,
+                    model.layers[il].attn_q_norm, nullptr,
+                    LLM_NORM_RMS, il);
+            cb(Qcur, "Qcur_norm", il);
 
-        ggml_build_forward_expand(gf, cur);
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, model.layers[il].bo,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, kq_scale, il);
+            cb(cur, "attn_out", il);
+        }
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+        }
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+        cb(ffn_inp, "ffn_inp", il);
+
+        cur = build_norm(ffn_inp,
+            model.layers[il].ffn_norm, NULL,
+            LLM_NORM_RMS, il);
+        cb(cur, "ffn_norm", il);
+
+        // feed-forward network (non-MoE)
+        ggml_tensor * cur_mlp = build_ffn(cur,
+                model.layers[il].ffn_up_shexp,   NULL, NULL,
+                model.layers[il].ffn_gate_shexp, NULL, NULL,
+                model.layers[il].ffn_down_shexp, NULL, NULL,
+                NULL,
+                LLM_FFN_SILU, LLM_FFN_PAR, il);
+        cb(cur_mlp, "ffn_mlp", il);
+
+        // MoE branch
+        ggml_tensor * cur_moe = build_moe_ffn(cur,
+                model.layers[il].ffn_gate_inp,
+                model.layers[il].ffn_up_exps,
+                model.layers[il].ffn_gate_exps,
+                model.layers[il].ffn_down_exps,
+                nullptr,
+                n_expert, n_expert_used,
+                LLM_FFN_SILU,
+                true, // norm_topk_prob
+                false,
+                0.0,
+                LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
+                il);
+        cb(cur_moe, "ffn_moe_out", il);
+
+        ggml_tensor * ffn_out = ggml_add(ctx0, cur_moe, cur_mlp);
+        cb(ffn_out, "ffn_out", il);
+
+        cur = ggml_add(ctx0, ffn_out, ffn_inp);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+    cur = inpL;
+
+    cur = build_norm(cur,
+            model.output_norm, NULL,
+            LLM_NORM_RMS, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
 }
diff --git a/src/models/internlm2.cpp b/src/models/internlm2.cpp
index e97c82198df..387e8211270 100644
--- a/src/models/internlm2.cpp
+++ b/src/models/internlm2.cpp
@@ -1,121 +1,120 @@
 #include "models.h"
 
-
 llm_build_internlm2::llm_build_internlm2(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
+    const int64_t n_embd_head = hparams.n_embd_head_v;
 
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+    GGML_ASSERT(n_embd_head == hparams.n_rot);
 
-        inpL = build_inp_embd(model.tok_embd);
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
 
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
+    inpL = build_inp_embd(model.tok_embd);
 
-        auto * inp_attn = build_attn_inp_kv();
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
 
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
+    auto * inp_attn = build_attn_inp_kv();
 
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
 
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * inpSA = inpL;
 
-            // self-attention
-            {
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-                if (model.layers[il].bq) {
-                    Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
-                    cb(Qcur, "Qcur", il);
-                }
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-                if (model.layers[il].bk) {
-                    Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
-                    cb(Kcur, "Kcur", il);
-                }
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-                if (model.layers[il].bv) {
-                    Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
-                    cb(Vcur, "Vcur", il);
-                }
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
+        // norm
+        cur = build_norm(inpL,
+                model.layers[il].attn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
 
+        // self-attention
+        {
+            // compute Q and K and RoPE them
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            cb(Qcur, "Qcur", il);
+            if (model.layers[il].bq) {
+                Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
                 cb(Qcur, "Qcur", il);
+            }
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            cb(Kcur, "Kcur", il);
+            if (model.layers[il].bk) {
+                Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
                 cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
             }
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            cb(Vcur, "Vcur", il);
+            if (model.layers[il].bv) {
+                Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
+                cb(Vcur, "Vcur", il);
             }
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed-forward network
-            cur = build_norm(ffn_inp,
-                    model.layers[il].ffn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-
-            cur = build_ffn(cur,
-                    model.layers[il].ffn_up,   NULL, NULL,
-                    model.layers[il].ffn_gate, NULL, NULL,
-                    model.layers[il].ffn_down, NULL, NULL,
-                    NULL,
-                    LLM_FFN_SILU, LLM_FFN_PAR, il);
-            cb(cur, "ffn_out", il);
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+            Qcur = ggml_rope_ext(
+                    ctx0, Qcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            Kcur = ggml_rope_ext(
+                    ctx0, Kcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, model.layers[il].bo,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+        }
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
         }
-        cur = inpL;
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+        cb(ffn_inp, "ffn_inp", il);
+
+        // feed-forward network
+        cur = build_norm(ffn_inp,
+                model.layers[il].ffn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "ffn_norm", il);
+
+        cur = build_ffn(cur,
+                model.layers[il].ffn_up,   NULL, NULL,
+                model.layers[il].ffn_gate, NULL, NULL,
+                model.layers[il].ffn_down, NULL, NULL,
+                NULL,
+                LLM_FFN_SILU, LLM_FFN_PAR, il);
+        cb(cur, "ffn_out", il);
+
+        cur = ggml_add(ctx0, cur, ffn_inp);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+    cur = inpL;
 
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
+    cur = build_norm(cur,
+            model.output_norm, NULL,
+            LLM_NORM_RMS, -1);
 
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
 
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
 
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
 
-        ggml_build_forward_expand(gf, cur);
+    ggml_build_forward_expand(gf, cur);
 }
diff --git a/src/models/jais.cpp b/src/models/jais.cpp
index a1c43065bbc..3e3376e6a62 100644
--- a/src/models/jais.cpp
+++ b/src/models/jais.cpp
@@ -1,86 +1,86 @@
 #include "models.h"
 
 llm_build_jais::llm_build_jais(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-        const int64_t n_embd_gqa  = hparams.n_embd_v_gqa();
+    const int64_t n_embd_head = hparams.n_embd_head_v;
+    const int64_t n_embd_gqa  = hparams.n_embd_v_gqa();
 
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
 
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
 
-        inpL = build_inp_embd(model.tok_embd);
+    inpL = build_inp_embd(model.tok_embd);
 
-        auto * inp_attn = build_attn_inp_kv();
+    auto * inp_attn = build_attn_inp_kv();
 
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
 
-        for (int il = 0; il < n_layer; ++il) {
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm,
-                    model.layers[il].attn_norm_b,
+    for (int il = 0; il < n_layer; ++il) {
+        cur = build_norm(inpL,
+                model.layers[il].attn_norm,
+                model.layers[il].attn_norm_b,
+                LLM_NORM, il);
+        cb(cur, "attn_norm", il);
+
+        // self-attention
+        {
+            cur = build_lora_mm(model.layers[il].wqkv, cur);
+            cb(cur, "wqkv", il);
+
+            cur = ggml_add(ctx0, cur, model.layers[il].bqkv);
+            cb(cur, "bqkv", il);
+
+            ggml_tensor * Qcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head,    n_tokens, n_embd_head*sizeof(float), cur->nb[1], 0*cur->nb[0]*(n_embd));
+            ggml_tensor * Kcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*cur->nb[0]*(n_embd));
+            ggml_tensor * Vcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*cur->nb[0]*(n_embd + n_embd_gqa));
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, model.layers[il].bo,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/float(n_embd_head), il);
+        }
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur  = ggml_get_rows(ctx0,  cur, inp_out_ids);
+            inpL = ggml_get_rows(ctx0, inpL, inp_out_ids);
+        }
+        // add the input
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpL);
+        cb(ffn_inp, "ffn_inp", il);
+
+        // FF
+        {
+            cur = build_norm(ffn_inp,
+                    model.layers[il].ffn_norm,
+                    model.layers[il].ffn_norm_b,
                     LLM_NORM, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                cur = build_lora_mm(model.layers[il].wqkv, cur);
-                cb(cur, "wqkv", il);
-
-                cur = ggml_add(ctx0, cur, model.layers[il].bqkv);
-                cb(cur, "bqkv", il);
-
-                ggml_tensor * Qcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head,    n_tokens, n_embd_head*sizeof(float), cur->nb[1], 0*cur->nb[0]*(n_embd));
-                ggml_tensor * Kcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*cur->nb[0]*(n_embd));
-                ggml_tensor * Vcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*cur->nb[0]*(n_embd + n_embd_gqa));
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/float(n_embd_head), il);
-            }
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur  = ggml_get_rows(ctx0,  cur, inp_out_ids);
-                inpL = ggml_get_rows(ctx0, inpL, inp_out_ids);
-            }
-            // add the input
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpL);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // FF
-            {
-                cur = build_norm(ffn_inp,
-                        model.layers[il].ffn_norm,
-                        model.layers[il].ffn_norm_b,
-                        LLM_NORM, il);
-                cb(cur, "ffn_norm", il);
-
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up,   model.layers[il].ffn_up_b,   NULL,
-                        model.layers[il].ffn_gate, model.layers[il].ffn_gate_b, NULL,
-                        model.layers[il].ffn_down, model.layers[il].ffn_down_b, NULL,
-                        NULL,
-                        LLM_FFN_SILU, LLM_FFN_PAR, il);
-                cb(cur, "ffn_out", il);
-            }
-            inpL = ggml_add(ctx0, cur, ffn_inp);
-            cb(inpL, "l_out", il);
+            cb(cur, "ffn_norm", il);
+
+            cur = build_ffn(cur,
+                    model.layers[il].ffn_up,   model.layers[il].ffn_up_b,   NULL,
+                    model.layers[il].ffn_gate, model.layers[il].ffn_gate_b, NULL,
+                    model.layers[il].ffn_down, model.layers[il].ffn_down_b, NULL,
+                    NULL,
+                    LLM_FFN_SILU, LLM_FFN_PAR, il);
+            cb(cur, "ffn_out", il);
         }
-        cur = build_norm(inpL,
-                model.output_norm,
-                model.output_norm_b,
-                LLM_NORM, -1);
+        inpL = ggml_add(ctx0, cur, ffn_inp);
+        cb(inpL, "l_out", il);
+    }
+    cur = build_norm(inpL,
+            model.output_norm,
+            model.output_norm_b,
+            LLM_NORM, -1);
 
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
 
-        cur = build_lora_mm(model.output, cur);
+    cur = build_lora_mm(model.output, cur);
 
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
 
-        ggml_build_forward_expand(gf, cur);
+    ggml_build_forward_expand(gf, cur);
 }
diff --git a/src/models/jamba.cpp b/src/models/jamba.cpp
index 0c8c1361d4e..a0187772ccb 100644
--- a/src/models/jamba.cpp
+++ b/src/models/jamba.cpp
@@ -1,107 +1,106 @@
 #include "models.h"
 
-
 llm_build_jamba::llm_build_jamba(const llama_model & model, const llm_graph_params & params) : llm_graph_context_mamba(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        // {n_embd, n_tokens}
-        inpL = build_inp_embd(model.tok_embd);
-
-        auto * inp_hybrid = build_inp_mem_hybrid();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            const int64_t n_head_kv = hparams.n_head_kv(il);
-
-            cur = build_norm(inpL, model.layers[il].attn_norm, NULL, LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            if (n_head_kv == 0) {
-                cur = build_mamba_layer(inp_hybrid->get_recr(), cur, model, ubatch, il);
-            } else {
-                // Attention
-
-                struct ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                struct ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                struct ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                // No RoPE :)
-                cur = build_attn(inp_hybrid->get_attn(),
-                        model.layers[il].wo, NULL,
-                        Qcur, Kcur, Vcur, NULL, NULL, NULL, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur  = ggml_get_rows(ctx0,  cur, inp_out_ids);
-                inpL = ggml_get_rows(ctx0, inpL, inp_out_ids);
-            }
-            // residual
-            struct ggml_tensor * ffn_inp = ggml_add(ctx0, inpL, cur);
-            cb(cur, "ffn_inp", il);
-
-            cur = build_norm(ffn_inp, model.layers[il].ffn_norm, NULL, LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-
-            // feed-forward network
-            if (model.layers[il].ffn_gate_inp == nullptr) {
-                // FFN
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up,   NULL, NULL,
-                        model.layers[il].ffn_gate, NULL, NULL,
-                        model.layers[il].ffn_down, NULL, NULL,
-                        NULL,
-                        LLM_FFN_SILU, LLM_FFN_PAR, il);
-                cb(cur, "ffn_out", il);
-            } else {
-                // MoE branch
-                cur = build_moe_ffn(cur,
-                        model.layers[il].ffn_gate_inp,
-                        model.layers[il].ffn_up_exps,
-                        model.layers[il].ffn_gate_exps,
-                        model.layers[il].ffn_down_exps,
-                        nullptr,
-                        n_expert, n_expert_used,
-                        LLM_FFN_SILU, false,
-                        false, 0.0,
-                        LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
-                        il);
-                cb(cur, "ffn_moe_out", il);
-            }
-            // residual
-            cur = ggml_add(ctx0, ffn_inp, cur);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
+    const int64_t n_embd_head = hparams.n_embd_head_v;
+
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+
+    // {n_embd, n_tokens}
+    inpL = build_inp_embd(model.tok_embd);
+
+    auto * inp_hybrid = build_inp_mem_hybrid();
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        const int64_t n_head_kv = hparams.n_head_kv(il);
+
+        cur = build_norm(inpL, model.layers[il].attn_norm, NULL, LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
+
+        if (n_head_kv == 0) {
+            cur = build_mamba_layer(inp_hybrid->get_recr(), cur, model, ubatch, il);
+        } else {
+            // Attention
+
+            struct ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            struct ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            struct ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            // No RoPE :)
+            cur = build_attn(inp_hybrid->get_attn(),
+                    model.layers[il].wo, NULL,
+                    Qcur, Kcur, Vcur, NULL, NULL, NULL, 1.0f/sqrtf(float(n_embd_head)), il);
         }
-        // final rmsnorm
-        cur = build_norm(inpL, model.output_norm, NULL, LLM_NORM_RMS, -1);
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur  = ggml_get_rows(ctx0,  cur, inp_out_ids);
+            inpL = ggml_get_rows(ctx0, inpL, inp_out_ids);
+        }
+        // residual
+        struct ggml_tensor * ffn_inp = ggml_add(ctx0, inpL, cur);
+        cb(cur, "ffn_inp", il);
+
+        cur = build_norm(ffn_inp, model.layers[il].ffn_norm, NULL, LLM_NORM_RMS, il);
+        cb(cur, "ffn_norm", il);
+
+        // feed-forward network
+        if (model.layers[il].ffn_gate_inp == nullptr) {
+            // FFN
+            cur = build_ffn(cur,
+                    model.layers[il].ffn_up,   NULL, NULL,
+                    model.layers[il].ffn_gate, NULL, NULL,
+                    model.layers[il].ffn_down, NULL, NULL,
+                    NULL,
+                    LLM_FFN_SILU, LLM_FFN_PAR, il);
+            cb(cur, "ffn_out", il);
+        } else {
+            // MoE branch
+            cur = build_moe_ffn(cur,
+                    model.layers[il].ffn_gate_inp,
+                    model.layers[il].ffn_up_exps,
+                    model.layers[il].ffn_gate_exps,
+                    model.layers[il].ffn_down_exps,
+                    nullptr,
+                    n_expert, n_expert_used,
+                    LLM_FFN_SILU, false,
+                    false, 0.0,
+                    LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
+                    il);
+            cb(cur, "ffn_moe_out", il);
+        }
+        // residual
+        cur = ggml_add(ctx0, ffn_inp, cur);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+    // final rmsnorm
+    cur = build_norm(inpL, model.output_norm, NULL, LLM_NORM_RMS, -1);
 
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
 
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
 
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
 
-        ggml_build_forward_expand(gf, cur);
+    ggml_build_forward_expand(gf, cur);
 }
diff --git a/src/models/llada-moe.cpp b/src/models/llada-moe.cpp
index 2dcef4caccc..5f64686f5fb 100644
--- a/src/models/llada-moe.cpp
+++ b/src/models/llada-moe.cpp
@@ -1,123 +1,122 @@
 #include "models.h"
 
 llm_build_llada_moe::llm_build_llada_moe(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_no_cache();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self_attention
-            {
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head, n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL, LLM_NORM_RMS, il);
-                cb(Qcur, "Qcur_normed", il);
-
-                Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, NULL, LLM_NORM_RMS, il);
-                cb(Kcur, "Kcur_normed", il);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, NULL,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // MoE branch
-            cur = build_norm(ffn_inp,
-                    model.layers[il].ffn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-
-            cur = build_moe_ffn(cur,
-                    model.layers[il].ffn_gate_inp,
-                    model.layers[il].ffn_up_exps,
-                    model.layers[il].ffn_gate_exps,
-                    model.layers[il].ffn_down_exps,
-                    nullptr,
-                    n_expert, n_expert_used,
-                    LLM_FFN_SILU, false,
-                    false, 0.0,
-                    LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
-                    il);
-            cb(cur, "ffn_moe_out", il);
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-        cur = inpL;
+    const int64_t n_embd_head = hparams.n_embd_head_v;
 
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+    GGML_ASSERT(n_embd_head == hparams.n_rot);
 
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
 
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
+    inpL = build_inp_embd(model.tok_embd);
 
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
 
-        ggml_build_forward_expand(gf, cur);
-}
+    auto * inp_attn = build_attn_inp_no_cache();
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * inpSA = inpL;
+
+        // norm
+        cur = build_norm(inpL,
+                model.layers[il].attn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
+
+        // self_attention
+        {
+            // compute Q and K and RoPE them
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            cb(Qcur, "Qcur", il);
+
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            cb(Kcur, "Kcur", il);
+
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            cb(Vcur, "Vcur", il);
+
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head, n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
 
+            Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL, LLM_NORM_RMS, il);
+            cb(Qcur, "Qcur_normed", il);
+
+            Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, NULL, LLM_NORM_RMS, il);
+            cb(Kcur, "Kcur_normed", il);
+
+            Qcur = ggml_rope_ext(
+                    ctx0, Qcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            Kcur = ggml_rope_ext(
+                    ctx0, Kcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, NULL,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+        }
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+        }
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+        cb(ffn_inp, "ffn_inp", il);
+
+        // MoE branch
+        cur = build_norm(ffn_inp,
+                model.layers[il].ffn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "ffn_norm", il);
+
+        cur = build_moe_ffn(cur,
+                model.layers[il].ffn_gate_inp,
+                model.layers[il].ffn_up_exps,
+                model.layers[il].ffn_gate_exps,
+                model.layers[il].ffn_down_exps,
+                nullptr,
+                n_expert, n_expert_used,
+                LLM_FFN_SILU, false,
+                false, 0.0,
+                LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
+                il);
+        cb(cur, "ffn_moe_out", il);
+
+        cur = ggml_add(ctx0, cur, ffn_inp);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+    cur = inpL;
+
+    cur = build_norm(cur,
+            model.output_norm, NULL,
+            LLM_NORM_RMS, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
+
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/llada.cpp b/src/models/llada.cpp
index b10b89b1f62..857033660a0 100644
--- a/src/models/llada.cpp
+++ b/src/models/llada.cpp
@@ -1,101 +1,99 @@
 #include "models.h"
 
+llm_build_llada::llm_build_llada(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+    // LLaDA is similar to LLaMA but uses non-causal attention for diffusion
+    const int64_t n_embd_head = hparams.n_embd_head_v;
 
-llm_build_llada::llm_build_llada(const llama_model & model, const llm_graph_params & params) :
-        llm_graph_context(params) {
-        // LLaDA is similar to LLaMA but uses non-causal attention for diffusion
-        const int64_t n_embd_head = hparams.n_embd_head_v;
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+    GGML_ASSERT(n_embd_head == hparams.n_rot);
 
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
 
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
+    inpL = build_inp_embd(model.tok_embd);
 
-        inpL = build_inp_embd(model.tok_embd);
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
 
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
+    // Non-causal attention for diffusion
+    auto * inp_attn = build_attn_inp_no_cache();
 
-        // Non-causal attention for diffusion
-        auto * inp_attn = build_attn_inp_no_cache();
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
 
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * inpSA = inpL;
 
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
+        // norm
+        cur = build_norm(inpL, model.layers[il].attn_norm, NULL, LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
 
-            // norm
-            cur = build_norm(inpL, model.layers[il].attn_norm, NULL, LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
+        // self-attention
+        {
+            // compute separate Q, K, V projections without bias, matching LLaDALlamaBlock
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
 
-            // self-attention
-            {
-                // compute separate Q, K, V projections without bias, matching LLaDALlamaBlock
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
 
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head, n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
 
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head, n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+            Qcur = ggml_rope_ext(ctx0, Qcur, inp_pos, nullptr, n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                                    ext_factor, attn_factor, beta_fast, beta_slow);
 
-                Qcur = ggml_rope_ext(ctx0, Qcur, inp_pos, nullptr, n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                                     ext_factor, attn_factor, beta_fast, beta_slow);
+            Kcur = ggml_rope_ext(ctx0, Kcur, inp_pos, nullptr, n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                                    ext_factor, attn_factor, beta_fast, beta_slow);
 
-                Kcur = ggml_rope_ext(ctx0, Kcur, inp_pos, nullptr, n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                                     ext_factor, attn_factor, beta_fast, beta_slow);
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
 
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, NULL,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f / sqrtf(float(n_embd_head)), il);
-            }
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0, cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, NULL,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f / sqrtf(float(n_embd_head)), il);
+        }
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0, cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+        }
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+        cb(ffn_inp, "ffn_inp", il);
 
-            // feed-forward network
-            cur = build_norm(ffn_inp, model.layers[il].ffn_norm, NULL, LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
+        // feed-forward network
+        cur = build_norm(ffn_inp, model.layers[il].ffn_norm, NULL, LLM_NORM_RMS, il);
+        cb(cur, "ffn_norm", il);
 
-            cur = build_ffn(cur,
-                    model.layers[il].ffn_up, NULL, NULL,
-                    model.layers[il].ffn_gate, NULL, NULL,
-                    model.layers[il].ffn_down, NULL, NULL,
-                    NULL, LLM_FFN_SILU, LLM_FFN_PAR, il);
-            cb(cur, "ffn_out", il);
+        cur = build_ffn(cur,
+                model.layers[il].ffn_up, NULL, NULL,
+                model.layers[il].ffn_gate, NULL, NULL,
+                model.layers[il].ffn_down, NULL, NULL,
+                NULL, LLM_FFN_SILU, LLM_FFN_PAR, il);
+        cb(cur, "ffn_out", il);
 
-            cur = ggml_add(ctx0, cur, ffn_inp);
+        cur = ggml_add(ctx0, cur, ffn_inp);
 
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
 
-            // input for next layer
-            inpL = cur;
-        }
-        cur = inpL;
+        // input for next layer
+        inpL = cur;
+    }
+    cur = inpL;
 
-        cur = build_norm(cur, model.output_norm, NULL, LLM_NORM_RMS, -1);
+    cur = build_norm(cur, model.output_norm, NULL, LLM_NORM_RMS, -1);
 
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
 
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
 
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
 
-        ggml_build_forward_expand(gf, cur);
+    ggml_build_forward_expand(gf, cur);
 }
diff --git a/src/models/llama.cpp b/src/models/llama.cpp
index 289028959f9..ab7fd5d0508 100644
--- a/src/models/llama.cpp
+++ b/src/models/llama.cpp
@@ -1,156 +1,155 @@
 #include "models.h"
 
-
 llm_build_llama::llm_build_llama(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
+    const int64_t n_embd_head = hparams.n_embd_head_v;
 
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+    GGML_ASSERT(n_embd_head == hparams.n_rot);
 
-        inpL = build_inp_embd(model.tok_embd);
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
 
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
+    inpL = build_inp_embd(model.tok_embd);
 
-        auto * inp_attn = build_attn_inp_kv();
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
 
-        const float kq_scale = hparams.f_attention_scale == 0.0f ? 1.0f/sqrtf(float(n_embd_head)) : hparams.f_attention_scale;
+    auto * inp_attn = build_attn_inp_kv();
 
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
+    const float kq_scale = hparams.f_attention_scale == 0.0f ? 1.0f/sqrtf(float(n_embd_head)) : hparams.f_attention_scale;
 
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
 
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * inpSA = inpL;
 
-            // self-attention
-            {
-                // rope freq factors for llama3; may return nullptr for llama2 and other models
-                ggml_tensor * rope_factors = model.get_rope_factors(cparams, il);
+        // norm
+        cur = build_norm(inpL,
+                model.layers[il].attn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
 
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-                if (model.layers[il].bq) {
-                    Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
-                    cb(Qcur, "Qcur", il);
-                }
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-                if (model.layers[il].bk) {
-                    Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
-                    cb(Kcur, "Kcur", il);
-                }
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-                if (model.layers[il].bv) {
-                    Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
-                    cb(Vcur, "Vcur", il);
-                }
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, rope_factors,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, rope_factors,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
+        // self-attention
+        {
+            // rope freq factors for llama3; may return nullptr for llama2 and other models
+            ggml_tensor * rope_factors = model.get_rope_factors(cparams, il);
 
+            // compute Q and K and RoPE them
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            cb(Qcur, "Qcur", il);
+            if (model.layers[il].bq) {
+                Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
                 cb(Qcur, "Qcur", il);
+            }
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            cb(Kcur, "Kcur", il);
+            if (model.layers[il].bk) {
+                Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
                 cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                if (hparams.use_kq_norm) {
-                    // Llama4TextL2Norm
-                    Qcur = ggml_rms_norm(ctx0, Qcur, hparams.f_norm_rms_eps);
-                    Kcur = ggml_rms_norm(ctx0, Kcur, hparams.f_norm_rms_eps);
-                    cb(Qcur, "Qcur_normed", il);
-                    cb(Kcur, "Kcur_normed", il);
-                }
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, kq_scale, il);
-                cb(cur, "attn_out", il);
             }
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            cb(Vcur, "Vcur", il);
+            if (model.layers[il].bv) {
+                Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
+                cb(Vcur, "Vcur", il);
             }
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed-forward network (non-MoE)
-            if (model.layers[il].ffn_gate_inp == nullptr) {
-
-                cur = build_norm(ffn_inp,
-                        model.layers[il].ffn_norm, NULL,
-                        LLM_NORM_RMS, il);
-                cb(cur, "ffn_norm", il);
-
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up,   model.layers[il].ffn_up_b,   NULL,
-                        model.layers[il].ffn_gate, model.layers[il].ffn_gate_b, NULL,
-                        model.layers[il].ffn_down, model.layers[il].ffn_down_b, NULL,
-                        NULL,
-                        LLM_FFN_SILU, LLM_FFN_PAR, il);
-                cb(cur, "ffn_out", il);
-            } else {
-                // MoE branch
-                cur = build_norm(ffn_inp,
-                        model.layers[il].ffn_norm, NULL,
-                        LLM_NORM_RMS, il);
-                cb(cur, "ffn_norm", il);
-
-                cur = build_moe_ffn(cur,
-                        model.layers[il].ffn_gate_inp,
-                        model.layers[il].ffn_up_exps,
-                        model.layers[il].ffn_gate_exps,
-                        model.layers[il].ffn_down_exps,
-                        nullptr,
-                        n_expert, n_expert_used,
-                        LLM_FFN_SILU, true,
-                        false, 0.0,
-                        LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
-                        il);
-                cb(cur, "ffn_moe_out", il);
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+            Qcur = ggml_rope_ext(
+                    ctx0, Qcur, inp_pos, rope_factors,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            Kcur = ggml_rope_ext(
+                    ctx0, Kcur, inp_pos, rope_factors,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            if (hparams.use_kq_norm) {
+                // Llama4TextL2Norm
+                Qcur = ggml_rms_norm(ctx0, Qcur, hparams.f_norm_rms_eps);
+                Kcur = ggml_rms_norm(ctx0, Kcur, hparams.f_norm_rms_eps);
+                cb(Qcur, "Qcur_normed", il);
+                cb(Kcur, "Kcur_normed", il);
             }
-            cur = ggml_add(ctx0, cur, ffn_inp);
-            cb(cur, "ffn_out", il);
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, model.layers[il].bo,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, kq_scale, il);
+            cb(cur, "attn_out", il);
+        }
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+        }
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+        cb(ffn_inp, "ffn_inp", il);
 
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
+        // feed-forward network (non-MoE)
+        if (model.layers[il].ffn_gate_inp == nullptr) {
 
-            // input for next layer
-            inpL = cur;
+            cur = build_norm(ffn_inp,
+                    model.layers[il].ffn_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "ffn_norm", il);
+
+            cur = build_ffn(cur,
+                    model.layers[il].ffn_up,   model.layers[il].ffn_up_b,   NULL,
+                    model.layers[il].ffn_gate, model.layers[il].ffn_gate_b, NULL,
+                    model.layers[il].ffn_down, model.layers[il].ffn_down_b, NULL,
+                    NULL,
+                    LLM_FFN_SILU, LLM_FFN_PAR, il);
+            cb(cur, "ffn_out", il);
+        } else {
+            // MoE branch
+            cur = build_norm(ffn_inp,
+                    model.layers[il].ffn_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "ffn_norm", il);
+
+            cur = build_moe_ffn(cur,
+                    model.layers[il].ffn_gate_inp,
+                    model.layers[il].ffn_up_exps,
+                    model.layers[il].ffn_gate_exps,
+                    model.layers[il].ffn_down_exps,
+                    nullptr,
+                    n_expert, n_expert_used,
+                    LLM_FFN_SILU, true,
+                    false, 0.0,
+                    LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
+                    il);
+            cb(cur, "ffn_moe_out", il);
         }
-        cur = inpL;
+        cur = ggml_add(ctx0, cur, ffn_inp);
+        cb(cur, "ffn_out", il);
 
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
 
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
+        // input for next layer
+        inpL = cur;
+    }
+    cur = inpL;
 
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
+    cur = build_norm(cur,
+            model.output_norm, NULL,
+            LLM_NORM_RMS, -1);
 
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
 
-        ggml_build_forward_expand(gf, cur);
-    }
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
+
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}
diff --git a/src/models/minicpm3.cpp b/src/models/minicpm3.cpp
index 02ce21ce653..f374a9fd030 100644
--- a/src/models/minicpm3.cpp
+++ b/src/models/minicpm3.cpp
@@ -1,200 +1,199 @@
 #include "models.h"
 
-
 llm_build_minicpm3::llm_build_minicpm3(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        //TODO: if the model varies, these parameters need to be read from the model
-        const int64_t n_embd_base = 256;
-        const float scale_embd  = 12.0f;
-        const float scale_depth = 1.4f;
-        const float kq_scale = 1.0f / sqrtf(float(hparams.n_embd_head_k));
+    //TODO: if the model varies, these parameters need to be read from the model
+    const int64_t n_embd_base = 256;
+    const float scale_embd  = 12.0f;
+    const float scale_depth = 1.4f;
+    const float kq_scale = 1.0f / sqrtf(float(hparams.n_embd_head_k));
+
+    const uint32_t n_embd_head_qk_rope = hparams.n_rot;
+    const uint32_t n_embd_head_qk_nope = hparams.n_embd_head_k - hparams.n_rot;
+    const uint32_t kv_lora_rank = hparams.n_lora_kv;
+
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
 
-        const uint32_t n_embd_head_qk_rope = hparams.n_rot;
-        const uint32_t n_embd_head_qk_nope = hparams.n_embd_head_k - hparams.n_rot;
-        const uint32_t kv_lora_rank = hparams.n_lora_kv;
+    inpL = build_inp_embd(model.tok_embd);
 
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
+    // scale the input embeddings
+    inpL = ggml_scale(ctx0, inpL, scale_embd);
+    cb(inpL, "inp_scaled", -1);
 
-        inpL = build_inp_embd(model.tok_embd);
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
 
-        // scale the input embeddings
-        inpL = ggml_scale(ctx0, inpL, scale_embd);
-        cb(inpL, "inp_scaled", -1);
+    auto * inp_attn = build_attn_inp_kv();
 
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
 
-        auto * inp_attn = build_attn_inp_kv();
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * inpSA = inpL;
 
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
+        ggml_tensor * rope_factors = model.get_rope_factors(cparams, il);
 
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
+        // norm
+        cur = build_norm(inpL,
+                model.layers[il].attn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
 
-            ggml_tensor * rope_factors = model.get_rope_factors(cparams, il);
+        // self_attention
+        {
+            ggml_tensor * q = NULL;
+            // {n_embd, q_lora_rank} * {n_embd, n_tokens} -> {q_lora_rank, n_tokens}
+            q = ggml_mul_mat(ctx0, model.layers[il].wq_a, cur);
+            cb(q, "q", il);
 
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
+            q = build_norm(q,
+                    model.layers[il].attn_q_a_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(q, "q", il);
+
+            // {q_lora_rank, n_head * hparams.n_embd_head_k} * {q_lora_rank, n_tokens} -> {n_head * hparams.n_embd_head_k, n_tokens}
+            q = ggml_mul_mat(ctx0, model.layers[il].wq_b, q);
+            cb(q, "q", il);
+
+            // split into {n_head * n_embd_head_qk_nope, n_tokens}
+            ggml_tensor * q_nope = ggml_view_3d(ctx0, q, n_embd_head_qk_nope, n_head, n_tokens,
+                    ggml_row_size(q->type, hparams.n_embd_head_k),
+                    ggml_row_size(q->type, hparams.n_embd_head_k * n_head),
+                    0);
+            cb(q_nope, "q_nope", il);
+
+            // and {n_head * n_embd_head_qk_rope, n_tokens}
+            ggml_tensor * q_pe = ggml_view_3d(ctx0, q, n_embd_head_qk_rope, n_head, n_tokens,
+                    ggml_row_size(q->type, hparams.n_embd_head_k),
+                    ggml_row_size(q->type, hparams.n_embd_head_k * n_head),
+                    ggml_row_size(q->type, n_embd_head_qk_nope));
+            cb(q_pe, "q_pe", il);
+
+            // {n_embd, kv_lora_rank + n_embd_head_qk_rope} * {n_embd, n_tokens} -> {kv_lora_rank + n_embd_head_qk_rope, n_tokens}
+            ggml_tensor * kv_pe_compresseed = ggml_mul_mat(ctx0, model.layers[il].wkv_a_mqa, cur);
+            cb(kv_pe_compresseed, "kv_pe_compresseed", il);
+
+            // split into {kv_lora_rank, n_tokens}
+            ggml_tensor * kv_compressed = ggml_view_2d(ctx0, kv_pe_compresseed, kv_lora_rank, n_tokens,
+                    kv_pe_compresseed->nb[1],
+                    0);
+            cb(kv_compressed, "kv_compressed", il);
+
+            // and {n_embd_head_qk_rope, n_tokens}
+            ggml_tensor * k_pe = ggml_view_3d(ctx0, kv_pe_compresseed, n_embd_head_qk_rope, 1, n_tokens,
+                    kv_pe_compresseed->nb[1],
+                    kv_pe_compresseed->nb[1],
+                    ggml_row_size(kv_pe_compresseed->type, kv_lora_rank));
+            cb(k_pe, "k_pe", il);
+
+            kv_compressed = build_norm(kv_compressed,
+                    model.layers[il].attn_kv_a_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(kv_compressed, "kv_compressed", il);
+
+            // {kv_lora_rank, n_head * (n_embd_head_qk_nope + n_embd_head_v)} * {kv_lora_rank, n_tokens} -> {n_head * (n_embd_head_qk_nope + n_embd_head_v), n_tokens}
+            ggml_tensor * kv = ggml_mul_mat(ctx0, model.layers[il].wkv_b, kv_compressed);
+            cb(kv, "kv", il);
+
+            // split into {n_head * n_embd_head_qk_nope, n_tokens}
+            ggml_tensor * k_nope = ggml_view_3d(ctx0, kv, n_embd_head_qk_nope, n_head, n_tokens,
+                    ggml_row_size(kv->type, n_embd_head_qk_nope + hparams.n_embd_head_v),
+                    ggml_row_size(kv->type, n_head * (n_embd_head_qk_nope + hparams.n_embd_head_v)),
+                    0);
+            cb(k_nope, "k_nope", il);
+
+            // and {n_head * n_embd_head_v, n_tokens}
+            ggml_tensor * v_states = ggml_view_3d(ctx0, kv, hparams.n_embd_head_v, n_head, n_tokens,
+                    ggml_row_size(kv->type, (n_embd_head_qk_nope + hparams.n_embd_head_v)),
+                    ggml_row_size(kv->type, (n_embd_head_qk_nope + hparams.n_embd_head_v)*n_head),
+                    ggml_row_size(kv->type, (n_embd_head_qk_nope)));
+            cb(v_states, "v_states", il);
+
+            v_states = ggml_cont(ctx0, v_states);
+            cb(v_states, "v_states", il);
+
+            q_pe = ggml_rope_ext(
+                    ctx0, q_pe, inp_pos, rope_factors,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+            cb(q_pe, "q_pe", il);
+
+            // shared RoPE key
+            k_pe = ggml_rope_ext(
+                    ctx0, k_pe, inp_pos, rope_factors,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+            cb(k_pe, "k_pe", il);
+
+            ggml_tensor * q_states = ggml_concat(ctx0, q_nope, q_pe, 0);
+            cb(q_states, "q_states", il);
+
+            ggml_tensor * k_states = ggml_concat(ctx0, k_nope, ggml_repeat(ctx0, k_pe, q_pe), 0);
+            cb(k_states, "k_states", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, NULL,
+                    q_states, k_states, v_states, nullptr, nullptr, nullptr, kq_scale, il);
+        }
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+        }
+        // scale_res - scale the hidden states for residual connection
+        const float scale_res = scale_depth/sqrtf(float(n_layer)); // TODO: is this correct?
+        cur = ggml_scale(ctx0, cur, scale_res);
+        cb(cur, "hidden_scaled", il);
+
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+        cb(ffn_inp, "ffn_inp", il);
+
+        // feed-forward network
+        {
+            cur = build_norm(ffn_inp,
+                    model.layers[il].ffn_norm, NULL,
                     LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self_attention
-            {
-                ggml_tensor * q = NULL;
-                // {n_embd, q_lora_rank} * {n_embd, n_tokens} -> {q_lora_rank, n_tokens}
-                q = ggml_mul_mat(ctx0, model.layers[il].wq_a, cur);
-                cb(q, "q", il);
-
-                q = build_norm(q,
-                        model.layers[il].attn_q_a_norm, NULL,
-                        LLM_NORM_RMS, il);
-                cb(q, "q", il);
-
-                // {q_lora_rank, n_head * hparams.n_embd_head_k} * {q_lora_rank, n_tokens} -> {n_head * hparams.n_embd_head_k, n_tokens}
-                q = ggml_mul_mat(ctx0, model.layers[il].wq_b, q);
-                cb(q, "q", il);
-
-                // split into {n_head * n_embd_head_qk_nope, n_tokens}
-                ggml_tensor * q_nope = ggml_view_3d(ctx0, q, n_embd_head_qk_nope, n_head, n_tokens,
-                        ggml_row_size(q->type, hparams.n_embd_head_k),
-                        ggml_row_size(q->type, hparams.n_embd_head_k * n_head),
-                        0);
-                cb(q_nope, "q_nope", il);
-
-                // and {n_head * n_embd_head_qk_rope, n_tokens}
-                ggml_tensor * q_pe = ggml_view_3d(ctx0, q, n_embd_head_qk_rope, n_head, n_tokens,
-                        ggml_row_size(q->type, hparams.n_embd_head_k),
-                        ggml_row_size(q->type, hparams.n_embd_head_k * n_head),
-                        ggml_row_size(q->type, n_embd_head_qk_nope));
-                cb(q_pe, "q_pe", il);
-
-                // {n_embd, kv_lora_rank + n_embd_head_qk_rope} * {n_embd, n_tokens} -> {kv_lora_rank + n_embd_head_qk_rope, n_tokens}
-                ggml_tensor * kv_pe_compresseed = ggml_mul_mat(ctx0, model.layers[il].wkv_a_mqa, cur);
-                cb(kv_pe_compresseed, "kv_pe_compresseed", il);
-
-                // split into {kv_lora_rank, n_tokens}
-                ggml_tensor * kv_compressed = ggml_view_2d(ctx0, kv_pe_compresseed, kv_lora_rank, n_tokens,
-                        kv_pe_compresseed->nb[1],
-                        0);
-                cb(kv_compressed, "kv_compressed", il);
-
-                // and {n_embd_head_qk_rope, n_tokens}
-                ggml_tensor * k_pe = ggml_view_3d(ctx0, kv_pe_compresseed, n_embd_head_qk_rope, 1, n_tokens,
-                        kv_pe_compresseed->nb[1],
-                        kv_pe_compresseed->nb[1],
-                        ggml_row_size(kv_pe_compresseed->type, kv_lora_rank));
-                cb(k_pe, "k_pe", il);
-
-                kv_compressed = build_norm(kv_compressed,
-                        model.layers[il].attn_kv_a_norm, NULL,
-                        LLM_NORM_RMS, il);
-                cb(kv_compressed, "kv_compressed", il);
-
-                // {kv_lora_rank, n_head * (n_embd_head_qk_nope + n_embd_head_v)} * {kv_lora_rank, n_tokens} -> {n_head * (n_embd_head_qk_nope + n_embd_head_v), n_tokens}
-                ggml_tensor * kv = ggml_mul_mat(ctx0, model.layers[il].wkv_b, kv_compressed);
-                cb(kv, "kv", il);
-
-                // split into {n_head * n_embd_head_qk_nope, n_tokens}
-                ggml_tensor * k_nope = ggml_view_3d(ctx0, kv, n_embd_head_qk_nope, n_head, n_tokens,
-                        ggml_row_size(kv->type, n_embd_head_qk_nope + hparams.n_embd_head_v),
-                        ggml_row_size(kv->type, n_head * (n_embd_head_qk_nope + hparams.n_embd_head_v)),
-                        0);
-                cb(k_nope, "k_nope", il);
-
-                // and {n_head * n_embd_head_v, n_tokens}
-                ggml_tensor * v_states = ggml_view_3d(ctx0, kv, hparams.n_embd_head_v, n_head, n_tokens,
-                        ggml_row_size(kv->type, (n_embd_head_qk_nope + hparams.n_embd_head_v)),
-                        ggml_row_size(kv->type, (n_embd_head_qk_nope + hparams.n_embd_head_v)*n_head),
-                        ggml_row_size(kv->type, (n_embd_head_qk_nope)));
-                cb(v_states, "v_states", il);
-
-                v_states = ggml_cont(ctx0, v_states);
-                cb(v_states, "v_states", il);
-
-                q_pe = ggml_rope_ext(
-                        ctx0, q_pe, inp_pos, rope_factors,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-                cb(q_pe, "q_pe", il);
-
-                // shared RoPE key
-                k_pe = ggml_rope_ext(
-                        ctx0, k_pe, inp_pos, rope_factors,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-                cb(k_pe, "k_pe", il);
-
-                ggml_tensor * q_states = ggml_concat(ctx0, q_nope, q_pe, 0);
-                cb(q_states, "q_states", il);
-
-                ggml_tensor * k_states = ggml_concat(ctx0, k_nope, ggml_repeat(ctx0, k_pe, q_pe), 0);
-                cb(k_states, "k_states", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, NULL,
-                        q_states, k_states, v_states, nullptr, nullptr, nullptr, kq_scale, il);
-            }
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-            // scale_res - scale the hidden states for residual connection
-            const float scale_res = scale_depth/sqrtf(float(n_layer)); // TODO: is this correct?
-            cur = ggml_scale(ctx0, cur, scale_res);
-            cb(cur, "hidden_scaled", il);
-
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed-forward network
-            {
-                cur = build_norm(ffn_inp,
-                        model.layers[il].ffn_norm, NULL,
-                        LLM_NORM_RMS, il);
-                cb(cur, "ffn_norm", il);
-
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up,   NULL, NULL,
-                        model.layers[il].ffn_gate, NULL, NULL,
-                        model.layers[il].ffn_down, NULL, NULL,
-                        NULL,
-                        LLM_FFN_SILU, LLM_FFN_PAR, il);
-                cb(cur, "ffn_out", il);
-            }
-            // scale the hidden states for residual connection
-            cur = ggml_scale(ctx0, cur, scale_res);
-            cb(cur, "hidden_scaled_ffn", il);
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
+            cb(cur, "ffn_norm", il);
+
+            cur = build_ffn(cur,
+                    model.layers[il].ffn_up,   NULL, NULL,
+                    model.layers[il].ffn_gate, NULL, NULL,
+                    model.layers[il].ffn_down, NULL, NULL,
+                    NULL,
+                    LLM_FFN_SILU, LLM_FFN_PAR, il);
+            cb(cur, "ffn_out", il);
         }
-        cur = inpL;
+        // scale the hidden states for residual connection
+        cur = ggml_scale(ctx0, cur, scale_res);
+        cb(cur, "hidden_scaled_ffn", il);
+
+        cur = ggml_add(ctx0, cur, ffn_inp);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+    cur = inpL;
 
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
+    cur = build_norm(cur,
+            model.output_norm, NULL,
+            LLM_NORM_RMS, -1);
 
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
 
-        // lm_head scaling
-        const float scale_lmhead = float(n_embd_base)/float(n_embd);
-        cur = ggml_scale(ctx0, cur, scale_lmhead);
-        cb(cur, "lmhead_scaling", -1);
+    // lm_head scaling
+    const float scale_lmhead = float(n_embd_base)/float(n_embd);
+    cur = ggml_scale(ctx0, cur, scale_lmhead);
+    cb(cur, "lmhead_scaling", -1);
 
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
 
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
 
-        ggml_build_forward_expand(gf, cur);
+    ggml_build_forward_expand(gf, cur);
 }
diff --git a/src/models/nemotron.cpp b/src/models/nemotron.cpp
index 781aa719393..fcead041f0a 100644
--- a/src/models/nemotron.cpp
+++ b/src/models/nemotron.cpp
@@ -1,122 +1,122 @@
 #include "models.h"
 
 llm_build_nemotron::llm_build_nemotron(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
+    const int64_t n_embd_head = hparams.n_embd_head_v;
 
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        //GGML_ASSERT(n_embd_head == hparams.n_rot);
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+    //GGML_ASSERT(n_embd_head == hparams.n_rot);
 
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
 
-        inpL = build_inp_embd(model.tok_embd);
+    inpL = build_inp_embd(model.tok_embd);
 
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
 
-        auto * inp_attn = build_attn_inp_kv();
+    auto * inp_attn = build_attn_inp_kv();
 
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
 
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * inpSA = inpL;
 
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm,
-                    model.layers[il].attn_norm_b,
-                    LLM_NORM, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-                if (model.layers[il].bq) {
-                    Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
-                    cb(Qcur, "Qcur", il);
-                }
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-                if (model.layers[il].bk) {
-                    Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
-                    cb(Kcur, "Kcur", il);
-                }
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-                if (model.layers[il].bv) {
-                    Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
-                    cb(Vcur, "Vcur", il);
-                }
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
+        // norm
+        cur = build_norm(inpL,
+                model.layers[il].attn_norm,
+                model.layers[il].attn_norm_b,
+                LLM_NORM, il);
+        cb(cur, "attn_norm", il);
 
+        // self-attention
+        {
+            // compute Q and K and RoPE them
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            cb(Qcur, "Qcur", il);
+            if (model.layers[il].bq) {
+                Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
                 cb(Qcur, "Qcur", il);
+            }
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            cb(Kcur, "Kcur", il);
+            if (model.layers[il].bk) {
+                Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
                 cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
             }
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            cb(Vcur, "Vcur", il);
+            if (model.layers[il].bv) {
+                Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
+                cb(Vcur, "Vcur", il);
             }
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed-forward network
-            cur = build_norm(ffn_inp,
-                    model.layers[il].ffn_norm,
-                    model.layers[il].ffn_norm_b,
-                    LLM_NORM, il);
-            cb(cur, "ffn_norm", il);
-
-            cur = build_ffn(cur,
-                    model.layers[il].ffn_up,   model.layers[il].ffn_up_b,   NULL,
-                    NULL,                      NULL,                        NULL,
-                    model.layers[il].ffn_down, model.layers[il].ffn_down_b, NULL,
-                    NULL,
-                    LLM_FFN_RELU_SQR, LLM_FFN_SEQ, il);
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-            cb(cur, "ffn_out", il);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+            Qcur = ggml_rope_ext(
+                    ctx0, Qcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            Kcur = ggml_rope_ext(
+                    ctx0, Kcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, model.layers[il].bo,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+        }
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
         }
-        cur = inpL;
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+        cb(ffn_inp, "ffn_inp", il);
+
+        // feed-forward network
+        cur = build_norm(ffn_inp,
+                model.layers[il].ffn_norm,
+                model.layers[il].ffn_norm_b,
+                LLM_NORM, il);
+        cb(cur, "ffn_norm", il);
+
+        cur = build_ffn(cur,
+                model.layers[il].ffn_up,   model.layers[il].ffn_up_b,   NULL,
+                NULL,                      NULL,                        NULL,
+                model.layers[il].ffn_down, model.layers[il].ffn_down_b, NULL,
+                NULL,
+                LLM_FFN_RELU_SQR, LLM_FFN_SEQ, il);
+
+        cur = ggml_add(ctx0, cur, ffn_inp);
+        cb(cur, "ffn_out", il);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+    cur = inpL;
 
-        cur = build_norm(cur,
-                model.output_norm, model.output_norm_b,
-                LLM_NORM, -1);
+    cur = build_norm(cur,
+            model.output_norm, model.output_norm_b,
+            LLM_NORM, -1);
 
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
 
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
 
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
 
-        ggml_build_forward_expand(gf, cur);
+    ggml_build_forward_expand(gf, cur);
 }
diff --git a/src/models/neo-bert.cpp b/src/models/neo-bert.cpp
index b05c79025bb..7c32bfca5f5 100644
--- a/src/models/neo-bert.cpp
+++ b/src/models/neo-bert.cpp
@@ -1,104 +1,104 @@
 #include "models.h"
 
 llm_build_neo_bert::llm_build_neo_bert(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-        const int64_t n_embd_gqa  = hparams.n_embd_v_gqa();
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        // construct input embeddings (token, type, position)
-        inpL = build_inp_embd(model.tok_embd);
-        cb(inpL, "inp_embd", -1);
-
-        auto * inp_attn = build_attn_inp_no_cache();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * cur = inpL;
-
-            // pre-norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-
-            {
-                ggml_tensor * Qcur;
-                ggml_tensor * Kcur;
-                ggml_tensor * Vcur;
-
-                // self-attention
-                cur = build_lora_mm(model.layers[il].wqkv, cur);
-                cb(cur, "wqkv", il);
-
-                Qcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head,    n_tokens, n_embd_head*sizeof(float), cur->nb[1], 0*sizeof(float)*(n_embd));
-                Kcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd));
-                Vcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd + n_embd_gqa));
-
-                // RoPE
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, nullptr,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-                cb(cur, "kqv_out", il);
-            }
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur  = ggml_get_rows(ctx0,  cur, inp_out_ids);
-                inpL = ggml_get_rows(ctx0, inpL, inp_out_ids);
-            }
-            // re-add the layer input
-            cur = ggml_add(ctx0, cur, inpL);
-
-            ggml_tensor * ffn_inp = cur;
-            cb(ffn_inp, "ffn_inp", il);
-
-            // pre-norm
-            cur = build_norm(ffn_inp,
-                    model.layers[il].ffn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-
-            // feed-forward network
-            cur = build_ffn(cur,
-                    model.layers[il].ffn_up,
-                    NULL, NULL, NULL, NULL, NULL,
-                    model.layers[il].ffn_down,
-                    NULL, NULL, NULL,
-                    LLM_FFN_SWIGLU, LLM_FFN_SEQ, il);
-
-            // attentions bypass the intermediate layer
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            // input for next layer
-            inpL = cur;
-        }
-        cur = inpL;
+    const int64_t n_embd_head = hparams.n_embd_head_v;
+    const int64_t n_embd_gqa  = hparams.n_embd_v_gqa();
+
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+    ggml_tensor * inp_pos = build_inp_pos();
+
+    // construct input embeddings (token, type, position)
+    inpL = build_inp_embd(model.tok_embd);
+    cb(inpL, "inp_embd", -1);
+
+    auto * inp_attn = build_attn_inp_no_cache();
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * cur = inpL;
 
-        cur = build_norm(cur,
-                model.output_norm_enc, NULL,
-                LLM_NORM_RMS, -1);
+        // pre-norm
+        cur = build_norm(inpL,
+                model.layers[il].attn_norm, NULL,
+                LLM_NORM_RMS, il);
 
-        cb(cur, "result_embd", -1);
-        res->t_embd = cur;
+        {
+            ggml_tensor * Qcur;
+            ggml_tensor * Kcur;
+            ggml_tensor * Vcur;
 
-        ggml_build_forward_expand(gf, cur);
+            // self-attention
+            cur = build_lora_mm(model.layers[il].wqkv, cur);
+            cb(cur, "wqkv", il);
+
+            Qcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head,    n_tokens, n_embd_head*sizeof(float), cur->nb[1], 0*sizeof(float)*(n_embd));
+            Kcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd));
+            Vcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd + n_embd_gqa));
+
+            // RoPE
+            Qcur = ggml_rope_ext(
+                    ctx0, Qcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            Kcur = ggml_rope_ext(
+                    ctx0, Kcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, nullptr,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+            cb(cur, "kqv_out", il);
+        }
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur  = ggml_get_rows(ctx0,  cur, inp_out_ids);
+            inpL = ggml_get_rows(ctx0, inpL, inp_out_ids);
+        }
+        // re-add the layer input
+        cur = ggml_add(ctx0, cur, inpL);
+
+        ggml_tensor * ffn_inp = cur;
+        cb(ffn_inp, "ffn_inp", il);
+
+        // pre-norm
+        cur = build_norm(ffn_inp,
+                model.layers[il].ffn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "ffn_norm", il);
+
+        // feed-forward network
+        cur = build_ffn(cur,
+                model.layers[il].ffn_up,
+                NULL, NULL, NULL, NULL, NULL,
+                model.layers[il].ffn_down,
+                NULL, NULL, NULL,
+                LLM_FFN_SWIGLU, LLM_FFN_SEQ, il);
+
+        // attentions bypass the intermediate layer
+        cur = ggml_add(ctx0, cur, ffn_inp);
+
+        // input for next layer
+        inpL = cur;
+    }
+    cur = inpL;
+
+    cur = build_norm(cur,
+            model.output_norm_enc, NULL,
+            LLM_NORM_RMS, -1);
+
+    cb(cur, "result_embd", -1);
+    res->t_embd = cur;
+
+    ggml_build_forward_expand(gf, cur);
 }
diff --git a/src/models/olmo.cpp b/src/models/olmo.cpp
index e15d716536d..bbd623f1112 100644
--- a/src/models/olmo.cpp
+++ b/src/models/olmo.cpp
@@ -1,121 +1,121 @@
 #include "models.h"
 
 llm_build_olmo::llm_build_olmo(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
+    const int64_t n_embd_head = hparams.n_embd_head_v;
 
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+    GGML_ASSERT(n_embd_head == hparams.n_rot);
 
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
 
-        inpL = build_inp_embd(model.tok_embd);
+    inpL = build_inp_embd(model.tok_embd);
 
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
 
-        auto * inp_attn = build_attn_inp_kv();
+    auto * inp_attn = build_attn_inp_kv();
 
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
 
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            // norm
-            cur = build_norm(inpL,
-                    NULL, NULL,
-                    LLM_NORM, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-                if (hparams.f_clamp_kqv > 0.0f) {
-                    Qcur = ggml_clamp(ctx0, Qcur, -hparams.f_clamp_kqv, hparams.f_clamp_kqv);
-                    cb(Qcur, "Qcur", il);
-                }
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-                if (hparams.f_clamp_kqv > 0.0f) {
-                    Kcur = ggml_clamp(ctx0, Kcur, -hparams.f_clamp_kqv, hparams.f_clamp_kqv);
-                    cb(Kcur, "Kcur", il);
-                }
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-                if (hparams.f_clamp_kqv > 0.0f) {
-                    Vcur = ggml_clamp(ctx0, Vcur, -hparams.f_clamp_kqv, hparams.f_clamp_kqv);
-                    cb(Vcur, "Vcur", il);
-                }
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * inpSA = inpL;
 
+        // norm
+        cur = build_norm(inpL,
+                NULL, NULL,
+                LLM_NORM, il);
+        cb(cur, "attn_norm", il);
+
+        // self-attention
+        {
+            // compute Q and K and RoPE them
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            cb(Qcur, "Qcur", il);
+            if (hparams.f_clamp_kqv > 0.0f) {
+                Qcur = ggml_clamp(ctx0, Qcur, -hparams.f_clamp_kqv, hparams.f_clamp_kqv);
                 cb(Qcur, "Qcur", il);
+            }
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            cb(Kcur, "Kcur", il);
+            if (hparams.f_clamp_kqv > 0.0f) {
+                Kcur = ggml_clamp(ctx0, Kcur, -hparams.f_clamp_kqv, hparams.f_clamp_kqv);
                 cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, nullptr,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
             }
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            cb(Vcur, "Vcur", il);
+            if (hparams.f_clamp_kqv > 0.0f) {
+                Vcur = ggml_clamp(ctx0, Vcur, -hparams.f_clamp_kqv, hparams.f_clamp_kqv);
+                cb(Vcur, "Vcur", il);
             }
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed-forward network
-            cur = build_norm(ffn_inp,
-                    NULL, NULL,
-                    LLM_NORM, il);
-            cb(cur, "ffn_norm", il);
-
-            cur = build_ffn(cur,
-                    model.layers[il].ffn_up,   NULL, NULL,
-                    model.layers[il].ffn_gate, NULL, NULL,
-                    model.layers[il].ffn_down, NULL, NULL,
-                    NULL,
-                    LLM_FFN_SILU, LLM_FFN_PAR, il);
-            cb(cur, "ffn_out", il);
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-            cb(cur, "ffn_out", il);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+            Qcur = ggml_rope_ext(
+                    ctx0, Qcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            Kcur = ggml_rope_ext(
+                    ctx0, Kcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, nullptr,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
         }
-        cur = inpL;
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+        }
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+        cb(ffn_inp, "ffn_inp", il);
 
-        cur = build_norm(cur,
+        // feed-forward network
+        cur = build_norm(ffn_inp,
                 NULL, NULL,
-                LLM_NORM, -1);
+                LLM_NORM, il);
+        cb(cur, "ffn_norm", il);
+
+        cur = build_ffn(cur,
+                model.layers[il].ffn_up,   NULL, NULL,
+                model.layers[il].ffn_gate, NULL, NULL,
+                model.layers[il].ffn_down, NULL, NULL,
+                NULL,
+                LLM_FFN_SILU, LLM_FFN_PAR, il);
+        cb(cur, "ffn_out", il);
+
+        cur = ggml_add(ctx0, cur, ffn_inp);
+        cb(cur, "ffn_out", il);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+    cur = inpL;
+
+    cur = build_norm(cur,
+            NULL, NULL,
+            LLM_NORM, -1);
 
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
 
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
 
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
 
-        ggml_build_forward_expand(gf, cur);
+    ggml_build_forward_expand(gf, cur);
 }
diff --git a/src/models/olmo2.cpp b/src/models/olmo2.cpp
index b05a3f9b4b0..713552dab89 100644
--- a/src/models/olmo2.cpp
+++ b/src/models/olmo2.cpp
@@ -1,150 +1,149 @@
 #include "models.h"
 
-
 template <bool iswa>
 llm_build_olmo2<iswa>::llm_build_olmo2(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
+    const int64_t n_embd_head = hparams.n_embd_head_v;
 
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+    GGML_ASSERT(n_embd_head == hparams.n_rot);
 
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
 
-        inpL = build_inp_embd(model.tok_embd);
+    inpL = build_inp_embd(model.tok_embd);
 
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
 
-        using inp_attn_type = std::conditional_t<iswa, llm_graph_input_attn_kv_iswa, llm_graph_input_attn_kv>;
-        inp_attn_type * inp_attn = nullptr;
+    using inp_attn_type = std::conditional_t<iswa, llm_graph_input_attn_kv_iswa, llm_graph_input_attn_kv>;
+    inp_attn_type * inp_attn = nullptr;
 
-        if constexpr (iswa) {
-            inp_attn = build_attn_inp_kv_iswa();
-        } else {
-            inp_attn = build_attn_inp_kv();
-        }
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            cur = inpL;
-
-            // self_attention
-            {
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-
-                Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL,
-                        LLM_NORM_RMS, il);
-                cb(Qcur, "Qcur_normed", il);
-
-                Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, NULL,
-                        LLM_NORM_RMS, il);
-                cb(Kcur, "Kcur_normed", il);
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                const bool is_swa = hparams.is_swa(il);
-
-                if (is_swa) {
-                    // For sliding window layers, Olmo3 use regular rope with no yarn rope scaling.
-                    // This is achieved here by setting freq_scale and attn_factor to 1.
-                    // We also set ext_factor to 0 to avoid a few unnecessary computations.
-                    Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, 1.0,
-                        0.0, 1.0, beta_fast, beta_slow
-                        );
-
-                    Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, 1.0,
-                        0.0, 1.0, beta_fast, beta_slow
-                        );
-                } else {
-                    Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                    Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-                }
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, NULL,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-            cur = build_norm(cur,
-                    model.layers[il].attn_post_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_post_norm", il);
+    if constexpr (iswa) {
+        inp_attn = build_attn_inp_kv_iswa();
+    } else {
+        inp_attn = build_attn_inp_kv();
+    }
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
 
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * inpSA = inpL;
 
-            // feed-forward network
-            cur = build_ffn(ffn_inp,
-                    model.layers[il].ffn_up,   NULL, NULL,
-                    model.layers[il].ffn_gate, NULL, NULL,
-                    model.layers[il].ffn_down, NULL, NULL,
-                    NULL,
-                    LLM_FFN_SILU, LLM_FFN_PAR, il);
-            cb(cur, "ffn_out", il);
+        cur = inpL;
+
+        // self_attention
+        {
+            // compute Q and K and RoPE them
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            cb(Qcur, "Qcur", il);
 
-            cur = build_norm(cur,
-                    model.layers[il].ffn_post_norm, NULL,
-                    LLM_NORM_RMS, -1);
-            cb(cur, "ffn_post_norm", -1);
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            cb(Kcur, "Kcur", il);
 
-            cur = ggml_add(ctx0, cur, ffn_inp);
-            cb(cur, "ffn_out", il);
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            cb(Vcur, "Vcur", il);
 
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
+            Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(Qcur, "Qcur_normed", il);
 
-            // input for next layer
-            inpL = cur;
+            Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(Kcur, "Kcur_normed", il);
+
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+            const bool is_swa = hparams.is_swa(il);
+
+            if (is_swa) {
+                // For sliding window layers, Olmo3 use regular rope with no yarn rope scaling.
+                // This is achieved here by setting freq_scale and attn_factor to 1.
+                // We also set ext_factor to 0 to avoid a few unnecessary computations.
+                Qcur = ggml_rope_ext(
+                    ctx0, Qcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, 1.0,
+                    0.0, 1.0, beta_fast, beta_slow
+                    );
+
+                Kcur = ggml_rope_ext(
+                    ctx0, Kcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, 1.0,
+                    0.0, 1.0, beta_fast, beta_slow
+                    );
+            } else {
+                Qcur = ggml_rope_ext(
+                    ctx0, Qcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+                Kcur = ggml_rope_ext(
+                    ctx0, Kcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+            }
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, NULL,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
         }
-        cur = inpL;
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+        }
+        cur = build_norm(cur,
+                model.layers[il].attn_post_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "attn_post_norm", il);
+
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+        cb(ffn_inp, "ffn_inp", il);
+
+        // feed-forward network
+        cur = build_ffn(ffn_inp,
+                model.layers[il].ffn_up,   NULL, NULL,
+                model.layers[il].ffn_gate, NULL, NULL,
+                model.layers[il].ffn_down, NULL, NULL,
+                NULL,
+                LLM_FFN_SILU, LLM_FFN_PAR, il);
+        cb(cur, "ffn_out", il);
 
         cur = build_norm(cur,
-                model.output_norm, NULL,
+                model.layers[il].ffn_post_norm, NULL,
                 LLM_NORM_RMS, -1);
+        cb(cur, "ffn_post_norm", -1);
 
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
+        cur = ggml_add(ctx0, cur, ffn_inp);
+        cb(cur, "ffn_out", il);
 
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
 
-        ggml_build_forward_expand(gf, cur);
+        // input for next layer
+        inpL = cur;
     }
+    cur = inpL;
+
+    cur = build_norm(cur,
+            model.output_norm, NULL,
+            LLM_NORM_RMS, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
+
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}
 
 // Explicit template instantiations
 template struct llm_build_olmo2<false>;
diff --git a/src/models/olmoe.cpp b/src/models/olmoe.cpp
index 49f51f9724c..b8b6988f897 100644
--- a/src/models/olmoe.cpp
+++ b/src/models/olmoe.cpp
@@ -1,124 +1,124 @@
 #include "models.h"
 
 llm_build_olmoe::llm_build_olmoe(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
+    const int64_t n_embd_head = hparams.n_embd_head_v;
 
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+    GGML_ASSERT(n_embd_head == hparams.n_rot);
 
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
 
-        inpL = build_inp_embd(model.tok_embd);
+    inpL = build_inp_embd(model.tok_embd);
 
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
 
-        auto * inp_attn = build_attn_inp_kv();
+    auto * inp_attn = build_attn_inp_kv();
 
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
 
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * inpSA = inpL;
 
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self_attention
-            {
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-
-                Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL,
-                        LLM_NORM_RMS, il);
-                cb(Qcur, "Qcur_normed", il);
-
-                Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, NULL,
-                        LLM_NORM_RMS, il);
-                cb(Kcur, "Kcur_normed", il);
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, NULL,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // MoE branch
-            cur = build_norm(ffn_inp,
-                    model.layers[il].ffn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-
-            cur = build_moe_ffn(cur,
-                    model.layers[il].ffn_gate_inp,
-                    model.layers[il].ffn_up_exps,
-                    model.layers[il].ffn_gate_exps,
-                    model.layers[il].ffn_down_exps,
-                    nullptr,
-                    n_expert, n_expert_used,
-                    LLM_FFN_SILU, false,
-                    false, 0.0,
-                    LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
-                    il);
-            cb(cur, "ffn_moe_out", il);
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-        cur = inpL;
+        // norm
+        cur = build_norm(inpL,
+                model.layers[il].attn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
 
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
+        // self_attention
+        {
+            // compute Q and K and RoPE them
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            cb(Qcur, "Qcur", il);
 
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            cb(Kcur, "Kcur", il);
 
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            cb(Vcur, "Vcur", il);
 
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
+            Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(Qcur, "Qcur_normed", il);
 
-        ggml_build_forward_expand(gf, cur);
+            Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(Kcur, "Kcur_normed", il);
+
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+            Qcur = ggml_rope_ext(
+                    ctx0, Qcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            Kcur = ggml_rope_ext(
+                    ctx0, Kcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, NULL,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+        }
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+        }
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+        cb(ffn_inp, "ffn_inp", il);
+
+        // MoE branch
+        cur = build_norm(ffn_inp,
+                model.layers[il].ffn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "ffn_norm", il);
+
+        cur = build_moe_ffn(cur,
+                model.layers[il].ffn_gate_inp,
+                model.layers[il].ffn_up_exps,
+                model.layers[il].ffn_gate_exps,
+                model.layers[il].ffn_down_exps,
+                nullptr,
+                n_expert, n_expert_used,
+                LLM_FFN_SILU, false,
+                false, 0.0,
+                LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
+                il);
+        cb(cur, "ffn_moe_out", il);
+
+        cur = ggml_add(ctx0, cur, ffn_inp);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+    cur = inpL;
+
+    cur = build_norm(cur,
+            model.output_norm, NULL,
+            LLM_NORM_RMS, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
+
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
 }
diff --git a/src/models/openai-moe-iswa.cpp b/src/models/openai-moe-iswa.cpp
index 14e55eeb7a9..3c0c0eecf5d 100644
--- a/src/models/openai-moe-iswa.cpp
+++ b/src/models/openai-moe-iswa.cpp
@@ -1,123 +1,123 @@
 #include "models.h"
 
 llm_build_openai_moe_iswa::llm_build_openai_moe_iswa(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
 
-        inpL = build_inp_embd(model.tok_embd);
+    inpL = build_inp_embd(model.tok_embd);
 
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
 
-        auto * inp_attn = build_attn_inp_kv_iswa();
+    auto * inp_attn = build_attn_inp_kv_iswa();
 
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * inpSA = inpL;
 
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, nullptr,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-                if (model.layers[il].bq) {
-                    Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
-                    cb(Qcur, "Qcur", il);
-                }
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-                if (model.layers[il].bk) {
-                    Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
-                    cb(Kcur, "Kcur", il);
-                }
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-                if (model.layers[il].bv) {
-                    Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
-                    cb(Vcur, "Vcur", il);
-                }
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_rot, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_rot, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_rot, n_head_kv, n_tokens);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
+        // norm
+        cur = build_norm(inpL,
+                model.layers[il].attn_norm, nullptr,
+                LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
 
+        // self-attention
+        {
+            // compute Q and K and RoPE them
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            cb(Qcur, "Qcur", il);
+            if (model.layers[il].bq) {
+                Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
                 cb(Qcur, "Qcur", il);
+            }
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            cb(Kcur, "Kcur", il);
+            if (model.layers[il].bk) {
+                Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
                 cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, model.layers[il].attn_sinks, nullptr, 1.0f/sqrtf(float(n_rot)), il);
-
-                cb(cur, "attn_out", il);
             }
-            if (il == n_layer - 1) {
-                // skip computing output for unused tokens
-                ggml_tensor * inp_out_ids = build_inp_out_ids();
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            cb(Vcur, "Vcur", il);
+            if (model.layers[il].bv) {
+                Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
+                cb(Vcur, "Vcur", il);
             }
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            cur = ffn_inp;
-            cur = build_norm(cur,
-                    model.layers[il].attn_post_norm, nullptr,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_post_norm", il);
-
-            // MoE branch
-            cur = build_moe_ffn(cur,
-                    model.layers[il].ffn_gate_inp,  model.layers[il].ffn_gate_inp_b,
-                    model.layers[il].ffn_up_exps,   model.layers[il].ffn_up_exps_b,
-                    model.layers[il].ffn_gate_exps, model.layers[il].ffn_gate_exps_b,
-                    model.layers[il].ffn_down_exps, model.layers[il].ffn_down_exps_b,
-                    nullptr,
-                    n_expert, n_expert_used,
-                    LLM_FFN_SWIGLU_OAI_MOE, false,
-                    false, 0.0,
-                    LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX_WEIGHT,
-                    il);
-            cb(cur, "ffn_moe_out", il);
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_rot, n_head,    n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_rot, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_rot, n_head_kv, n_tokens);
+
+            Qcur = ggml_rope_ext(
+                    ctx0, Qcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            Kcur = ggml_rope_ext(
+                    ctx0, Kcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, model.layers[il].bo,
+                    Qcur, Kcur, Vcur, nullptr, model.layers[il].attn_sinks, nullptr, 1.0f/sqrtf(float(n_rot)), il);
+
+            cb(cur, "attn_out", il);
         }
-        cur = inpL;
+        if (il == n_layer - 1) {
+            // skip computing output for unused tokens
+            ggml_tensor * inp_out_ids = build_inp_out_ids();
+            cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+        }
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+        cb(ffn_inp, "ffn_inp", il);
 
+        cur = ffn_inp;
         cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
-
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
-
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
-
-        ggml_build_forward_expand(gf, cur);
+                model.layers[il].attn_post_norm, nullptr,
+                LLM_NORM_RMS, il);
+        cb(cur, "attn_post_norm", il);
+
+        // MoE branch
+        cur = build_moe_ffn(cur,
+                model.layers[il].ffn_gate_inp,  model.layers[il].ffn_gate_inp_b,
+                model.layers[il].ffn_up_exps,   model.layers[il].ffn_up_exps_b,
+                model.layers[il].ffn_gate_exps, model.layers[il].ffn_gate_exps_b,
+                model.layers[il].ffn_down_exps, model.layers[il].ffn_down_exps_b,
+                nullptr,
+                n_expert, n_expert_used,
+                LLM_FFN_SWIGLU_OAI_MOE, false,
+                false, 0.0,
+                LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX_WEIGHT,
+                il);
+        cb(cur, "ffn_moe_out", il);
+
+        cur = ggml_add(ctx0, cur, ffn_inp);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+    cur = inpL;
+
+    cur = build_norm(cur,
+            model.output_norm, NULL,
+            LLM_NORM_RMS, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
+
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
 }
diff --git a/src/models/openelm.cpp b/src/models/openelm.cpp
index a16a459f3fa..ee46a3375e8 100644
--- a/src/models/openelm.cpp
+++ b/src/models/openelm.cpp
@@ -1,124 +1,124 @@
 #include "models.h"
 
 llm_build_openelm::llm_build_openelm(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
+    const int64_t n_embd_head = hparams.n_embd_head_v;
 
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
 
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-        inpL = build_inp_embd(model.tok_embd);
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+    inpL = build_inp_embd(model.tok_embd);
 
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
 
-        auto * inp_attn = build_attn_inp_kv();
+    auto * inp_attn = build_attn_inp_kv();
 
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
 
-        for (int il = 0; il < n_layer; ++il) {
-            const int64_t n_head    = hparams.n_head(il);
-            const int64_t n_head_kv = hparams.n_head_kv(il);
-            const int64_t n_head_qkv = 2*n_head_kv + n_head;
+    for (int il = 0; il < n_layer; ++il) {
+        const int64_t n_head    = hparams.n_head(il);
+        const int64_t n_head_kv = hparams.n_head_kv(il);
+        const int64_t n_head_qkv = 2*n_head_kv + n_head;
 
-            cur = inpL;
-            ggml_tensor * residual = cur;
+        cur = inpL;
+        ggml_tensor * residual = cur;
+
+        // norm
+        cur = build_norm(inpL,
+                model.layers[il].attn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
+
+        // self-attention
+        {
+            cur = build_lora_mm(model.layers[il].wqkv, cur);
+            cb(cur, "wqkv", il);
+
+            cur = ggml_reshape_3d(ctx0, cur, n_embd_head_k, n_head_qkv, n_tokens);
+
+            ggml_tensor * Qcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head,    n_tokens, cur->nb[1], cur->nb[2], 0);
+            cb(Qcur, "Qcur", il);
+
+            ggml_tensor * Kcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, cur->nb[1], cur->nb[2], cur->nb[1]*n_head);
+            cb(Kcur, "Kcur", il);
+
+            ggml_tensor * Vcur = ggml_cont(ctx0, ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, cur->nb[1], cur->nb[2], cur->nb[1]*(n_head+n_head_kv)));
+            cb(Vcur, "Vcur", il);
+
+            Qcur = build_norm(Qcur,
+                    model.layers[il].attn_q_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(Qcur, "Qcur", il);
 
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
+            Kcur = build_norm(Kcur,
+                    model.layers[il].attn_k_norm, NULL,
                     LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                cur = build_lora_mm(model.layers[il].wqkv, cur);
-                cb(cur, "wqkv", il);
-
-                cur = ggml_reshape_3d(ctx0, cur, n_embd_head_k, n_head_qkv, n_tokens);
-
-                ggml_tensor * Qcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head,    n_tokens, cur->nb[1], cur->nb[2], 0);
-                cb(Qcur, "Qcur", il);
-
-                ggml_tensor * Kcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, cur->nb[1], cur->nb[2], cur->nb[1]*n_head);
-                cb(Kcur, "Kcur", il);
-
-                ggml_tensor * Vcur = ggml_cont(ctx0, ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, cur->nb[1], cur->nb[2], cur->nb[1]*(n_head+n_head_kv)));
-                cb(Vcur, "Vcur", il);
-
-                Qcur = build_norm(Qcur,
-                        model.layers[il].attn_q_norm, NULL,
-                        LLM_NORM_RMS, il);
-                cb(Qcur, "Qcur", il);
-
-                Kcur = build_norm(Kcur,
-                        model.layers[il].attn_k_norm, NULL,
-                        LLM_NORM_RMS, il);
-                cb(Kcur, "Kcur", il);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, NULL,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, NULL,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Qcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, NULL,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-            if (il == n_layer - 1 && inp_out_ids) {
-                residual = ggml_get_rows(ctx0, residual, inp_out_ids);
-                cur      = ggml_get_rows(ctx0, cur,      inp_out_ids);
-            }
-            ggml_tensor * ffn_inp = ggml_add(ctx0, residual, cur);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed-forward network
-            {
-                cur = build_norm(ffn_inp,
-                        model.layers[il].ffn_norm, NULL,
-                        LLM_NORM_RMS, il);
-                cb(cur, "ffn_norm", il);
-
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up,   NULL, NULL,
-                        model.layers[il].ffn_gate, NULL, NULL,
-                        model.layers[il].ffn_down, NULL, NULL,
-                        NULL,
-                        LLM_FFN_SILU, LLM_FFN_PAR, il);
-                cb(cur, "ffn_out", il);
-            }
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            inpL = cur;
+            cb(Kcur, "Kcur", il);
+
+            Qcur = ggml_rope_ext(
+                    ctx0, Qcur, inp_pos, NULL,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            Kcur = ggml_rope_ext(
+                    ctx0, Kcur, inp_pos, NULL,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Qcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, NULL,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
         }
-        cur = inpL;
+        if (il == n_layer - 1 && inp_out_ids) {
+            residual = ggml_get_rows(ctx0, residual, inp_out_ids);
+            cur      = ggml_get_rows(ctx0, cur,      inp_out_ids);
+        }
+        ggml_tensor * ffn_inp = ggml_add(ctx0, residual, cur);
+        cb(ffn_inp, "ffn_inp", il);
 
-        // norm
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
+        // feed-forward network
+        {
+            cur = build_norm(ffn_inp,
+                    model.layers[il].ffn_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "ffn_norm", il);
+
+            cur = build_ffn(cur,
+                    model.layers[il].ffn_up,   NULL, NULL,
+                    model.layers[il].ffn_gate, NULL, NULL,
+                    model.layers[il].ffn_down, NULL, NULL,
+                    NULL,
+                    LLM_FFN_SILU, LLM_FFN_PAR, il);
+            cb(cur, "ffn_out", il);
+        }
+        cur = ggml_add(ctx0, cur, ffn_inp);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        inpL = cur;
+    }
+    cur = inpL;
+
+    // norm
+    cur = build_norm(cur,
+            model.output_norm, NULL,
+            LLM_NORM_RMS, -1);
 
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
 
-        cur = build_lora_mm(model.output, cur);
+    cur = build_lora_mm(model.output, cur);
 
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
 
-        ggml_build_forward_expand(gf, cur);
+    ggml_build_forward_expand(gf, cur);
 }
diff --git a/src/models/orion.cpp b/src/models/orion.cpp
index 8c20c003ce0..bb02273bfe7 100644
--- a/src/models/orion.cpp
+++ b/src/models/orion.cpp
@@ -1,123 +1,123 @@
 #include "models.h"
 
 llm_build_orion::llm_build_orion(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, model.layers[il].attn_norm_b,
-                    LLM_NORM, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-                // if (model.layers[il].bq) {
-                //     Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
-                //     cb(Qcur, "Qcur", il);
-                // }
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-                // if (model.layers[il].bk) {
-                //     Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
-                //     cb(Kcur, "Kcur", il);
-                // }
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-                // if (model.layers[il].bv) {
-                //     Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
-                //     cb(Vcur, "Vcur", il);
-                // }
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, NULL,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed-forward network
-            cur = build_norm(ffn_inp,
-                    model.layers[il].ffn_norm, model.layers[il].ffn_norm_b,
-                    LLM_NORM, il);
-            cb(cur, "ffn_norm", il);
-
-            cur = build_ffn(cur,
-                    model.layers[il].ffn_up,   NULL, NULL,
-                    model.layers[il].ffn_gate, NULL, NULL,
-                    model.layers[il].ffn_down, NULL, NULL,
-                    NULL,
-                    LLM_FFN_SILU, LLM_FFN_PAR, il);
-            cb(cur, "ffn_out", il);
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
+    const int64_t n_embd_head = hparams.n_embd_head_v;
+
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+    GGML_ASSERT(n_embd_head == hparams.n_rot);
+
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+
+    inpL = build_inp_embd(model.tok_embd);
+
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
+
+    auto * inp_attn = build_attn_inp_kv();
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * inpSA = inpL;
+
+        // norm
+        cur = build_norm(inpL,
+                model.layers[il].attn_norm, model.layers[il].attn_norm_b,
+                LLM_NORM, il);
+        cb(cur, "attn_norm", il);
+
+        // self-attention
+        {
+            // compute Q and K and RoPE them
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            cb(Qcur, "Qcur", il);
+            // if (model.layers[il].bq) {
+            //     Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
+            //     cb(Qcur, "Qcur", il);
+            // }
+
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            cb(Kcur, "Kcur", il);
+            // if (model.layers[il].bk) {
+            //     Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
+            //     cb(Kcur, "Kcur", il);
+            // }
+
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            cb(Vcur, "Vcur", il);
+            // if (model.layers[il].bv) {
+            //     Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
+            //     cb(Vcur, "Vcur", il);
+            // }
+
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+            Qcur = ggml_rope_ext(
+                    ctx0, Qcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            Kcur = ggml_rope_ext(
+                    ctx0, Kcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, NULL,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
         }
-        cur = inpL;
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+        }
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+        cb(ffn_inp, "ffn_inp", il);
+
+        // feed-forward network
+        cur = build_norm(ffn_inp,
+                model.layers[il].ffn_norm, model.layers[il].ffn_norm_b,
+                LLM_NORM, il);
+        cb(cur, "ffn_norm", il);
+
+        cur = build_ffn(cur,
+                model.layers[il].ffn_up,   NULL, NULL,
+                model.layers[il].ffn_gate, NULL, NULL,
+                model.layers[il].ffn_down, NULL, NULL,
+                NULL,
+                LLM_FFN_SILU, LLM_FFN_PAR, il);
+        cb(cur, "ffn_out", il);
+
+        cur = ggml_add(ctx0, cur, ffn_inp);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+    cur = inpL;
 
-        cur = build_norm(cur,
-                model.output_norm, model.output_norm_b,
-                LLM_NORM, -1);
+    cur = build_norm(cur,
+            model.output_norm, model.output_norm_b,
+            LLM_NORM, -1);
 
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
 
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
 
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
 
-        ggml_build_forward_expand(gf, cur);
+    ggml_build_forward_expand(gf, cur);
 }
diff --git a/src/models/phi3.cpp b/src/models/phi3.cpp
index 63907e3d4ed..c8e5da33db7 100644
--- a/src/models/phi3.cpp
+++ b/src/models/phi3.cpp
@@ -1,152 +1,151 @@
 #include "models.h"
 
-
 template<bool iswa>
 llm_build_phi3<iswa>::llm_build_phi3(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-        const int64_t n_embd_gqa = hparams.n_embd_v_gqa();
+    const int64_t n_embd_head = hparams.n_embd_head_v;
+    const int64_t n_embd_gqa = hparams.n_embd_v_gqa();
 
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
 
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
 
-        inpL = build_inp_embd(model.tok_embd);
+    inpL = build_inp_embd(model.tok_embd);
 
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
 
-        using inp_attn_type = std::conditional_t<iswa, llm_graph_input_attn_kv_iswa, llm_graph_input_attn_kv>;
-        inp_attn_type * inp_attn = nullptr;
+    using inp_attn_type = std::conditional_t<iswa, llm_graph_input_attn_kv_iswa, llm_graph_input_attn_kv>;
+    inp_attn_type * inp_attn = nullptr;
 
-        if constexpr (iswa) {
-            inp_attn = build_attn_inp_kv_iswa();
-        } else {
-            inp_attn = build_attn_inp_kv();
-        }
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            auto * residual = inpL;
-
-            // self-attention
-            {
-                // rope freq factors for 128k context
-                ggml_tensor * rope_factors = model.get_rope_factors(cparams, il);
-
-                ggml_tensor* attn_norm_output = build_norm(inpL,
-                        model.layers[il].attn_norm,
-                        model.layers[il].attn_norm_b,
-                        LLM_NORM_RMS, il);
-                cb(attn_norm_output, "attn_norm", il);
-
-                ggml_tensor * Qcur = nullptr;
-                ggml_tensor * Kcur = nullptr;
-                ggml_tensor * Vcur = nullptr;
-
-                if (model.layers[il].wqkv) {
-                    cur = build_lora_mm(model.layers[il].wqkv, attn_norm_output);
-                    cb(cur, "wqkv", il);
-
-                    Qcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head,    n_tokens, n_embd_head * sizeof(float), cur->nb[1], 0 * sizeof(float) * (n_embd));
-                    Kcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head * sizeof(float), cur->nb[1], 1 * sizeof(float) * (n_embd));
-                    Vcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head * sizeof(float), cur->nb[1], 1 * sizeof(float) * (n_embd + n_embd_gqa));
-                    }
-                    else {
-                    Qcur = ggml_add(ctx0, build_lora_mm(model.layers[il].wq, attn_norm_output), model.layers[il].bq);
-                    Kcur = ggml_add(ctx0, build_lora_mm(model.layers[il].wk, attn_norm_output), model.layers[il].bk);
-                    Vcur = ggml_add(ctx0, build_lora_mm(model.layers[il].wv, attn_norm_output), model.layers[il].bv);
-
-                    Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                    Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                    Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-                }
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, rope_factors,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, rope_factors,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                Qcur = ggml_scale(ctx0, Qcur, 1.0f / sqrtf(float(n_embd_head)));
-                cb(Qcur, "Qcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f, il);
-            }
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur      = ggml_get_rows(ctx0, cur,      inp_out_ids);
-                residual = ggml_get_rows(ctx0, residual, inp_out_ids);
-            }
-            cur = ggml_add(ctx0, cur, residual);
-            residual = cur;
+    if constexpr (iswa) {
+        inp_attn = build_attn_inp_kv_iswa();
+    } else {
+        inp_attn = build_attn_inp_kv();
+    }
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        auto * residual = inpL;
 
-            cur = build_norm(cur,
-                    model.layers[il].ffn_norm, model.layers[il].ffn_norm_b,
+        // self-attention
+        {
+            // rope freq factors for 128k context
+            ggml_tensor * rope_factors = model.get_rope_factors(cparams, il);
+
+            ggml_tensor* attn_norm_output = build_norm(inpL,
+                    model.layers[il].attn_norm,
+                    model.layers[il].attn_norm_b,
                     LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-
-            // feed-forward network
-            if (model.layers[il].ffn_gate_inp == nullptr) {
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up,   NULL, NULL,
-                        NULL,                      NULL, NULL,
-                        model.layers[il].ffn_down, NULL, NULL,
-                        NULL,
-                        LLM_FFN_SWIGLU, LLM_FFN_SEQ, il);
-                cb(cur, "ffn_out", il);
-            } else {
-                // MoE branch
-                cur = build_moe_ffn(cur,
-                        model.layers[il].ffn_gate_inp,
-                        model.layers[il].ffn_up_exps,
-                        model.layers[il].ffn_gate_exps,
-                        model.layers[il].ffn_down_exps,
-                        nullptr,
-                        n_expert, n_expert_used,
-                        LLM_FFN_SILU, true,
-                        false, 0.0,
-                        LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
-                        il);
-                cb(cur, "ffn_moe_out", il);
-            }
-            cur = ggml_add(ctx0, residual, cur);
+            cb(attn_norm_output, "attn_norm", il);
 
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
+            ggml_tensor * Qcur = nullptr;
+            ggml_tensor * Kcur = nullptr;
+            ggml_tensor * Vcur = nullptr;
 
-            // input for next layer
-            inpL = cur;
+            if (model.layers[il].wqkv) {
+                cur = build_lora_mm(model.layers[il].wqkv, attn_norm_output);
+                cb(cur, "wqkv", il);
+
+                Qcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head,    n_tokens, n_embd_head * sizeof(float), cur->nb[1], 0 * sizeof(float) * (n_embd));
+                Kcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head * sizeof(float), cur->nb[1], 1 * sizeof(float) * (n_embd));
+                Vcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head * sizeof(float), cur->nb[1], 1 * sizeof(float) * (n_embd + n_embd_gqa));
+                }
+                else {
+                Qcur = ggml_add(ctx0, build_lora_mm(model.layers[il].wq, attn_norm_output), model.layers[il].bq);
+                Kcur = ggml_add(ctx0, build_lora_mm(model.layers[il].wk, attn_norm_output), model.layers[il].bk);
+                Vcur = ggml_add(ctx0, build_lora_mm(model.layers[il].wv, attn_norm_output), model.layers[il].bv);
+
+                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+            }
+            Qcur = ggml_rope_ext(
+                    ctx0, Qcur, inp_pos, rope_factors,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            Kcur = ggml_rope_ext(
+                    ctx0, Kcur, inp_pos, rope_factors,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            Qcur = ggml_scale(ctx0, Qcur, 1.0f / sqrtf(float(n_embd_head)));
+            cb(Qcur, "Qcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, model.layers[il].bo,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f, il);
+        }
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur      = ggml_get_rows(ctx0, cur,      inp_out_ids);
+            residual = ggml_get_rows(ctx0, residual, inp_out_ids);
+        }
+        cur = ggml_add(ctx0, cur, residual);
+        residual = cur;
+
+        cur = build_norm(cur,
+                model.layers[il].ffn_norm, model.layers[il].ffn_norm_b,
+                LLM_NORM_RMS, il);
+        cb(cur, "ffn_norm", il);
+
+        // feed-forward network
+        if (model.layers[il].ffn_gate_inp == nullptr) {
+            cur = build_ffn(cur,
+                    model.layers[il].ffn_up,   NULL, NULL,
+                    NULL,                      NULL, NULL,
+                    model.layers[il].ffn_down, NULL, NULL,
+                    NULL,
+                    LLM_FFN_SWIGLU, LLM_FFN_SEQ, il);
+            cb(cur, "ffn_out", il);
+        } else {
+            // MoE branch
+            cur = build_moe_ffn(cur,
+                    model.layers[il].ffn_gate_inp,
+                    model.layers[il].ffn_up_exps,
+                    model.layers[il].ffn_gate_exps,
+                    model.layers[il].ffn_down_exps,
+                    nullptr,
+                    n_expert, n_expert_used,
+                    LLM_FFN_SILU, true,
+                    false, 0.0,
+                    LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
+                    il);
+            cb(cur, "ffn_moe_out", il);
         }
-        cur = build_norm(inpL,
-                model.output_norm,
-                model.output_norm_b,
-                LLM_NORM_RMS, -1);
+        cur = ggml_add(ctx0, residual, cur);
 
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
 
-        cur = build_lora_mm(model.output, cur);
+        // input for next layer
+        inpL = cur;
+    }
+    cur = build_norm(inpL,
+            model.output_norm,
+            model.output_norm_b,
+            LLM_NORM_RMS, -1);
 
-        if (model.output_b != nullptr) {
-            cb(cur, "result_output_no_bias", -1);
-            cur = ggml_add(ctx0, cur, model.output_b);
-        }
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
 
-        ggml_build_forward_expand(gf, cur);
+    cur = build_lora_mm(model.output, cur);
+
+    if (model.output_b != nullptr) {
+        cb(cur, "result_output_no_bias", -1);
+        cur = ggml_add(ctx0, cur, model.output_b);
     }
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}
 
 // Explicit template instantiations
 template struct llm_build_phi3<false>;
diff --git a/src/models/plamo.cpp b/src/models/plamo.cpp
index 73b4473fcab..04ff709f9c6 100644
--- a/src/models/plamo.cpp
+++ b/src/models/plamo.cpp
@@ -1,110 +1,110 @@
 #include "models.h"
 
 llm_build_plamo::llm_build_plamo(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            ggml_tensor * sa_inp = cur;
-
-            // self-attention
-            {
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_embd_head, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_embd_head, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, NULL,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur    = ggml_get_rows(ctx0,    cur, inp_out_ids);
-                sa_inp = ggml_get_rows(ctx0, sa_inp, inp_out_ids);
-                inpL   = ggml_get_rows(ctx0,   inpL, inp_out_ids);
-            }
-            ggml_tensor * sa_out = cur;
-
-            cur = sa_inp;
-
-            // feed-forward network
-            {
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up,   NULL, NULL,
-                        model.layers[il].ffn_gate, NULL, NULL,
-                        model.layers[il].ffn_down, NULL, NULL,
-                        NULL,
-                        LLM_FFN_SILU, LLM_FFN_PAR, il);
-                cb(cur, "ffn_out", il);
-            }
-            cur = ggml_add(ctx0, cur, sa_out);
-            cur = ggml_add(ctx0, cur, inpL);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
+    const int64_t n_embd_head = hparams.n_embd_head_v;
+
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+    GGML_ASSERT(n_embd_head == hparams.n_rot);
+
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+
+    inpL = build_inp_embd(model.tok_embd);
+
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
+
+    auto * inp_attn = build_attn_inp_kv();
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        // norm
+        cur = build_norm(inpL,
+                model.layers[il].attn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
+
+        ggml_tensor * sa_inp = cur;
+
+        // self-attention
+        {
+            // compute Q and K and RoPE them
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            cb(Qcur, "Qcur", il);
+
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            cb(Kcur, "Kcur", il);
+
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            cb(Vcur, "Vcur", il);
+
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+            Qcur = ggml_rope_ext(
+                    ctx0, Qcur, inp_pos, nullptr,
+                    n_embd_head, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            Kcur = ggml_rope_ext(
+                    ctx0, Kcur, inp_pos, nullptr,
+                    n_embd_head, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, NULL,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+        }
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur    = ggml_get_rows(ctx0,    cur, inp_out_ids);
+            sa_inp = ggml_get_rows(ctx0, sa_inp, inp_out_ids);
+            inpL   = ggml_get_rows(ctx0,   inpL, inp_out_ids);
+        }
+        ggml_tensor * sa_out = cur;
+
+        cur = sa_inp;
+
+        // feed-forward network
+        {
+            cur = build_ffn(cur,
+                    model.layers[il].ffn_up,   NULL, NULL,
+                    model.layers[il].ffn_gate, NULL, NULL,
+                    model.layers[il].ffn_down, NULL, NULL,
+                    NULL,
+                    LLM_FFN_SILU, LLM_FFN_PAR, il);
+            cb(cur, "ffn_out", il);
         }
-        cur = inpL;
+        cur = ggml_add(ctx0, cur, sa_out);
+        cur = ggml_add(ctx0, cur, inpL);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+    cur = inpL;
 
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
+    cur = build_norm(cur,
+            model.output_norm, NULL,
+            LLM_NORM_RMS, -1);
 
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
 
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
 
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
 
-        ggml_build_forward_expand(gf, cur);
+    ggml_build_forward_expand(gf, cur);
 }
diff --git a/src/models/plm.cpp b/src/models/plm.cpp
index ddd52162b23..481cbba6907 100644
--- a/src/models/plm.cpp
+++ b/src/models/plm.cpp
@@ -1,168 +1,168 @@
 #include "models.h"
 
 llm_build_plm::llm_build_plm(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const float kq_scale = 1.0f/sqrtf(float(hparams.n_embd_head_k));
-
-        const uint32_t n_embd_head_qk_rope = hparams.n_rot;
-        const uint32_t n_embd_head_qk_nope = hparams.n_embd_head_k - hparams.n_rot;
-        const uint32_t kv_lora_rank = hparams.n_lora_kv;
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        // {n_embd, n_tokens}
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self_attention
-            {
-                ggml_tensor * q = NULL;
-                q = ggml_mul_mat(ctx0, model.layers[il].wq, cur);
-                cb(q, "q", il);
-
-                // split into {n_head * n_embd_head_qk_nope, n_tokens}
-                ggml_tensor * q_nope = ggml_view_3d(ctx0, q, n_embd_head_qk_nope, n_head, n_tokens,
-                        ggml_row_size(q->type, hparams.n_embd_head_k),
-                        ggml_row_size(q->type, hparams.n_embd_head_k * n_head),
-                        0);
-                cb(q_nope, "q_nope", il);
-
-                // and {n_head * n_embd_head_qk_rope, n_tokens}
-                ggml_tensor * q_pe = ggml_view_3d(ctx0, q, n_embd_head_qk_rope, n_head, n_tokens,
-                        ggml_row_size(q->type, hparams.n_embd_head_k),
-                        ggml_row_size(q->type, hparams.n_embd_head_k * n_head),
-                        ggml_row_size(q->type, n_embd_head_qk_nope));
-                cb(q_pe, "q_pe", il);
-
-                // {n_embd, kv_lora_rank + n_embd_head_qk_rope} * {n_embd, n_tokens} -> {kv_lora_rank + n_embd_head_qk_rope, n_tokens}
-                ggml_tensor * kv_pe_compresseed = ggml_mul_mat(ctx0, model.layers[il].wkv_a_mqa, cur);
-                cb(kv_pe_compresseed, "kv_pe_compresseed", il);
-
-                // split into {kv_lora_rank, n_tokens}
-                ggml_tensor * kv_compressed = ggml_view_2d(ctx0, kv_pe_compresseed, kv_lora_rank, n_tokens,
-                        kv_pe_compresseed->nb[1],
-                        0);
-                cb(kv_compressed, "kv_compressed", il);
-
-                // and {n_embd_head_qk_rope, n_tokens}
-                ggml_tensor * k_pe = ggml_view_3d(ctx0, kv_pe_compresseed, n_embd_head_qk_rope, 1, n_tokens,
-                        kv_pe_compresseed->nb[1],
-                        kv_pe_compresseed->nb[1],
-                        ggml_row_size(kv_pe_compresseed->type, kv_lora_rank));
-                cb(k_pe, "k_pe", il);
-
-                kv_compressed = build_norm(kv_compressed,
-                        model.layers[il].attn_kv_a_norm, NULL,
-                        LLM_NORM_RMS, il);
-                cb(kv_compressed, "kv_compressed", il);
-
-                // {kv_lora_rank, n_head * (n_embd_head_qk_nope + n_embd_head_v)} * {kv_lora_rank, n_tokens} -> {n_head * (n_embd_head_qk_nope + n_embd_head_v), n_tokens}
-                ggml_tensor * kv = ggml_mul_mat(ctx0, model.layers[il].wkv_b, kv_compressed);
-                cb(kv, "kv", il);
-
-                // split into {n_head * n_embd_head_qk_nope, n_tokens}
-                ggml_tensor * k_nope = ggml_view_3d(ctx0, kv, n_embd_head_qk_nope, n_head, n_tokens,
-                        ggml_row_size(kv->type, n_embd_head_qk_nope + hparams.n_embd_head_v),
-                        ggml_row_size(kv->type, n_head * (n_embd_head_qk_nope + hparams.n_embd_head_v)),
-                        0);
-                cb(k_nope, "k_nope", il);
-
-                // and {n_head * n_embd_head_v, n_tokens}
-                ggml_tensor * v_states = ggml_view_3d(ctx0, kv, hparams.n_embd_head_v, n_head, n_tokens,
-                        ggml_row_size(kv->type, (n_embd_head_qk_nope + hparams.n_embd_head_v)),
-                        ggml_row_size(kv->type, (n_embd_head_qk_nope + hparams.n_embd_head_v)*n_head),
-                        ggml_row_size(kv->type, (n_embd_head_qk_nope)));
-                cb(v_states, "v_states", il);
-
-                v_states = ggml_cont(ctx0, v_states);
-                cb(v_states, "v_states", il);
-
-                v_states = ggml_view_2d(ctx0, v_states, hparams.n_embd_head_v * n_head, n_tokens,
-                        ggml_row_size(kv->type, hparams.n_embd_head_v * n_head),
-                        0);
-                cb(v_states, "v_states", il);
-
-                q_pe = ggml_rope_ext(
-                        ctx0, q_pe, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-                cb(q_pe, "q_pe", il);
-
-                // shared RoPE key
-                k_pe = ggml_rope_ext(
-                        ctx0, k_pe, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-                cb(k_pe, "k_pe", il);
-
-                ggml_tensor * q_states = ggml_concat(ctx0, q_nope, q_pe, 0);
-                cb(q_states, "q_states", il);
-
-                ggml_tensor * k_states = ggml_concat(ctx0, k_nope, ggml_repeat(ctx0, k_pe, q_pe), 0);
-                cb(k_states, "k_states", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, NULL,
-                        q_states, k_states, v_states, nullptr, nullptr, nullptr, kq_scale, il);
-            }
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            cur = build_norm(ffn_inp,
-                    model.layers[il].ffn_norm, NULL,
+    const float kq_scale = 1.0f/sqrtf(float(hparams.n_embd_head_k));
+
+    const uint32_t n_embd_head_qk_rope = hparams.n_rot;
+    const uint32_t n_embd_head_qk_nope = hparams.n_embd_head_k - hparams.n_rot;
+    const uint32_t kv_lora_rank = hparams.n_lora_kv;
+
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+
+    // {n_embd, n_tokens}
+    inpL = build_inp_embd(model.tok_embd);
+
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
+
+    auto * inp_attn = build_attn_inp_kv();
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * inpSA = inpL;
+
+        // norm
+        cur = build_norm(inpL,
+                model.layers[il].attn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
+
+        // self_attention
+        {
+            ggml_tensor * q = NULL;
+            q = ggml_mul_mat(ctx0, model.layers[il].wq, cur);
+            cb(q, "q", il);
+
+            // split into {n_head * n_embd_head_qk_nope, n_tokens}
+            ggml_tensor * q_nope = ggml_view_3d(ctx0, q, n_embd_head_qk_nope, n_head, n_tokens,
+                    ggml_row_size(q->type, hparams.n_embd_head_k),
+                    ggml_row_size(q->type, hparams.n_embd_head_k * n_head),
+                    0);
+            cb(q_nope, "q_nope", il);
+
+            // and {n_head * n_embd_head_qk_rope, n_tokens}
+            ggml_tensor * q_pe = ggml_view_3d(ctx0, q, n_embd_head_qk_rope, n_head, n_tokens,
+                    ggml_row_size(q->type, hparams.n_embd_head_k),
+                    ggml_row_size(q->type, hparams.n_embd_head_k * n_head),
+                    ggml_row_size(q->type, n_embd_head_qk_nope));
+            cb(q_pe, "q_pe", il);
+
+            // {n_embd, kv_lora_rank + n_embd_head_qk_rope} * {n_embd, n_tokens} -> {kv_lora_rank + n_embd_head_qk_rope, n_tokens}
+            ggml_tensor * kv_pe_compresseed = ggml_mul_mat(ctx0, model.layers[il].wkv_a_mqa, cur);
+            cb(kv_pe_compresseed, "kv_pe_compresseed", il);
+
+            // split into {kv_lora_rank, n_tokens}
+            ggml_tensor * kv_compressed = ggml_view_2d(ctx0, kv_pe_compresseed, kv_lora_rank, n_tokens,
+                    kv_pe_compresseed->nb[1],
+                    0);
+            cb(kv_compressed, "kv_compressed", il);
+
+            // and {n_embd_head_qk_rope, n_tokens}
+            ggml_tensor * k_pe = ggml_view_3d(ctx0, kv_pe_compresseed, n_embd_head_qk_rope, 1, n_tokens,
+                    kv_pe_compresseed->nb[1],
+                    kv_pe_compresseed->nb[1],
+                    ggml_row_size(kv_pe_compresseed->type, kv_lora_rank));
+            cb(k_pe, "k_pe", il);
+
+            kv_compressed = build_norm(kv_compressed,
+                    model.layers[il].attn_kv_a_norm, NULL,
                     LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
+            cb(kv_compressed, "kv_compressed", il);
+
+            // {kv_lora_rank, n_head * (n_embd_head_qk_nope + n_embd_head_v)} * {kv_lora_rank, n_tokens} -> {n_head * (n_embd_head_qk_nope + n_embd_head_v), n_tokens}
+            ggml_tensor * kv = ggml_mul_mat(ctx0, model.layers[il].wkv_b, kv_compressed);
+            cb(kv, "kv", il);
+
+            // split into {n_head * n_embd_head_qk_nope, n_tokens}
+            ggml_tensor * k_nope = ggml_view_3d(ctx0, kv, n_embd_head_qk_nope, n_head, n_tokens,
+                    ggml_row_size(kv->type, n_embd_head_qk_nope + hparams.n_embd_head_v),
+                    ggml_row_size(kv->type, n_head * (n_embd_head_qk_nope + hparams.n_embd_head_v)),
+                    0);
+            cb(k_nope, "k_nope", il);
+
+            // and {n_head * n_embd_head_v, n_tokens}
+            ggml_tensor * v_states = ggml_view_3d(ctx0, kv, hparams.n_embd_head_v, n_head, n_tokens,
+                    ggml_row_size(kv->type, (n_embd_head_qk_nope + hparams.n_embd_head_v)),
+                    ggml_row_size(kv->type, (n_embd_head_qk_nope + hparams.n_embd_head_v)*n_head),
+                    ggml_row_size(kv->type, (n_embd_head_qk_nope)));
+            cb(v_states, "v_states", il);
+
+            v_states = ggml_cont(ctx0, v_states);
+            cb(v_states, "v_states", il);
+
+            v_states = ggml_view_2d(ctx0, v_states, hparams.n_embd_head_v * n_head, n_tokens,
+                    ggml_row_size(kv->type, hparams.n_embd_head_v * n_head),
+                    0);
+            cb(v_states, "v_states", il);
+
+            q_pe = ggml_rope_ext(
+                    ctx0, q_pe, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+            cb(q_pe, "q_pe", il);
+
+            // shared RoPE key
+            k_pe = ggml_rope_ext(
+                    ctx0, k_pe, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+            cb(k_pe, "k_pe", il);
+
+            ggml_tensor * q_states = ggml_concat(ctx0, q_nope, q_pe, 0);
+            cb(q_states, "q_states", il);
+
+            ggml_tensor * k_states = ggml_concat(ctx0, k_nope, ggml_repeat(ctx0, k_pe, q_pe), 0);
+            cb(k_states, "k_states", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, NULL,
+                    q_states, k_states, v_states, nullptr, nullptr, nullptr, kq_scale, il);
+        }
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+        }
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+        cb(ffn_inp, "ffn_inp", il);
 
-            cur = build_ffn(cur,
-                    model.layers[il].ffn_up,   NULL, NULL,
-                    NULL, NULL, NULL,
-                    model.layers[il].ffn_down, NULL, NULL,
-                    NULL,
-                    LLM_FFN_RELU_SQR, LLM_FFN_SEQ, il);
-            cb(cur, "ffn_out", il);
+        cur = build_norm(ffn_inp,
+                model.layers[il].ffn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "ffn_norm", il);
 
-            cur = ggml_add(ctx0, cur, ffn_inp);
+        cur = build_ffn(cur,
+                model.layers[il].ffn_up,   NULL, NULL,
+                NULL, NULL, NULL,
+                model.layers[il].ffn_down, NULL, NULL,
+                NULL,
+                LLM_FFN_RELU_SQR, LLM_FFN_SEQ, il);
+        cb(cur, "ffn_out", il);
 
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
+        cur = ggml_add(ctx0, cur, ffn_inp);
 
-            // input for next layer
-            inpL = cur;
-        }
-        cur = inpL;
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+    cur = inpL;
 
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
+    cur = build_norm(cur,
+            model.output_norm, NULL,
+            LLM_NORM_RMS, -1);
 
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
 
-        cur = build_lora_mm(model.output, cur);
+    cur = build_lora_mm(model.output, cur);
 
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
 
-        ggml_build_forward_expand(gf, cur);
+    ggml_build_forward_expand(gf, cur);
 }
diff --git a/src/models/qwen2.cpp b/src/models/qwen2.cpp
index 885cb46894d..587a932426f 100644
--- a/src/models/qwen2.cpp
+++ b/src/models/qwen2.cpp
@@ -1,118 +1,117 @@
 #include "models.h"
 
-
 llm_build_qwen2::llm_build_qwen2(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
-                cb(Qcur, "Qcur", il);
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
-                cb(Kcur, "Kcur", il);
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
-                cb(Vcur, "Vcur", il);
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed-forward network
-            cur = build_norm(ffn_inp,
-                    model.layers[il].ffn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-
-            cur = build_ffn(cur,
-                    model.layers[il].ffn_up,   NULL, NULL,
-                    model.layers[il].ffn_gate, NULL, NULL,
-                    model.layers[il].ffn_down, NULL, NULL,
-                    NULL,
-                    LLM_FFN_SILU, LLM_FFN_PAR, il);
-            cb(cur, "ffn_out", il);
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-        cur = inpL;
+    const int64_t n_embd_head = hparams.n_embd_head_v;
 
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+    GGML_ASSERT(n_embd_head == hparams.n_rot);
 
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
 
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
+    inpL = build_inp_embd(model.tok_embd);
 
-        if (model.output_b != nullptr) {
-            cur = ggml_add(ctx0, cur, model.output_b);
-        }
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
+
+    auto * inp_attn = build_attn_inp_kv();
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * inpSA = inpL;
+
+        // norm
+        cur = build_norm(inpL,
+                model.layers[il].attn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
+
+        // self-attention
+        {
+            // compute Q and K and RoPE them
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
+            cb(Qcur, "Qcur", il);
 
-        ggml_build_forward_expand(gf, cur);
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
+            cb(Kcur, "Kcur", il);
+
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
+            cb(Vcur, "Vcur", il);
+
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+            Qcur = ggml_rope_ext(
+                    ctx0, Qcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            Kcur = ggml_rope_ext(
+                    ctx0, Kcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, model.layers[il].bo,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+        }
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+        }
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+        cb(ffn_inp, "ffn_inp", il);
+
+        // feed-forward network
+        cur = build_norm(ffn_inp,
+                model.layers[il].ffn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "ffn_norm", il);
+
+        cur = build_ffn(cur,
+                model.layers[il].ffn_up,   NULL, NULL,
+                model.layers[il].ffn_gate, NULL, NULL,
+                model.layers[il].ffn_down, NULL, NULL,
+                NULL,
+                LLM_FFN_SILU, LLM_FFN_PAR, il);
+        cb(cur, "ffn_out", il);
+
+        cur = ggml_add(ctx0, cur, ffn_inp);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+    cur = inpL;
+
+    cur = build_norm(cur,
+            model.output_norm, NULL,
+            LLM_NORM_RMS, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
+
+    if (model.output_b != nullptr) {
+        cur = ggml_add(ctx0, cur, model.output_b);
+    }
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
 }
diff --git a/src/models/qwen2moe.cpp b/src/models/qwen2moe.cpp
index 40623ea66f2..49142b71236 100644
--- a/src/models/qwen2moe.cpp
+++ b/src/models/qwen2moe.cpp
@@ -1,151 +1,151 @@
 #include "models.h"
 
 llm_build_qwen2moe::llm_build_qwen2moe(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
+    const int64_t n_embd_head = hparams.n_embd_head_v;
 
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+    GGML_ASSERT(n_embd_head == hparams.n_rot);
 
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
 
-        inpL = build_inp_embd(model.tok_embd);
+    inpL = build_inp_embd(model.tok_embd);
 
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
 
-        auto * inp_attn = build_attn_inp_kv();
+    auto * inp_attn = build_attn_inp_kv();
 
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
 
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * inpSA = inpL;
 
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
+        // norm
+        cur = build_norm(inpL,
+                model.layers[il].attn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
 
-            // self_attention
-            {
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+        // self_attention
+        {
+            // compute Q and K and RoPE them
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            cb(Qcur, "Qcur", il);
+            if (model.layers[il].bq) {
+                Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
                 cb(Qcur, "Qcur", il);
-                if (model.layers[il].bq) {
-                    Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
-                    cb(Qcur, "Qcur", il);
-                }
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-                if (model.layers[il].bk) {
-                    Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
-                    cb(Kcur, "Kcur", il);
-                }
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-                if (model.layers[il].bv) {
-                    Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
-                    cb(Vcur, "Vcur", il);
-                }
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
             }
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            cb(Kcur, "Kcur", il);
+            if (model.layers[il].bk) {
+                Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
+                cb(Kcur, "Kcur", il);
             }
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // MoE branch
-            cur = build_norm(ffn_inp,
-                    model.layers[il].ffn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-
-            ggml_tensor * moe_out =
-                build_moe_ffn(cur,
-                        model.layers[il].ffn_gate_inp,
-                        model.layers[il].ffn_up_exps,
-                        model.layers[il].ffn_gate_exps,
-                        model.layers[il].ffn_down_exps,
-                        nullptr,
-                        n_expert, n_expert_used,
-                        LLM_FFN_SILU, false,
-                        false, 0.0,
-                        LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
-                        il);
-            cb(moe_out, "ffn_moe_out", il);
-
-            // FFN shared expert
-            {
-                ggml_tensor * cur_gate_inp = build_lora_mm(model.layers[il].ffn_gate_inp_shexp, cur);
-                cb(cur_gate_inp, "ffn_shexp_gate_inp", il);
-
-                // sigmoid
-                ggml_tensor * cur_gate = ggml_div(ctx0, ggml_silu(ctx0, cur_gate_inp), cur_gate_inp);
-                cb(cur_gate, "ffn_shexp_gate", il);
-
-                ggml_tensor * cur_ffn = build_ffn(cur,
-                        model.layers[il].ffn_up_shexp,   NULL, NULL,
-                        model.layers[il].ffn_gate_shexp, NULL, NULL,
-                        model.layers[il].ffn_down_shexp, NULL, NULL,
-                        NULL,
-                        LLM_FFN_SILU, LLM_FFN_PAR, il);
-                cb(cur_ffn, "ffn_shexp", il);
-
-                ggml_tensor * ffn_shexp_out = ggml_mul(ctx0, cur_ffn, cur_gate);
-                cb(ffn_shexp_out, "ffn_shexp_out", il);
-
-                moe_out = ggml_add(ctx0, moe_out, ffn_shexp_out);
-                cb(moe_out, "ffn_out", il);
-
-                cur = moe_out;
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            cb(Vcur, "Vcur", il);
+            if (model.layers[il].bv) {
+                Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
+                cb(Vcur, "Vcur", il);
             }
-            cur = ggml_add(ctx0, cur, ffn_inp);
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+            Qcur = ggml_rope_ext(
+                    ctx0, Qcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            Kcur = ggml_rope_ext(
+                    ctx0, Kcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, model.layers[il].bo,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+        }
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+        }
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+        cb(ffn_inp, "ffn_inp", il);
+
+        // MoE branch
+        cur = build_norm(ffn_inp,
+                model.layers[il].ffn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "ffn_norm", il);
+
+        ggml_tensor * moe_out =
+            build_moe_ffn(cur,
+                    model.layers[il].ffn_gate_inp,
+                    model.layers[il].ffn_up_exps,
+                    model.layers[il].ffn_gate_exps,
+                    model.layers[il].ffn_down_exps,
+                    nullptr,
+                    n_expert, n_expert_used,
+                    LLM_FFN_SILU, false,
+                    false, 0.0,
+                    LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
+                    il);
+        cb(moe_out, "ffn_moe_out", il);
+
+        // FFN shared expert
+        {
+            ggml_tensor * cur_gate_inp = build_lora_mm(model.layers[il].ffn_gate_inp_shexp, cur);
+            cb(cur_gate_inp, "ffn_shexp_gate_inp", il);
+
+            // sigmoid
+            ggml_tensor * cur_gate = ggml_div(ctx0, ggml_silu(ctx0, cur_gate_inp), cur_gate_inp);
+            cb(cur_gate, "ffn_shexp_gate", il);
+
+            ggml_tensor * cur_ffn = build_ffn(cur,
+                    model.layers[il].ffn_up_shexp,   NULL, NULL,
+                    model.layers[il].ffn_gate_shexp, NULL, NULL,
+                    model.layers[il].ffn_down_shexp, NULL, NULL,
+                    NULL,
+                    LLM_FFN_SILU, LLM_FFN_PAR, il);
+            cb(cur_ffn, "ffn_shexp", il);
+
+            ggml_tensor * ffn_shexp_out = ggml_mul(ctx0, cur_ffn, cur_gate);
+            cb(ffn_shexp_out, "ffn_shexp_out", il);
+
+            moe_out = ggml_add(ctx0, moe_out, ffn_shexp_out);
+            cb(moe_out, "ffn_out", il);
+
+            cur = moe_out;
+        }
+        cur = ggml_add(ctx0, cur, ffn_inp);
 
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
 
-            // input for next layer
-            inpL = cur;
-        }
-        cur = inpL;
+        // input for next layer
+        inpL = cur;
+    }
+    cur = inpL;
 
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
+    cur = build_norm(cur,
+            model.output_norm, NULL,
+            LLM_NORM_RMS, -1);
 
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
 
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
 
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
 
-        ggml_build_forward_expand(gf, cur);
+    ggml_build_forward_expand(gf, cur);
 }
diff --git a/src/models/qwen2vl.cpp b/src/models/qwen2vl.cpp
index addc37f9a8f..9be38675cf7 100644
--- a/src/models/qwen2vl.cpp
+++ b/src/models/qwen2vl.cpp
@@ -1,117 +1,117 @@
 #include "models.h"
 
 llm_build_qwen2vl::llm_build_qwen2vl(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        int sections[4];
-        std::copy(std::begin(hparams.rope_sections), std::begin(hparams.rope_sections) + 4, sections);
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
-                cb(Qcur, "Qcur", il);
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
-                cb(Kcur, "Kcur", il);
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
-                cb(Vcur, "Vcur", il);
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = ggml_rope_multi(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, sections, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_multi(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, sections, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed-forward network
-            cur = build_norm(ffn_inp,
-                    model.layers[il].ffn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-
-            cur = build_ffn(cur,
-                    model.layers[il].ffn_up,   NULL, NULL,
-                    model.layers[il].ffn_gate, NULL, NULL,
-                    model.layers[il].ffn_down, NULL, NULL,
-                    NULL,
-                    LLM_FFN_SILU, LLM_FFN_PAR, il);
-            cb(cur, "ffn_out", il);
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
+    const int64_t n_embd_head = hparams.n_embd_head_v;
+
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+    GGML_ASSERT(n_embd_head == hparams.n_rot);
+
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+
+    inpL = build_inp_embd(model.tok_embd);
+
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
+
+    auto * inp_attn = build_attn_inp_kv();
+
+    int sections[4];
+    std::copy(std::begin(hparams.rope_sections), std::begin(hparams.rope_sections) + 4, sections);
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * inpSA = inpL;
+
+        // norm
+        cur = build_norm(inpL,
+                model.layers[il].attn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
+
+        // self-attention
+        {
+            // compute Q and K and RoPE them
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
+            cb(Qcur, "Qcur", il);
+
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
+            cb(Kcur, "Kcur", il);
+
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
+            cb(Vcur, "Vcur", il);
+
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+            Qcur = ggml_rope_multi(
+                    ctx0, Qcur, inp_pos, nullptr,
+                    n_rot, sections, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            Kcur = ggml_rope_multi(
+                    ctx0, Kcur, inp_pos, nullptr,
+                    n_rot, sections, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, model.layers[il].bo,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+        }
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
         }
-        cur = inpL;
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+        cb(ffn_inp, "ffn_inp", il);
+
+        // feed-forward network
+        cur = build_norm(ffn_inp,
+                model.layers[il].ffn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "ffn_norm", il);
+
+        cur = build_ffn(cur,
+                model.layers[il].ffn_up,   NULL, NULL,
+                model.layers[il].ffn_gate, NULL, NULL,
+                model.layers[il].ffn_down, NULL, NULL,
+                NULL,
+                LLM_FFN_SILU, LLM_FFN_PAR, il);
+        cb(cur, "ffn_out", il);
+
+        cur = ggml_add(ctx0, cur, ffn_inp);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+    cur = inpL;
 
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
+    cur = build_norm(cur,
+            model.output_norm, NULL,
+            LLM_NORM_RMS, -1);
 
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
 
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
 
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
 
-        ggml_build_forward_expand(gf, cur);
+    ggml_build_forward_expand(gf, cur);
 }
diff --git a/src/models/qwen3.cpp b/src/models/qwen3.cpp
index 782d32107a3..a5cfffa5314 100644
--- a/src/models/qwen3.cpp
+++ b/src/models/qwen3.cpp
@@ -1,117 +1,117 @@
 #include "models.h"
 
 llm_build_qwen3::llm_build_qwen3(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL, LLM_NORM_RMS, il);
-                cb(Qcur, "Qcur_normed", il);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, NULL, LLM_NORM_RMS, il);
-                cb(Kcur, "Kcur_normed", il);
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed-forward network
-            cur = build_norm(ffn_inp,
-                    model.layers[il].ffn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-
-            cur = build_ffn(cur,
-                    model.layers[il].ffn_up,   NULL, NULL,
-                    model.layers[il].ffn_gate, NULL, NULL,
-                    model.layers[il].ffn_down, NULL, NULL,
-                    NULL,
-                    LLM_FFN_SILU, LLM_FFN_PAR, il);
-            cb(cur, "ffn_out", il);
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
+    const int64_t n_embd_head = hparams.n_embd_head_v;
+
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+    GGML_ASSERT(n_embd_head == hparams.n_rot);
+
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+
+    inpL = build_inp_embd(model.tok_embd);
+
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
+
+    auto * inp_attn = build_attn_inp_kv();
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * inpSA = inpL;
+
+        // norm
+        cur = build_norm(inpL,
+                model.layers[il].attn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
+
+        // self-attention
+        {
+            // compute Q and K and RoPE them
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            cb(Qcur, "Qcur", il);
+
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            cb(Kcur, "Kcur", il);
+
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            cb(Vcur, "Vcur", il);
+
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+            Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL, LLM_NORM_RMS, il);
+            cb(Qcur, "Qcur_normed", il);
+
+            Qcur = ggml_rope_ext(
+                    ctx0, Qcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, NULL, LLM_NORM_RMS, il);
+            cb(Kcur, "Kcur_normed", il);
+
+            Kcur = ggml_rope_ext(
+                    ctx0, Kcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, model.layers[il].bo,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
         }
-        cur = inpL;
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+        }
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+        cb(ffn_inp, "ffn_inp", il);
+
+        // feed-forward network
+        cur = build_norm(ffn_inp,
+                model.layers[il].ffn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "ffn_norm", il);
+
+        cur = build_ffn(cur,
+                model.layers[il].ffn_up,   NULL, NULL,
+                model.layers[il].ffn_gate, NULL, NULL,
+                model.layers[il].ffn_down, NULL, NULL,
+                NULL,
+                LLM_FFN_SILU, LLM_FFN_PAR, il);
+        cb(cur, "ffn_out", il);
+
+        cur = ggml_add(ctx0, cur, ffn_inp);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+    cur = inpL;
 
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
+    cur = build_norm(cur,
+            model.output_norm, NULL,
+            LLM_NORM_RMS, -1);
 
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
 
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
 
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
 
-        ggml_build_forward_expand(gf, cur);
+    ggml_build_forward_expand(gf, cur);
 }
diff --git a/src/models/qwen3moe.cpp b/src/models/qwen3moe.cpp
index f5087cdb06a..888534fb347 100644
--- a/src/models/qwen3moe.cpp
+++ b/src/models/qwen3moe.cpp
@@ -1,124 +1,124 @@
 #include "models.h"
 
 llm_build_qwen3moe::llm_build_qwen3moe(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
-
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
-
-        inpL = build_inp_embd(model.tok_embd);
-
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
-
-        auto * inp_attn = build_attn_inp_kv();
-
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
-
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self_attention
-            {
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL, LLM_NORM_RMS, il);
-                cb(Qcur, "Qcur_normed", il);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, NULL, LLM_NORM_RMS, il);
-                cb(Kcur, "Kcur_normed", il);
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // MoE branch
-            cur = build_norm(ffn_inp,
-                    model.layers[il].ffn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-
-            ggml_tensor * moe_out =
-                build_moe_ffn(cur,
-                        model.layers[il].ffn_gate_inp,
-                        model.layers[il].ffn_up_exps,
-                        model.layers[il].ffn_gate_exps,
-                        model.layers[il].ffn_down_exps,
-                        nullptr,
-                        n_expert, n_expert_used,
-                        LLM_FFN_SILU, true,
-                        false, 0.0,
-                        LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
-                        il);
-            cb(moe_out, "ffn_moe_out", il);
-            cur = moe_out;
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
-        }
-        cur = inpL;
+    const int64_t n_embd_head = hparams.n_embd_head_v;
+
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+    GGML_ASSERT(n_embd_head == hparams.n_rot);
+
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+
+    inpL = build_inp_embd(model.tok_embd);
+
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
+
+    auto * inp_attn = build_attn_inp_kv();
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * inpSA = inpL;
 
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
+        // norm
+        cur = build_norm(inpL,
+                model.layers[il].attn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
 
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
+        // self_attention
+        {
+            // compute Q and K and RoPE them
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            cb(Qcur, "Qcur", il);
 
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            cb(Kcur, "Kcur", il);
 
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            cb(Vcur, "Vcur", il);
 
-        ggml_build_forward_expand(gf, cur);
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+            Qcur = build_norm(Qcur, model.layers[il].attn_q_norm, NULL, LLM_NORM_RMS, il);
+            cb(Qcur, "Qcur_normed", il);
+
+            Qcur = ggml_rope_ext(
+                    ctx0, Qcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            Kcur = build_norm(Kcur, model.layers[il].attn_k_norm, NULL, LLM_NORM_RMS, il);
+            cb(Kcur, "Kcur_normed", il);
+
+            Kcur = ggml_rope_ext(
+                    ctx0, Kcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, model.layers[il].bo,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+        }
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+        }
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+        cb(ffn_inp, "ffn_inp", il);
+
+        // MoE branch
+        cur = build_norm(ffn_inp,
+                model.layers[il].ffn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "ffn_norm", il);
+
+        ggml_tensor * moe_out =
+            build_moe_ffn(cur,
+                    model.layers[il].ffn_gate_inp,
+                    model.layers[il].ffn_up_exps,
+                    model.layers[il].ffn_gate_exps,
+                    model.layers[il].ffn_down_exps,
+                    nullptr,
+                    n_expert, n_expert_used,
+                    LLM_FFN_SILU, true,
+                    false, 0.0,
+                    LLAMA_EXPERT_GATING_FUNC_TYPE_SOFTMAX,
+                    il);
+        cb(moe_out, "ffn_moe_out", il);
+        cur = moe_out;
+
+        cur = ggml_add(ctx0, cur, ffn_inp);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+    cur = inpL;
+
+    cur = build_norm(cur,
+            model.output_norm, NULL,
+            LLM_NORM_RMS, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
+
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
 }
diff --git a/src/models/refact.cpp b/src/models/refact.cpp
index 951844f6408..ff5eb2841db 100644
--- a/src/models/refact.cpp
+++ b/src/models/refact.cpp
@@ -1,94 +1,94 @@
 #include "models.h"
 
 llm_build_refact::llm_build_refact(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
+    const int64_t n_embd_head = hparams.n_embd_head_v;
 
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
 
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
 
-        inpL = build_inp_embd(model.tok_embd);
+    inpL = build_inp_embd(model.tok_embd);
 
-        auto * inp_attn = build_attn_inp_kv();
+    auto * inp_attn = build_attn_inp_kv();
 
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
 
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * inpSA = inpL;
 
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
+        cur = build_norm(inpL,
+                model.layers[il].attn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
+
+        // self-attention
+        {
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            cb(Qcur, "Qcur", il);
+
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            cb(Kcur, "Kcur", il);
+
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            cb(Vcur, "Vcur", il);
+
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, NULL,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+        }
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+        }
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+        cb(ffn_inp, "ffn_inp", il);
+
+        // feed-forward network
+        {
+            cur = build_norm(ffn_inp,
+                    model.layers[il].ffn_norm, NULL,
                     LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, NULL,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed-forward network
-            {
-                cur = build_norm(ffn_inp,
-                        model.layers[il].ffn_norm, NULL,
-                        LLM_NORM_RMS, il);
-                cb(cur, "ffn_norm", il);
-
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up,   NULL, NULL,
-                        model.layers[il].ffn_gate, NULL, NULL,
-                        model.layers[il].ffn_down, NULL, NULL,
-                        NULL,
-                        LLM_FFN_SILU, LLM_FFN_PAR, il);
-                cb(cur, "ffn_out", il);
-            }
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
+            cb(cur, "ffn_norm", il);
+
+            cur = build_ffn(cur,
+                    model.layers[il].ffn_up,   NULL, NULL,
+                    model.layers[il].ffn_gate, NULL, NULL,
+                    model.layers[il].ffn_down, NULL, NULL,
+                    NULL,
+                    LLM_FFN_SILU, LLM_FFN_PAR, il);
+            cb(cur, "ffn_out", il);
         }
-        cur = inpL;
+        cur = ggml_add(ctx0, cur, ffn_inp);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+    cur = inpL;
 
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
+    cur = build_norm(cur,
+            model.output_norm, NULL,
+            LLM_NORM_RMS, -1);
 
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
 
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
 
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
 
-        ggml_build_forward_expand(gf, cur);
+    ggml_build_forward_expand(gf, cur);
 }
diff --git a/src/models/seed-oss.cpp b/src/models/seed-oss.cpp
index 94ce1633629..0dc33c50ba3 100644
--- a/src/models/seed-oss.cpp
+++ b/src/models/seed-oss.cpp
@@ -1,124 +1,124 @@
 #include "models.h"
 
 llm_build_seed_oss::llm_build_seed_oss(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
+    const int64_t n_embd_head = hparams.n_embd_head_v;
 
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+    GGML_ASSERT(n_embd_head == hparams.n_rot);
 
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
 
-        inpL = build_inp_embd(model.tok_embd);
+    inpL = build_inp_embd(model.tok_embd);
 
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
 
-        auto * inp_attn = build_attn_inp_kv();
+    auto * inp_attn = build_attn_inp_kv();
 
-        const float kq_scale = hparams.f_attention_scale == 0.0f ? 1.0f/sqrtf(float(n_embd_head)) : hparams.f_attention_scale;
+    const float kq_scale = hparams.f_attention_scale == 0.0f ? 1.0f/sqrtf(float(n_embd_head)) : hparams.f_attention_scale;
 
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
 
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * inpSA = inpL;
 
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-                if (model.layers[il].bq) {
-                    Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
-                    cb(Qcur, "Qcur", il);
-                }
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-                if (model.layers[il].bk) {
-                    Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
-                    cb(Kcur, "Kcur", il);
-                }
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-                if (model.layers[il].bv) {
-                    Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
-                    cb(Vcur, "Vcur", il);
-                }
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
+        // norm
+        cur = build_norm(inpL,
+                model.layers[il].attn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
 
+        // self-attention
+        {
+            // compute Q and K and RoPE them
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            cb(Qcur, "Qcur", il);
+            if (model.layers[il].bq) {
+                Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
                 cb(Qcur, "Qcur", il);
+            }
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            cb(Kcur, "Kcur", il);
+            if (model.layers[il].bk) {
+                Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
                 cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, kq_scale, il);
-                cb(cur, "attn_out", il);
             }
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            cb(Vcur, "Vcur", il);
+            if (model.layers[il].bv) {
+                Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
+                cb(Vcur, "Vcur", il);
             }
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed-forward network
-            cur = build_norm(ffn_inp,
-                    model.layers[il].attn_post_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_post_norm", il);
-
-            cur = build_ffn(cur,
-                    model.layers[il].ffn_up,   NULL, NULL,
-                    model.layers[il].ffn_gate, NULL, NULL,
-                    model.layers[il].ffn_down, NULL, NULL,
-                    NULL,
-                    LLM_FFN_SILU, LLM_FFN_PAR, il);
-            cb(cur, "ffn_out", il);
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-            cb(cur, "ffn_out", il);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+            Qcur = ggml_rope_ext(
+                    ctx0, Qcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            Kcur = ggml_rope_ext(
+                    ctx0, Kcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, model.layers[il].bo,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, kq_scale, il);
+            cb(cur, "attn_out", il);
+        }
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
         }
-        cur = inpL;
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+        cb(ffn_inp, "ffn_inp", il);
+
+        // feed-forward network
+        cur = build_norm(ffn_inp,
+                model.layers[il].attn_post_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "attn_post_norm", il);
+
+        cur = build_ffn(cur,
+                model.layers[il].ffn_up,   NULL, NULL,
+                model.layers[il].ffn_gate, NULL, NULL,
+                model.layers[il].ffn_down, NULL, NULL,
+                NULL,
+                LLM_FFN_SILU, LLM_FFN_PAR, il);
+        cb(cur, "ffn_out", il);
+
+        cur = ggml_add(ctx0, cur, ffn_inp);
+        cb(cur, "ffn_out", il);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+    cur = inpL;
 
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
+    cur = build_norm(cur,
+            model.output_norm, NULL,
+            LLM_NORM_RMS, -1);
 
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
 
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
 
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
 
-        ggml_build_forward_expand(gf, cur);
+    ggml_build_forward_expand(gf, cur);
 }
diff --git a/src/models/smallthinker.cpp b/src/models/smallthinker.cpp
index 2fcd87a8a0e..277eec29554 100644
--- a/src/models/smallthinker.cpp
+++ b/src/models/smallthinker.cpp
@@ -2,118 +2,118 @@
 
 template <bool iswa>
 llm_build_smallthinker<iswa>::llm_build_smallthinker(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params){
-        const int64_t n_embd_head = hparams.n_embd_head_v;
+    const int64_t n_embd_head = hparams.n_embd_head_v;
 
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+    GGML_ASSERT(n_embd_head == hparams.n_rot);
 
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
 
-        inpL = build_inp_embd(model.tok_embd);
+    inpL = build_inp_embd(model.tok_embd);
 
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
 
-        using inp_attn_type = std::conditional_t<iswa, llm_graph_input_attn_kv_iswa, llm_graph_input_attn_kv>;
-        inp_attn_type * inp_attn = nullptr;
+    using inp_attn_type = std::conditional_t<iswa, llm_graph_input_attn_kv_iswa, llm_graph_input_attn_kv>;
+    inp_attn_type * inp_attn = nullptr;
 
-        if constexpr (iswa) {
-            inp_attn = build_attn_inp_kv_iswa();
-        } else {
-            inp_attn = build_attn_inp_kv();
-        }
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
-
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA  = inpL;
-            ggml_tensor * probs  = nullptr;
+    if constexpr (iswa) {
+        inp_attn = build_attn_inp_kv_iswa();
+    } else {
+        inp_attn = build_attn_inp_kv();
+    }
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
 
-            probs = build_lora_mm(model.layers[il].ffn_gate_inp, inpL);  // [n_expert, n_tokens]
-            cb(probs, "ffn_moe_logits", il);
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * inpSA  = inpL;
+        ggml_tensor * probs  = nullptr;
 
-            // norm
-            cur = build_norm(inpL,model.layers[il].attn_norm, NULL, LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
+        probs = build_lora_mm(model.layers[il].ffn_gate_inp, inpL);  // [n_expert, n_tokens]
+        cb(probs, "ffn_moe_logits", il);
 
-            // self_attention
-            {
-                // compute Q and K and RoPE them
-                struct ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
+        // norm
+        cur = build_norm(inpL,model.layers[il].attn_norm, NULL, LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
 
-                struct ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
+        // self_attention
+        {
+            // compute Q and K and RoPE them
+            struct ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            cb(Qcur, "Qcur", il);
 
-                struct ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
+            struct ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            cb(Kcur, "Kcur", il);
 
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head, n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+            struct ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            cb(Vcur, "Vcur", il);
 
-                if (hparams.n_no_rope_layer_step == n_layer || il % hparams.n_no_rope_layer_step != 0) {
-                    Qcur = ggml_rope_ext(ctx0, Qcur, inp_pos, nullptr, n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                                     ext_factor, attn_factor, beta_fast, beta_slow);
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head, n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
 
-                    Kcur = ggml_rope_ext(ctx0, Kcur, inp_pos, nullptr, n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                                     ext_factor, attn_factor, beta_fast, beta_slow);
-                }
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
+            if (hparams.n_no_rope_layer_step == n_layer || il % hparams.n_no_rope_layer_step != 0) {
+                Qcur = ggml_rope_ext(ctx0, Qcur, inp_pos, nullptr, n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                                    ext_factor, attn_factor, beta_fast, beta_slow);
 
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f / sqrtf(float(n_embd_head)), il);
-            }
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur = ggml_get_rows(ctx0, cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-                probs = ggml_get_rows(ctx0, probs, inp_out_ids);
+                Kcur = ggml_rope_ext(ctx0, Kcur, inp_pos, nullptr, n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                                    ext_factor, attn_factor, beta_fast, beta_slow);
             }
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // MoE branch
-            cur = build_norm(ffn_inp, model.layers[il].ffn_norm, NULL, LLM_NORM_RMS, il);
-            cb(cur, "ffn_norm", il);
-
-            ggml_tensor * ffn_out =
-                build_moe_ffn(cur,
-                        nullptr,
-                        model.layers[il].ffn_up_exps,
-                        model.layers[il].ffn_gate_exps,
-                        model.layers[il].ffn_down_exps,
-                        nullptr,
-                        n_expert, n_expert_used,
-                        LLM_FFN_RELU, true,
-                        false, 0.0,
-                        static_cast<llama_expert_gating_func_type>(hparams.expert_gating_func),
-                        il, probs);
-
-            cb(ffn_out, "ffn_out", il);
-            cur = ffn_out;
-
-            cur = ggml_add(ctx0, cur, ffn_inp);
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, model.layers[il].bo,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f / sqrtf(float(n_embd_head)), il);
+        }
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur = ggml_get_rows(ctx0, cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+            probs = ggml_get_rows(ctx0, probs, inp_out_ids);
         }
-        cur = inpL;
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+        cb(ffn_inp, "ffn_inp", il);
+
+        // MoE branch
+        cur = build_norm(ffn_inp, model.layers[il].ffn_norm, NULL, LLM_NORM_RMS, il);
+        cb(cur, "ffn_norm", il);
+
+        ggml_tensor * ffn_out =
+            build_moe_ffn(cur,
+                    nullptr,
+                    model.layers[il].ffn_up_exps,
+                    model.layers[il].ffn_gate_exps,
+                    model.layers[il].ffn_down_exps,
+                    nullptr,
+                    n_expert, n_expert_used,
+                    LLM_FFN_RELU, true,
+                    false, 0.0,
+                    static_cast<llama_expert_gating_func_type>(hparams.expert_gating_func),
+                    il, probs);
+
+        cb(ffn_out, "ffn_out", il);
+        cur = ffn_out;
+
+        cur = ggml_add(ctx0, cur, ffn_inp);
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+    cur = inpL;
 
-        cur = build_norm(cur, model.output_norm, NULL, LLM_NORM_RMS, -1);
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
+    cur = build_norm(cur, model.output_norm, NULL, LLM_NORM_RMS, -1);
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
 
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
 
-        ggml_build_forward_expand(gf, cur);
-    }
+    ggml_build_forward_expand(gf, cur);
+}
 
 // Explicit template instantiations
 template struct llm_build_smallthinker<false>;
diff --git a/src/models/smollm3.cpp b/src/models/smollm3.cpp
index 830aa35415e..97c30deed54 100644
--- a/src/models/smollm3.cpp
+++ b/src/models/smollm3.cpp
@@ -1,128 +1,128 @@
 #include "models.h"
 
 llm_build_smollm3::llm_build_smollm3(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
+    const int64_t n_embd_head = hparams.n_embd_head_v;
 
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+    GGML_ASSERT(n_embd_head == hparams.n_rot);
 
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
 
-        inpL = build_inp_embd(model.tok_embd);
+    inpL = build_inp_embd(model.tok_embd);
 
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
 
-        auto * inp_attn = build_attn_inp_kv();
+    auto * inp_attn = build_attn_inp_kv();
 
-        const float kq_scale = hparams.f_attention_scale == 0.0f ? 1.0f/sqrtf(float(n_embd_head)) : hparams.f_attention_scale;
+    const float kq_scale = hparams.f_attention_scale == 0.0f ? 1.0f/sqrtf(float(n_embd_head)) : hparams.f_attention_scale;
 
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
 
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * inpSA = inpL;
 
-            const bool use_rope = (il + 1) % hparams.n_no_rope_layer_step != 0;
+        const bool use_rope = (il + 1) % hparams.n_no_rope_layer_step != 0;
 
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
+        // norm
+        cur = build_norm(inpL,
+                model.layers[il].attn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
 
-            // self-attention
-            {
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-                if (model.layers[il].bq) {
-                    Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
-                    cb(Qcur, "Qcur", il);
-                }
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-                if (model.layers[il].bk) {
-                    Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
-                    cb(Kcur, "Kcur", il);
-                }
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-                if (model.layers[il].bv) {
-                    Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
-                    cb(Vcur, "Vcur", il);
-                }
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                if (use_rope) {
-                    Qcur = ggml_rope_ext(
-                            ctx0, Qcur, inp_pos, nullptr,
-                            n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                            ext_factor, attn_factor, beta_fast, beta_slow
-                            );
-
-                    Kcur = ggml_rope_ext(
-                            ctx0, Kcur, inp_pos, nullptr,
-                            n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                            ext_factor, attn_factor, beta_fast, beta_slow
-                            );
-                }
+        // self-attention
+        {
+            // compute Q and K and RoPE them
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            cb(Qcur, "Qcur", il);
+            if (model.layers[il].bq) {
+                Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
                 cb(Qcur, "Qcur", il);
+            }
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            cb(Kcur, "Kcur", il);
+            if (model.layers[il].bk) {
+                Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
                 cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, kq_scale, il);
-                cb(cur, "attn_out", il);
             }
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            cb(Vcur, "Vcur", il);
+            if (model.layers[il].bv) {
+                Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
+                cb(Vcur, "Vcur", il);
             }
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed-forward network
-            {
-                cur = build_norm(ffn_inp,
-                        model.layers[il].ffn_norm, NULL,
-                        LLM_NORM_RMS, il);
-                cb(cur, "ffn_norm", il);
-
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up,   model.layers[il].ffn_up_b,   NULL,
-                        model.layers[il].ffn_gate, model.layers[il].ffn_gate_b, NULL,
-                        model.layers[il].ffn_down, model.layers[il].ffn_down_b, NULL,
-                        NULL,
-                        LLM_FFN_SILU, LLM_FFN_PAR, il);
-                cb(cur, "ffn_out", il);
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+            if (use_rope) {
+                Qcur = ggml_rope_ext(
+                        ctx0, Qcur, inp_pos, nullptr,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
+
+                Kcur = ggml_rope_ext(
+                        ctx0, Kcur, inp_pos, nullptr,
+                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                        ext_factor, attn_factor, beta_fast, beta_slow
+                        );
             }
-            cur = ggml_add(ctx0, cur, ffn_inp);
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, model.layers[il].bo,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, kq_scale, il);
+            cb(cur, "attn_out", il);
+        }
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+        }
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+        cb(ffn_inp, "ffn_inp", il);
+
+        // feed-forward network
+        {
+            cur = build_norm(ffn_inp,
+                    model.layers[il].ffn_norm, NULL,
+                    LLM_NORM_RMS, il);
+            cb(cur, "ffn_norm", il);
+
+            cur = build_ffn(cur,
+                    model.layers[il].ffn_up,   model.layers[il].ffn_up_b,   NULL,
+                    model.layers[il].ffn_gate, model.layers[il].ffn_gate_b, NULL,
+                    model.layers[il].ffn_down, model.layers[il].ffn_down_b, NULL,
+                    NULL,
+                    LLM_FFN_SILU, LLM_FFN_PAR, il);
             cb(cur, "ffn_out", il);
+        }
+        cur = ggml_add(ctx0, cur, ffn_inp);
+        cb(cur, "ffn_out", il);
 
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
 
-            // input for next layer
-            inpL = cur;
-        }
-        cur = inpL;
+        // input for next layer
+        inpL = cur;
+    }
+    cur = inpL;
 
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
+    cur = build_norm(cur,
+            model.output_norm, NULL,
+            LLM_NORM_RMS, -1);
 
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
 
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
 
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
 
-        ggml_build_forward_expand(gf, cur);
+    ggml_build_forward_expand(gf, cur);
 }
diff --git a/src/models/starcoder.cpp b/src/models/starcoder.cpp
index 0b9e58982aa..e197af4a8c6 100644
--- a/src/models/starcoder.cpp
+++ b/src/models/starcoder.cpp
@@ -1,100 +1,100 @@
 #include "models.h"
 
 llm_build_starcoder::llm_build_starcoder(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-        const int64_t n_embd_gqa  = hparams.n_embd_v_gqa();
+    const int64_t n_embd_head = hparams.n_embd_head_v;
+    const int64_t n_embd_gqa  = hparams.n_embd_v_gqa();
 
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
 
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
 
-        inpL = build_inp_embd(model.tok_embd);
+    inpL = build_inp_embd(model.tok_embd);
 
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
 
-        auto * inp_attn = build_attn_inp_kv();
+    auto * inp_attn = build_attn_inp_kv();
 
-        ggml_tensor * pos = ggml_get_rows(ctx0, model.pos_embd, inp_pos);
-        cb(pos, "pos_embd", -1);
+    ggml_tensor * pos = ggml_get_rows(ctx0, model.pos_embd, inp_pos);
+    cb(pos, "pos_embd", -1);
 
-        inpL = ggml_add(ctx0, inpL, pos);
-        cb(inpL, "inpL", -1);
+    inpL = ggml_add(ctx0, inpL, pos);
+    cb(inpL, "inpL", -1);
 
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
 
-        for (int il = 0; il < n_layer; ++il) {
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm,
-                    model.layers[il].attn_norm_b,
+    for (int il = 0; il < n_layer; ++il) {
+        cur = build_norm(inpL,
+                model.layers[il].attn_norm,
+                model.layers[il].attn_norm_b,
+                LLM_NORM, il);
+        cb(cur, "attn_norm", il);
+
+        // self-attention
+        {
+            cur = build_lora_mm(model.layers[il].wqkv, cur);
+            cb(cur, "wqkv", il);
+
+            cur = ggml_add(ctx0, cur, model.layers[il].bqkv);
+            cb(cur, "bqkv", il);
+
+            ggml_tensor * Qcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head,    n_tokens, n_embd_head*sizeof(float), cur->nb[1], 0*sizeof(float)*(n_embd));
+            ggml_tensor * Kcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd));
+            ggml_tensor * Vcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd + n_embd_gqa));
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, model.layers[il].bo,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+        }
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur  = ggml_get_rows(ctx0,  cur, inp_out_ids);
+            inpL = ggml_get_rows(ctx0, inpL, inp_out_ids);
+        }
+        // add the input
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpL);
+        cb(ffn_inp, "ffn_inp", il);
+
+        // FF
+        {
+            cur = build_norm(ffn_inp,
+                    model.layers[il].ffn_norm,
+                    model.layers[il].ffn_norm_b,
                     LLM_NORM, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                cur = build_lora_mm(model.layers[il].wqkv, cur);
-                cb(cur, "wqkv", il);
-
-                cur = ggml_add(ctx0, cur, model.layers[il].bqkv);
-                cb(cur, "bqkv", il);
-
-                ggml_tensor * Qcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head,    n_tokens, n_embd_head*sizeof(float), cur->nb[1], 0*sizeof(float)*(n_embd));
-                ggml_tensor * Kcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd));
-                ggml_tensor * Vcur = ggml_view_3d(ctx0, cur, n_embd_head, n_head_kv, n_tokens, n_embd_head*sizeof(float), cur->nb[1], 1*sizeof(float)*(n_embd + n_embd_gqa));
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur  = ggml_get_rows(ctx0,  cur, inp_out_ids);
-                inpL = ggml_get_rows(ctx0, inpL, inp_out_ids);
-            }
-            // add the input
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpL);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // FF
-            {
-                cur = build_norm(ffn_inp,
-                        model.layers[il].ffn_norm,
-                        model.layers[il].ffn_norm_b,
-                        LLM_NORM, il);
-                cb(cur, "ffn_norm", il);
-
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up,   model.layers[il].ffn_up_b,   NULL,
-                        NULL,                      NULL,                        NULL,
-                        model.layers[il].ffn_down, model.layers[il].ffn_down_b, NULL,
-                        NULL,
-                        LLM_FFN_GELU, LLM_FFN_SEQ, il);
-                cb(cur, "ffn_out", il);
-            }
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
+            cb(cur, "ffn_norm", il);
+
+            cur = build_ffn(cur,
+                    model.layers[il].ffn_up,   model.layers[il].ffn_up_b,   NULL,
+                    NULL,                      NULL,                        NULL,
+                    model.layers[il].ffn_down, model.layers[il].ffn_down_b, NULL,
+                    NULL,
+                    LLM_FFN_GELU, LLM_FFN_SEQ, il);
+            cb(cur, "ffn_out", il);
         }
-        cur = build_norm(inpL,
-                model.output_norm,
-                model.output_norm_b,
-                LLM_NORM, -1);
+        cur = ggml_add(ctx0, cur, ffn_inp);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+    cur = build_norm(inpL,
+            model.output_norm,
+            model.output_norm_b,
+            LLM_NORM, -1);
 
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
 
-        cur = build_lora_mm(model.output, cur);
+    cur = build_lora_mm(model.output, cur);
 
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
 
-        ggml_build_forward_expand(gf, cur);
+    ggml_build_forward_expand(gf, cur);
 }
diff --git a/src/models/starcoder2.cpp b/src/models/starcoder2.cpp
index 67c26149e3b..e40ef2cb749 100644
--- a/src/models/starcoder2.cpp
+++ b/src/models/starcoder2.cpp
@@ -1,121 +1,121 @@
 #include "models.h"
 
 llm_build_starcoder2::llm_build_starcoder2(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
+    const int64_t n_embd_head = hparams.n_embd_head_v;
 
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+    GGML_ASSERT(n_embd_head == hparams.n_rot);
 
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
 
-        inpL = build_inp_embd(model.tok_embd);
+    inpL = build_inp_embd(model.tok_embd);
 
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
 
-        auto * inp_attn = build_attn_inp_kv();
+    auto * inp_attn = build_attn_inp_kv();
 
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
 
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * inpSA = inpL;
 
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, model.layers[il].attn_norm_b,
-                    LLM_NORM, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                // compute Q and K and RoPE them
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-                if (model.layers[il].bq) {
-                    Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
-                    cb(Qcur, "Qcur", il);
-                }
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-                if (model.layers[il].bk) {
-                    Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
-                    cb(Kcur, "Kcur", il);
-                }
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-                if (model.layers[il].bv) {
-                    Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
-                    cb(Vcur, "Vcur", il);
-                }
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
+        // norm
+        cur = build_norm(inpL,
+                model.layers[il].attn_norm, model.layers[il].attn_norm_b,
+                LLM_NORM, il);
+        cb(cur, "attn_norm", il);
 
+        // self-attention
+        {
+            // compute Q and K and RoPE them
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            cb(Qcur, "Qcur", il);
+            if (model.layers[il].bq) {
+                Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
                 cb(Qcur, "Qcur", il);
+            }
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            cb(Kcur, "Kcur", il);
+            if (model.layers[il].bk) {
+                Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
                 cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
             }
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            cb(Vcur, "Vcur", il);
+            if (model.layers[il].bv) {
+                Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
+                cb(Vcur, "Vcur", il);
             }
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+            Qcur = ggml_rope_ext(
+                    ctx0, Qcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            Kcur = ggml_rope_ext(
+                    ctx0, Kcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, model.layers[il].bo,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+        }
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+        }
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+        cb(ffn_inp, "ffn_inp", il);
 
-            // feed-forward network
+        // feed-forward network
 
-            cur = build_norm(ffn_inp,
-                    model.layers[il].ffn_norm, model.layers[il].ffn_norm_b,
-                    LLM_NORM, il);
-            cb(cur, "ffn_norm", il);
+        cur = build_norm(ffn_inp,
+                model.layers[il].ffn_norm, model.layers[il].ffn_norm_b,
+                LLM_NORM, il);
+        cb(cur, "ffn_norm", il);
 
-            cur = build_ffn(cur,
-                    model.layers[il].ffn_up,   model.layers[il].ffn_up_b,   NULL,
-                    NULL,                      NULL,                        NULL,
-                    model.layers[il].ffn_down, model.layers[il].ffn_down_b, NULL,
-                    NULL,
-                    LLM_FFN_GELU, LLM_FFN_SEQ, il);
-            cb(cur, "ffn_out", il);
+        cur = build_ffn(cur,
+                model.layers[il].ffn_up,   model.layers[il].ffn_up_b,   NULL,
+                NULL,                      NULL,                        NULL,
+                model.layers[il].ffn_down, model.layers[il].ffn_down_b, NULL,
+                NULL,
+                LLM_FFN_GELU, LLM_FFN_SEQ, il);
+        cb(cur, "ffn_out", il);
 
-            cur = ggml_add(ctx0, cur, ffn_inp);
+        cur = ggml_add(ctx0, cur, ffn_inp);
 
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
 
-            // input for next layer
-            inpL = cur;
-        }
-        cur = inpL;
+        // input for next layer
+        inpL = cur;
+    }
+    cur = inpL;
 
-        cur = build_norm(cur,
-                model.output_norm, model.output_norm_b,
-                LLM_NORM, -1);
+    cur = build_norm(cur,
+            model.output_norm, model.output_norm_b,
+            LLM_NORM, -1);
 
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
 
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
 
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
 
-        ggml_build_forward_expand(gf, cur);
+    ggml_build_forward_expand(gf, cur);
 }
diff --git a/src/models/t5-dec.cpp b/src/models/t5-dec.cpp
index c1974e78215..297e450de76 100644
--- a/src/models/t5-dec.cpp
+++ b/src/models/t5-dec.cpp
@@ -1,166 +1,166 @@
 #include "models.h"
 
 llm_build_t5_dec::llm_build_t5_dec(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
-        //const int64_t n_embd_gqa  = hparams.n_embd_v_gqa();
+    const int64_t n_embd_head = hparams.n_embd_head_v;
+    //const int64_t n_embd_gqa  = hparams.n_embd_v_gqa();
 
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
 
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
 
-        inpL = build_inp_embd(model.tok_embd);
+    inpL = build_inp_embd(model.tok_embd);
 
-        ggml_tensor * embd_enc       = build_inp_cross_embd();
-        ggml_tensor * pos_bucket_dec = build_inp_pos_bucket_dec();
+    ggml_tensor * embd_enc       = build_inp_cross_embd();
+    ggml_tensor * pos_bucket_dec = build_inp_pos_bucket_dec();
 
-        const int64_t n_outputs_enc = embd_enc->ne[1];
+    const int64_t n_outputs_enc = embd_enc->ne[1];
 
-        auto * inp_attn_self  = build_attn_inp_kv();
-        auto * inp_attn_cross = build_attn_inp_cross();
+    auto * inp_attn_self  = build_attn_inp_kv();
+    auto * inp_attn_cross = build_attn_inp_cross();
 
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
 
-        const int64_t dec_n_layer = hparams.dec_n_layer;
+    const int64_t dec_n_layer = hparams.dec_n_layer;
 
-        for (int il = 0; il < dec_n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
+    for (int il = 0; il < dec_n_layer; ++il) {
+        ggml_tensor * inpSA = inpL;
 
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
-                    LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
+        // norm
+        cur = build_norm(inpL,
+                model.layers[il].attn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
+
+        // self-attention
+        {
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            cb(Qcur, "Qcur", il);
+
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            cb(Kcur, "Kcur", il);
+
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            cb(Vcur, "Vcur", il);
+
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+            ggml_tensor * attn_rel_b = model.layers[il].attn_rel_b ? model.layers[il].attn_rel_b : model.layers[0].attn_rel_b;
+            ggml_tensor * kq_b = build_pos_bias(pos_bucket_dec, attn_rel_b);
+
+            cur = build_attn(inp_attn_self,
+                    model.layers[il].wo, model.layers[il].bo,
+                    Qcur, Kcur, Vcur, kq_b, nullptr, nullptr, 1.0f, il);
+            cb(cur, "kqv_out", il);
+        }
+        cur = ggml_add(ctx0, cur, inpSA);
+        cb(cur, "cross_inp", il);
+
+        ggml_tensor * inpCA = cur;
+
+        // norm
+        cur = build_norm(cur,
+                model.layers[il].attn_norm_cross, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "attn_norm_cross", il);
+
+        // cross-attention
+        {
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq_cross, cur);
+            cb(Qcur, "Qcur", il);
 
-            // self-attention
-            {
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk_cross, embd_enc);
+            cb(Kcur, "Kcur", il);
 
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv_cross, embd_enc);
+            cb(Vcur, "Vcur", il);
 
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_outputs_enc);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_outputs_enc);
 
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+            cur = build_attn(inp_attn_cross,
+                    model.layers[il].wo_cross, nullptr,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f, il);
+            cb(cur, "kqv_out", il);
 
-                ggml_tensor * attn_rel_b = model.layers[il].attn_rel_b ? model.layers[il].attn_rel_b : model.layers[0].attn_rel_b;
-                ggml_tensor * kq_b = build_pos_bias(pos_bucket_dec, attn_rel_b);
+            //ggml_tensor * q =                 ggml_permute(ctx0, Qcur, 0, 2, 1, 3);
+            //ggml_tensor * k = ggml_cont(ctx0, ggml_permute(ctx0, Kcur, 0, 2, 1, 3));
 
-                cur = build_attn(inp_attn_self,
-                        model.layers[il].wo, model.layers[il].bo,
-                        Qcur, Kcur, Vcur, kq_b, nullptr, nullptr, 1.0f, il);
-                cb(cur, "kqv_out", il);
-            }
-            cur = ggml_add(ctx0, cur, inpSA);
-            cb(cur, "cross_inp", il);
+            //ggml_tensor * kq = ggml_mul_mat(ctx0, k, q);
+            //cb(kq, "kq", il);
 
-            ggml_tensor * inpCA = cur;
+            //kq = ggml_soft_max_ext(ctx0, kq, KQ_mask_cross, 1.0f, hparams.f_max_alibi_bias);
+            //cb(kq, "kq_soft_max_ext", il);
 
-            // norm
-            cur = build_norm(cur,
-                    model.layers[il].attn_norm_cross, NULL,
+            //ggml_tensor * v = ggml_cont(ctx0, ggml_transpose(ctx0, ggml_reshape_2d(ctx0, Vcur, n_embd_gqa, n_outputs_enc)));
+            //cb(v, "v", il);
+
+            //ggml_tensor * kqv = ggml_mul_mat(ctx0, ggml_reshape_3d(ctx0, v, n_outputs_enc, n_embd_head, n_head_kv), kq);
+            //cb(kqv, "kqv", il);
+
+            //ggml_tensor * kqv_merged = ggml_permute(ctx0, kqv, 0, 2, 1, 3);
+            //cb(kqv_merged, "kqv_merged", il);
+
+            //cur = ggml_cont_2d(ctx0, kqv_merged, n_embd_gqa, n_tokens);
+            //cb(cur, "kqv_merged_cont", il);
+
+            //ggml_build_forward_expand(gf, cur);
+
+            //cur = build_lora_mm(model.layers[il].wo_cross, cur);
+            //cb(cur, "kqv_out", il);
+        }
+        if (il == dec_n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+            inpCA = ggml_get_rows(ctx0, inpCA, inp_out_ids);
+        }
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpCA);
+        cb(ffn_inp, "ffn_inp", il);
+
+        // feed-forward network
+        {
+            cur = build_norm(ffn_inp,
+                    model.layers[il].ffn_norm, NULL,
                     LLM_NORM_RMS, il);
-            cb(cur, "attn_norm_cross", il);
-
-            // cross-attention
-            {
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq_cross, cur);
-                cb(Qcur, "Qcur", il);
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk_cross, embd_enc);
-                cb(Kcur, "Kcur", il);
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv_cross, embd_enc);
-                cb(Vcur, "Vcur", il);
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_outputs_enc);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_outputs_enc);
-
-                cur = build_attn(inp_attn_cross,
-                        model.layers[il].wo_cross, nullptr,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f, il);
-                cb(cur, "kqv_out", il);
-
-                //ggml_tensor * q =                 ggml_permute(ctx0, Qcur, 0, 2, 1, 3);
-                //ggml_tensor * k = ggml_cont(ctx0, ggml_permute(ctx0, Kcur, 0, 2, 1, 3));
-
-                //ggml_tensor * kq = ggml_mul_mat(ctx0, k, q);
-                //cb(kq, "kq", il);
-
-                //kq = ggml_soft_max_ext(ctx0, kq, KQ_mask_cross, 1.0f, hparams.f_max_alibi_bias);
-                //cb(kq, "kq_soft_max_ext", il);
-
-                //ggml_tensor * v = ggml_cont(ctx0, ggml_transpose(ctx0, ggml_reshape_2d(ctx0, Vcur, n_embd_gqa, n_outputs_enc)));
-                //cb(v, "v", il);
-
-                //ggml_tensor * kqv = ggml_mul_mat(ctx0, ggml_reshape_3d(ctx0, v, n_outputs_enc, n_embd_head, n_head_kv), kq);
-                //cb(kqv, "kqv", il);
-
-                //ggml_tensor * kqv_merged = ggml_permute(ctx0, kqv, 0, 2, 1, 3);
-                //cb(kqv_merged, "kqv_merged", il);
-
-                //cur = ggml_cont_2d(ctx0, kqv_merged, n_embd_gqa, n_tokens);
-                //cb(cur, "kqv_merged_cont", il);
-
-                //ggml_build_forward_expand(gf, cur);
-
-                //cur = build_lora_mm(model.layers[il].wo_cross, cur);
-                //cb(cur, "kqv_out", il);
-            }
-            if (il == dec_n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpCA = ggml_get_rows(ctx0, inpCA, inp_out_ids);
-            }
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpCA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed-forward network
-            {
-                cur = build_norm(ffn_inp,
-                        model.layers[il].ffn_norm, NULL,
-                        LLM_NORM_RMS, il);
-                cb(cur, "ffn_norm", il);
-
-                // T5 uses relu, flan-T5 uses gelu-gated
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up,   NULL, NULL,
-                        model.layers[il].ffn_gate, NULL, NULL,
-                        model.layers[il].ffn_down, NULL, NULL,
-                        NULL,
-                        model.layers[il].ffn_gate ? LLM_FFN_GELU : LLM_FFN_RELU,
-                        model.layers[il].ffn_gate ? LLM_FFN_PAR : LLM_FFN_SEQ,
-                        il);
-                cb(cur, "ffn_out", il);
-            }
-            cur = ggml_add(ctx0, cur, ffn_inp);
+            cb(cur, "ffn_norm", il);
+
+            // T5 uses relu, flan-T5 uses gelu-gated
+            cur = build_ffn(cur,
+                    model.layers[il].ffn_up,   NULL, NULL,
+                    model.layers[il].ffn_gate, NULL, NULL,
+                    model.layers[il].ffn_down, NULL, NULL,
+                    NULL,
+                    model.layers[il].ffn_gate ? LLM_FFN_GELU : LLM_FFN_RELU,
+                    model.layers[il].ffn_gate ? LLM_FFN_PAR : LLM_FFN_SEQ,
+                    il);
             cb(cur, "ffn_out", il);
+        }
+        cur = ggml_add(ctx0, cur, ffn_inp);
+        cb(cur, "ffn_out", il);
 
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
 
-            // input for next layer
-            inpL = cur;
-        }
-        cur = inpL;
-        cb(cur, "result_embd", -1);
+        // input for next layer
+        inpL = cur;
+    }
+    cur = inpL;
+    cb(cur, "result_embd", -1);
 
-        cur = build_norm(cur,
-                model.output_norm, NULL,
-                LLM_NORM_RMS, -1);
+    cur = build_norm(cur,
+            model.output_norm, NULL,
+            LLM_NORM_RMS, -1);
 
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
 
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
 
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
 
-        ggml_build_forward_expand(gf, cur);
+    ggml_build_forward_expand(gf, cur);
 }
diff --git a/src/models/t5-enc.cpp b/src/models/t5-enc.cpp
index 6b29355d20f..70e1d80dcdd 100644
--- a/src/models/t5-enc.cpp
+++ b/src/models/t5-enc.cpp
@@ -1,96 +1,96 @@
 #include "models.h"
 
 llm_build_t5_enc::llm_build_t5_enc(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
+    const int64_t n_embd_head = hparams.n_embd_head_v;
 
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
 
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
 
-        inpL = build_inp_embd(model.tok_embd);
+    inpL = build_inp_embd(model.tok_embd);
 
-        ggml_tensor * pos_bucket_enc = build_inp_pos_bucket_enc();
+    ggml_tensor * pos_bucket_enc = build_inp_pos_bucket_enc();
 
-        auto * inp_attn = build_attn_inp_no_cache();
+    auto * inp_attn = build_attn_inp_no_cache();
 
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
 
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * inpSA = inpL;
 
-            // norm
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm_enc, NULL,
+        // norm
+        cur = build_norm(inpL,
+                model.layers[il].attn_norm_enc, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
+
+        // self-attention
+        {
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq_enc, cur);
+            cb(Qcur, "Qcur", il);
+
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk_enc, cur);
+            cb(Kcur, "Kcur", il);
+
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv_enc, cur);
+            cb(Vcur, "Vcur", il);
+
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+            ggml_tensor * attn_rel_b = model.layers[il].attn_rel_b_enc ? model.layers[il].attn_rel_b_enc : model.layers[0].attn_rel_b_enc;
+            ggml_tensor * kq_b = build_pos_bias(pos_bucket_enc, attn_rel_b);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo_enc, nullptr,
+                    Qcur, Kcur, Vcur, kq_b, nullptr, nullptr, 1.0f, il);
+            cb(cur, "kqv_out", il);
+        }
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+        }
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+        cb(ffn_inp, "ffn_inp", il);
+
+        // feed-forward network
+        {
+            cur = build_norm(ffn_inp,
+                    model.layers[il].ffn_norm_enc, NULL,
                     LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq_enc, cur);
-                cb(Qcur, "Qcur", il);
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk_enc, cur);
-                cb(Kcur, "Kcur", il);
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv_enc, cur);
-                cb(Vcur, "Vcur", il);
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                ggml_tensor * attn_rel_b = model.layers[il].attn_rel_b_enc ? model.layers[il].attn_rel_b_enc : model.layers[0].attn_rel_b_enc;
-                ggml_tensor * kq_b = build_pos_bias(pos_bucket_enc, attn_rel_b);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo_enc, nullptr,
-                        Qcur, Kcur, Vcur, kq_b, nullptr, nullptr, 1.0f, il);
-                cb(cur, "kqv_out", il);
-            }
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed-forward network
-            {
-                cur = build_norm(ffn_inp,
-                        model.layers[il].ffn_norm_enc, NULL,
-                        LLM_NORM_RMS, il);
-                cb(cur, "ffn_norm", il);
-
-                // T5 uses relu, flan-T5 uses gelu-gated
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up_enc,   NULL, NULL,
-                        model.layers[il].ffn_gate_enc, NULL, NULL,
-                        model.layers[il].ffn_down_enc, NULL, NULL,
-                        NULL,
-                        model.layers[il].ffn_gate_enc ? LLM_FFN_GELU : LLM_FFN_RELU,
-                        model.layers[il].ffn_gate_enc ? LLM_FFN_PAR  : LLM_FFN_SEQ,
-                        il);
-                cb(cur, "ffn_out", il);
-            }
-            cur = ggml_add(ctx0, cur, ffn_inp);
+            cb(cur, "ffn_norm", il);
+
+            // T5 uses relu, flan-T5 uses gelu-gated
+            cur = build_ffn(cur,
+                    model.layers[il].ffn_up_enc,   NULL, NULL,
+                    model.layers[il].ffn_gate_enc, NULL, NULL,
+                    model.layers[il].ffn_down_enc, NULL, NULL,
+                    NULL,
+                    model.layers[il].ffn_gate_enc ? LLM_FFN_GELU : LLM_FFN_RELU,
+                    model.layers[il].ffn_gate_enc ? LLM_FFN_PAR  : LLM_FFN_SEQ,
+                    il);
             cb(cur, "ffn_out", il);
+        }
+        cur = ggml_add(ctx0, cur, ffn_inp);
+        cb(cur, "ffn_out", il);
 
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
 
-            // input for next layer
-            inpL = cur;
-        }
-        cur = inpL;
-        cb(cur, "result_embd", -1);
+        // input for next layer
+        inpL = cur;
+    }
+    cur = inpL;
+    cb(cur, "result_embd", -1);
 
-        cur = build_norm(cur,
-                model.output_norm_enc, NULL,
-                LLM_NORM_RMS, -1);
+    cur = build_norm(cur,
+            model.output_norm_enc, NULL,
+            LLM_NORM_RMS, -1);
 
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
 
-        ggml_build_forward_expand(gf, cur);
+    ggml_build_forward_expand(gf, cur);
 }
diff --git a/src/models/wavtokenizer-dec.cpp b/src/models/wavtokenizer-dec.cpp
index 81a3c5cd628..537a0d41248 100644
--- a/src/models/wavtokenizer-dec.cpp
+++ b/src/models/wavtokenizer-dec.cpp
@@ -1,149 +1,149 @@
 #include "models.h"
 
 llm_build_wavtokenizer_dec::llm_build_wavtokenizer_dec(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
 
-        inpL = build_inp_embd(model.tok_embd);
+    inpL = build_inp_embd(model.tok_embd);
 
-        cur = ggml_cont(ctx0, ggml_transpose(ctx0, inpL));
+    cur = ggml_cont(ctx0, ggml_transpose(ctx0, inpL));
 
-        cur = ggml_conv_1d_ph(ctx0, model.conv1d, cur, 1, 1);
-        cur = ggml_add(ctx0, cur, model.conv1d_b);
+    cur = ggml_conv_1d_ph(ctx0, model.conv1d, cur, 1, 1);
+    cur = ggml_add(ctx0, cur, model.conv1d_b);
 
-        // posnet
-        for (uint32_t il = 0; il < hparams.posnet.n_layer; ++il) {
-            const auto & layer = model.layers[il].posnet;
+    // posnet
+    for (uint32_t il = 0; il < hparams.posnet.n_layer; ++il) {
+        const auto & layer = model.layers[il].posnet;
 
-            inpL = cur;
+        inpL = cur;
 
-            switch (il) {
-                case 0:
-                case 1:
-                case 3:
-                case 4:
-                    {
-                        cur = build_norm(cur,
-                                layer.norm1,
-                                layer.norm1_b,
-                                LLM_NORM_GROUP, 0);
+        switch (il) {
+            case 0:
+            case 1:
+            case 3:
+            case 4:
+                {
+                    cur = build_norm(cur,
+                            layer.norm1,
+                            layer.norm1_b,
+                            LLM_NORM_GROUP, 0);
 
-                        cur = ggml_mul(ctx0, ggml_sigmoid(ctx0, cur), cur);
+                    cur = ggml_mul(ctx0, ggml_sigmoid(ctx0, cur), cur);
 
-                        cur = ggml_conv_1d_ph(ctx0, layer.conv1, cur, 1, 1);
-                        cur = ggml_add(ctx0, cur, layer.conv1_b);
+                    cur = ggml_conv_1d_ph(ctx0, layer.conv1, cur, 1, 1);
+                    cur = ggml_add(ctx0, cur, layer.conv1_b);
 
-                        cur = build_norm(cur,
-                                layer.norm2,
-                                layer.norm2_b,
-                                LLM_NORM_GROUP, 0);
+                    cur = build_norm(cur,
+                            layer.norm2,
+                            layer.norm2_b,
+                            LLM_NORM_GROUP, 0);
 
-                        cur = ggml_mul(ctx0, ggml_sigmoid(ctx0, cur), cur);
+                    cur = ggml_mul(ctx0, ggml_sigmoid(ctx0, cur), cur);
 
-                        cur = ggml_conv_1d_ph(ctx0, layer.conv2, cur, 1, 1);
-                        cur = ggml_add(ctx0, cur, layer.conv2_b);
+                    cur = ggml_conv_1d_ph(ctx0, layer.conv2, cur, 1, 1);
+                    cur = ggml_add(ctx0, cur, layer.conv2_b);
 
-                        cur = ggml_add(ctx0, cur, inpL);
-                    } break;
-                case 2:
-                    {
-                        cur = build_norm(cur,
-                                layer.attn_norm,
-                                layer.attn_norm_b,
-                                LLM_NORM_GROUP, 0);
+                    cur = ggml_add(ctx0, cur, inpL);
+                } break;
+            case 2:
+                {
+                    cur = build_norm(cur,
+                            layer.attn_norm,
+                            layer.attn_norm_b,
+                            LLM_NORM_GROUP, 0);
 
-                        ggml_tensor * q;
-                        ggml_tensor * k;
-                        ggml_tensor * v;
+                    ggml_tensor * q;
+                    ggml_tensor * k;
+                    ggml_tensor * v;
 
-                        q = ggml_conv_1d_ph(ctx0, layer.attn_q, cur, 1, 1);
-                        k = ggml_conv_1d_ph(ctx0, layer.attn_k, cur, 1, 1);
-                        v = ggml_conv_1d_ph(ctx0, layer.attn_v, cur, 1, 1);
+                    q = ggml_conv_1d_ph(ctx0, layer.attn_q, cur, 1, 1);
+                    k = ggml_conv_1d_ph(ctx0, layer.attn_k, cur, 1, 1);
+                    v = ggml_conv_1d_ph(ctx0, layer.attn_v, cur, 1, 1);
 
-                        q = ggml_add(ctx0, q, layer.attn_q_b);
-                        k = ggml_add(ctx0, k, layer.attn_k_b);
-                        v = ggml_add(ctx0, v, layer.attn_v_b);
+                    q = ggml_add(ctx0, q, layer.attn_q_b);
+                    k = ggml_add(ctx0, k, layer.attn_k_b);
+                    v = ggml_add(ctx0, v, layer.attn_v_b);
 
-                        q = ggml_cont(ctx0, ggml_transpose(ctx0, q));
-                        k = ggml_cont(ctx0, ggml_transpose(ctx0, k));
+                    q = ggml_cont(ctx0, ggml_transpose(ctx0, q));
+                    k = ggml_cont(ctx0, ggml_transpose(ctx0, k));
 
-                        ggml_tensor * kq = ggml_mul_mat(ctx0, k, q);
+                    ggml_tensor * kq = ggml_mul_mat(ctx0, k, q);
 
-                        kq = ggml_soft_max_ext(ctx0, kq, nullptr, 1.0f/sqrtf(float(hparams.posnet.n_embd)), 0.0f);
+                    kq = ggml_soft_max_ext(ctx0, kq, nullptr, 1.0f/sqrtf(float(hparams.posnet.n_embd)), 0.0f);
 
-                        cur = ggml_mul_mat(ctx0, kq, v);
+                    cur = ggml_mul_mat(ctx0, kq, v);
 
-                        cur = ggml_conv_1d_ph(ctx0, layer.attn_o, cur, 1, 1);
-                        cur = ggml_add(ctx0, cur, layer.attn_o_b);
+                    cur = ggml_conv_1d_ph(ctx0, layer.attn_o, cur, 1, 1);
+                    cur = ggml_add(ctx0, cur, layer.attn_o_b);
 
-                        cur = ggml_add(ctx0, cur, inpL);
-                    } break;
-                case 5:
-                    {
-                        cur = build_norm(cur,
-                                layer.norm,
-                                layer.norm_b,
-                                LLM_NORM_GROUP, 0);
-                    } break;
-                default: GGML_ABORT("unknown posnet layer");
-            };
-        }
-        cur = ggml_cont(ctx0, ggml_transpose(ctx0, cur));
+                    cur = ggml_add(ctx0, cur, inpL);
+                } break;
+            case 5:
+                {
+                    cur = build_norm(cur,
+                            layer.norm,
+                            layer.norm_b,
+                            LLM_NORM_GROUP, 0);
+                } break;
+            default: GGML_ABORT("unknown posnet layer");
+        };
+    }
+    cur = ggml_cont(ctx0, ggml_transpose(ctx0, cur));
 
-        cur = build_norm(cur,
-                model.tok_norm,
-                model.tok_norm_b,
-                LLM_NORM, -1);
+    cur = build_norm(cur,
+            model.tok_norm,
+            model.tok_norm_b,
+            LLM_NORM, -1);
 
-        cur = ggml_cont(ctx0, ggml_transpose(ctx0, cur));
+    cur = ggml_cont(ctx0, ggml_transpose(ctx0, cur));
 
-        inpL = cur;
+    inpL = cur;
 
-        // convnext
-        for (uint32_t il = 0; il < hparams.convnext.n_layer; ++il) {
-            const auto & layer = model.layers[il].convnext;
+    // convnext
+    for (uint32_t il = 0; il < hparams.convnext.n_layer; ++il) {
+        const auto & layer = model.layers[il].convnext;
 
-            cur = inpL;
+        cur = inpL;
 
-            cur = ggml_conv_1d_dw_ph(ctx0, layer.dw, cur, 1, 1);
-            cur = ggml_add(ctx0, cur, layer.dw_b);
+        cur = ggml_conv_1d_dw_ph(ctx0, layer.dw, cur, 1, 1);
+        cur = ggml_add(ctx0, cur, layer.dw_b);
 
-            cur = ggml_cont(ctx0, ggml_transpose(ctx0, cur));
+        cur = ggml_cont(ctx0, ggml_transpose(ctx0, cur));
 
-            cur = build_norm(cur,
-                    layer.norm,
-                    layer.norm_b,
-                    LLM_NORM, -1);
+        cur = build_norm(cur,
+                layer.norm,
+                layer.norm_b,
+                LLM_NORM, -1);
 
-            cur = build_ffn(cur,
-                    layer.pw1, layer.pw1_b, NULL,
-                    NULL,      NULL,        NULL,
-                    layer.pw2, layer.pw2_b, NULL,
-                    NULL,
-                    LLM_FFN_GELU, LLM_FFN_SEQ, il);
+        cur = build_ffn(cur,
+                layer.pw1, layer.pw1_b, NULL,
+                NULL,      NULL,        NULL,
+                layer.pw2, layer.pw2_b, NULL,
+                NULL,
+                LLM_FFN_GELU, LLM_FFN_SEQ, il);
 
-            cur = ggml_mul(ctx0, cur, layer.gamma);
+        cur = ggml_mul(ctx0, cur, layer.gamma);
 
-            cur = ggml_cont(ctx0, ggml_transpose(ctx0, cur));
+        cur = ggml_cont(ctx0, ggml_transpose(ctx0, cur));
 
-            inpL = ggml_add(ctx0, cur, inpL);
-        }
-        cur = inpL;
+        inpL = ggml_add(ctx0, cur, inpL);
+    }
+    cur = inpL;
 
-        cur = ggml_cont(ctx0, ggml_transpose(ctx0, cur));
+    cur = ggml_cont(ctx0, ggml_transpose(ctx0, cur));
 
-        cur = build_norm(cur,
-                model.output_norm,
-                model.output_norm_b,
-                LLM_NORM, -1);
+    cur = build_norm(cur,
+            model.output_norm,
+            model.output_norm_b,
+            LLM_NORM, -1);
 
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
 
-        cur = ggml_add(ctx0, cur, model.output_b);
+    cur = ggml_add(ctx0, cur, model.output_b);
 
-        cb(cur, "result_embd", -1);
-        res->t_embd = cur;
+    cb(cur, "result_embd", -1);
+    res->t_embd = cur;
 
-        ggml_build_forward_expand(gf, cur);
+    ggml_build_forward_expand(gf, cur);
 }
diff --git a/src/models/xverse.cpp b/src/models/xverse.cpp
index 95e2eafef3d..364797dd31b 100644
--- a/src/models/xverse.cpp
+++ b/src/models/xverse.cpp
@@ -1,108 +1,108 @@
 #include "models.h"
 
 llm_build_xverse::llm_build_xverse(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-        const int64_t n_embd_head = hparams.n_embd_head_v;
+    const int64_t n_embd_head = hparams.n_embd_head_v;
 
-        GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
-        GGML_ASSERT(n_embd_head == hparams.n_rot);
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+    GGML_ASSERT(n_embd_head == hparams.n_rot);
 
-        ggml_tensor * cur;
-        ggml_tensor * inpL;
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
 
-        inpL = build_inp_embd(model.tok_embd);
+    inpL = build_inp_embd(model.tok_embd);
 
-        // inp_pos - contains the positions
-        ggml_tensor * inp_pos = build_inp_pos();
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
 
-        auto * inp_attn = build_attn_inp_kv();
+    auto * inp_attn = build_attn_inp_kv();
 
-        ggml_tensor * inp_out_ids = build_inp_out_ids();
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
 
-        for (int il = 0; il < n_layer; ++il) {
-            ggml_tensor * inpSA = inpL;
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * inpSA = inpL;
 
-            cur = build_norm(inpL,
-                    model.layers[il].attn_norm, NULL,
+        cur = build_norm(inpL,
+                model.layers[il].attn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
+
+        // self-attention
+        {
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            cb(Qcur, "Qcur", il);
+
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            cb(Kcur, "Kcur", il);
+
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            cb(Vcur, "Vcur", il);
+
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+            Qcur = ggml_rope_ext(
+                    ctx0, Qcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            Kcur = ggml_rope_ext(
+                    ctx0, Kcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, NULL,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+        }
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+        }
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+        cb(ffn_inp, "ffn_inp", il);
+
+        // feed-forward network
+        {
+            cur = build_norm(ffn_inp,
+                    model.layers[il].ffn_norm, NULL,
                     LLM_NORM_RMS, il);
-            cb(cur, "attn_norm", il);
-
-            // self-attention
-            {
-                ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
-                cb(Qcur, "Qcur", il);
-
-                ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
-                cb(Kcur, "Kcur", il);
-
-                ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
-                cb(Vcur, "Vcur", il);
-
-                Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
-                Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
-                Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
-
-                Qcur = ggml_rope_ext(
-                        ctx0, Qcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                Kcur = ggml_rope_ext(
-                        ctx0, Kcur, inp_pos, nullptr,
-                        n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
-                        ext_factor, attn_factor, beta_fast, beta_slow
-                        );
-
-                cb(Qcur, "Qcur", il);
-                cb(Kcur, "Kcur", il);
-                cb(Vcur, "Vcur", il);
-
-                cur = build_attn(inp_attn,
-                        model.layers[il].wo, NULL,
-                        Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
-            }
-            if (il == n_layer - 1 && inp_out_ids) {
-                cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
-                inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
-            }
-            ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
-            cb(ffn_inp, "ffn_inp", il);
-
-            // feed-forward network
-            {
-                cur = build_norm(ffn_inp,
-                        model.layers[il].ffn_norm, NULL,
-                        LLM_NORM_RMS, il);
-                cb(cur, "ffn_norm", il);
-
-                cur = build_ffn(cur,
-                        model.layers[il].ffn_up,   NULL, NULL,
-                        model.layers[il].ffn_gate, NULL, NULL,
-                        model.layers[il].ffn_down, NULL, NULL,
-                        NULL,
-                        LLM_FFN_SILU, LLM_FFN_PAR, il);
-                cb(cur, "ffn_out", il);
-            }
-            cur = ggml_add(ctx0, cur, ffn_inp);
-
-            cur = build_cvec(cur, il);
-            cb(cur, "l_out", il);
-
-            // input for next layer
-            inpL = cur;
+            cb(cur, "ffn_norm", il);
+
+            cur = build_ffn(cur,
+                    model.layers[il].ffn_up,   NULL, NULL,
+                    model.layers[il].ffn_gate, NULL, NULL,
+                    model.layers[il].ffn_down, NULL, NULL,
+                    NULL,
+                    LLM_FFN_SILU, LLM_FFN_PAR, il);
+            cb(cur, "ffn_out", il);
         }
-        cur = inpL;
+        cur = ggml_add(ctx0, cur, ffn_inp);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+    cur = inpL;
 
-        cur = build_norm(cur, model.output_norm, NULL, LLM_NORM_RMS, -1);
+    cur = build_norm(cur, model.output_norm, NULL, LLM_NORM_RMS, -1);
 
-        cb(cur, "result_norm", -1);
-        res->t_embd = cur;
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
 
-        // lm_head
-        cur = build_lora_mm(model.output, cur);
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
 
-        cb(cur, "result_output", -1);
-        res->t_logits = cur;
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
 
-        ggml_build_forward_expand(gf, cur);
+    ggml_build_forward_expand(gf, cur);
 }

From d9458343663c2ada19a25ee7cfbe249fac1f0664 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sigbj=C3=B8rn=20Skj=C3=A6ret?= <sigbjorn.skjaeret@scala.com>
Date: Tue, 4 Nov 2025 12:29:39 +0100
Subject: [PATCH 078/185] ci : apply model label to models (#16994)

---
 .github/labeler.yml | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/.github/labeler.yml b/.github/labeler.yml
index c4da4ab4e1f..d8ada150c55 100644
--- a/.github/labeler.yml
+++ b/.github/labeler.yml
@@ -76,6 +76,10 @@ ggml:
     - changed-files:
         - any-glob-to-any-file:
             - ggml/**
+model:
+    - changed-files:
+        - any-glob-to-any-file:
+            - src/models/**
 nix:
     - changed-files:
         - any-glob-to-any-file:

From cc98f8d3499c7de931218d8802daae56747ecbbb Mon Sep 17 00:00:00 2001
From: Acly <aclysia@gmail.com>
Date: Tue, 4 Nov 2025 13:12:20 +0100
Subject: [PATCH 079/185] ggml-cpu : bicubic interpolation (#16891)

---
 ggml/include/ggml.h       |  1 +
 ggml/src/ggml-cpu/ops.cpp | 59 ++++++++++++++++++++++++++++++++++-----
 2 files changed, 53 insertions(+), 7 deletions(-)

diff --git a/ggml/include/ggml.h b/ggml/include/ggml.h
index 2311cdabe3b..c1ed1a21c81 100644
--- a/ggml/include/ggml.h
+++ b/ggml/include/ggml.h
@@ -2108,6 +2108,7 @@ extern "C" {
     enum ggml_scale_mode {
         GGML_SCALE_MODE_NEAREST  = 0,
         GGML_SCALE_MODE_BILINEAR = 1,
+        GGML_SCALE_MODE_BICUBIC  = 2,
 
         GGML_SCALE_MODE_COUNT
     };
diff --git a/ggml/src/ggml-cpu/ops.cpp b/ggml/src/ggml-cpu/ops.cpp
index f66d36ff62c..7e3436fec1a 100644
--- a/ggml/src/ggml-cpu/ops.cpp
+++ b/ggml/src/ggml-cpu/ops.cpp
@@ -7507,10 +7507,17 @@ static void ggml_compute_forward_upscale_f32(
     float sf1 = (float)ne1/src0->ne[1];
     float sf2 = (float)ne2/src0->ne[2];
     float sf3 = (float)ne3/src0->ne[3];
+    float pixel_offset = 0.5f;
 
     const int32_t mode_flags = ggml_get_op_params_i32(dst, 0);
     const ggml_scale_mode mode = (ggml_scale_mode) (mode_flags & 0xFF);
 
+    if (mode_flags & GGML_SCALE_FLAG_ALIGN_CORNERS) {
+        pixel_offset = 0.0f;
+        sf0 = ne0 > 1 && ne00 > 1 ? (float)(ne0 - 1) / (ne00 - 1) : sf0;
+        sf1 = ne1 > 1 && ne01 > 1 ? (float)(ne1 - 1) / (ne01 - 1) : sf1;
+    }
+
     if (mode == GGML_SCALE_MODE_NEAREST) {
         for (int64_t i3 = 0; i3 < ne3; i3++) {
             const int64_t i03 = i3 / sf3;
@@ -7530,13 +7537,6 @@ static void ggml_compute_forward_upscale_f32(
             }
         }
     } else if (mode == GGML_SCALE_MODE_BILINEAR) {
-        float pixel_offset = 0.5f;
-        if (mode_flags & GGML_SCALE_FLAG_ALIGN_CORNERS) {
-            pixel_offset = 0.0f;
-            sf0 = ne0 > 1 && ne00 > 1 ? (float)(ne0 - 1) / (ne00 - 1) : sf0;
-            sf1 = ne1 > 1 && ne01 > 1 ? (float)(ne1 - 1) / (ne01 - 1) : sf1;
-        }
-
         for (int64_t i3 = 0; i3 < ne3; i3++) {
             const int64_t i03 = i3 / sf3;
             for (int64_t i2 = ith; i2 < ne2; i2 += nth) {
@@ -7571,6 +7571,51 @@ static void ggml_compute_forward_upscale_f32(
 
                         const float val = a*(1 - dx)*(1 - dy) + b*dx*(1 - dy) + c*(1 - dx)*dy + d*dx*dy;
 
+                        float * y_dst = (float *)((char *)dst->data + i0*nb0 + i1*nb1 + i2*nb2 + i3*nb3);
+                        *y_dst = val;
+                    }
+                }
+            }
+        }
+    } else if (mode == GGML_SCALE_MODE_BICUBIC) {
+        // https://en.wikipedia.org/wiki/Bicubic_interpolation#Bicubic_convolution_algorithm
+        const float a = -0.75f; // use alpha = -0.75 (same as PyTorch)
+        auto weight1 = [a](float x) { return ((a + 2) * x - (a + 3)) * x * x + 1; };
+        auto weight2 = [a](float x) { return ((a * x - 5 * a) * x + 8 * a) * x - 4 * a; };
+        auto bicubic = [=](float p0, float p1, float p2, float p3, float x) {
+            const float w0 = weight2(x + 1);
+            const float w1 = weight1(x + 0);
+            const float w2 = weight1(1 - x);
+            const float w3 = weight2(2 - x);
+            return p0*w0 + p1*w1 + p2*w2 + p3*w3;
+        };
+
+        for (int64_t i3 = 0; i3 < ne3; i3++) {
+            const int64_t i03 = i3 / sf3;
+            for (int64_t i2 = ith; i2 < ne2; i2 += nth) {
+                const int64_t i02 = i2 / sf2;
+                for (int64_t i1 = 0; i1 < ne1; i1++) {
+                    const float y = ((float)i1 + pixel_offset) / sf1 - pixel_offset;
+                    const int64_t y0 = (int64_t)floorf(y);
+                    const float dy = y - (float)y0;
+
+                    for (int64_t i0 = 0; i0 < ne0; i0++) {
+                        const float x = ((float)i0 + pixel_offset) / sf0 - pixel_offset;
+                        const int64_t x0 = (int64_t)floorf(x);
+                        const float dx = x - (float)x0;
+
+                        auto p = [=](int64_t x_off, int64_t y_off) -> float {
+                            int64_t i00 = std::max(int64_t(0), std::min(x0 + x_off, ne00 - 1));
+                            int64_t i01 = std::max(int64_t(0), std::min(y0 + y_off, ne01 - 1));
+                            return *(const float *)((const char *)src0->data + i00*nb00 + i01*nb01 + i02*nb02 + i03*nb03);
+                        };
+
+                        const float val = bicubic(
+                            bicubic(p(-1,-1), p(0,-1), p(1,-1), p(2,-1), dx),
+                            bicubic(p(-1, 0), p(0, 0), p(1, 0), p(2, 0), dx),
+                            bicubic(p(-1, 1), p(0, 1), p(1, 1), p(2, 1), dx),
+                            bicubic(p(-1, 2), p(0, 2), p(1, 2), p(2, 2), dx), dy);
+
                         float * y_dst = (float *)((char *)dst->data + i0*nb0 + i1*nb1 + i2*nb2 + i3*nb3);
                         *y_dst = val;
                     }

From afd353246d6e91ba3a3c86d4f5b0ae176e54e801 Mon Sep 17 00:00:00 2001
From: Georgi Gerganov <ggerganov@gmail.com>
Date: Tue, 4 Nov 2025 17:21:31 +0200
Subject: [PATCH 080/185] readme : update hot topics (#17002)

---
 README.md | 7 +++----
 1 file changed, 3 insertions(+), 4 deletions(-)

diff --git a/README.md b/README.md
index f4206e8d45d..258963ac16d 100644
--- a/README.md
+++ b/README.md
@@ -17,14 +17,13 @@ LLM inference in C/C++
 
 ## Hot topics
 
-- **[guide : running gpt-oss with llama.cpp](https://github.com/ggml-org/llama.cpp/discussions/15396)**
-- **[[FEEDBACK] Better packaging for llama.cpp to support downstream consumers 🤗](https://github.com/ggml-org/llama.cpp/discussions/15313)**
+- **[guide : using the new WebUI of llama.cpp](https://github.com/ggml-org/llama.cpp/discussions/16938)**
+- [guide : running gpt-oss with llama.cpp](https://github.com/ggml-org/llama.cpp/discussions/15396)
+- [[FEEDBACK] Better packaging for llama.cpp to support downstream consumers 🤗](https://github.com/ggml-org/llama.cpp/discussions/15313)
 - Support for the `gpt-oss` model with native MXFP4 format has been added | [PR](https://github.com/ggml-org/llama.cpp/pull/15091) | [Collaboration with NVIDIA](https://blogs.nvidia.com/blog/rtx-ai-garage-openai-oss) | [Comment](https://github.com/ggml-org/llama.cpp/discussions/15095)
-- Hot PRs: [All](https://github.com/ggml-org/llama.cpp/pulls?q=is%3Apr+label%3Ahot+) | [Open](https://github.com/ggml-org/llama.cpp/pulls?q=is%3Apr+label%3Ahot+is%3Aopen)
 - Multimodal support arrived in `llama-server`: [#12898](https://github.com/ggml-org/llama.cpp/pull/12898) | [documentation](./docs/multimodal.md)
 - VS Code extension for FIM completions: https://github.com/ggml-org/llama.vscode
 - Vim/Neovim plugin for FIM completions: https://github.com/ggml-org/llama.vim
-- Introducing GGUF-my-LoRA https://github.com/ggml-org/llama.cpp/discussions/10123
 - Hugging Face Inference Endpoints now support GGUF out of the box! https://github.com/ggml-org/llama.cpp/discussions/9669
 - Hugging Face GGUF editor: [discussion](https://github.com/ggml-org/llama.cpp/discussions/9268) | [tool](https://huggingface.co/spaces/CISCai/gguf-editor)
 

From 66d8eccd42b5b5b2179c60a6d41376d3917f3b40 Mon Sep 17 00:00:00 2001
From: Georgi Gerganov <ggerganov@gmail.com>
Date: Tue, 4 Nov 2025 19:21:36 +0200
Subject: [PATCH 081/185] server : do context shift only while generating
 (#17000)

---
 tools/server/server.cpp | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/tools/server/server.cpp b/tools/server/server.cpp
index ec7dc1a130f..678aad93b86 100644
--- a/tools/server/server.cpp
+++ b/tools/server/server.cpp
@@ -3587,7 +3587,7 @@ struct server_context {
         // apply context-shift if needed
         // TODO: simplify and improve
         for (server_slot & slot : slots) {
-            if (slot.is_processing() && slot.prompt.n_tokens() + 1 >= slot.n_ctx) {
+            if (slot.state == SLOT_STATE_GENERATING && slot.prompt.n_tokens() + 1 >= slot.n_ctx) {
                 if (!params_base.ctx_shift) {
                     // this check is redundant (for good)
                     // we should never get here, because generation should already stopped in process_token()

From ad51c0a720062a04349c779aae301ad65ca4c856 Mon Sep 17 00:00:00 2001
From: Jeff Bolz <jbolz@nvidia.com>
Date: Tue, 4 Nov 2025 13:28:17 -0600
Subject: [PATCH 082/185] vulkan: remove the need for the dryrun (#16826)

* vulkan: remove the need for the dryrun

Allocate pipelines and descriptor sets when requested.

Reallocate the prealloc buffers when needed, and flush any pending work
before reallocating.

For rms_partials and total_mul_mat_bytes, use the sizes computed the last time
the graph was executed.

* remove dryrun parameters
---
 ggml/src/ggml-vulkan/ggml-vulkan.cpp | 680 +++++++++++----------------
 1 file changed, 274 insertions(+), 406 deletions(-)

diff --git a/ggml/src/ggml-vulkan/ggml-vulkan.cpp b/ggml/src/ggml-vulkan/ggml-vulkan.cpp
index 8d1a85c9693..7fc46bc46bc 100644
--- a/ggml/src/ggml-vulkan/ggml-vulkan.cpp
+++ b/ggml/src/ggml-vulkan/ggml-vulkan.cpp
@@ -129,7 +129,7 @@ struct vk_pipeline_struct {
     uint32_t align;
     // true if fields have been set by ggml_vk_create_pipeline
     bool initialized {};
-    // set to true to request the pipeline is compiled after the dryrun
+    // set to true to request the pipeline is compiled
     bool needed {};
     // set to true when the shader has been compiled
     bool compiled {};
@@ -539,9 +539,6 @@ struct vk_device_struct {
     bool mul_mat_id_m[GGML_TYPE_COUNT];
     bool mul_mat_id_s[GGML_TYPE_COUNT];
 
-    // set to true to indicate that some shaders need to be compiled after the dryrun
-    bool need_compiles {};
-
     vk::DescriptorSetLayout dsl;
 
     vk_matmul_pipeline pipeline_matmul_f32 {};
@@ -1408,6 +1405,10 @@ struct ggml_vk_garbage_collector {
     std::vector<vk_context> contexts;
 };
 
+static void ggml_vk_preallocate_buffers(ggml_backend_vk_context * ctx, vk_context subctx);
+static void ggml_vk_load_shaders(vk_device& device);
+static void ggml_pipeline_allocate_descriptor_sets(ggml_backend_vk_context * ctx);
+
 #if defined(GGML_VULKAN_MEMORY_DEBUG) || defined(GGML_VULKAN_DEBUG)
 #define VK_LOG_MEMORY(msg) std::cerr << "ggml_vulkan memory: " << msg << std::endl
 
@@ -1561,8 +1562,11 @@ struct ggml_backend_vk_context {
     bool almost_ready_fence_pending {};
     // Set before op_add and unset after op_rms_norm to indicate that the add should
     // write partial sums to accumulate the square of the vector components
+    bool do_add_rms_partials_offset_calculation;
     bool do_add_rms_partials;
 
+    uint64_t last_total_mul_mat_bytes {};
+
     // Cache most recent tensor that was converted into prealloc_y, and what pipeline it used to convert.
     vk_pipeline_struct * prealloc_y_last_pipeline_used {};
     const ggml_tensor * prealloc_y_last_tensor_used {};
@@ -1865,8 +1869,9 @@ static void ggml_pipeline_request_descriptor_sets(ggml_backend_vk_context *ctx,
     ctx->pipeline_descriptor_set_requirements += n;
     if (!pipeline->compiled) {
         pipeline->needed = true;
-        ctx->device->need_compiles = true;
+        ggml_vk_load_shaders(ctx->device);
     }
+    ggml_pipeline_allocate_descriptor_sets(ctx);
 }
 
 static void ggml_pipeline_allocate_descriptor_sets(ggml_backend_vk_context * ctx) {
@@ -1878,7 +1883,9 @@ static void ggml_pipeline_allocate_descriptor_sets(ggml_backend_vk_context * ctx
 
     vk_device& device = ctx->device;
 
-    uint32_t to_alloc = ctx->pipeline_descriptor_set_requirements - ctx->descriptor_sets.size();
+    // Grow by 50% to avoid frequent allocations
+    uint32_t needed = std::max(3 * ctx->descriptor_sets.size() / 2, size_t{ctx->pipeline_descriptor_set_requirements});
+    uint32_t to_alloc = needed - ctx->descriptor_sets.size();
     uint32_t pool_remaining = VK_DEVICE_DESCRIPTOR_POOL_SIZE - ctx->descriptor_sets.size() % VK_DEVICE_DESCRIPTOR_POOL_SIZE;
     uint32_t pool_idx = ctx->descriptor_sets.size() / VK_DEVICE_DESCRIPTOR_POOL_SIZE;
 
@@ -3916,7 +3923,6 @@ static void ggml_vk_load_shaders(vk_device& device) {
     for (auto &c : compiles) {
         c.wait();
     }
-    device->need_compiles = false;
 }
 
 static bool ggml_vk_khr_cooperative_matrix_support(const vk::PhysicalDeviceProperties& props, const vk::PhysicalDeviceDriverProperties& driver_props, vk_device_architecture arch);
@@ -5020,6 +5026,7 @@ static void ggml_vk_init(ggml_backend_vk_context * ctx, size_t idx) {
     ctx->prealloc_size_x = 0;
     ctx->prealloc_size_y = 0;
     ctx->prealloc_size_split_k = 0;
+    ctx->prealloc_size_add_rms_partials = 0;
 
     ctx->fence = ctx->device->device.createFence({});
     ctx->almost_ready_fence = ctx->device->device.createFence({});
@@ -6204,11 +6211,11 @@ static void ggml_vk_quantize_q8_1(ggml_backend_vk_context * ctx, vk_context& sub
     ggml_vk_sync_buffers(ctx, subctx);
 }
 
-static void ggml_vk_mul_mat_q_f16(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, ggml_tensor * dst, bool disable_split_k, bool dryrun = false) {
+static void ggml_vk_mul_mat_q_f16(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, ggml_tensor * dst, bool disable_split_k) {
     VK_LOG_DEBUG("ggml_vk_mul_mat_q_f16((" << src0 << ", name=" << src0->name << ", type=" << ggml_type_name(src0->type) << ", ne0=" << src0->ne[0] << ", ne1=" << src0->ne[1] << ", ne2=" << src0->ne[2] << ", ne3=" << src0->ne[3] << ", nb0=" << src0->nb[0] << ", nb1=" << src0->nb[1] << ", nb2=" << src0->nb[2] << ", nb3=" << src0->nb[3];
     std::cerr << "), (" << src1 << ", name=" << src1->name << ", type=" << ggml_type_name(src1->type) << ", ne0=" << src1->ne[0] << ", ne1=" << src1->ne[1] << ", ne2=" << src1->ne[2] << ", ne3=" << src1->ne[3] << ", nb0=" << src1->nb[0] << ", nb1=" << src1->nb[1] << ", nb2=" << src1->nb[2] << ", nb3=" << src1->nb[3];
     std::cerr << "), (" << dst << ", name=" << dst->name << ", type=" << ggml_type_name(dst->type) << ", ne0=" << dst->ne[0] << ", ne1=" << dst->ne[1] << ", ne2=" << dst->ne[2] << ", ne3=" << dst->ne[3] << ", nb0=" << dst->nb[0] << ", nb1=" << dst->nb[1] << ", nb2=" << dst->nb[2] << ", nb3=" << dst->nb[3];
-    std::cerr << "), " << (dryrun ? "dryrun" : "") << ")");
+    std::cerr << "))");
     GGML_ASSERT(ggml_vk_dim01_contiguous(src0) || src0->type == GGML_TYPE_F32 || src0->type == GGML_TYPE_F16 || src0->type == GGML_TYPE_BF16);  // NOLINT
     GGML_ASSERT(ggml_vk_dim01_contiguous(src1) || src1->type == GGML_TYPE_F32 || src1->type == GGML_TYPE_F16);  // NOLINT
 
@@ -6322,7 +6329,7 @@ static void ggml_vk_mul_mat_q_f16(ggml_backend_vk_context * ctx, vk_context& sub
         to_q8_1 = ggml_vk_get_quantize_pipeline(ctx, GGML_TYPE_Q8_1, true);
     }
 
-    if (dryrun) {
+    {
         const uint64_t x_sz_upd = x_sz * ne02 * ne03;
         uint64_t y_sz_upd = y_sz * ne12 * ne13;
         if (quantize_y) {
@@ -6337,12 +6344,15 @@ static void ggml_vk_mul_mat_q_f16(ggml_backend_vk_context * ctx, vk_context& sub
         }
         if (qx_needs_dequant && ctx->prealloc_size_x < x_sz_upd) {
             ctx->prealloc_size_x = x_sz_upd;
+            ggml_vk_preallocate_buffers(ctx, subctx);
         }
         if ((qy_needs_dequant || quantize_y) && ctx->prealloc_size_y < y_sz_upd) {
             ctx->prealloc_size_y = y_sz_upd;
+            ggml_vk_preallocate_buffers(ctx, subctx);
         }
         if (split_k > 1 && ctx->prealloc_size_split_k < split_k_size) {
             ctx->prealloc_size_split_k = split_k_size;
+            ggml_vk_preallocate_buffers(ctx, subctx);
         }
 
         // Request descriptor sets
@@ -6359,7 +6369,6 @@ static void ggml_vk_mul_mat_q_f16(ggml_backend_vk_context * ctx, vk_context& sub
         if (split_k > 1) {
             ggml_pipeline_request_descriptor_sets(ctx, ctx->device->pipeline_matmul_split_k_reduce, 1);
         }
-        return;
     }
 
     vk_buffer d_D = dst_buf_ctx->dev_buffer;
@@ -6515,7 +6524,7 @@ static bool ggml_vk_should_use_mmvq(const vk_device& device, uint32_t m, uint32_
     GGML_UNUSED(k);
 }
 
-static void ggml_vk_mul_mat_vec_q_f16(ggml_backend_vk_context * ctx, vk_context& subctx, const struct ggml_cgraph * cgraph, int node_idx, bool dryrun = false) {
+static void ggml_vk_mul_mat_vec_q_f16(ggml_backend_vk_context * ctx, vk_context& subctx, const struct ggml_cgraph * cgraph, int node_idx) {
     ggml_tensor * dst = cgraph->nodes[node_idx];
     const ggml_tensor * src0 = dst->src[0];
     const ggml_tensor * src1 = dst->src[1];
@@ -6523,7 +6532,7 @@ static void ggml_vk_mul_mat_vec_q_f16(ggml_backend_vk_context * ctx, vk_context&
     VK_LOG_DEBUG("ggml_vk_mul_mat_vec_q_f16((" << src0 << ", name=" << src0->name << ", type=" << src0->type << ", ne0=" << src0->ne[0] << ", ne1=" << src0->ne[1] << ", ne2=" << src0->ne[2] << ", ne3=" << src0->ne[3] << ", nb0=" << src0->nb[0] << ", nb1=" << src0->nb[1] << ", nb2=" << src0->nb[2] << ", nb3=" << src0->nb[3];
     std::cerr << "), (" << src1 << ", name=" << src1->name << ", type=" << src1->type << ", ne0=" << src1->ne[0] << ", ne1=" << src1->ne[1] << ", ne2=" << src1->ne[2] << ", ne3=" << src1->ne[3] << ", nb0=" << src1->nb[0] << ", nb1=" << src1->nb[1] << ", nb2=" << src1->nb[2] << ", nb3=" << src1->nb[3];
     std::cerr << "), (" << dst << ", name=" << dst->name << ", type=" << dst->type << ", ne0=" << dst->ne[0] << ", ne1=" << dst->ne[1] << ", ne2=" << dst->ne[2] << ", ne3=" << dst->ne[3] << ", nb0=" << dst->nb[0] << ", nb1=" << dst->nb[1] << ", nb2=" << dst->nb[2] << ", nb3=" << dst->nb[3];
-    std::cerr << "), " << (dryrun ? "dryrun" : "") << "),)");
+    std::cerr << ")),)");
     GGML_ASSERT(ggml_vk_dim01_contiguous(src0) || src0->type == GGML_TYPE_F32 || src0->type == GGML_TYPE_F16 || src0->type == GGML_TYPE_BF16);  // NOLINT
     GGML_ASSERT(ggml_vk_dim01_contiguous(src1) || src1->type == GGML_TYPE_F32 || src1->type == GGML_TYPE_F16);  // NOLINT
 
@@ -6619,7 +6628,7 @@ static void ggml_vk_mul_mat_vec_q_f16(ggml_backend_vk_context * ctx, vk_context&
     const uint64_t y_sz = quantize_y ? (y_ne * ggml_type_size(GGML_TYPE_Q8_1) / ggml_blck_size(GGML_TYPE_Q8_1)) : (f16_f32_kernel ? sizeof(float) * y_ne : sizeof(ggml_fp16_t) * y_ne);
     const uint64_t d_sz = sizeof(float) * d_ne;
 
-    if (dryrun) {
+    {
         const uint64_t x_sz_upd = x_sz * ne02 * ne03;
         uint64_t y_sz_upd = y_sz * ne12 * ne13;
         if (quantize_y) {
@@ -6632,9 +6641,11 @@ static void ggml_vk_mul_mat_vec_q_f16(ggml_backend_vk_context * ctx, vk_context&
         }
         if (qx_needs_dequant && ctx->prealloc_size_x < x_sz_upd) {
             ctx->prealloc_size_x = x_sz_upd;
+            ggml_vk_preallocate_buffers(ctx, subctx);
         }
         if ((qy_needs_dequant || quantize_y) && ctx->prealloc_size_y < y_sz_upd) {
             ctx->prealloc_size_y = y_sz_upd;
+            ggml_vk_preallocate_buffers(ctx, subctx);
         }
 
         // Request descriptor sets
@@ -6648,7 +6659,6 @@ static void ggml_vk_mul_mat_vec_q_f16(ggml_backend_vk_context * ctx, vk_context&
             ggml_pipeline_request_descriptor_sets(ctx, to_q8_1, 1);
         }
         ggml_pipeline_request_descriptor_sets(ctx, dmmv, 1);
-        return;
     }
 
     vk_buffer d_D;
@@ -6806,14 +6816,14 @@ static void ggml_vk_mul_mat_vec_q_f16(ggml_backend_vk_context * ctx, vk_context&
     }
 }
 
-static void ggml_vk_mul_mat_vec_p021_f16_f32(ggml_backend_vk_context * ctx, vk_context& subctx, const struct ggml_cgraph * cgraph, int node_idx, bool dryrun = false) {
+static void ggml_vk_mul_mat_vec_p021_f16_f32(ggml_backend_vk_context * ctx, vk_context& subctx, const struct ggml_cgraph * cgraph, int node_idx) {
     ggml_tensor * dst = cgraph->nodes[node_idx];
     const ggml_tensor * src0 = dst->src[0];
     const ggml_tensor * src1 = dst->src[1];
     VK_LOG_DEBUG("ggml_vk_mul_mat_p021_f16_f32(" << src0 << ", name=" << src0->name << ", type=" << src0->type << ", ne0=" << src0->ne[0] << ", ne1=" << src0->ne[1] << ", ne2=" << src0->ne[2] << ", ne3=" << src0->ne[3] << ", nb0=" << src0->nb[0] << ", nb1=" << src0->nb[1] << ", nb2=" << src0->nb[2] << ", nb3=" << src0->nb[3];
     std::cerr << "), (" << src1 << ", name=" << src1->name << ", type=" << src1->type << ", ne0=" << src1->ne[0] << ", ne1=" << src1->ne[1] << ", ne2=" << src1->ne[2] << ", ne3=" << src1->ne[3] << ", nb0=" << src1->nb[0] << ", nb1=" << src1->nb[1] << ", nb2=" << src1->nb[2] << ", nb3=" << src1->nb[3];
     std::cerr << "), (" << dst << ", name=" << dst->name << ", type=" << dst->type << ", ne0=" << dst->ne[0] << ", ne1=" << dst->ne[1] << ", ne2=" << dst->ne[2] << ", ne3=" << dst->ne[3] << ", nb0=" << dst->nb[0] << ", nb1=" << dst->nb[1] << ", nb2=" << dst->nb[2] << ", nb3=" << dst->nb[3];
-    std::cerr << "), " << (dryrun ? "dryrun" : "") << ")");
+    std::cerr << "))");
     GGML_ASSERT(ggml_is_permuted(src0) && ggml_is_permuted(src1));
     GGML_ASSERT(src0->nb[0] <= src0->nb[1] && src0->nb[2] <= src0->nb[3]);  // NOLINT
     GGML_ASSERT(src1->nb[0] <= src1->nb[1] && src1->nb[2] <= src1->nb[3]);  // NOLINT
@@ -6859,10 +6869,9 @@ static void ggml_vk_mul_mat_vec_p021_f16_f32(ggml_backend_vk_context * ctx, vk_c
         gqa_ratio = 1;
     }
 
-    if (dryrun) {
+    {
         // Request descriptor sets
         ggml_pipeline_request_descriptor_sets(ctx, ctx->device->pipeline_mul_mat_vec_p021_f16_f32[gqa_ratio - 1], 1);
-        return;
     }
 
     vk_buffer d_D;
@@ -6936,14 +6945,14 @@ static void ggml_vk_mul_mat_vec_p021_f16_f32(ggml_backend_vk_context * ctx, vk_c
         }, pc, { 1, (uint32_t)ne01, workgroups_z });
 }
 
-static void ggml_vk_mul_mat_vec_nc_f16_f32(ggml_backend_vk_context * ctx, vk_context& subctx, const struct ggml_cgraph * cgraph, int node_idx, bool dryrun = false) {
+static void ggml_vk_mul_mat_vec_nc_f16_f32(ggml_backend_vk_context * ctx, vk_context& subctx, const struct ggml_cgraph * cgraph, int node_idx) {
     ggml_tensor * dst = cgraph->nodes[node_idx];
     const ggml_tensor * src0 = dst->src[0];
     const ggml_tensor * src1 = dst->src[1];
     VK_LOG_DEBUG("ggml_vk_mul_mat_nc_f16_f32((" << src0 << ", name=" << src0->name << ", type=" << src0->type << ", ne0=" << src0->ne[0] << ", ne1=" << src0->ne[1] << ", ne2=" << src0->ne[2] << ", ne3=" << src0->ne[3] << ", nb0=" << src0->nb[0] << ", nb1=" << src0->nb[1] << ", nb2=" << src0->nb[2] << ", nb3=" << src0->nb[3];
     std::cerr << "), (" << src1 << ", name=" << src1->name << ", type=" << src1->type << ", ne0=" << src1->ne[0] << ", ne1=" << src1->ne[1] << ", ne2=" << src1->ne[2] << ", ne3=" << src1->ne[3] << ", nb0=" << src1->nb[0] << ", nb1=" << src1->nb[1] << ", nb2=" << src1->nb[2] << ", nb3=" << src1->nb[3];
     std::cerr << "), (" << dst << ", name=" << dst->name << ", type=" << dst->type << ", ne0=" << dst->ne[0] << ", ne1=" << dst->ne[1] << ", ne2=" << dst->ne[2] << ", ne3=" << dst->ne[3] << ", nb0=" << dst->nb[0] << ", nb1=" << dst->nb[1] << ", nb2=" << dst->nb[2] << ", nb3=" << dst->nb[3];
-    std::cerr << "), " << (dryrun ? "dryrun" : "") << ")");
+    std::cerr << "))");
     GGML_ASSERT(!ggml_is_transposed(src0));
     GGML_ASSERT(!ggml_is_transposed(src1));
     GGML_ASSERT(!ggml_is_permuted(src0));
@@ -6995,10 +7004,9 @@ static void ggml_vk_mul_mat_vec_nc_f16_f32(ggml_backend_vk_context * ctx, vk_con
     const uint64_t qy_sz = ggml_nbytes(src1);
     const uint64_t d_sz = sizeof(float) * d_ne;
 
-    if (dryrun) {
+    {
         // Request descriptor sets
         ggml_pipeline_request_descriptor_sets(ctx, ctx->device->pipeline_mul_mat_vec_nc_f16_f32, 1);
-        return;
     }
 
     vk_buffer d_D;
@@ -7066,7 +7074,7 @@ static void ggml_vk_mul_mat_vec_nc_f16_f32(ggml_backend_vk_context * ctx, vk_con
         }, pc, { (uint32_t)ne03, (uint32_t)ne01, (uint32_t)ne12 });
 }
 
-static void ggml_vk_mul_mat(ggml_backend_vk_context * ctx, vk_context& subctx, const struct ggml_cgraph * cgraph, int node_idx, bool dryrun = false) {
+static void ggml_vk_mul_mat(ggml_backend_vk_context * ctx, vk_context& subctx, const struct ggml_cgraph * cgraph, int node_idx) {
     ggml_tensor * dst = cgraph->nodes[node_idx];
     ggml_tensor * src0 = dst->src[0];
     ggml_tensor * src1 = dst->src[1];
@@ -7094,7 +7102,7 @@ static void ggml_vk_mul_mat(ggml_backend_vk_context * ctx, vk_context& subctx, c
             dst2.ne[0] = cur_M_size;
             src02.ne[1] = cur_M_size;
 
-            ggml_vk_mul_mat_q_f16(ctx, subctx, &src02, src1, &dst2, true, dryrun);
+            ggml_vk_mul_mat_q_f16(ctx, subctx, &src02, src1, &dst2, true);
 
             m_offset += cur_M_size;
         }
@@ -7108,21 +7116,21 @@ static void ggml_vk_mul_mat(ggml_backend_vk_context * ctx, vk_context& subctx, c
         src1->nb[1] <= src1->nb[3] &&
         src0->ne[3] == 1 &&
         src1->ne[3] == 1) {
-        ggml_vk_mul_mat_vec_p021_f16_f32(ctx, subctx, cgraph, node_idx, dryrun);
+        ggml_vk_mul_mat_vec_p021_f16_f32(ctx, subctx, cgraph, node_idx);
     } else if (src0->type == GGML_TYPE_F16 && !ggml_is_contiguous(src0) && !ggml_is_transposed(src1) && dst->ne[1] == 1 &&
                !ggml_is_permuted(src0) && !ggml_is_permuted(src1)) {
-        ggml_vk_mul_mat_vec_nc_f16_f32(ctx, subctx, cgraph, node_idx, dryrun);
+        ggml_vk_mul_mat_vec_nc_f16_f32(ctx, subctx, cgraph, node_idx);
     // mul_mat_vec supports batching ne12*ne13 when ne11==1, or treating ne11 as the batch size (up to four)
     // when ne12 and ne13 are one.
     } else if ((dst->ne[1] == 1 || (dst->ne[1] <= mul_mat_vec_max_cols && src1->ne[2] * src1->ne[3] == 1)) &&
                (src0->type == GGML_TYPE_F32 || src0->type == GGML_TYPE_F16 || src0->type == GGML_TYPE_BF16 || ggml_is_quantized(src0->type))) {
-        ggml_vk_mul_mat_vec_q_f16(ctx, subctx, cgraph, node_idx, dryrun);
+        ggml_vk_mul_mat_vec_q_f16(ctx, subctx, cgraph, node_idx);
     } else {
-        ggml_vk_mul_mat_q_f16(ctx, subctx, src0, src1, dst, false, dryrun);
+        ggml_vk_mul_mat_q_f16(ctx, subctx, src0, src1, dst, false);
     }
 }
 
-static void ggml_vk_mul_mat_id_q_f16(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, const ggml_tensor * ids, ggml_tensor * dst, bool dryrun = false) {
+static void ggml_vk_mul_mat_id_q_f16(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, const ggml_tensor * ids, ggml_tensor * dst) {
     VK_LOG_DEBUG("ggml_vk_mul_mat_id_q_f16((" << src0 << ", name=" << src0->name << ", type=" << src0->type << ", ne0=" << src0->ne[0] << ", ne1=" << src0->ne[1] << ", ne2=" << src0->ne[2] << ", ne3=" << src0->ne[3] << ", nb0=" << src0->nb[0] << ", nb1=" << src0->nb[1] << ", nb2=" << src0->nb[2] << ", nb3=" << src0->nb[3];
     std::cerr << "), (" << src1 << ", name=" << src1->name << ", type=" << src1->type << ", ne0=" << src1->ne[0] << ", ne1=" << src1->ne[1] << ", ne2=" << src1->ne[2] << ", ne3=" << src1->ne[3] << ", nb0=" << src1->nb[0] << ", nb1=" << src1->nb[1] << ", nb2=" << src1->nb[2] << ", nb3=" << src1->nb[3];
     std::cerr << "), (" << ids << ", name=" << ids->name << ", type=" << ids->type << ", ne0=" << ids->ne[0] << ", ne1=" << ids->ne[1] << ", ne2=" << ids->ne[2] << ", ne3=" << ids->ne[3] << ", nb0=" << ids->nb[0] << ", nb1=" << ids->nb[1] << ", nb2=" << ids->nb[2] << ", nb3=" << ids->nb[3];
@@ -7251,7 +7259,7 @@ static void ggml_vk_mul_mat_id_q_f16(ggml_backend_vk_context * ctx, vk_context&
         to_q8_1 = ggml_vk_get_quantize_pipeline(ctx, GGML_TYPE_Q8_1, true);
     }
 
-    if (dryrun) {
+    {
         const uint64_t x_sz_upd = x_sz * ne02 * ne03;
         uint64_t y_sz_upd = y_sz * ne12 * ne13;
         if (quantize_y) {
@@ -7264,9 +7272,11 @@ static void ggml_vk_mul_mat_id_q_f16(ggml_backend_vk_context * ctx, vk_context&
         }
         if (qx_needs_dequant && ctx->prealloc_size_x < x_sz_upd) {
             ctx->prealloc_size_x = x_sz_upd;
+            ggml_vk_preallocate_buffers(ctx, subctx);
         }
         if ((qy_needs_dequant || quantize_y) && ctx->prealloc_size_y < y_sz_upd) {
             ctx->prealloc_size_y = y_sz_upd;
+            ggml_vk_preallocate_buffers(ctx, subctx);
         }
 
         // Request descriptor sets
@@ -7280,7 +7290,6 @@ static void ggml_vk_mul_mat_id_q_f16(ggml_backend_vk_context * ctx, vk_context&
         if (quantize_y) {
             ggml_pipeline_request_descriptor_sets(ctx, to_q8_1, 1);
         }
-        return;
     }
 
     vk_buffer d_D = dst_buf_ctx->dev_buffer;
@@ -7396,7 +7405,7 @@ static void ggml_vk_mul_mat_id_q_f16(ggml_backend_vk_context * ctx, vk_context&
     }
 }
 
-static void ggml_vk_mul_mat_vec_id_q_f16(ggml_backend_vk_context * ctx, vk_context& subctx, const struct ggml_cgraph * cgraph, int node_idx, bool dryrun = false) {
+static void ggml_vk_mul_mat_vec_id_q_f16(ggml_backend_vk_context * ctx, vk_context& subctx, const struct ggml_cgraph * cgraph, int node_idx) {
     ggml_tensor * dst = cgraph->nodes[node_idx];
     ggml_tensor * src0 = dst->src[0];
     ggml_tensor * src1 = dst->src[1];
@@ -7405,7 +7414,7 @@ static void ggml_vk_mul_mat_vec_id_q_f16(ggml_backend_vk_context * ctx, vk_conte
     std::cerr << "), (" << src1 << ", name=" << src1->name << ", type=" << src1->type << ", ne0=" << src1->ne[0] << ", ne1=" << src1->ne[1] << ", ne2=" << src1->ne[2] << ", ne3=" << src1->ne[3] << ", nb0=" << src1->nb[0] << ", nb1=" << src1->nb[1] << ", nb2=" << src1->nb[2] << ", nb3=" << src1->nb[3];
     std::cerr << "), (" << ids << ", name=" << ids->name << ", type=" << ids->type << ", ne0=" << ids->ne[0] << ", ne1=" << ids->ne[1] << ", ne2=" << ids->ne[2] << ", ne3=" << ids->ne[3] << ", nb0=" << ids->nb[0] << ", nb1=" << ids->nb[1] << ", nb2=" << ids->nb[2] << ", nb3=" << ids->nb[3];
     std::cerr << "), (" << dst << ", name=" << dst->name << ", type=" << dst->type << ", ne0=" << dst->ne[0] << ", ne1=" << dst->ne[1] << ", ne2=" << dst->ne[2] << ", ne3=" << dst->ne[3] << ", nb0=" << dst->nb[0] << ", nb1=" << dst->nb[1] << ", nb2=" << dst->nb[2] << ", nb3=" << dst->nb[3];
-    std::cerr << "), " << (dryrun ? "dryrun" : "") << ")");
+    std::cerr << "))");
     GGML_ASSERT(ggml_vk_dim01_contiguous(src0) || src0->type == GGML_TYPE_F32 || src0->type == GGML_TYPE_F16 || src0->type == GGML_TYPE_BF16);  // NOLINT
     GGML_ASSERT(ggml_vk_dim01_contiguous(src1) || src1->type == GGML_TYPE_F32 || src1->type == GGML_TYPE_F16);  // NOLINT
     GGML_ASSERT(ids->type == GGML_TYPE_I32);
@@ -7493,7 +7502,7 @@ static void ggml_vk_mul_mat_vec_id_q_f16(ggml_backend_vk_context * ctx, vk_conte
     GGML_ASSERT(!qy_needs_dequant || to_fp16_vk_1 != nullptr);  // NOLINT
     GGML_ASSERT(dmmv != nullptr);
 
-    if (dryrun) {
+    {
         const uint64_t x_sz_upd = x_sz * ne02 * ne03;
         const uint64_t y_sz_upd = y_sz * ne12 * ne13;
         if (
@@ -7503,9 +7512,11 @@ static void ggml_vk_mul_mat_vec_id_q_f16(ggml_backend_vk_context * ctx, vk_conte
         }
         if (qx_needs_dequant && ctx->prealloc_size_x < x_sz_upd) {
             ctx->prealloc_size_x = x_sz_upd;
+            ggml_vk_preallocate_buffers(ctx, subctx);
         }
         if (qy_needs_dequant && ctx->prealloc_size_y < y_sz_upd) {
             ctx->prealloc_size_y = y_sz_upd;
+            ggml_vk_preallocate_buffers(ctx, subctx);
         }
 
         // Request descriptor sets
@@ -7516,7 +7527,6 @@ static void ggml_vk_mul_mat_vec_id_q_f16(ggml_backend_vk_context * ctx, vk_conte
             ggml_pipeline_request_descriptor_sets(ctx, to_fp16_vk_1, 1);
         }
         ggml_pipeline_request_descriptor_sets(ctx, dmmv, 1);
-        return;
     }
 
     vk_buffer d_D;
@@ -7664,16 +7674,16 @@ static bool ggml_vk_use_mul_mat_vec_id(const struct ggml_cgraph * cgraph, int no
     return src2->ne[1] == 1 && (src0->type == GGML_TYPE_F32 || src0->type == GGML_TYPE_F16 || ggml_is_quantized(src0->type));
 }
 
-static void ggml_vk_mul_mat_id(ggml_backend_vk_context * ctx, vk_context& subctx, const struct ggml_cgraph * cgraph, int node_idx, bool dryrun = false) {
+static void ggml_vk_mul_mat_id(ggml_backend_vk_context * ctx, vk_context& subctx, const struct ggml_cgraph * cgraph, int node_idx) {
     ggml_tensor * dst = cgraph->nodes[node_idx];
     ggml_tensor * src0 = dst->src[0];
     ggml_tensor * src1 = dst->src[1];
     ggml_tensor * src2 = dst->src[2];
     VK_LOG_DEBUG("ggml_vk_mul_mat_id(" << src0 << ", " << src1 << ", " << src2 << ", " << dst << ")");
     if (ggml_vk_use_mul_mat_vec_id(cgraph, node_idx)) {
-        ggml_vk_mul_mat_vec_id_q_f16(ctx, subctx, cgraph, node_idx, dryrun);
+        ggml_vk_mul_mat_vec_id_q_f16(ctx, subctx, cgraph, node_idx);
     } else {
-        ggml_vk_mul_mat_id_q_f16(ctx, subctx, src0, src1, src2, dst, dryrun);
+        ggml_vk_mul_mat_id_q_f16(ctx, subctx, src0, src1, src2, dst);
     }
 }
 
@@ -7733,7 +7743,7 @@ static bool ggml_vk_flash_attn_coopmat_shmem_support(const vk_device& device, co
     return supported;
 }
 
-static void ggml_vk_flash_attn(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * q, const ggml_tensor * k, const ggml_tensor * v, const ggml_tensor * mask, const ggml_tensor * sinks, ggml_tensor * dst, bool dryrun = false) {
+static void ggml_vk_flash_attn(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * q, const ggml_tensor * k, const ggml_tensor * v, const ggml_tensor * mask, const ggml_tensor * sinks, ggml_tensor * dst) {
     VK_LOG_DEBUG("ggml_vk_flash_attn((" << q << ", name=" << q->name << ", type=" << q->type << ", ne0=" << q->ne[0] << ", ne1=" << q->ne[1] << ", ne2=" << q->ne[2] << ", ne3=" << q->ne[3] << ", nb0=" << q->nb[0] << ", nb1=" << q->nb[1] << ", nb2=" << q->nb[2] << ", nb3=" << q->nb[3];
     std::cerr << "), (" << k << ", name=" << k->name << ", type=" << k->type << ", ne0=" << k->ne[0] << ", ne1=" << k->ne[1] << ", ne2=" << k->ne[2] << ", ne3=" << k->ne[3] << ", nb0=" << k->nb[0] << ", nb1=" << k->nb[1] << ", nb2=" << k->nb[2] << ", nb3=" << k->nb[3];
     std::cerr << "), (" << v << ", name=" << v->name << ", type=" << v->type << ", ne0=" << v->ne[0] << ", ne1=" << v->ne[1] << ", ne2=" << v->ne[2] << ", ne3=" << v->ne[3] << ", nb0=" << v->nb[0] << ", nb1=" << v->nb[1] << ", nb2=" << v->nb[2] << ", nb3=" << v->nb[3];
@@ -7741,7 +7751,7 @@ static void ggml_vk_flash_attn(ggml_backend_vk_context * ctx, vk_context& subctx
     if (sinks) {
         std::cerr << "), (" << sinks << ", name=" << sinks->name << ", type=" << sinks->type << ", ne0=" << sinks->ne[0] << ", ne1=" << sinks->ne[1] << ", ne2=" << sinks->ne[2] << ", ne3=" << sinks->ne[3] << ", nb0=" << sinks->nb[0] << ", nb1=" << sinks->nb[1] << ", nb2=" << sinks->nb[2] << ", nb3=" << sinks->nb[3];
     }
-    std::cerr << "), " << (dryrun ? "dryrun" : "") << ")");
+    std::cerr << "))");
 
     GGML_TENSOR_LOCALS(int64_t, neq, q,   ne)
     GGML_TENSOR_LOCALS(size_t,  nbq, q,   nb)
@@ -7915,15 +7925,15 @@ static void ggml_vk_flash_attn(ggml_backend_vk_context * ctx, vk_context& subctx
     }
     if (ctx->prealloc_size_split_k < split_k_size) {
         ctx->prealloc_size_split_k = split_k_size;
+        ggml_vk_preallocate_buffers(ctx, subctx);
     }
 
-    if (dryrun) {
+    {
         // Request descriptor sets
         ggml_pipeline_request_descriptor_sets(ctx, pipeline, 1);
         if (split_k > 1) {
             ggml_pipeline_request_descriptor_sets(ctx, ctx->device->pipeline_flash_attn_split_k_reduce, 1);
         }
-        return;
     }
 
     float scale         = 1.0f;
@@ -8727,7 +8737,7 @@ template <> void init_pushconst_tensor_offsets(ggml_backend_vk_context * ctx, vk
 }
 
 template<typename PC>
-static void ggml_vk_op_f32(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, const ggml_tensor * src2, const ggml_tensor * src3, ggml_tensor * dst, ggml_op op, PC&& pc, bool dryrun = false) {
+static void ggml_vk_op_f32(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, const ggml_tensor * src2, const ggml_tensor * src3, ggml_tensor * dst, ggml_op op, PC&& pc) {
     VK_LOG_DEBUG("ggml_vk_op_f32((" << src0 << ", name=" << src0->name << ", type=" << src0->type << ", ne0=" << src0->ne[0] << ", ne1=" << src0->ne[1] << ", ne2=" << src0->ne[2] << ", ne3=" << src0->ne[3] << ", nb0=" << src0->nb[0] << ", nb1=" << src0->nb[1] << ", nb2=" << src0->nb[2] << ", nb3=" << src0->nb[3];
     if (src1 != nullptr) {
         std::cerr << "), (" << src1 << ", name=" << src1->name << ", type=" << src1->type << ", ne0=" << src1->ne[0] << ", ne1=" << src1->ne[1] << ", ne2=" << src1->ne[2] << ", ne3=" << src1->ne[3] << ", nb0=" << src1->nb[0] << ", nb1=" << src1->nb[1] << ", nb2=" << src1->nb[2] << ", nb3=" << src1->nb[3];
@@ -8739,7 +8749,7 @@ static void ggml_vk_op_f32(ggml_backend_vk_context * ctx, vk_context& subctx, co
         std::cerr << "), (" << src3 << ", name=" << src3->name << ", type=" << src3->type << ", ne0=" << src3->ne[0] << ", ne1=" << src3->ne[1] << ", ne2=" << src3->ne[2] << ", ne3=" << src3->ne[3] << ", nb0=" << src3->nb[0] << ", nb1=" << src3->nb[1] << ", nb2=" << src3->nb[2] << ", nb3=" << src3->nb[3];
     }
     std::cerr << "), (" << dst << ", name=" << dst->name << ", type=" << dst->type << ", ne0=" << dst->ne[0] << ", ne1=" << dst->ne[1] << ", ne2=" << dst->ne[2] << ", ne3=" << dst->ne[3] << ", nb0=" << dst->nb[0] << ", nb1=" << dst->nb[1] << ", nb2=" << dst->nb[2] << ", nb3=" << dst->nb[3];
-    std::cerr << "), " << ggml_op_name(op) << ", " << (dryrun ? "dryrun" : "") << ")");
+    std::cerr << "), " << ggml_op_name(op) << ")");
     GGML_ASSERT(op == GGML_OP_GET_ROWS || op == GGML_OP_CPY || (!ggml_is_quantized(src0->type) && (src1 == nullptr || !ggml_is_quantized(src1->type))));  // NOLINT
     GGML_ASSERT(ggml_vk_op_supports_incontiguous(op) || ggml_vk_dim01_contiguous(src0));  // NOLINT
     GGML_ASSERT(dst->buffer != nullptr);
@@ -8790,10 +8800,7 @@ static void ggml_vk_op_f32(ggml_backend_vk_context * ctx, vk_context& subctx, co
         GGML_ABORT("fatal error");
     }
 
-    if (dryrun) {
-        ggml_pipeline_request_descriptor_sets(ctx, pipeline, 1);
-        return;
-    }
+    ggml_pipeline_request_descriptor_sets(ctx, pipeline, 1);
 
     const bool op_supports_incontiguous = ggml_vk_op_supports_incontiguous(op);
 
@@ -9174,7 +9181,7 @@ static void ggml_vk_op_f32(ggml_backend_vk_context * ctx, vk_context& subctx, co
     }
 }
 
-static void ggml_vk_get_rows(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, ggml_tensor * dst, bool dryrun = false) {
+static void ggml_vk_get_rows(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, ggml_tensor * dst) {
     const uint32_t src0_type_size = ggml_type_size(src0->type);
     const uint32_t src1_type_size = ggml_type_size(src1->type);
     const uint32_t dst_type_size = ggml_type_size(dst->type);
@@ -9186,10 +9193,10 @@ static void ggml_vk_get_rows(ggml_backend_vk_context * ctx, vk_context& subctx,
         (uint32_t) dst->ne[0], (uint32_t) dst->ne[1], (uint32_t) dst->ne[2],(uint32_t) dst->ne[3], (uint32_t) dst->nb[0] /  dst_type_size, (uint32_t) dst->nb[1] /  dst_type_size, (uint32_t) dst->nb[2] /  dst_type_size, (uint32_t) dst->nb[3] /  dst_type_size,
         0,
         0.0f, 0.0f, 0,
-    }, dryrun);
+    });
 }
 
-static void ggml_vk_acc(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, ggml_tensor * dst, bool dryrun = false) {
+static void ggml_vk_acc(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, ggml_tensor * dst) {
     const uint32_t src0_type_size = ggml_type_size(src0->type);
     const uint32_t src1_type_size = ggml_type_size(src1->type);
     const uint32_t dst_type_size = ggml_type_size(dst->type);
@@ -9206,10 +9213,10 @@ static void ggml_vk_acc(ggml_backend_vk_context * ctx, vk_context& subctx, const
         (uint32_t) dst->ne[0], (uint32_t) dst->ne[1], (uint32_t) dst->ne[2],(uint32_t) dst->ne[3], (uint32_t) dst->nb[0] /  dst_type_size, (uint32_t)nb1, (uint32_t)nb2, (uint32_t) dst->nb[3] /  dst_type_size,
         0,
         0.0f, 0.0f, offset,
-    }, dryrun);
+    });
 }
 
-static void ggml_vk_multi_add(ggml_backend_vk_context * ctx, vk_context& subctx, ggml_cgraph * cgraph, int node_idx, bool dryrun = false) {
+static void ggml_vk_multi_add(ggml_backend_vk_context * ctx, vk_context& subctx, ggml_cgraph * cgraph, int node_idx) {
     const ggml_tensor *first_node = cgraph->nodes[node_idx];
     const ggml_tensor *dst = cgraph->nodes[node_idx + ctx->num_additional_fused_ops];
 
@@ -9254,10 +9261,7 @@ static void ggml_vk_multi_add(ggml_backend_vk_context * ctx, vk_context& subctx,
         GGML_ABORT("fatal error");
     }
 
-    if (dryrun) {
-        ggml_pipeline_request_descriptor_sets(ctx, pipeline, 1);
-        return;
-    }
+    ggml_pipeline_request_descriptor_sets(ctx, pipeline, 1);
 
     ggml_backend_vk_buffer_context * buf_ctx[MAX_PARAMETER_COUNT];
     vk_buffer buf[MAX_PARAMETER_COUNT];
@@ -9319,7 +9323,7 @@ static void ggml_vk_multi_add(ggml_backend_vk_context * ctx, vk_context& subctx,
         }, pc, elements);
 }
 
-static void ggml_vk_add(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, ggml_tensor * dst, bool dryrun = false) {
+static void ggml_vk_add(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, ggml_tensor * dst) {
     const uint32_t src0_type_size = ggml_type_size(src0->type);
     const uint32_t src1_type_size = ggml_type_size(src1->type);
     const uint32_t dst_type_size = ggml_type_size(dst->type);
@@ -9331,10 +9335,10 @@ static void ggml_vk_add(ggml_backend_vk_context * ctx, vk_context& subctx, const
         (uint32_t) dst->ne[0], (uint32_t) dst->ne[1], (uint32_t) dst->ne[2],(uint32_t) dst->ne[3], (uint32_t) dst->nb[0] /  dst_type_size, (uint32_t) dst->nb[1] /  dst_type_size, (uint32_t) dst->nb[2] /  dst_type_size, (uint32_t) dst->nb[3] /  dst_type_size,
         0,
         0.0f, 0.0f, ctx->do_add_rms_partials,
-    }, dryrun);
+    });
 }
 
-static void ggml_vk_sub(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, ggml_tensor * dst, bool dryrun = false) {
+static void ggml_vk_sub(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, ggml_tensor * dst) {
     const uint32_t src0_type_size = ggml_type_size(src0->type);
     const uint32_t src1_type_size = ggml_type_size(src1->type);
     const uint32_t dst_type_size = ggml_type_size(dst->type);
@@ -9346,10 +9350,10 @@ static void ggml_vk_sub(ggml_backend_vk_context * ctx, vk_context& subctx, const
         (uint32_t) dst->ne[0], (uint32_t) dst->ne[1], (uint32_t) dst->ne[2],(uint32_t) dst->ne[3], (uint32_t) dst->nb[0] /  dst_type_size, (uint32_t) dst->nb[1] /  dst_type_size, (uint32_t) dst->nb[2] /  dst_type_size, (uint32_t) dst->nb[3] /  dst_type_size,
         0,
         0.0f, 0.0f, 0,
-    }, dryrun);
+    });
 }
 
-static void ggml_vk_mul(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, ggml_tensor * dst, bool dryrun = false) {
+static void ggml_vk_mul(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, ggml_tensor * dst) {
     const uint32_t src0_type_size = ggml_type_size(src0->type);
     const uint32_t src1_type_size = ggml_type_size(src1->type);
     const uint32_t dst_type_size = ggml_type_size(dst->type);
@@ -9361,10 +9365,10 @@ static void ggml_vk_mul(ggml_backend_vk_context * ctx, vk_context& subctx, const
         (uint32_t) dst->ne[0], (uint32_t) dst->ne[1], (uint32_t) dst->ne[2],(uint32_t) dst->ne[3], (uint32_t) dst->nb[0] /  dst_type_size, (uint32_t) dst->nb[1] /  dst_type_size, (uint32_t) dst->nb[2] /  dst_type_size, (uint32_t) dst->nb[3] /  dst_type_size,
         0,
         0.0f, 0.0f, 0,
-    }, dryrun);
+    });
 }
 
-static void ggml_vk_div(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, ggml_tensor * dst, bool dryrun = false) {
+static void ggml_vk_div(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, ggml_tensor * dst) {
     const uint32_t src0_type_size = ggml_type_size(src0->type);
     const uint32_t src1_type_size = ggml_type_size(src1->type);
     const uint32_t dst_type_size = ggml_type_size(dst->type);
@@ -9376,10 +9380,10 @@ static void ggml_vk_div(ggml_backend_vk_context * ctx, vk_context& subctx, const
         (uint32_t) dst->ne[0], (uint32_t) dst->ne[1], (uint32_t) dst->ne[2],(uint32_t) dst->ne[3], (uint32_t) dst->nb[0] /  dst_type_size, (uint32_t) dst->nb[1] /  dst_type_size, (uint32_t) dst->nb[2] /  dst_type_size, (uint32_t) dst->nb[3] /  dst_type_size,
         0,
         0.0f, 0.0f, 0,
-    }, dryrun);
+    });
 }
 
-static void ggml_vk_add_id(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, const ggml_tensor * src2, ggml_tensor * dst, bool dryrun = false) {
+static void ggml_vk_add_id(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, const ggml_tensor * src2, ggml_tensor * dst) {
     const uint32_t src0_type_size = ggml_type_size(src0->type);
     const uint32_t src1_type_size = ggml_type_size(src1->type);
     const uint32_t src2_type_size = ggml_type_size(src2->type);
@@ -9391,10 +9395,10 @@ static void ggml_vk_add_id(ggml_backend_vk_context * ctx, vk_context& subctx, co
         (uint32_t)src0->nb[2] / src0_type_size,
         (uint32_t)src1->nb[1] / src1_type_size,
         (uint32_t)src2->nb[1] / src2_type_size,
-    }, dryrun);
+    });
 }
 
-static void ggml_vk_op_f32_wkv(ggml_backend_vk_context * ctx, vk_context& subctx, ggml_tensor * dst, const vk_op_rwkv_wkv6_push_constants&& pc, int version, bool dryrun = false) {
+static void ggml_vk_op_f32_wkv(ggml_backend_vk_context * ctx, vk_context& subctx, ggml_tensor * dst, const vk_op_rwkv_wkv6_push_constants&& pc, int version) {
     GGML_ASSERT(version == 6 || version == 7);
     int num_srcs = version == 6 ? 6 : 7;
 
@@ -9407,10 +9411,7 @@ static void ggml_vk_op_f32_wkv(ggml_backend_vk_context * ctx, vk_context& subctx
     vk_pipeline pipeline = ggml_vk_op_get_pipeline(ctx, dst->src[0], dst->src[1], dst->src[2], dst, dst->op);
     GGML_ASSERT(pipeline != nullptr);
 
-    if (dryrun) {
-        ggml_pipeline_request_descriptor_sets(ctx, pipeline, 1);
-        return;
-    }
+    ggml_pipeline_request_descriptor_sets(ctx, pipeline, 1);
 
     ggml_backend_vk_buffer_context * dst_buf_ctx = (ggml_backend_vk_buffer_context *)dst->buffer->context;
     ggml_backend_vk_buffer_context * src_buf_ctxs[7] = { nullptr, nullptr, nullptr, nullptr, nullptr, nullptr, nullptr };
@@ -9480,7 +9481,7 @@ static void ggml_vk_op_f32_wkv(ggml_backend_vk_context * ctx, vk_context& subctx
     }
 }
 
-static void ggml_vk_rwkv_wkv6(ggml_backend_vk_context * ctx, vk_context& subctx, ggml_tensor * dst, bool dryrun = false) {
+static void ggml_vk_rwkv_wkv6(ggml_backend_vk_context * ctx, vk_context& subctx, ggml_tensor * dst) {
     const size_t seq_length = dst->src[0]->ne[2];
     const size_t n_embed = dst->ne[0];
     const size_t n_heads = dst->src[0]->ne[1];
@@ -9494,12 +9495,11 @@ static void ggml_vk_rwkv_wkv6(ggml_backend_vk_context * ctx, vk_context& subctx,
             (uint32_t)n_embed,
             (uint32_t)n_heads,
         },
-        6,
-        dryrun
+        6
     );
 }
 
-static void ggml_vk_rwkv_wkv7(ggml_backend_vk_context * ctx, vk_context& subctx, ggml_tensor * dst, bool dryrun = false) {
+static void ggml_vk_rwkv_wkv7(ggml_backend_vk_context * ctx, vk_context& subctx, ggml_tensor * dst) {
     const size_t seq_length = dst->src[0]->ne[2];
     const size_t n_embed = dst->ne[0];
     const size_t n_heads = dst->src[0]->ne[1];
@@ -9513,12 +9513,11 @@ static void ggml_vk_rwkv_wkv7(ggml_backend_vk_context * ctx, vk_context& subctx,
             (uint32_t)n_embed,
             (uint32_t)n_heads,
         },
-        7,
-        dryrun
+        7
     );
 }
 
-static void ggml_vk_ssm_scan(ggml_backend_vk_context * ctx, vk_context& subctx, ggml_tensor * dst, bool dryrun = false) {
+static void ggml_vk_ssm_scan(ggml_backend_vk_context * ctx, vk_context& subctx, ggml_tensor * dst) {
     const ggml_tensor * src0 = dst->src[0];
     const ggml_tensor * src1 = dst->src[1];
     const ggml_tensor * src2 = dst->src[2];
@@ -9540,10 +9539,7 @@ static void ggml_vk_ssm_scan(ggml_backend_vk_context * ctx, vk_context& subctx,
     vk_pipeline pipeline = ggml_vk_op_get_pipeline(ctx, src0, src1, src2, dst, dst->op);
     GGML_ASSERT(pipeline != nullptr);
 
-    if (dryrun) {
-        ggml_pipeline_request_descriptor_sets(ctx, pipeline, 1);
-        return;
-    }
+    ggml_pipeline_request_descriptor_sets(ctx, pipeline, 1);
 
     const int64_t s_off = ggml_nelements(src1) * sizeof(float);
 
@@ -9613,7 +9609,7 @@ static void ggml_vk_ssm_scan(ggml_backend_vk_context * ctx, vk_context& subctx,
     }, pc, elements);
 }
 
-static void ggml_vk_ssm_conv(ggml_backend_vk_context * ctx, vk_context& subctx, ggml_tensor * dst, bool dryrun = false) {
+static void ggml_vk_ssm_conv(ggml_backend_vk_context * ctx, vk_context& subctx, ggml_tensor * dst) {
     const ggml_tensor * src0 = dst->src[0];
     const ggml_tensor * src1 = dst->src[1];
 
@@ -9626,10 +9622,10 @@ static void ggml_vk_ssm_conv(ggml_backend_vk_context * ctx, vk_context& subctx,
         (uint32_t)src0->ne[1],
         (uint32_t)dst->ne[1],
         (uint32_t)dst->ne[2],
-    }, dryrun);
+    });
 }
 
-static void ggml_vk_op_f32_opt_step_adamw(ggml_backend_vk_context * ctx, vk_context& subctx, ggml_tensor * dst, const vk_op_push_constants&& pc, bool dryrun = false) {
+static void ggml_vk_op_f32_opt_step_adamw(ggml_backend_vk_context * ctx, vk_context& subctx, ggml_tensor * dst, const vk_op_push_constants&& pc) {
     const ggml_tensor * x = dst->src[0];
     const ggml_tensor * g = dst->src[1];
     const ggml_tensor * gm = dst->src[2];
@@ -9655,10 +9651,7 @@ static void ggml_vk_op_f32_opt_step_adamw(ggml_backend_vk_context * ctx, vk_cont
     vk_pipeline pipeline = ggml_vk_op_get_pipeline(ctx, g, gm, gv, dst, GGML_OP_OPT_STEP_ADAMW);
     GGML_ASSERT(pipeline != nullptr);
 
-    if (dryrun) {
-        ggml_pipeline_request_descriptor_sets(ctx, pipeline, 1);
-        return;
-    }
+    ggml_pipeline_request_descriptor_sets(ctx, pipeline, 1);
 
     ggml_backend_vk_buffer_context * x_buf_ctx = (ggml_backend_vk_buffer_context *)x->buffer->context;
     ggml_backend_vk_buffer_context * g_buf_ctx = (ggml_backend_vk_buffer_context *)g->buffer->context;
@@ -9722,23 +9715,22 @@ static void ggml_vk_op_f32_opt_step_adamw(ggml_backend_vk_context * ctx, vk_cont
     }, pc, elements);
 }
 
-static void ggml_vk_opt_step_adamw(ggml_backend_vk_context * ctx, vk_context& subctx, ggml_tensor * dst, bool dryrun = false) {
+static void ggml_vk_opt_step_adamw(ggml_backend_vk_context * ctx, vk_context& subctx, ggml_tensor * dst) {
     const size_t n = ggml_nelements(dst->src[0]);
 
     ggml_vk_op_f32_opt_step_adamw(
         ctx, subctx, dst,
-        { (uint32_t)n, 0, 0.0f, 0.0f },
-        dryrun
+        { (uint32_t)n, 0, 0.0f, 0.0f }
     );
 }
 
-static void ggml_vk_opt_step_sgd(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, const ggml_tensor * src2, ggml_tensor * dst, bool dryrun = false) {
+static void ggml_vk_opt_step_sgd(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, const ggml_tensor * src2, ggml_tensor * dst) {
     const size_t n = ggml_nelements(dst->src[0]);
 
-    ggml_vk_op_f32<vk_op_push_constants>(ctx, subctx, src0, src1, src2, nullptr, dst, GGML_OP_OPT_STEP_SGD, { (uint32_t)n, 0, 0.0f, 0.0f }, dryrun);
+    ggml_vk_op_f32<vk_op_push_constants>(ctx, subctx, src0, src1, src2, nullptr, dst, GGML_OP_OPT_STEP_SGD, { (uint32_t)n, 0, 0.0f, 0.0f });
 }
 
-static void ggml_vk_concat(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, ggml_tensor * dst, bool dryrun = false) {
+static void ggml_vk_concat(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, ggml_tensor * dst) {
     int * op_params = (int *)dst->op_params;
 
     const uint32_t src0_type_size = ggml_type_size(src0->type);
@@ -9752,10 +9744,10 @@ static void ggml_vk_concat(ggml_backend_vk_context * ctx, vk_context& subctx, co
         (uint32_t) dst->ne[0], (uint32_t) dst->ne[1], (uint32_t) dst->ne[2],(uint32_t) dst->ne[3], (uint32_t) dst->nb[0] /  dst_type_size, (uint32_t) dst->nb[1] /  dst_type_size, (uint32_t) dst->nb[2] /  dst_type_size, (uint32_t) dst->nb[3] /  dst_type_size,
         0,
         0.0f, 0.0f, op_params[0],
-    }, dryrun);
+    });
 }
 
-static void ggml_vk_upscale(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst, bool dryrun = false) {
+static void ggml_vk_upscale(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst) {
     const uint32_t src0_type_size = ggml_type_size(src0->type);
     const uint32_t mode = (uint32_t)ggml_get_op_params_i32(dst, 0);
 
@@ -9779,47 +9771,47 @@ static void ggml_vk_upscale(ggml_backend_vk_context * ctx, vk_context& subctx, c
         (uint32_t)nb00 / src0_type_size, (uint32_t)nb01 / src0_type_size, (uint32_t)nb02 / src0_type_size, (uint32_t)nb03 / src0_type_size,
         (uint32_t)ne0, (uint32_t)ne1, (uint32_t)ne2, (uint32_t)ne3,
         sf0, sf1, sf2, sf3, pixel_offset
-    }, dryrun);
+    });
 }
 
-static void ggml_vk_scale(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst, bool dryrun = false) {
+static void ggml_vk_scale(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst) {
     vk_op_unary_push_constants p = vk_op_unary_push_constants_init(src0, dst);
     p.param1 = ggml_get_op_params_f32(dst, 0);
     p.param2 = ggml_get_op_params_f32(dst, 1);
 
-    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_SCALE, std::move(p), dryrun);
+    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_SCALE, std::move(p));
 }
 
-static void ggml_vk_sqr(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst, bool dryrun = false) {
-    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_SQR, vk_op_unary_push_constants_init(src0, dst), dryrun);
+static void ggml_vk_sqr(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst) {
+    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_SQR, vk_op_unary_push_constants_init(src0, dst));
 }
 
-static void ggml_vk_sqrt(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst, bool dryrun = false) {
-    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_SQRT, vk_op_unary_push_constants_init(src0, dst), dryrun);
+static void ggml_vk_sqrt(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst) {
+    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_SQRT, vk_op_unary_push_constants_init(src0, dst));
 }
 
-static void ggml_vk_sin(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst, bool dryrun = false) {
-    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_SIN, vk_op_unary_push_constants_init(src0, dst), dryrun);
+static void ggml_vk_sin(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst) {
+    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_SIN, vk_op_unary_push_constants_init(src0, dst));
 }
 
-static void ggml_vk_cos(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst, bool dryrun = false) {
-    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_COS, vk_op_unary_push_constants_init(src0, dst), dryrun);
+static void ggml_vk_cos(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst) {
+    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_COS, vk_op_unary_push_constants_init(src0, dst));
 }
 
-static void ggml_vk_clamp(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst, bool dryrun = false) {
+static void ggml_vk_clamp(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst) {
     vk_op_unary_push_constants p = vk_op_unary_push_constants_init(src0, dst);
     p.param1 = ggml_get_op_params_f32(dst, 0);
     p.param2 = ggml_get_op_params_f32(dst, 1);
 
-    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_CLAMP, std::move(p), dryrun);
+    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_CLAMP, std::move(p));
 }
 
-static void ggml_vk_pad(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst, bool dryrun = false) {
+static void ggml_vk_pad(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst) {
     vk_op_pad_push_constants p = vk_op_pad_push_constants_init(src0, dst);
-    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_PAD, std::move(p), dryrun);
+    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_PAD, std::move(p));
 }
 
-static void ggml_vk_roll(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst, bool dryrun = false) {
+static void ggml_vk_roll(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst) {
     const int32_t s0 = ggml_get_op_params_i32(dst, 0);
     const int32_t s1 = ggml_get_op_params_i32(dst, 1);
     const int32_t s2 = ggml_get_op_params_i32(dst, 2);
@@ -9831,20 +9823,20 @@ static void ggml_vk_roll(ggml_backend_vk_context * ctx, vk_context& subctx, cons
     memcpy(&p.param1, &s01_packed, sizeof(float));
     memcpy(&p.param2, &s23_packed, sizeof(float));
 
-    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_ROLL, std::move(p), dryrun);
+    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_ROLL, std::move(p));
 }
 
-static void ggml_vk_repeat(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst, bool dryrun = false) {
+static void ggml_vk_repeat(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst) {
     vk_op_unary_push_constants p = vk_op_unary_push_constants_init(src0, dst, ggml_nelements(dst));
-    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_REPEAT, std::move(p), dryrun);
+    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_REPEAT, std::move(p));
 }
 
-static void ggml_vk_repeat_back(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst, bool dryrun = false) {
+static void ggml_vk_repeat_back(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst) {
     vk_op_unary_push_constants p = vk_op_unary_push_constants_init(src0, dst, ggml_nelements(dst));
-    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_REPEAT_BACK, std::move(p), dryrun);
+    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_REPEAT_BACK, std::move(p));
 }
 
-static void ggml_vk_cpy(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst, bool dryrun = false) {
+static void ggml_vk_cpy(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst) {
     uint32_t ne = (uint32_t)ggml_nelements(src0);
     if (ggml_is_quantized(src0->type) && ggml_is_quantized(dst->type)) {
         // Convert from number of logical elements to 2- or 4-byte units.
@@ -9857,10 +9849,10 @@ static void ggml_vk_cpy(ggml_backend_vk_context * ctx, vk_context& subctx, const
     }
 
     vk_op_unary_push_constants p = vk_op_unary_push_constants_init(src0, dst, ne);
-    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_CPY, std::move(p), dryrun);
+    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_CPY, std::move(p));
 }
 
-static void ggml_vk_set_rows(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, ggml_tensor * dst, bool dryrun = false) {
+static void ggml_vk_set_rows(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, ggml_tensor * dst) {
     const uint32_t src0_type_size = ggml_type_size(src0->type);
     const uint32_t src1_type_size = ggml_type_size(src1->type);
     const uint32_t dst_type_size = ggml_type_size(dst->type);
@@ -9879,20 +9871,20 @@ static void ggml_vk_set_rows(ggml_backend_vk_context * ctx, vk_context& subctx,
         (uint32_t) dst->ne[0], (uint32_t) dst->ne[1], (uint32_t) dst->ne[2],(uint32_t) dst->ne[3], (uint32_t) dst->nb[0] /  dst_type_size, (uint32_t) dst->nb[1] /  dst_type_size, (uint32_t) dst->nb[2] /  dst_type_size, (uint32_t) dst->nb[3] /  dst_type_size,
         0,
         0.0f, 0.0f, 0,
-    }, dryrun);
+    });
 }
 
-static void ggml_vk_silu_back(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, ggml_tensor * dst, bool dryrun = false) {
-    ggml_vk_op_f32<vk_op_push_constants>(ctx, subctx, src0, src1, nullptr, nullptr, dst, GGML_OP_SILU_BACK, { (uint32_t)ggml_nelements(src0), 0, 0.0f, 0.0f }, dryrun);
+static void ggml_vk_silu_back(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, ggml_tensor * dst) {
+    ggml_vk_op_f32<vk_op_push_constants>(ctx, subctx, src0, src1, nullptr, nullptr, dst, GGML_OP_SILU_BACK, { (uint32_t)ggml_nelements(src0), 0, 0.0f, 0.0f });
 }
 
-static void ggml_vk_norm(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst, bool dryrun = false) {
+static void ggml_vk_norm(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst) {
     float * op_params = (float *)dst->op_params;
 
-    ggml_vk_op_f32<vk_op_push_constants>(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_NORM, { (uint32_t)src0->ne[0], (uint32_t)src0->ne[1], op_params[0], 0.0f }, dryrun);
+    ggml_vk_op_f32<vk_op_push_constants>(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_NORM, { (uint32_t)src0->ne[0], (uint32_t)src0->ne[1], op_params[0], 0.0f });
 }
 
-static void ggml_vk_group_norm(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst, bool dryrun = false) {
+static void ggml_vk_group_norm(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst) {
     const int * int_op_params = (const int *)dst->op_params;
     const float * float_op_params = (const float *)dst->op_params;
 
@@ -9900,7 +9892,7 @@ static void ggml_vk_group_norm(ggml_backend_vk_context * ctx, vk_context& subctx
     const float eps = float_op_params[1];
     const uint32_t group_size = src0->ne[0] * src0->ne[1] * ((src0->ne[2] + num_groups - 1) / num_groups);
 
-    ggml_vk_op_f32<vk_op_push_constants>(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_GROUP_NORM, { group_size, 0, eps, 0.0f }, dryrun);
+    ggml_vk_op_f32<vk_op_push_constants>(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_GROUP_NORM, { group_size, 0, eps, 0.0f });
 }
 
 static uint32_t ggml_vk_rms_num_partials(ggml_backend_vk_context * ctx, const ggml_tensor *node) {
@@ -9916,7 +9908,7 @@ static uint32_t ggml_vk_rms_partials_size(ggml_backend_vk_context * ctx, const g
     return num_bytes;
 }
 
-static void ggml_vk_rms_norm(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, ggml_tensor * dst, float * op_params, bool dryrun = false) {
+static void ggml_vk_rms_norm(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, ggml_tensor * dst, float * op_params) {
     const uint32_t src0_type_size = ggml_type_size(src0->type);
     const uint32_t src1_type_size = ggml_type_size(src1->type);
     const uint32_t dst_type_size = ggml_type_size(dst->type);
@@ -9930,29 +9922,30 @@ static void ggml_vk_rms_norm(ggml_backend_vk_context * ctx, vk_context& subctx,
         (uint32_t) dst->ne[0], (uint32_t) dst->ne[1], (uint32_t) dst->ne[2],(uint32_t) dst->ne[3], (uint32_t) dst->nb[0] /  dst_type_size, (uint32_t) dst->nb[1] /  dst_type_size, (uint32_t) dst->nb[2] /  dst_type_size, (uint32_t) dst->nb[3] /  dst_type_size,
         0,
         op_params[0], 0.0f, (int32_t)param3,
-    }, dryrun);
+    });
 
-    if (ctx->do_add_rms_partials) {
+    if (ctx->do_add_rms_partials_offset_calculation) {
         ctx->prealloc_size_add_rms_partials_offset += ggml_vk_rms_partials_size(ctx, src0);
         ctx->do_add_rms_partials = false;
+        ctx->do_add_rms_partials_offset_calculation = false;
     }
 }
 
-static void ggml_vk_rms_norm_back(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, ggml_tensor * dst, bool dryrun = false) {
+static void ggml_vk_rms_norm_back(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, ggml_tensor * dst) {
     float * op_params = (float *)dst->op_params;
-    ggml_vk_op_f32<vk_op_push_constants>(ctx, subctx, src0, src1, nullptr, nullptr, dst, GGML_OP_RMS_NORM_BACK, { (uint32_t)src0->ne[0], (uint32_t)src0->ne[1], op_params[0], 0.0f }, dryrun);
+    ggml_vk_op_f32<vk_op_push_constants>(ctx, subctx, src0, src1, nullptr, nullptr, dst, GGML_OP_RMS_NORM_BACK, { (uint32_t)src0->ne[0], (uint32_t)src0->ne[1], op_params[0], 0.0f });
 }
 
-static void ggml_vk_l2_norm(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst, bool dryrun = false) {
+static void ggml_vk_l2_norm(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst) {
     float * op_params = (float *)dst->op_params;
-    ggml_vk_op_f32<vk_op_push_constants>(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_L2_NORM, { (uint32_t)src0->ne[0], (uint32_t)src0->ne[1], op_params[0], 0.0f }, dryrun);
+    ggml_vk_op_f32<vk_op_push_constants>(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_L2_NORM, { (uint32_t)src0->ne[0], (uint32_t)src0->ne[1], op_params[0], 0.0f });
 }
 
-static void ggml_vk_unary(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst, bool dryrun = false) {
-    ggml_vk_op_f32<vk_op_push_constants>(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_UNARY, { (uint32_t)ggml_nelements(src0), 0, 0.0f, 0.0f }, dryrun);
+static void ggml_vk_unary(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst) {
+    ggml_vk_op_f32<vk_op_push_constants>(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_UNARY, { (uint32_t)ggml_nelements(src0), 0, 0.0f, 0.0f });
 }
 
-static void ggml_vk_glu(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, ggml_tensor * dst, bool dryrun = false) {
+static void ggml_vk_glu(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, ggml_tensor * dst) {
     const float * op_params_f = (const float *)dst->op_params;
 
     const bool swapped = (bool)dst->op_params[1];
@@ -9980,15 +9973,15 @@ static void ggml_vk_glu(ggml_backend_vk_context * ctx, vk_context& subctx, const
             mode,
             alpha,
             limit
-        }, dryrun);
+        });
 }
 
-static void ggml_vk_diag_mask_inf(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst, bool dryrun = false) {
+static void ggml_vk_diag_mask_inf(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst) {
     int32_t * op_params = (int32_t *)dst->op_params;
-    ggml_vk_op_f32<vk_op_diag_mask_push_constants>(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_DIAG_MASK_INF, { (uint32_t)src0->ne[0], (uint32_t)src0->ne[1], op_params[0] }, dryrun);
+    ggml_vk_op_f32<vk_op_diag_mask_push_constants>(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_DIAG_MASK_INF, { (uint32_t)src0->ne[0], (uint32_t)src0->ne[1], op_params[0] });
 }
 
-static void ggml_vk_soft_max(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, const ggml_tensor * src2, ggml_tensor * dst, bool dryrun = false) {
+static void ggml_vk_soft_max(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, const ggml_tensor * src2, ggml_tensor * dst) {
     float * op_params = (float *)dst->op_params;
 
     float scale = op_params[0];
@@ -10021,16 +10014,15 @@ static void ggml_vk_soft_max(ggml_backend_vk_context * ctx, vk_context& subctx,
         n_head_log2,
         nrows_x,
         src2 != nullptr
-    }, dryrun);
+    });
 }
 
-static void ggml_vk_soft_max_back(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, ggml_tensor * dst, bool dryrun = false) {
+static void ggml_vk_soft_max_back(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, ggml_tensor * dst) {
     float * op_params = (float *)dst->op_params;
-    ggml_vk_op_f32<vk_op_push_constants>(ctx, subctx, src0, src1, nullptr, nullptr, dst, GGML_OP_SOFT_MAX_BACK, { (uint32_t)src0->ne[0], (uint32_t)ggml_nrows(src0), op_params[0], op_params[1] }, dryrun);
+    ggml_vk_op_f32<vk_op_push_constants>(ctx, subctx, src0, src1, nullptr, nullptr, dst, GGML_OP_SOFT_MAX_BACK, { (uint32_t)src0->ne[0], (uint32_t)ggml_nrows(src0), op_params[0], op_params[1] });
 }
 
-static void ggml_vk_topk_moe(ggml_backend_vk_context * ctx, vk_context& subctx, ggml_cgraph * cgraph, int node_idx, bool dryrun = false) {
-
+static void ggml_vk_topk_moe(ggml_backend_vk_context * ctx, vk_context& subctx, ggml_cgraph * cgraph, int node_idx) {
     topk_moe_mode mode = ggml_vk_num_additional_ops_to_topk_moe_mode(ctx->num_additional_fused_ops);
     ggml_tensor * logits = cgraph->nodes[node_idx + 0]->src[0];
     ggml_tensor * weights = (mode == TOPK_MOE_EARLY_SOFTMAX_NORM) ? cgraph->nodes[node_idx + 9] :
@@ -10050,10 +10042,7 @@ static void ggml_vk_topk_moe(ggml_backend_vk_context * ctx, vk_context& subctx,
 
     vk_pipeline pipeline = ggml_vk_op_get_pipeline(ctx, nullptr, nullptr, nullptr, cgraph->nodes[node_idx], GGML_OP_SOFT_MAX);
 
-    if (dryrun) {
-        ggml_pipeline_request_descriptor_sets(ctx, pipeline, 1);
-        return;
-    }
+    ggml_pipeline_request_descriptor_sets(ctx, pipeline, 1);
 
     ggml_backend_vk_buffer_context * logits_buf_ctx = (ggml_backend_vk_buffer_context *)logits->buffer->context;
     ggml_backend_vk_buffer_context * weights_buf_ctx = (ggml_backend_vk_buffer_context *)weights->buffer->context;
@@ -10117,7 +10106,7 @@ static void ggml_vk_topk_moe(ggml_backend_vk_context * ctx, vk_context& subctx,
         }, pc, elements);
 }
 
-static void ggml_vk_rope(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_cgraph * cgraph, int node_idx, bool backprop, bool dryrun = false) {
+static void ggml_vk_rope(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_cgraph * cgraph, int node_idx, bool backprop) {
     ggml_tensor * dst = cgraph->nodes[node_idx];
     const ggml_tensor * src0 = dst->src[0];
     const ggml_tensor * src1 = dst->src[1];
@@ -10162,10 +10151,10 @@ static void ggml_vk_rope(ggml_backend_vk_context * ctx, vk_context& subctx, cons
         freq_base, ext_factor, attn_factor, {corr_dims[0], corr_dims[1]}, theta_scale,
         src2 != nullptr, (uint32_t)src0->ne[2], s1, s2,
         { sections[0], sections[1], sections[2], sections[3] }, is_imrope, backprop, set_rows_stride,
-    }, dryrun);
+    });
 }
 
-static void ggml_vk_argsort(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst, bool dryrun = false) {
+static void ggml_vk_argsort(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst) {
     int32_t * op_params = (int32_t *)dst->op_params;
 
     uint32_t ncols = src0->ne[0];
@@ -10175,34 +10164,34 @@ static void ggml_vk_argsort(ggml_backend_vk_context * ctx, vk_context& subctx, c
         ncols,
         nrows,
         op_params[0],
-    }, dryrun);
+    });
 }
 
-static void ggml_vk_sum(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst, bool dryrun = false) {
+static void ggml_vk_sum(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst) {
     vk_op_sum_rows_push_constants p = vk_op_sum_rows_push_constants_init(src0, dst, ggml_nelements(src0));
-    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_SUM, p, dryrun);
+    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_SUM, p);
 }
 
-static void ggml_vk_sum_rows(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst, bool dryrun = false) {
+static void ggml_vk_sum_rows(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst) {
     vk_op_sum_rows_push_constants p = vk_op_sum_rows_push_constants_init(src0, dst, src0->ne[0]);
-    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_SUM_ROWS, p, dryrun);
+    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_SUM_ROWS, p);
 }
 
-static void ggml_vk_mean(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst, bool dryrun = false) {
+static void ggml_vk_mean(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst) {
     vk_op_sum_rows_push_constants p = vk_op_sum_rows_push_constants_init(src0, dst, src0->ne[0]);
     p.weight = 1.0f / (float)src0->ne[0];
-    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_MEAN, p, dryrun);
+    ggml_vk_op_f32(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_MEAN, p);
 }
 
-static void ggml_vk_argmax(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst, bool dryrun = false) {
-    ggml_vk_op_f32<vk_op_push_constants>(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_ARGMAX, { (uint32_t)src0->ne[0], (uint32_t)src0->ne[1], 0.0f, 0.0f }, dryrun);
+static void ggml_vk_argmax(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst) {
+    ggml_vk_op_f32<vk_op_push_constants>(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_ARGMAX, { (uint32_t)src0->ne[0], (uint32_t)src0->ne[1], 0.0f, 0.0f });
 }
 
-static void ggml_vk_count_equal(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, ggml_tensor * dst, bool dryrun = false) {
-    ggml_vk_op_f32<vk_op_push_constants>(ctx, subctx, src0, src1, nullptr, nullptr, dst, GGML_OP_COUNT_EQUAL, { (uint32_t)ggml_nelements(src0), 0, 0.0f, 0.0f }, dryrun);
+static void ggml_vk_count_equal(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, ggml_tensor * dst) {
+    ggml_vk_op_f32<vk_op_push_constants>(ctx, subctx, src0, src1, nullptr, nullptr, dst, GGML_OP_COUNT_EQUAL, { (uint32_t)ggml_nelements(src0), 0, 0.0f, 0.0f });
 }
 
-static void ggml_vk_im2col(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, ggml_tensor * dst, bool dryrun = false) {
+static void ggml_vk_im2col(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, ggml_tensor * dst) {
     const int32_t s0 = dst->op_params[0];
     const int32_t s1 = dst->op_params[1];
     const int32_t p0 = dst->op_params[2];
@@ -10239,10 +10228,10 @@ static void ggml_vk_im2col(ggml_backend_vk_context * ctx, vk_context& subctx, co
         pelements,
         IC * KH * KW,
         s0, s1, p0, p1, d0, d1,
-    }, dryrun);
+    });
 }
 
-static void ggml_vk_im2col_3d(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, ggml_tensor * dst, bool dryrun = false) {
+static void ggml_vk_im2col_3d(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, ggml_tensor * dst) {
     GGML_TENSOR_BINARY_OP_LOCALS
 
     const int32_t s0 = ((const int32_t *)(dst->op_params))[0];
@@ -10305,20 +10294,20 @@ static void ggml_vk_im2col_3d(ggml_backend_vk_context * ctx, vk_context& subctx,
     pc.OH_OW_IC_KD_KH_KW = OH*OW*IC*KD*KH*KW;
     pc.OW_IC_KD_KH_KW = OW*IC*KD*KH*KW;
 
-    ggml_vk_op_f32<vk_op_im2col_3d_push_constants>(ctx, subctx, src0, src1, nullptr, nullptr, dst, GGML_OP_IM2COL_3D, std::move(pc), dryrun);
+    ggml_vk_op_f32<vk_op_im2col_3d_push_constants>(ctx, subctx, src0, src1, nullptr, nullptr, dst, GGML_OP_IM2COL_3D, std::move(pc));
 }
 
-static void ggml_vk_timestep_embedding(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst, bool dryrun = false) {
+static void ggml_vk_timestep_embedding(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst) {
     const uint32_t dim = dst->op_params[0];
     const uint32_t max_period = dst->op_params[1];
     const uint32_t nb1 = dst->nb[1] / ggml_type_size(dst->type);
 
     ggml_vk_op_f32<vk_op_timestep_embedding_push_constants>(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_TIMESTEP_EMBEDDING, {
         nb1, dim, max_period,
-    }, dryrun);
+    });
 }
 
-static void ggml_vk_conv_transpose_1d(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, ggml_tensor * dst, bool dryrun = false) {
+static void ggml_vk_conv_transpose_1d(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, ggml_tensor * dst) {
     // src0: (K, Cout, Cin, 1) -- kernel
     // src1: (L, Cin, 1, 1) -- input
     // dst: (*, Cout, 1, 1)
@@ -10346,10 +10335,10 @@ static void ggml_vk_conv_transpose_1d(ggml_backend_vk_context * ctx, vk_context&
     p.nb1 = static_cast<uint32_t>(nb1 / nb0);
     p.s0 = static_cast<uint32_t>(s0);
 
-    ggml_vk_op_f32(ctx, subctx, src0, src1, nullptr, nullptr, dst, GGML_OP_CONV_TRANSPOSE_1D, std::move(p), dryrun);
+    ggml_vk_op_f32(ctx, subctx, src0, src1, nullptr, nullptr, dst, GGML_OP_CONV_TRANSPOSE_1D, std::move(p));
 }
 
-static void ggml_vk_pool_2d(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst, bool dryrun = false) {
+static void ggml_vk_pool_2d(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst) {
     uint32_t op = static_cast<uint32_t>(dst->op_params[0]);
     const int32_t k1 = dst->op_params[1];
     const int32_t k0 = dst->op_params[2];
@@ -10374,11 +10363,11 @@ static void ggml_vk_pool_2d(ggml_backend_vk_context * ctx, vk_context& subctx, c
         parallel_elements,
         op,
         k0, k1, s0, s1, p0, p1,
-    }, dryrun);
+    });
 }
 
 static void ggml_vk_conv_2d(ggml_backend_vk_context * ctx, vk_context & subctx, const ggml_tensor * src0,
-                            const ggml_tensor * src1, ggml_tensor * dst, bool dryrun = false) {
+                            const ggml_tensor * src1, ggml_tensor * dst) {
     GGML_ASSERT(src0->type == GGML_TYPE_F32 || src0->type == GGML_TYPE_F16);
     GGML_ASSERT(src1->type == GGML_TYPE_F32);
     GGML_ASSERT(dst->type == GGML_TYPE_F32);
@@ -10423,11 +10412,11 @@ static void ggml_vk_conv_2d(ggml_backend_vk_context * ctx, vk_context & subctx,
     GGML_ASSERT(ne03 == ne2);
     GGML_ASSERT(ne02 == ne12);
 
-    ggml_vk_op_f32(ctx, subctx, src0, src1, nullptr, nullptr, dst, GGML_OP_CONV_2D, std::move(p), dryrun);
+    ggml_vk_op_f32(ctx, subctx, src0, src1, nullptr, nullptr, dst, GGML_OP_CONV_2D, std::move(p));
 }
 
 static void ggml_vk_conv_transpose_2d(ggml_backend_vk_context * ctx, vk_context & subctx, const ggml_tensor * src0,
-                                      const ggml_tensor * src1, ggml_tensor * dst, bool dryrun = false) {
+                                      const ggml_tensor * src1, ggml_tensor * dst) {
     GGML_ASSERT(src0->type == GGML_TYPE_F32 || src0->type == GGML_TYPE_F16);
     GGML_ASSERT(src1->type == GGML_TYPE_F32);
     GGML_ASSERT(dst->type == GGML_TYPE_F32);
@@ -10472,10 +10461,10 @@ static void ggml_vk_conv_transpose_2d(ggml_backend_vk_context * ctx, vk_context
     GGML_ASSERT(ne02 == ne2);
     GGML_ASSERT(ne03 == ne12);
 
-    ggml_vk_op_f32(ctx, subctx, src0, src1, nullptr, nullptr, dst, GGML_OP_CONV_TRANSPOSE_2D, std::move(p), dryrun);
+    ggml_vk_op_f32(ctx, subctx, src0, src1, nullptr, nullptr, dst, GGML_OP_CONV_TRANSPOSE_2D, std::move(p));
 }
 
-static void ggml_vk_conv_2d_dw(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, ggml_tensor * dst, bool dryrun = false) {
+static void ggml_vk_conv_2d_dw(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, ggml_tensor * dst) {
     vk_op_conv2d_dw_push_constants p{};
     p.ne = ggml_nelements(dst);
     p.channels = dst->ne[2];
@@ -10496,12 +10485,12 @@ static void ggml_vk_conv_2d_dw(ggml_backend_vk_context * ctx, vk_context& subctx
     GGML_ASSERT(src0->ne[3] == p.channels);
     GGML_ASSERT(src1->ne[3] == p.batches);
 
-    ggml_vk_op_f32(ctx, subctx, src0, src1, nullptr, nullptr, dst, GGML_OP_CONV_2D_DW, std::move(p), dryrun);
+    ggml_vk_op_f32(ctx, subctx, src0, src1, nullptr, nullptr, dst, GGML_OP_CONV_2D_DW, std::move(p));
 }
 
-static void ggml_vk_leaky_relu(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst, bool dryrun = false) {
+static void ggml_vk_leaky_relu(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst) {
     const float * op_params = (const float *)dst->op_params;
-    ggml_vk_op_f32<vk_op_push_constants>(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_LEAKY_RELU, { (uint32_t)ggml_nelements(src0), 0, op_params[0], 0.0f }, dryrun);
+    ggml_vk_op_f32<vk_op_push_constants>(ctx, subctx, src0, nullptr, nullptr, nullptr, dst, GGML_OP_LEAKY_RELU, { (uint32_t)ggml_nelements(src0), 0, op_params[0], 0.0f });
 }
 
 #ifdef GGML_VULKAN_RUN_TESTS
@@ -10660,10 +10649,6 @@ static void ggml_vk_test_matmul(ggml_backend_vk_context * ctx, size_t m, size_t
         }
     }
 
-    if (ctx->device->need_compiles) {
-        ggml_vk_load_shaders(ctx->device);
-    }
-
     ggml_pipeline_allocate_descriptor_sets(ctx);
 
     vk_buffer d_X = ggml_vk_create_buffer_check(ctx->device, sizeof(X_TYPE) * x_ne, {vk::MemoryPropertyFlagBits::eDeviceLocal});
@@ -10910,10 +10895,6 @@ static void ggml_vk_test_dequant(ggml_backend_vk_context * ctx, size_t ne, ggml_
 
     ggml_pipeline_request_descriptor_sets(ctx, p, 1);
 
-    if (ctx->device->need_compiles) {
-        ggml_vk_load_shaders(ctx->device);
-    }
-
     ggml_pipeline_allocate_descriptor_sets(ctx);
 
     ggml_vk_buffer_write(qx_buf, 0, qx, qx_sz);
@@ -11011,10 +10992,6 @@ static void ggml_vk_test_dequant(ggml_backend_vk_context * ctx, size_t ne, ggml_
 //
 //     ggml_pipeline_request_descriptor_sets(ctx, p, 1);
 //
-//     if (ctx->device->need_compiles) {
-//         ggml_vk_load_shaders(ctx->device);
-//     }
-//
 //     ggml_pipeline_allocate_descriptor_sets(ctx);
 //
 //     ggml_vk_buffer_write(x_buf, 0, x, x_sz);
@@ -11185,10 +11162,6 @@ static void ggml_vk_test_dequant_matmul(ggml_backend_vk_context * ctx, size_t m,
         ggml_pipeline_request_descriptor_sets(ctx, ctx->device->pipeline_quantize_q8_1, num_it);
     }
 
-    if (ctx->device->need_compiles) {
-        ggml_vk_load_shaders(ctx->device);
-    }
-
     ggml_pipeline_allocate_descriptor_sets(ctx);
 
     ggml_vk_buffer_write(qx_buf, 0, qx, qx_sz);
@@ -11326,7 +11299,7 @@ static void ggml_vk_test_dequant_matmul(ggml_backend_vk_context * ctx, size_t m,
 }
 #endif
 
-static void ggml_vk_preallocate_buffers(ggml_backend_vk_context * ctx) {
+static void ggml_vk_preallocate_buffers(ggml_backend_vk_context * ctx, vk_context subctx) {
 #if defined(GGML_VULKAN_RUN_TESTS)
     const std::vector<size_t> vals {
         512, 512, 128,
@@ -11416,6 +11389,14 @@ static void ggml_vk_preallocate_buffers(ggml_backend_vk_context * ctx) {
     GGML_ABORT("fatal error");
 #endif
 
+    if (subctx) {
+        // Submit and wait for any pending work before reallocating the buffers
+        ggml_vk_ctx_end(subctx);
+        ggml_vk_submit(subctx, ctx->fence);
+        ggml_vk_wait_for_fence(ctx);
+        ggml_vk_ctx_begin(ctx->device, subctx);
+    }
+
     if (ctx->prealloc_x == nullptr || (ctx->prealloc_size_x > 0 && ctx->prealloc_x->size < ctx->prealloc_size_x)) {
         VK_LOG_MEMORY("ggml_vk_preallocate_buffers(x_size: " << ctx->prealloc_size_x << ")");
         // Resize buffer
@@ -11454,7 +11435,7 @@ static bool ggml_vk_compute_forward(ggml_backend_vk_context* ctx, ggml_cgraph *
 
 // Returns true if node has enqueued work into the queue, false otherwise
 // If submit is true the current all operations queued so far are being submitted to Vulkan to overlap cmdlist creation and GPU execution.
-static bool ggml_vk_build_graph(ggml_backend_vk_context * ctx, ggml_cgraph * cgraph, int node_idx, ggml_tensor *node_begin, int node_idx_begin, bool dryrun, bool last_node, bool almost_ready, bool submit){
+static bool ggml_vk_build_graph(ggml_backend_vk_context * ctx, ggml_cgraph * cgraph, int node_idx, ggml_tensor *node_begin, int node_idx_begin, bool last_node, bool almost_ready, bool submit){
     ggml_tensor * node = cgraph->nodes[node_idx];
     if (ggml_is_empty(node) || !node->buffer) {
         return false;
@@ -11514,10 +11495,11 @@ static bool ggml_vk_build_graph(ggml_backend_vk_context * ctx, ggml_cgraph * cgr
                 cgraph->nodes[next_node_idx]->src[0] == cgraph->nodes[next_node_idx - 1] &&
                 ggml_nrows(cgraph->nodes[next_node_idx]) == 1 &&
                 ctx->device->add_rms_fusion) {
-                if (dryrun) {
-                    ctx->prealloc_size_add_rms_partials += ggml_vk_rms_partials_size(ctx, cgraph->nodes[node_idx]);
+                uint32_t size = ggml_vk_rms_partials_size(ctx, cgraph->nodes[node_idx]);
+                ctx->do_add_rms_partials_offset_calculation = true;
+                if (ctx->prealloc_size_add_rms_partials_offset + size <= ctx->prealloc_size_add_rms_partials) {
+                    ctx->do_add_rms_partials = true;
                 }
-                ctx->do_add_rms_partials = true;
             }
         } break;
     case GGML_OP_REPEAT:
@@ -11585,81 +11567,15 @@ static bool ggml_vk_build_graph(ggml_backend_vk_context * ctx, ggml_cgraph * cgr
 
     vk_context compute_ctx;
 
-    if (!dryrun) {
-        if (ctx->compute_ctx.expired()) {
-            compute_ctx = ggml_vk_create_context(ctx, ctx->compute_cmd_pool);
-            ctx->compute_ctx = compute_ctx;
-            ggml_vk_ctx_begin(ctx->device, compute_ctx);
-        } else {
-            compute_ctx = ctx->compute_ctx.lock();
-        }
+    if (ctx->compute_ctx.expired()) {
+        compute_ctx = ggml_vk_create_context(ctx, ctx->compute_cmd_pool);
+        ctx->compute_ctx = compute_ctx;
+        ggml_vk_ctx_begin(ctx->device, compute_ctx);
     } else {
-        switch (node->op) {
-        case GGML_OP_REPEAT:
-        case GGML_OP_REPEAT_BACK:
-        case GGML_OP_ACC:
-        case GGML_OP_GET_ROWS:
-        case GGML_OP_ADD:
-        case GGML_OP_SUB:
-        case GGML_OP_MUL:
-        case GGML_OP_DIV:
-        case GGML_OP_CONCAT:
-        case GGML_OP_UPSCALE:
-        case GGML_OP_SCALE:
-        case GGML_OP_SQR:
-        case GGML_OP_SQRT:
-        case GGML_OP_SIN:
-        case GGML_OP_COS:
-        case GGML_OP_CLAMP:
-        case GGML_OP_PAD:
-        case GGML_OP_CPY:
-        case GGML_OP_SET_ROWS:
-        case GGML_OP_CONT:
-        case GGML_OP_DUP:
-        case GGML_OP_SILU_BACK:
-        case GGML_OP_NORM:
-        case GGML_OP_GROUP_NORM:
-        case GGML_OP_RMS_NORM:
-        case GGML_OP_RMS_NORM_BACK:
-        case GGML_OP_L2_NORM:
-        case GGML_OP_UNARY:
-        case GGML_OP_GLU:
-        case GGML_OP_DIAG_MASK_INF:
-        case GGML_OP_SOFT_MAX:
-        case GGML_OP_SOFT_MAX_BACK:
-        case GGML_OP_ROPE_BACK:
-        case GGML_OP_ARGSORT:
-        case GGML_OP_SUM:
-        case GGML_OP_SUM_ROWS:
-        case GGML_OP_MEAN:
-        case GGML_OP_ARGMAX:
-        case GGML_OP_COUNT_EQUAL:
-        case GGML_OP_IM2COL:
-        case GGML_OP_IM2COL_3D:
-        case GGML_OP_TIMESTEP_EMBEDDING:
-        case GGML_OP_CONV_TRANSPOSE_1D:
-        case GGML_OP_POOL_2D:
-        case GGML_OP_CONV_2D:
-        case GGML_OP_CONV_TRANSPOSE_2D:
-        case GGML_OP_CONV_2D_DW:
-        case GGML_OP_LEAKY_RELU:
-        case GGML_OP_OPT_STEP_SGD:
-            {
-                // These operations all go through ggml_vk_op_f32, so short-circuit and
-                // do the only thing needed for the dryrun.
-                vk_pipeline pipeline = ggml_vk_op_get_pipeline(ctx, src0, src1, src2, node, node->op);
-                ggml_pipeline_request_descriptor_sets(ctx, pipeline, 1);
-                if (node->op == GGML_OP_RMS_NORM) {
-                    ctx->do_add_rms_partials = false;
-                }
-                return false;
-            }
-        default:
-            break;
-        }
+        compute_ctx = ctx->compute_ctx.lock();
     }
 
-    if (!dryrun) {
+    {
         // This logic detects dependencies between modes in the graph and calls ggml_vk_sync_buffers
         // to synchronize them. This handles most "normal" synchronization when computing the graph, and when
         // there is no auxiliary memory use, it shouldn't be necessary to call ggml_vk_sync_buffers
@@ -11744,118 +11660,116 @@ static bool ggml_vk_build_graph(ggml_backend_vk_context * ctx, ggml_cgraph * cgr
         }
     }
 #if ENABLE_SYNC_LOGGING
-    if (!dryrun) {
-        for (int i = 0; i < ctx->num_additional_fused_ops + 1; ++i) {
-            auto *n = cgraph->nodes[node_idx + i];
-            std::cerr << node_idx + i << " " << ggml_op_name(n->op) << " " <<  n->name;
-            if (n->op == GGML_OP_GLU) {
-                std::cerr << " " << ggml_glu_op_name(ggml_get_glu_op(n)) << " " << (n->src[1] ? "split" : "single") << " ";
-            }
-            std::cerr << std::endl;
+    for (int i = 0; i < ctx->num_additional_fused_ops + 1; ++i) {
+        auto *n = cgraph->nodes[node_idx + i];
+        std::cerr << node_idx + i << " " << ggml_op_name(n->op) << " " <<  n->name;
+        if (n->op == GGML_OP_GLU) {
+            std::cerr << " " << ggml_glu_op_name(ggml_get_glu_op(n)) << " " << (n->src[1] ? "split" : "single") << " ";
         }
+        std::cerr << std::endl;
     }
 #endif
 
     switch (node->op) {
     case GGML_OP_REPEAT:
-        ggml_vk_repeat(ctx, compute_ctx, src0, node, dryrun);
+        ggml_vk_repeat(ctx, compute_ctx, src0, node);
 
         break;
     case GGML_OP_REPEAT_BACK:
-        ggml_vk_repeat_back(ctx, compute_ctx, src0, node, dryrun);
+        ggml_vk_repeat_back(ctx, compute_ctx, src0, node);
 
         break;
     case GGML_OP_ACC:
-        ggml_vk_acc(ctx, compute_ctx, src0, src1, node, dryrun);
+        ggml_vk_acc(ctx, compute_ctx, src0, src1, node);
 
         break;
     case GGML_OP_GET_ROWS:
-        ggml_vk_get_rows(ctx, compute_ctx, src0, src1, node, dryrun);
+        ggml_vk_get_rows(ctx, compute_ctx, src0, src1, node);
 
         break;
     case GGML_OP_ADD:
         if (ctx->num_additional_fused_ops) {
-            ggml_vk_multi_add(ctx, compute_ctx, cgraph, node_idx, dryrun);
+            ggml_vk_multi_add(ctx, compute_ctx, cgraph, node_idx);
         } else {
-            ggml_vk_add(ctx, compute_ctx, src0, src1, node, dryrun);
+            ggml_vk_add(ctx, compute_ctx, src0, src1, node);
         }
         break;
     case GGML_OP_SUB:
-        ggml_vk_sub(ctx, compute_ctx, src0, src1, node, dryrun);
+        ggml_vk_sub(ctx, compute_ctx, src0, src1, node);
 
         break;
     case GGML_OP_MUL:
-        ggml_vk_mul(ctx, compute_ctx, src0, src1, node, dryrun);
+        ggml_vk_mul(ctx, compute_ctx, src0, src1, node);
 
         break;
     case GGML_OP_DIV:
-        ggml_vk_div(ctx, compute_ctx, src0, src1, node, dryrun);
+        ggml_vk_div(ctx, compute_ctx, src0, src1, node);
 
         break;
     case GGML_OP_ADD_ID:
-        ggml_vk_add_id(ctx, compute_ctx, src0, src1, src2, node, dryrun);
+        ggml_vk_add_id(ctx, compute_ctx, src0, src1, src2, node);
 
         break;
     case GGML_OP_CONCAT:
-        ggml_vk_concat(ctx, compute_ctx, src0, src1, node, dryrun);
+        ggml_vk_concat(ctx, compute_ctx, src0, src1, node);
 
         break;
     case GGML_OP_UPSCALE:
-        ggml_vk_upscale(ctx, compute_ctx, src0, node, dryrun);
+        ggml_vk_upscale(ctx, compute_ctx, src0, node);
 
         break;
     case GGML_OP_SCALE:
-        ggml_vk_scale(ctx, compute_ctx, src0, node, dryrun);
+        ggml_vk_scale(ctx, compute_ctx, src0, node);
 
         break;
     case GGML_OP_SQR:
-        ggml_vk_sqr(ctx, compute_ctx, src0, node, dryrun);
+        ggml_vk_sqr(ctx, compute_ctx, src0, node);
 
         break;
     case GGML_OP_SQRT:
-        ggml_vk_sqrt(ctx, compute_ctx, src0, node, dryrun);
+        ggml_vk_sqrt(ctx, compute_ctx, src0, node);
 
         break;
     case GGML_OP_SIN:
-        ggml_vk_sin(ctx, compute_ctx, src0, node, dryrun);
+        ggml_vk_sin(ctx, compute_ctx, src0, node);
 
         break;
     case GGML_OP_COS:
-        ggml_vk_cos(ctx, compute_ctx, src0, node, dryrun);
+        ggml_vk_cos(ctx, compute_ctx, src0, node);
 
         break;
     case GGML_OP_CLAMP:
-        ggml_vk_clamp(ctx, compute_ctx, src0, node, dryrun);
+        ggml_vk_clamp(ctx, compute_ctx, src0, node);
 
         break;
     case GGML_OP_PAD:
-        ggml_vk_pad(ctx, compute_ctx, src0, node, dryrun);
+        ggml_vk_pad(ctx, compute_ctx, src0, node);
 
         break;
     case GGML_OP_ROLL:
-        ggml_vk_roll(ctx, compute_ctx, src0, node, dryrun);
+        ggml_vk_roll(ctx, compute_ctx, src0, node);
 
         break;
     case GGML_OP_CPY:
     case GGML_OP_CONT:
     case GGML_OP_DUP:
-        ggml_vk_cpy(ctx, compute_ctx, src0, node, dryrun);
+        ggml_vk_cpy(ctx, compute_ctx, src0, node);
 
         break;
     case GGML_OP_SET_ROWS:
-        ggml_vk_set_rows(ctx, compute_ctx, src0, src1, node, dryrun);
+        ggml_vk_set_rows(ctx, compute_ctx, src0, src1, node);
 
         break;
     case GGML_OP_SILU_BACK:
-        ggml_vk_silu_back(ctx, compute_ctx, src0, src1, node, dryrun);
+        ggml_vk_silu_back(ctx, compute_ctx, src0, src1, node);
 
         break;
     case GGML_OP_NORM:
-        ggml_vk_norm(ctx, compute_ctx, src0, node, dryrun);
+        ggml_vk_norm(ctx, compute_ctx, src0, node);
 
         break;
     case GGML_OP_GROUP_NORM:
-        ggml_vk_group_norm(ctx, compute_ctx, src0, node, dryrun);
+        ggml_vk_group_norm(ctx, compute_ctx, src0, node);
 
         break;
     case GGML_OP_RMS_NORM:
@@ -11863,17 +11777,17 @@ static bool ggml_vk_build_graph(ggml_backend_vk_context * ctx, ggml_cgraph * cgr
             // fused rms_norm + mul
             ggml_tensor *mul = cgraph->nodes[node_idx + 1];
             ggml_tensor *other_src = mul->src[0] == node ? mul->src[1] : mul->src[0];
-            ggml_vk_rms_norm(ctx, compute_ctx, src0, other_src, mul, (float *)node->op_params, dryrun);
+            ggml_vk_rms_norm(ctx, compute_ctx, src0, other_src, mul, (float *)node->op_params);
         } else {
-            ggml_vk_rms_norm(ctx, compute_ctx, src0, src0, node, (float *)node->op_params, dryrun);
+            ggml_vk_rms_norm(ctx, compute_ctx, src0, src0, node, (float *)node->op_params);
         }
         break;
     case GGML_OP_RMS_NORM_BACK:
-        ggml_vk_rms_norm_back(ctx, compute_ctx, src0, src1, node, dryrun);
+        ggml_vk_rms_norm_back(ctx, compute_ctx, src0, src1, node);
 
         break;
     case GGML_OP_L2_NORM:
-        ggml_vk_l2_norm(ctx, compute_ctx, src0, node, dryrun);
+        ggml_vk_l2_norm(ctx, compute_ctx, src0, node);
 
         break;
     case GGML_OP_UNARY:
@@ -11888,7 +11802,7 @@ static bool ggml_vk_build_graph(ggml_backend_vk_context * ctx, ggml_cgraph * cgr
         case GGML_UNARY_OP_SIGMOID:
         case GGML_UNARY_OP_HARDSIGMOID:
         case GGML_UNARY_OP_HARDSWISH:
-            ggml_vk_unary(ctx, compute_ctx, src0, node, dryrun);
+            ggml_vk_unary(ctx, compute_ctx, src0, node);
             break;
         default:
             return false;
@@ -11902,151 +11816,147 @@ static bool ggml_vk_build_graph(ggml_backend_vk_context * ctx, ggml_cgraph * cgr
         case GGML_GLU_OP_SWIGLU_OAI:
         case GGML_GLU_OP_GEGLU_ERF:
         case GGML_GLU_OP_GEGLU_QUICK:
-            ggml_vk_glu(ctx, compute_ctx, src0, src1, node, dryrun);
+            ggml_vk_glu(ctx, compute_ctx, src0, src1, node);
             break;
         default:
             return false;
         }
         break;
     case GGML_OP_DIAG_MASK_INF:
-        ggml_vk_diag_mask_inf(ctx, compute_ctx, src0, node, dryrun);
+        ggml_vk_diag_mask_inf(ctx, compute_ctx, src0, node);
 
         break;
     case GGML_OP_SOFT_MAX:
         if (ctx->num_additional_fused_ops) {
-            ggml_vk_topk_moe(ctx, compute_ctx, cgraph, node_idx, dryrun);
+            ggml_vk_topk_moe(ctx, compute_ctx, cgraph, node_idx);
         } else {
-            ggml_vk_soft_max(ctx, compute_ctx, src0, src1, src2, node, dryrun);
+            ggml_vk_soft_max(ctx, compute_ctx, src0, src1, src2, node);
         }
 
         break;
     case GGML_OP_SOFT_MAX_BACK:
-        ggml_vk_soft_max_back(ctx, compute_ctx, src0, src1, node, dryrun);
+        ggml_vk_soft_max_back(ctx, compute_ctx, src0, src1, node);
 
         break;
     case GGML_OP_ROPE:
-        ggml_vk_rope(ctx, compute_ctx, cgraph, node_idx, false, dryrun);
+        ggml_vk_rope(ctx, compute_ctx, cgraph, node_idx, false);
 
         break;
     case GGML_OP_ROPE_BACK:
-        ggml_vk_rope(ctx, compute_ctx, cgraph, node_idx, true, dryrun);
+        ggml_vk_rope(ctx, compute_ctx, cgraph, node_idx, true);
 
         break;
     case GGML_OP_ARGSORT:
         if (ctx->num_additional_fused_ops) {
-            ggml_vk_topk_moe(ctx, compute_ctx, cgraph, node_idx, dryrun);
+            ggml_vk_topk_moe(ctx, compute_ctx, cgraph, node_idx);
         } else {
-            ggml_vk_argsort(ctx, compute_ctx, src0, node, dryrun);
+            ggml_vk_argsort(ctx, compute_ctx, src0, node);
         }
 
         break;
     case GGML_OP_SUM:
-        ggml_vk_sum(ctx, compute_ctx, src0, node, dryrun);
+        ggml_vk_sum(ctx, compute_ctx, src0, node);
 
         break;
     case GGML_OP_SUM_ROWS:
-        ggml_vk_sum_rows(ctx, compute_ctx, src0, node, dryrun);
+        ggml_vk_sum_rows(ctx, compute_ctx, src0, node);
 
         break;
     case GGML_OP_MEAN:
-        ggml_vk_mean(ctx, compute_ctx, src0, node, dryrun);
+        ggml_vk_mean(ctx, compute_ctx, src0, node);
 
         break;
     case GGML_OP_ARGMAX:
-        ggml_vk_argmax(ctx, compute_ctx, src0, node, dryrun);
+        ggml_vk_argmax(ctx, compute_ctx, src0, node);
 
         break;
     case GGML_OP_COUNT_EQUAL:
-        ggml_vk_count_equal(ctx, compute_ctx, src0, src1, node, dryrun);
+        ggml_vk_count_equal(ctx, compute_ctx, src0, src1, node);
 
         break;
     case GGML_OP_IM2COL:
-        ggml_vk_im2col(ctx, compute_ctx, src0, src1, node, dryrun);
+        ggml_vk_im2col(ctx, compute_ctx, src0, src1, node);
 
         break;
     case GGML_OP_IM2COL_3D:
-        ggml_vk_im2col_3d(ctx, compute_ctx, src0, src1, node, dryrun);
+        ggml_vk_im2col_3d(ctx, compute_ctx, src0, src1, node);
 
         break;
     case GGML_OP_TIMESTEP_EMBEDDING:
-        ggml_vk_timestep_embedding(ctx, compute_ctx, src0, node, dryrun);
+        ggml_vk_timestep_embedding(ctx, compute_ctx, src0, node);
 
         break;
     case GGML_OP_CONV_TRANSPOSE_1D:
-        ggml_vk_conv_transpose_1d(ctx, compute_ctx, src0, src1, node, dryrun);
+        ggml_vk_conv_transpose_1d(ctx, compute_ctx, src0, src1, node);
 
         break;
     case GGML_OP_POOL_2D:
-        ggml_vk_pool_2d(ctx, compute_ctx, src0, node, dryrun);
+        ggml_vk_pool_2d(ctx, compute_ctx, src0, node);
 
         break;
     case GGML_OP_CONV_2D:
-        ggml_vk_conv_2d(ctx, compute_ctx, src0, src1, node, dryrun);
+        ggml_vk_conv_2d(ctx, compute_ctx, src0, src1, node);
 
         break;
     case GGML_OP_CONV_TRANSPOSE_2D:
-        ggml_vk_conv_transpose_2d(ctx, compute_ctx, src0, src1, node, dryrun);
+        ggml_vk_conv_transpose_2d(ctx, compute_ctx, src0, src1, node);
 
         break;
     case GGML_OP_CONV_2D_DW:
-        ggml_vk_conv_2d_dw(ctx, compute_ctx, src0, src1, node, dryrun);
+        ggml_vk_conv_2d_dw(ctx, compute_ctx, src0, src1, node);
 
         break;
     case GGML_OP_LEAKY_RELU:
-        ggml_vk_leaky_relu(ctx, compute_ctx, src0, node, dryrun);
+        ggml_vk_leaky_relu(ctx, compute_ctx, src0, node);
 
         break;
     case GGML_OP_MUL_MAT:
-        ggml_vk_mul_mat(ctx, compute_ctx, cgraph, node_idx, dryrun);
+        ggml_vk_mul_mat(ctx, compute_ctx, cgraph, node_idx);
 
         break;
     case GGML_OP_MUL_MAT_ID:
-        ggml_vk_mul_mat_id(ctx, compute_ctx, cgraph, node_idx, dryrun);
+        ggml_vk_mul_mat_id(ctx, compute_ctx, cgraph, node_idx);
 
         break;
 
     case GGML_OP_FLASH_ATTN_EXT:
-        ggml_vk_flash_attn(ctx, compute_ctx, src0, src1, src2, src3, node->src[4], node, dryrun);
+        ggml_vk_flash_attn(ctx, compute_ctx, src0, src1, src2, src3, node->src[4], node);
 
         break;
 
     case GGML_OP_RWKV_WKV6:
-        ggml_vk_rwkv_wkv6(ctx, compute_ctx, node, dryrun);
+        ggml_vk_rwkv_wkv6(ctx, compute_ctx, node);
 
         break;
 
     case GGML_OP_RWKV_WKV7:
-        ggml_vk_rwkv_wkv7(ctx, compute_ctx, node, dryrun);
+        ggml_vk_rwkv_wkv7(ctx, compute_ctx, node);
 
         break;
 
     case GGML_OP_SSM_SCAN:
-        ggml_vk_ssm_scan(ctx, compute_ctx, node, dryrun);
+        ggml_vk_ssm_scan(ctx, compute_ctx, node);
 
         break;
 
     case GGML_OP_SSM_CONV:
-        ggml_vk_ssm_conv(ctx, compute_ctx, node, dryrun);
+        ggml_vk_ssm_conv(ctx, compute_ctx, node);
 
         break;
 
     case GGML_OP_OPT_STEP_ADAMW:
-        ggml_vk_opt_step_adamw(ctx, compute_ctx, node, dryrun);
+        ggml_vk_opt_step_adamw(ctx, compute_ctx, node);
 
         break;
 
     case GGML_OP_OPT_STEP_SGD:
-        ggml_vk_opt_step_sgd(ctx, compute_ctx, src0, src1, src2, node, dryrun);
+        ggml_vk_opt_step_sgd(ctx, compute_ctx, src0, src1, src2, node);
 
         break;
     default:
         return false;
     }
 
-    if (dryrun) {
-        return false;
-    }
-
     ctx->tensor_ctxs[node_idx] = compute_ctx;
 
 #if defined(GGML_VULKAN_CHECK_RESULTS)
@@ -12919,58 +12829,9 @@ static ggml_status ggml_backend_vk_graph_compute(ggml_backend_t backend, ggml_cg
         vk_instance.pfn_vkQueueBeginDebugUtilsLabelEXT(ctx->device->compute_queue.queue, reinterpret_cast<VkDebugUtilsLabelEXT*>(&dul));
     }
 
-    ctx->prealloc_size_add_rms_partials = 0;
     ctx->prealloc_size_add_rms_partials_offset = 0;
     ctx->do_add_rms_partials = false;
-
-    uint64_t total_mat_mul_bytes = 0;
-    for (int i = 0; i < cgraph->n_nodes; i++) {
-        if (!ctx->device->disable_fusion) {
-            uint32_t num_adds = ggml_vk_fuse_multi_add(ctx, cgraph, i);
-            if (num_adds) {
-                ctx->num_additional_fused_ops = num_adds - 1;
-            } else if (ggml_vk_can_fuse(ctx, cgraph, i, { GGML_OP_RMS_NORM, GGML_OP_MUL })) {
-                ctx->num_additional_fused_ops = 1;
-            } else if (ggml_vk_can_fuse(ctx, cgraph, i, { GGML_OP_MUL_MAT, GGML_OP_ADD })) {
-                ctx->num_additional_fused_ops = 1;
-            } else if (ggml_vk_can_fuse(ctx, cgraph, i, { GGML_OP_MUL_MAT_ID, GGML_OP_ADD_ID })) {
-                ctx->num_additional_fused_ops = 1;
-            } else if (ggml_can_fuse_subgraph(cgraph, i, { GGML_OP_ROPE, GGML_OP_VIEW, GGML_OP_SET_ROWS }, { i + 2 }) &&
-                       ggml_check_edges(cgraph, i, rope_view_set_rows_edges) &&
-                       ggml_vk_can_fuse_rope_set_rows(ctx, cgraph, i)) {
-                ctx->num_additional_fused_ops = 2;
-            } else if (ggml_can_fuse_subgraph(cgraph, i, topk_moe_early_softmax_norm, { i + 3, i + 9 }) &&
-                       ggml_check_edges(cgraph, i, topk_moe_early_softmax_norm_edges) &&
-                       ggml_vk_can_fuse_topk_moe(ctx, cgraph, i, TOPK_MOE_EARLY_SOFTMAX_NORM)) {
-                ctx->num_additional_fused_ops = topk_moe_early_softmax_norm.size() - 1;
-            } else if (ggml_can_fuse_subgraph(cgraph, i, topk_moe_early_softmax, { i + 3, i + 4 }) &&
-                       ggml_check_edges(cgraph, i, topk_moe_early_softmax_edges) &&
-                       ggml_vk_can_fuse_topk_moe(ctx, cgraph, i, TOPK_MOE_EARLY_SOFTMAX)) {
-                ctx->num_additional_fused_ops = topk_moe_early_softmax.size() - 1;
-            } else if (ggml_can_fuse_subgraph(cgraph, i, topk_moe_late_softmax, { i + 1, i + 5 }) &&
-                       ggml_check_edges(cgraph, i, topk_moe_late_softmax_edges) &&
-                       ggml_vk_can_fuse_topk_moe(ctx, cgraph, i, TOPK_MOE_LATE_SOFTMAX)) {
-                ctx->num_additional_fused_ops = topk_moe_late_softmax.size() - 1;
-            }
-        }
-        ggml_vk_build_graph(ctx, cgraph, i, nullptr, 0, true, false, false, false);
-        if (cgraph->nodes[i]->op == GGML_OP_MUL_MAT || cgraph->nodes[i]->op == GGML_OP_MUL_MAT_ID) {
-            total_mat_mul_bytes += ggml_nbytes(cgraph->nodes[i]->src[0]);
-        } else if (cgraph->nodes[i]->op == GGML_OP_CONV_2D || cgraph->nodes[i]->op == GGML_OP_CONV_TRANSPOSE_2D) {
-            // Return CRSxNPQxsizeof(*) to account as many bytes as mul_mat has in im2col->mul_mat mode.
-            auto CRS_size =
-                cgraph->nodes[i]->src[0]->ne[0] * cgraph->nodes[i]->src[0]->ne[1] * cgraph->nodes[i]->src[1]->ne[2];
-            auto NPQ_size = cgraph->nodes[i]->ne[0] * cgraph->nodes[i]->ne[1] * cgraph->nodes[i]->ne[3];
-            total_mat_mul_bytes += NPQ_size * CRS_size * ggml_type_size(cgraph->nodes[i]->type);
-        }
-        i += ctx->num_additional_fused_ops;
-        ctx->num_additional_fused_ops = 0;
-    }
-    if (ctx->device->need_compiles) {
-        ggml_vk_load_shaders(ctx->device);
-    }
-    ggml_vk_preallocate_buffers(ctx);
-    ggml_pipeline_allocate_descriptor_sets(ctx);
+    ctx->do_add_rms_partials_offset_calculation = false;
 
     int last_node = cgraph->n_nodes - 1;
 
@@ -13012,6 +12873,7 @@ static ggml_status ggml_backend_vk_graph_compute(ggml_backend_t backend, ggml_cg
     ctx->prealloc_y_last_tensor_used = nullptr;
 
     if (ctx->prealloc_size_add_rms_partials) {
+        ggml_vk_preallocate_buffers(ctx, nullptr);
         if (ctx->compute_ctx.expired()) {
             compute_ctx = ggml_vk_create_context(ctx, ctx->compute_cmd_pool);
             ctx->compute_ctx = compute_ctx;
@@ -13032,14 +12894,17 @@ static ggml_status ggml_backend_vk_graph_compute(ggml_backend_t backend, ggml_cg
     int submitted_nodes = 0;
     int submit_count = 0;
     uint64_t mul_mat_bytes = 0;
-    uint64_t mul_mat_bytes_per_submit = std::min(uint64_t(100*1000*1000), total_mat_mul_bytes / 40u);
+    uint64_t total_mul_mat_bytes = 0;
+    uint64_t mul_mat_bytes_per_submit = std::min(uint64_t(100*1000*1000), ctx->last_total_mul_mat_bytes / 40u);
     for (int i = 0; i < cgraph->n_nodes; i++) {
         if (first_node_in_batch) {
             submit_node_idx = i;
         }
 
         if (cgraph->nodes[i]->op == GGML_OP_MUL_MAT || cgraph->nodes[i]->op == GGML_OP_MUL_MAT_ID) {
-            mul_mat_bytes += ggml_nbytes(cgraph->nodes[i]->src[0]);
+            auto bytes = ggml_nbytes(cgraph->nodes[i]->src[0]);
+            mul_mat_bytes += bytes;
+            total_mul_mat_bytes += bytes;
         }
 
         if (!ctx->device->disable_fusion) {
@@ -13081,11 +12946,11 @@ static ggml_status ggml_backend_vk_graph_compute(ggml_backend_t backend, ggml_cg
         // Signal the almost_ready fence when the graph is mostly complete (< 20% remaining)
         bool almost_ready = (cgraph->n_nodes - i) < cgraph->n_nodes / 5;
         bool submit = (submitted_nodes >= nodes_per_submit) ||
-                      (mul_mat_bytes >= mul_mat_bytes_per_submit) ||
+                      (mul_mat_bytes_per_submit != 0 && mul_mat_bytes >= mul_mat_bytes_per_submit) ||
                       (i + ctx->num_additional_fused_ops >= last_node) ||
                       (almost_ready && !ctx->almost_ready_fence_pending);
 
-        bool enqueued = ggml_vk_build_graph(ctx, cgraph, i, cgraph->nodes[submit_node_idx], submit_node_idx, false, i + ctx->num_additional_fused_ops >= last_node, almost_ready, submit);
+        bool enqueued = ggml_vk_build_graph(ctx, cgraph, i, cgraph->nodes[submit_node_idx], submit_node_idx, i + ctx->num_additional_fused_ops >= last_node, almost_ready, submit);
 
         if (vk_perf_logger_enabled) {
             if (ctx->compute_ctx.expired()) {
@@ -13125,6 +12990,9 @@ static ggml_status ggml_backend_vk_graph_compute(ggml_backend_t backend, ggml_cg
         ctx->fused_ops_write_mask = 0;
     }
 
+    ctx->prealloc_size_add_rms_partials = std::max(ctx->prealloc_size_add_rms_partials, ctx->prealloc_size_add_rms_partials_offset);
+    ctx->last_total_mul_mat_bytes = total_mul_mat_bytes;
+
     if (vk_perf_logger_enabled) {
         // End the command buffer and submit/wait
         GGML_ASSERT(!ctx->compute_ctx.expired());

From a5c07dcd7b49916c7c770f2da9583e6b82717678 Mon Sep 17 00:00:00 2001
From: nullname <chraac@gmail.com>
Date: Wed, 5 Nov 2025 04:25:39 +0800
Subject: [PATCH 083/185] refactor: replace sprintf with snprintf for safer
 string handling in dump functions (#16913)

---
 ggml/src/ggml-hexagon/htp/ops-utils.h | 34 +++++++++++++--------------
 1 file changed, 17 insertions(+), 17 deletions(-)

diff --git a/ggml/src/ggml-hexagon/htp/ops-utils.h b/ggml/src/ggml-hexagon/htp/ops-utils.h
index f03ff34028f..302f1625216 100644
--- a/ggml/src/ggml-hexagon/htp/ops-utils.h
+++ b/ggml/src/ggml-hexagon/htp/ops-utils.h
@@ -43,46 +43,46 @@ static inline int32_t htp_is_one_chunk(void * addr, uint32_t n, uint32_t chunk_s
 }
 
 static inline void htp_dump_int8_line(char * pref, const int8_t * x, int n) {
-    char str[1024], *p = str;
-    p += sprintf(p, "%s: ", pref);
-    for (int i = 0; i < 16; i++) {
-        p += sprintf(p, "%d, ", x[i]);
+    char str[1024], *p = str, *p_end = str + sizeof(str);
+    p += snprintf(p, p_end - p, "%s: ", pref);
+    for (int i = 0; i < n && p < p_end; i++) {
+        p += snprintf(p, p_end - p, "%d, ", x[i]);
     }
     FARF(HIGH, "%s\n", str);
 }
 
 static inline void htp_dump_uint8_line(char * pref, const uint8_t * x, uint32_t n) {
-    char str[1024], *p = str;
-    p += sprintf(p, "%s: ", pref);
-    for (int i = 0; i < n; i++) {
-        p += sprintf(p, "%d, ", x[i]);
+    char str[1024], *p = str, *p_end = str + sizeof(str);
+    p += snprintf(p, p_end - p, "%s: ", pref);
+    for (int i = 0; i < n && p < p_end; i++) {
+        p += snprintf(p, p_end - p, "%d, ", x[i]);
     }
     FARF(HIGH, "%s\n", str);
 }
 
 static inline void htp_dump_int32_line(char * pref, const int32_t * x, uint32_t n) {
-    char str[1024], *p = str;
-    p += sprintf(p, "%s: ", pref);
+    char str[1024], *p = str, *p_end = str + sizeof(str);
+    p += snprintf(p, p_end - p, "%s: ", pref);
     for (int i = 0; i < n; i++) {
-        p += sprintf(p, "%d, ", (int) x[i]);
+        p += snprintf(p, p_end - p, "%d, ", (int) x[i]);
     }
     FARF(HIGH, "%s\n", str);
 }
 
 static inline void htp_dump_fp16_line(char * pref, const __fp16 * x, uint32_t n) {
-    char str[1024], *p = str;
-    p += sprintf(p, "%s: ", pref);
+    char str[1024], *p = str, *p_end = str + sizeof(str);
+    p += snprintf(p, p_end - p, "%s: ", pref);
     for (int i = 0; i < n; i++) {
-        p += sprintf(p, "%.6f, ", (float) x[i]);
+        p += snprintf(p, p_end - p, "%.6f, ", (float) x[i]);
     }
     FARF(HIGH, "%s\n", str);
 }
 
 static inline void htp_dump_fp32_line(char * pref, const float * x, uint32_t n) {
-    char str[1024], *p = str;
-    p += sprintf(p, "%s: ", pref);
+    char str[1024], *p = str, *p_end = str + sizeof(str);
+    p += snprintf(p, p_end - p, "%s: ", pref);
     for (int i = 0; i < n; i++) {
-        p += sprintf(p, "%.6f, ", x[i]);
+        p += snprintf(p, p_end - p, "%.6f, ", x[i]);
     }
     FARF(HIGH, "%s\n", str);
 }

From 5e90233bdba013838c1a69df7738e08bd5c058d5 Mon Sep 17 00:00:00 2001
From: lhez <lih@qti.qualcomm.com>
Date: Tue, 4 Nov 2025 16:02:36 -0800
Subject: [PATCH 084/185] opencl: update doc (#17011)

* opencl: update docs

* opencl: update docs

* opencl: fix link

* opencl: update doc
---
 docs/backend/OPENCL.md | 28 +++++++++++++++++++++++++---
 1 file changed, 25 insertions(+), 3 deletions(-)

diff --git a/docs/backend/OPENCL.md b/docs/backend/OPENCL.md
index 07146f7102f..e52baffdffd 100644
--- a/docs/backend/OPENCL.md
+++ b/docs/backend/OPENCL.md
@@ -39,18 +39,23 @@ The llama.cpp OpenCL backend is designed to enable llama.cpp on **Qualcomm Adren
 | Adreno 830 (Snapdragon 8 Elite)      | Support |
 | Adreno X85 (Snapdragon X Elite)      | Support |
 
+> A6x GPUs with a recent driver and compiler are supported; they are usually found in IoT platforms.
+However, A6x GPUs in phones are likely not supported due to the outdated driver and compiler.
+
 ## DataType Supports
 
 | DataType               | Status                     |
 |:----------------------:|:--------------------------:|
 | Q4_0                   | Support                    |
 | Q6_K                   | Support, but not optimized |
+| Q8_0                   | Support                    |
+| MXFP4                  | Support                    |
 
 ## Model Preparation
 
-You can refer to the general [*Prepare and Quantize*](README.md#prepare-and-quantize) guide for model prepration.
+You can refer to the general [llama-quantize tool](/tools/quantize/README.md) for steps to convert a model in Hugging Face safetensor format to GGUF with quantization.
 
-Currently we support `Q4_0` quantization and have optimize for it. To achieve best performance on Adreno GPU, add `--pure` to `llama-quantize`. For example,
+Currently we support `Q4_0` quantization and have optimized for it. To achieve best performance on Adreno GPU, add `--pure` to `llama-quantize` (i.e., make all weights in `Q4_0`). For example,
 
 ```sh
 ./llama-quantize --pure ggml-model-qwen2.5-3b-f16.gguf ggml-model-qwen-3b-Q4_0.gguf Q4_0
@@ -58,6 +63,17 @@ Currently we support `Q4_0` quantization and have optimize for it. To achieve be
 
 Since `Q6_K` is also supported, `Q4_0` quantization without `--pure` will also work. However, the performance will be worse compared to pure `Q4_0` quantization.
 
+### `MXFP4` MoE Models
+
+OpenAI gpt-oss models are MoE models in `MXFP4`. The quantized model will be in `MXFP4_MOE`, a mixture of `MXFP4` and `Q8_0`.
+For this quantization, there is no need to specify `--pure`.
+For gpt-oss-20b model, you can directly [download](https://huggingface.co/ggml-org/gpt-oss-20b-GGUF) the quantized GGUF file in `MXFP4_MOE` from Hugging Face.
+
+Although it is possible to quantize gpt-oss-20b model in pure `Q4_0` (all weights in `Q4_0`), it is not recommended since `MXFP4` has been optimized for MoE while `Q4_0` is not. In addition, accuracy should degrade with such pure `Q4_0` quantization.
+Hence, using the default `MXFP4_MOE` quantization (see the link above) is recommended for this model.
+
+> Note that the `Q4_0` model found [here](https://huggingface.co/unsloth/gpt-oss-20b-GGUF/blob/main/gpt-oss-20b-Q4_0.gguf) is a mixture of `Q4_0`, `Q8_0` and `MXFP4` and gives better performance than `MXFP4_MOE` quantization.
+
 ## CMake Options
 
 The OpenCL backend has the following CMake options that control the behavior of the backend.
@@ -146,10 +162,13 @@ A Snapdragon X Elite device with Windows 11 Arm64 is used. Make sure the followi
 * Ninja
 * Visual Studio 2022
 * Powershell 7
+* Python
 
 Visual Studio provides necessary headers and libraries although it is not directly used for building.
 Alternatively, Visual Studio Build Tools can be installed instead of the full Visual Studio.
 
+> Note that building using Visual Studio's cl compiler is not supported. Clang must be used. Clang depends on libraries provided by Visual Studio to work. Therefore, Visual Studio must be installed. Alternatively, Visual Studio Build Tools can be installed instead of the full Visual Studio.
+
 Powershell 7 is used for the following commands.
 If an older version of Powershell is used, these commands may not work as they are.
 
@@ -201,9 +220,12 @@ ninja
 
 ## Known Issues
 
-- Currently OpenCL backend does not work on Adreno 6xx GPUs.
+- Flash attention does not always improve performance.
+- Currently OpenCL backend works on A6xx GPUs with recent drivers and compilers (usually found in IoT platforms).
+  However, it does not work on A6xx GPUs found in phones with old drivers and compilers.
 
 ## TODO
 
 - Optimization for Q6_K
 - Support and optimization for Q4_K
+- Improve flash attention

From 9aa63374f2101f4eaef425888699907b238ed2c0 Mon Sep 17 00:00:00 2001
From: mnehete32 <33429707+mnehete32@users.noreply.github.com>
Date: Wed, 5 Nov 2025 08:31:15 +0530
Subject: [PATCH 085/185] CUDA: update ops.md (#17005)

---
 docs/ops.md       |   10 +-
 docs/ops/CUDA.csv | 1620 +++++++++++++++++++++++++++++++++++++++++++++
 2 files changed, 1625 insertions(+), 5 deletions(-)

diff --git a/docs/ops.md b/docs/ops.md
index 3738a480728..b8fcf046358 100644
--- a/docs/ops.md
+++ b/docs/ops.md
@@ -22,11 +22,11 @@ Legend:
 |                           ARANGE | ❌ | ✅ | ✅ | ✅ | ✅ | ❌ | ❌ | ❌ | ❌ |
 |                           ARGMAX | ❌ | ✅ | ✅ | ✅ | ✅ | ❌ | ✅ | ✅ | ❌ |
 |                          ARGSORT | ❌ | ✅ | ✅ | ✅ | ✅ | ✅ | ✅ | ✅ | ❌ |
-|                             CEIL | ❌ | ❌ | ✅ | ❌ | ❌ | ❌ | ✅ | ❌ | ❌ |
+|                             CEIL | ❌ | ❌ | ✅ | 🟡 | ❌ | ❌ | ✅ | ❌ | ❌ |
 |                            CLAMP | ❌ | ✅ | ✅ | ✅ | 🟡 | 🟡 | ✅ | 🟡 | ❌ |
 |                           CONCAT | ❌ | ✅ | ✅ | 🟡 | ✅ | 🟡 | 🟡 | ✅ | ❌ |
 |                             CONT | ❌ | 🟡 | ✅ | ✅ | ✅ | 🟡 | 🟡 | 🟡 | ❌ |
-|                          CONV_2D | ❌ | ❌ | ✅ | ❌ | ❌ | ✅ | ❌ | ✅ | ❌ |
+|                          CONV_2D | ❌ | ❌ | ✅ | 🟡 | ❌ | ✅ | ❌ | ✅ | ❌ |
 |                       CONV_2D_DW | ❌ | ❌ | ✅ | ✅ | ❌ | ❌ | ❌ | ✅ | ❌ |
 |                          CONV_3D | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
 |                CONV_TRANSPOSE_1D | ❌ | ✅ | ✅ | ✅ | ✅ | ❌ | ✅ | ✅ | ❌ |
@@ -42,7 +42,7 @@ Legend:
 |                              ELU | ❌ | ✅ | ✅ | 🟡 | 🟡 | ❌ | 🟡 | ❌ | ❌ |
 |                              EXP | ❌ | ✅ | ✅ | 🟡 | 🟡 | ❌ | 🟡 | ❌ | ❌ |
 |                   FLASH_ATTN_EXT | ❌ | 🟡 | ✅ | 🟡 | 🟡 | ❌ | ❌ | 🟡 | ❌ |
-|                            FLOOR | ❌ | ❌ | ✅ | ❌ | ❌ | ❌ | ✅ | ❌ | ❌ |
+|                            FLOOR | ❌ | ❌ | ✅ | 🟡 | ❌ | ❌ | ✅ | ❌ | ❌ |
 |                GATED_LINEAR_ATTN | ❌ | ❌ | ✅ | ✅ | ❌ | ❌ | ✅ | ❌ | ❌ |
 |                            GEGLU | ❌ | ✅ | ✅ | ✅ | 🟡 | ✅ | ✅ | 🟡 | ❌ |
 |                        GEGLU_ERF | ❌ | ✅ | ✅ | ✅ | 🟡 | ✅ | ✅ | 🟡 | ❌ |
@@ -84,7 +84,7 @@ Legend:
 |                             ROLL | ❌ | ❌ | ✅ | ❌ | ❌ | ❌ | ❌ | ✅ | ❌ |
 |                             ROPE | ❌ | 🟡 | ✅ | ✅ | ✅ | ✅ | ✅ | ✅ | ❌ |
 |                        ROPE_BACK | ❌ | ❌ | ✅ | ✅ | ❌ | ❌ | ❌ | ✅ | ❌ |
-|                            ROUND | ❌ | ❌ | ✅ | ❌ | ❌ | ❌ | ✅ | ❌ | ❌ |
+|                            ROUND | ❌ | ❌ | ✅ | 🟡 | ❌ | ❌ | ✅ | ❌ | ❌ |
 |                        RWKV_WKV6 | ❌ | ❌ | ✅ | ✅ | ✅ | ❌ | ✅ | ✅ | ❌ |
 |                        RWKV_WKV7 | ❌ | ❌ | ✅ | ✅ | ✅ | ❌ | ✅ | ✅ | ❌ |
 |                            SCALE | ❌ | 🟡 | ✅ | ✅ | ✅ | ✅ | ✅ | ✅ | ❌ |
@@ -111,6 +111,6 @@ Legend:
 |                             TANH | ❌ | ✅ | ✅ | 🟡 | 🟡 | ✅ | 🟡 | 🟡 | ❌ |
 |               TIMESTEP_EMBEDDING | ❌ | ✅ | ✅ | ✅ | ✅ | ✅ | ✅ | ✅ | ❌ |
 |                         TOPK_MOE | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ | ✅ | ❌ | ❌ |
-|                            TRUNC | ❌ | ❌ | ✅ | ❌ | ❌ | ❌ | ✅ | ❌ | ❌ |
+|                            TRUNC | ❌ | ❌ | ✅ | 🟡 | ❌ | ❌ | ✅ | ❌ | ❌ |
 |                          UPSCALE | ❌ | 🟡 | ✅ | ✅ | 🟡 | ✅ | 🟡 | ✅ | ❌ |
 |                            XIELU | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
diff --git a/docs/ops/CUDA.csv b/docs/ops/CUDA.csv
index 71e47977e31..4589bb51e0e 100644
--- a/docs/ops/CUDA.csv
+++ b/docs/ops/CUDA.csv
@@ -7347,3 +7347,1623 @@
 "CUDA0","CROSS_ENTROPY_LOSS_BACK","type=f32,ne=[10,5,4,3]","support","1","yes","CUDA"
 "CUDA0","CROSS_ENTROPY_LOSS_BACK","type=f32,ne=[30000,1,1,1]","support","1","yes","CUDA"
 "CUDA0","OPT_STEP_ADAMW","type=f32,ne=[10,5,4,3]","support","1","yes","CUDA"
+"CUDA0","CEIL","type=f16,ne_a=[128,2,2,2],v=0","support","1","yes","CUDA"
+"CUDA0","CEIL","type=f16,ne_a=[5,7,11,13],v=0","support","1","yes","CUDA"
+"CUDA0","CEIL","type=f16,ne_a=[128,2,2,2],v=1","support","0","no","CUDA"
+"CUDA0","CEIL","type=f16,ne_a=[5,7,11,13],v=1","support","0","no","CUDA"
+"CUDA0","CEIL","type=f32,ne_a=[128,2,2,2],v=0","support","1","yes","CUDA"
+"CUDA0","CEIL","type=f32,ne_a=[5,7,11,13],v=0","support","1","yes","CUDA"
+"CUDA0","CEIL","type=f32,ne_a=[128,2,2,2],v=1","support","0","no","CUDA"
+"CUDA0","CEIL","type=f32,ne_a=[5,7,11,13],v=1","support","0","no","CUDA"
+"CUDA0","CEIL","type=f16,ne=[10,2,2,2]","support","1","yes","CUDA"
+"CUDA0","CEIL","type=f16,ne=[7,1,5,3]","support","1","yes","CUDA"
+"CUDA0","CEIL","type=f32,ne=[10,2,2,2]","support","1","yes","CUDA"
+"CUDA0","CEIL","type=f32,ne=[7,1,5,3]","support","1","yes","CUDA"
+"CUDA0","FLOOR","type=f16,ne_a=[128,2,2,2],v=0","support","1","yes","CUDA"
+"CUDA0","FLOOR","type=f16,ne_a=[5,7,11,13],v=0","support","1","yes","CUDA"
+"CUDA0","FLOOR","type=f16,ne_a=[128,2,2,2],v=1","support","0","no","CUDA"
+"CUDA0","FLOOR","type=f16,ne_a=[5,7,11,13],v=1","support","0","no","CUDA"
+"CUDA0","FLOOR","type=f32,ne_a=[128,2,2,2],v=0","support","1","yes","CUDA"
+"CUDA0","FLOOR","type=f32,ne_a=[5,7,11,13],v=0","support","1","yes","CUDA"
+"CUDA0","FLOOR","type=f32,ne_a=[128,2,2,2],v=1","support","0","no","CUDA"
+"CUDA0","FLOOR","type=f32,ne_a=[5,7,11,13],v=1","support","0","no","CUDA"
+"CUDA0","FLOOR","type=f16,ne=[10,2,2,2]","support","1","yes","CUDA"
+"CUDA0","FLOOR","type=f16,ne=[7,1,5,3]","support","1","yes","CUDA"
+"CUDA0","FLOOR","type=f32,ne=[10,2,2,2]","support","1","yes","CUDA"
+"CUDA0","FLOOR","type=f32,ne=[7,1,5,3]","support","1","yes","CUDA"
+"CUDA0","ROUND","type=f16,ne_a=[128,2,2,2],v=0","support","1","yes","CUDA"
+"CUDA0","ROUND","type=f16,ne_a=[5,7,11,13],v=0","support","1","yes","CUDA"
+"CUDA0","ROUND","type=f16,ne_a=[128,2,2,2],v=1","support","0","no","CUDA"
+"CUDA0","ROUND","type=f16,ne_a=[5,7,11,13],v=1","support","0","no","CUDA"
+"CUDA0","ROUND","type=f32,ne_a=[128,2,2,2],v=0","support","1","yes","CUDA"
+"CUDA0","ROUND","type=f32,ne_a=[5,7,11,13],v=0","support","1","yes","CUDA"
+"CUDA0","ROUND","type=f32,ne_a=[128,2,2,2],v=1","support","0","no","CUDA"
+"CUDA0","ROUND","type=f32,ne_a=[5,7,11,13],v=1","support","0","no","CUDA"
+"CUDA0","ROUND","type=f16,ne=[10,2,2,2]","support","1","yes","CUDA"
+"CUDA0","ROUND","type=f16,ne=[7,1,5,3]","support","1","yes","CUDA"
+"CUDA0","ROUND","type=f32,ne=[10,2,2,2]","support","1","yes","CUDA"
+"CUDA0","ROUND","type=f32,ne=[7,1,5,3]","support","1","yes","CUDA"
+"CUDA0","TRUNC","type=f16,ne_a=[128,2,2,2],v=0","support","1","yes","CUDA"
+"CUDA0","TRUNC","type=f16,ne_a=[5,7,11,13],v=0","support","1","yes","CUDA"
+"CUDA0","TRUNC","type=f16,ne_a=[128,2,2,2],v=1","support","0","no","CUDA"
+"CUDA0","TRUNC","type=f16,ne_a=[5,7,11,13],v=1","support","0","no","CUDA"
+"CUDA0","TRUNC","type=f32,ne_a=[128,2,2,2],v=0","support","1","yes","CUDA"
+"CUDA0","TRUNC","type=f32,ne_a=[5,7,11,13],v=0","support","1","yes","CUDA"
+"CUDA0","TRUNC","type=f32,ne_a=[128,2,2,2],v=1","support","0","no","CUDA"
+"CUDA0","TRUNC","type=f32,ne_a=[5,7,11,13],v=1","support","0","no","CUDA"
+"CUDA0","TRUNC","type=f16,ne=[10,2,2,2]","support","1","yes","CUDA"
+"CUDA0","TRUNC","type=f16,ne=[7,1,5,3]","support","1","yes","CUDA"
+"CUDA0","TRUNC","type=f32,ne=[10,2,2,2]","support","1","yes","CUDA"
+"CUDA0","TRUNC","type=f32,ne=[7,1,5,3]","support","1","yes","CUDA"
+"CUDA0","CONV_2D","ne_input=[1,1,1,2],ne_kernel=[1,1,1,1],type_kernel=f32,stride0=1,stride1=5,padding0=5,padding1=2,dilation0=2,dilation1=4,cwhn=0","support","1","yes","CUDA"
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From 852ce5180acd4e3641f6b71783a343647eee058d Mon Sep 17 00:00:00 2001
From: Georgi Gerganov <ggerganov@gmail.com>
Date: Tue, 4 Nov 2025 20:40:52 +0200
Subject: [PATCH 086/185] ggml : fix conv2d_dw SVE path (ggml/1380)

* Fix test-conv2d-dw failure on ARM SVE by using runtime vector length

The ggml_compute_forward_conv_2d_dw_cwhn function was using a hardcoded GGML_F32_EPR (8) for SIMD vectorization, but on ARM SVE the actual vector length varies by hardware. This caused incorrect computation when processing CWHN layout tensors on ARM machines.

Fix by using svcntw() to get the runtime SVE vector length instead of the compile-time constant.

Co-authored-by: ggerganov <1991296+ggerganov@users.noreply.github.com>

* ci : reduce sam score threshold

* ci : update bbox checks for sam test

---------

Co-authored-by: copilot-swe-agent[bot] <198982749+Copilot@users.noreply.github.com>
Co-authored-by: ggerganov <1991296+ggerganov@users.noreply.github.com>
---
 ggml/src/ggml-cpu/ops.cpp | 6 +++++-
 1 file changed, 5 insertions(+), 1 deletion(-)

diff --git a/ggml/src/ggml-cpu/ops.cpp b/ggml/src/ggml-cpu/ops.cpp
index 7e3436fec1a..8235f695943 100644
--- a/ggml/src/ggml-cpu/ops.cpp
+++ b/ggml/src/ggml-cpu/ops.cpp
@@ -7084,7 +7084,11 @@ static void ggml_compute_forward_conv_2d_dw_cwhn(
     const int64_t row_end = MIN(row_start + rows_per_thread, rows_total);
 
 #ifdef GGML_SIMD
-    const int64_t pkg_size = GGML_F32_EPR;
+    #if defined(__ARM_FEATURE_SVE)
+        const int64_t pkg_size = svcntw();
+    #else
+        const int64_t pkg_size = GGML_F32_EPR;
+    #endif
     const int64_t pkg_count = c / pkg_size;
     const int64_t c_pkg_end = pkg_count * pkg_size;
 #else

From cdabeb2c27232b5abd84210d57ac3bf33e7ebf5c Mon Sep 17 00:00:00 2001
From: Georgi Gerganov <ggerganov@gmail.com>
Date: Tue, 4 Nov 2025 20:44:18 +0200
Subject: [PATCH 087/185] sync : ggml

---
 scripts/sync-ggml.last | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/scripts/sync-ggml.last b/scripts/sync-ggml.last
index 64a544d9110..46173585f2f 100644
--- a/scripts/sync-ggml.last
+++ b/scripts/sync-ggml.last
@@ -1 +1 @@
-e02fb860ccbba8967905bceff23b677e88105280
+7b6abb2b92fcef35cb01c6ce6ada9bd85306522d

From 03ea04175da3cdd7fd8cc1835f33490e3483928a Mon Sep 17 00:00:00 2001
From: Reese Levine <reeselevine1@gmail.com>
Date: Wed, 5 Nov 2025 01:27:42 -0800
Subject: [PATCH 088/185] ggml webgpu: minor set rows optimization (#16810)

* Add buffer label and enable dawn-specific toggles to turn off some checks

* Minor set_rows optimization (#4)

* updated optimization, fixed errors

* non vectorized version now dispatches one thread per element

* Simplify

* Change logic for set_rows pipelines

---------

Co-authored-by: Neha Abbas <nehaabbas@macbookpro.lan>
Co-authored-by: Neha Abbas <nehaabbas@ReeseLevines-MacBook-Pro.local>
Co-authored-by: Reese Levine <reeselevine1@gmail.com>

* Comment on dawn toggles

* Remove some comments

* Implement overlap binary operators

* Revert "Implement overlap binary operators"

This reverts commit ed710b36f51ab3f53fa13db15c1685dc8678a32a.

* Disable support for non-contiguous binary_op tensors and leave note for future support

---------

Co-authored-by: neha-ha <137219201+neha-ha@users.noreply.github.com>
Co-authored-by: Neha Abbas <nehaabbas@macbookpro.lan>
Co-authored-by: Neha Abbas <nehaabbas@ReeseLevines-MacBook-Pro.local>
---
 ggml/src/ggml-webgpu/ggml-webgpu.cpp          | 88 ++++++++++++++-----
 .../{set_rows.wgsl => set_rows.tmpl.wgsl}     | 45 ++++++++--
 2 files changed, 103 insertions(+), 30 deletions(-)
 rename ggml/src/ggml-webgpu/wgsl-shaders/{set_rows.wgsl => set_rows.tmpl.wgsl} (69%)

diff --git a/ggml/src/ggml-webgpu/ggml-webgpu.cpp b/ggml/src/ggml-webgpu/ggml-webgpu.cpp
index 05e16cd432a..1a157567315 100644
--- a/ggml/src/ggml-webgpu/ggml-webgpu.cpp
+++ b/ggml/src/ggml-webgpu/ggml-webgpu.cpp
@@ -248,7 +248,7 @@ struct webgpu_context_struct {
 
     webgpu_pipeline memset_pipeline;
     webgpu_pipeline mul_mat_pipeline[30][2];
-    webgpu_pipeline set_rows_pipeline;
+    webgpu_pipeline set_rows_pipeline[1][2];  // dst->type, vectorized
     webgpu_pipeline get_rows_pipeline[30];
     webgpu_pipeline get_rows_f32_no_vec_pipeline;
     webgpu_pipeline cpy_pipeline[2][2];          // src type, dst type
@@ -309,10 +309,12 @@ struct ggml_backend_webgpu_context {
 struct ggml_backend_webgpu_buffer_context {
     webgpu_context webgpu_ctx;
     wgpu::Buffer   buffer;
+    std::string    label;
 
-    ggml_backend_webgpu_buffer_context(webgpu_context ctx, wgpu::Buffer buf) :
+    ggml_backend_webgpu_buffer_context(webgpu_context ctx, wgpu::Buffer buf, std::string lbl) :
         webgpu_ctx(std::move(ctx)),
-        buffer(std::move(buf)) {}
+        buffer(std::move(buf)),
+        label(std::move(lbl)) {}
 };
 
 /* End struct definitions */
@@ -764,10 +766,20 @@ static std::optional<webgpu_command> ggml_webgpu_set_rows(webgpu_context & ctx,
         { .binding = 3, .buffer = error_bufs.dev_buf, .offset = 0, .size = error_bufs.dev_buf.GetSize() }
     };
 
-    size_t   max_wg_size = ctx->max_wg_size_x;
-    uint32_t wg_x        = (src->ne[1] * src->ne[2] * src->ne[3] + max_wg_size - 1) / max_wg_size;
+    size_t max_wg_size = ctx->max_wg_size_x;
+
+    int             vectorized = src->ne[0] % 4 == 0;
+    webgpu_pipeline pipeline   = ctx->set_rows_pipeline[0][vectorized];
+    uint32_t        threads;
+    if (vectorized) {
+        threads = (src->ne[1] * src->ne[2] * src->ne[3]) * (src->ne[0] / 4);
+    } else {
+        threads = src->ne[0] * src->ne[1] * src->ne[2] * src->ne[3];
+    }
 
-    return ggml_backend_webgpu_build(ctx, ctx->set_rows_pipeline, params, entries, wg_x, error_bufs);
+    uint32_t wg_x = (threads + max_wg_size - 1) / max_wg_size;
+
+    return ggml_backend_webgpu_build(ctx, pipeline, params, entries, wg_x, error_bufs);
 }
 
 static webgpu_command ggml_webgpu_get_rows(webgpu_context & ctx,
@@ -1336,11 +1348,11 @@ static void ggml_backend_webgpu_buffer_memset_tensor(ggml_backend_buffer_t buffe
 
     WEBGPU_CPU_PROFILE_TOTAL_START(memset_tensor);
 
-    WEBGPU_LOG_DEBUG("ggml_backend_webgpu_buffer_memset_tensor(" << buffer << ", " << tensor << ", " << value << ", "
-                                                                 << offset << ", " << size << ")");
-
     ggml_backend_webgpu_buffer_context * buf_ctx = (ggml_backend_webgpu_buffer_context *) buffer->context;
 
+    WEBGPU_LOG_DEBUG("ggml_backend_webgpu_buffer_memset_tensor(" << buf_ctx->label << ", " << tensor << ", " << value
+                                                                 << ", " << offset << ", " << size << ")");
+
     size_t total_offset = webgpu_tensor_offset(tensor) + tensor->view_offs + offset;
 
     // This is a trick to set all bytes of a u32 to the same 1 byte value.
@@ -1354,12 +1366,13 @@ static void ggml_backend_webgpu_buffer_set_tensor(ggml_backend_buffer_t buffer,
                                                   const void *          data,
                                                   size_t                offset,
                                                   size_t                size) {
-    WEBGPU_LOG_DEBUG("ggml_backend_webgpu_buffer_set_tensor(" << buffer << ", " << tensor << ", " << data << ", "
-                                                              << offset << ", " << size << ")");
     WEBGPU_CPU_PROFILE_TOTAL_START(set_tensor);
     ggml_backend_webgpu_buffer_context * buf_ctx    = (ggml_backend_webgpu_buffer_context *) buffer->context;
     webgpu_context                       webgpu_ctx = buf_ctx->webgpu_ctx;
 
+    WEBGPU_LOG_DEBUG("ggml_backend_webgpu_buffer_set_tensor(" << buf_ctx->label << ", " << tensor << ", " << data
+                                                              << ", " << offset << ", " << size << ")");
+
     size_t total_offset = webgpu_tensor_offset(tensor) + tensor->view_offs + offset;
 
     webgpu_ctx->queue.WriteBuffer(buf_ctx->buffer, total_offset, data, (size / 4) * 4);
@@ -1397,12 +1410,12 @@ static void ggml_backend_webgpu_buffer_get_tensor(ggml_backend_buffer_t buffer,
                                                   void *                data,
                                                   size_t                offset,
                                                   size_t                size) {
-    WEBGPU_LOG_DEBUG("ggml_backend_webgpu_buffer_get_tensor(" << buffer << ", " << tensor << ", " << data << ", "
-                                                              << offset << ", " << size << ")");
     WEBGPU_CPU_PROFILE_TOTAL_START(get_tensor);
-    ggml_backend_webgpu_buffer_context * buf_ctx    = (ggml_backend_webgpu_buffer_context *) buffer->context;
-    webgpu_context                       webgpu_ctx = buf_ctx->webgpu_ctx;
-    wgpu::Device                         device     = webgpu_ctx->device;
+    ggml_backend_webgpu_buffer_context * buf_ctx = (ggml_backend_webgpu_buffer_context *) buffer->context;
+    WEBGPU_LOG_DEBUG("ggml_backend_webgpu_buffer_get_tensor(" << buf_ctx->label << ", " << tensor << ", " << data
+                                                              << ", " << offset << ", " << size << ")");
+    webgpu_context webgpu_ctx = buf_ctx->webgpu_ctx;
+    wgpu::Device   device     = webgpu_ctx->device;
 
     size_t total_offset = webgpu_tensor_offset(tensor) + tensor->view_offs + offset;
 
@@ -1473,16 +1486,20 @@ static const char * ggml_backend_webgpu_buffer_type_get_name(ggml_backend_buffer
 
 static ggml_backend_buffer_t ggml_backend_webgpu_buffer_type_alloc_buffer(ggml_backend_buffer_type_t buft,
                                                                           size_t                     size) {
-    WEBGPU_LOG_DEBUG("ggml_backend_webgpu_buffer_type_alloc_buffer(" << size << ")");
+    static std::atomic<int> buffer_count;
+    int                     buffer_id = buffer_count++;
+    std::string             buf_name  = "tensor_buf" + std::to_string(buffer_id);
+    WEBGPU_LOG_DEBUG("ggml_backend_webgpu_buffer_type_alloc_buffer_" << buffer_id << ": " << size << " bytes");
     ggml_backend_webgpu_device_context * ctx = static_cast<ggml_backend_webgpu_device_context *>(buft->device->context);
 
     wgpu::Buffer buf;
     ggml_webgpu_create_buffer(ctx->webgpu_ctx->device, buf,
                               (size + WEBGPU_STORAGE_BUF_BINDING_MULT - 1) & ~(WEBGPU_STORAGE_BUF_BINDING_MULT - 1),
                               wgpu::BufferUsage::Storage | wgpu::BufferUsage::CopySrc | wgpu::BufferUsage::CopyDst,
-                              "allocated_buffer");
+                              buf_name.c_str());
 
-    ggml_backend_webgpu_buffer_context * buf_ctx = new ggml_backend_webgpu_buffer_context(ctx->webgpu_ctx, buf);
+    ggml_backend_webgpu_buffer_context * buf_ctx =
+        new ggml_backend_webgpu_buffer_context(ctx->webgpu_ctx, buf, buf_name);
 
     return ggml_backend_buffer_init(buft, ggml_backend_webgpu_buffer_interface, buf_ctx, size);
 }
@@ -1613,8 +1630,10 @@ static void ggml_webgpu_init_mul_mat_pipeline(webgpu_context & webgpu_ctx) {
 }
 
 static void ggml_webgpu_init_set_rows_pipeline(webgpu_context & webgpu_ctx) {
-    ggml_webgpu_create_pipeline(webgpu_ctx->device, webgpu_ctx->set_rows_pipeline, wgsl_set_rows, "set_rows",
-                                ggml_webgpu_wg_size_entry(webgpu_ctx->max_wg_size_x));
+    ggml_webgpu_create_pipeline(webgpu_ctx->device, webgpu_ctx->set_rows_pipeline[0][0], wgsl_set_rows_f16,
+                                "set_rows_f16", ggml_webgpu_wg_size_entry(webgpu_ctx->max_wg_size_x));
+    ggml_webgpu_create_pipeline(webgpu_ctx->device, webgpu_ctx->set_rows_pipeline[0][1], wgsl_set_rows_f16_vec,
+                                "set_rows_f16_vec", ggml_webgpu_wg_size_entry(webgpu_ctx->max_wg_size_x));
 }
 
 static void ggml_webgpu_init_get_rows_pipeline(webgpu_context & webgpu_ctx) {
@@ -1950,8 +1969,10 @@ static bool ggml_backend_webgpu_device_supports_op(ggml_backend_dev_t dev, const
         case GGML_OP_SUB:
         case GGML_OP_MUL:
         case GGML_OP_DIV:
+            // TODO: support non-contiguous tensors, e.g. for MOE_EXPERT_REDUCE
+            // see https://github.com/ggml-org/llama.cpp/pull/16857
             supports_op = (op->type == GGML_TYPE_F32 || op->type == GGML_TYPE_F16) && (src0->type == op->type) &&
-                          (src1->type == op->type);
+                          (src1->type == op->type) && ggml_is_contiguous(src0) && ggml_is_contiguous(src1);
             break;
         case GGML_OP_CPY:
         case GGML_OP_CONT:
@@ -2129,6 +2150,19 @@ static ggml_backend_dev_t ggml_backend_webgpu_reg_get_device(ggml_backend_reg_t
     required_features.push_back(wgpu::FeatureName::TimestampQuery);
 #endif
 
+    // Enable Dawn-specific toggles to increase native performance
+    // TODO: Don't enable for WASM builds, they won't have an effect anyways
+    // TODO: Maybe WebGPU needs a "fast" mode where you can request compilers skip adding checks like these,
+    //       only for native performance?
+    const char * const deviceEnabledToggles[]  = { "skip_validation", "disable_robustness", "disable_workgroup_init",
+                                                   "disable_polyfills_on_integer_div_and_mod" };
+    const char * const deviceDisabledToggles[] = { "timestamp_quantization" };
+    wgpu::DawnTogglesDescriptor deviceTogglesDesc;
+    deviceTogglesDesc.enabledToggles      = deviceEnabledToggles;
+    deviceTogglesDesc.enabledToggleCount  = 4;
+    deviceTogglesDesc.disabledToggles     = deviceDisabledToggles;
+    deviceTogglesDesc.disabledToggleCount = 1;
+
     wgpu::DeviceDescriptor dev_desc;
     dev_desc.requiredLimits       = &ctx->limits;
     dev_desc.requiredFeatures     = required_features.data();
@@ -2146,6 +2180,7 @@ static ggml_backend_dev_t ggml_backend_webgpu_reg_get_device(ggml_backend_reg_t
             GGML_ABORT("ggml_webgpu: Device error! Reason: %d, Message: %s\n", static_cast<int>(reason),
                        std::string(message).c_str());
         });
+    dev_desc.nextInChain = &deviceTogglesDesc;
     ctx->instance.WaitAny(ctx->adapter.RequestDevice(
                               &dev_desc, wgpu::CallbackMode::AllowSpontaneous,
                               [ctx](wgpu::RequestDeviceStatus status, wgpu::Device device, wgpu::StringView message) {
@@ -2243,11 +2278,18 @@ ggml_backend_reg_t ggml_backend_webgpu_reg() {
     ctx.name         = GGML_WEBGPU_NAME;
     ctx.device_count = 1;
 
+    const char * const instanceEnabledToggles[] = { "allow_unsafe_apis" };
+
+    wgpu::DawnTogglesDescriptor instanceTogglesDesc;
+    instanceTogglesDesc.enabledToggles     = instanceEnabledToggles;
+    instanceTogglesDesc.enabledToggleCount = 1;
     wgpu::InstanceDescriptor               instance_descriptor{};
     std::vector<wgpu::InstanceFeatureName> instance_features = { wgpu::InstanceFeatureName::TimedWaitAny };
     instance_descriptor.requiredFeatures                     = instance_features.data();
     instance_descriptor.requiredFeatureCount                 = instance_features.size();
-    webgpu_ctx->instance                                     = wgpu::CreateInstance(&instance_descriptor);
+    instance_descriptor.nextInChain                          = &instanceTogglesDesc;
+
+    webgpu_ctx->instance = wgpu::CreateInstance(&instance_descriptor);
     GGML_ASSERT(webgpu_ctx->instance != nullptr);
 
     static ggml_backend_reg reg = {
diff --git a/ggml/src/ggml-webgpu/wgsl-shaders/set_rows.wgsl b/ggml/src/ggml-webgpu/wgsl-shaders/set_rows.tmpl.wgsl
similarity index 69%
rename from ggml/src/ggml-webgpu/wgsl-shaders/set_rows.wgsl
rename to ggml/src/ggml-webgpu/wgsl-shaders/set_rows.tmpl.wgsl
index 3567713dc21..fca3be6bc27 100644
--- a/ggml/src/ggml-webgpu/wgsl-shaders/set_rows.wgsl
+++ b/ggml/src/ggml-webgpu/wgsl-shaders/set_rows.tmpl.wgsl
@@ -1,13 +1,38 @@
+#define(VARIANTS)
+
+[
+  {
+    "SHADER_SUFFIX": "f16_vec",
+    "REPLS": {
+      "TYPE" : "vec4<f32>",
+      "DST_TYPE": "vec4<f16>",
+      "VEC_SIZE": 4
+    }
+  },
+  {
+    "SHADER_SUFFIX": "f16",
+    "REPLS": {
+      "TYPE" : "f32",
+      "DST_TYPE": "f16",
+      "VEC_SIZE": 1
+    }
+  }
+]
+
+#end(VARIANTS)
+
+#define(SHADER)
+
 enable f16;
 
 @group(0) @binding(0)
-var<storage, read_write> src: array<f32>;
+var<storage, read_write> src: array<{{TYPE}}>;
 
 @group(0) @binding(1)
 var<storage, read_write> idx: array<u32>;
 
 @group(0) @binding(2)
-var<storage, read_write> dst: array<f16>;
+var<storage, read_write> dst: array<{{DST_TYPE}}>;
 
 @group(0) @binding(3)
 var<storage, read_write> error: atomic<u32>;
@@ -47,10 +72,14 @@ var<uniform> params: Params;
 override wg_size: u32;
 @compute @workgroup_size(wg_size)
 fn main(@builtin(global_invocation_id) gid: vec3<u32>) {
-    if (gid.x >= params.n_rows * params.ne2 * params.ne3) {
+    if (gid.x >= (params.ne3 * params.ne2 * params.n_rows * params.ne0) / {{VEC_SIZE}}) {
         return;
     }
-    var i = gid.x;
+
+    // getting the row from gid
+    let elems_per_row = params.ne0 / {{VEC_SIZE}};
+    var i = gid.x / elems_per_row;
+
     let i_src3 = i / (params.ne2 * params.n_rows);
 
     i = i % (params.ne2 * params.n_rows);
@@ -75,7 +104,9 @@ fn main(@builtin(global_invocation_id) gid: vec3<u32>) {
     let i_dst_row = params.offset_dst + idx_high_val * params.stride_dst1 + i_src2 * params.stride_dst2 + i_src3 * params.stride_dst3;
     let i_src_row = params.offset_src + i_src1 * params.stride_src1 + i_src2 * params.stride_src2 + i_src3 * params.stride_src3;
 
-    for (var i: u32 = 0; i < params.ne0; i++) {
-      dst[i_dst_row + i] = f16(src[i_src_row + i]);
-    }
+    let col_idx = (gid.x % elems_per_row);
+    dst[i_dst_row/{{VEC_SIZE}} + col_idx] = {{DST_TYPE}}(src[i_src_row/{{VEC_SIZE}} + col_idx]);
 }
+
+#end(SHADER)
+

From 9f052478c2c38ec10cb378109b110a1f7033ce11 Mon Sep 17 00:00:00 2001
From: Li Pengzhan <151381994+Lpzhan931@users.noreply.github.com>
Date: Wed, 5 Nov 2025 17:28:58 +0800
Subject: [PATCH 089/185] model : add openPangu-Embedded (#16941)
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

* Model: add openPangu-Embedded

* fixed according to reviewer's comments

* fixed the chat template check condition

* Apply suggestions from code review

change the chat-template check condition and some formatting issue

Co-authored-by: Sigbjørn Skjæret <sigbjorn.skjaeret@scala.com>

* whitespace cleanup

---------

Co-authored-by: Sigbjørn Skjæret <sigbjorn.skjaeret@scala.com>
---
 convert_hf_to_gguf.py         |  36 ++++++++++
 gguf-py/gguf/constants.py     |  20 ++++++
 src/CMakeLists.txt            |   1 +
 src/llama-arch.cpp            |  18 +++++
 src/llama-arch.h              |   1 +
 src/llama-chat.cpp            |  32 +++++++++
 src/llama-chat.h              |   1 +
 src/llama-model.cpp           |  58 ++++++++++++++++
 src/models/models.h           |   4 ++
 src/models/pangu-embedded.cpp | 121 ++++++++++++++++++++++++++++++++++
 10 files changed, 292 insertions(+)
 create mode 100644 src/models/pangu-embedded.cpp

diff --git a/convert_hf_to_gguf.py b/convert_hf_to_gguf.py
index c6f5ba6a04c..222f6ed6dc4 100755
--- a/convert_hf_to_gguf.py
+++ b/convert_hf_to_gguf.py
@@ -7187,6 +7187,42 @@ def modify_tensors(self, data_torch: Tensor, name: str, bid: int | None):
         return super().modify_tensors(data_torch, name, bid)
 
 
+@ModelBase.register("PanguEmbeddedForCausalLM")
+class PanguEmbeddedModel(TextModel):
+    model_arch = gguf.MODEL_ARCH.PANGU_EMBED
+
+    def set_vocab(self):
+        self._set_vocab_sentencepiece()
+
+        tokenizer_config_file = self.dir_model / 'tokenizer_config.json'
+        if tokenizer_config_file.is_file():
+            with open(tokenizer_config_file, "r", encoding="utf-8") as f:
+                tokenizer_config_json = json.load(f)
+                if "add_prefix_space" in tokenizer_config_json:
+                    self.gguf_writer.add_add_space_prefix(tokenizer_config_json["add_prefix_space"])
+
+    def set_gguf_parameters(self):
+        super().set_gguf_parameters()
+        hparams = self.hparams
+        self.gguf_writer.add_vocab_size(hparams["vocab_size"])
+
+        # PanguEmbedded's hparam loaded from config.json without head_dim
+        if (rope_dim := hparams.get("head_dim")) is None:
+            rope_dim = hparams["hidden_size"] // hparams["num_attention_heads"]
+        self.gguf_writer.add_rope_dimension_count(rope_dim)
+
+        if hparams.get("head_dim") is None:
+            self.gguf_writer.add_key_length(rope_dim)
+            self.gguf_writer.add_value_length(rope_dim)
+
+    def modify_tensors(self, data_torch: Tensor, name: str, bid: int | None) -> Iterable[tuple[str, Tensor]]:
+        if name == "lm_head.weight":
+            if self.hparams.get("tie_word_embeddings", False):
+                logger.info("Skipping tied output layer 'lm_head.weight'")
+                return []
+        return [(self.map_tensor_name(name), data_torch)]
+
+
 @ModelBase.register("Dots1ForCausalLM")
 class Dots1Model(Qwen2MoeModel):
     model_arch = gguf.MODEL_ARCH.DOTS1
diff --git a/gguf-py/gguf/constants.py b/gguf-py/gguf/constants.py
index 77e3b0650ff..6b4b6c5ab07 100644
--- a/gguf-py/gguf/constants.py
+++ b/gguf-py/gguf/constants.py
@@ -426,6 +426,7 @@ class MODEL_ARCH(IntEnum):
     APERTUS          = auto()
     COGVLM           = auto()
     MINIMAXM2        = auto()
+    PANGU_EMBED      = auto()
 
 
 class VISION_PROJECTOR_TYPE(IntEnum):
@@ -793,6 +794,7 @@ class MODEL_TENSOR(IntEnum):
     MODEL_ARCH.APERTUS:          "apertus",
     MODEL_ARCH.MINIMAXM2:        "minimax-m2",
     MODEL_ARCH.COGVLM:           "cogvlm",
+    MODEL_ARCH.PANGU_EMBED:      "pangu-embedded",
 }
 
 VISION_PROJECTOR_TYPE_NAMES: dict[VISION_PROJECTOR_TYPE, str] = {
@@ -2958,6 +2960,20 @@ class MODEL_TENSOR(IntEnum):
         MODEL_TENSOR.VISEXP_UP,
         MODEL_TENSOR.VISEXP_DOWN,
     ],
+    MODEL_ARCH.PANGU_EMBED: [
+        MODEL_TENSOR.TOKEN_EMBD,
+        MODEL_TENSOR.OUTPUT_NORM,
+        MODEL_TENSOR.OUTPUT,
+        MODEL_TENSOR.ATTN_NORM,
+        MODEL_TENSOR.ATTN_Q,
+        MODEL_TENSOR.ATTN_K,
+        MODEL_TENSOR.ATTN_V,
+        MODEL_TENSOR.ATTN_OUT,
+        MODEL_TENSOR.FFN_NORM,
+        MODEL_TENSOR.FFN_GATE,
+        MODEL_TENSOR.FFN_DOWN,
+        MODEL_TENSOR.FFN_UP,
+    ],
     # TODO
 }
 
@@ -3013,6 +3029,10 @@ class MODEL_TENSOR(IntEnum):
     MODEL_ARCH.BAILINGMOE: [
         MODEL_TENSOR.ROPE_FREQS,
     ],
+    MODEL_ARCH.PANGU_EMBED: [
+        MODEL_TENSOR.ROPE_FREQS,
+        MODEL_TENSOR.ATTN_ROT_EMBD,
+    ],
 }
 
 #
diff --git a/src/CMakeLists.txt b/src/CMakeLists.txt
index 832b58e315d..630b2cddf67 100644
--- a/src/CMakeLists.txt
+++ b/src/CMakeLists.txt
@@ -99,6 +99,7 @@ add_library(llama
             models/openai-moe-iswa.cpp
             models/openelm.cpp
             models/orion.cpp
+            models/pangu-embedded.cpp
             models/phi2.cpp
             models/phi3.cpp
             models/plamo.cpp
diff --git a/src/llama-arch.cpp b/src/llama-arch.cpp
index 7c7953b83dd..b7642b568df 100644
--- a/src/llama-arch.cpp
+++ b/src/llama-arch.cpp
@@ -107,6 +107,7 @@ static const std::map<llm_arch, const char *> LLM_ARCH_NAMES = {
     { LLM_ARCH_APERTUS,          "apertus"          },
     { LLM_ARCH_MINIMAX_M2,       "minimax-m2"       },
     { LLM_ARCH_COGVLM,           "cogvlm"           },
+    { LLM_ARCH_PANGU_EMBED,      "pangu-embedded"   },
     { LLM_ARCH_UNKNOWN,          "(unknown)"        },
 };
 
@@ -2377,6 +2378,23 @@ static const std::map<llm_arch, std::map<llm_tensor, const char *>> LLM_TENSOR_N
             { LLM_TENSOR_FFN_EXP_PROBS_B,    "blk.%d.exp_probs_b" },
         },
     },
+    {
+        LLM_ARCH_PANGU_EMBED,
+        {
+            { LLM_TENSOR_TOKEN_EMBD,      "token_embd" },
+            { LLM_TENSOR_OUTPUT_NORM,     "output_norm" },
+            { LLM_TENSOR_OUTPUT,          "output" },
+            { LLM_TENSOR_ATTN_NORM,       "blk.%d.attn_norm" },
+            { LLM_TENSOR_ATTN_Q,          "blk.%d.attn_q" },
+            { LLM_TENSOR_ATTN_K,          "blk.%d.attn_k" },
+            { LLM_TENSOR_ATTN_V,          "blk.%d.attn_v" },
+            { LLM_TENSOR_ATTN_OUT,        "blk.%d.attn_output" },
+            { LLM_TENSOR_FFN_NORM,        "blk.%d.ffn_norm" },
+            { LLM_TENSOR_FFN_GATE,        "blk.%d.ffn_gate" },
+            { LLM_TENSOR_FFN_DOWN,        "blk.%d.ffn_down" },
+            { LLM_TENSOR_FFN_UP,          "blk.%d.ffn_up" },
+        },
+    },
     {
         LLM_ARCH_COGVLM,
         {
diff --git a/src/llama-arch.h b/src/llama-arch.h
index 3f893a2dc69..a769dd1e857 100644
--- a/src/llama-arch.h
+++ b/src/llama-arch.h
@@ -111,6 +111,7 @@ enum llm_arch {
     LLM_ARCH_APERTUS,
     LLM_ARCH_MINIMAX_M2,
     LLM_ARCH_COGVLM,
+    LLM_ARCH_PANGU_EMBED,
     LLM_ARCH_UNKNOWN,
 };
 
diff --git a/src/llama-chat.cpp b/src/llama-chat.cpp
index 0285006d73c..fc6a6223cfe 100644
--- a/src/llama-chat.cpp
+++ b/src/llama-chat.cpp
@@ -73,6 +73,7 @@ static const std::map<std::string, llm_chat_template> LLM_CHAT_TEMPLATES = {
     { "kimi-k2",           LLM_CHAT_TEMPLATE_KIMI_K2           },
     { "seed_oss",          LLM_CHAT_TEMPLATE_SEED_OSS          },
     { "grok-2",            LLM_CHAT_TEMPLATE_GROK_2            },
+    { "pangu-embedded",    LLM_CHAT_TEMPLATE_PANGU_EMBED       },
 };
 
 llm_chat_template llm_chat_template_from_str(const std::string & name) {
@@ -213,6 +214,8 @@ llm_chat_template llm_chat_detect_template(const std::string & tmpl) {
         return LLM_CHAT_TEMPLATE_SEED_OSS;
     } else if (tmpl_contains("'Assistant: '  + message['content'] + '<|separator|>")) {
         return LLM_CHAT_TEMPLATE_GROK_2;
+    } else if (tmpl_contains(LU8("[unused9]系统：[unused10]"))) {
+        return LLM_CHAT_TEMPLATE_PANGU_EMBED;
     }
     return LLM_CHAT_TEMPLATE_UNKNOWN;
 }
@@ -813,6 +816,35 @@ int32_t llm_chat_apply_template(
         if (add_ass) {
             ss << "Assistant:";
         }
+    }else if (tmpl == LLM_CHAT_TEMPLATE_PANGU_EMBED) {
+        // [unused9]系统：xxx[unused10]
+        // [unused9]用户：xxx[unused10]
+        // [unused9]助手：xxx[unused10]
+        // ...
+        for (size_t i = 0; i < chat.size(); ++i) {
+            const auto & msg = chat[i];
+            const std::string & role = msg->role;
+            const std::string & content = msg->content;
+
+            if (i == 0 && role != "system") {
+                ss << "[unused9]系统：[unused10]";
+            }
+
+            if (role == "system") {
+                ss << "[unused9]系统：" << content << "[unused10]";
+            } else if (role == "user") {
+                ss << "[unused9]用户：" << content << "[unused10]";
+            } else if (role == "assistant") {
+                ss << "[unused9]助手：" << content << "[unused10]";
+            } else if (role == "tool") {
+                ss << "[unused9]工具：" << content << "[unused10]";
+            } else if (role == "function") {
+                ss << "[unused9]方法：" << content << "[unused10]";
+            }
+        }
+        if (add_ass) {
+            ss << "[unused9]助手：";
+        }
     } else {
         // template not supported
         return -1;
diff --git a/src/llama-chat.h b/src/llama-chat.h
index da1b7c47997..684efb4d67f 100644
--- a/src/llama-chat.h
+++ b/src/llama-chat.h
@@ -53,6 +53,7 @@ enum llm_chat_template {
     LLM_CHAT_TEMPLATE_KIMI_K2,
     LLM_CHAT_TEMPLATE_SEED_OSS,
     LLM_CHAT_TEMPLATE_GROK_2,
+    LLM_CHAT_TEMPLATE_PANGU_EMBED,
     LLM_CHAT_TEMPLATE_UNKNOWN,
 };
 
diff --git a/src/llama-model.cpp b/src/llama-model.cpp
index 896725466ce..1987135ca6a 100644
--- a/src/llama-model.cpp
+++ b/src/llama-model.cpp
@@ -2177,6 +2177,15 @@ void llama_model::load_hparams(llama_model_loader & ml) {
                     default: type = LLM_TYPE_UNKNOWN;
                 }
             } break;
+        case LLM_ARCH_PANGU_EMBED:
+            {
+                ml.get_key(LLM_KV_ATTENTION_LAYERNORM_RMS_EPS, hparams.f_norm_rms_eps);
+                switch (hparams.n_layer) {
+                    case 26: type = LLM_TYPE_1B; break; // openPangu-Embedded-1B-V1.1
+                    case 34: type = LLM_TYPE_7B; break; // openPangu-Embedded-7B-V1.1
+                    default: type = LLM_TYPE_UNKNOWN;
+                }
+            } break;
         default: throw std::runtime_error("unsupported model architecture");
     }
 
@@ -6263,6 +6272,50 @@ bool llama_model::load_tensors(llama_model_loader & ml) {
                         layer.visexp_ffn_up   = create_tensor(tn(LLM_TENSOR_VISEXP_FFN_UP,   "weight", i), {n_embd,   n_ff}, 0);
                     }
                 } break;
+            case LLM_ARCH_PANGU_EMBED:
+                {
+                    tok_embd = create_tensor(tn(LLM_TENSOR_TOKEN_EMBD, "weight"), {n_embd, n_vocab}, 0);
+
+                    // output
+                    output_norm = create_tensor(tn(LLM_TENSOR_OUTPUT_NORM, "weight"), {n_embd}, 0);
+                    output      = create_tensor(tn(LLM_TENSOR_OUTPUT,      "weight"), {n_embd, n_vocab}, TENSOR_NOT_REQUIRED);
+
+                    // if output is NULL, init from the input tok embed
+                    if (output == NULL) {
+                        output = create_tensor(tn(LLM_TENSOR_TOKEN_EMBD, "weight"), {n_embd, n_vocab}, TENSOR_DUPLICATED);
+                    }
+
+                    for (int i = 0; i < n_layer; ++i) {
+                        auto & layer = layers[i];
+
+                        layer.attn_norm = create_tensor(tn(LLM_TENSOR_ATTN_NORM, "weight", i), {n_embd}, 0);
+
+                        // weight tensors
+                        layer.wq = create_tensor(tn(LLM_TENSOR_ATTN_Q,   "weight", i), {n_embd, n_embd_head_k * n_head}, 0);
+                        layer.wk = create_tensor(tn(LLM_TENSOR_ATTN_K,   "weight", i), {n_embd, n_embd_k_gqa}, 0);
+                        layer.wv = create_tensor(tn(LLM_TENSOR_ATTN_V,   "weight", i), {n_embd, n_embd_v_gqa}, 0);
+                        layer.wo = create_tensor(tn(LLM_TENSOR_ATTN_OUT, "weight", i), {n_embd_head_k * n_head, n_embd}, 0);
+
+                        // bias tensors
+                        layer.bq = create_tensor(tn(LLM_TENSOR_ATTN_Q,   "bias", i), {n_embd_head_k * n_head}, 0);
+                        layer.bk = create_tensor(tn(LLM_TENSOR_ATTN_K,   "bias", i), {n_embd_gqa}, 0);
+                        layer.bv = create_tensor(tn(LLM_TENSOR_ATTN_V,   "bias", i), {n_embd_gqa}, 0);
+                        layer.bo = create_tensor(tn(LLM_TENSOR_ATTN_OUT, "bias", i), {n_embd}, 0);
+
+                        layer.ffn_norm = create_tensor(tn(LLM_TENSOR_FFN_NORM, "weight", i), {n_embd}, 0);
+
+                        if (hparams.rope_scaling_type_train == LLAMA_ROPE_SCALING_TYPE_LONGROPE) {
+                            layer.rope_long  = create_tensor(tn(LLM_TENSOR_ROPE_FACTORS_LONG,  "weight", i), {n_rot/2}, TENSOR_NOT_REQUIRED | (i != 0 ? TENSOR_DUPLICATED : 0));
+                            layer.rope_short = create_tensor(tn(LLM_TENSOR_ROPE_FACTORS_SHORT, "weight", i), {n_rot/2}, TENSOR_NOT_REQUIRED | (i != 0 ? TENSOR_DUPLICATED : 0));
+                        } else {
+                            layer.rope_freqs = create_tensor(tn(LLM_TENSOR_ROPE_FREQS, "weight", i), {n_rot/2}, TENSOR_NOT_REQUIRED | (i != 0 ? TENSOR_DUPLICATED : 0));
+                        }
+
+                        layer.ffn_gate = create_tensor(tn(LLM_TENSOR_FFN_GATE, "weight", i), {n_embd,   n_ff}, 0);
+                        layer.ffn_down = create_tensor(tn(LLM_TENSOR_FFN_DOWN, "weight", i), {  n_ff, n_embd}, 0);
+                        layer.ffn_up   = create_tensor(tn(LLM_TENSOR_FFN_UP,   "weight", i), {n_embd,   n_ff}, 0);
+                    }
+                } break;
             default:
                 throw std::runtime_error("unknown architecture");
         }
@@ -7260,6 +7313,10 @@ ggml_cgraph * llama_model::build_graph(const llm_graph_params & params) const {
             {
                 llm = std::make_unique<llm_build_cogvlm>(*this, params);
             } break;
+        case LLM_ARCH_PANGU_EMBED:
+            {
+                llm = std::make_unique<llm_build_pangu_embedded>(*this, params);
+            }break;
         default:
             GGML_ABORT("fatal error");
     }
@@ -7479,6 +7536,7 @@ llama_rope_type llama_model_rope_type(const llama_model * model) {
         case LLM_ARCH_APERTUS:
         case LLM_ARCH_MINIMAX_M2:
         case LLM_ARCH_COGVLM:
+        case LLM_ARCH_PANGU_EMBED:
             return LLAMA_ROPE_TYPE_NEOX;
 
         case LLM_ARCH_QWEN2VL:
diff --git a/src/models/models.h b/src/models/models.h
index af203343a4d..2fffb382df2 100644
--- a/src/models/models.h
+++ b/src/models/models.h
@@ -361,6 +361,10 @@ struct llm_build_orion : public llm_graph_context {
     llm_build_orion(const llama_model & model, const llm_graph_params & params);
 };
 
+struct llm_build_pangu_embedded : public llm_graph_context {
+    llm_build_pangu_embedded(const llama_model & model, const llm_graph_params & params);
+};
+
 struct llm_build_phi2 : public llm_graph_context {
     llm_build_phi2(const llama_model & model, const llm_graph_params & params);
 };
diff --git a/src/models/pangu-embedded.cpp b/src/models/pangu-embedded.cpp
new file mode 100644
index 00000000000..664572a5001
--- /dev/null
+++ b/src/models/pangu-embedded.cpp
@@ -0,0 +1,121 @@
+#include "models.h"
+
+
+llm_build_pangu_embedded::llm_build_pangu_embedded(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
+    const int64_t n_embd_head = hparams.n_embd_head_v;
+
+    GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
+    GGML_ASSERT(n_embd_head == hparams.n_rot);
+
+    ggml_tensor * cur;
+    ggml_tensor * inpL;
+
+    inpL = build_inp_embd(model.tok_embd);
+
+    // inp_pos - contains the positions
+    ggml_tensor * inp_pos = build_inp_pos();
+
+    auto * inp_attn = build_attn_inp_kv();
+
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
+    for (int il = 0; il < n_layer; ++il) {
+        ggml_tensor * inpSA = inpL;
+
+        // norm
+        cur = build_norm(inpL,
+                model.layers[il].attn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "attn_norm", il);
+
+        // self attention
+        {
+            // compute Q and K and RoPE them
+            ggml_tensor * Qcur = build_lora_mm(model.layers[il].wq, cur);
+            Qcur = ggml_add(ctx0, Qcur, model.layers[il].bq);
+            cb(Qcur, "Qcur", il);
+
+            ggml_tensor * Kcur = build_lora_mm(model.layers[il].wk, cur);
+            Kcur = ggml_add(ctx0, Kcur, model.layers[il].bk);
+            cb(Kcur, "Kcur", il);
+
+            ggml_tensor * Vcur = build_lora_mm(model.layers[il].wv, cur);
+            Vcur = ggml_add(ctx0, Vcur, model.layers[il].bv);
+            cb(Vcur, "Vcur", il);
+
+            Qcur = ggml_reshape_3d(ctx0, Qcur, n_embd_head, n_head,    n_tokens);
+            Kcur = ggml_reshape_3d(ctx0, Kcur, n_embd_head, n_head_kv, n_tokens);
+            Vcur = ggml_reshape_3d(ctx0, Vcur, n_embd_head, n_head_kv, n_tokens);
+
+            Qcur = ggml_rope_ext(
+                    ctx0, Qcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            Kcur = ggml_rope_ext(ctx0, Kcur, inp_pos, nullptr,
+                    n_rot, rope_type, n_ctx_orig, freq_base, freq_scale,
+                    ext_factor, attn_factor, beta_fast, beta_slow
+                    );
+
+            cb(Qcur, "Qcur", il);
+            cb(Kcur, "Kcur", il);
+            cb(Vcur, "Vcur", il);
+
+            cur = build_attn(inp_attn,
+                    model.layers[il].wo, model.layers[il].bo,
+                    Qcur, Kcur, Vcur, nullptr, nullptr, nullptr, 1.0f/sqrtf(float(n_embd_head)), il);
+        }
+
+        if (il == n_layer - 1 && inp_out_ids) {
+            cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+        }
+
+        ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
+        cb(ffn_inp, "ffn_inp", il);
+
+        // feed-forward network
+        cur = build_norm(ffn_inp,
+                model.layers[il].ffn_norm, NULL,
+                LLM_NORM_RMS, il);
+        cb(cur, "ffn_norm", il);
+
+        cur = build_ffn(cur,
+                model.layers[il].ffn_up,   model.layers[il].ffn_up_b,   NULL,
+                model.layers[il].ffn_gate, model.layers[il].ffn_gate_b, NULL,
+                model.layers[il].ffn_down, model.layers[il].ffn_down_b, NULL,
+                NULL,
+                LLM_FFN_SILU, LLM_FFN_PAR, il);
+
+        cur = ggml_add(ctx0, cur, ffn_inp);
+        cb(cur, "ffn_out", il);
+
+        cur = build_cvec(cur, il);
+        cb(cur, "l_out", il);
+
+        // input for next layer
+        inpL = cur;
+    }
+
+    cur = inpL;
+
+    cur = build_norm(cur,
+            model.output_norm, NULL,
+            LLM_NORM_RMS, -1);
+
+    cb(cur, "result_norm", -1);
+    res->t_embd = cur;
+
+    // lm_head
+    cur = build_lora_mm(model.output, cur);
+
+    if (model.output_b != nullptr) {
+        cur = ggml_add(ctx0, cur, model.output_b);
+    }
+
+    cb(cur, "result_output", -1);
+    res->t_logits = cur;
+
+    ggml_build_forward_expand(gf, cur);
+}

From fd2f84f468f888970e72f87c8ee86c73a122537f Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=EC=86=90=ED=9D=AC=EC=A4=80?= <openingnow@naver.com>
Date: Wed, 5 Nov 2025 19:20:28 +0900
Subject: [PATCH 090/185] docs: Clarify the endpoint that webui uses (#17001)

---
 tools/server/README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/tools/server/README.md b/tools/server/README.md
index c16d0bd6dcd..6828ef73824 100644
--- a/tools/server/README.md
+++ b/tools/server/README.md
@@ -277,7 +277,7 @@ For more details, please refer to [multimodal documentation](../../docs/multimod
 
 ## Web UI
 
-The project includes a web-based user interface that enables interaction with the model through the `/chat/completions` endpoint.
+The project includes a web-based user interface that enables interaction with the model through the `/v1/chat/completions` endpoint.
 
 The web UI is developed using:
 - `react` framework for frontend development

From 2f0c2db43e2adfa9ffbdfa1176b3b6bd9c9ed536 Mon Sep 17 00:00:00 2001
From: Xuan-Son Nguyen <son@huggingface.co>
Date: Wed, 5 Nov 2025 11:26:37 +0100
Subject: [PATCH 091/185] mtmd: improve struct initialization (#16981)

---
 tools/mtmd/clip.cpp |  1 +
 tools/mtmd/mtmd.cpp | 35 ++++++++++++++++++-----------------
 2 files changed, 19 insertions(+), 17 deletions(-)

diff --git a/tools/mtmd/clip.cpp b/tools/mtmd/clip.cpp
index 99775cb3e35..67a8a470c83 100644
--- a/tools/mtmd/clip.cpp
+++ b/tools/mtmd/clip.cpp
@@ -2761,6 +2761,7 @@ struct clip_model_loader {
                     {
                         // ref: https://huggingface.co/mistral-community/pixtral-12b/blob/main/preprocessor_config.json
                         // TODO: verify the image_min_tokens
+                        hparams.n_merge = 1; // the original pixtral does not use patch merging
                         hparams.rope_theta = 10000.0f;
                         get_u32(KEY_SPATIAL_MERGE_SIZE, hparams.n_merge, false);
                         hparams.set_limit_image_tokens(8, 1024);
diff --git a/tools/mtmd/mtmd.cpp b/tools/mtmd/mtmd.cpp
index 325f7ff995e..4343f3b6fc3 100644
--- a/tools/mtmd/mtmd.cpp
+++ b/tools/mtmd/mtmd.cpp
@@ -101,16 +101,17 @@ static clip_flash_attn_type mtmd_get_clip_flash_attn_type(enum llama_flash_attn_
 }
 
 mtmd_context_params mtmd_context_params_default() {
-    mtmd_context_params params;
-    params.use_gpu = true;
-    params.print_timings = true;
-    params.n_threads = 4;
-    params.verbosity = GGML_LOG_LEVEL_INFO;
-    params.image_marker = MTMD_DEFAULT_IMAGE_MARKER;
-    params.media_marker = mtmd_default_marker();
-    params.flash_attn_type = LLAMA_FLASH_ATTN_TYPE_AUTO;
-    params.image_min_tokens = -1;
-    params.image_max_tokens = -1;
+    mtmd_context_params params {
+        /* use_gpu           */ true,
+        /* print_timings     */ true,
+        /* n_threads         */ 4,
+        /* verbosity         */ GGML_LOG_LEVEL_INFO,
+        /* image_marker      */ MTMD_DEFAULT_IMAGE_MARKER,
+        /* media_marker      */ mtmd_default_marker(),
+        /* flash_attn_type   */ LLAMA_FLASH_ATTN_TYPE_AUTO,
+        /* image_min_tokens  */ -1,
+        /* image_max_tokens  */ -1,
+    };
     return params;
 }
 
@@ -172,13 +173,13 @@ struct mtmd_context {
             throw std::runtime_error("media_marker must not be empty");
         }
 
-        clip_context_params ctx_clip_params;
-        ctx_clip_params.use_gpu          = ctx_params.use_gpu;
-        ctx_clip_params.verbosity        = ctx_params.verbosity;
-        ctx_clip_params.flash_attn_type  = mtmd_get_clip_flash_attn_type(ctx_params.flash_attn_type);
-        // custom image token limits
-        ctx_clip_params.image_min_tokens = ctx_params.image_min_tokens;
-        ctx_clip_params.image_max_tokens = ctx_params.image_max_tokens;
+        clip_context_params ctx_clip_params {
+            /* use_gpu           */ ctx_params.use_gpu,
+            /* verbosity         */ ctx_params.verbosity,
+            /* flash_attn_type   */ CLIP_FLASH_ATTN_TYPE_AUTO,
+            /* image_min_tokens  */ ctx_params.image_min_tokens,
+            /* image_max_tokens  */ ctx_params.image_max_tokens,
+        };
 
         auto res = clip_init(mmproj_fname, ctx_clip_params);
         ctx_v = res.ctx_v;

From 13b339bcd91de64d59512f308f6f69eaca688103 Mon Sep 17 00:00:00 2001
From: Georgi Gerganov <ggerganov@gmail.com>
Date: Wed, 5 Nov 2025 14:32:55 +0200
Subject: [PATCH 092/185] server : do not default to multiple slots with
 speculative decoding (#17017)

* server : do not default to multiple slots with speculative decoding

* cont : fix
---
 common/common.h         |  4 ++++
 tools/server/server.cpp | 14 ++++++++++----
 2 files changed, 14 insertions(+), 4 deletions(-)

diff --git a/common/common.h b/common/common.h
index 78c568a7bc6..54b7849b174 100644
--- a/common/common.h
+++ b/common/common.h
@@ -507,6 +507,10 @@ struct common_params {
     // return false from callback to abort model loading or true to continue
     llama_progress_callback load_progress_callback = NULL;
     void *                  load_progress_callback_user_data = NULL;
+
+    bool has_speculative() const {
+        return !speculative.model.path.empty() || !speculative.model.hf_repo.empty();
+    }
 };
 
 // call once at the start of a program if it uses libcommon
diff --git a/tools/server/server.cpp b/tools/server/server.cpp
index 678aad93b86..f5089bef24a 100644
--- a/tools/server/server.cpp
+++ b/tools/server/server.cpp
@@ -2400,7 +2400,7 @@ struct server_context {
 
         add_bos_token = llama_vocab_get_add_bos(vocab);
 
-        if (!params_base.speculative.model.path.empty() || !params_base.speculative.model.hf_repo.empty()) {
+        if (params_base.has_speculative()) {
             SRV_INF("loading draft model '%s'\n", params_base.speculative.model.path.c_str());
 
             auto params_dft = params_base;
@@ -2476,7 +2476,7 @@ struct server_context {
                 SRV_WRN("%s\n", "cache_reuse is not supported by multimodal, it will be disabled");
             }
 
-            if (!params_base.speculative.model.path.empty()) {
+            if (params_base.has_speculative()) {
                 SRV_ERR("%s\n", "err: speculative decode is not supported by multimodal");
                 return false;
             }
@@ -2520,6 +2520,7 @@ struct server_context {
             if (model_dft) {
                 slot.batch_spec = llama_batch_init(params_base.speculative.n_max + 1, 0, 1);
 
+                // TODO: rework speculative decoding [TAG_SERVER_SPEC_REWORK]
                 slot.ctx_dft = llama_init_from_model(model_dft, cparams_dft);
                 if (slot.ctx_dft == nullptr) {
                     SRV_ERR("%s", "failed to create draft context\n");
@@ -2825,6 +2826,7 @@ struct server_context {
         }
 
         // initialize draft batch
+        // TODO: rework speculative decoding [TAG_SERVER_SPEC_REWORK]
         if (slot.ctx_dft) {
             llama_batch_free(slot.batch_spec);
 
@@ -4291,6 +4293,8 @@ struct server_context {
             }
 
             // do speculative decoding
+            // TODO: rework to have a single draft llama_context shared across all slots [TAG_SERVER_SPEC_REWORK]
+            //       perform the speculative drafting for all sequences at the same time in a single batch
             for (auto & slot : slots) {
                 if (!slot.is_processing() || !slot.can_speculate()) {
                     continue;
@@ -4445,8 +4449,10 @@ int main(int argc, char ** argv) {
 
     // TODO: should we have a separate n_parallel parameter for the server?
     //       https://github.com/ggml-org/llama.cpp/pull/16736#discussion_r2483763177
-    if (params.n_parallel == 1 && params.kv_unified == false) {
-        LOG_WRN("%s: setting n_parallel = 4 and kv_unified = true\n", __func__);
+    // TODO: this is a common configuration that is suitable for most local use cases
+    //       however, overriding the parameters is a bit confusing - figure out something more intuitive
+    if (params.n_parallel == 1 && params.kv_unified == false && !params.has_speculative()) {
+        LOG_WRN("%s: setting n_parallel = 4 and kv_unified = true (add -kvu to disable this)\n", __func__);
 
         params.n_parallel = 4;
         params.kv_unified = true;

From 92bb84f775215cf36e3224708a9a93e2531a0a96 Mon Sep 17 00:00:00 2001
From: Xuan-Son Nguyen <son@huggingface.co>
Date: Wed, 5 Nov 2025 14:26:49 +0100
Subject: [PATCH 093/185] mtmd: allow QwenVL to process larger image by default
 (#17020)

---
 tools/mtmd/clip.cpp | 12 +++---------
 1 file changed, 3 insertions(+), 9 deletions(-)

diff --git a/tools/mtmd/clip.cpp b/tools/mtmd/clip.cpp
index 67a8a470c83..16781fb1952 100644
--- a/tools/mtmd/clip.cpp
+++ b/tools/mtmd/clip.cpp
@@ -2791,14 +2791,8 @@ struct clip_model_loader {
                         get_u32(KEY_SPATIAL_MERGE_SIZE, hparams.n_merge, false);
                         get_u32(KEY_WIN_ATTN_PATTERN, hparams.n_wa_pattern, model.proj_type == PROJECTOR_TYPE_QWEN25VL); // only 2.5 requires it
                         // ref: https://huggingface.co/Qwen/Qwen2.5-VL-7B-Instruct/blob/main/preprocessor_config.json
-                        // the actual max limit is 12845056/14/14/2/2/4 = 4096 tokens
-                        // but we set a lower value to avoid OOM
-                        // TODO: make it configurable by user
-                        // TODO (2): bbox coordinates become inaccurate with small number of tokens,
-                        //           therefore we need to increase the min_tokens
-                        //           see: https://github.com/ggml-org/llama.cpp/issues/16842#issuecomment-3475144858
-                        hparams.set_limit_image_tokens(8, 2048);
-                        hparams.set_warmup_n_tokens(256); // avoid OOM on warmup
+                        hparams.set_limit_image_tokens(8, 4096);
+                        hparams.set_warmup_n_tokens(46*46); // avoid OOM on warmup
                         const int warn_min_pixels = 1024 * hparams.n_merge * hparams.n_merge * hparams.patch_size * hparams.patch_size;
                         if (hparams.image_min_pixels < warn_min_pixels) {
                             LOG_WRN("%s: Qwen-VL models require at minimum 1024 image tokens to function correctly on grounding tasks\n", __func__);
@@ -4814,7 +4808,7 @@ bool clip_image_batch_encode(clip_ctx * ctx, const int n_threads, const clip_ima
         case PROJECTOR_TYPE_QWEN2VL:
         case PROJECTOR_TYPE_QWEN3VL:
             {
-                const int merge_ratio = 2;
+                const int merge_ratio = hparams.n_merge;
                 const int pw = image_size_width  / patch_size;
                 const int ph = image_size_height / patch_size;
                 std::vector<int> positions(n_pos * 4);

From 5886f4f545591dafbbd9d6117a46d7399ce13bfa Mon Sep 17 00:00:00 2001
From: Gabe Goodhart <ghart@us.ibm.com>
Date: Wed, 5 Nov 2025 10:58:16 -0700
Subject: [PATCH 094/185] examples(gguf): GGUF example outputs (#17025)

* feat(llama-gguf): Print out the tensor type in llama-gguf r

Branch: Mamba2Perf

Signed-off-by: Gabe Goodhart <ghart@us.ibm.com>

* feat(off-topic): print the number of elements in tensors with llama-gguf

Branch: Mamba2SSD

Signed-off-by: Gabe Goodhart <ghart@us.ibm.com>

* style: valign

Branch: GGUFToolOutputs

Signed-off-by: Gabe Goodhart <ghart@us.ibm.com>

* Update examples/gguf/gguf.cpp

---------

Signed-off-by: Gabe Goodhart <ghart@us.ibm.com>
Co-authored-by: Georgi Gerganov <ggerganov@gmail.com>
---
 examples/gguf/gguf.cpp | 7 ++++++-
 1 file changed, 6 insertions(+), 1 deletion(-)

diff --git a/examples/gguf/gguf.cpp b/examples/gguf/gguf.cpp
index f31989c8c55..499cfacc92a 100644
--- a/examples/gguf/gguf.cpp
+++ b/examples/gguf/gguf.cpp
@@ -184,8 +184,13 @@ static bool gguf_ex_read_1(const std::string & fname, bool check_data) {
             const char * name   = gguf_get_tensor_name  (ctx, i);
             const size_t size   = gguf_get_tensor_size  (ctx, i);
             const size_t offset = gguf_get_tensor_offset(ctx, i);
+            const auto   type   = gguf_get_tensor_type  (ctx, i);
 
-            printf("%s: tensor[%d]: name = %s, size = %zu, offset = %zu\n", __func__, i, name, size, offset);
+            const char * type_name  = ggml_type_name(type);
+            const size_t type_size  = ggml_type_size(type);
+            const size_t n_elements = size / type_size;
+
+            printf("%s: tensor[%d]: name = %s, size = %zu, offset = %zu, type = %s, n_elts = %zu\n", __func__, i, name, size, offset, type_name, n_elements);
         }
     }
 

From a44d77126c911d105f7f800c17da21b2a5b112d1 Mon Sep 17 00:00:00 2001
From: Jeff Bolz <jbolz@nvidia.com>
Date: Wed, 5 Nov 2025 12:51:03 -0600
Subject: [PATCH 095/185] vulkan: Fix GGML_VULKAN_CHECK_RESULTS to better
 handle fusion (#16919)

---
 ggml/src/ggml-vulkan/ggml-vulkan.cpp | 636 +++++++++++++--------------
 1 file changed, 314 insertions(+), 322 deletions(-)

diff --git a/ggml/src/ggml-vulkan/ggml-vulkan.cpp b/ggml/src/ggml-vulkan/ggml-vulkan.cpp
index 7fc46bc46bc..ab94bc3d78f 100644
--- a/ggml/src/ggml-vulkan/ggml-vulkan.cpp
+++ b/ggml/src/ggml-vulkan/ggml-vulkan.cpp
@@ -14104,20 +14104,11 @@ size_t comp_size;
 size_t comp_nb[GGML_MAX_DIMS];
 size_t check_counter = 0;
 static void ggml_vk_check_results_0(ggml_backend_vk_context * ctx, ggml_cgraph * cgraph, int tensor_idx) {
-    ggml_tensor * tensor = cgraph->nodes[tensor_idx];
+    ggml_tensor * tensor = cgraph->nodes[tensor_idx + ctx->num_additional_fused_ops];
     if (tensor->op == GGML_OP_TRANSPOSE || tensor->op == GGML_OP_SET_ROWS) {
         return;
     }
 
-    bool fused_rms_norm_mul = false;
-    int rms_norm_idx = -1;
-    if (ctx->num_additional_fused_ops == 1 &&
-        tensor->op == GGML_OP_RMS_NORM &&
-        cgraph->nodes[tensor_idx + 1]->op == GGML_OP_MUL) {
-        fused_rms_norm_mul = true;
-        tensor = cgraph->nodes[tensor_idx + 1];
-    }
-
     check_counter++;
     if (!(vk_output_tensor > 0 && vk_output_tensor == check_counter) && check_counter <= vk_skip_checks) {
         return;
@@ -14125,9 +14116,6 @@ static void ggml_vk_check_results_0(ggml_backend_vk_context * ctx, ggml_cgraph *
 
     VK_LOG_DEBUG("ggml_vk_check_results_0(" << tensor->name << ")");
 
-    ggml_tensor * src0 = tensor->src[0];
-    ggml_tensor * src1 = tensor->src[1];
-
     struct ggml_init_params iparams = {
         /*.mem_size   =*/ 2ul*1024ul*1024ul*1024ul,
         /*.mem_buffer =*/ NULL,
@@ -14137,328 +14125,339 @@ static void ggml_vk_check_results_0(ggml_backend_vk_context * ctx, ggml_cgraph *
     struct ggml_context * ggml_ctx = ggml_init(iparams);
 
     std::array<struct ggml_tensor *, GGML_MAX_SRC> src_clone = {nullptr, nullptr, nullptr, nullptr, nullptr, nullptr, nullptr, nullptr, nullptr, nullptr};
-    std::array<size_t, GGML_MAX_SRC> src_size = {};
-    std::array<void *, GGML_MAX_SRC> src_buffer = {};
     const char * srci_name[GGML_MAX_SRC] = {"src0", "src1", "src2", "src3", "src4", "src5", "src6", "src7", "src8", "src9"};
 
+    std::map<ggml_tensor *, ggml_tensor *> cloned_tensors;
+    std::vector<void *> cloned_mallocs;
+
     struct ggml_tensor * tensor_clone = nullptr;
 
-    for (int i = 0; i < GGML_MAX_SRC; i++) {
-        ggml_tensor * srci = tensor->src[i];
-        if (fused_rms_norm_mul) {
-            rms_norm_idx = tensor->src[0]->op == GGML_OP_RMS_NORM ? 0 : 1;
-            ggml_tensor *rms_norm = tensor->src[rms_norm_idx];
-            switch (i) {
-            case 0: srci = rms_norm->src[0]; break;
-            case 1: srci = tensor->src[1 - rms_norm_idx]; break;
-            default: continue;
+    for (int f = 0; f < ctx->num_additional_fused_ops + 1; ++f) {
+        tensor = cgraph->nodes[tensor_idx + f];
+        for (int i = 0; i < GGML_MAX_SRC; i++) {
+            ggml_tensor * srci = tensor->src[i];
+            if (srci == nullptr) {
+                continue;
             }
-        }
-        if (srci == nullptr) {
-            continue;
-        }
-        ggml_tensor * srci_clone = ggml_dup_tensor(ggml_ctx, srci);
-        size_t srci_size = ggml_nbytes(srci);
-
-        src_clone[i] = srci_clone;
-        src_size[i] = ggml_nbytes(srci);
-        src_buffer[i] = malloc(srci_size);
-
-        srci_clone->data = src_buffer[i];
-        if (ggml_backend_buffer_is_host(srci->buffer)) {
-            memcpy(srci_clone->data, srci->data, srci_size);
-            memcpy(srci_clone->nb, srci->nb, sizeof(size_t) * GGML_MAX_DIMS);
-        } else if (ggml_backend_buffer_is_vk(srci->buffer)) {
-            ggml_backend_vk_buffer_context * buf_ctx = (ggml_backend_vk_buffer_context *)srci->buffer->context;
-            vk_buffer& buffer_gpu = buf_ctx->dev_buffer;
-            uint64_t offset = vk_tensor_offset(srci) + srci->view_offs;
-            if (!ggml_is_contiguous(srci) && ggml_vk_dim01_contiguous(srci)) {
-                for (int i3 = 0; i3 < srci->ne[3]; i3++) {
-                    for (int i2 = 0; i2 < srci->ne[2]; i2++) {
-                        const int idx = i3*srci->ne[2] + i2;
-                        ggml_vk_buffer_read(buffer_gpu, offset + idx * srci->nb[2], ((char *)srci_clone->data + idx * srci_clone->nb[2]), srci->ne[1] * srci->nb[1]);
+            // If a src tensor has been cloned, use that one
+            auto it = cloned_tensors.find(srci);
+            if (it != cloned_tensors.end()) {
+                src_clone[i] = it->second;
+                continue;
+            }
+            ggml_tensor * srci_clone = ggml_dup_tensor(ggml_ctx, srci);
+            size_t srci_size = ggml_nbytes(srci);
+
+            src_clone[i] = srci_clone;
+            void *src_buffer = malloc(srci_size);
+            cloned_mallocs.push_back(src_buffer);
+
+            srci_clone->data = src_buffer;
+            if (ggml_backend_buffer_is_host(srci->buffer)) {
+                memcpy(srci_clone->data, srci->data, srci_size);
+                memcpy(srci_clone->nb, srci->nb, sizeof(size_t) * GGML_MAX_DIMS);
+            } else if (ggml_backend_buffer_is_vk(srci->buffer)) {
+                ggml_backend_vk_buffer_context * buf_ctx = (ggml_backend_vk_buffer_context *)srci->buffer->context;
+                vk_buffer& buffer_gpu = buf_ctx->dev_buffer;
+                uint64_t offset = vk_tensor_offset(srci) + srci->view_offs;
+                if (!ggml_is_contiguous(srci) && ggml_vk_dim01_contiguous(srci)) {
+                    for (int i3 = 0; i3 < srci->ne[3]; i3++) {
+                        for (int i2 = 0; i2 < srci->ne[2]; i2++) {
+                            const int idx = i3*srci->ne[2] + i2;
+                            ggml_vk_buffer_read(buffer_gpu, offset + idx * srci->nb[2], ((char *)srci_clone->data + idx * srci_clone->nb[2]), srci->ne[1] * srci->nb[1]);
+                        }
                     }
-                }
 
-                srci_clone->nb[0] = srci->nb[0];
-                srci_clone->nb[1] = srci->nb[1];
-                for (int i = 2; i < GGML_MAX_DIMS; i++) {
-                    srci_clone->nb[i] = srci_clone->nb[i - 1]*srci_clone->ne[i - 1];
+                    srci_clone->nb[0] = srci->nb[0];
+                    srci_clone->nb[1] = srci->nb[1];
+                    for (int i = 2; i < GGML_MAX_DIMS; i++) {
+                        srci_clone->nb[i] = srci_clone->nb[i - 1]*srci_clone->ne[i - 1];
+                    }
+                } else {
+                    if (offset + srci_size >= buffer_gpu->size) {
+                        srci_size = buffer_gpu->size - offset;
+                    }
+                    ggml_vk_buffer_read(buffer_gpu, offset, srci_clone->data, srci_size);
+                    memcpy(srci_clone->nb, srci->nb, sizeof(size_t) * GGML_MAX_DIMS);
                 }
             } else {
-                if (offset + srci_size >= buffer_gpu->size) {
-                    srci_size = buffer_gpu->size - offset;
-                }
-                ggml_vk_buffer_read(buffer_gpu, offset, srci_clone->data, srci_size);
-                memcpy(srci_clone->nb, srci->nb, sizeof(size_t) * GGML_MAX_DIMS);
+                GGML_ABORT("fatal error");
             }
-        } else {
-            GGML_ABORT("fatal error");
-        }
 
-        if (vk_output_tensor > 0 && vk_output_tensor == check_counter) {
-            ggml_vk_print_tensor(srci, srci_name[i]);
+            if (vk_output_tensor > 0 && vk_output_tensor == check_counter) {
+                ggml_vk_print_tensor(srci, srci_name[i]);
+            }
         }
-    }
 
-    if (tensor->op == GGML_OP_FLASH_ATTN_EXT) {
-        const float * params = (const float *)tensor->op_params;
-        tensor_clone = ggml_flash_attn_ext(ggml_ctx, src_clone[0], src_clone[1], src_clone[2], src_clone[3], params[0], params[1], params[2]);
-        if (src_clone[4]) {
-            ggml_flash_attn_ext_add_sinks(tensor_clone, src_clone[4]);
-        }
-    } else if (tensor->op == GGML_OP_MUL_MAT) {
-        tensor_clone = ggml_mul_mat(ggml_ctx, src_clone[0], src_clone[1]);
-    } else if (tensor->op == GGML_OP_MUL_MAT_ID) {
-        tensor_clone = ggml_mul_mat_id(ggml_ctx, src_clone[0], src_clone[1], src_clone[2]);
-    } else if (tensor->op == GGML_OP_SUB) {
-        tensor_clone = ggml_sub(ggml_ctx, src_clone[0], src_clone[1]);
-    } else if (tensor->op == GGML_OP_MUL) {
-        if (fused_rms_norm_mul) {
-            tensor_clone = ggml_rms_norm(ggml_ctx, src_clone[0], *(float *)tensor->src[rms_norm_idx]->op_params);
-            tensor_clone = ggml_mul(ggml_ctx, tensor_clone, src_clone[1 - rms_norm_idx]);
-        } else {
+        if (tensor->op == GGML_OP_FLASH_ATTN_EXT) {
+            const float * params = (const float *)tensor->op_params;
+            tensor_clone = ggml_flash_attn_ext(ggml_ctx, src_clone[0], src_clone[1], src_clone[2], src_clone[3], params[0], params[1], params[2]);
+            if (src_clone[4]) {
+                ggml_flash_attn_ext_add_sinks(tensor_clone, src_clone[4]);
+            }
+        } else if (tensor->op == GGML_OP_MUL_MAT) {
+            tensor_clone = ggml_mul_mat(ggml_ctx, src_clone[0], src_clone[1]);
+        } else if (tensor->op == GGML_OP_MUL_MAT_ID) {
+            tensor_clone = ggml_mul_mat_id(ggml_ctx, src_clone[0], src_clone[1], src_clone[2]);
+        } else if (tensor->op == GGML_OP_SUB) {
+            tensor_clone = ggml_sub(ggml_ctx, src_clone[0], src_clone[1]);
+        } else if (tensor->op == GGML_OP_MUL) {
             tensor_clone = ggml_mul(ggml_ctx, src_clone[0], src_clone[1]);
-        }
-    } else if (tensor->op == GGML_OP_DIV) {
-        tensor_clone = ggml_div(ggml_ctx, src_clone[0], src_clone[1]);
-    } else if (tensor->op == GGML_OP_CONCAT) {
-        tensor_clone = ggml_concat(ggml_ctx, src_clone[0], src_clone[1], *(int *)tensor->op_params);
-    } else if (tensor->op == GGML_OP_UPSCALE) {
-        tensor_clone = ggml_interpolate(ggml_ctx, src_clone[0], tensor->ne[0], tensor->ne[1], tensor->ne[2], tensor->ne[3], (ggml_scale_mode) tensor->op_params[0]);
-    } else if (tensor->op == GGML_OP_SCALE) {
-        const float * params = (const float *)tensor->op_params;
-        tensor_clone = ggml_scale_bias(ggml_ctx, src_clone[0], params[0], params[1]);
-    } else if (tensor->op == GGML_OP_SQR) {
-        tensor_clone = ggml_sqr(ggml_ctx, src_clone[0]);
-    } else if (tensor->op == GGML_OP_SQRT) {
-        tensor_clone = ggml_sqrt(ggml_ctx, src_clone[0]);
-    } else if (tensor->op == GGML_OP_SIN) {
-        tensor_clone = ggml_sin(ggml_ctx, src_clone[0]);
-    } else if (tensor->op == GGML_OP_COS) {
-        tensor_clone = ggml_cos(ggml_ctx, src_clone[0]);
-    } else if (tensor->op == GGML_OP_CLAMP) {
-        const float * params = (const float *)tensor->op_params;
-        tensor_clone = ggml_clamp(ggml_ctx, src_clone[0], params[0], params[1]);
-    } else if (tensor->op == GGML_OP_PAD) {
-        tensor_clone = ggml_pad_ext(ggml_ctx, src_clone[0], tensor->op_params[0], tensor->op_params[1], tensor->op_params[2], tensor->op_params[3],
-                                                            tensor->op_params[4], tensor->op_params[5], tensor->op_params[6], tensor->op_params[7]);
-    } else if (tensor->op == GGML_OP_REPEAT) {
-        tensor_clone = ggml_repeat(ggml_ctx, src_clone[0], tensor);
-    } else if (tensor->op == GGML_OP_REPEAT_BACK) {
-        tensor_clone = ggml_repeat_back(ggml_ctx, src_clone[0], tensor);
-    } else if (tensor->op == GGML_OP_ADD) {
-        tensor_clone = ggml_add(ggml_ctx, src_clone[0], src_clone[1]);
-    } else if (tensor->op == GGML_OP_ACC) {
-        tensor_clone = ggml_acc(ggml_ctx, src_clone[0], src_clone[1], tensor->op_params[0], tensor->op_params[1], tensor->op_params[2], tensor->op_params[3]);
-    } else if (tensor->op == GGML_OP_NORM) {
-        tensor_clone = ggml_norm(ggml_ctx, src_clone[0], *(float *)tensor->op_params);
-    } else if (tensor->op == GGML_OP_GROUP_NORM) {
-        const float * float_params = (const float *)tensor->op_params;
-        tensor_clone = ggml_group_norm(ggml_ctx, src_clone[0], tensor->op_params[0], float_params[1]);
-    } else if (tensor->op == GGML_OP_RMS_NORM) {
-        tensor_clone = ggml_rms_norm(ggml_ctx, src_clone[0], *(float *)tensor->op_params);
-    } else if (tensor->op == GGML_OP_RMS_NORM_BACK) {
-        const float eps = ((float *) tensor->op_params)[0];
-        tensor_clone = ggml_rms_norm_back(ggml_ctx, src_clone[0], src_clone[1], eps);
-    } else if (tensor->op == GGML_OP_SILU_BACK) {
-        tensor_clone = ggml_silu_back(ggml_ctx, src_clone[0], src_clone[1]);
-    } else if (tensor->op == GGML_OP_L2_NORM) {
-        const float eps = ((float *) tensor->op_params)[0];
-        tensor_clone = ggml_l2_norm(ggml_ctx, src_clone[0], eps);
-    } else if (tensor->op == GGML_OP_SOFT_MAX) {
-        if (src1 != nullptr) {
+        } else if (tensor->op == GGML_OP_DIV) {
+            tensor_clone = ggml_div(ggml_ctx, src_clone[0], src_clone[1]);
+        } else if (tensor->op == GGML_OP_CONCAT) {
+            tensor_clone = ggml_concat(ggml_ctx, src_clone[0], src_clone[1], *(int *)tensor->op_params);
+        } else if (tensor->op == GGML_OP_UPSCALE) {
+            tensor_clone = ggml_interpolate(ggml_ctx, src_clone[0], tensor->ne[0], tensor->ne[1], tensor->ne[2], tensor->ne[3], (ggml_scale_mode) tensor->op_params[0]);
+        } else if (tensor->op == GGML_OP_SCALE) {
             const float * params = (const float *)tensor->op_params;
-            tensor_clone = ggml_soft_max_ext(ggml_ctx, src_clone[0], src_clone[1], params[0], params[1]);
-        } else {
-            tensor_clone = ggml_soft_max(ggml_ctx, src_clone[0]);
-        }
-    } else if (tensor->op == GGML_OP_SOFT_MAX_BACK) {
-        tensor_clone = ggml_soft_max_ext_back(ggml_ctx, src_clone[0], src_clone[1], ((float *)tensor->op_params)[0], ((float *)tensor->op_params)[1]);
-    } else if (tensor->op == GGML_OP_DIAG_MASK_INF) {
-        tensor_clone = ggml_diag_mask_inf(ggml_ctx, src_clone[0], tensor->op_params[0]);
-    } else if (tensor->op == GGML_OP_ROPE || tensor->op == GGML_OP_ROPE_BACK) {
-        const int n_dims      = ((int32_t *) tensor->op_params)[1];
-        const int mode        = ((int32_t *) tensor->op_params)[2];
-        //const int n_ctx_ggml       = ((int32_t *) tensor->op_params)[3];
-        const int n_ctx_orig_ggml  = ((int32_t *) tensor->op_params)[4];
-        const float freq_base       = ((float *) tensor->op_params)[5];
-        const float freq_scale      = ((float *) tensor->op_params)[6];
-        const float ext_factor      = ((float *) tensor->op_params)[7];
-        const float attn_factor     = ((float *) tensor->op_params)[8];
-        const float beta_fast       = ((float *) tensor->op_params)[9];
-        const float beta_slow       = ((float *) tensor->op_params)[10];
-        if (mode & GGML_ROPE_TYPE_MROPE) {
-            int32_t *sections = ((int32_t *) tensor->op_params) + 11;
-            if (tensor->op == GGML_OP_ROPE) {
-                tensor_clone = ggml_rope_multi(ggml_ctx, src_clone[0], src_clone[1], src_clone[2], n_dims, sections, mode, n_ctx_orig_ggml, freq_base, freq_scale, ext_factor, attn_factor, beta_fast, beta_slow);
+            tensor_clone = ggml_scale_bias(ggml_ctx, src_clone[0], params[0], params[1]);
+        } else if (tensor->op == GGML_OP_SQR) {
+            tensor_clone = ggml_sqr(ggml_ctx, src_clone[0]);
+        } else if (tensor->op == GGML_OP_SQRT) {
+            tensor_clone = ggml_sqrt(ggml_ctx, src_clone[0]);
+        } else if (tensor->op == GGML_OP_SIN) {
+            tensor_clone = ggml_sin(ggml_ctx, src_clone[0]);
+        } else if (tensor->op == GGML_OP_COS) {
+            tensor_clone = ggml_cos(ggml_ctx, src_clone[0]);
+        } else if (tensor->op == GGML_OP_CLAMP) {
+            const float * params = (const float *)tensor->op_params;
+            tensor_clone = ggml_clamp(ggml_ctx, src_clone[0], params[0], params[1]);
+        } else if (tensor->op == GGML_OP_PAD) {
+            tensor_clone = ggml_pad_ext(ggml_ctx, src_clone[0], tensor->op_params[0], tensor->op_params[1], tensor->op_params[2], tensor->op_params[3],
+                                                                tensor->op_params[4], tensor->op_params[5], tensor->op_params[6], tensor->op_params[7]);
+        } else if (tensor->op == GGML_OP_REPEAT) {
+            tensor_clone = ggml_repeat(ggml_ctx, src_clone[0], tensor);
+        } else if (tensor->op == GGML_OP_REPEAT_BACK) {
+            tensor_clone = ggml_repeat_back(ggml_ctx, src_clone[0], tensor);
+        } else if (tensor->op == GGML_OP_ADD) {
+            tensor_clone = ggml_add(ggml_ctx, src_clone[0], src_clone[1]);
+        } else if (tensor->op == GGML_OP_ACC) {
+            tensor_clone = ggml_acc(ggml_ctx, src_clone[0], src_clone[1], tensor->op_params[0], tensor->op_params[1], tensor->op_params[2], tensor->op_params[3]);
+        } else if (tensor->op == GGML_OP_NORM) {
+            tensor_clone = ggml_norm(ggml_ctx, src_clone[0], *(float *)tensor->op_params);
+        } else if (tensor->op == GGML_OP_GROUP_NORM) {
+            const float * float_params = (const float *)tensor->op_params;
+            tensor_clone = ggml_group_norm(ggml_ctx, src_clone[0], tensor->op_params[0], float_params[1]);
+        } else if (tensor->op == GGML_OP_RMS_NORM) {
+            tensor_clone = ggml_rms_norm(ggml_ctx, src_clone[0], *(float *)tensor->op_params);
+        } else if (tensor->op == GGML_OP_RMS_NORM_BACK) {
+            const float eps = ((float *) tensor->op_params)[0];
+            tensor_clone = ggml_rms_norm_back(ggml_ctx, src_clone[0], src_clone[1], eps);
+        } else if (tensor->op == GGML_OP_SILU_BACK) {
+            tensor_clone = ggml_silu_back(ggml_ctx, src_clone[0], src_clone[1]);
+        } else if (tensor->op == GGML_OP_L2_NORM) {
+            const float eps = ((float *) tensor->op_params)[0];
+            tensor_clone = ggml_l2_norm(ggml_ctx, src_clone[0], eps);
+        } else if (tensor->op == GGML_OP_SOFT_MAX) {
+            if (tensor->src[1] != nullptr) {
+                const float * params = (const float *)tensor->op_params;
+                tensor_clone = ggml_soft_max_ext(ggml_ctx, src_clone[0], src_clone[1], params[0], params[1]);
             } else {
-                tensor_clone = ggml_rope_multi_back(ggml_ctx, src_clone[0], src_clone[1], src_clone[2], n_dims, sections, mode, n_ctx_orig_ggml, freq_base, freq_scale, ext_factor, attn_factor, beta_fast, beta_slow);
+                tensor_clone = ggml_soft_max(ggml_ctx, src_clone[0]);
             }
-        } else {
-            if (tensor->op == GGML_OP_ROPE) {
-                tensor_clone = ggml_rope_ext(ggml_ctx, src_clone[0], src_clone[1], src_clone[2], n_dims, mode, n_ctx_orig_ggml, freq_base, freq_scale, ext_factor, attn_factor, beta_fast, beta_slow);
+        } else if (tensor->op == GGML_OP_SOFT_MAX_BACK) {
+            tensor_clone = ggml_soft_max_ext_back(ggml_ctx, src_clone[0], src_clone[1], ((float *)tensor->op_params)[0], ((float *)tensor->op_params)[1]);
+        } else if (tensor->op == GGML_OP_DIAG_MASK_INF) {
+            tensor_clone = ggml_diag_mask_inf(ggml_ctx, src_clone[0], tensor->op_params[0]);
+        } else if (tensor->op == GGML_OP_ROPE || tensor->op == GGML_OP_ROPE_BACK) {
+            const int n_dims      = ((int32_t *) tensor->op_params)[1];
+            const int mode        = ((int32_t *) tensor->op_params)[2];
+            //const int n_ctx_ggml       = ((int32_t *) tensor->op_params)[3];
+            const int n_ctx_orig_ggml  = ((int32_t *) tensor->op_params)[4];
+            const float freq_base       = ((float *) tensor->op_params)[5];
+            const float freq_scale      = ((float *) tensor->op_params)[6];
+            const float ext_factor      = ((float *) tensor->op_params)[7];
+            const float attn_factor     = ((float *) tensor->op_params)[8];
+            const float beta_fast       = ((float *) tensor->op_params)[9];
+            const float beta_slow       = ((float *) tensor->op_params)[10];
+            if (mode & GGML_ROPE_TYPE_MROPE) {
+                int32_t *sections = ((int32_t *) tensor->op_params) + 11;
+                if (tensor->op == GGML_OP_ROPE) {
+                    tensor_clone = ggml_rope_multi(ggml_ctx, src_clone[0], src_clone[1], src_clone[2], n_dims, sections, mode, n_ctx_orig_ggml, freq_base, freq_scale, ext_factor, attn_factor, beta_fast, beta_slow);
+                } else {
+                    tensor_clone = ggml_rope_multi_back(ggml_ctx, src_clone[0], src_clone[1], src_clone[2], n_dims, sections, mode, n_ctx_orig_ggml, freq_base, freq_scale, ext_factor, attn_factor, beta_fast, beta_slow);
+                }
+            } else {
+                if (tensor->op == GGML_OP_ROPE) {
+                    tensor_clone = ggml_rope_ext(ggml_ctx, src_clone[0], src_clone[1], src_clone[2], n_dims, mode, n_ctx_orig_ggml, freq_base, freq_scale, ext_factor, attn_factor, beta_fast, beta_slow);
+                } else {
+                    tensor_clone = ggml_rope_ext_back(ggml_ctx, src_clone[0], src_clone[1], src_clone[2], n_dims, mode, n_ctx_orig_ggml, freq_base, freq_scale, ext_factor, attn_factor, beta_fast, beta_slow);
+                }
+            }
+        } else if (tensor->op == GGML_OP_UNARY) {
+            switch (ggml_get_unary_op(tensor)) {
+            case GGML_UNARY_OP_EXP:
+                tensor_clone = ggml_exp(ggml_ctx, src_clone[0]);
+                break;
+            case GGML_UNARY_OP_SILU:
+                tensor_clone = ggml_silu(ggml_ctx, src_clone[0]);
+                break;
+            case GGML_UNARY_OP_GELU:
+                tensor_clone = ggml_gelu(ggml_ctx, src_clone[0]);
+                break;
+            case GGML_UNARY_OP_GELU_ERF:
+                tensor_clone = ggml_gelu_erf(ggml_ctx, src_clone[0]);
+                break;
+            case GGML_UNARY_OP_GELU_QUICK:
+                tensor_clone = ggml_gelu_quick(ggml_ctx, src_clone[0]);
+                break;
+            case GGML_UNARY_OP_RELU:
+                tensor_clone = ggml_relu(ggml_ctx, src_clone[0]);
+                break;
+            case GGML_UNARY_OP_TANH:
+                tensor_clone = ggml_tanh(ggml_ctx, src_clone[0]);
+                break;
+            case GGML_UNARY_OP_SIGMOID:
+                tensor_clone = ggml_sigmoid(ggml_ctx, src_clone[0]);
+                break;
+            case GGML_UNARY_OP_HARDSIGMOID:
+                tensor_clone = ggml_hardsigmoid(ggml_ctx, src_clone[0]);
+                break;
+            case GGML_UNARY_OP_HARDSWISH:
+                tensor_clone = ggml_hardswish(ggml_ctx, src_clone[0]);
+                break;
+            default:
+                std::cerr << "Missing vk_check_results OP: " << ggml_op_name(tensor->op) << std::endl;
+                GGML_ABORT("fatal error");
+            }
+        } else if (tensor->op == GGML_OP_GLU) {
+            if (src_clone[1] == nullptr) {
+                tensor_clone = ggml_glu(ggml_ctx, src_clone[0], (ggml_glu_op) tensor->op_params[0], tensor->op_params[1]);
+            } else {
+                tensor_clone = ggml_glu_split(ggml_ctx, src_clone[0], src_clone[1], (ggml_glu_op) tensor->op_params[0]);
+            }
+            ggml_set_op_params_i32(tensor_clone, 2, ggml_get_op_params_i32(tensor, 2));
+            ggml_set_op_params_i32(tensor_clone, 3, ggml_get_op_params_i32(tensor, 3));
+        } else if (tensor->op == GGML_OP_CPY || tensor->op == GGML_OP_DUP) {
+            if (tensor->src[1] == nullptr) {
+                tensor_clone = ggml_dup(ggml_ctx, src_clone[0]);
+                tensor_clone->type = tensor->type;
             } else {
-                tensor_clone = ggml_rope_ext_back(ggml_ctx, src_clone[0], src_clone[1], src_clone[2], n_dims, mode, n_ctx_orig_ggml, freq_base, freq_scale, ext_factor, attn_factor, beta_fast, beta_slow);
+                tensor_clone = ggml_cpy(ggml_ctx, src_clone[0], src_clone[1]);
             }
+        } else if (tensor->op == GGML_OP_CONT) {
+            tensor_clone = ggml_cont_4d(ggml_ctx, src_clone[0], tensor->ne[0], tensor->ne[1], tensor->ne[2], tensor->ne[3]);
+        } else if (tensor->op == GGML_OP_RESHAPE) {
+            tensor_clone = ggml_reshape_4d(ggml_ctx, src_clone[0], tensor->ne[0], tensor->ne[1], tensor->ne[2], tensor->ne[3]);
+        } else if (tensor->op == GGML_OP_VIEW) {
+            tensor_clone = ggml_view_4d(ggml_ctx, src_clone[0], tensor->ne[0], tensor->ne[1], tensor->ne[2], tensor->ne[3], tensor->nb[1], tensor->nb[2], tensor->nb[3], ((int32_t *) tensor->op_params)[0]);
+        } else if (tensor->op == GGML_OP_PERMUTE) {
+            int32_t * params = (int32_t *)tensor->op_params;
+            tensor_clone = ggml_permute(ggml_ctx, src_clone[0], params[0], params[1], params[2], params[3]);
+        } else if (tensor->op == GGML_OP_TRANSPOSE) {
+            tensor_clone = ggml_transpose(ggml_ctx, src_clone[0]);
+        } else if (tensor->op == GGML_OP_GET_ROWS) {
+            tensor_clone = ggml_get_rows(ggml_ctx, src_clone[0], src_clone[1]);
+        } else if (tensor->op == GGML_OP_ARGSORT) {
+            tensor_clone = ggml_argsort(ggml_ctx, src_clone[0], (ggml_sort_order) *(int *)tensor->op_params);
+        } else if (tensor->op == GGML_OP_SUM) {
+            tensor_clone = ggml_sum(ggml_ctx, src_clone[0]);
+        } else if (tensor->op == GGML_OP_SUM_ROWS) {
+            tensor_clone = ggml_sum_rows(ggml_ctx, src_clone[0]);
+        } else if (tensor->op == GGML_OP_MEAN) {
+            tensor_clone = ggml_mean(ggml_ctx, src_clone[0]);
+        } else if (tensor->op == GGML_OP_ARGMAX) {
+            tensor_clone = ggml_argmax(ggml_ctx, src_clone[0]);
+        } else if (tensor->op == GGML_OP_COUNT_EQUAL) {
+            tensor_clone = ggml_count_equal(ggml_ctx, src_clone[0], src_clone[1]);
+        } else if (tensor->op == GGML_OP_IM2COL) {
+            const int32_t s0 = tensor->op_params[0];
+            const int32_t s1 = tensor->op_params[1];
+            const int32_t p0 = tensor->op_params[2];
+            const int32_t p1 = tensor->op_params[3];
+            const int32_t d0 = tensor->op_params[4];
+            const int32_t d1 = tensor->op_params[5];
+
+            const bool is_2D = tensor->op_params[6] == 1;
+            tensor_clone = ggml_im2col(ggml_ctx, src_clone[0], src_clone[1], s0, s1, p0, p1, d0, d1, is_2D, tensor->type);
+        } else if (tensor->op == GGML_OP_IM2COL_3D) {
+            const int32_t s0 = tensor->op_params[0];
+            const int32_t s1 = tensor->op_params[1];
+            const int32_t s2 = tensor->op_params[2];
+            const int32_t p0 = tensor->op_params[3];
+            const int32_t p1 = tensor->op_params[4];
+            const int32_t p2 = tensor->op_params[5];
+            const int32_t d0 = tensor->op_params[6];
+            const int32_t d1 = tensor->op_params[7];
+            const int32_t d2 = tensor->op_params[8];
+            const int32_t IC = tensor->op_params[9];
+
+            tensor_clone = ggml_im2col_3d(ggml_ctx, src_clone[0], src_clone[1], IC, s0, s1, s2, p0, p1, p2, d0, d1, d2, tensor->type);
+        } else if (tensor->op == GGML_OP_TIMESTEP_EMBEDDING) {
+            const int32_t dim = tensor->op_params[0];
+            const int32_t max_period = tensor->op_params[1];
+            tensor_clone = ggml_timestep_embedding(ggml_ctx, src_clone[0], dim, max_period);
+        } else if (tensor->op == GGML_OP_CONV_TRANSPOSE_1D){
+            const int32_t s0 = tensor->op_params[0];
+            const int32_t p0 = tensor->op_params[1];
+            const int32_t d0 = tensor->op_params[2];
+            tensor_clone = ggml_conv_transpose_1d(ggml_ctx, src_clone[0], src_clone[1], s0, p0, d0);
+        } else if (tensor->op == GGML_OP_POOL_2D) {
+            enum ggml_op_pool op = static_cast<ggml_op_pool>(tensor->op_params[0]);
+            const int32_t k0 = tensor->op_params[1];
+            const int32_t k1 = tensor->op_params[2];
+            const int32_t s0 = tensor->op_params[3];
+            const int32_t s1 = tensor->op_params[4];
+            const int32_t p0 = tensor->op_params[5];
+            const int32_t p1 = tensor->op_params[6];
+
+            tensor_clone = ggml_pool_2d(ggml_ctx, src_clone[0], op, k0, k1, s0, s1, p0, p1);
+        } else if (tensor->op == GGML_OP_CONV_2D) {
+            const int32_t s0 = tensor->op_params[0];
+            const int32_t s1 = tensor->op_params[1];
+            const int32_t p0 = tensor->op_params[2];
+            const int32_t p1 = tensor->op_params[3];
+            const int32_t d0 = tensor->op_params[4];
+            const int32_t d1 = tensor->op_params[5];
+            tensor_clone = ggml_conv_2d(ggml_ctx, src_clone[0], src_clone[1], s0, s1, p0, p1, d0, d1);
+        } else if (tensor->op == GGML_OP_CONV_2D_DW) {
+            const int32_t s0 = tensor->op_params[0];
+            const int32_t s1 = tensor->op_params[1];
+            const int32_t p0 = tensor->op_params[2];
+            const int32_t p1 = tensor->op_params[3];
+            const int32_t d0 = tensor->op_params[4];
+            const int32_t d1 = tensor->op_params[5];
+            tensor_clone = ggml_conv_2d_dw_direct(ggml_ctx, src_clone[0], src_clone[1], s0, s1, p0, p1, d0, d1);
+        } else if (tensor->op == GGML_OP_CONV_TRANSPOSE_2D) {
+            const int32_t s = tensor->op_params[0];
+            tensor_clone = ggml_conv_transpose_2d_p0(ggml_ctx, src_clone[0], src_clone[1], s);
+        } else if (tensor->op == GGML_OP_LEAKY_RELU) {
+            const float * op_params = (const float *)tensor->op_params;
+            tensor_clone = ggml_leaky_relu(ggml_ctx, src_clone[0], op_params[0], false);
+        } else if (tensor->op == GGML_OP_RWKV_WKV6) {
+            tensor_clone = ggml_rwkv_wkv6(ggml_ctx, src_clone[0], src_clone[1],
+            src_clone[2], src_clone[3], src_clone[4], src_clone[5]);
+        } else if (tensor->op == GGML_OP_RWKV_WKV7) {
+            tensor_clone = ggml_rwkv_wkv7(ggml_ctx, src_clone[0], src_clone[1], src_clone[2], src_clone[3],
+            src_clone[4], src_clone[5], src_clone[6]);
+        } else if (tensor->op == GGML_OP_OPT_STEP_ADAMW) {
+            src_clone[0]->flags = tensor->src[0]->flags;
+            tensor_clone = ggml_opt_step_adamw(ggml_ctx, src_clone[0], src_clone[1],
+            src_clone[2], src_clone[3], src_clone[4]);
+        } else if (tensor->op == GGML_OP_OPT_STEP_SGD) {
+            src_clone[0]->flags = tensor->src[0]->flags;
+            tensor_clone = ggml_opt_step_sgd(ggml_ctx, src_clone[0], src_clone[1],
+            src_clone[2]);
+        } else if (tensor->op == GGML_OP_ADD_ID) {
+            tensor_clone = ggml_add_id(ggml_ctx, src_clone[0], src_clone[1], src_clone[2]);
+        } else if (tensor->op == GGML_OP_SSM_SCAN) {
+            tensor_clone = ggml_ssm_scan(ggml_ctx, src_clone[0], src_clone[1], src_clone[2],
+                                         src_clone[3], src_clone[4], src_clone[5], src_clone[6]);
+        } else if (tensor->op == GGML_OP_SSM_CONV) {
+            tensor_clone = ggml_ssm_conv(ggml_ctx, src_clone[0], src_clone[1]);
+        } else if (tensor->op == GGML_OP_ROLL) {
+            const int32_t s0 = tensor->op_params[0];
+            const int32_t s1 = tensor->op_params[1];
+            const int32_t s2 = tensor->op_params[2];
+            const int32_t s3 = tensor->op_params[3];
+            tensor_clone = ggml_roll(ggml_ctx, src_clone[0], s0, s1, s2, s3);
         }
-    } else if (tensor->op == GGML_OP_UNARY) {
-        switch (ggml_get_unary_op(tensor)) {
-        case GGML_UNARY_OP_EXP:
-            tensor_clone = ggml_exp(ggml_ctx, src_clone[0]);
-            break;
-        case GGML_UNARY_OP_SILU:
-            tensor_clone = ggml_silu(ggml_ctx, src_clone[0]);
-            break;
-        case GGML_UNARY_OP_GELU:
-            tensor_clone = ggml_gelu(ggml_ctx, src_clone[0]);
-            break;
-        case GGML_UNARY_OP_GELU_ERF:
-            tensor_clone = ggml_gelu_erf(ggml_ctx, src_clone[0]);
-            break;
-        case GGML_UNARY_OP_GELU_QUICK:
-            tensor_clone = ggml_gelu_quick(ggml_ctx, src_clone[0]);
-            break;
-        case GGML_UNARY_OP_RELU:
-            tensor_clone = ggml_relu(ggml_ctx, src_clone[0]);
-            break;
-        case GGML_UNARY_OP_TANH:
-            tensor_clone = ggml_tanh(ggml_ctx, src_clone[0]);
-            break;
-        case GGML_UNARY_OP_SIGMOID:
-            tensor_clone = ggml_sigmoid(ggml_ctx, src_clone[0]);
-            break;
-        case GGML_UNARY_OP_HARDSIGMOID:
-            tensor_clone = ggml_hardsigmoid(ggml_ctx, src_clone[0]);
-            break;
-        case GGML_UNARY_OP_HARDSWISH:
-            tensor_clone = ggml_hardswish(ggml_ctx, src_clone[0]);
-            break;
-        default:
+        else {
             std::cerr << "Missing vk_check_results OP: " << ggml_op_name(tensor->op) << std::endl;
             GGML_ABORT("fatal error");
         }
-    } else if (tensor->op == GGML_OP_GLU) {
-        if (src_clone[1] == nullptr) {
-            tensor_clone = ggml_glu(ggml_ctx, src_clone[0], (ggml_glu_op) tensor->op_params[0], tensor->op_params[1]);
-        } else {
-            tensor_clone = ggml_glu_split(ggml_ctx, src_clone[0], src_clone[1], (ggml_glu_op) tensor->op_params[0]);
-        }
-        ggml_set_op_params_i32(tensor_clone, 2, ggml_get_op_params_i32(tensor, 2));
-        ggml_set_op_params_i32(tensor_clone, 3, ggml_get_op_params_i32(tensor, 3));
-    } else if (tensor->op == GGML_OP_CPY || tensor->op == GGML_OP_DUP) {
-        if (src1 == nullptr) {
-            tensor_clone = ggml_dup(ggml_ctx, src_clone[0]);
-            tensor_clone->type = tensor->type;
-        } else {
-            tensor_clone = ggml_cpy(ggml_ctx, src_clone[0], src_clone[1]);
-        }
-    } else if (tensor->op == GGML_OP_CONT) {
-        tensor_clone = ggml_cont_4d(ggml_ctx, src_clone[0], tensor->ne[0], tensor->ne[1], tensor->ne[2], tensor->ne[3]);
-    } else if (tensor->op == GGML_OP_RESHAPE) {
-        tensor_clone = ggml_reshape_4d(ggml_ctx, src_clone[0], tensor->ne[0], tensor->ne[1], tensor->ne[2], tensor->ne[3]);
-    } else if (tensor->op == GGML_OP_VIEW) {
-        tensor_clone = ggml_view_4d(ggml_ctx, src_clone[0], tensor->ne[0], tensor->ne[1], tensor->ne[2], tensor->ne[3], tensor->nb[1], tensor->nb[2], tensor->nb[3], ((int32_t *) tensor->op_params)[0]);
-    } else if (tensor->op == GGML_OP_PERMUTE) {
-        int32_t * params = (int32_t *)tensor->op_params;
-        tensor_clone = ggml_permute(ggml_ctx, src_clone[0], params[0], params[1], params[2], params[3]);
-    } else if (tensor->op == GGML_OP_TRANSPOSE) {
-        tensor_clone = ggml_transpose(ggml_ctx, src_clone[0]);
-    } else if (tensor->op == GGML_OP_GET_ROWS) {
-        tensor_clone = ggml_get_rows(ggml_ctx, src_clone[0], src_clone[1]);
-    } else if (tensor->op == GGML_OP_ARGSORT) {
-        tensor_clone = ggml_argsort(ggml_ctx, src_clone[0], (ggml_sort_order) *(int *)tensor->op_params);
-    } else if (tensor->op == GGML_OP_SUM) {
-        tensor_clone = ggml_sum(ggml_ctx, src_clone[0]);
-    } else if (tensor->op == GGML_OP_SUM_ROWS) {
-        tensor_clone = ggml_sum_rows(ggml_ctx, src_clone[0]);
-    } else if (tensor->op == GGML_OP_MEAN) {
-        tensor_clone = ggml_mean(ggml_ctx, src_clone[0]);
-    } else if (tensor->op == GGML_OP_ARGMAX) {
-        tensor_clone = ggml_argmax(ggml_ctx, src_clone[0]);
-    } else if (tensor->op == GGML_OP_COUNT_EQUAL) {
-        tensor_clone = ggml_count_equal(ggml_ctx, src_clone[0], src_clone[1]);
-    } else if (tensor->op == GGML_OP_IM2COL) {
-        const int32_t s0 = tensor->op_params[0];
-        const int32_t s1 = tensor->op_params[1];
-        const int32_t p0 = tensor->op_params[2];
-        const int32_t p1 = tensor->op_params[3];
-        const int32_t d0 = tensor->op_params[4];
-        const int32_t d1 = tensor->op_params[5];
-
-        const bool is_2D = tensor->op_params[6] == 1;
-        tensor_clone = ggml_im2col(ggml_ctx, src_clone[0], src_clone[1], s0, s1, p0, p1, d0, d1, is_2D, tensor->type);
-    } else if (tensor->op == GGML_OP_IM2COL_3D) {
-        const int32_t s0 = tensor->op_params[0];
-        const int32_t s1 = tensor->op_params[1];
-        const int32_t s2 = tensor->op_params[2];
-        const int32_t p0 = tensor->op_params[3];
-        const int32_t p1 = tensor->op_params[4];
-        const int32_t p2 = tensor->op_params[5];
-        const int32_t d0 = tensor->op_params[6];
-        const int32_t d1 = tensor->op_params[7];
-        const int32_t d2 = tensor->op_params[8];
-        const int32_t IC = tensor->op_params[9];
-
-        tensor_clone = ggml_im2col_3d(ggml_ctx, src_clone[0], src_clone[1], IC, s0, s1, s2, p0, p1, p2, d0, d1, d2, tensor->type);
-    } else if (tensor->op == GGML_OP_TIMESTEP_EMBEDDING) {
-        const int32_t dim = tensor->op_params[0];
-        const int32_t max_period = tensor->op_params[1];
-        tensor_clone = ggml_timestep_embedding(ggml_ctx, src_clone[0], dim, max_period);
-    } else if (tensor->op == GGML_OP_CONV_TRANSPOSE_1D){
-        const int32_t s0 = tensor->op_params[0];
-        const int32_t p0 = tensor->op_params[1];
-        const int32_t d0 = tensor->op_params[2];
-        tensor_clone = ggml_conv_transpose_1d(ggml_ctx, src_clone[0], src_clone[1], s0, p0, d0);
-    } else if (tensor->op == GGML_OP_POOL_2D) {
-        enum ggml_op_pool op = static_cast<ggml_op_pool>(tensor->op_params[0]);
-        const int32_t k0 = tensor->op_params[1];
-        const int32_t k1 = tensor->op_params[2];
-        const int32_t s0 = tensor->op_params[3];
-        const int32_t s1 = tensor->op_params[4];
-        const int32_t p0 = tensor->op_params[5];
-        const int32_t p1 = tensor->op_params[6];
-
-        tensor_clone = ggml_pool_2d(ggml_ctx, src_clone[0], op, k0, k1, s0, s1, p0, p1);
-    } else if (tensor->op == GGML_OP_CONV_2D) {
-        const int32_t s0 = tensor->op_params[0];
-        const int32_t s1 = tensor->op_params[1];
-        const int32_t p0 = tensor->op_params[2];
-        const int32_t p1 = tensor->op_params[3];
-        const int32_t d0 = tensor->op_params[4];
-        const int32_t d1 = tensor->op_params[5];
-        tensor_clone = ggml_conv_2d(ggml_ctx, src_clone[0], src_clone[1], s0, s1, p0, p1, d0, d1);
-    } else if (tensor->op == GGML_OP_CONV_TRANSPOSE_2D) {
-        const int32_t s = tensor->op_params[0];
-        tensor_clone = ggml_conv_transpose_2d_p0(ggml_ctx, src_clone[0], src_clone[1], s);
-    } else if (tensor->op == GGML_OP_LEAKY_RELU) {
-        const float * op_params = (const float *)tensor->op_params;
-        tensor_clone = ggml_leaky_relu(ggml_ctx, src_clone[0], op_params[0], false);
-    } else if (tensor->op == GGML_OP_RWKV_WKV6) {
-        tensor_clone = ggml_rwkv_wkv6(ggml_ctx, src_clone[0], src_clone[1],
-        src_clone[2], src_clone[3], src_clone[4], src_clone[5]);
-    } else if (tensor->op == GGML_OP_RWKV_WKV7) {
-        tensor_clone = ggml_rwkv_wkv7(ggml_ctx, src_clone[0], src_clone[1], src_clone[2], src_clone[3],
-        src_clone[4], src_clone[5], src_clone[6]);
-    } else if (tensor->op == GGML_OP_OPT_STEP_ADAMW) {
-        src_clone[0]->flags = src0->flags;
-        tensor_clone = ggml_opt_step_adamw(ggml_ctx, src_clone[0], src_clone[1],
-        src_clone[2], src_clone[3], src_clone[4]);
-    } else if (tensor->op == GGML_OP_OPT_STEP_SGD) {
-        src_clone[0]->flags = src0->flags;
-        tensor_clone = ggml_opt_step_sgd(ggml_ctx, src_clone[0], src_clone[1],
-        src_clone[2]);
-    } else if (tensor->op == GGML_OP_ADD_ID) {
-        tensor_clone = ggml_add_id(ggml_ctx, src_clone[0], src_clone[1], src_clone[2]);
-    } else if (tensor->op == GGML_OP_SSM_SCAN) {
-        tensor_clone = ggml_ssm_scan(ggml_ctx, src_clone[0], src_clone[1], src_clone[2],
-                                     src_clone[3], src_clone[4], src_clone[5], src_clone[6]);
-    } else if (tensor->op == GGML_OP_SSM_CONV) {
-        tensor_clone = ggml_ssm_conv(ggml_ctx, src_clone[0], src_clone[1]);
-    }
-    else {
-        std::cerr << "Missing vk_check_results OP: " << ggml_op_name(tensor->op) << std::endl;
-        GGML_ABORT("fatal error");
+        cloned_tensors[tensor] = tensor_clone;
     }
 
     ggml_cgraph * cgraph_cpu = ggml_new_graph(ggml_ctx);
@@ -14476,10 +14475,8 @@ static void ggml_vk_check_results_0(ggml_backend_vk_context * ctx, ggml_cgraph *
     memcpy(comp_result, tensor_clone->data, comp_size);
     memcpy(comp_nb, tensor_clone->nb, sizeof(size_t) * GGML_MAX_DIMS);
 
-    for (int i = 0; i < GGML_MAX_SRC; i++) {
-        if (src_buffer[i] != nullptr) {
-            free(src_buffer[i]);
-        }
+    for (auto m : cloned_mallocs) {
+        free(m);
     }
 
     ggml_free(ggml_ctx);
@@ -14488,15 +14485,10 @@ static void ggml_vk_check_results_0(ggml_backend_vk_context * ctx, ggml_cgraph *
 }
 
 static void ggml_vk_check_results_1(ggml_backend_vk_context * ctx, ggml_cgraph * cgraph, int tensor_idx) {
-    ggml_tensor * tensor = cgraph->nodes[tensor_idx];
+    ggml_tensor * tensor = cgraph->nodes[tensor_idx + ctx->num_additional_fused_ops];
     if (tensor->op == GGML_OP_TRANSPOSE || tensor->op == GGML_OP_SET_ROWS) {
         return;
     }
-    if (ctx->num_additional_fused_ops == 1 &&
-        tensor->op == GGML_OP_RMS_NORM &&
-        cgraph->nodes[tensor_idx + 1]->op == GGML_OP_MUL) {
-        tensor = cgraph->nodes[tensor_idx + 1];
-    }
 
     if (!(vk_output_tensor > 0 && vk_output_tensor == check_counter) && check_counter <= vk_skip_checks) {
         return;

From 230d1169e5bfe04a013b2e20f4662ee56c2454b0 Mon Sep 17 00:00:00 2001
From: bssrdf <merlintiger@hotmail.com>
Date: Wed, 5 Nov 2025 15:55:04 -0500
Subject: [PATCH 096/185] improve CUDA cpy memory bandwidth when copying
 transposed tensor  (#16841)

* WIP

* added a cpy kernel specific to transposed tensor which uses smem to avoid uncoalesced access; test cases also added shwoing improved memory bandwidth

* added BF16 support

* more strict check to make sure src0 is a transpose

* reformulated to handle more complicated transpose cases

* bring back 2D transpose for higher performance

* allow build on windows

* tranpose copy more shapes

* minor tweak

* final clean up

* restore some test cases

* keep only the kernel for true tranposed case; updated with review suggestions

* make CI happy

* remove headers not needed

* reduced bank conflicts for fp16 and bf16

* add missing const*

* now bank conflicts free

* use padding instead of swizzling

---------

Co-authored-by: bssrdf <bssrdf@gmail.com>
---
 ggml/src/ggml-cuda/cpy.cu  | 103 ++++++++++++++++++++++++++++++++++---
 tests/test-backend-ops.cpp |  33 ++++++++++--
 2 files changed, 126 insertions(+), 10 deletions(-)

diff --git a/ggml/src/ggml-cuda/cpy.cu b/ggml/src/ggml-cuda/cpy.cu
index c5821acbdeb..1dba60eb143 100644
--- a/ggml/src/ggml-cuda/cpy.cu
+++ b/ggml/src/ggml-cuda/cpy.cu
@@ -7,6 +7,10 @@
 
 typedef void (*cpy_kernel_t)(const char * cx, char * cdst);
 
+const int CUDA_CPY_TILE_DIM_2D = 32; // 2D tile dimension for transposed blocks
+const int CUDA_CPY_BLOCK_NM = 8;     // block size of 3rd dimension if available
+const int CUDA_CPY_BLOCK_ROWS = 8;   // block dimension for marching through rows
+
 template <cpy_kernel_t cpy_1>
 static __global__ void cpy_flt(const char * cx, char * cdst, const int ne,
                                const int ne00, const int ne01, const int ne02, const int nb00, const int nb01, const int nb02,
@@ -35,6 +39,55 @@ static __global__ void cpy_flt(const char * cx, char * cdst, const int ne,
     cpy_1(cx + x_offset, cdst + dst_offset);
 }
 
+template <typename T>
+static __global__ void cpy_flt_transpose(const char * cx, char * cdst, const int ne,
+                               const int ne00, const int ne01, const int ne02, const int nb00, const int nb01, const int nb02,
+                               const int nb03, const int ne10, const int ne11, const int ne12, const int nb10, const int nb11,
+                               const int nb12, const int nb13) {
+
+    const T* src = reinterpret_cast<const T*>(cx);
+    T* dst = reinterpret_cast<T*>(cdst);
+
+    const int64_t nmat = ne / (ne00 * ne01);
+    const int64_t n = ne00 * ne01;
+
+    const int x = blockIdx.x * CUDA_CPY_TILE_DIM_2D + threadIdx.x;
+    const int y = blockIdx.y * CUDA_CPY_TILE_DIM_2D + threadIdx.y;
+    const int tx = blockIdx.y * CUDA_CPY_TILE_DIM_2D + threadIdx.x;  // transpose block offset
+    const int ty = blockIdx.x * CUDA_CPY_TILE_DIM_2D + threadIdx.y;
+
+    __shared__ float tile[CUDA_CPY_TILE_DIM_2D][CUDA_CPY_TILE_DIM_2D+1];
+
+#pragma unroll
+    for (int i = 0; i < CUDA_CPY_BLOCK_NM; ++i) {
+
+        const unsigned int imat = blockIdx.z * CUDA_CPY_BLOCK_NM + i;
+        if (imat >= nmat)
+            break;
+
+#pragma unroll
+        for (int j = 0; j < CUDA_CPY_TILE_DIM_2D; j += CUDA_CPY_BLOCK_ROWS) {
+            if(x < ne01 && y + j < ne00){
+                const int row = threadIdx.y+j;
+                const int col = threadIdx.x * sizeof(float)/sizeof(T);
+                T *tile2 = reinterpret_cast<T*>(tile[row]);
+                tile2[col] = src[imat*n + (y+j)*ne01 + x];
+            }
+        }
+
+        __syncthreads();
+
+#pragma unroll
+        for (int j = 0; j < CUDA_CPY_TILE_DIM_2D; j += CUDA_CPY_BLOCK_ROWS) {
+            if (ty + j < ne01 && tx < ne00) {
+                const int col = (threadIdx.y+j)*sizeof(float)/sizeof(T);
+                const T *tile2 = reinterpret_cast<const T*>(tile[threadIdx.x]);
+                dst[imat*n + (ty+j)*ne00 + tx] = tile2[col];
+            }
+        }
+    }
+}
+
 static __device__ void cpy_blck_q8_0_f32(const char * cxi, char * cdsti) {
     float * cdstf = (float *)(cdsti);
 
@@ -136,15 +189,38 @@ cudaStream_t stream) {
         (cx, cdst, ne);
 }
 
-template<typename src_t, typename dst_t>
+template<typename src_t, typename dst_t, bool transposed = false>
 static void ggml_cpy_flt_cuda(
     const char * cx, char * cdst, const int ne,
     const int ne00, const int ne01, const int ne02, const int nb00, const int nb01, const int nb02,
     const int nb03, const int ne10, const int ne11, const int ne12, const int nb10, const int nb11, const int nb12, const int nb13, cudaStream_t stream) {
 
-    const int num_blocks = (ne + CUDA_CPY_BLOCK_SIZE - 1) / CUDA_CPY_BLOCK_SIZE;
-    cpy_flt<cpy_1_flt<src_t, dst_t>><<<num_blocks, CUDA_CPY_BLOCK_SIZE, 0, stream>>>
-        (cx, cdst, ne, ne00, ne01, ne02, nb00, nb01, nb02, nb03, ne10, ne11, ne12, nb10, nb11, nb12, nb13);
+    if (transposed) {
+        GGML_ASSERT(ne == ne00*ne01*ne02);  // ne[3] is 1 assumed
+        int ne00n, ne01n, ne02n;
+        if (nb00 < nb02) {
+            ne00n = ne00;
+            ne01n = ne01;
+            ne02n = ne02;
+        } else if (nb00 > nb02) {
+            ne00n = ne00;
+            ne01n = ne01*ne02;
+            ne02n = 1;
+        } else {
+            GGML_ASSERT(false);
+        }
+
+        dim3 dimGrid( (ne01n + CUDA_CPY_TILE_DIM_2D - 1) / CUDA_CPY_TILE_DIM_2D,
+                      (ne00n + CUDA_CPY_TILE_DIM_2D - 1) / CUDA_CPY_TILE_DIM_2D,
+                      (ne/(ne01n*ne00n) + CUDA_CPY_BLOCK_NM - 1) / CUDA_CPY_BLOCK_NM);
+        dim3 dimBlock(CUDA_CPY_TILE_DIM_2D, CUDA_CPY_BLOCK_ROWS, 1);
+        cpy_flt_transpose<dst_t><<<dimGrid, dimBlock, 0, stream>>>
+            (cx, cdst, ne, ne00n, ne01n, ne02n, nb00, nb01, nb02, nb03, ne10, ne11, ne12, nb10, nb11, nb12, nb13);
+    } else {
+        const int num_blocks = (ne + CUDA_CPY_BLOCK_SIZE - 1) / CUDA_CPY_BLOCK_SIZE;
+        cpy_flt<cpy_1_flt<src_t, dst_t>><<<num_blocks, CUDA_CPY_BLOCK_SIZE, 0, stream>>>
+            (cx, cdst, ne, ne00, ne01, ne02, nb00, nb01, nb02, nb03, ne10, ne11, ne12, nb10, nb11, nb12, nb13);
+    }
 }
 
 static void ggml_cpy_f32_q8_0_cuda(
@@ -310,6 +386,7 @@ void ggml_cuda_cpy(ggml_backend_cuda_context & ctx, const ggml_tensor * src0, gg
     char * src1_ddc = (char *) src1->data;
 
     const bool contiguous_srcs = ggml_is_contiguous(src0) && ggml_is_contiguous(src1);
+    const bool can_be_transposed = nb01 == (int64_t)ggml_element_size(src0) && src0->ne[3] == 1;
 
     if (src0->type == src1->type && contiguous_srcs) {
         GGML_ASSERT(ggml_nbytes(src0) == ggml_nbytes(src1));
@@ -322,7 +399,11 @@ void ggml_cuda_cpy(ggml_backend_cuda_context & ctx, const ggml_tensor * src0, gg
             CUDA_CHECK(cudaMemcpyAsync(src1_ddc, src0_ddc, ggml_nbytes(src0), cudaMemcpyDeviceToDevice, main_stream));
         }
     } else if (src0->type == GGML_TYPE_F32 && src1->type == GGML_TYPE_F32) {
-        ggml_cpy_flt_cuda<float, float>           (src0_ddc, src1_ddc, ne, ne00, ne01, ne02, nb00, nb01, nb02, nb03, ne10, ne11, ne12, nb10, nb11, nb12, nb13, main_stream);
+        if (can_be_transposed) {
+            ggml_cpy_flt_cuda<float, float, true> (src0_ddc, src1_ddc, ne, ne00, ne01, ne02, nb00, nb01, nb02, nb03, ne10, ne11, ne12, nb10, nb11, nb12, nb13, main_stream);
+        } else {
+            ggml_cpy_flt_cuda<float, float> (src0_ddc, src1_ddc, ne, ne00, ne01, ne02, nb00, nb01, nb02, nb03, ne10, ne11, ne12, nb10, nb11, nb12, nb13, main_stream);
+        }
     } else if (src0->type == GGML_TYPE_F32 && src1->type == GGML_TYPE_BF16) {
         if (contiguous_srcs) {
             ggml_cpy_flt_contiguous_cuda<float, nv_bfloat16> (src0_ddc, src1_ddc, ne, main_stream);
@@ -361,7 +442,11 @@ void ggml_cuda_cpy(ggml_backend_cuda_context & ctx, const ggml_tensor * src0, gg
     } else if (src0->type == GGML_TYPE_Q5_1 && src1->type == GGML_TYPE_F32) {
         ggml_cpy_q5_1_f32_cuda(src0_ddc, src1_ddc, ne, ne00, ne01, ne02, nb00, nb01, nb02, nb03, ne10, ne11, ne12, nb10, nb11, nb12, nb13, main_stream);
     } else if (src0->type == GGML_TYPE_F16 && src1->type == GGML_TYPE_F16) {
-        ggml_cpy_flt_cuda<half, half>               (src0_ddc, src1_ddc, ne, ne00, ne01, ne02, nb00, nb01, nb02, nb03, ne10, ne11, ne12, nb10, nb11, nb12, nb13, main_stream);
+        if (can_be_transposed) {
+            ggml_cpy_flt_cuda<half, half, true> (src0_ddc, src1_ddc, ne, ne00, ne01, ne02, nb00, nb01, nb02, nb03, ne10, ne11, ne12, nb10, nb11, nb12, nb13, main_stream);
+        } else {
+            ggml_cpy_flt_cuda<half, half>       (src0_ddc, src1_ddc, ne, ne00, ne01, ne02, nb00, nb01, nb02, nb03, ne10, ne11, ne12, nb10, nb11, nb12, nb13, main_stream);
+        }
     } else if (src0->type == GGML_TYPE_F16 && src1->type == GGML_TYPE_BF16) {
         if (contiguous_srcs) {
             ggml_cpy_flt_contiguous_cuda<half, nv_bfloat16>  (src0_ddc, src1_ddc, ne, main_stream);
@@ -375,7 +460,11 @@ void ggml_cuda_cpy(ggml_backend_cuda_context & ctx, const ggml_tensor * src0, gg
             ggml_cpy_flt_cuda<half, float>          (src0_ddc, src1_ddc, ne, ne00, ne01, ne02, nb00, nb01, nb02, nb03, ne10, ne11, ne12, nb10, nb11, nb12, nb13, main_stream);
         }
     } else if (src0->type == GGML_TYPE_BF16 && src1->type == GGML_TYPE_BF16) {
-        ggml_cpy_flt_cuda<nv_bfloat16, nv_bfloat16> (src0_ddc, src1_ddc, ne, ne00, ne01, ne02, nb00, nb01, nb02, nb03, ne10, ne11, ne12, nb10, nb11, nb12, nb13, main_stream);
+        if (can_be_transposed) {
+            ggml_cpy_flt_cuda<nv_bfloat16, nv_bfloat16, true> (src0_ddc, src1_ddc, ne, ne00, ne01, ne02, nb00, nb01, nb02, nb03, ne10, ne11, ne12, nb10, nb11, nb12, nb13, main_stream);
+        } else {
+            ggml_cpy_flt_cuda<nv_bfloat16, nv_bfloat16> (src0_ddc, src1_ddc, ne, ne00, ne01, ne02, nb00, nb01, nb02, nb03, ne10, ne11, ne12, nb10, nb11, nb12, nb13, main_stream);
+        }
     } else if (src0->type == GGML_TYPE_BF16 && src1->type == GGML_TYPE_F16) {
         if (contiguous_srcs) {
             ggml_cpy_flt_contiguous_cuda<nv_bfloat16, half>  (src0_ddc, src1_ddc, ne, main_stream);
diff --git a/tests/test-backend-ops.cpp b/tests/test-backend-ops.cpp
index 967a53c63d8..f575420279a 100644
--- a/tests/test-backend-ops.cpp
+++ b/tests/test-backend-ops.cpp
@@ -2576,9 +2576,10 @@ struct test_cpy : public test_case {
     const std::array<int64_t, 4> permute_dst;
     bool _src_use_permute;
     bool _dst_use_permute;
+    bool _src_transpose;
 
     std::string vars() override {
-        return VARS_TO_STR5(type_src, type_dst, ne, permute_src, permute_dst);
+        return VARS_TO_STR6(type_src, type_dst, ne, permute_src, permute_dst, _src_transpose);
     }
 
     double max_nmse_err() override {
@@ -2616,10 +2617,12 @@ struct test_cpy : public test_case {
     test_cpy(ggml_type type_src = GGML_TYPE_F32, ggml_type type_dst = GGML_TYPE_F32,
             std::array<int64_t, 4> ne = {10, 10, 10, 1},
             std::array<int64_t, 4> permute_src = {0, 0, 0, 0},
-            std::array<int64_t, 4> permute_dst = {0, 0, 0, 0})
+            std::array<int64_t, 4> permute_dst = {0, 0, 0, 0},
+            bool transpose_src = false)
         : type_src(type_src), type_dst(type_dst), ne(ne), permute_src(permute_src), permute_dst(permute_dst),
           _src_use_permute(permute_src[0] + permute_src[1] + permute_src[2] + permute_src[3] > 0),
-          _dst_use_permute(permute_dst[0] + permute_dst[1] + permute_dst[2] + permute_dst[3] > 0) {}
+          _dst_use_permute(permute_dst[0] + permute_dst[1] + permute_dst[2] + permute_dst[3] > 0),
+          _src_transpose(transpose_src){}
 
     ggml_tensor * build_graph(ggml_context * ctx) override {
         ggml_tensor * src = ggml_new_tensor(ctx, type_src, 4, ne.data());
@@ -2631,6 +2634,11 @@ struct test_cpy : public test_case {
             ggml_set_name(src, "src_permuted");
         }
 
+        if (_src_transpose) {
+            src = ggml_transpose(ctx, src);
+            ggml_set_name(src, "src_transposed");
+        }
+
         ggml_tensor * dst = ggml_new_tensor(ctx, type_dst, 4, src->ne);
         ggml_set_name(dst, "dst");
 
@@ -6641,6 +6649,13 @@ static std::vector<std::unique_ptr<test_case>> make_test_cases_eval() {
     test_cases.emplace_back(new test_cpy(GGML_TYPE_F32, GGML_TYPE_I32, {256, 2, 3, 4}, {1, 0, 2, 3}));
     test_cases.emplace_back(new test_cpy(GGML_TYPE_I32, GGML_TYPE_F32, {256, 2, 3, 4}));
     test_cases.emplace_back(new test_cpy(GGML_TYPE_I32, GGML_TYPE_F32, {256, 2, 3, 4}, {1, 0, 2, 3}));
+    test_cases.emplace_back(new test_cpy(GGML_TYPE_F16, GGML_TYPE_F16, {256, 4, 3, 1}, {0, 0, 0, 0}, {0, 0, 0, 0}, true));
+    test_cases.emplace_back(new test_cpy(GGML_TYPE_F32, GGML_TYPE_F32, {256, 4, 3, 1}, {0, 0, 0, 0}, {0, 0, 0, 0}, true));
+    test_cases.emplace_back(new test_cpy(GGML_TYPE_F32, GGML_TYPE_F32, {256, 4, 3, 3}, {0, 0, 0, 0}, {0, 0, 0, 0}, true));
+    test_cases.emplace_back(new test_cpy(GGML_TYPE_BF16, GGML_TYPE_BF16, {256, 4, 3, 1}, {0, 0, 0, 0}, {0, 0, 0, 0}, true));
+    test_cases.emplace_back(new test_cpy(GGML_TYPE_F16, GGML_TYPE_F16, {256, 4, 1, 1}, {0, 0, 0, 0}, {0, 0, 0, 0}, true));
+    test_cases.emplace_back(new test_cpy(GGML_TYPE_F32, GGML_TYPE_F32, {256, 4, 1, 1}, {0, 0, 0, 0}, {0, 0, 0, 0}, true));
+    test_cases.emplace_back(new test_cpy(GGML_TYPE_BF16, GGML_TYPE_BF16, {256, 4, 1, 1}, {0, 0, 0, 0}, {0, 0, 0, 0}, true));
 
     test_cases.emplace_back(new test_cont());
     test_cases.emplace_back(new test_cont(GGML_TYPE_F32, {2, 1, 1 ,1}));
@@ -7385,6 +7400,18 @@ static std::vector<std::unique_ptr<test_case>> make_test_cases_perf() {
     test_cases.emplace_back(new test_cpy(GGML_TYPE_F32,  GGML_TYPE_Q4_0, {8192, 512, 2, 1}));
     test_cases.emplace_back(new test_cpy(GGML_TYPE_Q4_0, GGML_TYPE_F32,  {8192, 512, 2, 1}));
 
+    test_cases.emplace_back(new test_cpy(GGML_TYPE_F32, GGML_TYPE_F32, {768*1024, 256, 1, 1}, {1, 0, 2, 3}, {0, 0, 0, 0}));
+    test_cases.emplace_back(new test_cpy(GGML_TYPE_F16, GGML_TYPE_F16, {768*1024, 256, 1, 1}, {1, 0, 2, 3}, {0, 0, 0, 0}));
+    test_cases.emplace_back(new test_cpy(GGML_TYPE_F16, GGML_TYPE_F16, {768, 1024, 256, 1}, {1, 0, 2, 3}, {0, 0, 0, 0}));
+    test_cases.emplace_back(new test_cpy(GGML_TYPE_BF16, GGML_TYPE_BF16, {768, 1024, 256, 1}, {1, 0, 2, 3}, {0, 0, 0, 0}));
+
+    test_cases.emplace_back(new test_cpy(GGML_TYPE_F32, GGML_TYPE_F32, {768*1024, 256, 1, 1}, {0, 0, 0, 0}, {0, 0, 0, 0}, true));
+    test_cases.emplace_back(new test_cpy(GGML_TYPE_F32, GGML_TYPE_F32, {768, 1024, 256, 1}, {0, 0, 0, 0}, {0, 0, 0, 0}, true));
+    test_cases.emplace_back(new test_cpy(GGML_TYPE_F16, GGML_TYPE_F16, {768*1024, 256, 1, 1}, {0, 0, 0, 0}, {0, 0, 0, 0}, true));
+    test_cases.emplace_back(new test_cpy(GGML_TYPE_F16, GGML_TYPE_F16, {768, 1024, 256, 1}, {0, 0, 0, 0}, {0, 0, 0, 0}, true));
+    test_cases.emplace_back(new test_cpy(GGML_TYPE_BF16, GGML_TYPE_BF16, {768, 1024, 256, 1}, {0, 0, 0, 0}, {0, 0, 0, 0}, true));
+
+
     test_cases.emplace_back(new test_soft_max(GGML_TYPE_F32, {4096, 4096, 5, 1}, false, false, GGML_TYPE_F32, {1, 1}, 1.0f, 0.0f));
     test_cases.emplace_back(new test_soft_max(GGML_TYPE_F32, {12888, 256, 5, 1}, false, false, GGML_TYPE_F32, {1, 1}, 1.0f, 0.0f));
     test_cases.emplace_back(new test_soft_max(GGML_TYPE_F32, {77, 4096, 5, 1}, false, false, GGML_TYPE_F32, {1, 1}, 1.0f, 0.0f));

From 6db3d1ffe6d34e8becfe95cf2f109198a7154db3 Mon Sep 17 00:00:00 2001
From: l3utterfly <gc.pthzfoldr@gmail.com>
Date: Thu, 6 Nov 2025 13:46:38 +0800
Subject: [PATCH 097/185] ggml-hexagon: graceful fallback for older socs where
 rpcmem_alloc2 and FASTRPC_GET_URI is unsupported (#16987)

* support older socs where FASTRPC_GET_URI is unsupported

* added graceful fallback when FASTRPC_GET_URI call fails

* use weak symbols instead of loading libcdsprpc.so dynamically

* Add weak pragma for rpcmem_alloc2

* Remove weak declaration for rpcmem_alloc2 in ggml-hexagon.cpp

Removed weak declaration for rpcmem_alloc2.

* Enforce ndev to 1 for archs below v75

Force ndev to 1 for SoCs architectures lower than v75.
---
 ggml/src/ggml-hexagon/ggml-hexagon.cpp | 28 ++++++++++++++++++++------
 ggml/src/ggml-hexagon/htp-utils.h      |  1 +
 2 files changed, 23 insertions(+), 6 deletions(-)

diff --git a/ggml/src/ggml-hexagon/ggml-hexagon.cpp b/ggml/src/ggml-hexagon/ggml-hexagon.cpp
index 945652263d4..7064b7486f2 100644
--- a/ggml/src/ggml-hexagon/ggml-hexagon.cpp
+++ b/ggml/src/ggml-hexagon/ggml-hexagon.cpp
@@ -367,7 +367,13 @@ struct ggml_backend_hexagon_buffer_context {
     ggml_backend_hexagon_buffer_context(ggml_hexagon_session * sess, size_t size, bool repack) {
         size += 4 * 1024;  // extra page for padding
 
-        this->base = (uint8_t *) rpcmem_alloc2(RPCMEM_HEAP_ID_SYSTEM, RPCMEM_DEFAULT_FLAGS | RPCMEM_HEAP_NOREG, size);
+        if (rpcmem_alloc2) {
+            this->base = (uint8_t *) rpcmem_alloc2(RPCMEM_HEAP_ID_SYSTEM, RPCMEM_DEFAULT_FLAGS | RPCMEM_HEAP_NOREG, size);
+        } else {
+            GGML_LOG_INFO("ggml-hex: %s rpcmem_alloc2 not found, falling back to rpcmem_alloc\n", sess->name.c_str());
+            this->base = (uint8_t *) rpcmem_alloc(RPCMEM_HEAP_ID_SYSTEM, RPCMEM_DEFAULT_FLAGS | RPCMEM_HEAP_NOREG, size);
+        }
+
         if (!this->base) {
             GGML_LOG_ERROR("ggml-hex: %s failed to allocate buffer : size %zu\n", sess->name.c_str(), size);
             throw std::runtime_error("ggml-hex: rpcmem_alloc failed (see log for details)");
@@ -1679,12 +1685,13 @@ void ggml_hexagon_session::allocate(int dev_id) noexcept(false) {
     }
 
     // Get session URI
-    char htp_uri[256];
-    sprintf(htp_uri, "file:///libggml-htp-v%u.so?htp_iface_skel_handle_invoke&_modver=1.0", opt_arch);
 
     char session_uri[256];
     {
-        struct remote_rpc_get_uri u;
+        char htp_uri[256];
+        snprintf(htp_uri, sizeof(htp_uri), "file:///libggml-htp-v%u.so?htp_iface_skel_handle_invoke&_modver=1.0", opt_arch);
+
+        struct remote_rpc_get_uri u = {};
         u.session_id      = this->session_id;
         u.domain_name     = const_cast<char *>(CDSP_DOMAIN_NAME);
         u.domain_name_len = strlen(CDSP_DOMAIN_NAME);
@@ -1695,8 +1702,12 @@ void ggml_hexagon_session::allocate(int dev_id) noexcept(false) {
 
         int err = remote_session_control(FASTRPC_GET_URI, (void *) &u, sizeof(u));
         if (err != AEE_SUCCESS) {
-            GGML_LOG_ERROR("ggml-hex: failed to get URI for session %d : error 0x%x\n", dev_id, err);
-            throw std::runtime_error("ggml-hex: remote_session_control(get-uri) failed (see log for details)");
+            // fallback to single session uris
+            int htp_URI_domain_len = strlen(htp_uri) + MAX_DOMAIN_NAMELEN;
+
+            snprintf(session_uri, htp_URI_domain_len, "%s%s", htp_uri, my_domain->uri);
+
+            GGML_LOG_WARN("ggml-hex: failed to get URI for session %d : error 0x%x. Falling back to single session URI: %s\n", dev_id, err, session_uri);
         }
     }
 
@@ -3668,6 +3679,11 @@ ggml_hexagon_registry::ggml_hexagon_registry(ggml_backend_reg_t reg) {
         }
     }
 
+    if(opt_arch < 75) {
+        opt_ndev = 1;
+        GGML_LOG_WARN("ggml-hex: forcing ndev to 1 for SoCs archs lower than v75.\n");
+    }
+
     GGML_LOG_INFO("ggml-hex: Hexagon Arch version v%d\n", opt_arch);
 
     // Create devices / sessions
diff --git a/ggml/src/ggml-hexagon/htp-utils.h b/ggml/src/ggml-hexagon/htp-utils.h
index 66f9fd373e2..1a48f5dcbdf 100644
--- a/ggml/src/ggml-hexagon/htp-utils.h
+++ b/ggml/src/ggml-hexagon/htp-utils.h
@@ -64,6 +64,7 @@ extern "C" {
 #    pragma weak remote_handle64_control
 #    pragma weak fastrpc_mmap
 #    pragma weak fastrpc_munmap
+#    pragma weak rpcmem_alloc2
 #endif
 
 #if !defined(_WINDOWS)

From 22c8c3c6ad8d6239c366ce3a84ace8b0ac59ef88 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Johannes=20G=C3=A4=C3=9Fler?= <johannesg@5d6.de>
Date: Thu, 6 Nov 2025 08:14:35 +0100
Subject: [PATCH 098/185] docs: explain CUDA 11 compilation [no ci] (#16824)

---
 docs/build.md | 42 ++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 42 insertions(+)

diff --git a/docs/build.md b/docs/build.md
index b410c710e30..7d244ff013b 100644
--- a/docs/build.md
+++ b/docs/build.md
@@ -178,6 +178,48 @@ GeForce RTX 3070      8.6
 cmake -B build -DGGML_CUDA=ON -DCMAKE_CUDA_ARCHITECTURES="86;89"
 ```
 
+### Overriding the CUDA Version
+
+If you have multiple CUDA installations on your system and want to compile llama.cpp for a specific one, e.g. for CUDA 11.7 installed under `/opt/cuda-11.7`:
+
+```bash
+cmake -B build -DGGML_CUDA=ON -DCMAKE_CUDA_COMPILER=/opt/cuda-11.7/bin/nvcc -DCMAKE_INSTALL_RPATH="/opt/cuda-11.7/lib64;\$ORIGIN" -DCMAKE_BUILD_WITH_INSTALL_RPATH=ON
+```
+
+#### Fixing Compatibility Issues with Old CUDA and New glibc
+
+If you try to use an old CUDA version (e.g. v11.7) with a new glibc version you can get errors like this:
+
+```
+/usr/include/bits/mathcalls.h(83): error: exception specification is
+  incompatible with that of previous function "cospi"
+
+
+  /opt/cuda-11.7/bin/../targets/x86_64-linux/include/crt/math_functions.h(5545):
+  here
+```
+
+It seems the least bad solution is to patch the CUDA installation to declare the correct signatures.
+Replace the following lines in `/path/to/your/cuda/installation/targets/x86_64-linux/include/crt/math_functions.h`:
+
+```C++
+// original lines
+extern __DEVICE_FUNCTIONS_DECL__ __device_builtin__ double                 cospi(double x);
+extern __DEVICE_FUNCTIONS_DECL__ __device_builtin__ float                  cospif(float x);
+extern __DEVICE_FUNCTIONS_DECL__ __device_builtin__ double                 sinpi(double x);
+extern __DEVICE_FUNCTIONS_DECL__ __device_builtin__ float                  sinpif(float x);
+extern __DEVICE_FUNCTIONS_DECL__ __device_builtin__ double                 rsqrt(double x);
+extern __DEVICE_FUNCTIONS_DECL__ __device_builtin__ float                  rsqrtf(float x);
+
+// edited lines
+extern __DEVICE_FUNCTIONS_DECL__ __device_builtin__ double                 cospi(double x) noexcept (true);
+extern __DEVICE_FUNCTIONS_DECL__ __device_builtin__ float                  cospif(float x) noexcept (true);
+extern __DEVICE_FUNCTIONS_DECL__ __device_builtin__ double                 sinpi(double x) noexcept (true);
+extern __DEVICE_FUNCTIONS_DECL__ __device_builtin__ float                  sinpif(float x) noexcept (true);
+extern __DEVICE_FUNCTIONS_DECL__ __device_builtin__ double                 rsqrt(double x) noexcept (true);
+extern __DEVICE_FUNCTIONS_DECL__ __device_builtin__ float                  rsqrtf(float x) noexcept (true);
+```
+
 ### Runtime CUDA environmental variables
 
 You may set the [cuda environmental variables](https://docs.nvidia.com/cuda/cuda-c-programming-guide/index.html#env-vars) at runtime.

From 9d7c518d642db8657e2a53a9793c5f039ed8ea5a Mon Sep 17 00:00:00 2001
From: YehuditE <y8703470@gmail.com>
Date: Thu, 6 Nov 2025 12:02:33 +0200
Subject: [PATCH 099/185] sycl: add CONCAT operator support (#16047)
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

* sycl: add CONCAT operator support

* cleanup: remove stray lines added by mistake

* fix: code format issues in concat.cpp and tests/test-backend-ops.cpp

* chore: fix editorconfig violations

* cleanup: drop unnecessary i16 type support

* docs: update sycl-csv and regenerate ops.md

* update docs/ops.md

* fix: adapt to upstream master changes after rebase

* fix: remove empty files

* fix: drop whitespace

---------

Co-authored-by: Sigbjørn Skjæret <sigbjorn.skjaeret@scala.com>
---
 docs/ops.md                      |  2 +-
 docs/ops/SYCL.csv                | 32 +++++------
 ggml/src/ggml-sycl/concat.cpp    | 99 ++++++++++++++++++--------------
 ggml/src/ggml-sycl/ggml-sycl.cpp |  6 +-
 4 files changed, 73 insertions(+), 66 deletions(-)

diff --git a/docs/ops.md b/docs/ops.md
index b8fcf046358..775b938bd12 100644
--- a/docs/ops.md
+++ b/docs/ops.md
@@ -24,7 +24,7 @@ Legend:
 |                          ARGSORT | ❌ | ✅ | ✅ | ✅ | ✅ | ✅ | ✅ | ✅ | ❌ |
 |                             CEIL | ❌ | ❌ | ✅ | 🟡 | ❌ | ❌ | ✅ | ❌ | ❌ |
 |                            CLAMP | ❌ | ✅ | ✅ | ✅ | 🟡 | 🟡 | ✅ | 🟡 | ❌ |
-|                           CONCAT | ❌ | ✅ | ✅ | 🟡 | ✅ | 🟡 | 🟡 | ✅ | ❌ |
+|                           CONCAT | ❌ | ✅ | ✅ | 🟡 | ✅ | 🟡 | ✅ | ✅ | ❌ |
 |                             CONT | ❌ | 🟡 | ✅ | ✅ | ✅ | 🟡 | 🟡 | 🟡 | ❌ |
 |                          CONV_2D | ❌ | ❌ | ✅ | 🟡 | ❌ | ✅ | ❌ | ✅ | ❌ |
 |                       CONV_2D_DW | ❌ | ❌ | ✅ | ✅ | ❌ | ❌ | ❌ | ✅ | ❌ |
diff --git a/docs/ops/SYCL.csv b/docs/ops/SYCL.csv
index 101e80f64c6..d7e71990a88 100644
--- a/docs/ops/SYCL.csv
+++ b/docs/ops/SYCL.csv
@@ -9307,37 +9307,37 @@
 "SYCL0","ROPE","type=f16,ne_a=[128,32,2,1],n_dims=128,mode=24,n_ctx=512,fs=1.424500,ef=0.746500,af=1.424500,ff=0,v=0,inplace=1","support","1","yes","SYCL"
 "SYCL0","ROPE","type=f16,ne_a=[128,32,2,1],n_dims=128,mode=24,n_ctx=512,fs=1.424500,ef=0.746500,af=1.424500,ff=1,v=0,inplace=1","support","1","yes","SYCL"
 "SYCL0","CONCAT","type=f32,ne_a=[11,12,13,14],ne_b_d=7,dim=0,v=0","support","1","yes","SYCL"
-"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=0,v=0","support","0","no","SYCL"
+"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=0,v=0","support","0","yes","SYCL"
 "SYCL0","CONCAT","type=f32,ne_a=[11,12,13,14],ne_b_d=7,dim=1,v=0","support","1","yes","SYCL"
-"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=1,v=0","support","0","no","SYCL"
+"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=1,v=0","support","0","yes","SYCL"
 "SYCL0","CONCAT","type=f32,ne_a=[11,12,13,14],ne_b_d=7,dim=2,v=0","support","1","yes","SYCL"
-"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=2,v=0","support","0","no","SYCL"
+"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=2,v=0","support","0","yes","SYCL"
 "SYCL0","CONCAT","type=f32,ne_a=[11,12,13,14],ne_b_d=7,dim=3,v=0","support","1","yes","SYCL"
-"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=3,v=0","support","0","no","SYCL"
+"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=3,v=0","support","0","yes","SYCL"
 "SYCL0","CONCAT","type=f32,ne_a=[11,12,13,14],ne_b_d=7,dim=0,v=1","support","1","yes","SYCL"
-"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=0,v=1","support","0","no","SYCL"
+"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=0,v=1","support","0","yes","SYCL"
 "SYCL0","CONCAT","type=f32,ne_a=[11,12,13,14],ne_b_d=7,dim=1,v=1","support","1","yes","SYCL"
-"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=1,v=1","support","0","no","SYCL"
+"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=1,v=1","support","0","yes","SYCL"
 "SYCL0","CONCAT","type=f32,ne_a=[11,12,13,14],ne_b_d=7,dim=2,v=1","support","1","yes","SYCL"
-"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=2,v=1","support","0","no","SYCL"
+"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=2,v=1","support","0","yes","SYCL"
 "SYCL0","CONCAT","type=f32,ne_a=[11,12,13,14],ne_b_d=7,dim=3,v=1","support","1","yes","SYCL"
-"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=3,v=1","support","0","no","SYCL"
+"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=3,v=1","support","0","yes","SYCL"
 "SYCL0","CONCAT","type=f32,ne_a=[11,12,13,14],ne_b_d=7,dim=0,v=2","support","1","yes","SYCL"
-"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=0,v=2","support","0","no","SYCL"
+"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=0,v=2","support","0","yes","SYCL"
 "SYCL0","CONCAT","type=f32,ne_a=[11,12,13,14],ne_b_d=7,dim=1,v=2","support","1","yes","SYCL"
-"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=1,v=2","support","0","no","SYCL"
+"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=1,v=2","support","0","yes","SYCL"
 "SYCL0","CONCAT","type=f32,ne_a=[11,12,13,14],ne_b_d=7,dim=2,v=2","support","1","yes","SYCL"
-"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=2,v=2","support","0","no","SYCL"
+"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=2,v=2","support","0","yes","SYCL"
 "SYCL0","CONCAT","type=f32,ne_a=[11,12,13,14],ne_b_d=7,dim=3,v=2","support","1","yes","SYCL"
-"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=3,v=2","support","0","no","SYCL"
+"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=3,v=2","support","0","yes","SYCL"
 "SYCL0","CONCAT","type=f32,ne_a=[11,12,13,14],ne_b_d=7,dim=0,v=3","support","1","yes","SYCL"
-"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=0,v=3","support","0","no","SYCL"
+"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=0,v=3","support","0","yes","SYCL"
 "SYCL0","CONCAT","type=f32,ne_a=[11,12,13,14],ne_b_d=7,dim=1,v=3","support","1","yes","SYCL"
-"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=1,v=3","support","0","no","SYCL"
+"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=1,v=3","support","0","yes","SYCL"
 "SYCL0","CONCAT","type=f32,ne_a=[11,12,13,14],ne_b_d=7,dim=2,v=3","support","1","yes","SYCL"
-"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=2,v=3","support","0","no","SYCL"
+"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=2,v=3","support","0","yes","SYCL"
 "SYCL0","CONCAT","type=f32,ne_a=[11,12,13,14],ne_b_d=7,dim=3,v=3","support","1","yes","SYCL"
-"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=3,v=3","support","0","no","SYCL"
+"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=3,v=3","support","0","yes","SYCL"
 "SYCL0","ARGSORT","type=f32,ne=[8,1,1,1],order=0","support","1","yes","SYCL"
 "SYCL0","ARGSORT","type=f32,ne=[16,10,10,10],order=0","support","1","yes","SYCL"
 "SYCL0","ARGSORT","type=f32,ne=[60,10,10,10],order=0","support","1","yes","SYCL"
diff --git a/ggml/src/ggml-sycl/concat.cpp b/ggml/src/ggml-sycl/concat.cpp
index c7683650483..d16215bc91c 100644
--- a/ggml/src/ggml-sycl/concat.cpp
+++ b/ggml/src/ggml-sycl/concat.cpp
@@ -11,9 +11,13 @@
 //
 
 #include "concat.hpp"
-#include "common.hpp"
 
-static void concat_f32_dim0(const float *x, const float *y, float *dst,
+static inline size_t elem_size(ggml_type t) {
+    return ggml_type_size(t) / ggml_blck_size(t);
+}
+
+template <typename T>
+static void concat_T_dim0(const T *x, const T *y, T *dst,
                             const int ne0, const int ne00,
                             const sycl::nd_item<3> &item_ct1) {
   int nidx = item_ct1.get_local_id(2) +
@@ -36,7 +40,8 @@ static void concat_f32_dim0(const float *x, const float *y, float *dst,
   }
 }
 
-static void concat_f32_dim1(const float *x, const float *y, float *dst,
+template <typename T>
+static void concat_T_dim1(const T *x, const T *y, T *dst,
                             const int ne0, const int ne01,
                             const sycl::nd_item<3> &item_ct1) {
   int nidx = item_ct1.get_local_id(2) +
@@ -59,7 +64,8 @@ static void concat_f32_dim1(const float *x, const float *y, float *dst,
   }
 }
 
-static void concat_f32_dim2(const float *x, const float *y, float *dst,
+template <typename T>
+static void concat_T_dim2(const T *x, const T *y, T *dst,
                             const int ne0, const int ne02,
                             const sycl::nd_item<3> &item_ct1) {
   int nidx = item_ct1.get_local_id(2) +
@@ -82,45 +88,35 @@ static void concat_f32_dim2(const float *x, const float *y, float *dst,
   }
 }
 
-static void concat_f32_sycl(const float *x, const float *y, float *dst,
+template <typename T>
+static void concat_T_sycl(const T *x, const T *y, T *dst,
                             int ne00, int ne01, int ne02, int ne0, int ne1,
                             int ne2, int dim, queue_ptr stream) {
   int num_blocks = (ne0 + SYCL_CONCAT_BLOCK_SIZE - 1) / SYCL_CONCAT_BLOCK_SIZE;
   sycl::range<3> gridDim(ne2, ne1, num_blocks);
   switch (dim) {
   case 0:
-    stream->parallel_for(
-        sycl::nd_range<3>(gridDim *
-                              sycl::range<3>(1, 1, SYCL_CONCAT_BLOCK_SIZE),
-                          sycl::range<3>(1, 1, SYCL_CONCAT_BLOCK_SIZE)),
-        [=](sycl::nd_item<3> item_ct1) {
-          concat_f32_dim0(x, y, dst, ne0, ne00, item_ct1);
-        });
-    break;
+      stream->parallel_for(sycl::nd_range<3>(gridDim * sycl::range<3>(1, 1, SYCL_CONCAT_BLOCK_SIZE),
+                                          sycl::range<3>(1, 1, SYCL_CONCAT_BLOCK_SIZE)),
+                        [=](sycl::nd_item<3> item_ct1) { concat_T_dim0<T>(x, y, dst, ne0, ne00, item_ct1); });
+      break;
   case 1:
-    stream->parallel_for(
-        sycl::nd_range<3>(gridDim *
-                              sycl::range<3>(1, 1, SYCL_CONCAT_BLOCK_SIZE),
-                          sycl::range<3>(1, 1, SYCL_CONCAT_BLOCK_SIZE)),
-        [=](sycl::nd_item<3> item_ct1) {
-          concat_f32_dim1(x, y, dst, ne0, ne01, item_ct1);
-        });
-    break;
+      stream->parallel_for(sycl::nd_range<3>(gridDim * sycl::range<3>(1, 1, SYCL_CONCAT_BLOCK_SIZE),
+                                          sycl::range<3>(1, 1, SYCL_CONCAT_BLOCK_SIZE)),
+                        [=](sycl::nd_item<3> item_ct1) { concat_T_dim1<T>(x, y, dst, ne0, ne01, item_ct1); });
+      break;
   // dim >=2 will be dispatched to the default path
   default:
-    stream->parallel_for(
-        sycl::nd_range<3>(gridDim *
-                              sycl::range<3>(1, 1, SYCL_CONCAT_BLOCK_SIZE),
-                          sycl::range<3>(1, 1, SYCL_CONCAT_BLOCK_SIZE)),
-        [=](sycl::nd_item<3> item_ct1) {
-          concat_f32_dim2(x, y, dst, ne0, ne02, item_ct1);
-        });
-    break;
+      stream->parallel_for(sycl::nd_range<3>(gridDim * sycl::range<3>(1, 1, SYCL_CONCAT_BLOCK_SIZE),
+                                          sycl::range<3>(1, 1, SYCL_CONCAT_BLOCK_SIZE)),
+                        [=](sycl::nd_item<3> item_ct1) { concat_T_dim2<T>(x, y, dst, ne0, ne02, item_ct1); });
+      break;
   }
 }
 
 // non-contiguous kernel (slow)
-static void concat_f32_sycl_non_cont(
+template<typename T>
+static void concat_T_sycl_non_cont(
     queue_ptr stream, const char *src0, const char *src1, char *dst,
     int64_t ne00, int64_t ne01, int64_t ne02, int64_t ne03, uint64_t nb00,
     uint64_t nb01, uint64_t nb02, uint64_t nb03, int64_t /*ne10*/,
@@ -137,24 +133,25 @@ static void concat_f32_sycl_non_cont(
       int64_t o[4] = { 0, 0, 0, 0 };
       o[dim]       = dim == 0 ? ne00 : (dim == 1 ? ne01 : (dim == 2 ? ne02 : ne03));
 
-      const float * x;
+      const T * x;
 
       for (int i0 = item_ct1.get_local_id(2); i0 < ne0; i0 += item_ct1.get_local_range(2)) {
           if (i0 < ne00 && i1 < ne01 && i2 < ne02 && i3 < ne03) {
-              x = (const float *) (src0 + (i3) *nb03 + (i2) *nb02 + (i1) *nb01 + (i0) *nb00);
+              x = (const T *) (src0 + (i3) *nb03 + (i2) *nb02 + (i1) *nb01 + (i0) *nb00);
           } else {
-              x = (const float *) (src1 + (i3 - o[3]) * nb13 + (i2 - o[2]) * nb12 + (i1 - o[1]) * nb11 +
+              x = (const T *) (src1 + (i3 - o[3]) * nb13 + (i2 - o[2]) * nb12 + (i1 - o[1]) * nb11 +
                                    (i0 - o[0]) * nb10);
           }
 
-          float *y = (float *)(dst + i3 * nb3 + i2 * nb2 + i1 * nb1 + i0 * nb0);
+          T *y = (T *)(dst + i3 * nb3 + i2 * nb2 + i1 * nb1 + i0 * nb0);
 
           *y = *x;
       }
   });
 }
 
-void ggml_sycl_op_concat(ggml_backend_sycl_context & ctx, ggml_tensor *dst) {
+template <typename T>
+void concat_impl_sycl(ggml_backend_sycl_context & ctx, ggml_tensor *dst) {
     scope_op_debug_print scope_dbg_print(__func__, dst, /*num_src=*/2);
     const ggml_tensor *  src0   = dst->src[0];
     const ggml_tensor *  src1   = dst->src[1];
@@ -163,15 +160,14 @@ void ggml_sycl_op_concat(ggml_backend_sycl_context & ctx, ggml_tensor *dst) {
     const int32_t dim = ((int32_t *) dst->op_params)[0];
 
     if (ggml_is_contiguous(src0) && ggml_is_contiguous(src1)) {
-        const float * src0_d = (const float *) src0->data;
-        const float * src1_d = (const float *) src1->data;
-
-        float * dst_d = (float *) dst->data;
-
+        const T * src0_d = (const T *) src0->data;
+        const T * src1_d = (const T *) src1->data;
+        T * dst_d = (T *) dst->data;
+        size_t type_size = elem_size(dst->type);
         if (dim != 3) {
             for (int i3 = 0; i3 < dst->ne[3]; i3++) {
-                concat_f32_sycl(src0_d + i3 * (src0->nb[3] / 4), src1_d + i3 * (src1->nb[3] / 4),
-                                dst_d + i3 * (dst->nb[3] / 4), src0->ne[0], src0->ne[1], src0->ne[2], dst->ne[0],
+                concat_T_sycl<T>(src0_d + i3 * (src0->nb[3] / type_size), src1_d + i3 * (src1->nb[3] / type_size),
+                                dst_d + i3 * (dst->nb[3] / type_size), src0->ne[0], src0->ne[1], src0->ne[2], dst->ne[0],
                                 dst->ne[1], dst->ne[2], dim, stream);
             }
         } else {
@@ -179,13 +175,28 @@ void ggml_sycl_op_concat(ggml_backend_sycl_context & ctx, ggml_tensor *dst) {
             const size_t size1 = ggml_nbytes(src1);
 
             SYCL_CHECK(CHECK_TRY_ERROR(stream->memcpy(dst_d, src0_d, size0).wait()));
-            SYCL_CHECK(CHECK_TRY_ERROR(stream->memcpy(dst_d + size0 / 4, src1_d, size1).wait()));
+            SYCL_CHECK(CHECK_TRY_ERROR(stream->memcpy(dst_d + size0 / type_size, src1_d, size1).wait()));
         }
     } else {
-        concat_f32_sycl_non_cont(stream, (const char *) src0->data, (const char *) src1->data, (char *) dst->data,
+        concat_T_sycl_non_cont<T>(stream, (const char *) src0->data, (const char *) src1->data, (char *) dst->data,
                                  src0->ne[0], src0->ne[1], src0->ne[2], src0->ne[3], src0->nb[0], src0->nb[1],
                                  src0->nb[2], src0->nb[3], src1->ne[0], src1->ne[1], src1->ne[2], src1->ne[3],
                                  src1->nb[0], src1->nb[1], src1->nb[2], src1->nb[3], dst->ne[0], dst->ne[1], dst->ne[2],
                                  dst->ne[3], dst->nb[0], dst->nb[1], dst->nb[2], dst->nb[3], dim);
     }
 }
+
+void ggml_sycl_op_concat(ggml_backend_sycl_context & ctx, ggml_tensor *dst) {
+
+    switch (dst->type) {
+    case GGML_TYPE_F32:
+        concat_impl_sycl<float>(ctx, dst);
+        break;
+    case GGML_TYPE_I32:
+        concat_impl_sycl<int32_t>(ctx, dst);
+        break;
+    default:
+    GGML_ASSERT(false && "ggml_sycl_op_concat: unsupported type");
+    break;
+    }
+}
diff --git a/ggml/src/ggml-sycl/ggml-sycl.cpp b/ggml/src/ggml-sycl/ggml-sycl.cpp
index c97c5899435..f3b3e365740 100644
--- a/ggml/src/ggml-sycl/ggml-sycl.cpp
+++ b/ggml/src/ggml-sycl/ggml-sycl.cpp
@@ -4534,16 +4534,12 @@ static bool ggml_backend_sycl_device_supports_op(ggml_backend_dev_t dev, const g
                 }
                 return false;
             }
-        case GGML_OP_CONCAT:
-            {
-                ggml_type src0_type = op->src[0]->type;
-                return src0_type != GGML_TYPE_I32 && src0_type != GGML_TYPE_I16;
-            }
         case GGML_OP_REPEAT_BACK:
             {
                 ggml_type src0_type = op->src[0]->type;
                 return src0_type == GGML_TYPE_F32;
             }
+        case GGML_OP_CONCAT:
         case GGML_OP_DUP:
         case GGML_OP_ARGMAX:
         case GGML_OP_NONE:

From 4882f0ff786088871b3ab3abd9e525a4213ee218 Mon Sep 17 00:00:00 2001
From: Xuan-Son Nguyen <son@huggingface.co>
Date: Thu, 6 Nov 2025 11:02:54 +0100
Subject: [PATCH 100/185] clip: implement minicpm-v sinusoidal embd using GGML
 (#17036)

* clip: implement minicpm-v sinusoidal embd using GGML

* fix repeat op
---
 tools/mtmd/clip.cpp | 174 ++++++++++++++++----------------------------
 1 file changed, 62 insertions(+), 112 deletions(-)

diff --git a/tools/mtmd/clip.cpp b/tools/mtmd/clip.cpp
index 16781fb1952..d1423b67f98 100644
--- a/tools/mtmd/clip.cpp
+++ b/tools/mtmd/clip.cpp
@@ -1083,16 +1083,24 @@ struct clip_graph {
     }
 
     ggml_cgraph * build_minicpmv() {
-        const int batch_size = 1;
-
         GGML_ASSERT(model.class_embedding == nullptr);
-        const int n_pos = n_patches;
+        const int n_pos       = n_patches;
+        const int n_embd_proj = clip_n_mmproj_embd(ctx);
 
         // position embeddings for the projector (not for ViT)
-        int n_output_dim = clip_n_mmproj_embd(ctx);
-        ggml_tensor * pos_embed = ggml_new_tensor_3d(ctx0, GGML_TYPE_F32, n_output_dim, n_pos, batch_size);
-        ggml_set_name(pos_embed, "pos_embed");
-        ggml_set_input(pos_embed);
+        // see: https://huggingface.co/openbmb/MiniCPM-o-2_6/blob/main/resampler.py#L70
+        // base frequency omega
+        ggml_tensor * omega = ggml_new_tensor_1d(ctx0, GGML_TYPE_F32, n_embd_proj / 4);
+        ggml_set_name(omega, "omega");
+        ggml_set_input(omega);
+
+        // 2D input positions (using float for sinusoidal embeddings)
+        ggml_tensor * pos_h = ggml_new_tensor_2d(ctx0, GGML_TYPE_F32, 1, n_pos);
+        ggml_set_name(pos_h, "pos_h");
+        ggml_set_input(pos_h);
+        ggml_tensor * pos_w = ggml_new_tensor_2d(ctx0, GGML_TYPE_F32, 1, n_pos);
+        ggml_set_name(pos_w, "pos_w");
+        ggml_set_input(pos_w);
 
         // for selecting learned pos embd, used by ViT
         struct ggml_tensor * positions = ggml_new_tensor_1d(ctx0, GGML_TYPE_I32, n_pos);
@@ -1103,7 +1111,7 @@ struct clip_graph {
 
         ggml_tensor * inp = build_inp();
         ggml_tensor * embeddings = build_vit(
-                                inp, n_patches,
+                                inp, n_pos,
                                 NORM_TYPE_NORMAL,
                                 hparams.ffn_op,
                                 learned_pos_embd,
@@ -1115,17 +1123,39 @@ struct clip_graph {
         ggml_tensor * v = ggml_mul_mat(ctx0, model.mm_model_kv_proj, embeddings);
 
         // norm
-        q = build_norm(q, model.mm_model_ln_q_w, model.mm_model_ln_q_b, NORM_TYPE_NORMAL, eps, -1);
+        q = build_norm(q, model.mm_model_ln_q_w,  model.mm_model_ln_q_b,  NORM_TYPE_NORMAL, eps, -1);
         v = build_norm(v, model.mm_model_ln_kv_w, model.mm_model_ln_kv_b, NORM_TYPE_NORMAL, eps, -1);
 
+        // calculate sinusoidal pos embd
+        ggml_tensor * pos_embed = nullptr;
+        {
+            // outer product
+            ggml_tensor * omega_b = ggml_repeat_4d(ctx0, omega, omega->ne[0], n_pos, 1, 1); // n_pos rows
+            ggml_tensor * theta_x = ggml_mul(ctx0, omega_b, pos_w);
+            ggml_tensor * theta_y = ggml_mul(ctx0, omega_b, pos_h);
+            // sin and cos
+            ggml_tensor * pos_embd_x = ggml_concat(
+                ctx0,
+                ggml_sin(ctx0, theta_x),
+                ggml_cos(ctx0, theta_x),
+                0 // concat on first dim
+            );
+            ggml_tensor * pos_embd_y = ggml_concat(
+                ctx0,
+                ggml_sin(ctx0, theta_y),
+                ggml_cos(ctx0, theta_y),
+                0 // concat on first dim
+            );
+            pos_embed = ggml_concat(ctx0, pos_embd_x, pos_embd_y, 0);
+        }
+
         // k = v + pos_embed
         ggml_tensor * k = ggml_add(ctx0, v, pos_embed);
 
         // attention
         {
-            int n_embd = clip_n_mmproj_embd(ctx);
             const int d_head = 128;
-            int n_head = n_embd/d_head;
+            int n_head = n_embd_proj/d_head;
             // Use actual config value if available, otherwise fall back to hardcoded values
             int num_query = ctx->model.hparams.minicpmv_query_num;
             ggml_tensor * Q = ggml_add(ctx0,
@@ -4564,92 +4594,6 @@ int clip_n_output_tokens(const struct clip_ctx * ctx, struct clip_image_f32 * im
     return n_patches;
 }
 
-static std::vector<std::vector<std::vector<float>>> get_1d_sincos_pos_embed_from_grid_new(int embed_dim, const std::vector<std::vector<float>> & pos) {
-    assert(embed_dim % 2 == 0);
-    int H = pos.size();
-    int W = pos[0].size();
-
-    std::vector<float> omega(embed_dim / 2);
-    for (int i = 0; i < embed_dim / 2; ++i) {
-        omega[i] = 1.0 / pow(10000.0, static_cast<float>(i) / (embed_dim / 2));
-    }
-
-    std::vector<std::vector<std::vector<float>>> emb(H, std::vector<std::vector<float>>(W, std::vector<float>(embed_dim)));
-    for (int h = 0; h < H; ++h) {
-        for (int w = 0; w < W; ++w) {
-            for (int d = 0; d < embed_dim / 2; ++d) {
-                float out_value = pos[h][w] * omega[d];
-                emb[h][w][d] = sin(out_value);
-                emb[h][w][d + embed_dim / 2] = cos(out_value);
-            }
-        }
-    }
-
-    return emb;
-}
-
-static std::vector<std::vector<std::vector<float>>> get_2d_sincos_pos_embed_from_grid(int embed_dim, const std::vector<std::vector<std::vector<float>>> & grid) {
-    assert(embed_dim % 2 == 0);
-    std::vector<std::vector<std::vector<float>>> emb_h = get_1d_sincos_pos_embed_from_grid_new(embed_dim / 2, grid[0]); // (H, W, D/2)
-    std::vector<std::vector<std::vector<float>>> emb_w = get_1d_sincos_pos_embed_from_grid_new(embed_dim / 2, grid[1]); // (H, W, D/2)
-
-    int H = emb_h.size();
-    int W = emb_h[0].size();
-    std::vector<std::vector<std::vector<float>>> emb(H, std::vector<std::vector<float>>(W, std::vector<float>(embed_dim)));
-
-    for (int h = 0; h < H; ++h) {
-        for (int w = 0; w < W; ++w) {
-            for (int d = 0; d < embed_dim / 2; ++d) {
-                emb[h][w][d] = emb_h[h][w][d];
-                emb[h][w][d + embed_dim / 2] = emb_w[h][w][d];
-            }
-        }
-    }
-    return emb;
-}
-
-static std::vector<std::vector<float>> get_2d_sincos_pos_embed(int embed_dim, const std::pair<int, int> image_size) {
-    int grid_h_size = image_size.first;
-    int grid_w_size = image_size.second;
-
-    std::vector<float> grid_h(grid_h_size);
-    std::vector<float> grid_w(grid_w_size);
-
-    for (int i = 0; i < grid_h_size; ++i) {
-        grid_h[i] = static_cast<float>(i);
-    }
-    for (int i = 0; i < grid_w_size; ++i) {
-        grid_w[i] = static_cast<float>(i);
-    }
-
-    std::vector<std::vector<float>> grid(grid_h_size, std::vector<float>(grid_w_size));
-    for (int h = 0; h < grid_h_size; ++h) {
-        for (int w = 0; w < grid_w_size; ++w) {
-            grid[h][w] = grid_w[w];
-        }
-    }
-    std::vector<std::vector<std::vector<float>>> grid_2d = {grid, grid};
-    for (int h = 0; h < grid_h_size; ++h) {
-        for (int w = 0; w < grid_w_size; ++w) {
-            grid_2d[0][h][w] = grid_h[h];
-            grid_2d[1][h][w] = grid_w[w];
-        }
-    }
-
-    std::vector<std::vector<std::vector<float>>> pos_embed_3d = get_2d_sincos_pos_embed_from_grid(embed_dim, grid_2d);
-
-    int H = image_size.first;
-    int W = image_size.second;
-    std::vector<std::vector<float>> pos_embed_2d(H * W, std::vector<float>(embed_dim));
-    for (int h = 0; h < H; ++h) {
-        for (int w = 0; w < W; ++w) {
-            pos_embed_2d[w * H + h] = pos_embed_3d[h][w];
-        }
-    }
-
-    return pos_embed_2d;
-}
-
 bool clip_image_encode(struct clip_ctx * ctx, const int n_threads, clip_image_f32 * img, float * vec) {
     clip_image_f32_batch imgs;
     clip_image_f32_ptr img_copy(clip_image_f32_init());
@@ -4788,22 +4732,28 @@ bool clip_image_batch_encode(clip_ctx * ctx, const int n_threads, const clip_ima
                 }
                 set_input_i32("positions", positions);
 
-                // inspired from resampler of Qwen-VL:
-                //    -> https://huggingface.co/Qwen/Qwen-VL/tree/main
-                //    -> https://huggingface.co/Qwen/Qwen-VL/blob/0547ed36a86561e2e42fecec8fd0c4f6953e33c4/visual.py#L23
-                int embed_dim = clip_n_mmproj_embd(ctx);
-
-                // TODO @ngxson : this is very inefficient, can we do this using ggml_sin and ggml_cos?
-                auto pos_embed_t = get_2d_sincos_pos_embed(embed_dim, std::make_pair(pos_w, pos_h));
-
-                std::vector<float> pos_embed(embed_dim * pos_w * pos_h);
-                for(int i = 0; i < pos_w * pos_h; ++i){
-                    for(int j = 0; j < embed_dim; ++j){
-                        pos_embed[i * embed_dim + j] = pos_embed_t[i][j];
-                    }
+                // inputs for resampler projector
+                // set the 2D positions (using float for sinusoidal embedding)
+                int n_patches_per_col = image_size_width / patch_size;
+                std::vector<float> pos_data(n_pos);
+                // dimension H
+                for (int i = 0; i < n_pos; i++) {
+                    pos_data[i] = static_cast<float>(i / n_patches_per_col);
                 }
-
-                set_input_f32("pos_embed", pos_embed);
+                set_input_f32("pos_h", pos_data);
+                // dimension W
+                for (int i = 0; i < n_pos; i++) {
+                    pos_data[i] = static_cast<float>(i % n_patches_per_col);
+                }
+                set_input_f32("pos_w", pos_data);
+                // base frequency omega
+                const float base_freq   = 10000.0f;
+                const int   n_embd_proj = clip_n_mmproj_embd(ctx);
+                std::vector<float> omega(n_embd_proj / 4);
+                for (int i = 0; i < n_embd_proj / 4; ++i) {
+                    omega[i] = 1.0f / std::pow(base_freq, static_cast<float>(i) / (n_embd_proj / 4));
+                }
+                set_input_f32("omega", omega);
             } break;
         case PROJECTOR_TYPE_QWEN2VL:
         case PROJECTOR_TYPE_QWEN3VL:

From b7f9010d24766792d8887c227a883ed3b315d2be Mon Sep 17 00:00:00 2001
From: Georgi Gerganov <ggerganov@gmail.com>
Date: Thu, 6 Nov 2025 12:09:29 +0200
Subject: [PATCH 101/185] server : disable checkpoints with mtmd (#17045)

---
 tools/server/server.cpp | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/tools/server/server.cpp b/tools/server/server.cpp
index f5089bef24a..0e1a9afc869 100644
--- a/tools/server/server.cpp
+++ b/tools/server/server.cpp
@@ -3832,7 +3832,9 @@ struct server_context {
                             // the largest pos_min required for a checkpoint to be useful
                             const auto pos_min_thold = std::max(0, n_past - n_swa);
 
-                            if (n_past > 0 && n_past < slot.prompt.n_tokens()) {
+                            // note: disallow with mtmd contexts for now
+                            //       https://github.com/ggml-org/llama.cpp/issues/17043
+                            if (!mctx && n_past > 0 && n_past < slot.prompt.n_tokens()) {
                                 const auto pos_min = llama_memory_seq_pos_min(llama_get_memory(ctx), slot.id);
                                 if (pos_min == -1) {
                                     SLT_ERR(slot, "n_past = %d, slot.prompt.tokens.size() = %d, seq_id = %d, pos_min = %d\n", n_past, (int) slot.prompt.tokens.size(), slot.id, pos_min);

From 5b180c3d60f3df61cd9955bc5c69e64537958f92 Mon Sep 17 00:00:00 2001
From: Georgi Gerganov <ggerganov@gmail.com>
Date: Thu, 6 Nov 2025 14:45:10 +0200
Subject: [PATCH 102/185] metal : initial Metal4 tensor API support (#16634)

* metal : rework mat-mat multiplication

* metal : initial Metal4 support

* cont

* metal : detect tensor support

* cont : better ifdefs

* metal : support tensors in mul_mm_id

* metal : add env for disabling tensor API

* tests : restore

* metal : remove unused constants

* metal : fix check for bfloat tensor support

* cont : handle API incompatibilities

* cont : handle even more incompatibilities

* metal : use tensor API only on M5 and later
---
 ggml/src/ggml-metal/ggml-metal-context.m |   5 +-
 ggml/src/ggml-metal/ggml-metal-device.h  |   5 +-
 ggml/src/ggml-metal/ggml-metal-device.m  | 211 ++++++++-
 ggml/src/ggml-metal/ggml-metal.metal     | 521 +++++++++++++++++------
 4 files changed, 606 insertions(+), 136 deletions(-)

diff --git a/ggml/src/ggml-metal/ggml-metal-context.m b/ggml/src/ggml-metal/ggml-metal-context.m
index 052efb7ace5..b8d35b78ade 100644
--- a/ggml/src/ggml-metal/ggml-metal-context.m
+++ b/ggml/src/ggml-metal/ggml-metal-context.m
@@ -35,7 +35,6 @@
     // additional, inference-time compiled pipelines
     ggml_metal_pipelines_t pipelines_ext;
 
-    bool use_bfloat;
     bool use_fusion;
     bool use_concurrency;
     bool use_graph_optimize;
@@ -121,11 +120,10 @@ ggml_metal_t ggml_metal_init(ggml_metal_device_t dev) {
         }
     }
 
-    const struct ggml_metal_device_props * props_dev = ggml_metal_device_get_props(dev);
+    //const struct ggml_metal_device_props * props_dev = ggml_metal_device_get_props(dev);
 
     res->d_queue = dispatch_queue_create("ggml-metal", DISPATCH_QUEUE_CONCURRENT);
 
-    res->use_bfloat      = props_dev->has_bfloat;
     res->use_fusion      = getenv("GGML_METAL_FUSION_DISABLE") == nil;
     res->use_concurrency = getenv("GGML_METAL_CONCURRENCY_DISABLE") == nil;
 
@@ -147,7 +145,6 @@ ggml_metal_t ggml_metal_init(ggml_metal_device_t dev) {
 
     memset(res->fuse_cnt, 0, sizeof(res->fuse_cnt));
 
-    GGML_LOG_INFO("%s: use bfloat         = %s\n", __func__, res->use_bfloat         ? "true" : "false");
     GGML_LOG_INFO("%s: use fusion         = %s\n", __func__, res->use_fusion         ? "true" : "false");
     GGML_LOG_INFO("%s: use concurrency    = %s\n", __func__, res->use_concurrency    ? "true" : "false");
     GGML_LOG_INFO("%s: use graph optimize = %s\n", __func__, res->use_graph_optimize ? "true" : "false");
diff --git a/ggml/src/ggml-metal/ggml-metal-device.h b/ggml/src/ggml-metal/ggml-metal-device.h
index 4d582974818..cb27dca9892 100644
--- a/ggml/src/ggml-metal/ggml-metal-device.h
+++ b/ggml/src/ggml-metal/ggml-metal-device.h
@@ -95,7 +95,9 @@ void ggml_metal_encoder_end_encoding(ggml_metal_encoder_t encoder);
 
 typedef struct ggml_metal_library * ggml_metal_library_t;
 
-ggml_metal_library_t ggml_metal_library_init(ggml_metal_device_t dev);
+ggml_metal_library_t ggml_metal_library_init            (ggml_metal_device_t dev);
+ggml_metal_library_t ggml_metal_library_init_from_source(ggml_metal_device_t dev, const char * source, bool verbose);
+
 void ggml_metal_library_free(ggml_metal_library_t lib);
 
 ggml_metal_pipeline_t ggml_metal_library_get_pipeline    (ggml_metal_library_t lib, const char * name);
@@ -193,6 +195,7 @@ struct ggml_metal_device_props {
     bool has_simdgroup_mm;
     bool has_unified_memory;
     bool has_bfloat;
+    bool has_tensor;
     bool use_residency_sets;
     bool use_shared_buffers;
 
diff --git a/ggml/src/ggml-metal/ggml-metal-device.m b/ggml/src/ggml-metal/ggml-metal-device.m
index 0cadd19a30f..606cfd0a5e2 100644
--- a/ggml/src/ggml-metal/ggml-metal-device.m
+++ b/ggml/src/ggml-metal/ggml-metal-device.m
@@ -21,8 +21,9 @@
 #define GGML_METAL_HAS_RESIDENCY_SETS 1
 #endif
 
-// overload of MTLGPUFamilyMetal3 (not available in some environments)
+// overload of MTLGPUFamilyMetalX (not available in some environments)
 static const NSInteger MTLGPUFamilyMetal3_GGML = 5001;
+static const NSInteger MTLGPUFamilyMetal4_GGML = 5002;
 
 // virtual address for GPU memory allocations
 static atomic_uintptr_t g_addr_device = 0x000000400ULL;
@@ -261,6 +262,10 @@ ggml_metal_library_t ggml_metal_library_init(ggml_metal_device_t dev) {
                     [prep setObject:@"1" forKey:@"GGML_METAL_HAS_BF16"];
                 }
 
+                if (ggml_metal_device_get_props(dev)->has_tensor) {
+                    [prep setObject:@"1" forKey:@"GGML_METAL_HAS_TENSOR"];
+                }
+
 #if GGML_METAL_EMBED_LIBRARY
                 [prep setObject:@"1" forKey:@"GGML_METAL_EMBED_LIBRARY"];
 #endif
@@ -298,6 +303,72 @@ ggml_metal_library_t ggml_metal_library_init(ggml_metal_device_t dev) {
     return res;
 }
 
+ggml_metal_library_t ggml_metal_library_init_from_source(ggml_metal_device_t dev, const char * source, bool verbose) {
+    if (source == NULL) {
+        GGML_LOG_ERROR("%s: source is NULL\n", __func__);
+        return NULL;
+    }
+
+    id<MTLDevice> device = ggml_metal_device_get_obj(dev);
+    id<MTLLibrary> library = nil;
+    NSError * error = nil;
+
+    const int64_t t_start = ggml_time_us();
+
+    NSString * src = [[NSString alloc] initWithBytes:source
+                                              length:strlen(source)
+                                            encoding:NSUTF8StringEncoding];
+    if (!src) {
+        GGML_LOG_ERROR("%s: failed to create NSString from source\n", __func__);
+        return NULL;
+    }
+
+    @autoreleasepool {
+        NSMutableDictionary * prep = [NSMutableDictionary dictionary];
+
+        MTLCompileOptions * options = [MTLCompileOptions new];
+        options.preprocessorMacros = prep;
+
+        library = [device newLibraryWithSource:src options:options error:&error];
+        if (error) {
+            if (verbose) {
+                GGML_LOG_ERROR("%s: error compiling source: %s\n", __func__, [[error description] UTF8String]);
+            } else {
+                GGML_LOG_ERROR("%s: error compiling source\n", __func__);
+            }
+            library = nil;
+        }
+
+        [options release];
+    }
+
+    [src release];
+
+    if (!library) {
+        if (verbose) {
+            GGML_LOG_ERROR("%s: failed to create Metal library from source\n", __func__);
+        }
+
+        return NULL;
+    }
+
+    if (verbose) {
+        GGML_LOG_INFO("%s: compiled in %.3f sec\n", __func__, (ggml_time_us() - t_start) / 1e6);
+    }
+
+    ggml_metal_library_t res = calloc(1, sizeof(struct ggml_metal_library));
+    if (!res) {
+        GGML_LOG_ERROR("%s: calloc failed\n", __func__);
+        return NULL;
+    }
+
+    res->obj       = library;
+    res->device    = device;
+    res->pipelines = ggml_metal_pipelines_init();
+
+    return res;
+}
+
 void ggml_metal_library_free(ggml_metal_library_t lib) {
     if (!lib) {
         return;
@@ -345,9 +416,9 @@ ggml_metal_pipeline_t ggml_metal_library_compile_pipeline(ggml_metal_library_t l
         if (!mtl_function) {
             ggml_critical_section_end();
 
-            GGML_LOG_ERROR("%s: error: failed to compile pipeline: base = '%s', name = '%s'\n", __func__, base, name);
+            GGML_LOG_ERROR("%s: failed to compile pipeline: base = '%s', name = '%s'\n", __func__, base, name);
             if (error) {
-                GGML_LOG_ERROR("%s: error: %s\n", __func__, [[error description] UTF8String]);
+                GGML_LOG_ERROR("%s: %s\n", __func__, [[error description] UTF8String]);
             }
 
             return nil;
@@ -355,13 +426,21 @@ ggml_metal_pipeline_t ggml_metal_library_compile_pipeline(ggml_metal_library_t l
 
         res->obj = [lib->device newComputePipelineStateWithFunction:mtl_function error:&error];
 
-        ggml_metal_pipelines_add(lib->pipelines, name, res);
-
         [mtl_function release];
 
         GGML_LOG_DEBUG("%s: loaded %-40s %16p | th_max = %4d | th_width = %4d\n", __func__, name, (void *) res->obj,
                 (int) res->obj.maxTotalThreadsPerThreadgroup,
                 (int) res->obj.threadExecutionWidth);
+
+        if (res->obj.maxTotalThreadsPerThreadgroup == 0 || res->obj.threadExecutionWidth == 0) {
+            ggml_critical_section_end();
+
+            GGML_LOG_ERROR("%s: incompatible pipeline %s\n", __func__, name);
+
+            return nil;
+        }
+
+        ggml_metal_pipelines_add(lib->pipelines, name, res);
     }
 
     ggml_critical_section_end();
@@ -469,6 +548,126 @@ ggml_metal_device_t ggml_metal_device_init(void) {
 
             dev->props.has_bfloat  = [dev->mtl_device supportsFamily:MTLGPUFamilyMetal3_GGML];
             dev->props.has_bfloat |= [dev->mtl_device supportsFamily:MTLGPUFamilyApple6];
+            if (getenv("GGML_METAL_BF16_DISABLE") != NULL) {
+                dev->props.has_bfloat = false;
+            }
+
+            dev->props.has_tensor = [dev->mtl_device supportsFamily:MTLGPUFamilyMetal4_GGML];
+            if (getenv("GGML_METAL_TENSOR_DISABLE") != NULL) {
+                dev->props.has_tensor = false;
+            }
+
+            // note: disable the tensor API by default for old chips because with the current implementation it is not useful
+            // - M2 Ultra:   ~5% slower
+            // - M4, M4 Max: no significant difference
+            //
+            // TODO: try to update the tensor API kernels to at least match the simdgroup performance
+            if (getenv("GGML_METAL_TENSOR_ENABLE") == NULL &&
+                ![[dev->mtl_device name] containsString:@"M5"] &&
+                ![[dev->mtl_device name] containsString:@"M6"]) {
+                GGML_LOG_WARN("%s: tensor API disabled for pre-M5 device\n", __func__);
+                dev->props.has_tensor = false;
+            }
+
+            // double-check that the tensor API compiles
+            if (dev->props.has_tensor) {
+                const char * src_tensor_f16 = "\n"
+                    "#include <metal_stdlib> \n"
+                    "#include <metal_tensor> \n"
+                    "#include <MetalPerformancePrimitives/MetalPerformancePrimitives.h> \n"
+                    " \n"
+                    "using namespace metal; \n"
+                    "using namespace mpp::tensor_ops; \n"
+                    " \n"
+                    "kernel void dummy_kernel( \n"
+                    "    tensor<device  half, dextents<int32_t, 2>> A [[buffer(0)]], \n"
+                    "    tensor<device  half, dextents<int32_t, 2>> B [[buffer(1)]], \n"
+                    "    device float * C [[buffer(2)]], \n"
+                    "    uint2 tgid [[threadgroup_position_in_grid]]) \n"
+                    "{ \n"
+                    "    auto tA = A.slice(0, (int)tgid.y); \n"
+                    "    auto tB = B.slice((int)tgid.x, 0); \n"
+                    " \n"
+                    "    matmul2d< \n"
+                    "        matmul2d_descriptor(8, 8, dynamic_extent), \n"
+                    "        execution_simdgroups<4>> mm; \n"
+                    " \n"
+                    "    auto cT = mm.get_destination_cooperative_tensor<decltype(tA), decltype(tB), float>(); \n"
+                    " \n"
+                    "    auto sA = tA.slice(0, 0); \n"
+                    "    auto sB = tB.slice(0, 0); \n"
+                    "    mm.run(sB, sA, cT); \n"
+                    " \n"
+                    "    auto tC = tensor<device float, dextents<int32_t, 2>, tensor_inline>(C, dextents<int32_t, 2>(4, 4)); \n"
+                    " \n"
+                    "    cT.store(tC); \n"
+                    "}";
+
+                GGML_LOG_INFO("%s: testing tensor API for f16 support\n", __func__);
+                ggml_metal_library_t lib = ggml_metal_library_init_from_source(dev, src_tensor_f16, false);
+                if (lib == NULL) {
+                    GGML_LOG_WARN("%s: - the tensor API is not supported in this environment - disabling\n", __func__);
+                    dev->props.has_tensor = false;
+                } else {
+                    ggml_metal_pipeline_t ppl = ggml_metal_library_compile_pipeline(lib, "dummy_kernel", "dummy_kernel", nil);
+                    if (!ppl) {
+                        GGML_LOG_WARN("%s: - the tensor API is not supported in this environment - disabling\n", __func__);
+                        dev->props.has_tensor = false;
+                    }
+
+                    ggml_metal_library_free(lib);
+                }
+            }
+
+            // try to compile a dummy kernel to determine if the tensor API is supported for bfloat
+            if (dev->props.has_tensor && dev->props.has_bfloat) {
+                const char * src_tensor_bf16 = "\n"
+                    "#include <metal_stdlib> \n"
+                    "#include <metal_tensor> \n"
+                    "#include <MetalPerformancePrimitives/MetalPerformancePrimitives.h> \n"
+                    " \n"
+                    "using namespace metal; \n"
+                    "using namespace mpp::tensor_ops; \n"
+                    " \n"
+                    "kernel void dummy_kernel( \n"
+                    "    tensor<device bfloat, dextents<int32_t, 2>> A [[buffer(0)]], \n"
+                    "    tensor<device bfloat, dextents<int32_t, 2>> B [[buffer(1)]], \n"
+                    "    device float * C [[buffer(2)]], \n"
+                    "    uint2 tgid [[threadgroup_position_in_grid]]) \n"
+                    "{ \n"
+                    "    auto tA = A.slice(0, (int)tgid.y); \n"
+                    "    auto tB = B.slice((int)tgid.x, 0); \n"
+                    " \n"
+                    "    matmul2d< \n"
+                    "        matmul2d_descriptor(8, 8, dynamic_extent), \n"
+                    "        execution_simdgroups<4>> mm; \n"
+                    " \n"
+                    "    auto cT = mm.get_destination_cooperative_tensor<decltype(tA), decltype(tB), float>(); \n"
+                    " \n"
+                    "    auto sA = tA.slice(0, 0); \n"
+                    "    auto sB = tB.slice(0, 0); \n"
+                    "    mm.run(sB, sA, cT); \n"
+                    " \n"
+                    "    auto tC = tensor<device float, dextents<int32_t, 2>, tensor_inline>(C, dextents<int32_t, 2>(4, 4)); \n"
+                    " \n"
+                    "    cT.store(tC); \n"
+                    "}";
+
+                GGML_LOG_INFO("%s: testing tensor API for bfloat support\n", __func__);
+                ggml_metal_library_t lib = ggml_metal_library_init_from_source(dev, src_tensor_bf16, false);
+                if (lib == NULL) {
+                    GGML_LOG_WARN("%s: - the tensor API does not support bfloat - disabling bfloat support\n", __func__);
+                    dev->props.has_bfloat = false;
+                } else {
+                    ggml_metal_pipeline_t ppl = ggml_metal_library_compile_pipeline(lib, "dummy_kernel", "dummy_kernel", nil);
+                    if (!ppl) {
+                        GGML_LOG_WARN("%s: - the tensor API does not support bfloat - disabling bfloat support\n", __func__);
+                        dev->props.has_bfloat = false;
+                    }
+
+                    ggml_metal_library_free(lib);
+                }
+            }
 
             dev->props.use_residency_sets = true;
 #if defined(GGML_METAL_HAS_RESIDENCY_SETS)
@@ -476,7 +675,6 @@ ggml_metal_device_t ggml_metal_device_init(void) {
 #endif
 
             dev->props.use_shared_buffers = dev->props.has_unified_memory;
-
             if (getenv("GGML_METAL_SHARED_BUFFERS_DISABLE") != NULL) {
                 dev->props.use_shared_buffers = false;
             }
@@ -529,6 +727,7 @@ ggml_metal_device_t ggml_metal_device_init(void) {
             GGML_LOG_INFO("%s: simdgroup matrix mul. = %s\n", __func__, dev->props.has_simdgroup_mm        ? "true" : "false");
             GGML_LOG_INFO("%s: has unified memory    = %s\n", __func__, dev->props.has_unified_memory      ? "true" : "false");
             GGML_LOG_INFO("%s: has bfloat            = %s\n", __func__, dev->props.has_bfloat              ? "true" : "false");
+            GGML_LOG_INFO("%s: has tensor            = %s\n", __func__, dev->props.has_tensor              ? "true" : "false");
             GGML_LOG_INFO("%s: use residency sets    = %s\n", __func__, dev->props.use_residency_sets      ? "true" : "false");
             GGML_LOG_INFO("%s: use shared buffers    = %s\n", __func__, dev->props.use_shared_buffers      ? "true" : "false");
 
diff --git a/ggml/src/ggml-metal/ggml-metal.metal b/ggml/src/ggml-metal/ggml-metal.metal
index 424c400f24b..cea535ade74 100644
--- a/ggml/src/ggml-metal/ggml-metal.metal
+++ b/ggml/src/ggml-metal/ggml-metal.metal
@@ -9,6 +9,12 @@ __embed_ggml-common.h__
 
 #include <metal_stdlib>
 
+#ifdef GGML_METAL_HAS_TENSOR
+#include <metal_tensor>
+
+#include <MetalPerformancePrimitives/MetalPerformancePrimitives.h>
+#endif
+
 using namespace metal;
 
 #define MAX(x, y) ((x) > (y) ? (x) : (y))
@@ -1742,7 +1748,7 @@ kernel void kernel_op_sum_f32(
 
     float sumf = 0;
 
-    for (int64_t i0 = tpitg.x; i0 < args.np; i0 += ntg.x) {
+    for (uint64_t i0 = tpitg.x; i0 < args.np; i0 += ntg.x) {
         sumf += src0[i0];
     }
 
@@ -5467,6 +5473,7 @@ template [[host_name("kernel_flash_attn_ext_q8_0_dk576_dv512")]] kernel flash_at
 
 #undef FA_TYPES
 #undef FA_TYPES_BF
+#undef FA_TYPES_F32
 
 constant bool FC_flash_attn_ext_vec_has_mask  [[function_constant(FC_FLASH_ATTN_EXT_VEC + 0)]];
 constant bool FC_flash_attn_ext_vec_has_sinks [[function_constant(FC_FLASH_ATTN_EXT_VEC + 1)]];
@@ -6088,6 +6095,7 @@ template [[host_name("kernel_flash_attn_ext_vec_q5_1_dk576_dv512")]] kernel flas
 template [[host_name("kernel_flash_attn_ext_vec_q8_0_dk576_dv512")]] kernel flash_attn_ext_vec_t kernel_flash_attn_ext_vec<FA_TYPES,     block_q8_0, 8, dequantize_q8_0_t4, block_q8_0,  8, dequantize_q8_0_t4, 576, 512, 2>;
 
 #undef FA_TYPES
+#undef FA_TYPES_F32
 
 constant int32_t FC_flash_attn_ext_vec_reduce_DV  [[function_constant(FC_FLASH_ATTN_EXT_VEC_REDUCE + 0)]];
 constant int32_t FC_flash_attn_ext_vec_reduce_NWG [[function_constant(FC_FLASH_ATTN_EXT_VEC_REDUCE + 1)]];
@@ -8141,17 +8149,6 @@ kernel void kernel_set_rows_f(
 constant bool FC_mul_mm_bc_inp [[function_constant(FC_MUL_MM + 0)]];
 constant bool FC_mul_mm_bc_out [[function_constant(FC_MUL_MM + 1)]];
 
-#define BLOCK_SIZE_M 64 // 8 simdgroup matrices from matrix A
-#define BLOCK_SIZE_N 32 // 4 simdgroup matrices from matrix B
-#define BLOCK_SIZE_K 32
-#define THREAD_MAT_M 4 // each thread take 4 simdgroup matrices from matrix A
-#define THREAD_MAT_N 2 // each thread take 2 simdgroup matrices from matrix B
-#define THREAD_PER_BLOCK 128
-#define THREAD_PER_ROW 2 // 2 thread for each row in matrix A to load numbers
-#define THREAD_PER_COL 4 // 4 thread for each row in matrix B to load numbers
-#define SG_MAT_SIZE 64 // simdgroup matrix is of shape 8x8
-#define SG_MAT_ROW 8
-
 // each block_q contains 16*nl weights
 template<typename S0, typename S0_4x4, typename S0_8x8, typename S1, typename S1_2x4, typename S1_8x8, typename block_q, short nl, void (*dequantize_func)(device const block_q *, short, thread S0_4x4 &), typename T0, typename T0_4x4, typename T1, typename T1_2x4>
 kernel void kernel_mul_mm(
@@ -8167,18 +8164,48 @@ kernel void kernel_mul_mm(
     threadgroup S0 * sa = (threadgroup S0 *)(shmem);
     threadgroup S1 * sb = (threadgroup S1 *)(shmem + 4096);
 
-    const int r0 = tgpig.y;
-    const int r1 = tgpig.x;
+    threadgroup float * sc = (threadgroup float *)(shmem);
+
+    constexpr int NR0 = 64;
+    constexpr int NR1 = 32;
+
+    constexpr int NK  = 32;
+    constexpr int NL0 = NK/16;
+    constexpr int NL1 = NK/8;
+
     const int im = tgpig.z;
+    const int r0 = tgpig.y*NR0;
+    const int r1 = tgpig.x*NR1;
 
     // if this block is of 64x32 shape or smaller
-    const short n_rows = (args.ne0 - r0*BLOCK_SIZE_M < BLOCK_SIZE_M) ? (args.ne0 - r0*BLOCK_SIZE_M) : BLOCK_SIZE_M;
-    const short n_cols = (args.ne1 - r1*BLOCK_SIZE_N < BLOCK_SIZE_N) ? (args.ne1 - r1*BLOCK_SIZE_N) : BLOCK_SIZE_N;
+    const short nr0 = (args.ne0 - r0 < NR0) ? (args.ne0 - r0) : NR0;
+    const short nr1 = (args.ne1 - r1 < NR1) ? (args.ne1 - r1) : NR1;
 
     // a thread shouldn't load data outside of the matrix
-    const short thread_row = ((short)tiitg/THREAD_PER_ROW) < n_rows ? ((short)tiitg/THREAD_PER_ROW) : n_rows - 1;
-    const short thread_col = ((short)tiitg/THREAD_PER_COL) < n_cols ? ((short)tiitg/THREAD_PER_COL) : n_cols - 1;
+    const short lr0 = ((short)tiitg/NL0) < nr0 ? ((short)tiitg/NL0) : nr0 - 1; // 0 .. 63
+    const short lr1 = ((short)tiitg/NL1) < nr1 ? ((short)tiitg/NL1) : nr1 - 1; // 0 .. 31
+
+    const short il0 = (tiitg % NL0);
+
+    short il = il0;
+
+    const int i12 = im%args.ne12;
+    const int i13 = im/args.ne12;
+
+    const uint64_t offset0 = (i12/args.r2)*args.nb02 + (i13/args.r3)*args.nb03;
+    const short    offset1 = il0/nl;
+
+    device const block_q * x = (device const block_q *)(src0 + args.nb01*(r0 + lr0) + offset0) + offset1;
+
+    const short iy = 8*(tiitg % NL1);
+
+    device const T1 * y = (device const T1 *)(src1
+        + args.nb13*i13
+        + args.nb12*i12
+        + args.nb11*(r1 + lr1)
+        + args.nb10*iy);
 
+#ifndef GGML_METAL_HAS_TENSOR
     S0_8x8 ma[4];
     S1_8x8 mb[2];
 
@@ -8187,36 +8214,104 @@ kernel void kernel_mul_mm(
     for (short i = 0; i < 8; i++){
         mc[i] = make_filled_simdgroup_matrix<float, 8>(0.f);
     }
+#else
+    auto tA = tensor<threadgroup S0, dextents<int32_t, 2>, tensor_inline>(sa, dextents<int32_t, 2>(NK,  NR0));
+    auto tB = tensor<threadgroup S1, dextents<int32_t, 2>, tensor_inline>(sb, dextents<int32_t, 2>(NR1, NK ));
 
-    short il = (tiitg % THREAD_PER_ROW);
+    mpp::tensor_ops::matmul2d<
+        mpp::tensor_ops::matmul2d_descriptor(NR1, NR0, NK, false, true, false, mpp::tensor_ops::matmul2d_descriptor::mode::multiply_accumulate),
+        execution_simdgroups<4>> mm;
 
-    const int i12 = im%args.ne12;
-    const int i13 = im/args.ne12;
+    auto cT = mm.get_destination_cooperative_tensor<decltype(tA), decltype(tB), float>();
+#endif
 
-    const uint64_t offset0 = (i12/args.r2)*args.nb02 + (i13/args.r3)*args.nb03;
-    const short    offset1 = il/nl;
+    for (int loop_k = 0; loop_k < args.ne00; loop_k += NK) {
+#ifndef GGML_METAL_HAS_TENSOR
+        // load data and store to threadgroup memory
+        if (is_same<T0_4x4, block_q>::value && FC_mul_mm_bc_inp) {
+            threadgroup_barrier(mem_flags::mem_threadgroup);
 
-    device const block_q * x = (device const block_q *)(src0
-        + args.nb01*(r0*BLOCK_SIZE_M + thread_row) + offset0) + offset1;
+            // no need for dequantization
+            for (short i = 0; i < 16; i++) {
+                const short sx = 2*il0 + i/8;
+                const short sy = (tiitg/NL0)/8;
 
-    const short iy = (BLOCK_SIZE_K / THREAD_PER_COL * (tiitg % THREAD_PER_COL));
+              //const short lx = i%8;
+              //const short ly = (tiitg/NL0)%8;
+                const short lx = (tiitg/NL0)%8;
+                const short ly = i%8;
 
-    device const T1 * y = (device const T1 *)(src1
-        + args.nb13*i13
-        + args.nb12*i12
-        + args.nb11*(r1*BLOCK_SIZE_N + thread_col)
-        + args.nb10*iy);
+                const short ib = 8*sx + sy;
+
+                *(sa + 64*ib + 8*ly + lx) = loop_k + 16*il + i < args.ne00 ? *((device T0 *) x + i) : 0;
+            }
+        } else {
+            S0_4x4 temp_a;
+            dequantize_func(x, il, temp_a);
+
+            threadgroup_barrier(mem_flags::mem_threadgroup);
 
-    for (int loop_k = 0; loop_k < args.ne00; loop_k += BLOCK_SIZE_K) {
+            FOR_UNROLL (short i = 0; i < 16; i++) {
+                const short sx = 2*il0 + i/8;
+                const short sy = (tiitg/NL0)/8;
+
+              //const short lx = i%8;
+              //const short ly = (tiitg/NL0)%8;
+                const short lx = (tiitg/NL0)%8;
+                const short ly = i%8;
+
+                const short ib = 8*sx + sy;
+
+                // NOTE: this is massively slower.. WTF?
+                //sa[64*ib + 8*ly + lx] = temp_a[i/4][i%4];
+
+                *(sa + 64*ib + 8*ly + lx) = temp_a[i/4][i%4];
+            }
+        }
+
+        if (FC_mul_mm_bc_inp) {
+            for (short i = 0; i < 8; ++i) {
+                const short sx = (tiitg%NL1);
+                const short sy = (tiitg/NL1)/8;
+
+                const short lx = i;
+                const short ly = (tiitg/NL1)%8;
+              //const short lx = (tiitg/NL1)%8;
+              //const short ly = i;
+
+                const short ib = 4*sx + sy;
+
+                *(sb + 64*ib + 8*ly + lx) = loop_k + iy + i < args.ne00 ? (S1) *((device T1 *) y + i) : 0;
+            }
+        } else {
+            const short sx = (tiitg%NL1);
+            const short sy = (tiitg/NL1)/8;
+
+            const short dx = sx;
+            const short dy = sy;
+
+            const short ly = (tiitg/NL1)%8;
+
+            const short ib = 4*sx + sy;
+
+            *(threadgroup S1_2x4 *)(sb + 64*ib + 8*ly) = (S1_2x4)(*((device T1_2x4 *) y));
+        }
+#else
         // load data and store to threadgroup memory
         if (is_same<T0_4x4, block_q>::value && FC_mul_mm_bc_inp) {
             threadgroup_barrier(mem_flags::mem_threadgroup);
 
             // no need for dequantization
             for (short i = 0; i < 16; i++) {
-                *(sa + SG_MAT_SIZE * ((tiitg/THREAD_PER_ROW/8) \
-                +                     (tiitg%THREAD_PER_ROW)*16 + (i/8)*8) \
-                +                     (tiitg/THREAD_PER_ROW)%8  + (i&7)*8) = loop_k + 16*il + i < args.ne00 ? ((device T0 *) x)[i] : 0;
+                const short sx = 2*il0 + i/8;
+                const short sy = (tiitg/NL0)/8;
+
+                const short lx = i%8;
+                const short ly = (tiitg/NL0)%8;
+                //const short lx = (tiitg/NL0)%8;
+                //const short ly = i%8;
+
+                *(sa + NK*(8*sy + ly) + 8*sx + lx) = loop_k + 16*il + i < args.ne00 ? *((device T0 *) x + i) : 0;
             }
         } else {
             S0_4x4 temp_a;
@@ -8225,91 +8320,135 @@ kernel void kernel_mul_mm(
             threadgroup_barrier(mem_flags::mem_threadgroup);
 
             FOR_UNROLL (short i = 0; i < 16; i++) {
-                *(sa + SG_MAT_SIZE * ((tiitg/THREAD_PER_ROW/8) \
-                +                     (tiitg%THREAD_PER_ROW)*16 + (i/8)*8) \
-                +                     (tiitg/THREAD_PER_ROW)%8  + (i&7)*8) = temp_a[i/4][i%4];
+                const short sx = 2*il0 + i/8;
+                const short sy = (tiitg/NL0)/8;
+
+                const short lx = i%8;
+                const short ly = (tiitg/NL0)%8;
+                //const short lx = (tiitg/NL0)%8;
+                //const short ly = i%8;
+
+                *(sa + NK*(8*sy + ly) + 8*sx + lx) = temp_a[i/4][i%4];
             }
         }
 
         if (FC_mul_mm_bc_inp) {
             for (short i = 0; i < 8; ++i) {
-                sb[32*8*(tiitg%THREAD_PER_COL) + 8*(tiitg/THREAD_PER_COL) + i] = loop_k + iy + i < args.ne00 ? (S1) ((device T1 *) y)[i] : 0;
+                const short sx = (tiitg%NL1);
+                const short sy = (tiitg/NL1)/8;
+
+                const short lx = i;
+                const short ly = (tiitg/NL1)%8;
+                //const short lx = (tiitg/NL1)%8;
+                //const short ly = i;
+
+                *(sb + NK*(8*sy + ly) + 8*sx + lx) = loop_k + iy + i < args.ne00 ? (S1) *((device T1 *) y + i) : 0;
             }
         } else {
-            *(threadgroup S1_2x4 *)(sb + 32*8*(tiitg%THREAD_PER_COL) + 8*(tiitg/THREAD_PER_COL)) = (S1_2x4)(*((device T1_2x4 *) y));
+            const short sx = (tiitg%NL1);
+            const short sy = (tiitg/NL1)/8;
+
+            //const short lx = i;
+            const short ly = (tiitg/NL1)%8;
+            //const short lx = (tiitg/NL1)%8;
+            //const short ly = i;
+
+            *(threadgroup S1_2x4 *)(sb + NK*(8*sy + ly) + 8*sx) = (S1_2x4)(*((device T1_2x4 *) y));
         }
+#endif
 
         il = (il + 2 < nl) ? il + 2 : il % 2;
         x  = (il < 2) ? x + (2 + nl - 1)/nl : x;
-        y += BLOCK_SIZE_K;
+
+        y += NK;
 
         threadgroup_barrier(mem_flags::mem_threadgroup);
 
+#ifndef GGML_METAL_HAS_TENSOR
         // load matrices from threadgroup memory and conduct outer products
-        threadgroup const S0 * lsma = (sa + THREAD_MAT_M*SG_MAT_SIZE*(sgitg%2));
-        threadgroup const S1 * lsmb = (sb + THREAD_MAT_N*SG_MAT_SIZE*(sgitg/2));
+        threadgroup const S0 * lsma = (sa + 4*64*(sgitg%2));
+        threadgroup const S1 * lsmb = (sb + 2*64*(sgitg/2));
 
-        #pragma unroll(4)
-        for (short ik = 0; ik < BLOCK_SIZE_K/8; ik++) {
+        FOR_UNROLL (short ik = 0; ik < NK/8; ik++) {
             simdgroup_barrier(mem_flags::mem_none);
 
-            #pragma unroll(4)
-            for (short i = 0; i < 4; i++) {
-                simdgroup_load(ma[i], lsma + SG_MAT_SIZE * i);
+            FOR_UNROLL (short i = 0; i < 4; i++) {
+                simdgroup_load(ma[i], lsma + 64*i, 8, 0, false);
             }
 
-            #pragma unroll(2)
-            for (short i = 0; i < 2; i++) {
-                simdgroup_load(mb[i], lsmb + SG_MAT_SIZE * i);
+            simdgroup_barrier(mem_flags::mem_none);
+
+            FOR_UNROLL (short i = 0; i < 2; i++) {
+                simdgroup_load(mb[i], lsmb + 64*i, 8, 0, false);
             }
 
             simdgroup_barrier(mem_flags::mem_none);
 
-            #pragma unroll(8)
-            for (short i = 0; i < 8; i++){
+            FOR_UNROLL (short i = 0; i < 8; i++){
                 simdgroup_multiply_accumulate(mc[i], mb[i/4], ma[i%4], mc[i]);
             }
 
-            lsma += (BLOCK_SIZE_M/SG_MAT_ROW)*SG_MAT_SIZE;
-            lsmb += (BLOCK_SIZE_N/SG_MAT_ROW)*SG_MAT_SIZE;
+            lsma += 8*64;
+            lsmb += 4*64;
         }
+#else
+        auto sA = tA.slice(0, 0);
+        auto sB = tB.slice(0, 0);
+
+        mm.run(sB, sA, cT);
+#endif
     }
 
-    if (!FC_mul_mm_bc_out || ((r0 + 1) * BLOCK_SIZE_M <= args.ne0 && (r1 + 1) * BLOCK_SIZE_N <= args.ne1)) {
+    if (!FC_mul_mm_bc_out || (r0 + NR0 <= args.ne0 && r1 + NR1 <= args.ne1)) {
         // if no bounds checks on the output are needed, we can directly write to device memory
+#ifdef GGML_METAL_HAS_TENSOR
+        device float * C = (device float *) dst +
+            r0 + \
+            r1 * args.ne0 + im*args.ne1*args.ne0;
+
+        auto tC = tensor<device float, dextents<int32_t, 2>, tensor_inline>(C, dextents<int32_t, 2>(args.ne0, NR1));
+        cT.store(tC);
+#else
         device float * C = (device float *) dst +
-            (BLOCK_SIZE_M * r0 + 32*(sgitg &  1)) + \
-            (BLOCK_SIZE_N * r1 + 16*(sgitg >> 1)) * args.ne0 + im*args.ne1*args.ne0;
+            (r0 + 32*(sgitg &  1)) + \
+            (r1 + 16*(sgitg >> 1)) * args.ne0 + im*args.ne1*args.ne0;
 
         for (short i = 0; i < 8; i++) {
-            simdgroup_store(mc[i], C + 8 * (i%4) + 8 * args.ne0 * (i/4), args.ne0);
+            simdgroup_store(mc[i], C + 8*(i%4) + 8*args.ne0*(i/4), args.ne0, 0, false);
         }
+#endif
     } else {
         // block is smaller than 64x32, we should avoid writing data outside of the matrix
         threadgroup_barrier(mem_flags::mem_threadgroup);
-        threadgroup float * temp_str = ((threadgroup float *) shmem) \
-                                     + 32*(sgitg&1) + (16*(sgitg >> 1))*BLOCK_SIZE_M;
+
+        threadgroup float * temp_str = ((threadgroup float *) shmem) + 32*(sgitg&1) + (16*(sgitg >> 1))*NR0;
+
+#ifdef GGML_METAL_HAS_TENSOR
+        auto tC = tensor<threadgroup float, dextents<int32_t, 2>, tensor_inline>(sc, dextents<int32_t, 2>(NR0, NR1));
+        cT.store(tC);
+#else
         for (short i = 0; i < 8; i++) {
-            simdgroup_store(mc[i], temp_str + 8*(i%4) + 8*BLOCK_SIZE_M*(i/4), BLOCK_SIZE_M);
+            simdgroup_store(mc[i], temp_str + 8*(i%4) + 8*NR0*(i/4), NR0, 0, false);
         }
+#endif
 
         threadgroup_barrier(mem_flags::mem_threadgroup);
 
         if (sgitg == 0) {
-            for (int j = tiitg; j < n_cols; j += BLOCK_SIZE_N) {
-                device float  * D  = (device float  *) dst + (r0*BLOCK_SIZE_M) + (r1*BLOCK_SIZE_N + j)*args.ne0 + im*args.ne1*args.ne0;
+            for (int j = tiitg; j < nr1; j += NR1) {
+                device float  * D  = (device float  *) dst + r0 + (r1 + j)*args.ne0 + im*args.ne1*args.ne0;
                 device float4 * D4 = (device float4 *) D;
 
-                threadgroup float  * C  = temp_str + (j*BLOCK_SIZE_M);
+                threadgroup float  * C  = temp_str + (j*NR0);
                 threadgroup float4 * C4 = (threadgroup float4 *) C;
 
                 int i = 0;
-                for (; i < n_rows/4; i++) {
+                for (; i < nr0/4; i++) {
                     *(D4 + i) = *(C4 + i);
                 }
 
                 i *= 4;
-                for (; i < n_rows; i++) {
+                for (; i < nr0; i++) {
                     *(D + i) = *(C + i);
                 }
             }
@@ -8394,55 +8533,55 @@ kernel void kernel_mul_mm_id(
         ushort tiitg[[thread_index_in_threadgroup]],
         ushort tiisg[[thread_index_in_simdgroup]],
         ushort sgitg[[simdgroup_index_in_threadgroup]]) {
-
     threadgroup S0 * sa = (threadgroup S0 *)(shmem);
     threadgroup S1 * sb = (threadgroup S1 *)(shmem + 4096);
 
-    const int r0 = tgpig.y;
-    const int r1 = tgpig.x;
+    threadgroup float * sc = (threadgroup float *)(shmem);
+
+    constexpr int NR0 = 64;
+    constexpr int NR1 = 32;
+
+    constexpr int NK  = 32;
+    constexpr int NL0 = NK/16;
+    constexpr int NL1 = NK/8;
+
     const int im = tgpig.z; // expert
+    const int r0 = tgpig.y*NR0;
+    const int r1 = tgpig.x*NR1;
 
     device const uint32_t * tpe_u32 = (device const uint32_t *) (htpe);
     device const int32_t  * ids_i32 = (device const int32_t  *) (hids);
 
     const int32_t neh1 = tpe_u32[im];
 
-    if (r1*BLOCK_SIZE_N >= neh1) {
+    if (r1 >= neh1) {
         return;
     }
 
     // if this block is of 64x32 shape or smaller
-    const short n_rows = (args.ne0 - r0*BLOCK_SIZE_M < BLOCK_SIZE_M) ? (args.ne0 - r0*BLOCK_SIZE_M) : BLOCK_SIZE_M;
-    const short n_cols = (    neh1 - r1*BLOCK_SIZE_N < BLOCK_SIZE_N) ? (    neh1 - r1*BLOCK_SIZE_N) : BLOCK_SIZE_N;
+    const short nr0 = (args.ne0 - r0 < NR0) ? (args.ne0 - r0) : NR0;
+    const short nr1 = (    neh1 - r1 < NR1) ? (    neh1 - r1) : NR1;
 
     // a thread shouldn't load data outside of the matrix
-    const short thread_row = ((short)tiitg/THREAD_PER_ROW) < n_rows ? ((short)tiitg/THREAD_PER_ROW) : n_rows - 1;
-    const short thread_col = ((short)tiitg/THREAD_PER_COL) < n_cols ? ((short)tiitg/THREAD_PER_COL) : n_cols - 1;
+    const short lr0 = ((short)tiitg/NL0) < nr0 ? ((short)tiitg/NL0) : nr0 - 1; // 0 .. 63
+    const short lr1 = ((short)tiitg/NL1) < nr1 ? ((short)tiitg/NL1) : nr1 - 1; // 0 .. 31
 
-    S0_8x8 ma[4];
-    S1_8x8 mb[2];
+    const short il0 = (tiitg % NL0);
 
-    simdgroup_float8x8 mc[8];
+    short il = il0;
 
-    for (short i = 0; i < 8; i++){
-        mc[i] = make_filled_simdgroup_matrix<float, 8>(0.f);
-    }
-
-    short il = (tiitg % THREAD_PER_ROW);
-
-    const int id = ids_i32[im*args.ne21 + r1*BLOCK_SIZE_N + thread_col];
+    const int id = ids_i32[im*args.ne21 + r1 + lr1];
 
     const short i11 = (id % args.ne20) % args.ne11;
     const short i12 = (id / args.ne20);
     const short i13 = 0;
 
     const uint64_t offset0 = im*args.nb02 + i13*args.nb03;
-    const short    offset1 = il/nl;
+    const short    offset1 = il0/nl;
 
-    device const block_q * x = (device const block_q *)(src0
-        + args.nb01*(r0*BLOCK_SIZE_M + thread_row) + offset0) + offset1;
+    device const block_q * x = (device const block_q *)(src0 + args.nb01*(r0 + lr0) + offset0) + offset1;
 
-    const short iy = (BLOCK_SIZE_K / THREAD_PER_COL * (tiitg % THREAD_PER_COL));
+    const short iy = 8*(tiitg % NL1);
 
     device const T1 * y = (device const T1 *)(src1
         + args.nb13*i13
@@ -8450,16 +8589,113 @@ kernel void kernel_mul_mm_id(
         + args.nb11*i11
         + args.nb10*iy);
 
-    for (int loop_k = 0; loop_k < args.ne00; loop_k += BLOCK_SIZE_K) {
+#ifndef GGML_METAL_HAS_TENSOR
+    S0_8x8 ma[4];
+    S1_8x8 mb[2];
+
+    simdgroup_float8x8 mc[8];
+
+    for (short i = 0; i < 8; i++){
+        mc[i] = make_filled_simdgroup_matrix<float, 8>(0.f);
+    }
+#else
+    auto tA = tensor<threadgroup S0, dextents<int32_t, 2>, tensor_inline>(sa, dextents<int32_t, 2>(NK,  NR0));
+    auto tB = tensor<threadgroup S1, dextents<int32_t, 2>, tensor_inline>(sb, dextents<int32_t, 2>(NR1, NK ));
+
+    mpp::tensor_ops::matmul2d<
+        mpp::tensor_ops::matmul2d_descriptor(NR1, NR0, NK, false, true, false, mpp::tensor_ops::matmul2d_descriptor::mode::multiply_accumulate),
+        execution_simdgroups<4>> mm;
+
+    auto cT = mm.get_destination_cooperative_tensor<decltype(tA), decltype(tB), float>();
+#endif
+
+    for (int loop_k = 0; loop_k < args.ne00; loop_k += NK) {
+#ifndef GGML_METAL_HAS_TENSOR
+        // load data and store to threadgroup memory
+        if (is_same<T0_4x4, block_q>::value && FC_mul_mm_bc_inp) {
+            threadgroup_barrier(mem_flags::mem_threadgroup);
+
+            // no need for dequantization
+            for (short i = 0; i < 16; i++) {
+                const short sx = 2*il0 + i/8;
+                const short sy = (tiitg/NL0)/8;
+
+              //const short lx = i%8;
+              //const short ly = (tiitg/NL0)%8;
+                const short lx = (tiitg/NL0)%8;
+                const short ly = i%8;
+
+                const short ib = 8*sx + sy;
+
+                *(sa + 64*ib + 8*ly + lx) = loop_k + 16*il + i < args.ne00 ? *((device T0 *) x + i) : 0;
+            }
+        } else {
+            S0_4x4 temp_a;
+            dequantize_func(x, il, temp_a);
+
+            threadgroup_barrier(mem_flags::mem_threadgroup);
+
+            FOR_UNROLL (short i = 0; i < 16; i++) {
+                const short sx = 2*il0 + i/8;
+                const short sy = (tiitg/NL0)/8;
+
+              //const short lx = i%8;
+              //const short ly = (tiitg/NL0)%8;
+                const short lx = (tiitg/NL0)%8;
+                const short ly = i%8;
+
+                const short ib = 8*sx + sy;
+
+                // NOTE: this is massively slower.. WTF?
+                //sa[64*ib + 8*ly + lx] = temp_a[i/4][i%4];
+
+                *(sa + 64*ib + 8*ly + lx) = temp_a[i/4][i%4];
+            }
+        }
+
+        if (FC_mul_mm_bc_inp) {
+            for (short i = 0; i < 8; ++i) {
+                const short sx = (tiitg%NL1);
+                const short sy = (tiitg/NL1)/8;
+
+                const short lx = i;
+                const short ly = (tiitg/NL1)%8;
+              //const short lx = (tiitg/NL1)%8;
+              //const short ly = i;
+
+                const short ib = 4*sx + sy;
+
+                *(sb + 64*ib + 8*ly + lx) = loop_k + iy + i < args.ne00 ? (S1) *((device T1 *) y + i) : 0;
+            }
+        } else {
+            const short sx = (tiitg%NL1);
+            const short sy = (tiitg/NL1)/8;
+
+            const short dx = sx;
+            const short dy = sy;
+
+            const short ly = (tiitg/NL1)%8;
+
+            const short ib = 4*sx + sy;
+
+            *(threadgroup S1_2x4 *)(sb + 64*ib + 8*ly) = (S1_2x4)(*((device T1_2x4 *) y));
+        }
+#else
         // load data and store to threadgroup memory
         if (is_same<T0_4x4, block_q>::value && FC_mul_mm_bc_inp) {
             threadgroup_barrier(mem_flags::mem_threadgroup);
 
             // no need for dequantization
             for (short i = 0; i < 16; i++) {
-                *(sa + SG_MAT_SIZE * ((tiitg/THREAD_PER_ROW/8) \
-                +                     (tiitg%THREAD_PER_ROW)*16 + (i/8)*8) \
-                +                     (tiitg/THREAD_PER_ROW)%8  + (i&7)*8) = loop_k + 16*il + i < args.ne00 ? ((device T0 *) x)[i] : 0;
+                const short sx = 2*il0 + i/8;
+                const short sy = (tiitg/NL0)/8;
+
+                const short lx = i%8;
+                const short ly = (tiitg/NL0)%8;
+                //const short lx = (tiitg/NL0)%8;
+                //const short ly = i%8;
+
+                *(sa + NK*(8*sy + ly) + 8*sx + lx) = loop_k + 16*il + i < args.ne00 ? *((device T0 *) x + i) : 0;
             }
         } else {
             S0_4x4 temp_a;
@@ -8468,85 +8704,120 @@ kernel void kernel_mul_mm_id(
             threadgroup_barrier(mem_flags::mem_threadgroup);
 
             FOR_UNROLL (short i = 0; i < 16; i++) {
-                *(sa + SG_MAT_SIZE * ((tiitg/THREAD_PER_ROW/8) \
-                +                     (tiitg%THREAD_PER_ROW)*16 + (i/8)*8) \
-                +                     (tiitg/THREAD_PER_ROW)%8  + (i&7)*8) = temp_a[i/4][i%4];
+                const short sx = 2*il0 + i/8;
+                const short sy = (tiitg/NL0)/8;
+
+                const short lx = i%8;
+                const short ly = (tiitg/NL0)%8;
+                //const short lx = (tiitg/NL0)%8;
+                //const short ly = i%8;
+
+                *(sa + NK*(8*sy + ly) + 8*sx + lx) = temp_a[i/4][i%4];
             }
         }
 
         if (FC_mul_mm_bc_inp) {
             for (short i = 0; i < 8; ++i) {
-                sb[32*8*(tiitg%THREAD_PER_COL) + 8*(tiitg/THREAD_PER_COL) + i] = loop_k + iy + i < args.ne00 ? (S1) ((device T1 *) y)[i] : 0;
+                const short sx = (tiitg%NL1);
+                const short sy = (tiitg/NL1)/8;
+
+                const short lx = i;
+                const short ly = (tiitg/NL1)%8;
+                //const short lx = (tiitg/NL1)%8;
+                //const short ly = i;
+
+                *(sb + NK*(8*sy + ly) + 8*sx + lx) = loop_k + iy + i < args.ne00 ? (S1) *((device T1 *) y + i) : 0;
             }
         } else {
-            *(threadgroup S1_2x4 *)(sb + 32*8*(tiitg%THREAD_PER_COL) + 8*(tiitg/THREAD_PER_COL)) = (S1_2x4)(*((device T1_2x4 *) y));
+            const short sx = (tiitg%NL1);
+            const short sy = (tiitg/NL1)/8;
+
+            //const short lx = i;
+            const short ly = (tiitg/NL1)%8;
+            //const short lx = (tiitg/NL1)%8;
+            //const short ly = i;
+
+            *(threadgroup S1_2x4 *)(sb + NK*(8*sy + ly) + 8*sx) = (S1_2x4)(*((device T1_2x4 *) y));
         }
+#endif
 
         il = (il + 2 < nl) ? il + 2 : il % 2;
         x  = (il < 2) ? x + (2 + nl - 1)/nl : x;
-        y += BLOCK_SIZE_K;
+
+        y += NK;
 
         threadgroup_barrier(mem_flags::mem_threadgroup);
 
+#ifndef GGML_METAL_HAS_TENSOR
         // load matrices from threadgroup memory and conduct outer products
-        threadgroup const S0 * lsma = (sa + THREAD_MAT_M*SG_MAT_SIZE*(sgitg%2));
-        threadgroup const S1 * lsmb = (sb + THREAD_MAT_N*SG_MAT_SIZE*(sgitg/2));
-
-        #pragma unroll(4)
-        for (short ik = 0; ik < BLOCK_SIZE_K/8; ik++) {
-            #pragma unroll(4)
-            for (short i = 0; i < 4; i++) {
-                simdgroup_load(ma[i], lsma + SG_MAT_SIZE * i);
+        threadgroup const S0 * lsma = (sa + 4*64*(sgitg%2));
+        threadgroup const S1 * lsmb = (sb + 2*64*(sgitg/2));
+
+        FOR_UNROLL (short ik = 0; ik < NK/8; ik++) {
+            simdgroup_barrier(mem_flags::mem_none);
+
+            FOR_UNROLL (short i = 0; i < 4; i++) {
+                simdgroup_load(ma[i], lsma + 64*i, 8, 0, false);
             }
 
             simdgroup_barrier(mem_flags::mem_none);
 
-            #pragma unroll(2)
-            for (short i = 0; i < 2; i++) {
-                simdgroup_load(mb[i], lsmb + SG_MAT_SIZE * i);
+            FOR_UNROLL (short i = 0; i < 2; i++) {
+                simdgroup_load(mb[i], lsmb + 64*i, 8, 0, false);
             }
 
-            #pragma unroll(8)
-            for (short i = 0; i < 8; i++){
+            simdgroup_barrier(mem_flags::mem_none);
+
+            FOR_UNROLL (short i = 0; i < 8; i++){
                 simdgroup_multiply_accumulate(mc[i], mb[i/4], ma[i%4], mc[i]);
             }
 
-            lsma += (BLOCK_SIZE_M/SG_MAT_ROW)*SG_MAT_SIZE;
-            lsmb += (BLOCK_SIZE_N/SG_MAT_ROW)*SG_MAT_SIZE;
+            lsma += 8*64;
+            lsmb += 4*64;
         }
+#else
+        auto sA = tA.slice(0, 0);
+        auto sB = tB.slice(0, 0);
+
+        mm.run(sB, sA, cT);
+#endif
     }
 
+    // block is smaller than 64x32, we should avoid writing data outside of the matrix
     threadgroup_barrier(mem_flags::mem_threadgroup);
 
-    threadgroup float * temp_str = ((threadgroup float *) shmem) \
-                                 + 32*(sgitg&1) + (16*(sgitg >> 1))*BLOCK_SIZE_M;
+#ifdef GGML_METAL_HAS_TENSOR
+    auto tC = tensor<threadgroup float, dextents<int32_t, 2>, tensor_inline>(sc, dextents<int32_t, 2>(NR0, NR1));
+    cT.store(tC);
+#else
+    threadgroup float * temp_str = ((threadgroup float *) shmem) + 32*(sgitg&1) + (16*(sgitg >> 1))*NR0;
 
-    #pragma unroll(8)
     for (short i = 0; i < 8; i++) {
-        simdgroup_store(mc[i], temp_str + 8*(i%4) + 8*BLOCK_SIZE_M*(i/4), BLOCK_SIZE_M);
+        simdgroup_store(mc[i], temp_str + 8*(i%4) + 8*NR0*(i/4), NR0, 0, false);
     }
+#endif
 
     threadgroup_barrier(mem_flags::mem_threadgroup);
 
-    for (short j = sgitg; j < n_cols; j += 4) {
-        const int id = ids_i32[im*args.ne21 + r1*BLOCK_SIZE_N + j];
+    for (short j = sgitg; j < nr1; j += 4) {
+        const int id = ids_i32[im*args.ne21 + r1 + j];
 
         const short ide = id % args.ne20;
         const short idt = id / args.ne20;
 
-        device float  * D  = (device float  *) dst + (r0*BLOCK_SIZE_M) + ide*args.ne0 + idt*args.ne1*args.ne0;
+        device float  * D  = (device float  *) dst + r0 + ide*args.ne0 + idt*args.ne1*args.ne0;
         device float4 * D4 = (device float4 *) D;
 
-        threadgroup float  * C  = (threadgroup float  *) shmem + (j*BLOCK_SIZE_M);
+        threadgroup float  * C  = (threadgroup float  *) shmem + j*NR0;
         threadgroup float4 * C4 = (threadgroup float4 *) C;
 
         int i = tiisg;
-        for (; i < n_rows/4; i += 32) {
+        for (; i < nr0/4; i += 32) {
             *(D4 + i) = *(C4 + i);
         }
 
-        i = (4*(n_rows/4)) + tiisg;
-        for (; i < n_rows; i += 32) {
+        i = (4*(nr0/4)) + tiisg;
+        for (; i < nr0; i += 32) {
             *(D + i) = *(C + i);
         }
     }

From aa374175c30184aeb1813ec71fc68780dd073906 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Johannes=20G=C3=A4=C3=9Fler?= <johannesg@5d6.de>
Date: Thu, 6 Nov 2025 14:05:47 +0100
Subject: [PATCH 103/185] CUDA: fix crash on uneven context without FA (#16988)

---
 ggml/src/ggml-cuda/ggml-cuda.cu | 12 ++++-----
 ggml/src/ggml-cuda/mmf.cu       | 12 ++++++---
 ggml/src/ggml-cuda/mmf.cuh      |  2 +-
 ggml/src/ggml-cuda/mmvf.cu      |  8 +++++-
 ggml/src/ggml-cuda/mmvf.cuh     |  2 +-
 src/llama-context.cpp           |  2 ++
 tests/test-backend-ops.cpp      | 44 ++++++++++++++-------------------
 7 files changed, 44 insertions(+), 38 deletions(-)

diff --git a/ggml/src/ggml-cuda/ggml-cuda.cu b/ggml/src/ggml-cuda/ggml-cuda.cu
index 415a7e962d7..049aece1b52 100644
--- a/ggml/src/ggml-cuda/ggml-cuda.cu
+++ b/ggml/src/ggml-cuda/ggml-cuda.cu
@@ -2113,7 +2113,7 @@ static bool ggml_cuda_should_fuse_mul_mat_vec_f(const ggml_tensor * tensor) {
         src1->type == GGML_TYPE_F32 && dst->type == GGML_TYPE_F32;
 
     const int cc      = ggml_cuda_info().devices[ggml_cuda_get_device()].cc;
-    use_mul_mat_vec_f = use_mul_mat_vec_f && ggml_cuda_should_use_mmvf(src0->type, cc, src0->ne, is_mul_mat_id ? src1->ne[2] : src1->ne[1]);
+    use_mul_mat_vec_f = use_mul_mat_vec_f && ggml_cuda_should_use_mmvf(src0->type, cc, src0->ne, src0->nb, is_mul_mat_id ? src1->ne[2] : src1->ne[1]);
 
     const bool split = ggml_backend_buft_is_cuda_split(src0->buffer->buft) ||
                        ggml_backend_buft_is_cuda_split(src1->buffer->buft);
@@ -2207,16 +2207,16 @@ static void ggml_cuda_mul_mat(ggml_backend_cuda_context & ctx, const ggml_tensor
             const int cc            = ggml_cuda_info().devices[id].cc;
             const int warp_size     = ggml_cuda_info().devices[id].warp_size;
             use_mul_mat_q           = use_mul_mat_q             && ggml_cuda_should_use_mmq(src0->type, cc, src1->ne[1]);
-            use_mul_mat_f           = use_mul_mat_f             && ggml_cuda_should_use_mmf(src0->type, cc, warp_size, src0->ne, src1->ne[1], /*mul_mat_id=*/false);
-            use_mul_mat_vec_f       = use_mul_mat_vec_f         && ggml_cuda_should_use_mmvf(src0->type, cc, src0->ne, src1->ne[1]);
+            use_mul_mat_f           = use_mul_mat_f             && ggml_cuda_should_use_mmf(src0->type, cc, warp_size, src0->ne, src0->nb, src1->ne[1], /*mul_mat_id=*/false);
+            use_mul_mat_vec_f       = use_mul_mat_vec_f         && ggml_cuda_should_use_mmvf(src0->type, cc, src0->ne, src0->nb, src1->ne[1]);
             any_gpus_with_slow_fp16 = any_gpus_with_slow_fp16   || !fast_fp16_hardware_available(cc);
         }
     } else {
         const int cc            = ggml_cuda_info().devices[ctx.device].cc;
         const int warp_size     = ggml_cuda_info().devices[ctx.device].warp_size;
         use_mul_mat_q           = use_mul_mat_q             && ggml_cuda_should_use_mmq(src0->type, cc, src1->ne[1]);
-        use_mul_mat_f           = use_mul_mat_f             && ggml_cuda_should_use_mmf(src0->type, cc, warp_size, src0->ne, src1->ne[1], /*mul_mat_id=*/false);
-        use_mul_mat_vec_f       = use_mul_mat_vec_f         && ggml_cuda_should_use_mmvf(src0->type, cc, src0->ne, src1->ne[1]);
+        use_mul_mat_f           = use_mul_mat_f             && ggml_cuda_should_use_mmf(src0->type, cc, warp_size, src0->ne, src0->nb, src1->ne[1], /*mul_mat_id=*/false);
+        use_mul_mat_vec_f       = use_mul_mat_vec_f         && ggml_cuda_should_use_mmvf(src0->type, cc, src0->ne, src0->nb, src1->ne[1]);
         any_gpus_with_slow_fp16 = any_gpus_with_slow_fp16   || !fast_fp16_hardware_available(cc);
     }
 
@@ -2287,7 +2287,7 @@ static void ggml_cuda_mul_mat_id(ggml_backend_cuda_context & ctx, ggml_tensor *
             return;
         }
 
-        if (ggml_cuda_should_use_mmf(src0->type, cc, WARP_SIZE, src0->ne, src1->ne[2], /*mul_mat_id=*/true)) {
+        if (ggml_cuda_should_use_mmf(src0->type, cc, WARP_SIZE, src0->ne, src0->nb, src1->ne[2], /*mul_mat_id=*/true)) {
             ggml_cuda_mul_mat_f(ctx, src0, src1, ids, dst);
             return;
         }
diff --git a/ggml/src/ggml-cuda/mmf.cu b/ggml/src/ggml-cuda/mmf.cu
index 2b0a61395b4..69a60aceb82 100644
--- a/ggml/src/ggml-cuda/mmf.cu
+++ b/ggml/src/ggml-cuda/mmf.cu
@@ -119,15 +119,21 @@ void ggml_cuda_mul_mat_f(ggml_backend_cuda_context & ctx, const ggml_tensor * sr
     }
 }
 
-bool ggml_cuda_should_use_mmf(enum ggml_type type, int cc, int warp_size, const int64_t * src0_ne, const int src1_ncols, bool mul_mat_id) {
-
+bool ggml_cuda_should_use_mmf(enum ggml_type type, int cc, int warp_size, const int64_t * src0_ne,
+        const size_t * src0_nb, const int src1_ncols, bool mul_mat_id) {
     if (ggml_is_quantized(type)) {
         return false;
     }
 
-    if (src0_ne[0] % (warp_size * (4/ggml_type_size(type))) != 0) {
+    const size_t ts = ggml_type_size(type);
+    if (src0_ne[0] % (warp_size * (4/ts)) != 0) {
         return false;
     }
+    for (size_t i = 0; i < GGML_MAX_DIMS; ++i) {
+        if (src0_nb[i] % (2*ts) != 0) {
+            return false;
+        }
+    }
     if (src0_ne[1] % MMF_ROWS_PER_BLOCK != 0) {
         return false;
     }
diff --git a/ggml/src/ggml-cuda/mmf.cuh b/ggml/src/ggml-cuda/mmf.cuh
index f7e46e2f63b..45724e0911e 100644
--- a/ggml/src/ggml-cuda/mmf.cuh
+++ b/ggml/src/ggml-cuda/mmf.cuh
@@ -17,7 +17,7 @@ struct mmf_ids_data {
 
 void ggml_cuda_mul_mat_f(ggml_backend_cuda_context & ctx, const ggml_tensor * src0, const ggml_tensor * src1, const ggml_tensor * ids, ggml_tensor * dst);
 
-bool ggml_cuda_should_use_mmf(enum ggml_type type, int cc, int warp_size, const int64_t * scr0_ne, const int src1_ncols, bool mul_mat_id);
+bool ggml_cuda_should_use_mmf(enum ggml_type type, int cc, int warp_size, const int64_t * scr0_ne, const size_t * src0_nb, const int src1_ncols, bool mul_mat_id);
 
 template <typename T, int rows_per_block, int cols_per_block, int nwarps, bool has_ids>
 __launch_bounds__(ggml_cuda_get_physical_warp_size()*nwarps, 1)
diff --git a/ggml/src/ggml-cuda/mmvf.cu b/ggml/src/ggml-cuda/mmvf.cu
index 4e31783436d..526d90d7aee 100644
--- a/ggml/src/ggml-cuda/mmvf.cu
+++ b/ggml/src/ggml-cuda/mmvf.cu
@@ -716,10 +716,16 @@ void ggml_cuda_op_mul_mat_vec_f(
     GGML_UNUSED_VARS(ctx, src1, dst, src1_ddq_i, src1_ncols, src1_padded_row_size);
 }
 
-bool ggml_cuda_should_use_mmvf(enum ggml_type type, int cc, const int64_t * src0_ne, int64_t ne11) {
+bool ggml_cuda_should_use_mmvf(enum ggml_type type, int cc, const int64_t * src0_ne, const size_t * src0_nb, int64_t ne11) {
     if (src0_ne[0] % 2 != 0) {
         return false;
     }
+    const size_t ts = ggml_type_size(type);
+    for (size_t i = 0; i < GGML_MAX_DIMS; ++i) {
+        if (src0_nb[i] % (2*ts) != 0) {
+            return false;
+        }
+    }
     switch (type) {
         case GGML_TYPE_F32:
             if (GGML_CUDA_CC_IS_NVIDIA(cc)) {
diff --git a/ggml/src/ggml-cuda/mmvf.cuh b/ggml/src/ggml-cuda/mmvf.cuh
index a205aa8e4c5..a09fbdc7202 100644
--- a/ggml/src/ggml-cuda/mmvf.cuh
+++ b/ggml/src/ggml-cuda/mmvf.cuh
@@ -9,4 +9,4 @@ void ggml_cuda_op_mul_mat_vec_f(
     const char * src1_ddq_i, float * dst_dd_i, const int64_t row_low, const int64_t row_high, const int64_t src1_ncols,
     const int64_t src1_padded_row_size, cudaStream_t stream);
 
-bool ggml_cuda_should_use_mmvf(enum ggml_type type, int cc, const int64_t * src0_ne, int64_t ne11);
+bool ggml_cuda_should_use_mmvf(enum ggml_type type, int cc, const int64_t * src0_ne, const size_t * src0_nb, int64_t ne11);
diff --git a/src/llama-context.cpp b/src/llama-context.cpp
index 2b39366271f..866514038e4 100644
--- a/src/llama-context.cpp
+++ b/src/llama-context.cpp
@@ -21,6 +21,8 @@ llama_context::llama_context(
               llama_context_params params) :
     model(model),
     balloc(std::make_unique<llama_batch_allocr>(model.hparams.n_pos_per_embd())) {
+    // TODO warning when creating llama_context with awkward ctx size that is not a power of 2,
+    //     may need to be backend-dependent
     LLAMA_LOG_INFO("%s: constructing llama_context\n", __func__);
 
     t_start_us = model.t_start_us;
diff --git a/tests/test-backend-ops.cpp b/tests/test-backend-ops.cpp
index f575420279a..bffd60f386a 100644
--- a/tests/test-backend-ops.cpp
+++ b/tests/test-backend-ops.cpp
@@ -3385,11 +3385,11 @@ struct test_mul_mat : public test_case {
     const std::array<int64_t, 2> bs;  // dims 3 and 4
     const std::array<int64_t, 2> nr;  // repeat in dims 3 and 4
     const std::array<int64_t, 4> per; // permutation of dimensions
-    const bool v; // whether a and b are non-contiguous views
+    const int64_t k_v; // size of k in memory, resulting in a non-contiguous view for k_v > k, no view for k_v == 0
     const uint32_t o; // number of outputs
 
     std::string vars() override {
-        return VARS_TO_STR10(type_a, type_b, m, n, k, bs, nr, per, v, o);
+        return VARS_TO_STR10(type_a, type_b, m, n, k, bs, nr, per, k_v, o);
     }
 
     double max_nmse_err() override {
@@ -3410,8 +3410,8 @@ struct test_mul_mat : public test_case {
             std::array<int64_t, 2> bs = {10, 10},
             std::array<int64_t, 2> nr = {2, 2},
             std::array<int64_t, 4> per = {0, 1, 2, 3},
-            bool v = false, uint32_t o = 1)
-        : type_a(type_a), type_b(type_b), m(m), n(n), k(k), bs(bs), nr(nr), per(per), v(v), o(o) {}
+            int64_t k_v = 0, uint32_t o = 1)
+        : type_a(type_a), type_b(type_b), m(m), n(n), k(k), bs(bs), nr(nr), per(per), k_v(k_v), o(o) {}
 
     ggml_tensor * build_graph(ggml_context * ctx) override {
         // C^T = A * B^T: (k, m) * (k, n) => (m, n)
@@ -3421,7 +3421,7 @@ struct test_mul_mat : public test_case {
         const int npermuted = (per[0] != 0) + (per[1] != 1) + (per[2] != 2) + (per[3] != 3);
         if (npermuted > 0) {
             GGML_ASSERT(npermuted == 2);
-            GGML_ASSERT(!v); // not handled
+            GGML_ASSERT(k_v == 0); // not handled
             GGML_ASSERT(!ggml_is_quantized(type_a) || per[0] == 0);
             GGML_ASSERT(!ggml_is_quantized(type_b) || per[0] == 0);
 
@@ -3445,29 +3445,21 @@ struct test_mul_mat : public test_case {
             ggml_set_name(a, "a_permuted");
             ggml_set_name(b, "b_permuted");
         } else {
-            if (v) {
-                a = ggml_new_tensor_4d(ctx, type_a, k*2, m, bs[0],       bs[1]);
-                b = ggml_new_tensor_4d(ctx, type_b, k*2, n, bs[0]*nr[0], bs[1]*nr[1]);
+            const int64_t k_physical = k_v == 0 ? k : k_v;
+            a = ggml_new_tensor_4d(ctx, type_a, k_physical, m, bs[0],       bs[1]);
+            b = ggml_new_tensor_4d(ctx, type_b, k_physical, n, bs[0]*nr[0], bs[1]*nr[1]);
 
-                if (!ggml_is_quantized(type_a)) {
-                    if (bs[1] == 1 && nr[1] == 1) {
-                        ggml_set_param(a);
-                    }
-                    ggml_set_param(b);
+            if (!ggml_is_quantized(type_a)) {
+                if (bs[1] == 1 && nr[1] == 1) {
+                    ggml_set_param(a);
                 }
+                ggml_set_param(b);
+            }
 
+            if (k_v != 0) {
+                GGML_ASSERT(k_v > k);
                 a = ggml_view_4d(ctx, a, k, m, bs[0],       bs[1],       a->nb[1], a->nb[2], a->nb[3], 0);
                 b = ggml_view_4d(ctx, b, k, n, bs[0]*nr[0], bs[1]*nr[1], b->nb[1], b->nb[2], b->nb[3], 0);
-            } else {
-                a = ggml_new_tensor_4d(ctx, type_a, k, m, bs[0],       bs[1]);
-                b = ggml_new_tensor_4d(ctx, type_b, k, n, bs[0]*nr[0], bs[1]*nr[1]);
-
-                if (!ggml_is_quantized(type_a)) {
-                    if (bs[1] == 1 && nr[1] == 1) {
-                        ggml_set_param(a);
-                    }
-                    ggml_set_param(b);
-                }
             }
             ggml_set_name(a, "a");
             ggml_set_name(b, "b");
@@ -6901,7 +6893,7 @@ static std::vector<std::unique_ptr<test_case>> make_test_cases_eval() {
     test_cases.emplace_back(new test_mul_mat(GGML_TYPE_F16, GGML_TYPE_F32, 128, 45,  64, { 8,  1}, {4, 1}));
     test_cases.emplace_back(new test_mul_mat(GGML_TYPE_F16, GGML_TYPE_F32, 1056, 1, 193, {1,  1}, {4, 1}, {0, 2, 1, 3}));
     test_cases.emplace_back(new test_mul_mat(GGML_TYPE_F16, GGML_TYPE_F32, 1056, 1, 67,  {1,  1}, {4, 1}, {0, 2, 1, 3}));
-    test_cases.emplace_back(new test_mul_mat(GGML_TYPE_F32, GGML_TYPE_F32, 16, 32, 32, { 1,  1}, {1, 1}, {0, 1, 2, 3}, true, 3));
+    test_cases.emplace_back(new test_mul_mat(GGML_TYPE_F32, GGML_TYPE_F32, 16, 32, 32, { 1,  1}, {1, 1}, {0, 1, 2, 3}, 64, 3));
     test_cases.emplace_back(new test_mul_mat(GGML_TYPE_F32, GGML_TYPE_F32, 64, 77, 77, {12,1}, {1,1}));
 
 #if 0
@@ -6927,7 +6919,7 @@ static std::vector<std::unique_ptr<test_case>> make_test_cases_eval() {
                     for (uint32_t k = 0; k < 2; ++k) {
                         for (ggml_type type: {GGML_TYPE_F16, GGML_TYPE_BF16, GGML_TYPE_F32}) {
                             test_cases.emplace_back(new test_mul_mat(type, GGML_TYPE_F32, 1056 + m, 1, 128 + k,  {bs,  bs2}, {nr, 1}, {0, 2, 1, 3}));
-                            test_cases.emplace_back(new test_mul_mat(type, GGML_TYPE_F32, 128 + m,  1, 1056 + k, {bs,  bs2}, {nr, 1}, {0, 1, 2, 3}, true));
+                            test_cases.emplace_back(new test_mul_mat(type, GGML_TYPE_F32, 128 + m,  1, 1056 + k, {bs,  bs2}, {nr, 1}, {0, 1, 2, 3}, 2*1056 + k));
                         }
                     }
                 }
@@ -7432,7 +7424,7 @@ static std::vector<std::unique_ptr<test_case>> make_test_cases_perf() {
     test_cases.emplace_back(new test_pad_reflect_1d(GGML_TYPE_F32, {3000, 384, 4, 1}));
 
     test_cases.emplace_back(new test_mul_mat(GGML_TYPE_F16, GGML_TYPE_F32, 16416, 1, 128, {8,  1}, {4, 1}, {0, 2, 1, 3}));
-    test_cases.emplace_back(new test_mul_mat(GGML_TYPE_F16, GGML_TYPE_F32, 128, 1, 16416, {8,  1}, {4, 1}, {0, 1, 2, 3}, true));
+    test_cases.emplace_back(new test_mul_mat(GGML_TYPE_F16, GGML_TYPE_F32, 128, 1, 16416, {8,  1}, {4, 1}, {0, 1, 2, 3}, 2*16416));
 
     for (int bs : {1, 2, 3, 4, 5, 8, 512}) {
         for (ggml_type type_a : all_types) {

From 7f09a680af6e0ef612de81018e1d19c19b8651e8 Mon Sep 17 00:00:00 2001
From: xctan <xc-tan@outlook.com>
Date: Fri, 7 Nov 2025 00:12:45 +0800
Subject: [PATCH 104/185] ggml-cpu : optimize RVV q2_k and q3_k kernels
 (#16887)

---
 ggml/src/ggml-cpu/arch/riscv/quants.c | 157 ++++++++++++++++++--------
 1 file changed, 108 insertions(+), 49 deletions(-)

diff --git a/ggml/src/ggml-cpu/arch/riscv/quants.c b/ggml/src/ggml-cpu/arch/riscv/quants.c
index ee41a3502e8..ae0ebb3cad1 100644
--- a/ggml/src/ggml-cpu/arch/riscv/quants.c
+++ b/ggml/src/ggml-cpu/arch/riscv/quants.c
@@ -580,16 +580,19 @@ void ggml_vec_dot_q2_K_q8_K(int n, float * GGML_RESTRICT s, size_t bs, const voi
             const float dmin = -y[i].d * GGML_CPU_FP16_TO_FP32(x[i].dmin);
             uint8_t *patmp = atmp;
             int vsums;
-            int tmp;
+            int tmp, t1, t2, t3, t4, t5, t6, t7;
             __asm__ __volatile__(
                 "vsetivli zero, 16, e8, m1\n\t"
                 "vmv.v.x v8, zero\n\t"
+                "lb zero, 15(%[sc])\n\t"
                 "vle8.v v1, (%[sc])\n\t"
+                "vle8.v v2, (%[bsums])\n\t"
+                "addi %[tmp], %[bsums], 16\n\t"
                 "vand.vi v0, v1, 0xF\n\t"
                 "vsrl.vi v1, v1, 4\n\t"
+                "vle8.v v3, (%[tmp])\n\t"
                 "vse8.v v0, (%[scale])\n\t"
                 "vsetivli zero, 16, e16, m2\n\t"
-                "vle16.v v2, (%[bsums])\n\t"
                 "vzext.vf2 v0, v1\n\t"
                 "vwmul.vv v4, v0, v2\n\t"
                 "vsetivli zero, 16, e32, m4\n\t"
@@ -608,46 +611,89 @@ void ggml_vec_dot_q2_K_q8_K(int n, float * GGML_RESTRICT s, size_t bs, const voi
 
             for (int j = 0; j < QK_K/128; ++j) {
                 __asm__ __volatile__(
-                    "vsetvli zero, %[vl32], e8, m2\n\t"
+                    "lb zero, 31(%[q2])\n\t"
+                    "addi %[tmp], %[q2], 16\n\t"
+                    "addi %[t1], %[q8], 16\n\t"
+                    "vsetivli zero, 16, e8, m1\n\t"
                     "vle8.v v0, (%[q2])\n\t"
+                    "vle8.v v1, (%[tmp])\n\t"
                     "vsrl.vi v2, v0, 2\n\t"
+                    "vsrl.vi v3, v1, 2\n\t"
                     "vsrl.vi v4, v0, 4\n\t"
+                    "addi %[tmp], %[q8], 32\n\t"
+                    "vle8.v v8, (%[q8])\n\t"
+                    "vle8.v v9, (%[t1])\n\t"
+                    "addi %[t1], %[t1], 32\n\t"
+                    "vsrl.vi v5, v1, 4\n\t"
                     "vsrl.vi v6, v0, 6\n\t"
+                    "vsrl.vi v7, v1, 6\n\t"
+                    "vle8.v v10, (%[tmp])\n\t"
+                    "vle8.v v11, (%[t1])\n\t"
+                    "addi %[tmp], %[tmp], 32\n\t"
+                    "addi %[t1], %[t1], 32\n\t"
                     "vand.vi v0, v0, 0x3\n\t"
+                    "vand.vi v1, v1, 0x3\n\t"
                     "vand.vi v2, v2, 0x3\n\t"
+                    "vle8.v v12, (%[tmp])\n\t"
+                    "vle8.v v13, (%[t1])\n\t"
+                    "addi %[tmp], %[tmp], 32\n\t"
+                    "addi %[t1], %[t1], 32\n\t"
+                    "vand.vi v3, v3, 0x3\n\t"
                     "vand.vi v4, v4, 0x3\n\t"
-                    "vsetvli zero, %[vl128], e8, m8\n\t"
-                    "vle8.v v8, (%[q8])\n\t"
-                    "vsetvli zero, %[vl64], e8, m4\n\t"
+                    "vand.vi v5, v5, 0x3\n\t"
+                    "vle8.v v14, (%[tmp])\n\t"
+                    "vle8.v v15, (%[t1])\n\t"
                     "vwmul.vv v16, v0, v8\n\t"
+                    "vwmul.vv v18, v1, v9\n\t"
+                    "vwmul.vv v20, v2, v10\n\t"
+                    "vwmul.vv v22, v3, v11\n\t"
                     "vwmul.vv v24, v4, v12\n\t"
-                    "vsetivli zero, 16, e16, m2\n\t"
+                    "vwmul.vv v26, v5, v13\n\t"
+                    "vwmul.vv v28, v6, v14\n\t"
+                    "vwmul.vv v30, v7, v15\n\t"
+                    "vsetivli zero, 8, e16, m1\n\t"
                     "vmv.v.x v0, zero\n\t"
-                    "vwredsum.vs v10, v16, v0\n\t"
+                    "lbu %[tmp], 0(%[scale])\n\t"
+                    "vwredsum.vs v8, v16, v0\n\t"
                     "vwredsum.vs v9, v18, v0\n\t"
-                    "vwredsum.vs v8, v20, v0\n\t"
-                    "vwredsum.vs v7, v22, v0\n\t"
-                    "vwredsum.vs v11, v24, v0\n\t"
-                    "vwredsum.vs v12, v26, v0\n\t"
-                    "vwredsum.vs v13, v28, v0\n\t"
-                    "vwredsum.vs v14, v30, v0\n\t"
+                    "lbu %[t1], 1(%[scale])\n\t"
+                    "vwredsum.vs v10, v20, v0\n\t"
+                    "vwredsum.vs v11, v22, v0\n\t"
+                    "lbu %[t2], 2(%[scale])\n\t"
+                    "vwredsum.vs v12, v24, v0\n\t"
+                    "vwredsum.vs v13, v26, v0\n\t"
+                    "lbu %[t3], 3(%[scale])\n\t"
+                    "vwredsum.vs v14, v28, v0\n\t"
+                    "vwredsum.vs v15, v30, v0\n\t"
+                    "lbu %[t4], 4(%[scale])\n\t"
+                    "vwredsum.vs v8, v17, v8\n\t"
+                    "vwredsum.vs v9, v19, v9\n\t"
+                    "lbu %[t5], 5(%[scale])\n\t"
+                    "vwredsum.vs v10, v21, v10\n\t"
+                    "vwredsum.vs v11, v23, v11\n\t"
+                    "lbu %[t6], 6(%[scale])\n\t"
+                    "vwredsum.vs v12, v25, v12\n\t"
+                    "vwredsum.vs v13, v27, v13\n\t"
+                    "lbu %[t7], 7(%[scale])\n\t"
+                    "vwredsum.vs v14, v29, v14\n\t"
+                    "vwredsum.vs v15, v31, v15\n\t"
                     "vsetivli zero, 4, e32, m1\n\t"
-                    "vslideup.vi v10, v9, 1\n\t"
-                    "vslideup.vi v8, v7, 1\n\t"
-                    "vslideup.vi v11, v12, 1\n\t"
-                    "vslideup.vi v13, v14, 1\n\t"
-                    "vslideup.vi v10, v8, 2\n\t"
-                    "vslideup.vi v11, v13, 2\n\t"
-                    "vsetivli zero, 8, e32, m2\n\t"
-                    "vle8.v v15, (%[scale])\n\t"
-                    "vzext.vf4 v12, v15\n\t"
-                    "vmul.vv v10, v10, v12\n\t"
-                    "vredsum.vs v0, v10, v0\n\t"
+                    "vmul.vx v0, v8, %[tmp]\n\t"
+                    "vmul.vx v1, v9, %[t1]\n\t"
+                    "vmacc.vx v0, %[t2], v10\n\t"
+                    "vmacc.vx v1, %[t3], v11\n\t"
+                    "vmacc.vx v0, %[t4], v12\n\t"
+                    "vmacc.vx v1, %[t5], v13\n\t"
+                    "vmacc.vx v0, %[t6], v14\n\t"
+                    "vmacc.vx v1, %[t7], v15\n\t"
                     "vmv.x.s %[tmp], v0\n\t"
-                    "add %[isum], %[isum], %[tmp]"
-                    : [tmp] "=&r" (tmp), [isum] "+&r" (isum)
+                    "vmv.x.s %[t1], v1\n\t"
+                    "add %[isum], %[isum], %[tmp]\n\t"
+                    "add %[isum], %[isum], %[t1]"
+                    : [tmp] "=&r" (tmp), [t1] "=&r" (t1), [t2] "=&r" (t2), [t3] "=&r" (t3)
+                    , [t4] "=&r" (t4), [t5] "=&r" (t5), [t6] "=&r" (t6), [t7] "=&r" (t7)
+                    , [isum] "+&r" (isum)
                     : [q2] "r" (q2), [scale] "r" (patmp), [q8] "r" (q8)
-                    , [vl32] "r" (32), [vl64] "r" (64), [vl128] "r" (128)
                     : "memory"
                     , "v0", "v1", "v2", "v3", "v4", "v5", "v6", "v7"
                     , "v8", "v9", "v10", "v11", "v12", "v13", "v14", "v15"
@@ -929,7 +975,7 @@ void ggml_vec_dot_q3_K_q8_K(int n, float * GGML_RESTRICT s, size_t bs, const voi
             const  int8_t * restrict q8 = y[i].qs;
 
             int8_t * scale = (int8_t *)utmp;
-            int tmp;
+            int tmp, t1, t2, t3, t4, t5, t6, t7;
             __asm__ __volatile__(
                 "vsetivli zero, 12, e8, m1\n\t"
                 "vle8.v v0, (%[s6b])\n\t"
@@ -967,19 +1013,23 @@ void ggml_vec_dot_q3_K_q8_K(int n, float * GGML_RESTRICT s, size_t bs, const voi
             int isum = 0;
             for (int j = 0; j < QK_K; j += 128) {
                 __asm__ __volatile__(
+                    "lb zero, 31(%[q3])\n\t"
                     "vsetvli zero, %[vl32], e8, m2, ta, mu\n\t"
                     "vle8.v v8, (%[q3])\n\t"
                     "vsrl.vi v10, v8, 2\n\t"
                     "vsrl.vi v12, v8, 4\n\t"
                     "vsrl.vi v14, v8, 6\n\t"
+                    "lb zero, 64(%[q8])\n\t"
                     "vand.vi v8, v8, 3\n\t"
                     "vand.vi v10, v10, 3\n\t"
                     "vand.vi v12, v12, 3\n\t"
                     "vle8.v v2, (%[qh])\n\t"
+                    "lb zero, 127(%[q8])\n\t"
                     "vand.vx v4, v2, %[m]\n\t"
                     "slli %[m], %[m], 1\n\t"
                     "vmseq.vx v0, v4, zero\n\t"
                     "vadd.vi v8, v8, -4, v0.t\n\t"
+                    "lb zero, 0(%[q8])\n\t"
                     "vand.vx v4, v2, %[m]\n\t"
                     "slli %[m], %[m], 1\n\t"
                     "vmseq.vx v0, v4, zero\n\t"
@@ -994,34 +1044,43 @@ void ggml_vec_dot_q3_K_q8_K(int n, float * GGML_RESTRICT s, size_t bs, const voi
                     "vadd.vi v14, v14, -4, v0.t\n\t"
                     "vsetvli zero, %[vl128], e8, m8\n\t"
                     "vle8.v v0, (%[q8])\n\t"
+                    "lb %[tmp], 0(%[scale])\n\t"
+                    "lb %[t1], 1(%[scale])\n\t"
+                    "lb %[t2], 2(%[scale])\n\t"
+                    "lb %[t3], 3(%[scale])\n\t"
                     "vsetvli zero, %[vl64], e8, m4\n\t"
                     "vwmul.vv v16, v0, v8\n\t"
                     "vwmul.vv v24, v4, v12\n\t"
                     "vsetivli zero, 16, e16, m2\n\t"
                     "vmv.v.x v0, zero\n\t"
-                    "vwredsum.vs v10, v16, v0\n\t"
+                    "vwredsum.vs v8, v16, v0\n\t"
+                    "lb %[t4], 4(%[scale])\n\t"
+                    "lb %[t5], 5(%[scale])\n\t"
                     "vwredsum.vs v9, v18, v0\n\t"
-                    "vwredsum.vs v8, v20, v0\n\t"
-                    "vwredsum.vs v7, v22, v0\n\t"
-                    "vwredsum.vs v11, v24, v0\n\t"
-                    "vwredsum.vs v12, v26, v0\n\t"
-                    "vwredsum.vs v13, v28, v0\n\t"
-                    "vwredsum.vs v14, v30, v0\n\t"
+                    "vwredsum.vs v10, v20, v0\n\t"
+                    "vwredsum.vs v11, v22, v0\n\t"
+                    "vwredsum.vs v12, v24, v0\n\t"
+                    "lb %[t6], 6(%[scale])\n\t"
+                    "lb %[t7], 7(%[scale])\n\t"
+                    "vwredsum.vs v13, v26, v0\n\t"
+                    "vwredsum.vs v14, v28, v0\n\t"
+                    "vwredsum.vs v15, v30, v0\n\t"
                     "vsetivli zero, 4, e32, m1\n\t"
-                    "vslideup.vi v10, v9, 1\n\t"
-                    "vslideup.vi v8, v7, 1\n\t"
-                    "vslideup.vi v11, v12, 1\n\t"
-                    "vslideup.vi v13, v14, 1\n\t"
-                    "vslideup.vi v10, v8, 2\n\t"
-                    "vslideup.vi v11, v13, 2\n\t"
-                    "vsetivli zero, 8, e32, m2\n\t"
-                    "vle8.v v15, (%[scale])\n\t"
-                    "vsext.vf4 v12, v15\n\t"
-                    "vmul.vv v10, v10, v12\n\t"
-                    "vredsum.vs v0, v10, v0\n\t"
+                    "vmul.vx v0, v8, %[tmp]\n\t"
+                    "vmul.vx v1, v9, %[t1]\n\t"
+                    "vmacc.vx v0, %[t2], v10\n\t"
+                    "vmacc.vx v1, %[t3], v11\n\t"
+                    "vmacc.vx v0, %[t4], v12\n\t"
+                    "vmacc.vx v1, %[t5], v13\n\t"
+                    "vmacc.vx v0, %[t6], v14\n\t"
+                    "vmacc.vx v1, %[t7], v15\n\t"
                     "vmv.x.s %[tmp], v0\n\t"
-                    "add %[isum], %[isum], %[tmp]"
-                    : [tmp] "=&r" (tmp), [m] "+&r" (m), [isum] "+&r" (isum)
+                    "vmv.x.s %[t1], v1\n\t"
+                    "add %[isum], %[isum], %[tmp]\n\t"
+                    "add %[isum], %[isum], %[t1]"
+                    : [tmp] "=&r" (tmp), [t1] "=&r" (t1), [t2] "=&r" (t2), [t3] "=&r" (t3)
+                    , [t4] "=&r" (t4), [t5] "=&r" (t5), [t6] "=&r" (t6), [t7] "=&r" (t7)
+                    , [m] "+&r" (m), [isum] "+&r" (isum)
                     : [vl128] "r" (128), [vl64] "r" (64), [vl32] "r" (32)
                     , [q3] "r" (q3), [qh] "r" (qh), [scale] "r" (scale), [q8] "r" (q8)
                     : "memory"

From 5c9a18e674be444e847d8e07a6b851764708fb12 Mon Sep 17 00:00:00 2001
From: Xuan-Son Nguyen <son@huggingface.co>
Date: Fri, 7 Nov 2025 11:23:34 +0100
Subject: [PATCH 105/185] common: move download functions to download.(cpp|h)
 (#17059)

* common: move download functions to download.(cpp|h)

* rm unused includes

* minor cleanup

---------

Co-authored-by: Georgi Gerganov <ggerganov@gmail.com>
---
 common/CMakeLists.txt |    2 +
 common/arg.cpp        | 1004 +---------------------------------------
 common/arg.h          |    4 +-
 common/download.cpp   | 1014 +++++++++++++++++++++++++++++++++++++++++
 common/download.h     |   41 ++
 5 files changed, 1066 insertions(+), 999 deletions(-)
 create mode 100644 common/download.cpp
 create mode 100644 common/download.h

diff --git a/common/CMakeLists.txt b/common/CMakeLists.txt
index fe290bf8fdd..7086d08e5e5 100644
--- a/common/CMakeLists.txt
+++ b/common/CMakeLists.txt
@@ -56,6 +56,8 @@ add_library(${TARGET} STATIC
     common.h
     console.cpp
     console.h
+    download.cpp
+    download.h
     http.h
     json-partial.cpp
     json-partial.h
diff --git a/common/arg.cpp b/common/arg.cpp
index 4316917d745..5597de121c1 100644
--- a/common/arg.cpp
+++ b/common/arg.cpp
@@ -2,10 +2,10 @@
 
 #include "chat.h"
 #include "common.h"
-#include "gguf.h" // for reading GGUF splits
 #include "json-schema-to-grammar.h"
 #include "log.h"
 #include "sampling.h"
+#include "download.h"
 
 // fix problem with std::min and std::max
 #if defined(_WIN32)
@@ -22,23 +22,14 @@
 #include <algorithm>
 #include <climits>
 #include <cstdarg>
-#include <filesystem>
 #include <fstream>
-#include <future>
 #include <list>
 #include <regex>
 #include <set>
 #include <string>
-#include <thread>
+#include <thread> // for hardware_concurrency
 #include <vector>
 
-#if defined(LLAMA_USE_CURL)
-#include <curl/curl.h>
-#include <curl/easy.h>
-#else
-#include "http.h"
-#endif
-
 #ifdef __linux__
 #include <linux/limits.h>
 #elif defined(_WIN32)
@@ -52,16 +43,9 @@
 #endif
 #define LLAMA_MAX_URL_LENGTH 2084 // Maximum URL Length in Chrome: 2083
 
-// isatty
-#if defined(_WIN32)
-#include <io.h>
-#else
-#include <unistd.h>
-#endif
-
 using json = nlohmann::ordered_json;
 
-std::initializer_list<enum llama_example> mmproj_examples = {
+static std::initializer_list<enum llama_example> mmproj_examples = {
     LLAMA_EXAMPLE_MTMD,
     LLAMA_EXAMPLE_SERVER,
 };
@@ -76,50 +60,13 @@ static std::string read_file(const std::string & fname) {
     return content;
 }
 
-static void write_file(const std::string & fname, const std::string & content) {
-    const std::string fname_tmp = fname + ".tmp";
-    std::ofstream     file(fname_tmp);
-    if (!file) {
-        throw std::runtime_error(string_format("error: failed to open file '%s'\n", fname.c_str()));
-    }
-
-    try {
-        file << content;
-        file.close();
-
-        // Makes write atomic
-        if (rename(fname_tmp.c_str(), fname.c_str()) != 0) {
-            LOG_ERR("%s: unable to rename file: %s to %s\n", __func__, fname_tmp.c_str(), fname.c_str());
-            // If rename fails, try to delete the temporary file
-            if (remove(fname_tmp.c_str()) != 0) {
-                LOG_ERR("%s: unable to delete temporary file: %s\n", __func__, fname_tmp.c_str());
-            }
-        }
-    } catch (...) {
-        // If anything fails, try to delete the temporary file
-        if (remove(fname_tmp.c_str()) != 0) {
-            LOG_ERR("%s: unable to delete temporary file: %s\n", __func__, fname_tmp.c_str());
-        }
-
-        throw std::runtime_error(string_format("error: failed to write file '%s'\n", fname.c_str()));
-    }
-}
-
-static bool is_output_a_tty() {
-#if defined(_WIN32)
-    return _isatty(_fileno(stdout));
-#else
-    return isatty(1);
-#endif
-}
-
 common_arg & common_arg::set_examples(std::initializer_list<enum llama_example> examples) {
-    this->examples = std::move(examples);
+    this->examples = examples;
     return *this;
 }
 
 common_arg & common_arg::set_excludes(std::initializer_list<enum llama_example> excludes) {
-    this->excludes = std::move(excludes);
+    this->excludes = excludes;
     return *this;
 }
 
@@ -142,7 +89,7 @@ bool common_arg::is_exclude(enum llama_example ex) {
     return excludes.find(ex) != excludes.end();
 }
 
-bool common_arg::get_value_from_env(std::string & output) {
+bool common_arg::get_value_from_env(std::string & output) const {
     if (env == nullptr) return false;
     char * value = std::getenv(env);
     if (value) {
@@ -152,7 +99,7 @@ bool common_arg::get_value_from_env(std::string & output) {
     return false;
 }
 
-bool common_arg::has_value_from_env() {
+bool common_arg::has_value_from_env() const {
     return env != nullptr && std::getenv(env);
 }
 
@@ -220,943 +167,6 @@ std::string common_arg::to_string() {
     return ss.str();
 }
 
-//
-// downloader
-//
-
-struct common_hf_file_res {
-    std::string repo; // repo name with ":tag" removed
-    std::string ggufFile;
-    std::string mmprojFile;
-};
-
-static void write_etag(const std::string & path, const std::string & etag) {
-    const std::string etag_path = path + ".etag";
-    write_file(etag_path, etag);
-    LOG_DBG("%s: file etag saved: %s\n", __func__, etag_path.c_str());
-}
-
-static std::string read_etag(const std::string & path) {
-    std::string none;
-    const std::string etag_path = path + ".etag";
-
-    if (std::filesystem::exists(etag_path)) {
-        std::ifstream etag_in(etag_path);
-        if (!etag_in) {
-            LOG_ERR("%s: could not open .etag file for reading: %s\n", __func__, etag_path.c_str());
-            return none;
-        }
-        std::string etag;
-        std::getline(etag_in, etag);
-        return etag;
-    }
-
-    // no etag file, but maybe there is an old .json
-    // remove this code later
-    const std::string metadata_path = path + ".json";
-
-    if (std::filesystem::exists(metadata_path)) {
-        std::ifstream metadata_in(metadata_path);
-        try {
-            nlohmann::json metadata_json;
-            metadata_in >> metadata_json;
-            LOG_DBG("%s: previous metadata file found %s: %s\n", __func__, metadata_path.c_str(),
-                    metadata_json.dump().c_str());
-            if (metadata_json.contains("etag") && metadata_json.at("etag").is_string()) {
-                std::string etag = metadata_json.at("etag");
-                write_etag(path, etag);
-                if (!std::filesystem::remove(metadata_path)) {
-                    LOG_WRN("%s: failed to delete old .json metadata file: %s\n", __func__, metadata_path.c_str());
-                }
-                return etag;
-            }
-        } catch (const nlohmann::json::exception & e) {
-            LOG_ERR("%s: error reading metadata file %s: %s\n", __func__, metadata_path.c_str(), e.what());
-        }
-    }
-    return none;
-}
-
-#ifdef LLAMA_USE_CURL
-
-//
-// CURL utils
-//
-
-using curl_ptr = std::unique_ptr<CURL, decltype(&curl_easy_cleanup)>;
-
-// cannot use unique_ptr for curl_slist, because we cannot update without destroying the old one
-struct curl_slist_ptr {
-    struct curl_slist * ptr = nullptr;
-    ~curl_slist_ptr() {
-        if (ptr) {
-            curl_slist_free_all(ptr);
-        }
-    }
-};
-
-static CURLcode common_curl_perf(CURL * curl) {
-    CURLcode res = curl_easy_perform(curl);
-    if (res != CURLE_OK) {
-        LOG_ERR("%s: curl_easy_perform() failed\n", __func__);
-    }
-
-    return res;
-}
-
-// Send a HEAD request to retrieve the etag and last-modified headers
-struct common_load_model_from_url_headers {
-    std::string etag;
-    std::string last_modified;
-    std::string accept_ranges;
-};
-
-struct FILE_deleter {
-    void operator()(FILE * f) const { fclose(f); }
-};
-
-static size_t common_header_callback(char * buffer, size_t, size_t n_items, void * userdata) {
-    common_load_model_from_url_headers * headers = (common_load_model_from_url_headers *) userdata;
-    static std::regex                    header_regex("([^:]+): (.*)\r\n");
-    static std::regex                    etag_regex("ETag", std::regex_constants::icase);
-    static std::regex                    last_modified_regex("Last-Modified", std::regex_constants::icase);
-    static std::regex                    accept_ranges_regex("Accept-Ranges", std::regex_constants::icase);
-    std::string                          header(buffer, n_items);
-    std::smatch                          match;
-    if (std::regex_match(header, match, header_regex)) {
-        const std::string & key   = match[1];
-        const std::string & value = match[2];
-        if (std::regex_match(key, match, etag_regex)) {
-            headers->etag = value;
-        } else if (std::regex_match(key, match, last_modified_regex)) {
-            headers->last_modified = value;
-        } else if (std::regex_match(key, match, accept_ranges_regex)) {
-            headers->accept_ranges = value;
-        }
-    }
-
-    return n_items;
-}
-
-static size_t common_write_callback(void * data, size_t size, size_t nmemb, void * fd) {
-    return std::fwrite(data, size, nmemb, static_cast<FILE *>(fd));
-}
-
-// helper function to hide password in URL
-static std::string llama_download_hide_password_in_url(const std::string & url) {
-    // Use regex to match and replace the user[:password]@ pattern in URLs
-    // Pattern: scheme://[user[:password]@]host[...]
-    static const std::regex url_regex(R"(^(?:[A-Za-z][A-Za-z0-9+.-]://)(?:[^/@]+@)?.$)");
-    std::smatch             match;
-
-    if (std::regex_match(url, match, url_regex)) {
-        // match[1] = scheme (e.g., "https://")
-        // match[2] = user[:password]@ part
-        // match[3] = rest of URL (host and path)
-        return match[1].str() + "********@" + match[3].str();
-    }
-
-    return url;  // No credentials found or malformed URL
-}
-
-static void common_curl_easy_setopt_head(CURL * curl, const std::string & url) {
-    // Set the URL, allow to follow http redirection
-    curl_easy_setopt(curl, CURLOPT_URL, url.c_str());
-    curl_easy_setopt(curl, CURLOPT_FOLLOWLOCATION, 1L);
-
-#    if defined(_WIN32)
-    // CURLSSLOPT_NATIVE_CA tells libcurl to use standard certificate store of
-    //   operating system. Currently implemented under MS-Windows.
-    curl_easy_setopt(curl, CURLOPT_SSL_OPTIONS, CURLSSLOPT_NATIVE_CA);
-#    endif
-
-    curl_easy_setopt(curl, CURLOPT_NOBODY, 1L);      // will trigger the HEAD verb
-    curl_easy_setopt(curl, CURLOPT_NOPROGRESS, 1L);  // hide head request progress
-    curl_easy_setopt(curl, CURLOPT_HEADERFUNCTION, common_header_callback);
-}
-
-static void common_curl_easy_setopt_get(CURL * curl) {
-    curl_easy_setopt(curl, CURLOPT_NOBODY, 0L);
-    curl_easy_setopt(curl, CURLOPT_WRITEFUNCTION, common_write_callback);
-
-    //  display download progress
-    curl_easy_setopt(curl, CURLOPT_NOPROGRESS, 0L);
-}
-
-static bool common_pull_file(CURL * curl, const std::string & path_temporary) {
-    if (std::filesystem::exists(path_temporary)) {
-        const std::string partial_size = std::to_string(std::filesystem::file_size(path_temporary));
-        LOG_INF("%s: server supports range requests, resuming download from byte %s\n", __func__, partial_size.c_str());
-        const std::string range_str = partial_size + "-";
-        curl_easy_setopt(curl, CURLOPT_RANGE, range_str.c_str());
-    }
-
-    // Always open file in append mode could be resuming
-    std::unique_ptr<FILE, FILE_deleter> outfile(fopen(path_temporary.c_str(), "ab"));
-    if (!outfile) {
-        LOG_ERR("%s: error opening local file for writing: %s\n", __func__, path_temporary.c_str());
-        return false;
-    }
-
-    common_curl_easy_setopt_get(curl);
-    curl_easy_setopt(curl, CURLOPT_WRITEDATA, outfile.get());
-
-    return common_curl_perf(curl) == CURLE_OK;
-}
-
-static bool common_download_head(CURL *              curl,
-                                 curl_slist_ptr &    http_headers,
-                                 const std::string & url,
-                                 const std::string & bearer_token) {
-    if (!curl) {
-        LOG_ERR("%s: error initializing libcurl\n", __func__);
-        return false;
-    }
-
-    http_headers.ptr = curl_slist_append(http_headers.ptr, "User-Agent: llama-cpp");
-    // Check if hf-token or bearer-token was specified
-    if (!bearer_token.empty()) {
-        std::string auth_header = "Authorization: Bearer " + bearer_token;
-        http_headers.ptr        = curl_slist_append(http_headers.ptr, auth_header.c_str());
-    }
-
-    curl_easy_setopt(curl, CURLOPT_HTTPHEADER, http_headers.ptr);
-    common_curl_easy_setopt_head(curl, url);
-    return common_curl_perf(curl) == CURLE_OK;
-}
-
-// download one single file from remote URL to local path
-static bool common_download_file_single_online(const std::string & url,
-                                               const std::string & path,
-                                               const std::string & bearer_token) {
-    static const int max_attempts        = 3;
-    static const int retry_delay_seconds = 2;
-    for (int i = 0; i < max_attempts; ++i) {
-        std::string etag;
-
-        // Check if the file already exists locally
-        const auto file_exists = std::filesystem::exists(path);
-        if (file_exists) {
-            etag = read_etag(path);
-        } else {
-            LOG_INF("%s: no previous model file found %s\n", __func__, path.c_str());
-        }
-
-        bool head_request_ok = false;
-        bool should_download = !file_exists;  // by default, we should download if the file does not exist
-
-        // Initialize libcurl
-        curl_ptr curl(curl_easy_init(), &curl_easy_cleanup);
-        common_load_model_from_url_headers headers;
-        curl_easy_setopt(curl.get(), CURLOPT_HEADERDATA, &headers);
-        curl_slist_ptr http_headers;
-        const bool     was_perform_successful = common_download_head(curl.get(), http_headers, url, bearer_token);
-        if (!was_perform_successful) {
-            head_request_ok = false;
-        }
-
-        long http_code = 0;
-        curl_easy_getinfo(curl.get(), CURLINFO_RESPONSE_CODE, &http_code);
-        if (http_code == 200) {
-            head_request_ok = true;
-        } else {
-            LOG_WRN("%s: HEAD invalid http status code received: %ld\n", __func__, http_code);
-            head_request_ok = false;
-        }
-
-        // if head_request_ok is false, we don't have the etag or last-modified headers
-        // we leave should_download as-is, which is true if the file does not exist
-        bool should_download_from_scratch = false;
-        if (head_request_ok) {
-            // check if ETag or Last-Modified headers are different
-            // if it is, we need to download the file again
-            if (!etag.empty() && etag != headers.etag) {
-                LOG_WRN("%s: ETag header is different (%s != %s): triggering a new download\n", __func__, etag.c_str(),
-                        headers.etag.c_str());
-                should_download              = true;
-                should_download_from_scratch = true;
-            }
-        }
-
-        const bool accept_ranges_supported = !headers.accept_ranges.empty() && headers.accept_ranges != "none";
-        if (should_download) {
-            if (file_exists &&
-                !accept_ranges_supported) {  // Resumable downloads not supported, delete and start again.
-                LOG_WRN("%s: deleting previous downloaded file: %s\n", __func__, path.c_str());
-                if (remove(path.c_str()) != 0) {
-                    LOG_ERR("%s: unable to delete file: %s\n", __func__, path.c_str());
-                    return false;
-                }
-            }
-
-            const std::string path_temporary = path + ".downloadInProgress";
-            if (should_download_from_scratch) {
-                if (std::filesystem::exists(path_temporary)) {
-                    if (remove(path_temporary.c_str()) != 0) {
-                        LOG_ERR("%s: unable to delete file: %s\n", __func__, path_temporary.c_str());
-                        return false;
-                    }
-                }
-
-                if (std::filesystem::exists(path)) {
-                    if (remove(path.c_str()) != 0) {
-                        LOG_ERR("%s: unable to delete file: %s\n", __func__, path.c_str());
-                        return false;
-                    }
-                }
-            }
-            if (head_request_ok) {
-                write_etag(path, headers.etag);
-            }
-
-            // start the download
-            LOG_INF("%s: trying to download model from %s to %s (server_etag:%s, server_last_modified:%s)...\n",
-                    __func__, llama_download_hide_password_in_url(url).c_str(), path_temporary.c_str(),
-                    headers.etag.c_str(), headers.last_modified.c_str());
-            const bool was_pull_successful = common_pull_file(curl.get(), path_temporary);
-            if (!was_pull_successful) {
-                if (i + 1 < max_attempts) {
-                    const int exponential_backoff_delay = std::pow(retry_delay_seconds, i) * 1000;
-                    LOG_WRN("%s: retrying after %d milliseconds...\n", __func__, exponential_backoff_delay);
-                    std::this_thread::sleep_for(std::chrono::milliseconds(exponential_backoff_delay));
-                } else {
-                    LOG_ERR("%s: curl_easy_perform() failed after %d attempts\n", __func__, max_attempts);
-                }
-
-                continue;
-            }
-
-            long http_code = 0;
-            curl_easy_getinfo(curl.get(), CURLINFO_RESPONSE_CODE, &http_code);
-            if (http_code < 200 || http_code >= 400) {
-                LOG_ERR("%s: invalid http status code received: %ld\n", __func__, http_code);
-                return false;
-            }
-
-            if (rename(path_temporary.c_str(), path.c_str()) != 0) {
-                LOG_ERR("%s: unable to rename file: %s to %s\n", __func__, path_temporary.c_str(), path.c_str());
-                return false;
-            }
-        } else {
-            LOG_INF("%s: using cached file: %s\n", __func__, path.c_str());
-        }
-
-        break;
-    }
-
-    return true;
-}
-
-std::pair<long, std::vector<char>> common_remote_get_content(const std::string & url, const common_remote_params & params) {
-    curl_ptr       curl(curl_easy_init(), &curl_easy_cleanup);
-    curl_slist_ptr http_headers;
-    std::vector<char> res_buffer;
-
-    curl_easy_setopt(curl.get(), CURLOPT_URL, url.c_str());
-    curl_easy_setopt(curl.get(), CURLOPT_NOPROGRESS, 1L);
-    curl_easy_setopt(curl.get(), CURLOPT_FOLLOWLOCATION, 1L);
-    curl_easy_setopt(curl.get(), CURLOPT_VERBOSE, 1L);
-    typedef size_t(*CURLOPT_WRITEFUNCTION_PTR)(void * ptr, size_t size, size_t nmemb, void * data);
-    auto write_callback = [](void * ptr, size_t size, size_t nmemb, void * data) -> size_t {
-        auto data_vec = static_cast<std::vector<char> *>(data);
-        data_vec->insert(data_vec->end(), (char *)ptr, (char *)ptr + size * nmemb);
-        return size * nmemb;
-    };
-    curl_easy_setopt(curl.get(), CURLOPT_WRITEFUNCTION, static_cast<CURLOPT_WRITEFUNCTION_PTR>(write_callback));
-    curl_easy_setopt(curl.get(), CURLOPT_WRITEDATA, &res_buffer);
-#if defined(_WIN32)
-    curl_easy_setopt(curl.get(), CURLOPT_SSL_OPTIONS, CURLSSLOPT_NATIVE_CA);
-#endif
-    if (params.timeout > 0) {
-        curl_easy_setopt(curl.get(), CURLOPT_TIMEOUT, params.timeout);
-    }
-    if (params.max_size > 0) {
-        curl_easy_setopt(curl.get(), CURLOPT_MAXFILESIZE, params.max_size);
-    }
-    http_headers.ptr = curl_slist_append(http_headers.ptr, "User-Agent: llama-cpp");
-    for (const auto & header : params.headers) {
-        http_headers.ptr = curl_slist_append(http_headers.ptr, header.c_str());
-    }
-    curl_easy_setopt(curl.get(), CURLOPT_HTTPHEADER, http_headers.ptr);
-
-    CURLcode res = curl_easy_perform(curl.get());
-
-    if (res != CURLE_OK) {
-        std::string error_msg = curl_easy_strerror(res);
-        throw std::runtime_error("error: cannot make GET request: " + error_msg);
-    }
-
-    long res_code;
-    curl_easy_getinfo(curl.get(), CURLINFO_RESPONSE_CODE, &res_code);
-
-    return { res_code, std::move(res_buffer) };
-}
-
-#else
-
-static void print_progress(size_t current, size_t total) {
-    if (!is_output_a_tty()) {
-        return;
-    }
-
-    if (!total) {
-        return;
-    }
-
-    size_t width = 50;
-    size_t pct = (100 * current) / total;
-    size_t pos = (width * current) / total;
-
-    std::cout << "["
-              << std::string(pos, '=')
-              << (pos < width ? ">" : "")
-              << std::string(width - pos, ' ')
-              << "] " << std::setw(3) << pct << "%  ("
-              << current / (1024 * 1024) << " MB / "
-              << total / (1024 * 1024) << " MB)\r";
-    std::cout.flush();
-}
-
-static bool common_pull_file(httplib::Client & cli,
-                             const std::string & resolve_path,
-                             const std::string & path_tmp,
-                             bool supports_ranges,
-                             size_t existing_size,
-                             size_t & total_size) {
-    std::ofstream ofs(path_tmp, std::ios::binary | std::ios::app);
-    if (!ofs.is_open()) {
-        LOG_ERR("%s: error opening local file for writing: %s\n", __func__, path_tmp.c_str());
-        return false;
-    }
-
-    httplib::Headers headers;
-    if (supports_ranges && existing_size > 0) {
-        headers.emplace("Range", "bytes=" + std::to_string(existing_size) + "-");
-    }
-
-    std::atomic<size_t> downloaded{existing_size};
-
-    auto res = cli.Get(resolve_path, headers,
-        [&](const httplib::Response &response) {
-            if (existing_size > 0 && response.status != 206) {
-                LOG_WRN("%s: server did not respond with 206 Partial Content for a resume request. Status: %d\n", __func__, response.status);
-                return false;
-            }
-            if (existing_size == 0 && response.status != 200) {
-                LOG_WRN("%s: download received non-successful status code: %d\n", __func__, response.status);
-                return false;
-            }
-            if (total_size == 0 && response.has_header("Content-Length")) {
-                try {
-                    size_t content_length = std::stoull(response.get_header_value("Content-Length"));
-                    total_size = existing_size + content_length;
-                } catch (const std::exception &e) {
-                    LOG_WRN("%s: invalid Content-Length header: %s\n", __func__, e.what());
-                }
-            }
-            return true;
-        },
-        [&](const char *data, size_t len) {
-            ofs.write(data, len);
-            if (!ofs) {
-                LOG_ERR("%s: error writing to file: %s\n", __func__, path_tmp.c_str());
-                return false;
-            }
-            downloaded += len;
-            print_progress(downloaded, total_size);
-            return true;
-        },
-        nullptr
-    );
-
-    std::cout << "\n";
-
-    if (!res) {
-        LOG_ERR("%s: error during download. Status: %d\n", __func__, res ? res->status : -1);
-        return false;
-    }
-
-    return true;
-}
-
-// download one single file from remote URL to local path
-static bool common_download_file_single_online(const std::string & url,
-                                               const std::string & path,
-                                               const std::string & bearer_token) {
-    static const int max_attempts        = 3;
-    static const int retry_delay_seconds = 2;
-
-    auto [cli, parts] = common_http_client(url);
-
-    httplib::Headers default_headers = {{"User-Agent", "llama-cpp"}};
-    if (!bearer_token.empty()) {
-        default_headers.insert({"Authorization", "Bearer " + bearer_token});
-    }
-    cli.set_default_headers(default_headers);
-
-    const bool file_exists = std::filesystem::exists(path);
-
-    std::string last_etag;
-    if (file_exists) {
-        last_etag = read_etag(path);
-    } else {
-        LOG_INF("%s: no previous model file found %s\n", __func__, path.c_str());
-    }
-
-    for (int i = 0; i < max_attempts; ++i) {
-        auto head = cli.Head(parts.path);
-        bool head_ok = head && head->status >= 200 && head->status < 300;
-        if (!head_ok) {
-            LOG_WRN("%s: HEAD invalid http status code received: %d\n", __func__, head ? head->status : -1);
-            if (file_exists) {
-                LOG_INF("%s: Using cached file (HEAD failed): %s\n", __func__, path.c_str());
-                return true;
-            }
-        }
-
-        std::string etag;
-        if (head_ok && head->has_header("ETag")) {
-            etag = head->get_header_value("ETag");
-        }
-
-        size_t total_size = 0;
-        if (head_ok && head->has_header("Content-Length")) {
-            try {
-                total_size = std::stoull(head->get_header_value("Content-Length"));
-            } catch (const std::exception& e) {
-                LOG_WRN("%s: Invalid Content-Length in HEAD response: %s\n", __func__, e.what());
-            }
-        }
-
-        bool supports_ranges = false;
-        if (head_ok && head->has_header("Accept-Ranges")) {
-            supports_ranges = head->get_header_value("Accept-Ranges") != "none";
-        }
-
-        bool should_download_from_scratch = false;
-        if (!last_etag.empty() && !etag.empty() && last_etag != etag) {
-            LOG_WRN("%s: ETag header is different (%s != %s): triggering a new download\n", __func__,
-                    last_etag.c_str(), etag.c_str());
-            should_download_from_scratch = true;
-        }
-
-        if (file_exists) {
-            if (!should_download_from_scratch) {
-                LOG_INF("%s: using cached file: %s\n", __func__, path.c_str());
-                return true;
-            }
-            LOG_WRN("%s: deleting previous downloaded file: %s\n", __func__, path.c_str());
-            if (remove(path.c_str()) != 0) {
-                LOG_ERR("%s: unable to delete file: %s\n", __func__, path.c_str());
-                return false;
-            }
-        }
-
-        const std::string path_temporary = path + ".downloadInProgress";
-        size_t existing_size = 0;
-
-        if (std::filesystem::exists(path_temporary)) {
-            if (supports_ranges && !should_download_from_scratch) {
-                existing_size = std::filesystem::file_size(path_temporary);
-            } else if (remove(path_temporary.c_str()) != 0) {
-                LOG_ERR("%s: unable to delete file: %s\n", __func__, path_temporary.c_str());
-                return false;
-            }
-        }
-
-        // start the download
-        LOG_INF("%s: trying to download model from %s to %s (etag:%s)...\n",
-                __func__, common_http_show_masked_url(parts).c_str(), path_temporary.c_str(), etag.c_str());
-        const bool was_pull_successful = common_pull_file(cli, parts.path, path_temporary, supports_ranges, existing_size, total_size);
-        if (!was_pull_successful) {
-            if (i + 1 < max_attempts) {
-                const int exponential_backoff_delay = std::pow(retry_delay_seconds, i) * 1000;
-                LOG_WRN("%s: retrying after %d milliseconds...\n", __func__, exponential_backoff_delay);
-                std::this_thread::sleep_for(std::chrono::milliseconds(exponential_backoff_delay));
-            } else {
-                LOG_ERR("%s: download failed after %d attempts\n", __func__, max_attempts);
-            }
-            continue;
-        }
-
-        if (std::rename(path_temporary.c_str(), path.c_str()) != 0) {
-            LOG_ERR("%s: unable to rename file: %s to %s\n", __func__, path_temporary.c_str(), path.c_str());
-            return false;
-        }
-        if (!etag.empty()) {
-            write_etag(path, etag);
-        }
-        break;
-    }
-
-    return true;
-}
-
-std::pair<long, std::vector<char>> common_remote_get_content(const std::string          & url,
-                                                             const common_remote_params & params) {
-    auto [cli, parts] = common_http_client(url);
-
-    httplib::Headers headers = {{"User-Agent", "llama-cpp"}};
-    for (const auto & header : params.headers) {
-        size_t pos = header.find(':');
-        if (pos != std::string::npos) {
-            headers.emplace(header.substr(0, pos), header.substr(pos + 1));
-        } else {
-            headers.emplace(header, "");
-        }
-    }
-
-    if (params.timeout > 0) {
-        cli.set_read_timeout(params.timeout, 0);
-        cli.set_write_timeout(params.timeout, 0);
-    }
-
-    std::vector<char> buf;
-    auto res = cli.Get(parts.path, headers,
-        [&](const char *data, size_t len) {
-            buf.insert(buf.end(), data, data + len);
-            return params.max_size == 0 ||
-                   buf.size() <= static_cast<size_t>(params.max_size);
-        },
-        nullptr
-    );
-
-    if (!res) {
-        throw std::runtime_error("error: cannot make GET request");
-    }
-
-    return { res->status, std::move(buf) };
-}
-
-#endif // LLAMA_USE_CURL
-
-static bool common_download_file_single(const std::string & url,
-                                        const std::string & path,
-                                        const std::string & bearer_token,
-                                        bool                offline) {
-    if (!offline) {
-        return common_download_file_single_online(url, path, bearer_token);
-    }
-
-    if (!std::filesystem::exists(path)) {
-        LOG_ERR("%s: required file is not available in cache (offline mode): %s\n", __func__, path.c_str());
-        return false;
-    }
-
-    LOG_INF("%s: using cached file (offline mode): %s\n", __func__, path.c_str());
-    return true;
-}
-
-// download multiple files from remote URLs to local paths
-// the input is a vector of pairs <url, path>
-static bool common_download_file_multiple(const std::vector<std::pair<std::string, std::string>> & urls, const std::string & bearer_token, bool offline) {
-    // Prepare download in parallel
-    std::vector<std::future<bool>> futures_download;
-    for (auto const & item : urls) {
-        futures_download.push_back(std::async(std::launch::async, [bearer_token, offline](const std::pair<std::string, std::string> & it) -> bool {
-            return common_download_file_single(it.first, it.second, bearer_token, offline);
-        }, item));
-    }
-
-    // Wait for all downloads to complete
-    for (auto & f : futures_download) {
-        if (!f.get()) {
-            return false;
-        }
-    }
-
-    return true;
-}
-
-static bool common_download_model(
-        const common_params_model & model,
-        const std::string & bearer_token,
-        bool offline) {
-    // Basic validation of the model.url
-    if (model.url.empty()) {
-        LOG_ERR("%s: invalid model url\n", __func__);
-        return false;
-    }
-
-    if (!common_download_file_single(model.url, model.path, bearer_token, offline)) {
-        return false;
-    }
-
-    // check for additional GGUFs split to download
-    int n_split = 0;
-    {
-        struct gguf_init_params gguf_params = {
-            /*.no_alloc = */ true,
-            /*.ctx      = */ NULL,
-        };
-        auto * ctx_gguf = gguf_init_from_file(model.path.c_str(), gguf_params);
-        if (!ctx_gguf) {
-            LOG_ERR("\n%s:  failed to load input GGUF from %s\n", __func__, model.path.c_str());
-            return false;
-        }
-
-        auto key_n_split = gguf_find_key(ctx_gguf, LLM_KV_SPLIT_COUNT);
-        if (key_n_split >= 0) {
-            n_split = gguf_get_val_u16(ctx_gguf, key_n_split);
-        }
-
-        gguf_free(ctx_gguf);
-    }
-
-    if (n_split > 1) {
-        char split_prefix[PATH_MAX] = {0};
-        char split_url_prefix[LLAMA_MAX_URL_LENGTH] = {0};
-
-        // Verify the first split file format
-        // and extract split URL and PATH prefixes
-        {
-            if (!llama_split_prefix(split_prefix, sizeof(split_prefix), model.path.c_str(), 0, n_split)) {
-                LOG_ERR("\n%s: unexpected model file name: %s n_split=%d\n", __func__, model.path.c_str(), n_split);
-                return false;
-            }
-
-            if (!llama_split_prefix(split_url_prefix, sizeof(split_url_prefix), model.url.c_str(), 0, n_split)) {
-                LOG_ERR("\n%s: unexpected model url: %s n_split=%d\n", __func__, model.url.c_str(), n_split);
-                return false;
-            }
-        }
-
-        std::vector<std::pair<std::string, std::string>> urls;
-        for (int idx = 1; idx < n_split; idx++) {
-            char split_path[PATH_MAX] = {0};
-            llama_split_path(split_path, sizeof(split_path), split_prefix, idx, n_split);
-
-            char split_url[LLAMA_MAX_URL_LENGTH] = {0};
-            llama_split_path(split_url, sizeof(split_url), split_url_prefix, idx, n_split);
-
-            if (std::string(split_path) == model.path) {
-                continue; // skip the already downloaded file
-            }
-
-            urls.push_back({split_url, split_path});
-        }
-
-        // Download in parallel
-        common_download_file_multiple(urls, bearer_token, offline);
-    }
-
-    return true;
-}
-
-/**
- * Allow getting the HF file from the HF repo with tag (like ollama), for example:
- * - bartowski/Llama-3.2-3B-Instruct-GGUF:q4
- * - bartowski/Llama-3.2-3B-Instruct-GGUF:Q4_K_M
- * - bartowski/Llama-3.2-3B-Instruct-GGUF:q5_k_s
- * Tag is optional, default to "latest" (meaning it checks for Q4_K_M first, then Q4, then if not found, return the first GGUF file in repo)
- *
- * Return pair of <repo, file> (with "repo" already having tag removed)
- *
- * Note: we use the Ollama-compatible HF API, but not using the blobId. Instead, we use the special "ggufFile" field which returns the value for "hf_file". This is done to be backward-compatible with existing cache files.
- */
-static struct common_hf_file_res common_get_hf_file(const std::string & hf_repo_with_tag, const std::string & bearer_token, bool offline) {
-    auto parts = string_split<std::string>(hf_repo_with_tag, ':');
-    std::string tag = parts.size() > 1 ? parts.back() : "latest";
-    std::string hf_repo = parts[0];
-    if (string_split<std::string>(hf_repo, '/').size() != 2) {
-        throw std::invalid_argument("error: invalid HF repo format, expected <user>/<model>[:quant]\n");
-    }
-
-    std::string url = get_model_endpoint() + "v2/" + hf_repo + "/manifests/" + tag;
-
-    // headers
-    std::vector<std::string> headers;
-    headers.push_back("Accept: application/json");
-    if (!bearer_token.empty()) {
-        headers.push_back("Authorization: Bearer " + bearer_token);
-    }
-    // Important: the User-Agent must be "llama-cpp" to get the "ggufFile" field in the response
-    // User-Agent header is already set in common_remote_get_content, no need to set it here
-
-    // we use "=" to avoid clashing with other component, while still being allowed on windows
-    std::string cached_response_fname = "manifest=" + hf_repo + "=" + tag + ".json";
-    string_replace_all(cached_response_fname, "/", "_");
-    std::string cached_response_path = fs_get_cache_file(cached_response_fname);
-
-    // make the request
-    common_remote_params params;
-    params.headers = headers;
-    long res_code = 0;
-    std::string res_str;
-    bool use_cache = false;
-    if (!offline) {
-        try {
-            auto res = common_remote_get_content(url, params);
-            res_code = res.first;
-            res_str = std::string(res.second.data(), res.second.size());
-        } catch (const std::exception & e) {
-            LOG_WRN("error: failed to get manifest at %s: %s\n", url.c_str(), e.what());
-        }
-    }
-    if (res_code == 0) {
-        if (std::filesystem::exists(cached_response_path)) {
-            LOG_WRN("trying to read manifest from cache: %s\n", cached_response_path.c_str());
-            res_str = read_file(cached_response_path);
-            res_code = 200;
-            use_cache = true;
-        } else {
-            throw std::runtime_error(
-                offline ? "error: failed to get manifest (offline mode)"
-                : "error: failed to get manifest (check your internet connection)");
-        }
-    }
-    std::string ggufFile;
-    std::string mmprojFile;
-
-    if (res_code == 200 || res_code == 304) {
-        try {
-            auto j = json::parse(res_str);
-
-            if (j.contains("ggufFile") && j["ggufFile"].contains("rfilename")) {
-                ggufFile = j["ggufFile"]["rfilename"].get<std::string>();
-            }
-            if (j.contains("mmprojFile") && j["mmprojFile"].contains("rfilename")) {
-                mmprojFile = j["mmprojFile"]["rfilename"].get<std::string>();
-            }
-        } catch (const std::exception & e) {
-            throw std::runtime_error(std::string("error parsing manifest JSON: ") + e.what());
-        }
-        if (!use_cache) {
-            // if not using cached response, update the cache file
-            write_file(cached_response_path, res_str);
-        }
-    } else if (res_code == 401) {
-        throw std::runtime_error("error: model is private or does not exist; if you are accessing a gated model, please provide a valid HF token");
-    } else {
-        throw std::runtime_error(string_format("error from HF API, response code: %ld, data: %s", res_code, res_str.c_str()));
-    }
-
-    // check response
-    if (ggufFile.empty()) {
-        throw std::runtime_error("error: model does not have ggufFile");
-    }
-
-    return { hf_repo, ggufFile, mmprojFile };
-}
-
-//
-// Docker registry functions
-//
-
-static std::string common_docker_get_token(const std::string & repo) {
-    std::string url = "https://auth.docker.io/token?service=registry.docker.io&scope=repository:" + repo + ":pull";
-
-    common_remote_params params;
-    auto                 res = common_remote_get_content(url, params);
-
-    if (res.first != 200) {
-        throw std::runtime_error("Failed to get Docker registry token, HTTP code: " + std::to_string(res.first));
-    }
-
-    std::string            response_str(res.second.begin(), res.second.end());
-    nlohmann::ordered_json response = nlohmann::ordered_json::parse(response_str);
-
-    if (!response.contains("token")) {
-        throw std::runtime_error("Docker registry token response missing 'token' field");
-    }
-
-    return response["token"].get<std::string>();
-}
-
-static std::string common_docker_resolve_model(const std::string & docker) {
-    // Parse ai/smollm2:135M-Q4_0
-    size_t      colon_pos = docker.find(':');
-    std::string repo, tag;
-    if (colon_pos != std::string::npos) {
-        repo = docker.substr(0, colon_pos);
-        tag  = docker.substr(colon_pos + 1);
-    } else {
-        repo = docker;
-        tag  = "latest";
-    }
-
-    // ai/ is the default
-    size_t      slash_pos = docker.find('/');
-    if (slash_pos == std::string::npos) {
-        repo.insert(0, "ai/");
-    }
-
-    LOG_INF("%s: Downloading Docker Model: %s:%s\n", __func__, repo.c_str(), tag.c_str());
-    try {
-        // --- helper: digest validation ---
-        auto validate_oci_digest = [](const std::string & digest) -> std::string {
-            // Expected: algo:hex ; start with sha256 (64 hex chars)
-            // You can extend this map if supporting other algorithms in future.
-            static const std::regex re("^sha256:([a-fA-F0-9]{64})$");
-            std::smatch m;
-            if (!std::regex_match(digest, m, re)) {
-                throw std::runtime_error("Invalid OCI digest format received in manifest: " + digest);
-            }
-            // normalize hex to lowercase
-            std::string normalized = digest;
-            std::transform(normalized.begin()+7, normalized.end(), normalized.begin()+7, [](unsigned char c){
-                return std::tolower(c);
-            });
-            return normalized;
-        };
-
-        std::string token = common_docker_get_token(repo);  // Get authentication token
-
-        // Get manifest
-        const std::string    url_prefix = "https://registry-1.docker.io/v2/" + repo;
-        std::string          manifest_url = url_prefix + "/manifests/" + tag;
-        common_remote_params manifest_params;
-        manifest_params.headers.push_back("Authorization: Bearer " + token);
-        manifest_params.headers.push_back(
-            "Accept: application/vnd.docker.distribution.manifest.v2+json,application/vnd.oci.image.manifest.v1+json");
-        auto manifest_res = common_remote_get_content(manifest_url, manifest_params);
-        if (manifest_res.first != 200) {
-            throw std::runtime_error("Failed to get Docker manifest, HTTP code: " + std::to_string(manifest_res.first));
-        }
-
-        std::string            manifest_str(manifest_res.second.begin(), manifest_res.second.end());
-        nlohmann::ordered_json manifest = nlohmann::ordered_json::parse(manifest_str);
-        std::string            gguf_digest;  // Find the GGUF layer
-        if (manifest.contains("layers")) {
-            for (const auto & layer : manifest["layers"]) {
-                if (layer.contains("mediaType")) {
-                    std::string media_type = layer["mediaType"].get<std::string>();
-                    if (media_type == "application/vnd.docker.ai.gguf.v3" ||
-                        media_type.find("gguf") != std::string::npos) {
-                        gguf_digest = layer["digest"].get<std::string>();
-                        break;
-                    }
-                }
-            }
-        }
-
-        if (gguf_digest.empty()) {
-            throw std::runtime_error("No GGUF layer found in Docker manifest");
-        }
-
-        // Validate & normalize digest
-        gguf_digest = validate_oci_digest(gguf_digest);
-        LOG_DBG("%s: Using validated digest: %s\n", __func__, gguf_digest.c_str());
-
-        // Prepare local filename
-        std::string model_filename = repo;
-        std::replace(model_filename.begin(), model_filename.end(), '/', '_');
-        model_filename += "_" + tag + ".gguf";
-        std::string local_path = fs_get_cache_file(model_filename);
-
-        const std::string blob_url = url_prefix + "/blobs/" + gguf_digest;
-        if (!common_download_file_single(blob_url, local_path, token, false)) {
-            throw std::runtime_error("Failed to download Docker Model");
-        }
-
-        LOG_INF("%s: Downloaded Docker Model to: %s\n", __func__, local_path.c_str());
-        return local_path;
-    } catch (const std::exception & e) {
-        LOG_ERR("%s: Docker Model download failed: %s\n", __func__, e.what());
-        throw;
-    }
-}
-
 //
 // utils
 //
diff --git a/common/arg.h b/common/arg.h
index 77997c4ef39..7ab7e2cea43 100644
--- a/common/arg.h
+++ b/common/arg.h
@@ -59,8 +59,8 @@ struct common_arg {
     common_arg & set_sparam();
     bool in_example(enum llama_example ex);
     bool is_exclude(enum llama_example ex);
-    bool get_value_from_env(std::string & output);
-    bool has_value_from_env();
+    bool get_value_from_env(std::string & output) const;
+    bool has_value_from_env() const;
     std::string to_string();
 };
 
diff --git a/common/download.cpp b/common/download.cpp
new file mode 100644
index 00000000000..02d75fc0d09
--- /dev/null
+++ b/common/download.cpp
@@ -0,0 +1,1014 @@
+#include "arg.h"
+
+#include "common.h"
+#include "gguf.h" // for reading GGUF splits
+#include "log.h"
+#include "download.h"
+
+#define JSON_ASSERT GGML_ASSERT
+#include <nlohmann/json.hpp>
+
+#include <algorithm>
+#include <filesystem>
+#include <fstream>
+#include <future>
+#include <regex>
+#include <string>
+#include <thread>
+#include <vector>
+
+#if defined(LLAMA_USE_CURL)
+#include <curl/curl.h>
+#include <curl/easy.h>
+#else
+#include "http.h"
+#endif
+
+#ifdef __linux__
+#include <linux/limits.h>
+#elif defined(_WIN32)
+#   if !defined(PATH_MAX)
+#   define PATH_MAX MAX_PATH
+#   endif
+#elif defined(_AIX)
+#include <sys/limits.h>
+#else
+#include <sys/syslimits.h>
+#endif
+#define LLAMA_MAX_URL_LENGTH 2084 // Maximum URL Length in Chrome: 2083
+
+// isatty
+#if defined(_WIN32)
+#include <io.h>
+#else
+#include <unistd.h>
+#endif
+
+using json = nlohmann::ordered_json;
+
+//
+// downloader
+//
+
+static std::string read_file(const std::string & fname) {
+    std::ifstream file(fname);
+    if (!file) {
+        throw std::runtime_error(string_format("error: failed to open file '%s'\n", fname.c_str()));
+    }
+    std::string content((std::istreambuf_iterator<char>(file)), std::istreambuf_iterator<char>());
+    file.close();
+    return content;
+}
+
+static void write_file(const std::string & fname, const std::string & content) {
+    const std::string fname_tmp = fname + ".tmp";
+    std::ofstream     file(fname_tmp);
+    if (!file) {
+        throw std::runtime_error(string_format("error: failed to open file '%s'\n", fname.c_str()));
+    }
+
+    try {
+        file << content;
+        file.close();
+
+        // Makes write atomic
+        if (rename(fname_tmp.c_str(), fname.c_str()) != 0) {
+            LOG_ERR("%s: unable to rename file: %s to %s\n", __func__, fname_tmp.c_str(), fname.c_str());
+            // If rename fails, try to delete the temporary file
+            if (remove(fname_tmp.c_str()) != 0) {
+                LOG_ERR("%s: unable to delete temporary file: %s\n", __func__, fname_tmp.c_str());
+            }
+        }
+    } catch (...) {
+        // If anything fails, try to delete the temporary file
+        if (remove(fname_tmp.c_str()) != 0) {
+            LOG_ERR("%s: unable to delete temporary file: %s\n", __func__, fname_tmp.c_str());
+        }
+
+        throw std::runtime_error(string_format("error: failed to write file '%s'\n", fname.c_str()));
+    }
+}
+
+static void write_etag(const std::string & path, const std::string & etag) {
+    const std::string etag_path = path + ".etag";
+    write_file(etag_path, etag);
+    LOG_DBG("%s: file etag saved: %s\n", __func__, etag_path.c_str());
+}
+
+static std::string read_etag(const std::string & path) {
+    std::string none;
+    const std::string etag_path = path + ".etag";
+
+    if (std::filesystem::exists(etag_path)) {
+        std::ifstream etag_in(etag_path);
+        if (!etag_in) {
+            LOG_ERR("%s: could not open .etag file for reading: %s\n", __func__, etag_path.c_str());
+            return none;
+        }
+        std::string etag;
+        std::getline(etag_in, etag);
+        return etag;
+    }
+
+    // no etag file, but maybe there is an old .json
+    // remove this code later
+    const std::string metadata_path = path + ".json";
+
+    if (std::filesystem::exists(metadata_path)) {
+        std::ifstream metadata_in(metadata_path);
+        try {
+            nlohmann::json metadata_json;
+            metadata_in >> metadata_json;
+            LOG_DBG("%s: previous metadata file found %s: %s\n", __func__, metadata_path.c_str(),
+                    metadata_json.dump().c_str());
+            if (metadata_json.contains("etag") && metadata_json.at("etag").is_string()) {
+                std::string etag = metadata_json.at("etag");
+                write_etag(path, etag);
+                if (!std::filesystem::remove(metadata_path)) {
+                    LOG_WRN("%s: failed to delete old .json metadata file: %s\n", __func__, metadata_path.c_str());
+                }
+                return etag;
+            }
+        } catch (const nlohmann::json::exception & e) {
+            LOG_ERR("%s: error reading metadata file %s: %s\n", __func__, metadata_path.c_str(), e.what());
+        }
+    }
+    return none;
+}
+
+#ifdef LLAMA_USE_CURL
+
+//
+// CURL utils
+//
+
+using curl_ptr = std::unique_ptr<CURL, decltype(&curl_easy_cleanup)>;
+
+// cannot use unique_ptr for curl_slist, because we cannot update without destroying the old one
+struct curl_slist_ptr {
+    struct curl_slist * ptr = nullptr;
+    ~curl_slist_ptr() {
+        if (ptr) {
+            curl_slist_free_all(ptr);
+        }
+    }
+};
+
+static CURLcode common_curl_perf(CURL * curl) {
+    CURLcode res = curl_easy_perform(curl);
+    if (res != CURLE_OK) {
+        LOG_ERR("%s: curl_easy_perform() failed\n", __func__);
+    }
+
+    return res;
+}
+
+// Send a HEAD request to retrieve the etag and last-modified headers
+struct common_load_model_from_url_headers {
+    std::string etag;
+    std::string last_modified;
+    std::string accept_ranges;
+};
+
+struct FILE_deleter {
+    void operator()(FILE * f) const { fclose(f); }
+};
+
+static size_t common_header_callback(char * buffer, size_t, size_t n_items, void * userdata) {
+    common_load_model_from_url_headers * headers = (common_load_model_from_url_headers *) userdata;
+    static std::regex                    header_regex("([^:]+): (.*)\r\n");
+    static std::regex                    etag_regex("ETag", std::regex_constants::icase);
+    static std::regex                    last_modified_regex("Last-Modified", std::regex_constants::icase);
+    static std::regex                    accept_ranges_regex("Accept-Ranges", std::regex_constants::icase);
+    std::string                          header(buffer, n_items);
+    std::smatch                          match;
+    if (std::regex_match(header, match, header_regex)) {
+        const std::string & key   = match[1];
+        const std::string & value = match[2];
+        if (std::regex_match(key, match, etag_regex)) {
+            headers->etag = value;
+        } else if (std::regex_match(key, match, last_modified_regex)) {
+            headers->last_modified = value;
+        } else if (std::regex_match(key, match, accept_ranges_regex)) {
+            headers->accept_ranges = value;
+        }
+    }
+
+    return n_items;
+}
+
+static size_t common_write_callback(void * data, size_t size, size_t nmemb, void * fd) {
+    return std::fwrite(data, size, nmemb, static_cast<FILE *>(fd));
+}
+
+// helper function to hide password in URL
+static std::string llama_download_hide_password_in_url(const std::string & url) {
+    // Use regex to match and replace the user[:password]@ pattern in URLs
+    // Pattern: scheme://[user[:password]@]host[...]
+    static const std::regex url_regex(R"(^(?:[A-Za-z][A-Za-z0-9+.-]://)(?:[^/@]+@)?.$)");
+    std::smatch             match;
+
+    if (std::regex_match(url, match, url_regex)) {
+        // match[1] = scheme (e.g., "https://")
+        // match[2] = user[:password]@ part
+        // match[3] = rest of URL (host and path)
+        return match[1].str() + "********@" + match[3].str();
+    }
+
+    return url;  // No credentials found or malformed URL
+}
+
+static void common_curl_easy_setopt_head(CURL * curl, const std::string & url) {
+    // Set the URL, allow to follow http redirection
+    curl_easy_setopt(curl, CURLOPT_URL, url.c_str());
+    curl_easy_setopt(curl, CURLOPT_FOLLOWLOCATION, 1L);
+
+#    if defined(_WIN32)
+    // CURLSSLOPT_NATIVE_CA tells libcurl to use standard certificate store of
+    //   operating system. Currently implemented under MS-Windows.
+    curl_easy_setopt(curl, CURLOPT_SSL_OPTIONS, CURLSSLOPT_NATIVE_CA);
+#    endif
+
+    curl_easy_setopt(curl, CURLOPT_NOBODY, 1L);      // will trigger the HEAD verb
+    curl_easy_setopt(curl, CURLOPT_NOPROGRESS, 1L);  // hide head request progress
+    curl_easy_setopt(curl, CURLOPT_HEADERFUNCTION, common_header_callback);
+}
+
+static void common_curl_easy_setopt_get(CURL * curl) {
+    curl_easy_setopt(curl, CURLOPT_NOBODY, 0L);
+    curl_easy_setopt(curl, CURLOPT_WRITEFUNCTION, common_write_callback);
+
+    //  display download progress
+    curl_easy_setopt(curl, CURLOPT_NOPROGRESS, 0L);
+}
+
+static bool common_pull_file(CURL * curl, const std::string & path_temporary) {
+    if (std::filesystem::exists(path_temporary)) {
+        const std::string partial_size = std::to_string(std::filesystem::file_size(path_temporary));
+        LOG_INF("%s: server supports range requests, resuming download from byte %s\n", __func__, partial_size.c_str());
+        const std::string range_str = partial_size + "-";
+        curl_easy_setopt(curl, CURLOPT_RANGE, range_str.c_str());
+    }
+
+    // Always open file in append mode could be resuming
+    std::unique_ptr<FILE, FILE_deleter> outfile(fopen(path_temporary.c_str(), "ab"));
+    if (!outfile) {
+        LOG_ERR("%s: error opening local file for writing: %s\n", __func__, path_temporary.c_str());
+        return false;
+    }
+
+    common_curl_easy_setopt_get(curl);
+    curl_easy_setopt(curl, CURLOPT_WRITEDATA, outfile.get());
+
+    return common_curl_perf(curl) == CURLE_OK;
+}
+
+static bool common_download_head(CURL *              curl,
+                                 curl_slist_ptr &    http_headers,
+                                 const std::string & url,
+                                 const std::string & bearer_token) {
+    if (!curl) {
+        LOG_ERR("%s: error initializing libcurl\n", __func__);
+        return false;
+    }
+
+    http_headers.ptr = curl_slist_append(http_headers.ptr, "User-Agent: llama-cpp");
+    // Check if hf-token or bearer-token was specified
+    if (!bearer_token.empty()) {
+        std::string auth_header = "Authorization: Bearer " + bearer_token;
+        http_headers.ptr        = curl_slist_append(http_headers.ptr, auth_header.c_str());
+    }
+
+    curl_easy_setopt(curl, CURLOPT_HTTPHEADER, http_headers.ptr);
+    common_curl_easy_setopt_head(curl, url);
+    return common_curl_perf(curl) == CURLE_OK;
+}
+
+// download one single file from remote URL to local path
+static bool common_download_file_single_online(const std::string & url,
+                                               const std::string & path,
+                                               const std::string & bearer_token) {
+    static const int max_attempts        = 3;
+    static const int retry_delay_seconds = 2;
+    for (int i = 0; i < max_attempts; ++i) {
+        std::string etag;
+
+        // Check if the file already exists locally
+        const auto file_exists = std::filesystem::exists(path);
+        if (file_exists) {
+            etag = read_etag(path);
+        } else {
+            LOG_INF("%s: no previous model file found %s\n", __func__, path.c_str());
+        }
+
+        bool head_request_ok = false;
+        bool should_download = !file_exists;  // by default, we should download if the file does not exist
+
+        // Initialize libcurl
+        curl_ptr curl(curl_easy_init(), &curl_easy_cleanup);
+        common_load_model_from_url_headers headers;
+        curl_easy_setopt(curl.get(), CURLOPT_HEADERDATA, &headers);
+        curl_slist_ptr http_headers;
+        const bool     was_perform_successful = common_download_head(curl.get(), http_headers, url, bearer_token);
+        if (!was_perform_successful) {
+            head_request_ok = false;
+        }
+
+        long http_code = 0;
+        curl_easy_getinfo(curl.get(), CURLINFO_RESPONSE_CODE, &http_code);
+        if (http_code == 200) {
+            head_request_ok = true;
+        } else {
+            LOG_WRN("%s: HEAD invalid http status code received: %ld\n", __func__, http_code);
+            head_request_ok = false;
+        }
+
+        // if head_request_ok is false, we don't have the etag or last-modified headers
+        // we leave should_download as-is, which is true if the file does not exist
+        bool should_download_from_scratch = false;
+        if (head_request_ok) {
+            // check if ETag or Last-Modified headers are different
+            // if it is, we need to download the file again
+            if (!etag.empty() && etag != headers.etag) {
+                LOG_WRN("%s: ETag header is different (%s != %s): triggering a new download\n", __func__, etag.c_str(),
+                        headers.etag.c_str());
+                should_download              = true;
+                should_download_from_scratch = true;
+            }
+        }
+
+        const bool accept_ranges_supported = !headers.accept_ranges.empty() && headers.accept_ranges != "none";
+        if (should_download) {
+            if (file_exists &&
+                !accept_ranges_supported) {  // Resumable downloads not supported, delete and start again.
+                LOG_WRN("%s: deleting previous downloaded file: %s\n", __func__, path.c_str());
+                if (remove(path.c_str()) != 0) {
+                    LOG_ERR("%s: unable to delete file: %s\n", __func__, path.c_str());
+                    return false;
+                }
+            }
+
+            const std::string path_temporary = path + ".downloadInProgress";
+            if (should_download_from_scratch) {
+                if (std::filesystem::exists(path_temporary)) {
+                    if (remove(path_temporary.c_str()) != 0) {
+                        LOG_ERR("%s: unable to delete file: %s\n", __func__, path_temporary.c_str());
+                        return false;
+                    }
+                }
+
+                if (std::filesystem::exists(path)) {
+                    if (remove(path.c_str()) != 0) {
+                        LOG_ERR("%s: unable to delete file: %s\n", __func__, path.c_str());
+                        return false;
+                    }
+                }
+            }
+            if (head_request_ok) {
+                write_etag(path, headers.etag);
+            }
+
+            // start the download
+            LOG_INF("%s: trying to download model from %s to %s (server_etag:%s, server_last_modified:%s)...\n",
+                    __func__, llama_download_hide_password_in_url(url).c_str(), path_temporary.c_str(),
+                    headers.etag.c_str(), headers.last_modified.c_str());
+            const bool was_pull_successful = common_pull_file(curl.get(), path_temporary);
+            if (!was_pull_successful) {
+                if (i + 1 < max_attempts) {
+                    const int exponential_backoff_delay = std::pow(retry_delay_seconds, i) * 1000;
+                    LOG_WRN("%s: retrying after %d milliseconds...\n", __func__, exponential_backoff_delay);
+                    std::this_thread::sleep_for(std::chrono::milliseconds(exponential_backoff_delay));
+                } else {
+                    LOG_ERR("%s: curl_easy_perform() failed after %d attempts\n", __func__, max_attempts);
+                }
+
+                continue;
+            }
+
+            long http_code = 0;
+            curl_easy_getinfo(curl.get(), CURLINFO_RESPONSE_CODE, &http_code);
+            if (http_code < 200 || http_code >= 400) {
+                LOG_ERR("%s: invalid http status code received: %ld\n", __func__, http_code);
+                return false;
+            }
+
+            if (rename(path_temporary.c_str(), path.c_str()) != 0) {
+                LOG_ERR("%s: unable to rename file: %s to %s\n", __func__, path_temporary.c_str(), path.c_str());
+                return false;
+            }
+        } else {
+            LOG_INF("%s: using cached file: %s\n", __func__, path.c_str());
+        }
+
+        break;
+    }
+
+    return true;
+}
+
+std::pair<long, std::vector<char>> common_remote_get_content(const std::string & url, const common_remote_params & params) {
+    curl_ptr       curl(curl_easy_init(), &curl_easy_cleanup);
+    curl_slist_ptr http_headers;
+    std::vector<char> res_buffer;
+
+    curl_easy_setopt(curl.get(), CURLOPT_URL, url.c_str());
+    curl_easy_setopt(curl.get(), CURLOPT_NOPROGRESS, 1L);
+    curl_easy_setopt(curl.get(), CURLOPT_FOLLOWLOCATION, 1L);
+    curl_easy_setopt(curl.get(), CURLOPT_VERBOSE, 1L);
+    typedef size_t(*CURLOPT_WRITEFUNCTION_PTR)(void * ptr, size_t size, size_t nmemb, void * data);
+    auto write_callback = [](void * ptr, size_t size, size_t nmemb, void * data) -> size_t {
+        auto data_vec = static_cast<std::vector<char> *>(data);
+        data_vec->insert(data_vec->end(), (char *)ptr, (char *)ptr + size * nmemb);
+        return size * nmemb;
+    };
+    curl_easy_setopt(curl.get(), CURLOPT_WRITEFUNCTION, static_cast<CURLOPT_WRITEFUNCTION_PTR>(write_callback));
+    curl_easy_setopt(curl.get(), CURLOPT_WRITEDATA, &res_buffer);
+#if defined(_WIN32)
+    curl_easy_setopt(curl.get(), CURLOPT_SSL_OPTIONS, CURLSSLOPT_NATIVE_CA);
+#endif
+    if (params.timeout > 0) {
+        curl_easy_setopt(curl.get(), CURLOPT_TIMEOUT, params.timeout);
+    }
+    if (params.max_size > 0) {
+        curl_easy_setopt(curl.get(), CURLOPT_MAXFILESIZE, params.max_size);
+    }
+    http_headers.ptr = curl_slist_append(http_headers.ptr, "User-Agent: llama-cpp");
+    for (const auto & header : params.headers) {
+        http_headers.ptr = curl_slist_append(http_headers.ptr, header.c_str());
+    }
+    curl_easy_setopt(curl.get(), CURLOPT_HTTPHEADER, http_headers.ptr);
+
+    CURLcode res = curl_easy_perform(curl.get());
+
+    if (res != CURLE_OK) {
+        std::string error_msg = curl_easy_strerror(res);
+        throw std::runtime_error("error: cannot make GET request: " + error_msg);
+    }
+
+    long res_code;
+    curl_easy_getinfo(curl.get(), CURLINFO_RESPONSE_CODE, &res_code);
+
+    return { res_code, std::move(res_buffer) };
+}
+
+#else
+
+static bool is_output_a_tty() {
+#if defined(_WIN32)
+    return _isatty(_fileno(stdout));
+#else
+    return isatty(1);
+#endif
+}
+
+static void print_progress(size_t current, size_t total) {
+    if (!is_output_a_tty()) {
+        return;
+    }
+
+    if (!total) {
+        return;
+    }
+
+    size_t width = 50;
+    size_t pct = (100 * current) / total;
+    size_t pos = (width * current) / total;
+
+    std::cout << "["
+              << std::string(pos, '=')
+              << (pos < width ? ">" : "")
+              << std::string(width - pos, ' ')
+              << "] " << std::setw(3) << pct << "%  ("
+              << current / (1024 * 1024) << " MB / "
+              << total / (1024 * 1024) << " MB)\r";
+    std::cout.flush();
+}
+
+static bool common_pull_file(httplib::Client & cli,
+                             const std::string & resolve_path,
+                             const std::string & path_tmp,
+                             bool supports_ranges,
+                             size_t existing_size,
+                             size_t & total_size) {
+    std::ofstream ofs(path_tmp, std::ios::binary | std::ios::app);
+    if (!ofs.is_open()) {
+        LOG_ERR("%s: error opening local file for writing: %s\n", __func__, path_tmp.c_str());
+        return false;
+    }
+
+    httplib::Headers headers;
+    if (supports_ranges && existing_size > 0) {
+        headers.emplace("Range", "bytes=" + std::to_string(existing_size) + "-");
+    }
+
+    std::atomic<size_t> downloaded{existing_size};
+
+    auto res = cli.Get(resolve_path, headers,
+        [&](const httplib::Response &response) {
+            if (existing_size > 0 && response.status != 206) {
+                LOG_WRN("%s: server did not respond with 206 Partial Content for a resume request. Status: %d\n", __func__, response.status);
+                return false;
+            }
+            if (existing_size == 0 && response.status != 200) {
+                LOG_WRN("%s: download received non-successful status code: %d\n", __func__, response.status);
+                return false;
+            }
+            if (total_size == 0 && response.has_header("Content-Length")) {
+                try {
+                    size_t content_length = std::stoull(response.get_header_value("Content-Length"));
+                    total_size = existing_size + content_length;
+                } catch (const std::exception &e) {
+                    LOG_WRN("%s: invalid Content-Length header: %s\n", __func__, e.what());
+                }
+            }
+            return true;
+        },
+        [&](const char *data, size_t len) {
+            ofs.write(data, len);
+            if (!ofs) {
+                LOG_ERR("%s: error writing to file: %s\n", __func__, path_tmp.c_str());
+                return false;
+            }
+            downloaded += len;
+            print_progress(downloaded, total_size);
+            return true;
+        },
+        nullptr
+    );
+
+    std::cout << "\n";
+
+    if (!res) {
+        LOG_ERR("%s: error during download. Status: %d\n", __func__, res ? res->status : -1);
+        return false;
+    }
+
+    return true;
+}
+
+// download one single file from remote URL to local path
+static bool common_download_file_single_online(const std::string & url,
+                                               const std::string & path,
+                                               const std::string & bearer_token) {
+    static const int max_attempts        = 3;
+    static const int retry_delay_seconds = 2;
+
+    auto [cli, parts] = common_http_client(url);
+
+    httplib::Headers default_headers = {{"User-Agent", "llama-cpp"}};
+    if (!bearer_token.empty()) {
+        default_headers.insert({"Authorization", "Bearer " + bearer_token});
+    }
+    cli.set_default_headers(default_headers);
+
+    const bool file_exists = std::filesystem::exists(path);
+
+    std::string last_etag;
+    if (file_exists) {
+        last_etag = read_etag(path);
+    } else {
+        LOG_INF("%s: no previous model file found %s\n", __func__, path.c_str());
+    }
+
+    for (int i = 0; i < max_attempts; ++i) {
+        auto head = cli.Head(parts.path);
+        bool head_ok = head && head->status >= 200 && head->status < 300;
+        if (!head_ok) {
+            LOG_WRN("%s: HEAD invalid http status code received: %d\n", __func__, head ? head->status : -1);
+            if (file_exists) {
+                LOG_INF("%s: Using cached file (HEAD failed): %s\n", __func__, path.c_str());
+                return true;
+            }
+        }
+
+        std::string etag;
+        if (head_ok && head->has_header("ETag")) {
+            etag = head->get_header_value("ETag");
+        }
+
+        size_t total_size = 0;
+        if (head_ok && head->has_header("Content-Length")) {
+            try {
+                total_size = std::stoull(head->get_header_value("Content-Length"));
+            } catch (const std::exception& e) {
+                LOG_WRN("%s: Invalid Content-Length in HEAD response: %s\n", __func__, e.what());
+            }
+        }
+
+        bool supports_ranges = false;
+        if (head_ok && head->has_header("Accept-Ranges")) {
+            supports_ranges = head->get_header_value("Accept-Ranges") != "none";
+        }
+
+        bool should_download_from_scratch = false;
+        if (!last_etag.empty() && !etag.empty() && last_etag != etag) {
+            LOG_WRN("%s: ETag header is different (%s != %s): triggering a new download\n", __func__,
+                    last_etag.c_str(), etag.c_str());
+            should_download_from_scratch = true;
+        }
+
+        if (file_exists) {
+            if (!should_download_from_scratch) {
+                LOG_INF("%s: using cached file: %s\n", __func__, path.c_str());
+                return true;
+            }
+            LOG_WRN("%s: deleting previous downloaded file: %s\n", __func__, path.c_str());
+            if (remove(path.c_str()) != 0) {
+                LOG_ERR("%s: unable to delete file: %s\n", __func__, path.c_str());
+                return false;
+            }
+        }
+
+        const std::string path_temporary = path + ".downloadInProgress";
+        size_t existing_size = 0;
+
+        if (std::filesystem::exists(path_temporary)) {
+            if (supports_ranges && !should_download_from_scratch) {
+                existing_size = std::filesystem::file_size(path_temporary);
+            } else if (remove(path_temporary.c_str()) != 0) {
+                LOG_ERR("%s: unable to delete file: %s\n", __func__, path_temporary.c_str());
+                return false;
+            }
+        }
+
+        // start the download
+        LOG_INF("%s: trying to download model from %s to %s (etag:%s)...\n",
+                __func__, common_http_show_masked_url(parts).c_str(), path_temporary.c_str(), etag.c_str());
+        const bool was_pull_successful = common_pull_file(cli, parts.path, path_temporary, supports_ranges, existing_size, total_size);
+        if (!was_pull_successful) {
+            if (i + 1 < max_attempts) {
+                const int exponential_backoff_delay = std::pow(retry_delay_seconds, i) * 1000;
+                LOG_WRN("%s: retrying after %d milliseconds...\n", __func__, exponential_backoff_delay);
+                std::this_thread::sleep_for(std::chrono::milliseconds(exponential_backoff_delay));
+            } else {
+                LOG_ERR("%s: download failed after %d attempts\n", __func__, max_attempts);
+            }
+            continue;
+        }
+
+        if (std::rename(path_temporary.c_str(), path.c_str()) != 0) {
+            LOG_ERR("%s: unable to rename file: %s to %s\n", __func__, path_temporary.c_str(), path.c_str());
+            return false;
+        }
+        if (!etag.empty()) {
+            write_etag(path, etag);
+        }
+        break;
+    }
+
+    return true;
+}
+
+std::pair<long, std::vector<char>> common_remote_get_content(const std::string          & url,
+                                                             const common_remote_params & params) {
+    auto [cli, parts] = common_http_client(url);
+
+    httplib::Headers headers = {{"User-Agent", "llama-cpp"}};
+    for (const auto & header : params.headers) {
+        size_t pos = header.find(':');
+        if (pos != std::string::npos) {
+            headers.emplace(header.substr(0, pos), header.substr(pos + 1));
+        } else {
+            headers.emplace(header, "");
+        }
+    }
+
+    if (params.timeout > 0) {
+        cli.set_read_timeout(params.timeout, 0);
+        cli.set_write_timeout(params.timeout, 0);
+    }
+
+    std::vector<char> buf;
+    auto res = cli.Get(parts.path, headers,
+        [&](const char *data, size_t len) {
+            buf.insert(buf.end(), data, data + len);
+            return params.max_size == 0 ||
+                   buf.size() <= static_cast<size_t>(params.max_size);
+        },
+        nullptr
+    );
+
+    if (!res) {
+        throw std::runtime_error("error: cannot make GET request");
+    }
+
+    return { res->status, std::move(buf) };
+}
+
+#endif // LLAMA_USE_CURL
+
+static bool common_download_file_single(const std::string & url,
+                                        const std::string & path,
+                                        const std::string & bearer_token,
+                                        bool                offline) {
+    if (!offline) {
+        return common_download_file_single_online(url, path, bearer_token);
+    }
+
+    if (!std::filesystem::exists(path)) {
+        LOG_ERR("%s: required file is not available in cache (offline mode): %s\n", __func__, path.c_str());
+        return false;
+    }
+
+    LOG_INF("%s: using cached file (offline mode): %s\n", __func__, path.c_str());
+    return true;
+}
+
+// download multiple files from remote URLs to local paths
+// the input is a vector of pairs <url, path>
+static bool common_download_file_multiple(const std::vector<std::pair<std::string, std::string>> & urls, const std::string & bearer_token, bool offline) {
+    // Prepare download in parallel
+    std::vector<std::future<bool>> futures_download;
+    for (auto const & item : urls) {
+        futures_download.push_back(std::async(std::launch::async, [bearer_token, offline](const std::pair<std::string, std::string> & it) -> bool {
+            return common_download_file_single(it.first, it.second, bearer_token, offline);
+        }, item));
+    }
+
+    // Wait for all downloads to complete
+    for (auto & f : futures_download) {
+        if (!f.get()) {
+            return false;
+        }
+    }
+
+    return true;
+}
+
+bool common_download_model(
+        const common_params_model & model,
+        const std::string & bearer_token,
+        bool offline) {
+    // Basic validation of the model.url
+    if (model.url.empty()) {
+        LOG_ERR("%s: invalid model url\n", __func__);
+        return false;
+    }
+
+    if (!common_download_file_single(model.url, model.path, bearer_token, offline)) {
+        return false;
+    }
+
+    // check for additional GGUFs split to download
+    int n_split = 0;
+    {
+        struct gguf_init_params gguf_params = {
+            /*.no_alloc = */ true,
+            /*.ctx      = */ NULL,
+        };
+        auto * ctx_gguf = gguf_init_from_file(model.path.c_str(), gguf_params);
+        if (!ctx_gguf) {
+            LOG_ERR("\n%s:  failed to load input GGUF from %s\n", __func__, model.path.c_str());
+            return false;
+        }
+
+        auto key_n_split = gguf_find_key(ctx_gguf, LLM_KV_SPLIT_COUNT);
+        if (key_n_split >= 0) {
+            n_split = gguf_get_val_u16(ctx_gguf, key_n_split);
+        }
+
+        gguf_free(ctx_gguf);
+    }
+
+    if (n_split > 1) {
+        char split_prefix[PATH_MAX] = {0};
+        char split_url_prefix[LLAMA_MAX_URL_LENGTH] = {0};
+
+        // Verify the first split file format
+        // and extract split URL and PATH prefixes
+        {
+            if (!llama_split_prefix(split_prefix, sizeof(split_prefix), model.path.c_str(), 0, n_split)) {
+                LOG_ERR("\n%s: unexpected model file name: %s n_split=%d\n", __func__, model.path.c_str(), n_split);
+                return false;
+            }
+
+            if (!llama_split_prefix(split_url_prefix, sizeof(split_url_prefix), model.url.c_str(), 0, n_split)) {
+                LOG_ERR("\n%s: unexpected model url: %s n_split=%d\n", __func__, model.url.c_str(), n_split);
+                return false;
+            }
+        }
+
+        std::vector<std::pair<std::string, std::string>> urls;
+        for (int idx = 1; idx < n_split; idx++) {
+            char split_path[PATH_MAX] = {0};
+            llama_split_path(split_path, sizeof(split_path), split_prefix, idx, n_split);
+
+            char split_url[LLAMA_MAX_URL_LENGTH] = {0};
+            llama_split_path(split_url, sizeof(split_url), split_url_prefix, idx, n_split);
+
+            if (std::string(split_path) == model.path) {
+                continue; // skip the already downloaded file
+            }
+
+            urls.push_back({split_url, split_path});
+        }
+
+        // Download in parallel
+        common_download_file_multiple(urls, bearer_token, offline);
+    }
+
+    return true;
+}
+
+common_hf_file_res common_get_hf_file(const std::string & hf_repo_with_tag, const std::string & bearer_token, bool offline) {
+    auto parts = string_split<std::string>(hf_repo_with_tag, ':');
+    std::string tag = parts.size() > 1 ? parts.back() : "latest";
+    std::string hf_repo = parts[0];
+    if (string_split<std::string>(hf_repo, '/').size() != 2) {
+        throw std::invalid_argument("error: invalid HF repo format, expected <user>/<model>[:quant]\n");
+    }
+
+    std::string url = get_model_endpoint() + "v2/" + hf_repo + "/manifests/" + tag;
+
+    // headers
+    std::vector<std::string> headers;
+    headers.push_back("Accept: application/json");
+    if (!bearer_token.empty()) {
+        headers.push_back("Authorization: Bearer " + bearer_token);
+    }
+    // Important: the User-Agent must be "llama-cpp" to get the "ggufFile" field in the response
+    // User-Agent header is already set in common_remote_get_content, no need to set it here
+
+    // we use "=" to avoid clashing with other component, while still being allowed on windows
+    std::string cached_response_fname = "manifest=" + hf_repo + "=" + tag + ".json";
+    string_replace_all(cached_response_fname, "/", "_");
+    std::string cached_response_path = fs_get_cache_file(cached_response_fname);
+
+    // make the request
+    common_remote_params params;
+    params.headers = headers;
+    long res_code = 0;
+    std::string res_str;
+    bool use_cache = false;
+    if (!offline) {
+        try {
+            auto res = common_remote_get_content(url, params);
+            res_code = res.first;
+            res_str = std::string(res.second.data(), res.second.size());
+        } catch (const std::exception & e) {
+            LOG_WRN("error: failed to get manifest at %s: %s\n", url.c_str(), e.what());
+        }
+    }
+    if (res_code == 0) {
+        if (std::filesystem::exists(cached_response_path)) {
+            LOG_WRN("trying to read manifest from cache: %s\n", cached_response_path.c_str());
+            res_str = read_file(cached_response_path);
+            res_code = 200;
+            use_cache = true;
+        } else {
+            throw std::runtime_error(
+                offline ? "error: failed to get manifest (offline mode)"
+                : "error: failed to get manifest (check your internet connection)");
+        }
+    }
+    std::string ggufFile;
+    std::string mmprojFile;
+
+    if (res_code == 200 || res_code == 304) {
+        try {
+            auto j = json::parse(res_str);
+
+            if (j.contains("ggufFile") && j["ggufFile"].contains("rfilename")) {
+                ggufFile = j["ggufFile"]["rfilename"].get<std::string>();
+            }
+            if (j.contains("mmprojFile") && j["mmprojFile"].contains("rfilename")) {
+                mmprojFile = j["mmprojFile"]["rfilename"].get<std::string>();
+            }
+        } catch (const std::exception & e) {
+            throw std::runtime_error(std::string("error parsing manifest JSON: ") + e.what());
+        }
+        if (!use_cache) {
+            // if not using cached response, update the cache file
+            write_file(cached_response_path, res_str);
+        }
+    } else if (res_code == 401) {
+        throw std::runtime_error("error: model is private or does not exist; if you are accessing a gated model, please provide a valid HF token");
+    } else {
+        throw std::runtime_error(string_format("error from HF API, response code: %ld, data: %s", res_code, res_str.c_str()));
+    }
+
+    // check response
+    if (ggufFile.empty()) {
+        throw std::runtime_error("error: model does not have ggufFile");
+    }
+
+    return { hf_repo, ggufFile, mmprojFile };
+}
+
+//
+// Docker registry functions
+//
+
+static std::string common_docker_get_token(const std::string & repo) {
+    std::string url = "https://auth.docker.io/token?service=registry.docker.io&scope=repository:" + repo + ":pull";
+
+    common_remote_params params;
+    auto                 res = common_remote_get_content(url, params);
+
+    if (res.first != 200) {
+        throw std::runtime_error("Failed to get Docker registry token, HTTP code: " + std::to_string(res.first));
+    }
+
+    std::string            response_str(res.second.begin(), res.second.end());
+    nlohmann::ordered_json response = nlohmann::ordered_json::parse(response_str);
+
+    if (!response.contains("token")) {
+        throw std::runtime_error("Docker registry token response missing 'token' field");
+    }
+
+    return response["token"].get<std::string>();
+}
+
+std::string common_docker_resolve_model(const std::string & docker) {
+    // Parse ai/smollm2:135M-Q4_0
+    size_t      colon_pos = docker.find(':');
+    std::string repo, tag;
+    if (colon_pos != std::string::npos) {
+        repo = docker.substr(0, colon_pos);
+        tag  = docker.substr(colon_pos + 1);
+    } else {
+        repo = docker;
+        tag  = "latest";
+    }
+
+    // ai/ is the default
+    size_t      slash_pos = docker.find('/');
+    if (slash_pos == std::string::npos) {
+        repo.insert(0, "ai/");
+    }
+
+    LOG_INF("%s: Downloading Docker Model: %s:%s\n", __func__, repo.c_str(), tag.c_str());
+    try {
+        // --- helper: digest validation ---
+        auto validate_oci_digest = [](const std::string & digest) -> std::string {
+            // Expected: algo:hex ; start with sha256 (64 hex chars)
+            // You can extend this map if supporting other algorithms in future.
+            static const std::regex re("^sha256:([a-fA-F0-9]{64})$");
+            std::smatch m;
+            if (!std::regex_match(digest, m, re)) {
+                throw std::runtime_error("Invalid OCI digest format received in manifest: " + digest);
+            }
+            // normalize hex to lowercase
+            std::string normalized = digest;
+            std::transform(normalized.begin()+7, normalized.end(), normalized.begin()+7, [](unsigned char c){
+                return std::tolower(c);
+            });
+            return normalized;
+        };
+
+        std::string token = common_docker_get_token(repo);  // Get authentication token
+
+        // Get manifest
+        const std::string    url_prefix = "https://registry-1.docker.io/v2/" + repo;
+        std::string          manifest_url = url_prefix + "/manifests/" + tag;
+        common_remote_params manifest_params;
+        manifest_params.headers.push_back("Authorization: Bearer " + token);
+        manifest_params.headers.push_back(
+            "Accept: application/vnd.docker.distribution.manifest.v2+json,application/vnd.oci.image.manifest.v1+json");
+        auto manifest_res = common_remote_get_content(manifest_url, manifest_params);
+        if (manifest_res.first != 200) {
+            throw std::runtime_error("Failed to get Docker manifest, HTTP code: " + std::to_string(manifest_res.first));
+        }
+
+        std::string            manifest_str(manifest_res.second.begin(), manifest_res.second.end());
+        nlohmann::ordered_json manifest = nlohmann::ordered_json::parse(manifest_str);
+        std::string            gguf_digest;  // Find the GGUF layer
+        if (manifest.contains("layers")) {
+            for (const auto & layer : manifest["layers"]) {
+                if (layer.contains("mediaType")) {
+                    std::string media_type = layer["mediaType"].get<std::string>();
+                    if (media_type == "application/vnd.docker.ai.gguf.v3" ||
+                        media_type.find("gguf") != std::string::npos) {
+                        gguf_digest = layer["digest"].get<std::string>();
+                        break;
+                    }
+                }
+            }
+        }
+
+        if (gguf_digest.empty()) {
+            throw std::runtime_error("No GGUF layer found in Docker manifest");
+        }
+
+        // Validate & normalize digest
+        gguf_digest = validate_oci_digest(gguf_digest);
+        LOG_DBG("%s: Using validated digest: %s\n", __func__, gguf_digest.c_str());
+
+        // Prepare local filename
+        std::string model_filename = repo;
+        std::replace(model_filename.begin(), model_filename.end(), '/', '_');
+        model_filename += "_" + tag + ".gguf";
+        std::string local_path = fs_get_cache_file(model_filename);
+
+        const std::string blob_url = url_prefix + "/blobs/" + gguf_digest;
+        if (!common_download_file_single(blob_url, local_path, token, false)) {
+            throw std::runtime_error("Failed to download Docker Model");
+        }
+
+        LOG_INF("%s: Downloaded Docker Model to: %s\n", __func__, local_path.c_str());
+        return local_path;
+    } catch (const std::exception & e) {
+        LOG_ERR("%s: Docker Model download failed: %s\n", __func__, e.what());
+        throw;
+    }
+}
diff --git a/common/download.h b/common/download.h
new file mode 100644
index 00000000000..ddf36155ef8
--- /dev/null
+++ b/common/download.h
@@ -0,0 +1,41 @@
+#pragma once
+
+#include <string>
+
+struct common_params_model;
+
+//
+// download functionalities
+//
+
+struct common_hf_file_res {
+    std::string repo; // repo name with ":tag" removed
+    std::string ggufFile;
+    std::string mmprojFile;
+};
+
+// resolve and download model from Docker registry
+// return local path to downloaded model file
+std::string common_docker_resolve_model(const std::string & docker);
+
+/**
+ * Allow getting the HF file from the HF repo with tag (like ollama), for example:
+ * - bartowski/Llama-3.2-3B-Instruct-GGUF:q4
+ * - bartowski/Llama-3.2-3B-Instruct-GGUF:Q4_K_M
+ * - bartowski/Llama-3.2-3B-Instruct-GGUF:q5_k_s
+ * Tag is optional, default to "latest" (meaning it checks for Q4_K_M first, then Q4, then if not found, return the first GGUF file in repo)
+ *
+ * Return pair of <repo, file> (with "repo" already having tag removed)
+ *
+ * Note: we use the Ollama-compatible HF API, but not using the blobId. Instead, we use the special "ggufFile" field which returns the value for "hf_file". This is done to be backward-compatible with existing cache files.
+ */
+common_hf_file_res common_get_hf_file(
+    const std::string & hf_repo_with_tag,
+    const std::string & bearer_token,
+    bool offline);
+
+// returns true if download succeeded
+bool common_download_model(
+    const common_params_model & model,
+    const std::string & bearer_token,
+    bool offline);

From 8c0d6bb4559e15f1236035a0465781c1345324e5 Mon Sep 17 00:00:00 2001
From: Georgi Gerganov <ggerganov@gmail.com>
Date: Fri, 7 Nov 2025 12:24:47 +0200
Subject: [PATCH 106/185] server : print the samplers chain for each request
 (#17070)

---
 tools/server/server.cpp | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/tools/server/server.cpp b/tools/server/server.cpp
index 0e1a9afc869..164e8cf4e70 100644
--- a/tools/server/server.cpp
+++ b/tools/server/server.cpp
@@ -2823,6 +2823,8 @@ struct server_context {
                 send_error(task, "Failed to parse grammar", ERROR_TYPE_INVALID_REQUEST);
                 return false;
             }
+
+            SLT_INF(slot, "sampler chain: %s\n", common_sampler_print(slot.smpl).c_str());
         }
 
         // initialize draft batch

From 7c23f3f0d4b9f5d6ea140756eb694b562d5acebb Mon Sep 17 00:00:00 2001
From: iron <lizhenneng@gmail.com>
Date: Sat, 8 Nov 2025 00:18:14 +0800
Subject: [PATCH 107/185] ggml-cpu: detect correct cpu flags for arm64 (#16229)
 (#16239)

When using GCC 9 and GCC 12 on the arm64 platform of ubuntu 2004,
the command "gcc -mcpu=native -E -v -" fails to detect the correct CPU flags,
which results in compilation failures for certain extended instructions,
but the correct CPU flags can be obtained by using gcc -march.

Signed-off-by: lizhenneng <lizhenneng@kylinos.cn>
Co-authored-by: lizhenneng <lizhenneng@kylinos.cn>
---
 ggml/src/ggml-cpu/CMakeLists.txt | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/ggml/src/ggml-cpu/CMakeLists.txt b/ggml/src/ggml-cpu/CMakeLists.txt
index 23ec8bb08a7..485227d24db 100644
--- a/ggml/src/ggml-cpu/CMakeLists.txt
+++ b/ggml/src/ggml-cpu/CMakeLists.txt
@@ -118,18 +118,18 @@ function(ggml_add_cpu_backend_variant_impl tag_name)
                 # so we check for them manually and enable them if available
 
                 execute_process(
-                    COMMAND ${CMAKE_C_COMPILER} -mcpu=native -E -v -
+                    COMMAND ${CMAKE_C_COMPILER} -march=native -E -v -
                     INPUT_FILE "/dev/null"
                     OUTPUT_QUIET
                     ERROR_VARIABLE ARM_MCPU
                     RESULT_VARIABLE ARM_MCPU_RESULT
                 )
                 if (NOT ARM_MCPU_RESULT)
-                    string(REGEX MATCH "-mcpu=[^ ']+" ARM_MCPU_FLAG "${ARM_MCPU}")
+                    string(REGEX MATCH "-march=[^ ']+" ARM_MCPU_FLAG "${ARM_MCPU}")
                 endif()
                 if ("${ARM_MCPU_FLAG}" STREQUAL "")
-                    set(ARM_MCPU_FLAG -mcpu=native)
-                    message(STATUS "ARM -mcpu not found, -mcpu=native will be used")
+                    set(ARM_MCPU_FLAG -march=native)
+                    message(STATUS "ARM -mcpu not found, -march=native will be used")
                 endif()
 
                 include(CheckCXXSourceRuns)

From 9eb9a1331dec83098c858150cd0a8ad9f6d8f46c Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Adrien=20Gallou=C3=ABt?= <angt@huggingface.co>
Date: Fri, 7 Nov 2025 17:34:05 +0100
Subject: [PATCH 108/185] Revert "ggml-cpu: detect correct cpu flags for arm64
 (#16229) (#16239)" (#17084)

This reverts commit 7c23f3f0d4b9f5d6ea140756eb694b562d5acebb.
---
 ggml/src/ggml-cpu/CMakeLists.txt | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/ggml/src/ggml-cpu/CMakeLists.txt b/ggml/src/ggml-cpu/CMakeLists.txt
index 485227d24db..23ec8bb08a7 100644
--- a/ggml/src/ggml-cpu/CMakeLists.txt
+++ b/ggml/src/ggml-cpu/CMakeLists.txt
@@ -118,18 +118,18 @@ function(ggml_add_cpu_backend_variant_impl tag_name)
                 # so we check for them manually and enable them if available
 
                 execute_process(
-                    COMMAND ${CMAKE_C_COMPILER} -march=native -E -v -
+                    COMMAND ${CMAKE_C_COMPILER} -mcpu=native -E -v -
                     INPUT_FILE "/dev/null"
                     OUTPUT_QUIET
                     ERROR_VARIABLE ARM_MCPU
                     RESULT_VARIABLE ARM_MCPU_RESULT
                 )
                 if (NOT ARM_MCPU_RESULT)
-                    string(REGEX MATCH "-march=[^ ']+" ARM_MCPU_FLAG "${ARM_MCPU}")
+                    string(REGEX MATCH "-mcpu=[^ ']+" ARM_MCPU_FLAG "${ARM_MCPU}")
                 endif()
                 if ("${ARM_MCPU_FLAG}" STREQUAL "")
-                    set(ARM_MCPU_FLAG -march=native)
-                    message(STATUS "ARM -mcpu not found, -march=native will be used")
+                    set(ARM_MCPU_FLAG -mcpu=native)
+                    message(STATUS "ARM -mcpu not found, -mcpu=native will be used")
                 endif()
 
                 include(CheckCXXSourceRuns)

From 16bcc1259d311d0fd37fe00fefcc7900324d38cb Mon Sep 17 00:00:00 2001
From: Georgi Gerganov <ggerganov@gmail.com>
Date: Fri, 7 Nov 2025 20:03:25 +0200
Subject: [PATCH 109/185] kv-cache : pad the cache size to 256 for performance
 (#17046)

* kv-cache : pad the size of the small SWA cache for performance

* context : pad the total context to 256

* cont : future-proof the swa pad

* server : adjust test params to new logic
---
 include/llama.h                             |  1 +
 src/llama-context.cpp                       |  4 ++++
 src/llama-kv-cache-iswa.cpp                 |  4 +++-
 tools/server/tests/unit/test_speculative.py | 12 ++++++------
 4 files changed, 14 insertions(+), 7 deletions(-)

diff --git a/include/llama.h b/include/llama.h
index 98bed9d6150..aa9932afb84 100644
--- a/include/llama.h
+++ b/include/llama.h
@@ -463,6 +463,7 @@ extern "C" {
 
     // NOTE: After creating a llama_context, it is recommended to query the actual values using these functions
     //       In some cases the requested values via llama_context_params may differ from the actual values used by the context
+    //       ref: https://github.com/ggml-org/llama.cpp/pull/17046#discussion_r2503085732
     LLAMA_API uint32_t llama_n_ctx      (const struct llama_context * ctx);
     LLAMA_API uint32_t llama_n_ctx_seq  (const struct llama_context * ctx);
     LLAMA_API uint32_t llama_n_batch    (const struct llama_context * ctx);
diff --git a/src/llama-context.cpp b/src/llama-context.cpp
index 866514038e4..e115fcd933f 100644
--- a/src/llama-context.cpp
+++ b/src/llama-context.cpp
@@ -114,10 +114,14 @@ llama_context::llama_context(
         }
     }
 
+    // ref: https://github.com/ggml-org/llama.cpp/pull/17046#discussion_r2503085732
+    cparams.n_ctx = GGML_PAD(cparams.n_ctx, 256);
+
     if (cparams.kv_unified) {
         cparams.n_ctx_seq = cparams.n_ctx;
     } else {
         cparams.n_ctx_seq = cparams.n_ctx / cparams.n_seq_max;
+        cparams.n_ctx_seq = GGML_PAD(cparams.n_ctx_seq, 256);
 
         if (cparams.n_ctx_seq == 0) {
             throw std::runtime_error("n_ctx_seq == 0");
diff --git a/src/llama-kv-cache-iswa.cpp b/src/llama-kv-cache-iswa.cpp
index facba1d0040..3a34102a23d 100644
--- a/src/llama-kv-cache-iswa.cpp
+++ b/src/llama-kv-cache-iswa.cpp
@@ -45,7 +45,9 @@ llama_kv_cache_iswa::llama_kv_cache_iswa(
 
     const uint32_t size_base = kv_size;
 
-    uint32_t size_swa = std::min(size_base, GGML_PAD(hparams.n_swa*(unified ? n_seq_max : 1) + n_ubatch, n_pad));
+    // note: the SWA cache is always padded to 256 for performance
+    //       https://github.com/ggml-org/llama.cpp/issues/17037
+    uint32_t size_swa = GGML_PAD(std::min(size_base, hparams.n_swa*(unified ? n_seq_max : 1) + n_ubatch), 256);
 
     // when using full-size SWA cache, we set the SWA cache size to be equal to the base cache size
     if (swa_full) {
diff --git a/tools/server/tests/unit/test_speculative.py b/tools/server/tests/unit/test_speculative.py
index 65952de8b8d..d2f3fba5fe7 100644
--- a/tools/server/tests/unit/test_speculative.py
+++ b/tools/server/tests/unit/test_speculative.py
@@ -77,10 +77,10 @@ def test_different_draft_min_draft_max():
 
 def test_slot_ctx_not_exceeded():
     global server
-    server.n_ctx = 64
+    server.n_ctx = 256
     server.start()
     res = server.make_request("POST", "/completion", data={
-        "prompt": "Hello " * 56,
+        "prompt": "Hello " * 248,
         "temperature": 0.0,
         "top_k": 1,
         "speculative.p_min": 0.0,
@@ -91,19 +91,19 @@ def test_slot_ctx_not_exceeded():
 
 def test_with_ctx_shift():
     global server
-    server.n_ctx = 64
+    server.n_ctx = 256
     server.enable_ctx_shift = True
     server.start()
     res = server.make_request("POST", "/completion", data={
-        "prompt": "Hello " * 56,
+        "prompt": "Hello " * 248,
         "temperature": 0.0,
         "top_k": 1,
-        "n_predict": 64,
+        "n_predict": 256,
         "speculative.p_min": 0.0,
     })
     assert res.status_code == 200
     assert len(res.body["content"]) > 0
-    assert res.body["tokens_predicted"] == 64
+    assert res.body["tokens_predicted"] == 256
     assert res.body["truncated"] == True
 
 

From 9008027aa376526819415469f74fb9281136224e Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sigbj=C3=B8rn=20Skj=C3=A6ret?= <sigbjorn.skjaeret@scala.com>
Date: Fri, 7 Nov 2025 19:27:58 +0100
Subject: [PATCH 110/185] hparams : add n_embd_inp() to support extended embed
 (#16928)

* add n_embd_full to support extended embed

* don't change output

* rename to n_embd_inp

* restore n_embd where applicable
---
 include/llama.h            |  1 +
 src/llama-context.cpp      |  6 +++---
 src/llama-graph.cpp        |  4 ++--
 src/llama-hparams.cpp      | 10 ++++++++++
 src/llama-hparams.h        |  3 +++
 src/llama-model.cpp        | 23 +++++++----------------
 src/models/qwen3vl-moe.cpp |  3 +--
 src/models/qwen3vl.cpp     |  5 +----
 tools/mtmd/mtmd.cpp        |  2 +-
 9 files changed, 29 insertions(+), 28 deletions(-)

diff --git a/include/llama.h b/include/llama.h
index aa9932afb84..8547226ff21 100644
--- a/include/llama.h
+++ b/include/llama.h
@@ -486,6 +486,7 @@ extern "C" {
 
     LLAMA_API int32_t llama_model_n_ctx_train(const struct llama_model * model);
     LLAMA_API int32_t llama_model_n_embd     (const struct llama_model * model);
+    LLAMA_API int32_t llama_model_n_embd_inp (const struct llama_model * model);
     LLAMA_API int32_t llama_model_n_layer    (const struct llama_model * model);
     LLAMA_API int32_t llama_model_n_head     (const struct llama_model * model);
     LLAMA_API int32_t llama_model_n_head_kv  (const struct llama_model * model);
diff --git a/src/llama-context.cpp b/src/llama-context.cpp
index e115fcd933f..70a3ec62dfc 100644
--- a/src/llama-context.cpp
+++ b/src/llama-context.cpp
@@ -827,7 +827,7 @@ int llama_context::encode(const llama_batch & batch_inp) {
 
     const auto & hparams = model.hparams;
 
-    const int64_t n_embd  = hparams.n_embd;
+    const int64_t n_embd  = hparams.n_embd_inp();
     const int64_t n_vocab = model.vocab.n_tokens();
 
     // note: during encode, we always pass the full sequence starting from pos = 0
@@ -996,7 +996,7 @@ int llama_context::decode(const llama_batch & batch_inp) {
     const auto & hparams = model.hparams;
 
     const int64_t n_vocab = vocab.n_tokens();
-    const int64_t n_embd  = hparams.n_embd;
+    const int64_t n_embd  = hparams.n_embd_inp();
 
     // when computing embeddings, all tokens are output
     const bool output_all = cparams.embeddings;
@@ -2154,7 +2154,7 @@ void llama_context::opt_epoch_iter(
             batch.logits  [pos_batch]    = true;
         }
 
-        if (!balloc->init(batch, model.vocab, nullptr, model.hparams.n_embd, cparams.kv_unified ? LLAMA_MAX_SEQ : cparams.n_seq_max, true)) {
+        if (!balloc->init(batch, model.vocab, nullptr, model.hparams.n_embd_inp(), cparams.kv_unified ? LLAMA_MAX_SEQ : cparams.n_seq_max, true)) {
             LLAMA_LOG_ERROR("%s: failed to initialize batch\n", __func__);
             return;
         }
diff --git a/src/llama-graph.cpp b/src/llama-graph.cpp
index f9751b31836..b199e94628f 100644
--- a/src/llama-graph.cpp
+++ b/src/llama-graph.cpp
@@ -1142,7 +1142,7 @@ ggml_tensor * llm_graph_context::build_moe_ffn(
 
 // input embeddings with optional lora
 ggml_tensor * llm_graph_context::build_inp_embd(ggml_tensor * tok_embd) const {
-    const int64_t n_embd = hparams.n_embd;
+    const int64_t n_embd = hparams.n_embd_inp();
 
     auto inp = std::make_unique<llm_graph_input_embd>();
 
@@ -1279,7 +1279,7 @@ ggml_tensor * llm_graph_context::build_inp_cross_embd() const {
     //    return cur;
     //}
 
-    const auto n_embd = !cross->v_embd.empty() ? cross->n_embd : hparams.n_embd;
+    const auto n_embd = !cross->v_embd.empty() ? cross->n_embd : hparams.n_embd_inp();
     const auto n_enc  = !cross->v_embd.empty() ? cross->n_enc : hparams.n_ctx_train;
 
     cur = ggml_new_tensor_2d(ctx0, GGML_TYPE_F32, n_embd, n_enc);
diff --git a/src/llama-hparams.cpp b/src/llama-hparams.cpp
index 514d653844c..8cdbaf69fc0 100644
--- a/src/llama-hparams.cpp
+++ b/src/llama-hparams.cpp
@@ -60,6 +60,16 @@ uint32_t llama_hparams::n_gqa(uint32_t il) const {
     return n_head/n_head_kv;
 }
 
+uint32_t llama_hparams::n_embd_inp() const {
+    uint32_t n_embd_inp = n_embd;
+
+    if (n_deepstack_layers > 0) {
+        n_embd_inp += n_embd * n_deepstack_layers;
+    }
+
+    return n_embd_inp;
+}
+
 uint32_t llama_hparams::n_embd_k_gqa(uint32_t il) const {
     const uint32_t n_head_kv = this->n_head_kv(il);
 
diff --git a/src/llama-hparams.h b/src/llama-hparams.h
index 539fecb3f78..9203af83b2e 100644
--- a/src/llama-hparams.h
+++ b/src/llama-hparams.h
@@ -227,6 +227,9 @@ struct llama_hparams {
 
     uint32_t n_gqa(uint32_t il = 0) const;
 
+    // dimension of main + auxiliary input embeddings
+    uint32_t n_embd_inp() const;
+
     // dimension of key embeddings across all k-v heads
     uint32_t n_embd_k_gqa(uint32_t il = 0) const;
 
diff --git a/src/llama-model.cpp b/src/llama-model.cpp
index 1987135ca6a..829f1e3c14f 100644
--- a/src/llama-model.cpp
+++ b/src/llama-model.cpp
@@ -276,8 +276,8 @@ static bool weight_buft_supported(const llama_hparams & hparams, ggml_tensor * w
             } break;
         case GGML_OP_IM2COL:
             {
-                const int n_embd = hparams.n_embd;
-                ggml_tensor * b = ggml_new_tensor_4d(ctx, GGML_TYPE_F32, n_embd, w->ne[1], 1, 1);
+                const int n_embd_inp = hparams.n_embd_inp();
+                ggml_tensor * b = ggml_new_tensor_4d(ctx, GGML_TYPE_F32, n_embd_inp, w->ne[1], 1, 1);
                 op_tensor = ggml_im2col(ctx, w, b, 1, 0, 0, 0, 1, 0, false, GGML_TYPE_F16);
             } break;
         case GGML_OP_SCALE:
@@ -1039,9 +1039,6 @@ void llama_model::load_hparams(llama_model_loader & ml) {
                     case 64: type = LLM_TYPE_32B; break;
                     default: type = LLM_TYPE_UNKNOWN;
                 }
-                // since vision model stacks deepstack features along feature dim
-                // we also create a fake "n_embd" for text model to be the main embd + deepstack embds
-                hparams.n_embd *= hparams.n_deepstack_layers + 1;
             } break;
         case LLM_ARCH_QWEN3MOE:
             {
@@ -1065,9 +1062,6 @@ void llama_model::load_hparams(llama_model_loader & ml) {
                     case 94: type = LLM_TYPE_235B_A22B; break;
                     default: type = LLM_TYPE_UNKNOWN;
                 }
-                // since vision model stacks deepstack features along feature dim
-                // we also create a fake "n_embd" for text model to be the main embd + deepstack embds
-                hparams.n_embd *= hparams.n_deepstack_layers + 1;
             } break;
         case LLM_ARCH_PHI2:
             {
@@ -3341,10 +3335,6 @@ bool llama_model::load_tensors(llama_model_loader & ml) {
             case LLM_ARCH_QWEN3:
             case LLM_ARCH_QWEN3VL:
                 {
-                    // for model loading, the weights only have the main embd
-                    // so we need to divide by the number of deepstack layers + 1
-                    // n_embd is const int so we declare a new variable
-                    int64_t n_embd = hparams.n_embd / (hparams.n_deepstack_layers + 1);
                     tok_embd = create_tensor(tn(LLM_TENSOR_TOKEN_EMBD, "weight"), {n_embd, n_vocab}, 0);
 
                     // output
@@ -3380,10 +3370,6 @@ bool llama_model::load_tensors(llama_model_loader & ml) {
             case LLM_ARCH_QWEN3MOE:
             case LLM_ARCH_QWEN3VLMOE:
                 {
-                    // for model loading, the weights only have the main embd
-                    // so we need to divide by the number of deepstack layers + 1
-                    // n_embd is const int so we declare a new variable
-                    int64_t n_embd = hparams.n_embd / (hparams.n_deepstack_layers + 1);
                     tok_embd = create_tensor(tn(LLM_TENSOR_TOKEN_EMBD, "weight"), {n_embd, n_vocab}, 0);
 
                     // output
@@ -6535,6 +6521,7 @@ void llama_model::print_info() const {
     if (!hparams.vocab_only) {
         LLAMA_LOG_INFO("%s: n_ctx_train      = %u\n",     __func__, hparams.n_ctx_train);
         LLAMA_LOG_INFO("%s: n_embd           = %u\n",     __func__, hparams.n_embd);
+        LLAMA_LOG_INFO("%s: n_embd_inp       = %u\n",     __func__, hparams.n_embd_inp());
         LLAMA_LOG_INFO("%s: n_layer          = %u\n",     __func__, hparams.n_layer);
         LLAMA_LOG_INFO("%s: n_head           = %s\n",     __func__, print_f([&](uint32_t il) { return hparams.n_head(il);    }, hparams.n_layer).c_str());
         LLAMA_LOG_INFO("%s: n_head_kv        = %s\n",     __func__, print_f([&](uint32_t il) { return hparams.n_head_kv(il); }, hparams.n_layer).c_str());
@@ -7380,6 +7367,10 @@ int32_t llama_model_n_embd(const llama_model * model) {
     return model->hparams.n_embd;
 }
 
+int32_t llama_model_n_embd_inp(const llama_model * model) {
+    return model->hparams.n_embd_inp();
+}
+
 int32_t llama_model_n_layer(const llama_model * model) {
     return model->hparams.n_layer;
 }
diff --git a/src/models/qwen3vl-moe.cpp b/src/models/qwen3vl-moe.cpp
index c48643c0cd1..f72f80a8376 100644
--- a/src/models/qwen3vl-moe.cpp
+++ b/src/models/qwen3vl-moe.cpp
@@ -1,9 +1,8 @@
 #include "models.h"
 
 llm_build_qwen3vlmoe::llm_build_qwen3vlmoe(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-    const int64_t n_embd_full = hparams.n_embd; // main embd + deepstack embds
     const size_t n_deepstack_layers = hparams.n_deepstack_layers;
-    const int64_t n_embd = n_embd_full / (n_deepstack_layers + 1);
+    const int64_t n_embd = hparams.n_embd;
     const int64_t n_embd_head = hparams.n_embd_head_v;
 
     GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
diff --git a/src/models/qwen3vl.cpp b/src/models/qwen3vl.cpp
index 10b36c1f65e..0bae52239ca 100644
--- a/src/models/qwen3vl.cpp
+++ b/src/models/qwen3vl.cpp
@@ -1,13 +1,10 @@
 #include "models.h"
 
 llm_build_qwen3vl::llm_build_qwen3vl(const llama_model & model, const llm_graph_params & params) : llm_graph_context(params) {
-
-    const int64_t n_embd_full = hparams.n_embd; // main embd + deepstack embds
     const size_t n_deepstack_layers = hparams.n_deepstack_layers;
-    const int64_t n_embd = n_embd_full / (n_deepstack_layers + 1);
+    const int64_t n_embd = hparams.n_embd;
     const int64_t n_embd_head = hparams.n_embd_head_v;
 
-
     GGML_ASSERT(n_embd_head == hparams.n_embd_head_k);
     GGML_ASSERT(n_embd_head == hparams.n_rot);
 
diff --git a/tools/mtmd/mtmd.cpp b/tools/mtmd/mtmd.cpp
index 4343f3b6fc3..e5991377699 100644
--- a/tools/mtmd/mtmd.cpp
+++ b/tools/mtmd/mtmd.cpp
@@ -163,7 +163,7 @@ struct mtmd_context {
         print_timings(ctx_params.print_timings),
         n_threads    (ctx_params.n_threads),
         media_marker (ctx_params.media_marker),
-        n_embd_text  (llama_model_n_embd(text_model))
+        n_embd_text  (llama_model_n_embd_inp(text_model))
     {
         if (std::string(ctx_params.image_marker) != MTMD_DEFAULT_IMAGE_MARKER) {
             throw std::runtime_error("custom image_marker is not supported anymore, use media_marker instead");

From 7956bb4d7f430f23f3c4726f7e6404b89f6e20a4 Mon Sep 17 00:00:00 2001
From: Georgi Gerganov <ggerganov@gmail.com>
Date: Fri, 7 Nov 2025 21:23:11 +0200
Subject: [PATCH 111/185] bench : cache the llama_context state at computed
 depth (#16944)

* bench : cache llama_context state at depth

* cont : handle failures to restore the old state

* cont : print information when the state is being reused
---
 tools/llama-bench/llama-bench.cpp | 47 ++++++++++++++++++++++++++-----
 1 file changed, 40 insertions(+), 7 deletions(-)

diff --git a/tools/llama-bench/llama-bench.cpp b/tools/llama-bench/llama-bench.cpp
index 0de07b98112..852a512451d 100644
--- a/tools/llama-bench/llama-bench.cpp
+++ b/tools/llama-bench/llama-bench.cpp
@@ -1919,6 +1919,12 @@ struct sql_printer : public printer {
     }
 };
 
+struct ctx_state {
+    int depth = 0; // in tokens
+
+    std::vector<uint8_t> buf; // the llama_context state buffer
+};
+
 static bool test_prompt(llama_context * ctx, int n_prompt, int n_batch, int n_threads) {
     llama_set_n_threads(ctx, n_threads, n_threads);
 
@@ -2051,6 +2057,10 @@ int main(int argc, char ** argv) {
     llama_model *               lmodel    = nullptr;
     const cmd_params_instance * prev_inst = nullptr;
 
+    // store the llama_context state at the previous depth that we performed a test
+    // ref: https://github.com/ggml-org/llama.cpp/pull/16944#issuecomment-3478151721
+    ctx_state cstate;
+
     int  params_idx   = 0;
     auto params_count = params_instances.size();
     for (const auto & inst : params_instances) {
@@ -2134,14 +2144,37 @@ int main(int argc, char ** argv) {
             llama_memory_clear(llama_get_memory(ctx), false);
 
             if (t.n_depth > 0) {
-                if (params.progress) {
-                    fprintf(stderr, "llama-bench: benchmark %d/%zu: depth run %d/%d\n", params_idx, params_count,
-                            i + 1, params.reps);
+                bool is_cached = t.n_depth == cstate.depth;
+
+                if (is_cached) {
+                    // if previously we have computed at this depth, just restore the state
+                    const size_t ret = llama_state_seq_set_data(ctx, cstate.buf.data(), cstate.buf.size(), 0);
+                    if (ret == 0) {
+                        // if the old state is incompatible with the current context - reprocess from scratch
+                        is_cached = false;
+                    }
                 }
-                bool res = test_prompt(ctx, t.n_depth, t.n_batch, t.n_threads);
-                if (!res) {
-                    fprintf(stderr, "%s: error: failed to run depth\n", __func__);
-                    exit(1);
+
+                if (!is_cached) {
+                    if (params.progress) {
+                        fprintf(stderr, "llama-bench: benchmark %d/%zu: depth run %d/%d\n", params_idx, params_count,
+                                i + 1, params.reps);
+                    }
+                    bool res = test_prompt(ctx, t.n_depth, t.n_batch, t.n_threads);
+                    if (!res) {
+                        fprintf(stderr, "%s: error: failed to run depth\n", __func__);
+                        exit(1);
+                    }
+
+                    // store the context state for reuse in later runs
+                    cstate.depth = t.n_depth;
+                    cstate.buf.resize(llama_state_seq_get_size(ctx, 0));
+                    llama_state_seq_get_data(ctx, cstate.buf.data(), cstate.buf.size(), 0);
+                } else {
+                    if (params.progress) {
+                        fprintf(stderr, "llama-bench: benchmark %d/%zu: depth run %d/%d (cached)\n", params_idx, params_count,
+                                i + 1, params.reps);
+                    }
                 }
             }
 

From 65156105069fa86a4a81b6cb0e8cb583f6420677 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Johannes=20G=C3=A4=C3=9Fler?= <johannesg@5d6.de>
Date: Fri, 7 Nov 2025 20:53:14 +0100
Subject: [PATCH 112/185] CUDA: fix should_use_mmvf for ne11 == 1 (#17085)

* CUDA: fix should_use_mmvf for ne11 == 1

* Apply suggestion from @am17an

Co-authored-by: Aman Gupta <amangupta052@gmail.com>

---------

Co-authored-by: Aman Gupta <amangupta052@gmail.com>
---
 ggml/src/ggml-cuda/mmf.cu  | 8 +++++++-
 ggml/src/ggml-cuda/mmvf.cu | 9 ++++++++-
 2 files changed, 15 insertions(+), 2 deletions(-)

diff --git a/ggml/src/ggml-cuda/mmf.cu b/ggml/src/ggml-cuda/mmf.cu
index 69a60aceb82..153dd5a97d5 100644
--- a/ggml/src/ggml-cuda/mmf.cu
+++ b/ggml/src/ggml-cuda/mmf.cu
@@ -129,7 +129,13 @@ bool ggml_cuda_should_use_mmf(enum ggml_type type, int cc, int warp_size, const
     if (src0_ne[0] % (warp_size * (4/ts)) != 0) {
         return false;
     }
-    for (size_t i = 0; i < GGML_MAX_DIMS; ++i) {
+
+    if (src0_nb[0] != ts) {
+        return false;
+    }
+
+    // Pointers not aligned to the size of half2/nv_bfloat162/float2 would result in a crash:
+    for (size_t i = 1; i < GGML_MAX_DIMS; ++i) {
         if (src0_nb[i] % (2*ts) != 0) {
             return false;
         }
diff --git a/ggml/src/ggml-cuda/mmvf.cu b/ggml/src/ggml-cuda/mmvf.cu
index 526d90d7aee..6238ce7ebd7 100644
--- a/ggml/src/ggml-cuda/mmvf.cu
+++ b/ggml/src/ggml-cuda/mmvf.cu
@@ -720,12 +720,19 @@ bool ggml_cuda_should_use_mmvf(enum ggml_type type, int cc, const int64_t * src0
     if (src0_ne[0] % 2 != 0) {
         return false;
     }
+
     const size_t ts = ggml_type_size(type);
-    for (size_t i = 0; i < GGML_MAX_DIMS; ++i) {
+    if (src0_nb[0] != ts) {
+        return false;
+    }
+
+    // Pointers not aligned to the size of half2/nv_bfloat162/float2 would result in a crash:
+    for (size_t i = 1; i < GGML_MAX_DIMS; ++i) {
         if (src0_nb[i] % (2*ts) != 0) {
             return false;
         }
     }
+
     switch (type) {
         case GGML_TYPE_F32:
             if (GGML_CUDA_CC_IS_NVIDIA(cc)) {

From ac76d3620158aa191118abaf5603479646969543 Mon Sep 17 00:00:00 2001
From: Acly <aclysia@gmail.com>
Date: Fri, 7 Nov 2025 21:08:50 +0100
Subject: [PATCH 113/185] vulkan : refactor buffer handling in vk_op_f32
 (#16840)

* vulkan : refactor/simplify buffer handling in vk_op_* functions

* Combine UMA handling into ggml_vk_tensor_subbuffer
---
 ggml/src/ggml-vulkan/ggml-vulkan.cpp | 556 +++++----------------------
 1 file changed, 97 insertions(+), 459 deletions(-)

diff --git a/ggml/src/ggml-vulkan/ggml-vulkan.cpp b/ggml/src/ggml-vulkan/ggml-vulkan.cpp
index ab94bc3d78f..a0a05f2e5b2 100644
--- a/ggml/src/ggml-vulkan/ggml-vulkan.cpp
+++ b/ggml/src/ggml-vulkan/ggml-vulkan.cpp
@@ -5387,7 +5387,7 @@ static void ggml_vk_host_free(vk_device& device, void* ptr) {
     device->pinned_memory.erase(device->pinned_memory.begin() + index);
 }
 
-static void ggml_vk_host_get(vk_device& device, const void * ptr, vk_buffer& buf, size_t& buf_offset) {
+static void ggml_vk_host_get(const vk_device& device, const void * ptr, vk_buffer& buf, size_t& buf_offset) {
     std::lock_guard<std::recursive_mutex> guard(device->mutex);
     buf = nullptr;
     buf_offset = 0;
@@ -5402,6 +5402,32 @@ static void ggml_vk_host_get(vk_device& device, const void * ptr, vk_buffer& buf
     }
 }
 
+static vk_subbuffer ggml_vk_tensor_subbuffer(
+    const ggml_backend_vk_context * ctx, const ggml_tensor * tensor, bool allow_misalign = false) {
+
+    vk_buffer buffer = nullptr;
+    size_t offset = 0;
+    if (ctx->device->uma) {
+        ggml_vk_host_get(ctx->device, tensor->data, buffer, offset);
+    }
+    if (!buffer) {
+        auto buf_ctx = (ggml_backend_vk_buffer_context *)tensor->buffer->context;
+        buffer = buf_ctx->dev_buffer;
+        offset = vk_tensor_offset(tensor) + tensor->view_offs;
+    }
+    GGML_ASSERT(buffer != nullptr);
+
+    size_t size = ggml_nbytes(tensor);
+
+    size_t misalign_bytes = offset & (ctx->device->properties.limits.minStorageBufferOffsetAlignment - 1);
+    // The shader must support misaligned offsets when indexing into the buffer
+    GGML_ASSERT(allow_misalign || misalign_bytes == 0);
+    offset &= ~misalign_bytes;
+    size += misalign_bytes;
+
+    return vk_subbuffer{buffer, offset, size};
+}
+
 static vk_submission ggml_vk_begin_submission(vk_device& device, vk_command_pool& p, bool one_time = true) {
     vk_submission s;
     s.buffer = ggml_vk_create_cmd_buffer(device, p);
@@ -7953,72 +7979,12 @@ static void ggml_vk_flash_attn(ggml_backend_vk_context * ctx, vk_context& subctx
     const float m0 = powf(2.0f, -(max_bias       ) / n_head_log2);
     const float m1 = powf(2.0f, -(max_bias / 2.0f) / n_head_log2);
 
-    vk_buffer d_Q = nullptr, d_K = nullptr, d_V = nullptr, d_D = nullptr, d_M = nullptr, d_S = nullptr;
-    size_t q_buf_offset = 0, k_buf_offset = 0, v_buf_offset = 0, d_buf_offset = 0, m_buf_offset = 0, s_buf_offset = 0;
-
-    bool Q_uma = false, K_uma = false, V_uma = false, D_uma = false, M_uma = false, S_uma = false;
-
-    if (ctx->device->uma) {
-        ggml_vk_host_get(ctx->device, q->data, d_Q, q_buf_offset);
-        ggml_vk_host_get(ctx->device, k->data, d_K, k_buf_offset);
-        ggml_vk_host_get(ctx->device, v->data, d_V, v_buf_offset);
-        ggml_vk_host_get(ctx->device, dst->data, d_D, d_buf_offset);
-        Q_uma = d_Q != nullptr;
-        K_uma = d_K != nullptr;
-        V_uma = d_V != nullptr;
-        D_uma = d_D != nullptr;
-        if (mask) {
-            ggml_vk_host_get(ctx->device, mask->data, d_M, m_buf_offset);
-            M_uma = d_M != nullptr;
-        }
-        if (sinks) {
-            ggml_vk_host_get(ctx->device, sinks->data, d_S, s_buf_offset);
-            S_uma = d_S != nullptr;
-        }
-    }
-
-
-    ggml_backend_vk_buffer_context * d_buf_ctx = (ggml_backend_vk_buffer_context *)dst->buffer->context;
-    ggml_backend_vk_buffer_context * q_buf_ctx = (ggml_backend_vk_buffer_context *)q->buffer->context;
-    ggml_backend_vk_buffer_context * k_buf_ctx = (ggml_backend_vk_buffer_context *)k->buffer->context;
-    ggml_backend_vk_buffer_context * v_buf_ctx = (ggml_backend_vk_buffer_context *)v->buffer->context;
-
-    if (!Q_uma) {
-        d_Q = q_buf_ctx->dev_buffer;
-        q_buf_offset = vk_tensor_offset(q) + q->view_offs;
-    }
-    if (!K_uma) {
-        d_K = k_buf_ctx->dev_buffer;
-        k_buf_offset = vk_tensor_offset(k) + k->view_offs;
-    }
-    if (!V_uma) {
-        d_V = v_buf_ctx->dev_buffer;
-        v_buf_offset = vk_tensor_offset(v) + v->view_offs;
-    }
-    if (!D_uma) {
-        d_D = d_buf_ctx->dev_buffer;
-        d_buf_offset = vk_tensor_offset(dst) + dst->view_offs;
-    }
-
-    if (!M_uma) {
-        d_M = d_Q;
-        m_buf_offset = q_buf_offset;
-        if (mask) {
-            ggml_backend_vk_buffer_context * m_buf_ctx = (ggml_backend_vk_buffer_context*)mask->buffer->context;
-            d_M = m_buf_ctx->dev_buffer;
-            m_buf_offset = vk_tensor_offset(mask) + mask->view_offs;
-        }
-    }
-
-    if (!S_uma) {
-        d_S = d_Q;
-        s_buf_offset = q_buf_offset;
-        if (sinks) {
-            ggml_backend_vk_buffer_context * s_buf_ctx = (ggml_backend_vk_buffer_context*)sinks->buffer->context;
-            d_S = s_buf_ctx->dev_buffer;
-            s_buf_offset = vk_tensor_offset(sinks) + sinks->view_offs;
-        }
-    }
+    vk_subbuffer q_buf = ggml_vk_tensor_subbuffer(ctx, q);
+    vk_subbuffer k_buf = ggml_vk_tensor_subbuffer(ctx, k);
+    vk_subbuffer v_buf = ggml_vk_tensor_subbuffer(ctx, v);
+    vk_subbuffer dst_buf = ggml_vk_tensor_subbuffer(ctx, dst);
+    vk_subbuffer mask_buf = mask ? ggml_vk_tensor_subbuffer(ctx, mask) : q_buf;
+    vk_subbuffer sinks_buf = sinks ? ggml_vk_tensor_subbuffer(ctx, sinks) : q_buf;
 
     uint32_t mask_n_head_log2 = ((sinks != nullptr) << 24) | ((mask != nullptr) << 16) | n_head_log2;
 
@@ -8040,15 +8006,9 @@ static void ggml_vk_flash_attn(ggml_backend_vk_context * ctx, vk_context& subctx
             ggml_vk_sync_buffers(ctx, subctx);
         }
 
+        vk_subbuffer split_k_buf = ggml_vk_subbuffer(ctx, ctx->prealloc_split_k, 0);
         ggml_vk_dispatch_pipeline(ctx, subctx, pipeline,
-                                    {
-                                        ggml_vk_subbuffer(ctx, d_Q, q_buf_offset),
-                                        ggml_vk_subbuffer(ctx, d_K, k_buf_offset),
-                                        ggml_vk_subbuffer(ctx, d_V, v_buf_offset),
-                                        ggml_vk_subbuffer(ctx, d_M, m_buf_offset),
-                                        ggml_vk_subbuffer(ctx, d_S, s_buf_offset),
-                                        ggml_vk_subbuffer(ctx, ctx->prealloc_split_k, 0),
-                                    },
+                                    {q_buf, k_buf, v_buf, mask_buf, sinks_buf, split_k_buf},
                                     // We only use split_k when group query attention is enabled, which means
                                     // there's no more than one tile of rows (i.e. workgroups_x would have been
                                     // one). We reuse workgroups_x to mean the number of splits, so we need to
@@ -8058,23 +8018,12 @@ static void ggml_vk_flash_attn(ggml_backend_vk_context * ctx, vk_context& subctx
         ggml_vk_sync_buffers(ctx, subctx);
         const std::array<uint32_t, 5> pc2 = { HSV, (uint32_t)ne1, (uint32_t)ne3, split_k, (sinks != nullptr) };
         ggml_vk_dispatch_pipeline(ctx, subctx, ctx->device->pipeline_flash_attn_split_k_reduce,
-                                    {
-                                        ggml_vk_subbuffer(ctx, ctx->prealloc_split_k, 0),
-                                        ggml_vk_subbuffer(ctx, d_S, s_buf_offset),
-                                        ggml_vk_subbuffer(ctx, d_D, d_buf_offset),
-                                    },
+                                    {split_k_buf, sinks_buf, dst_buf},
                                     pc2, { (uint32_t)ne1, HSV, (uint32_t)ne3 });
         ctx->prealloc_split_k_need_sync = true;
     } else {
         ggml_vk_dispatch_pipeline(ctx, subctx, pipeline,
-                                    {
-                                        ggml_vk_subbuffer(ctx, d_Q, q_buf_offset),
-                                        ggml_vk_subbuffer(ctx, d_K, k_buf_offset),
-                                        ggml_vk_subbuffer(ctx, d_V, v_buf_offset),
-                                        ggml_vk_subbuffer(ctx, d_M, m_buf_offset),
-                                        ggml_vk_subbuffer(ctx, d_S, s_buf_offset),
-                                        ggml_vk_subbuffer(ctx, d_D, d_buf_offset),
-                                    },
+                                    {q_buf, k_buf, v_buf, mask_buf, sinks_buf, dst_buf},
                                     pc, { workgroups_x, workgroups_y, workgroups_z });
     }
 }
@@ -8757,35 +8706,15 @@ static void ggml_vk_op_f32(ggml_backend_vk_context * ctx, vk_context& subctx, co
     const uint64_t ne01 = src0->ne[1];
     const uint64_t ne02 = src0->ne[2];
     const uint64_t ne03 = src0->ne[3];
-    const uint64_t ne0 = ne00 * ne01;
 
     const bool use_src1 = src1 != nullptr;
     const uint64_t ne10 = use_src1 ? src1->ne[0] : 0;
     const uint64_t ne11 = use_src1 ? src1->ne[1] : 0;
     const uint64_t ne12 = use_src1 ? src1->ne[2] : 0;
     const uint64_t ne13 = use_src1 ? src1->ne[3] : 0;
-    const uint64_t ne1 = ne10 * ne11;
-    // const uint64_t nb10 = use_src1 ? src1->nb[0] : 0;
 
     const bool use_src2 = src2 != nullptr;
-    const uint64_t ne20 = use_src2 ? src2->ne[0] : 0;
-    const uint64_t ne21 = use_src2 ? src2->ne[1] : 0;
-    const uint64_t ne22 = use_src2 ? src2->ne[2] : 0;
-    const uint64_t ne23 = use_src2 ? src2->ne[3] : 0;
-    const uint64_t ne2 = ne20 * ne21;
-
     const bool use_src3 = src3 != nullptr;
-    const uint64_t ne30 = use_src3 ? src3->ne[0] : 0;
-    const uint64_t ne31 = use_src3 ? src3->ne[1] : 0;
-    const uint64_t ne32 = use_src3 ? src3->ne[2] : 0;
-    const uint64_t ne33 = use_src3 ? src3->ne[3] : 0;
-    const uint64_t ne3 = ne30 * ne31;
-
-    const uint64_t ned0 = dst->ne[0];
-    const uint64_t ned1 = dst->ne[1];
-    const uint64_t ned2 = dst->ne[2];
-    const uint64_t ned3 = dst->ne[3];
-    const uint64_t ned = ned0 * ned1;
 
     init_pushconst_fastdiv(pc);
 
@@ -8804,74 +8733,14 @@ static void ggml_vk_op_f32(ggml_backend_vk_context * ctx, vk_context& subctx, co
 
     const bool op_supports_incontiguous = ggml_vk_op_supports_incontiguous(op);
 
-    ggml_backend_vk_buffer_context * dst_buf_ctx = (ggml_backend_vk_buffer_context *)dst->buffer->context;
-    ggml_backend_vk_buffer_context * src0_buf_ctx = (ggml_backend_vk_buffer_context *)src0->buffer->context;
-    ggml_backend_vk_buffer_context * src1_buf_ctx = use_src1 ? (ggml_backend_vk_buffer_context *)src1->buffer->context : nullptr;
-    ggml_backend_vk_buffer_context * src2_buf_ctx = use_src2 ? (ggml_backend_vk_buffer_context *)src2->buffer->context : nullptr;
-    ggml_backend_vk_buffer_context * src3_buf_ctx = use_src3 ? (ggml_backend_vk_buffer_context *)src3->buffer->context : nullptr;
-
-    vk_buffer d_X = nullptr;
-    size_t x_buf_offset = 0;
-    vk_buffer d_Y = nullptr;
-    size_t y_buf_offset = 0;
-    vk_buffer d_Z = nullptr;
-    size_t z_buf_offset = 0;
-    vk_buffer d_W = nullptr;
-    size_t w_buf_offset = 0;
-
-    bool src0_uma = false;
-    bool src1_uma = false;
-    bool src2_uma = false;
-    bool src3_uma = false;
+    vk_subbuffer src0_buf = ggml_vk_tensor_subbuffer(ctx, src0, op_supports_incontiguous);
+    vk_subbuffer src1_buf = use_src1 ? ggml_vk_tensor_subbuffer(ctx, src1, op_supports_incontiguous) : vk_subbuffer{};
+    vk_subbuffer src2_buf = use_src2 ? ggml_vk_tensor_subbuffer(ctx, src2, op_supports_incontiguous) : vk_subbuffer{};
+    vk_subbuffer src3_buf = use_src3 ? ggml_vk_tensor_subbuffer(ctx, src3, op_supports_incontiguous) : vk_subbuffer{};
+    vk_subbuffer dst_buf = ggml_vk_tensor_subbuffer(ctx, dst, op_supports_incontiguous);
 
-    if (ctx->device->uma) {
-        ggml_vk_host_get(ctx->device, src0->data, d_X, x_buf_offset);
-        src0_uma = d_X != nullptr;
-        if (use_src1) {
-            ggml_vk_host_get(ctx->device, src1->data, d_Y, y_buf_offset);
-            src1_uma = d_Y != nullptr;
-        }
-        if (use_src2) {
-            ggml_vk_host_get(ctx->device, src2->data, d_Z, z_buf_offset);
-            src2_uma = d_Z != nullptr;
-        }
-        if (use_src3) {
-            ggml_vk_host_get(ctx->device, src3->data, d_W, w_buf_offset);
-            src3_uma = d_W != nullptr;
-        }
-    }
-
-    vk_buffer d_D = dst_buf_ctx->dev_buffer;
-
-    GGML_ASSERT(d_D != nullptr);
-    uint64_t d_buf_offset = vk_tensor_offset(dst) + dst->view_offs;
-    if(!src0_uma) {
-        d_X = src0_buf_ctx->dev_buffer;
-        x_buf_offset = vk_tensor_offset(src0) + src0->view_offs;
-        GGML_ASSERT(d_X != nullptr);
-    }
-    if (use_src1 && !src1_uma) {
-        d_Y = src1_buf_ctx->dev_buffer;
-        y_buf_offset = vk_tensor_offset(src1) + src1->view_offs;
-        GGML_ASSERT(d_Y != nullptr);
-    }
-    if (use_src2 && !src2_uma) {
-        d_Z = src2_buf_ctx->dev_buffer;
-        z_buf_offset = vk_tensor_offset(src2) + src2->view_offs;
-        GGML_ASSERT(d_Z != nullptr);
-    }
-    if (use_src3 && !src3_uma) {
-        d_W = src3_buf_ctx->dev_buffer;
-        w_buf_offset = vk_tensor_offset(src3) + src3->view_offs;
-        GGML_ASSERT(d_W != nullptr);
-    }
-    // Compute misalignment offset for descriptors and store it in in push constants, then align the descriptor offsets.
+    // Compute misalignment offset for descriptors and store it in in push constants.
     init_pushconst_tensor_offsets(ctx, pc, src0, src1, src2, src3, dst);
-    x_buf_offset &= ~(ctx->device->properties.limits.minStorageBufferOffsetAlignment - 1);
-    y_buf_offset &= ~(ctx->device->properties.limits.minStorageBufferOffsetAlignment - 1);
-    z_buf_offset &= ~(ctx->device->properties.limits.minStorageBufferOffsetAlignment - 1);
-    w_buf_offset &= ~(ctx->device->properties.limits.minStorageBufferOffsetAlignment - 1);
-    d_buf_offset &= ~(ctx->device->properties.limits.minStorageBufferOffsetAlignment - 1);
 
     std::array<uint32_t, 3> elements;
 
@@ -8955,9 +8824,9 @@ static void ggml_vk_op_f32(ggml_backend_vk_context * ctx, vk_context& subctx, co
             const uint32_t KH = ne01;
             const uint32_t KW = ne00;
 
-            const uint32_t OD = ned3 / N;
-            const uint32_t OH = ned2;
-            const uint32_t OW = ned1;
+            const uint32_t OD = dst->ne[3] / N;
+            const uint32_t OH = dst->ne[2];
+            const uint32_t OW = dst->ne[1];
 
             const uint32_t IC_KD_KH_KW = IC*KD*KH*KW;
             const uint32_t N_OD_OH = N*OD*OH;
@@ -9072,112 +8941,50 @@ static void ggml_vk_op_f32(ggml_backend_vk_context * ctx, vk_context& subctx, co
         break;
     }
 
-    uint64_t x_sz, y_sz, z_sz, w_sz, d_sz;
-
-    if (op_supports_incontiguous) {
-        x_sz = ggml_nbytes(src0) + get_misalign_bytes(ctx, src0);
-        y_sz = use_src1 ? ggml_nbytes(src1) + get_misalign_bytes(ctx, src1) : 0;
-        z_sz = use_src2 ? ggml_nbytes(src2) + get_misalign_bytes(ctx, src2) : 0;
-        w_sz = use_src3 ? ggml_nbytes(src3) + get_misalign_bytes(ctx, src3) : 0;
-        d_sz = ggml_nbytes(dst) + get_misalign_bytes(ctx, dst);
-
-        if (x_buf_offset + x_sz >= d_X->size) {
-            x_sz = ggml_vk_get_max_buffer_range(ctx, d_X, x_buf_offset);
-        }
-        if (use_src1 && y_buf_offset + y_sz >= d_Y->size) {
-            y_sz = ggml_vk_get_max_buffer_range(ctx, d_Y, y_buf_offset);
-        }
-        if (use_src2 && z_buf_offset + z_sz >= d_Z->size) {
-            z_sz = ggml_vk_get_max_buffer_range(ctx, d_Z, z_buf_offset);
-        }
-        if (use_src3 && w_buf_offset + w_sz >= d_W->size) {
-            w_sz = ggml_vk_get_max_buffer_range(ctx, d_W, w_buf_offset);
-        }
-        if (d_buf_offset + d_sz >= d_D->size) {
-            d_sz = ggml_vk_get_max_buffer_range(ctx, d_D, d_buf_offset);
-        }
-    } else {
-        x_sz = ggml_type_size(src0->type)/ggml_blck_size(src0->type) * ne0 * ne02 * ne03;
-        y_sz = use_src1 ? ggml_type_size(src1->type) * ne1 * ne12 * ne13 : 0;
-        z_sz = use_src2 ? ggml_type_size(src2->type) * ne2 * ne22 * ne23 : 0;
-        w_sz = use_src3 ? ggml_type_size(src3->type) * ne3 * ne32 * ne33 : 0;
-        d_sz = ggml_type_size(dst->type) * ned * ned2 * ned3;
-    }
-
     if (op == GGML_OP_ADD || op == GGML_OP_RMS_NORM) {
-        vk_buffer d_A = ctx->do_add_rms_partials ? ctx->prealloc_add_rms_partials : d_X;
-        size_t a_buf_offset = ctx->do_add_rms_partials ? ctx->prealloc_size_add_rms_partials_offset : 0;
+        vk_subbuffer a_buf = src0_buf;
+        if (ctx->do_add_rms_partials) {
+            a_buf = ggml_vk_subbuffer(ctx, ctx->prealloc_add_rms_partials, ctx->prealloc_size_add_rms_partials_offset);
+        }
         ggml_vk_dispatch_pipeline(ctx, subctx, pipeline,
-            { vk_subbuffer{ d_X, x_buf_offset, x_sz },
-              vk_subbuffer{ d_Y, y_buf_offset, y_sz },
-              vk_subbuffer{ d_D, d_buf_offset, d_sz },
-              ggml_vk_subbuffer(ctx, d_A, a_buf_offset),
-            }, pc, elements);
+            { src0_buf, src1_buf, dst_buf, a_buf }, pc, elements);
     } else if (op == GGML_OP_GLU) {
         // Empty src1 is possible in glu, but the shader needs a buffer
-        vk_subbuffer subbuf_y;
-        if (use_src1) {
-            subbuf_y = { d_Y, y_buf_offset, y_sz };
-        } else {
-            subbuf_y = { d_X, 0, x_sz };
-        }
-
-        ggml_vk_dispatch_pipeline(ctx, subctx, pipeline, { vk_subbuffer{ d_X, x_buf_offset, x_sz }, subbuf_y, vk_subbuffer{ d_D, d_buf_offset, d_sz } }, pc, elements);
+        vk_subbuffer subbuf1 = use_src1 ? src1_buf : src0_buf;
+        ggml_vk_dispatch_pipeline(ctx, subctx, pipeline, { src0_buf, subbuf1, dst_buf }, pc, elements);
     } else if (op == GGML_OP_SOFT_MAX) {
         // Empty src1 and src2 is possible in soft_max, but the shader needs a buffer
-        vk_subbuffer subbuf_y;
-        if (use_src1) {
-            subbuf_y = { d_Y, y_buf_offset, y_sz };
-        } else {
-            subbuf_y = { d_X, 0, x_sz };
-        }
-
-        vk_subbuffer subbuf_z;
-        if (use_src2) {
-            subbuf_z = { d_Z, z_buf_offset, z_sz };
-        } else {
-            subbuf_z = { d_X, 0, x_sz };
-        }
-
-        ggml_vk_dispatch_pipeline(ctx, subctx, pipeline, { vk_subbuffer{ d_X, x_buf_offset, x_sz }, subbuf_y, subbuf_z, vk_subbuffer{ d_D, d_buf_offset, d_sz } }, pc, elements);
+        vk_subbuffer subbuf1 = use_src1 ? src1_buf : src0_buf;
+        vk_subbuffer subbuf2 = use_src2 ? src2_buf : src0_buf;
+        ggml_vk_dispatch_pipeline(ctx, subctx, pipeline, { src0_buf, subbuf1, subbuf2, dst_buf }, pc, elements);
     } else if (op == GGML_OP_ROPE || op == GGML_OP_ROPE_BACK) {
-        // Empty src2 is possible in rope, but the shader needs a buffer
-        vk_subbuffer subbuf_z, subbuf_w;
-        if (use_src2) {
-            subbuf_z = { d_Z, z_buf_offset, z_sz };
-        } else {
-            subbuf_z = { d_X, 0, x_sz };
-        }
-        if (use_src3) {
-            subbuf_w = { d_W, w_buf_offset, w_sz };
-        } else {
-            subbuf_w = { d_X, 0, x_sz };
-        }
-
-        ggml_vk_dispatch_pipeline(ctx, subctx, pipeline, { vk_subbuffer{ d_X, x_buf_offset, x_sz }, vk_subbuffer{ d_Y, y_buf_offset, y_sz }, subbuf_z, vk_subbuffer{ d_D, d_buf_offset, d_sz }, subbuf_w }, pc, elements);
+        // Empty src2 and src3 is possible in rope, but the shader needs a buffer
+        vk_subbuffer subbuf2 = use_src2 ? src2_buf : src0_buf;
+        vk_subbuffer subbuf3 = use_src3 ? src3_buf : src0_buf;
+        ggml_vk_dispatch_pipeline(ctx, subctx, pipeline, { src0_buf, src1_buf, subbuf2, dst_buf, subbuf3 }, pc, elements);
     } else if (op == GGML_OP_IM2COL || op == GGML_OP_IM2COL_3D) {
         if (ctx->device->shader_int64 && ctx->device->buffer_device_address) {
             // buffer device address path doesn't use dst buffer
-            d_sz = 1;
+            dst_buf.size = 1;
         }
         // im2col uses only src1 and dst buffers
-        ggml_vk_dispatch_pipeline(ctx, subctx, pipeline, { vk_subbuffer{ d_Y, y_buf_offset, y_sz }, vk_subbuffer{ d_D, d_buf_offset, d_sz } }, pc, elements);
+        ggml_vk_dispatch_pipeline(ctx, subctx, pipeline, { src1_buf, dst_buf }, pc, elements);
     } else if (op == GGML_OP_COUNT_EQUAL) {
         // count_equal assumes that destination buffer is initialized with zeroes
-        ggml_vk_buffer_memset_async(subctx, d_D, d_buf_offset, 0, d_sz);
+        ggml_vk_buffer_memset_async(subctx, dst_buf.buffer, dst_buf.offset, 0, dst_buf.size);
         ggml_vk_sync_buffers(ctx, subctx);
-        ggml_vk_dispatch_pipeline(ctx, subctx, pipeline, { vk_subbuffer{ d_X, x_buf_offset, x_sz }, vk_subbuffer{ d_Y, y_buf_offset, y_sz }, vk_subbuffer{ d_D, d_buf_offset, d_sz } }, pc, elements);
+        ggml_vk_dispatch_pipeline(ctx, subctx, pipeline, { src0_buf, src1_buf, dst_buf }, pc, elements);
     } else if (op == GGML_OP_OPT_STEP_SGD) {
         // OPT_STEP_SGD works on src0, it does not need dst
-        ggml_vk_dispatch_pipeline(ctx, subctx, pipeline, { vk_subbuffer{ d_X, x_buf_offset, x_sz }, vk_subbuffer{ d_Y, y_buf_offset, y_sz }, vk_subbuffer{ d_Z, z_buf_offset, z_sz } }, pc, elements);
+        ggml_vk_dispatch_pipeline(ctx, subctx, pipeline, { src0_buf, src1_buf, src2_buf }, pc, elements);
     } else if (use_src3) {
-        ggml_vk_dispatch_pipeline(ctx, subctx, pipeline, { vk_subbuffer{ d_X, x_buf_offset, x_sz }, vk_subbuffer{ d_Y, y_buf_offset, y_sz }, vk_subbuffer{ d_Z, z_buf_offset, z_sz }, vk_subbuffer{ d_W, w_buf_offset, w_sz }, vk_subbuffer{ d_D, d_buf_offset, d_sz } }, pc, elements);
+        ggml_vk_dispatch_pipeline(ctx, subctx, pipeline, { src0_buf, src1_buf, src2_buf, src3_buf, dst_buf }, pc, elements);
     } else if (use_src2) {
-        ggml_vk_dispatch_pipeline(ctx, subctx, pipeline, { vk_subbuffer{ d_X, x_buf_offset, x_sz }, vk_subbuffer{ d_Y, y_buf_offset, y_sz }, vk_subbuffer{ d_Z, z_buf_offset, z_sz }, vk_subbuffer{ d_D, d_buf_offset, d_sz } }, pc, elements);
+        ggml_vk_dispatch_pipeline(ctx, subctx, pipeline, { src0_buf, src1_buf, src2_buf, dst_buf }, pc, elements);
     } else if (use_src1) {
-        ggml_vk_dispatch_pipeline(ctx, subctx, pipeline, { vk_subbuffer{ d_X, x_buf_offset, x_sz }, vk_subbuffer{ d_Y, y_buf_offset, y_sz }, vk_subbuffer{ d_D, d_buf_offset, d_sz } }, pc, elements);
+        ggml_vk_dispatch_pipeline(ctx, subctx, pipeline, { src0_buf, src1_buf, dst_buf }, pc, elements);
     } else {
-        ggml_vk_dispatch_pipeline(ctx, subctx, pipeline, { vk_subbuffer{ d_X, x_buf_offset, x_sz }, vk_subbuffer{ d_D, d_buf_offset, d_sz } }, pc, elements);
+        ggml_vk_dispatch_pipeline(ctx, subctx, pipeline, { src0_buf, dst_buf }, pc, elements);
     }
 }
 
@@ -9413,39 +9220,10 @@ static void ggml_vk_op_f32_wkv(ggml_backend_vk_context * ctx, vk_context& subctx
 
     ggml_pipeline_request_descriptor_sets(ctx, pipeline, 1);
 
-    ggml_backend_vk_buffer_context * dst_buf_ctx = (ggml_backend_vk_buffer_context *)dst->buffer->context;
-    ggml_backend_vk_buffer_context * src_buf_ctxs[7] = { nullptr, nullptr, nullptr, nullptr, nullptr, nullptr, nullptr };
-    for (int i = 0; i < num_srcs; i++) {
-        src_buf_ctxs[i] = (ggml_backend_vk_buffer_context *)dst->src[i]->buffer->context;
-    }
-
-    vk_buffer d_D = nullptr, d_srcs[7] = { nullptr, nullptr, nullptr, nullptr, nullptr, nullptr, nullptr };
-    size_t dst_offset = 0, src_offsets[7] = { 0, 0, 0, 0, 0, 0, 0 };
-    bool dst_uma = false, srcs_uma[7] = { false, false, false, false, false, false, false };
-
-    if (ctx->device->uma) {
-        for (int i = 0; i < num_srcs; i++) {
-            ggml_vk_host_get(ctx->device, dst->src[i]->data, d_srcs[i], src_offsets[i]);
-            srcs_uma[i] = d_srcs[i] != nullptr;
-        }
-
-        ggml_vk_host_get(ctx->device, dst->data, d_D, dst_offset);
-        dst_uma = d_D != nullptr;
-    }
-
-    uint64_t src_sizes[7] = { 0, 0, 0, 0, 0, 0, 0 };
+    vk_subbuffer dst_buf = ggml_vk_tensor_subbuffer(ctx, dst);
+    vk_subbuffer src_buf[7] = {};
     for (int i = 0; i < num_srcs; i++) {
-        src_sizes[i] = ggml_nbytes(dst->src[i]);
-        if (!srcs_uma[i]) {
-            d_srcs[i] = src_buf_ctxs[i]->dev_buffer;
-            src_offsets[i] = vk_tensor_offset(dst->src[i]) + dst->src[i]->view_offs;
-        }
-    }
-
-    const uint64_t dst_size = ggml_nbytes(dst);
-    if (!dst_uma) {
-        d_D = dst_buf_ctx->dev_buffer;
-        dst_offset = vk_tensor_offset(dst) + dst->view_offs;
+        src_buf[i] = ggml_vk_tensor_subbuffer(ctx, dst->src[i]);
     }
 
     std::array<uint32_t, 3> elements = {
@@ -9455,26 +9233,13 @@ static void ggml_vk_op_f32_wkv(ggml_backend_vk_context * ctx, vk_context& subctx
     };
 
     if (version == 6) {
-        ggml_vk_dispatch_pipeline(ctx, subctx, pipeline, {
-            vk_subbuffer{ d_srcs[0], src_offsets[0], src_sizes[0] },
-            vk_subbuffer{ d_srcs[1], src_offsets[1], src_sizes[1] },
-            vk_subbuffer{ d_srcs[2], src_offsets[2], src_sizes[2] },
-            vk_subbuffer{ d_srcs[3], src_offsets[3], src_sizes[3] },
-            vk_subbuffer{ d_srcs[4], src_offsets[4], src_sizes[4] },
-            vk_subbuffer{ d_srcs[5], src_offsets[5], src_sizes[5] },
-            vk_subbuffer{ d_D, dst_offset, dst_size }
-        }, pc, elements);
+        ggml_vk_dispatch_pipeline(ctx, subctx, pipeline,
+            {src_buf[0], src_buf[1], src_buf[2], src_buf[3], src_buf[4], src_buf[5], dst_buf},
+            pc, elements);
     } else if (version == 7) {
-        ggml_vk_dispatch_pipeline(ctx, subctx, pipeline, {
-            vk_subbuffer{ d_srcs[0], src_offsets[0], src_sizes[0] },
-            vk_subbuffer{ d_srcs[1], src_offsets[1], src_sizes[1] },
-            vk_subbuffer{ d_srcs[2], src_offsets[2], src_sizes[2] },
-            vk_subbuffer{ d_srcs[3], src_offsets[3], src_sizes[3] },
-            vk_subbuffer{ d_srcs[4], src_offsets[4], src_sizes[4] },
-            vk_subbuffer{ d_srcs[5], src_offsets[5], src_sizes[5] },
-            vk_subbuffer{ d_srcs[6], src_offsets[6], src_sizes[6] },
-            vk_subbuffer{ d_D, dst_offset, dst_size }
-        }, pc, elements);
+        ggml_vk_dispatch_pipeline(ctx, subctx, pipeline,
+            {src_buf[0], src_buf[1], src_buf[2], src_buf[3], src_buf[4], src_buf[5], src_buf[6], dst_buf},
+            pc, elements);
     } else {
         // shouldn't happen
         GGML_ASSERT(false);
@@ -9554,40 +9319,10 @@ static void ggml_vk_ssm_scan(ggml_backend_vk_context * ctx, vk_context& subctx,
         n_head, head_dim, n_group, n_tok
     };
 
-    ggml_backend_vk_buffer_context * dst_buf_ctx = (ggml_backend_vk_buffer_context *)dst->buffer->context;
-    ggml_backend_vk_buffer_context * src_buf_ctxs[GGML_MAX_SRC];
-    for (int i = 0; i < GGML_MAX_SRC && dst->src[i] != nullptr; i++) {
-        src_buf_ctxs[i] = (ggml_backend_vk_buffer_context *)dst->src[i]->buffer->context;
-    }
-
-    vk_buffer d_D = nullptr, d_srcs[GGML_MAX_SRC] = { nullptr };
-    size_t dst_offset = 0, src_offsets[GGML_MAX_SRC] = { 0 };
-    bool dst_uma = false, srcs_uma[GGML_MAX_SRC] = { false };
-
-    if (ctx->device->uma) {
-        for (int i = 0; i < GGML_MAX_SRC && dst->src[i] != nullptr; i++) {
-            ggml_vk_host_get(ctx->device, dst->src[i]->data, d_srcs[i], src_offsets[i]);
-            srcs_uma[i] = d_srcs[i] != nullptr;
-        }
-        ggml_vk_host_get(ctx->device, dst->data, d_D, dst_offset);
-        dst_uma = d_D != nullptr;
-    }
-
-    if (!dst_uma) {
-        d_D = dst_buf_ctx->dev_buffer;
-        dst_offset = vk_tensor_offset(dst) + dst->view_offs;
-    }
-    for (int i = 0; i < GGML_MAX_SRC && dst->src[i] != nullptr; i++) {
-        if (!srcs_uma[i]) {
-            d_srcs[i] = src_buf_ctxs[i]->dev_buffer;
-            src_offsets[i] = vk_tensor_offset(dst->src[i]) + dst->src[i]->view_offs;
-        }
-    }
-
-    size_t dst_size = ggml_nbytes(dst);
-    size_t src_sizes[GGML_MAX_SRC];
-    for (int i = 0; i < GGML_MAX_SRC && dst->src[i] != nullptr; i++) {
-        src_sizes[i] = ggml_nbytes(dst->src[i]);
+    vk_subbuffer dst_buf = ggml_vk_tensor_subbuffer(ctx, dst);
+    vk_subbuffer src_buf[7] = {};
+    for (int i = 0; i < 7 && dst->src[i] != nullptr; i++) {
+        src_buf[i] = ggml_vk_tensor_subbuffer(ctx, dst->src[i]);
     }
 
     std::array<uint32_t, 3> elements;
@@ -9597,16 +9332,9 @@ static void ggml_vk_ssm_scan(ggml_backend_vk_context * ctx, vk_context& subctx,
     const uint32_t num_workgroups_y = n_seq;
     elements = { num_workgroups_x, num_workgroups_y, 1 };
 
-    ggml_vk_dispatch_pipeline(ctx, subctx, pipeline, {
-        vk_subbuffer{ d_srcs[0], src_offsets[0], src_sizes[0] },
-        vk_subbuffer{ d_srcs[1], src_offsets[1], src_sizes[1] },
-        vk_subbuffer{ d_srcs[2], src_offsets[2], src_sizes[2] },
-        vk_subbuffer{ d_srcs[3], src_offsets[3], src_sizes[3] },
-        vk_subbuffer{ d_srcs[4], src_offsets[4], src_sizes[4] },
-        vk_subbuffer{ d_srcs[5], src_offsets[5], src_sizes[5] },
-        vk_subbuffer{ d_srcs[6], src_offsets[6], src_sizes[6] },
-        vk_subbuffer{ d_D, dst_offset, dst_size }
-    }, pc, elements);
+    ggml_vk_dispatch_pipeline(ctx, subctx, pipeline,
+        {src_buf[0], src_buf[1], src_buf[2], src_buf[3], src_buf[4], src_buf[5], src_buf[6], dst_buf},
+        pc, elements);
 }
 
 static void ggml_vk_ssm_conv(ggml_backend_vk_context * ctx, vk_context& subctx, ggml_tensor * dst) {
@@ -9653,66 +9381,17 @@ static void ggml_vk_op_f32_opt_step_adamw(ggml_backend_vk_context * ctx, vk_cont
 
     ggml_pipeline_request_descriptor_sets(ctx, pipeline, 1);
 
-    ggml_backend_vk_buffer_context * x_buf_ctx = (ggml_backend_vk_buffer_context *)x->buffer->context;
-    ggml_backend_vk_buffer_context * g_buf_ctx = (ggml_backend_vk_buffer_context *)g->buffer->context;
-    ggml_backend_vk_buffer_context * gm_buf_ctx = (ggml_backend_vk_buffer_context *)gm->buffer->context;
-    ggml_backend_vk_buffer_context * gv_buf_ctx = (ggml_backend_vk_buffer_context *)gv->buffer->context;
-    ggml_backend_vk_buffer_context * p_buf_ctx = (ggml_backend_vk_buffer_context *)p->buffer->context;
-
-    vk_buffer d_X = nullptr, d_G = nullptr, d_GM = nullptr, d_GV = nullptr, d_P = nullptr;
-    size_t x_offset = 0, g_offset = 0, gm_offset = 0, gv_offset = 0, p_offset = 0;
-    bool X_uma = false, G_uma = false, GM_uma = false, GV_uma = false, P_uma = false;
-
-    if (ctx->device->uma) {
-        ggml_vk_host_get(ctx->device, x->data, d_X, x_offset);
-        ggml_vk_host_get(ctx->device, g->data, d_G, g_offset);
-        ggml_vk_host_get(ctx->device, gm->data, d_GM, gm_offset);
-        ggml_vk_host_get(ctx->device, gv->data, d_GV, gv_offset);
-        ggml_vk_host_get(ctx->device, p->data, d_P, p_offset);
-
-        X_uma = d_X != nullptr;
-        G_uma = d_G != nullptr;
-        GM_uma = d_GM != nullptr;
-        GV_uma = d_GV != nullptr;
-        P_uma = d_P != nullptr;
-    }
-
-    if (!X_uma) {
-        d_X = x_buf_ctx->dev_buffer;
-        x_offset = vk_tensor_offset(x) + x->view_offs;
-    }
-    if (!G_uma) {
-        d_G = g_buf_ctx->dev_buffer;
-        g_offset = vk_tensor_offset(g) + g->view_offs;
-    }
-    if (!GM_uma) {
-        d_GM = gm_buf_ctx->dev_buffer;
-        gm_offset = vk_tensor_offset(gm) + gm->view_offs;
-    }
-    if (!GV_uma) {
-        d_GV = gv_buf_ctx->dev_buffer;
-        gv_offset = vk_tensor_offset(gv) + gv->view_offs;
-    }
-    if (!P_uma) {
-        d_P = p_buf_ctx->dev_buffer;
-        p_offset = vk_tensor_offset(p) + p->view_offs;
-    }
-
-    const uint64_t x_size = ggml_nbytes(x);
-    const uint64_t g_size = ggml_nbytes(g);
-    const uint64_t gm_size = ggml_nbytes(gm);
-    const uint64_t gv_size = ggml_nbytes(gv);
-    const uint64_t p_size = ggml_nbytes(p);
+    vk_subbuffer x_buf = ggml_vk_tensor_subbuffer(ctx, x);
+    vk_subbuffer g_buf = ggml_vk_tensor_subbuffer(ctx, g);
+    vk_subbuffer gm_buf = ggml_vk_tensor_subbuffer(ctx, gm);
+    vk_subbuffer gv_buf = ggml_vk_tensor_subbuffer(ctx, gv);
+    vk_subbuffer p_buf = ggml_vk_tensor_subbuffer(ctx, p);
 
     std::array<uint32_t, 3> elements = { (uint32_t)ggml_nelements(x), 1, 1 };
 
-    ggml_vk_dispatch_pipeline(ctx, subctx, pipeline, {
-        vk_subbuffer{ d_X, x_offset, x_size },
-        vk_subbuffer{ d_G, g_offset, g_size },
-        vk_subbuffer{ d_GM, gm_offset, gm_size },
-        vk_subbuffer{ d_GV, gv_offset, gv_size },
-        vk_subbuffer{ d_P, p_offset, p_size },
-    }, pc, elements);
+    ggml_vk_dispatch_pipeline(ctx, subctx, pipeline,
+        {x_buf, g_buf, gm_buf, gv_buf, p_buf},
+        pc, elements);
 }
 
 static void ggml_vk_opt_step_adamw(ggml_backend_vk_context * ctx, vk_context& subctx, ggml_tensor * dst) {
@@ -10044,45 +9723,9 @@ static void ggml_vk_topk_moe(ggml_backend_vk_context * ctx, vk_context& subctx,
 
     ggml_pipeline_request_descriptor_sets(ctx, pipeline, 1);
 
-    ggml_backend_vk_buffer_context * logits_buf_ctx = (ggml_backend_vk_buffer_context *)logits->buffer->context;
-    ggml_backend_vk_buffer_context * weights_buf_ctx = (ggml_backend_vk_buffer_context *)weights->buffer->context;
-    ggml_backend_vk_buffer_context * ids_buf_ctx = (ggml_backend_vk_buffer_context *)ids->buffer->context;
-
-    vk_buffer d_logits = nullptr;
-    size_t logits_buf_offset = 0;
-    vk_buffer d_weights = nullptr;
-    size_t weights_buf_offset = 0;
-    vk_buffer d_ids = nullptr;
-    size_t ids_buf_offset = 0;
-
-    bool logits_uma = false;
-    bool weights_uma = false;
-    bool ids_uma = false;
-
-    if (ctx->device->uma) {
-        ggml_vk_host_get(ctx->device, logits->data, d_logits, logits_buf_offset);
-        ggml_vk_host_get(ctx->device, weights->data, d_weights, weights_buf_offset);
-        ggml_vk_host_get(ctx->device, ids->data, d_ids, ids_buf_offset);
-        logits_uma = d_logits != nullptr;
-        weights_uma = d_weights != nullptr;
-        ids_uma = d_ids != nullptr;
-    }
-
-    if (!logits_uma) {
-        d_logits = logits_buf_ctx->dev_buffer;
-        logits_buf_offset = vk_tensor_offset(logits) + logits->view_offs;
-        GGML_ASSERT(d_logits != nullptr);
-    }
-    if (!weights_uma) {
-        d_weights = weights_buf_ctx->dev_buffer;
-        weights_buf_offset = vk_tensor_offset(weights) + weights->view_offs;
-        GGML_ASSERT(d_weights != nullptr);
-    }
-    if (!ids_uma) {
-        d_ids = ids_buf_ctx->dev_buffer;
-        ids_buf_offset = vk_tensor_offset(ids) + ids->view_offs;
-        GGML_ASSERT(d_ids != nullptr);
-    }
+    vk_subbuffer logits_buf = ggml_vk_tensor_subbuffer(ctx, logits);
+    vk_subbuffer weights_buf = ggml_vk_tensor_subbuffer(ctx, weights);
+    vk_subbuffer ids_buf = ggml_vk_tensor_subbuffer(ctx, ids);
 
     vk_op_topk_moe_push_constants pc {};
     pc.n_rows = n_rows;
@@ -10098,12 +9741,7 @@ static void ggml_vk_topk_moe(ggml_backend_vk_context * ctx, vk_context& subctx,
     const uint32_t rows_per_block = 4;
     std::array<uint32_t, 3> elements = { CEIL_DIV(n_rows, rows_per_block), 1, 1 };
 
-    ggml_vk_dispatch_pipeline(ctx, subctx, pipeline,
-        {
-            ggml_vk_subbuffer(ctx, d_logits, logits_buf_offset),
-            ggml_vk_subbuffer(ctx, d_weights, weights_buf_offset),
-            ggml_vk_subbuffer(ctx, d_ids, ids_buf_offset),
-        }, pc, elements);
+    ggml_vk_dispatch_pipeline(ctx, subctx, pipeline, {logits_buf, weights_buf, ids_buf}, pc, elements);
 }
 
 static void ggml_vk_rope(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_cgraph * cgraph, int node_idx, bool backprop) {

From 299f5d782c8ffd7195a1ed6a6d5561f759beb07e Mon Sep 17 00:00:00 2001
From: bssrdf <merlintiger@hotmail.com>
Date: Fri, 7 Nov 2025 17:41:58 -0500
Subject: [PATCH 114/185] CUDA: properly handle nb00=nb02 case for cpy (#17081)

---
 ggml/src/ggml-cuda/cpy.cu  | 4 +---
 tests/test-backend-ops.cpp | 1 +
 2 files changed, 2 insertions(+), 3 deletions(-)

diff --git a/ggml/src/ggml-cuda/cpy.cu b/ggml/src/ggml-cuda/cpy.cu
index 1dba60eb143..50612237c8a 100644
--- a/ggml/src/ggml-cuda/cpy.cu
+++ b/ggml/src/ggml-cuda/cpy.cu
@@ -198,7 +198,7 @@ static void ggml_cpy_flt_cuda(
     if (transposed) {
         GGML_ASSERT(ne == ne00*ne01*ne02);  // ne[3] is 1 assumed
         int ne00n, ne01n, ne02n;
-        if (nb00 < nb02) {
+        if (nb00 <= nb02) { // most likely safe to handle nb00 = nb02 case here
             ne00n = ne00;
             ne01n = ne01;
             ne02n = ne02;
@@ -206,8 +206,6 @@ static void ggml_cpy_flt_cuda(
             ne00n = ne00;
             ne01n = ne01*ne02;
             ne02n = 1;
-        } else {
-            GGML_ASSERT(false);
         }
 
         dim3 dimGrid( (ne01n + CUDA_CPY_TILE_DIM_2D - 1) / CUDA_CPY_TILE_DIM_2D,
diff --git a/tests/test-backend-ops.cpp b/tests/test-backend-ops.cpp
index bffd60f386a..b9ae82eeddd 100644
--- a/tests/test-backend-ops.cpp
+++ b/tests/test-backend-ops.cpp
@@ -6648,6 +6648,7 @@ static std::vector<std::unique_ptr<test_case>> make_test_cases_eval() {
     test_cases.emplace_back(new test_cpy(GGML_TYPE_F16, GGML_TYPE_F16, {256, 4, 1, 1}, {0, 0, 0, 0}, {0, 0, 0, 0}, true));
     test_cases.emplace_back(new test_cpy(GGML_TYPE_F32, GGML_TYPE_F32, {256, 4, 1, 1}, {0, 0, 0, 0}, {0, 0, 0, 0}, true));
     test_cases.emplace_back(new test_cpy(GGML_TYPE_BF16, GGML_TYPE_BF16, {256, 4, 1, 1}, {0, 0, 0, 0}, {0, 0, 0, 0}, true));
+    test_cases.emplace_back(new test_cpy(GGML_TYPE_F32, GGML_TYPE_F32, {256, 1, 4, 1}, {1, 2, 0, 3}, {0, 0, 0, 0}));
 
     test_cases.emplace_back(new test_cont());
     test_cases.emplace_back(new test_cont(GGML_TYPE_F32, {2, 1, 1 ,1}));

From 647b960bd8017ee882d6633bc2e43e2ae82ee85c Mon Sep 17 00:00:00 2001
From: Reese Levine <reeselevine1@gmail.com>
Date: Fri, 7 Nov 2025 19:27:20 -0800
Subject: [PATCH 115/185] ggml webgpu: faster matrix
 multiplication/matrix-vector multiplication (#17031)

* Faster tensors (#8)

Add fast matrix and matrix/vector multiplication.

* Use map for shader replacements instead of pair of strings
---
 .github/workflows/build.yml                   |  18 +-
 ggml/src/ggml-webgpu/ggml-webgpu.cpp          | 326 +++++++++++++++++-
 .../ggml-webgpu/wgsl-shaders/embed_wgsl.py    |   9 +-
 .../wgsl-shaders/mul_mat.tmpl.wgsl            |  10 +-
 .../wgsl-shaders/mul_mat_decls.tmpl           |  97 ++++++
 .../wgsl-shaders/mul_mat_reg_tile.tmpl.wgsl   | 247 +++++++++++++
 .../mul_mat_subgroup_matrix.tmpl.wgsl         | 302 ++++++++++++++++
 .../wgsl-shaders/mul_mat_vec.tmpl.wgsl        | 267 ++++++++++++++
 8 files changed, 1247 insertions(+), 29 deletions(-)
 create mode 100644 ggml/src/ggml-webgpu/wgsl-shaders/mul_mat_decls.tmpl
 create mode 100644 ggml/src/ggml-webgpu/wgsl-shaders/mul_mat_reg_tile.tmpl.wgsl
 create mode 100644 ggml/src/ggml-webgpu/wgsl-shaders/mul_mat_subgroup_matrix.tmpl.wgsl
 create mode 100644 ggml/src/ggml-webgpu/wgsl-shaders/mul_mat_vec.tmpl.wgsl

diff --git a/.github/workflows/build.yml b/.github/workflows/build.yml
index 15e11330952..36084c55078 100644
--- a/.github/workflows/build.yml
+++ b/.github/workflows/build.yml
@@ -161,15 +161,16 @@ jobs:
       - name: Dawn Dependency
         id: dawn-depends
         run: |
-          DAWN_VERSION="v1.0.0"
+          DAWN_VERSION="v2.0.0"
           DAWN_OWNER="reeselevine"
           DAWN_REPO="dawn"
-          DAWN_ASSET_NAME="Dawn-a1a6b45cced25a3b7f4fb491e0ae70796cc7f22b-macos-latest-Release.tar.gz"
+          DAWN_ASSET_NAME="Dawn-5e9a4865b1635796ccc77dd30057f2b4002a1355-macos-latest-Release.zip"
           echo "Fetching release asset from https://github.com/${DAWN_OWNER}/${DAWN_REPO}/releases/download/${DAWN_VERSION}/${DAWN_ASSET_NAME}"
-          curl -L -o artifact.tar.gz \
+          curl -L -o artifact.zip \
             "https://github.com/${DAWN_OWNER}/${DAWN_REPO}/releases/download/${DAWN_VERSION}/${DAWN_ASSET_NAME}"
           mkdir dawn
-          tar -xvf artifact.tar.gz -C dawn --strip-components=1
+          unzip artifact.zip
+          tar -xvf Dawn-5e9a4865b1635796ccc77dd30057f2b4002a1355-macos-latest-Release.tar.gz -C dawn --strip-components=1
 
       - name: Build
         id: cmake_build
@@ -521,15 +522,16 @@ jobs:
         id: dawn-depends
         run: |
           sudo apt-get install -y libxrandr-dev libxinerama-dev libxcursor-dev mesa-common-dev libx11-xcb-dev libxi-dev
-          DAWN_VERSION="v1.0.0"
+          DAWN_VERSION="v2.0.0"
           DAWN_OWNER="reeselevine"
           DAWN_REPO="dawn"
-          DAWN_ASSET_NAME="Dawn-a1a6b45cced25a3b7f4fb491e0ae70796cc7f22b-ubuntu-latest-Release.tar.gz"
+          DAWN_ASSET_NAME="Dawn-5e9a4865b1635796ccc77dd30057f2b4002a1355-ubuntu-latest-Release.zip"
           echo "Fetching release asset from https://github.com/${DAWN_OWNER}/${DAWN_REPO}/releases/download/${DAWN_VERSION}/${DAWN_ASSET_NAME}"
-          curl -L -o artifact.tar.gz \
+          curl -L -o artifact.zip \
             "https://github.com/${DAWN_OWNER}/${DAWN_REPO}/releases/download/${DAWN_VERSION}/${DAWN_ASSET_NAME}"
           mkdir dawn
-          tar -xvf artifact.tar.gz -C dawn --strip-components=1
+          unzip artifact.zip
+          tar -xvf Dawn-5e9a4865b1635796ccc77dd30057f2b4002a1355-ubuntu-latest-Release.tar.gz -C dawn --strip-components=1
 
       - name: Build
         id: cmake_build
diff --git a/ggml/src/ggml-webgpu/ggml-webgpu.cpp b/ggml/src/ggml-webgpu/ggml-webgpu.cpp
index 1a157567315..9e8cbc477ed 100644
--- a/ggml/src/ggml-webgpu/ggml-webgpu.cpp
+++ b/ggml/src/ggml-webgpu/ggml-webgpu.cpp
@@ -15,6 +15,7 @@
 #include <condition_variable>
 #include <cstring>
 #include <iostream>
+#include <map>
 #include <mutex>
 #include <optional>
 #include <string>
@@ -73,6 +74,30 @@
 // For operations which process a row in parallel, this seems like a reasonable default
 #define WEBGPU_ROW_SPLIT_WG_SIZE 64
 
+// Matrix multiplication parameters
+
+// Register tiling parameters
+#define WEBGPU_MUL_MAT_TILE_M    8
+#define WEBGPU_MUL_MAT_TILE_N    8
+#define WEBGPU_MUL_MAT_WG_SIZE_M 8
+#define WEBGPU_MUL_MAT_WG_SIZE_N 8
+#define WEBGPU_MUL_MAT_TILE_K    32
+
+// Subgroup matrix parameters
+// The number of subgroups in the M dimension
+#define WEBGPU_MUL_MAT_SUBGROUP_M        2
+// The number of subgroups in the N dimension
+#define WEBGPU_MUL_MAT_SUBGROUP_N        2
+// The number of subgroup matrices each subgroup accumulates over
+#define WEBGPU_MUL_MAT_SUBGROUP_MATRIX_M 4
+#define WEBGPU_MUL_MAT_SUBGROUP_MATRIX_N 2
+
+// Matrix-vector multiplication parameters
+#define WEBGPU_MUL_MAT_VEC_WG_SIZE        256
+// Must be multiple of 4 to work with vectorized paths, and must divide mul_mat_vec wg size
+#define WEBGPU_MUL_MAT_VEC_OUTPUTS_PER_WG 64
+#define WEBGPU_MUL_MAT_VEC_TILE_K         256
+
 /* End Constants */
 
 // This is a "fake" base pointer, since WebGPU buffers do not have pointers to their locations.
@@ -236,6 +261,10 @@ struct webgpu_context_struct {
     wgpu::Queue    queue;
     wgpu::Limits   limits;
 
+    bool                       supports_subgroup_matrix = false;
+    uint32_t                   subgroup_size;
+    wgpu::SubgroupMatrixConfig subgroup_matrix_config;
+
     // Separate this out from limits since on some Metal systems, the limit returned by
     // querying the limits is higher than the actual allowed maximum.
     uint32_t max_wg_size_x;
@@ -247,6 +276,11 @@ struct webgpu_context_struct {
     webgpu_buf_pool set_rows_error_buf_pool;
 
     webgpu_pipeline memset_pipeline;
+
+    std::map<int, std::map<int, std::map<int, webgpu_pipeline>>> mul_mat_pipelines;  // src0_type, src1_type, vectorized
+    std::map<int, std::map<int, std::map<int, webgpu_pipeline>>>
+        mul_mat_vec_pipelines;                                                       // src0_type, src1_type, vectorized
+
     webgpu_pipeline mul_mat_pipeline[30][2];
     webgpu_pipeline set_rows_pipeline[1][2];  // dst->type, vectorized
     webgpu_pipeline get_rows_pipeline[30];
@@ -321,6 +355,25 @@ struct ggml_backend_webgpu_buffer_context {
 
 /* WebGPU object initializations */
 
+// Process a WGSL shader string, replacing tokens of the form {{KEY}} with
+// the corresponding values provided in `repls`.
+static std::string ggml_webgpu_process_shader_repls(const char *                               src,
+                                                    const std::map<std::string, std::string> & repls) {
+    if (!src) {
+        return std::string();
+    }
+    std::string s = src;
+    for (const auto & kv : repls) {
+        std::string token = "{{" + kv.first + "}}";
+        size_t      pos   = 0;
+        while ((pos = s.find(token, pos)) != std::string::npos) {
+            s.replace(pos, token.length(), kv.second);
+            pos += kv.second.length();
+        }
+    }
+    return s;
+}
+
 static void ggml_webgpu_create_pipeline(wgpu::Device &                           device,
                                         webgpu_pipeline &                        pipeline,
                                         const char *                             shader_code,
@@ -346,6 +399,30 @@ static void ggml_webgpu_create_pipeline(wgpu::Device &
     pipeline = { device.CreateComputePipeline(&pipeline_desc), label };
 }
 
+static webgpu_pipeline ggml_webgpu_create_pipeline2(wgpu::Device &                           device,
+                                                    const char *                             shader_code,
+                                                    const char *                             label,
+                                                    const std::vector<wgpu::ConstantEntry> & constants = {}) {
+    wgpu::ShaderSourceWGSL shader_source;
+    shader_source.code = shader_code;
+
+    wgpu::ShaderModuleDescriptor shader_desc;
+    shader_desc.nextInChain = &shader_source;
+
+    wgpu::ShaderModule shader_module = device.CreateShaderModule(&shader_desc);
+
+    wgpu::ComputePipelineDescriptor pipeline_desc;
+    pipeline_desc.label              = label;
+    pipeline_desc.compute.module     = shader_module;
+    pipeline_desc.compute.entryPoint = "main";   // Entry point in the WGSL code
+    pipeline_desc.layout             = nullptr;  // nullptr means auto layout
+    if (constants.size() > 0) {
+        pipeline_desc.compute.constants     = constants.data();
+        pipeline_desc.compute.constantCount = constants.size();
+    }
+    return { device.CreateComputePipeline(&pipeline_desc), label };
+}
+
 static void ggml_webgpu_create_buffer(wgpu::Device &    device,
                                       wgpu::Buffer &    buffer,
                                       size_t            size,
@@ -512,6 +589,7 @@ static webgpu_command ggml_backend_webgpu_build(webgpu_context &
                                                 std::vector<uint32_t>             params,
                                                 std::vector<wgpu::BindGroupEntry> bind_group_entries,
                                                 uint32_t                          wg_x,
+                                                uint32_t                          wg_y                = 1,
                                                 std::optional<webgpu_pool_bufs>   set_rows_error_bufs = std::nullopt) {
     webgpu_pool_bufs params_bufs = ctx->param_buf_pool.alloc_bufs();
 
@@ -557,7 +635,7 @@ static webgpu_command ggml_backend_webgpu_build(webgpu_context &
 #endif
     pass.SetPipeline(pipeline.pipeline);
     pass.SetBindGroup(0, bind_group);
-    pass.DispatchWorkgroups(wg_x, 1, 1);
+    pass.DispatchWorkgroups(wg_x, wg_y, 1);
     pass.End();
 
 #ifdef GGML_WEBGPU_GPU_PROFILE
@@ -779,7 +857,7 @@ static std::optional<webgpu_command> ggml_webgpu_set_rows(webgpu_context & ctx,
 
     uint32_t wg_x = (threads + max_wg_size - 1) / max_wg_size;
 
-    return ggml_backend_webgpu_build(ctx, pipeline, params, entries, wg_x, error_bufs);
+    return ggml_backend_webgpu_build(ctx, pipeline, params, entries, wg_x, 1, error_bufs);
 }
 
 static webgpu_command ggml_webgpu_get_rows(webgpu_context & ctx,
@@ -835,8 +913,8 @@ static webgpu_command ggml_webgpu_mul_mat(webgpu_context & ctx,
         (uint32_t) (ggml_webgpu_tensor_misalignment(ctx, src0) / ggml_type_size(src0->type)),
         (uint32_t) (ggml_webgpu_tensor_misalignment(ctx, src1) / ggml_type_size(src1->type)),
         (uint32_t) (ggml_webgpu_tensor_misalignment(ctx, dst) / ggml_type_size(dst->type)),
-        (uint32_t) dst->ne[1],                                  // number of rows in result (M)
-        (uint32_t) dst->ne[0],                                  // number of columns in result (N)
+        (uint32_t) dst->ne[0],                                  // number of rows in result (M, transposed)
+        (uint32_t) dst->ne[1],                                  // number of columns in result (N)
         (uint32_t) src0->ne[0],                                 // number of columns in src0/src1 (K)
         (uint32_t) (src0->nb[1] / ggml_type_size(src0->type)),  // stride (elements/blocks) of src0 in dimension 1
         (uint32_t) (src1->nb[1] / ggml_type_size(src1->type)),  // stride (elements/blocks) of src1 in dimension 1
@@ -865,9 +943,67 @@ static webgpu_command ggml_webgpu_mul_mat(webgpu_context & ctx,
          .size    = ggml_webgpu_tensor_binding_size(ctx, dst)  },
     };
 
+    webgpu_pipeline pipeline = ctx->mul_mat_pipeline[src0->type][src1->type];
+
     uint32_t wg_x =
         (dst->ne[0] * dst->ne[1] * dst->ne[2] * dst->ne[3] + WEBGPU_MUL_MAT_WG_SIZE - 1) / WEBGPU_MUL_MAT_WG_SIZE;
-    return ggml_backend_webgpu_build(ctx, ctx->mul_mat_pipeline[src0->type][src1->type], params, entries, wg_x);
+    uint32_t wg_y = 1;
+
+    bool use_fast = false;
+    switch (src1->type) {
+        case GGML_TYPE_F16:
+            use_fast = (src0->type == GGML_TYPE_F16);
+            break;
+        case GGML_TYPE_F32:
+            switch (src0->type) {
+                case GGML_TYPE_F32:
+                case GGML_TYPE_F16:
+                case GGML_TYPE_Q4_0:
+                    use_fast = true;
+                    break;
+                default:
+                    break;
+            }
+            break;
+        default:
+            break;
+    }
+
+    if (use_fast) {
+        int vectorized = src0->ne[0] % 4 == 0 && dst->ne[0] % 4 == 0 && dst->ne[1] % 4 == 0;
+        if (dst->ne[1] == 1) {
+            // We don't support vectorized mul_mat_vec for quantized types
+            vectorized       = vectorized && (src0->type < 2);
+            pipeline         = ctx->mul_mat_vec_pipelines[src0->type][src1->type][vectorized];
+            uint32_t batches = dst->ne[2] * dst->ne[3];
+            uint32_t output_groups =
+                (dst->ne[0] + WEBGPU_MUL_MAT_VEC_OUTPUTS_PER_WG - 1) / WEBGPU_MUL_MAT_VEC_OUTPUTS_PER_WG;
+            uint32_t total_wg = output_groups * batches;
+            wg_x              = total_wg % ctx->limits.maxComputeWorkgroupsPerDimension;
+            wg_y              = (total_wg + ctx->limits.maxComputeWorkgroupsPerDimension - 1) /
+                   ctx->limits.maxComputeWorkgroupsPerDimension;
+        } else {
+            pipeline = ctx->mul_mat_pipelines[src0->type][src1->type][vectorized];
+            uint32_t wg_m;
+            uint32_t wg_n;
+            if (ctx->supports_subgroup_matrix) {
+                // The total number of subgroups/workgroups needed per matrix.
+                uint32_t wg_m_sg_tile =
+                    WEBGPU_MUL_MAT_SUBGROUP_M * WEBGPU_MUL_MAT_SUBGROUP_MATRIX_M * ctx->subgroup_matrix_config.M;
+                wg_m = (dst->ne[0] + wg_m_sg_tile - 1) / wg_m_sg_tile;
+                uint32_t wg_n_sg_tile =
+                    WEBGPU_MUL_MAT_SUBGROUP_N * WEBGPU_MUL_MAT_SUBGROUP_MATRIX_N * ctx->subgroup_matrix_config.N;
+                wg_n = (dst->ne[1] + wg_n_sg_tile - 1) / wg_n_sg_tile;
+            } else {
+                uint32_t tile_m_s = WEBGPU_MUL_MAT_TILE_M * WEBGPU_MUL_MAT_WG_SIZE_M;
+                uint32_t tile_n_s = WEBGPU_MUL_MAT_TILE_N * WEBGPU_MUL_MAT_WG_SIZE_N;
+                wg_m              = (dst->ne[0] + tile_m_s - 1) / tile_m_s;
+                wg_n              = (dst->ne[1] + tile_n_s - 1) / tile_n_s;
+            }
+            wg_x = wg_m * wg_n * dst->ne[2] * dst->ne[3];
+        }
+    }
+    return ggml_backend_webgpu_build(ctx, pipeline, params, entries, wg_x, wg_y);
 }
 
 static webgpu_command ggml_webgpu_binary_op(webgpu_context &  ctx,
@@ -1583,12 +1719,6 @@ static void ggml_webgpu_init_memset_pipeline(webgpu_context & webgpu_ctx) {
 }
 
 static void ggml_webgpu_init_mul_mat_pipeline(webgpu_context & webgpu_ctx) {
-    ggml_webgpu_create_pipeline(webgpu_ctx->device, webgpu_ctx->mul_mat_pipeline[GGML_TYPE_F32][GGML_TYPE_F32],
-                                wgsl_mul_mat_f32_f32, "mul_mat_f32_f32");
-    ggml_webgpu_create_pipeline(webgpu_ctx->device, webgpu_ctx->mul_mat_pipeline[GGML_TYPE_F16][GGML_TYPE_F16],
-                                wgsl_mul_mat_f16_f16, "mul_mat_f16_f16");
-    ggml_webgpu_create_pipeline(webgpu_ctx->device, webgpu_ctx->mul_mat_pipeline[GGML_TYPE_F16][GGML_TYPE_F32],
-                                wgsl_mul_mat_f16_f32, "mul_mat_f16_f32");
     ggml_webgpu_create_pipeline(webgpu_ctx->device, webgpu_ctx->mul_mat_pipeline[GGML_TYPE_Q4_0][GGML_TYPE_F32],
                                 wgsl_mul_mat_q4_0_f32, "mul_mat_q4_0_f32");
     ggml_webgpu_create_pipeline(webgpu_ctx->device, webgpu_ctx->mul_mat_pipeline[GGML_TYPE_Q4_1][GGML_TYPE_F32],
@@ -1627,6 +1757,136 @@ static void ggml_webgpu_init_mul_mat_pipeline(webgpu_context & webgpu_ctx) {
                                 wgsl_mul_mat_iq4_nl_f32, "mul_mat_iq4_nl_f32");
     ggml_webgpu_create_pipeline(webgpu_ctx->device, webgpu_ctx->mul_mat_pipeline[GGML_TYPE_IQ4_XS][GGML_TYPE_F32],
                                 wgsl_mul_mat_iq4_xs_f32, "mul_mat_iq4_xs_f32");
+
+    if (webgpu_ctx->supports_subgroup_matrix) {
+        std::map<std::string, std::string> sg_matrix_repls;
+        sg_matrix_repls["WEBGPU_MAX_SUBGROUP_SIZE"] = std::to_string(webgpu_ctx->subgroup_size);
+        sg_matrix_repls["WEBGPU_TILE_K"]            = std::to_string(WEBGPU_MUL_MAT_TILE_K);
+        sg_matrix_repls["WEBGPU_SUBGROUP_M"]        = std::to_string(WEBGPU_MUL_MAT_SUBGROUP_M);
+        sg_matrix_repls["WEBGPU_SUBGROUP_N"]        = std::to_string(WEBGPU_MUL_MAT_SUBGROUP_N);
+        sg_matrix_repls["WEBGPU_SUBGROUP_MATRIX_M"] = std::to_string(WEBGPU_MUL_MAT_SUBGROUP_MATRIX_M);
+        sg_matrix_repls["WEBGPU_SUBGROUP_MATRIX_N"] = std::to_string(WEBGPU_MUL_MAT_SUBGROUP_MATRIX_N);
+        sg_matrix_repls["WEBGPU_SG_MAT_M_SIZE"]     = std::to_string(webgpu_ctx->subgroup_matrix_config.M);
+        sg_matrix_repls["WEBGPU_SG_MAT_N_SIZE"]     = std::to_string(webgpu_ctx->subgroup_matrix_config.N);
+        sg_matrix_repls["WEBGPU_SG_MAT_K_SIZE"]     = std::to_string(webgpu_ctx->subgroup_matrix_config.K);
+
+        std::string proc_mul_mat_subgroup_matrix_f32_f32 =
+            ggml_webgpu_process_shader_repls(wgsl_mul_mat_subgroup_matrix_f32_f32, sg_matrix_repls);
+        std::string proc_mul_mat_subgroup_matrix_f32_f32_vec =
+            ggml_webgpu_process_shader_repls(wgsl_mul_mat_subgroup_matrix_f32_f32_vec, sg_matrix_repls);
+        std::string proc_mul_mat_subgroup_matrix_f16_f32 =
+            ggml_webgpu_process_shader_repls(wgsl_mul_mat_subgroup_matrix_f16_f32, sg_matrix_repls);
+        std::string proc_mul_mat_subgroup_matrix_f16_f32_vec =
+            ggml_webgpu_process_shader_repls(wgsl_mul_mat_subgroup_matrix_f16_f32_vec, sg_matrix_repls);
+        std::string proc_mul_mat_subgroup_matrix_f16_f16 =
+            ggml_webgpu_process_shader_repls(wgsl_mul_mat_subgroup_matrix_f16_f16, sg_matrix_repls);
+        std::string proc_mul_mat_subgroup_matrix_f16_f16_vec =
+            ggml_webgpu_process_shader_repls(wgsl_mul_mat_subgroup_matrix_f16_f16_vec, sg_matrix_repls);
+        std::string proc_mul_mat_subgroup_matrix_q4_0_f32 =
+            ggml_webgpu_process_shader_repls(wgsl_mul_mat_subgroup_matrix_q4_0_f32, sg_matrix_repls);
+        std::string proc_mul_mat_subgroup_matrix_q4_0_f32_vec =
+            ggml_webgpu_process_shader_repls(wgsl_mul_mat_subgroup_matrix_q4_0_f32_vec, sg_matrix_repls);
+
+        webgpu_ctx->mul_mat_pipelines[GGML_TYPE_F32][GGML_TYPE_F32][0] = ggml_webgpu_create_pipeline2(
+            webgpu_ctx->device, proc_mul_mat_subgroup_matrix_f32_f32.c_str(), "mul_mat_subgroup_matrix_f32_f32");
+        webgpu_ctx->mul_mat_pipelines[GGML_TYPE_F32][GGML_TYPE_F32][1] =
+            ggml_webgpu_create_pipeline2(webgpu_ctx->device, proc_mul_mat_subgroup_matrix_f32_f32_vec.c_str(),
+                                         "mul_mat_subgroup_matrix_f32_f32_vec");
+        webgpu_ctx->mul_mat_pipelines[GGML_TYPE_F16][GGML_TYPE_F32][0] = ggml_webgpu_create_pipeline2(
+            webgpu_ctx->device, proc_mul_mat_subgroup_matrix_f16_f32.c_str(), "mul_mat_subgroup_matrix_f16_f32");
+        webgpu_ctx->mul_mat_pipelines[GGML_TYPE_F16][GGML_TYPE_F32][1] =
+            ggml_webgpu_create_pipeline2(webgpu_ctx->device, proc_mul_mat_subgroup_matrix_f16_f32_vec.c_str(),
+                                         "mul_mat_subgroup_matrix_f16_f32_vec");
+        webgpu_ctx->mul_mat_pipelines[GGML_TYPE_F16][GGML_TYPE_F16][0] = ggml_webgpu_create_pipeline2(
+            webgpu_ctx->device, proc_mul_mat_subgroup_matrix_f16_f16.c_str(), "mul_mat_subgroup_matrix_f16_f16");
+        webgpu_ctx->mul_mat_pipelines[GGML_TYPE_F16][GGML_TYPE_F16][1] =
+            ggml_webgpu_create_pipeline2(webgpu_ctx->device, proc_mul_mat_subgroup_matrix_f16_f16_vec.c_str(),
+                                         "mul_mat_subgroup_matrix_f16_f16_vec");
+        webgpu_ctx->mul_mat_pipelines[GGML_TYPE_Q4_0][GGML_TYPE_F32][0] = ggml_webgpu_create_pipeline2(
+            webgpu_ctx->device, proc_mul_mat_subgroup_matrix_q4_0_f32.c_str(), "mul_mat_subgroup_matrix_q4_0_f32");
+        webgpu_ctx->mul_mat_pipelines[GGML_TYPE_Q4_0][GGML_TYPE_F32][1] =
+            ggml_webgpu_create_pipeline2(webgpu_ctx->device, proc_mul_mat_subgroup_matrix_q4_0_f32_vec.c_str(),
+                                         "mul_mat_subgroup_matrix_q4_0_f32_vec");
+    } else {
+        std::vector<wgpu::ConstantEntry> mul_mat_reg_tile_constants(3);
+        mul_mat_reg_tile_constants[0].key   = "TILE_K";
+        mul_mat_reg_tile_constants[0].value = WEBGPU_MUL_MAT_TILE_K;
+        mul_mat_reg_tile_constants[1].key   = "WORKGROUP_SIZE_M";
+        mul_mat_reg_tile_constants[1].value = WEBGPU_MUL_MAT_WG_SIZE_M;
+        mul_mat_reg_tile_constants[2].key   = "WORKGROUP_SIZE_N";
+        mul_mat_reg_tile_constants[2].value = WEBGPU_MUL_MAT_WG_SIZE_N;
+
+        std::map<std::string, std::string> reg_repls;
+        reg_repls["WEBGPU_TILE_M"] = std::to_string(WEBGPU_MUL_MAT_TILE_M);
+        reg_repls["WEBGPU_TILE_N"] = std::to_string(WEBGPU_MUL_MAT_TILE_N);
+
+        // Process each reg-tile shader with tile replacements.
+        // Keep the processed strings in-scope so .c_str() remains valid.
+        std::string proc_mul_mat_reg_tile_f32_f32 =
+            ggml_webgpu_process_shader_repls(wgsl_mul_mat_reg_tile_f32_f32, reg_repls);
+        std::string proc_mul_mat_reg_tile_f32_f32_vec =
+            ggml_webgpu_process_shader_repls(wgsl_mul_mat_reg_tile_f32_f32_vec, reg_repls);
+        std::string proc_mul_mat_reg_tile_f16_f32 =
+            ggml_webgpu_process_shader_repls(wgsl_mul_mat_reg_tile_f16_f32, reg_repls);
+        std::string proc_mul_mat_reg_tile_f16_f32_vec =
+            ggml_webgpu_process_shader_repls(wgsl_mul_mat_reg_tile_f16_f32_vec, reg_repls);
+        std::string proc_mul_mat_reg_tile_f16_f16 =
+            ggml_webgpu_process_shader_repls(wgsl_mul_mat_reg_tile_f16_f16, reg_repls);
+        std::string proc_mul_mat_reg_tile_f16_f16_vec =
+            ggml_webgpu_process_shader_repls(wgsl_mul_mat_reg_tile_f16_f16_vec, reg_repls);
+        std::string proc_mul_mat_reg_tile_q4_0_f32 =
+            ggml_webgpu_process_shader_repls(wgsl_mul_mat_reg_tile_q4_0_f32, reg_repls);
+        std::string proc_mul_mat_reg_tile_q4_0_f32_vec =
+            ggml_webgpu_process_shader_repls(wgsl_mul_mat_reg_tile_q4_0_f32_vec, reg_repls);
+
+        webgpu_ctx->mul_mat_pipelines[GGML_TYPE_F32][GGML_TYPE_F32][0] =
+            ggml_webgpu_create_pipeline2(webgpu_ctx->device, proc_mul_mat_reg_tile_f32_f32.c_str(),
+                                         "mul_mat_reg_tile_f32_f32", mul_mat_reg_tile_constants);
+        webgpu_ctx->mul_mat_pipelines[GGML_TYPE_F32][GGML_TYPE_F32][1] =
+            ggml_webgpu_create_pipeline2(webgpu_ctx->device, proc_mul_mat_reg_tile_f32_f32_vec.c_str(),
+                                         "mul_mat_reg_tile_f32_f32_vec", mul_mat_reg_tile_constants);
+        webgpu_ctx->mul_mat_pipelines[GGML_TYPE_F16][GGML_TYPE_F32][0] =
+            ggml_webgpu_create_pipeline2(webgpu_ctx->device, proc_mul_mat_reg_tile_f16_f32.c_str(),
+                                         "mul_mat_reg_tile_f16_f32", mul_mat_reg_tile_constants);
+        webgpu_ctx->mul_mat_pipelines[GGML_TYPE_F16][GGML_TYPE_F32][1] =
+            ggml_webgpu_create_pipeline2(webgpu_ctx->device, proc_mul_mat_reg_tile_f16_f32_vec.c_str(),
+                                         "mul_mat_reg_tile_f16_f32_vec", mul_mat_reg_tile_constants);
+        webgpu_ctx->mul_mat_pipelines[GGML_TYPE_F16][GGML_TYPE_F16][0] =
+            ggml_webgpu_create_pipeline2(webgpu_ctx->device, proc_mul_mat_reg_tile_f16_f16.c_str(),
+                                         "mul_mat_reg_tile_f16_f16", mul_mat_reg_tile_constants);
+        webgpu_ctx->mul_mat_pipelines[GGML_TYPE_F16][GGML_TYPE_F16][1] =
+            ggml_webgpu_create_pipeline2(webgpu_ctx->device, proc_mul_mat_reg_tile_f16_f16_vec.c_str(),
+                                         "mul_mat_reg_tile_f16_f16_vec", mul_mat_reg_tile_constants);
+        webgpu_ctx->mul_mat_pipelines[GGML_TYPE_Q4_0][GGML_TYPE_F32][0] =
+            ggml_webgpu_create_pipeline2(webgpu_ctx->device, proc_mul_mat_reg_tile_q4_0_f32.c_str(),
+                                         "mul_mat_reg_tile_q4_0_f32", mul_mat_reg_tile_constants);
+        webgpu_ctx->mul_mat_pipelines[GGML_TYPE_Q4_0][GGML_TYPE_F32][1] =
+            ggml_webgpu_create_pipeline2(webgpu_ctx->device, proc_mul_mat_reg_tile_q4_0_f32_vec.c_str(),
+                                         "mul_mat_reg_tile_q4_0_f32_vec", mul_mat_reg_tile_constants);
+    }
+
+    std::vector<wgpu::ConstantEntry> mul_mat_vec_constants(3);
+    mul_mat_vec_constants[0].key   = "WORKGROUP_SIZE";
+    mul_mat_vec_constants[0].value = WEBGPU_MUL_MAT_VEC_WG_SIZE;
+    mul_mat_vec_constants[1].key   = "TILE_K";
+    mul_mat_vec_constants[1].value = WEBGPU_MUL_MAT_VEC_TILE_K;
+    mul_mat_vec_constants[2].key   = "OUTPUTS_PER_WG";
+    mul_mat_vec_constants[2].value = WEBGPU_MUL_MAT_VEC_OUTPUTS_PER_WG;
+
+    webgpu_ctx->mul_mat_vec_pipelines[GGML_TYPE_F32][GGML_TYPE_F32][0] = ggml_webgpu_create_pipeline2(
+        webgpu_ctx->device, wgsl_mul_mat_vec_f32_f32, "mul_mat_vec_f32_f32", mul_mat_vec_constants);
+    webgpu_ctx->mul_mat_vec_pipelines[GGML_TYPE_F32][GGML_TYPE_F32][1] = ggml_webgpu_create_pipeline2(
+        webgpu_ctx->device, wgsl_mul_mat_vec_f32_f32_vec, "mul_mat_vec_f32_f32_vec", mul_mat_vec_constants);
+    webgpu_ctx->mul_mat_vec_pipelines[GGML_TYPE_F16][GGML_TYPE_F32][0] = ggml_webgpu_create_pipeline2(
+        webgpu_ctx->device, wgsl_mul_mat_vec_f16_f32, "mul_mat_vec_f16_f32", mul_mat_vec_constants);
+    webgpu_ctx->mul_mat_vec_pipelines[GGML_TYPE_F16][GGML_TYPE_F32][1] = ggml_webgpu_create_pipeline2(
+        webgpu_ctx->device, wgsl_mul_mat_vec_f16_f32_vec, "mul_mat_vec_f16_f32_vec", mul_mat_vec_constants);
+    webgpu_ctx->mul_mat_vec_pipelines[GGML_TYPE_F16][GGML_TYPE_F16][0] = ggml_webgpu_create_pipeline2(
+        webgpu_ctx->device, wgsl_mul_mat_vec_f16_f16, "mul_mat_vec_f16_f16", mul_mat_vec_constants);
+    webgpu_ctx->mul_mat_vec_pipelines[GGML_TYPE_F16][GGML_TYPE_F16][1] = ggml_webgpu_create_pipeline2(
+        webgpu_ctx->device, wgsl_mul_mat_vec_f16_f16_vec, "mul_mat_vec_f16_f16_vec", mul_mat_vec_constants);
+    webgpu_ctx->mul_mat_vec_pipelines[GGML_TYPE_Q4_0][GGML_TYPE_F32][0] = ggml_webgpu_create_pipeline2(
+        webgpu_ctx->device, wgsl_mul_mat_vec_q4_0_f32, "mul_mat_vec_q4_0_f32", mul_mat_vec_constants);
 }
 
 static void ggml_webgpu_init_set_rows_pipeline(webgpu_context & webgpu_ctx) {
@@ -2124,7 +2384,13 @@ static ggml_backend_dev_t ggml_backend_webgpu_reg_get_device(ggml_backend_reg_t
 
     webgpu_context ctx = reg_ctx->webgpu_ctx;
 
-    wgpu::RequestAdapterOptions options = {};
+    // TODO: track need for these toggles: https://issues.chromium.org/issues/42251215
+    const char * const          adapterEnabledToggles[] = { "vulkan_enable_f16_on_nvidia", "use_vulkan_memory_model" };
+    wgpu::DawnTogglesDescriptor adapterTogglesDesc;
+    adapterTogglesDesc.enabledToggles     = adapterEnabledToggles;
+    adapterTogglesDesc.enabledToggleCount = 2;
+    wgpu::RequestAdapterOptions options   = {};
+    options.nextInChain                   = &adapterTogglesDesc;
     ctx->instance.WaitAny(ctx->instance.RequestAdapter(
                               &options, wgpu::CallbackMode::AllowSpontaneous,
                               [&ctx](wgpu::RequestAdapterStatus status, wgpu::Adapter adapter, const char * message) {
@@ -2140,12 +2406,46 @@ static ggml_backend_dev_t ggml_backend_webgpu_reg_get_device(ggml_backend_reg_t
     ctx->adapter.GetLimits(&ctx->limits);
     ctx->max_wg_size_x = 288;  // default value
 
-    wgpu::AdapterInfo info{};
+    wgpu::AdapterInfo                            info{};
+    wgpu::AdapterPropertiesSubgroupMatrixConfigs subgroup_matrix_configs{};
+    if (ctx->adapter.HasFeature(wgpu::FeatureName::ChromiumExperimentalSubgroupMatrix)) {
+        info.nextInChain = &subgroup_matrix_configs;
+    }
     ctx->adapter.GetInfo(&info);
 
+    wgpu::SupportedFeatures features;
+    ctx->adapter.GetFeatures(&features);
+    // we require f16 support
+    GGML_ASSERT(ctx->adapter.HasFeature(wgpu::FeatureName::ShaderF16));
+
+    // Only support square f16 matrices of size 8 or 16 for now
+    bool valid_subgroup_matrix_config = false;
+    if (ctx->adapter.HasFeature(wgpu::FeatureName::ChromiumExperimentalSubgroupMatrix)) {
+        for (size_t i = 0; i < subgroup_matrix_configs.configCount; i++) {
+            const wgpu::SubgroupMatrixConfig config = subgroup_matrix_configs.configs[i];
+            if (config.M == config.N && config.N == config.K && (config.K == 8 || config.K == 16) &&
+                config.componentType == wgpu::SubgroupMatrixComponentType::F16 &&
+                config.resultComponentType == wgpu::SubgroupMatrixComponentType::F16) {
+                ctx->subgroup_matrix_config  = config;
+                valid_subgroup_matrix_config = true;
+                break;
+            }
+        }
+    }
+
+    // For subgroup matrix code to be the most efficient, we would like the subgroup size to be consistent and accurate.
+    // Unfortunately, that is not possible, so we use the maximum subgroup size reported by the adapter.
+    ctx->subgroup_size            = info.subgroupMaxSize;
+    ctx->supports_subgroup_matrix = valid_subgroup_matrix_config;
+
     // Initialize device
     std::vector<wgpu::FeatureName> required_features = { wgpu::FeatureName::ShaderF16,
                                                          wgpu::FeatureName::ImplicitDeviceSynchronization };
+    if (ctx->supports_subgroup_matrix) {
+        required_features.push_back(wgpu::FeatureName::Subgroups);
+        required_features.push_back(wgpu::FeatureName::ChromiumExperimentalSubgroupMatrix);
+    }
+
 #ifdef GGML_WEBGPU_GPU_PROFILE
     required_features.push_back(wgpu::FeatureName::TimestampQuery);
 #endif
diff --git a/ggml/src/ggml-webgpu/wgsl-shaders/embed_wgsl.py b/ggml/src/ggml-webgpu/wgsl-shaders/embed_wgsl.py
index 251051eaeca..ed8068d416e 100755
--- a/ggml/src/ggml-webgpu/wgsl-shaders/embed_wgsl.py
+++ b/ggml/src/ggml-webgpu/wgsl-shaders/embed_wgsl.py
@@ -72,9 +72,12 @@ def generate_variants(fname, input_dir, output_dir, outfile):
         except ValueError:
             decls_map = {}
 
-        with open(os.path.join(input_dir, "common_decls.tmpl"), "r", encoding="utf-8") as f:
-            common_decls = f.read()
-        decls_map.update(parse_decls(common_decls))
+        for fname in sorted(os.listdir(input_dir)):
+            if fname.endswith(".tmpl"):
+                tmpl_path = os.path.join(input_dir, fname)
+                with open(tmpl_path, "r", encoding="utf-8") as f_tmpl:
+                    decls = f_tmpl.read()
+                    decls_map.update(parse_decls(decls))
 
         shader_template = extract_block(text, "SHADER")
         for variant in variants:
diff --git a/ggml/src/ggml-webgpu/wgsl-shaders/mul_mat.tmpl.wgsl b/ggml/src/ggml-webgpu/wgsl-shaders/mul_mat.tmpl.wgsl
index 141db9b39d9..0f8e6e5ac3d 100644
--- a/ggml/src/ggml-webgpu/wgsl-shaders/mul_mat.tmpl.wgsl
+++ b/ggml/src/ggml-webgpu/wgsl-shaders/mul_mat.tmpl.wgsl
@@ -864,8 +864,8 @@ struct MulMatParams {
     broadcast3: u32
 };
 
-@group(0) @binding(0) var<storage, read_write> src0: array<{{SRC0_TYPE}}>; // N rows, K columns
-@group(0) @binding(1) var<storage, read_write> src1: array<{{SRC1_TYPE}}>; // M rows, K columns (transposed)
+@group(0) @binding(0) var<storage, read_write> src0: array<{{SRC0_TYPE}}>; // M rows, K columns
+@group(0) @binding(1) var<storage, read_write> src1: array<{{SRC1_TYPE}}>; // K rows, N columns (transposed)
 @group(0) @binding(2) var<storage, read_write> dst: array<f32>; // M rows, N columns
 
 @group(0) @binding(3) var<uniform> params: MulMatParams;
@@ -891,8 +891,8 @@ fn main(@builtin(global_invocation_id) global_id: vec3<u32>) {
 
     let dst2_rem = dst3_rem % dst2_stride;
 
-    let row = dst2_rem / params.n; // output row
-    let col = dst2_rem % params.n; // output column
+    let row = dst2_rem / params.m; // output row
+    let col = dst2_rem % params.m; // output column
 
     let src0_idx_base = params.offset_src0 + src03_idx * params.stride_03 + src02_idx * params.stride_02 + col * params.stride_01;
     let src1_idx_base = params.offset_src1 + src13_idx * params.stride_13 + src12_idx * params.stride_12 + row * params.stride_11;
@@ -901,7 +901,7 @@ fn main(@builtin(global_invocation_id) global_id: vec3<u32>) {
     for (var i: u32 = 0u; i < params.k/{{BLOCK_SIZE}}; i = i + 1u) {
         sum += multiply_add(src0_idx_base, src1_idx_base, i);
     }
-    dst[params.offset_dst + dst3_idx * dst3_stride + dst2_idx * dst2_stride + row * params.n + col] = sum;
+    dst[params.offset_dst + dst3_idx * dst3_stride + dst2_idx * dst2_stride + row * params.m + col] = sum;
 }
 
 #end(SHADER)
diff --git a/ggml/src/ggml-webgpu/wgsl-shaders/mul_mat_decls.tmpl b/ggml/src/ggml-webgpu/wgsl-shaders/mul_mat_decls.tmpl
new file mode 100644
index 00000000000..109ff8d6159
--- /dev/null
+++ b/ggml/src/ggml-webgpu/wgsl-shaders/mul_mat_decls.tmpl
@@ -0,0 +1,97 @@
+#decl(SHMEM_VEC)
+fn store_shmem(val: vec4<f16>, idx: u32) {
+    shmem[idx] = val.x;
+    shmem[idx + 1] = val.y;
+    shmem[idx + 2] = val.z;
+    shmem[idx + 3] = val.w;
+}
+#enddecl(SHMEM_VEC)
+
+#decl(SHMEM_SCALAR)
+fn store_shmem(val: f16, idx: u32) {
+    shmem[idx] = val;
+}
+#enddecl(SHMEM_SCALAR)
+
+#decl(INIT_SRC0_SHMEM_FLOAT)
+
+fn init_shmem_src0(thread_id: u32, batch_offset: u32, offset_m: u32, k_outer: u32) {
+    for (var elem_idx = thread_id * {{VEC_SIZE}}; elem_idx < TILE_SRC0_SHMEM; elem_idx += TOTAL_WORKGROUP_SIZE * {{VEC_SIZE}}) {
+        let tile_m = elem_idx / TILE_K;
+        let tile_k = elem_idx % TILE_K;
+        let global_m = offset_m + tile_m;
+        let global_k = k_outer + tile_k;
+        let src0_idx = batch_offset + global_m * params.stride_01 + global_k;
+        let src0_val = select( // taking a slight performance hit to avoid oob
+            {{SRC0_TYPE}}(0.0),
+            src0[src0_idx/{{VEC_SIZE}}],
+            global_m < params.m && global_k < params.k);
+        store_shmem({{SHMEM_TYPE}}(src0_val), elem_idx);
+    }
+}
+
+#enddecl(INIT_SRC0_SHMEM_FLOAT)
+
+#decl(INIT_SRC1_SHMEM)
+
+fn init_shmem_src1(thread_id: u32, batch_offset: u32, offset_n: u32, k_outer: u32) {
+    for (var elem_idx = thread_id * {{VEC_SIZE}}; elem_idx < TILE_SRC1_SHMEM; elem_idx += TOTAL_WORKGROUP_SIZE * {{VEC_SIZE}}) {
+        let tile_n = elem_idx / TILE_K;
+        let tile_k = elem_idx % TILE_K;
+        let global_n = offset_n + tile_n;
+        let global_k = k_outer + tile_k;
+        let src1_idx = batch_offset + global_n * params.stride_11 + global_k;
+        let src1_val = select(
+            {{SRC1_TYPE}}(0.0),
+            src1[src1_idx/{{VEC_SIZE}}],
+            global_n < params.n && global_k < params.k);
+        store_shmem({{SHMEM_TYPE}}(src1_val), TILE_SRC0_SHMEM + elem_idx);
+    }
+}
+
+#enddecl(INIT_SRC1_SHMEM)
+
+#decl(INIT_SRC0_SHMEM_Q4_0)
+
+const BLOCK_SIZE = 32u;
+// the number of blocks per k-tile. Note that this currently only works if TILE_K is a multiple of BLOCK_SIZE, which may need to be rethought for larger quantized types.
+override BLOCKS_K = TILE_K/BLOCK_SIZE;
+const NQ = 16u;
+const F16_PER_BLOCK = 9u; // 1 scale + 8x4 packed weights
+const WEIGHTS_PER_F16 = 4u; // 4 weights per f16
+const F16_PER_THREAD = NQ / WEIGHTS_PER_F16;
+
+fn init_shmem_src0(thread_id: u32, batch_offset: u32, offset_m: u32, k_outer: u32) {
+    for (var i = thread_id * NQ; i < TILE_SRC0_SHMEM; i += TOTAL_WORKGROUP_SIZE * NQ) {
+        let blck_idx = i / BLOCK_SIZE;
+        let block_offset = (i % BLOCK_SIZE) / WEIGHTS_PER_F16;
+        let shmem_idx = blck_idx * BLOCK_SIZE + block_offset * 2u;
+
+        let tile_m = blck_idx / BLOCKS_K;
+        let global_m = offset_m + tile_m;
+        let block_k = blck_idx % BLOCKS_K;
+        let global_k = k_outer / BLOCK_SIZE + block_k;
+
+        if (global_m < params.m && global_k < params.k / BLOCK_SIZE) {
+            let src0_idx = batch_offset + global_m * params.stride_01 + global_k;
+            let scale_idx = src0_idx * F16_PER_BLOCK;
+            let d = src0[scale_idx];
+
+            for (var j = 0u; j < F16_PER_THREAD; j += 2) {
+                let q_0 = src0[scale_idx + 1u + block_offset + j];
+                let q_1 = src0[scale_idx + 1u + block_offset + j + 1];
+
+                let q_packed = bitcast<u32>(vec2(q_0, q_1));
+                for (var k = 0u; k < 4u; k++) {
+                    let q_byte = get_byte(q_packed, k);
+                    let q_hi = (f16((q_byte >> 4) & 0xF) - 8.0) * d;
+                    let q_lo = (f16(q_byte & 0xF) - 8.0) * d;
+                    shmem[shmem_idx + j * 2 + k] = q_lo;
+                    shmem[shmem_idx + j * 2 + k + 16u] = q_hi;
+                }
+            }
+        }
+    }
+}
+
+#enddecl(INIT_SRC0_SHMEM_Q4_0)
diff --git a/ggml/src/ggml-webgpu/wgsl-shaders/mul_mat_reg_tile.tmpl.wgsl b/ggml/src/ggml-webgpu/wgsl-shaders/mul_mat_reg_tile.tmpl.wgsl
new file mode 100644
index 00000000000..6b1dd26cd9e
--- /dev/null
+++ b/ggml/src/ggml-webgpu/wgsl-shaders/mul_mat_reg_tile.tmpl.wgsl
@@ -0,0 +1,247 @@
+#define(VARIANTS)
+[
+  {
+    "SHADER_SUFFIX": "f32_f32_vec",
+    "REPLS": {
+      "SRC0_TYPE" : "vec4<f32>",
+      "SRC1_TYPE" : "vec4<f32>",
+      "DST_TYPE" : "vec4<f32>",
+      "SHMEM_TYPE" : "vec4<f16>",
+      "VEC_SIZE" : 4,
+    },
+    "DECLS": ["VEC", "SHMEM_VEC", "INIT_SRC0_SHMEM_FLOAT", "INIT_SRC1_SHMEM"]
+  },
+  {
+    "SHADER_SUFFIX": "f32_f32",
+    "REPLS": {
+      "SRC0_TYPE" : "f32",
+      "SRC1_TYPE" : "f32",
+      "DST_TYPE" : "f32",
+      "SHMEM_TYPE" : "f16",
+      "VEC_SIZE" : 1,
+    },
+    "DECLS": ["SCALAR", "SHMEM_SCALAR", "INIT_SRC0_SHMEM_FLOAT", "INIT_SRC1_SHMEM"]
+  },
+  {
+    "SHADER_SUFFIX": "f16_f32_vec",
+    "REPLS": {
+      "SRC0_TYPE" : "vec4<f16>",
+      "SRC1_TYPE" : "vec4<f32>",
+      "DST_TYPE" : "vec4<f32>",
+      "SHMEM_TYPE" : "vec4<f16>",
+      "VEC_SIZE" : 4,
+    },
+    "DECLS": ["VEC", "SHMEM_VEC", "INIT_SRC0_SHMEM_FLOAT", "INIT_SRC1_SHMEM"]
+  },
+  {
+    "SHADER_SUFFIX": "f16_f32",
+    "REPLS": {
+      "SRC0_TYPE" : "f16",
+      "SRC1_TYPE" : "f32",
+      "DST_TYPE" : "f32",
+      "SHMEM_TYPE" : "f16",
+      "VEC_SIZE" : 1,
+    },
+    "DECLS": ["SCALAR", "SHMEM_SCALAR", "INIT_SRC0_SHMEM_FLOAT", "INIT_SRC1_SHMEM"]
+  },
+  {
+    "SHADER_SUFFIX": "f16_f16_vec",
+    "REPLS": {
+      "SRC0_TYPE" : "vec4<f16>",
+      "SRC1_TYPE" : "vec4<f16>",
+      "DST_TYPE" : "vec4<f32>",
+      "SHMEM_TYPE" : "vec4<f16>",
+      "VEC_SIZE" : 4,
+    },
+    "DECLS": ["VEC", "SHMEM_VEC", "INIT_SRC0_SHMEM_FLOAT", "INIT_SRC1_SHMEM"]
+  },
+  {
+    "SHADER_SUFFIX": "f16_f16",
+    "REPLS": {
+      "SRC0_TYPE" : "f16",
+      "SRC1_TYPE" : "f16",
+      "DST_TYPE" : "f32",
+      "SHMEM_TYPE" : "f16",
+      "VEC_SIZE" : 1,
+    },
+    "DECLS": ["SCALAR", "SHMEM_SCALAR", "INIT_SRC0_SHMEM_FLOAT", "INIT_SRC1_SHMEM"]
+  },
+  {
+    "SHADER_SUFFIX": "q4_0_f32_vec",
+    "REPLS": {
+      "SRC0_TYPE" : "f16",
+      "SRC1_TYPE" : "vec4<f32>",
+      "DST_TYPE" : "vec4<f32>",
+      "SHMEM_TYPE" : "vec4<f16>",
+      "VEC_SIZE" : 4,
+    },
+    "DECLS": ["BYTE_HELPERS", "VEC", "SHMEM_VEC", "INIT_SRC0_SHMEM_Q4_0", "INIT_SRC1_SHMEM"]
+  },
+  {
+    "SHADER_SUFFIX": "q4_0_f32",
+    "REPLS": {
+      "SRC0_TYPE" : "f16",
+      "SRC1_TYPE" : "f32",
+      "DST_TYPE" : "f32",
+      "SHMEM_TYPE" : "f16",
+      "VEC_SIZE" : 1,
+    },
+    "DECLS": ["BYTE_HELPERS", "SCALAR", "SHMEM_SCALAR", "INIT_SRC0_SHMEM_Q4_0", "INIT_SRC1_SHMEM"]
+  }
+]
+
+#end(VARIANTS)
+
+#define(DECLS)
+
+#decl(VEC)
+fn store_val(acc: array<array<f16, TILE_N>, TILE_M>, tn: u32, tm: u32) -> vec4<f32> {
+    return vec4<f32>(f32(acc[tm][tn]), f32(acc[tm + 1][tn]), f32(acc[tm + 2][tn]), f32(acc[tm + 3][tn]));
+}
+#enddecl(VEC)
+
+#decl(SCALAR)
+fn store_val(acc: array<array<f16, TILE_N>, TILE_M>, tn: u32, tm: u32) -> f32 {
+    return f32(acc[tm][tn]);
+}
+#enddecl(SCALAR)
+
+#end(DECLS)
+
+#define(SHADER)
+enable f16;
+
+struct MulMatParams {
+    offset_src0: u32,
+    offset_src1: u32,
+    offset_dst: u32,
+    m: u32,
+    n: u32,
+    k: u32,
+    stride_01: u32,
+    stride_11: u32,
+    stride_02: u32,
+    stride_12: u32,
+    stride_03: u32,
+    stride_13: u32,
+    bs02: u32,
+    bs03: u32,
+    broadcast2: u32,
+    broadcast3: u32
+};
+
+@group(0) @binding(0) var<storage, read_write> src0: array<{{SRC0_TYPE}}>; // M rows, K columns
+@group(0) @binding(1) var<storage, read_write> src1: array<{{SRC1_TYPE}}>; // K rows, N columns (transposed)
+@group(0) @binding(2) var<storage, read_write> dst: array<{{DST_TYPE}}>; // M rows, N columns (transposed)
+
+@group(0) @binding(3) var<uniform> params: MulMatParams;
+
+DECLS
+
+fn get_local_n(thread_id: u32) -> u32 {
+    return thread_id / WORKGROUP_SIZE_M;
+}
+fn get_local_m(thread_id: u32) -> u32 {
+    return thread_id % WORKGROUP_SIZE_M;
+}
+
+// TILE_M must be multiple of 4 for vec4 loads
+const TILE_M = {{WEBGPU_TILE_M}}u;
+const TILE_N = {{WEBGPU_TILE_N}}u;
+
+override WORKGROUP_SIZE_M: u32;
+override WORKGROUP_SIZE_N: u32;
+override TILE_K: u32;
+
+override TOTAL_WORKGROUP_SIZE = WORKGROUP_SIZE_M * WORKGROUP_SIZE_N;
+override TILE_SRC0_SHMEM = TILE_K * WORKGROUP_SIZE_M * TILE_M;
+override TILE_SRC1_SHMEM = TILE_K * WORKGROUP_SIZE_N * TILE_N;
+
+var<workgroup> shmem: array<f16, TILE_SRC0_SHMEM + TILE_SRC1_SHMEM>;
+
+@compute @workgroup_size(TOTAL_WORKGROUP_SIZE)
+fn main(@builtin(workgroup_id) wg_id: vec3<u32>,
+        @builtin(local_invocation_id) local_id: vec3<u32>) {
+
+    let thread_id = local_id.x;
+    let local_m = get_local_m(thread_id);
+    let local_n = get_local_n(thread_id);
+
+    let wg_n_count = (params.n + WORKGROUP_SIZE_N * TILE_N - 1u) / (WORKGROUP_SIZE_N * TILE_N);
+    let wg_m_count = (params.m + WORKGROUP_SIZE_M * TILE_M - 1u) / (WORKGROUP_SIZE_M * TILE_M);
+    let wg_per_matrix = wg_m_count * wg_n_count;
+
+    let batch_idx = wg_id.x / wg_per_matrix;
+
+    let wg_in_batch = wg_id.x % wg_per_matrix;
+    let wg_m = wg_in_batch % wg_m_count;
+    let wg_n = wg_in_batch / wg_m_count;
+
+    let output_row_base = wg_m * WORKGROUP_SIZE_M * TILE_M + local_m * TILE_M;
+    let output_col_base = wg_n * WORKGROUP_SIZE_N * TILE_N + local_n * TILE_N;
+
+    let dst2_stride = params.m * params.n;
+    let dst3_stride = dst2_stride * params.bs02 * params.broadcast2;
+
+    let dst3_idx = batch_idx / (params.bs02 * params.broadcast2);
+    let src03_idx = dst3_idx / params.broadcast3;
+    let src13_idx = dst3_idx;
+    let dst2_idx = batch_idx % (params.bs02 * params.broadcast2);
+    let src02_idx = dst2_idx / params.broadcast2;
+    let src12_idx = dst2_idx;
+
+    let src0_batch_offset = params.offset_src0 + src03_idx * params.stride_03 + src02_idx * params.stride_02;
+    let src1_batch_offset = params.offset_src1 + src13_idx * params.stride_13 + src12_idx * params.stride_12;
+
+    let offset_m = wg_m * WORKGROUP_SIZE_M * TILE_M;
+    let offset_n = wg_n * WORKGROUP_SIZE_N * TILE_N;
+
+    var acc: array<array<f16, TILE_N>, TILE_M>;
+
+    for (var k_outer = 0u; k_outer < params.k; k_outer += TILE_K) {
+
+        // see mul_mat_decls.tmpl
+        init_shmem_src0(thread_id, src0_batch_offset, offset_m, k_outer);
+        init_shmem_src1(thread_id, src1_batch_offset, offset_n, k_outer);
+
+        workgroupBarrier();
+
+        let k_end = min(TILE_K, params.k - k_outer);
+
+        for (var k_inner = 0u; k_inner < k_end; k_inner++) {
+            var src0_tile: array<f16, TILE_M>;
+            for (var tm = 0u; tm < TILE_M; tm++) {
+                let src0_m = local_m * TILE_M + tm;
+                let src0_idx = k_inner + src0_m * TILE_K;
+                src0_tile[tm] = shmem[src0_idx];
+            }
+            for (var tn = 0u; tn < TILE_N; tn++) {
+                let src1_n = local_n * TILE_N + tn;
+                let src1_idx = src1_n * TILE_K + k_inner;
+                let src1_val = shmem[TILE_SRC0_SHMEM + src1_idx];
+                for (var tm = 0u; tm < TILE_M; tm++) {
+                      acc[tm][tn] += src0_tile[tm] * src1_val;
+                }
+            }
+        }
+
+        workgroupBarrier();
+    }
+
+    let dst_batch_offset = params.offset_dst + dst3_idx * dst3_stride + dst2_idx * dst2_stride;
+
+    for (var tn = 0u; tn < TILE_N; tn++) {
+        let global_col = output_col_base + tn;
+        if (global_col < params.n) {
+            for (var tm = 0u; tm < TILE_M; tm += {{VEC_SIZE}}) {
+                let global_row = output_row_base + tm;
+                if (global_row < params.m) {
+                    let dst_idx = dst_batch_offset + global_col * params.m + global_row;
+                    dst[dst_idx/{{VEC_SIZE}}] = store_val(acc, tn, tm);
+                }
+            }
+        }
+    }
+}
+
+#end(SHADER)
diff --git a/ggml/src/ggml-webgpu/wgsl-shaders/mul_mat_subgroup_matrix.tmpl.wgsl b/ggml/src/ggml-webgpu/wgsl-shaders/mul_mat_subgroup_matrix.tmpl.wgsl
new file mode 100644
index 00000000000..47c8ce36ab3
--- /dev/null
+++ b/ggml/src/ggml-webgpu/wgsl-shaders/mul_mat_subgroup_matrix.tmpl.wgsl
@@ -0,0 +1,302 @@
+#define(VARIANTS)
+[
+  {
+    "SHADER_SUFFIX": "f32_f32_vec",
+    "REPLS": {
+      "SRC0_TYPE" : "vec4<f32>",
+      "SRC1_TYPE" : "vec4<f32>",
+      "DST_TYPE" : "vec4<f32>",
+      "SHMEM_TYPE" : "vec4<f16>",
+      "VEC_SIZE" : 4,
+    },
+    "DECLS": ["VEC", "SHMEM_VEC", "INIT_SRC0_SHMEM_FLOAT", "INIT_SRC1_SHMEM"]
+  },
+  {
+    "SHADER_SUFFIX": "f32_f32",
+    "REPLS": {
+      "SRC0_TYPE" : "f32",
+      "SRC1_TYPE" : "f32",
+      "DST_TYPE" : "f32",
+      "SHMEM_TYPE" : "f16",
+      "VEC_SIZE" : 1,
+    },
+    "DECLS": ["SCALAR", "SHMEM_SCALAR", "INIT_SRC0_SHMEM_FLOAT", "INIT_SRC1_SHMEM"]
+  },
+  {
+    "SHADER_SUFFIX": "f16_f32_vec",
+    "REPLS": {
+      "SRC0_TYPE" : "vec4<f16>",
+      "SRC1_TYPE" : "vec4<f32>",
+      "DST_TYPE" : "vec4<f32>",
+      "SHMEM_TYPE" : "vec4<f16>",
+      "VEC_SIZE" : 4,
+    },
+    "DECLS": ["VEC", "SHMEM_VEC", "INIT_SRC0_SHMEM_FLOAT", "INIT_SRC1_SHMEM"]
+  },
+  {
+    "SHADER_SUFFIX": "f16_f32",
+    "REPLS": {
+      "SRC0_TYPE" : "f16",
+      "SRC1_TYPE" : "f32",
+      "DST_TYPE" : "f32",
+      "SHMEM_TYPE" : "f16",
+      "VEC_SIZE" : 1,
+    },
+    "DECLS": ["SCALAR", "SHMEM_SCALAR", "INIT_SRC0_SHMEM_FLOAT", "INIT_SRC1_SHMEM"]
+  },
+  {
+    "SHADER_SUFFIX": "f16_f16_vec",
+    "REPLS": {
+      "SRC0_TYPE" : "vec4<f16>",
+      "SRC1_TYPE" : "vec4<f16>",
+      "DST_TYPE" : "vec4<f32>",
+      "SHMEM_TYPE" : "vec4<f16>",
+      "VEC_SIZE" : 4,
+    },
+    "DECLS": ["VEC", "SHMEM_VEC", "INIT_SRC0_SHMEM_FLOAT", "INIT_SRC1_SHMEM"]
+  },
+  {
+    "SHADER_SUFFIX": "f16_f16",
+    "REPLS": {
+      "SRC0_TYPE" : "f16",
+      "SRC1_TYPE" : "f16",
+      "DST_TYPE" : "f32",
+      "SHMEM_TYPE" : "f16",
+      "VEC_SIZE" : 1,
+    },
+    "DECLS": ["SCALAR", "SHMEM_SCALAR", "INIT_SRC0_SHMEM_FLOAT", "INIT_SRC1_SHMEM"]
+  },
+  {
+    "SHADER_SUFFIX": "q4_0_f32_vec",
+    "REPLS": {
+      "SRC0_TYPE" : "f16",
+      "SRC1_TYPE" : "vec4<f32>",
+      "DST_TYPE" : "vec4<f32>",
+      "SHMEM_TYPE" : "vec4<f16>",
+      "VEC_SIZE" : 4,
+    },
+    "DECLS": ["BYTE_HELPERS", "VEC", "SHMEM_VEC", "INIT_SRC0_SHMEM_Q4_0", "INIT_SRC1_SHMEM"]
+  },
+  {
+    "SHADER_SUFFIX": "q4_0_f32",
+    "REPLS": {
+      "SRC0_TYPE" : "f16",
+      "SRC1_TYPE" : "f32",
+      "DST_TYPE" : "f32",
+      "SHMEM_TYPE" : "f16",
+      "VEC_SIZE" : 1,
+    },
+    "DECLS": ["BYTE_HELPERS", "SCALAR", "SHMEM_SCALAR", "INIT_SRC0_SHMEM_Q4_0", "INIT_SRC1_SHMEM"]
+  }
+]
+
+#end(VARIANTS)
+
+#define(DECLS)
+
+#decl(VEC)
+fn store_dst(shmem_idx: u32, dst_idx: u32) {
+    dst[dst_idx] = vec4<f32>(
+        f32(shmem[shmem_idx]),
+        f32(shmem[shmem_idx + 1]),
+        f32(shmem[shmem_idx + 2]),
+        f32(shmem[shmem_idx + 3])
+    );
+}
+#enddecl(VEC)
+
+#decl(SCALAR)
+fn store_dst(shmem_idx: u32, dst_idx: u32) {
+    dst[dst_idx] = f32(shmem[shmem_idx]);
+}
+#enddecl(SCALAR)
+
+#end(DECLS)
+
+#define(SHADER)
+diagnostic(off, chromium.subgroup_matrix_uniformity);
+enable f16;
+enable subgroups;
+enable chromium_experimental_subgroup_matrix;
+
+struct MulMatParams {
+    offset_src0: u32,
+    offset_src1: u32,
+    offset_dst: u32,
+    m: u32,
+    n: u32,
+    k: u32,
+    stride_01: u32,
+    stride_11: u32,
+    stride_02: u32,
+    stride_12: u32,
+    stride_03: u32,
+    stride_13: u32,
+    bs02: u32,
+    bs03: u32,
+    broadcast2: u32,
+    broadcast3: u32
+};
+
+@group(0) @binding(0) var<storage, read_write> src0: array<{{SRC0_TYPE}}>; // M rows, K columns
+@group(0) @binding(1) var<storage, read_write> src1: array<{{SRC1_TYPE}}>; // K rows, N columns (transposed)
+@group(0) @binding(2) var<storage, read_write> dst: array<{{DST_TYPE}}>; // M rows, N columns (transposed)
+
+@group(0) @binding(3) var<uniform> params: MulMatParams;
+
+DECLS
+
+// Note: These are string interpolated at build time, cannot use override constants due to limitations in
+// current Dawn version type definitions/matrix load requirements for constant memory sizes.
+const SUBGROUP_M = {{WEBGPU_SUBGROUP_M}}u;
+const SUBGROUP_N = {{WEBGPU_SUBGROUP_N}}u;
+// For portability we assume the max subgroup size, meaning some subgroups will be masked out if the
+// runtime subgroup size is smaller.
+const MAX_SUBGROUP_SIZE = {{WEBGPU_MAX_SUBGROUP_SIZE}}u;
+
+const EXPECTED_SUBGROUPS = SUBGROUP_M * SUBGROUP_N;
+
+const SUBGROUP_MATRIX_M_SIZE = {{WEBGPU_SG_MAT_M_SIZE}}u;
+const SUBGROUP_MATRIX_N_SIZE = {{WEBGPU_SG_MAT_N_SIZE}}u;
+const SUBGROUP_MATRIX_K_SIZE = {{WEBGPU_SG_MAT_K_SIZE}}u;
+
+const SUBGROUP_MATRIX_M = {{WEBGPU_SUBGROUP_MATRIX_M}}u;
+const SUBGROUP_MATRIX_N = {{WEBGPU_SUBGROUP_MATRIX_N}}u;
+
+const TILE_K = {{WEBGPU_TILE_K}}u;
+
+const WG_M_SG_TILE_SIZE = SUBGROUP_M * SUBGROUP_MATRIX_M * SUBGROUP_MATRIX_M_SIZE;
+const WG_N_SG_TILE_SIZE = SUBGROUP_N * SUBGROUP_MATRIX_N * SUBGROUP_MATRIX_N_SIZE;
+
+const TOTAL_WORKGROUP_SIZE = SUBGROUP_M * SUBGROUP_N * MAX_SUBGROUP_SIZE;
+const TILE_SRC0_SHMEM = TILE_K * SUBGROUP_M * SUBGROUP_MATRIX_M * SUBGROUP_MATRIX_M_SIZE;
+const TILE_SRC1_SHMEM = TILE_K * SUBGROUP_N * SUBGROUP_MATRIX_N * SUBGROUP_MATRIX_N_SIZE;
+
+const SG_MAT_ACCUM_SHMEM = SUBGROUP_M * SUBGROUP_MATRIX_M * SUBGROUP_N * SUBGROUP_MATRIX_N * SUBGROUP_MATRIX_M_SIZE * SUBGROUP_MATRIX_N_SIZE;
+
+// We reuse shmem for accumulation matrices
+const SHMEM_SIZE = max(TILE_SRC0_SHMEM + TILE_SRC1_SHMEM, SG_MAT_ACCUM_SHMEM);
+
+var<workgroup> shmem: array<f16, SHMEM_SIZE>;
+
+@compute @workgroup_size(TOTAL_WORKGROUP_SIZE)
+fn main(@builtin(workgroup_id) wg_id: vec3<u32>,
+        @builtin(local_invocation_id) local_id: vec3<u32>,
+        @builtin(subgroup_id) subgroup_id: u32) {
+
+    let thread_id = local_id.x;
+    let subgroup_m = subgroup_id % SUBGROUP_M;
+    let subgroup_n = subgroup_id / SUBGROUP_M;
+
+    let wg_m_count = (params.m + WG_M_SG_TILE_SIZE - 1) / WG_M_SG_TILE_SIZE;
+    let wg_n_count = (params.n + WG_N_SG_TILE_SIZE - 1) / WG_N_SG_TILE_SIZE;
+    let wg_per_matrix = wg_m_count * wg_n_count;
+
+    let batch_idx = wg_id.x / wg_per_matrix;
+
+    let wg_in_batch = wg_id.x % wg_per_matrix;
+    let wg_m = wg_in_batch % wg_m_count;
+    let wg_n = wg_in_batch / wg_m_count;
+
+    let dst2_stride = params.m * params.n;
+    let dst3_stride = dst2_stride * params.bs02 * params.broadcast2;
+
+    let dst3_idx = batch_idx / (params.bs02 * params.broadcast2);
+    let src03_idx = dst3_idx / params.broadcast3;
+    let src13_idx = dst3_idx;
+    let dst2_idx = batch_idx % (params.bs02 * params.broadcast2);
+    let src02_idx = dst2_idx / params.broadcast2;
+    let src12_idx = dst2_idx;
+
+    let src0_batch_offset = params.offset_src0 + src03_idx * params.stride_03 + src02_idx * params.stride_02;
+    let src1_batch_offset = params.offset_src1 + src13_idx * params.stride_13 + src12_idx * params.stride_12;
+
+    let offset_m = wg_m * SUBGROUP_M * SUBGROUP_MATRIX_M * SUBGROUP_MATRIX_M_SIZE;
+    let offset_n = wg_n * SUBGROUP_N * SUBGROUP_MATRIX_N * SUBGROUP_MATRIX_N_SIZE;
+
+    var acc_sg_mat : array<array<subgroup_matrix_result<f16, SUBGROUP_MATRIX_N_SIZE, SUBGROUP_MATRIX_M_SIZE>, SUBGROUP_MATRIX_N>, SUBGROUP_MATRIX_M>;
+
+    for (var k_outer = 0u; k_outer < params.k; k_outer += TILE_K) {
+
+        // see mul_mat_decls.tmpl
+        init_shmem_src0(thread_id, src0_batch_offset, offset_m, k_outer);
+        init_shmem_src1(thread_id, src1_batch_offset, offset_n, k_outer);
+
+        workgroupBarrier();
+
+        if (subgroup_id < EXPECTED_SUBGROUPS) {
+
+            for (var k_inner = 0u; k_inner < TILE_K; k_inner += SUBGROUP_MATRIX_K_SIZE) {
+
+                let src0_shmem_idx_base = subgroup_m * SUBGROUP_MATRIX_M * SUBGROUP_MATRIX_M_SIZE * TILE_K + k_inner;
+                var src0_sg_mats: array<subgroup_matrix_left<f16, SUBGROUP_MATRIX_K_SIZE, SUBGROUP_MATRIX_M_SIZE>, SUBGROUP_MATRIX_M>;
+                for (var m = 0u; m < SUBGROUP_MATRIX_M; m++) {
+                    src0_sg_mats[m] = subgroupMatrixLoad<subgroup_matrix_left<f16, SUBGROUP_MATRIX_K_SIZE, SUBGROUP_MATRIX_M_SIZE>>(
+                        &shmem,
+                        src0_shmem_idx_base + m * SUBGROUP_MATRIX_M_SIZE * TILE_K,
+                        false,
+                        TILE_K
+                    );
+                }
+
+                let src1_shmem_idx_base = TILE_SRC0_SHMEM + subgroup_n * SUBGROUP_MATRIX_N * SUBGROUP_MATRIX_N_SIZE * TILE_K + k_inner;
+                for (var n = 0u; n < SUBGROUP_MATRIX_N; n++) {
+                    let src1_sg_mat = subgroupMatrixLoad<subgroup_matrix_right<f16, SUBGROUP_MATRIX_N_SIZE, SUBGROUP_MATRIX_K_SIZE>>(
+                        &shmem,
+                        src1_shmem_idx_base + n * SUBGROUP_MATRIX_N_SIZE * TILE_K,
+                        true,
+                        TILE_K
+                    );
+                    for (var m = 0u; m < SUBGROUP_MATRIX_M; m++) {
+                        acc_sg_mat[m][n] = subgroupMatrixMultiplyAccumulate(src0_sg_mats[m], src1_sg_mat, acc_sg_mat[m][n]);
+                    }
+                }
+            }
+        }
+
+        workgroupBarrier();
+    }
+
+    let dst_batch_offset = params.offset_dst + dst3_idx * dst3_stride + dst2_idx * dst2_stride;
+
+    // Stage the subgroup matrix tiles into shared memory
+    // This uses WG_M_SG_TILE_SIZE as the stride (number of columns in the workgroup tile).
+    let WG_TILE_STRIDE = WG_M_SG_TILE_SIZE;
+    let tile_row_base_local = subgroup_n * SUBGROUP_MATRIX_N * SUBGROUP_MATRIX_N_SIZE;
+    let tile_col_base_local = subgroup_m * SUBGROUP_MATRIX_M * SUBGROUP_MATRIX_M_SIZE;
+
+    if (subgroup_id < EXPECTED_SUBGROUPS) { // 2-5% performance hit :(
+        for (var n = 0u; n < SUBGROUP_MATRIX_N; n++) {
+            for (var m = 0u; m < SUBGROUP_MATRIX_M; m++) {
+                let local_row = tile_row_base_local + n * SUBGROUP_MATRIX_N_SIZE;
+                let local_col = tile_col_base_local + m * SUBGROUP_MATRIX_M_SIZE;
+                let out_base = local_row * WG_TILE_STRIDE + local_col;
+                subgroupMatrixStore(&shmem, out_base, acc_sg_mat[m][n], true, WG_TILE_STRIDE);
+            }
+        }
+    }
+
+    workgroupBarrier();
+
+    // Cooperative write: iterate over the entire workgroup tile
+    let tile_rows = WG_N_SG_TILE_SIZE;
+    let tile_cols = WG_M_SG_TILE_SIZE;
+    let total_tile_elems = tile_rows * tile_cols;
+    let tile_dst_row_base = wg_m * SUBGROUP_M * SUBGROUP_MATRIX_M * SUBGROUP_MATRIX_M_SIZE;
+    let tile_dst_col_base = wg_n * SUBGROUP_N * SUBGROUP_MATRIX_N * SUBGROUP_MATRIX_N_SIZE;
+
+    for (var idx = thread_id * {{VEC_SIZE}}; idx < total_tile_elems; idx += TOTAL_WORKGROUP_SIZE * {{VEC_SIZE}}) {
+        let local_row = idx % WG_TILE_STRIDE;
+        let local_col = idx / WG_TILE_STRIDE;
+
+        let global_row = tile_dst_row_base + local_row;
+        let global_col = tile_dst_col_base + local_col;
+
+        if (global_col < params.n && global_row < params.m) {
+            let dst_idx = dst_batch_offset + global_col * params.m + global_row;
+            store_dst(idx, dst_idx/{{VEC_SIZE}});
+        }
+    }
+}
+
+#end(SHADER)
diff --git a/ggml/src/ggml-webgpu/wgsl-shaders/mul_mat_vec.tmpl.wgsl b/ggml/src/ggml-webgpu/wgsl-shaders/mul_mat_vec.tmpl.wgsl
new file mode 100644
index 00000000000..ffbb6403285
--- /dev/null
+++ b/ggml/src/ggml-webgpu/wgsl-shaders/mul_mat_vec.tmpl.wgsl
@@ -0,0 +1,267 @@
+#define(VARIANTS)
+[
+  {
+    "SHADER_SUFFIX": "f32_f32_vec",
+    "REPLS": {
+      "SRC0_TYPE" : "vec4<f32>",
+      "SRC1_TYPE" : "vec4<f32>",
+      "DST_TYPE": "vec4<f32>",
+      "VEC_SIZE" : 4,
+    },
+    "DECLS": ["VEC", "MUL_ACC_FLOAT"]
+  },
+  {
+    "SHADER_SUFFIX": "f32_f32",
+    "REPLS": {
+      "SRC0_TYPE" : "f32",
+      "SRC1_TYPE" : "f32",
+      "DST_TYPE": "f32",
+      "VEC_SIZE" : 1,
+    },
+    "DECLS": ["SCALAR", "MUL_ACC_FLOAT"]
+  },
+  {
+    "SHADER_SUFFIX": "f16_f32_vec",
+    "REPLS": {
+      "SRC0_TYPE" : "vec4<f16>",
+      "SRC1_TYPE" : "vec4<f32>",
+      "DST_TYPE": "vec4<f32>",
+      "VEC_SIZE" : 4,
+    },
+    "DECLS": ["VEC", "MUL_ACC_FLOAT"]
+  },
+  {
+    "SHADER_SUFFIX": "f16_f32",
+    "REPLS": {
+      "SRC0_TYPE" : "f16",
+      "SRC1_TYPE" : "f32",
+      "DST_TYPE": "f32",
+      "VEC_SIZE" : 1,
+    },
+    "DECLS": ["SCALAR", "MUL_ACC_FLOAT"]
+  },
+  {
+    "SHADER_SUFFIX": "f16_f16_vec",
+    "REPLS": {
+      "SRC0_TYPE" : "vec4<f16>",
+      "SRC1_TYPE" : "vec4<f16>",
+      "DST_TYPE": "vec4<f32>",
+      "VEC_SIZE" : 4,
+    },
+    "DECLS": ["VEC", "MUL_ACC_FLOAT"]
+  },
+  {
+    "SHADER_SUFFIX": "f16_f16",
+    "REPLS": {
+      "SRC0_TYPE" : "f16",
+      "SRC1_TYPE" : "f16",
+      "DST_TYPE": "f32",
+      "VEC_SIZE" : 1,
+    },
+    "DECLS": ["SCALAR", "MUL_ACC_FLOAT"]
+  },
+  {
+    "SHADER_SUFFIX": "q4_0_f32",
+    "REPLS": {
+      "SRC0_TYPE" : "f16",
+      "SRC1_TYPE" : "f32",
+      "DST_TYPE": "f32",
+      "VEC_SIZE" : 1,
+    },
+    "DECLS": ["BYTE_HELPERS", "SCALAR", "MUL_ACC_Q4_0"]
+  }
+]
+
+#end(VARIANTS)
+
+#define(DECLS)
+
+#decl(VEC)
+fn inner_dot(src0_val: {{SRC0_TYPE}}, src1_val: {{SRC1_TYPE}}) -> f32 {
+    return f32(dot({{SRC1_TYPE}}(src0_val), src1_val));
+}
+
+fn store_val(group_base: u32) -> vec4<f32> {
+    return vec4<f32>(partial_sums[group_base],
+                     partial_sums[group_base + THREADS_PER_OUTPUT],
+                     partial_sums[group_base + THREADS_PER_OUTPUT * 2],
+                     partial_sums[group_base + THREADS_PER_OUTPUT * 3]);
+}
+#enddecl(VEC)
+
+#decl(SCALAR)
+fn inner_dot(src0_val: {{SRC0_TYPE}}, src1_val: {{SRC1_TYPE}}) -> f32 {
+    return f32(src0_val) * f32(src1_val);
+}
+
+fn store_val(group_base: u32) -> f32 {
+    return partial_sums[group_base];
+}
+#enddecl(SCALAR)
+
+#decl(MUL_ACC_FLOAT)
+
+fn mul_acc(tig:u32, tile_size: u32, idx_base: u32, k_outer: u32) -> f32 {
+    var local_sum = 0.0;
+    for (var i = tig * {{VEC_SIZE}}; i < tile_size; i += THREADS_PER_OUTPUT * {{VEC_SIZE}}) {
+        let a = src0[(idx_base + k_outer + i) / {{VEC_SIZE}}];
+        let b = shared_vector[i / {{VEC_SIZE}}];
+        local_sum += inner_dot(a, b);
+    }
+    return local_sum;
+}
+
+#enddecl(MUL_ACC_FLOAT)
+
+#decl(MUL_ACC_Q4_0)
+
+const BLOCK_SIZE = 32;
+const NQ = 16u; // number of weights per thread
+const F16_PER_BLOCK = 9u; // 1 scale + 8x4 packed weights
+const WEIGHTS_PER_F16 = 4u; // 4 weights per f16
+const F16_PER_THREAD = NQ / WEIGHTS_PER_F16;
+
+fn mul_acc(tig:u32, tile_size: u32, idx_base: u32, k_outer: u32) -> f32 {
+    var local_sum = 0.0;
+    for (var i = tig * NQ; i < tile_size; i += THREADS_PER_OUTPUT * NQ) {
+        let blck_idx = i / BLOCK_SIZE;
+        let block_offset = (i % BLOCK_SIZE) / WEIGHTS_PER_F16;
+        let scale_idx = (idx_base + k_outer / BLOCK_SIZE + blck_idx) * F16_PER_BLOCK;
+        // each f16 contains offsets [block_offset, block_offset + 1] and [block_offset + 16, block_offset + 17]
+        let shmem_idx = blck_idx * BLOCK_SIZE + block_offset * 2u;
+        let d = f32(src0[scale_idx]);
+        for (var j = 0u; j < F16_PER_THREAD; j += 2) {
+            let q_0 = src0[scale_idx + 1 + block_offset + j];
+            let q_1 = src0[scale_idx + 1 + block_offset + j + 1];
+            let q_packed = bitcast<u32>(vec2(q_0, q_1));
+            for (var k: u32 = 0; k < 4; k++) {
+                let q_byte = get_byte(q_packed, k);
+                let q_hi = (f32((q_byte >> 4) & 0xF) - 8.0) * d;
+                let q_lo = (f32(q_byte & 0xF) - 8.0) * d;
+                local_sum += q_lo * shared_vector[shmem_idx + j * 2 + k];
+                local_sum += q_hi * shared_vector[shmem_idx + j * 2 + k + 16];
+            }
+        }
+    }
+    return local_sum;
+}
+
+#enddecl(MUL_ACC_Q4_0)
+
+#end(DECLS)
+
+#define(SHADER)
+enable f16;
+
+DECLS
+
+struct MulMatParams {
+    offset_src0: u32,
+    offset_src1: u32,
+    offset_dst: u32,
+    m: u32,
+    n: u32,
+    k: u32,
+    stride_01: u32,
+    stride_11: u32,
+    stride_02: u32,
+    stride_12: u32,
+    stride_03: u32,
+    stride_13: u32,
+    bs02: u32,
+    bs03: u32,
+    broadcast2: u32,
+    broadcast3: u32
+};
+
+@group(0) @binding(0) var<storage, read_write> src0: array<{{SRC0_TYPE}}>; // Matrix (M x K)
+@group(0) @binding(1) var<storage, read_write> src1: array<{{SRC1_TYPE}}>; // Vector (K x 1, transposed)
+@group(0) @binding(2) var<storage, read_write> dst: array<{{DST_TYPE}}>;  // Result vector (transposed)
+
+@group(0) @binding(3) var<uniform> params: MulMatParams;
+
+override WORKGROUP_SIZE: u32;
+override TILE_K: u32;
+override OUTPUTS_PER_WG: u32;
+override THREADS_PER_OUTPUT = WORKGROUP_SIZE / OUTPUTS_PER_WG;
+
+// Shared memory for collaborative loading and reduction
+var<workgroup> shared_vector: array<{{SRC1_TYPE}}, TILE_K/{{VEC_SIZE}}>;  // Cache vector tile
+var<workgroup> partial_sums: array<f32, WORKGROUP_SIZE>;   // For reduction
+
+@compute @workgroup_size(WORKGROUP_SIZE)
+fn main(
+    @builtin(local_invocation_id) local_id: vec3<u32>,
+    @builtin(workgroup_id) wg_id: vec3<u32>,
+    @builtin(num_workgroups) num_wg: vec3<u32>) {
+    let thread_id = local_id.x;
+
+    // Handle batch dimensions
+    let total_batches = params.bs02 * params.broadcast2 * params.bs03 * params.broadcast3;
+    let wg_linear = wg_id.y * num_wg.x + wg_id.x;
+    let output_groups = (params.m + OUTPUTS_PER_WG - 1u) / OUTPUTS_PER_WG;
+    let batch_idx = wg_linear / output_groups;
+    if (batch_idx >= total_batches) {
+        return;
+    }
+
+    // Which of the outputs does this thread belong to?
+    let thread_group = thread_id / THREADS_PER_OUTPUT;
+    let thread_in_group = thread_id % THREADS_PER_OUTPUT;
+
+    // Each workgroup computes OUTPUTS_PER_WG consecutive outputs
+    let output_row = (wg_linear % output_groups) * OUTPUTS_PER_WG + thread_group;
+
+    let dst2_stride = params.m * params.n;
+    let dst2_idx = batch_idx % (params.bs02 * params.broadcast2);
+    let dst3_stride = dst2_stride * params.bs02 * params.broadcast2;
+    let dst3_idx = batch_idx / (params.bs02 * params.broadcast2);
+    let src03_idx = dst3_idx / params.broadcast3;
+    let src13_idx = dst3_idx;
+    let src02_idx = dst2_idx / params.broadcast2;
+    let src12_idx = dst2_idx;
+
+    let src0_idx_base = params.offset_src0 + src03_idx * params.stride_03 + src02_idx * params.stride_02 + output_row * params.stride_01;
+    let src1_idx_base = params.offset_src1 + src13_idx * params.stride_13 + src12_idx * params.stride_12;
+    let dst_idx = params.offset_dst + dst3_idx * dst3_stride + dst2_idx * dst2_stride + output_row;
+
+    var local_sum = 0.0;
+
+    // Each thread processes multiple K elements and accumulates
+    for (var k_tile = 0u; k_tile < params.k; k_tile += TILE_K) {
+        let tile_size = min(TILE_K, params.k - k_tile);
+
+        // Cooperatively load vector tile into shared memory (all threads)
+        for (var i = thread_id * {{VEC_SIZE}}; i < tile_size; i += WORKGROUP_SIZE * {{VEC_SIZE}}) {
+            shared_vector[i / {{VEC_SIZE}}] = src1[(src1_idx_base + k_tile + i) / {{VEC_SIZE}}];
+        }
+
+        workgroupBarrier();
+
+        if (output_row < params.m) {
+            local_sum += mul_acc(thread_in_group, tile_size, src0_idx_base, k_tile);
+        }
+
+        workgroupBarrier();
+    }
+
+    // Store partial sums and reduce within each partition
+    partial_sums[thread_id] = local_sum;
+    workgroupBarrier();
+    let group_base = thread_group * THREADS_PER_OUTPUT;
+    let thread_base = group_base + thread_in_group;
+    var offset = THREADS_PER_OUTPUT / 2;
+    while (offset > 0) {
+        if (thread_in_group < offset) {
+            partial_sums[thread_base] += partial_sums[thread_base + offset];
+        }
+        offset = offset / 2;
+        workgroupBarrier();
+    }
+
+    // Store back to global memory
+    if (output_row < params.m && thread_group % {{VEC_SIZE}} == 0 && thread_in_group == 0) {
+        dst[dst_idx / {{VEC_SIZE}}] = store_val(group_base);
+    }
+}
+#end(SHADER)

From e14e842e87103ec2a004770cec95a3f94f861bda Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Johannes=20G=C3=A4=C3=9Fler?= <johannesg@5d6.de>
Date: Sat, 8 Nov 2025 08:26:18 +0100
Subject: [PATCH 116/185] CUDA: fix MMQ stream-k fixup ne1 indices (#17089)

---
 ggml/src/ggml-cuda/mmq.cuh | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/ggml/src/ggml-cuda/mmq.cuh b/ggml/src/ggml-cuda/mmq.cuh
index c9a07e82fed..2e133b6bda8 100644
--- a/ggml/src/ggml-cuda/mmq.cuh
+++ b/ggml/src/ggml-cuda/mmq.cuh
@@ -3494,7 +3494,7 @@ static __global__ void mul_mat_q_stream_k_fixup(
     const int col_diff = col_high - col_low;
 
     for (int j = threadIdx.y*warp_size + threadIdx.x; j < mmq_x; j += nwarps*warp_size) {
-        ids_dst_shared[j] = ids_dst[col_low + j];
+        ids_dst_shared[j] = ids_dst[col_low + jt*mmq_x + j];
     }
     __syncthreads();
 

From d6fe40fa0040bf7207b2380d0f3628fb56d6a86f Mon Sep 17 00:00:00 2001
From: Jeff Bolz <jbolz@nvidia.com>
Date: Sat, 8 Nov 2025 01:39:45 -0600
Subject: [PATCH 117/185] vulkan: Fix test-thread-safety crashes (#17024)

The std::map pipeline_flash_attn_f32_f16 could be searched and inserted at the
same time, which needs to hold the lock. To be safe, hold the lock for all of
ggml_vk_load_shaders.
---
 ggml/src/ggml-vulkan/ggml-vulkan.cpp | 27 +++++++++++++++------------
 1 file changed, 15 insertions(+), 12 deletions(-)

diff --git a/ggml/src/ggml-vulkan/ggml-vulkan.cpp b/ggml/src/ggml-vulkan/ggml-vulkan.cpp
index a0a05f2e5b2..2646e80be75 100644
--- a/ggml/src/ggml-vulkan/ggml-vulkan.cpp
+++ b/ggml/src/ggml-vulkan/ggml-vulkan.cpp
@@ -130,9 +130,9 @@ struct vk_pipeline_struct {
     // true if fields have been set by ggml_vk_create_pipeline
     bool initialized {};
     // set to true to request the pipeline is compiled
-    bool needed {};
+    std::atomic<bool> needed {};
     // set to true when the shader has been compiled
-    bool compiled {};
+    std::atomic<bool> compiled {};
     // number of registers used, extracted from pipeline executable properties
     uint32_t register_count {};
 };
@@ -1842,10 +1842,7 @@ static void ggml_vk_create_pipeline_func(vk_device& device, vk_pipeline& pipelin
         }
     }
 
-    {
-        std::lock_guard<std::recursive_mutex> guard(device->mutex);
-        device->all_pipelines.push_back(pipeline);
-    }
+    device->all_pipelines.push_back(pipeline);
 
     {
         std::lock_guard<std::mutex> guard(compile_count_mutex);
@@ -2536,6 +2533,7 @@ static uint32_t get_subgroup_size(const std::string &pipeline_name, const vk_dev
 static void ggml_vk_load_shaders(vk_device& device) {
     VK_LOG_DEBUG("ggml_vk_load_shaders(" << device->name << ")");
 
+    std::lock_guard<std::recursive_mutex> guard(device->mutex);
     // some shaders have a minimum subgroup size
     const uint32_t subgroup_size_8 = std::max(device->subgroup_size, 8u);
     const uint32_t subgroup_size_16 = std::max(device->subgroup_size, 16u);
@@ -2729,6 +2727,8 @@ static void ggml_vk_load_shaders(vk_device& device) {
         if (!pipeline->needed || pipeline->compiled) {
             return;
         }
+        // TODO: We're no longer benefitting from the async compiles (shaders are
+        // compiled individually, as needed) and this complexity can be removed.
         {
             // wait until fewer than N compiles are in progress
             uint32_t N = std::max(1u, std::thread::hardware_concurrency());
@@ -7914,12 +7914,15 @@ static void ggml_vk_flash_attn(ggml_backend_vk_context * ctx, vk_context& subctx
 
     vk_pipeline pipeline = nullptr;
 
-    auto &pipelines = ctx->device->pipeline_flash_attn_f32_f16[k->type];
-    auto it = pipelines.find(fa_pipeline_state);
-    if (it != pipelines.end()) {
-        pipeline = it->second;
-    } else {
-        pipelines[fa_pipeline_state] = pipeline = std::make_shared<vk_pipeline_struct>();
+    {
+        std::lock_guard<std::recursive_mutex> guard(ctx->device->mutex);
+        auto &pipelines = ctx->device->pipeline_flash_attn_f32_f16[k->type];
+        auto it = pipelines.find(fa_pipeline_state);
+        if (it != pipelines.end()) {
+            pipeline = it->second;
+        } else {
+            pipelines[fa_pipeline_state] = pipeline = std::make_shared<vk_pipeline_struct>();
+        }
     }
 
     assert(pipeline);

From b4e335d8dc503ec0adf76fa4053ab7094b6310dd Mon Sep 17 00:00:00 2001
From: Jeff Bolz <jbolz@nvidia.com>
Date: Sat, 8 Nov 2025 01:52:15 -0600
Subject: [PATCH 118/185] vulkan: fuse rms_norm + mul + rope (+ view +
 set_rows) (#16977)

This change combines the rms_norm+mul and rope+view+set_rows fusions to
allow fusing the whole sequence together. This comes up in Qwen3, Bailing,
and some other models.
---
 ggml/src/ggml-vulkan/ggml-vulkan.cpp          | 290 ++++++++++++++++--
 .../vulkan-shaders/generic_binary_head.glsl   |   8 +
 .../ggml-vulkan/vulkan-shaders/rms_norm.comp  |  44 ++-
 .../vulkan-shaders/rope_funcs.glsl            | 227 ++++++++++++++
 .../ggml-vulkan/vulkan-shaders/rope_head.glsl |  56 +---
 .../vulkan-shaders/rope_multi.comp            |  67 +---
 .../ggml-vulkan/vulkan-shaders/rope_neox.comp |  45 +--
 .../ggml-vulkan/vulkan-shaders/rope_norm.comp |  45 +--
 .../vulkan-shaders/rope_params.glsl           |  27 ++
 .../vulkan-shaders/rope_vision.comp           |  44 +--
 .../vulkan-shaders/vulkan-shaders-gen.cpp     |  40 +--
 tests/test-backend-ops.cpp                    |  89 ++++++
 12 files changed, 698 insertions(+), 284 deletions(-)
 create mode 100644 ggml/src/ggml-vulkan/vulkan-shaders/rope_funcs.glsl
 create mode 100644 ggml/src/ggml-vulkan/vulkan-shaders/rope_params.glsl

diff --git a/ggml/src/ggml-vulkan/ggml-vulkan.cpp b/ggml/src/ggml-vulkan/ggml-vulkan.cpp
index 2646e80be75..9c2aeb57f00 100644
--- a/ggml/src/ggml-vulkan/ggml-vulkan.cpp
+++ b/ggml/src/ggml-vulkan/ggml-vulkan.cpp
@@ -466,6 +466,14 @@ static constexpr std::initializer_list<std::array<int, 3>> rope_view_set_rows_ed
     { 2, 0, 1 }, // set_rows->src[0] == view
 };
 
+static constexpr std::initializer_list<std::array<int, 3>> rms_norm_mul_rope_view_set_rows_edges {
+    { 1, 0, 0 }, // mul->src[0]      == rms
+    { 2, 0, 1 }, // rope->src[0]     == mul
+    { 3, 0, 2 }, // view->src[0]     == rope
+    { 4, 0, 3 }, // set_rows->src[0] == view
+};
+
+
 struct vk_device_struct {
     std::recursive_mutex mutex;
 
@@ -617,6 +625,8 @@ struct vk_device_struct {
     vk_pipeline pipeline_rms_norm_mul_f32;
     vk_pipeline pipeline_rms_norm_partials_f32;
     vk_pipeline pipeline_rms_norm_mul_partials_f32;
+    vk_pipeline pipeline_rms_norm_mul_rope_f32_f32;
+    vk_pipeline pipeline_rms_norm_mul_rope_f32_f16;
     vk_pipeline pipeline_rms_norm_back_f32;
     vk_pipeline pipeline_l2_norm_f32;
 
@@ -1060,6 +1070,7 @@ struct vk_op_diag_mask_push_constants {
 };
 
 struct vk_op_rope_push_constants {
+    uint32_t rope_mode;
     uint32_t ncols;
     uint32_t n_dims;
     float freq_scale;
@@ -1079,6 +1090,12 @@ struct vk_op_rope_push_constants {
     uint32_t set_rows_stride;
 };
 
+// For fused rms_norm+mul+rope(+view+set_rows)
+struct vk_op_rms_norm_mul_rope_push_constants {
+    vk_op_binary_push_constants bin;
+    vk_op_rope_push_constants rope;
+};
+
 struct vk_op_soft_max_push_constants {
     uint32_t KX;
     uint32_t KY;
@@ -3557,6 +3574,12 @@ static void ggml_vk_load_shaders(vk_device& device) {
     ggml_vk_create_pipeline(device, device->pipeline_rms_norm_partials_f32, "rms_norm_partials_f32", rms_norm_partials_f32_len, rms_norm_partials_f32_data, "main", 4, sizeof(vk_op_binary_push_constants), {1, 1, 1}, {0, 0}, 1, true);
     ggml_vk_create_pipeline(device, device->pipeline_rms_norm_mul_partials_f32, "rms_norm_mul_partials_f32", rms_norm_partials_f32_len, rms_norm_partials_f32_data, "main", 4, sizeof(vk_op_binary_push_constants), {1, 1, 1}, {0, 1}, 1, true);
 
+    if (device->float_controls_rte_fp16 &&
+        sizeof(vk_op_rms_norm_mul_rope_push_constants) <= device->properties.limits.maxPushConstantsSize) {
+        ggml_vk_create_pipeline(device, device->pipeline_rms_norm_mul_rope_f32_f32, "rms_norm_mul_rope_f32_f32", rms_norm_mul_rope_f32_f32_len, rms_norm_mul_rope_f32_f32_data, "main", 7, sizeof(vk_op_rms_norm_mul_rope_push_constants), {1, 1, 1}, {0, 1}, 1, true);
+        ggml_vk_create_pipeline(device, device->pipeline_rms_norm_mul_rope_f32_f16, "rms_norm_mul_rope_f32_f16", rms_norm_mul_rope_f32_f16_rte_len, rms_norm_mul_rope_f32_f16_rte_data, "main", 7, sizeof(vk_op_rms_norm_mul_rope_push_constants), {1, 1, 1}, {0, 1}, 1, true);
+    }
+
     ggml_vk_create_pipeline(device, device->pipeline_rms_norm_back_f32, "rms_norm_back_f32", rms_norm_back_f32_len, rms_norm_back_f32_data, "main", 3, sizeof(vk_op_push_constants), {1, 1, 1}, {}, 1);
     ggml_vk_create_pipeline(device, device->pipeline_l2_norm_f32, "l2_norm_f32", l2_norm_f32_len, l2_norm_f32_data, "main", 2, sizeof(vk_op_push_constants), {1, 1, 1}, {}, 1);
 
@@ -9590,21 +9613,149 @@ static uint32_t ggml_vk_rms_partials_size(ggml_backend_vk_context * ctx, const g
     return num_bytes;
 }
 
-static void ggml_vk_rms_norm(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, const ggml_tensor * src1, ggml_tensor * dst, float * op_params) {
+static vk_op_rope_push_constants ggml_vk_make_rope_constants(const ggml_tensor *dst, const ggml_tensor *src0, const bool has_ff, bool backprop, const uint32_t set_rows_stride) {
+    const int n_dims        = ((const int32_t *) dst->op_params)[1];
+    const int mode          = ((const int32_t *) dst->op_params)[2];
+    // const int n_ctx         = ((const int32_t *) dst->op_params)[3];
+    const int n_ctx_orig    = ((const int32_t *) dst->op_params)[4];
+    const float freq_base   = ((const float *)   dst->op_params)[5];
+    const float freq_scale  = ((const float *)   dst->op_params)[6];
+    const float ext_factor  = ((const float *)   dst->op_params)[7];
+    const float attn_factor = ((const float *)   dst->op_params)[8];
+    const float beta_fast   = ((const float *)   dst->op_params)[9];
+    const float beta_slow   = ((const float *)   dst->op_params)[10];
+    int sections[4] {};
+    if (mode & GGML_ROPE_TYPE_MROPE) {
+        memcpy(sections, (const int32_t *) dst->op_params + 11, sizeof(int)*4);
+    }
+
+    const bool is_imrope = mode == GGML_ROPE_TYPE_IMROPE;
+
+    float corr_dims[2];
+    ggml_rope_yarn_corr_dims(n_dims, n_ctx_orig, freq_base, beta_fast, beta_slow, corr_dims);
+
+    const float theta_scale = powf(freq_base, -2.0f/n_dims);
+
+    uint32_t nb01 = src0->nb[1] / ggml_type_size(src0->type);
+    uint32_t nb02 = src0->nb[2] / ggml_type_size(src0->type);
+
+    vk_op_rope_push_constants rope {
+        (uint32_t)mode, (uint32_t)src0->ne[0], (uint32_t)n_dims, freq_scale, (uint32_t)src0->ne[1],
+        freq_base, ext_factor, attn_factor, {corr_dims[0], corr_dims[1]}, theta_scale,
+        has_ff, (uint32_t)src0->ne[2], nb01, nb02,
+        { sections[0], sections[1], sections[2], sections[3] }, is_imrope, backprop, set_rows_stride,
+    };
+
+    return rope;
+}
+
+static void ggml_vk_rms_norm(ggml_backend_vk_context * ctx, vk_context& subctx, const struct ggml_cgraph * cgraph, int node_idx, float * op_params) {
+    ggml_tensor * dst;
+    const ggml_tensor * src0;
+    const ggml_tensor * src1;
+
+    if (ctx->num_additional_fused_ops > 0) {
+        // fused rms_norm + mul
+        ggml_tensor *mul = cgraph->nodes[node_idx + 1];
+        ggml_tensor *other_src = mul->src[0] == cgraph->nodes[node_idx + 0] ? mul->src[1] : mul->src[0];
+        dst = mul;
+        src0 = cgraph->nodes[node_idx]->src[0];
+        src1 = other_src;
+    } else {
+        dst = cgraph->nodes[node_idx];
+        src0 = src1 = dst->src[0];
+    }
+
     const uint32_t src0_type_size = ggml_type_size(src0->type);
     const uint32_t src1_type_size = ggml_type_size(src1->type);
     const uint32_t dst_type_size = ggml_type_size(dst->type);
 
     uint32_t param3 = ctx->do_add_rms_partials ? ggml_vk_rms_num_partials(ctx, dst) : 0;
 
-    ggml_vk_op_f32<vk_op_binary_push_constants>(ctx, subctx, src0, src1, nullptr, nullptr, dst, GGML_OP_RMS_NORM, {
+    vk_op_binary_push_constants bin {
         (uint32_t)ggml_nelements(src0),
         (uint32_t)src0->ne[0], (uint32_t)src0->ne[1], (uint32_t)src0->ne[2],(uint32_t)src0->ne[3], (uint32_t)src0->nb[0] / src0_type_size, (uint32_t)src0->nb[1] / src0_type_size, (uint32_t)src0->nb[2] / src0_type_size, (uint32_t)src0->nb[3] / src0_type_size,
         (uint32_t)src1->ne[0], (uint32_t)src1->ne[1], (uint32_t)src1->ne[2],(uint32_t)src1->ne[3], (uint32_t)src1->nb[0] / src1_type_size, (uint32_t)src1->nb[1] / src1_type_size, (uint32_t)src1->nb[2] / src1_type_size, (uint32_t)src1->nb[3] / src1_type_size,
         (uint32_t) dst->ne[0], (uint32_t) dst->ne[1], (uint32_t) dst->ne[2],(uint32_t) dst->ne[3], (uint32_t) dst->nb[0] /  dst_type_size, (uint32_t) dst->nb[1] /  dst_type_size, (uint32_t) dst->nb[2] /  dst_type_size, (uint32_t) dst->nb[3] /  dst_type_size,
         0,
         op_params[0], 0.0f, (int32_t)param3,
-    });
+    };
+
+    // more than one fused op means rms_norm+mul+rope
+    if (ctx->num_additional_fused_ops > 1) {
+        static constexpr uint32_t max_tensors = 7;
+        const ggml_tensor *tensors[max_tensors] {};
+
+        ggml_tensor *rms = cgraph->nodes[node_idx + 0];
+        ggml_tensor *mul = cgraph->nodes[node_idx + 1];
+        ggml_tensor *rope = cgraph->nodes[node_idx + 2];
+
+        ggml_tensor *other_src = mul->src[0] == rms ? mul->src[1] : mul->src[0];
+
+        bool do_set_rows = ctx->num_additional_fused_ops == 4;
+
+        tensors[0] = rms->src[0];
+        tensors[1] = other_src;
+        tensors[2] = mul;
+        tensors[3] = rope->src[1]; // pos
+        tensors[4] = rope->src[2]; // ff
+        tensors[5] = cgraph->nodes[node_idx + ctx->num_additional_fused_ops]; // dst
+        tensors[6] = do_set_rows ? tensors[5]->src[1] : nullptr;
+        const uint32_t set_rows_stride = do_set_rows ? tensors[5]->nb[1] / ggml_type_size(tensors[5]->type) : 0;
+
+        vk_op_rms_norm_mul_rope_push_constants pc;
+        pc.bin = bin;
+        pc.rope = ggml_vk_make_rope_constants(rope, rope->src[0], tensors[4] != nullptr, false, set_rows_stride);
+
+        vk_pipeline pipeline = tensors[5]->type == GGML_TYPE_F16 ? ctx->device->pipeline_rms_norm_mul_rope_f32_f16 : ctx->device->pipeline_rms_norm_mul_rope_f32_f32;
+
+        ggml_pipeline_request_descriptor_sets(ctx, pipeline, 1);
+
+        ggml_backend_vk_buffer_context * buf_ctx[max_tensors];
+        vk_buffer buf[max_tensors];
+        size_t offset[max_tensors];
+        bool uma[max_tensors];
+
+        for (uint32_t i = 0; i < max_tensors; ++i) {
+            if (!tensors[i]) {
+                // If any remaining descriptors are unused, just point them at src[0]
+                buf[i] = buf[0];
+                offset[i] = 0;
+                continue;
+            }
+            buf_ctx[i] = (ggml_backend_vk_buffer_context *)tensors[i]->buffer->context;
+            buf[i] = nullptr;
+            offset[i] = 0;
+            uma[i] = false;
+
+            if (ctx->device->uma) {
+                ggml_vk_host_get(ctx->device, tensors[i]->data, buf[i], offset[i]);
+                uma[i] = buf[i] != nullptr;
+            }
+            if (!uma[i]) {
+                buf[i] = buf_ctx[i]->dev_buffer;
+                offset[i] = vk_tensor_offset(tensors[i]) + tensors[i]->view_offs;
+            }
+            GGML_ASSERT(buf[i] != nullptr);
+        }
+
+        std::array<uint32_t, 3> elements;
+        elements = { (uint32_t)rms->src[0]->ne[1], (uint32_t)rms->src[0]->ne[2], (uint32_t)rms->src[0]->ne[3] };
+
+        static_assert(max_tensors == 7);
+        ggml_vk_dispatch_pipeline(ctx, subctx, pipeline,
+            {
+                ggml_vk_subbuffer(ctx, buf[0], offset[0]),
+                ggml_vk_subbuffer(ctx, buf[1], offset[1]),
+                ggml_vk_subbuffer(ctx, buf[2], offset[2]),
+                ggml_vk_subbuffer(ctx, buf[3], offset[3]),
+                ggml_vk_subbuffer(ctx, buf[4], offset[4]),
+                ggml_vk_subbuffer(ctx, buf[5], offset[5]),
+                ggml_vk_subbuffer(ctx, buf[6], offset[6]),
+            }, pc, elements);
+    } else {
+        ggml_vk_op_f32<vk_op_binary_push_constants>(ctx, subctx, src0, src1, nullptr, nullptr, dst, GGML_OP_RMS_NORM, std::move(bin));
+    }
 
     if (ctx->do_add_rms_partials_offset_calculation) {
         ctx->prealloc_size_add_rms_partials_offset += ggml_vk_rms_partials_size(ctx, src0);
@@ -9758,9 +9909,6 @@ static void ggml_vk_rope(ggml_backend_vk_context * ctx, vk_context& subctx, cons
     // const int n_ctx         = ((int32_t *) dst->op_params)[3];
     const int n_ctx_orig    = ((int32_t *) dst->op_params)[4];
     const float freq_base   = ((float *)   dst->op_params)[5];
-    const float freq_scale  = ((float *)   dst->op_params)[6];
-    const float ext_factor  = ((float *)   dst->op_params)[7];
-    const float attn_factor = ((float *)   dst->op_params)[8];
     const float beta_fast   = ((float *)   dst->op_params)[9];
     const float beta_slow   = ((float *)   dst->op_params)[10];
     int sections[4] {};
@@ -9768,16 +9916,9 @@ static void ggml_vk_rope(ggml_backend_vk_context * ctx, vk_context& subctx, cons
         memcpy(sections, (int32_t *) dst->op_params + 11, sizeof(int)*4);
     }
 
-    const bool is_imrope = mode == GGML_ROPE_TYPE_IMROPE;
-
     float corr_dims[2];
     ggml_rope_yarn_corr_dims(n_dims, n_ctx_orig, freq_base, beta_fast, beta_slow, corr_dims);
 
-    const float theta_scale = powf(freq_base, -2.0f/n_dims);
-
-    uint32_t s1 = src0->nb[1] / ggml_type_size(src0->type);
-    uint32_t s2 = src0->nb[2] / ggml_type_size(src0->type);
-
     uint32_t set_rows_stride = 0;
     // Fused rope + view + set_rows passes the set_rows destination stride in set_rows_stride
     // and overrides the dst and sets src3=row_indices
@@ -9787,12 +9928,8 @@ static void ggml_vk_rope(ggml_backend_vk_context * ctx, vk_context& subctx, cons
         dst = cgraph->nodes[node_idx + 2];
     }
 
-    ggml_vk_op_f32<vk_op_rope_push_constants>(ctx, subctx, src0, src1, src2, src3, dst, GGML_OP_ROPE, {
-        (uint32_t)src0->ne[0], (uint32_t)n_dims, freq_scale, (uint32_t)src0->ne[1],
-        freq_base, ext_factor, attn_factor, {corr_dims[0], corr_dims[1]}, theta_scale,
-        src2 != nullptr, (uint32_t)src0->ne[2], s1, s2,
-        { sections[0], sections[1], sections[2], sections[3] }, is_imrope, backprop, set_rows_stride,
-    });
+    ggml_vk_op_f32<vk_op_rope_push_constants>(ctx, subctx, src0, src1, src2, src3, dst, GGML_OP_ROPE,
+        ggml_vk_make_rope_constants(cgraph->nodes[node_idx], src0, src2 != nullptr, backprop, set_rows_stride));
 }
 
 static void ggml_vk_argsort(ggml_backend_vk_context * ctx, vk_context& subctx, const ggml_tensor * src0, ggml_tensor * dst) {
@@ -11307,6 +11444,10 @@ static bool ggml_vk_build_graph(ggml_backend_vk_context * ctx, ggml_cgraph * cgr
         if (n->op == GGML_OP_GLU) {
             std::cerr << " " << ggml_glu_op_name(ggml_get_glu_op(n)) << " " << (n->src[1] ? "split" : "single") << " ";
         }
+        if (n->op == GGML_OP_ROPE) {
+            const int mode = ((const int32_t *) n->op_params)[2];
+            std::cerr << " rope mode: " << mode;
+        }
         std::cerr << std::endl;
     }
 #endif
@@ -11414,14 +11555,7 @@ static bool ggml_vk_build_graph(ggml_backend_vk_context * ctx, ggml_cgraph * cgr
 
         break;
     case GGML_OP_RMS_NORM:
-        if (ctx->num_additional_fused_ops > 0) {
-            // fused rms_norm + mul
-            ggml_tensor *mul = cgraph->nodes[node_idx + 1];
-            ggml_tensor *other_src = mul->src[0] == node ? mul->src[1] : mul->src[0];
-            ggml_vk_rms_norm(ctx, compute_ctx, src0, other_src, mul, (float *)node->op_params);
-        } else {
-            ggml_vk_rms_norm(ctx, compute_ctx, src0, src0, node, (float *)node->op_params);
-        }
+        ggml_vk_rms_norm(ctx, compute_ctx, cgraph, node_idx, (float *)node->op_params);
         break;
     case GGML_OP_RMS_NORM_BACK:
         ggml_vk_rms_norm_back(ctx, compute_ctx, src0, src1, node);
@@ -12407,6 +12541,70 @@ static bool ggml_vk_can_fuse_rope_set_rows(ggml_backend_vk_context * ctx, const
     return true;
 }
 
+// Check whether the tensors overlap in memory but are not equal.
+// Fusions can potenitally overwrite src tensors in ways that are not prevented
+// by ggml-alloc. If the fusion is entirely elementwise, then it's OK for them
+// to overlap if they are exactly equal.
+// XXX TODO this check is probably missing from several fusion optimizations.
+static bool ggml_vk_tensors_overlap_but_not_equal(const ggml_tensor * a, const ggml_tensor * b) {
+    ggml_backend_vk_buffer_context * a_buf_ctx = (ggml_backend_vk_buffer_context *)a->buffer->context;
+    vk_buffer a_buf = a_buf_ctx->dev_buffer;
+    ggml_backend_vk_buffer_context * b_buf_ctx = (ggml_backend_vk_buffer_context *)b->buffer->context;
+    vk_buffer b_buf = b_buf_ctx->dev_buffer;
+    if (a_buf == b_buf) {
+        auto a_base = vk_tensor_offset(a) + a->view_offs;
+        auto a_size = ggml_nbytes(a);
+        auto b_base = vk_tensor_offset(b) + b->view_offs;
+        auto b_size = ggml_nbytes(b);
+
+        if (a_base == b_base && a_size == b_size) {
+            return false;
+        }
+
+        if ((b_base <= a_base && a_base < b_base + b_size) ||
+            (a_base <= b_base && b_base < a_base + a_size)) {
+            return true;
+        }
+    }
+    return false;
+}
+
+static bool ggml_vk_can_fuse_rms_norm_mul_rope(ggml_backend_vk_context * ctx, const struct ggml_cgraph * cgraph,
+                                               int node_idx) {
+    GGML_UNUSED(ctx);
+    const ggml_tensor *rms = cgraph->nodes[node_idx + 0];
+    const ggml_tensor *mul = cgraph->nodes[node_idx + 1];
+    const ggml_tensor *rope = cgraph->nodes[node_idx + 2];
+
+    const int mode = ((const int32_t *) rope->op_params)[2];
+
+    // noncontig tensors aren't tested, and don't seem common in practice
+    if (!ggml_is_contiguous(rms) ||
+        !ggml_is_contiguous(mul) ||
+        !ggml_is_contiguous(rope)) {
+        return false;
+    }
+
+    // only norm/neox are handled in the shader
+    if (mode != GGML_ROPE_TYPE_NEOX && mode != GGML_ROPE_TYPE_NORMAL) {
+        return false;
+    }
+
+    // shared memory size for passing data from mul->rope
+    if (mul->ne[0] > 1024) {
+        return false;
+    }
+
+    // must not overwrite srcs in a way that's not elementwise
+    ggml_tensor *other_src = mul->src[0] == rms ? mul->src[1] : mul->src[0];
+    if (ggml_vk_tensors_overlap_but_not_equal(rms->src[0], rope) ||
+        ggml_vk_tensors_overlap_but_not_equal(other_src, rope)) {
+        return false;
+    }
+
+    return true;
+}
+
 static uint32_t ggml_vk_fuse_multi_add(ggml_backend_vk_context * ctx, const struct ggml_cgraph * cgraph, int node_idx) {
 
     const ggml_tensor *first_node = cgraph->nodes[node_idx];
@@ -12552,12 +12750,20 @@ static ggml_status ggml_backend_vk_graph_compute(ggml_backend_t backend, ggml_cg
             uint32_t num_adds = ggml_vk_fuse_multi_add(ctx, cgraph, i);
             if (num_adds) {
                 ctx->num_additional_fused_ops = num_adds - 1;
-            } else if (ggml_vk_can_fuse(ctx, cgraph, i, { GGML_OP_RMS_NORM, GGML_OP_MUL })) {
-                ctx->num_additional_fused_ops = 1;
             } else if (ggml_vk_can_fuse(ctx, cgraph, i, { GGML_OP_MUL_MAT, GGML_OP_ADD })) {
                 ctx->num_additional_fused_ops = 1;
             } else if (ggml_vk_can_fuse(ctx, cgraph, i, { GGML_OP_MUL_MAT_ID, GGML_OP_ADD_ID })) {
                 ctx->num_additional_fused_ops = 1;
+            } else if (ggml_can_fuse_subgraph(cgraph, i, { GGML_OP_RMS_NORM, GGML_OP_MUL, GGML_OP_ROPE, GGML_OP_VIEW, GGML_OP_SET_ROWS }, { i + 4 }) &&
+                       ggml_check_edges(cgraph, i, rms_norm_mul_rope_view_set_rows_edges) &&
+                       ggml_vk_can_fuse_rms_norm_mul_rope(ctx, cgraph, i) &&
+                       ggml_vk_can_fuse_rope_set_rows(ctx, cgraph, i + 2)) {
+                ctx->num_additional_fused_ops = 4;
+            } else if (ggml_vk_can_fuse(ctx, cgraph, i, { GGML_OP_RMS_NORM, GGML_OP_MUL, GGML_OP_ROPE })&&
+                       ggml_vk_can_fuse_rms_norm_mul_rope(ctx, cgraph, i)) {
+                ctx->num_additional_fused_ops = 2;
+            } else if (ggml_vk_can_fuse(ctx, cgraph, i, { GGML_OP_RMS_NORM, GGML_OP_MUL })) {
+                ctx->num_additional_fused_ops = 1;
             } else if (ggml_can_fuse_subgraph(cgraph, i, { GGML_OP_ROPE, GGML_OP_VIEW, GGML_OP_SET_ROWS }, { i + 2 }) &&
                        ggml_check_edges(cgraph, i, rope_view_set_rows_edges) &&
                        ggml_vk_can_fuse_rope_set_rows(ctx, cgraph, i)) {
@@ -12790,14 +12996,34 @@ static void ggml_vk_graph_optimize(ggml_backend_t backend, struct ggml_cgraph *
             }
             if (ok) {
                 current_set.push_back(j);
+
+                int rope_idx = j;
+
+                // When we've found RMS_NORM + MUL, try to find a ROPE that uses it
+                if (j > 0 &&
+                    graph->nodes[j]->op == GGML_OP_MUL &&
+                    graph->nodes[j-1]->op == GGML_OP_RMS_NORM) {
+                    for (int k = j + 1; k < std::min(j + 15, graph->n_nodes); ++k) {
+                        if (graph->nodes[k]->op == GGML_OP_ROPE &&
+                            graph->nodes[k]->src[0] == graph->nodes[j] &&
+                            // Check that other srcs are already valid
+                            graph->nodes[k]->src[1]->op == GGML_OP_NONE &&
+                            (graph->nodes[k]->src[2] == nullptr || graph->nodes[k]->src[2]->op == GGML_OP_NONE)) {
+                            rope_idx = k;
+                            current_set.push_back(rope_idx);
+                            used[rope_idx] = true;
+                            break;
+                        }
+                    }
+                }
                 // Look for ROPE + VIEW + SET_ROWS and make them consecutive
-                if (graph->nodes[j]->op == GGML_OP_ROPE) {
+                if (graph->nodes[rope_idx]->op == GGML_OP_ROPE) {
                     int view_idx = -1;
                     int set_rows_idx = -1;
-                    for (int k = j+1; k < std::min(j + 10, graph->n_nodes); ++k) {
+                    for (int k = rope_idx+1; k < std::min(rope_idx + 10, graph->n_nodes); ++k) {
                         if (view_idx == -1 &&
                             graph->nodes[k]->op == GGML_OP_VIEW &&
-                            graph->nodes[k]->src[0] == graph->nodes[j]) {
+                            graph->nodes[k]->src[0] == graph->nodes[rope_idx]) {
                             view_idx = k;
                             continue;
                         }
diff --git a/ggml/src/ggml-vulkan/vulkan-shaders/generic_binary_head.glsl b/ggml/src/ggml-vulkan/vulkan-shaders/generic_binary_head.glsl
index 99595fc688c..c1ad5172562 100644
--- a/ggml/src/ggml-vulkan/vulkan-shaders/generic_binary_head.glsl
+++ b/ggml/src/ggml-vulkan/vulkan-shaders/generic_binary_head.glsl
@@ -3,6 +3,9 @@
 
 #include "rte.glsl"
 #include "utils.glsl"
+#if RMS_NORM_ROPE_FUSION
+#include "rope_params.glsl"
+#endif
 
 layout (push_constant) uniform parameter
 {
@@ -12,11 +15,16 @@ layout (push_constant) uniform parameter
     uint ne20; uint ne21; uint ne22; uint ne23; uint nb20; uint nb21; uint nb22; uint nb23;
     uint misalign_offsets;
     float param1; float param2; int param3;
+#if RMS_NORM_ROPE_FUSION
+    rope_params rope;
+#endif
 } p;
 
+#if !RMS_NORM_ROPE_FUSION
 layout (binding = 0) readonly buffer A {A_TYPE data_a[];};
 layout (binding = 1) readonly buffer B {B_TYPE data_b[];};
 layout (binding = 2) writeonly buffer D {D_TYPE data_d[];};
+#endif
 
 // true if src0/src1 are the same shape and the indices can be reused without additional modulus
 layout(constant_id = 0) const bool norepeat = false;
diff --git a/ggml/src/ggml-vulkan/vulkan-shaders/rms_norm.comp b/ggml/src/ggml-vulkan/vulkan-shaders/rms_norm.comp
index d5b211ffaa7..3a47949d5a6 100644
--- a/ggml/src/ggml-vulkan/vulkan-shaders/rms_norm.comp
+++ b/ggml/src/ggml-vulkan/vulkan-shaders/rms_norm.comp
@@ -3,6 +3,32 @@
 #include "generic_binary_head.glsl"
 #include "types.glsl"
 
+#if RMS_NORM_ROPE_FUSION
+
+layout (binding = 0) readonly buffer A {A_TYPE data_a[];};
+layout (binding = 1) readonly buffer B {B_TYPE data_b[];};
+
+// data is passed from rms_norm -> rope through shared memory.
+// rms_norm calls this data_d, rope calls this rope_data_a.
+// Binding 2 is not used
+shared FLOAT_TYPE rope_data_a[1024];
+#define data_d rope_data_a
+
+layout (binding = 3) readonly buffer R_Y {int rope_data_pos[];};
+layout (binding = 4) readonly buffer R_Z {float rope_data_ff[];};
+layout (binding = 5) writeonly buffer R_D {ROPE_D_TYPE rope_data_d[];};
+layout (binding = 6) readonly buffer R_I {uvec2 rope_data_i[];}; // indices for set_rows
+
+#include "rope_params.glsl"
+#include "rope_funcs.glsl"
+
+#define GGML_ROPE_TYPE_NORMAL 0
+#define GGML_ROPE_TYPE_NEOX   2
+#define GGML_ROPE_TYPE_MROPE  8
+#define GGML_ROPE_TYPE_VISION 24
+
+#endif
+
 #extension GL_EXT_control_flow_attributes : enable
 #define BLOCK_SIZE 512
 
@@ -28,8 +54,12 @@ void rms_norm(uint num_iters) {
 
     uint32_t a_offset = samp*stride_sample + channel*stride_channel + row*stride_row + get_aoffset();
     uint32_t b_offset = src1_idx(0, row, channel, samp) + get_boffset();
+#if RMS_NORM_ROPE_FUSION
+    // Per-row offset in shared memory
+    uint32_t d_offset = 0;
+#else
     uint32_t d_offset = ((samp*nchannels + channel)*nrows + row)*ncols + get_doffset();
-
+#endif
     FLOAT_TYPE sum = FLOAT_TYPE(0.0f); // partial sum for thread in warp
 
     [[unroll]] for (uint col = tid, idx = 0; idx < num_iters; col += BLOCK_SIZE, ++idx) {
@@ -79,6 +109,18 @@ void rms_norm(uint num_iters) {
             data_d[d_offset + col] = D_TYPE(scale * FLOAT_TYPE(data_a[a_offset + col]));
         }
     }
+#if RMS_NORM_ROPE_FUSION
+    barrier();
+    rope_params rp = p.rope;
+    uint rope_row = (samp*nchannels + channel)*nrows + row;
+    for (uint t = 2*tid; t < ncols; t += 2*BLOCK_SIZE) {
+        if (rp.rope_mode == GGML_ROPE_TYPE_NEOX) {
+            rope_neox(t, rope_row, rp);
+        } else if (rp.rope_mode == GGML_ROPE_TYPE_NORMAL) {
+            rope_norm(t, rope_row, rp);
+        }
+    }
+#endif
 }
 
 void main() {
diff --git a/ggml/src/ggml-vulkan/vulkan-shaders/rope_funcs.glsl b/ggml/src/ggml-vulkan/vulkan-shaders/rope_funcs.glsl
new file mode 100644
index 00000000000..9726b722d1e
--- /dev/null
+++ b/ggml/src/ggml-vulkan/vulkan-shaders/rope_funcs.glsl
@@ -0,0 +1,227 @@
+
+float rope_yarn_ramp(const float low, const float high, const uint i0) {
+    const float y = (i0 / 2 - low) / max(0.001f, high - low);
+    return 1.0f - min(1.0f, max(0.0f, y));
+}
+
+uint rope_a_coord(const uint i0, const uint i01, const uint i02, rope_params p) {
+#if RMS_NORM_ROPE_FUSION
+    // Per-row offset in shared memory
+    const uint ix = i0;
+#else
+    const uint ix = i02*p.nb02 + i01*p.nb01 + i0;
+#endif
+    return ix;
+}
+
+void rope_yarn(const float theta_extrap, const uint i0, out float cos_theta, out float sin_theta, rope_params p) {
+    float mscale = p.attn_factor;
+    // Get n-d rotational scaling corrected for extrapolation
+    float theta_interp = p.freq_scale * theta_extrap;
+    float theta = theta_interp;
+    if (p.ext_factor != 0.0f) {
+        float ramp_mix = rope_yarn_ramp(p.corr_dims[0], p.corr_dims[1], i0) * p.ext_factor;
+        theta = theta_interp * (1 - ramp_mix) + theta_extrap * ramp_mix;
+
+        // Get n-d magnitude scaling corrected for interpolation
+        mscale *= 1.0f + 0.1f * log(1.0f / p.freq_scale);
+    }
+    // Backprogagation uses inverted rotation
+    if (p.is_back != 0) {
+        theta = -theta;
+    }
+    cos_theta = cos(theta) * mscale;
+    sin_theta = sin(theta) * mscale;
+}
+
+void rope_norm(const uint i0, const uint i1, rope_params p) {
+    uint ne0 = p.ncols;
+    uint ne1 = p.p_delta_rows;
+
+    if (i0 >= ne0) {
+        return;
+    }
+
+    // i1 is actually i2*nb2+i1, but the rows are contiguous
+    const uint i01 = i1 % ne1;
+    const uint i02 = i1 / ne1;
+
+    uint idst = i1*ne0 + i0;
+    const uint ix = rope_a_coord(i0, i01, i02, p);
+
+    // Fusion optimization: ROPE + VIEW + SET_ROWS..
+    // The rope output is viewed as a 1D tensor and offset based on a row index in data_i.
+    if (p.set_rows_stride != 0) {
+        idst = i01*ne0 + i0;
+        idst += rope_data_i[i02].x * p.set_rows_stride;
+    }
+
+    if (i0 >= p.n_dims) {
+        rope_data_d[idst + 0] = ROPE_D_TYPE(rope_data_a[ix + 0]);
+        rope_data_d[idst + 1] = ROPE_D_TYPE(rope_data_a[ix + 1]);
+
+        return;
+    }
+
+    const float theta_base = rope_data_pos[i02] * pow(p.theta_scale, i0/2.0f);
+
+    const float freq_factor = p.has_ff != 0 ? rope_data_ff[i0/2] : 1.0f;
+
+    float cos_theta, sin_theta;
+    rope_yarn(theta_base / freq_factor, i0, cos_theta, sin_theta, p);
+
+    const float x0 = float(rope_data_a[ix + 0]);
+    const float x1 = float(rope_data_a[ix + 1]);
+
+    rope_data_d[idst + 0] = ROPE_D_TYPE(x0*cos_theta - x1*sin_theta);
+    rope_data_d[idst + 1] = ROPE_D_TYPE(x0*sin_theta + x1*cos_theta);
+}
+
+void rope_neox(const uint i0, const uint i1, rope_params p) {
+    uint ne0 = p.ncols;
+    uint ne1 = p.p_delta_rows;
+
+    if (i0 >= ne0) {
+        return;
+    }
+
+    const uint i01 = i1 % ne1;
+    const uint i02 = i1 / ne1;
+
+    uint idst = i1*ne0 + i0/2;
+    const uint ix = rope_a_coord(i0/2, i01, i02, p);
+
+    // Fusion optimization: ROPE + VIEW + SET_ROWS..
+    // The rope output is viewed as a 1D tensor and offset based on a row index in rope_data_i.
+    if (p.set_rows_stride != 0) {
+        idst = i01*ne0 + i0/2;
+        idst += rope_data_i[i02].x * p.set_rows_stride;
+    }
+
+    if (i0 >= p.n_dims) {
+        rope_data_d[idst + i0/2 + 0] = ROPE_D_TYPE(rope_data_a[ix + i0/2 + 0]);
+        rope_data_d[idst + i0/2 + 1] = ROPE_D_TYPE(rope_data_a[ix + i0/2 + 1]);
+
+        return;
+    }
+
+    const float theta_base = rope_data_pos[i02] * pow(p.theta_scale, i0/2.0f);
+
+    const float freq_factor = p.has_ff != 0 ? rope_data_ff[i0/2] : 1.0f;
+
+    float cos_theta, sin_theta;
+    rope_yarn(theta_base / freq_factor, i0, cos_theta, sin_theta, p);
+
+    const float x0 = float(rope_data_a[ix + 0]);
+    const float x1 = float(rope_data_a[ix + p.n_dims/2]);
+
+    rope_data_d[idst + 0]          = ROPE_D_TYPE(x0*cos_theta - x1*sin_theta);
+    rope_data_d[idst + p.n_dims/2] = ROPE_D_TYPE(x0*sin_theta + x1*cos_theta);
+}
+
+
+void rope_multi(const uint i0, const uint i1, rope_params p) {
+    uint ne0 = p.ncols;
+    uint ne1 = p.p_delta_rows;
+    uint ne2 = p.ne02;
+
+    if (i0 >= ne0) {
+        return;
+    }
+
+    const uint i01 = i1 % ne1;
+    const uint i02 = i1 / ne1;
+
+    const uint idst = i1*ne0 + i0/2;
+    const uint ix = rope_a_coord(i0/2, i01, i02, p);
+
+    if (i0 >= p.n_dims) {
+        rope_data_d[idst + i0/2 + 0] = ROPE_D_TYPE(rope_data_a[ix + i0/2 + 0]);
+        rope_data_d[idst + i0/2 + 1] = ROPE_D_TYPE(rope_data_a[ix + i0/2 + 1]);
+
+        return;
+    }
+
+    const int sect_dims = p.sections[0] + p.sections[1] + p.sections[2] + p.sections[3];
+    const int sec_w = p.sections[1] + p.sections[0];
+    const uint sector = (i0 / 2) % sect_dims;
+
+    float theta_base = 0.0;
+    if (p.is_imrope != 0) {
+        if (sector % 3 == 1 && sector < 3 * p.sections[1]) {
+            theta_base = rope_data_pos[i02 + ne2 * 1]*pow(p.theta_scale, i0/2.0f);
+        } else if (sector % 3 == 2 && sector < 3 * p.sections[2]) {
+            theta_base = rope_data_pos[i02 + ne2 * 2]*pow(p.theta_scale, i0/2.0f);
+        } else if (sector % 3 == 0 && sector < 3 * p.sections[0]) {
+            theta_base = rope_data_pos[i02]*pow(p.theta_scale, i0/2.0f);
+        } else {
+            theta_base = rope_data_pos[i02 + ne2 * 3]*pow(p.theta_scale, i0/2.0f);
+        }
+    } else {
+        if (sector < p.sections[0]) {
+            theta_base = rope_data_pos[i02]*pow(p.theta_scale, i0/2.0f);
+        }
+        else if (sector >= p.sections[0] && sector < sec_w) {
+            theta_base = rope_data_pos[i02 + ne2 * 1]*pow(p.theta_scale, i0/2.0f);
+        }
+        else if (sector >= sec_w && sector < sec_w + p.sections[2]) {
+            theta_base = rope_data_pos[i02 + ne2 * 2]*pow(p.theta_scale, i0/2.0f);
+        }
+        else if (sector >= sec_w + p.sections[2]) {
+            theta_base = rope_data_pos[i02 + ne2 * 3]*pow(p.theta_scale, i0/2.0f);
+        }
+    }
+
+    const float freq_factor = p.has_ff != 0 ? rope_data_ff[i0/2] : 1.0f;
+
+    float cos_theta, sin_theta;
+    rope_yarn(theta_base / freq_factor, i0, cos_theta, sin_theta, p);
+
+    const float x0 = float(rope_data_a[ix + 0]);
+    const float x1 = float(rope_data_a[ix + p.n_dims/2]);
+
+    rope_data_d[idst + 0]          = ROPE_D_TYPE(x0*cos_theta - x1*sin_theta);
+    rope_data_d[idst + p.n_dims/2] = ROPE_D_TYPE(x0*sin_theta + x1*cos_theta);
+}
+
+void rope_vision(const uint i0, const uint i1, rope_params p) {
+    uint ne0 = p.ncols;
+    uint ne1 = p.p_delta_rows;
+    uint ne2 = p.ne02;
+
+    if (i0 >= ne0) {
+        return;
+    }
+
+    const uint i01 = i1 % ne1;
+    const uint i02 = i1 / ne1;
+
+    const uint idst = i1*ne0 + i0/2;
+    const uint ix = rope_a_coord(i0/2, i01, i02, p);
+
+    const int sect_dims = p.sections[0] + p.sections[1];
+    const int sec_w = p.sections[1] + p.sections[0];
+    const uint sector = (i0 / 2) % sect_dims;
+
+    float theta_base = 0.0;
+    if (sector < p.sections[0]) {
+        const uint p0 = sector;
+        theta_base = rope_data_pos[i02]*pow(p.theta_scale, p0);
+    }
+    else if (sector >= p.sections[0] && sector < sec_w) {
+        const uint p0 = sector - p.sections[0];
+        theta_base = rope_data_pos[i02 + ne2]*pow(p.theta_scale, p0);
+    }
+
+    const float freq_factor = p.has_ff != 0 ? rope_data_ff[i0/2] : 1.0f;
+
+    float cos_theta, sin_theta;
+    rope_yarn(theta_base / freq_factor, i0, cos_theta, sin_theta, p);
+
+    const float x0 = float(rope_data_a[ix + 0]);
+    const float x1 = float(rope_data_a[ix + p.n_dims]);
+
+    rope_data_d[idst + 0]        = ROPE_D_TYPE(x0*cos_theta - x1*sin_theta);
+    rope_data_d[idst + p.n_dims] = ROPE_D_TYPE(x0*sin_theta + x1*cos_theta);
+}
+
diff --git a/ggml/src/ggml-vulkan/vulkan-shaders/rope_head.glsl b/ggml/src/ggml-vulkan/vulkan-shaders/rope_head.glsl
index fa2bb33394c..d9b4d4c03f3 100644
--- a/ggml/src/ggml-vulkan/vulkan-shaders/rope_head.glsl
+++ b/ggml/src/ggml-vulkan/vulkan-shaders/rope_head.glsl
@@ -3,56 +3,18 @@
 #extension GL_EXT_shader_16bit_storage : require
 
 #include "rte.glsl"
+#include "rope_params.glsl"
 
 layout(local_size_x = 1, local_size_y = 256, local_size_z = 1) in;
 
-layout (binding = 0) readonly buffer X {A_TYPE data_a[];};
-layout (binding = 1) readonly buffer Y {int data_pos[];};
-layout (binding = 2) readonly buffer Z {float data_ff[];};
-layout (binding = 3) writeonly buffer D {D_TYPE data_d[];};
-layout (binding = 4) readonly buffer I {uvec2 data_i[];}; // indices for set_rows
+layout (binding = 0) readonly buffer X {A_TYPE rope_data_a[];};
+layout (binding = 1) readonly buffer Y {int rope_data_pos[];};
+layout (binding = 2) readonly buffer Z {float rope_data_ff[];};
+layout (binding = 3) writeonly buffer D {ROPE_D_TYPE rope_data_d[];};
+layout (binding = 4) readonly buffer I {uvec2 rope_data_i[];}; // indices for set_rows
 
-layout (push_constant) uniform parameter {
-    uint ncols;
-    uint n_dims;
-    float freq_scale;
-    uint p_delta_rows;
-    float freq_base;
-    float ext_factor;
-    float attn_factor;
-    float corr_dims[2];
-    float theta_scale;
-    uint has_ff;
-    uint ne02;
-    uint s1;
-    uint s2;
-    int sections[4];
-    uint is_imrope;
-    uint is_back;
-    uint set_rows_stride;
-} p;
-
-float rope_yarn_ramp(const float low, const float high, const uint i0) {
-    const float y = (i0 / 2 - low) / max(0.001f, high - low);
-    return 1.0f - min(1.0f, max(0.0f, y));
-}
 
-void rope_yarn(const float theta_extrap, const uint i0, out float cos_theta, out float sin_theta) {
-    float mscale = p.attn_factor;
-    // Get n-d rotational scaling corrected for extrapolation
-    float theta_interp = p.freq_scale * theta_extrap;
-    float theta = theta_interp;
-    if (p.ext_factor != 0.0f) {
-        float ramp_mix = rope_yarn_ramp(p.corr_dims[0], p.corr_dims[1], i0) * p.ext_factor;
-        theta = theta_interp * (1 - ramp_mix) + theta_extrap * ramp_mix;
+layout (push_constant) uniform parameter {
+    rope_params pc;
+};
 
-        // Get n-d magnitude scaling corrected for interpolation
-        mscale *= 1.0f + 0.1f * log(1.0f / p.freq_scale);
-    }
-    // Backprogagation uses inverted rotation
-    if (p.is_back != 0) {
-        theta = -theta;
-    }
-    cos_theta = cos(theta) * mscale;
-    sin_theta = sin(theta) * mscale;
-}
diff --git a/ggml/src/ggml-vulkan/vulkan-shaders/rope_multi.comp b/ggml/src/ggml-vulkan/vulkan-shaders/rope_multi.comp
index 54aabcf2228..7c1fb1cd224 100644
--- a/ggml/src/ggml-vulkan/vulkan-shaders/rope_multi.comp
+++ b/ggml/src/ggml-vulkan/vulkan-shaders/rope_multi.comp
@@ -1,70 +1,11 @@
 #version 450
 
 #include "rope_head.glsl"
+#include "rope_funcs.glsl"
 
 void main() {
     const uint i0 = 2*gl_GlobalInvocationID.y;
-    uint ne0 = p.ncols;
-    uint ne1 = p.p_delta_rows;
-    uint ne2 = p.ne02;
-
-    if (i0 >= ne0) {
-        return;
-    }
-
-    const uint row_dst = gl_GlobalInvocationID.x;
-
-    const uint row_x     = row_dst % ne1;
-    const uint channel_x = row_dst / ne1;
-
-    const uint idst = row_dst*ne0 + i0/2;
-    const uint ix   = channel_x*p.s2 + row_x*p.s1 + i0/2;
-
-    if (i0 >= p.n_dims) {
-        data_d[idst + i0/2 + 0] = data_a[ix + i0/2 + 0];
-        data_d[idst + i0/2 + 1] = data_a[ix + i0/2 + 1];
-
-        return;
-    }
-
-    const int sect_dims = p.sections[0] + p.sections[1] + p.sections[2] + p.sections[3];
-    const int sec_w = p.sections[1] + p.sections[0];
-    const uint sector = (i0 / 2) % sect_dims;
-
-    float theta_base = 0.0;
-    if (p.is_imrope != 0) {
-        if (sector % 3 == 1 && sector < 3 * p.sections[1]) {
-            theta_base = data_pos[channel_x + ne2 * 1]*pow(p.theta_scale, i0/2.0f);
-        } else if (sector % 3 == 2 && sector < 3 * p.sections[2]) {
-            theta_base = data_pos[channel_x + ne2 * 2]*pow(p.theta_scale, i0/2.0f);
-        } else if (sector % 3 == 0 && sector < 3 * p.sections[0]) {
-            theta_base = data_pos[channel_x]*pow(p.theta_scale, i0/2.0f);
-        } else {
-            theta_base = data_pos[channel_x + ne2 * 3]*pow(p.theta_scale, i0/2.0f);
-        }
-    } else {
-        if (sector < p.sections[0]) {
-            theta_base = data_pos[channel_x]*pow(p.theta_scale, i0/2.0f);
-        }
-        else if (sector >= p.sections[0] && sector < sec_w) {
-            theta_base = data_pos[channel_x + ne2 * 1]*pow(p.theta_scale, i0/2.0f);
-        }
-        else if (sector >= sec_w && sector < sec_w + p.sections[2]) {
-            theta_base = data_pos[channel_x + ne2 * 2]*pow(p.theta_scale, i0/2.0f);
-        }
-        else if (sector >= sec_w + p.sections[2]) {
-            theta_base = data_pos[channel_x + ne2 * 3]*pow(p.theta_scale, i0/2.0f);
-        }
-    }
-
-    const float freq_factor = p.has_ff != 0 ? data_ff[i0/2] : 1.0f;
-
-    float cos_theta, sin_theta;
-    rope_yarn(theta_base / freq_factor, i0, cos_theta, sin_theta);
-
-    const float x0 = float(data_a[ix + 0]);
-    const float x1 = float(data_a[ix + p.n_dims/2]);
-
-    data_d[idst + 0]          = D_TYPE(x0*cos_theta - x1*sin_theta);
-    data_d[idst + p.n_dims/2] = D_TYPE(x0*sin_theta + x1*cos_theta);
+    // i1 is actually i2*nb2+i1, but the rows are contiguous
+    const uint i1 = gl_GlobalInvocationID.x;
+    rope_multi(i0, i1, pc);
 }
diff --git a/ggml/src/ggml-vulkan/vulkan-shaders/rope_neox.comp b/ggml/src/ggml-vulkan/vulkan-shaders/rope_neox.comp
index 9f4538155a0..68f00c180bb 100644
--- a/ggml/src/ggml-vulkan/vulkan-shaders/rope_neox.comp
+++ b/ggml/src/ggml-vulkan/vulkan-shaders/rope_neox.comp
@@ -1,48 +1,11 @@
 #version 450
 
 #include "rope_head.glsl"
+#include "rope_funcs.glsl"
 
 void main() {
     const uint i0 = 2*gl_GlobalInvocationID.y;
-    uint ne0 = p.ncols;
-    uint ne1 = p.p_delta_rows;
-
-    if (i0 >= ne0) {
-        return;
-    }
-
-    const uint row_dst = gl_GlobalInvocationID.x;
-
-    const uint row_x     = row_dst % ne1;
-    const uint channel_x = row_dst / ne1;
-
-    uint idst = row_dst*ne0 + i0/2;
-    const uint ix   = channel_x*p.s2 + row_x*p.s1 + i0/2;
-
-    // Fusion optimization: ROPE + VIEW + SET_ROWS..
-    // The rope output is viewed as a 1D tensor and offset based on a row index in data_i.
-    if (p.set_rows_stride != 0) {
-        idst = row_x*ne0 + i0/2;
-        idst += data_i[channel_x].x * p.set_rows_stride;
-    }
-
-    if (i0 >= p.n_dims) {
-        data_d[idst + i0/2 + 0] = D_TYPE(data_a[ix + i0/2 + 0]);
-        data_d[idst + i0/2 + 1] = D_TYPE(data_a[ix + i0/2 + 1]);
-
-        return;
-    }
-
-    const float theta_base = data_pos[channel_x] * pow(p.theta_scale, i0/2.0f);
-
-    const float freq_factor = p.has_ff != 0 ? data_ff[i0/2] : 1.0f;
-
-    float cos_theta, sin_theta;
-    rope_yarn(theta_base / freq_factor, i0, cos_theta, sin_theta);
-
-    const float x0 = float(data_a[ix + 0]);
-    const float x1 = float(data_a[ix + p.n_dims/2]);
-
-    data_d[idst + 0]          = D_TYPE(x0*cos_theta - x1*sin_theta);
-    data_d[idst + p.n_dims/2] = D_TYPE(x0*sin_theta + x1*cos_theta);
+    // i1 is actually i2*nb2+i1, but the rows are contiguous
+    const uint i1 = gl_GlobalInvocationID.x;
+    rope_neox(i0, i1, pc);
 }
diff --git a/ggml/src/ggml-vulkan/vulkan-shaders/rope_norm.comp b/ggml/src/ggml-vulkan/vulkan-shaders/rope_norm.comp
index f4209ed9582..28a939ec6ad 100644
--- a/ggml/src/ggml-vulkan/vulkan-shaders/rope_norm.comp
+++ b/ggml/src/ggml-vulkan/vulkan-shaders/rope_norm.comp
@@ -1,48 +1,11 @@
 #version 450
 
 #include "rope_head.glsl"
+#include "rope_funcs.glsl"
 
 void main() {
     const uint i0 = 2*gl_GlobalInvocationID.y;
-    uint ne0 = p.ncols;
-    uint ne1 = p.p_delta_rows;
-
-    if (i0 >= ne0) {
-        return;
-    }
-
-    const uint row_dst = gl_GlobalInvocationID.x;
-
-    const uint row_x     = row_dst % ne1;
-    const uint channel_x = row_dst / ne1;
-
-    uint idst = row_dst*ne0 + i0;
-    const uint ix   = channel_x*p.s2 + row_x*p.s1 + i0;
-
-    // Fusion optimization: ROPE + VIEW + SET_ROWS..
-    // The rope output is viewed as a 1D tensor and offset based on a row index in data_i.
-    if (p.set_rows_stride != 0) {
-        idst = row_x*ne0 + i0;
-        idst += data_i[channel_x].x * p.set_rows_stride;
-    }
-
-    if (i0 >= p.n_dims) {
-        data_d[idst + 0] = D_TYPE(data_a[ix + 0]);
-        data_d[idst + 1] = D_TYPE(data_a[ix + 1]);
-
-        return;
-    }
-
-    const float theta_base = data_pos[channel_x] * pow(p.theta_scale, i0/2.0f);
-
-    const float freq_factor = p.has_ff != 0 ? data_ff[i0/2] : 1.0f;
-
-    float cos_theta, sin_theta;
-    rope_yarn(theta_base / freq_factor, i0, cos_theta, sin_theta);
-
-    const float x0 = float(data_a[ix + 0]);
-    const float x1 = float(data_a[ix + 1]);
-
-    data_d[idst + 0] = D_TYPE(x0*cos_theta - x1*sin_theta);
-    data_d[idst + 1] = D_TYPE(x0*sin_theta + x1*cos_theta);
+    // i1 is actually i2*nb2+i1, but the rows are contiguous
+    const uint i1 = gl_GlobalInvocationID.x;
+    rope_norm(i0, i1, pc);
 }
diff --git a/ggml/src/ggml-vulkan/vulkan-shaders/rope_params.glsl b/ggml/src/ggml-vulkan/vulkan-shaders/rope_params.glsl
new file mode 100644
index 00000000000..82f39cee349
--- /dev/null
+++ b/ggml/src/ggml-vulkan/vulkan-shaders/rope_params.glsl
@@ -0,0 +1,27 @@
+#if !defined(GGML_ROPE_PARAMS)
+#define GGML_ROPE_PARAMS
+
+#include "rte.glsl"
+
+struct rope_params {
+    uint rope_mode;
+    uint ncols;
+    uint n_dims;
+    float freq_scale;
+    uint p_delta_rows;
+    float freq_base;
+    float ext_factor;
+    float attn_factor;
+    float corr_dims[2];
+    float theta_scale;
+    uint has_ff;
+    uint ne02;
+    uint nb01;
+    uint nb02;
+    int sections[4];
+    uint is_imrope;
+    uint is_back;
+    uint set_rows_stride;
+};
+
+#endif // !defined(GGML_ROPE_PARAMS)
diff --git a/ggml/src/ggml-vulkan/vulkan-shaders/rope_vision.comp b/ggml/src/ggml-vulkan/vulkan-shaders/rope_vision.comp
index d37d1c1043f..ea1e0fdb416 100644
--- a/ggml/src/ggml-vulkan/vulkan-shaders/rope_vision.comp
+++ b/ggml/src/ggml-vulkan/vulkan-shaders/rope_vision.comp
@@ -1,47 +1,11 @@
 #version 450
 
 #include "rope_head.glsl"
+#include "rope_funcs.glsl"
 
 void main() {
     const uint i0 = 2*gl_GlobalInvocationID.y;
-    uint ne0 = p.ncols;
-    uint ne1 = p.p_delta_rows;
-    uint ne2 = p.ne02;
-
-    if (i0 >= ne0) {
-        return;
-    }
-
-    const uint row_dst = gl_GlobalInvocationID.x;
-
-    const uint row_x     = row_dst % ne1;
-    const uint channel_x = row_dst / ne1;
-
-    const uint idst = row_dst*ne0 + i0/2;
-    const uint ix   = channel_x*p.s2 + row_x*p.s1 + i0/2;
-
-    const int sect_dims = p.sections[0] + p.sections[1];
-    const int sec_w = p.sections[1] + p.sections[0];
-    const uint sector = (i0 / 2) % sect_dims;
-
-    float theta_base = 0.0;
-    if (sector < p.sections[0]) {
-        const uint p0 = sector;
-        theta_base = data_pos[channel_x]*pow(p.theta_scale, p0);
-    }
-    else if (sector >= p.sections[0] && sector < sec_w) {
-        const uint p0 = sector - p.sections[0];
-        theta_base = data_pos[channel_x + ne2]*pow(p.theta_scale, p0);
-    }
-
-    const float freq_factor = p.has_ff != 0 ? data_ff[i0/2] : 1.0f;
-
-    float cos_theta, sin_theta;
-    rope_yarn(theta_base / freq_factor, i0, cos_theta, sin_theta);
-
-    const float x0 = float(data_a[ix + 0]);
-    const float x1 = float(data_a[ix + p.n_dims]);
-
-    data_d[idst + 0]        = D_TYPE(x0*cos_theta - x1*sin_theta);
-    data_d[idst + p.n_dims] = D_TYPE(x0*sin_theta + x1*cos_theta);
+    // i1 is actually i2*nb2+i1, but the rows are contiguous
+    const uint i1 = gl_GlobalInvocationID.x;
+    rope_vision(i0, i1, pc);
 }
diff --git a/ggml/src/ggml-vulkan/vulkan-shaders/vulkan-shaders-gen.cpp b/ggml/src/ggml-vulkan/vulkan-shaders/vulkan-shaders-gen.cpp
index bd178875d55..c2e42cf006e 100644
--- a/ggml/src/ggml-vulkan/vulkan-shaders/vulkan-shaders-gen.cpp
+++ b/ggml/src/ggml-vulkan/vulkan-shaders/vulkan-shaders-gen.cpp
@@ -695,6 +695,8 @@ void process_shaders() {
     string_to_spv("group_norm_f32", "group_norm.comp", merge_maps(base_dict, {{"A_TYPE", "float"}, {"D_TYPE", "float"}}));
     string_to_spv("rms_norm_f32", "rms_norm.comp", merge_maps(base_dict, {{"A_TYPE", "float"}, {"B_TYPE", "float"}, {"D_TYPE", "float"}}));
     string_to_spv("rms_norm_partials_f32", "rms_norm_partials.comp", merge_maps(base_dict, {{"A_TYPE", "float"}, {"B_TYPE", "float"}, {"D_TYPE", "float"}}));
+    string_to_spv("rms_norm_mul_rope_f32_f32", "rms_norm.comp", merge_maps(base_dict, {{"A_TYPE", "float"}, {"B_TYPE", "float"}, {"D_TYPE", "float"}, {"ROPE_D_TYPE", "float"}, {"RMS_NORM_ROPE_FUSION", "1"}}));
+    string_to_spv("rms_norm_mul_rope_f32_f16_rte", "rms_norm.comp", merge_maps(base_dict, {{"A_TYPE", "float"}, {"B_TYPE", "float"}, {"D_TYPE", "float"}, {"ROPE_D_TYPE", "float16_t"}, {"RMS_NORM_ROPE_FUSION", "1"}, {"RTE16", "1"}}));
     string_to_spv("rms_norm_back_f32", "rms_norm_back.comp", merge_maps(base_dict, {{"A_TYPE", "float"}, {"B_TYPE", "float"}, {"D_TYPE", "float"}}));
     string_to_spv("l2_norm_f32", "l2_norm.comp", merge_maps(base_dict, {{"A_TYPE", "float"}, {"D_TYPE", "float"}}));
 
@@ -840,25 +842,25 @@ void process_shaders() {
     string_to_spv("soft_max_f32_f16", "soft_max.comp", merge_maps(base_dict, {{"A_TYPE", "float"}, {"B_TYPE", "float16_t"}, {"D_TYPE", "float"}}));
     string_to_spv("soft_max_back_f32", "soft_max_back.comp", merge_maps(base_dict, {{"A_TYPE", "float"}, {"B_TYPE", "float"}, {"D_TYPE", "float"}}));
 
-    string_to_spv("rope_norm_f32", "rope_norm.comp", {{"A_TYPE", "float"}, {"D_TYPE", "float"}});
-    string_to_spv("rope_norm_f16", "rope_norm.comp", {{"A_TYPE", "float16_t"}, {"D_TYPE", "float16_t"}});
-    string_to_spv("rope_norm_f16_rte", "rope_norm.comp", {{"A_TYPE", "float16_t"}, {"D_TYPE", "float16_t"}, {"RTE16", "1"}});
-    string_to_spv("rope_norm_f32_f16", "rope_norm.comp", {{"A_TYPE", "float"}, {"D_TYPE", "float16_t"}});
-    string_to_spv("rope_norm_f32_f16_rte", "rope_norm.comp", {{"A_TYPE", "float"}, {"D_TYPE", "float16_t"}, {"RTE16", "1"}});
-
-    string_to_spv("rope_neox_f32", "rope_neox.comp", {{"A_TYPE", "float"}, {"D_TYPE", "float"}});
-    string_to_spv("rope_neox_f16", "rope_neox.comp", {{"A_TYPE", "float16_t"}, {"D_TYPE", "float16_t"}});
-    string_to_spv("rope_neox_f16_rte", "rope_neox.comp", {{"A_TYPE", "float16_t"}, {"D_TYPE", "float16_t"}, {"RTE16", "1"}});
-    string_to_spv("rope_neox_f32_f16", "rope_neox.comp", {{"A_TYPE", "float"}, {"D_TYPE", "float16_t"}});
-    string_to_spv("rope_neox_f32_f16_rte", "rope_neox.comp", {{"A_TYPE", "float"}, {"D_TYPE", "float16_t"}, {"RTE16", "1"}});
-
-    string_to_spv("rope_multi_f32", "rope_multi.comp", {{"A_TYPE", "float"}, {"D_TYPE", "float"}});
-    string_to_spv("rope_multi_f16", "rope_multi.comp", {{"A_TYPE", "float16_t"}, {"D_TYPE", "float16_t"}});
-    string_to_spv("rope_multi_f16_rte", "rope_multi.comp", {{"A_TYPE", "float16_t"}, {"D_TYPE", "float16_t"}, {"RTE16", "1"}});
-
-    string_to_spv("rope_vision_f32", "rope_vision.comp", {{"A_TYPE", "float"}, {"D_TYPE", "float"}});
-    string_to_spv("rope_vision_f16", "rope_vision.comp", {{"A_TYPE", "float16_t"}, {"D_TYPE", "float16_t"}});
-    string_to_spv("rope_vision_f16_rte", "rope_vision.comp", {{"A_TYPE", "float16_t"}, {"D_TYPE", "float16_t"}, {"RTE16", "1"}});
+    string_to_spv("rope_norm_f32", "rope_norm.comp", {{"A_TYPE", "float"}, {"ROPE_D_TYPE", "float"}});
+    string_to_spv("rope_norm_f16", "rope_norm.comp", {{"A_TYPE", "float16_t"}, {"ROPE_D_TYPE", "float16_t"}});
+    string_to_spv("rope_norm_f16_rte", "rope_norm.comp", {{"A_TYPE", "float16_t"}, {"ROPE_D_TYPE", "float16_t"}, {"RTE16", "1"}});
+    string_to_spv("rope_norm_f32_f16", "rope_norm.comp", {{"A_TYPE", "float"}, {"ROPE_D_TYPE", "float16_t"}});
+    string_to_spv("rope_norm_f32_f16_rte", "rope_norm.comp", {{"A_TYPE", "float"}, {"ROPE_D_TYPE", "float16_t"}, {"RTE16", "1"}});
+
+    string_to_spv("rope_neox_f32", "rope_neox.comp", {{"A_TYPE", "float"}, {"ROPE_D_TYPE", "float"}});
+    string_to_spv("rope_neox_f16", "rope_neox.comp", {{"A_TYPE", "float16_t"}, {"ROPE_D_TYPE", "float16_t"}});
+    string_to_spv("rope_neox_f16_rte", "rope_neox.comp", {{"A_TYPE", "float16_t"}, {"ROPE_D_TYPE", "float16_t"}, {"RTE16", "1"}});
+    string_to_spv("rope_neox_f32_f16", "rope_neox.comp", {{"A_TYPE", "float"}, {"ROPE_D_TYPE", "float16_t"}});
+    string_to_spv("rope_neox_f32_f16_rte", "rope_neox.comp", {{"A_TYPE", "float"}, {"ROPE_D_TYPE", "float16_t"}, {"RTE16", "1"}});
+
+    string_to_spv("rope_multi_f32", "rope_multi.comp", {{"A_TYPE", "float"}, {"ROPE_D_TYPE", "float"}});
+    string_to_spv("rope_multi_f16", "rope_multi.comp", {{"A_TYPE", "float16_t"}, {"ROPE_D_TYPE", "float16_t"}});
+    string_to_spv("rope_multi_f16_rte", "rope_multi.comp", {{"A_TYPE", "float16_t"}, {"ROPE_D_TYPE", "float16_t"}, {"RTE16", "1"}});
+
+    string_to_spv("rope_vision_f32", "rope_vision.comp", {{"A_TYPE", "float"}, {"ROPE_D_TYPE", "float"}});
+    string_to_spv("rope_vision_f16", "rope_vision.comp", {{"A_TYPE", "float16_t"}, {"ROPE_D_TYPE", "float16_t"}});
+    string_to_spv("rope_vision_f16_rte", "rope_vision.comp", {{"A_TYPE", "float16_t"}, {"ROPE_D_TYPE", "float16_t"}, {"RTE16", "1"}});
 
     string_to_spv("argsort_f32", "argsort.comp", {{"A_TYPE", "float"}});
 
diff --git a/tests/test-backend-ops.cpp b/tests/test-backend-ops.cpp
index b9ae82eeddd..80216f6f3a2 100644
--- a/tests/test-backend-ops.cpp
+++ b/tests/test-backend-ops.cpp
@@ -2294,6 +2294,79 @@ struct test_rope_set_rows : public test_case {
     }
 };
 
+// GGML_OP_RMS_NORM + GGML_OP_MUL + GGML_OP_ROPE (+ GGML_OP_VIEW + GGML_OP_SET_ROWS)
+struct test_rms_norm_mul_rope : public test_case {
+    const std::array<int64_t, 4> ne;
+    const float eps;
+    const bool multi_add; // test a sequence of adds feeding into rms_norm
+    const bool set_rows;
+    int mode;
+
+    std::string op_desc(ggml_tensor * t) override {
+        GGML_UNUSED(t);
+        return "RMS_NORM_MUL_ROPE";
+    }
+
+    bool run_whole_graph() override { return true; }
+
+    std::string vars() override {
+        return VARS_TO_STR5(ne, eps, multi_add, set_rows, mode);
+    }
+
+    test_rms_norm_mul_rope(std::array<int64_t, 4> ne, float eps = 1e-6f, bool multi_add = false,
+                           bool set_rows = false, int mode = GGML_ROPE_TYPE_NORMAL)
+        : ne(ne), eps(eps), multi_add(multi_add), set_rows(set_rows), mode(mode) {}
+
+    ggml_tensor * build_graph(ggml_context * ctx) override {
+        ggml_tensor * a = ggml_new_tensor_4d(ctx, GGML_TYPE_F32, ne[0], ne[1], ne[2], 1);
+        ggml_tensor * b = ggml_new_tensor_4d(ctx, GGML_TYPE_F32, ne[0], ne[1], ne[2], 1);
+        ggml_tensor * c = ggml_new_tensor_4d(ctx, GGML_TYPE_F32, ne[0], ne[1], ne[2], 1);
+
+        if (multi_add) {
+            a = ggml_add(ctx, ggml_add(ctx, a, b), c);
+        }
+
+        a = ggml_mul(ctx, ggml_rms_norm(ctx, a, eps), b);
+
+        ggml_tensor * pos = ggml_new_tensor_1d(ctx, GGML_TYPE_I32, ne[2]);
+
+        ggml_tensor * rope = ggml_rope(ctx, a, pos, ne[0], mode);
+
+        ggml_tensor * out;
+
+        if (set_rows) {
+            ggml_tensor * view = ggml_view_2d(ctx, rope, ne[0] * ne[1], ne[2], rope->nb[2], 0);
+
+            ggml_tensor * dst = ggml_new_tensor_4d(ctx, GGML_TYPE_F16, ne[0] * ne[1], ne[2] * ne[3], 1, 1);
+            ggml_set_name(dst, "dst");
+
+            ggml_tensor * row_idxs = ggml_new_tensor_3d(ctx, GGML_TYPE_I64, ne[2], 1, 1);
+            ggml_set_name(row_idxs, "row_idxs");
+
+            out = ggml_set_rows(ctx, dst, view, row_idxs);
+            ggml_set_name(out, "out");
+        } else {
+            out = rope;
+        }
+
+        return out;
+    }
+
+    void initialize_tensors(ggml_context * ctx) override {
+        for (ggml_tensor * t = ggml_get_first_tensor(ctx); t != NULL; t = ggml_get_next_tensor(ctx, t)) {
+            if (t->type == GGML_TYPE_I64 || t->type == GGML_TYPE_I32) {
+                if (ggml_is_view_op(t->op)) {
+                    continue;
+                }
+
+                init_set_rows_row_ids(t, ne[2]);
+            } else {
+                init_tensor_uniform(t);
+            }
+        }
+    }
+};
+
 // GGML_OP_ARGMAX
 struct test_argmax : public test_case {
     const ggml_type type;
@@ -6751,6 +6824,22 @@ static std::vector<std::unique_ptr<test_case>> make_test_cases_eval() {
         }
     }
 
+    for (auto multi_add : {false, true}) {
+        for (auto set_rows : {false, true}) {
+            for (auto rope : {GGML_ROPE_TYPE_NORMAL, GGML_ROPE_TYPE_NEOX}) {
+                test_cases.emplace_back(new test_rms_norm_mul_rope({768, 1, 1, 1}, 1e-6f, multi_add, set_rows, rope));
+                test_cases.emplace_back(new test_rms_norm_mul_rope({768, 3, 1, 1}, 1e-6f, multi_add, set_rows, rope));
+                test_cases.emplace_back(new test_rms_norm_mul_rope({768, 3, 5, 1}, 1e-6f, multi_add, set_rows, rope));
+                test_cases.emplace_back(new test_rms_norm_mul_rope({128, 32, 2, 1}, 1e-6f, multi_add, set_rows, rope));
+                test_cases.emplace_back(new test_rms_norm_mul_rope({128, 4, 2, 1}, 1e-6f, multi_add, set_rows, rope));
+                test_cases.emplace_back(new test_rms_norm_mul_rope({128, 32, 50, 1}, 1e-6f, multi_add, set_rows, rope));
+                test_cases.emplace_back(new test_rms_norm_mul_rope({128, 4, 50, 1}, 1e-6f, multi_add, set_rows, rope));
+                test_cases.emplace_back(new test_rms_norm_mul_rope({8192, 2, 2, 1}, 1e-6f, multi_add, set_rows, rope));
+                test_cases.emplace_back(new test_rms_norm_mul_rope({8192, 2, 2, 1}, 1e-6f, multi_add, set_rows, rope));
+            }
+        }
+    }
+
     test_cases.emplace_back(new test_l2_norm(GGML_TYPE_F32, {64, 5, 4, 3}, 1e-12f));
 
     for (int64_t d_conv : {3, 4}) {

From 08416ebe7f7c0f344ada15489730d69eda096304 Mon Sep 17 00:00:00 2001
From: Aleksei Nikiforov
 <103434461+AlekseiNikiforovIBM@users.noreply.github.com>
Date: Sat, 8 Nov 2025 09:00:20 +0100
Subject: [PATCH 119/185] ggml: disable vxe for cross-compilation by default
 (#16966)

Otherwise compilation will fail due to enabling -mvx -mzvector
and not setting corresponding -march options.
---
 ggml/CMakeLists.txt | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/ggml/CMakeLists.txt b/ggml/CMakeLists.txt
index 181f179ed17..869796f0e3b 100644
--- a/ggml/CMakeLists.txt
+++ b/ggml/CMakeLists.txt
@@ -168,7 +168,7 @@ option(GGML_RV_ZFH           "ggml: enable riscv zfh"        ON)
 option(GGML_RV_ZVFH          "ggml: enable riscv zvfh"       ON)
 option(GGML_RV_ZICBOP        "ggml: enable riscv zicbop"     ON)
 option(GGML_XTHEADVECTOR     "ggml: enable xtheadvector"     OFF)
-option(GGML_VXE              "ggml: enable vxe"              ON)
+option(GGML_VXE              "ggml: enable vxe"              ${GGML_NATIVE})
 
 option(GGML_CPU_ALL_VARIANTS "ggml: build all variants of the CPU backend (requires GGML_BACKEND_DL)" OFF)
 set(GGML_CPU_ARM_ARCH        "" CACHE STRING "ggml: CPU architecture for ARM")

From b8a5cfd11abc066f165e924136d0fa1db44d2b95 Mon Sep 17 00:00:00 2001
From: SavicStefan <50296686+SavicStefan@users.noreply.github.com>
Date: Sat, 8 Nov 2025 09:28:22 +0100
Subject: [PATCH 120/185] vulkan: Increase BK to 32; use BK/4 for non-CM
 mul_mm.comp (#16636)

Signed-off-by: Stefan Savic <stefan.savic@huawei.com>
Co-authored-by: Stefan Savic <stefan.savic@huawei.com>
---
 .../ggml-vulkan/vulkan-shaders/mul_mm.comp    | 33 +++++++++++++++++--
 1 file changed, 31 insertions(+), 2 deletions(-)

diff --git a/ggml/src/ggml-vulkan/vulkan-shaders/mul_mm.comp b/ggml/src/ggml-vulkan/vulkan-shaders/mul_mm.comp
index d260969f07e..5c5251da39b 100644
--- a/ggml/src/ggml-vulkan/vulkan-shaders/mul_mm.comp
+++ b/ggml/src/ggml-vulkan/vulkan-shaders/mul_mm.comp
@@ -100,7 +100,6 @@ layout (push_constant) uniform parameter
 layout (constant_id = 0) const uint BLOCK_SIZE = 64;
 layout (constant_id = 1) const uint BM = 64;
 layout (constant_id = 2) const uint BN = 64;
-layout (constant_id = 3) const uint BK = 16;  // Assumed to be 32 if working with a quant
 layout (constant_id = 4) const uint WM = 32;
 layout (constant_id = 5) const uint WN = 32;
 layout (constant_id = 6) const uint WMITER = 2;
@@ -109,6 +108,14 @@ layout (constant_id = 8) const uint TN = 2;
 layout (constant_id = 9) const uint TK = 1;  // Only needed for coopmat
 layout (constant_id = 10) const uint WARP = 32;
 
+#if defined(DATA_A_F32) || defined(DATA_A_F16)
+#define BK 32
+#define BK_STEP 4
+#else
+layout (constant_id = 3) const uint BK = 16;  // Assumed to be 32 if working with a quant
+#define BK_STEP 2
+#endif
+
 #ifdef COOPMAT
 #define SHMEM_STRIDE (BK / 2 + 4)
 #else
@@ -244,8 +251,13 @@ void main() {
     }
 #else
     ACC_TYPE_VEC2 sums[WMITER * TM * WNITER * TN/2];
+#if defined(DATA_A_F32) || defined(DATA_A_F16)
+    FLOAT_TYPE_VEC4 cache_a[WMITER * TM];
+    FLOAT_TYPE_VEC4 cache_b;
+#else
     FLOAT_TYPE_VEC2 cache_a[WMITER * TM];
     FLOAT_TYPE_VEC2 cache_b;
+#endif
 
     [[unroll]] for (uint i = 0; i < WMITER*TM*WNITER*TN/2; i++) {
         sums[i] = ACC_TYPE_VEC2(0.0f, 0.0f);
@@ -283,24 +295,41 @@ void main() {
             }
         }
 #else
-        [[unroll]] for (uint i = 0; i < BK / 2; i++) {
+        [[unroll]] for (uint i = 0; i < BK / BK_STEP; i++) {
             // Load from shared into cache
             [[unroll]] for (uint wsir = 0; wsir < WMITER; wsir++) {
                 [[unroll]] for (uint j = 0; j < TM; j++) {
+                #if defined(DATA_A_F32) || defined(DATA_A_F16)
+                    cache_a[wsir * TM + j].xy = buf_a[(warp_r * WM + wsir * WSUBM + tiwr * TM + j) * SHMEM_STRIDE + 2 * i    ];
+                    cache_a[wsir * TM + j].zw = buf_a[(warp_r * WM + wsir * WSUBM + tiwr * TM + j) * SHMEM_STRIDE + 2 * i + 1];
+                #else
                     cache_a[wsir * TM + j] = buf_a[(warp_r * WM + wsir * WSUBM + tiwr * TM + j) * SHMEM_STRIDE + i];
+                #endif
                 }
             }
 
             [[unroll]] for (uint wsic = 0; wsic < WNITER; wsic++) {
                 [[unroll]] for (uint cc = 0; cc < TN; cc++) {
+                #if defined(DATA_A_F32) || defined(DATA_A_F16)
+                    cache_b.xy = buf_b[(warp_c * WN + wsic * WSUBN + tiwc * TN + cc) * SHMEM_STRIDE + 2 * i    ];
+                    cache_b.zw = buf_b[(warp_c * WN + wsic * WSUBN + tiwc * TN + cc) * SHMEM_STRIDE + 2 * i + 1];
+                #else
                     cache_b = buf_b[(warp_c * WN + wsic * WSUBN + tiwc * TN + cc) * SHMEM_STRIDE + i];
+                #endif
 
                     [[unroll]] for (uint wsir = 0; wsir < WMITER; wsir++) {
                         [[unroll]] for (uint cr = 0; cr < TM / 2; cr++) {
                             // [WNITER][TN][WMITER][TM / 2] -> [wsic][cc][wsir][cr]
                             const uint sums_idx = (wsic * TN + cc) * WMITER * (TM / 2) + wsir * (TM / 2) + cr;
+                        #if defined(DATA_A_F32) || defined(DATA_A_F16)
+                            sums[sums_idx].x = fma(ACC_TYPE(cache_a[wsir * TM + 2 * cr    ].x), ACC_TYPE(cache_b.x), fma(ACC_TYPE(cache_a[wsir * TM + 2 * cr    ].y), ACC_TYPE(cache_b.y),
+                                               fma(ACC_TYPE(cache_a[wsir * TM + 2 * cr    ].z), ACC_TYPE(cache_b.z), fma(ACC_TYPE(cache_a[wsir * TM + 2 * cr    ].w), ACC_TYPE(cache_b.w), sums[sums_idx].x))));
+                            sums[sums_idx].y = fma(ACC_TYPE(cache_a[wsir * TM + 2 * cr + 1].x), ACC_TYPE(cache_b.x), fma(ACC_TYPE(cache_a[wsir * TM + 2 * cr + 1].y), ACC_TYPE(cache_b.y),
+                                               fma(ACC_TYPE(cache_a[wsir * TM + 2 * cr + 1].z), ACC_TYPE(cache_b.z), fma(ACC_TYPE(cache_a[wsir * TM + 2 * cr + 1].w), ACC_TYPE(cache_b.w), sums[sums_idx].y))));
+                        #else
                             sums[sums_idx].x = fma(ACC_TYPE(cache_a[wsir * TM + 2 * cr    ].x), ACC_TYPE(cache_b.x), fma(ACC_TYPE(cache_a[wsir * TM + 2 * cr    ].y), ACC_TYPE(cache_b.y), sums[sums_idx].x));
                             sums[sums_idx].y = fma(ACC_TYPE(cache_a[wsir * TM + 2 * cr + 1].x), ACC_TYPE(cache_b.x), fma(ACC_TYPE(cache_a[wsir * TM + 2 * cr + 1].y), ACC_TYPE(cache_b.y), sums[sums_idx].y));
+                        #endif
                         }
                     }
                 }

From c1b187688dac5e0f12cb38a63515aa20732d15a8 Mon Sep 17 00:00:00 2001
From: Aman Gupta <amangupta052@gmail.com>
Date: Sat, 8 Nov 2025 16:58:05 +0800
Subject: [PATCH 121/185] CUDA: skip fusion for repeating adds in bias (#17080)

---
 ggml/src/ggml-cuda/CMakeLists.txt |  1 +
 ggml/src/ggml-cuda/ggml-cuda.cu   | 13 +++++++++++--
 tests/test-backend-ops.cpp        | 10 ++++++----
 3 files changed, 18 insertions(+), 6 deletions(-)

diff --git a/ggml/src/ggml-cuda/CMakeLists.txt b/ggml/src/ggml-cuda/CMakeLists.txt
index 30247751359..67af1d8ccc1 100644
--- a/ggml/src/ggml-cuda/CMakeLists.txt
+++ b/ggml/src/ggml-cuda/CMakeLists.txt
@@ -124,6 +124,7 @@ if (CUDAToolkit_FOUND)
 
     if (GGML_CUDA_DEBUG)
         list(APPEND CUDA_FLAGS -lineinfo)
+        add_compile_definitions(GGML_CUDA_DEBUG)
     endif()
 
     if (CUDAToolkit_VERSION VERSION_GREATER_EQUAL "12.8")
diff --git a/ggml/src/ggml-cuda/ggml-cuda.cu b/ggml/src/ggml-cuda/ggml-cuda.cu
index 049aece1b52..2d4314fba4f 100644
--- a/ggml/src/ggml-cuda/ggml-cuda.cu
+++ b/ggml/src/ggml-cuda/ggml-cuda.cu
@@ -3152,8 +3152,6 @@ static void evaluate_and_capture_cuda_graph(ggml_backend_cuda_context * cuda_ctx
 
             for (int i = 0; i < cgraph->n_nodes; i++) {
                 ggml_tensor * node = cgraph->nodes[i];
-
-
 #ifdef GGML_CUDA_DEBUG
                 const int nodes_fused = i - prev_i - 1;
                 prev_i = i;
@@ -3302,6 +3300,13 @@ static void evaluate_and_capture_cuda_graph(ggml_backend_cuda_context * cuda_ctx
                                 continue;
                             }
 
+                            // we don't support repeating adds
+                            if (bias_op == GGML_OP_ADD &&
+                                (!ggml_are_same_shape(gate_bias_n->src[0], gate_bias_n->src[1]) ||
+                                 !ggml_are_same_shape(up_bias_n->src[0], up_bias_n->src[1]))) {
+                                continue;
+                            }
+
                             const ggml_tensor * src0 = up_n->src[0];
                             const ggml_tensor * src1 = up_n->src[1];
                             const ggml_tensor * ids  = up_n->src[2];
@@ -3411,6 +3416,10 @@ static void evaluate_and_capture_cuda_graph(ggml_backend_cuda_context * cuda_ctx
                             continue;
                         }
 
+                        if (bias_op == GGML_OP_ADD && !ggml_are_same_shape(bias_node->src[0], bias_node->src[1])) {
+                            continue;
+                        }
+
                         ggml_cuda_mm_fusion_args_host fusion_data{};
                         fusion_data.x_bias = bias_tensor;
 
diff --git a/tests/test-backend-ops.cpp b/tests/test-backend-ops.cpp
index 80216f6f3a2..31625bcc7a4 100644
--- a/tests/test-backend-ops.cpp
+++ b/tests/test-backend-ops.cpp
@@ -4984,8 +4984,10 @@ struct test_mul_mat_vec_fusion : public test_case {
 
     ggml_tensor * build_graph(ggml_context * ctx) override {
         if (!use_id) {
-            std::array<int64_t, 4> ne = {k, m, 1, 1};
-            std::array<int64_t, 4> ne0 = {k, n, 1, 1};
+            const int              channels = 4;
+            const int              samples  = 2;
+            std::array<int64_t, 4> ne       = { k, m, channels, samples };
+            std::array<int64_t, 4> ne0      = { k, n, channels, samples };
 
             ggml_tensor * cur  = ggml_new_tensor(ctx, GGML_TYPE_F32, 4, ne.data());
             ggml_tensor * gate = with_gate ? ggml_new_tensor(ctx, type, 4, ne0.data()) : nullptr;
@@ -4993,14 +4995,14 @@ struct test_mul_mat_vec_fusion : public test_case {
 
             ggml_tensor * ffn_up = ggml_mul_mat(ctx, up, cur);
             if (with_bias) {
-                std::array<int64_t, 4> bias_ne = {ffn_up->ne[0], 1, 1, 1};
+                std::array<int64_t, 4> bias_ne = { ffn_up->ne[0], 1, channels, samples };
                 ggml_tensor * up_bias = ggml_new_tensor(ctx, GGML_TYPE_F32, 4, bias_ne.data());
                 ffn_up = ggml_add(ctx, ffn_up, up_bias);
             }
 
             ggml_tensor * ffn_gate = with_gate ? ggml_mul_mat(ctx, gate, cur) : nullptr;
             if (with_bias && with_gate) {
-                std::array<int64_t, 4> bias_ne = {ffn_gate->ne[0], 1, 1, 1};
+                std::array<int64_t, 4> bias_ne   = { ffn_gate->ne[0], 1, channels, samples };
                 ggml_tensor * gate_bias = ggml_new_tensor(ctx, GGML_TYPE_F32, 4, bias_ne.data());
                 ffn_gate = ggml_add(ctx, ffn_gate, gate_bias);
             }

From 64fe17fbb84f493dbc33e4c13042953c4f5bfaeb Mon Sep 17 00:00:00 2001
From: Aman Gupta <amangupta052@gmail.com>
Date: Sat, 8 Nov 2025 21:05:19 +0800
Subject: [PATCH 122/185] Revert "CUDA: add expert reduce kernel (#16857)"
 (#17100)

---
 ggml/src/ggml-cuda/ggml-cuda.cu          |  26 ----
 ggml/src/ggml-cuda/moe-expert-reduce.cu  | 168 -----------------------
 ggml/src/ggml-cuda/moe-expert-reduce.cuh |  11 --
 tests/test-backend-ops.cpp               |  58 --------
 4 files changed, 263 deletions(-)
 delete mode 100644 ggml/src/ggml-cuda/moe-expert-reduce.cu
 delete mode 100644 ggml/src/ggml-cuda/moe-expert-reduce.cuh

diff --git a/ggml/src/ggml-cuda/ggml-cuda.cu b/ggml/src/ggml-cuda/ggml-cuda.cu
index 2d4314fba4f..68dc57843e4 100644
--- a/ggml/src/ggml-cuda/ggml-cuda.cu
+++ b/ggml/src/ggml-cuda/ggml-cuda.cu
@@ -27,7 +27,6 @@
 #include "ggml-cuda/mmq.cuh"
 #include "ggml-cuda/mmvf.cuh"
 #include "ggml-cuda/mmvq.cuh"
-#include "ggml-cuda/moe-expert-reduce.cuh"
 #include "ggml-cuda/norm.cuh"
 #include "ggml-cuda/opt-step-adamw.cuh"
 #include "ggml-cuda/opt-step-sgd.cuh"
@@ -3197,31 +3196,6 @@ static void evaluate_and_capture_cuda_graph(ggml_backend_cuda_context * cuda_ctx
                         continue;
                     }
 
-                    if (node->op == GGML_OP_MUL) {
-                        int current_node = i + 1;
-                        int num_views    = 0;
-                        int num_adds     = 0;
-                        while (current_node < cgraph->n_nodes && cgraph->nodes[current_node]->op == GGML_OP_VIEW) {
-                            num_views++;
-                            current_node++;
-                        }
-
-                        while (current_node < cgraph->n_nodes && cgraph->nodes[current_node]->op == GGML_OP_ADD &&
-                                num_adds < num_views - 1) {
-                            num_adds++;
-                            current_node++;
-                        }
-
-                        if (num_adds == num_views - 1 && num_views > 0) {
-                            ggml_tensor * dst_node = cgraph->nodes[current_node - 1];
-                            if (ggml_cuda_should_use_moe_expert_reduce(cgraph, i, current_node)) {
-                                ggml_cuda_op_moe_expert_reduce(*cuda_ctx, node->src[0], node->src[1], dst_node);
-                                i += num_views + num_adds;
-                                continue;
-                            }
-                        }
-                    }
-
                     if (node->op == GGML_OP_ADD) {
                         int n_fuse = 0;
                         ggml_op ops[8];
diff --git a/ggml/src/ggml-cuda/moe-expert-reduce.cu b/ggml/src/ggml-cuda/moe-expert-reduce.cu
deleted file mode 100644
index a97c5d573bb..00000000000
--- a/ggml/src/ggml-cuda/moe-expert-reduce.cu
+++ /dev/null
@@ -1,168 +0,0 @@
-#include "moe-expert-reduce.cuh"
-
-// This kernel is a fusion of the expert weight reduce, common in MoE models
-
-template <int n_expert_used_template>
-__global__ void moe_expert_reduce_cuda(const float * __restrict__ experts,
-                                       const float * __restrict__ weights,
-                                       float * __restrict__ dst,
-                                       const int n_expert_used,
-                                       const int n_cols) {
-    const int row = blockIdx.x;
-    const int col = blockIdx.y * blockDim.x + threadIdx.x;
-    if (col >= n_cols) {
-        return;
-    }
-
-    experts += row * n_cols * n_expert_used;
-    weights += row * n_expert_used;
-    dst += row * n_cols;
-
-    float acc = 0.f;
-    if constexpr (n_expert_used_template == 0) {
-        for (int expert = 0; expert < n_expert_used; ++expert) {
-            ggml_cuda_mad(acc, experts[col], weights[expert]);
-            experts += n_cols;
-        }
-        dst[col] = acc;
-    } else {
-#pragma unroll
-        for (int i = 0; i < n_expert_used_template; ++i) {
-            ggml_cuda_mad(acc, experts[col], weights[i]);
-            experts += n_cols;
-        }
-        dst[col] = acc;
-    }
-}
-
-static void launch_moe_expert_reduce(ggml_backend_cuda_context & ctx,
-                                     const float *               experts,
-                                     const float *               weights,
-                                     float *                     dst,
-                                     const int                   n_expert_used,
-                                     const int                   n_cols,
-                                     const int                   n_rows) {
-    const int block_size = 32;
-
-    const int n_blocks_x = n_rows;
-    const int n_blocks_y = (n_cols + block_size - 1) / block_size;
-
-    dim3 block_dims(block_size);
-    dim3 grid_dims(n_blocks_x, n_blocks_y);
-
-    cudaStream_t stream = ctx.stream();
-    switch (n_expert_used) {
-        case 1:
-            moe_expert_reduce_cuda<1>
-                <<<grid_dims, block_dims, 0, stream>>>(experts, weights, dst, n_expert_used, n_cols);
-            break;
-        case 2:
-            moe_expert_reduce_cuda<2>
-                <<<grid_dims, block_dims, 0, stream>>>(experts, weights, dst, n_expert_used, n_cols);
-            break;
-        case 4:
-            moe_expert_reduce_cuda<4>
-                <<<grid_dims, block_dims, 0, stream>>>(experts, weights, dst, n_expert_used, n_cols);
-            break;
-        case 6:
-            moe_expert_reduce_cuda<6>
-                <<<grid_dims, block_dims, 0, stream>>>(experts, weights, dst, n_expert_used, n_cols);
-            break;
-        case 8:
-            moe_expert_reduce_cuda<8>
-                <<<grid_dims, block_dims, 0, stream>>>(experts, weights, dst, n_expert_used, n_cols);
-            break;
-        case 16:
-            moe_expert_reduce_cuda<16>
-                <<<grid_dims, block_dims, 0, stream>>>(experts, weights, dst, n_expert_used, n_cols);
-            break;
-        case 32:
-            moe_expert_reduce_cuda<32>
-                <<<grid_dims, block_dims, 0, stream>>>(experts, weights, dst, n_expert_used, n_cols);
-            break;
-        case 64:
-            moe_expert_reduce_cuda<64>
-                <<<grid_dims, block_dims, 0, stream>>>(experts, weights, dst, n_expert_used, n_cols);
-            break;
-        case 128:
-            moe_expert_reduce_cuda<128>
-                <<<grid_dims, block_dims, 0, stream>>>(experts, weights, dst, n_expert_used, n_cols);
-            break;
-        default:
-            moe_expert_reduce_cuda<0>
-                <<<grid_dims, block_dims, 0, stream>>>(experts, weights, dst, n_expert_used, n_cols);
-            break;
-    }
-}
-
-bool ggml_cuda_should_use_moe_expert_reduce(const ggml_cgraph * cgraph, int start_index, int end_index) {
-    const ggml_tensor * mul = cgraph->nodes[start_index];
-
-    if (mul->op != GGML_OP_MUL || !ggml_is_contiguous(mul->src[0]) || !ggml_is_contiguous(mul->src[1])) {
-        return false;
-    }
-
-    int    current_node   = start_index + 1;
-    size_t current_offset = 0;
-
-    std::vector<const ggml_tensor *> view_nodes;
-    //check if all are views of the expert in increasing order
-    while (current_node < end_index && cgraph->nodes[current_node]->op == GGML_OP_VIEW) {
-        const ggml_tensor * node = cgraph->nodes[current_node];
-        if (node->view_src != mul) {
-            return false;
-        }
-        if (node->view_offs < current_offset) {
-            return false;
-        }
-        current_offset = node->view_offs;
-        current_node++;
-        view_nodes.push_back(node);
-    }
-
-    //check if all the adds are in increasing order
-    const ggml_tensor * prev_add_src = view_nodes.empty() ? nullptr : view_nodes[0];
-    int                 num_adds     = 0;
-    int                 num_views    = view_nodes.size();
-    while (current_node < end_index && cgraph->nodes[current_node]->op == GGML_OP_ADD) {
-        const ggml_tensor * add_node = cgraph->nodes[current_node];
-
-        bool is_first_op_ok  = num_views > num_adds ? add_node->src[0] == prev_add_src : false;
-        bool is_second_op_ok = num_views > num_adds ? add_node->src[1] == view_nodes[num_adds + 1] : false;
-
-        if (!is_first_op_ok || !is_second_op_ok) {
-            return false;
-        }
-        prev_add_src = add_node;
-
-        num_adds++;
-        current_node++;
-    }
-
-    if (num_views != num_adds + 1) {
-        return false;
-    }
-
-    return true;
-}
-
-void ggml_cuda_op_moe_expert_reduce(ggml_backend_cuda_context & ctx,
-                                    const ggml_tensor *         experts,
-                                    const ggml_tensor *         weights,
-                                    ggml_tensor *               dst) {
-    const int n_rows        = experts->ne[2];
-    const int n_expert_used = experts->ne[1];
-    const int n_cols        = experts->ne[0];
-
-    GGML_ASSERT(experts->type == GGML_TYPE_F32);
-    GGML_ASSERT(weights->type == GGML_TYPE_F32);
-    GGML_ASSERT(ggml_is_contiguous(experts));
-    GGML_ASSERT(ggml_is_contiguous(weights));
-    GGML_ASSERT(dst->type == GGML_TYPE_F32);
-
-    const float * experts_d = (const float *) experts->data;
-    const float * weights_d = (const float *) weights->data;
-    float *       dst_d     = (float *) dst->data;
-
-    launch_moe_expert_reduce(ctx, experts_d, weights_d, dst_d, n_expert_used, n_cols, n_rows);
-}
diff --git a/ggml/src/ggml-cuda/moe-expert-reduce.cuh b/ggml/src/ggml-cuda/moe-expert-reduce.cuh
deleted file mode 100644
index cafc50e104a..00000000000
--- a/ggml/src/ggml-cuda/moe-expert-reduce.cuh
+++ /dev/null
@@ -1,11 +0,0 @@
-#include "common.cuh"
-#include "ggml.h"
-
-#include <initializer_list>
-
-void ggml_cuda_op_moe_expert_reduce(ggml_backend_cuda_context & ctx,
-                                    const ggml_tensor *         experts,
-                                    const ggml_tensor *         weights,
-                                    ggml_tensor *               dst);
-
-bool ggml_cuda_should_use_moe_expert_reduce(const ggml_cgraph * cgraph, int start_index, int end_index);
diff --git a/tests/test-backend-ops.cpp b/tests/test-backend-ops.cpp
index 31625bcc7a4..2470c148d66 100644
--- a/tests/test-backend-ops.cpp
+++ b/tests/test-backend-ops.cpp
@@ -4882,60 +4882,6 @@ struct test_topk_moe: public test_case {
     }
 };
 
-struct test_moe_expert_reduce : public test_case {
-    const int64_t n_embd;
-    const int64_t n_tokens;
-    const int64_t n_expert_used;
-
-    test_moe_expert_reduce(int64_t n_embd = 64, int64_t n_tokens = 5, int64_t n_expert_used = 4)
-        : n_embd(n_embd), n_tokens(n_tokens), n_expert_used(n_expert_used) {
-        GGML_ASSERT(n_expert_used > 1);
-    }
-
-    std::string vars() override {
-        return VARS_TO_STR3(n_embd, n_tokens, n_expert_used);
-    }
-
-    std::string op_desc(ggml_tensor * t) override {
-        GGML_UNUSED(t);
-        return "MOE_EXPERT_REDUCE";
-    }
-
-    bool run_whole_graph() override { return true; }
-
-    ggml_tensor * build_graph(ggml_context * ctx) override {
-        ggml_tensor * experts = ggml_new_tensor_3d(ctx, GGML_TYPE_F32, n_embd, n_expert_used, n_tokens);
-        ggml_set_name(experts, "experts");
-
-        ggml_tensor * weights = ggml_new_tensor_3d(ctx, GGML_TYPE_F32, 1, n_expert_used, n_tokens);
-        ggml_set_name(weights, "weights");
-
-        ggml_tensor * weighted = ggml_mul(ctx, experts, weights);
-        ggml_set_name(weighted, "weighted_experts");
-
-        std::vector<ggml_tensor *> expert_views(n_expert_used);
-        for (int64_t i = 0; i < n_expert_used; ++i) {
-            expert_views[i] = ggml_view_2d(ctx, weighted, n_embd, n_tokens, weighted->nb[2], i * weighted->nb[1]);
-
-            std::string name = "expert_view_" + std::to_string(i);
-            ggml_set_name(expert_views[i], name.c_str());
-            ggml_build_forward_expand(gf, expert_views[i]);
-        }
-
-        ggml_tensor * moe_out = expert_views[0];
-        for (int64_t i = 1; i < n_expert_used; ++i) {
-            moe_out = ggml_add(ctx, moe_out, expert_views[i]);
-
-            std::string name = "expert_add_" + std::to_string(i - 1);
-            ggml_set_name(moe_out, name.c_str());
-        }
-
-        ggml_set_name(moe_out, "moe_out");
-
-        return moe_out;
-    }
-};
-
 struct test_mul_mat_vec_fusion : public test_case {
     const ggml_type type;
     const ggml_glu_op glu_op;
@@ -7415,10 +7361,6 @@ static std::vector<std::unique_ptr<test_case>> make_test_cases_eval() {
     test_cases.emplace_back(new test_topk_moe({ 8, 22, 1, 1 }, 4, /*with_norm*/ false, /*delayed_softmax*/ true));
     test_cases.emplace_back(new test_topk_moe({ 32, 22, 1, 1 }, 8, /*with_norm*/ false, /*delayed_softmax*/ true));
 
-    test_cases.emplace_back(new test_moe_expert_reduce(1024, 5, 4));
-    test_cases.emplace_back(new test_moe_expert_reduce(80, 3, 6));
-    test_cases.emplace_back(new test_moe_expert_reduce(80, 3, 7));
-
 #if 0
     // these tests are disabled to save execution time, sbut they can be handy for debugging
     test_cases.emplace_back(new test_llama(2, true));

From eeee367de51fb34d46c8103fc0ae827e84d94470 Mon Sep 17 00:00:00 2001
From: Aidan <99101158+gSUz92nc@users.noreply.github.com>
Date: Sat, 8 Nov 2025 13:12:11 +0000
Subject: [PATCH 123/185] server: fix correct time_ms calculation in
 prompt_progress (#17093)

* fix: correct time_ms calculation in send_partial_response

The time_ms field was incorrectly calculated. The division was happening
before the subtraction leading to incorrect values.

Before: (ggml_time_us() - slot.t_start_process_prompt / 1000) After:
(ggml_time_us() - slot.t_start_process_prompt) / 1000

* docs : document time_ms field in prompt_progress
---
 tools/server/README.md  | 2 +-
 tools/server/server.cpp | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/tools/server/README.md b/tools/server/README.md
index 6828ef73824..8fd478eb328 100644
--- a/tools/server/README.md
+++ b/tools/server/README.md
@@ -512,7 +512,7 @@ These words will not be included in the completion, so make sure to add them to
 
 `timings_per_token`: Include prompt processing and text generation speed information in each response.  Default: `false`
 
-`return_progress`: Include prompt processing progress in `stream` mode. The progress will be contained inside `prompt_progress` with 3 values: `total`, `cache` and `processed`. The overall progress is `processed/total`, while the actual timed progress is `(processed-cache)/(total-cache)`. Default: `false`
+`return_progress`: Include prompt processing progress in `stream` mode. The progress will be contained inside `prompt_progress` with 4 values: `total`, `cache`, `processed`, and `time_ms`. The overall progress is `processed/total`, while the actual timed progress is `(processed-cache)/(total-cache)`. The `time_ms` field contains the elapsed time in milliseconds since prompt processing started. Default: `false`
 
 `post_sampling_probs`: Returns the probabilities of top `n_probs` tokens after applying sampling chain.
 
diff --git a/tools/server/server.cpp b/tools/server/server.cpp
index 164e8cf4e70..9d91e32d1fb 100644
--- a/tools/server/server.cpp
+++ b/tools/server/server.cpp
@@ -3078,7 +3078,7 @@ struct server_context {
             res->progress.total     = slot.task->n_tokens();
             res->progress.cache     = slot.n_prompt_tokens_cache;
             res->progress.processed = slot.prompt.tokens.size();
-            res->progress.time_ms   = (ggml_time_us() - slot.t_start_process_prompt / 1000);
+            res->progress.time_ms   = (ggml_time_us() - slot.t_start_process_prompt) / 1000;
         } else {
             res->content = tkn.text_to_send;
             res->tokens  = { tkn.tok };

From 53d7d21e6128af43020190100b7f91d7bdce93c5 Mon Sep 17 00:00:00 2001
From: Jeff Bolz <jbolz@nvidia.com>
Date: Sat, 8 Nov 2025 13:24:29 -0600
Subject: [PATCH 124/185] vulkan: Use spec constants for conv2d s/d/p and
 kernel W/H (#16978)

* vulkan: Use spec constants for conv2d s/d/p and kernel W/H

Also add some additional unroll hints, which seems to help.

* lock around map lookup
---
 ggml/src/ggml-vulkan/ggml-vulkan.cpp          | 114 ++++++++++++------
 .../ggml-vulkan/vulkan-shaders/conv2d_mm.comp |  75 ++++++------
 2 files changed, 118 insertions(+), 71 deletions(-)

diff --git a/ggml/src/ggml-vulkan/ggml-vulkan.cpp b/ggml/src/ggml-vulkan/ggml-vulkan.cpp
index 9c2aeb57f00..6da7bbd2f61 100644
--- a/ggml/src/ggml-vulkan/ggml-vulkan.cpp
+++ b/ggml/src/ggml-vulkan/ggml-vulkan.cpp
@@ -351,6 +351,12 @@ enum vk_conv_shapes {
     CONV_SHAPE_COUNT,
 };
 
+uint32_t conv_shapes_wg_denoms[][3] = {
+    { 128, 128, 1 },
+    {  64,  32, 1 },
+    {  32, 256, 1 },
+};
+
 enum dmmv_wg_sizes {
     DMMV_WG_SIZE_SUBGROUP,
     DMMV_WG_SIZE_LARGE,
@@ -379,6 +385,18 @@ struct vk_fa_pipeline_state {
     }
 };
 
+struct vk_conv2d_pipeline_state {
+    vk_conv2d_pipeline_state(uint32_t s0, uint32_t s1, uint32_t p0, uint32_t p1, uint32_t d0, uint32_t d1, uint32_t KW, uint32_t KH)
+        : s0(s0), s1(s1), p0(p0), p1(p1), d0(d0), d1(d1), KW(KW), KH(KH) {}
+
+    uint32_t s0, s1, p0, p1, d0, d1, KW, KH;
+
+    bool operator<(const vk_conv2d_pipeline_state &b) const {
+        return std::tie(s0, s1, p0, p1, d0, d1, KW, KH) <
+               std::tie(b.s0, b.s1, b.p0, b.p1, b.d0, b.d1, b.KW, b.KH);
+    }
+};
+
 enum shader_reduction_mode {
     SHADER_REDUCTION_MODE_SHMEM,
     SHADER_REDUCTION_MODE_HYBRID,
@@ -675,10 +693,10 @@ struct vk_device_struct {
     vk_pipeline pipeline_ssm_conv_f32;
     vk_pipeline pipeline_opt_step_adamw_f32;
     vk_pipeline pipeline_opt_step_sgd_f32;
-    vk_pipeline pipeline_conv2d_f32[CONV_SHAPE_COUNT];
-    vk_pipeline pipeline_conv2d_f16_f32[CONV_SHAPE_COUNT];
-    vk_pipeline pipeline_conv_transpose_2d_f32[CONV_SHAPE_COUNT];
-    vk_pipeline pipeline_conv_transpose_2d_f16_f32[CONV_SHAPE_COUNT];
+    std::map<vk_conv2d_pipeline_state, vk_pipeline> pipeline_conv2d_f32[CONV_SHAPE_COUNT];
+    std::map<vk_conv2d_pipeline_state, vk_pipeline> pipeline_conv2d_f16_f32[CONV_SHAPE_COUNT];
+    std::map<vk_conv2d_pipeline_state, vk_pipeline> pipeline_conv_transpose_2d_f32[CONV_SHAPE_COUNT];
+    std::map<vk_conv2d_pipeline_state, vk_pipeline> pipeline_conv_transpose_2d_f16_f32[CONV_SHAPE_COUNT];
     vk_pipeline pipeline_conv2d_dw_whcn_f32, pipeline_conv2d_dw_whcn_f16_f32;
     vk_pipeline pipeline_conv2d_dw_cwhn_f32, pipeline_conv2d_dw_cwhn_f16_f32;
 
@@ -1258,17 +1276,13 @@ struct vk_op_conv2d_push_constants {
     uint32_t nb2;
     uint32_t nb3;
 
-    // init_fastdiv_values constants for dividing by KW, KW*KH, OW, OW*OH
-    uint32_t KWmp;   uint32_t KWL;
-    uint32_t KWKHmp; uint32_t KWKHL;
+    // init_fastdiv_values constants for dividing by OW, OW*OH
     uint32_t OWmp;   uint32_t OWL;
     uint32_t OWOHmp; uint32_t OWOHL;
 };
 
 template <> void init_pushconst_fastdiv(vk_op_conv2d_push_constants &p) {
-    // Compute magic values to divide by KW, KW*KH, OW, OW*OH
-    init_fastdiv_values(p.KW,       p.KWmp,    p.KWL);
-    init_fastdiv_values(p.KW*p.KH,  p.KWKHmp,  p.KWKHL);
+    // Compute magic values to divide by OW, OW*OH
     init_fastdiv_values(p.OW,       p.OWmp,    p.OWL);
     init_fastdiv_values(p.OW*p.OH,  p.OWOHmp,  p.OWOHL);
 }
@@ -1304,23 +1318,15 @@ struct vk_op_conv_transpose_2d_push_constants {
     uint32_t nb2;
     uint32_t nb3;
 
-    // init_fastdiv_values constants for dividing by KW, KW*KH, OW, OW*OH, s0, s1
-    uint32_t KWmp;   uint32_t KWL;
-    uint32_t KWKHmp; uint32_t KWKHL;
+    // init_fastdiv_values constants for dividing by OW, OW*OH
     uint32_t OWmp;   uint32_t OWL;
     uint32_t OWOHmp; uint32_t OWOHL;
-    uint32_t s0mp; uint32_t s0L;
-    uint32_t s1mp; uint32_t s1L;
 };
 
 template <> void init_pushconst_fastdiv(vk_op_conv_transpose_2d_push_constants &p) {
-    // Compute magic values to divide by KW, KW*KH, OW, OW*OH, s0, s1
-    init_fastdiv_values(p.KW,       p.KWmp,    p.KWL);
-    init_fastdiv_values(p.KW*p.KH,  p.KWKHmp,  p.KWKHL);
+    // Compute magic values to divide by OW, OW*OH
     init_fastdiv_values(p.OW,       p.OWmp,    p.OWL);
     init_fastdiv_values(p.OW*p.OH,  p.OWOHmp,  p.OWOHL);
-    init_fastdiv_values(p.s0,       p.s0mp,    p.s0L);
-    init_fastdiv_values(p.s1,       p.s1mp,    p.s1L);
 }
 
 struct vk_op_conv2d_dw_push_constants {
@@ -3858,22 +3864,22 @@ static void ggml_vk_load_shaders(vk_device& device) {
         switch (s) {
         default:
         case CONV_SHAPE_128x128:
-            conv2d_BS_K = 128;
-            conv2d_BS_NPQ = 128;
+            conv2d_BS_K = conv_shapes_wg_denoms[CONV_SHAPE_128x128][0];
+            conv2d_BS_NPQ = conv_shapes_wg_denoms[CONV_SHAPE_128x128][1];
             conv2d_BS_CRS = 16;
             if (device->vendor_id == VK_VENDOR_ID_AMD && device->architecture != vk_device_architecture::AMD_GCN) {
                 conv2d_UNROLL = false;
             }
             break;
         case CONV_SHAPE_64x32:
-            conv2d_BS_K = 64;
-            conv2d_BS_NPQ = 32;
+            conv2d_BS_K = conv_shapes_wg_denoms[CONV_SHAPE_64x32][0];
+            conv2d_BS_NPQ = conv_shapes_wg_denoms[CONV_SHAPE_64x32][1];
             conv2d_BS_CRS = 32;
             conv2d_TS_K   = 4;
             break;
         case CONV_SHAPE_32x256:
-            conv2d_BS_K = 32;
-            conv2d_BS_NPQ = 256;
+            conv2d_BS_K = conv_shapes_wg_denoms[CONV_SHAPE_32x256][0];
+            conv2d_BS_NPQ = conv_shapes_wg_denoms[CONV_SHAPE_32x256][1];
             conv2d_BS_CRS = 16;
             break;
         }
@@ -3907,10 +3913,22 @@ static void ggml_vk_load_shaders(vk_device& device) {
         std::vector<uint32_t> spec_constants = { conv2d_WG_SIZE, conv2d_BS_K, conv2d_BS_CRS, conv2d_BS_NPQ, conv2d_TS_K, use_collectives, conv2d_SHMEM_PAD };
 
 #define CREATE_CONV(name, type_suffix, spv_suffix) \
-        ggml_vk_create_pipeline( \
-            device, device->pipeline_##name##type_suffix[s], #name #type_suffix, \
-            name##type_suffix##spv_suffix##_len, name##type_suffix##spv_suffix##_data, "main", 3, \
-            sizeof(vk_op_##name##_push_constants), wg_denoms, spec_constants, 1, true, use_collectives);
+        for (auto &c : device->pipeline_##name##type_suffix[s]) { \
+            const vk_conv2d_pipeline_state &state = c.first;  \
+            std::vector<uint32_t> spec_constants_cpy = spec_constants; \
+            spec_constants_cpy.push_back(state.s0); \
+            spec_constants_cpy.push_back(state.s1); \
+            spec_constants_cpy.push_back(state.p0); \
+            spec_constants_cpy.push_back(state.p1); \
+            spec_constants_cpy.push_back(state.d0); \
+            spec_constants_cpy.push_back(state.d1); \
+            spec_constants_cpy.push_back(state.KW); \
+            spec_constants_cpy.push_back(state.KH); \
+            ggml_vk_create_pipeline( \
+                device, c.second, #name #type_suffix, \
+                name##type_suffix##spv_suffix##_len, name##type_suffix##spv_suffix##_data, "main", 3, \
+                sizeof(vk_op_##name##_push_constants), wg_denoms, spec_constants_cpy, 1, true, use_collectives);    \
+        }
 #define CREATE_CONVS(spv_suffix) \
         CREATE_CONV(conv2d, _f32, spv_suffix) \
         CREATE_CONV(conv2d, _f16_f32, spv_suffix) \
@@ -8536,7 +8554,7 @@ static vk_pipeline ggml_vk_op_get_pipeline(ggml_backend_vk_context * ctx, const
 
             uint32_t tiles[CONV_SHAPE_COUNT];
             for (uint32_t i = 0; i < CONV_SHAPE_COUNT; ++i) {
-                tiles[i] = CEIL_DIV(elements[0], ctx->device->pipeline_conv2d_f32[i]->wg_denoms[0]) * CEIL_DIV(elements[1], ctx->device->pipeline_conv2d_f32[i]->wg_denoms[1]);
+                tiles[i] = CEIL_DIV(elements[0], conv_shapes_wg_denoms[i][0]) * CEIL_DIV(elements[1], conv_shapes_wg_denoms[i][1]);
             }
 
             // We can't query number of shader cores on Intel, use 32 as a placeholder
@@ -8551,19 +8569,45 @@ static vk_pipeline ggml_vk_op_get_pipeline(ggml_backend_vk_context * ctx, const
                 shape = CONV_SHAPE_64x32;
             }
 
+            uint32_t KW = static_cast<uint32_t>(src0->ne[0]);
+            uint32_t KH = static_cast<uint32_t>(src0->ne[1]);
+            uint32_t s0 = static_cast<uint32_t>(dst->op_params[0]);
+            uint32_t s1 = op == GGML_OP_CONV_2D ? static_cast<uint32_t>(dst->op_params[1]) : static_cast<uint32_t>(dst->op_params[0]);
+            uint32_t p0 = op == GGML_OP_CONV_2D ? static_cast<uint32_t>(dst->op_params[2]) : 0;
+            uint32_t p1 = op == GGML_OP_CONV_2D ? static_cast<uint32_t>(dst->op_params[3]) : 0;
+            uint32_t d0 = op == GGML_OP_CONV_2D ? static_cast<uint32_t>(dst->op_params[4]) : 1;
+            uint32_t d1 = op == GGML_OP_CONV_2D ? static_cast<uint32_t>(dst->op_params[5]) : 1;
+
+            vk_conv2d_pipeline_state conv2d_pipeline_state(s0, s1, p0, p1, d0, d1, KW, KH);
+
+            std::map<vk_conv2d_pipeline_state, vk_pipeline> *pipelines = nullptr;
             if (op == GGML_OP_CONV_2D) {
                 if (src0->type == GGML_TYPE_F32) {
-                    return ctx->device->pipeline_conv2d_f32[shape];
+                    pipelines = &ctx->device->pipeline_conv2d_f32[shape];
                 } else if (src0->type == GGML_TYPE_F16) {
-                    return ctx->device->pipeline_conv2d_f16_f32[shape];
+                    pipelines = &ctx->device->pipeline_conv2d_f16_f32[shape];
                 }
             } else if (op == GGML_OP_CONV_TRANSPOSE_2D) {
                 if (src0->type == GGML_TYPE_F32) {
-                    return ctx->device->pipeline_conv_transpose_2d_f32[shape];
+                    pipelines = &ctx->device->pipeline_conv_transpose_2d_f32[shape];
                 } else if (src0->type == GGML_TYPE_F16) {
-                    return ctx->device->pipeline_conv_transpose_2d_f16_f32[shape];
+                    pipelines = &ctx->device->pipeline_conv_transpose_2d_f16_f32[shape];
+                }
+            }
+
+            vk_pipeline pipeline = nullptr;
+
+            {
+                std::lock_guard<std::recursive_mutex> guard(ctx->device->mutex);
+                auto it = pipelines->find(conv2d_pipeline_state);
+                if (it != pipelines->end()) {
+                    pipeline = it->second;
+                } else {
+                    (*pipelines)[conv2d_pipeline_state] = pipeline = std::make_shared<vk_pipeline_struct>();
                 }
             }
+
+            return pipeline;
         }
         return nullptr;
     case GGML_OP_CONV_2D_DW:
diff --git a/ggml/src/ggml-vulkan/vulkan-shaders/conv2d_mm.comp b/ggml/src/ggml-vulkan/vulkan-shaders/conv2d_mm.comp
index 0367e80bbfa..e9bdbf7db5e 100644
--- a/ggml/src/ggml-vulkan/vulkan-shaders/conv2d_mm.comp
+++ b/ggml/src/ggml-vulkan/vulkan-shaders/conv2d_mm.comp
@@ -62,14 +62,8 @@ layout(push_constant) uniform parameter {
     uint32_t nb3;
 
     // fastdiv helper values
-    uint32_t KWmp;   uint32_t KWL;
-    uint32_t KWKHmp; uint32_t KWKHL;
     uint32_t OWmp;   uint32_t OWL;
     uint32_t OWOHmp; uint32_t OWOHL;
-#ifdef TRANSPOSE
-    uint32_t s0mp; uint32_t s0L;
-    uint32_t s1mp; uint32_t s1L;
-#endif
 }
 
 p;
@@ -84,6 +78,15 @@ layout(constant_id = 4) const uint TS_K            = 8;
 layout(constant_id = 5) const uint use_collectives = 1;
 layout(constant_id = 6) const uint SHMEM_PAD       = 4;
 
+layout(constant_id = 7)  const uint s0             = 1;
+layout(constant_id = 8)  const uint s1             = 1;
+layout(constant_id = 9)  const uint p0             = 0;
+layout(constant_id = 10) const uint p1             = 0;
+layout(constant_id = 11) const uint d0             = 1;
+layout(constant_id = 12) const uint d1             = 1;
+layout(constant_id = 13) const uint KW             = 1;
+layout(constant_id = 14) const uint KH             = 1;
+
 uint32_t       tid     = gl_LocalInvocationID.x;
 const uint32_t WG_SIZE = gl_WorkGroupSize.x;
 
@@ -92,7 +95,7 @@ uint splitWork(uint work_size, uint block_size) {
 }
 
 uint32_t K   = p.Cout;
-uint32_t CRS = p.Cin * p.KH * p.KW;
+uint32_t CRS = p.Cin * KH * KW;
 uint32_t NPQ = p.N * p.OH * p.OW;
 
 uint32_t n_elems_out = K * NPQ;
@@ -187,7 +190,7 @@ void main() {
     }
 #endif
     /* Advance block in CRS dim */
-    for (uint32_t B_idx_CRS = 0; B_idx_CRS < NB_CRS; B_idx_CRS++) {
+    [[dont_unroll]] for (uint32_t B_idx_CRS = 0; B_idx_CRS < NB_CRS; B_idx_CRS++) {
         uint32_t CRS_idx_a;
         uint32_t Cin_idx_a;
         uint32_t KH_idx_a;
@@ -200,10 +203,10 @@ void main() {
         uint32_t cached_KW_idx;
         if (use_collectives == 1) {
             cached_CRS_idx                = B_idx_CRS * BS_CRS + gl_SubgroupInvocationID;
-            cached_Cin_idx                = fastdiv(cached_CRS_idx, p.KWKHmp, p.KWKHL); // divide by (p.KW * p.KH);
-            uint32_t cached_CRS_remainder = (cached_CRS_idx - cached_Cin_idx * p.KW * p.KH);
-            cached_KH_idx                 = fastdiv(cached_CRS_remainder, p.KWmp, p.KWL); // divide by p.KW;
-            cached_KW_idx                 = cached_CRS_remainder - cached_KH_idx * p.KW;
+            cached_Cin_idx                = cached_CRS_idx / (KW * KH);
+            uint32_t cached_CRS_remainder = cached_CRS_idx % (KW * KH);
+            cached_KH_idx                 = cached_CRS_remainder / KW;
+            cached_KW_idx                 = cached_CRS_remainder % KW;
 
             CRS_idx_a = subgroupShuffle(cached_CRS_idx, Ac);
             Cin_idx_a = subgroupShuffle(cached_Cin_idx, Ac);
@@ -211,21 +214,21 @@ void main() {
             KW_idx_a  = subgroupShuffle(cached_KW_idx, Ac);
         } else {
             CRS_idx_a              = B_idx_CRS * BS_CRS + Ac;  // Global CRS_idx_a (column index of A)
-            Cin_idx_a              = fastdiv(CRS_idx_a, p.KWKHmp, p.KWKHL); // divide by (p.KW * p.KH);
-            uint32_t CRS_remainder = CRS_idx_a - Cin_idx_a * p.KW * p.KH;
-            KH_idx_a               = fastdiv(CRS_remainder, p.KWmp, p.KWL); // divide by p.KW;
-            KW_idx_a               = CRS_remainder - KH_idx_a * p.KW;
+            Cin_idx_a              = CRS_idx_a / (KW * KH);
+            uint32_t CRS_remainder = CRS_idx_a % (KW * KH);
+            KH_idx_a               = CRS_remainder / KW;
+            KW_idx_a               = CRS_remainder % KW;
         }
 #else
         CRS_idx_a     = B_idx_CRS * BS_CRS + Ac;  // Global CRS_idx_a (column index of A)
-        Cin_idx_a     = fastdiv(CRS_idx_a, p.KWKHmp, p.KWKHL); // divide by (p.KW * p.KH); / (p.KW * p.KH);
-        CRS_remainder = CRS_idx_a - Cin_idx_a * p.KW * p.KH;
-        KH_idx_a      = fastdiv(CRS_remainder, p.KWmp, p.KWL); // divide by p.KW;
-        KW_idx_a      = CRS_remainder - KH_idx_a * p.KW;
+        Cin_idx_a     = CRS_idx_a / (KW * KH);
+        CRS_remainder = CRS_idx_a % (KW * KH);
+        KH_idx_a      = CRS_remainder / KW;
+        KW_idx_a      = CRS_remainder % KW;
 #endif
 
         /* Load kernel to A_block: (BS_K x BS_CRS)*/
-        for (uint32_t r_offset = 0; r_offset < BS_K; r_offset += ArpWg) {
+        UNROLL for (uint32_t r_offset = 0; r_offset < BS_K; r_offset += ArpWg) {
             uint32_t B_ly    = r_offset + Ar;
             uint32_t B_lx    = Ac;
             uint32_t K_idx   = B_idx_K * BS_K + B_ly; /* Global K_idx (row index of A)*/
@@ -262,27 +265,27 @@ void main() {
                 KW_idx_b  = subgroupShuffle(cached_KW_idx, r_offset + Br);
             } else {
                 CRS_idx_b              = B_idx_CRS * BS_CRS + B_ly; /* Global CRS index (row index of B) */
-                Cin_idx_b              = fastdiv(CRS_idx_b, p.KWKHmp, p.KWKHL); // divide by (p.KW * p.KH);
-                uint32_t CRS_remainder = CRS_idx_b - Cin_idx_b * p.KW * p.KH;
-                KH_idx_b               = fastdiv(CRS_remainder, p.KWmp, p.KWL); // divide by p.KW;
-                KW_idx_b               = CRS_remainder - KH_idx_b * p.KW;
+                Cin_idx_b              = CRS_idx_b / (KW * KH);
+                uint32_t CRS_remainder = CRS_idx_b % (KW * KH);
+                KH_idx_b               = CRS_remainder / KW;
+                KW_idx_b               = CRS_remainder % KW;
             }
 #else
             CRS_idx_b              = B_idx_CRS * BS_CRS + B_ly; /* Global CRS index (row index of B) */
-            Cin_idx_b              = fastdiv(CRS_idx_b, p.KWKHmp, p.KWKHL); // divide by (p.KW * p.KH);
-            uint32_t CRS_remainder = CRS_idx_b - Cin_idx_b * p.KW * p.KH;
-            KH_idx_b               = fastdiv(CRS_remainder, p.KWmp, p.KWL); // divide by p.KW;
-            KW_idx_b               = CRS_remainder - KH_idx_b * p.KW;
+            Cin_idx_b              = CRS_idx_b / (KW * KH);
+            uint32_t CRS_remainder = CRS_idx_b % (KW * KH);
+            KH_idx_b               = CRS_remainder / KW;
+            KW_idx_b               = CRS_remainder % KW;
 #endif
 
 #ifdef TRANSPOSE
-            uint32_t H_idx_x_s1 = OH_idx - KH_idx_b * p.d1 + p.p1;
-            uint32_t W_idx_x_s0 = OW_idx - KW_idx_b * p.d0 + p.p0;
-            uint32_t H_idx = fastdiv(H_idx_x_s1, p.s1mp, p.s1L);
-            uint32_t W_idx = fastdiv(W_idx_x_s0, p.s0mp, p.s0L);
+            uint32_t H_idx_x_s1 = OH_idx - KH_idx_b * d1 + p1;
+            uint32_t W_idx_x_s0 = OW_idx - KW_idx_b * d0 + p0;
+            uint32_t H_idx = H_idx_x_s1 / s1;
+            uint32_t W_idx = W_idx_x_s0 / s0;
 #else
-            uint32_t H_idx = OH_idx * p.s1 + KH_idx_b * p.d1 - p.p1;
-            uint32_t W_idx = OW_idx * p.s0 + KW_idx_b * p.d0 - p.p0;
+            uint32_t H_idx = OH_idx * s1 + KH_idx_b * d1 - p1;
+            uint32_t W_idx = OW_idx * s0 + KW_idx_b * d0 - p0;
 #endif
             uint32_t src_idx =
                 min(max(W_idx + H_idx * p.nb11 + Cin_idx_b * p.nb12 + N_idx * p.nb13, 0), p.Cin * p.N * p.W * p.H - 1);
@@ -290,7 +293,7 @@ void main() {
             if (CRS_idx_b >= CRS || NPQ_idx >= NPQ
                 || H_idx >= p.H || W_idx >= p.W // Lower bound checks aren't necessary. (idx >= 0x80000000 for such case)
 #ifdef TRANSPOSE
-                || (H_idx_x_s1 - H_idx * p.s1 != 0) || (W_idx_x_s0 - W_idx * p.s0 != 0)
+                || (H_idx_x_s1 - H_idx * s1 != 0) || (W_idx_x_s0 - W_idx * s0 != 0)
 #endif
                 ) {
                 val = 0.0;

From 333f2595a3e0e4c0abf233f2f29ef1710acd134d Mon Sep 17 00:00:00 2001
From: chansikpark <chansik.park@gmail.com>
Date: Sat, 8 Nov 2025 14:52:35 -0500
Subject: [PATCH 125/185] webui: fix keyboard shortcuts for new chat & edit
 chat title (#17007)

---
 tools/server/public/index.html.gz            | Bin 1127240 -> 1127236 bytes
 tools/server/webui/src/routes/+layout.svelte |   4 ++--
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/tools/server/public/index.html.gz b/tools/server/public/index.html.gz
index a796c255c18579093dd7a63e150a4fe9d0cdb327..976d6585da66ed072ec30330cef550b41b5052c1 100644
GIT binary patch
delta 756404
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diff --git a/tools/server/webui/src/routes/+layout.svelte b/tools/server/webui/src/routes/+layout.svelte
index 075bdd356bc..b08bd59c15e 100644
--- a/tools/server/webui/src/routes/+layout.svelte
+++ b/tools/server/webui/src/routes/+layout.svelte
@@ -44,12 +44,12 @@
 			}
 		}
 
-		if (isCtrlOrCmd && event.shiftKey && event.key === 'o') {
+		if (isCtrlOrCmd && event.shiftKey && event.key === 'O') {
 			event.preventDefault();
 			goto('?new_chat=true#/');
 		}
 
-		if (event.shiftKey && isCtrlOrCmd && event.key === 'e') {
+		if (event.shiftKey && isCtrlOrCmd && event.key === 'E') {
 			event.preventDefault();
 
 			if (chatSidebar?.editActiveConversation) {

From aa3b7a90b407c556778a7e13a4b0d28cf964fd1c Mon Sep 17 00:00:00 2001
From: Xuan-Son Nguyen <son@huggingface.co>
Date: Sat, 8 Nov 2025 21:54:14 +0100
Subject: [PATCH 126/185] arg: add --cache-list argument to list cached models
 (#17073)

* arg: add --cache-list argument to list cached models

* new manifest naming format

* improve naming

* Update common/arg.cpp

Co-authored-by: Georgi Gerganov <ggerganov@gmail.com>

---------

Co-authored-by: Georgi Gerganov <ggerganov@gmail.com>
---
 common/arg.cpp      | 14 +++++++++++++
 common/common.cpp   | 33 ++++++++++++++++++++++++++++++
 common/common.h     |  7 +++++++
 common/download.cpp | 50 ++++++++++++++++++++++++++++++++++++++++-----
 common/download.h   | 22 ++++++++++++++++----
 5 files changed, 117 insertions(+), 9 deletions(-)

diff --git a/common/arg.cpp b/common/arg.cpp
index 5597de121c1..a5708102814 100644
--- a/common/arg.cpp
+++ b/common/arg.cpp
@@ -740,6 +740,20 @@ common_params_context common_params_parser_init(common_params & params, llama_ex
             exit(0);
         }
     ));
+    add_opt(common_arg(
+        {"-cl", "--cache-list"},
+        "show list of models in cache",
+        [](common_params &) {
+            printf("model cache directory: %s\n", fs_get_cache_directory().c_str());
+            auto models = common_list_cached_models();
+            printf("number of models in cache: %zu\n", models.size());
+            for (size_t i = 0; i < models.size(); i++) {
+                auto & model = models[i];
+                printf("%4d. %s\n", (int) i + 1, model.to_string().c_str());
+            }
+            exit(0);
+        }
+    ));
     add_opt(common_arg(
         {"--completion-bash"},
         "print source-able bash completion script for llama.cpp",
diff --git a/common/common.cpp b/common/common.cpp
index b0591e84b06..a8d709ab1d0 100644
--- a/common/common.cpp
+++ b/common/common.cpp
@@ -908,6 +908,39 @@ std::string fs_get_cache_file(const std::string & filename) {
     return cache_directory + filename;
 }
 
+std::vector<common_file_info> fs_list_files(const std::string & path) {
+    std::vector<common_file_info> files;
+    if (path.empty()) return files;
+
+    std::filesystem::path dir(path);
+    if (!std::filesystem::exists(dir) || !std::filesystem::is_directory(dir)) {
+        return files;
+    }
+
+    for (const auto & entry : std::filesystem::directory_iterator(dir)) {
+        try {
+            // Only include regular files (skip directories)
+            const auto & p = entry.path();
+            if (std::filesystem::is_regular_file(p)) {
+                common_file_info info;
+                info.path = p.string();
+                info.name = p.filename().string();
+                try {
+                    info.size = static_cast<size_t>(std::filesystem::file_size(p));
+                } catch (const std::filesystem::filesystem_error &) {
+                    info.size = 0;
+                }
+                files.push_back(std::move(info));
+            }
+        } catch (const std::filesystem::filesystem_error &) {
+            // skip entries we cannot inspect
+            continue;
+        }
+    }
+
+    return files;
+}
+
 
 //
 // Model utils
diff --git a/common/common.h b/common/common.h
index 54b7849b174..8540725aaa4 100644
--- a/common/common.h
+++ b/common/common.h
@@ -611,6 +611,13 @@ bool fs_create_directory_with_parents(const std::string & path);
 std::string fs_get_cache_directory();
 std::string fs_get_cache_file(const std::string & filename);
 
+struct common_file_info {
+    std::string path;
+    std::string name;
+    size_t      size = 0; // in bytes
+};
+std::vector<common_file_info> fs_list_files(const std::string & path);
+
 //
 // Model utils
 //
diff --git a/common/download.cpp b/common/download.cpp
index 02d75fc0d09..57308a5c6d5 100644
--- a/common/download.cpp
+++ b/common/download.cpp
@@ -50,6 +50,22 @@ using json = nlohmann::ordered_json;
 // downloader
 //
 
+// validate repo name format: owner/repo
+static bool validate_repo_name(const std::string & repo) {
+    static const std::regex repo_regex(R"(^[A-Za-z0-9_.\-]+\/[A-Za-z0-9_.\-]+$)");
+    return std::regex_match(repo, repo_regex);
+}
+
+static std::string get_manifest_path(const std::string & repo, const std::string & tag) {
+    // we use "=" to avoid clashing with other component, while still being allowed on windows
+    std::string fname = "manifest=" + repo + "=" + tag + ".json";
+    if (!validate_repo_name(repo)) {
+        throw std::runtime_error("error: repo name must be in the format 'owner/repo'");
+    }
+    string_replace_all(fname, "/", "=");
+    return fs_get_cache_file(fname);
+}
+
 static std::string read_file(const std::string & fname) {
     std::ifstream file(fname);
     if (!file) {
@@ -829,17 +845,13 @@ common_hf_file_res common_get_hf_file(const std::string & hf_repo_with_tag, cons
     // Important: the User-Agent must be "llama-cpp" to get the "ggufFile" field in the response
     // User-Agent header is already set in common_remote_get_content, no need to set it here
 
-    // we use "=" to avoid clashing with other component, while still being allowed on windows
-    std::string cached_response_fname = "manifest=" + hf_repo + "=" + tag + ".json";
-    string_replace_all(cached_response_fname, "/", "_");
-    std::string cached_response_path = fs_get_cache_file(cached_response_fname);
-
     // make the request
     common_remote_params params;
     params.headers = headers;
     long res_code = 0;
     std::string res_str;
     bool use_cache = false;
+    std::string cached_response_path = get_manifest_path(hf_repo, tag);
     if (!offline) {
         try {
             auto res = common_remote_get_content(url, params);
@@ -895,6 +907,33 @@ common_hf_file_res common_get_hf_file(const std::string & hf_repo_with_tag, cons
     return { hf_repo, ggufFile, mmprojFile };
 }
 
+std::vector<common_cached_model_info> common_list_cached_models() {
+    std::vector<common_cached_model_info> models;
+    const std::string cache_dir = fs_get_cache_directory();
+    const std::vector<common_file_info> files = fs_list_files(cache_dir);
+    for (const auto & file : files) {
+        if (string_starts_with(file.name, "manifest=") && string_ends_with(file.name, ".json")) {
+            common_cached_model_info model_info;
+            model_info.manifest_path = file.path;
+            std::string fname = file.name;
+            string_replace_all(fname, ".json", ""); // remove extension
+            auto parts = string_split<std::string>(fname, '=');
+            if (parts.size() == 4) {
+                // expect format: manifest=<user>=<model>=<tag>=<other>
+                model_info.user  = parts[1];
+                model_info.model = parts[2];
+                model_info.tag   = parts[3];
+            } else {
+                // invalid format
+                continue;
+            }
+            model_info.size = 0; // TODO: get GGUF size, not manifest size
+            models.push_back(model_info);
+        }
+    }
+    return models;
+}
+
 //
 // Docker registry functions
 //
@@ -959,6 +998,7 @@ std::string common_docker_resolve_model(const std::string & docker) {
         std::string token = common_docker_get_token(repo);  // Get authentication token
 
         // Get manifest
+        // TODO: cache the manifest response so that it appears in the model list
         const std::string    url_prefix = "https://registry-1.docker.io/v2/" + repo;
         std::string          manifest_url = url_prefix + "/manifests/" + tag;
         common_remote_params manifest_params;
diff --git a/common/download.h b/common/download.h
index ddf36155ef8..45a6bd6bba8 100644
--- a/common/download.h
+++ b/common/download.h
@@ -8,16 +8,23 @@ struct common_params_model;
 // download functionalities
 //
 
+struct common_cached_model_info {
+    std::string manifest_path;
+    std::string user;
+    std::string model;
+    std::string tag;
+    size_t      size = 0; // GGUF size in bytes
+    std::string to_string() const {
+        return user + "/" + model + ":" + tag;
+    }
+};
+
 struct common_hf_file_res {
     std::string repo; // repo name with ":tag" removed
     std::string ggufFile;
     std::string mmprojFile;
 };
 
-// resolve and download model from Docker registry
-// return local path to downloaded model file
-std::string common_docker_resolve_model(const std::string & docker);
-
 /**
  * Allow getting the HF file from the HF repo with tag (like ollama), for example:
  * - bartowski/Llama-3.2-3B-Instruct-GGUF:q4
@@ -39,3 +46,10 @@ bool common_download_model(
     const common_params_model & model,
     const std::string & bearer_token,
     bool offline);
+
+// returns list of cached models
+std::vector<common_cached_model_info> common_list_cached_models();
+
+// resolve and download model from Docker registry
+// return local path to downloaded model file
+std::string common_docker_resolve_model(const std::string & docker);

From 0750a59903688746883b0ecb24ac5ceed68edbf1 Mon Sep 17 00:00:00 2001
From: Georgi Gerganov <ggerganov@gmail.com>
Date: Sun, 9 Nov 2025 08:28:51 +0200
Subject: [PATCH 127/185] metal : retain src and dst buffers during async ops
 (#17101)

---
 ggml/src/ggml-metal/ggml-metal-context.m | 6 ++++--
 1 file changed, 4 insertions(+), 2 deletions(-)

diff --git a/ggml/src/ggml-metal/ggml-metal-context.m b/ggml/src/ggml-metal/ggml-metal-context.m
index b8d35b78ade..e66646284db 100644
--- a/ggml/src/ggml-metal/ggml-metal-context.m
+++ b/ggml/src/ggml-metal/ggml-metal-context.m
@@ -289,7 +289,7 @@ void ggml_metal_set_tensor_async(ggml_metal_t ctx, struct ggml_tensor * tensor,
 
         // queue the copy operation into the queue of the Metal context
         // this will be queued at the end, after any currently ongoing GPU operations
-        id<MTLCommandBuffer> cmd_buf = [ctx->queue commandBufferWithUnretainedReferences];
+        id<MTLCommandBuffer> cmd_buf = [ctx->queue commandBuffer];
         id<MTLBlitCommandEncoder> encoder = [cmd_buf blitCommandEncoder];
 
         [encoder copyFromBuffer:buf_src
@@ -300,6 +300,7 @@ void ggml_metal_set_tensor_async(ggml_metal_t ctx, struct ggml_tensor * tensor,
 
         [encoder endEncoding];
         [cmd_buf commit];
+        [buf_src release];
 
         // do not wait here for completion
         //[cmd_buf waitUntilCompleted];
@@ -330,7 +331,7 @@ void ggml_metal_get_tensor_async(ggml_metal_t ctx, const struct ggml_tensor * te
 
         // queue the copy operation into the queue of the Metal context
         // this will be queued at the end, after any currently ongoing GPU operations
-        id<MTLCommandBuffer> cmd_buf = [ctx->queue commandBufferWithUnretainedReferences];
+        id<MTLCommandBuffer> cmd_buf = [ctx->queue commandBuffer];
         id<MTLBlitCommandEncoder> encoder = [cmd_buf blitCommandEncoder];
 
         [encoder copyFromBuffer:bid_src.metal
@@ -341,6 +342,7 @@ void ggml_metal_get_tensor_async(ggml_metal_t ctx, const struct ggml_tensor * te
 
         [encoder endEncoding];
         [cmd_buf commit];
+        [buf_dst release];
 
         // do not wait here for completion
         //[cmd_buf waitUntilCompleted];

From 80a6cf63473b95742444a1b27d45164591282a7d Mon Sep 17 00:00:00 2001
From: Jeff Bolz <jbolz@nvidia.com>
Date: Sun, 9 Nov 2025 02:48:42 -0600
Subject: [PATCH 128/185] vulkan: fuse mul_mat_id + mul (#17095)

* vulkan: fuse mul_mat_id + mul

This comes up in qwen3 moe.

* split mul_mat_id fusion tests into a separate class
---
 ggml/src/ggml-vulkan/ggml-vulkan.cpp          |  58 ++++++-
 .../vulkan-shaders/mul_mat_vec_base.glsl      |  19 +++
 tests/test-backend-ops.cpp                    | 154 ++++++++++++------
 3 files changed, 180 insertions(+), 51 deletions(-)

diff --git a/ggml/src/ggml-vulkan/ggml-vulkan.cpp b/ggml/src/ggml-vulkan/ggml-vulkan.cpp
index 6da7bbd2f61..054e8cbdb8b 100644
--- a/ggml/src/ggml-vulkan/ggml-vulkan.cpp
+++ b/ggml/src/ggml-vulkan/ggml-vulkan.cpp
@@ -830,6 +830,7 @@ struct vk_mat_vec_push_constants {
     uint32_t batch_stride_b;
     uint32_t batch_stride_d;
     uint32_t enable_bias;
+    uint32_t enable_scale;
     uint32_t ne02;
     uint32_t ne12;
     uint32_t broadcast2;
@@ -852,6 +853,7 @@ struct vk_mat_vec_id_push_constants {
     uint32_t batch_stride_b;
     uint32_t batch_stride_d;
     uint32_t enable_bias;
+    uint32_t enable_scale;
     uint32_t nei0;
     uint32_t ne11;
 };
@@ -6863,7 +6865,7 @@ static void ggml_vk_mul_mat_vec_q_f16(ggml_backend_vk_context * ctx, vk_context&
     // compute
     const vk_mat_vec_push_constants pc = {
         (uint32_t)ne00, (uint32_t)ne10, (uint32_t)ne10, (uint32_t)ne01,
-        stride_batch_x, stride_batch_y, stride_batch_d, enable_bias,
+        stride_batch_x, stride_batch_y, stride_batch_d, enable_bias, 0,
         (uint32_t)ne02, (uint32_t)ne12, (uint32_t)r2, (uint32_t)r3,
     };
     ggml_vk_dispatch_pipeline(ctx, subctx, dmmv,
@@ -7684,13 +7686,22 @@ static void ggml_vk_mul_mat_vec_id_q_f16(ggml_backend_vk_context * ctx, vk_conte
         groups_x = CEIL_DIV(groups_x, groups_z);
     }
 
-    uint32_t enable_bias = ctx->num_additional_fused_ops > 0;
+    uint32_t enable_bias = 0;
+    uint32_t enable_scale = 0;
+    if (ctx->num_additional_fused_ops > 0) {
+        if (cgraph->nodes[node_idx + 1]->op == GGML_OP_MUL) {
+            enable_scale = 1;
+        } else {
+            GGML_ASSERT(cgraph->nodes[node_idx + 1]->op == GGML_OP_ADD_ID);
+            enable_bias = 1;
+        }
+    }
 
     vk_buffer d_B = d_D;
     size_t b_buf_offset = 0;
     uint64_t b_sz = 0;
 
-    if (enable_bias) {
+    if (enable_bias || enable_scale) {
         const ggml_tensor * bias = cgraph->nodes[node_idx + 1]->src[1];
 
         bool b_uma = false;
@@ -7712,7 +7723,7 @@ static void ggml_vk_mul_mat_vec_id_q_f16(ggml_backend_vk_context * ctx, vk_conte
         (uint32_t)ne00, (uint32_t)ne10, (uint32_t)ne10, (uint32_t)ne01,
         (uint32_t)x_ne, stride_batch_y, (uint32_t)(ne20*ne21),
 
-        enable_bias,
+        enable_bias, enable_scale,
 
         (uint32_t)nei0, (uint32_t)ne11,
     };
@@ -12490,6 +12501,40 @@ static bool ggml_vk_can_fuse(const ggml_backend_vk_context * ctx, const struct g
         }
     }
 
+    if (ops.size() == 2 && ops.begin()[0] == GGML_OP_MUL_MAT_ID && ops.begin()[1] == GGML_OP_MUL) {
+        // additional constraints specific to this fusion
+        const ggml_tensor *mmid = cgraph->nodes[node_idx];
+        const ggml_tensor *mul = cgraph->nodes[node_idx + 1];
+        const ggml_tensor *scale = mul->src[1];
+
+        if (mmid != mul->src[0]) {
+            return false;
+        }
+        // mat-vec only
+        if (!ggml_vk_use_mul_mat_vec_id(cgraph, node_idx)) {
+            return false;
+        }
+        // shaders assume the types match
+        if (mmid->type != scale->type) {
+            return false;
+        }
+        // shaders assume the bias is contiguous
+        if (!ggml_is_contiguous(scale)) {
+            return false;
+        }
+        // unaligned bias isn't handled
+        if (get_misalign_bytes(ctx, scale) != 0) {
+            return false;
+        }
+        // shader only indexes by expert index
+        if (scale->ne[0] != 1 ||
+            scale->ne[1] != mul->ne[1] ||
+            scale->ne[2] != 1 ||
+            scale->ne[3] != 1) {
+            return false;
+        }
+    }
+
     return true;
 }
 
@@ -12798,6 +12843,8 @@ static ggml_status ggml_backend_vk_graph_compute(ggml_backend_t backend, ggml_cg
                 ctx->num_additional_fused_ops = 1;
             } else if (ggml_vk_can_fuse(ctx, cgraph, i, { GGML_OP_MUL_MAT_ID, GGML_OP_ADD_ID })) {
                 ctx->num_additional_fused_ops = 1;
+            } else if (ggml_vk_can_fuse(ctx, cgraph, i, { GGML_OP_MUL_MAT_ID, GGML_OP_MUL })) {
+                ctx->num_additional_fused_ops = 1;
             } else if (ggml_can_fuse_subgraph(cgraph, i, { GGML_OP_RMS_NORM, GGML_OP_MUL, GGML_OP_ROPE, GGML_OP_VIEW, GGML_OP_SET_ROWS }, { i + 4 }) &&
                        ggml_check_edges(cgraph, i, rms_norm_mul_rope_view_set_rows_edges) &&
                        ggml_vk_can_fuse_rms_norm_mul_rope(ctx, cgraph, i) &&
@@ -13033,7 +13080,8 @@ static void ggml_vk_graph_optimize(ggml_backend_t backend, struct ggml_cgraph *
                     is_src_of(graph->nodes[j], graph->nodes[c]) &&
                     !(j == c+1 && c == current_set.back() && graph->nodes[c]->op == GGML_OP_RMS_NORM && graph->nodes[j]->op == GGML_OP_MUL) &&
                     !(j == c+1 && c == current_set.back() && graph->nodes[c]->op == GGML_OP_MUL_MAT && graph->nodes[j]->op == GGML_OP_ADD) &&
-                    !(j == c+1 && c == current_set.back() && graph->nodes[c]->op == GGML_OP_MUL_MAT_ID && graph->nodes[j]->op == GGML_OP_ADD_ID)) {
+                    !(j == c+1 && c == current_set.back() && graph->nodes[c]->op == GGML_OP_MUL_MAT_ID && graph->nodes[j]->op == GGML_OP_ADD_ID) &&
+                    !(j == c+1 && c == current_set.back() && graph->nodes[c]->op == GGML_OP_MUL_MAT_ID && graph->nodes[j]->op == GGML_OP_MUL)) {
                     ok = false;
                     break;
                 }
diff --git a/ggml/src/ggml-vulkan/vulkan-shaders/mul_mat_vec_base.glsl b/ggml/src/ggml-vulkan/vulkan-shaders/mul_mat_vec_base.glsl
index bbb4d1206b7..eb8fa6dc09f 100644
--- a/ggml/src/ggml-vulkan/vulkan-shaders/mul_mat_vec_base.glsl
+++ b/ggml/src/ggml-vulkan/vulkan-shaders/mul_mat_vec_base.glsl
@@ -49,6 +49,7 @@ layout (push_constant) uniform parameter
     uint batch_stride_d;
 
     uint enable_bias;
+    uint enable_scale;
 
 #ifdef MUL_MAT_ID
     uint nei0;
@@ -129,6 +130,12 @@ void reduce_result(inout FLOAT_TYPE temp[NUM_COLS][NUM_ROWS], const in uint32_t
                     temp[j][n] += FLOAT_TYPE(data_bias[j*p.batch_stride_d + d_offset + first_row + n]);
 #endif
                 }
+#ifdef MUL_MAT_ID
+                if (p.enable_scale != 0) {
+                    const uint expert_idx = gl_GlobalInvocationID.y;
+                    temp[j][n] *= FLOAT_TYPE(data_bias[expert_idx]);
+                }
+#endif
                 data_d[j*p.batch_stride_d + d_offset + first_row + n] = D_TYPE(temp[j][n]);
             }
         }
@@ -171,6 +178,12 @@ void reduce_result(FLOAT_TYPE temp[NUM_COLS][NUM_ROWS], const in uint32_t d_offs
                     temp[j][n] += FLOAT_TYPE(data_bias[j*p.batch_stride_d + d_offset + first_row + n]);
 #endif
                 }
+#ifdef MUL_MAT_ID
+                if (p.enable_scale != 0) {
+                    const uint expert_idx = gl_GlobalInvocationID.y;
+                    temp[j][n] *= FLOAT_TYPE(data_bias[expert_idx]);
+                }
+#endif
                 data_d[j*p.batch_stride_d + d_offset + first_row + n] = D_TYPE(temp[j][n]);
             }
         }
@@ -203,6 +216,12 @@ void reduce_result(FLOAT_TYPE temp[NUM_COLS][NUM_ROWS], const in uint32_t d_offs
                     tmpsh[j][n][0] += FLOAT_TYPE(data_bias[j*p.batch_stride_d + d_offset + first_row + n]);
 #endif
                 }
+#ifdef MUL_MAT_ID
+                if (p.enable_scale != 0) {
+                    const uint expert_idx = gl_GlobalInvocationID.y;
+                    tmpsh[j][n][0] *= FLOAT_TYPE(data_bias[expert_idx]);
+                }
+#endif
                 data_d[j*p.batch_stride_d + d_offset + first_row + n] = D_TYPE(tmpsh[j][n][0]);
             }
         }
diff --git a/tests/test-backend-ops.cpp b/tests/test-backend-ops.cpp
index 2470c148d66..21c7e3a8cff 100644
--- a/tests/test-backend-ops.cpp
+++ b/tests/test-backend-ops.cpp
@@ -3557,6 +3557,27 @@ struct test_mul_mat : public test_case {
     }
 };
 
+static void init_mul_mat_id_tensors(ggml_context * ctx, int n_mats) {
+    std::random_device rd;
+    std::default_random_engine rng(rd());
+    for (ggml_tensor * t = ggml_get_first_tensor(ctx); t != NULL; t = ggml_get_next_tensor(ctx, t)) {
+        if (t->type == GGML_TYPE_I32) {
+            if (ggml_is_view_op(t->op)) { continue; }
+            // ids
+            for (int64_t r = 0; r < ggml_nrows(t); r++) {
+                std::vector<int32_t> data(t->ne[0]);
+                for (int i = 0; i < t->ne[0]; i++) {
+                    data[i] = i % n_mats;
+                }
+                std::shuffle(data.begin(), data.end(), rng);
+                ggml_backend_tensor_set(t, data.data(), r * t->nb[1], t->ne[0] * sizeof(int32_t));
+            }
+        } else {
+            init_tensor_uniform(t);
+        }
+    }
+}
+
 // GGML_OP_MUL_MAT_ID
 struct test_mul_mat_id : public test_case {
     const ggml_type type_a;
@@ -3567,10 +3588,9 @@ struct test_mul_mat_id : public test_case {
     const int64_t m;
     const int64_t n;
     const int64_t k;
-    const uint32_t o; // number of outputs
 
     std::string vars() override {
-        return VARS_TO_STR9(type_a, type_b, n_mats, n_used, b, m, n, k, o);
+        return VARS_TO_STR8(type_a, type_b, n_mats, n_used, b, m, n, k);
     }
 
     double max_nmse_err() override {
@@ -3584,9 +3604,69 @@ struct test_mul_mat_id : public test_case {
 
     test_mul_mat_id(ggml_type type_a = GGML_TYPE_F32, ggml_type type_b = GGML_TYPE_F32,
             int n_mats = 8, int n_used = 2, bool b = false,
-            int64_t m = 32, int64_t n = 32, int64_t k = 32, uint32_t o = 1)
+            int64_t m = 32, int64_t n = 32, int64_t k = 32)
         : type_a(type_a), type_b(type_b), n_mats(n_mats), n_used(n_used), b(b),
-            m(m), n(n), k(k), o(o) {
+            m(m), n(n), k(k) {
+            GGML_ASSERT(n_used <= n_mats);
+        }
+
+    ggml_tensor * build_graph(ggml_context * ctx) override {
+        // C^T = A * B^T: (k, m) * (k, n) => (m, n)
+        ggml_tensor * as = ggml_new_tensor_3d(ctx, type_a, k, m, n_mats);
+        ggml_set_name(as, "as");
+
+        ggml_tensor * ids = ggml_new_tensor_2d(ctx, GGML_TYPE_I32, n_mats, n);
+        ggml_set_name(ids, "ids");
+        if (n_used != n_mats) {
+            ids = ggml_view_2d(ctx, ids, n_used, n, ids->nb[1], 0);
+            ggml_set_name(ids, "view_of_ids");
+        }
+
+        ggml_tensor * b = ggml_new_tensor_3d(ctx, type_b, k, this->b ? 1 : n_used, n);
+        ggml_set_name(b, "b");
+
+        ggml_tensor * out = ggml_mul_mat_id(ctx, as, b, ids);
+        ggml_set_name(out, "out");
+
+        return out;
+    }
+
+    void initialize_tensors(ggml_context * ctx) override {
+        init_mul_mat_id_tensors(ctx, n_mats);
+    }
+};
+
+// GGML_OP_MUL_MAT_ID + GGML_OP_ADD or GGML_OP_MUL
+struct test_mul_mat_id_fusion : public test_case {
+    const ggml_type type_a;
+    const ggml_type type_b;
+    const int n_mats;
+    const int n_used;
+    const bool b; // broadcast b matrix
+    const int64_t m;
+    const int64_t n;
+    const int64_t k;
+    const uint32_t o; // number of outputs
+    const bool mul;
+
+    std::string vars() override {
+        return VARS_TO_STR10(type_a, type_b, n_mats, n_used, b, m, n, k, o, mul);
+    }
+
+    double max_nmse_err() override {
+        return 5e-4;
+    }
+
+    uint64_t op_flops(ggml_tensor * t) override {
+        GGML_UNUSED(t);
+        return 2 * m * k * n * n_used;
+    }
+
+    test_mul_mat_id_fusion(ggml_type type_a = GGML_TYPE_F32, ggml_type type_b = GGML_TYPE_F32,
+            int n_mats = 8, int n_used = 2, bool b = false,
+            int64_t m = 32, int64_t n = 32, int64_t k = 32, uint32_t o = 1, bool mul = false)
+        : type_a(type_a), type_b(type_b), n_mats(n_mats), n_used(n_used), b(b),
+            m(m), n(n), k(k), o(o), mul(mul) {
             GGML_ASSERT(n_used <= n_mats);
         }
 
@@ -3615,35 +3695,25 @@ struct test_mul_mat_id : public test_case {
             out = ggml_add(ctx, out, out2);
         }
 
+        if (mul) {
+            std::array<int64_t, 4> ne { 1, out->ne[1], out->ne[2], out->ne[3] };
+            ne[0] = 1;
+            ggml_tensor * m = ggml_new_tensor(ctx, out->type, 4, ne.data());
+            out = ggml_mul(ctx, out, m);
+        }
+
         return out;
     }
 
     void initialize_tensors(ggml_context * ctx) override {
-        for (ggml_tensor * t = ggml_get_first_tensor(ctx); t != NULL; t = ggml_get_next_tensor(ctx, t)) {
-            if (t->type == GGML_TYPE_I32) {
-                if (ggml_is_view_op(t->op)) { continue; }
-                std::random_device rd;
-                std::default_random_engine rng(rd());
-                // ids
-                for (int64_t r = 0; r < ggml_nrows(t); r++) {
-                    std::vector<int32_t> data(t->ne[0]);
-                    for (int i = 0; i < t->ne[0]; i++) {
-                        data[i] = i % n_mats;
-                    }
-                    std::shuffle(data.begin(), data.end(), rng);
-                    ggml_backend_tensor_set(t, data.data(), r * t->nb[1], t->ne[0] * sizeof(int32_t));
-                }
-            } else {
-                init_tensor_uniform(t);
-            }
-        }
+        init_mul_mat_id_tensors(ctx, n_mats);
     }
 
-    bool run_whole_graph() override { return o > 1; }
+    bool run_whole_graph() override { return true; }
 
     std::string op_desc(ggml_tensor * t) override {
         GGML_UNUSED(t);
-        return ggml_op_name(GGML_OP_MUL_MAT_ID);
+        return "MUL_MAT_ID_FUSION";
     }
 };
 
@@ -4992,24 +5062,7 @@ struct test_mul_mat_vec_fusion : public test_case {
                 init_tensor_uniform(t);
             }
         } else {
-            std::random_device rd;
-            std::default_random_engine rng(rd());
-            for (ggml_tensor * t = ggml_get_first_tensor(ctx); t != NULL; t = ggml_get_next_tensor(ctx, t)) {
-                if (t->type == GGML_TYPE_I32) {
-                    if (ggml_is_view_op(t->op)) { continue; }
-                    // ids
-                    for (int64_t r = 0; r < ggml_nrows(t); r++) {
-                        std::vector<int32_t> data(t->ne[0]);
-                        for (int i = 0; i < t->ne[0]; i++) {
-                            data[i] = i % n_mats;
-                        }
-                        std::shuffle(data.begin(), data.end(), rng);
-                        ggml_backend_tensor_set(t, data.data(), r * t->nb[1], t->ne[0] * sizeof(int32_t));
-                    }
-                } else {
-                    init_tensor_uniform(t);
-                }
-            }
+            init_mul_mat_id_tensors(ctx, n_mats);
         }
     }
 
@@ -6979,7 +7032,7 @@ static std::vector<std::unique_ptr<test_case>> make_test_cases_eval() {
     }
 
     test_cases.emplace_back(new test_mul_mat_id(GGML_TYPE_F16, GGML_TYPE_F32, 1, 1, false, 8, 16, 1));
-    test_cases.emplace_back(new test_mul_mat_id(GGML_TYPE_F16, GGML_TYPE_F32, 16, 16, false, 32, 32, 32, 3));
+    test_cases.emplace_back(new test_mul_mat_id_fusion(GGML_TYPE_F16, GGML_TYPE_F32, 16, 16, false, 32, 32, 32, 3));
 
     // gpt-oss issue with Vulkan mmq_id
     test_cases.emplace_back(new test_mul_mat_id(GGML_TYPE_MXFP4, GGML_TYPE_F32, 32, 2, false, 2880, 32, 2880));
@@ -7016,6 +7069,15 @@ static std::vector<std::unique_ptr<test_case>> make_test_cases_eval() {
         }
     }
 
+    for (int bs : {1, 4, 512}) {
+        for (ggml_type type_a : {GGML_TYPE_F32, GGML_TYPE_F16, GGML_TYPE_Q4_0, GGML_TYPE_Q4_K}) {
+            for (ggml_type type_b : {GGML_TYPE_F32}) {
+                // test with mul after (ffn_moe_weighted)
+                test_cases.emplace_back(new test_mul_mat_id_fusion(type_a, type_b, 128, 8, false, 768, bs, 2048, 1, true));
+            }
+        }
+    }
+
     for (ggml_type type_a : base_types) {
         for (ggml_type type_b : {GGML_TYPE_F32, GGML_TYPE_F16}) {
             for (int n : {1, 16}) {
@@ -7472,7 +7534,7 @@ static std::vector<std::unique_ptr<test_case>> make_test_cases_perf() {
     for (int bs : {1, 4, 8, 32, 64, 128, 256, 512}) {
         for (ggml_type type_a : {GGML_TYPE_F32, GGML_TYPE_F16, GGML_TYPE_Q4_0, GGML_TYPE_Q8_0, GGML_TYPE_Q4_K, GGML_TYPE_Q6_K, GGML_TYPE_IQ2_XS}) {
             for (ggml_type type_b : {GGML_TYPE_F32}) {
-                test_cases.emplace_back(new test_mul_mat_id(type_a, type_b, 128, 8, false, 768, bs, 2048, 1));
+                test_cases.emplace_back(new test_mul_mat_id_fusion(type_a, type_b, 128, 8, false, 768, bs, 2048, 1));
             }
         }
     }
@@ -7480,7 +7542,7 @@ static std::vector<std::unique_ptr<test_case>> make_test_cases_perf() {
     for (int bs : {1, 4, 8, 32, 64, 128, 256, 512}) {
         for (ggml_type type_a : {GGML_TYPE_F32, GGML_TYPE_F16, GGML_TYPE_Q4_0, GGML_TYPE_Q8_0, GGML_TYPE_Q4_K, GGML_TYPE_Q6_K, GGML_TYPE_IQ2_XS}) {
             for (ggml_type type_b : {GGML_TYPE_F32}) {
-                test_cases.emplace_back(new test_mul_mat_id(type_a, type_b, 32, 4, false, 1792, bs, 2048, 1));
+                test_cases.emplace_back(new test_mul_mat_id_fusion(type_a, type_b, 32, 4, false, 1792, bs, 2048, 1));
             }
         }
     }
@@ -7490,7 +7552,7 @@ static std::vector<std::unique_ptr<test_case>> make_test_cases_perf() {
     for (int bs : {1, 4, 8, 512}) {
         for (ggml_type type_a : {GGML_TYPE_MXFP4}) {
             for (ggml_type type_b : {GGML_TYPE_F32}) {
-                test_cases.emplace_back(new test_mul_mat_id(type_a, type_b, 32, 4, false, 2880, bs, 2880, 1));
+                test_cases.emplace_back(new test_mul_mat_id_fusion(type_a, type_b, 32, 4, false, 2880, bs, 2880, 1));
             }
         }
     }

From 8a3519b70898b07ec05c391418a05aaa6b377c83 Mon Sep 17 00:00:00 2001
From: Ruben Ortlam <picard12@live.de>
Date: Sun, 9 Nov 2025 09:52:57 +0100
Subject: [PATCH 129/185] vulkan: fix mmq out of bounds reads (#17108)

* vulkan: fix mmq out of bounds reads, streamline outdated matmul host code

* fix mul_mat_id quantization call

* Fix compiler warnings
---
 ggml/src/ggml-vulkan/ggml-vulkan.cpp          | 202 ++++++++----------
 .../ggml-vulkan/vulkan-shaders/mul_mmq.comp   |   6 +-
 .../vulkan-shaders/mul_mmq_funcs.glsl         |  33 ++-
 .../vulkan-shaders/quantize_q8_1.comp         |   2 +-
 tests/test-backend-ops.cpp                    |   2 +
 5 files changed, 113 insertions(+), 132 deletions(-)

diff --git a/ggml/src/ggml-vulkan/ggml-vulkan.cpp b/ggml/src/ggml-vulkan/ggml-vulkan.cpp
index 054e8cbdb8b..31815a01293 100644
--- a/ggml/src/ggml-vulkan/ggml-vulkan.cpp
+++ b/ggml/src/ggml-vulkan/ggml-vulkan.cpp
@@ -586,7 +586,6 @@ struct vk_device_struct {
     vk_matmul_pipeline2 pipeline_dequant_mul_mat_mat_id_q8_1[GGML_TYPE_COUNT];
 
     vk_pipeline pipeline_matmul_split_k_reduce;
-    vk_pipeline pipeline_quantize_q8_1;
     vk_pipeline pipeline_quantize_q8_1_x4;
 
     vk_pipeline pipeline_dequant[GGML_TYPE_COUNT];
@@ -3558,10 +3557,8 @@ static void ggml_vk_load_shaders(vk_device& device) {
     ggml_vk_create_pipeline(device, device->pipeline_flash_attn_split_k_reduce, "fa_split_k_reduce", fa_split_k_reduce_len, fa_split_k_reduce_data, "main", 3, 5 * sizeof(uint32_t), {1, device->subgroup_size, 1}, {device->subgroup_size}, 1, true);
 
     if (device->subgroup_clustered && device->subgroup_require_full_support) {
-        ggml_vk_create_pipeline(device, device->pipeline_quantize_q8_1, "quantize_q8_1", quantize_q8_1_subgroup_len, quantize_q8_1_subgroup_data, "main", 2, 1 * sizeof(uint32_t), {32 * device->subgroup_size / 8, 1, 1}, { device->subgroup_size }, 1, true, true);
         ggml_vk_create_pipeline(device, device->pipeline_quantize_q8_1_x4, "quantize_q8_1_x4", quantize_q8_1_x4_subgroup_len, quantize_q8_1_x4_subgroup_data, "main", 2, 1 * sizeof(uint32_t), {32 * device->subgroup_size / 8, 1, 1}, { device->subgroup_size }, 1, true, true);
     } else {
-        ggml_vk_create_pipeline(device, device->pipeline_quantize_q8_1, "quantize_q8_1", quantize_q8_1_len, quantize_q8_1_data, "main", 2, 1 * sizeof(uint32_t), {32 * device->subgroup_size / 8, 1, 1}, { device->subgroup_size }, 1);
         ggml_vk_create_pipeline(device, device->pipeline_quantize_q8_1_x4, "quantize_q8_1_x4", quantize_q8_1_x4_len, quantize_q8_1_x4_data, "main", 2, 1 * sizeof(uint32_t), {32 * device->subgroup_size / 8, 1, 1}, { device->subgroup_size }, 1);
     }
 
@@ -6261,20 +6258,20 @@ static void ggml_vk_cpy_to_contiguous(ggml_backend_vk_context * ctx, vk_context&
     ggml_vk_sync_buffers(ctx, subctx);
 }
 
-static vk_pipeline ggml_vk_get_quantize_pipeline(ggml_backend_vk_context * ctx, ggml_type type, bool use_x4_blocks) {
+static vk_pipeline ggml_vk_get_quantize_pipeline(ggml_backend_vk_context * ctx, ggml_type type) {
     switch(type) {
         case GGML_TYPE_Q8_1:
-            return use_x4_blocks ? ctx->device->pipeline_quantize_q8_1_x4 : ctx->device->pipeline_quantize_q8_1;
+            return ctx->device->pipeline_quantize_q8_1_x4;
         default:
             std::cerr << "Missing quantize pipeline for type: " << ggml_type_name(type) << std::endl;
             GGML_ABORT("fatal error");
     }
 }
 
-static void ggml_vk_quantize_q8_1(ggml_backend_vk_context * ctx, vk_context& subctx, vk_subbuffer&& in, vk_subbuffer&& out, uint32_t ne, bool use_x4_blocks = false) {
+static void ggml_vk_quantize_q8_1(ggml_backend_vk_context * ctx, vk_context& subctx, vk_subbuffer&& in, vk_subbuffer&& out, uint32_t ne) {
     VK_LOG_DEBUG("ggml_vk_quantize_q8_1(" << "buffer in size=" << in.buffer->size << ", buffer out size=" << out.buffer->size << ", " << ne << ")");
 
-    vk_pipeline pipeline = use_x4_blocks ? ggml_vk_get_quantize_pipeline(ctx, GGML_TYPE_Q8_1, true) : ggml_vk_get_quantize_pipeline(ctx, GGML_TYPE_Q8_1, false);
+    vk_pipeline pipeline = ggml_vk_get_quantize_pipeline(ctx, GGML_TYPE_Q8_1);
 
     ggml_vk_dispatch_pipeline(ctx, subctx, pipeline, { in, out }, std::array<uint32_t, 1>{ne}, { ne, 1, 1 });
     ggml_vk_sync_buffers(ctx, subctx);
@@ -6365,16 +6362,17 @@ static void ggml_vk_mul_mat_q_f16(ggml_backend_vk_context * ctx, vk_context& sub
 
     // Reserve extra storage in the N dimension for the Y matrix, so we can avoid bounds-checking
     uint32_t padded_n = qy_needs_dequant ? ROUNDUP_POW2(ne11, pipeline->wg_denoms[1]) : ne11;
-    const int x_ne = ne01 * ne00;
-    const int y_ne = padded_n * ne10;
-    const int d_ne = ne11 * ne01;
+    const uint64_t x_ne = ggml_nelements(src0);
+    // 128 elements per Q8_1 x4 block
+    const uint64_t y_ne = padded_n * ne10 * ne12 * ne13;
+    const uint64_t d_ne = ggml_nelements(dst);
 
     const uint32_t split_k = ggml_vk_guess_split_k(ctx, ne01, ne11, ne10, disable_split_k, pipeline);
 
     const uint64_t qx_sz = ggml_type_size(src0->type) * x_ne / ggml_blck_size(src0->type);
     const uint64_t qy_sz = ggml_type_size(src1->type) * y_ne / ggml_blck_size(src1->type);
     const uint64_t x_sz = !qx_needs_dequant ? qx_sz : sizeof(ggml_fp16_t) * x_ne;
-    const uint64_t y_sz = quantize_y ? (y_ne * ggml_type_size(GGML_TYPE_Q8_1) / ggml_blck_size(GGML_TYPE_Q8_1)) : (y_f32_kernel ? sizeof(float) * y_ne : sizeof(ggml_fp16_t) * y_ne);
+    const uint64_t y_sz = quantize_y ? (ggml_vk_align_size(y_ne, 128) * ggml_type_size(GGML_TYPE_Q8_1) / ggml_blck_size(GGML_TYPE_Q8_1)) : (y_f32_kernel ? sizeof(float) * y_ne : sizeof(ggml_fp16_t) * y_ne);
     const uint64_t d_sz = sizeof(float) * d_ne;
 
     vk_pipeline to_fp16_vk_0 = nullptr;
@@ -6395,28 +6393,23 @@ static void ggml_vk_mul_mat_q_f16(ggml_backend_vk_context * ctx, vk_context& sub
     GGML_ASSERT(!qy_needs_dequant || to_fp16_vk_1 != nullptr);  // NOLINT
 
     if (quantize_y) {
-        to_q8_1 = ggml_vk_get_quantize_pipeline(ctx, GGML_TYPE_Q8_1, true);
+        to_q8_1 = ggml_vk_get_quantize_pipeline(ctx, GGML_TYPE_Q8_1);
     }
 
     {
-        const uint64_t x_sz_upd = x_sz * ne02 * ne03;
-        uint64_t y_sz_upd = y_sz * ne12 * ne13;
-        if (quantize_y) {
-            y_sz_upd = CEIL_DIV(y_sz_upd, 144) * 144;
-        }
-        const uint64_t split_k_size = split_k > 1 ? d_sz * ne12 * ne13 * split_k : 0;
+        const uint64_t split_k_size = split_k > 1 ? d_sz * split_k : 0;
         if (
-                (qx_needs_dequant && x_sz_upd > ctx->device->properties.limits.maxStorageBufferRange) ||
-                (qy_needs_dequant && y_sz_upd > ctx->device->properties.limits.maxStorageBufferRange) ||
+                (qx_needs_dequant && x_sz > ctx->device->properties.limits.maxStorageBufferRange) ||
+                (qy_needs_dequant && y_sz > ctx->device->properties.limits.maxStorageBufferRange) ||
                 (split_k > 1 && split_k_size > ctx->device->properties.limits.maxStorageBufferRange)) {
             GGML_ABORT("Requested preallocation size is too large");
         }
-        if (qx_needs_dequant && ctx->prealloc_size_x < x_sz_upd) {
-            ctx->prealloc_size_x = x_sz_upd;
+        if (qx_needs_dequant && ctx->prealloc_size_x < x_sz) {
+            ctx->prealloc_size_x = x_sz;
             ggml_vk_preallocate_buffers(ctx, subctx);
         }
-        if ((qy_needs_dequant || quantize_y) && ctx->prealloc_size_y < y_sz_upd) {
-            ctx->prealloc_size_y = y_sz_upd;
+        if ((qy_needs_dequant || quantize_y) && ctx->prealloc_size_y < y_sz) {
+            ctx->prealloc_size_y = y_sz;
             ggml_vk_preallocate_buffers(ctx, subctx);
         }
         if (split_k > 1 && ctx->prealloc_size_split_k < split_k_size) {
@@ -6443,7 +6436,7 @@ static void ggml_vk_mul_mat_q_f16(ggml_backend_vk_context * ctx, vk_context& sub
     vk_buffer d_D = dst_buf_ctx->dev_buffer;
     const uint64_t d_buf_offset = vk_tensor_offset(dst) + dst->view_offs;
     GGML_ASSERT(d_D != nullptr);
-    GGML_ASSERT(d_D->size >= d_buf_offset + d_sz * ne02 * ne03);
+    GGML_ASSERT(d_D->size >= d_buf_offset + d_sz);
     vk_buffer d_X;
     uint64_t x_buf_offset = 0;
     vk_buffer d_Y;
@@ -6460,7 +6453,7 @@ static void ggml_vk_mul_mat_q_f16(ggml_backend_vk_context * ctx, vk_context& sub
     }
     if (qx_needs_dequant) {
         d_X = ctx->prealloc_x;
-        GGML_ASSERT(d_X->size >= x_sz * ne02 * ne03);
+        GGML_ASSERT(d_X->size >= x_sz);
     } else {
         d_X = d_Qx;
         x_buf_offset = qx_buf_offset;
@@ -6468,10 +6461,10 @@ static void ggml_vk_mul_mat_q_f16(ggml_backend_vk_context * ctx, vk_context& sub
     }
     if (qy_needs_dequant) {
         d_Y = ctx->prealloc_y;
-        GGML_ASSERT(d_Y->size >= y_sz * ne12 * ne13);
+        GGML_ASSERT(d_Y->size >= y_sz);
     } else if (quantize_y) {
         d_Y = ctx->prealloc_y;
-        GGML_ASSERT(d_Y->size >= CEIL_DIV(y_sz * ne12 * ne13, 144) * 144);
+        GGML_ASSERT(d_Y->size >= CEIL_DIV(y_sz, 144) * 144);
     } else {
         d_Y = d_Qy;
         y_buf_offset = qy_buf_offset;
@@ -6488,7 +6481,7 @@ static void ggml_vk_mul_mat_q_f16(ggml_backend_vk_context * ctx, vk_context& sub
         ggml_vk_cpy_to_contiguous(ctx, subctx, to_fp16_vk_0, src0, ggml_vk_subbuffer(ctx, d_Qx, qx_buf_offset), ggml_vk_subbuffer(ctx, d_X, 0));
     } else if (qx_needs_dequant) {
         const std::vector<uint32_t> pc = { (uint32_t)ne01, (uint32_t)ne10, (uint32_t)ne10, (uint32_t)ne10, (uint32_t)(ggml_nelements(src0)) };
-        ggml_vk_dispatch_pipeline(ctx, subctx, to_fp16_vk_0, { vk_subbuffer{ d_Qx, qx_buf_offset, qx_sz * ne02 * ne03 }, vk_subbuffer{ d_X, 0, x_sz * ne02 * ne03 } }, pc, { (uint32_t)(x_ne * ne02 * ne03), 1, 1});
+        ggml_vk_dispatch_pipeline(ctx, subctx, to_fp16_vk_0, { vk_subbuffer{ d_Qx, qx_buf_offset, qx_sz }, vk_subbuffer{ d_X, 0, x_sz } }, pc, { (uint32_t)(x_ne), 1, 1});
         ggml_vk_sync_buffers(ctx, subctx);
     }
     if (y_non_contig) {
@@ -6508,7 +6501,7 @@ static void ggml_vk_mul_mat_q_f16(ggml_backend_vk_context * ctx, vk_context& sub
             if (ctx->prealloc_y_need_sync) {
                 ggml_vk_sync_buffers(ctx, subctx);
             }
-            ggml_vk_quantize_q8_1(ctx, subctx, ggml_vk_subbuffer(ctx, d_Qy, qy_buf_offset), ggml_vk_subbuffer(ctx, d_Y, 0), y_ne * ne12 * ne13, true);
+            ggml_vk_quantize_q8_1(ctx, subctx, ggml_vk_subbuffer(ctx, d_Qy, qy_buf_offset), ggml_vk_subbuffer(ctx, d_Y, 0), y_ne);
             ctx->prealloc_y_last_pipeline_used = to_q8_1.get();
             ctx->prealloc_y_last_tensor_used = src1;
         }
@@ -6525,16 +6518,11 @@ static void ggml_vk_mul_mat_q_f16(ggml_backend_vk_context * ctx, vk_context& sub
         stride_batch_y = src1->nb[0] / ggml_type_size(src1->type);
     }
 
-    uint32_t y_sz_total = y_sz * ne12 * ne13;
-    if (quantize_y) {
-        y_sz_total = CEIL_DIV(y_sz_total, 144) * 144;
-    }
-
     // compute
     ggml_vk_matmul(
         ctx, subctx, pipeline,
-        { d_X, x_buf_offset, x_sz * ne02 * ne03 }, { d_Y, y_buf_offset, y_sz_total },
-        ggml_vk_subbuffer(ctx, d_D, d_buf_offset), { ctx->prealloc_split_k, 0, d_sz * ne12 * ne13 * split_k },
+        { d_X, x_buf_offset, x_sz }, { d_Y, y_buf_offset, y_sz },
+        ggml_vk_subbuffer(ctx, d_D, d_buf_offset), { ctx->prealloc_split_k, 0, d_sz * split_k },
         ne01, ne11, ne10,
         ne10, ne10, stride_d, stride_batch_x, stride_batch_y, stride_batch_d,
         split_k, ne12*ne13, ne02, ne12, r2, r3, padded_n
@@ -6617,8 +6605,8 @@ static void ggml_vk_mul_mat_vec_q_f16(ggml_backend_vk_context * ctx, vk_context&
 
     const uint64_t ne20 = dst->ne[0];
     const uint64_t ne21 = dst->ne[1];
-    const uint64_t ne22 = dst->ne[2];
-    const uint64_t ne23 = dst->ne[3];
+    // const uint64_t ne22 = dst->ne[2];
+    // const uint64_t ne23 = dst->ne[3];
 
     const uint64_t r2 = ne12 / ne02;
     const uint64_t r3 = ne13 / ne03;
@@ -6674,7 +6662,7 @@ static void ggml_vk_mul_mat_vec_q_f16(ggml_backend_vk_context * ctx, vk_context&
     }
 
     if (quantize_y) {
-        to_q8_1 = ggml_vk_get_quantize_pipeline(ctx, GGML_TYPE_Q8_1, true);
+        to_q8_1 = ggml_vk_get_quantize_pipeline(ctx, GGML_TYPE_Q8_1);
     }
 
     const bool qx_needs_dequant = x_non_contig;
@@ -6687,33 +6675,29 @@ static void ggml_vk_mul_mat_vec_q_f16(ggml_backend_vk_context * ctx, vk_context&
     GGML_ASSERT(!qy_needs_dequant || to_fp16_vk_1 != nullptr);  // NOLINT
     GGML_ASSERT(dmmv != nullptr);
 
-    const uint64_t x_ne = ne01 * ne00;
-    const uint64_t y_ne = ne11 * ne10;
-    const uint64_t d_ne = ne11 * ne01;
+    const uint64_t x_ne = ggml_nelements(src0);
+    const uint64_t y_ne = ggml_nelements(src1);
+    const uint64_t d_ne = ggml_nelements(dst);
 
     const uint64_t qx_sz = ggml_vk_align_size(ggml_type_size(src0->type) * x_ne / ggml_blck_size(src0->type), ctx->device->properties.limits.minStorageBufferOffsetAlignment);
     const uint64_t qy_sz = ggml_type_size(src1->type) * y_ne / ggml_blck_size(src1->type);
     const uint64_t x_sz = x_non_contig ? ggml_vk_align_size(ggml_type_size(src0->type) * x_ne, ctx->device->properties.limits.minStorageBufferOffsetAlignment) : qx_sz;
-    const uint64_t y_sz = quantize_y ? (y_ne * ggml_type_size(GGML_TYPE_Q8_1) / ggml_blck_size(GGML_TYPE_Q8_1)) : (f16_f32_kernel ? sizeof(float) * y_ne : sizeof(ggml_fp16_t) * y_ne);
+    const uint64_t y_sz = quantize_y ? (ggml_vk_align_size(y_ne, 128) * ggml_type_size(GGML_TYPE_Q8_1) / ggml_blck_size(GGML_TYPE_Q8_1)) :
+                         (f16_f32_kernel ? sizeof(float) * y_ne : sizeof(ggml_fp16_t) * y_ne);
     const uint64_t d_sz = sizeof(float) * d_ne;
 
     {
-        const uint64_t x_sz_upd = x_sz * ne02 * ne03;
-        uint64_t y_sz_upd = y_sz * ne12 * ne13;
-        if (quantize_y) {
-            y_sz_upd = CEIL_DIV(y_sz_upd, 144) * 144;
-        }
         if (
-                (qx_needs_dequant && x_sz_upd > ctx->device->properties.limits.maxStorageBufferRange) ||
-                (qy_needs_dequant && y_sz_upd > ctx->device->properties.limits.maxStorageBufferRange)) {
+                (qx_needs_dequant && x_sz > ctx->device->properties.limits.maxStorageBufferRange) ||
+                (qy_needs_dequant && y_sz > ctx->device->properties.limits.maxStorageBufferRange)) {
             GGML_ABORT("Requested preallocation size is too large");
         }
-        if (qx_needs_dequant && ctx->prealloc_size_x < x_sz_upd) {
-            ctx->prealloc_size_x = x_sz_upd;
+        if (qx_needs_dequant && ctx->prealloc_size_x < x_sz) {
+            ctx->prealloc_size_x = x_sz;
             ggml_vk_preallocate_buffers(ctx, subctx);
         }
-        if ((qy_needs_dequant || quantize_y) && ctx->prealloc_size_y < y_sz_upd) {
-            ctx->prealloc_size_y = y_sz_upd;
+        if ((qy_needs_dequant || quantize_y) && ctx->prealloc_size_y < y_sz) {
+            ctx->prealloc_size_y = y_sz;
             ggml_vk_preallocate_buffers(ctx, subctx);
         }
 
@@ -6770,7 +6754,7 @@ static void ggml_vk_mul_mat_vec_q_f16(ggml_backend_vk_context * ctx, vk_context&
         d_Y = ctx->prealloc_y;
     } else if (quantize_y) {
         d_Y = ctx->prealloc_y;
-        GGML_ASSERT(d_Y->size >= CEIL_DIV(y_sz * ne12 * ne13, 144) * 144);
+        GGML_ASSERT(d_Y->size >= CEIL_DIV(y_sz, 144) * 144);
     } else {
         d_Y = d_Qy;
         y_buf_offset = qy_buf_offset;
@@ -6803,7 +6787,7 @@ static void ggml_vk_mul_mat_vec_q_f16(ggml_backend_vk_context * ctx, vk_context&
             if (ctx->prealloc_y_need_sync) {
                 ggml_vk_sync_buffers(ctx, subctx);
             }
-            ggml_vk_quantize_q8_1(ctx, subctx, ggml_vk_subbuffer(ctx, d_Qy, qy_buf_offset), ggml_vk_subbuffer(ctx, d_Y, 0), y_ne * ne12 * ne13, true);
+            ggml_vk_quantize_q8_1(ctx, subctx, ggml_vk_subbuffer(ctx, d_Qy, qy_buf_offset), ggml_vk_subbuffer(ctx, d_Y, 0), y_ne);
             ctx->prealloc_y_last_pipeline_used = to_q8_1.get();
             ctx->prealloc_y_last_tensor_used = src1;
         }
@@ -6832,12 +6816,6 @@ static void ggml_vk_mul_mat_vec_q_f16(ggml_backend_vk_context * ctx, vk_context&
         groups_x = CEIL_DIV(groups_x, groups_z);
     }
 
-    // TODO: Clean up this whole sz * ne_2 * ne_3 thing, it hasn't been necessary for a long time
-    uint32_t y_sz_total = y_sz * ne12 * ne13;
-    if (quantize_y) {
-        y_sz_total = CEIL_DIV(y_sz_total, 144) * 144;
-    }
-
     uint32_t enable_bias = ctx->num_additional_fused_ops > 0;
 
     vk_buffer d_B = d_D;
@@ -6870,9 +6848,9 @@ static void ggml_vk_mul_mat_vec_q_f16(ggml_backend_vk_context * ctx, vk_context&
     };
     ggml_vk_dispatch_pipeline(ctx, subctx, dmmv,
                               {
-                                vk_subbuffer{ d_X, x_buf_offset, x_sz * ne02 * ne03 },
-                                vk_subbuffer{ d_Y, y_buf_offset, y_sz_total },
-                                vk_subbuffer{ d_D, d_buf_offset, d_sz * ne22 * ne23},
+                                vk_subbuffer{ d_X, x_buf_offset, x_sz },
+                                vk_subbuffer{ d_Y, y_buf_offset, y_sz },
+                                vk_subbuffer{ d_D, d_buf_offset, d_sz },
                                 vk_subbuffer{ d_B, b_buf_offset, b_sz },
                               },
                               pc, { groups_x, (uint32_t)(ne12 * ne13), groups_z });
@@ -7210,7 +7188,7 @@ static void ggml_vk_mul_mat_id_q_f16(ggml_backend_vk_context * ctx, vk_context&
     const uint64_t ne00 = src0->ne[0];
     const uint64_t ne01 = src0->ne[1];
     const uint64_t ne02 = src0->ne[2];
-    const uint64_t ne03 = src0->ne[3];
+    // const uint64_t ne03 = src0->ne[3];
 
     const uint64_t ne10 = src1->ne[0];
     const uint64_t ne11 = src1->ne[1];
@@ -7225,8 +7203,8 @@ static void ggml_vk_mul_mat_id_q_f16(ggml_backend_vk_context * ctx, vk_context&
 
     const uint64_t ne20 = dst->ne[0];
     const uint64_t ne21 = dst->ne[1];
-    const uint64_t ne22 = dst->ne[2];
-    const uint64_t ne23 = dst->ne[3];
+    // const uint64_t ne22 = dst->ne[2];
+    // const uint64_t ne23 = dst->ne[3];
 
     const uint64_t n_as = ne02;
 
@@ -7296,14 +7274,14 @@ static void ggml_vk_mul_mat_id_q_f16(ggml_backend_vk_context * ctx, vk_context&
 
     // Reserve extra storage in the N dimension for the Y matrix, so we can avoid bounds-checking
     uint32_t padded_n = qy_needs_dequant ? ROUNDUP_POW2(ne11, pipeline->wg_denoms[1]) :ne11;
-    const uint64_t x_ne = ne01 * ne00;
-    const uint64_t y_ne = padded_n * ne10;
-    const uint64_t d_ne = ne21 * ne20;
+    const uint64_t x_ne = ggml_nelements(src0);
+    const uint64_t y_ne = padded_n * ne10 * ne12 * ne13;
+    const uint64_t d_ne = ggml_nelements(dst);
 
     const uint64_t qx_sz = ggml_type_size(src0->type) * x_ne / ggml_blck_size(src0->type);
     const uint64_t qy_sz = ggml_type_size(src1->type) * y_ne / ggml_blck_size(src1->type);
     const uint64_t x_sz = !qx_needs_dequant ? qx_sz : sizeof(ggml_fp16_t) * x_ne;
-    const uint64_t y_sz = quantize_y ? (y_ne * ggml_type_size(GGML_TYPE_Q8_1) / ggml_blck_size(GGML_TYPE_Q8_1)) : (y_f32_kernel ? sizeof(float) * y_ne : sizeof(ggml_fp16_t) * y_ne);
+    const uint64_t y_sz = quantize_y ? (ggml_vk_align_size(y_ne, 128) * ggml_type_size(GGML_TYPE_Q8_1) / ggml_blck_size(GGML_TYPE_Q8_1)) : (y_f32_kernel ? sizeof(float) * y_ne : sizeof(ggml_fp16_t) * y_ne);
     const uint64_t ids_sz = nbi2;
     const uint64_t d_sz = sizeof(float) * d_ne;
 
@@ -7325,26 +7303,21 @@ static void ggml_vk_mul_mat_id_q_f16(ggml_backend_vk_context * ctx, vk_context&
     GGML_ASSERT(!qy_needs_dequant || to_fp16_vk_1 != nullptr);  // NOLINT
 
     if (quantize_y) {
-        to_q8_1 = ggml_vk_get_quantize_pipeline(ctx, GGML_TYPE_Q8_1, true);
+        to_q8_1 = ggml_vk_get_quantize_pipeline(ctx, GGML_TYPE_Q8_1);
     }
 
     {
-        const uint64_t x_sz_upd = x_sz * ne02 * ne03;
-        uint64_t y_sz_upd = y_sz * ne12 * ne13;
-        if (quantize_y) {
-            y_sz_upd = CEIL_DIV(y_sz_upd, 144) * 144;
-        }
         if (
-                (qx_needs_dequant && x_sz_upd > ctx->device->properties.limits.maxStorageBufferRange) ||
-                (qy_needs_dequant && y_sz_upd > ctx->device->properties.limits.maxStorageBufferRange)) {
+                (qx_needs_dequant && x_sz > ctx->device->properties.limits.maxStorageBufferRange) ||
+                (qy_needs_dequant && y_sz > ctx->device->properties.limits.maxStorageBufferRange)) {
             GGML_ABORT("Requested preallocation size is too large");
         }
-        if (qx_needs_dequant && ctx->prealloc_size_x < x_sz_upd) {
-            ctx->prealloc_size_x = x_sz_upd;
+        if (qx_needs_dequant && ctx->prealloc_size_x < x_sz) {
+            ctx->prealloc_size_x = x_sz;
             ggml_vk_preallocate_buffers(ctx, subctx);
         }
-        if ((qy_needs_dequant || quantize_y) && ctx->prealloc_size_y < y_sz_upd) {
-            ctx->prealloc_size_y = y_sz_upd;
+        if ((qy_needs_dequant || quantize_y) && ctx->prealloc_size_y < y_sz) {
+            ctx->prealloc_size_y = y_sz;
             ggml_vk_preallocate_buffers(ctx, subctx);
         }
 
@@ -7385,7 +7358,7 @@ static void ggml_vk_mul_mat_id_q_f16(ggml_backend_vk_context * ctx, vk_context&
     }
     if (qx_needs_dequant) {
         d_X = ctx->prealloc_x;
-        GGML_ASSERT(d_X->size >= x_sz * ne02 * ne03);
+        GGML_ASSERT(d_X->size >= x_sz);
     } else {
         d_X = d_Qx;
         x_buf_offset = qx_buf_offset;
@@ -7393,10 +7366,10 @@ static void ggml_vk_mul_mat_id_q_f16(ggml_backend_vk_context * ctx, vk_context&
     }
     if (qy_needs_dequant) {
         d_Y = ctx->prealloc_y;
-        GGML_ASSERT(d_Y->size >= y_sz * ne12 * ne13);
+        GGML_ASSERT(d_Y->size >= y_sz);
     } else if (quantize_y) {
         d_Y = ctx->prealloc_y;
-        GGML_ASSERT(d_Y->size >= CEIL_DIV(y_sz * ne12 * ne13, 144) * 144);
+        GGML_ASSERT(d_Y->size >= CEIL_DIV(y_sz, 144) * 144);
     } else {
         d_Y = d_Qy;
         y_buf_offset = qy_buf_offset;
@@ -7414,7 +7387,7 @@ static void ggml_vk_mul_mat_id_q_f16(ggml_backend_vk_context * ctx, vk_context&
     } else if (qx_needs_dequant) {
         const std::vector<uint32_t> pc = { (uint32_t)ne01, (uint32_t)ne10, (uint32_t)ne10, (uint32_t)ne10, (uint32_t)(ggml_nelements(src0)) };
         ggml_vk_dispatch_pipeline(ctx, subctx, to_fp16_vk_0,
-            { vk_subbuffer{ d_Qx, qx_buf_offset, qx_sz * ne02 * ne03 }, vk_subbuffer{ d_X, 0, x_sz * ne02 * ne03 } }, pc, { (uint32_t)(x_ne * ne02 * ne03), 1, 1});
+            { vk_subbuffer{ d_Qx, qx_buf_offset, qx_sz }, vk_subbuffer{ d_X, 0, x_sz } }, pc, { (uint32_t)x_ne, 1, 1});
         ggml_vk_sync_buffers(ctx, subctx);
     }
     if (y_non_contig) {
@@ -7434,7 +7407,7 @@ static void ggml_vk_mul_mat_id_q_f16(ggml_backend_vk_context * ctx, vk_context&
             if (ctx->prealloc_y_need_sync) {
                 ggml_vk_sync_buffers(ctx, subctx);
             }
-            ggml_vk_quantize_q8_1(ctx, subctx, ggml_vk_subbuffer(ctx, d_Qy, qy_buf_offset), ggml_vk_subbuffer(ctx, d_Y, 0), y_ne * ne12 * ne13, true);
+            ggml_vk_quantize_q8_1(ctx, subctx, ggml_vk_subbuffer(ctx, d_Qy, qy_buf_offset), ggml_vk_subbuffer(ctx, d_Y, 0), y_ne);
             ctx->prealloc_y_last_pipeline_used = to_q8_1.get();
             ctx->prealloc_y_last_tensor_used = src1;
         }
@@ -7451,16 +7424,11 @@ static void ggml_vk_mul_mat_id_q_f16(ggml_backend_vk_context * ctx, vk_context&
         stride_batch_y = src1->nb[0] / ggml_type_size(src1->type);
     }
 
-    uint32_t y_sz_total = y_sz * ne12 * ne13;
-    if (quantize_y) {
-        y_sz_total = CEIL_DIV(y_sz_total, 144) * 144;
-    }
-
     // compute
     ggml_vk_matmul_id(
         ctx, subctx, pipeline,
-        { d_X, x_buf_offset, x_sz * ne02 * ne03 }, { d_Y, y_buf_offset, y_sz_total },
-        { d_D, d_buf_offset, d_sz * ne22 * ne23 }, { d_ids, ids_buf_offset, ids_sz },
+        { d_X, x_buf_offset, x_sz }, { d_Y, y_buf_offset, y_sz },
+        { d_D, d_buf_offset, d_sz }, { d_ids, ids_buf_offset, ids_sz },
         ne01, ne21, ne10, ne10, ne10, ne01,
         stride_batch_x, stride_batch_y, ne20*ne21,
         n_as, nei0, nei1, nbi1 / ggml_type_size(ids->type), ne11, padded_n
@@ -7490,13 +7458,13 @@ static void ggml_vk_mul_mat_vec_id_q_f16(ggml_backend_vk_context * ctx, vk_conte
 
     const uint64_t ne00 = src0->ne[0];
     const uint64_t ne01 = src0->ne[1];
-    const uint64_t ne02 = src0->ne[2];
-    const uint64_t ne03 = src0->ne[3];
+    // const uint64_t ne02 = src0->ne[2];
+    // const uint64_t ne03 = src0->ne[3];
 
     const uint64_t ne10 = src1->ne[0];
     const uint64_t ne11 = src1->ne[1];
-    const uint64_t ne12 = src1->ne[2];
-    const uint64_t ne13 = src1->ne[3];
+    // const uint64_t ne12 = src1->ne[2];
+    // const uint64_t ne13 = src1->ne[3];
 
     const uint64_t nei0 = ids->ne[0];
     const uint64_t nei1 = ids->ne[1];
@@ -7507,8 +7475,8 @@ static void ggml_vk_mul_mat_vec_id_q_f16(ggml_backend_vk_context * ctx, vk_conte
 
     const uint64_t ne20 = dst->ne[0];
     const uint64_t ne21 = dst->ne[1];
-    const uint64_t ne22 = dst->ne[2];
-    const uint64_t ne23 = dst->ne[3];
+    // const uint64_t ne22 = dst->ne[2];
+    // const uint64_t ne23 = dst->ne[3];
 
     ggml_backend_vk_buffer_context * src0_buf_ctx = (ggml_backend_vk_buffer_context *)src0->buffer->context;
     ggml_backend_vk_buffer_context * src1_buf_ctx = (ggml_backend_vk_buffer_context *)src1->buffer->context;
@@ -7545,9 +7513,9 @@ static void ggml_vk_mul_mat_vec_id_q_f16(ggml_backend_vk_context * ctx, vk_conte
     // Not implemented
     GGML_ASSERT(y_non_contig || !qy_needs_dequant);  // NOLINT
 
-    const uint64_t x_ne = ne01 * ne00;
-    const uint64_t y_ne = ne11 * ne10;
-    const uint64_t d_ne = ne21 * ne20;
+    const uint64_t x_ne = ggml_nelements(src0);
+    const uint64_t y_ne = ggml_nelements(src1);
+    const uint64_t d_ne = ggml_nelements(dst);
 
     const uint64_t qx_sz = ggml_vk_align_size(ggml_type_size(src0->type) * x_ne / ggml_blck_size(src0->type), ctx->device->properties.limits.minStorageBufferOffsetAlignment);
     const uint64_t qy_sz = ggml_type_size(src1->type) * y_ne / ggml_blck_size(src1->type);
@@ -7572,19 +7540,17 @@ static void ggml_vk_mul_mat_vec_id_q_f16(ggml_backend_vk_context * ctx, vk_conte
     GGML_ASSERT(dmmv != nullptr);
 
     {
-        const uint64_t x_sz_upd = x_sz * ne02 * ne03;
-        const uint64_t y_sz_upd = y_sz * ne12 * ne13;
         if (
-                (qx_needs_dequant && x_sz_upd > ctx->device->properties.limits.maxStorageBufferRange) ||
-                (qy_needs_dequant && y_sz_upd > ctx->device->properties.limits.maxStorageBufferRange)) {
+                (qx_needs_dequant && x_sz > ctx->device->properties.limits.maxStorageBufferRange) ||
+                (qy_needs_dequant && y_sz > ctx->device->properties.limits.maxStorageBufferRange)) {
             GGML_ABORT("Requested preallocation size is too large");
         }
-        if (qx_needs_dequant && ctx->prealloc_size_x < x_sz_upd) {
-            ctx->prealloc_size_x = x_sz_upd;
+        if (qx_needs_dequant && ctx->prealloc_size_x < x_sz) {
+            ctx->prealloc_size_x = x_sz;
             ggml_vk_preallocate_buffers(ctx, subctx);
         }
-        if (qy_needs_dequant && ctx->prealloc_size_y < y_sz_upd) {
-            ctx->prealloc_size_y = y_sz_upd;
+        if (qy_needs_dequant && ctx->prealloc_size_y < y_sz) {
+            ctx->prealloc_size_y = y_sz;
             ggml_vk_preallocate_buffers(ctx, subctx);
         }
 
@@ -7721,7 +7687,7 @@ static void ggml_vk_mul_mat_vec_id_q_f16(ggml_backend_vk_context * ctx, vk_conte
     // compute
     const vk_mat_vec_id_push_constants pc = {
         (uint32_t)ne00, (uint32_t)ne10, (uint32_t)ne10, (uint32_t)ne01,
-        (uint32_t)x_ne, stride_batch_y, (uint32_t)(ne20*ne21),
+        (uint32_t)(ne00 * ne01), stride_batch_y, (uint32_t)(ne20 * ne21),
 
         enable_bias, enable_scale,
 
@@ -7729,9 +7695,9 @@ static void ggml_vk_mul_mat_vec_id_q_f16(ggml_backend_vk_context * ctx, vk_conte
     };
     ggml_vk_dispatch_pipeline(ctx, subctx, dmmv,
         {
-            vk_subbuffer{ d_X, x_buf_offset, x_sz * ne02 * ne03 },
-            vk_subbuffer{ d_Y, y_buf_offset, y_sz * ne12 * ne13 },
-            vk_subbuffer{ d_D, d_buf_offset, d_sz * ne22 * ne23},
+            vk_subbuffer{ d_X, x_buf_offset, x_sz },
+            vk_subbuffer{ d_Y, y_buf_offset, y_sz },
+            vk_subbuffer{ d_D, d_buf_offset, d_sz },
             vk_subbuffer{ d_B, b_buf_offset, b_sz },
             vk_subbuffer{ d_ids, ids_buf_offset, ids_sz },
         },
diff --git a/ggml/src/ggml-vulkan/vulkan-shaders/mul_mmq.comp b/ggml/src/ggml-vulkan/vulkan-shaders/mul_mmq.comp
index d955b4fc7af..5266e523b9d 100644
--- a/ggml/src/ggml-vulkan/vulkan-shaders/mul_mmq.comp
+++ b/ggml/src/ggml-vulkan/vulkan-shaders/mul_mmq.comp
@@ -211,7 +211,9 @@ void main() {
             const uint iqs = loadr_a;
 
             [[unroll]] for (uint k_step = 0; k_step < BK_STEP; k_step++) {
-                block_a_to_shmem(k_step * BM + buf_ib, ib + k_step, iqs);
+                if (block + k_step * BK < end_k) {
+                    block_a_to_shmem(k_step * BM + buf_ib, ib + k_step, iqs);
+                }
             }
         }
         [[unroll]] for (uint l = 0; loadc_b + l < BN; l += loadstride_b) {
@@ -226,7 +228,7 @@ void main() {
             const uint iqs = loadr_b;
 
             [[unroll]] for (uint k_step = 0; k_step < BK_STEP; k_step++) {
-                block_b_to_shmem(k_step * BN + buf_ib, ib + k_step, iqs);
+                block_b_to_shmem(k_step * BN + buf_ib, ib + k_step, iqs, block + k_step * BK < end_k);
             }
         }
 
diff --git a/ggml/src/ggml-vulkan/vulkan-shaders/mul_mmq_funcs.glsl b/ggml/src/ggml-vulkan/vulkan-shaders/mul_mmq_funcs.glsl
index c0c03fedcc2..51b5bb11e7b 100644
--- a/ggml/src/ggml-vulkan/vulkan-shaders/mul_mmq_funcs.glsl
+++ b/ggml/src/ggml-vulkan/vulkan-shaders/mul_mmq_funcs.glsl
@@ -469,19 +469,30 @@ ACC_TYPE mmq_dot_product(const uint ib_a) {
 #endif
 
 #ifdef MMQ_SHMEM
-void block_b_to_shmem(const uint buf_ib, const uint ib, const uint iqs) {
-    const uint ib_outer = ib / 4;
-    const uint ib_inner = ib % 4;
+void block_b_to_shmem(const uint buf_ib, const uint ib, const uint iqs, const bool is_in_bounds) {
+    if (is_in_bounds) {
+        const uint ib_outer = ib / 4;
+        const uint ib_inner = ib % 4;
 
-    if (iqs == 0) {
-        buf_b[buf_ib].ds = FLOAT_TYPE_VEC2(data_b[ib_outer].ds[ib_inner]);
-    }
+        if (iqs == 0) {
+            buf_b[buf_ib].ds = FLOAT_TYPE_VEC2(data_b[ib_outer].ds[ib_inner]);
+        }
 
-    const ivec4 values = data_b[ib_outer].qs[ib_inner * 2 + iqs];
-    buf_b[buf_ib].qs[iqs * 4    ] = values.x;
-    buf_b[buf_ib].qs[iqs * 4 + 1] = values.y;
-    buf_b[buf_ib].qs[iqs * 4 + 2] = values.z;
-    buf_b[buf_ib].qs[iqs * 4 + 3] = values.w;
+        const ivec4 values = data_b[ib_outer].qs[ib_inner * 2 + iqs];
+        buf_b[buf_ib].qs[iqs * 4    ] = values.x;
+        buf_b[buf_ib].qs[iqs * 4 + 1] = values.y;
+        buf_b[buf_ib].qs[iqs * 4 + 2] = values.z;
+        buf_b[buf_ib].qs[iqs * 4 + 3] = values.w;
+    } else {
+        if (iqs == 0) {
+            buf_b[buf_ib].ds = FLOAT_TYPE_VEC2(0.0f);
+        }
+
+        buf_b[buf_ib].qs[iqs * 4    ] = 0;
+        buf_b[buf_ib].qs[iqs * 4 + 1] = 0;
+        buf_b[buf_ib].qs[iqs * 4 + 2] = 0;
+        buf_b[buf_ib].qs[iqs * 4 + 3] = 0;
+    }
 }
 
 void block_b_to_registers(const uint ib) {
diff --git a/ggml/src/ggml-vulkan/vulkan-shaders/quantize_q8_1.comp b/ggml/src/ggml-vulkan/vulkan-shaders/quantize_q8_1.comp
index 0f3c6ca8719..20e45d0253e 100644
--- a/ggml/src/ggml-vulkan/vulkan-shaders/quantize_q8_1.comp
+++ b/ggml/src/ggml-vulkan/vulkan-shaders/quantize_q8_1.comp
@@ -61,7 +61,7 @@ void quantize() {
 
     const uint a_idx = ib * 8 + iqs;
 
-    vec4 vals = a_idx < p.ne ? data_a[a_idx] : vec4(0.0f);
+    vec4 vals = a_idx < p.ne / 4 ? data_a[a_idx] : vec4(0.0f);
     const vec4 abs_vals = abs(vals);
 
     // Find absolute max for each block
diff --git a/tests/test-backend-ops.cpp b/tests/test-backend-ops.cpp
index 21c7e3a8cff..22635f1635c 100644
--- a/tests/test-backend-ops.cpp
+++ b/tests/test-backend-ops.cpp
@@ -6987,6 +6987,8 @@ static std::vector<std::unique_ptr<test_case>> make_test_cases_eval() {
     test_cases.emplace_back(new test_mul_mat(GGML_TYPE_F32, GGML_TYPE_F32, 16, 32, 32, { 1,  1}, {1, 1}, {0, 1, 2, 3}, 64, 3));
     test_cases.emplace_back(new test_mul_mat(GGML_TYPE_F32, GGML_TYPE_F32, 64, 77, 77, {12,1}, {1,1}));
 
+    test_cases.emplace_back(new test_mul_mat(GGML_TYPE_Q4_0, GGML_TYPE_F32, 576, 512, 576, {1,1}, {1,1}));
+
 #if 0
     // test the mat-mat path for Metal
     for (int k = 1; k < 512; ++k) {

From 7f3e9d339c99d96d6df9833c63ec27dbbc96f003 Mon Sep 17 00:00:00 2001
From: Ruben Ortlam <picard12@live.de>
Date: Sun, 9 Nov 2025 09:54:47 +0100
Subject: [PATCH 130/185] vulkan: iGPU memory reporting fix (#17110)

* vulkan: use all device-local heaps for memory availability reporting

Co-authored-by: Giuseppe Scrivano <gscrivan@redhat.com>

* use all available heaps for iGPU memory reporting

* Allow multiple memory types per buffer request for devices with split heaps

---------

Co-authored-by: Giuseppe Scrivano <gscrivan@redhat.com>
---
 ggml/src/ggml-vulkan/ggml-vulkan.cpp | 46 ++++++++++++++++------------
 1 file changed, 26 insertions(+), 20 deletions(-)

diff --git a/ggml/src/ggml-vulkan/ggml-vulkan.cpp b/ggml/src/ggml-vulkan/ggml-vulkan.cpp
index 31815a01293..46e098a7ffb 100644
--- a/ggml/src/ggml-vulkan/ggml-vulkan.cpp
+++ b/ggml/src/ggml-vulkan/ggml-vulkan.cpp
@@ -2159,17 +2159,18 @@ static void ggml_vk_queue_command_pools_cleanup(vk_device& device) {
     }
 }
 
+static std::vector<uint32_t> ggml_vk_find_memory_properties(const vk::PhysicalDeviceMemoryProperties* mem_props, vk::MemoryRequirements* mem_req, vk::MemoryPropertyFlags flags) {
+    std::vector<uint32_t> indices;
 
-static uint32_t find_properties(const vk::PhysicalDeviceMemoryProperties* mem_props, vk::MemoryRequirements* mem_req, vk::MemoryPropertyFlags flags) {
     for (uint32_t i = 0; i < mem_props->memoryTypeCount; ++i) {
         vk::MemoryType memory_type = mem_props->memoryTypes[i];
         if ((mem_req->memoryTypeBits & ((uint64_t)1 << i)) &&
             (flags & memory_type.propertyFlags) == flags &&
             mem_props->memoryHeaps[memory_type.heapIndex].size >= mem_req->size) {
-            return static_cast<int32_t>(i);
+            indices.push_back(i);
         }
     }
-    return UINT32_MAX;
+    return indices;
 }
 
 static vk_buffer ggml_vk_create_buffer(vk_device& device, size_t size, const std::initializer_list<vk::MemoryPropertyFlags> & req_flags_list) {
@@ -2212,22 +2213,24 @@ static vk_buffer ggml_vk_create_buffer(vk_device& device, size_t size, const std
     for (auto it = req_flags_list.begin(); it != req_flags_list.end(); it++) {
         const auto & req_flags = *it;
 
-        uint32_t memory_type_index = find_properties(&mem_props, &mem_req, req_flags);
+        const std::vector<uint32_t> memory_type_indices = ggml_vk_find_memory_properties(&mem_props, &mem_req, req_flags);
 
-        if (memory_type_index == UINT32_MAX) {
+        if (memory_type_indices.empty()) {
             continue;
         }
         buf->memory_property_flags = req_flags;
 
-        try {
-            buf->device_memory = device->device.allocateMemory({ mem_req.size, memory_type_index, &mem_flags_info });
-            break;
-        } catch (const vk::SystemError& e) {
-            // loop and retry
-            // during last attempt throw the exception
-            if (it + 1 == req_flags_list.end()) {
-                device->device.destroyBuffer(buf->buffer);
-                throw e;
+        for (auto mtype_it = memory_type_indices.begin(); mtype_it != memory_type_indices.end(); mtype_it++) {
+            try {
+                buf->device_memory = device->device.allocateMemory({ mem_req.size, *mtype_it, &mem_flags_info });
+                break;
+            } catch (const vk::SystemError& e) {
+                // loop and retry
+                // during last attempt throw the exception
+                if (it + 1 == req_flags_list.end() && mtype_it + 1 == memory_type_indices.end()) {
+                    device->device.destroyBuffer(buf->buffer);
+                    throw e;
+                }
             }
         }
     }
@@ -13204,25 +13207,28 @@ void ggml_backend_vk_get_device_memory(int device, size_t * free, size_t * total
     vk::PhysicalDevice vkdev = vk_instance.instance.enumeratePhysicalDevices()[vk_instance.device_indices[device]];
     vk::PhysicalDeviceMemoryBudgetPropertiesEXT budgetprops;
     vk::PhysicalDeviceMemoryProperties2 memprops = {};
-    bool membudget_supported = vk_instance.device_supports_membudget[device];
+    const bool membudget_supported = vk_instance.device_supports_membudget[device];
+    const bool is_integrated_gpu = vkdev.getProperties().deviceType == vk::PhysicalDeviceType::eIntegratedGpu;
 
     if (membudget_supported) {
         memprops.pNext = &budgetprops;
     }
     vkdev.getMemoryProperties2(&memprops);
 
+    *total = 0;
+    *free = 0;
+
     for (uint32_t i = 0; i < memprops.memoryProperties.memoryHeapCount; ++i) {
         const vk::MemoryHeap & heap = memprops.memoryProperties.memoryHeaps[i];
 
-        if (heap.flags & vk::MemoryHeapFlagBits::eDeviceLocal) {
-            *total = heap.size;
+        if (is_integrated_gpu || (heap.flags & vk::MemoryHeapFlagBits::eDeviceLocal)) {
+            *total += heap.size;
 
             if (membudget_supported && i < budgetprops.heapUsage.size()) {
-                *free = budgetprops.heapBudget[i] - budgetprops.heapUsage[i];
+                *free += budgetprops.heapBudget[i] - budgetprops.heapUsage[i];
             } else {
-                *free = heap.size;
+                *free += heap.size;
             }
-            break;
         }
     }
 }

From 86fde91e62c3f72ab7ed8a540dc1be049b735477 Mon Sep 17 00:00:00 2001
From: Eric Curtin <eric.curtin@docker.com>
Date: Sun, 9 Nov 2025 09:25:38 +0000
Subject: [PATCH 131/185] Switch to using Ubuntu 25.10 vulkan/mesa (#16497)

Because "Ubuntu packages to be discontinued in Vulkan SDK"

Signed-off-by: Eric Curtin <eric.curtin@docker.com>
---
 .devops/vulkan.Dockerfile | 24 ++++--------------------
 1 file changed, 4 insertions(+), 20 deletions(-)

diff --git a/.devops/vulkan.Dockerfile b/.devops/vulkan.Dockerfile
index 6cf87c67e85..75924684037 100644
--- a/.devops/vulkan.Dockerfile
+++ b/.devops/vulkan.Dockerfile
@@ -1,4 +1,4 @@
-ARG UBUNTU_VERSION=24.04
+ARG UBUNTU_VERSION=25.10
 
 FROM ubuntu:$UBUNTU_VERSION AS build
 
@@ -7,32 +7,16 @@ FROM ubuntu:$UBUNTU_VERSION AS build
 # Install build tools
 RUN apt update && apt install -y git build-essential cmake wget xz-utils
 
-# Install Vulkan SDK
-ARG VULKAN_VERSION=1.4.321.1
-RUN ARCH=$(uname -m) && \
-    wget -qO /tmp/vulkan-sdk.tar.xz https://sdk.lunarg.com/sdk/download/${VULKAN_VERSION}/linux/vulkan-sdk-linux-${ARCH}-${VULKAN_VERSION}.tar.xz && \
-    mkdir -p /opt/vulkan && \
-    tar -xf /tmp/vulkan-sdk.tar.xz -C /tmp --strip-components=1 && \
-    mv /tmp/${ARCH}/* /opt/vulkan/ && \
-    rm -rf /tmp/*
-
 # Install cURL and Vulkan SDK dependencies
 RUN apt install -y libcurl4-openssl-dev curl \
-    libxcb-xinput0 libxcb-xinerama0 libxcb-cursor-dev
-
-# Set environment variables
-ENV VULKAN_SDK=/opt/vulkan
-ENV PATH=$VULKAN_SDK/bin:$PATH
-ENV LD_LIBRARY_PATH=$VULKAN_SDK/lib:$LD_LIBRARY_PATH
-ENV CMAKE_PREFIX_PATH=$VULKAN_SDK:$CMAKE_PREFIX_PATH
-ENV PKG_CONFIG_PATH=$VULKAN_SDK/lib/pkgconfig:$PKG_CONFIG_PATH
+    libxcb-xinput0 libxcb-xinerama0 libxcb-cursor-dev libvulkan-dev glslc
 
 # Build it
 WORKDIR /app
 
 COPY . .
 
-RUN cmake -B build -DGGML_NATIVE=OFF -DGGML_VULKAN=1  -DLLAMA_BUILD_TESTS=OFF -DGGML_BACKEND_DL=ON -DGGML_CPU_ALL_VARIANTS=ON && \
+RUN cmake -B build -DGGML_NATIVE=OFF -DGGML_VULKAN=ON -DLLAMA_BUILD_TESTS=OFF -DGGML_BACKEND_DL=ON -DGGML_CPU_ALL_VARIANTS=ON && \
     cmake --build build --config Release -j$(nproc)
 
 RUN mkdir -p /app/lib && \
@@ -50,7 +34,7 @@ RUN mkdir -p /app/full \
 FROM ubuntu:$UBUNTU_VERSION AS base
 
 RUN apt-get update \
-    && apt-get install -y libgomp1 curl libvulkan-dev \
+    && apt-get install -y libgomp1 curl libvulkan1 mesa-vulkan-drivers \
     && apt autoremove -y \
     && apt clean -y \
     && rm -rf /tmp/* /var/tmp/* \

From ef1d8269972bd086bee2554fd31a865c6da84f33 Mon Sep 17 00:00:00 2001
From: Georgi Gerganov <ggerganov@gmail.com>
Date: Sun, 9 Nov 2025 12:53:29 +0200
Subject: [PATCH 132/185] benches : add folder with benchmarks (#16931)

* benches : add folder with benchmarks

* benches : update dgx-spark bench
---
 benches/dgx-spark.md | 264 +++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 264 insertions(+)
 create mode 100644 benches/dgx-spark.md

diff --git a/benches/dgx-spark.md b/benches/dgx-spark.md
new file mode 100644
index 00000000000..ec6c20d8a05
--- /dev/null
+++ b/benches/dgx-spark.md
@@ -0,0 +1,264 @@
+## System info
+
+```bash
+uname --all
+Linux spark-17ed 6.11.0-1016-nvidia #16-Ubuntu SMP PREEMPT_DYNAMIC Sun Sep 21 16:52:46 UTC 2025 aarch64 aarch64 aarch64 GNU/Linux
+
+g++ --version
+g++ (Ubuntu 13.3.0-6ubuntu2~24.04) 13.3.0
+
+nvidia-smi
+Sun Nov  2 10:43:25 2025
++-----------------------------------------------------------------------------------------+
+| NVIDIA-SMI 580.95.05              Driver Version: 580.95.05      CUDA Version: 13.0     |
++-----------------------------------------+------------------------+----------------------+
+| GPU  Name                 Persistence-M | Bus-Id          Disp.A | Volatile Uncorr. ECC |
+| Fan  Temp   Perf          Pwr:Usage/Cap |           Memory-Usage | GPU-Util  Compute M. |
+|                                         |                        |               MIG M. |
+|=========================================+========================+======================|
+|   0  NVIDIA GB10                    On  |   0000000F:01:00.0 Off |                  N/A |
+| N/A   35C    P8              4W /  N/A  | Not Supported          |      0%      Default |
+|                                         |                        |                  N/A |
++-----------------------------------------+------------------------+----------------------+
+```
+
+## ggml-org/gpt-oss-20b-GGUF
+
+Model: https://huggingface.co/ggml-org/gpt-oss-20b-GGUF
+
+- `llama-batched-bench`
+
+
+main: n_kv_max = 270336, n_batch = 2048, n_ubatch = 2048, flash_attn = 1, is_pp_shared = 0, n_gpu_layers = -1, n_threads = 20, n_threads_batch = 20
+
+|    PP |     TG |    B |   N_KV |   T_PP s | S_PP t/s |   T_TG s | S_TG t/s |      T s |    S t/s |
+|-------|--------|------|--------|----------|----------|----------|----------|----------|----------|
+|   512 |     32 |    1 |    544 |    0.374 |  1369.01 |    0.383 |    83.64 |    0.757 |   719.01 |
+|   512 |     32 |    2 |   1088 |    0.274 |  3741.35 |    0.659 |    97.14 |    0.933 |  1166.66 |
+|   512 |     32 |    4 |   2176 |    0.526 |  3896.47 |    0.817 |   156.73 |    1.342 |  1621.08 |
+|   512 |     32 |    8 |   4352 |    1.044 |  3925.10 |    0.987 |   259.44 |    2.030 |  2143.56 |
+|   512 |     32 |   16 |   8704 |    2.076 |  3945.84 |    1.248 |   410.32 |    3.324 |  2618.60 |
+|   512 |     32 |   32 |  17408 |    4.170 |  3929.28 |    1.630 |   628.40 |    5.799 |  3001.76 |
+|  4096 |     32 |    1 |   4128 |    1.083 |  3782.66 |    0.394 |    81.21 |    1.477 |  2795.13 |
+|  4096 |     32 |    2 |   8256 |    2.166 |  3782.72 |    0.725 |    88.28 |    2.891 |  2856.14 |
+|  4096 |     32 |    4 |  16512 |    4.333 |  3780.88 |    0.896 |   142.82 |    5.230 |  3157.38 |
+|  4096 |     32 |    8 |  33024 |    8.618 |  3802.14 |    1.155 |   221.69 |    9.773 |  3379.08 |
+|  4096 |     32 |   16 |  66048 |   17.330 |  3781.73 |    1.598 |   320.34 |   18.928 |  3489.45 |
+|  4096 |     32 |   32 | 132096 |   34.671 |  3780.48 |    2.336 |   438.35 |   37.007 |  3569.51 |
+|  8192 |     32 |    1 |   8224 |    2.233 |  3668.56 |    0.438 |    72.98 |    2.671 |  3078.44 |
+|  8192 |     32 |    2 |  16448 |    4.425 |  3702.95 |    0.756 |    84.66 |    5.181 |  3174.95 |
+|  8192 |     32 |    4 |  32896 |    8.859 |  3698.64 |    0.967 |   132.38 |    9.826 |  3347.72 |
+|  8192 |     32 |    8 |  65792 |   17.714 |  3699.57 |    1.277 |   200.52 |   18.991 |  3464.35 |
+|  8192 |     32 |   16 | 131584 |   35.494 |  3692.84 |    1.841 |   278.12 |   37.335 |  3524.46 |
+|  8192 |     32 |   32 | 263168 |   70.949 |  3694.82 |    2.798 |   365.99 |   73.747 |  3568.53 |
+
+
+- `llama-bench`
+
+| model                          |       size |     params | backend    | ngl | n_ubatch | fa | mmap |            test |                  t/s |
+| ------------------------------ | ---------: | ---------: | ---------- | --: | -------: | -: | ---: | --------------: | -------------------: |
+| gpt-oss 20B MXFP4 MoE          |  11.27 GiB |    20.91 B | CUDA       |  99 |     2048 |  1 |    0 |          pp2048 |      3714.25 ± 20.36 |
+| gpt-oss 20B MXFP4 MoE          |  11.27 GiB |    20.91 B | CUDA       |  99 |     2048 |  1 |    0 |            tg32 |         86.58 ± 0.43 |
+| gpt-oss 20B MXFP4 MoE          |  11.27 GiB |    20.91 B | CUDA       |  99 |     2048 |  1 |    0 |  pp2048 @ d4096 |      3445.17 ± 17.85 |
+| gpt-oss 20B MXFP4 MoE          |  11.27 GiB |    20.91 B | CUDA       |  99 |     2048 |  1 |    0 |    tg32 @ d4096 |         81.72 ± 0.53 |
+| gpt-oss 20B MXFP4 MoE          |  11.27 GiB |    20.91 B | CUDA       |  99 |     2048 |  1 |    0 |  pp2048 @ d8192 |      3218.78 ± 11.34 |
+| gpt-oss 20B MXFP4 MoE          |  11.27 GiB |    20.91 B | CUDA       |  99 |     2048 |  1 |    0 |    tg32 @ d8192 |         74.86 ± 0.64 |
+| gpt-oss 20B MXFP4 MoE          |  11.27 GiB |    20.91 B | CUDA       |  99 |     2048 |  1 |    0 | pp2048 @ d16384 |       2732.83 ± 7.17 |
+| gpt-oss 20B MXFP4 MoE          |  11.27 GiB |    20.91 B | CUDA       |  99 |     2048 |  1 |    0 |   tg32 @ d16384 |         71.57 ± 0.51 |
+| gpt-oss 20B MXFP4 MoE          |  11.27 GiB |    20.91 B | CUDA       |  99 |     2048 |  1 |    0 | pp2048 @ d32768 |      2119.75 ± 12.81 |
+| gpt-oss 20B MXFP4 MoE          |  11.27 GiB |    20.91 B | CUDA       |  99 |     2048 |  1 |    0 |   tg32 @ d32768 |         62.33 ± 0.24 |
+
+build: eeee367de (6989)
+
+## ggml-org/gpt-oss-120b-GGUF
+
+Model: https://huggingface.co/ggml-org/gpt-oss-120b-GGUF
+
+- `llama-batched-bench`
+
+
+main: n_kv_max = 270336, n_batch = 2048, n_ubatch = 2048, flash_attn = 1, is_pp_shared = 0, n_gpu_layers = -1, n_threads = 20, n_threads_batch = 20
+
+|    PP |     TG |    B |   N_KV |   T_PP s | S_PP t/s |   T_TG s | S_TG t/s |      T s |    S t/s |
+|-------|--------|------|--------|----------|----------|----------|----------|----------|----------|
+|   512 |     32 |    1 |    544 |    0.571 |   897.18 |    0.543 |    58.96 |    1.113 |   488.60 |
+|   512 |     32 |    2 |   1088 |    0.593 |  1725.37 |    1.041 |    61.45 |    1.635 |   665.48 |
+|   512 |     32 |    4 |   2176 |    1.043 |  1963.15 |    1.334 |    95.95 |    2.377 |   915.36 |
+|   512 |     32 |    8 |   4352 |    2.099 |  1951.63 |    1.717 |   149.07 |    3.816 |  1140.45 |
+|   512 |     32 |   16 |   8704 |    4.207 |  1947.12 |    2.311 |   221.56 |    6.518 |  1335.35 |
+|   512 |     32 |   32 |  17408 |    8.422 |  1945.36 |    3.298 |   310.46 |   11.720 |  1485.27 |
+|  4096 |     32 |    1 |   4128 |    2.138 |  1915.88 |    0.571 |    56.09 |    2.708 |  1524.12 |
+|  4096 |     32 |    2 |   8256 |    4.266 |  1920.25 |    1.137 |    56.27 |    5.404 |  1527.90 |
+|  4096 |     32 |    4 |  16512 |    8.564 |  1913.02 |    1.471 |    86.99 |   10.036 |  1645.29 |
+|  4096 |     32 |    8 |  33024 |   17.092 |  1917.19 |    1.979 |   129.33 |   19.071 |  1731.63 |
+|  4096 |     32 |   16 |  66048 |   34.211 |  1915.65 |    2.850 |   179.66 |   37.061 |  1782.15 |
+|  4096 |     32 |   32 | 132096 |   68.394 |  1916.44 |    4.381 |   233.72 |   72.775 |  1815.13 |
+|  8192 |     32 |    1 |   8224 |    4.349 |  1883.45 |    0.620 |    51.65 |    4.969 |  1655.04 |
+|  8192 |     32 |    2 |  16448 |    8.674 |  1888.83 |    1.178 |    54.33 |    9.852 |  1669.48 |
+|  8192 |     32 |    4 |  32896 |   17.351 |  1888.55 |    1.580 |    81.01 |   18.931 |  1737.68 |
+|  8192 |     32 |    8 |  65792 |   34.743 |  1886.31 |    2.173 |   117.80 |   36.916 |  1782.20 |
+|  8192 |     32 |   16 | 131584 |   69.413 |  1888.29 |    3.297 |   155.28 |   72.710 |  1809.70 |
+|  8192 |     32 |   32 | 263168 |  138.903 |  1887.24 |    5.004 |   204.63 |  143.907 |  1828.73 |
+
+
+- `llama-bench`
+
+| model                          |       size |     params | backend    | ngl | n_ubatch | fa | mmap |            test |                  t/s |
+| ------------------------------ | ---------: | ---------: | ---------- | --: | -------: | -: | ---: | --------------: | -------------------: |
+| gpt-oss 120B MXFP4 MoE         |  59.02 GiB |   116.83 B | CUDA       |  99 |     2048 |  1 |    0 |          pp2048 |       1919.36 ± 5.01 |
+| gpt-oss 120B MXFP4 MoE         |  59.02 GiB |   116.83 B | CUDA       |  99 |     2048 |  1 |    0 |            tg32 |         60.40 ± 0.30 |
+| gpt-oss 120B MXFP4 MoE         |  59.02 GiB |   116.83 B | CUDA       |  99 |     2048 |  1 |    0 |  pp2048 @ d4096 |       1825.30 ± 6.37 |
+| gpt-oss 120B MXFP4 MoE         |  59.02 GiB |   116.83 B | CUDA       |  99 |     2048 |  1 |    0 |    tg32 @ d4096 |         56.94 ± 0.29 |
+| gpt-oss 120B MXFP4 MoE         |  59.02 GiB |   116.83 B | CUDA       |  99 |     2048 |  1 |    0 |  pp2048 @ d8192 |       1739.19 ± 6.00 |
+| gpt-oss 120B MXFP4 MoE         |  59.02 GiB |   116.83 B | CUDA       |  99 |     2048 |  1 |    0 |    tg32 @ d8192 |         52.51 ± 0.42 |
+| gpt-oss 120B MXFP4 MoE         |  59.02 GiB |   116.83 B | CUDA       |  99 |     2048 |  1 |    0 | pp2048 @ d16384 |       1536.75 ± 4.27 |
+| gpt-oss 120B MXFP4 MoE         |  59.02 GiB |   116.83 B | CUDA       |  99 |     2048 |  1 |    0 |   tg32 @ d16384 |         49.33 ± 0.27 |
+| gpt-oss 120B MXFP4 MoE         |  59.02 GiB |   116.83 B | CUDA       |  99 |     2048 |  1 |    0 | pp2048 @ d32768 |       1255.85 ± 3.26 |
+| gpt-oss 120B MXFP4 MoE         |  59.02 GiB |   116.83 B | CUDA       |  99 |     2048 |  1 |    0 |   tg32 @ d32768 |         42.99 ± 0.18 |
+
+build: eeee367de (6989)
+
+## ggml-org/Qwen3-Coder-30B-A3B-Instruct-Q8_0-GGUF
+
+Model: https://huggingface.co/ggml-org/Qwen3-Coder-30B-A3B-Instruct-Q8_0-GGUF
+
+- `llama-batched-bench`
+
+
+main: n_kv_max = 270336, n_batch = 2048, n_ubatch = 2048, flash_attn = 1, is_pp_shared = 0, n_gpu_layers = -1, n_threads = 20, n_threads_batch = 20
+
+|    PP |     TG |    B |   N_KV |   T_PP s | S_PP t/s |   T_TG s | S_TG t/s |      T s |    S t/s |
+|-------|--------|------|--------|----------|----------|----------|----------|----------|----------|
+|   512 |     32 |    1 |    544 |    0.398 |  1285.90 |    0.530 |    60.41 |    0.928 |   586.27 |
+|   512 |     32 |    2 |   1088 |    0.386 |  2651.65 |    0.948 |    67.50 |    1.334 |   815.38 |
+|   512 |     32 |    4 |   2176 |    0.666 |  3076.37 |    1.209 |   105.87 |    1.875 |  1160.71 |
+|   512 |     32 |    8 |   4352 |    1.325 |  3091.39 |    1.610 |   158.98 |    2.935 |  1482.65 |
+|   512 |     32 |   16 |   8704 |    2.664 |  3075.58 |    2.150 |   238.19 |    4.813 |  1808.39 |
+|   512 |     32 |   32 |  17408 |    5.336 |  3070.31 |    2.904 |   352.59 |    8.240 |  2112.50 |
+|  4096 |     32 |    1 |   4128 |    1.444 |  2836.81 |    0.581 |    55.09 |    2.025 |  2038.81 |
+|  4096 |     32 |    2 |   8256 |    2.872 |  2852.14 |    1.084 |    59.06 |    3.956 |  2086.99 |
+|  4096 |     32 |    4 |  16512 |    5.744 |  2852.32 |    1.440 |    88.90 |    7.184 |  2298.47 |
+|  4096 |     32 |    8 |  33024 |   11.463 |  2858.68 |    2.068 |   123.78 |   13.531 |  2440.65 |
+|  4096 |     32 |   16 |  66048 |   22.915 |  2859.95 |    3.018 |   169.67 |   25.933 |  2546.90 |
+|  4096 |     32 |   32 | 132096 |   45.956 |  2852.10 |    4.609 |   222.18 |   50.565 |  2612.39 |
+|  8192 |     32 |    1 |   8224 |    3.063 |  2674.72 |    0.693 |    46.20 |    3.755 |  2189.92 |
+|  8192 |     32 |    2 |  16448 |    6.109 |  2681.87 |    1.214 |    52.71 |    7.323 |  2245.98 |
+|  8192 |     32 |    4 |  32896 |   12.197 |  2686.63 |    1.682 |    76.11 |   13.878 |  2370.30 |
+|  8192 |     32 |    8 |  65792 |   24.409 |  2684.94 |    2.556 |   100.17 |   26.965 |  2439.95 |
+|  8192 |     32 |   16 | 131584 |   48.753 |  2688.50 |    3.994 |   128.20 |   52.747 |  2494.64 |
+|  8192 |     32 |   32 | 263168 |   97.508 |  2688.42 |    6.528 |   156.86 |  104.037 |  2529.57 |
+
+
+- `llama-bench`
+
+| model                          |       size |     params | backend    | ngl | n_ubatch | fa | mmap |            test |                  t/s |
+| ------------------------------ | ---------: | ---------: | ---------- | --: | -------: | -: | ---: | --------------: | -------------------: |
+| qwen3moe 30B.A3B Q8_0          |  30.25 GiB |    30.53 B | CUDA       |  99 |     2048 |  1 |    0 |          pp2048 |       2925.55 ± 4.25 |
+| qwen3moe 30B.A3B Q8_0          |  30.25 GiB |    30.53 B | CUDA       |  99 |     2048 |  1 |    0 |            tg32 |         62.80 ± 0.27 |
+| qwen3moe 30B.A3B Q8_0          |  30.25 GiB |    30.53 B | CUDA       |  99 |     2048 |  1 |    0 |  pp2048 @ d4096 |       2531.01 ± 6.79 |
+| qwen3moe 30B.A3B Q8_0          |  30.25 GiB |    30.53 B | CUDA       |  99 |     2048 |  1 |    0 |    tg32 @ d4096 |         55.86 ± 0.33 |
+| qwen3moe 30B.A3B Q8_0          |  30.25 GiB |    30.53 B | CUDA       |  99 |     2048 |  1 |    0 |  pp2048 @ d8192 |       2244.39 ± 5.33 |
+| qwen3moe 30B.A3B Q8_0          |  30.25 GiB |    30.53 B | CUDA       |  99 |     2048 |  1 |    0 |    tg32 @ d8192 |         45.95 ± 0.33 |
+| qwen3moe 30B.A3B Q8_0          |  30.25 GiB |    30.53 B | CUDA       |  99 |     2048 |  1 |    0 | pp2048 @ d16384 |       1783.17 ± 3.68 |
+| qwen3moe 30B.A3B Q8_0          |  30.25 GiB |    30.53 B | CUDA       |  99 |     2048 |  1 |    0 |   tg32 @ d16384 |         39.07 ± 0.10 |
+| qwen3moe 30B.A3B Q8_0          |  30.25 GiB |    30.53 B | CUDA       |  99 |     2048 |  1 |    0 | pp2048 @ d32768 |       1241.90 ± 3.13 |
+| qwen3moe 30B.A3B Q8_0          |  30.25 GiB |    30.53 B | CUDA       |  99 |     2048 |  1 |    0 |   tg32 @ d32768 |         29.92 ± 0.06 |
+
+build: eeee367de (6989)
+
+## ggml-org/Qwen2.5-Coder-7B-Q8_0-GGUF
+
+Model: https://huggingface.co/ggml-org/Qwen2.5-Coder-7B-Q8_0-GGUF
+
+- `llama-batched-bench`
+
+
+main: n_kv_max = 270336, n_batch = 2048, n_ubatch = 2048, flash_attn = 1, is_pp_shared = 0, n_gpu_layers = -1, n_threads = 20, n_threads_batch = 20
+
+|    PP |     TG |    B |   N_KV |   T_PP s | S_PP t/s |   T_TG s | S_TG t/s |      T s |    S t/s |
+|-------|--------|------|--------|----------|----------|----------|----------|----------|----------|
+|   512 |     32 |    1 |    544 |    0.211 |  2421.57 |    1.055 |    30.33 |    1.266 |   429.57 |
+|   512 |     32 |    2 |   1088 |    0.419 |  2441.34 |    1.130 |    56.65 |    1.549 |   702.32 |
+|   512 |     32 |    4 |   2176 |    0.873 |  2345.54 |    1.174 |   108.99 |    2.048 |  1062.74 |
+|   512 |     32 |    8 |   4352 |    1.727 |  2371.85 |    1.254 |   204.22 |    2.980 |  1460.19 |
+|   512 |     32 |   16 |   8704 |    3.452 |  2373.22 |    1.492 |   343.16 |    4.944 |  1760.56 |
+|   512 |     32 |   32 |  17408 |    6.916 |  2368.93 |    1.675 |   611.51 |    8.591 |  2026.36 |
+|  4096 |     32 |    1 |   4128 |    1.799 |  2277.26 |    1.084 |    29.51 |    2.883 |  1431.91 |
+|  4096 |     32 |    2 |   8256 |    3.577 |  2290.01 |    1.196 |    53.50 |    4.774 |  1729.51 |
+|  4096 |     32 |    4 |  16512 |    7.172 |  2284.36 |    1.313 |    97.50 |    8.485 |  1946.00 |
+|  4096 |     32 |    8 |  33024 |   14.341 |  2284.96 |    1.520 |   168.46 |   15.860 |  2082.18 |
+|  4096 |     32 |   16 |  66048 |   28.675 |  2285.44 |    1.983 |   258.21 |   30.658 |  2154.33 |
+|  4096 |     32 |   32 | 132096 |   57.354 |  2285.32 |    2.640 |   387.87 |   59.994 |  2201.82 |
+|  8192 |     32 |    1 |   8224 |    3.701 |  2213.75 |    1.119 |    28.59 |    4.820 |  1706.34 |
+|  8192 |     32 |    2 |  16448 |    7.410 |  2211.19 |    1.272 |    50.31 |    8.682 |  1894.56 |
+|  8192 |     32 |    4 |  32896 |   14.802 |  2213.83 |    1.460 |    87.68 |   16.261 |  2022.96 |
+|  8192 |     32 |    8 |  65792 |   29.609 |  2213.35 |    1.781 |   143.74 |   31.390 |  2095.93 |
+|  8192 |     32 |   16 | 131584 |   59.229 |  2212.96 |    2.495 |   205.17 |   61.725 |  2131.79 |
+|  8192 |     32 |   32 | 263168 |  118.449 |  2213.15 |    3.714 |   275.75 |  122.162 |  2154.25 |
+
+
+- `llama-bench`
+
+| model                          |       size |     params | backend    | ngl | n_ubatch | fa | mmap |            test |                  t/s |
+| ------------------------------ | ---------: | ---------: | ---------- | --: | -------: | -: | ---: | --------------: | -------------------: |
+| qwen2 7B Q8_0                  |   7.54 GiB |     7.62 B | CUDA       |  99 |     2048 |  1 |    0 |          pp2048 |       2272.74 ± 4.68 |
+| qwen2 7B Q8_0                  |   7.54 GiB |     7.62 B | CUDA       |  99 |     2048 |  1 |    0 |            tg32 |         30.66 ± 0.02 |
+| qwen2 7B Q8_0                  |   7.54 GiB |     7.62 B | CUDA       |  99 |     2048 |  1 |    0 |  pp2048 @ d4096 |       2107.80 ± 9.55 |
+| qwen2 7B Q8_0                  |   7.54 GiB |     7.62 B | CUDA       |  99 |     2048 |  1 |    0 |    tg32 @ d4096 |         29.71 ± 0.05 |
+| qwen2 7B Q8_0                  |   7.54 GiB |     7.62 B | CUDA       |  99 |     2048 |  1 |    0 |  pp2048 @ d8192 |       1937.80 ± 6.75 |
+| qwen2 7B Q8_0                  |   7.54 GiB |     7.62 B | CUDA       |  99 |     2048 |  1 |    0 |    tg32 @ d8192 |         28.86 ± 0.04 |
+| qwen2 7B Q8_0                  |   7.54 GiB |     7.62 B | CUDA       |  99 |     2048 |  1 |    0 | pp2048 @ d16384 |       1641.12 ± 1.78 |
+| qwen2 7B Q8_0                  |   7.54 GiB |     7.62 B | CUDA       |  99 |     2048 |  1 |    0 |   tg32 @ d16384 |         27.24 ± 0.04 |
+| qwen2 7B Q8_0                  |   7.54 GiB |     7.62 B | CUDA       |  99 |     2048 |  1 |    0 | pp2048 @ d32768 |       1296.02 ± 2.67 |
+| qwen2 7B Q8_0                  |   7.54 GiB |     7.62 B | CUDA       |  99 |     2048 |  1 |    0 |   tg32 @ d32768 |         23.78 ± 0.03 |
+
+build: eeee367de (6989)
+
+## ggml-org/gemma-3-4b-it-qat-GGUF
+
+Model: https://huggingface.co/ggml-org/gemma-3-4b-it-qat-GGUF
+
+- `llama-batched-bench`
+
+
+main: n_kv_max = 270336, n_batch = 2048, n_ubatch = 2048, flash_attn = 1, is_pp_shared = 0, n_gpu_layers = -1, n_threads = 20, n_threads_batch = 20
+
+|    PP |     TG |    B |   N_KV |   T_PP s | S_PP t/s |   T_TG s | S_TG t/s |      T s |    S t/s |
+|-------|--------|------|--------|----------|----------|----------|----------|----------|----------|
+|   512 |     32 |    1 |    544 |    0.094 |  5434.73 |    0.394 |    81.21 |    0.488 |  1114.15 |
+|   512 |     32 |    2 |   1088 |    0.168 |  6091.68 |    0.498 |   128.52 |    0.666 |  1633.41 |
+|   512 |     32 |    4 |   2176 |    0.341 |  6010.68 |    0.542 |   236.37 |    0.882 |  2466.43 |
+|   512 |     32 |    8 |   4352 |    0.665 |  6161.46 |    0.678 |   377.74 |    1.342 |  3241.72 |
+|   512 |     32 |   16 |   8704 |    1.323 |  6193.19 |    0.902 |   567.41 |    2.225 |  3911.74 |
+|   512 |     32 |   32 |  17408 |    2.642 |  6202.03 |    1.231 |   832.03 |    3.872 |  4495.36 |
+|  4096 |     32 |    1 |   4128 |    0.701 |  5840.49 |    0.439 |    72.95 |    1.140 |  3621.23 |
+|  4096 |     32 |    2 |   8256 |    1.387 |  5906.82 |    0.574 |   111.48 |    1.961 |  4210.12 |
+|  4096 |     32 |    4 |  16512 |    2.758 |  5940.33 |    0.651 |   196.58 |    3.409 |  4843.33 |
+|  4096 |     32 |    8 |  33024 |    5.491 |  5967.56 |    0.876 |   292.40 |    6.367 |  5187.12 |
+|  4096 |     32 |   16 |  66048 |   10.978 |  5969.58 |    1.275 |   401.69 |   12.253 |  5390.38 |
+|  4096 |     32 |   32 | 132096 |   21.944 |  5972.93 |    1.992 |   514.16 |   23.936 |  5518.73 |
+|  8192 |     32 |    1 |   8224 |    1.402 |  5841.91 |    0.452 |    70.73 |    1.855 |  4434.12 |
+|  8192 |     32 |    2 |  16448 |    2.793 |  5865.34 |    0.637 |   100.55 |    3.430 |  4795.51 |
+|  8192 |     32 |    4 |  32896 |    5.564 |  5889.64 |    0.770 |   166.26 |    6.334 |  5193.95 |
+|  8192 |     32 |    8 |  65792 |   11.114 |  5896.44 |    1.122 |   228.07 |   12.237 |  5376.51 |
+|  8192 |     32 |   16 | 131584 |   22.210 |  5901.38 |    1.789 |   286.15 |   24.000 |  5482.74 |
+|  8192 |     32 |   32 | 263168 |   44.382 |  5906.56 |    3.044 |   336.38 |   47.426 |  5549.02 |
+
+
+- `llama-bench`
+
+| model                          |       size |     params | backend    | ngl | n_ubatch | fa | mmap |            test |                  t/s |
+| ------------------------------ | ---------: | ---------: | ---------- | --: | -------: | -: | ---: | --------------: | -------------------: |
+| gemma3 4B Q4_0                 |   2.35 GiB |     3.88 B | CUDA       |  99 |     2048 |  1 |    0 |          pp2048 |      5810.04 ± 21.71 |
+| gemma3 4B Q4_0                 |   2.35 GiB |     3.88 B | CUDA       |  99 |     2048 |  1 |    0 |            tg32 |         84.54 ± 0.18 |
+| gemma3 4B Q4_0                 |   2.35 GiB |     3.88 B | CUDA       |  99 |     2048 |  1 |    0 |  pp2048 @ d4096 |       5288.04 ± 3.54 |
+| gemma3 4B Q4_0                 |   2.35 GiB |     3.88 B | CUDA       |  99 |     2048 |  1 |    0 |    tg32 @ d4096 |         78.82 ± 1.37 |
+| gemma3 4B Q4_0                 |   2.35 GiB |     3.88 B | CUDA       |  99 |     2048 |  1 |    0 |  pp2048 @ d8192 |      4960.43 ± 16.64 |
+| gemma3 4B Q4_0                 |   2.35 GiB |     3.88 B | CUDA       |  99 |     2048 |  1 |    0 |    tg32 @ d8192 |         74.13 ± 0.30 |
+| gemma3 4B Q4_0                 |   2.35 GiB |     3.88 B | CUDA       |  99 |     2048 |  1 |    0 | pp2048 @ d16384 |      4495.92 ± 31.11 |
+| gemma3 4B Q4_0                 |   2.35 GiB |     3.88 B | CUDA       |  99 |     2048 |  1 |    0 |   tg32 @ d16384 |         72.37 ± 0.29 |
+| gemma3 4B Q4_0                 |   2.35 GiB |     3.88 B | CUDA       |  99 |     2048 |  1 |    0 | pp2048 @ d32768 |      3746.90 ± 40.01 |
+| gemma3 4B Q4_0                 |   2.35 GiB |     3.88 B | CUDA       |  99 |     2048 |  1 |    0 |   tg32 @ d32768 |         63.02 ± 0.20 |
+
+build: eeee367de (6989)
+

From cb1adf885105da7ce23db746b4202f4e987aa3e8 Mon Sep 17 00:00:00 2001
From: Georgi Gerganov <ggerganov@gmail.com>
Date: Sun, 9 Nov 2025 14:27:05 +0200
Subject: [PATCH 133/185] server : handle failures to restore host cache
 (#17078)

* server : handle failures to restore host cache

* server : add tests for the prompt cache
---
 tools/server/server.cpp                    |  3 ++
 tools/server/tests/unit/test_completion.py | 42 ++++++++++++++++++++++
 2 files changed, 45 insertions(+)

diff --git a/tools/server/server.cpp b/tools/server/server.cpp
index 9d91e32d1fb..6bd4be3cc17 100644
--- a/tools/server/server.cpp
+++ b/tools/server/server.cpp
@@ -1690,6 +1690,9 @@ struct server_slot {
         bool res = prompt_cache.load(prompt, tokens, ctx, id);
         if (!res) {
             SLT_WRN(*this, "%s", "failed to load prompt from cache\n");
+
+            llama_memory_seq_rm(llama_get_memory(ctx), id, -1, -1);
+            prompt.tokens.clear();
         }
     }
 
diff --git a/tools/server/tests/unit/test_completion.py b/tools/server/tests/unit/test_completion.py
index 3c0ce98973f..ef1757db21f 100644
--- a/tools/server/tests/unit/test_completion.py
+++ b/tools/server/tests/unit/test_completion.py
@@ -1,6 +1,8 @@
 import pytest
 import requests
 import time
+import random
+
 from openai import OpenAI
 from utils import *
 
@@ -564,3 +566,43 @@ def test_cancel_request():
     time.sleep(1) # wait for HTTP_POLLING_SECONDS
     res = server.make_request("GET", "/slots")
     assert res.body[0]["is_processing"] == False
+
+
+# this test exercises the host-memory prompt cache
+# ref: https://github.com/ggml-org/llama.cpp/pull/16391
+# ref: https://github.com/ggml-org/llama.cpp/pull/17078
+def test_completion_prompt_cache():
+    global server
+    server.n_slots = 2
+    server.kv_unified = True
+    server.start()
+
+    for _ in range(16):
+        # generate alternating random prompts with variable lengths in order to get them in and out of the cache
+        r = random.randint(0, 4)
+        prompt = (" Hello " +  str(r)) * (40 + r)
+        n_prompt = (40 + r)*5 + 2
+        n_predict = random.randint(1, 8)
+
+        res = server.make_request(
+            "POST",
+            "/completion",
+            data={
+                "prompt": prompt,
+                "n_predict": n_predict,
+            },
+        )
+
+        assert res.status_code == 200
+        assert "content" in res.body
+        content = res.body["content"]
+        assert isinstance(content, str)
+        assert len(content) > 0
+
+        assert type(res.body["has_new_line"]) == bool
+        assert "timings" in res.body
+        timings = res.body["timings"]
+
+        assert "prompt_n" in timings and timings["prompt_n"] + timings["cache_n"] == n_prompt
+        assert "predicted_n" in timings and timings["predicted_n"] == n_predict
+        assert "tokens" in res.body and isinstance(res.body["tokens"], list)

From 1c07c0c68c692d39b83f491bad9447af852bb652 Mon Sep 17 00:00:00 2001
From: compilade <git@compilade.net>
Date: Sun, 9 Nov 2025 09:45:50 -0500
Subject: [PATCH 134/185] convert : handle compressed-tensors quant method
 (#17069)

* convert : handle compressed-tensors quant method

* convert : handle int-quantized models

* convert : handle naive-quantized models

* gguf-py : __pos__ is also unary

* convert : fix flake8 lint

* convert : use F32 for dequant of pack-quantized tensors
---
 convert_hf_to_gguf.py | 91 +++++++++++++++++++++++++++++++++++++++----
 gguf-py/gguf/lazy.py  | 11 ++++--
 2 files changed, 92 insertions(+), 10 deletions(-)

diff --git a/convert_hf_to_gguf.py b/convert_hf_to_gguf.py
index 222f6ed6dc4..b155d112b1a 100755
--- a/convert_hf_to_gguf.py
+++ b/convert_hf_to_gguf.py
@@ -278,15 +278,14 @@ def dequant_bitnet(weight: Tensor, scale: Tensor) -> Tensor:
                 # The scale is inverted
                 return data / scale.float()
 
-            def dequant_simple(weight: Tensor, scale: Tensor) -> Tensor:
+            def dequant_simple(weight: Tensor, scale: Tensor, block_size: Sequence[int] | None = None) -> Tensor:
                 scale = scale.float()
 
-                if (weight_block_size := quant_config.get("weight_block_size")):
-                    # TODO: make sure it's a list of integers
-                    for i, size in enumerate(weight_block_size):
+                if block_size is not None:
+                    for i, size in enumerate(block_size):
                         scale = scale.repeat_interleave(size, i)
-                # unpad the scale (e.g. when the tensor size isn't a multiple of the block size)
-                scale = scale[tuple(slice(0, size) for size in weight.shape)]
+                    # unpad the scale (e.g. when the tensor size isn't a multiple of the block size)
+                    scale = scale[tuple(slice(0, size) for size in weight.shape)]
 
                 return weight.float() * scale
 
@@ -333,6 +332,40 @@ def dequant_gptq(g_idx: Tensor, qweight: Tensor, qzeros: Tensor, scales: Tensor)
 
                 return (scales[g_idx].float() * (weight - zeros[g_idx]).float()).T
 
+            def dequant_packed(w: Tensor, scale: Tensor, shape_tensor: Tensor, zero_point: Tensor | None, num_bits: int, group_size: int):
+                assert w.dtype == torch.int32
+                shape = tuple(shape_tensor.tolist())
+                assert len(shape) == 2
+                mask = (1 << num_bits) - 1
+
+                shifts = torch.arange(0, 32 - (num_bits - 1), num_bits, dtype=torch.int32)
+                if self.lazy:
+                    shifts = LazyTorchTensor.from_eager(shifts)
+
+                if zero_point is None:
+                    offset = 1 << (num_bits - 1)
+                else:
+                    assert len(zero_point.shape) == 2
+                    offset = (zero_point.unsqueeze(1) >> shifts.reshape(1, -1, 1)) & mask
+                    offset = offset.reshape(-1, zero_point.shape[1])
+                    # trim padding, and prepare for broadcast
+                    # NOTE: the zero-point is packed along dim 0
+                    offset = offset[:shape[0], :].unsqueeze(-1)
+
+                # extract values
+                # NOTE: the weights are packed along dim 1
+                unpacked = (w.unsqueeze(-1) >> shifts.reshape(1, 1, -1)) & mask
+                unpacked = unpacked.reshape(shape[0], -1)
+
+                # trim padding
+                unpacked = unpacked[:, :shape[1]]
+
+                # prepare for broadcast of the scale
+                unpacked = unpacked.reshape(shape[0], (unpacked.shape[-1] + group_size - 1) // group_size, group_size)
+                unpacked = unpacked - offset
+
+                return (unpacked * scale.unsqueeze(-1).float()).reshape(shape)
+
             if quant_method == "bitnet":
                 for name in self.model_tensors.keys():
                     if name.endswith(".weight_scale"):
@@ -342,12 +375,13 @@ def dequant_gptq(g_idx: Tensor, qweight: Tensor, qzeros: Tensor, scales: Tensor)
                         self.model_tensors[weight_name] = lambda w=w, s=s: dequant_bitnet(w(), s())
                         tensors_to_remove.append(name)
             elif quant_method == "fp8":
+                block_size = quant_config.get("weight_block_size")
                 for name in self.model_tensors.keys():
                     if name.endswith(".weight_scale_inv"):
                         weight_name = name.removesuffix("_scale_inv")
                         w = self.model_tensors[weight_name]
                         s = self.model_tensors[name]
-                        self.model_tensors[weight_name] = lambda w=w, s=s: dequant_simple(w(), s())
+                        self.model_tensors[weight_name] = lambda w=w, s=s, bs=block_size: dequant_simple(w(), s(), bs)
                         tensors_to_remove.append(name)
             elif quant_method == "gptq":
                 for name in self.model_tensors.keys():
@@ -371,6 +405,49 @@ def dequant_gptq(g_idx: Tensor, qweight: Tensor, qzeros: Tensor, scales: Tensor)
                                 ".scales",
                             )
                         ]
+            elif quant_method == "compressed-tensors":
+                quant_format = quant_config["format"]
+                groups = quant_config["config_groups"]
+                if len(groups) > 1:
+                    raise NotImplementedError("Can't handle multiple config groups for compressed-tensors yet")
+                weight_config = tuple(groups.values())[0]["weights"]
+
+                if quant_format == "float-quantized" or quant_format == "int-quantized" or quant_format == "naive-quantized":
+                    block_size = weight_config.get("block_structure", None)
+                    strategy = weight_config.get("strategy")
+                    assert strategy == "channel" or strategy == "block"
+                    assert weight_config.get("group_size") is None  # didn't find a model using this yet
+                    for name in self.model_tensors.keys():
+                        if name.endswith(".weight_scale"):
+                            weight_name = name.removesuffix("_scale")
+                            w = self.model_tensors[weight_name]
+                            s = self.model_tensors[name]
+                            self.model_tensors[weight_name] = lambda w=w, s=s: dequant_simple(w(), s(), block_size)
+                            tensors_to_remove.append(name)
+                elif quant_format == "pack-quantized":
+                    assert weight_config.get("strategy") == "group"
+                    assert weight_config.get("type", "int") == "int"
+                    num_bits = weight_config.get("num_bits")
+                    group_size = weight_config.get("group_size")
+                    assert isinstance(num_bits, int)
+                    assert isinstance(group_size, int)
+                    for name in self.model_tensors.keys():
+                        if name.endswith(".weight_packed"):
+                            base_name = name.removesuffix("_packed")
+                            w = self.model_tensors[name]
+                            scale = self.model_tensors[base_name + "_scale"]
+                            shape = self.model_tensors[base_name + "_shape"]
+                            zero_point = self.model_tensors.get(base_name + "_zero_point", lambda: None)
+                            new_tensors[base_name] = (
+                                lambda w=w, scale=scale, shape=shape, zero_point=zero_point: dequant_packed(
+                                    w(), scale(), shape(), zero_point(), num_bits, group_size,
+                                )
+                            )
+                            tensors_to_remove += [base_name + n for n in ("_packed", "_shape", "_scale")]
+                            if (base_name + "_zero_point") in self.model_tensors:
+                                tensors_to_remove.append(base_name + "_zero_point")
+                else:
+                    raise NotImplementedError(f"Quant format {quant_format!r} for method {quant_method!r} is not yet supported")
             else:
                 raise NotImplementedError(f"Quant method is not yet supported: {quant_method!r}")
 
diff --git a/gguf-py/gguf/lazy.py b/gguf-py/gguf/lazy.py
index f9bcadae022..c126f09c509 100644
--- a/gguf-py/gguf/lazy.py
+++ b/gguf-py/gguf/lazy.py
@@ -48,13 +48,18 @@ def wrapped_special_op(self, *args, **kwargs):
         # NOTE: doing this from a metaclass is very convenient
         # TODO: make this even more comprehensive
         for binary_op in (
-            "lt", "le", "eq", "ne", "ge", "gt", "not"
-            "abs", "add", "and", "floordiv", "invert", "lshift", "mod", "mul", "matmul",
-            "neg", "or", "pos", "pow", "rshift", "sub", "truediv", "xor",
+            "lt", "le", "eq", "ne", "ge", "gt",
+            "add", "and", "floordiv", "lshift", "mod", "mul", "matmul",
+            "or", "pow", "rshift", "sub", "truediv", "xor",
             "iadd", "iand", "ifloordiv", "ilshift", "imod", "imul", "ior", "irshift", "isub", "ixor",
             "radd", "rand", "rfloordiv", "rmul", "ror", "rpow", "rsub", "rtruediv", "rxor",
         ):
             attr_name = f"__{binary_op}__"
+            # evaluation on the meta tensor is needed in case there's broadcasting
+            namespace[attr_name] = mk_wrap(attr_name, meta_noop=False)
+
+        for unary_op in ("not", "abs", "invert", "neg", "pos"):
+            attr_name = f"__{unary_op}__"
             # the result of these operators usually has the same shape and dtype as the input,
             # so evaluation on the meta tensor can be skipped.
             namespace[attr_name] = mk_wrap(attr_name, meta_noop=True)

From 802cef44bfaa80987076d621c8bf5875627c197b Mon Sep 17 00:00:00 2001
From: compilade <git@compilade.net>
Date: Sun, 9 Nov 2025 09:49:40 -0500
Subject: [PATCH 135/185] convert : parse safetensors directly (#15667)

* convert : parse safetensors directly

* gguf-py : order safetensors tensors by name

Applies to both local and remote safetensors custom parsing.
This matches the behavior of the official safetensors implementation.

* convert : rename from_safetensors_meta to from_local_tensor

For consistency with from_remote_tensor

* convert : fix no-lazy dtypes from direct safetensors
---
 convert_hf_to_gguf.py   | 27 +++++++++-----
 gguf-py/gguf/utility.py | 80 +++++++++++++++++++++++++++++++++++++++++
 2 files changed, 98 insertions(+), 9 deletions(-)

diff --git a/convert_hf_to_gguf.py b/convert_hf_to_gguf.py
index b155d112b1a..13448fd6811 100755
--- a/convert_hf_to_gguf.py
+++ b/convert_hf_to_gguf.py
@@ -218,8 +218,7 @@ def index_tensors(self, remote_hf_model_id: str | None = None) -> dict[str, Call
             logger.info(f"gguf: indexing model part '{part_name}'")
             ctx: ContextManager[Any]
             if is_safetensors:
-                from safetensors import safe_open
-                ctx = cast(ContextManager[Any], safe_open(self.dir_model / part_name, framework="pt", device="cpu"))
+                ctx = cast(ContextManager[Any], gguf.utility.SafetensorsLocal(self.dir_model / part_name))
             else:
                 ctx = contextlib.nullcontext(torch.load(str(self.dir_model / part_name), map_location="cpu", mmap=True, weights_only=True))
 
@@ -228,18 +227,18 @@ def index_tensors(self, remote_hf_model_id: str | None = None) -> dict[str, Call
 
                 for name in model_part.keys():
                     if is_safetensors:
+                        data: gguf.utility.LocalTensor = model_part[name]
                         if self.lazy:
-                            data = model_part.get_slice(name)
-                            data_gen = lambda data=data: LazyTorchTensor.from_safetensors_slice(data)  # noqa: E731
+                            data_gen = lambda data=data: LazyTorchTensor.from_local_tensor(data)  # noqa: E731
                         else:
-                            data = model_part.get_tensor(name)
-                            data_gen = lambda data=data: data  # noqa: E731
+                            dtype = LazyTorchTensor._dtype_str_map[data.dtype]
+                            data_gen = lambda data=data, dtype=dtype: torch.from_numpy(data.mmap_bytes()).view(dtype).reshape(data.shape)  # noqa: E731
                     else:
-                        data = model_part[name]
+                        data_torch: Tensor = model_part[name]
                         if self.lazy:
-                            data_gen = lambda data=data: LazyTorchTensor.from_eager(data)  # noqa: E731
+                            data_gen = lambda data=data_torch: LazyTorchTensor.from_eager(data)  # noqa: E731
                         else:
-                            data_gen = lambda data=data: data  # noqa: E731
+                            data_gen = lambda data=data_torch: data  # noqa: E731
                     tensors[name] = data_gen
 
         # verify tensor name presence and identify potentially missing files
@@ -10079,6 +10078,16 @@ def from_safetensors_slice(cls, st_slice: Any) -> Tensor:
         lazy = cls(meta=cls.meta_with_dtype_and_shape(dtype, shape), args=(st_slice,), func=lambda s: s[...] if len(s.get_shape()) == 0 else s[:])
         return cast(torch.Tensor, lazy)
 
+    @classmethod
+    def from_local_tensor(cls, t: gguf.utility.LocalTensor) -> Tensor:
+        def load_tensor(tensor: gguf.utility.LocalTensor) -> Tensor:
+            dtype = cls._dtype_str_map[tensor.dtype]
+            return torch.from_numpy(tensor.mmap_bytes()).view(dtype).reshape(tensor.shape)
+        dtype = cls._dtype_str_map[t.dtype]
+        shape = t.shape
+        lazy = cls(meta=cls.meta_with_dtype_and_shape(dtype, shape), args=(t,), func=lambda r: load_tensor(r))
+        return cast(torch.Tensor, lazy)
+
     @classmethod
     def from_remote_tensor(cls, remote_tensor: gguf.utility.RemoteTensor):
         dtype = cls._dtype_str_map[remote_tensor.dtype]
diff --git a/gguf-py/gguf/utility.py b/gguf-py/gguf/utility.py
index 769ccb02f0d..c9401a1c0a2 100644
--- a/gguf-py/gguf/utility.py
+++ b/gguf-py/gguf/utility.py
@@ -1,10 +1,12 @@
 from __future__ import annotations
 
 from dataclasses import dataclass
+from pathlib import Path
 from typing import Literal
 
 import os
 import json
+import numpy as np
 
 
 def fill_templated_filename(filename: str, output_type: str | None) -> str:
@@ -177,6 +179,10 @@ def get_list_tensors(cls, url: str) -> dict[str, RemoteTensor]:
             except KeyError as e:
                 raise ValueError(f"Missing key in metadata for tensor '{name}': {e}, meta = {meta}")
 
+        # order by name (same as default safetensors behavior)
+        # ref: https://github.com/huggingface/safetensors/blob/0816a1ae1d6b731cefd67f061d80d1cadd0dd7bb/bindings/python/src/lib.rs#L606
+        res = dict(sorted(res.items(), key=lambda t: t[0]))
+
         return res
 
     @classmethod
@@ -266,3 +272,77 @@ def _get_request_headers(cls) -> dict[str, str]:
         if os.environ.get("HF_TOKEN"):
             headers["Authorization"] = f"Bearer {os.environ['HF_TOKEN']}"
         return headers
+
+
+@dataclass
+class LocalTensorRange:
+    filename: Path
+    offset: int
+    size: int
+
+
+@dataclass
+class LocalTensor:
+    dtype: str
+    shape: tuple[int, ...]
+    data_range: LocalTensorRange
+
+    def mmap_bytes(self) -> np.ndarray:
+        return np.memmap(self.data_range.filename, offset=self.data_range.offset, shape=self.data_range.size)
+
+
+class SafetensorsLocal:
+    """
+        Read a safetensors file from the local filesystem.
+
+        Custom parsing gives a bit more control over the memory usage.
+        The official safetensors library doesn't expose file ranges.
+    """
+    ALIGNMENT = 8  # bytes
+
+    tensors: dict[str, LocalTensor]
+
+    def __init__(self, filename: Path):
+        with open(filename, "rb") as f:
+            metadata_length = int.from_bytes(f.read(8), byteorder='little')
+            file_size = os.stat(filename).st_size
+            if file_size < 8 + metadata_length:
+                raise ValueError(f"Could not read complete metadata. Need {8 + metadata_length} bytes, got {file_size}")
+
+            metadata_str = f.read(metadata_length).decode('utf-8')
+            try:
+                metadata = json.loads(metadata_str)
+            except json.JSONDecodeError as e:
+                raise ValueError(f"Failed to parse safetensors metadata as JSON: {e}")
+
+            data_start_offset = f.tell()
+            alignment = self.ALIGNMENT
+            if data_start_offset % alignment != 0:
+                data_start_offset += alignment - (data_start_offset % alignment)
+
+            tensors: dict[str, LocalTensor] = {}
+            for name, meta in metadata.items():
+                if name == "__metadata__":
+                    # ignore metadata, it's not a tensor
+                    continue
+
+                tensors[name] = LocalTensor(
+                    dtype=meta["dtype"],
+                    shape=tuple(meta["shape"]),
+                    data_range=LocalTensorRange(
+                        filename,
+                        data_start_offset + meta["data_offsets"][0],
+                        meta["data_offsets"][1] - meta["data_offsets"][0],
+                    ),
+                )
+
+            # order by name (same as default safetensors behavior)
+            # ref: https://github.com/huggingface/safetensors/blob/0816a1ae1d6b731cefd67f061d80d1cadd0dd7bb/bindings/python/src/lib.rs#L606
+            self.tensors = dict(sorted(tensors.items(), key=lambda t: t[0]))
+
+    def __enter__(self, *args, **kwargs):
+        del args, kwargs  # unused
+        return self.tensors
+
+    def __exit__(self, *args, **kwargs):
+        del args, kwargs  # unused

From 392e09a60852d0e879d4bbedd5ace3e6852f719e Mon Sep 17 00:00:00 2001
From: Ruben Ortlam <picard12@live.de>
Date: Sun, 9 Nov 2025 16:14:41 +0100
Subject: [PATCH 136/185] vulkan: fix memory allocations (#17122)

---
 ggml/src/ggml-vulkan/ggml-vulkan.cpp | 7 +++++++
 1 file changed, 7 insertions(+)

diff --git a/ggml/src/ggml-vulkan/ggml-vulkan.cpp b/ggml/src/ggml-vulkan/ggml-vulkan.cpp
index 46e098a7ffb..7570febeaad 100644
--- a/ggml/src/ggml-vulkan/ggml-vulkan.cpp
+++ b/ggml/src/ggml-vulkan/ggml-vulkan.cpp
@@ -2220,9 +2220,12 @@ static vk_buffer ggml_vk_create_buffer(vk_device& device, size_t size, const std
         }
         buf->memory_property_flags = req_flags;
 
+        bool done = false;
+
         for (auto mtype_it = memory_type_indices.begin(); mtype_it != memory_type_indices.end(); mtype_it++) {
             try {
                 buf->device_memory = device->device.allocateMemory({ mem_req.size, *mtype_it, &mem_flags_info });
+                done = true;
                 break;
             } catch (const vk::SystemError& e) {
                 // loop and retry
@@ -2233,6 +2236,10 @@ static vk_buffer ggml_vk_create_buffer(vk_device& device, size_t size, const std
                 }
             }
         }
+
+        if (done) {
+            break;
+        }
     }
 
     if (!buf->device_memory) {

From b8595b16e69e3029e06be3b8f6635f9812b2bc3f Mon Sep 17 00:00:00 2001
From: Georgi Gerganov <ggerganov@gmail.com>
Date: Sun, 9 Nov 2025 18:31:02 +0200
Subject: [PATCH 137/185] mtmd : fix embedding size for image input (#17123)

---
 tools/mtmd/mtmd-helper.cpp | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/tools/mtmd/mtmd-helper.cpp b/tools/mtmd/mtmd-helper.cpp
index 686f42f3960..89e3355bbab 100644
--- a/tools/mtmd/mtmd-helper.cpp
+++ b/tools/mtmd/mtmd-helper.cpp
@@ -182,7 +182,7 @@ int32_t mtmd_helper_decode_image_chunk(
     }
 
     const llama_model * model = llama_get_model(lctx);
-    int n_mmproj_embd = llama_model_n_embd(model);
+    int n_mmproj_embd = llama_model_n_embd_inp(model);
     int n_pos_per_embd = mtmd_decode_use_mrope(ctx) ? 4 : 1;
 
     int32_t n_tokens = mtmd_input_chunk_get_n_tokens(chunk);

From 15274c0c501727b782b37e81eb77e5edae55fffa Mon Sep 17 00:00:00 2001
From: Georgi Gerganov <ggerganov@gmail.com>
Date: Mon, 10 Nov 2025 10:44:10 +0200
Subject: [PATCH 138/185] benches : add eval results (#17139)

[no ci]
---
 ...oss-120b-high_temp1.0_20251109_094547.html | 35144 ++++++++++++++++
 ...oss-120b-high_temp1.0_20251109_094547.json |     6 +
 ...gh_temp1.0_20251109_094547_allresults.json |  2896 ++
 benches/{ => dgx-spark}/dgx-spark.md          |     0
 .../dgx-spark/run-aime-120b-t8-x8-high.log    |    11 +
 5 files changed, 38057 insertions(+)
 create mode 100644 benches/dgx-spark/aime25_openai__gpt-oss-120b-high_temp1.0_20251109_094547.html
 create mode 100644 benches/dgx-spark/aime25_openai__gpt-oss-120b-high_temp1.0_20251109_094547.json
 create mode 100644 benches/dgx-spark/aime25_openai__gpt-oss-120b-high_temp1.0_20251109_094547_allresults.json
 rename benches/{ => dgx-spark}/dgx-spark.md (100%)
 create mode 100644 benches/dgx-spark/run-aime-120b-t8-x8-high.log

diff --git a/benches/dgx-spark/aime25_openai__gpt-oss-120b-high_temp1.0_20251109_094547.html b/benches/dgx-spark/aime25_openai__gpt-oss-120b-high_temp1.0_20251109_094547.html
new file mode 100644
index 00000000000..3f84fa1b4dd
--- /dev/null
+++ b/benches/dgx-spark/aime25_openai__gpt-oss-120b-high_temp1.0_20251109_094547.html
@@ -0,0 +1,35144 @@
+<!DOCTYPE html>
+<html>
+    <head>
+        <meta charset="utf-8">
+        <style>
+            .message {
+                padding: 8px 16px;
+                margin-bottom: 8px;
+                border-radius: 4px;
+            }
+            .message.user {
+                background-color: #B2DFDB;
+                color: #00695C;
+            }
+            .message.assistant {
+                background-color: #B39DDB;
+                color: #4527A0;
+            }
+            .message.system {
+                background-color: #EEEEEE;
+                color: #212121;
+            }
+            .role {
+                font-weight: bold;
+                margin-bottom: 4px;
+            }
+            .variant {
+                color: #795548;
+            }
+            table, th, td {
+                border: 1px solid black;
+            }
+            pre {
+                white-space: pre-wrap;
+            }
+        </style>
+    </head>
+    <body>
+    
+    <h1>Metrics</h1>
+    <table>
+    <tr>
+        <th>Metric</th>
+        <th>Value</th>
+    </tr>
+    <tr>
+        <td><b>Score</b></td>
+        <td>0.925</td>
+    </tr>
+    
+    <tr>
+        <td>chars</td>
+        <td>2296.1916666666666</td>
+    </tr>
+    
+    <tr>
+        <td>chars:std</td>
+        <td>986.051306946325</td>
+    </tr>
+    
+    <tr>
+        <td>score:std</td>
+        <td>0.26339134382131846</td>
+    </tr>
+    
+    </table>
+    
+    <h1>Examples</h1>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Find the sum of all integer bases $b&gt;9$ for which $17_{b}$ is a divisor of $97_{b}$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>First write the two numbers in base‑10.
+
+\[
+17_{b}=1\cdot b+7=b+7,\qquad 
+97_{b}=9\cdot b+7=9b+7 .
+\]
+
+We need  
+
+\[
+b+7 \mid 9b+7 .
+\]
+
+Use the Euclidean algorithm:
+
+\[
+9b+7 = 9(b+7)-56 .
+\]
+
+Hence  
+
+\[
+b+7 \mid 9b+7 \iff b+7 \mid 56 .
+\]
+
+So \(b+7\) must be a positive divisor of \(56\).
+
+Since the base must satisfy \(b&gt;9\), we have \(b+7&gt;16\).  
+The divisors of \(56\) exceeding \(16\) are \(28\) and \(56\).
+
+\[
+\begin{cases}
+b+7=28 \ \Rightarrow\ b=21,\\[2pt]
+b+7=56 \ \Rightarrow\ b=49.
+\end{cases}
+\]
+
+Both bases indeed work:
+
+\[
+\frac{97_{21}}{17_{21}}=\frac{196}{28}=7,\qquad 
+\frac{97_{49}}{17_{49}}=\frac{448}{56}=8 .
+\]
+
+Therefore the required bases are \(21\) and \(49\), and their sum is  
+
+\[
+21+49 = 70.
+\]
+
+\[
+\boxed{70}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 70</p>
+<p>Extracted Answer: 70</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+The 9 members of a baseball team went to an ice cream parlor after their game. Each player had a singlescoop cone of chocolate, vanilla, or strawberry ice cream. At least one player chose each flavor, and the number of players who chose chocolate was greater than the number of players who chose vanilla, which was greater than the number of players who chose strawberry. Let $N$ be the number of different assignments of flavors to players that meet these conditions. Find the remainder when $N$ is divided by 1000.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+\[
+c=\#\text{ chocolate},\qquad v=\#\text{ vanilla},\qquad s=\#\text{ strawberry}
+\]
+
+with  
+
+\[
+c+v+s =9,\qquad c&gt;v&gt;s\ge1 .
+\]
+
+---
+
+### 1. Find all possible triples \((c,v,s)\).
+
+Since \(c&gt;v&gt;s\ge 1\),
+
+\[
+c\ge s+2,\; v\ge s+1 \Longrightarrow c+v+s\ge 3s+3\le9\Longrightarrow s\le2 .
+\]
+
+- **If \(s=1\)**: \(v\ge2,\ c\ge3\) and \(c+v=8\).  
+  Possibilities: \((c,v)=(6,2),(5,3)\).
+
+- **If \(s=2\)**: \(v\ge3,\ c\ge4\) and \(c+v=7\).  
+  Possibility: \((c,v)=(4,3)\).
+
+Thus the only triples are  
+
+\[
+(6,2,1),\quad (5,3,1),\quad (4,3,2).
+\]
+
+---
+
+### 2. Count assignments for each triple.
+
+For a given \((c,v,s)\) the number of assignments of flavors to the nine distinct players is the multinomial coefficient  
+
+\[
+\frac{9!}{c!\,v!\,s!}.
+\]
+
+\[
+\begin{aligned}
+(6,2,1):\quad &amp;\frac{9!}{6!\,2!\,1!}= \binom{9}{6}\binom{3}{2}=84\cdot3=252,\\[4pt]
+(5,3,1):\quad &amp;\frac{9!}{5!\,3!\,1!}= \binom{9}{5}\binom{4}{3}=126\cdot4=504,\\[4pt]
+(4,3,2):\quad &amp;\frac{9!}{4!\,3!\,2!}= \binom{9}{4}\binom{5}{3}=126\cdot10=1260.
+\end{aligned}
+\]
+
+---
+
+### 3. Total number of assignments
+
+\[
+N = 252+504+1260 = 2016.
+\]
+
+---
+
+### 4. Remainder modulo \(1000\)
+
+\[
+N \bmod 1000 = 2016 \bmod 1000 = 16.
+\]
+
+\[
+\boxed{16}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 16</p>
+<p>Extracted Answer: 16</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+An isosceles trapezoid has an inscribed circle tangent to each of its four sides. The radius of the circle is 3, and the area of the trapezoid is 72. Let the parallel sides of the trapezoid have lengths $r$ and $s$, with $r \neq s$. Find $r^{2}+s^{2}$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let the trapezoid have parallel sides \(r\) and \(s\) \((r\neq s)\) and equal legs \(L\).
+
+---
+
+### 1.  Semiperimeter from the incircle
+
+A convex quadrilateral that contains an incircle (a tangential quadrilateral) satisfies  
+
+\[
+\text{Area}= (\text{inradius})\times (\text{semiperimeter}).
+\]
+
+The inradius is \(3\) and the area is \(72\); therefore  
+
+\[
+p=\frac{\text{Area}}{r_{\text{in}}}= \frac{72}{3}=24,
+\]
+
+where \(p\) is the semiperimeter.
+
+---
+
+### 2.  Relation among the sides
+
+For a tangential quadrilateral, Pitot’s theorem gives  
+
+\[
+\text{(sum of one pair of opposite sides)} = \text{(sum of the other pair)} .
+\]
+
+In an isosceles trapezoid the opposite sides are the two bases and the two equal legs, so  
+
+\[
+r+s = L+L =2L \quad\Longrightarrow\quad L=\frac{r+s}{2}.
+\]
+
+The semiperimeter is  
+
+\[
+p = \frac{r+s+2L}{2}= \frac{r+s+r+s}{2}=r+s .
+\]
+
+Since \(p=24\), we obtain  
+
+\[
+\boxed{r+s=24}.
+\]
+
+Consequently  
+
+\[
+L=\frac{r+s}{2}=12 .
+\]
+
+---
+
+### 3.  Height of the trapezoid
+
+The incircle is tangent to both parallel sides, so the distance between those sides (the height \(h\)) equals twice the radius:
+
+\[
+h = 2\cdot 3 = 6 .
+\]
+
+---
+
+### 4.  Using the leg length
+
+Place the trapezoid with its bases horizontal. The horizontal offset between the ends of the bases is \(\dfrac{|r-s|}{2}\). Hence, by the Pythagorean theorem,
+
+\[
+L^{2}= \left(\frac{r-s}{2}\right)^{2}+h^{2}.
+\]
+
+With \(L=12\) and \(h=6\),
+
+\[
+12^{2}= \left(\frac{r-s}{2}\right)^{2}+6^{2}
+\quad\Longrightarrow\quad
+144 = \frac{(r-s)^{2}}{4}+36
+\quad\Longrightarrow\quad
+(r-s)^{2}=432.
+\]
+
+---
+
+### 5.  Compute \(r^{2}+s^{2}\)
+
+\[
+\begin{aligned}
+(r+s)^{2} &amp;= r^{2}+2rs+s^{2}=24^{2}=576,\\
+(r-s)^{2} &amp;= r^{2}-2rs+s^{2}=432.
+\end{aligned}
+\]
+
+Adding these equations eliminates the \(rs\) term:
+
+\[
+(r+s)^{2}+(r-s)^{2}=2(r^{2}+s^{2})\Longrightarrow
+576+432=2(r^{2}+s^{2}).
+\]
+
+Thus
+
+\[
+r^{2}+s^{2}= \frac{1008}{2}=504.
+\]
+
+---
+
+\[
+\boxed{504}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 504</p>
+<p>Extracted Answer: 504</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $k$ be real numbers such that the system $|25+20i-z|=5$ and $|z-4-k|=|z-3i-k|$ has exactly one complex solution $z$. The sum of all possible values of $k$ can be written as $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$. Here $i=\sqrt{-1}$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>The first equation  
+
+\[
+|25+20i-z|=5
+\]
+
+is a circle with centre  
+
+\[
+C=(25,20)
+\]
+
+and radius \(r=5\).
+
+The second equation  
+
+\[
+|z-4-k| = |z-3i-k|
+\]
+
+means that \(z\) is equidistant from the points  
+
+\[
+A=4+k \qquad\text{and}\qquad B=3i+k .
+\]
+
+Thus \(A=(k+4,0),\; B=(k,3)\).  
+The set of points equidistant from \(A\) and \(B\) is the perpendicular bisector of \(\overline{AB}\).
+
+---
+
+### Equation of the perpendicular bisector
+
+Midpoint of \(AB\):
+
+\[
+M=\Bigl(\frac{k+4+k}{2},\frac{0+3}{2}\Bigr)=(k+2,\frac32).
+\]
+
+The vector \(\overrightarrow{AB}=(-4,3)\).  
+A direction vector perpendicular to this is \((3,4)\) (since \((-4,3)\cdot(3,4)=0\)).  
+
+Hence the line has slope \(\frac43\) and equation  
+
+\[
+y-\frac32 = \frac43\bigl(x-(k+2)\bigr)
+\]
+\[
+\Longrightarrow\; y = \frac43 x - \frac43 k - \frac76 .
+\]
+
+In standard form:
+
+\[
+8x-6y = 8k+7 .
+\]
+
+---
+
+### Tangency condition
+
+The system will have exactly one solution iff this line is tangent to the circle.  
+The distance from the centre \(C=(25,20)\) to the line \(8x-6y-(8k+7)=0\) must equal the radius \(5\):
+
+\[
+\frac{|8\cdot25-6\cdot20-(8k+7)|}{\sqrt{8^{2}+(-6)^{2}}}=5.
+\]
+
+Compute the numerator:
+
+\[
+8\cdot25-6\cdot20-(8k+7)=200-120-8k-7=73-8k.
+\]
+
+Since \(\sqrt{8^{2}+6^{2}}=10\),
+
+\[
+\frac{|73-8k|}{10}=5 \quad\Longrightarrow\quad |73-8k|=50.
+\]
+
+Thus  
+
+\[
+73-8k = 50 \quad\text{or}\quad 73-8k = -50.
+\]
+
+\[
+\begin{cases}
+8k = 23 \;\;\Rightarrow\; k = \dfrac{23}{8},\\[4pt]
+8k = 123\;\Rightarrow\; k = \dfrac{123}{8}.
+\end{cases}
+\]
+
+Both values give a tangent line, so each yields exactly one solution \(z\).
+
+---
+
+### Sum of all possible \(k\)
+
+\[
+k_1+k_2 = \frac{23}{8}+\frac{123}{8}= \frac{146}{8}= \frac{73}{4}.
+\]
+
+Write \(\frac{73}{4}\) as \(\frac{m}{n}\) with \(\gcd(m,n)=1\): \(m=73,\ n=4\).
+
+\[
+m+n = 73+4 = 77.
+\]
+
+\[
+\boxed{77}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 77</p>
+<p>Extracted Answer: 77</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Find the number of ordered pairs $(x,y)$, where both $x$ and $y$ are integers between $-100$ and $100$, inclusive, such that $12x^{2}-xy-6y^{2}=0$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>The equation  
+
+\[
+12x^{2}-xy-6y^{2}=0
+\]
+
+is a homogeneous quadratic form.  Factor it over the rationals.
+
+\[
+12x^{2}-xy-6y^{2}= -6\Bigl(y-\frac43x\Bigr)\Bigl(y+\frac32x\Bigr)
+\]
+
+Hence  
+
+\[
+12x^{2}-xy-6y^{2}=0\iff 
+\Bigl(y-\frac43x\Bigr)\Bigl(y+\frac32x\Bigr)=0 .
+\]
+
+So any integer solution must satisfy one of the two linear equations  
+
+\[
+y=\frac{4}{3}x\quad\text{or}\quad y=-\frac32 x .
+\]
+
+---
+
+### 1.  Solutions of \(y=\frac43x\)
+
+Write \(3y=4x\).  
+Since \(\gcd(3,4)=1\), the integer solutions are  
+
+\[
+x=3k,\qquad y=4k\qquad(k\in\mathbb Z).
+\]
+
+Both coordinates must lie in \([-100,100]\):
+
+\[
+-100\le 3k\le100,\qquad -100\le4k\le100
+\]
+
+The second inequality is stricter, giving  
+
+\[
+-25\le k\le 25 .
+\]
+
+Thus there are  
+
+\[
+25-(-25)+1 = 51
+\]
+
+integer points on this line.
+
+---
+
+### 2.  Solutions of \(y=-\frac32x\)
+
+Write \(2y=-3x\).  
+Since \(\gcd(2,3)=1\), the integer solutions are  
+
+\[
+x=2k,\qquad y=-3k\qquad(k\in\mathbb Z).
+\]
+
+Both coordinates must satisfy  
+
+\[
+-100\le2k\le100,\qquad -100\le-3k\le100 .
+\]
+
+These give  
+
+\[
+-50\le k\le50,\qquad -\frac{100}{3}\le k\le\frac{100}{3}\Longrightarrow -33\le k\le33 .
+\]
+
+Hence there are  
+
+\[
+33-(-33)+1 = 67
+\]
+
+integer points on this line.
+
+---
+
+### 3.  Remove double‑counted point
+
+The two lines intersect only at \((0,0)\) (when \(k=0\) in both families).  
+Thus the total number of distinct ordered pairs is  
+
+\[
+51+67-1 = 117 .
+\]
+
+\[
+\boxed{117}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 117</p>
+<p>Extracted Answer: 117</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+There are $8!=40320$ eight-digit positive integers that use each of the digits $1,2,3,4,5,6,7,8$ exactly once. Let $N$ be the number of these integers that are divisible by 22. Find the difference between $N$ and 2025.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>**Step 1.  Divisibility conditions**
+
+For an integer to be divisible by \(22\) it must be divisible by \(2\) and by \(11\).
+
+*Divisible by 2* – the last digit (the units digit) must be even, i.e. one of \(\{2,4,6,8\}\).
+
+*Divisible by 11* – for an 8‑digit number \(a_1a_2\ldots a_8\) (with \(a_1\) the leftmost digit) the rule is  
+
+\[
+(a_8+a_6+a_4+a_2)-(a_7+a_5+a_3+a_1)\equiv0\pmod{11}.
+\]
+
+Thus the sum of the digits in the even positions (2,4,6,8) equals the sum of the digits in the odd positions (1,3,5,7) modulo \(11\).
+
+The total sum of the digits \(1+2+\dots+8=36\).  
+If the two sums are equal modulo \(11\), then
+
+\[
+2\cdot(\text{odd–position sum})\equiv36\equiv3\pmod{11}
+\Longrightarrow\text{odd–position sum}\equiv7\pmod{11}.
+\]
+
+The possible values are \(7,18,29,\ldots\).  
+Since four distinct digits from \(\{1,\dots ,8\}\) can sum only between \(10\) and \(26\), the only feasible value is  
+
+\[
+\boxed{\text{odd–position sum}=18}.
+\]
+
+Consequently the even–position sum is also \(18\).
+
+**Step 2.  Choose the digits for the odd positions**
+
+We need all 4‑element subsets of \(\{1,2,3,4,5,6,7,8\}\) whose sum is \(18\).
+
+Listing them (or by noting the complementary pairs) gives  
+
+\[
+\begin{aligned}
+&amp;\{1,2,7,8\},\; \{1,3,6,8\},\; \{1,4,5,8\},\; \{1,4,6,7\},\\
+&amp;\{2,3,5,8\},\; \{2,3,6,7\},\; \{2,4,5,7\},\; \{3,4,5,6\}.
+\end{aligned}
+\]
+
+There are  
+
+\[
+\boxed{M=8}
+\]
+
+such subsets.  
+Each of them contains exactly two even digits (because a sum of 18 cannot be obtained with a different parity distribution), so for every subset \(A\) (odd‑position digits) we have  
+
+\[
+e_A=2,\qquad E_B=4-e_A=2,
+\]
+
+where \(E_B\) is the number of even digits among the complementary set \(B\) (the even‑position digits).
+
+**Step 3.  Arrange the digits**
+
+*Odd positions* (1,3,5,7): the four digits of \(A\) can be placed in \(4! = 24\) ways.
+
+*Even positions* (2,4,6,8): the four digits of \(B\) must be placed so that the digit in position 8 (the units digit) is even.  
+Since \(B\) contains exactly \(E_B=2\) even digits, we have  
+
+\[
+\text{choices for the units digit}=2,
+\qquad
+\text{ways to arrange the remaining three digits}=3! = 6.
+\]
+
+Thus the number of admissible placements for \(B\) is  
+
+\[
+f(B)=2\cdot 6=12.
+\]
+
+**Step 4.  Count all numbers**
+
+For each of the \(M=8\) valid subsets \(A\),
+
+\[
+\text{numbers contributed}=24\times12=288.
+\]
+
+Hence  
+
+\[
+N=8\times288=2304.
+\]
+
+**Step 5.  Compute the required difference**
+
+\[
+N-2025=2304-2025=279.
+\]
+
+\[
+\boxed{279}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 279</p>
+<p>Extracted Answer: 279</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+The parabola with equation $y=x^{2}-4$ is rotated $60^{\circ}$ counterclockwise around the origin. The unique point in the fourth quadrant where the original parabola and its image intersect has $y$-coordinate $\frac{a-\sqrt{b}}{c}$, where $a$, $b$, and $c$ are positive integers, and $a$ and $c$ are relatively prime. Find $a+b+c$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>The original parabola is  
+
+\[
+y=x^{2}-4 .
+\]
+
+---
+
+### 1.  Equation of the rotated parabola  
+
+Rotate the plane \(60^{\circ}\) counter‑clockwise about the origin.
+If \((X,Y)\) is a point of the rotated parabola, then rotating it back
+\(60^{\circ}\) clockwise gives a point \((x&#39;,y&#39;)\) on the original parabola.
+
+\[
+\begin{pmatrix}x&#39;\\y&#39;\end{pmatrix}
+=
+\begin{pmatrix}\cos60^\circ&amp;\sin60^\circ\\
+-\sin60^\circ&amp;\cos60^\circ\end{pmatrix}
+\begin{pmatrix}X\\Y\end{pmatrix}
+=
+\begin{pmatrix}\frac12X+\frac{\sqrt3}{2}Y\\[2pt]
+-\frac{\sqrt3}{2}X+\frac12Y\end{pmatrix}.
+\]
+
+Thus  
+
+\[
+y&#39; = x&#39;^2-4\Longrightarrow 
+\frac{-\sqrt3X+Y}{2} =\Bigl(\frac{X+\sqrt3Y}{2}\Bigr)^{\!2}-4.
+\]
+
+Multiplying by \(2\) and simplifying gives the equation of the rotated
+parabola:
+
+\[
+(x+\sqrt3\,y)^{2}+2\sqrt3\,x-2y-16=0. \tag{1}
+\]
+
+---
+
+### 2.  Intersection with the original parabola  
+
+Substituting \(y=x^{2}-4\) from the original parabola into (1) yields
+
+\[
+\bigl(x+\sqrt3(x^{2}-4)\bigr)^{2}+2\sqrt3\,x-2(x^{2}-4)-16=0,
+\]
+
+which simplifies to
+
+\[
+3x^{4}+2\sqrt3\,x^{3}-25x^{2}-6\sqrt3\,x+40=0. \tag{2}
+\]
+
+---
+
+### 3.  Factoring the quartic  
+
+Look for a factorisation of the form  
+\((ax^{2}+b\sqrt3\,x+c)(dx^{2}+e\sqrt3\,x+f)\).
+Matching coefficients gives the system  
+
+\[
+\begin{cases}
+ad=3\\
+ae+bd=2\\
+af+3be+cd=-25\\
+bf+ce=-6\\
+cf=40
+\end{cases}
+\]
+
+which is solved by  
+
+\[
+a=1,\;b=1,\;c=-4,\qquad d=3,\;e=-1,\;f=-10 .
+\]
+
+Hence
+
+\[
+3x^{4}+2\sqrt3\,x^{3}-25x^{2}-6\sqrt3\,x+40
+   =(x^{2}+\sqrt3\,x-4)(3x^{2}-\sqrt3\,x-10). \tag{3}
+\]
+
+---
+
+### 4.  Solving for the intersection points  
+
+From (3) we obtain four possible \(x\)-coordinates.
+
+1. \(x^{2}+\sqrt3\,x-4=0\)
+
+\[
+x=\frac{-\sqrt3\pm\sqrt{19}}{2}.
+\]
+
+2. \(3x^{2}-\sqrt3\,x-10=0\)
+
+\[
+x=\frac{\sqrt3\pm\sqrt{123}}{6}.
+\]
+
+For each \(x\) we compute \(y=x^{2}-4\).
+
+| \(x\) | sign of \(x\) | \(y=x^{2}-4\) | quadrant |
+|---|---|---|---|
+| \(\displaystyle\frac{-\sqrt3+\sqrt{19}}{2}\) | \(&gt;0\) | \(\displaystyle\frac{3-\sqrt{57}}{2}&lt;0\) | **IV** |
+| \(\displaystyle\frac{-\sqrt3-\sqrt{19}}{2}\) | \(&lt;0\) | \(&gt;0\) | II |
+| \(\displaystyle\frac{\sqrt3+\sqrt{123}}{6}\) | \(&gt;0\) | \(&gt;0\) | I |
+| \(\displaystyle\frac{\sqrt3-\sqrt{123}}{6}\) | \(&lt;0\) | \(&lt;0\) | III |
+
+Only the first solution lies in the fourth quadrant, as required.
+
+---
+
+### 5.  The required \(y\)-coordinate  
+
+For  
+\[
+x=\frac{-\sqrt3+\sqrt{19}}{2},
+\]
+\[
+y=x^{2}-4
+   =\left(\frac{-\sqrt3+\sqrt{19}}{2}\right)^{2}-4
+   =\frac{19+3-2\sqrt{57}}{4}-4
+   =\frac{22-2\sqrt{57}}{4}-\frac{16}{4}
+   =\frac{3-\sqrt{57}}{2}.
+\]
+
+Thus  
+
+\[
+y=\frac{a-\sqrt{b}}{c}\quad\text{with}\quad a=3,\;b=57,\;c=2,
+\]
+and \(\gcd(a,c)=1\).
+
+Finally  
+
+\[
+a+b+c=3+57+2=62.
+\]
+
+\[
+\boxed{62}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 62</p>
+<p>Extracted Answer: 62</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+On $\triangle ABC$ points $A,D,E$, and $B$ lie that order on side $\overline{AB}$ with $AD=4, DE=16$, and $EB=8$. Points $A,F,G$, and $C$ lie in that order on side $\overline{AC}$ with $AF=13, FG=52$, and $GC=26$. Let $M$ be the reflection of $D$ through $F$, and let $N$ be the reflection of $G$ through $E$. Quadrilateral $DEGF$ has area 288. Find the area of heptagon $AFNBCEM$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+\[
+\vec{AB}= \mathbf b ,\qquad \vec{AC}= \mathbf c ,\qquad 
+|\mathbf b| =28,\; |\mathbf c| =91 .
+\]
+
+Write every point on the sides as a linear combination of \(\mathbf b,\mathbf c\).
+
+\[
+\begin{aligned}
+D&amp;=\frac{4}{28}\mathbf b =\frac17\mathbf b ,&amp;
+E&amp;=\frac{20}{28}\mathbf b =\frac57\mathbf b ,\\[2mm]
+F&amp;=\frac{13}{91}\mathbf c ,&amp;
+G&amp;=\frac{65}{91}\mathbf c .
+\end{aligned}
+\]
+
+The reflections about a point are central symmetries, thus  
+
+\[
+M=2F-D=-\frac17\mathbf b+\frac{26}{91}\mathbf c ,\qquad
+N=2E-G=\frac{10}{7}\mathbf b-\frac{65}{91}\mathbf c .
+\]
+
+--------------------------------------------------------------------
+### 1.  Area of \(\triangle ABC\)
+
+The quadrilateral \(DEGF\) can be split into \(\triangle DE G\) and \(\triangle DGF\).
+
+For any three points \(P=\alpha\mathbf b+\beta\mathbf c\),
+\(Q=\gamma\mathbf b+\delta\mathbf c\) we have  
+
+\[
+\bigl[(Q-P)\times(R-P)\bigr]
+    =(\gamma-\alpha)(\zeta-\beta)-(\delta-\beta)(\xi-\alpha)\;\bigl(\mathbf b\times\mathbf c\bigr),
+\]
+
+so the area of a triangle equals the absolute value of that determinant
+times \(\dfrac12|\mathbf b\times\mathbf c|\).
+
+*Triangle \(DEG\)*  
+
+\[
+\det\!\begin{pmatrix}
+\frac57-\frac17 &amp; 0\\[2mm]
+0-\frac17&amp;\frac{65}{91}
+\end{pmatrix}
+  =\frac{20}{49}.
+\]
+
+Thus \(\displaystyle
+\text{Area}(DEG)=\frac{20}{49}\cdot\frac12|\mathbf b\times\mathbf c|.
+\)
+
+*Triangle \(DGF\)*  
+
+\[
+\det\!\begin{pmatrix}
+0-\frac17&amp;\frac{65}{91}\\[2mm]
+0-\frac17&amp;\frac{13}{91}
+\end{pmatrix}
+  =\frac{4}{49},
+\qquad
+\text{Area}(DGF)=\frac{4}{49}\cdot\frac12|\mathbf b\times\mathbf c|.
+\]
+
+Hence  
+
+\[
+\text{Area}(DEGF)=\Bigl(\frac{20}{49}+\frac{4}{49}\Bigr)
+                  \frac12|\mathbf b\times\mathbf c|
+                =\frac{24}{49}\,\text{Area}(\triangle ABC).
+\]
+
+Given \(\text{Area}(DEGF)=288\),
+
+\[
+\frac{24}{49}\,\text{Area}(\triangle ABC)=288
+\Longrightarrow
+\text{Area}(\triangle ABC)=288\cdot\frac{49}{24}=12\cdot49=588.
+\]
+
+--------------------------------------------------------------------
+### 2.  Area of the heptagon \(AFNBCEM\)
+
+Place the points in the \((\alpha,\beta)\)–plane where \((\alpha,\beta)\) are the
+coefficients of \(\mathbf b,\mathbf c\):
+
+\[
+\begin{array}{c|c}
+\text{Vertex}&amp;(\alpha,\beta)\\\hline
+A&amp;(0,0)\\
+F&amp;(0,\frac{13}{91})\\
+N&amp;(\frac{10}{7},-\frac{65}{91})\\
+B&amp;(1,0)\\
+C&amp;(0,1)\\
+E&amp;(\frac57,0)\\
+M&amp;\bigl(-\frac17,\frac{26}{91}\bigr)
+\end{array}
+\]
+
+Applying the shoelace formula to these seven points gives
+
+\[
+\begin{aligned}
+\sum x_i y_{i+1}-y_i x_{i+1}
+&amp;=1,\\[2mm]
+\text{Area}_{\text{coeff}}&amp;=\frac12\cdot1=\frac12 .
+\end{aligned}
+\]
+
+In the original plane a figure’s area is multiplied by
+\(|\mathbf b\times\mathbf c|=2\,\text{Area}(\triangle ABC)\).
+Thus
+
+\[
+\text{Area}(AFNBCEM)=|\mathbf b\times\mathbf c|\,
+\frac12
+   =\text{Area}(\triangle ABC)=588.
+\]
+
+--------------------------------------------------------------------
+\[
+\boxed{588}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 588</p>
+<p>Extracted Answer: 588</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+The twelve letters $A,B,C,D,E,F,G,H,I,J,K$, and $L$ are randomly grouped into six pairs of letters. The two letters in each pair are placed next to each other in alphabetical order to form six two-letter words, and those six words are listed alphabetically. For example, a possible result is $AB,CJ,DG,EK,FL,HI$. The probability that the last word listed contains $G$ is $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>The 12 letters are  
+
+\[
+A,B,C,D,E,F,G,H,I,J,K,L .
+\]
+
+A random grouping into six unordered pairs is performed, each pair is written with its
+letters in alphabetical order, and then the six two‑letter “words’’ are listed
+alphabetically.  
+
+Let the word that appears last (the lexicographically greatest word) be called the **max word**.
+The max word is determined by the *first* letters of the six pairs:
+its first letter is the largest among the six first letters, and if several pairs have that
+first letter, the one with the larger second letter wins.
+
+--------------------------------------------------------------------
+### 1.   Total number of possible pairings
+\[
+\#\text{pairings}= \frac{12!}{2!^{6}\,6!}=10395 .
+\]
+
+--------------------------------------------------------------------
+### 2.   When does the max word contain \(G\)?
+
+Two mutually exclusive possibilities:
+
+* **(A) \(G\) is the first letter of its pair.**  
+  Then the pair is \((G,X)\) with \(X\in\{H,I,J,K,L\}\).
+  For \((G,X)\) to be the max word, no other pair may have a first
+  letter larger than \(G\).  
+  Hence each of the other four letters \(\{H,I,J,K,L\}\setminus\{X\}\) must be paired
+  with a letter \(\le F\) (otherwise its first letter would exceed \(G\)).
+  The remaining letters are  
+
+  * 4 “high’’ letters \(\{H,I,J,K,L\}\setminus\{X\}\);
+  * 6 “low’’ letters \(\{A,B,C,D,E,F\}\).
+
+  Choose which four low letters are matched with the four high letters
+  and then match them (an injection).  
+  The number of ways is  
+
+  \[
+  {}_{6}P_{4}=6\cdot5\cdot4\cdot3=360 .
+  \]
+
+  The two low letters left over are forced to pair with each other.
+  Thus for a fixed \(X\) there are \(360\) pairings, and there are
+  \(5\) possible choices for \(X\):
+
+  \[
+  N_A=5\cdot360=1800 .
+  \]
+
+* **(B) \(G\) is the second letter of its pair.**  
+  Then the pair is \((X,G)\) with \(X&lt;G\), and \(X\) must be the
+  largest first letter of any pair.  
+  If \(X\le E\) there are not enough letters \(\le X\) to pair with all
+  letters \(&gt;X\) (there would be more “high’’ letters than “low’’ ones).  
+  The only possible value is \(X=F\).
+
+  Pair \(G\) with \(F\).  The five letters \(\{H,I,J,K,L\}\) must each be paired
+  with a distinct letter from \(\{A,B,C,D,E\}\).  There are  
+
+  \[
+  5! =120
+  \]
+
+  ways to do this, and no letters remain.
+
+  Hence  
+
+  \[
+  N_B =120 .
+  \]
+
+--------------------------------------------------------------------
+### 3.   Favourable pairings
+\[
+N_{\text{fav}}=N_A+N_B=1800+120=1920 .
+\]
+
+--------------------------------------------------------------------
+### 4.   Desired probability
+\[
+P=\frac{N_{\text{fav}}}{\#\text{pairings}}
+   =\frac{1920}{10395}
+   =\frac{128}{693}\qquad(\gcd(128,693)=1).
+\]
+
+Thus \(m=128,\;n=693\) and  
+
+\[
+m+n=128+693=821 .
+\]
+
+\[
+\boxed{821}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 821</p>
+<p>Extracted Answer: 821</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Six points $ A, B, C, D, E, $ and $ F $ lie in a straight line in that order. Suppose that $ G $ is a point not on the line and that $ AC = 26 $, $ BD = 22 $, $ CE = 31 $, $ DF = 33 $, $ AF = 73 $, $ CG = 40 $, and $ DG = 30 $. Find the area of $ \triangle BGE $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let the line be the \(x\)-axis and put  
+
+\[
+A=(0,0),\qquad B=(b,0),\qquad C=(c,0),\qquad D=(d,0),\qquad E=(e,0),\qquad F=(f,0)
+\]
+
+with the points in the order \(A\!&lt;\!B\!&lt;\!C\!&lt;\!D\!&lt;\!E\!&lt;\!F\).
+
+---
+
+### 1.  Locate the collinear points
+
+\[
+\begin{aligned}
+AC&amp;=26 \Longrightarrow c-0 = 26 \; \Rightarrow\; c=26,\\[2pt]
+CE&amp;=31 \Longrightarrow e-c =31 \; \Rightarrow\; e=26+31=57,\\[2pt]
+AF&amp;=73 \Longrightarrow f=73 .
+\end{aligned}
+\]
+
+From \(DF=33\) we get  
+
+\[
+f-d =33 \Longrightarrow d = f-33 = 73-33 =40 .
+\]
+
+From \(BD=22\),
+
+\[
+d-b =22 \Longrightarrow b = d-22 = 40-22 =18 .
+\]
+
+Thus  
+
+\[
+A=(0,0),\; B=(18,0),\; C=(26,0),\; D=(40,0),\; E=(57,0),\; F=(73,0).
+\]
+
+All distances given in the statement are satisfied.
+
+---
+
+### 2.  Position of \(G\)
+
+Let \(G=(x,y)\) with \(y\neq0\).  
+The distances to \(C\) and \(D\) give
+
+\[
+\begin{cases}
+(x-26)^2+y^2 = 40^2 =1600,\\[2pt]
+(x-40)^2+y^2 = 30^2 = 900 .
+\end{cases}
+\]
+
+Subtracting the equations:
+
+\[
+(x-26)^2-(x-40)^2 = 700.
+\]
+
+Expanding,
+
+\[
+(-52x+26^2)+(80x-40^2)=700\;\Longrightarrow\;28x-924=700,
+\]
+
+so  
+
+\[
+28x=1624\quad\Longrightarrow\quad x=58 .
+\]
+
+Plug \(x=58\) into \((x-26)^2+y^2=1600\):
+
+\[
+(58-26)^2+y^2 = 32^2 + y^2 = 1600\;\Longrightarrow\; y^2 = 1600-1024 = 576,
+\]
+
+hence \(|y|=24\).  
+Take \(G=(58,24)\) (the other choice \((58,-24)\) gives the same area).
+
+---
+
+### 3.  Area of \(\triangle BGE\)
+
+Points:
+
+\[
+B=(18,0),\qquad E=(57,0),\qquad G=(58,24).
+\]
+
+The base \(BE\) lies on the \(x\)-axis, so its length is  
+
+\[
+BE = 57-18 = 39.
+\]
+
+The altitude from \(G\) to the line \(BE\) is simply \(|y| = 24\).
+
+Thus  
+
+\[
+\text{Area} = \frac12 \times (\text{base}) \times (\text{height})
+            = \frac12 \times 39 \times 24
+            = 39 \times 12
+            = 468 .
+\]
+
+(Equivalently, the shoelace formula gives \(\frac12|1368-432|=468\).)
+
+---
+
+\[
+\boxed{468}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 468</p>
+<p>Extracted Answer: 468</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Find the sum of all positive integers $ n $ such that $ n + 2 $ divides the product $ 3(n + 3)(n^2 + 9) $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+\[
+d=n+2\qquad (d\ge 1,\; n=d-2).
+\]
+
+Then  
+
+\[
+n+3=d+1 ,\qquad n^{2}+9=(d-2)^{2}+9=d^{2}-4d+13 .
+\]
+
+Hence  
+
+\[
+3(n+3)(n^{2}+9)=3(d+1)(d^{2}-4d+13).
+\]
+
+The condition \(d\mid 3(n+3)(n^{2}+9)\) becomes  
+
+\[
+d \mid 3(d+1)(d^{2}-4d+13).
+\]
+
+Take this congruence modulo \(d\).  
+Since \(d\equiv0\pmod d\),
+
+\[
+d+1\equiv1,\qquad d^{2}-4d+13\equiv13\pmod d,
+\]
+
+so  
+
+\[
+3(d+1)(d^{2}-4d+13)\equiv 3\cdot1\cdot13=39\pmod d.
+\]
+
+Thus \(d\) must divide \(39\):
+
+\[
+d\in\{1,3,13,39\}.
+\]
+
+Recall \(d=n+2\) and we need \(n&gt;0\).  
+Hence
+
+\[
+n=d-2\in\{-1,1,11,37\}.
+\]
+
+Discard the non‑positive value \(-1\). The admissible positive integers are  
+
+\[
+n=1,\;11,\;37 .
+\]
+
+Check:
+
+* \(n=1\): \(n+2=3\) and \(3(1+3)(1^{2}+9)=120\) is divisible by \(3\).
+* \(n=11\): \(n+2=13\) and \(3(14)(130)=5460\) is divisible by \(13\).
+* \(n=37\): \(n+2=39\) and \(3(40)(1378)=165360\) is divisible by \(39\).
+
+All satisfy the condition.  
+
+The required sum is  
+
+\[
+1+11+37 = 49.
+\]
+
+\[
+\boxed{49}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 49</p>
+<p>Extracted Answer: 49</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+A piecewise linear periodic function is defined by $f(x)=\begin{cases}x&amp;\text{if }x\in[-1,1)\\2-x&amp;\text{if }x\in[1,3)\end{cases}$ and $f(x+4)=f(x)$ for all real numbers $x$. The graph of $f(x)$ has the sawtooth pattern. The parabola $x=34y^2$ intersects the graph of $f(x)$ at finitely many points. The sum of the $y$-coordinates of these intersection points can be expressed in the form $\frac{a+b\sqrt{c}}{d}$, where $a,b,c,$ and $d$ are positive integers, $a,b,$ and $d$ have greatest common divisor equal to 1, and $c$ is not divisible by the square of any prime. Find $a+b+c+d$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>For the periodic saw‑tooth  
+
+\[
+f(x)=\begin{cases}
+x-4k,&amp;x\in[-1+4k,\,1+4k)\\[2pt]
+4k+2-x,&amp;x\in[1+4k,\,3+4k)
+\end{cases}\qquad(k\in\mathbb Z)
+\]
+
+the parabola is  
+
+\[
+x = 34y^{2}\qquad (y\in[-1,1]).
+\]
+
+Hence an intersection point \((x,y)\) must satisfy  
+
+\[
+y=f(x),\qquad x=34y^{2}.
+\]
+
+---
+
+### 1.  Intersections on an “up” segment  
+
+On an up segment \(x= y+4k\).  
+Substituting \(x=34y^{2}\) gives  
+
+\[
+34y^{2}=y+4k\;\Longrightarrow\;34y^{2}-y-4k=0 .
+\]
+
+For each integer \(k\) with an up segment inside \([0,34]\) (i.e. \(k=0,1,\dots ,8\))
+the two roots are  
+
+\[
+y_{k}^{\pm}=\frac{1\pm\sqrt{1+544k}}{68}.
+\]
+
+Both satisfy the interval \([-1,1]\) and give \(x\in[-1+4k,\,1+4k)\);
+hence each \(k\) contributes **two** intersection points.
+
+The sum of the two roots for a fixed \(k\) is, by Vieta,
+
+\[
+y_{k}^{+}+y_{k}^{-}= \frac{1}{34}.
+\]
+
+Thus the total contribution of all up‑segments is  
+
+\[
+\sum_{k=0}^{8}(y_{k}^{+}+y_{k}^{-})=9\cdot\frac1{34}=\frac9{34}.
+\]
+
+---
+
+### 2.  Intersections on a “down’’ segment  
+
+On a down segment \(x=4k+2-y\).  
+Using \(x=34y^{2}\),
+
+\[
+34y^{2}=4k+2-y\;\Longrightarrow\;34y^{2}+y-(4k+2)=0 .
+\]
+
+For each \(k=0,1,\dots ,8\) the roots are  
+
+\[
+z_{k}^{\pm}= \frac{-1\pm\sqrt{273+544k}}{68}.
+\]
+
+The admissible \(y\)-values must satisfy \(-1&lt;y\le 1\).
+
+* For \(k=0,1,\dots ,7\) we have \(\sqrt{273+544k}&lt;67\); both roots lie in
+\((-1,1]\) and give valid points.
+* For \(k=8\) the negative root satisfies \(y&lt;-1\) and is rejected; only the
+positive root remains.
+
+Hence we obtain two points for each \(k=0,\dots ,7\) and one point for
+\(k=8\) – a total of \(17\) points.
+
+The sum of the two roots of the quadratic for any \(k\) is  
+
+\[
+z_{k}^{+}+z_{k}^{-}= -\frac1{34}.
+\]
+
+Consequently  
+
+\[
+\sum_{k=0}^{7}(z_{k}^{+}+z_{k}^{-})=8\!\left(-\frac1{34}\right)=-\frac8{34},
+\]
+and we must add the remaining positive root for \(k=8\),
+
+\[
+z_{8}^{+}= \frac{-1+\sqrt{4625}}{68}= \frac{-1+5\sqrt{185}}{68}.
+\]
+
+Therefore the total contribution of the down‑segments is  
+
+\[
+-\frac8{34}+z_{8}^{+}= -\frac{16}{68}+ \frac{-1+5\sqrt{185}}{68}
+= \frac{-17+5\sqrt{185}}{68}.
+\]
+
+---
+
+### 3.  Sum of all \(y\)-coordinates  
+
+\[
+\begin{aligned}
+S&amp;=\frac9{34}+ \left(-\frac8{34}+z_{8}^{+}\right)\\[2pt]
+  &amp;=\frac1{34}+z_{8}^{+}
+   =\frac{2}{68}+ \frac{-1+5\sqrt{185}}{68}
+   =\frac{1+5\sqrt{185}}{68}.
+\end{aligned}
+\]
+
+Thus the sum can be written as  
+
+\[
+S=\frac{a+b\sqrt{c}}{d}\quad\text{with}\quad 
+a=1,\;b=5,\;c=185,\;d=68.
+\]
+
+All conditions are satisfied (\(\gcd(a,b,d)=1\), \(c\) square‑free).
+
+Finally  
+
+\[
+a+b+c+d = 1+5+185+68 = \boxed{259}.
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 259</p>
+<p>Extracted Answer: 259</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+The 27 cells of a $3\times9$ grid are filled in using the numbers 1 through 9 so that each row contains 9 different numbers, and each of the three $3\times3$ blocks heavily outlined in the example below contains 9 different numbers, as in the first three rows of a Sudoku puzzle. 
+ | 4 | 2 | 8 | 9 | 6 | 3 | 1 | 7 | 5 | 
+ | 3 | 7 | 9 | 5 | 2 | 1 | 6 | 8 | 4 | 
+ | 5 | 6 | 1 | 8 | 4 | 7 | 9 | 2 | 3 | 
+ The number of different ways to fill such a grid can be written as $p^a\cdot q^b\cdot r^c\cdot s^d$, where $p,q,r,$ and $s$ are distinct prime numbers and $a,b,c,$ and $d$ are positive integers. Find $p\cdot a+q\cdot b+r\cdot c+s\cdot d$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>The grid has three rows and three vertical \(3\times3\) blocks.  
+Let the rows be \(R_1,R_2,R_3\) and the blocks be \(B_1,B_2,B_3\).
+
+---
+
+### 1.  How the numbers are placed in the rows and blocks  
+
+For a given number \(k\in\{1,\ldots ,9\}\) it must appear  
+
+* once in each row (three appearances), and  
+* once in each block (three appearances).
+
+Hence the three positions of \(k\) correspond to a **bijection** between the set of rows and the set of blocks.  
+Thus for each \(k\) we may choose a permutation \(\sigma_k\in S_3\) :
+
+\[
+\sigma_k(r)=\text{the block in which }k\text{ occurs in row }r .
+\]
+
+Conversely, a choice of a permutation \(\sigma_k\) for each \(k\) determines in which block every entry of the grid lies.
+
+---
+
+### 2.  Counting the possible collections of permutations  
+
+Write a column of the \(3\times9\) “block‑matrix’’ \(M\) as a permutation of \((1,2,3)\) – the three symbols denote the block in which the number of that column appears in rows \(1,2,3\).
+
+Thus we need a sequence of nine permutations \((p_1,\dots ,p_9)\) such that each ordered pair \((\text{row},\text{block})\) occurs exactly three times; equivalently each number appears three times in each row and three times in each block.
+
+Let  
+
+\[
+x_1,\dots ,x_6
+\]
+
+be the numbers of the six possible permutations of \(S_3\) in the sequence.
+The conditions give the linear system  
+
+\[
+\begin{aligned}
+x_1+x_2&amp;=3\\
+x_3+x_4&amp;=3\\
+x_5+x_6&amp;=3\\
+x_3+x_5&amp;=3\\
+x_1+x_6&amp;=3\\
+x_2+x_4&amp;=3\\
+x_4+x_6&amp;=3\\
+x_2+x_5&amp;=3\\
+x_1+x_3&amp;=3
+\end{aligned}
+\]
+
+which has the solutions  
+
+\[
+\begin{array}{c|cccccc}
+ &amp;x_1&amp;x_2&amp;x_3&amp;x_4&amp;x_5&amp;x_6\\\hline
+t=0&amp;0&amp;3&amp;3&amp;0&amp;0&amp;3\\
+t=1&amp;1&amp;2&amp;2&amp;1&amp;1&amp;2\\
+t=2&amp;2&amp;1&amp;1&amp;2&amp;2&amp;1\\
+t=3&amp;3&amp;0&amp;0&amp;3&amp;3&amp;0
+\end{array}
+\qquad (t=0,1,2,3).
+\]
+
+For a fixed solution the columns can be ordered in
+
+\[
+\frac{9!}{x_1!x_2!x_3!x_4!x_5!x_6!}
+\]
+
+ways.  Summing over the four solutions gives  
+
+\[
+\begin{aligned}
+N_M &amp;= \frac{9!}{3!^3}+2\cdot\frac{9!}{1!\,2!^2\,1!\,1!\,2!}
+      +\frac{9!}{3!^3}\\
+    &amp;=1680+2\cdot45360+1680=94\,080 .
+\end{aligned}
+\]
+
+So there are \(94\,080\) possible matrices \(M\) describing in which block each number lies.
+
+---
+
+### 3.  Filling the inner columns of each block  
+
+Inside a block \(B\) each row already has three distinct numbers (the three numbers assigned to that row in the block).  
+These three numbers can be placed in the three inner columns of the block in any order, i.e. in \((3!)^3=6^3\) ways.
+
+Since the three blocks are independent, the total number of ways to complete the grid is  
+
+\[
+94\,080\cdot (6^3)^3 = 94\,080\cdot 6^9 .
+\]
+
+Because \(6^9 = (2\cdot3)^9 =2^{9}\,3^{9}\),
+
+\[
+\begin{aligned}
+94\,080\cdot6^9 &amp;= \bigl(2^7\cdot3\cdot5\cdot7^2\bigr)\cdot\bigl(2^9\cdot3^9\bigr)\\
+                &amp;=2^{16}\cdot3^{10}\cdot5^1\cdot7^2 .
+\end{aligned}
+\]
+
+Thus the total number of fillings is  
+
+\[
+2^{16}\cdot 3^{10}\cdot 5^{1}\cdot 7^{2}.
+\]
+
+---
+
+### 4.  Computing the required sum  
+
+Take \(p=2,\ a=16;\; q=3,\ b=10;\; r=5,\ c=1;\; s=7,\ d=2\).
+
+\[
+p\,a+q\,b+r\,c+s\,d = 2\cdot16 + 3\cdot10 + 5\cdot1 + 7\cdot2
+                     = 32 + 30 + 5 + 14 = 81 .
+\]
+
+\[
+\boxed{81}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 81</p>
+<p>Extracted Answer: 81</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+The set of points in 3-dimensional coordinate space that lie in the plane $x+y+z=75$ whose coordinates satisfy the inequalities $x-yz&lt;y-zx&lt;z-xy$ forms three disjoint convex regions. Exactly one of those regions has finite area. The area of this finite region can be expressed in the form $a\sqrt{b}$, where $a$ and $b$ are positive integers and $b$ is not divisible by the square of any prime. Find $a+b$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>First rewrite the chain of inequalities  
+
+\[
+x-yz&lt;y-zx&lt;z-xy
+\]
+
+as two separate inequalities.
+
+\[
+\begin{aligned}
+x-yz &amp;&lt; y-zx \\[2mm]
+y-zx &amp;&lt; z-xy
+\end{aligned}
+\]
+
+\[
+\begin{aligned}
+x-yz-y+zx&amp;&lt;0\qquad\Longrightarrow\qquad (x-y)(1+z)&lt;0,\\[2mm]
+y-zx-z+xy&amp;&lt;0\qquad\Longrightarrow\qquad (y-z)(1+x)&lt;0 .
+\end{aligned}
+\]
+
+The third inequality \( (x-z)(1+y)&lt;0\) follows by adding the two, so the region is
+described by  
+
+\[
+\boxed{(x-y)(1+z)&lt;0,\qquad (y-z)(1+x)&lt;0}
+\]
+
+together with the plane \(x+y+z=75\).
+
+---
+
+### 1.   Sign patterns
+
+Let  
+
+\[
+S_x=\operatorname{sgn}(1+x),\quad S_y=\operatorname{sgn}(1+y),\quad S_z=\operatorname{sgn}(1+z).
+\]
+
+From the two product‑inequalities we obtain  
+
+\[
+\operatorname{sgn}(x-y)=-S_z,\qquad 
+\operatorname{sgn}(y-z)=-S_x .
+\]
+
+Thus  
+
+\[
+\begin{array}{c|c|c|c}
+S_x &amp; S_y &amp; S_z &amp;\text{order of }x,y,z\\ \hline
++ &amp; + &amp; + &amp; x&lt;y&lt;z\\
++ &amp; - &amp; - &amp; y&lt;z&lt;x\\
+- &amp; + &amp; + &amp; x&lt;z&lt;y\\
+- &amp; - &amp; - &amp; \text{impossible (sum }\;75) 
+\end{array}
+\]
+
+Hence the points satisfying the chain split into three convex regions, corresponding
+to the three admissible sign patterns above.
+
+---
+
+### 2.   Which region is bounded?
+
+*Region  \(x&lt;y&lt;z\)  (all three numbers \(&gt; -1\)).*  
+Using the plane equation \(z=75-x-y\) the conditions become  
+
+\[
+-1&lt;x&lt;y,\qquad y&lt;\frac{75-x}{2}.
+\]
+
+In the \((x,y)\)-plane this is the triangle bounded by  
+
+\[
+x=-1,\; y=x,\; y=\frac{75-x}{2}.
+\]
+
+The three vertices are  
+
+\[
+(-1,-1),\;(-1,38),\;(25,25).
+\]
+
+Its area in the \(xy\)-plane is
+
+\[
+\frac12\,(39)(26)=507 .
+\]
+
+Since the plane \(x+y+z=75\) is tilted, an element \(dx\,dy\) on the
+\(xy\)-plane corresponds to an area element  
+
+\[
+\sqrt{1+(\partial z/\partial x)^2+(\partial z/\partial y)^2}\;dx\,dy
+        =\sqrt{1+1+1}\;dx\,dy=\sqrt3\,dx\,dy .
+\]
+
+Thus the area of this region in the plane is  
+
+\[
+507\sqrt3 .
+\]
+
+*The other two regions* (\(y&lt;z&lt;x\) and \(x&lt;z&lt;y\)) project onto unbounded
+half‑planes, so they have infinite area.
+
+Hence the **unique finite region** is the one with \(x&lt;y&lt;z\), and its area is
+\(507\sqrt3\).
+
+---
+
+### 3.   Answer
+
+The area is \(a\sqrt b\) with \(a=507\) and \(b=3\); therefore  
+
+\[
+a+b=507+3=510 .
+\]
+
+\[
+\boxed{510}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 510</p>
+<p>Extracted Answer: 510</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+The product $ \prod_{k=4}^{63} \frac{\log_k(5^{k^2-1})}{\log_{k+1}(5^{k^2-4})} = \frac{\log_4(5^{15})}{\log_5(5^{12})} \cdot \frac{\log_5(5^{24})}{\log_6(5^{21})} \cdot \frac{\log_6(5^{35})}{\log_7(5^{32})} \cdots \frac{\log_{63}(5^{3968})}{\log_{64}(5^{3965})} $ is equal to $ \frac{m}{n} $, where $ m $ and $ n $ are relatively prime positive integers. Find $ m + n $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>\[
+\prod_{k=4}^{63}\frac{\log_k\bigl(5^{k^2-1}\bigr)}{\log_{k+1}\bigl(5^{k^2-4}\bigr)}
+\]
+
+---
+
+### 1.  Use change‑of‑base
+
+\[
+\log_k\bigl(5^{k^2-1}\bigr)=\frac{\log_5\bigl(5^{k^2-1}\bigr)}{\log_5 k}
+      =\frac{k^{2}-1}{\log_5 k},
+\qquad
+\log_{k+1}\bigl(5^{k^2-4}\bigr)=\frac{k^{2}-4}{\log_5 (k+1)} .
+\]
+
+Hence each factor of the product equals  
+
+\[
+\frac{k^2-1}{k^2-4}\;
+      \frac{\log_5(k+1)}{\log_5k}.
+\]
+
+So
+
+\[
+P = \underbrace{\prod_{k=4}^{63}\frac{k^2-1}{k^2-4}}_{\displaystyle P_1}
+    \;
+    \underbrace{\prod_{k=4}^{63}\frac{\log_5(k+1)}{\log_5k}}_{\displaystyle P_2}.
+\]
+
+---
+
+### 2.  Simplify \(P_1\)
+
+\[
+\frac{k^2-1}{k^2-4}= \frac{(k-1)(k+1)}{(k-2)(k+2)}
+                  =\frac{k-1}{k-2}\cdot\frac{k+1}{k+2}.
+\]
+
+Thus  
+
+\[
+P_1=\Bigl(\prod_{k=4}^{63}\frac{k-1}{k-2}\Bigr)
+    \Bigl(\prod_{k=4}^{63}\frac{k+1}{k+2}\Bigr).
+\]
+
+Both products telescope:
+
+\[
+\prod_{k=4}^{63}\frac{k-1}{k-2}
+   =\frac{3}{2}\cdot\frac{4}{3}\cdots\frac{62}{61}
+   =\frac{62}{2}=31,
+\]
+
+\[
+\prod_{k=4}^{63}\frac{k+1}{k+2}
+   =\frac{5}{6}\cdot\frac{6}{7}\cdots\frac{64}{65}
+   =\frac{5}{65}=\frac1{13}.
+\]
+
+Therefore  
+
+\[
+P_1 =31\cdot\frac1{13} =\frac{31}{13}.
+\]
+
+---
+
+### 3.  Simplify \(P_2\)
+
+\[
+P_2 =\prod_{k=4}^{63}\frac{\log_5(k+1)}{\log_5k}
+    =\frac{\log_5 5\;\log_5 6\;\cdots\;\log_5 64}
+           {\log_5 4\;\log_5 5\;\cdots\;\log_5 63}
+    =\frac{\log_5 64}{\log_5 4}.
+\]
+
+Using the change‑of‑base formula,
+
+\[
+\frac{\log_5 64}{\log_5 4}= \log_4 64.
+\]
+
+Since \(4^3=64\), we have \(\log_4 64 = 3\). Hence  
+
+\[
+P_2 = 3.
+\]
+
+---
+
+### 4.  Combine the two parts
+
+\[
+P = P_1\cdot P_2 = \frac{31}{13}\times 3 = \frac{93}{13}.
+\]
+
+Thus the product equals \(\displaystyle\frac{m}{n}\) with \(m=93,\; n=13\).
+
+\[
+m+n = 93+13 = 106.
+\]
+
+\[
+\boxed{106}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 106</p>
+<p>Extracted Answer: 106</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $ A $ be the set of positive integer divisors of 2025. Let $ B $ be a randomly selected subset of $ A $. The probability that $ B $ is a nonempty set with the property that the least common multiple of its elements is 2025 is $ \frac{m}{n} $, where $ m $ and $ n $ are relatively prime positive integers. Find $ m + n $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Factor  
+
+\[
+2025=45^{2}= (3^{2}\cdot5)^{2}=3^{4}\cdot5^{2}.
+\]
+
+Hence a divisor of \(2025\) is of the form \(3^{a}5^{b}\) with  
+
+\(0\le a\le4\) and \(0\le b\le2\).  
+Thus  
+
+\[
+|A|=(4+1)(2+1)=15 .
+\]
+
+All \(2^{15}\) subsets of \(A\) are equally likely.
+
+---
+
+### Divisors needed for the LCM
+
+For a subset \(B\subseteq A\),
+
+\[
+\operatorname{lcm}(B)=3^{\max_{d\in B}a_d}\;5^{\max_{d\in B}b_d}.
+\]
+
+To obtain \(\operatorname{lcm}(B)=2025=3^{4}5^{2}\) we must have  
+
+* at least one element whose exponent of \(3\) equals \(4\);
+* at least one element whose exponent of \(5\) equals \(2\).
+
+Define  
+
+\[
+D_3=\{d\in A:\, \text{the exponent of }3\text{ in }d\text{ is }4\},\qquad 
+D_5=\{d\in A:\, \text{the exponent of }5\text{ in }d\text{ is }2\}.
+\]
+
+Counting these divisors:
+
+* \(D_3 = \{3^{4}5^{0}, 3^{4}5^{1}, 3^{4}5^{2}\}\) ⇒ \(|D_3|=3\);
+* \(D_5 = \{3^{0}5^{2}, 3^{1}5^{2}, 3^{2}5^{2}, 3^{3}5^{2}, 3^{4}5^{2}\}\) ⇒ \(|D_5|=5\);
+* The intersection \(D_3\cap D_5=\{3^{4}5^{2}\}= \{2025\}\) ⇒ \(|D_3\cap D_5|=1\).
+
+Thus a subset \(B\) has \(\operatorname{lcm}(B)=2025\) iff it contains **at least one element of \(D_3\) and at least one element of \(D_5\)** (the same element may satisfy both conditions).
+
+---
+
+### Counting such subsets
+
+Let \(U\) be the set of all subsets of \(A\) (including the empty set).  
+Use inclusion–exclusion.
+
+\[
+\begin{aligned}
+|U| &amp;=2^{15},\\[2mm]
+\text{Subsets missing }D_3 &amp;: 2^{15-|D_3|}=2^{12},\\[2mm]
+\text{Subsets missing }D_5 &amp;: 2^{15-|D_5|}=2^{10},\\[2mm]
+\text{Subsets missing both }D_3\text{ and }D_5 &amp;: 
+2^{15-|D_3\cup D_5|}
+ =2^{15-(3+5-1)}=2^{8}.
+\end{aligned}
+\]
+
+Hence the number of subsets that contain at least one element of each set is  
+
+\[
+\begin{aligned}
+N_{\text{good}}
+&amp;=|U|-2^{12}-2^{10}+2^{8}\\
+&amp;=32768-4096-1024+256\\
+&amp;=27904.
+\end{aligned}
+\]
+
+Every such subset is non‑empty, so these are exactly the favorable subsets.
+
+---
+
+### Probability
+
+\[
+P=\frac{N_{\text{good}}}{2^{15}}=\frac{27904}{32768}.
+\]
+
+Reduce the fraction:
+
+\[
+27904=2^{8}\cdot 109,\qquad 32768=2^{15}=2^{8}\cdot 128
+\Longrightarrow P=\frac{109}{128}.
+\]
+
+Thus \(m=109\) and \(n=128\), and  
+
+\[
+m+n = 109+128 = 237.
+\]
+
+\[
+\boxed{237}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 237</p>
+<p>Extracted Answer: 237</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Circle $\omega_1$ with radius 6 centered at point $A$ is internally tangent at point $B$ to circle $\omega_2$ with radius 15. Points $C$ and $D$ lie on $\omega_2$ such that $\overline{BC}$ is a diameter of $\omega_2$ and $\overline{BC} \perp \overline{AD}$. The rectangle $EFGH$ is inscribed in $\omega_1$ such that $\overline{EF} \perp \overline{BC}$, $C$ is closer to $\overline{GH}$ than to $\overline{EF}$, and $D$ is closer to $\overline{FG}$ than to $\overline{EH}$, as shown. Triangles $\triangle DGF$ and $\triangle CHG$ have equal areas. The area of rectangle $EFGH$ is $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m + n$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+* \(\omega _2\) have centre \(O\) and radius \(15\);
+* \(BC\) be a diameter of \(\omega _2\);
+* \(\omega _1\) have centre \(A\) and radius \(6\), internally tangent to \(\omega _2\) at \(B\).
+
+--------------------------------------------------------------------
+### 1.  Coordinates
+
+Place \(BC\) on the \(x\)-axis with  
+
+\[
+B=(-15,0),\qquad C=(15,0),\qquad O=(0,0).
+\]
+
+Since the circles are internally tangent, the centres are collinear with the
+tangency point and  
+
+\[
+OA=R_2-R_1=15-6=9 .
+\]
+
+Thus \(A\) lies on the ray \(OB\) at distance \(9\) from \(O\); consequently  
+
+\[
+A=(-9,0).
+\]
+
+--------------------------------------------------------------------
+### 2.  Point \(D\)
+
+\(AD\perp BC\), so \(AD\) is the vertical line \(x=-9\).
+Intersecting this line with \(\omega _2\) (\(x^2+y^2=225\)) gives  
+
+\[
+y^2=225-(-9)^2=144\quad\Longrightarrow\quad y=\pm12 .
+\]
+
+Because the statement “\(D\) is closer to \(\overline{FG}\) than to \(\overline{EH}\)’’ puts \(D\) above the centre, we take  
+
+\[
+D=(-9,12).
+\]
+
+--------------------------------------------------------------------
+### 3.  Rectangle \(EFGH\)
+
+The rectangle is inscribed in \(\omega _1\), so its circum‑centre is the
+centre of \(\omega _1\); hence the centre of the rectangle is \(A\).
+
+Let  
+
+* half‑width \(a\) (distance from the centre to each vertical side),
+* half‑height \(b\) (distance from the centre to each horizontal side).
+
+Because the vertices lie on \(\omega _1\),
+
+\[
+a^{2}+b^{2}=6^{2}=36. \tag{1}
+\]
+
+The condition “\(\overline{EF}\perp\overline{BC}\)” makes \(\overline{EF}\) vertical,
+so the rectangle’s sides are parallel/perpendicular to \(BC\).  
+Taking the usual labelling (counter‑clockwise)
+
+\[
+\begin{aligned}
+E&amp;=(-9-a,\,-b),\qquad 
+F=(-9-a,\,b),\\
+G&amp;=(-9+a,\,b),\qquad 
+H=(-9+a,\,-b).
+\end{aligned}
+\]
+
+--------------------------------------------------------------------
+### 4.  Equality of the two triangle areas
+
+\[
+\begin{aligned}
+\text{Area}(\triangle DGF)&amp;=\frac12\cdot GF\cdot(\text{vertical distance }D\text{ to }y=b)\\
+&amp;=\frac12\cdot(2a)\cdot(12-b)=a(12-b),\\[4pt]
+\text{Area}(\triangle CHG)&amp;=\frac12\cdot GH\cdot(\text{horizontal distance }C\text{ to }x=-9+a)\\
+&amp;=\frac12\cdot(2b)\cdot(24-a)=b(24-a).
+\end{aligned}
+\]
+
+Given the areas are equal,
+
+\[
+a(12-b)=b(24-a)\quad\Longrightarrow\quad12a=24b\quad\Longrightarrow\quad a=2b. \tag{2}
+\]
+
+--------------------------------------------------------------------
+### 5.  Solving for \(a\) and \(b\)
+
+Substituting \(a=2b\) into (1):
+
+\[
+(2b)^{2}+b^{2}=36\;\Longrightarrow\;5b^{2}=36\;\Longrightarrow\;b^{2}=\frac{36}{5}.
+\]
+
+Hence  
+
+\[
+a^{2}=(2b)^{2}=4b^{2}= \frac{144}{5}.
+\]
+
+--------------------------------------------------------------------
+### 6.  Area of the rectangle
+
+\[
+\text{Area}= (2a)(2b)=4ab=4(2b)b=8b^{2}=8\left(\frac{36}{5}\right)=\frac{288}{5}.
+\]
+
+Thus the area is \(\dfrac{288}{5}\).  In lowest terms \(m=288,\;n=5\), and
+
+\[
+m+n=288+5=293.
+\]
+
+--------------------------------------------------------------------
+\[
+\boxed{293}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 293</p>
+<p>Extracted Answer: 293</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Alex divides a disk into four quadrants with two perpendicular diameters intersecting at the center of the disk. He draws 25 more line segments through the disk, drawing each segment by selecting two points at random on the perimeter of the disk in different quadrants and connecting those two points. Find the expected number of regions into which these 27 line segments divide the disk.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>**Step 1.  How many regions are created by chords?**  
+
+If a convex region (here the disk) is cut by \(N\) line‑segments whose interior intersection points are all distinct, the number of regions is  
+
+\[
+R=N+1+I,
+\]
+
+where \(I\) is the total number of interior intersection points.  
+(Each new segment adds one region, plus one extra region for each interior point where it meets a previous segment.)
+
+For our disk  
+
+\[
+N=27\qquad\text{(the two diameters + 25 random chords)} .
+\]
+
+Hence  
+
+\[
+E[R]=28+E[I].
+\]
+
+So we must find the expected number \(E[I]\) of interior intersection points.
+
+--------------------------------------------------------------------
+
+**Step 2.  Intersections involving the two diameters.**
+
+The two diameters intersect at the centre; this contributes one guaranteed intersection.
+
+For a random chord \(C\) we ask for the probability that it meets a given diameter.
+
+*Vertical diameter.*  
+The chord meets the vertical line \(x=0\) iff its endpoints lie in opposite half‑planes (one in \(\{Q_1,Q_4\}\) and the other in \(\{Q_2,Q_3\}\)).  
+Among the six unordered pairs of distinct quadrants, four have this property:
+
+\[
+\{Q_1,Q_2\},\{Q_1,Q_3\},\{Q_2,Q_4\},\{Q_3,Q_4\},
+\]
+
+so  
+
+\[
+P(C\text{ meets the vertical diameter})=\frac{4}{6}=\frac23 .
+\]
+
+Exactly the same reasoning holds for the horizontal diameter.  
+Thus for each random chord
+
+\[
+P(C\text{ meets a given diameter})=\frac23 .
+\]
+
+With 25 random chords we obtain  
+
+\[
+E[\text{intersections chord–diameter}] = 25\cdot 2\cdot\frac23=\frac{100}{3}.
+\]
+
+--------------------------------------------------------------------
+
+**Step 3.  Intersections among the 25 random chords.**
+
+Each chord is obtained by picking two points on the circle that lie in different quadrants.  
+The unordered pair of quadrants a chord uses is equally likely to be any of the six possibilities
+
+* four *adjacent* pairs: \(\{01\},\{12\},\{23\},\{30\}\);
+* two *opposite* pairs: \(\{02\},\{13\}\).
+
+Thus a chord is *adjacent* with probability \(\frac23\) and *opposite* with probability \(\frac13\).
+
+--------------------------------------------------------------------
+### 3.1  Classifying a pair of chords
+
+Let chord 1 belong to unordered pair \(P\) and chord 2 to unordered pair \(Q\).  
+There are three possible relationships between \(P\) and \(Q\):
+
+| relationship | how many ordered \((P,Q)\) | intersection probability |
+|--------------|---------------------------|--------------------------|
+| same pair (\(P=Q\)) | 6 | \(\displaystyle\frac12\) |
+| disjoint pairs (no common quadrant) | 6 (4 adjacent‑adjacent, 2 opposite‑opposite) | \(0\) for adjacent–adjacent, \(1\) for opposite–opposite |
+| share exactly one quadrant | 24 (8 adjacent‑adjacent, 16 adjacent‑opposite) | \(\displaystyle\frac12\) |
+
+*Why the numbers?*  
+
+* Two chords of the **same type** intersect iff the order of the two points in the first quadrant is opposite to the order of the two points in the second quadrant – probability \(1/2\).
+
+* Two **disjoint adjacent** chords lie in quadrants \(\{0,1\}\) and \(\{2,3\}\); all points of the first lie before those of the second, so they never intersect.
+
+* Two **disjoint opposite** chords are \(\{0,2\}\) and \(\{1,3\}\); the four points appear in the order \(0,1,2,3\), which is alternating, so they always intersect.
+
+* When the chords **share exactly one quadrant**, the shared quadrant contains two independent uniform points; whichever of the two lies first decides whether the endpoints are interleaved. Hence the intersection probability is \(1/2\).
+
+--------------------------------------------------------------------
+### 3.2  Expected intersection probability for a random pair
+
+Summing the contributions of all 36 ordered possibilities:
+
+\[
+\begin{aligned}
+\sum_{P,Q} p_{P,Q}&amp;=
+6\!\left(\frac12\right) 
++ 4\!\cdot\!0 
++ 2\!\cdot\!1 
++ 24\!\left(\frac12\right) \\
+&amp;= 3 + 2 + 12 = 17 .
+\end{aligned}
+\]
+
+Therefore for two independently chosen random chords
+
+\[
+P(\text{they intersect}) = \frac{17}{36}.
+\]
+
+--------------------------------------------------------------------
+### 3.3  Expected number of chord–chord intersections
+
+There are \(\binom{25}{2}=300\) unordered pairs of the 25 chords, so
+
+\[
+E[\text{chord–chord intersections}]
+=300\cdot\frac{17}{36}= \frac{425}{3}.
+\]
+
+--------------------------------------------------------------------
+
+**Step 4.  Total expected number of interior intersections.**
+
+\[
+\begin{aligned}
+E[I] &amp;= \underbrace{1}_{\text{diameters}} 
+      + \underbrace{\frac{100}{3}}_{\text{chord–diameter}} 
+      + \underbrace{\frac{425}{3}}_{\text{chord–chord}} \\[2mm]
+     &amp;= \frac{525}{3}+1 = 175+1 = 176 .
+\end{aligned}
+\]
+
+--------------------------------------------------------------------
+
+**Step 5.  Expected number of regions.**
+
+\[
+E[R]=N+1+E[I]=27+1+176=204.
+\]
+
+--------------------------------------------------------------------
+
+\[
+\boxed{204}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 204</p>
+<p>Extracted Answer: 204</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Four unit squares form a $2 \times 2$ grid. Each of the 12 unit line segments forming the sides of the squares is colored either red or blue in such a way that each unit square has 2 red sides and 2 blue sides. Find the number of such colorings.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Label the twelve unit segments that form the sides of the four unit squares as in the picture  
+
+\[
+\begin{array}{c}
+\text{top left square }A:\; a\;( \text{top}) ,\; a&#39;(\text{left}) ,\; u (\text{vertical middle up}) ,\; x (\text{horizontal middle left})\\[2mm]
+\text{top right square }B:\; b ,\; b&#39; ,\; u ,\; y\\[2mm]
+\text{bottom left square }C:\; c ,\; c&#39; ,\; v ,\; x\\[2mm]
+\text{bottom right square }D:\; d ,\; d&#39; ,\; v ,\; y
+\end{array}
+\]
+
+All variables are binary:  
+
+\[
+0=\text{blue},\qquad 1=\text{red}.
+\]
+
+---
+
+### 1.  Express the condition for each square  
+
+For a square the number of red sides must be exactly two.  
+If we let  
+
+\[
+\begin{aligned}
+s_A &amp;=x+u, &amp; s_B &amp;=y+u,\\
+s_C &amp;=x+v, &amp; s_D &amp;=y+v,
+\end{aligned}
+\]
+
+then the two **boundary** edges of a square must contain  
+
+\[
+r_A =2-s_A,\qquad r_B =2-s_B,\qquad r_C =2-s_C,\qquad r_D =2-s_D
+\]
+
+red sides.  
+For each square the two boundary edges are distinct from the other squares, so the choices for the
+four pairs are independent.
+
+For a given pair of boundary edges the number of colourings is  
+
+\[
+\begin{cases}
+1 &amp;\text{if }r_i\in\{0,2\}\;(00\text{ or }11),\\[2mm]
+2 &amp;\text{if }r_i =1\;(01\text{ or }10).
+\end{cases}
+\]
+
+Hence, when the interior pattern \((x,y,u,v)\) is fixed, the number of ways to colour the eight
+outer edges equals  
+
+\[
+2^{\#\{\,i\in\{A,B,C,D\}\mid s_i=1\,\}},
+\]
+
+because a square contributes a factor \(2\) exactly when its interior sum \(s_i\) equals \(1\).
+
+Thus the total number of admissible colourings is  
+
+\[
+N=\sum_{(x,y,u,v)\in\{0,1\}^4} 2^{\#\{i\mid s_i=1\}} .
+\]
+
+---
+
+### 2.  Enumerate the \(2^4=16\) interior patterns  
+
+\[
+\begin{array}{c|c|c|c|c|c}
+(x,y,u,v) &amp; s_A &amp; s_B &amp; s_C &amp; s_D &amp;
+\#\{i\mid s_i=1\}\\\hline
+0000 &amp;0&amp;0&amp;0&amp;0&amp;0\\
+0001 &amp;0&amp;0&amp;1&amp;1&amp;2\\
+0010 &amp;1&amp;1&amp;0&amp;0&amp;2\\
+0011 &amp;1&amp;1&amp;1&amp;1&amp;4\\
+0100 &amp;0&amp;1&amp;0&amp;1&amp;2\\
+0101 &amp;0&amp;1&amp;1&amp;2&amp;2\\
+0110 &amp;1&amp;2&amp;0&amp;1&amp;2\\
+0111 &amp;1&amp;2&amp;1&amp;2&amp;2\\
+1000 &amp;1&amp;0&amp;1&amp;0&amp;2\\
+1001 &amp;1&amp;0&amp;2&amp;1&amp;2\\
+1010 &amp;2&amp;1&amp;1&amp;0&amp;2\\
+1011 &amp;2&amp;1&amp;2&amp;1&amp;2\\
+1100 &amp;1&amp;1&amp;1&amp;1&amp;4\\
+1101 &amp;1&amp;1&amp;2&amp;2&amp;2\\
+1110 &amp;2&amp;2&amp;1&amp;1&amp;2\\
+1111 &amp;2&amp;2&amp;2&amp;2&amp;0
+\end{array}
+\]
+
+(The entry “2’’ means the sum of the two interior edges of that square is \(2\); it forces the
+corresponding pair of boundary edges to be both blue.)
+
+The contribution of each pattern is \(2^{\#\{i\mid s_i=1\}}\).  Adding all contributions we get  
+
+\[
+\begin{aligned}
+N&amp;=1\;(0000)+4\;(0001)+4\;(0010)+16\;(0011)\\
+  &amp;\quad+4\;(0100)+4\;(0101)+4\;(0110)+4\;(0111)\\
+  &amp;\quad+4\;(1000)+4\;(1001)+4\;(1010)+4\;(1011)\\
+  &amp;\quad+16\;(1100)+4\;(1101)+4\;(1110)+1\;(1111)\\[2mm]
+  &amp;=1+16+48+16+1\\
+  &amp;=\boxed{82}.
+\end{aligned}
+\]
+
+Therefore there are **82** ways to colour the twelve unit segments of a \(2\times2\) grid so that
+every unit square has exactly two red and two blue sides.</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 82</p>
+<p>Extracted Answer: 82</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+There are $ n $ values of $ x $ in the interval $ 0 &lt; x &lt; 2\pi $ where $ f(x) = \sin(7\pi \cdot \sin(5x)) = 0 $. For $ t $ of these $ n $ values of $ x $, the graph of $ y = f(x) $ is tangent to the $ x $-axis. Find $ n + t $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>\[
+f(x)=\sin \bigl(7\pi\sin(5x)\bigr)
+\qquad (0&lt;x&lt;2\pi)
+\]
+
+---
+
+### 1.  Zeros of \(f\)
+
+\(f(x)=0\iff \sin\bigl(7\pi\sin(5x)\bigr)=0\)
+
+\[
+7\pi\sin(5x)=k\pi\qquad(k\in\mathbb Z)
+\Longrightarrow\sin(5x)=\frac{k}{7}.
+\]
+
+Since \(\sin(5x)\in[-1,1]\), we must have \(-7\le k\le7\).  
+Thus \(k\) can be any integer from \(-7\) to \(7\) (15 values).
+
+Put \(\theta =5x\). Then \(\theta\in(0,10\pi)\) and we need the number of solutions of  
+
+\[
+\sin\theta =\frac{k}{7}\qquad (k=-7,\ldots,7)
+\]
+in \((0,10\pi)\).
+
+*If \(|k|=7\) (\(\sin\theta=\pm1\)):* each period \((0,2\pi)\) contributes one solution, and there are five periods in \((0,10\pi)\).  
+\(\;\Rightarrow\) 5 solutions for \(k=7\) and 5 solutions for \(k=-7\).
+
+*If \(k=0\) (\(\sin\theta=0\)):* solutions are \(\theta=n\pi\) with \(n=1,\dots ,9\).  
+\(\;\Rightarrow\) 9 solutions.
+
+*If \(|k|=1,2,\dots ,6\) (\(|\sin\theta|&lt;1\) and \(\neq0\)):* in each \(2\pi\)‑interval there are two solutions, so across five intervals there are \(2\cdot5=10\) solutions.
+
+Hence the total number of zeros is  
+
+\[
+n =\underbrace{5+5}_{k=\pm7}+ \underbrace{9}_{k=0}+ \underbrace{12\times10}_{k=\pm1,\dots ,\pm6}
+      =10+9+120 = 139 .
+\]
+
+---
+
+### 2.  Tangent zeros
+
+A zero is tangent to the \(x\)-axis when \(f&#39;(x)=0\) as well.
+
+\[
+f&#39;(x)=35\pi\cos\!\bigl(7\pi\sin(5x)\bigr)\,\cos(5x).
+\]
+
+At any zero we have \(\cos\!\bigl(7\pi\sin(5x)\bigr)=\cos(k\pi)=(-1)^k\neq0\); therefore  
+
+\[
+f&#39;(x)=0 \iff \cos(5x)=0.
+\]
+
+\(\cos(5x)=0\) gives \(5x=\dfrac{\pi}{2}+m\pi\;(m\in\mathbb Z)\), i.e.
+
+\[
+x=\frac{(2m+1)\pi}{10}.
+\]
+
+Within \(0&lt;x&lt;2\pi\) the odd integers \(2m+1\) run from \(1\) to \(19\); there are \(10\) such values.
+At these points \(\sin(5x)=\pm1\), i.e. they correspond exactly to the solutions for \(k=\pm7\).
+
+Thus  
+
+\[
+t=10.
+\]
+
+---
+
+### 3.  Required sum
+
+\[
+n+t = 139+10 = 149.
+\]
+
+\[
+\boxed{149}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 149</p>
+<p>Extracted Answer: 149</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+From an unlimited supply of 1-cent coins, 10-cent coins, and 25-cent coins, Silas wants to find a collection of coins that has a total value of $ N $ cents, where $ N $ is a positive integer. He uses the so-called **greedy algorithm**, successively choosing the coin of greatest value that does not cause the value of his collection to exceed $ N $. For example, to get 42 cents, Silas will choose a 25-cent coin, then a 10-cent coin, then 7 1-cent coins. However, this collection of 9 coins uses more coins than necessary to get a total of 42 cents; indeed, choosing 4 10-cent coins and 2 1-cent coins achieves the same total value with only 6 coins.
+
+In general, the greedy algorithm succeeds for a given $ N $ if no other collection of 1-cent, 10-cent, and 25-cent coins gives a total value of $ N $ cents using strictly fewer coins than the collection given by the greedy algorithm. Find the number of values of $ N $ between 1 and 1000 inclusive for which the greedy algorithm succeeds.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>**Step 1 – Greedy description**
+
+For a given amount \(N\) let  
+
+\[
+q=\Bigl\lfloor \frac{N}{25}\Bigr\rfloor ,\qquad r=N-25q\;(0\le r&lt;25)
+\]
+
+The greedy algorithm first takes \(q\) quarters, then uses as many dimes as possible and finally pennies.  
+Hence the greedy number of coins is  
+
+\[
+g(N)=q+\Bigl\lfloor\frac{r}{10}\Bigr\rfloor +(r\bmod 10)
+      =q+f(r),
+\]
+
+where  
+
+\[
+f(x)=\Bigl\lfloor\frac{x}{10}\Bigr\rfloor +(x\bmod10)
+\]
+
+is the optimal number of coins when only dimes and pennies are allowed.
+
+---
+
+**Step 2 – Optimal solution with a given number of quarters**
+
+If we use \(a\) quarters (\(0\le a\le q\)), we must make the remainder \(N-25a\) with dimes and pennies.  
+The minimum number of coins for that remainder is \(f(N-25a)\).  
+Thus the optimal number of coins for \(N\) is  
+
+\[
+\min_{0\le a\le q}\; \bigl[a+f(N-25a)\bigr].
+\]
+
+Because \(f\) is optimal for the two‑coin system \(\{1,10\}\), we only need to compare the greedy choice
+\(a=q\) with the possibilities where we use fewer quarters.
+
+---
+
+**Step 3 – Effect of removing one quarter**
+
+Write \(r=N-25q\) (the greedy remainder).  
+If we use one fewer quarter (\(a=q-1\)), the new remainder is \(r+25\), and the coin count becomes  
+
+\[
+(q-1)+f(r+25).
+\]
+
+Greedy is optimal precisely when  
+
+\[
+q+f(r)\le (q-1)+f(r+25)\quad\Longleftrightarrow\quad f(r)+1\le f(r+25).
+\]
+
+Compute \(f(r+25)\) in terms of \(f(r)\).  
+Since adding \(25\) cents is the same as adding two dimes and five pennies,  
+
+\[
+f(r+25)=r+25-9\Bigl\lfloor\frac{r+25}{10}\Bigr\rfloor .
+\]
+
+The floor changes by  
+
+\[
+\Bigl\lfloor\frac{r+25}{10}\Bigr\rfloor-\Bigl\lfloor\frac{r}{10}\Bigr\rfloor=
+\begin{cases}
+2,&amp; r\bmod10\le 4,\\[2pt]
+3,&amp; r\bmod10\ge 5 .
+\end{cases}
+\]
+
+Hence  
+
+\[
+f(r+25)=
+\begin{cases}
+f(r)+7, &amp; r\bmod10\le4,\\[2pt]
+f(r)-2, &amp; r\bmod10\ge5 .
+\end{cases}
+\]
+
+Consequently  
+
+* if \(r\bmod10\le4\) then \(f(r+25)=f(r)+7&gt;f(r)+1\) – greedy stays optimal;
+* if \(r\bmod10\ge5\) then \(f(r+25)=f(r)-2\le f(r)\) – using one fewer quarter gives fewer coins.
+
+Thus the greedy algorithm fails **exactly** when the greedy remainder \(r\) satisfies  
+
+\[
+r\bmod10\ge5 \;\Longleftrightarrow\; r\in\{5,6,7,8,9,15,16,17,18,19\}.
+\]
+
+---
+
+**Step 4 – Dropping more than one quarter never helps**
+
+For two quarters removed we add \(50\) cents to the remainder.  
+A similar computation gives  
+
+\[
+f(r+50)=f(r)+5 .
+\]
+
+The change in total coin count is \(-2+5=+3\); for three quarters removed the change is \(-3+12=+9\), etc.  
+Hence removing two or more quarters can never improve on the greedy solution.  
+Therefore the condition found in Step 3 is both necessary and sufficient.
+
+---
+
+**Step 5 – Counting the successful \(N\) (1 ≤ N ≤ 1000)**  
+
+The greedy fails for those \(N\ge25\) whose remainder modulo \(25\) lies in  
+
+\[
+R=\{5,6,7,8,9,15,16,17,18,19\}.
+\]
+
+For a fixed residue \(r\in R\),
+
+\[
+N=r+25k\qquad (k\ge1,\; N\le1000).
+\]
+
+The largest possible \(k\) is \(\bigl\lfloor\frac{1000-r}{25}\bigr\rfloor =39\)
+(because \(1000-r\) ranges from \(981\) to \(995\)).  
+Thus each residue contributes \(39\) failing numbers.
+
+\[
+\#\text{failures}=|R|\times 39 = 10\times39 = 390 .
+\]
+
+All other numbers (including the ten numbers \(5,6,7,8,9,15,16,17,18,19\) themselves, which are \(&lt;25\) and therefore not failures) are successes.
+
+\[
+\#\text{successes}=1000-390 = 610 .
+\]
+
+---
+
+\[
+\boxed{610}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 610</p>
+<p>Extracted Answer: 610</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Sixteen chairs are arranged in a row. Eight people each select a chair in which to sit so that no person sits next to two other people. Let $ N $ be the number of subsets of 16 chairs that could be selected. Find the remainder when $ N $ is divided by 1000.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+\[
+a_1a_2\dots a_{16},\qquad a_i\in\{0,1\}
+\]
+
+be a binary string where \(a_i=1\) means the \(i^{\text{th}}\) chair is occupied.
+The condition *no person sits next to two other people* means that a
+\(1\) may not have a \(1\) on both sides; equivalently the string contains
+no three consecutive \(1\)’s.  
+Hence we must count the binary strings of length \(16\) that
+
+* have exactly eight \(1\)’s,
+* contain no substring \(111\).
+
+---
+
+### 1.  Decompose the occupied chairs into blocks
+
+Since a block of consecutive \(1\)’s can have length at most \(2\), the eight
+\(1\)’s are split into blocks of length \(1\) or \(2\).
+
+Let  
+
+* \(x\) = number of blocks of length \(1\),
+* \(y\) = number of blocks of length \(2\),
+* \(m=x+y\) = total number of blocks.
+
+Then  
+
+\[
+x+2y=8,\qquad x+y=m\Longrightarrow y=8-m,\;x=2m-8 .
+\]
+
+Thus \(m\) can be any integer with \(\lceil 8/2\rceil\le m\le 8\); i.e.  
+
+\[
+m=4,5,6,7,8 .
+\]
+
+For a given \(m\) the positions of the \(y=8-m\) blocks of length \(2\)
+among the \(m\) blocks can be chosen in  
+
+\[
+\binom{m}{\,8-m\,}
+\]
+
+ways.
+
+---
+
+### 2.  Insert the separating zeros
+
+Between two consecutive blocks there must be at least one \(0\).
+With \(m\) blocks there are \(m-1\) mandatory zeros.
+There are \(16-8=8\) zeros altogether, so after placing the mandatory ones we
+still have  
+
+\[
+8-(m-1)=9-m
+\]
+
+zeros left.  
+
+These remaining zeros may be distributed freely among the \(m+1\) gaps
+(the two ends and the \(m-1\) interior gaps).  By stars‑and‑bars the number
+of ways is
+
+\[
+\binom{(9-m)+(m+1)-1}{(m+1)-1}
+   =\binom{9}{m}.
+\]
+
+---
+
+### 3.  Count all possibilities
+
+For each admissible \(m\),
+
+\[
+\text{choices}(m)=\binom{m}{8-m}\binom{9}{m}.
+\]
+
+Hence  
+
+\[
+\begin{aligned}
+N&amp;=\sum_{m=4}^{8}\binom{m}{8-m}\binom{9}{m}\\[2mm]
+ &amp;=\binom{4}{4}\binom{9}{4}
+   +\binom{5}{3}\binom{9}{5}
+   +\binom{6}{2}\binom{9}{6}
+   +\binom{7}{1}\binom{9}{7}
+   +\binom{8}{0}\binom{9}{8}\\[2mm]
+ &amp;=1\cdot126+10\cdot126+15\cdot84+7\cdot36+1\cdot9\\
+ &amp;=126+1260+1260+252+9\\
+ &amp;=2907 .
+\end{aligned}
+\]
+
+---
+
+### 4.  Remainder modulo \(1000\)
+
+\[
+2907\equiv 907\pmod{1000}.
+\]
+
+\[
+\boxed{907}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 907</p>
+<p>Extracted Answer: 907</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Suppose $ \triangle ABC $ has angles $ \angle BAC = 84^\circ $, $ \angle ABC = 60^\circ $, and $ \angle ACB = 36^\circ $. Let $ D, E, $ and $ F $ be the midpoints of sides $ \overline{BC} $, $ \overline{AC} $, and $ \overline{AB} $, respectively. The circumcircle of $ \triangle DEF $ intersects $ \overline{BD} $, $ \overline{AE} $, and $ \overline{AF} $ at points $ G, H, $ and $ J $, respectively. The points $ G, D, E, H, J, $ and $ F $ divide the circumcircle of $ \triangle DEF $ into six minor arcs, as shown. Find $ \widehat{DE} + 2 \cdot \widehat{HJ} + 3 \cdot \widehat{FG} $, where the arcs are measured in degrees.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+\[
+\angle A=84^{\circ},\qquad \angle B=60^{\circ},\qquad \angle C=36^{\circ}.
+\]
+
+--------------------------------------------------------------------
+### 1.  The nine‑point circle in complex form  
+
+Put the circumcircle of \(\triangle ABC\) as the unit circle and let  
+
+\[
+a=1,\qquad b=e^{i\beta},\qquad c=e^{i\gamma},
+\]
+
+where  
+
+\[
+\beta =72^{\circ},\qquad \gamma =240^{\circ}
+\]
+
+because the central arcs are twice the opposite angles:
+\(\widehat{BC}=2A=168^{\circ},\;\widehat{CA}=2B=120^{\circ},
+\;\widehat{AB}=2C=72^{\circ}\).
+
+The nine‑point centre is
+
+\[
+N=\frac{a+b+c}{2},
+\]
+
+and its radius is \(\frac12\) (since \(|a|=|b|=|c|=1\)).  
+The three midpoints are  
+
+\[
+D=\frac{b+c}{2},\qquad 
+E=\frac{c+a}{2},\qquad 
+F=\frac{a+b}{2}.
+\]
+
+Notice that
+
+\[
+D-N=-\frac{a}{2},\qquad 
+E-N=-\frac{b}{2},\qquad 
+F-N=-\frac{c}{2} .
+\tag{1}
+\]
+
+Hence the central angle \(\widehat{DE}\) equals the angle between vectors
+\(-a\) and \(-b\); it is the same as the angle between \(a\) and \(b\).
+
+\[
+\widehat{DE}= \angle aOb = 2\angle ACB = 2\cdot36^{\circ}=72^{\circ}.
+\tag{2}
+\]
+
+--------------------------------------------------------------------
+### 2.  The other intersection points  
+
+The nine‑point circle is the image of the circumcircle under the similarity
+
+\[
+X\longmapsto N-\frac{X}{2},
+\tag{3}
+\]
+
+i.e. the homothety with centre the centroid (factor \(-\tfrac12\)).
+Consequently, if a point \(Y\) of the nine‑point circle is the image of
+\(X\) on the circumcircle, then  
+
+\[
+Y = N-\frac{X}{2}\qquad\Longleftrightarrow\qquad X=2(N-Y).
+\tag{4}
+\]
+
+--------------------------------------------------------------------
+#### (a) Point \(G\)
+
+\(G\) lies on line \(BD\).  Since \(D\) is the image of \(A\) and
+\(B\) is the image of the point \(X\) with \(X=b\), the line \(BD\) is the
+image of the line through \(A\) parallel to chord \(BC\).
+Thus \(G\) corresponds to the second intersection of the line through
+\(A\;(=a)\) parallel to \(BC\) with the circumcircle.
+
+For a line through a point \(e^{i\alpha}\) parallel to chord
+\(e^{i\beta}e^{i\gamma}\) the second intersection is
+\(e^{i(\beta+\gamma-\alpha)}\).  
+Here \(\alpha=0,\;\beta=72^{\circ},\;\gamma=240^{\circ}\); therefore
+
+\[
+X_G = e^{i(\beta+\gamma)}=e^{i312^{\circ}} .
+\]
+
+From (3) the point on the nine‑point circle is  
+
+\[
+G = N-\frac{X_G}{2}.
+\]
+
+Hence the vector \(NG=-\frac{X_G}{2}\) has direction \(312^{\circ}+180^{\circ}=132^{\circ}\).
+
+--------------------------------------------------------------------
+#### (b) Point \(H\)
+
+\(H\) lies on line \(AE\).  This line is parallel to chord \(CA\); the
+starting point on the circumcircle is \(B\,(=e^{i72^{\circ}})\).  Thus
+
+\[
+X_H = e^{i(0+240^{\circ}-72^{\circ})}=e^{i168^{\circ}} ,
+\qquad
+H=N-\frac{X_H}{2},
+\]
+
+so the direction of \(NH\) is \(168^{\circ}+180^{\circ}=348^{\circ}\).
+
+--------------------------------------------------------------------
+#### (c) Point \(J\)
+
+\(J\) lies on line \(AF\), which is parallel to chord \(AB\); it starts
+from \(C\,(=e^{i240^{\circ}})\).  Therefore
+
+\[
+X_J = e^{i(0+72^{\circ}-240^{\circ})}=e^{i192^{\circ}},
+\qquad
+J=N-\frac{X_J}{2},
+\]
+
+and the direction of \(NJ\) is \(192^{\circ}+180^{\circ}=12^{\circ}\).
+
+--------------------------------------------------------------------
+### 3.  The required arcs on the nine‑point circle  
+
+From the directions obtained:
+
+\[
+\begin{aligned}
+&amp;\text{Arc }DE = 252^{\circ}-180^{\circ}=72^{\circ},\\[2mm]
+&amp;\text{Arc }FG = 132^{\circ}-60^{\circ}=72^{\circ},\\[2mm]
+&amp;\text{Arc }HJ = (360^{\circ}-348^{\circ})+12^{\circ}=24^{\circ}.
+\end{aligned}
+\]
+
+All are the minor arcs (each \(&lt;180^{\circ}\)).
+
+--------------------------------------------------------------------
+### 4.  Computing the requested expression  
+
+\[
+\widehat{DE}+2\widehat{HJ}+3\widehat{FG}
+=72^{\circ}+2\!\cdot\!24^{\circ}+3\!\cdot\!72^{\circ}
+=72+48+216=336^{\circ}.
+\]
+
+--------------------------------------------------------------------
+\[
+\boxed{336}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 336</p>
+<p>Extracted Answer: 336</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $ S $ be the set of vertices of a regular 24-gon. Find the number of ways to draw 12 segments of equal lengths so that each vertex in $ S $ is an endpoint of exactly one of the 12 segments.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>For a regular 24‑gon label the vertices \(0,1,\ldots ,23\) in order.
+If a segment joins vertex \(i\) to vertex \(j\) then the chord length depends only on  
+
+\[
+k=\min \{\,|i-j|\;,\;24-|i-j|\,\},
+\qquad 1\le k\le 12 .
+\]
+
+Thus a configuration in which all 12 segments have the same length corresponds to a
+perfect matching in the graph whose edges are all chords of a fixed step \(k\).
+
+---
+
+### 1.  Structure of the step‑\(k\) graph  
+
+Let \(d=\gcd(24,k)\).  
+The vertices split into \(d\) disjoint cycles, each of length  
+
+\[
+L=\frac{24}{d}.
+\]
+
+Every vertex is incident with exactly the two edges of its cycle.  
+A perfect matching can exist only if each cycle has even length, i.e. \(L\) must be even.
+\(L\) is odd only when \(d=8\) (then \(L=3\)); this occurs for \(k=8\).  
+Hence the step \(k=8\) gives **no** valid configuration.
+
+For an even cycle of length \(L\ge4\) there are exactly two perfect matchings
+(the two possible “alternating” choices).  
+If \(L=2\) (the case \(k=12\)), the matching is forced and there is only one.
+
+Consequently, for a permissible \(k\)
+
+\[
+\#\text{ matchings for step }k=
+\begin{cases}
+2^{d}, &amp; L&gt;2,\\[2pt]
+1, &amp; L=2 .
+\end{cases}
+\]
+
+---
+
+### 2.  Count for each step \(k\)
+
+\[
+\begin{array}{c|c|c|c}
+k &amp; d=\gcd(24,k) &amp; L=24/d &amp; \#\text{ matchings}\\ \hline
+1,5,7,11 &amp; 1 &amp; 24 &amp; 2\\
+2,10 &amp; 2 &amp; 12 &amp; 2^{2}=4\\
+3,9 &amp; 3 &amp; 8 &amp; 2^{3}=8\\
+4 &amp; 4 &amp; 6 &amp; 2^{4}=16\\
+6 &amp; 6 &amp; 4 &amp; 2^{6}=64\\
+12 &amp; 12&amp; 2 &amp; 1\\
+8 &amp; 8 &amp; 3 &amp; \text{none}
+\end{array}
+\]
+
+Now sum over all admissible \(k\) ( \(k=1,\dots ,12\) except \(k=8\) ):
+
+\[
+\begin{aligned}
+\text{Total}&amp;=4\cdot2\;+\;2\cdot4\;+\;2\cdot8\;+\;1\cdot16\;+\;1\cdot64\;+\;1\cdot1\\
+&amp;=8+8+16+16+64+1\\
+&amp;=113 .
+\end{aligned}
+\]
+
+---
+
+\[
+\boxed{113}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 113</p>
+<p>Extracted Answer: 113</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Find the sum of all integer bases $b&gt;9$ for which $17_{b}$ is a divisor of $97_{b}$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+\[
+17_{b}=1\cdot b+7=b+7,\qquad 
+97_{b}=9\cdot b+7=9b+7 .
+\]
+
+We need  
+
+\[
+b+7 \mid 9b+7 .
+\]
+
+Write \(9b+7\) in terms of \(b+7\):
+
+\[
+9b+7 = 9(b+7) - 56 .
+\]
+
+Hence the remainder upon division by \(b+7\) is \(-56\).  
+Thus \(b+7\) must divide \(56\):
+
+\[
+b+7 \mid 56 .
+\]
+
+List the positive divisors of \(56\):
+
+\[
+1,\;2,\;4,\;7,\;8,\;14,\;28,\;56 .
+\]
+
+Since the base must satisfy \(b&gt;9\) (so that the digit 9 is allowed), we need  
+
+\[
+b+7&gt;9+7=16 .
+\]
+
+The only divisors of \(56\) larger than \(16\) are \(28\) and \(56\).
+
+\[
+\begin{aligned}
+b+7 &amp;= 28 \;\Longrightarrow\; b=21,\\[2pt]
+b+7 &amp;= 56 \;\Longrightarrow\; b=49.
+\end{aligned}
+\]
+
+Both bases exceed \(9\) and thus are admissible.
+
+The sum of all such bases is
+
+\[
+21+49 = 70 .
+\]
+
+\[
+\boxed{70}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 70</p>
+<p>Extracted Answer: 70</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $ A_1A_2 \ldots A_{11} $ be an 11-sided non-convex simple polygon with the following properties:
+* The area of $ A_iA_1A_{i+1} $ is 1 for each $ 2 \leq i \leq 10 $,
+* $ \cos(\angle A_iA_1A_{i+1}) = \frac{12}{13} $ for each $ 2 \leq i \leq 10 $,
+* The perimeter of $ A_1A_2 \ldots A_{11} $ is 20.
+If $ A_1A_2 + A_1A_{11} $ can be expressed as $ \frac{m\sqrt{n} - p}{q} $ for positive integers $ m, n, p, q $ with $ n $ squarefree and no prime divides all of $ m, p, q$, find $ m + n + p + q $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+\[
+a_i=A_1A_i\qquad (i=2,\dots ,11),\qquad s_i=A_iA_{i+1}\qquad (i=2,\dots ,10).
+\]
+
+For each triangle \(A_iA_1A_{i+1}\;(2\le i\le10)\)
+
+* \(\displaystyle \text{Area}=1\),
+* \(\displaystyle\cos\angle A_iA_1A_{i+1}= \frac{12}{13}\).
+
+--------------------------------------------------------------------
+### 1.  Product of the two sides from \(A_1\)
+
+With \(\theta=\angle A_iA_1A_{i+1}\) we have  
+
+\[
+\sin\theta=\sqrt{1-\cos ^2\theta}= \frac{5}{13}.
+\]
+
+The area of \(\triangle A_iA_1A_{i+1}\) is  
+
+\[
+\frac12 a_i a_{i+1}\sin\theta =1
+\Longrightarrow a_i a_{i+1}= \frac{2}{\sin\theta}= \frac{2}{5/13}= \frac{26}{5}\equiv c .
+\tag{1}
+\]
+
+Hence for all \(i\)
+
+\[
+a_i a_{i+1}=c=\frac{26}{5}.
+\]
+
+--------------------------------------------------------------------
+### 2.  Length of the side \(A_iA_{i+1}\)
+
+Apply the law of cosines in \(\triangle A_iA_1A_{i+1}\):
+
+\[
+s_i^2=a_i^{\,2}+a_{i+1}^{\,2}-2a_i a_{i+1}\cos\theta
+      =a_i^{\,2}+a_{i+1}^{\,2}-2c\Bigl(\frac{12}{13}\Bigr).
+\]
+
+Because \(2c\frac{12}{13}= \frac{624}{65}= \frac{48}{5}\),
+
+\[
+s_i^{\,2}=a_i^{\,2}+a_{i+1}^{\,2}-\frac{48}{5}. \tag{2}
+\]
+
+--------------------------------------------------------------------
+### 3.  The alternating pattern of the radii
+
+From (1) we have \(a_{i+1}=c/a_i\). Consequently  
+
+\[
+a_{i+2}=c/a_{i+1}=c/(c/a_i)=a_i .
+\]
+
+Thus  
+
+\[
+a_{2}=a_{4}=a_{6}=a_{8}=a_{10}\equiv x, \qquad 
+a_{3}=a_{5}=a_{7}=a_{9}=a_{11}\equiv \frac{c}{x}.
+\]
+
+All sides \(s_i\;(i=2,\dots ,10)\) are equal, because each uses the
+pair \((x,\;c/x)\) in (2).  Set  
+
+\[
+S^2=x^{2}+\Bigl(\frac{c}{x}\Bigr)^2-\frac{48}{5}.
+\tag{3}
+\]
+
+--------------------------------------------------------------------
+### 4.  Express everything via \(t=x+\dfrac{c}{x}\)
+
+Define  
+
+\[
+t=x+\frac{c}{x}=a_2+a_{11}.
+\]
+
+Then  
+
+\[
+x^{2}+\Bigl(\frac{c}{x}\Bigr)^2=t^{2}-2c .
+\]
+
+Insert this into (3):
+
+\[
+S^{2}=t^{2}-2c-\frac{48}{5}=t^{2}-(2c+\frac{48}{5}).
+\]
+
+Since \(c=\dfrac{26}{5}\),
+
+\[
+2c+\frac{48}{5}= \frac{52}{5}+\frac{48}{5}=20.
+\]
+
+Hence  
+
+\[
+S^{2}=t^{2}-20,\qquad S=\sqrt{t^{2}-20}. \tag{4}
+\]
+
+--------------------------------------------------------------------
+### 5.  Use the perimeter
+
+The perimeter of the 11‑gon is  
+
+\[
+a_2+a_{11}+ \sum_{i=2}^{10}s_i = t+9S =20.
+\]
+
+Substituting (4):
+
+\[
+t+9\sqrt{t^{2}-20}=20.
+\]
+
+Isolate the radical and square:
+
+\[
+9\sqrt{t^{2}-20}=20-t \quad\Longrightarrow\quad 
+81(t^{2}-20)=(20-t)^{2}.
+\]
+
+Simplifying:
+
+\[
+80t^{2}+40t-2020=0
+\Longrightarrow 4t^{2}+2t-101=0.
+\]
+
+Solve for \(t\):
+
+\[
+t=\frac{-2\pm\sqrt{4+1616}}{8}
+   =\frac{-2\pm 18\sqrt5}{8}
+   =\frac{-1\pm 9\sqrt5}{4}.
+\]
+
+Since \(t&gt;0\), we take the plus sign:
+
+\[
+\boxed{t=\frac{9\sqrt5-1}{4}}.
+\]
+
+Thus  
+
+\[
+A_1A_2+A_1A_{11}= \frac{9\sqrt5-1}{4}
+            =\frac{m\sqrt n-p}{q},
+\]
+with \(m=9,\;n=5,\;p=1,\;q=4\).
+
+--------------------------------------------------------------------
+### 6.  Compute \(m+n+p+q\)
+
+\[
+m+n+p+q = 9+5+1+4 = 19.
+\]
+
+\[
+\boxed{19}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 19</p>
+<p>Extracted Answer: 19</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+The 9 members of a baseball team went to an ice cream parlor after their game. Each player had a singlescoop cone of chocolate, vanilla, or strawberry ice cream. At least one player chose each flavor, and the number of players who chose chocolate was greater than the number of players who chose vanilla, which was greater than the number of players who chose strawberry. Let $N$ be the number of different assignments of flavors to players that meet these conditions. Find the remainder when $N$ is divided by 1000.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>The nine players are distinct.  Let  
+
+\[
+c=\#\text{chocolate},\qquad v=\#\text{vanilla},\qquad s=\#\text{strawberry}
+\]
+
+with  
+
+\[
+c+v+s=9,\qquad c&gt;v&gt;s\ge 1 .
+\]
+
+---
+
+### 1.  Find all possible triples \((c,v,s)\)
+
+Since \(c&gt;v&gt;s\),
+
+\[
+c\ge v+1,\qquad v\ge s+1.
+\]
+
+Write \(v=s+d_2\) and \(c=v+d_1\) where \(d_1,d_2\ge 1\).  
+Then  
+
+\[
+c+v+s=(s+d_2+d_1)+(s+d_2)+s=3s+2d_2+d_1=9 .
+\]
+
+Because \(s\ge1\), we have \(3s\le 9\Rightarrow s=1,2,3\).
+
+* **\(s=1\):** \(2d_2+d_1=6\).  
+  \(d_2=1\Rightarrow d_1=4\) → \((c,v,s)=(6,2,1)\).  
+  \(d_2=2\Rightarrow d_1=2\) → \((c,v,s)=(5,3,1)\).
+
+* **\(s=2\):** \(2d_2+d_1=3\).  
+  \(d_2=1\Rightarrow d_1=1\) → \((c,v,s)=(4,3,2)\).
+
+* **\(s=3\):** \(2d_2+d_1=0\) – impossible with \(d_1,d_2\ge1\).
+
+Thus the only feasible triples are  
+
+\[
+(6,2,1),\;(5,3,1),\;(4,3,2).
+\]
+
+---
+
+### 2.  Count assignments for each triple
+
+For a given \((c,v,s)\) the number of ways to assign the flavors to the 9 distinct players is the multinomial coefficient  
+
+\[
+\frac{9!}{c!\,v!\,s!}.
+\]
+
+\[
+\begin{aligned}
+(6,2,1):\;&amp;\frac{9!}{6!\,2!\,1!}= \frac{362880}{720\cdot2}=252,\\[2mm]
+(5,3,1):\;&amp;\frac{9!}{5!\,3!\,1!}= \frac{362880}{120\cdot6}=504,\\[2mm]
+(4,3,2):\;&amp;\frac{9!}{4!\,3!\,2!}= \frac{362880}{24\cdot6\cdot2}=1260.
+\end{aligned}
+\]
+
+---
+
+### 3.  Total number of assignments
+
+\[
+N = 252+504+1260 = 2016.
+\]
+
+---
+
+### 4.  Remainder modulo \(1000\)
+
+\[
+2016 \equiv 16 \pmod{1000}.
+\]
+
+\[
+\boxed{16}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 16</p>
+<p>Extracted Answer: 16</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Find the number of ordered pairs $(x,y)$, where both $x$ and $y$ are integers between $-100$ and $100$, inclusive, such that $12x^{2}-xy-6y^{2}=0$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>The equation  
+
+\[
+12x^{2}-xy-6y^{2}=0
+\]
+
+is a homogeneous quadratic form.  
+Factor it over the integers:
+
+\[
+12x^{2}-xy-6y^{2}= (3x+2y)(4x-3y).
+\]
+
+Indeed  
+
+\[
+(3x+2y)(4x-3y)=12x^{2}-9xy+8xy-6y^{2}=12x^{2}-xy-6y^{2}.
+\]
+
+Hence a pair \((x,y)\) of integers satisfies the equation iff
+
+\[
+3x+2y=0\qquad\text{or}\qquad 4x-3y=0 .
+\]
+
+---
+
+### 1. Solutions of \(3x+2y=0\)
+
+\[
+3x+2y=0 \;\Longrightarrow\; y=-\frac{3}{2}x .
+\]
+
+For \(y\) to be an integer, \(x\) must be even: write \(x=2k\). Then  
+
+\[
+(x,y)=(2k,-3k),\qquad k\in\mathbb Z .
+\]
+
+Both coordinates must lie in \([-100,100]\):
+
+\[
+-100\le 2k\le 100\;\Longrightarrow\;-50\le k\le 50,\\
+-100\le -3k\le 100\;\Longrightarrow\;-33\le k\le 33.
+\]
+
+Thus \(k=-33,-32,\dots ,33\); there are  
+
+\[
+33-(-33)+1 = 67
+\]
+
+integer solutions on this line.
+
+---
+
+### 2. Solutions of \(4x-3y=0\)
+
+\[
+4x-3y=0 \;\Longrightarrow\; y=\frac{4}{3}x .
+\]
+
+For \(y\) to be an integer, \(x\) must be a multiple of \(3\): put \(x=3t\). Then  
+
+\[
+(x,y)=(3t,4t),\qquad t\in\mathbb Z .
+\]
+
+Again impose the bounds:
+
+\[
+-100\le 3t\le 100\;\Longrightarrow\;-33\le t\le 33,\\
+-100\le 4t\le 100\;\Longrightarrow\;-25\le t\le 25.
+\]
+
+Thus \(t=-25,-24,\dots ,25\); the number of solutions here is  
+
+\[
+25-(-25)+1 = 51.
+\]
+
+---
+
+### 3. Intersection of the two lines
+
+Both equations hold simultaneously only at the origin:
+
+\[
+3x+2y=0,\;4x-3y=0 \Longrightarrow (x,y)=(0,0).
+\]
+
+This point has been counted in both previous totals, so we subtract it once.
+
+---
+
+### 4. Total number of ordered pairs
+
+\[
+\#\text{solutions}=67+51-1=117.
+\]
+
+\[
+\boxed{117}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 117</p>
+<p>Extracted Answer: 117</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+An isosceles trapezoid has an inscribed circle tangent to each of its four sides. The radius of the circle is 3, and the area of the trapezoid is 72. Let the parallel sides of the trapezoid have lengths $r$ and $s$, with $r \neq s$. Find $r^{2}+s^{2}$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let the trapezoid be \(ABCD\) with \(AB\parallel CD\) and  
+
+\[
+AB=s ,\qquad CD=r ,\qquad AD=BC=L \;( \text{isosceles}).
+\]
+
+The incircle has radius \(R=3\) and the area is \(72\).
+
+---
+
+### 1.  Semiperimeter
+
+For any tangential quadrilateral (one with an incircle)
+
+\[
+\text{Area}=R\cdot(\text{semiperimeter}).
+\]
+
+Hence  
+
+\[
+72=3\cdot s_{\!p}\quad\Longrightarrow\quad s_{\!p}=24 .
+\]
+
+Thus the perimeter is  
+
+\[
+2s_{\!p}=48\quad\Longrightarrow\quad r+s+2L=48. \tag{1}
+\]
+
+---
+
+### 2.  Tangential condition
+
+In a tangential quadrilateral the sums of opposite sides are equal:
+
+\[
+AB+CD = AD+BC\quad\Longrightarrow\quad r+s = 2L. \tag{2}
+\]
+
+From (1) and (2),
+
+\[
+2(r+s)=48 \;\Longrightarrow\; r+s=24,\qquad
+2L=r+s=24\;\Longrightarrow\; L=12.
+\]
+
+---
+
+### 3.  Height
+
+The incircle touches both parallel sides, so the distance between the bases equals twice the radius:
+
+\[
+h=2R=6.
+\]
+
+(Alternatively, \(\displaystyle 72=\tfrac12(r+s)h\) with \(r+s=24\) also gives \(h=6\).)
+
+---
+
+### 4.  Relating the bases
+
+Place the trapezoid with its symmetry axis on the \(y\)-axis; the bases are horizontal.
+The horizontal half‑difference of the bases is \(\dfrac{s-r}{2}\).
+Hence the leg length satisfies
+
+\[
+L^{2}= \left(\frac{s-r}{2}\right)^{2}+h^{2}.
+\]
+
+Using \(L=12,\;h=6\),
+
+\[
+12^{2}= \frac{(s-r)^{2}}{4}+6^{2}
+\quad\Longrightarrow\quad
+\frac{(s-r)^{2}}{4}=108
+\quad\Longrightarrow\quad
+s-r=12\sqrt3. \tag{3}
+\]
+
+---
+
+### 5.  Solving for \(r\) and \(s\)
+
+\[
+\begin{cases}
+r+s=24,\\[2pt]
+s-r=12\sqrt3,
+\end{cases}
+\qquad\Longrightarrow\qquad
+\begin{aligned}
+s&amp;=\frac{24+12\sqrt3}{2}=12+6\sqrt3,\\
+r&amp;=\frac{24-12\sqrt3}{2}=12-6\sqrt3.
+\end{aligned}
+\]
+
+---
+
+### 6.  Required sum of squares
+
+\[
+\begin{aligned}
+r^{2}+s^{2}
+&amp;=(12-6\sqrt3)^{2}+(12+6\sqrt3)^{2}\\
+&amp;= \bigl(144-144\sqrt3+108\bigr)+\bigl(144+144\sqrt3+108\bigr)\\
+&amp;= 504.
+\end{aligned}
+\]
+
+\[
+\boxed{504}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 504</p>
+<p>Extracted Answer: 504</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $ \triangle ABC $ be a right triangle with $ \angle A = 90^\circ $ and $ BC = 38 $. There exist points $ K $ and $ L $ inside the triangle such that $ AK = AL = BK = CL = KL = 14. $ The area of the quadrilateral $ BKLC $ can be expressed as $ n \sqrt{3} $ for some positive integer $ n $. Find $ n $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+* \(A=(0,0)\),  
+* \(B=(u,0)\) on the \(x\)-axis,  
+* \(C=(0,v)\) on the \(y\)-axis.  
+
+Since \(\angle A=90^{\circ}\), \(BC=38\) gives  
+
+\[
+u^{2}+v^{2}=38^{2}=1444\tag{1}
+\]
+
+---
+
+### 1.  The equilateral triangle \(AKL\)
+
+The conditions  
+
+\[
+AK=AL=KL=14
+\]
+
+show that \(\triangle AKL\) is equilateral.  
+Let the direction of \(\overrightarrow{AK}\) form an angle \(\theta\) with the
+positive \(x\)-axis. Then
+
+\[
+K=(14\cos\theta,\;14\sin\theta),\qquad 
+L=(14\cos(\theta+60^\circ),\;14\sin(\theta+60^\circ)).\tag{2}
+\]
+
+---
+
+### 2.  Using \(BK=14\) and \(CL=14\)
+
+\[
+BK^{2}= (u-14\cos\theta)^2+(14\sin\theta)^2=14^{2}
+\]
+
+\[
+\Longrightarrow\; u=28\cos\theta.\tag{3}
+\]
+
+Similarly  
+
+\[
+CL^{2}= (14\cos(\theta+60^\circ))^{2}+(v-14\sin(\theta+60^\circ))^{2}=14^{2}
+\]
+
+\[
+\Longrightarrow\; v=28\sin(\theta+60^\circ).\tag{4}
+\]
+
+---
+
+### 3.  Determining \(\theta\)
+
+Insert (3) and (4) into (1):
+
+\[
+(28\cos\theta)^{2}+(28\sin(\theta+60^\circ))^{2}=1444
+\]
+\[
+\Longrightarrow\;\cos^{2}\theta+\sin^{2}(\theta+60^\circ)=\frac{361}{196}.
+\]
+
+Using \(\sin(\theta+60^\circ)=\tfrac12\sin\theta+\tfrac{\sqrt3}{2}\cos\theta\),
+the equation reduces to  
+
+\[
+6\cos^{2}\theta+2\sqrt3\sin\theta\cos\theta= \frac{312}{49}.
+\]
+
+Solving gives \(\cos\theta=\frac{13}{14}\) (the other root gives the same
+triangle with the legs interchanged).  
+
+Hence  
+
+\[
+u=28\cos\theta=28\cdot\frac{13}{14}=26,\qquad
+v=28\sin(\theta+60^\circ)=28\cdot\frac{4\sqrt3}{7}=16\sqrt3 .
+\]
+
+Thus  
+
+\[
+AB=26,\qquad AC=16\sqrt3,\qquad BC=38.
+\]
+
+From (2) we obtain the coordinates of the interior points
+
+\[
+K=(13,\;3\sqrt3),\qquad L=(2,\;8\sqrt3).
+\]
+
+---
+
+### 4.  Area of \(BKLC\)
+
+Use the shoelace formula for the polygon \(B(26,0),K(13,3\sqrt3),L(2,8\sqrt3),C(0,16\sqrt3)\):
+
+\[
+\begin{aligned}
+S_1&amp;=26\cdot3\sqrt3+13\cdot8\sqrt3+2\cdot16\sqrt3+0\cdot0=214\sqrt3,\\
+S_2&amp;=0\cdot13+3\sqrt3\cdot2+8\sqrt3\cdot0+16\sqrt3\cdot26=422\sqrt3.
+\end{aligned}
+\]
+
+\[
+\text{Area}=\frac12|S_2-S_1|
+          =\frac12(422-214)\sqrt3
+          =104\sqrt3 .
+\]
+
+Therefore the area can be written as \(n\sqrt3\) with  
+
+\[
+\boxed{n=104}.
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 104</p>
+<p>Extracted Answer: None</p>
+<p>Score: 0.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+There are $8!=40320$ eight-digit positive integers that use each of the digits $1,2,3,4,5,6,7,8$ exactly once. Let $N$ be the number of these integers that are divisible by 22. Find the difference between $N$ and 2025.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>For an eight‑digit number formed by a permutation of  
+
+\[
+\{1,2,3,4,5,6,7,8\}
+\]
+
+let  
+
+\[
+a_1a_2a_3a_4a_5a_6a_7a_8
+\]
+
+be its digits (left to right).  
+A number is divisible by \(22\iff\) it is divisible by \(2\) and by \(11\).
+
+---
+
+### 1.  Divisibility by 2  
+
+The last digit \(a_8\) must be even, so \(a_8\in\{2,4,6,8\}\).
+
+---
+
+### 2.  Divisibility by 11  
+
+For an 8‑digit number the rule for 11 is  
+
+\[
+(a_1+a_3+a_5+a_7)-(a_2+a_4+a_6+a_8)\equiv 0\pmod{11}.
+\]
+
+Since the total sum of the digits is  
+
+\[
+1+2+\cdots+8 = 36,
+\]
+
+let  
+
+\[
+S_{\text{odd}}=a_1+a_3+a_5+a_7,\qquad 
+S_{\text{even}}=a_2+a_4+a_6+a_8 .
+\]
+
+Then \(S_{\text{odd}}+S_{\text{even}}=36\) and the condition gives  
+
+\[
+S_{\text{odd}}-S_{\text{even}}\equiv0\pmod{11}.
+\]
+
+The only possible values for \(S_{\text{odd}}-S_{\text{even}}\) are \(-22,0,22\);   
+\(-22\) would give \(S_{\text{odd}}=7\) and \(22\) would give \(S_{\text{odd}}=29\), both impossible because a sum of four distinct digits from \(\{1,\dots ,8\}\) cannot be smaller than \(10\) nor larger than \(26\).  
+Hence
+
+\[
+S_{\text{odd}} = S_{\text{even}} = 18 .
+\]
+
+Thus the four digits in the odd positions must sum to \(18\); the same holds for the even positions.
+
+---
+
+### 3.  Choosing the four digits for the odd positions  
+
+We need 4‑element subsets of \(\{1,\dots ,8\}\) whose sum is \(18\).  
+A quick enumeration gives the eight subsets
+
+\[
+\begin{aligned}
+&amp;\{1,2,7,8\},\{1,3,6,8\},\{1,4,5,8\},\{1,4,6,7\},\\
+&amp;\{2,3,5,8\},\{2,3,6,7\},\{2,4,5,7\},\{3,4,5,6\}.
+\end{aligned}
+\]
+
+Each contains exactly two even digits (the set \(\{2,4,6,8\}\)) and two odd digits.  
+Hence every admissible odd‑position set has **2 even digits**.
+
+Let a chosen subset be \(S\) (the odd‑position digits) and its complement \(S^c\) (the even‑position digits).
+
+---
+
+### 4.  Arranging the digits  
+
+* The four digits of \(S\) can be placed in the odd positions \((1,3,5,7)\) in \(4! = 24\) ways.  
+* The four digits of \(S^c\) must fill the even positions \((2,4,6,8)\) with the extra requirement that the last digit \(a_8\) be even.  
+  Since \(S^c\) contains exactly \(2\) even digits, we have  
+
+\[
+\text{choices for }a_8 = 2,\qquad
+\text{arrangements of the remaining three even‑position digits}=3! = 6 .
+\]
+
+Thus for each set \(S\)
+
+\[
+\#\text{numbers}=4!\times(2\times3!) = 24\times12 = 288.
+\]
+
+---
+
+### 5.  Total number \(N\)
+
+There are \(8\) possible subsets \(S\); consequently
+
+\[
+N = 8 \times 288 = 2304 .
+\]
+
+---
+
+### 6.  Required difference
+
+\[
+N-2025 = 2304-2025 = 279 .
+\]
+
+\[
+\boxed{279}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 279</p>
+<p>Extracted Answer: 279</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $k$ be real numbers such that the system $|25+20i-z|=5$ and $|z-4-k|=|z-3i-k|$ has exactly one complex solution $z$. The sum of all possible values of $k$ can be written as $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$. Here $i=\sqrt{-1}$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+\[
+C=25+20i,\qquad r=5 ,
+\]
+
+so  
+
+\[
+|C-z|=5
+\]
+
+is the circle with centre \(C\) and radius \(5\).
+
+The second condition  
+
+\[
+|z-4-k|=|z-3i-k|
+\]
+
+means that \(z\) is equally distant from the points  
+
+\[
+P_1=4+k\quad(\text{on the real axis}), \qquad   
+P_2=k+3i .
+\]
+
+Hence the locus of \(z\) is the perpendicular bisector of the segment \(\overline{P_1P_2}\); this is a straight line.
+
+---
+
+### 1. Equation of the line
+
+Write \(z=x+yi\).  
+
+\[
+(x-(4+k))^2+y^2=(x-k)^2+(y-3)^2 .
+\]
+
+Expanding and simplifying gives  
+
+\[
+-8(x-k)+16=-6y+9,
+\]
+
+\[
+-8x+8k+6y+7=0 .
+\]
+
+Thus the line \(L(k)\) is  
+
+\[
+-8x+6y+8k+7=0 \qquad\text{or}\qquad 8x-6y=8k+7 .
+\]
+
+All such lines have slope \(\dfrac{4}{3}\); they are a family of parallel lines depending on \(k\).
+
+---
+
+### 2. Tangency condition
+
+The system has exactly one solution precisely when the line \(L(k)\) is tangent to the circle \(|z-C|=5\).  
+
+For a line \(Ax+By+C=0\) the distance from a point \((x_0,y_0)\) is  
+
+\[
+d=\frac{|Ax_0+By_0+C|}{\sqrt{A^2+B^2}} .
+\]
+
+Here \(A=-8,\;B=6,\;C=8k+7\) and the centre of the circle is \((25,20)\). Hence
+
+\[
+d(k)=\frac{\bigl|-8\cdot25+6\cdot20+(8k+7)\bigr|}{\sqrt{(-8)^2+6^2}}
+      =\frac{|8k-73|}{10}.
+\]
+
+Tangency requires \(d(k)=r=5\):
+
+\[
+\frac{|8k-73|}{10}=5\quad\Longrightarrow\quad|8k-73|=50 .
+\]
+
+Thus  
+
+\[
+8k-73=50\quad\text{or}\quad8k-73=-50,
+\]
+
+\[
+k=\frac{123}{8},\qquad k=\frac{23}{8}.
+\]
+
+Both values make the line tangent, giving exactly one intersection point with the circle.
+
+---
+
+### 3. Sum of the possible \(k\)
+
+\[
+\frac{123}{8}+\frac{23}{8}= \frac{146}{8}= \frac{73}{4}.
+\]
+
+Write \(\dfrac{73}{4}\) as \(\dfrac{m}{n}\) with \(\gcd(m,n)=1\); then \(m=73,\;n=4\).
+
+\[
+m+n = 73+4 = 77.
+\]
+
+\[
+\boxed{77}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 77</p>
+<p>Extracted Answer: 77</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+The twelve letters $A,B,C,D,E,F,G,H,I,J,K$, and $L$ are randomly grouped into six pairs of letters. The two letters in each pair are placed next to each other in alphabetical order to form six two-letter words, and those six words are listed alphabetically. For example, a possible result is $AB,CJ,DG,EK,FL,HI$. The probability that the last word listed contains $G$ is $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let the letters be  
+
+\[
+A&lt;B&lt;C&lt;D&lt;E&lt;F&lt;G&lt;H&lt;I&lt;J&lt;K&lt;L .
+\]
+
+In a random pairing each pair is written with its smaller letter first, so a
+pair \(\{x,y\}\;(x&lt;y)\) becomes the word \(xy\).
+The six words are then listed alphabetically; the last word is the
+lexicographically largest of the six two‑letter words.
+
+Because the first letters of the six words are all different (each letter can
+appear as the smaller element of at most one pair), the largest word is the
+pair whose **smaller** element is the largest among the six smaller elements.
+Hence the last word contains \(G\) precisely when the pair containing \(G\)
+has the largest smaller element.
+
+---
+
+### 1.  Choose the partner of \(G\)
+
+\(G\) can be paired with any of the other 11 letters, each with probability
+\(\frac1{11}\).
+
+*If \(G\) is paired with a letter larger than \(G\)*  
+(let the partner be \(X\in\{H,I,J,K,L\}\)).  
+Then the smaller element of the \(G\!-\!X\) pair is \(G\).
+
+The remaining 10 letters consist of  
+
+- 6 letters \(\{A,B,C,D,E,F\}\) smaller than \(G\) (call them “low”),  
+- 4 letters among \(\{H,I,J,K,L\}\setminus\{X\}\) larger than \(G\) (call them “high”).
+
+For the pair \(G\!-\!X\) to have the largest smaller element, no other pair
+may have a smaller element \(\ge G\); i.e. no “high” letter may be the smaller
+letter of its pair.  Hence each high letter must be matched with a low
+letter.  
+
+Number of matchings of the 10 remaining letters with no high–high pair:
+
+\[
+\binom{6}{4}\,4!\;(=15\cdot24)=360 .
+\]
+
+Total matchings of 10 letters: \((10-1)!!=945\).
+Thus
+
+\[
+P(\text{lexicographically largest pair }|\,G\!-\!X,\;X&gt;G)=\frac{360}{945}
+=\frac{8}{21}.
+\]
+
+Since there are 5 possible partners larger than \(G\),
+
+\[
+\sum_{X&gt;G}\frac1{11}\cdot\frac{8}{21}=5\cdot\frac{1}{11}\cdot\frac{8}{21}
+=\frac{40}{231}.
+\]
+
+*If \(G\) is paired with a letter smaller than \(G\)*  
+the only possible partner is \(F\); for any smaller partner there are fewer
+than five letters below it, making it impossible for its pair to have the
+largest smaller element.
+
+When \(G\) is paired with \(F\), the smaller element of the pair is \(F\).
+The other 10 letters are  
+
+\[
+\{A,B,C,D,E\}\ (\text{low})\quad\text{and}\quad\{H,I,J,K,L\}\ (\text{high}).
+\]
+
+All five high letters must be paired with the five low letters; otherwise a
+high letter would become a smaller element.  The number of such matchings is
+\(5!=120\).  Hence
+
+\[
+P(\text{largest pair }|\,G\!-\!F)=\frac{120}{945}=\frac{8}{63},
+\]
+and the contribution is \(\displaystyle\frac1{11}\cdot\frac{8}{63}
+= \frac{8}{693}\).
+
+No other partner of \(G\) can work, so the total probability that the last
+word contains \(G\) is
+
+\[
+\frac{40}{231}+\frac{8}{693}
+=\frac{120}{693}+\frac{8}{693}
+=\frac{128}{693}.
+\]
+
+The fraction \(\frac{128}{693}\) is already in lowest terms.  
+Thus \(m=128,\ n=693\) and
+
+\[
+m+n = 128+693 = 821.
+\]
+
+\[
+\boxed{821}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 821</p>
+<p>Extracted Answer: 821</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+On $\triangle ABC$ points $A,D,E$, and $B$ lie that order on side $\overline{AB}$ with $AD=4, DE=16$, and $EB=8$. Points $A,F,G$, and $C$ lie in that order on side $\overline{AC}$ with $AF=13, FG=52$, and $GC=26$. Let $M$ be the reflection of $D$ through $F$, and let $N$ be the reflection of $G$ through $E$. Quadrilateral $DEGF$ has area 288. Find the area of heptagon $AFNBCEM$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>**Solution**
+
+--------------------------------------------------------------------
+
+### 1.  The ratios on the two sides  
+
+\[
+AB=AD+DE+EB=4+16+8=28,\qquad 
+AC=AF+FG+GC=13+52+26=91 .
+\]
+
+\[
+\frac{AD}{AB}=\frac{4}{28}=\frac17,\qquad 
+\frac{AF}{AC}= \frac{13}{91}= \frac17 .
+\]
+
+Hence  
+
+\[
+\frac{AD}{AB}= \frac{AF}{AC}= \frac17\qquad\Longrightarrow\qquad 
+DF\parallel BC .
+\]
+
+Similarly  
+
+\[
+\frac{AE}{AB}= \frac{20}{28}= \frac57,\qquad 
+\frac{AG}{AC}= \frac{65}{91}= \frac57 ,
+\]
+
+so  
+
+\[
+\frac{AE}{AB}= \frac{AG}{AC}= \frac57\qquad\Longrightarrow\qquad 
+EG\parallel BC .
+\]
+
+Let  
+
+\[
+p=\frac17,\qquad q=\frac57 .
+\]
+
+--------------------------------------------------------------------
+
+### 2.  Area of \(\triangle ABC\)
+
+Because \(DF\parallel EG\parallel BC\), the quadrilateral \(DEGF\) is the
+region of \(\triangle ABC\) between the two lines through \(D\) and \(E\)
+parallel to \(BC\).  
+
+Triangles \(ADF\) and \(AEG\) are similar to \(\triangle ABC\) with similarity
+ratios \(p\) and \(q\) respectively, so
+
+\[
+[ADF]=p^{2}[ABC],\qquad[AEG]=q^{2}[ABC].
+\]
+
+Hence  
+
+\[
+[DEGF]=[AEG]-[ADF]=(q^{2}-p^{2})[ABC]
+        =\Bigl(\frac{5^{2}}{7^{2}}-\frac{1^{2}}{7^{2}}\Bigr)[ABC]
+        =\frac{24}{49}[ABC].
+\]
+
+Given \([DEGF]=288\),
+
+\[
+[ABC]=288\cdot\frac{49}{24}=12\cdot 49 =\boxed{588}.
+\]
+
+--------------------------------------------------------------------
+
+### 3.  Coordinates
+
+Place  
+
+\[
+A=(0,0),\qquad B=(28,0),\qquad C=(c,\,42)
+\]
+
+(the height is \(42\) because \([ABC]=\frac12\cdot28\cdot42=588\)).  
+Using the ratios \(p,q\),
+
+\[
+\begin{aligned}
+D &amp;=pB=(4,0),                   &amp;E&amp;=qB=(20,0),\\[2mm]
+F &amp;=pC=\Bigl(\frac{c}{7},6\Bigr), &amp;
+G &amp;=qC=\Bigl(\frac{5c}{7},30\Bigr).
+\end{aligned}
+\]
+
+Reflections give  
+
+\[
+M=2F-D=\Bigl(\frac{2c}{7}-4,\;12\Bigr),\qquad 
+N=2E-G=\Bigl(40-\frac{5c}{7},\;-30\Bigr).
+\]
+
+--------------------------------------------------------------------
+
+### 4.  Area of the heptagon \(AFNBCEM\)
+
+List the vertices in order:
+
+\[
+\begin{array}{c|c}
+\text{Vertex}&amp;(x,y)\\ \hline
+A&amp;(0,0)\\
+F&amp;\bigl(\frac{c}{7},6\bigr)\\
+N&amp;\bigl(40-\frac{5c}{7},-30\bigr)\\
+B&amp;(28,0)\\
+C&amp;(c,42)\\
+E&amp;(20,0)\\
+M&amp;\bigl(\frac{2c}{7}-4,12\bigr)
+\end{array}
+\]
+
+Apply the Shoelace formula.  The sum  
+
+\[
+\sum_{i=1}^{7}\bigl(x_i y_{i+1}-y_i x_{i+1}\bigr)
+\]  
+
+(with \(x_8=x_1,\;y_8=y_1\)) simplifies dramatically:
+
+\[
+\begin{aligned}
+&amp;0\\
+&amp;\;-\;240\\
+&amp;\;+\;840\\
+&amp;\;+\;1176\\
+&amp;\;-\;840\\
+&amp;\;+\;240\\
+&amp;0
+\end{aligned}
+\qquad =\;1176 .
+\]
+
+Thus
+
+\[
+[AFNBCEM]=\frac12\cdot1176=588 .
+\]
+
+The result does **not** depend on the unknown coordinate \(c\); the
+cancellation occurs because the vectors \(DF\) and \(EG\) are parallel to
+\(BC\).
+
+--------------------------------------------------------------------
+
+### 5.  Answer
+
+\[
+\boxed{588}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 588</p>
+<p>Extracted Answer: 588</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+The parabola with equation $y=x^{2}-4$ is rotated $60^{\circ}$ counterclockwise around the origin. The unique point in the fourth quadrant where the original parabola and its image intersect has $y$-coordinate $\frac{a-\sqrt{b}}{c}$, where $a$, $b$, and $c$ are positive integers, and $a$ and $c$ are relatively prime. Find $a+b+c$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+\[
+P:\;y=x^{2}-4
+\]
+
+and rotate \(P\) \(60^{\circ}\) counter‑clockwise about the origin.  
+If \((x,y)\) lies on the rotated curve, then there is a point \((u,v)\) on
+\(P\) such that  
+
+\[
+\begin{pmatrix}x\\y\end{pmatrix}=R\begin{pmatrix}u\\v\end{pmatrix},
+\qquad 
+R=\begin{pmatrix}\tfrac12&amp;-\tfrac{\sqrt3}{2}\\[2pt]\tfrac{\sqrt3}{2}&amp;\tfrac12\end{pmatrix}.
+\]
+
+Equivalently, a point \((x,y)\) is on both curves iff
+
+\[
+y=x^{2}-4 \qquad\text{and}\qquad 
+R^{T}\!\begin{pmatrix}x\\y\end{pmatrix}
+   =\begin{pmatrix}x&#39;\\y&#39;\end{pmatrix}
+\text{ satisfies }y&#39;=(x&#39;)^{2}-4,
+\]
+
+where  
+
+\[
+R^{T}= \begin{pmatrix}\tfrac12&amp;\tfrac{\sqrt3}{2}\\[2pt]-\tfrac{\sqrt3}{2}&amp;\tfrac12\end{pmatrix},
+\quad 
+x&#39;=\frac{x}{2}+\frac{\sqrt3\,y}{2},\qquad
+y&#39;=-\frac{\sqrt3\,x}{2}+\frac{y}{2}.
+\]
+
+Using \(y=x^{2}-4\),
+
+\[
+x&#39;=\frac{\sqrt3 x^{2}+x-4\sqrt3}{2},\qquad 
+y&#39;=\frac{x^{2}-\sqrt3 x-4}{2}.
+\]
+
+The condition \(y&#39;=(x&#39;)^{2}-4\) yields  
+
+\[
+\frac{x^{2}-\sqrt3 x-4}{2}
+   =\Bigl(\frac{\sqrt3 x^{2}+x-4\sqrt3}{2}\Bigr)^{2}-4 .
+\]
+
+Multiplying by \(2\) and simplifying gives the quartic
+
+\[
+3x^{4}+2\sqrt3\,x^{3}-25x^{2}-6\sqrt3\,x+40=0.
+\]
+
+Factor this over \(\mathbb{Q}(\sqrt3)\):
+
+\[
+\begin{aligned}
+3x^{4}+2\sqrt3\,x^{3}-25x^{2}-6\sqrt3\,x+40
+&amp;=(x^{2}+\sqrt3\,x-4)(3x^{2}-\sqrt3\,x-10).
+\end{aligned}
+\]
+
+Hence the possible \(x\)-coordinates are the roots of the two quadratics.
+
+\[
+\begin{cases}
+x^{2}+\sqrt3\,x-4=0 &amp;\Longrightarrow
+\displaystyle x=\frac{-\sqrt3\pm\sqrt{19}}2,\\[6pt]
+3x^{2}-\sqrt3\,x-10=0 &amp;\Longrightarrow
+\displaystyle x=\frac{\sqrt3\pm\sqrt{123}}6 .
+\end{cases}
+\]
+
+We need a point in the fourth quadrant, i.e. \(x&gt;0\) and \(y=x^{2}-4&lt;0\).
+Only  
+
+\[
+x=\frac{-\sqrt3+\sqrt{19}}2\;(&gt;0,\;&lt;2)
+\]
+
+satisfies this.  Its \(y\)-coordinate is
+
+\[
+\begin{aligned}
+y&amp;=x^{2}-4
+   =\frac{(-\sqrt3+\sqrt{19})^{2}}{4}-4
+   =\frac{22-2\sqrt{57}}4-4\\
+  &amp;=\frac{11-\sqrt{57}}2-4
+   =\frac{3-\sqrt{57}}2 .
+\end{aligned}
+\]
+
+Thus  
+
+\[
+y=\frac{a-\sqrt{b}}{c}\quad\text{with}\quad a=3,\;b=57,\;c=2,
+\]
+
+and \(a\) and \(c\) are relatively prime.  
+
+Finally
+
+\[
+a+b+c=3+57+2=62.
+\]
+
+\[
+\boxed{62}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 62</p>
+<p>Extracted Answer: 62</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+The set of points in 3-dimensional coordinate space that lie in the plane $x+y+z=75$ whose coordinates satisfy the inequalities $x-yz&lt;y-zx&lt;z-xy$ forms three disjoint convex regions. Exactly one of those regions has finite area. The area of this finite region can be expressed in the form $a\sqrt{b}$, where $a$ and $b$ are positive integers and $b$ is not divisible by the square of any prime. Find $a+b$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>\[
+\begin{aligned}
+&amp;x-yz&lt;y-zx&lt;z-xy \\
+\Longleftrightarrow\;&amp;x-yz&lt;y-zx\quad\text{and}\quad y-zx&lt;z-xy  \\
+\Longleftrightarrow\;&amp;(x-y)(1+z)&lt;0\quad\text{and}\quad (y-z)(1+x)&lt;0 .
+\end{aligned}
+\]
+
+Hence  
+
+\[
+\begin{cases}
+(x-y)(1+z)&lt;0,\\[2pt]
+(y-z)(1+x)&lt;0 .
+\end{cases}
+\]
+
+Each product being negative means the two factors have opposite signs.  
+Thus we have four possible sign‑combinations:
+
+\[
+\begin{array}{c|c|c}
+\text{Case}&amp; (x-y,\;1+z) &amp; (y-z,\;1+x)\\ \hline
+\text{I}&amp; (+,\; -) &amp; (+,\; -)\\
+\text{II}&amp; (+,\; -) &amp; (-,\; +)\\
+\text{III}&amp; (-,\; +) &amp; (+,\; -)\\
+\text{IV}&amp; (-,\; +) &amp; (-,\; +)
+\end{array}
+\]
+
+Translating them into linear inequalities:
+
+\[
+\begin{aligned}
+\text{I}&amp;:\; x&gt;y,\;z&lt;-1,\;y&gt;z,\;x&lt;-1 \qquad\text{(impossible since }x+y+z=75)\\
+\text{II}&amp;:\; x&gt;y,\;z&lt;-1,\;y&lt;z,\;x&gt;-1 \\
+\text{III}&amp;:\; x&lt;y,\;z&gt;-1,\;y&gt;z,\;x&lt;-1 \\
+\text{IV}&amp;:\; x&lt;y,\;z&gt;-1,\;y&lt;z,\;x&gt;-1 .
+\end{aligned}
+\]
+
+Thus three non‑empty convex regions arise from cases II, III, IV.
+Cases II and III are unbounded, while case IV gives a bounded region.
+
+---
+
+### Bounded region (case IV)
+
+Case IV is equivalent to  
+
+\[
+-1&lt;x&lt;y&lt;z ,\qquad x+y+z=75 .
+\]
+
+The boundary of this region in the plane \(x+y+z=75\) consists of the three lines  
+
+\[
+\begin{cases}
+x=-1,\\[2pt]
+y=x,\\[2pt]
+z=y .
+\end{cases}
+\]
+
+Intersecting each pair of lines with the plane gives the vertices
+
+\[
+\begin{aligned}
+A &amp;: x=-1,\;y=-1 \;\Rightarrow\;z=77 ,&amp;&amp;A(-1,-1,77),\\
+B &amp;: x=-1,\;z=y \;\Rightarrow\;y=z=38 ,&amp;&amp;B(-1,38,38),\\
+C &amp;: y=x,\;z=y \;\Rightarrow\;x=y=z=25 ,&amp;&amp;C(25,25,25).
+\end{aligned}
+\]
+
+Hence the finite region is the triangle \(ABC\).
+
+---
+
+### Area of the triangle
+
+Vectors along two sides:
+
+\[
+\begin{aligned}
+\vec{AB}&amp;=B-A=(0,39,-39),\\
+\vec{AC}&amp;=C-A=(26,26,-52).
+\end{aligned}
+\]
+
+\[
+\vec{AB}\times\vec{AC}=(-1014,-1014,-1014)
+\quad\Longrightarrow\quad 
+\bigl\lVert\vec{AB}\times\vec{AC}\bigr\rVert
+=1014\sqrt3 .
+\]
+
+Therefore
+
+\[
+\text{Area}= \frac12\bigl\lVert\vec{AB}\times\vec{AC}\bigr\rVert
+           =\frac12\cdot1014\sqrt3
+           =507\sqrt3 .
+\]
+
+Thus the area is \(a\sqrt b\) with \(a=507,\;b=3\), and
+
+\[
+a+b=507+3=510.
+\]
+
+\[
+\boxed{510}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 510</p>
+<p>Extracted Answer: 510</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+A piecewise linear periodic function is defined by $f(x)=\begin{cases}x&amp;\text{if }x\in[-1,1)\\2-x&amp;\text{if }x\in[1,3)\end{cases}$ and $f(x+4)=f(x)$ for all real numbers $x$. The graph of $f(x)$ has the sawtooth pattern. The parabola $x=34y^2$ intersects the graph of $f(x)$ at finitely many points. The sum of the $y$-coordinates of these intersection points can be expressed in the form $\frac{a+b\sqrt{c}}{d}$, where $a,b,c,$ and $d$ are positive integers, $a,b,$ and $d$ have greatest common divisor equal to 1, and $c$ is not divisible by the square of any prime. Find $a+b+c+d$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>First write the equation for the intersection points.
+
+The parabola is  
+
+\[
+x=34y^{2},
+\]
+
+and the periodic saw‑tooth satisfies  
+
+\[
+f(x+4)=f(x),\qquad   
+f(x)=\begin{cases}
+x,&amp;-1\le x&lt;1,\\[2pt]
+2-x,&amp;1\le x&lt;3 .
+\end{cases}
+\]
+
+Hence an intersection must satisfy  
+
+\[
+y=f(34y^{2}). \tag{1}
+\]
+
+--------------------------------------------------------------------
+### 1.  Express \(f\) using the modulus
+
+For any real \(x\) let  
+
+\[
+t=(x+1)\pmod 4,\qquad 0\le t&lt;4 .
+\]
+
+Then  
+
+\[
+f(x)=
+\begin{cases}
+t-1,&amp;0\le t&lt;2,\\[2pt]
+3-t,&amp;2\le t&lt;4 .
+\end{cases}
+\]
+
+Put \(x=34y^{2}\).  Let  
+
+\[
+s=34y^{2}+1,\qquad t=s\pmod4 .
+\]
+
+--------------------------------------------------------------------
+### 2.  Two linear possibilities
+
+*If \(0\le t&lt;2\) (the “rising” part) then \(y=t-1\) and  
+\(t=y+1\).  Hence  
+
+\[
+34y^{2}+1=4n+y+1\quad\Longrightarrow\quad 34y^{2}-y-4n=0,\tag{2}
+\]
+
+with the condition \(y\in[-1,1)\).
+
+*If \(2\le t&lt;4\) (the “falling” part) then \(y=3-t\) and  
+\(t=3-y\).  Hence  
+
+\[
+34y^{2}+1=4n+3-y\quad\Longrightarrow\quad 34y^{2}+y-(2+4n)=0,\tag{3}
+\]
+
+with the condition \(y\in(-1,1]\).
+
+Here \(n\) is the integer \(\displaystyle n=\Big\lfloor\frac{34y^{2}+1}{4}\Big\rfloor\).
+Since \(0\le 34y^{2}+1\le 35\), we must have \(0\le n\le 8\).
+
+--------------------------------------------------------------------
+### 3.  Solve the quadratics
+
+**From (2):**  
+
+\[
+y=\frac{1\pm\sqrt{1+544n}}{68}\qquad (n=0,1,\dots ,8).
+\]
+
+Both roots lie in \([-1,1)\); for each \(n\) their sum is  
+
+\[
+\frac{1}{34}.
+\]
+
+Thus  
+
+\[
+S_I=\sum_{n=0}^{8}\frac1{34}= \frac{9}{34}. \tag{4}
+\]
+
+**From (3):**  
+
+\[
+y=\frac{-1\pm\sqrt{273+544n}}{68}\qquad (n=0,1,\dots ,8).
+\]
+
+For \(n=0,\dots ,7\) both roots satisfy \((-1,1]\); for \(n=8\) the
+negative root is \(\le -1\) and must be discarded.
+Hence for \(n=0,\dots ,7\) each pair sums to \(-\dfrac1{34}\), and we add
+the single remaining root for \(n=8\):
+
+\[
+S_{II}=8\!\left(-\frac1{34}\right)+\frac{-1+\sqrt{4625}}{68}
+        =-\frac{8}{34}+\frac{-1+5\sqrt{185}}{68}. \tag{5}
+\]
+
+--------------------------------------------------------------------
+### 4.  Total sum of \(y\)-coordinates
+
+\[
+\begin{aligned}
+S &amp;=S_I+S_{II}\\
+  &amp;=\frac{9}{34}-\frac{8}{34}+\frac{-1+5\sqrt{185}}{68}\\
+  &amp;=\frac{1}{34}+\frac{-1+5\sqrt{185}}{68}\\[2pt]
+  &amp;=\frac{2-1+5\sqrt{185}}{68}
+   =\frac{1+5\sqrt{185}}{68}.
+\end{aligned}
+\]
+
+Thus the sum can be written as \(\displaystyle \frac{a+b\sqrt{c}}{d}\) with  
+
+\[
+a=1,\qquad b=5,\qquad c=185,\qquad d=68,
+\]
+
+where \(a,b,d\) are coprime and \(c\) is square‑free.
+
+Finally  
+
+\[
+a+b+c+d = 1+5+185+68 = 259.
+\]
+
+\[
+\boxed{259}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 259</p>
+<p>Extracted Answer: 259</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $N$ denote the number of ordered triples of positive integers $(a,b,c)$ such that $a,b,c\leq3^6$ and $a^3+b^3+c^3$ is a multiple of $3^7$. Find the remainder when $N$ is divided by $1000$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>The condition  
+
+\[
+a^3+b^3+c^3\equiv 0\pmod {3^7}\qquad (3^7=2187)
+\]
+
+depends only on the residues of \(a,b,c\) modulo \(3^7\).  
+Write each number as  
+
+\[
+a=3^{3\alpha}q,\qquad \alpha\in\{0,1,2\},\;q\in Q,
+\]
+
+where  
+
+* \(Q\) = the set of cubic residues among units modulo \(3^7\);  
+  \(|Q|=486\);
+* for \(\alpha=0,1,2\) the sets  
+
+\[
+R_\alpha =\{3^{3\alpha}q\;|\;q\in Q\}
+\]
+
+have sizes  
+
+\[
+|R_0|=486,\;|R_1|=162,\;|R_2|=54 .
+\]
+
+All numbers divisible by \(27\) contribute \(0\) to the sum, so we only need the
+ordered triples whose components lie in  
+
+\[
+R=R_0\cup R_1\cup R_2 .
+\]
+
+Denote  
+
+\[
+M_2 =\#\{(x,y)\in R^2 : x+y\equiv 0\},\qquad 
+M_3 =\#\{(x,y,z)\in R^3 : x+y+z\equiv 0\}.
+\]
+
+Because \(-x\in R\) for every \(x\in R\), we have \(M_2=|R|=702\).
+
+The total number of required triples of positive integers is  
+
+\[
+\begin{aligned}
+N&amp;=27^3      \;(\text{all three multiples of }27) \\
+  &amp;\quad+ 3\cdot27\cdot M_2 \;(\text{exactly two non‑multiples of }27)\\
+  &amp;\quad+ M_3 .
+\end{aligned}
+\]
+
+Thus  
+
+\[
+N=19683+81\cdot702+M_3=19683+56862+M_3 .
+\]
+
+--------------------------------------------------------------------
+### Computing \(M_3\)
+
+Let  
+
+\[
+f(z)=\mathbf 1_R(z),\qquad
+F(t)=\sum_{z\in\mathbf Z/3^7\mathbf Z}f(z) e^{2\pi i t z/3^7}
+\]
+
+be the Fourier transform of the indicator of \(R\).  
+Then
+
+\[
+M_3=\frac1{3^7}\sum_{t=0}^{3^7-1}F(t)^3 .
+\]
+
+Writing \(R\) as \(Q\cup27Q\cup729Q\) and using that each element of
+\(R_\alpha\) is obtained from \(|Q|/3^\alpha\) elements of \(Q\), we obtain
+
+\[
+F(t)=\sum_{\alpha=0}^{2}\frac1{3^{\alpha}}
+        \sum_{q\in Q} e^{2\pi i t\cdot3^{3\alpha} q/3^7}.
+\]
+
+The inner sums are evaluated with the three characters of order 3 on
+\((\mathbf Z/3^7\mathbf Z)^\times\).  One finds that \(F(t)\) depends only on
+\(v=v_3(t)\) (the 3‑adic valuation of \(t\)):
+
+\[
+\begin{array}{c|c|c}
+v &amp;\text{number of }t &amp;F(t)\\\hline
+0 &amp;1458 &amp; -27\\
+1 &amp;486  &amp; 54\\
+2 &amp;162  &amp; 54\bigl(1+\operatorname{Re}A\bigr)\\
+3 &amp;54   &amp; -27\\
+4 &amp;18   &amp; 216\\
+5 &amp;6    &amp; 216+162\,\operatorname{Re}A\\
+6 &amp;2    &amp; -27
+\end{array}
+\]
+
+where  
+
+\[
+A=3e^{2\pi i/9}=3\zeta_9,\qquad 
+\operatorname{Re}A=3\cos\frac{2\pi}{9}.
+\]
+
+From the values
+\[
+\operatorname{Re}A=3\cos\frac{2\pi}{9},\qquad
+\cos\frac{2\pi}{9}+ \cos\frac{4\pi}{9}+ \cos\frac{8\pi}{9}=0,
+\]
+one obtains  
+
+\[
+\sum_{i=1}^3 (1+r_i)^3=\frac{267}{8},\qquad
+\sum_{i=1}^3\Bigl(\frac43+r_i\Bigr)^3=\frac{3671}{72},
+\]
+where \(r_1,r_2,r_3\) are the three real numbers
+\(3\cos\frac{2\pi}{9},\,3\cos\frac{4\pi}{9},\,3\cos\frac{8\pi}{9}\).
+
+Carrying out the sum
+
+\[
+\sum_{t}F(t)^3
+ =702^3-1514\cdot27^3+486\cdot54^3+18\cdot216^3
+   +54^4\!\left(\frac{267}{8}\right)+8\,503\,056\!\left(\frac{3671}{72}\right)
+ =1\,291\,401\,630 .
+\]
+
+Since \(3^7=2187\),
+
+\[
+M_3=\frac{1\,291\,401\,630}{2187}=590\,490 .
+\]
+
+--------------------------------------------------------------------
+### Final count
+
+\[
+\begin{aligned}
+N &amp;=19683+56862+590490\\
+  &amp;=667\,035 .
+\end{aligned}
+\]
+
+The problem asks for \(N\bmod 1000\):
+
+\[
+\boxed{35}.
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 735</p>
+<p>Extracted Answer: 35</p>
+<p>Score: 0.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+The 27 cells of a $3\times9$ grid are filled in using the numbers 1 through 9 so that each row contains 9 different numbers, and each of the three $3\times3$ blocks heavily outlined in the example below contains 9 different numbers, as in the first three rows of a Sudoku puzzle. 
+ | 4 | 2 | 8 | 9 | 6 | 3 | 1 | 7 | 5 | 
+ | 3 | 7 | 9 | 5 | 2 | 1 | 6 | 8 | 4 | 
+ | 5 | 6 | 1 | 8 | 4 | 7 | 9 | 2 | 3 | 
+ The number of different ways to fill such a grid can be written as $p^a\cdot q^b\cdot r^c\cdot s^d$, where $p,q,r,$ and $s$ are distinct prime numbers and $a,b,c,$ and $d$ are positive integers. Find $p\cdot a+q\cdot b+r\cdot c+s\cdot d$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>**Step 1 –   What the conditions mean**
+
+The grid has three rows and nine columns.  
+The columns are grouped into three \(3\times3\) blocks  
+
+\[
+B_{1}=\{1,2,3\},\qquad B_{2}=\{4,5,6\},\qquad B_{3}=\{7,8,9\}.
+\]
+
+For each row we must use the numbers \(1,2,\dots ,9\) exactly once, and for each
+block the nine cells of that block must also contain the numbers \(1,\dots ,9\) exactly once.
+
+Hence for each digit \(d\) :
+
+* it appears once in each of the three rows,  
+* it appears once in each of the three blocks.
+
+Consequently the three positions of a digit form a **bijection** between rows and blocks.
+Let \(\sigma _d\in S_{3}\) be the permutation defined by
+
+\[
+\sigma _d(i)=\text{the block that contains }d\text{ in row }i .
+\]
+
+Thus each digit contributes one ‘1’ in the \(3\times3\) permutation matrix of \(\sigma _d\).
+
+--------------------------------------------------------------------
+
+**Step 2 –   The matrix condition**
+
+If we add the nine permutation matrices of the nine digits we obtain a matrix
+\(M\) whose entry \(M_{i,b}\) counts how many digits lie in row \(i\) and block \(b\).
+The block condition says that each block must contain each digit once, i.e. each
+cell \((i,b)\) must contain exactly three digits. Therefore
+
+\[
+M=3J,\qquad J=\begin{pmatrix}1&amp;1&amp;1\\1&amp;1&amp;1\\1&amp;1&amp;1\end{pmatrix}.
+\]
+
+So we must write \(3J\) as a sum of nine (not‑necessarily distinct) permutation
+matrices of size \(3\).
+
+--------------------------------------------------------------------
+
+**Step 3 –   Types of permutations**
+
+\(S_{3}\) has six elements:
+
+\[
+\begin{aligned}
+&amp;\text{id},\;(12),\;(13),\;(23),\;(123),\;(132).
+\end{aligned}
+\]
+
+Let  
+
+\[
+a=x_{\text{id}}=x_{(123)}=x_{(132)},\qquad
+b=x_{(12)}=x_{(13)}=x_{(23)} .
+\]
+
+Counting the contributions of each type to the nine entries of \(M\) gives the
+system  
+
+\[
+\begin{cases}
+a+b=3\\[2pt]
+a+b=3\\[2pt]
+a+b=3\\[2pt]
+a+b=3,
+\end{cases}
+\qquad\Longrightarrow\qquad a+b=3 .
+\]
+
+Hence \(a\) may be \(0,1,2,3\) and \(b=3-a\).  For a fixed value of \(a\),
+
+\[
+\begin{aligned}
+x_{\text{id}}&amp;=a,\\
+x_{(123)}&amp;=a,\\
+x_{(132)}&amp;=a,\\
+x_{(12)}&amp;=x_{(13)}=x_{(23)}&amp;=3-a .
+\end{aligned}
+\]
+
+--------------------------------------------------------------------
+
+**Step 4 –   Assigning the nine digits to the permutations**
+
+The nine digits are distinct, so for a given \(a\) the number of ways to give the
+six permutation types to the digits is the multinomial coefficient
+
+\[
+N_a=\frac{9!}{a!\,a!\,a!\,(3-a)!\,(3-a)!\,(3-a)!}
+    =\frac{9!}{a!^{3}(3-a)!^{3}} .
+\]
+
+Summing over the four possible values of \(a\),
+
+\[
+\sum_{a=0}^{3}N_a
+   =\frac{9!}{0!^{3}3!^{3}}+\frac{9!}{1!^{3}2!^{3}}
+    +\frac{9!}{2!^{3}1!^{3}}+\frac{9!}{3!^{3}0!^{3}}
+   =94\,080 .
+\]
+
+--------------------------------------------------------------------
+
+**Step 5 –   Ordering inside each row‑block**
+
+For a fixed assignment of the permutations, each of the nine
+\( ( \text{row},\text{block} )\) cells contains exactly three different digits.
+These three digits can be placed in the three columns of that cell in any order,
+i.e. in \(3! = 6\) ways, independently of the other cells.
+Hence we obtain an extra factor \((3!)^{9}=6^{9}\).
+
+Thus the total number of admissible \(3\times9\) grids is
+
+\[
+N = 94\,080\cdot 6^{9}
+   =9!\cdot 6^{6}\cdot 56 .
+\]
+
+--------------------------------------------------------------------
+
+**Step 6 –   Prime factorisation**
+
+\[
+\begin{aligned}
+9! &amp;=2^{7}\,3^{4}\,5\,7,\\
+6^{6}&amp;=(2\cdot3)^{6}=2^{6}\,3^{6},\\
+56 &amp;=2^{3}\,7 .
+\end{aligned}
+\]
+
+Multiplying gives  
+
+\[
+N=2^{7+6+3}\,3^{4+6}\,5^{1}\,7^{1+1}
+  =2^{16}\,3^{10}\,5^{1}\,7^{2}.
+\]
+
+Thus we may write  
+
+\[
+N = p^{a}\,q^{b}\,r^{c}\,s^{d}
+\quad\text{with}\quad
+p=2,\;a=16;\;\; q=3,\;b=10;\;\; r=5,\;c=1;\;\; s=7,\;d=2 .
+\]
+
+--------------------------------------------------------------------
+
+**Step 7 –   Required sum**
+
+\[
+p\cdot a+q\cdot b+r\cdot c+s\cdot d
+ =2\cdot16+3\cdot10+5\cdot1+7\cdot2
+ =32+30+5+14=81 .
+\]
+
+--------------------------------------------------------------------
+
+\[
+\boxed{81}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 81</p>
+<p>Extracted Answer: 81</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Six points $ A, B, C, D, E, $ and $ F $ lie in a straight line in that order. Suppose that $ G $ is a point not on the line and that $ AC = 26 $, $ BD = 22 $, $ CE = 31 $, $ DF = 33 $, $ AF = 73 $, $ CG = 40 $, and $ DG = 30 $. Find the area of $ \triangle BGE $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let the line containing \(A,B,C,D,E,F\) be the \(x\)-axis.
+
+\[
+A=(0,0),\qquad B=(b,0),\ C=(c,0),\ D=(d,0),\ E=(e,0),\ F=(f,0)
+\]
+
+From the given distances along the line  
+
+\[
+\begin{aligned}
+AC&amp;=c-a=26 \Longrightarrow c=26,\\
+BD&amp;=d-b=22,\\
+CE&amp;=e-c=31 \Longrightarrow e=26+31=57,\\
+DF&amp;=f-d=33,\\
+AF&amp;=f-a=73 \Longrightarrow f=73 .
+\end{aligned}
+\]
+
+From \(DF=33\) we get \(d=f-33=73-33=40\).  
+Then \(BD=22\) gives \(b=d-22=40-22=18\).
+
+Thus the collinear points are
+
+\[
+A(0),\ B(18),\ C(26),\ D(40),\ E(57),\ F(73).
+\]
+
+---
+
+### Coordinates of \(G\)
+
+Let \(G=(x,y)\) with \(y\neq0\).  
+We know
+
+\[
+\begin{cases}
+(CG)^2=(x-26)^2+y^2=40^2=1600,\\
+(DG)^2=(x-40)^2+y^2=30^2=900 .
+\end{cases}
+\]
+
+Subtracting the equations:
+
+\[
+(x-26)^2-(x-40)^2 = 1600-900=700 .
+\]
+
+Compute the left side:
+
+\[
+\bigl(x^2-52x+676\bigr)-\bigl(x^2-80x+1600\bigr)=28x-924 .
+\]
+
+Hence \(28x-924=700\) giving  
+
+\[
+x=\frac{1624}{28}=58.
+\]
+
+Now use \((x-40)^2+y^2=900\):
+
+\[
+(58-40)^2+y^2=900\Longrightarrow 18^2+y^2=900\Longrightarrow y^2=576.
+\]
+
+Thus \(y=\pm24\).  The sign does not affect the area; we take \(y=24\).
+
+Therefore  
+
+\[
+G=(58,24)\;(\text{or }(58,-24)).
+\]
+
+---
+
+### Area of \(\triangle BGE\)
+
+Points:
+\[
+B=(18,0),\qquad G=(58,24),\qquad E=(57,0).
+\]
+
+Since \(B\) and \(E\) lie on the \(x\)-axis, the base \(BE\) has length  
+
+\[
+BE = 57-18 = 39.
+\]
+
+The altitude from \(G\) to the \(x\)-axis is \(|y|=24\).
+
+Hence
+
+\[
+\text{Area}=\frac12\cdot (\text{base})\cdot (\text{height})
+          =\frac12\cdot 39\cdot 24
+          =468.
+\]
+
+\[
+\boxed{468}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 468</p>
+<p>Extracted Answer: 468</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let the sequence of rationals $ x_1, x_2, \ldots $ be defined such that $ x_1 = \frac{25}{11} $ and
+$ x_{k+1} = \frac{1}{3} \left( x_k + \frac{1}{x_k} - 1 \right). $
+$ x_{2025} $ can be expressed as $ \frac{m}{n} $ for relatively prime positive integers $ m $ and $ n $. Find the remainder when $ m + n $ is divided by 1000.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>\[
+x_{k+1}= \frac{x_k+\frac1{x_k}-1}{3},\qquad x_1=\frac{25}{11}
+\]
+
+---
+
+### 1.  A convenient substitution  
+
+Let  
+
+\[
+y_k=\frac{x_k-1}{x_k+1}\qquad\Longleftrightarrow\qquad 
+x_k=\frac{1+y_k}{1-y_k}.
+\]
+
+Then a short computation gives  
+
+\[
+y_{k+1}= \frac{3y_k^{\,2}-1}{2}. \tag{1}
+\]
+
+Thus we only have to iterate the quadratic map (1).
+
+---
+
+### 2.  Scaling  
+
+Define  
+
+\[
+u_k=\frac32\,y_k .
+\]
+
+From (1)
+
+\[
+u_{k+1}=u_k^{2}-\frac34 .\tag{2}
+\]
+
+Let  
+
+\[
+u_k=\frac{a_k}{12^{\,2^{k-1}}},\qquad a_1=7 .
+\]
+
+Because the denominator squares each step, indeed  
+
+\[
+12^{\,2^{k}}=(12^{\,2^{k-1}})^2 .
+\]
+
+Using (2) one checks that  
+
+\[
+a_{k+1}=a_k^{2}-\frac34\cdot12^{\,2^{k}} .
+\]
+
+Only the denominator grows; the exact value of the numerator is not needed later.
+
+---
+
+### 3.  Returning to \(x_k\)
+
+Since \(y_k=\frac{2}{3}u_k\),
+
+\[
+x_k=\frac{1+y_k}{1-y_k}
+     =\frac{3+2u_k}{3-2u_k}
+     =\frac{3\cdot12^{\,2^{k-1}}+2a_k}
+            {3\cdot12^{\,2^{k-1}}-2a_k}.
+\]
+
+Hence for any \(k\),
+
+\[
+x_k=\frac{M_k}{N_k},\qquad 
+M_k+N_k =6\cdot12^{\,2^{k-1}} .
+\]
+
+In particular
+
+\[
+m+n = M_{2025}+N_{2025}= 6\cdot 12^{\,2^{2024}} .
+\]
+
+---
+
+### 4.  Computing \(6\cdot12^{2^{2024}}\pmod{1000}\)
+
+We need \(6\cdot12^{K}\pmod{1000}\) where \(K=2^{2024}\).
+
+Because \(1000=8\cdot125\) we work modulo 8 and 125.
+
+*Modulo 8*:  
+\(12\equiv4\pmod8\), and \(4^{2}=0\pmod8\).  
+Since \(K\ge2\), \(12^{K}\equiv0\pmod8\) ⇒ the whole expression is \(0\pmod8\).
+
+*Modulo 125*:  \(\gcd(12,125)=1\) and \(\phi(125)=100\).  
+Thus \(12^{100}\equiv1\pmod{125}\); we need \(K\bmod100\).
+
+The powers of 2 modulo 100 repeat with period 20 for exponents \(\ge2\).  
+\(2024\equiv4\pmod{20}\), so \(2^{2024}\equiv2^{4}=16\pmod{100}\).  
+Hence \(12^{K}\equiv12^{16}\pmod{125}\).
+
+Compute:
+\[
+12^{2}\equiv19,\;12^{4}\equiv111,\;12^{8}\equiv71,\;12^{16}\equiv71^{2}\equiv41\pmod{125}.
+\]
+
+Thus \(6\cdot12^{K}\equiv6\cdot41=246\equiv121\pmod{125}\).
+
+Now solve the CRT:
+\[
+X\equiv0\pmod8,\qquad X\equiv121\pmod{125}.
+\]
+
+Let \(X=8t\). Then \(8t\equiv121\pmod{125}\Rightarrow t\equiv47\cdot121\equiv62\pmod{125}\) (since \(8^{-1}\equiv47\pmod{125}\)).  
+Thus \(X=8\cdot62=496\pmod{1000}\).
+
+Therefore
+
+\[
+m+n \equiv 496 \pmod{1000}.
+\]
+
+---
+
+\[
+\boxed{496}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 248</p>
+<p>Extracted Answer: 496</p>
+<p>Score: 0.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Find the sum of all positive integers $ n $ such that $ n + 2 $ divides the product $ 3(n + 3)(n^2 + 9) $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+\[
+m=n+2\qquad (m&gt;2)
+\]
+
+Then  
+
+\[
+n+2=m,\qquad n+3=m+1,\qquad n^{2}+9=(m-2)^{2}+9=m^{2}-4m+13 .
+\]
+
+The condition  
+
+\[
+n+2\mid 3(n+3)(n^{2}+9)
+\]
+
+becomes  
+
+\[
+m \mid 3(m+1)(m^{2}-4m+13). \tag{1}
+\]
+
+--------------------------------------------------------------------
+### 1.  Using the gcd with 3
+
+Because  
+
+\[
+\gcd(m,m+1)=1,
+\]
+
+any prime divisor of \(m\) cannot come from the factor \(m+1\).  
+The only possible common factor of \(m\) with the whole right‑hand side of (1) is the factor \(3\).
+
+Let  
+
+\[
+d=\gcd(m,3),\qquad m=d\cdot m&#39;,\qquad \gcd(m&#39;,3)=1 .
+\]
+
+Then (1) is equivalent to  
+
+\[
+d m&#39; \mid 3(m+1)(m^{2}-4m+13)
+      = d\Bigl(\frac{3}{d}\Bigr)(m+1)(m^{2}-4m+13).
+\]
+
+Cancelling \(d\) gives  
+
+\[
+m&#39; \mid \Bigl(\frac{3}{d}\Bigr)(m+1)(m^{2}-4m+13).\tag{2}
+\]
+
+Since \(\gcd(m&#39;,m+1)=1\) and also \(\gcd(m&#39;,3)=1\), the factor \((m+1)\) and the possible remaining factor \(\frac{3}{d}\) cannot help the divisibility. Hence (2) reduces to  
+
+\[
+m&#39; \mid (m^{2}-4m+13). \tag{3}
+\]
+
+--------------------------------------------------------------------
+### 2.  Reduce modulo \(m\)
+
+\[
+m^{2}-4m+13 \equiv 13\pmod{m},
+\]
+
+so (3) is equivalent to  
+
+\[
+m&#39; \mid 13.
+\]
+
+Recall \(m&#39; =\dfrac{m}{\gcd(m,3)}\).  Therefore
+
+\[
+\frac{m}{\gcd(m,3)}\mid 13.
+\]
+
+--------------------------------------------------------------------
+### 3.  Solve the two possibilities
+
+**(i)  \(\gcd(m,3)=1\) (i.e. \(3\nmid m\)).**  
+Then \(\displaystyle m\mid13\).  
+With \(m&gt;2\), the only possibility is \(m=13\).
+
+**(ii)  \(\gcd(m,3)=3\) (i.e. \(m=3k\)).**  
+Then \(\displaystyle k\mid13\).  
+Thus \(k=1\) or \(k=13\), giving \(m=3\) or \(m=39\).
+
+--------------------------------------------------------------------
+### 4.  Return to \(n\)
+
+\[
+n=m-2\; \Longrightarrow\; 
+\begin{cases}
+m=3 &amp;\Rightarrow n=1,\\[2pt]
+m=13 &amp;\Rightarrow n=11,\\[2pt]
+m=39 &amp;\Rightarrow n=37.
+\end{cases}
+\]
+
+All three values satisfy the original divisibility (direct verification shows \(3\mid120\), \(13\mid5460\), \(39\mid165360\)).
+
+--------------------------------------------------------------------
+### 5.  Sum of all such \(n\)
+
+\[
+1+11+37 = 49.
+\]
+
+\[
+\boxed{49}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 49</p>
+<p>Extracted Answer: 49</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+The product $ \prod_{k=4}^{63} \frac{\log_k(5^{k^2-1})}{\log_{k+1}(5^{k^2-4})} = \frac{\log_4(5^{15})}{\log_5(5^{12})} \cdot \frac{\log_5(5^{24})}{\log_6(5^{21})} \cdot \frac{\log_6(5^{35})}{\log_7(5^{32})} \cdots \frac{\log_{63}(5^{3968})}{\log_{64}(5^{3965})} $ is equal to $ \frac{m}{n} $, where $ m $ and $ n $ are relatively prime positive integers. Find $ m + n $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>First rewrite each factor using the change–of–base formula  
+
+\[
+\log_a b=\frac{\ln b}{\ln a}.
+\]
+
+\[
+\frac{\log_k\bigl(5^{k^{2}-1}\bigr)}{\log_{k+1}\bigl(5^{k^{2}-4}\bigr)}
+   =\frac{\dfrac{\ln5^{\,k^{2}-1}}{\ln k}}
+          {\dfrac{\ln5^{\,k^{2}-4}}{\ln (k+1)}}
+   =\frac{(k^{2}-1)\ln5}{\ln k}\cdot\frac{\ln(k+1)}{(k^{2}-4)\ln5}
+   =\frac{k^{2}-1}{k^{2}-4}\cdot\frac{\ln(k+1)}{\ln k}.
+\]
+
+Hence
+
+\[
+P=\prod_{k=4}^{63}\frac{k^{2}-1}{k^{2}-4}
+   \cdot\prod_{k=4}^{63}\frac{\ln(k+1)}{\ln k}.
+\]
+
+---
+
+### 1.  The logarithmic product
+
+\[
+\prod_{k=4}^{63}\frac{\ln(k+1)}{\ln k}
+   =\frac{\ln64}{\ln4}
+   =\log_{4}64=3.
+\]
+
+(The terms cancel telescopically.)
+
+---
+
+### 2.  The rational product  
+
+Factor each term:
+
+\[
+\frac{k^{2}-1}{k^{2}-4}
+   =\frac{(k-1)(k+1)}{(k-2)(k+2)}
+   =\frac{k-1}{k-2}\cdot\frac{k+1}{k+2}.
+\]
+
+Thus
+
+\[
+\prod_{k=4}^{63}\frac{k^{2}-1}{k^{2}-4}
+ =\Bigl(\prod_{k=4}^{63}\frac{k-1}{k-2}\Bigr)
+  \Bigl(\prod_{k=4}^{63}\frac{k+1}{k+2}\Bigr).
+\]
+
+The first product telescopes:
+
+\[
+\prod_{k=4}^{63}\frac{k-1}{k-2}
+ =\frac{3}{2}\cdot\frac{4}{3}\cdot\cdots\cdot\frac{62}{61}
+ =\frac{62}{2}=31.
+\]
+
+The second product also telescopes:
+
+\[
+\prod_{k=4}^{63}\frac{k+1}{k+2}
+ =\frac{5}{6}\cdot\frac{6}{7}\cdot\cdots\cdot\frac{64}{65}
+ =\frac{5}{65}=\frac{1}{13}.
+\]
+
+Therefore
+
+\[
+\prod_{k=4}^{63}\frac{k^{2}-1}{k^{2}-4}
+   =31\cdot\frac{1}{13}=\frac{31}{13}.
+\]
+
+---
+
+### 3.  Combine the two parts
+
+\[
+P=\frac{31}{13}\times3=\frac{93}{13}.
+\]
+
+The fraction is already in lowest terms (\(\gcd(93,13)=1\)).  
+Thus \(m=93\), \(n=13\) and
+
+\[
+m+n=93+13=106.
+\]
+
+\[
+\boxed{106}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 106</p>
+<p>Extracted Answer: 106</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Four unit squares form a $2 \times 2$ grid. Each of the 12 unit line segments forming the sides of the squares is colored either red or blue in such a way that each unit square has 2 red sides and 2 blue sides. Find the number of such colorings.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let the four unit squares be  
+
+\[
+\begin{array}{c|c}
+\text{TL}&amp;\text{TR}\\\hline
+\text{BL}&amp;\text{BR}
+\end{array}
+\]
+
+and denote the twelve unit edges as follows  
+
+* Horizontal edges:  
+
+\[
+\begin{aligned}
+&amp;h_{1}= \text{top of TL},\qquad h_{2}= \text{top of TR},\\
+&amp;h_{3}= \text{middle left},\qquad h_{4}= \text{middle right},\\
+&amp;h_{5}= \text{bottom of BL},\qquad h_{6}= \text{bottom of BR}.
+\end{aligned}
+\]
+
+* Vertical edges:  
+
+\[
+\begin{aligned}
+&amp;v_{1}= \text{left of TL},\qquad v_{2}= \text{left of BL},\\
+&amp;v_{3}= \text{middle top},\qquad v_{4}= \text{middle bottom},\\
+&amp;v_{5}= \text{right of TR},\qquad v_{6}= \text{right of BR}.
+\end{aligned}
+\]
+
+For each square the sum of the red edges must be \(2\).
+Writing a red edge as \(1\) and a blue edge as \(0\),
+
+\[
+\begin{aligned}
+\text{TL}&amp;:\;h_{1}+h_{3}+v_{1}+v_{3}=2,\\
+\text{TR}&amp;:\;h_{2}+h_{4}+v_{3}+v_{5}=2,\\
+\text{BL}&amp;:\;h_{3}+h_{5}+v_{2}+v_{4}=2,\\
+\text{BR}&amp;:\;h_{4}+h_{6}+v_{4}+v_{6}=2.
+\end{aligned}
+\]
+
+The four **interior** edges are \(h_{3},h_{4},v_{3},v_{4}\); the other eight edges lie on the outer
+boundary.  
+
+Fix the colours of the interior edges:
+\[
+a=h_{3},\qquad b=h_{4},\qquad c=v_{3},\qquad d=v_{4}\in\{0,1\}.
+\]
+
+Then for each square we know the required sum of its two boundary edges:
+
+\[
+\begin{aligned}
+h_{1}+v_{1}&amp;=2-(a+c),\\
+h_{2}+v_{5}&amp;=2-(b+c),\\
+h_{5}+v_{2}&amp;=2-(a+d),\\
+h_{6}+v_{6}&amp;=2-(b+d).
+\end{aligned}
+\]
+
+If the right‑hand side equals \(2\) or \(0\) the two boundary edges are forced to be
+both red or both blue – exactly one choice.  
+If it equals \(1\) the two edges must be of opposite colours – two choices.
+
+Hence, for a fixed interior vector \((a,b,c,d)\) the number of admissible colourings of the
+boundary edges is  
+
+\[
+2^{\,k(a,b,c,d)},
+\]
+
+where \(k\) is the number of squares whose interior‑edge sum equals \(1\); i.e.
+
+\[
+k=(a\oplus c)+(b\oplus c)+(a\oplus d)+(b\oplus d),
+\]
+(\(\oplus\) denotes XOR).
+
+Therefore the total number of colourings is  
+
+\[
+\sum_{a,b,c,d\in\{0,1\}}2^{k}
+= \sum_{c,d} \Bigl(\sum_{a}2^{\,a\oplus c + a\oplus d}\Bigr)^{2}.
+\]
+
+For the four possibilities of \((c,d)\) we have
+
+\[
+\begin{array}{c|c}
+(c,d) &amp; \displaystyle\sum_{a}2^{a\oplus c + a\oplus d} \\ \hline
+(0,0) &amp; 1+4 = 5\\
+(1,1) &amp; 4+1 = 5\\
+(0,1),(1,0) &amp; 2+2 = 4
+\end{array}
+\]
+
+Thus
+
+\[
+\text{total}=2\cdot5^{2}+2\cdot4^{2}=2\cdot25+2\cdot16=50+32=82.
+\]
+
+Hence there are  
+
+\[
+\boxed{82}
+\]
+
+different colourings of the twelve unit edges so that each of the four unit squares has
+exactly two red and two blue sides.</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 82</p>
+<p>Extracted Answer: 82</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $ A $ be the set of positive integer divisors of 2025. Let $ B $ be a randomly selected subset of $ A $. The probability that $ B $ is a nonempty set with the property that the least common multiple of its elements is 2025 is $ \frac{m}{n} $, where $ m $ and $ n $ are relatively prime positive integers. Find $ m + n $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>The divisors of  
+
+\[
+2025 = 3^{4}\cdot5^{2}
+\]
+
+are obtained by choosing the exponent of \(3\) from \(\{0,1,2,3,4\}\) and the exponent of \(5\) from \(\{0,1,2\}\).  
+Hence  
+
+\[
+|A|=(4+1)(2+1)=15 .
+\]
+
+---
+
+### Condition for the LCM to be \(2025\)
+
+For a non‑empty subset \(B\subseteq A\),
+
+\[
+\operatorname{lcm}(B)=2025 \iff
+\begin{cases}
+\text{some element of }B\text{ has }3\text{-exponent }4,\\[2pt]
+\text{some element of }B\text{ has }5\text{-exponent }2.
+\end{cases}
+\]
+
+Define  
+
+\[
+S_3=\{81,\,405,\,2025\} \quad (\text{divisors with }3^4) ,
+\]
+\[
+S_5=\{25,\,75,\,225,\,675,\,2025\} \quad (\text{divisors with }5^2).
+\]
+
+Thus \(B\) must intersect both \(S_3\) and \(S_5\).
+
+---
+
+### Counting favorable subsets
+
+Let \(U=S_3\cup S_5\).  
+\(|S_3|=3,\;|S_5|=5,\;|S_3\cap S_5|=1\) (the element \(2025\)), so
+
+\[
+|U|=3+5-1=7.
+\]
+
+The remaining divisors of \(2025\) (those not in \(U\)) are \(15-7=8\) in number and can be chosen freely.
+
+Number of subsets of \(U\) that contain at least one element of \(S_3\) **and** at least one element of \(S_5\):
+
+\[
+\begin{aligned}
+&amp;2^{7}\;(\text{all subsets of }U)\\
+&amp;\quad-2^{4}\;(\text{subsets with no }S_3)\\
+&amp;\quad-2^{2}\;(\text{subsets with no }S_5)\\
+&amp;\quad+2^{0}\;(\text{subsets with neither }S_3\text{ nor }S_5)\\[2pt]
+&amp;=128-16-4+1=109 .
+\end{aligned}
+\]
+
+For each of these \(109\) choices, any subset of the other 8 divisors may be added, giving a factor \(2^{8}=256\).
+
+Hence the number of favorable subsets is  
+
+\[
+N=109\cdot256=27904.
+\]
+
+---
+
+### Probability
+
+All subsets of \(A\) (including the empty set) number  
+
+\[
+2^{15}=32768.
+\]
+
+Thus
+
+\[
+P=\frac{N}{2^{15}}=\frac{27904}{32768}.
+\]
+
+Dividing numerator and denominator by their greatest common divisor \(256\),
+
+\[
+P=\frac{27904/256}{32768/256}=\frac{109}{128}.
+\]
+
+So \(\displaystyle m=109,\;n=128\) and
+
+\[
+m+n=109+128=237.
+\]
+
+\[
+\boxed{237}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 237</p>
+<p>Extracted Answer: 237</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $ABCDE$ be a convex pentagon with $AB=14, BC=7, CD=24, DE=13, EA=26,$ and $\angle B=\angle E=60^\circ$. For each point $X$ in the plane, define $f(X)=AX+BX+CX+DX+EX$. The least possible value of $f(X)$ can be expressed as $m+n\sqrt{p}$, where $m$ and $n$ are positive integers and $p$ is not divisible by the square of any prime. Find $m+n+p$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>\[
+\boxed{45}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 60</p>
+<p>Extracted Answer: 45</p>
+<p>Score: 0.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Circle $\omega_1$ with radius 6 centered at point $A$ is internally tangent at point $B$ to circle $\omega_2$ with radius 15. Points $C$ and $D$ lie on $\omega_2$ such that $\overline{BC}$ is a diameter of $\omega_2$ and $\overline{BC} \perp \overline{AD}$. The rectangle $EFGH$ is inscribed in $\omega_1$ such that $\overline{EF} \perp \overline{BC}$, $C$ is closer to $\overline{GH}$ than to $\overline{EF}$, and $D$ is closer to $\overline{FG}$ than to $\overline{EH}$, as shown. Triangles $\triangle DGF$ and $\triangle CHG$ have equal areas. The area of rectangle $EFGH$ is $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m + n$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let the centre of the large circle \(\omega _2\) be the origin \(O(0,0)\).
+Since \(BC\) is a diameter of \(\omega _2\), take  
+
+\[
+B=(15,0),\qquad C=(-15,0),\qquad O=(0,0).
+\]
+
+Because \(\omega _1\) (radius \(6\)) is internally tangent to \(\omega _2\) at \(B\),
+its centre \(A\) lies on \(OB\) with  
+
+\[
+OA=15-6=9\quad\Longrightarrow\quad A=(9,0).
+\]
+
+The condition \(AD\perp BC\) forces \(AD\) to be vertical through \(x=9\).
+Intersecting this line with \(\omega _2\) (\(x^{2}+y^{2}=225\)) gives  
+
+\[
+D=(9,12)\text{ or }(9,-12).
+\]
+
+Since later we need \(D\) to be nearer the side \(\overline{FG}\) than to \(\overline{EH}\),
+\(D\) must lie **below** the rectangle; hence  
+
+\[
+D=(9,-12).
+\]
+
+---
+
+### The rectangle
+
+A rectangle inscribed in a circle has its centre at the circle’s centre.
+Thus the centre of rectangle \(EFGH\) is \(A(9,0)\).
+
+Let  
+
+* \(w\) = horizontal distance from \(A\) to each vertical side,
+* \(h\) = vertical distance from \(A\) to each horizontal side.
+
+Then the vertices are  
+
+\[
+\begin{aligned}
+E&amp;(9+w,\;h),\qquad F&amp;(9+w,\;-h),\\
+G&amp;(9-w,\;-h),\qquad H&amp;(9-w,\;h).
+\end{aligned}
+\]
+
+Because the rectangle is inscribed in \(\omega _1\),
+
+\[
+w^{2}+h^{2}=6^{2}=36. \tag{1}
+\]
+
+The side \(\overline{EF}\) is vertical, so \(\overline{EF}\perp BC\) (which is horizontal).
+
+- \(C(-15,0)\) is left of the rectangle, so its distances to the two vertical sides are  
+
+\[
+\operatorname{dist}(C,\overline{GH}) =| -15-(9-w)| =24-w,
+\]
+\[
+\operatorname{dist}(C,\overline{EF}) =| -15-(9+w)| =24+w,
+\]
+
+hence \(C\) is indeed closer to \(\overline{GH}\) than to \(\overline{EF}\).
+
+- \(D(9,-12)\) is below the rectangle; its distances to the horizontal sides are  
+
+\[
+\operatorname{dist}(D,\overline{FG}) =|-12-(-h)| =12-h,
+\]
+\[
+\operatorname{dist}(D,\overline{EH}) =|-12-h| =12+h,
+\]
+
+so \(D\) is closer to \(\overline{FG}\) than to \(\overline{EH}\) as required.
+
+---
+
+### Equality of the two triangle areas
+
+\[
+\triangle DGF:\quad 
+\text{base}=GF=2w,\;
+\text{height}=12-h\;\Longrightarrow\;
+[ DGF]=\tfrac12(2w)(12-h)=w(12-h).
+\]
+
+\[
+\triangle CHG:\quad 
+\text{base}=HG=2h,\;
+\text{height}=24-w\;\Longrightarrow\;
+[ CHG]=\tfrac12(2h)(24-w)=h(24-w).
+\]
+
+Given \([DGF]=[CHG]\),
+
+\[
+w(12-h)=h(24-w)\;\Longrightarrow\;12w=24h\;\Longrightarrow\; w=2h. \tag{2}
+\]
+
+---
+
+### Solving for \(w\) and \(h\)
+
+Substituting \(w=2h\) into (1),
+
+\[
+(2h)^{2}+h^{2}=36\;\Longrightarrow\;5h^{2}=36\;\Longrightarrow\;h^{2}=\frac{36}{5}.
+\]
+
+Hence  
+
+\[
+h=\frac{6}{\sqrt5},\qquad 
+w=2h=\frac{12}{\sqrt5}.
+\]
+
+---
+
+### Area of the rectangle
+
+\[
+\text{Area}= (2w)(2h)=4wh
+   =4\!\left(\frac{12}{\sqrt5}\right)\!\left(\frac{6}{\sqrt5}\right)
+   =\frac{288}{5}.
+\]
+
+Thus \(\displaystyle \frac{m}{n}= \frac{288}{5}\) with \(m,n\) relatively prime.
+Hence  
+
+\[
+m+n=288+5=293.
+\]
+
+\[
+\boxed{293}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 293</p>
+<p>Extracted Answer: 293</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+There are $ n $ values of $ x $ in the interval $ 0 &lt; x &lt; 2\pi $ where $ f(x) = \sin(7\pi \cdot \sin(5x)) = 0 $. For $ t $ of these $ n $ values of $ x $, the graph of $ y = f(x) $ is tangent to the $ x $-axis. Find $ n + t $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>\[
+f(x)=\sin\bigl(7\pi\sin(5x)\bigr),\qquad 0&lt;x&lt;2\pi .
+\]
+
+---
+
+### 1.  Zeros of \(f\)
+
+\[
+f(x)=0\iff \sin\bigl(7\pi\sin(5x)\bigr)=0
+\iff 7\pi\sin(5x)=k\pi\;(k\in\mathbb Z)
+\iff \sin(5x)=\frac{k}{7}.
+\]
+
+Because \(|\sin(5x)|\le1\), we must have \(|k|\le7\); thus  
+
+\[
+k\in\{-7,-6,\dots ,0,\dots ,6,7\}.
+\]
+
+Set \(\theta=5x\).  Then \(x\in(0,2\pi)\) gives \(\theta\in(0,10\pi)\).
+Hence we must count the solutions of
+
+\[
+\sin\theta=\frac{k}{7},\qquad \theta\in(0,10\pi),
+\]
+for every integer \(k\) with \(|k|\le7\).
+
+---
+
+### 2.  Number of solutions for each \(k\)
+
+* **\(k=0\):** \(\sin\theta=0\Rightarrow\theta=n\pi\).  
+  In \((0,10\pi)\) we have \(n=1,2,\dots ,9\): **9 solutions**.
+
+* **\(k=\pm7\):** \(\sin\theta=\pm1\).  
+  Each period \(2\pi\) contributes one solution, so over five periods we get **5 solutions** for \(\sin\theta=1\) and **5** for \(\sin\theta=-1\): **10 solutions**.
+
+* **\(k=\pm1,\pm2,\pm3,\pm4,\pm5,\pm6\):** \(\sin\theta=a\) with \(|a|&lt;1,\;a\neq0\).  
+  In each period there are two solutions, therefore over five periods we obtain **10 solutions** for each such \(k\).
+
+There are \(12\) values of \(k\) with \(\pm1,\dots ,\pm6\); they give  
+\(12\times10=120\) solutions.
+
+Hence the total number of zeros is  
+
+\[
+n = 9\;(k=0) + 10\;(k=\pm7) + 120\;(k=\pm1,\dots ,\pm6) = 139 .
+\]
+
+---
+
+### 3.  Points where the graph is tangent to the \(x\)-axis
+
+A zero is a point of tangency when \(f&#39;(x)=0\) as well.
+
+\[
+f&#39;(x)=\cos\bigl(7\pi\sin(5x)\bigr)\cdot 7\pi\cdot5\cos(5x)
+     =35\pi\cos(5x)\,\cos\bigl(7\pi\sin(5x)\bigr).
+\]
+
+At any zero we have \(\sin(5x)=k/7\) and thus
+\(\cos\bigl(7\pi\sin(5x)\bigr)=\cos(k\pi)=(-1)^k\neq0\).
+Consequently  
+
+\[
+f&#39;(x)=0\iff \cos(5x)=0.
+\]
+
+\(\cos(5x)=0\) implies \(\sin(5x)=\pm1\), i.e. the cases \(k=\pm7\).
+Therefore the tangency points are precisely the solutions for
+\(\sin(5x)=\pm1\).
+
+From the count above there are **5** solutions for \(\sin(5x)=1\) and **5**
+for \(\sin(5x)=-1\); altogether
+
+\[
+t = 10 .
+\]
+
+---
+
+### 4.  Required sum
+
+\[
+n+t = 139+10 = 149.
+\]
+
+\[
+\boxed{149}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 149</p>
+<p>Extracted Answer: 149</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Sixteen chairs are arranged in a row. Eight people each select a chair in which to sit so that no person sits next to two other people. Let $ N $ be the number of subsets of 16 chairs that could be selected. Find the remainder when $ N $ is divided by 1000.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let the chairs be numbered \(1,2,\ldots ,16\).
+Choosing the chairs for the eight people is the same as writing a binary
+string of length \(16\) with exactly eight \(1\)’s (occupied chairs) and eight
+\(0\)’s (empty chairs).
+
+The condition “no person sits next to two other people’’ means that we may
+not have three consecutive occupied chairs; i.e. the binary string must contain
+no substring \(111\).
+
+---
+
+### 1.  Decompose the 1’s into blocks  
+
+Since three consecutive 1’s are forbidden, any maximal block of consecutive
+1’s has length \(1\) or \(2\).
+Let  
+
+* \(a\) = number of blocks of length \(1\),  
+* \(b\) = number of blocks of length \(2\).
+
+Then  
+
+\[
+a+2b = 8,\qquad a,b\ge 0 .
+\]
+
+Hence the possible values are  
+
+\[
+\begin{array}{c|c|c}
+b &amp; a &amp; r=a+b\\ \hline
+0&amp;8&amp;8\\
+1&amp;6&amp;7\\
+2&amp;4&amp;6\\
+3&amp;2&amp;5\\
+4&amp;0&amp;4
+\end{array}
+\]
+
+Here \(r\) is the total number of blocks of 1’s.
+
+For a fixed \(r\) the number of ways to decide which of the \(r\) blocks are
+length \(2\) is \(\displaystyle\binom{r}{b}\) (choose the \(b\) blocks of
+size \(2\)).  
+
+---
+
+### 2.  Insert the zeros  
+
+There are \(8\) zeros.  
+Between any two consecutive blocks of 1’s there must be at least one zero,
+so the \(r-1\) internal gaps each receive one zero.  
+After this we have  
+
+\[
+8-(r-1)=9-r
+\]
+
+zeros left to distribute freely among the \(r+1\) gaps (the two ends plus the
+\(r-1\) internal gaps).  
+
+The number of non‑negative integer solutions of  
+
+\[
+z_0+z_1+\cdots+z_r = 9-r
+\]
+
+is  
+
+\[
+\binom{(9-r)+(r+1)-1}{(r+1)-1}= \binom{9}{r}.
+\]
+
+Thus for a given \(r\) (equivalently a given \(b\)) we have  
+
+\[
+\binom{r}{b}\binom{9}{r}
+\]
+
+valid strings.
+
+---
+
+### 3.  Sum over all possibilities  
+
+Recall \(r=8-b\).  Summing over \(b=0,1,2,3,4\):
+
+\[
+\begin{aligned}
+N &amp;=\sum_{b=0}^{4}\binom{8-b}{b}\binom{9}{8-b}  \\
+  &amp;=\binom{8}{0}\binom{9}{8}+
+    \binom{7}{1}\binom{9}{7}+
+    \binom{6}{2}\binom{9}{6}+
+    \binom{5}{3}\binom{9}{5}+
+    \binom{4}{4}\binom{9}{4}  \\
+  &amp;=1\cdot9+7\cdot36+15\cdot84+10\cdot126+1\cdot126 \\
+  &amp;=9+252+1260+1260+126 \\
+  &amp;=2907 .
+\end{aligned}
+\]
+
+---
+
+### 4.  Modulo \(1000\)
+
+\[
+2907\equiv 907\pmod{1000}.
+\]
+
+\[
+\boxed{907}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 907</p>
+<p>Extracted Answer: 907</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Alex divides a disk into four quadrants with two perpendicular diameters intersecting at the center of the disk. He draws 25 more line segments through the disk, drawing each segment by selecting two points at random on the perimeter of the disk in different quadrants and connecting those two points. Find the expected number of regions into which these 27 line segments divide the disk.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>The disk is cut by line–segments (chords).  
+If a new chord meets \(k\) already drawn chords in the interior, it splits
+\(k+1\) existing regions, so the total number of regions after all chords are drawn is  
+
+\[
+R = 1 + (\text{number of chords}) + (\text{number of interior intersections}).
+\]
+
+There are \(27\) chords in total (the two diameters plus the \(25\) random chords), so  
+
+\[
+\mathbb E[R]=28+\mathbb E[I],
+\]
+
+where \(I\) is the number of interior intersection points.
+
+--------------------------------------------------------------------
+### 1.  Intersections involving a diameter  
+
+A fixed diameter (say the vertical one) is intersected iff the two
+end–points of the chord lie in opposite half–planes \((x&gt;0\) and \(x&lt;0)\).
+For a chord whose endpoints are required to lie in **different quadrants**
+\[
+P(\text{opposite }x\text{-signs})=\frac12,\qquad 
+P(\text{different quadrants})=\frac34,
+\]
+hence  
+
+\[
+p_D=P(\text{intersects a given diameter}\mid\text{different quadrants})
+      =\frac{1/2}{3/4}= \frac23 .
+\]
+
+Thus each random chord meets the vertical diameter with probability \(2/3\)
+and also meets the horizontal diameter with probability \(2/3\).  
+The expected number of intersections between the \(25\) random chords
+and the two diameters is  
+
+\[
+25\bigl(2\cdot\tfrac23\bigr)=\frac{100}{3}.
+\]
+
+The two diameters intersect each other once, so the total expected
+intersection count contributed by the diameters is  
+
+\[
+1+\frac{100}{3}.
+\]
+
+--------------------------------------------------------------------
+### 2.  Intersections between two random chords  
+
+Write each chord only by the **pair of quadrants** that its two endpoints
+occupy.  For a chord whose endpoints are in different quadrants the
+unordered pair of quadrants is uniformly distributed over the six possible
+pairs:
+
+* four **adjacent** pairs \(\{1,2\},\{2,3\},\{3,4\},\{4,1\}\);
+* two **opposite** pairs \(\{1,3\},\{2,4\}\).
+
+Thus each random chord is adjacent with probability \(\tfrac23\) and opposite
+with probability \(\tfrac13\).
+
+Consider two chords and classify them according to the relationship of the
+quadrants they use.
+
+| case | description | intersection probability |
+|------|-------------|---------------------------|
+| AA–same | both are the same adjacent pair (e.g. \(\{1,2\}\) and \(\{1,2\}\)) | \(\tfrac12\) |
+| AA–share | adjacent pairs sharing one quadrant (e.g. \(\{1,2\},\{2,3\}\)) | \(\tfrac12\) |
+| AA–disjoint | adjacent pairs using opposite quadrants (e.g. \(\{1,2\},\{3,4\}\)) | \(0\) |
+| OO–same | both are the same opposite pair (e.g. \(\{1,3\},\{1,3\}\)) | \(\tfrac12\) |
+| OO–disjoint | opposite pairs \(\{1,3\},\{2,4\}\) | \(1\) |
+| AO (any) | one adjacent, one opposite (they always share one quadrant) | \(\tfrac12\) |
+
+All of the probabilities above are obtained by looking at the possible
+orderings of the four points inside their quadrants; each ordering is
+equally likely and the intersecting orderings are exactly half of them
+(when both chords involve a common quadrant) or forced (when the quadrants
+are disjoint).
+
+Let  
+
+* \(a=p_{AA\;{\rm same}}=\tfrac12\),  
+* \(b=p_{AA\;{\rm share}}=\tfrac12\),  
+* \(c=p_{OO\;{\rm same}}=\tfrac12\),  
+* \(d=p_{AO}=\tfrac12\).
+
+From the probabilities of picking each type we obtain
+
+\[
+\begin{aligned}
+p_{RR}
+&amp;=P(\text{intersection of two random chords})\\
+&amp;=\frac{2a+4b+c+8d+1}{18}
+   =\frac{2\cdot\frac12+4\cdot\frac12+\frac12+8\cdot\frac12+1}{18}
+   =\frac{17}{36}.
+\end{aligned}
+\]
+
+Hence the expected number of intersections among the \(25\) random chords is  
+
+\[
+\binom{25}{2}\,p_{RR}=300\cdot\frac{17}{36}
+      =\frac{425}{3}.
+\]
+
+--------------------------------------------------------------------
+### 3.  Total expected intersections
+
+\[
+\mathbb E[I]=
+\underbrace{1}_{\text{diameters}}+
+\underbrace{\frac{100}{3}}_{\text{diameters–random chords}}+
+\underbrace{\frac{425}{3}}_{\text{random–random}}=
+\frac{525}{3}+1=176 .
+\]
+
+--------------------------------------------------------------------
+### 4.  Expected number of regions
+
+\[
+\mathbb E[R]=28+\mathbb E[I]=28+176=204.
+\]
+
+--------------------------------------------------------------------
+\[
+\boxed{204}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 204</p>
+<p>Extracted Answer: 204</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+From an unlimited supply of 1-cent coins, 10-cent coins, and 25-cent coins, Silas wants to find a collection of coins that has a total value of $ N $ cents, where $ N $ is a positive integer. He uses the so-called **greedy algorithm**, successively choosing the coin of greatest value that does not cause the value of his collection to exceed $ N $. For example, to get 42 cents, Silas will choose a 25-cent coin, then a 10-cent coin, then 7 1-cent coins. However, this collection of 9 coins uses more coins than necessary to get a total of 42 cents; indeed, choosing 4 10-cent coins and 2 1-cent coins achieves the same total value with only 6 coins.
+
+In general, the greedy algorithm succeeds for a given $ N $ if no other collection of 1-cent, 10-cent, and 25-cent coins gives a total value of $ N $ cents using strictly fewer coins than the collection given by the greedy algorithm. Find the number of values of $ N $ between 1 and 1000 inclusive for which the greedy algorithm succeeds.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>**Step 1 –  Formulating the optimal problem**
+
+Let  
+
+\[
+a=\text{ number of 1‑cent coins},\qquad 
+b=\text{ number of 10‑cent coins},\qquad 
+c=\text{ number of 25‑cent coins}.
+\]
+
+We must have  
+
+\[
+a+10b+25c=N,\qquad a,b,c\ge 0 .
+\]
+
+The total number of coins is  
+
+\[
+T=a+b+c
+  =(N-10b-25c)+b+c
+  =N-9b-24c.
+\]
+
+Thus minimizing the number of coins is the same as **maximising**  
+
+\[
+9b+24c\qquad\text{subject to }10b+25c\le N .
+\]
+
+--------------------------------------------------------------------
+
+**Step 2 –  The greedy solution**
+
+The greedy algorithm first uses as many 25‑cent coins as possible,
+then as many 10‑cent coins, and finally 1‑cent coins.  
+Write  
+
+\[
+N=25q+r,\qquad 0\le r&lt;25 .
+\]
+
+The greedy representation is  
+
+\[
+c_{\text{g}}=q,\qquad b_{\text{g}}=\Big\lfloor\frac{r}{10}\Big\rfloor,
+\qquad a_{\text{g}}=r\bmod 10,
+\]
+
+and the greedy number of coins is  
+
+\[
+G(N)=q+\Big\lfloor\frac{r}{10}\Big\rfloor+(r\bmod10).
+\]
+
+--------------------------------------------------------------------
+
+**Step 3 –  When can we do better?**
+
+Suppose we try to use **one fewer** 25‑cent coin.  
+Then we have \(c=q-1\) and the remainder becomes \(r+25\).
+The new numbers of 10‑ and 1‑cent coins are  
+
+\[
+b&#39;=\Big\lfloor\frac{r+25}{10}\Big\rfloor,\qquad   
+a&#39;= (r+25)\bmod 10 .
+\]
+
+The total number of coins after dropping one 25‑cent coin is  
+
+\[
+A(N)=(q-1)+b&#39;+a&#39;.
+\]
+
+The difference is
+
+\[
+A(N)-G(N)=-1+\Big\lfloor\frac{r+25}{10}\Big\rfloor-\Big\lfloor\frac{r}{10}\Big\rfloor
+            +(r+25\bmod10)-(r\bmod10).
+\]
+
+Write \(r=10k+s\) with \(0\le s\le 9\).  Then  
+
+\[
+\Big\lfloor\frac{r+25}{10}\Big\rfloor-\Big\lfloor\frac{r}{10}\Big\rfloor=
+\begin{cases}
+2,&amp; s\le 4,\\[2pt]
+3,&amp; s\ge 5,
+\end{cases}
+\]
+
+and \((r+25\bmod10)-(r\bmod10)=5\) in either case.  
+Hence  
+
+\[
+A(N)-G(N)= -1 + \Delta +5 = 4+\Delta,
+\]
+
+where \(\Delta=2\) or \(3\).  Consequently  
+
+\[
+A(N)-G(N)=\begin{cases}
+ 6,&amp; s\le 4,\\
+ 3,&amp; s\ge 5 .
+\end{cases}
+\]
+
+Thus **dropping one 25‑cent coin reduces the total number of coins
+iff the ones‑digit \(s\) of the remainder \(r\) is at least 5**.
+
+That is, the greedy algorithm fails exactly when  
+
+\[
+r\equiv 5,6,7,8,9,15,16,17,18,19\pmod{25},
+\]
+
+i.e. when the remainder after using the maximal number of 25‑cent coins has units digit \(5,6,7,8,\) or \(9\).
+
+--------------------------------------------------------------------
+
+**Step 4 –  Dropping more than one 25‑cent coin never helps**
+
+If we drop a second 25‑cent coin, the units digit of the new remainder
+flips between \(s\) and \(s+5\pmod{10}\).  Consequently the increase in the
+number of 10‑cent coins alternates between **2** and **3**.
+A short computation (or the formula \(\Delta(k)=24k-9\sum T_i\) where each
+\(T_i\in\{2,3\}\)) shows that after two or more drops the total number of
+coins is never smaller than the greedy count; the only possible improvement
+is the single‑drop case described above.
+
+--------------------------------------------------------------------
+
+**Step 5 –  Counting the successful values**
+
+The greedy algorithm succeeds for all \(N\) that are **not** of the above
+failing form, and also for \(N&lt;25\) (there are no 25‑cent coins to drop).
+
+*There are 10 “bad’’ residues modulo 25*:  
+
+\[
+5,6,7,8,9,15,16,17,18,19.
+\]
+
+For each integer \(q\ge 1\) the numbers \(N=25q+r\) with such an \(r\) are
+failures.  
+
+\[
+\text{Number of blocks with }q\ge 1\text{: } \left\lfloor\frac{1000}{25}\right\rfloor=40.
+\]
+
+The last block (\(q=40\)) contains only \(N=1000\) (remainder 0), which is
+not a failure.  Hence the failing blocks are those with \(q=1,2,\dots,39\).
+
+\[
+\text{Failures}=39\;\times\;10 = 390.
+\]
+
+All the remaining numbers succeed:
+
+\[
+\text{Successes}=1000-390=610.
+\]
+
+--------------------------------------------------------------------
+
+\[
+\boxed{610}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 610</p>
+<p>Extracted Answer: 610</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $ A_1A_2 \ldots A_{11} $ be an 11-sided non-convex simple polygon with the following properties:
+* The area of $ A_iA_1A_{i+1} $ is 1 for each $ 2 \leq i \leq 10 $,
+* $ \cos(\angle A_iA_1A_{i+1}) = \frac{12}{13} $ for each $ 2 \leq i \leq 10 $,
+* The perimeter of $ A_1A_2 \ldots A_{11} $ is 20.
+If $ A_1A_2 + A_1A_{11} $ can be expressed as $ \frac{m\sqrt{n} - p}{q} $ for positive integers $ m, n, p, q $ with $ n $ squarefree and no prime divides all of $ m, p, q$, find $ m + n + p + q $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>For every \(2\le i\le 10\) the triangle \(A_iA_1A_{i+1}\) has  
+
+\[
+[\,A_iA_1A_{i+1}\,]=\frac12 \,A_1A_i\cdot A_1A_{i+1}\sin\angle A_iA_1A_{i+1}=1
+\]
+
+and  
+
+\[
+\cos\angle A_iA_1A_{i+1}= \frac{12}{13}.
+\]
+
+---
+
+### 1.  The angle \(\angle A_iA_1A_{i+1}\)
+
+\[
+\sin\theta=\sqrt{1-\cos^{2}\theta}=\sqrt{1-\Big(\frac{12}{13}\Big)^2}=
+\frac{5}{13}.
+\]
+
+Thus \(\theta=\angle A_iA_1A_{i+1}\) is the same for all \(i\) and  
+
+\[
+\frac12\;A_1A_i\;A_1A_{i+1}\;\frac{5}{13}=1
+\Longrightarrow
+A_1A_i\;A_1A_{i+1}= \frac{26}{5}.\tag{1}
+\]
+
+Denote \(a_i=A_1A_i\).  Then (1) gives  
+
+\[
+a_i a_{i+1}=C,\qquad C:=\frac{26}{5}, \qquad 2\le i\le10.
+\]
+
+---
+
+### 2.  Alternating values of the radii
+
+From \(a_i a_{i+1}=C\) we obtain  
+
+\[
+a_{i+1}= \frac C{a_i},\qquad 
+a_{i+2}= \frac C{a_{i+1}} = a_i .
+\]
+
+Hence the distances from \(A_1\) repeat with period \(2\):
+\[
+a_2=a_4=\dots =a_{10}=x,\qquad
+a_3=a_5=\dots =a_{11}=y,
+\]
+with
+\[
+xy=C=\frac{26}{5}.\tag{2}
+\]
+
+Thus \(A_1A_2=x,\;A_1A_{11}=y\) and we must find \(x+y\).
+
+---
+
+### 3.  Length of a side \(A_iA_{i+1}\;(2\le i\le10)\)
+
+In triangle \(A_iA_1A_{i+1}\) we know the two sides \(a_i,a_{i+1}\) and the angle \(\theta\) at \(A_1\).  By the law of cosines
+
+\[
+d^2:=A_iA_{i+1}^{\,2}=a_i^{2}+a_{i+1}^{2}
+-2a_i a_{i+1}\cos\theta.
+\]
+
+Since \(\cos\theta=\frac{12}{13}\) and \(a_i a_{i+1}=C\),
+
+\[
+d^{2}=a_i^{2}+a_{i+1}^{2}
+-\frac{24}{13}C.
+\]
+
+Using (2) we have \(C=\frac{26}{5}\), so \(\frac{24}{13}C=\frac{48}{5}\).
+Now \(a_i^{2}+a_{i+1}^{2}=(a_i+a_{i+1})^{2}-2a_i a_{i+1}=
+S^{2}-2C\) where \(S:=x+y\).  Hence
+
+\[
+d^{2}=S^{2}-2C-\frac{48}{5}
+=S^{2}-\frac{52}{5}-\frac{48}{5}
+=S^{2}-20. \tag{3}
+\]
+
+All nine sides \(A_iA_{i+1}\;(i=2,\dots ,10)\) have the same length \(d\).
+
+---
+
+### 4.  The perimeter
+
+The polygon has edges  
+
+\[
+A_1A_2=x,\; A_{11}A_1=y,\;
+\underbrace{A_2A_3,\dots ,A_{10}A_{11}}_{9\ \text{edges of length }d}.
+\]
+
+Thus the given perimeter \(20\) yields
+
+\[
+x+y+9d=20\quad\Longrightarrow\quad S+9\sqrt{S^{2}-20}=20,
+\]
+using (3) for \(d\).
+
+---
+
+### 5.  Solving for \(S\)
+
+\[
+9\sqrt{S^{2}-20}=20-S\quad (S\le20).
+\]
+
+Squaring:
+
+\[
+81(S^{2}-20)=(20-S)^{2}
+\]
+\[
+81S^{2}-1620=S^{2}-40S+400
+\]
+\[
+80S^{2}+40S-2020=0
+\]
+\[
+4S^{2}+2S-101=0.
+\]
+
+The quadratic gives
+
+\[
+S=\frac{-2\pm\sqrt{4+1616}}{8}
+   =\frac{-2\pm\sqrt{1620}}{8}
+   =\frac{-2\pm18\sqrt5}{8}.
+\]
+
+Only the positive root is admissible:
+
+\[
+S=\frac{-2+18\sqrt5}{8}
+   =\frac{9\sqrt5-1}{4}.
+\]
+
+Thus  
+
+\[
+A_1A_2+A_1A_{11}=x+y=S=\frac{9\sqrt5-1}{4}.
+\]
+
+---
+
+### 6.  Required sum \(m+n+p+q\)
+
+The expression is \(\displaystyle\frac{m\sqrt{n}-p}{q}\) with  
+
+\[
+m=9,\qquad n=5\ (\text{square‑free}),\qquad p=1,\qquad q=4.
+\]
+
+Hence  
+
+\[
+m+n+p+q=9+5+1+4=19.
+\]
+
+\[
+\boxed{19}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 19</p>
+<p>Extracted Answer: 19</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+There are exactly three positive real numbers $ k $ such that the function
+$ f(x) = \frac{(x - 18)(x - 72)(x - 98)(x - k)}{x} $
+defined over the positive real numbers achieves its minimum value at exactly two positive real numbers $ x $. Find the sum of these three values of $ k $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>\[
+\boxed{564}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 240</p>
+<p>Extracted Answer: 564</p>
+<p>Score: 0.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Find the sum of all integer bases $b&gt;9$ for which $17_{b}$ is a divisor of $97_{b}$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+\[
+17_b = 1\cdot b+7 = b+7 ,\qquad 
+97_b = 9\cdot b+7 .
+\]
+
+We need the integer bases \(b&gt;9\) for which \(b+7\) divides \(9b+7\).
+
+---
+
+### 1.  Express the divisibility condition
+
+\[
+9b+7 \equiv 0\pmod{b+7}.
+\]
+
+Write \(b = (b+7)-7\).  Set \(t=b+7\) (so \(t&gt;16\) because \(b&gt;9\)). Then  
+
+\[
+9b+7 = 9(t-7)+7 = 9t-63+7 = 9t-56.
+\]
+
+Hence  
+
+\[
+9t-56 \equiv 0 \pmod{t}\quad\Longrightarrow\quad -56\equiv0\pmod{t}.
+\]
+
+Thus  
+
+\[
+t \mid 56\qquad\text{or}\qquad b+7 \mid 56.
+\]
+
+---
+
+### 2.  Find possible values of \(b\)
+
+The positive divisors of \(56\) are  
+
+\[
+1,\,2,\,4,\,7,\,8,\,14,\,28,\,56 .
+\]
+
+Since \(b+7 &gt; 16\) (because \(b&gt;9\)), the only admissible divisors are  
+
+\[
+b+7 = 28 \quad\text{or}\quad b+7 = 56 .
+\]
+
+Therefore  
+
+\[
+\begin{aligned}
+b+7 = 28 &amp;\;\Rightarrow\; b = 21,\\[2pt]
+b+7 = 56 &amp;\;\Rightarrow\; b = 49.
+\end{aligned}
+\]
+
+Both bases are greater than \(9\) and the digits \(1,7,9\) are all less than each base, so the representations \(17_b\) and \(97_b\) are valid.
+
+---
+
+### 3.  Verify the divisibility
+
+*For \(b=21\):*  
+
+\[
+17_{21}=21+7=28,\qquad 97_{21}=9\cdot21+7=196,\qquad \frac{196}{28}=7.
+\]
+
+*For \(b=49\):*  
+
+\[
+17_{49}=49+7=56,\qquad 97_{49}=9\cdot49+7=448,\qquad \frac{448}{56}=8.
+\]
+
+Both are indeed integers.
+
+---
+
+### 4.  Sum of all such bases
+
+\[
+21+49 = 70.
+\]
+
+\[
+\boxed{70}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 70</p>
+<p>Extracted Answer: 70</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Suppose $ \triangle ABC $ has angles $ \angle BAC = 84^\circ $, $ \angle ABC = 60^\circ $, and $ \angle ACB = 36^\circ $. Let $ D, E, $ and $ F $ be the midpoints of sides $ \overline{BC} $, $ \overline{AC} $, and $ \overline{AB} $, respectively. The circumcircle of $ \triangle DEF $ intersects $ \overline{BD} $, $ \overline{AE} $, and $ \overline{AF} $ at points $ G, H, $ and $ J $, respectively. The points $ G, D, E, H, J, $ and $ F $ divide the circumcircle of $ \triangle DEF $ into six minor arcs, as shown. Find $ \widehat{DE} + 2 \cdot \widehat{HJ} + 3 \cdot \widehat{FG} $, where the arcs are measured in degrees.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>**Step 1.  Identify the nine–point circle**
+
+The midpoints \(D,E,F\) of the sides of \(\triangle ABC\) together with the three feet of the
+altitudes lie on the **nine‑point circle** of \(\triangle ABC\).
+Hence  
+
+\[
+G=\text{foot of the altitude from }A\text{ on }BC,\qquad   
+H=\text{foot from }B\text{ on }AC,\qquad   
+J=\text{foot from }C\text{ on }AB .
+\]
+
+The centre \(N\) of the nine‑point circle is the midpoint of the circumcentre \(O\) and
+the orthocentre \(H_{\!o}\);
+if we take the circumradius \(R=1\) and place the circumcentre at the origin,
+the vertices are  
+
+\[
+A=1,\qquad B=e^{i2C}=e^{i72^\circ},\qquad C=e^{i(2C+2A)}=e^{i240^\circ}.
+\]
+
+Thus  
+
+\[
+N=\frac{A+B+C}{2},\qquad R_{9}= \frac{R}{2}= \frac12 .
+\]
+
+The radii to the three midpoints are  
+
+\[
+\overrightarrow{ND}= \frac{B+C}{2}-\frac{A+B+C}{2}= -\frac{A}{2},\qquad 
+\overrightarrow{NE}= -\frac{B}{2},\qquad 
+\overrightarrow{NF}= -\frac{C}{2}.
+\]
+
+Consequently  
+
+\[
+\widehat{DE}= \angle( ND,NE)=\angle(A,B)=2\angle C=2\cdot 36^\circ=72^\circ .
+\tag{1}
+\]
+
+--------------------------------------------------------------------
+
+**Step 2.  Coordinates of the feet of the altitudes**
+
+For an acute triangle with vertex angles \(\alpha =\angle A,\ \beta=\angle B,\ \gamma=\angle C\),
+
+\[
+\begin{aligned}
+G&amp;= D+\frac{\sin(\beta-\gamma)}{2\sin\alpha}\,(B-C),\\[2mm]
+H&amp;= E+\frac{\sin(\gamma-\alpha)}{2\sin\beta}\,(C-A),\\[2mm]
+J&amp;= F+\frac{\sin(\alpha-\beta)}{2\sin\gamma}\,(A-B).
+\end{aligned}
+\tag{2}
+\]
+
+These formulas follow from the usual expression for the foot of an altitude as a
+weighted average of the two endpoints of the side.
+
+With \(\alpha=84^\circ,\ \beta=60^\circ,\ \gamma=36^\circ\) we obtain
+
+\[
+\begin{aligned}
+t&amp;=\frac{\sin(\beta-\gamma)}{2\sin\alpha}
+   =\frac{\sin24^\circ}{2\sin84^\circ}\approx0.2045,\\[2mm]
+u&amp;=\frac{\sin(\gamma-\alpha)}{2\sin\beta}
+   =\frac{\sin(-48^\circ)}{2\sin60^\circ}\approx-0.4290,\\[2mm]
+v&amp;=\frac{\sin(\alpha-\beta)}{2\sin\gamma}
+   =\frac{\sin24^\circ}{2\sin36^\circ}\approx0.3460 .
+\end{aligned}
+\]
+
+Hence  
+
+\[
+\begin{aligned}
+G&amp;=D+t\,(B-C),\\
+H&amp;=E+u\,(C-A),\\
+J&amp;=F+v\,(A-B).
+\end{aligned}
+\]
+
+--------------------------------------------------------------------
+
+**Step 3.  Central angles of the required arcs**
+
+The vectors from the nine‑point centre are
+
+\[
+\begin{aligned}
+\overrightarrow{NG}&amp;= \overrightarrow{ND}+t\,(B-C)
+                    =-\frac{A}{2}+t\,(B-C),\\[1mm]
+\overrightarrow{NF}&amp;=-\frac{C}{2},\\[1mm]
+\overrightarrow{NH}&amp;= -\frac{B}{2}+u\,(C-A),\\[1mm]
+\overrightarrow{NJ}&amp;= -\frac{C}{2}+v\,(A-B).
+\end{aligned}
+\]
+
+Computing their arguments (or using dot‑product formulas) gives
+
+\[
+\begin{aligned}
+\arg(\overrightarrow{ND}) &amp;=180^\circ,\\
+\arg(\overrightarrow{NG}) &amp;=132^\circ,\\
+\arg(\overrightarrow{NF}) &amp;= 60^\circ,\\
+\arg(\overrightarrow{NE}) &amp;=252^\circ,\\
+\arg(\overrightarrow{NH}) &amp;=-12^\circ\;(=348^\circ),\\
+\arg(\overrightarrow{NJ}) &amp;= 12^\circ .
+\end{aligned}
+\]
+
+Therefore the minor central arcs are
+
+\[
+\begin{aligned}
+\widehat{FG}&amp;=|\arg(NF)-\arg(NG)|
+            =|60^\circ-132^\circ|=72^\circ,\\[2mm]
+\widehat{HJ}&amp;=|\arg(NJ)-\arg(NH)|
+            =|12^\circ-(-12^\circ)|
+            =24^\circ,
+\end{aligned}
+\tag{3}
+\]
+
+and we already have \(\widehat{DE}=72^\circ\) from (1).
+
+--------------------------------------------------------------------
+
+**Step 4.  Form the required combination**
+
+\[
+\begin{aligned}
+\widehat{DE}+2\widehat{HJ}+3\widehat{FG}
+ &amp;= 72^\circ+2\cdot24^\circ+3\cdot72^\circ\\
+ &amp;= 72^\circ+48^\circ+216^\circ\\
+ &amp;= 336^\circ .
+\end{aligned}
+\]
+
+--------------------------------------------------------------------
+
+\[
+\boxed{336}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 336</p>
+<p>Extracted Answer: 336</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $ S $ be the set of vertices of a regular 24-gon. Find the number of ways to draw 12 segments of equal lengths so that each vertex in $ S $ is an endpoint of exactly one of the 12 segments.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Number the vertices of the regular \(24\)-gon by  
+\(0,1,\dots ,23\) (mod \(24\)).  
+
+For two vertices \(i\) and \(j\) let  
+
+\[
+d(i,j)=\min \{|i-j|,\;24-|i-j|\}\qquad (1\le d\le 12)
+\]
+
+be the step (or the number of sides) between them.  
+The Euclidean length of the segment \(ij\) depends only on this step;
+segments have the same length **iff** they have the same step \(d\).
+
+--------------------------------------------------------------------
+### 1.  The graph of a fixed step
+
+Fix a step \(d\;(1\le d\le 12)\).  
+All possible segments of that length are the edges  
+
+\[
+\{i,i+d\}, \qquad i=0,1,\dots ,23 .
+\]
+
+Thus we obtain the circulant graph  
+
+\[
+G_d=(V,E_d),\qquad V=\{0,1,\dots ,23\},\;
+E_d=\{\{i,i+d\}\mid i\in\mathbb Z_{24}\}.
+\]
+
+Each vertex is adjacent to \(i+d\) and to \(i-d\); therefore every
+vertex has degree \(2\).  
+The graph \(G_d\) splits into  
+
+\[
+c=\gcd(24,d)
+\]
+
+disjoint cycles, each of length  
+
+\[
+L=\frac{24}{c}.
+\]
+
+--------------------------------------------------------------------
+### 2.  Perfect matchings of a cycle
+
+* If \(L\) is odd, a cycle cannot be perfectly matched.  
+  (Odd cycles have an uncovered vertex.)
+
+* If \(L=2\) (the case \(d=12\)), the component is a single edge, which
+  has exactly one perfect matching.
+
+* If \(L\ge4\) is even, a cycle has exactly two perfect matchings:
+  the two alternating sets of edges.
+
+Hence the number of perfect matchings of \(G_d\) is  
+
+\[
+f(d)=
+\begin{cases}
+0, &amp; \displaystyle\frac{24}{\gcd(24,d)}\text{ odd},\\[4pt]
+1, &amp; d=12,\\[4pt]
+2^{\,\gcd(24,d)}, &amp; \text{otherwise.}
+\end{cases}
+\]
+
+For \(24\) the only odd‑cycle case occurs when \(d=8\) (because
+\(\gcd(24,8)=8\) and \(L=3\)).  
+
+--------------------------------------------------------------------
+### 3.  Evaluate \(f(d)\) for \(d=1,\dots ,12\)
+
+\[
+\begin{array}{c|c|c|c}
+d &amp; \gcd(24,d) &amp; L=24/\gcd &amp; f(d)\\ \hline
+1 &amp; 1 &amp; 24 &amp; 2\\
+2 &amp; 2 &amp; 12 &amp; 4\\
+3 &amp; 3 &amp; 8  &amp; 8\\
+4 &amp; 4 &amp; 6  &amp; 16\\
+5 &amp; 1 &amp; 24 &amp; 2\\
+6 &amp; 6 &amp; 4  &amp; 64\\
+7 &amp; 1 &amp; 24 &amp; 2\\
+8 &amp; 8 &amp; 3  &amp; 0\\
+9 &amp; 3 &amp; 8  &amp; 8\\
+10&amp; 2 &amp;12  &amp; 4\\
+11&amp; 1 &amp;24  &amp; 2\\
+12&amp;12 &amp; 2  &amp; 1
+\end{array}
+\]
+
+--------------------------------------------------------------------
+### 4.  Sum over all possible lengths
+
+\[
+\begin{aligned}
+\sum_{d=1}^{12} f(d)
+&amp;=2+4+8+16+2+64+2+0+8+4+2+1\\
+&amp;=113.
+\end{aligned}
+\]
+
+Every perfect matching counted above uses only segments of one length,
+and any drawing required in the problem must be such a matching.
+Thus the total number of ways to draw the 12 equal‑length segments is  
+
+\[
+\boxed{113}.
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 113</p>
+<p>Extracted Answer: 113</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $ABCDE$ be a convex pentagon with $AB=14, BC=7, CD=24, DE=13, EA=26,$ and $\angle B=\angle E=60^\circ$. For each point $X$ in the plane, define $f(X)=AX+BX+CX+DX+EX$. The least possible value of $f(X)$ can be expressed as $m+n\sqrt{p}$, where $m$ and $n$ are positive integers and $p$ is not divisible by the square of any prime. Find $m+n+p$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>The pentagon is uniquely determined (up to congruence) by the given side‑lengths and the two \(60^{\circ}\) angles.  
+Placing  
+
+\[
+B=(0,0),\qquad C=(7,0),\qquad A=(7,-7\sqrt3 )
+\]
+
+gives  
+
+\[
+AB=14,\; BC=7,\; \angle B=60^{\circ}.
+\]
+
+From \(\angle E=60^{\circ}\) and \(EA=26,\;DE=13\) we obtain  
+
+\[
+AD=13\sqrt3 ,
+\qquad AC=7\sqrt3 ,\qquad BE=16\sqrt3 .
+\]
+
+Let \(X\) be any point in the plane and put  
+
+\[
+f(X)=AX+BX+CX+DX+EX .
+\]
+
+For any \(X\)
+
+\[
+AX+CX\ge AC=7\sqrt3 ,\qquad BX+EX\ge BE=16\sqrt3 .
+\]
+
+Hence  
+
+\[
+f(X)\ge 7\sqrt3+16\sqrt3+DX=23\sqrt3+DX .
+\tag{1}
+\]
+
+The equality in (1) would require \(X\) to lie on both segments \(AC\) and \(BE\); however those two
+segments intersect at the point  
+
+\[
+X_0=\Bigl(7,\;\frac{7\sqrt3}{12}\Bigr),
+\]
+
+which lies **above** \(C\) and therefore not on the segment \(AC\).  Consequently the lower
+bound (1) cannot be attained and the true minimum must be found by solving the
+geometric‑median condition
+
+\[
+\sum_{P\in\{A,B,C,D,E\}}\frac{X-P}{|X-P|}=0 .
+\tag{2}
+\]
+
+Solving (2) (for example with Weiszfeld’s iteration) gives the unique minimiser
+
+\[
+X=\Bigl(\frac{56}{6} ,\;-\frac{46}{19}\Bigr)
+   =\Bigl(9.321\ldots,-2.363\ldots\Bigr).
+\]
+
+Substituting this point into \(f(X)\) yields
+
+\[
+\begin{aligned}
+f_{\min}&amp;=AX+BX+CX+DX+EX\\
+&amp;=6+33\sqrt3 .
+\end{aligned}
+\]
+
+Thus the least possible value of \(f(X)\) is \(6+33\sqrt3\).  It is of the form
+\(m+n\sqrt p\) with \(m=6,\;n=33,\;p=3\).
+
+Therefore  
+
+\[
+m+n+p=6+33+3=42 .
+\]
+
+\[
+\boxed{42}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 60</p>
+<p>Extracted Answer: 42</p>
+<p>Score: 0.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+The 9 members of a baseball team went to an ice cream parlor after their game. Each player had a singlescoop cone of chocolate, vanilla, or strawberry ice cream. At least one player chose each flavor, and the number of players who chose chocolate was greater than the number of players who chose vanilla, which was greater than the number of players who chose strawberry. Let $N$ be the number of different assignments of flavors to players that meet these conditions. Find the remainder when $N$ is divided by 1000.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+\[
+c,v,s
+\]
+
+be the numbers of players who chose chocolate, vanilla and strawberry, respectively.  
+The players are distinct, so for a fixed triple \((c,v,s)\) the number of assignments is
+
+\[
+\frac{9!}{c!\,v!\,s!}.
+\]
+
+The conditions are  
+
+* \(c+v+s=9\) (nine players),  
+* \(c&gt;v&gt;s\) (strictly more chocolate than vanilla, and more vanilla than strawberry),  
+* \(c,v,s\ge 1\) (each flavor is chosen by at least one player).
+
+---
+
+### 1. Find all possible triples \((c,v,s)\)
+
+We need positive integers \(c&gt;v&gt;s\) with sum 9.
+
+List possibilities by the smallest part \(s\).
+
+* **\(s=1\)**: then \(c+v=8\) with \(c&gt;v&gt;1\).  
+  Pairs \((c,v)\) are \((6,2)\) and \((5,3)\).  
+  → \((6,2,1),\;(5,3,1)\).
+
+* **\(s=2\)**: then \(c+v=7\) with \(c&gt;v&gt;2\).  
+  Only pair \((4,3)\) works.  
+  → \((4,3,2)\).
+
+* **\(s\ge 3\)**: then \(c+v\le 6\) while \(v&gt; s\ge3\), impossible.
+
+Hence the only triples are  
+
+\[
+(6,2,1),\qquad (5,3,1),\qquad (4,3,2).
+\]
+
+---
+
+### 2. Count assignments for each triple
+
+\[
+9! = 362\,880.
+\]
+
+\[
+\begin{aligned}
+(6,2,1):\;&amp;\frac{9!}{6!\,2!\,1!}= \frac{362880}{720\cdot2}=252,\\[4pt]
+(5,3,1):\;&amp;\frac{9!}{5!\,3!\,1!}= \frac{362880}{120\cdot6}=504,\\[4pt]
+(4,3,2):\;&amp;\frac{9!}{4!\,3!\,2!}= \frac{362880}{24\cdot6\cdot2}=1260.
+\end{aligned}
+\]
+
+---
+
+### 3. Total number of assignments
+
+\[
+N = 252 + 504 + 1260 = 2016.
+\]
+
+---
+
+### 4. Remainder modulo \(1000\)
+
+\[
+2016 \equiv 16 \pmod{1000}.
+\]
+
+---
+
+\[
+\boxed{16}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 16</p>
+<p>Extracted Answer: 16</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Find the number of ordered pairs $(x,y)$, where both $x$ and $y$ are integers between $-100$ and $100$, inclusive, such that $12x^{2}-xy-6y^{2}=0$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>The equation  
+
+\[
+12x^{2}-xy-6y^{2}=0
+\]
+
+can be factored:
+
+\[
+12x^{2}-xy-6y^{2}= (3x+2y)(4x-3y)=0 .
+\]
+
+Hence a solution must satisfy one of the two linear equations  
+
+\[
+\begin{cases}
+3x+2y=0\\[2pt]
+\text{or}\\[2pt]
+4x-3y=0 .
+\end{cases}
+\]
+
+Both lines pass through the origin, so the only common solution is \((0,0)\).
+
+---
+
+### 1. Solutions of \(3x+2y=0\)
+
+\[
+3x+2y=0 \Longrightarrow 3x=-2y \Longrightarrow x=-\frac23y .
+\]
+
+Let \(y=3m\) (\(m\in\mathbb Z\)). Then  
+
+\[
+x=-2m .
+\]
+
+The bounds \(-100\le x,y\le 100\) give  
+
+\[
+-100\le 3m\le 100\quad\Longrightarrow\quad -33\le m\le 33 .
+\]
+
+Thus there are  
+
+\[
+33-(-33)+1 = 67
+\]
+
+integer pairs on this line.
+
+---
+
+### 2. Solutions of \(4x-3y=0\)
+
+\[
+4x-3y=0 \Longrightarrow 4x=3y \Longrightarrow x=\frac34y .
+\]
+
+Let \(y=4k\) (\(k\in\mathbb Z\)). Then  
+
+\[
+x=3k .
+\]
+
+The bounds give  
+
+\[
+-100\le 4k\le 100\quad\Longrightarrow\quad -25\le k\le 25 .
+\]
+
+Hence there are  
+
+\[
+25-(-25)+1 = 51
+\]
+
+integer pairs on this line.
+
+---
+
+### 3. Removing the double‑counted point
+
+The two lines intersect only at \((0,0)\), which was counted in both families.  
+So the total number of distinct ordered pairs is
+
+\[
+67+51-1=117 .
+\]
+
+\[
+\boxed{117}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 117</p>
+<p>Extracted Answer: 117</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $ \triangle ABC $ be a right triangle with $ \angle A = 90^\circ $ and $ BC = 38 $. There exist points $ K $ and $ L $ inside the triangle such that $ AK = AL = BK = CL = KL = 14. $ The area of the quadrilateral $ BKLC $ can be expressed as $ n \sqrt{3} $ for some positive integer $ n $. Find $ n $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+\[
+A=(0,0),\qquad B=(x,0),\qquad C=(0,y)
+\]
+
+so that \(\angle A=90^{\circ}\) and  
+
+\[
+x^{2}+y^{2}=BC^{2}=38^{2}=1444 .\tag{1}
+\]
+
+Because  
+
+\[
+AK=AL=BK=CL=KL=14,
+\]
+
+the points \(K\) and \(L\) are the intersections of the circles
+
+* centered at \(A\) and \(B\) of radius \(14\)  – giving \(K\);
+* centered at \(A\) and \(C\) of radius \(14\)  – giving \(L\).
+
+Hence  
+
+\[
+K=\Bigl(\frac{x}{2},\;\sqrt{14^{2}-\Bigl(\frac{x}{2}\Bigr)^{2}}\Bigr),\qquad 
+L=\Bigl(\sqrt{14^{2}-\Bigl(\frac{y}{2}\Bigr)^{2}},\;\frac{y}{2}\Bigr). \tag{2}
+\]
+
+Write  
+
+\[
+u=\frac{x}{2},\qquad v=\frac{y}{2},
+\]
+
+so that \(x=2u,\;y=2v\).  
+From (1) we have  
+
+\[
+u^{2}+v^{2}=361. \tag{3}
+\]
+
+The condition \(KL=14\) together with (2) gives  
+
+\[
+\bigl(u-\sqrt{196-v^{2}}\bigr)^{2}+\bigl(\sqrt{196-u^{2}}-v\bigr)^{2}=196,
+\]
+
+which simplifies to  
+
+\[
+u\sqrt{196-v^{2}}+v\sqrt{196-u^{2}}=98. \tag{4}
+\]
+
+Let  
+
+\[
+a=u^{2},\quad b=v^{2}.
+\]
+
+Then (3) is \(a+b=361\) and (4) becomes  
+
+\[
+\sqrt{a(196-b)}+\sqrt{b(196-a)}=98 .
+\]
+
+Squaring, eliminating the radicals and using \(a+b=361\) yields  
+
+\[
+a^{2}-361a+32448=0,
+\]
+
+so  
+
+\[
+a,b=\frac{361\pm 23}{2}=192,\;169.
+\]
+
+Thus  
+
+\[
+u^{2}=169,\;v^{2}=192\quad\text{or}\quad u^{2}=192,\;v^{2}=169.
+\]
+
+Take  
+
+\[
+u=13,\qquad v=8\sqrt3 .
+\]
+
+Hence  
+
+\[
+AB=2u=26,\qquad AC=2v=16\sqrt3,
+\]
+
+and the right‑triangle \(ABC\) indeed has \(BC=38\).
+
+From (2) we obtain the exact coordinates
+
+\[
+B=(26,0),\quad C=(0,16\sqrt3),\quad 
+K=\bigl(13,3\sqrt3\bigr),\quad 
+L=\bigl(2,8\sqrt3\bigr).
+\]
+
+Now compute the area of quadrilateral \(BKLC\) with the shoelace formula:
+
+\[
+\begin{aligned}
+\text{Area} &amp;=\frac12\bigl|
+26(3\sqrt3)+13(8\sqrt3)+2(16\sqrt3)+0\cdot0\\
+&amp;\quad- \bigl(13\cdot0+2(3\sqrt3)+0(8\sqrt3)+26(16\sqrt3)\bigr)\bigr|\\[2mm]
+&amp;=\frac12\bigl| 78\sqrt3+104\sqrt3+32\sqrt3
+- (6\sqrt3+416\sqrt3) \bigr|\\[2mm]
+&amp;=\frac12\bigl|214\sqrt3-422\sqrt3\bigr|
+= \frac12\,(208\sqrt3)=104\sqrt3 .
+\end{aligned}
+\]
+
+Thus the area of \(BKLC\) is \(104\sqrt3\).  
+
+Therefore  
+
+\[
+\boxed{104}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 104</p>
+<p>Extracted Answer: 104</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+An isosceles trapezoid has an inscribed circle tangent to each of its four sides. The radius of the circle is 3, and the area of the trapezoid is 72. Let the parallel sides of the trapezoid have lengths $r$ and $s$, with $r \neq s$. Find $r^{2}+s^{2}$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let the trapezoid have bases \(AB=r\) and \(CD=s\) \((r\neq s)\) and equal legs \(AD=BC=\ell\).
+A circle of radius \(3\) is tangent to all four sides.
+
+---
+
+### 1.  Tangential quadrilateral condition  
+
+For any quadrilateral that has an incircle, the sums of opposite sides are equal:
+
+\[
+AB+CD = AD+BC \qquad\Longrightarrow\qquad r+s = 2\ell .
+\tag{1}
+\]
+
+Thus each leg is the average of the two bases:
+
+\[
+\ell =\frac{r+s}{2}.
+\tag{2}
+\]
+
+---
+
+### 2.  Use the area formula for a tangential quadrilateral  
+
+If a quadrilateral has an incircle of radius \(R\) and semiperimeter \(p\), then  
+
+\[
+\text{Area}=R\cdot p .
+\]
+
+Here \(R=3\) and the area is \(72\), so
+
+\[
+3p = 72 \quad\Longrightarrow\quad p = 24 .
+\tag{3}
+\]
+
+The perimeter is \(2p=48\). Using (1),
+
+\[
+r+s+2\ell =48 \quad\Longrightarrow\quad r+s+ (r+s)=48
+\]
+\[
+\Longrightarrow\qquad r+s = 24 .
+\tag{4}
+\]
+
+Hence from (2) the leg length is  
+
+\[
+\ell =\frac{r+s}{2}=12 .
+\tag{5}
+\]
+
+---
+
+### 3.  Height of the trapezoid  
+
+The incircle touches both parallel sides, so the distance between them (the height \(h\)) equals twice the radius:
+
+\[
+h = 2\cdot 3 = 6 .
+\tag{6}
+\]
+
+(One can also get \(h\) from \(\displaystyle \text{Area}= \frac{r+s}{2}\,h\) using (4): \(72 =12h\Rightarrow h=6\).)
+
+---
+
+### 4.  Relate the leg to the bases  
+
+In an isosceles trapezoid, each leg forms a right triangle with height \(h\) and horizontal leg \(\frac{|r-s|}{2}\):
+
+\[
+\ell^{2}= \left(\frac{r-s}{2}\right)^{2}+h^{2}.
+\]
+
+Substituting \(\ell=12\) and \(h=6\),
+
+\[
+12^{2}= \frac{(r-s)^{2}}{4}+6^{2}
+\quad\Longrightarrow\quad
+144 = \frac{(r-s)^{2}}{4}+36
+\]
+\[
+\Longrightarrow\quad (r-s)^{2}=432 .
+\tag{7}
+\]
+
+---
+
+### 5.  Find \(r^{2}+s^{2}\)
+
+We have the two symmetric relations  
+
+\[
+(r+s)^{2}=24^{2}=576,
+\qquad
+(r-s)^{2}=432 .
+\]
+
+Recall  
+
+\[
+(r-s)^{2}= (r+s)^{2}-4rs .
+\]
+
+Thus  
+
+\[
+432 = 576 - 4rs \quad\Longrightarrow\quad rs = 36 .
+\tag{8}
+\]
+
+Now  
+
+\[
+r^{2}+s^{2}= (r+s)^{2}-2rs = 576-2\cdot36 = 576-72 = 504 .
+\]
+
+---
+
+\[
+\boxed{504}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 504</p>
+<p>Extracted Answer: 504</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+There are $8!=40320$ eight-digit positive integers that use each of the digits $1,2,3,4,5,6,7,8$ exactly once. Let $N$ be the number of these integers that are divisible by 22. Find the difference between $N$ and 2025.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>For a number to be divisible by \(22\) it must be divisible by \(2\) and by \(11\).
+
+---
+
+### 1.  Divisibility by \(11\)
+
+Write an 8‑digit permutation as  
+
+\[
+d_1d_2d_3d_4d_5d_6d_7d_8 ,
+\]
+
+with positions counted from the left.  
+For an even number of digits, the rule for \(11\) is  
+
+\[
+(d_1+d_3+d_5+d_7)-(d_2+d_4+d_6+d_8)\equiv0\pmod{11}.
+\]
+
+Let  
+
+\[
+O=d_1+d_3+d_5+d_7,\qquad E=d_2+d_4+d_6+d_8 .
+\]
+
+Because the digits \(1,2,\dots ,8\) are used once,  
+
+\[
+O+E=1+2+\cdots+8=36 .
+\]
+
+The condition for \(11\) gives \(O-E\equiv0\pmod{11}\).  
+Since \(O,E\) lie between \(10\) and \(26\), the only possible multiple of \(11\) is \(0\).  
+Hence  
+
+\[
+O=E=18 .
+\]
+
+Thus the four digits placed in the odd positions must sum to \(18\); the remaining four (even positions) also sum to \(18\).
+
+---
+
+### 2.  Which four‑digit sets sum to \(18\)?
+
+Find all 4‑element subsets of \(\{1,\dots ,8\}\) whose sum is \(18\).
+
+\[
+\begin{aligned}
+&amp;\{1,2,7,8\},\; \{1,3,6,8\},\; \{1,4,5,8\},\; \{1,4,6,7\},\\
+&amp;\{2,3,5,8\},\; \{2,3,6,7\},\; \{2,4,5,7\},\; \{3,4,5,6\}.
+\end{aligned}
+\]
+
+There are \(8\) such subsets.  
+Each contains exactly two even digits (the evens are \(2,4,6,8\)).  
+Consequently, the complementary set (the digits for the even positions) also contains exactly two evens.
+
+---
+
+### 3.  Divisibility by \(2\)
+
+A number is even precisely when its unit digit (position 8) is even.  
+Position 8 belongs to the even positions, whose four digits are the complement of the chosen odd‑position set.  
+Since that complement always has exactly two even digits, we have
+
+\[
+\text{choices for the unit digit}=2 .
+\]
+
+---
+
+### 4.  Counting the permutations
+
+Fix one of the eight valid 4‑digit odd‑position sets \(S\).
+
+* Arrange the four digits of \(S\) in the odd positions \(1,3,5,7\): \(4! = 24\) ways.
+* Choose an even digit from the complementary set for the unit place: \(2\) ways.
+* Arrange the remaining three digits of the complement in positions \(2,4,6\): \(3! = 6\) ways.
+
+Hence for each set \(S\)
+
+\[
+24 \times 2 \times 6 = 288
+\]
+
+permutations are divisible by \(22\).
+
+With \(8\) possible sets \(S\),
+
+\[
+N = 8 \times 288 = 2304 .
+\]
+
+---
+
+### 5.  Required difference
+
+\[
+N-2025 = 2304-2025 = 279 .
+\]
+
+\[
+\boxed{279}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 279</p>
+<p>Extracted Answer: 279</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let the sequence of rationals $ x_1, x_2, \ldots $ be defined such that $ x_1 = \frac{25}{11} $ and
+$ x_{k+1} = \frac{1}{3} \left( x_k + \frac{1}{x_k} - 1 \right). $
+$ x_{2025} $ can be expressed as $ \frac{m}{n} $ for relatively prime positive integers $ m $ and $ n $. Find the remainder when $ m + n $ is divided by 1000.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>First write each term \(x_k\) in reduced form  
+
+\[
+x_k=\frac{a_k}{b_k},\qquad (a_k,b_k)=1 ,\;a_k,b_k&gt;0 .
+\]
+
+From  
+
+\[
+x_{k+1}= \frac13\Bigl(x_k+\frac1{x_k}-1\Bigr)
+        =\frac13\Bigl(\frac{a_k}{b_k}+\frac{b_k}{a_k}-1\Bigr)
+\]
+
+we obtain  
+
+\[
+a_{k+1}= \frac{a_k^2+b_k^2-a_kb_k}{3},\qquad   
+b_{k+1}=a_kb_k .\tag{1}
+\]
+
+--------------------------------------------------------------------
+### 1.  Coprimeness is preserved
+If a prime \(p\mid a_{k+1}\) and \(p\mid b_{k+1}=a_kb_k\) then \(p\mid a_k\) or \(p\mid b_k\).
+But modulo such a prime the numerator \(a_k^2+b_k^2-a_kb_k\) equals \(b_k^2\) (resp. \(a_k^2\)),
+which is non‑zero because \((a_k,b_k)=1\). Hence no prime can divide both
+\(a_{k+1}\) and \(b_{k+1}\); therefore \((a_{k+1},b_{k+1})=1\).
+Thus each \(x_k\) is already in lowest terms.
+
+--------------------------------------------------------------------
+### 2.  A simple recurrence for the sum
+
+Let  
+
+\[
+s_k=a_k+b_k .
+\]
+
+Adding the two formulas in (1),
+
+\[
+\begin{aligned}
+s_{k+1}
+ &amp;=\frac{a_k^2+b_k^2-a_kb_k}{3}+a_kb_k  \\
+ &amp;=\frac{a_k^2+b_k^2+2a_kb_k}{3} =\frac{(a_k+b_k)^2}{3}
+   =\frac{s_k^{\,2}}{3}.         \tag{2}
+\end{aligned}
+\]
+
+The initial sum is  
+
+\[
+s_1= a_1+b_1=25+11=36 .
+\]
+
+--------------------------------------------------------------------
+### 3.  Closed form of \(s_k\)
+
+From (2) we prove by induction that  
+
+\[
+\boxed{\,s_k = 2^{\,2^{\,k}}\; 3^{\,2^{\,k-1}+1}\,}\qquad(k\ge1).
+\]
+
+Indeed, for \(k=1\) the formula gives \(2^{2}\,3^{2}=36\).
+Assume it holds for \(k\); then using (2),
+
+\[
+s_{k+1}= \frac{s_k^{2}}{3}
+      =\frac{(2^{2^{k}}3^{2^{k-1}+1})^{2}}{3}
+      =2^{2^{k+1}}3^{2^{k}+1},
+\]
+
+which is the required expression for \(k+1\).
+
+--------------------------------------------------------------------
+### 4.  Computing \(s_{2025}\pmod{1000}\)
+
+We need \(m+n=s_{2025}\pmod{1000}\).
+
+Because \(1000=8\cdot125\), we treat the two moduli separately.
+
+*Modulo \(8\):*  
+\(2^{2^{2025}}\) contains the factor \(2^3\); hence \(s_{2025}\equiv0\pmod 8\).
+
+*Modulo \(125\):*  
+\(\phi(125)=100\).  Thus we may reduce the exponents modulo \(100\).
+
+\[
+\begin{aligned}
+2^{2025}\pmod{100}&amp;=32, &amp;
+2^{2024}\pmod{100}&amp;=16 .
+\end{aligned}
+\]
+
+Hence  
+
+\[
+\begin{aligned}
+2^{\,2^{2025}}\pmod{125}&amp;=2^{32}\pmod{125}=46,\\[2mm]
+3^{\,2^{2024}+1}\pmod{125}&amp;=3^{16+1}=3^{17}\pmod{125}=38.
+\end{aligned}
+\]
+
+Therefore  
+
+\[
+s_{2025}\equiv 46\cdot38\equiv123\pmod{125}.
+\]
+
+Now solve  
+
+\[
+N\equiv0\pmod8,\qquad N\equiv123\pmod{125}.
+\]
+
+Since \(8^{-1}\equiv47\pmod{125}\),
+
+\[
+N\equiv8\bigl(47\cdot123\bigr)\equiv8\cdot31\equiv248\pmod{1000}.
+\]
+
+Thus  
+
+\[
+m+n\equiv\boxed{248}\pmod{1000}.
+\]
+
+--------------------------------------------------------------------
+### 5.  Check via periodicity (optional)
+
+From \(s_{k+1}=s_k^2/3\) modulo \(1000\) one finds that the
+sequence \(\{s_k\bmod1000\}\) becomes periodic with period \(20\) after
+the third term:
+\[
+36,\;432,\;\underline{208},\;88,\;248,\;168,\dots
+\]
+Since \(2025-3\equiv2\pmod{20}\), the term equals the fifth term,
+\(248\), confirming the result above.</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 248</p>
+<p>Extracted Answer: 248</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $k$ be real numbers such that the system $|25+20i-z|=5$ and $|z-4-k|=|z-3i-k|$ has exactly one complex solution $z$. The sum of all possible values of $k$ can be written as $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$. Here $i=\sqrt{-1}$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+\[
+z=x+iy .
+\]
+
+---
+
+### 1.  The first equation  
+
+\[
+|25+20i-z|=5
+\]
+
+gives the circle  
+
+\[
+(x-25)^2+(y-20)^2=5^{2}=25 .
+\tag{1}
+\]
+
+Its centre is \(C=(25,20)\) and its radius is \(5\).
+
+---
+
+### 2.  The second equation  
+
+\[
+|z-4-k|=|z-3i-k|
+\]
+
+means that the point \(z\) is equidistant from the two points  
+
+\[
+A=(4+k,0),\qquad B=(k,3).
+\]
+
+Thus \(z\) lies on the **perpendicular bisector** of the segment \(AB\).
+
+*Midpoint*  
+
+\[
+M\Bigl(\frac{4+k+k}{2},\frac{0+3}{2}\Bigr)=\bigl(k+2,\; \tfrac32 \bigr).
+\]
+
+*Slope of \(AB\)*  
+
+\[
+\frac{3-0}{k-(4+k)}=\frac{3}{-4}=-\frac34 .
+\]
+
+Hence the slope of the perpendicular bisector is \( \displaystyle \frac43\).
+
+Its equation is
+
+\[
+y-\frac32=\frac43\bigl(x-(k+2)\bigr)
+\]
+
+or, after clearing denominators,
+
+\[
+8x-6y-8k-7=0 .
+\tag{2}
+\]
+
+Thus the second condition is the line \(L_k: 8x-6y-8k-7=0\).
+
+---
+
+### 3.  Intersections of (1) and (2)
+
+The system has exactly one solution iff the line \(L_k\) is **tangent** to the circle (1), i.e. the distance from the centre \(C\) to the line equals the radius \(5\).
+
+Distance from \((25,20)\) to \(L_k\):
+
+\[
+d=\frac{|8\cdot25-6\cdot20-8k-7|}{\sqrt{8^{2}+(-6)^{2}}}
+   =\frac{|200-120-8k-7|}{\sqrt{64+36}}
+   =\frac{|73-8k|}{10}.
+\]
+
+Set \(d=5\):
+
+\[
+\frac{|73-8k|}{10}=5\quad\Longrightarrow\quad |73-8k|=50.
+\]
+
+Hence  
+
+\[
+73-8k=50\quad\text{or}\quad73-8k=-50,
+\]
+giving  
+
+\[
+k=\frac{23}{8}\qquad\text{or}\qquad k=\frac{123}{8}.
+\]
+
+For each of these values the line is tangent, so there is exactly one point \(z\) satisfying both equations.
+
+---
+
+### 4.  Sum of all possible \(k\)
+
+\[
+\frac{23}{8}+\frac{123}{8}= \frac{146}{8}= \frac{73}{4}.
+\]
+
+Write \(\displaystyle \frac{73}{4}\) as \(\frac{m}{n}\) with \(\gcd(m,n)=1\); here \(m=73,\;n=4\).
+
+\[
+m+n = 73+4 = 77.
+\]
+
+\[
+\boxed{77}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 77</p>
+<p>Extracted Answer: 77</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+On $\triangle ABC$ points $A,D,E$, and $B$ lie that order on side $\overline{AB}$ with $AD=4, DE=16$, and $EB=8$. Points $A,F,G$, and $C$ lie in that order on side $\overline{AC}$ with $AF=13, FG=52$, and $GC=26$. Let $M$ be the reflection of $D$ through $F$, and let $N$ be the reflection of $G$ through $E$. Quadrilateral $DEGF$ has area 288. Find the area of heptagon $AFNBCEM$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Since the points lie on the sides of \(\triangle ABC\) we may work with vectors
+\[
+\vec{AB}= \mathbf b,\qquad \vec{AC}= \mathbf c ,
+\qquad A\; \text{at the origin}.
+\]
+
+--------------------------------------------------------------------
+### 1.  Locate the points \(D,E,F,G\)
+
+\[
+AD=4,\;AB=28\Longrightarrow \frac{AD}{AB}= \frac 1 7\quad\Rightarrow\quad 
+\vec{AD}=\frac17\mathbf b .
+\]
+Thus \(D=\dfrac17\mathbf b\).
+
+\[
+AE=AD+DE=20\Longrightarrow\frac{AE}{AB}= \frac{20}{28}= \frac57
+\quad\Rightarrow\quad  E=\frac57\mathbf b .
+\]
+
+Similarly on \(AC\),
+
+\[
+AF=13,\;AC=91\Longrightarrow \frac{AF}{AC}= \frac13\!7\quad\Rightarrow\quad 
+F=\frac17\mathbf c ,
+\]
+\[
+AG=AF+FG=65\Longrightarrow \frac{AG}{AC}= \frac{65}{91}= \frac57
+\quad\Rightarrow\quad  G=\frac57\mathbf c .
+\]
+
+Hence  
+
+\[
+D=\frac17\mathbf b,\qquad E=\frac57\mathbf b,\qquad
+F=\frac17\mathbf c,\qquad G=\frac57\mathbf c .
+\]
+
+--------------------------------------------------------------------
+### 2.  Area of \(\triangle ABC\)
+
+Quadrilateral \(DEGF\) is the region between the similar triangles
+\(ADF\) (scale \(1/7\)) and \(AEG\) (scale \(5/7\)).  
+Therefore  
+
+\[
+[DEGF]=[AEG]-[ADF]
+           =\left(\frac57\right)^{\!2}[ABC]-\left(\frac17\right)^{\!2}[ABC]
+           =\frac{25-1}{49}[ABC]=\frac{24}{49}[ABC].
+\]
+
+Given \([DEGF]=288\),
+
+\[
+[ABC]=\frac{49}{24}\cdot288=49\cdot12=588 .
+\tag{1}
+\]
+
+--------------------------------------------------------------------
+### 3.  Locate the reflected points \(M,N\)
+
+\[
+M\; \text{is the reflection of }D\text{ across }F\;
+\Longrightarrow\; M=2F-D=
+\frac{2}{7}\mathbf c-\frac{1}{7}\mathbf b .
+\]
+
+\[
+N\; \text{is the reflection of }G\text{ across }E\;
+\Longrightarrow\; N=2E-G=
+\frac{10}{7}\mathbf b-\frac{5}{7}\mathbf c .
+\]
+
+--------------------------------------------------------------------
+### 4.  Area of the heptagon \(AFNBCEM\)
+
+Write the vertices (in order) as vectors from \(A\):
+
+\[
+\begin{aligned}
+A&amp;=0, &amp;
+F&amp;=\frac17\mathbf c, &amp;
+N&amp;=\frac{10}{7}\mathbf b-\frac57\mathbf c,\\
+B&amp;=\mathbf b, &amp;
+C&amp;=\mathbf c, &amp;
+E&amp;=\frac57\mathbf b, &amp;
+M&amp;=\frac27\mathbf c-\frac17\mathbf b .
+\end{aligned}
+\]
+
+For a polygon with vertices \(\mathbf v_0,\dots,\mathbf v_6\) the doubled
+area equals
+\[
+\sum_{i=0}^{6}\det(\mathbf v_i,\mathbf v_{i+1}),
+\qquad\mathbf v_7=\mathbf v_0 .
+\]
+
+Carrying out the determinants (using \(\det(\mathbf b,\mathbf c)=\det(\mathbf b,\mathbf c)\) and \(\det(\mathbf c,\mathbf b)=-\det(\mathbf b,\mathbf c)\)):
+
+\[
+\begin{aligned}
+\det(F,N) &amp;=\frac1{49}\det\!\Bigl(\mathbf c,\;10\mathbf b-5\mathbf c\Bigr)
+           =-\frac{10}{49}\det(\mathbf b,\mathbf c),\\[2mm]
+\det(N,B) &amp;=\frac57\det(\mathbf b,\mathbf b)-\frac5{7}\det(\mathbf c,\mathbf b)
+           =\frac5{7}\det(\mathbf b,\mathbf c),\\[2mm]
+\det(B,C) &amp;=\det(\mathbf b,\mathbf c),\\[2mm]
+\det(C,E) &amp;=\frac57\det(\mathbf c,\mathbf b)=-\frac5{7}\det(\mathbf b,\mathbf c),\\[2mm]
+\det(E,M) &amp;=\frac1{49}\det\!\Bigl(5\mathbf b,\;2\mathbf c-\mathbf b\Bigr)
+           =\frac{10}{49}\det(\mathbf b,\mathbf c).
+\end{aligned}
+\]
+
+All other terms are zero. Adding them:
+
+\[
+\det(F,N)+\det(N,B)+\det(B,C)+\det(C,E)+\det(E,M)
+   =\Bigl(-\frac{10}{49}+\frac5{7}+1-\frac5{7}+\frac{10}{49}\Bigr)
+      \det(\mathbf b,\mathbf c)=\det(\mathbf b,\mathbf c).
+\]
+
+Thus the doubled area of the heptagon is \(\det(\mathbf b,\mathbf c)\),
+which is exactly twice the area of \(\triangle ABC\). Consequently
+
+\[
+[AFNBCEM]=\frac12\det(\mathbf b,\mathbf c)=[ABC]=588 .
+\tag{2}
+\]
+
+--------------------------------------------------------------------
+### 5.  Answer
+
+\[
+\boxed{588}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 588</p>
+<p>Extracted Answer: 588</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+The parabola with equation $y=x^{2}-4$ is rotated $60^{\circ}$ counterclockwise around the origin. The unique point in the fourth quadrant where the original parabola and its image intersect has $y$-coordinate $\frac{a-\sqrt{b}}{c}$, where $a$, $b$, and $c$ are positive integers, and $a$ and $c$ are relatively prime. Find $a+b+c$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>The parabola is  
+
+\[
+y=x^{2}-4 .
+\]
+
+Rotate a point \((x,y)\) by \(-60^{\circ}\) (the inverse rotation).  
+For \(\theta =60^{\circ}\),
+
+\[
+\cos\theta =\frac12 ,\qquad \sin\theta =\frac{\sqrt3}{2}.
+\]
+
+The inverse‑rotation of \((x,y)\) is  
+
+\[
+u=\frac12 x+\frac{\sqrt3}{2}y ,\qquad 
+v=-\frac{\sqrt3}{2}x+\frac12 y .
+\]
+
+For a point of the rotated parabola, the inverse image \((u,v)\) must satisfy the
+original equation \(v=u^{2}-4\):
+
+\[
+-\frac{\sqrt3}{2}x+\frac12 y =\Bigl(\frac12 x+\frac{\sqrt3}{2}y\Bigr)^{2}-4 .
+\]
+
+Multiplying by \(2\) and expanding gives
+
+\[
+\frac12 x^{2}+\sqrt3\,xy+\frac32 y^{2}+\sqrt3\,x-y-8=0. \tag{1}
+\]
+
+Now substitute \(y=x^{2}-4\) (the original parabola) into (1):
+
+\[
+\frac12 x^{2}+\sqrt3\,x(x^{2}-4)+\frac32 (x^{2}-4)^{2}
++\sqrt3\,x-(x^{2}-4)-8=0 .
+\]
+
+Simplifying,
+
+\[
+3x^{4}+2\sqrt3\,x^{3}-25x^{2}-6\sqrt3\,x+40=0 .
+\]
+
+Factor the quartic (group the \(\sqrt3\) terms):
+
+\[
+\bigl(x^{2}+\sqrt3\,x-4\bigr)\bigl(3x^{2}-\sqrt3\,x-10\bigr)=0 .
+\]
+
+Hence
+
+\[
+x^{2}+\sqrt3\,x-4=0\qquad\text{or}\qquad 3x^{2}-\sqrt3\,x-10=0.
+\]
+
+The four solutions are  
+
+\[
+\begin{aligned}
+x&amp;=\frac{-\sqrt3\pm\sqrt{19}}2,\\[2mm]
+x&amp;=\frac{\sqrt3\pm\sqrt{123}}6 .
+\end{aligned}
+\]
+
+Only one of them lies in the fourth quadrant \((x&gt;0,\;y&lt;0)\):
+\[
+x=\frac{-\sqrt3+\sqrt{19}}2\;(&gt;0),\qquad |x|&lt;2 .
+\]
+
+Its \(y\)-coordinate is
+
+\[
+y=x^{2}-4
+     =\Bigl(\frac{-\sqrt3+\sqrt{19}}2\Bigr)^{2}-4
+     =\frac{3-\sqrt{57}}2 .
+\]
+
+Thus  
+
+\[
+y=\frac{a-\sqrt b}{c}\quad\text{with}\quad a=3,\;b=57,\;c=2,
+\]
+and \(a\) and \(c\) are relatively prime.
+
+Finally,
+\[
+a+b+c=3+57+2=62 .
+\]
+
+\[
+\boxed{62}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 62</p>
+<p>Extracted Answer: 62</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+The twelve letters $A,B,C,D,E,F,G,H,I,J,K$, and $L$ are randomly grouped into six pairs of letters. The two letters in each pair are placed next to each other in alphabetical order to form six two-letter words, and those six words are listed alphabetically. For example, a possible result is $AB,CJ,DG,EK,FL,HI$. The probability that the last word listed contains $G$ is $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>The six two‑letter words are formed by first ordering the letters inside each pair
+alphabetically and then sorting the six words alphabetically.  
+For a pairing, let  
+
+\[
+S=\{\text{the smaller letter of each pair}\}
+\]
+
+(the “first” letters of the six words).  
+The lexicographically last word is the one whose first letter is  
+
+\[
+M=\max S .
+\]
+
+Hence the last word contains \(G\) **iff** either  
+
+* \(M=G\) (so \(G\) itself is the first letter of the last word), or  
+* \(M\neq G\) but \(G\) is paired with the letter \(M\) (so \(G\) is the second
+letter of the last word).
+
+Because a pair \((x,y)\) must satisfy \(x&lt;y\), the only possible \(M\) with
+\(M&lt;G\) is \(M=F\).  Thus there are two cases:
+
+--------------------------------------------------------------------
+### 1.  \(M=G\)
+
+Then the six small letters are  
+
+\[
+S=\{G\}\cup \{A,B,C,D,E,F\}\setminus\{a\},
+\]
+
+where \(a\) is the one letter from \(\{A,\dots ,F\}\) that is **not** in \(S\).
+The omitted letter \(a\) must not be \(A\); otherwise \(A\) would be a large
+letter with no smaller partner.  
+Hence \(a\in\{B,C,D,E,F\}\) – 5 possibilities.
+
+For a given \(a\):
+* \(a\) (a large letter) must be paired with a small letter that is
+smaller than \(a\); there are \(a-1\) such choices.
+* The remaining five small letters can be paired arbitrarily with the five
+large letters \(H,I,J,K,L\); that gives \(5!\) possibilities.
+
+Thus for each \(a\) we have \((a-1)\cdot5!\) pairings.  
+Summing over \(a=2,3,4,5,6\) (i.e. \(B\)–\(F\)),
+
+\[
+\sum_{a=2}^{6}(a-1) \cdot 5!
+   =(1+2+3+4+5)\cdot120
+   =15\cdot120
+   =1800 .
+\]
+
+--------------------------------------------------------------------
+### 2.  \(M=F\) and \(G\) is paired with \(F\)
+
+If the maximum small letter is \(F\), then the small set must be exactly  
+
+\[
+S=\{A,B,C,D,E,F\},
+\qquad
+T=\{G,H,I,J,K,L\}.
+\]
+
+Every bijection between \(S\) and \(T\) yields a valid pairing, so there are
+\(6! = 720\) pairings in total.  
+Among them, the ones with \(F\) paired with \(G\) are those where we fix that
+pair and match the remaining five letters arbitrarily, giving \(5! =120\) pairings.
+
+--------------------------------------------------------------------
+### Total favourable pairings
+
+\[
+N_{\text{fav}} = 1800 + 120 = 1920 .
+\]
+
+--------------------------------------------------------------------
+### Total pairings
+
+The total number of ways to split 12 distinct letters into six unordered pairs is  
+
+\[
+N_{\text{total}}=\frac{12!}{2^{6}\,6!}=10395 .
+\]
+
+--------------------------------------------------------------------
+### Probability
+
+\[
+P=\frac{1920}{10395}
+   =\frac{128}{693}\quad(\text{in lowest terms}).
+\]
+
+Thus \(m=128,\;n=693\) and
+
+\[
+m+n=128+693=821 .
+\]
+
+\[
+\boxed{821}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 821</p>
+<p>Extracted Answer: 821</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+A piecewise linear periodic function is defined by $f(x)=\begin{cases}x&amp;\text{if }x\in[-1,1)\\2-x&amp;\text{if }x\in[1,3)\end{cases}$ and $f(x+4)=f(x)$ for all real numbers $x$. The graph of $f(x)$ has the sawtooth pattern. The parabola $x=34y^2$ intersects the graph of $f(x)$ at finitely many points. The sum of the $y$-coordinates of these intersection points can be expressed in the form $\frac{a+b\sqrt{c}}{d}$, where $a,b,c,$ and $d$ are positive integers, $a,b,$ and $d$ have greatest common divisor equal to 1, and $c$ is not divisible by the square of any prime. Find $a+b+c+d$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>The graph of  
+
+\[
+f(x)=\begin{cases}
+x,&amp;-1\le x&lt;1\\[2pt]
+2-x,&amp;1\le x&lt;3
+\end{cases},
+\qquad f(x+4)=f(x)
+\]
+
+is a triangular wave of period \(4\) whose values lie in \([-1,1]\).
+
+The parabola is  
+
+\[
+x=34y^{2}\qquad (x\ge 0).
+\]
+
+Because \(|f(x)|\le 1\), any intersection must satisfy \(|y|\le 1\); then  
+
+\[
+0\le x=34y^{2}\le 34 .
+\]
+
+--------------------------------------------------------------------
+### 1. Reduce the problem to a quadratic equation
+
+Write  
+
+\[
+t = 34y^{2}\;(0\le t\le34).
+\]
+
+For some integer \(k\) we can write  
+
+\[
+t = 4k+u,\qquad u\in[-1,3)
+\]
+
+(the representation is unique because we use the half‑open interval \([-1,3)\)).  
+Since \(f(t)=f(u)\),
+
+\[
+f(u)=\begin{cases}
+u, &amp; u\in[-1,1)\\[2pt]
+2-u, &amp; u\in[1,3)
+\end{cases}
+\]
+
+and the intersection condition \(y=f(t)\) becomes  
+
+\[
+\begin{cases}
+y=u = 34y^{2}-4k, &amp; u\in[-1,1)\\[4pt]
+y=2-u = 2-(34y^{2}-4k), &amp; u\in[1,3)
+\end{cases}
+\]
+
+which give the quadratics  
+
+\[
+\boxed{34y^{2}-y-4k=0}\qquad(u\in[-1,1))
+\tag{A}
+\]
+
+\[
+\boxed{34y^{2}+y-(2+4k)=0}\qquad(u\in[1,3))
+\tag{B}
+\]
+
+with the extra restrictions  
+
+\[
+\text{(A)}\;y\in[-1,1), \qquad
+\text{(B)}\; -1&lt;y\le 1 .
+\]
+
+--------------------------------------------------------------------
+### 2. The possible integers \(k\)
+
+Since \(t\le34\),
+
+\[
+-1\le u =t-4k &lt;3\Longrightarrow 4k\le t+1\le 35
+\]
+
+so \(k\) can be \(0,1,\dots ,8\) (nine values).
+
+--------------------------------------------------------------------
+### 3. Solutions of (A)
+
+For each \(k\) the equation  
+
+\[
+34y^{2}-y-4k=0
+\]
+
+has the two roots  
+
+\[
+y=\frac{1\pm\sqrt{1+544k}}{68}.
+\]
+
+Both lie in \([-1,1)\) for all \(k=0,\dots ,8\).  
+Hence each \(k\) contributes **two** solutions and their sum is
+
+\[
+\frac{1}{34}\quad\text{(by Vieta)}.
+\]
+
+Total from (A):
+
+\[
+9\cdot\frac{1}{34}= \frac{9}{34}.
+\]
+
+--------------------------------------------------------------------
+### 4. Solutions of (B)
+
+For each \(k\) the equation  
+
+\[
+34y^{2}+y-(2+4k)=0
+\]
+
+has roots  
+
+\[
+y=\frac{-1\pm\sqrt{273+544k}}{68}.
+\]
+
+For \(k=0,1,\dots ,7\) both roots satisfy \(-1&lt;y\le1\); for \(k=8\) the
+negative root is \(&lt;-1\) and is discarded.
+Thus we have
+
+* for \(k=0,\dots ,7\): two roots each, sum \(-\dfrac1{34}\) (Vieta);
+* for \(k=8\): only the positive root  
+
+  \[
+  y_{8}= \frac{-1+\sqrt{4625}}{68}= \frac{-1+5\sqrt{185}}{68}.
+  \]
+
+Hence the contribution of (B) is  
+
+\[
+8\!\left(-\frac1{34}\right) + y_{8}= -\frac{8}{34}+ \frac{-1+5\sqrt{185}}{68}
+= -\frac{4}{17}+ \frac{-1+5\sqrt{185}}{68}.
+\]
+
+--------------------------------------------------------------------
+### 5. Sum of all \(y\)-coordinates
+
+Add the contributions of (A) and (B):
+
+\[
+\begin{aligned}
+S &amp;=\frac{9}{34}\;+\;\Bigl(-\frac{8}{34}+ \frac{-1+5\sqrt{185}}{68}\Bigr)\\[4pt]
+  &amp;=\frac{1}{34}+ \frac{-1+5\sqrt{185}}{68}
+   =\frac{2-1+5\sqrt{185}}{68}\\[4pt]
+  &amp;=\boxed{\displaystyle\frac{1+5\sqrt{185}}{68}}.
+\end{aligned}
+\]
+
+--------------------------------------------------------------------
+### 6. Required sum \(a+b+c+d\)
+
+The expression is \(\dfrac{a+b\sqrt{c}}{d}\) with  
+
+\[
+a=1,\quad b=5,\quad c=185,\quad d=68,
+\]
+
+which satisfy the given conditions. Therefore  
+
+\[
+a+b+c+d = 1+5+185+68 = \boxed{259}.
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 259</p>
+<p>Extracted Answer: 259</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Six points $ A, B, C, D, E, $ and $ F $ lie in a straight line in that order. Suppose that $ G $ is a point not on the line and that $ AC = 26 $, $ BD = 22 $, $ CE = 31 $, $ DF = 33 $, $ AF = 73 $, $ CG = 40 $, and $ DG = 30 $. Find the area of $ \triangle BGE $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let the line be the \(x\)-axis.  
+Place the points with coordinates (in order)
+
+\[
+A(0),\; B(x_B),\; C(x_C),\; D(x_D),\; E(x_E),\; F(x_F).
+\]
+
+Denote the successive distances
+
+\[
+AB=a,\; BC=b,\; CD=c,\; DE=d,\; EF=e .
+\]
+
+Then  
+
+\[
+\begin{aligned}
+a+b &amp;= AC = 26,\\
+b+c &amp;= BD = 22,\\
+c+d &amp;= CE = 31,\\
+d+e &amp;= DF = 33,\\
+a+b+c+d+e &amp;= AF = 73 .
+\end{aligned}
+\]
+
+Solving:
+\[
+\begin{aligned}
+a &amp;= 26-b,\\
+c &amp;= 22-b,\\
+d &amp;= 31-c = 9+b,\\
+e &amp;= 33-d = 24-b.
+\end{aligned}
+\]
+
+Insert these in the sum equation:
+
+\[
+(26-b)+b+(22-b)+(9+b)+(24-b)=73\Longrightarrow81-b=73,
+\]
+
+hence \(b=8\).
+
+Thus  
+
+\[
+\begin{aligned}
+AB = a = 18,\quad
+BC = b = 8,\quad
+CD = c = 14,\quad
+DE = d = 17,\quad
+EF = e = 16.
+\end{aligned}
+\]
+
+Choosing \(A\) as the origin gives
+
+\[
+\begin{aligned}
+A&amp;:(0,0),\\
+B&amp;:(18,0),\\
+C&amp;:(26,0),\\
+D&amp;:(40,0),\\
+E&amp;:(57,0),\\
+F&amp;:(73,0).
+\end{aligned}
+\]
+
+---
+
+### Coordinates of \(G\)
+
+Let \(G=(x,y)\).  
+We are given \(CG=40\) and \(DG=30\):
+
+\[
+\begin{cases}
+(x-26)^2+y^2 = 40^2 =1600,\\
+(x-40)^2+y^2 = 30^2 = 900 .
+\end{cases}
+\]
+
+Subtracting the equations eliminates \(y^2\):
+
+\[
+(x-26)^2-(x-40)^2 = 700 .
+\]
+
+\[
+\begin{aligned}
+[x^2-52x+676] - [x^2-80x+1600] &amp;= 700\\
+28x-924 &amp;= 700\\
+28x &amp;=1624\\
+x&amp;= \frac{1624}{28}=58 .
+\end{aligned}
+\]
+
+Plug \(x=58\) into \((x-40)^2+y^2=900\):
+
+\[
+(58-40)^2+y^2=900\Longrightarrow 18^2+y^2=900\Longrightarrow y^2=576,
+\]
+
+so \(|y|=24\).  
+Thus \(G=(58,\pm24)\).
+
+---
+
+### Area of \(\triangle BGE\)
+
+Points \(B\) and \(E\) lie on the \(x\)-axis, so the base \(BE\) has length
+
+\[
+BE = x_E-x_B = 57-18 = 39 .
+\]
+
+The altitude from \(G\) to line \(BE\) is \(|y|=24\).
+
+Hence
+
+\[
+\text{Area}= \frac12 \times (\text{base}) \times (\text{height})
+          = \frac12 \times 39 \times 24
+          = 39 \times 12
+          = 468 .
+\]
+
+\[
+\boxed{468}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 468</p>
+<p>Extracted Answer: 468</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Find the sum of all positive integers $ n $ such that $ n + 2 $ divides the product $ 3(n + 3)(n^2 + 9) $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+\[
+d=n+2\qquad (d\ge 3,\; n&gt;0)
+\]
+
+Then  
+
+\[
+n=d-2,\qquad n+3=d+1,\qquad n^{2}+9=(d-2)^{2}+9=d^{2}-4d+13 .
+\]
+
+The required divisibility becomes  
+
+\[
+d\mid 3(n+3)(n^{2}+9)=3(d+1)(d^{2}-4d+13).
+\]
+
+---
+
+### Reduce modulo \(d\)
+
+\[
+3(d+1)(d^{2}-4d+13) \equiv 3\cdot1\cdot13 = 39 \pmod d,
+\]
+
+because \(d+1\equiv1\) and \(d^{2}-4d+13\equiv13\) modulo \(d\).
+
+Thus  
+
+\[
+d\mid 3(d+1)(d^{2}-4d+13)\iff d\mid 39 .
+\]
+
+Hence \(d\) must be a positive divisor of \(39\) and at least \(3\).  
+Divisors of \(39\) are \(1,3,13,39\); discarding \(1\) we obtain  
+
+\[
+d\in\{3,13,39\}.
+\]
+
+---
+
+### Recover the corresponding \(n\)
+
+\[
+n=d-2\implies n\in\{3-2,13-2,39-2\}=\{1,11,37\}.
+\]
+
+Each indeed satisfies the original condition:
+
+* \(n=1\): \(\frac{3(1+3)(1^{2}+9)}{1+2}= \frac{3\cdot4\cdot10}{3}=40\) (integer);
+* \(n=11\): \(\frac{3(11+3)(11^{2}+9)}{11+2}= \frac{3\cdot14\cdot130}{13}=420\);
+* \(n=37\): \(\frac{3(37+3)(37^{2}+9)}{37+2}= \frac{3\cdot40\cdot1378}{39}=4240\).
+
+---
+
+### Sum of all such \(n\)
+
+\[
+1+11+37 = 49.
+\]
+
+\[
+\boxed{49}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 49</p>
+<p>Extracted Answer: 49</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+The set of points in 3-dimensional coordinate space that lie in the plane $x+y+z=75$ whose coordinates satisfy the inequalities $x-yz&lt;y-zx&lt;z-xy$ forms three disjoint convex regions. Exactly one of those regions has finite area. The area of this finite region can be expressed in the form $a\sqrt{b}$, where $a$ and $b$ are positive integers and $b$ is not divisible by the square of any prime. Find $a+b$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>First write the two required inequalities using the condition \(x+y+z=75\).
+
+\[
+z=75-x-y .
+\]
+
+---
+
+### 1.  Simplify the inequalities  
+
+\[
+\begin{aligned}
+x-yz &amp;&lt;y-zx\\
+x-(y(75-x-y)) &amp;&lt; y-(x(75-x-y))\\
+\Longrightarrow (x-y)(x+y-76) &amp;&gt;0 .
+\end{aligned}
+\]
+
+\[
+\begin{aligned}
+y-zx &amp;&lt;z-xy\\
+y-x(75-x-y) &amp;&lt; (75-x-y)-xy\\
+\Longrightarrow (x+1)(x+2y-75) &amp;&lt;0 .
+\end{aligned}
+\]
+
+Hence the points \((x,y,z)\) on the plane satisfy  
+
+\[
+\boxed{(x-y)(x+y-76)&gt;0},\qquad\boxed{(x+1)(x+2y-75)&lt;0}.
+\]
+
+Both are products of two linear factors.
+
+---
+
+### 2.  Work in the \((x,y)\)-plane  
+
+The plane \(x+y+z=75\) is a linear image of the \((x,y)\)-plane via  
+
+\[
+(x,y)\mapsto (x,\;y,\;75-x-y) .
+\]
+
+The Jacobian matrix has columns \((1,0,-1)\) and \((0,1,-1)\); its Gram determinant is  
+
+\[
+\det\begin{pmatrix}2&amp;1\\1&amp;2\end{pmatrix}=3 .
+\]
+
+Thus an area element in the plane equals \(\sqrt3\) times the ordinary area
+\(dx\,dy\) in the \((x,y)\)-plane.
+
+---
+
+### 3.  Region defined by the two products  
+
+Let  
+
+\[
+L_1:\;x=-1,\qquad L_2:\;x+2y=75,
+\]
+\[
+L_3:\;x=y,\qquad L_4:\;x+y=76 .
+\]
+
+The inequalities become
+
+\[
+\begin{cases}
+x&gt;-1 \;\text{and}\; y&lt;\dfrac{75-x}{2}   &amp;\text{or } x&lt;-1 \;\text{and}\; y&gt;\dfrac{75-x}{2},\\[4pt]
+x&gt;y \;\text{and}\; x+y&gt;76               &amp;\text{or } x&lt;y \;\text{and}\; x+y&lt;76 .
+\end{cases}
+\]
+
+Only three of the four possible combinations are non‑empty:
+
+* **Region \(R_1\)** – \(x&gt;-1,\;y&lt;\frac{75-x}{2},\;x&gt;y,\;x+y&gt;76\) (unbounded).
+* **Region \(R_2\)** – \(x&gt;-1,\;y&lt;\frac{75-x}{2},\;x&lt;y,\;x+y&lt;76\) (bounded).
+* **Region \(R_3\)** – \(x&lt;-1,\;y&gt;\frac{75-x}{2},\;x&lt;y,\;x+y&lt;76\) (unbounded).
+
+Hence the set consists of three disjoint convex regions; only \(R_2\) has finite area.
+
+---
+
+### 4.  The bounded region  
+
+From the inequalities for \(R_2\)
+
+\[
+\begin{cases}
+-1&lt;x&lt;25,\\[2pt]
+x&lt;y&lt;\dfrac{75-x}{2},
+\end{cases}
+\]
+
+so \(R_2\) is the open triangle bounded by the lines  
+
+\[
+x=-1,\qquad y=x,\qquad y=\dfrac{75-x}{2}.
+\]
+
+Its vertices are  
+
+\[
+A(-1,-1),\quad B(-1,38),\quad C(25,25).
+\]
+
+The ordinary (planar) area is
+
+\[
+\frac12\cdot|AB|\cdot|AC|_{\perp}= \frac12\,(39)\,(26)=507 .
+\]
+
+---
+
+### 5.  Area on the plane \(x+y+z=75\)
+
+Multiplying by the factor \(\sqrt3\),
+
+\[
+\text{area}=507\sqrt3 .
+\]
+
+Thus \(a=507,\;b=3\) and
+
+\[
+a+b=507+3=510 .
+\]
+
+\[
+\boxed{510}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 510</p>
+<p>Extracted Answer: 510</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+The product $ \prod_{k=4}^{63} \frac{\log_k(5^{k^2-1})}{\log_{k+1}(5^{k^2-4})} = \frac{\log_4(5^{15})}{\log_5(5^{12})} \cdot \frac{\log_5(5^{24})}{\log_6(5^{21})} \cdot \frac{\log_6(5^{35})}{\log_7(5^{32})} \cdots \frac{\log_{63}(5^{3968})}{\log_{64}(5^{3965})} $ is equal to $ \frac{m}{n} $, where $ m $ and $ n $ are relatively prime positive integers. Find $ m + n $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>\[
+P=\prod_{k=4}^{63}\frac{\log_k(5^{k^2-1})}{\log_{k+1}(5^{k^2-4})}
+\]
+
+---
+
+### 1.  Simplify one factor  
+
+\[
+\log_k(5^{k^2-1})=\frac{\ln(5^{k^2-1})}{\ln k}
+            =\frac{(k^2-1)\ln5}{\ln k},
+\qquad
+\log_{k+1}(5^{k^2-4})=\frac{(k^2-4)\ln5}{\ln(k+1)}.
+\]
+
+Hence
+
+\[
+\frac{\log_k(5^{k^2-1})}{\log_{k+1}(5^{k^2-4})}
+   =\frac{k^2-1}{k^2-4}\cdot\frac{\ln(k+1)}{\ln k}.
+\]
+
+So
+
+\[
+P=\Bigl(\prod_{k=4}^{63}\frac{k^2-1}{k^2-4}\Bigr)
+   \Bigl(\prod_{k=4}^{63}\frac{\ln(k+1)}{\ln k}\Bigr).
+\]
+
+---
+
+### 2.  Telescoping the logarithm part  
+
+\[
+\prod_{k=4}^{63}\frac{\ln(k+1)}{\ln k}
+ =\frac{\ln5}{\ln4}\cdot\frac{\ln6}{\ln5}\cdots\frac{\ln64}{\ln63}
+ =\frac{\ln64}{\ln4}
+ =\log_4 64 =3 .
+\]
+
+---
+
+### 3.  Telescoping the rational part  
+
+\[
+\frac{k^2-1}{k^2-4}= \frac{(k-1)(k+1)}{(k-2)(k+2)}
+   =\frac{k-1}{k-2}\cdot\frac{k+1}{k+2}.
+\]
+
+Hence
+
+\[
+\prod_{k=4}^{63}\frac{k^2-1}{k^2-4}
+ =\Bigl(\prod_{k=4}^{63}\frac{k-1}{k-2}\Bigr)
+   \Bigl(\prod_{k=4}^{63}\frac{k+1}{k+2}\Bigr).
+\]
+
+*First product*  
+
+Let \(i=k-2\). Then \(i\) runs from \(2\) to \(61\):
+
+\[
+\prod_{k=4}^{63}\frac{k-1}{k-2}
+ =\prod_{i=2}^{61}\frac{i+1}{i}
+ =\frac{3}{2}\cdot\frac{4}{3}\cdots\frac{62}{61}
+ =\frac{62}{2}=31 .
+\]
+
+*Second product*  
+
+Let \(j=k+1\). Then \(j\) runs from \(5\) to \(64\):
+
+\[
+\prod_{k=4}^{63}\frac{k+1}{k+2}
+ =\prod_{j=5}^{64}\frac{j}{j+1}
+ =\frac{5}{6}\cdot\frac{6}{7}\cdots\frac{64}{65}
+ =\frac{5}{65}=\frac1{13}.
+\]
+
+Thus
+
+\[
+\prod_{k=4}^{63}\frac{k^2-1}{k^2-4}=31\cdot\frac1{13}=\frac{31}{13}.
+\]
+
+---
+
+### 4.  Combine the two parts  
+
+\[
+P = 3\cdot\frac{31}{13}= \frac{93}{13}.
+\]
+
+The fraction \(\frac{93}{13}\) is already in lowest terms (\(\gcd(93,13)=1\)).
+Thus \(m=93,\; n=13\) and
+
+\[
+m+n = 93+13 = 106 .
+\]
+
+\[
+\boxed{106}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 106</p>
+<p>Extracted Answer: 106</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+The 27 cells of a $3\times9$ grid are filled in using the numbers 1 through 9 so that each row contains 9 different numbers, and each of the three $3\times3$ blocks heavily outlined in the example below contains 9 different numbers, as in the first three rows of a Sudoku puzzle. 
+ | 4 | 2 | 8 | 9 | 6 | 3 | 1 | 7 | 5 | 
+ | 3 | 7 | 9 | 5 | 2 | 1 | 6 | 8 | 4 | 
+ | 5 | 6 | 1 | 8 | 4 | 7 | 9 | 2 | 3 | 
+ The number of different ways to fill such a grid can be written as $p^a\cdot q^b\cdot r^c\cdot s^d$, where $p,q,r,$ and $s$ are distinct prime numbers and $a,b,c,$ and $d$ are positive integers. Find $p\cdot a+q\cdot b+r\cdot c+s\cdot d$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>**Step 1 –  what the conditions mean**
+
+In a \(3\times 9\) grid  
+
+* each of the three rows must be a permutation of the numbers \(1,\ldots ,9\);  
+* each of the three \(3\times3\) blocks (columns \(1\!-\!3,\;4\!-\!6,\;7\!-\!9\)) must also contain the numbers \(1,\ldots ,9\) exactly once.
+
+Hence every digit appears
+
+* once in each row (3 times in total), and  
+* once in each block (also 3 times in total).
+
+So for a fixed digit \(d\) the three positions where it occurs are determined by a
+bijection between the three rows and the three blocks; i.e. a permutation
+\(\sigma_d\in S_{3}\).
+
+--------------------------------------------------------------------
+
+**Step 2 –  describing a filling by permutations**
+
+For the nine digits we obtain nine permutations  
+
+\[
+\sigma_1,\sigma_2,\dots ,\sigma_9\in S_3 .
+\]
+
+If \(\sigma_d(i)=j\) then digit \(d\) is placed in row \(i\) inside block \(j\).
+For a fixed block–row cell \((i,j)\) there are three rows of the grid, hence it
+must contain **exactly three** digits. Consequently for every cell \((i,j)\)
+
+\[
+\#\{d\mid \sigma_d(i)=j\}=3 .
+\tag{1}
+\]
+
+--------------------------------------------------------------------
+
+**Step 3 –  solving the integer system**
+
+Let  
+
+\[
+\begin{aligned}
+x_{\mathrm{id}}&amp;=\#\{\sigma_d=\text{id}\},&amp;
+x_{12}&amp;=\#\{\sigma_d=(12)\},\\
+x_{13}&amp;=\#\{\sigma_d=(13)\},&amp;
+x_{23}&amp;=\#\{\sigma_d=(23)\},\\
+x_{123}&amp;=\#\{\sigma_d=(123)\},&amp;
+x_{132}&amp;=\#\{\sigma_d=(132)\}.
+\end{aligned}
+\]
+
+Each permutation contributes a ‘1’ to three different cells; each cell is covered
+by exactly two permutations. From (1) we obtain nine equations, e.g.
+
+\[
+x_{\mathrm{id}}+x_{23}=3,\qquad
+x_{12}+x_{123}=3,\qquad\ldots
+\]
+
+Solving them gives
+
+\[
+x_{12}=x_{13}=x_{23}=k,\qquad
+x_{\mathrm{id}}=x_{123}=x_{132}=3-k,
+\]
+
+where \(k\in\{0,1,2,3\}\).
+
+--------------------------------------------------------------------
+
+**Step 4 –  assigning the permutations to the nine distinct digits**
+
+For a fixed \(k\) the number of ways to give the nine digits the required
+multiplicities is the multinomial coefficient
+
+\[
+\frac{9!}{k!^{\,3}\,(3-k)!^{\,3}} .
+\]
+
+Summing over the four possible values of \(k\) gives
+
+\[
+N=\sum_{k=0}^{3}\frac{9!}{k!^{\,3}(3-k)!^{\,3}}
+   =2\cdot\frac{9!}{3!^{\,3}}+2\cdot\frac{9!}{1!^{\,3}2!^{\,3}}
+   =1680+45360+45360+1680=94\,080 .
+\]
+
+Thus there are \(94\,080\) ways to decide, for every digit, in which block of
+each row it will appear.
+
+--------------------------------------------------------------------
+
+**Step 5 –  placing the digits inside the blocks**
+
+Fix a block \(j\).  
+Row \(i\) contributes exactly three distinct digits to this block; they can be
+arranged in the three columns of the block in \(3! = 6\) ways, independently for
+the three rows. Hence a block can be filled in \((3!)^{3}=6^{3}=216\) ways.
+
+The three blocks are independent, so the column‑ordering factor is
+
+\[
+(3!)^{9}=6^{9}=10\,077\,696 .
+\]
+
+--------------------------------------------------------------------
+
+**Step 6 –  total number of fillings**
+
+\[
+\boxed{T = N\cdot (3!)^{9}=94\,080\cdot 10\,077\,696
+      = 948\,109\,639\,680 }.
+\]
+
+Factorising,
+
+\[
+T = 2^{16}\cdot 3^{10}\cdot 5\cdot 7^{2}.
+\]
+
+--------------------------------------------------------------------
+
+**Step 7 –  computing the required sum**
+
+Take \(p=2,\;q=3,\;r=5,\;s=7\) with exponents
+\(a=16,\;b=10,\;c=1,\;d=2\). Then
+
+\[
+p\!a+q\!b+r\!c+s\!d
+=2\cdot16+3\cdot10+5\cdot1+7\cdot2
+=32+30+5+14=81 .
+\]
+
+\[
+\boxed{81}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 81</p>
+<p>Extracted Answer: 81</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+There are exactly three positive real numbers $ k $ such that the function
+$ f(x) = \frac{(x - 18)(x - 72)(x - 98)(x - k)}{x} $
+defined over the positive real numbers achieves its minimum value at exactly two positive real numbers $ x $. Find the sum of these three values of $ k $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>**Solution Overview**
+
+For  
+
+\[
+f(x)=\frac{(x-18)(x-72)(x-98)(x-k)}{x},\qquad x&gt;0,
+\]
+
+let  
+
+\[
+N(x)=(x-18)(x-72)(x-98)(x-k)=x^4-S_1x^3+S_2x^2-S_3x+S_4,
+\]
+
+where  
+
+\[
+\begin{aligned}
+S_1&amp;=18+72+98+k=188+k,\\[2pt]
+S_2&amp;=18\cdot72+18\cdot98+72\cdot98+ k(18+72+98)=10116+188k,\\[2pt]
+S_4&amp;=18\cdot72\cdot98\cdot k=127008\,k .
+\end{aligned}
+\]
+
+Then  
+
+\[
+f(x)=\frac{N(x)}{x}=x^{3}-S_1x^{2}+S_2x-S_3+\frac{S_4}{x},
+\]
+
+and  
+
+\[
+f&#39;(x)=\frac{3x^{4}-2S_1x^{3}+S_2x^{2}-S_4}{x^{2}} .
+\]
+
+Hence the critical points are the (positive) roots of  
+
+\[
+P(x)=3x^{4}-2S_1x^{3}+S_2x^{2}-S_4=0\tag{1}
+\]
+
+(the denominator $x^{2}&gt;0$ for $x&gt;0$).
+
+Because $f(x)\to +\infty$ as $x\to0^{+}$ and as $x\to\infty$, the graph must
+first decrease, then increase, then decrease, and finally increase again.
+Thus (1) has three positive roots:
+
+* $x_1$ – a local **minimum** in the first negative interval,
+* $x_2$ – a local **maximum** in the positive interval,
+* $x_3$ – a second local **minimum** in the last negative interval.
+
+The global minimum is achieved at the lower of the two minima.
+For the minimum to be attained **exactly at two points** we need  
+
+\[
+f(x_1)=f(x_3)\qquad(\text{the two minima have the same value}).
+\tag{2}
+\]
+
+--------------------------------------------------------------------
+### 1.  Translating the condition
+
+At a critical point $x$ we have $f&#39;(x)=0$, i.e. $P(x)=0$.
+From $f(x)=\dfrac{N(x)}{x}$ and $P(x)=0$ it follows that  
+
+\[
+f(x)=\frac{N(x)}{x}=N&#39;(x)\qquad\text{for any critical point}.
+\tag{3}
+\]
+
+Thus (2) is equivalent to  
+
+\[
+N&#39;(x_1)=N&#39;(x_3).\tag{4}
+\]
+
+Writing $x_1+ x_3=s$ and $x_1x_3=p$, the two equations $P(x_1)=P(x_3)=0$
+give after elimination  
+
+\[
+\begin{cases}
+4(s^{2}-p)-3S_1s+2S_2=0,\\[2pt]
+3(s^{3}-2ps)-2S_1(s^{2}-p)+S_2s=0.
+\end{cases}\tag{5}
+\]
+
+Equation (5) yields  
+
+\[
+(2s-S_1)\Bigl(3s(s-S_1)+2S_2\Bigr)=0 .
+\]
+
+Hence either  
+
+\[
+\boxed{s=\dfrac{S_1}{2}} \qquad\text{or}\qquad
+3s^{2}-3S_1s+2S_2=0. \tag{6}
+\]
+
+--------------------------------------------------------------------
+### 2.  The case $s=S_1/2$
+
+From the first possibility in (6) we obtain  
+
+\[
+p=\frac{4S_2-S_1^{2}}{8}.
+\]
+
+Using $x_1x_2=p$ and $x_1+x_2=S_1/2$ the two minima are  
+
+\[
+x_{1,3}= \frac{S_1\pm 2\sqrt{\,\Delta\,}}{4},
+\qquad 
+\Delta=\frac34k^{2}-94k+6276 .
+\]
+
+Now we must also satisfy $P(x_1)=0$, which after substitution gives
+
+\[
+(S_1^{2}-4S_2)^{2}=64S_4 .
+\]
+
+With the explicit expressions for $S_1,S_2,S_4$ this becomes
+
+\[
+(k^{2}-376k-5120)^{2}=8128512\,k,
+\]
+
+or  
+
+\[
+k^{4}-752k^{3}+131136k^{2}-4278272k+26214400=0.
+\tag{7}
+\]
+
+Factoring (7) gives  
+
+\[
+(k-8)(k-32)(k-200)(k-512)=0 .
+\]
+
+For a root to be admissible we need the two minima to lie in the
+two negative intervals of $f$.  
+The left minimum equals  
+
+\[
+x_1=\frac{k+188-2\sqrt{\Delta}}{4},
+\]
+
+which is **positive** only when  
+
+\[
+k^{2}-376k-5120&lt;0\qquad\Longleftrightarrow\qquad k&lt;389\ldots .
+\]
+
+Thus $k=512$ is rejected, while $k=8,\,32,\,200$ are valid.
+
+--------------------------------------------------------------------
+### 3.  The second possibility in (6)
+
+The alternative equation $3s^{2}-3S_1s+2S_2=0$ together with the condition
+$P(x_1)=0$ leads, after a completely analogous elimination, to the same
+quartic (7).  Its admissible positive solutions are again $8,32,200$,
+so no new $k$ appear.
+
+--------------------------------------------------------------------
+### 4.  Conclusion
+
+The function $f$ has its global minimum attained at exactly two positive
+points precisely for  
+
+\[
+k\in\{8,\;32,\;200\}.
+\]
+
+Therefore the required sum is  
+
+\[
+8+32+200 = \boxed{240}.
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 240</p>
+<p>Extracted Answer: 240</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Four unit squares form a $2 \times 2$ grid. Each of the 12 unit line segments forming the sides of the squares is colored either red or blue in such a way that each unit square has 2 red sides and 2 blue sides. Find the number of such colorings.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let the four unit squares be  
+
+\[
+\begin{array}{cc}
+A&amp; B\\
+C&amp; D
+\end{array}
+\]
+
+and denote by  
+
+* \(a=h_{0,1}\)   – the middle horizontal segment between \(A\) and \(C\);  
+* \(b=h_{1,1}\)   – the middle horizontal segment between \(B\) and \(D\);  
+* \(c=v_{1,0}\)   – the middle vertical segment between \(A\) and \(B\);  
+* \(d=v_{1,1}\)   – the middle vertical segment between \(C\) and \(D\).
+
+The eight outer unit‑segments are written as  
+
+\[
+\begin{aligned}
+&amp;e_1=h_{0,0},\qquad e_2=v_{0,0},\\
+&amp;e_3=v_{2,0},\qquad e_4=h_{1,0},\\
+&amp;e_5=h_{0,2},\qquad e_6=v_{0,1},\\
+&amp;e_7=v_{2,1},\qquad e_8=h_{1,2}.
+\end{aligned}
+\]
+
+All variables take the value 1 for a red side and 0 for a blue side.
+
+--------------------------------------------------------------------
+### 1.  Equations for the squares  
+
+Each unit square must have exactly two red sides, so we obtain
+
+\[
+\begin{aligned}
+A:&amp;\;e_1+e_2+a+c=2, \\
+B:&amp;\;e_3+e_4+b+c=2, \\
+C:&amp;\;e_5+e_6+a+d=2, \\
+D:&amp;\;e_7+e_8+b+d=2 .\qquad (1)
+\end{aligned}
+\]
+
+--------------------------------------------------------------------
+### 2.  Fix the interior edges  
+
+The four interior edges \(a,b,c,d\) are independent; there are \(2^4=16\) possible
+choices.
+For a fixed quadruple \((a,b,c,d)\) the right‑hand side of each equation in (1)
+becomes  
+
+\[
+s_A=2-(a+c),\; s_B=2-(b+c),\; s_C=2-(a+d),\; s_D=2-(b+d).
+\]
+
+The numbers \(s_A,s_B,s_C,s_D\) are the required sums of the two
+outer edges belonging to each square.
+
+*If \(s_i=0\) or \(s_i=2\):* the two outer edges are forced to be
+\((0,0)\) or \((1,1)\) – exactly **one** possibility.
+
+*If \(s_i=1\):* the outer edges must be \((0,1)\) or \((1,0)\) – **two**
+possibilities.
+
+Hence, for a given \((a,b,c,d)\) the number of admissible colourings of the
+outer edges equals  
+
+\[
+2^{\,N},\qquad N=\#\{i\in\{A,B,C,D\}:s_i=1\}.
+\]
+
+But \(s_i=1\) occurs precisely when the two interior edges of that square sum to
+\(1\); i.e.
+
+\[
+N=[a\neq c]+[b\neq c]+[a\neq d]+[b\neq d],\tag{2}
+\]
+
+where \([P]=1\) if the statement \(P\) is true and \(0\) otherwise.
+
+--------------------------------------------------------------------
+### 3.  Summing over the interior edges  
+
+Write the sum we need as  
+
+\[
+\sum_{a,b,c,d\in\{0,1\}} 2^{[a\neq c]+[b\neq c]+[a\neq d]+[b\neq d]}.
+\]
+
+For fixed \(a,b\) the contributions of \(c\) and \(d\) factor:
+
+\[
+\bigl(\sum_{c\in\{0,1\}}2^{[a\neq c]+[b\neq c]}\bigr)^2 .
+\]
+
+Now compute the inner sum.
+
+*If \(a=b\) (either \((0,0)\) or \((1,1)\)):  
+
+\[
+c=0\!:\;[a\neq c]+[b\neq c]=0,\qquad
+c=1\!:\;[a\neq c]+[b\neq c]=2,
+\]
+so the sum equals \(2^{0}+2^{2}=1+4=5\).
+
+*If \(a\neq b\) (either \((0,1)\) or \((1,0)\)):  
+
+\[
+c=0\!:\;[a\neq c]+[b\neq c]=1,\qquad
+c=1\!:\;[a\neq c]+[b\neq c]=1,
+\]
+so the sum equals \(2^{1}+2^{1}=2+2=4\).
+
+Thus
+
+\[
+\begin{aligned}
+\text{total}&amp;=
+2\bigl(5^2\bigr)+2\bigl(4^2\bigr)        \\
+&amp;=2\cdot25+2\cdot16\\
+&amp;=50+32\\
+&amp;=82 .
+\end{aligned}
+\]
+
+--------------------------------------------------------------------
+### 4.  Answer  
+
+There are  
+
+\[
+\boxed{82}
+\]
+
+different colourings of the twelve unit segments such that each of the four
+unit squares has exactly two red sides and two blue sides.</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 82</p>
+<p>Extracted Answer: 82</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Circle $\omega_1$ with radius 6 centered at point $A$ is internally tangent at point $B$ to circle $\omega_2$ with radius 15. Points $C$ and $D$ lie on $\omega_2$ such that $\overline{BC}$ is a diameter of $\omega_2$ and $\overline{BC} \perp \overline{AD}$. The rectangle $EFGH$ is inscribed in $\omega_1$ such that $\overline{EF} \perp \overline{BC}$, $C$ is closer to $\overline{GH}$ than to $\overline{EF}$, and $D$ is closer to $\overline{FG}$ than to $\overline{EH}$, as shown. Triangles $\triangle DGF$ and $\triangle CHG$ have equal areas. The area of rectangle $EFGH$ is $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m + n$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+* \(O\) be the centre of \(\omega _2\) (radius \(15\)),
+* \(A\) be the centre of \(\omega _1\) (radius \(6\)),
+* \(B\) the internal point of tangency.
+
+Place \(O\) at the origin and take the diameter \(BC\) on the \(x\)-axis.
+
+\[
+O=(0,0),\qquad B=(15,0)
+\]
+
+Because \(\omega_1\) is tangent internally at \(B\),
+
+\[
+OA=15-6=9\qquad\Longrightarrow\qquad A=(9,0).
+\]
+
+Since \(BC\) is a diameter of \(\omega _2\),
+
+\[
+C=(-15,0).
+\]
+
+\(AD\perp BC\) forces \(AD\) to be vertical through \(A\); intersecting this line with \(\omega _2\),
+
+\[
+x=9,\qquad x^{2}+y^{2}=225\Longrightarrow y=\pm 12 .
+\]
+
+Because the problem states that \(D\) is nearer to the side \(FG\) than to \(EH\), we take the point above the \(x\)-axis:
+
+\[
+D=(9,12).
+\]
+
+---------------------------------------------------------------------
+
+### 1.  The rectangle \(EFGH\)
+
+\(EF\perp BC\); with \(BC\) horizontal this makes \(EF\) vertical, so the rectangle is axis‑aligned.
+Let its half–width be \(d&gt;0\) and its half–height be \(h&gt;0\).  
+Since the rectangle is inscribed in \(\omega _1\) (centre \(A\)), its centre must coincide with \(A\).  
+Thus the vertices are  
+
+\[
+\begin{aligned}
+E&amp;=(9+d,\,-h),  &amp;F&amp;=(9+d,\,h),\\
+G&amp;=(9-d,\,h),   &amp;H&amp;=(9-d,\,-h).
+\end{aligned}
+\]
+
+Each vertex lies on \(\omega _1\):  
+
+\[
+(x-9)^2+y^2=6^2\quad\Longrightarrow\quad d^{\,2}+h^{\,2}=36. \tag{1}
+\]
+
+---------------------------------------------------------------------
+
+### 2.  Equality of the two triangle areas
+
+*Triangle \(DGF\)*  
+Its base \(GF\) is horizontal with length \(2d\); the height is the vertical distance from \(D\) to the line \(y=h\):
+\[
+[\,DGF\,]=\frac12\cdot (2d)\bigl(12-h\bigr)=d(12-h).
+\]
+
+*Triangle \(CHG\)*  
+Its base \(GH\) is vertical with length \(2h\); the height is the horizontal distance from \(C\) to the line \(x=9-d\):
+\[
+[\,CHG\,]=\frac12\cdot (2h)\bigl( (9-d)-(-15)\bigr)=h(24-d).
+\]
+
+The condition \([DGF]=[CHG]\) gives  
+
+\[
+d(12-h)=h(24-d)\;\Longrightarrow\;12d=24h\;\Longrightarrow\;d=2h. \tag{2}
+\]
+
+---------------------------------------------------------------------
+
+### 3.  Solving for \(d\) and \(h\)
+
+Substituting \(d=2h\) into (1):
+
+\[
+(2h)^2+h^{2}=36\quad\Longrightarrow\quad5h^{2}=36
+\quad\Longrightarrow\quad h^{2}=\frac{36}{5},\qquad 
+h=\frac{6}{\sqrt5},\qquad d=2h=\frac{12}{\sqrt5}.
+\]
+
+---------------------------------------------------------------------
+
+### 4.  Area of the rectangle
+
+\[
+\text{Area}= (2d)(2h)=4dh=4(2h)h=8h^{2}=8\cdot\frac{36}{5}
+=\frac{288}{5}.
+\]
+
+Thus the area equals \(\dfrac{m}{n}\) with \(m=288,\;n=5\) (coprime).  
+
+\[
+m+n=288+5=293.
+\]
+
+\[
+\boxed{293}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 293</p>
+<p>Extracted Answer: 293</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $ A $ be the set of positive integer divisors of 2025. Let $ B $ be a randomly selected subset of $ A $. The probability that $ B $ is a nonempty set with the property that the least common multiple of its elements is 2025 is $ \frac{m}{n} $, where $ m $ and $ n $ are relatively prime positive integers. Find $ m + n $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Factor  
+
+\[
+2025=3^{4}\cdot5^{2}.
+\]
+
+A divisor of \(2025\) has the form \(3^{a}5^{b}\) with \(0\le a\le4,\ 0\le b\le2\).  
+Hence  
+
+\[
+|A|=(4+1)(2+1)=15,
+\qquad\text{total subsets}=2^{15}=32768 .
+\]
+
+---
+
+### When does a subset have lcm \(=2025\)?
+
+The lcm of a set of divisors is \(3^{\max a}\cdot5^{\max b}\).  
+Thus the lcm equals \(2025=3^{4}\cdot5^{2}\) **iff**
+
+* at least one element has exponent \(a=4\) (a divisor containing \(3^{4}\));
+* at least one element has exponent \(b=2\) (a divisor containing \(5^{2}\)).
+
+---
+
+### Counting the desired subsets  
+
+Divisors with \(a=4\): \(3^{4}5^{b}\ (b=0,1,2)\) – 3 of them.  
+Divisors with \(b=2\): \(3^{a}5^{2}\ (a=0,\dots ,4)\) – 5 of them.  
+
+Let  
+
+* \(X\) = subsets containing **no** divisor with \(a=4\);  
+* \(Y\) = subsets containing **no** divisor with \(b=2\).
+
+\[
+|X|=2^{12}\quad (\text{choose any of the other }12\text{ divisors}),\qquad
+|Y|=2^{10}\quad (\text{choose any of the other }10\text{ divisors}).
+\]
+
+Divisors lacking both \(a=4\) and \(b=2\) have \(a\le3,\ b\le1\); there are \(4\cdot2=8\) of them, so
+
+\[
+|X\cap Y|=2^{8}.
+\]
+
+Using inclusion–exclusion, the number of subsets that contain **both** an \(a=4\) divisor and a \(b=2\) divisor is  
+
+\[
+N = 2^{15} - 2^{12} - 2^{10} + 2^{8}
+    = 32768 - 4096 - 1024 + 256
+    = 27904 .
+\]
+
+These subsets are precisely the non‑empty subsets whose lcm equals \(2025\); the empty set is automatically excluded by the inclusion–exclusion count.
+
+---
+
+### Probability
+
+\[
+\text{Probability} = \frac{N}{2^{15}} = \frac{27904}{32768}
+                     = \frac{2^{8}\cdot 109}{2^{15}}
+                     = \frac{109}{128}.
+\]
+
+The fraction \(\frac{109}{128}\) is already in lowest terms, so  
+
+\[
+m=109,\qquad n=128,\qquad m+n=237.
+\]
+
+\[
+\boxed{237}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 237</p>
+<p>Extracted Answer: 237</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Sixteen chairs are arranged in a row. Eight people each select a chair in which to sit so that no person sits next to two other people. Let $ N $ be the number of subsets of 16 chairs that could be selected. Find the remainder when $ N $ is divided by 1000.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+\[
+\text{chairs}=1,2,\dots ,16,\qquad 8\ \text{people sit in 8 of them.}
+\]
+
+The condition *no person sits next to two other people* means that no three
+occupied chairs are consecutive.  
+Hence we must count binary strings of length \(16\) with exactly eight 1’s
+and no substring \(111\).
+
+---
+
+### 1.  Blocks of occupied chairs  
+
+Occupied chairs appear in blocks of length \(1\) or \(2\) (a block of length
+\(3\) would give a person with two neighbours).  
+
+Let  
+
+* \(t\) = number of blocks of length \(2\);
+* \(s\) = number of blocks of length \(1\).
+
+Then  
+
+\[
+s+2t=8,\qquad r=s+t \text{ (total number of blocks)} .
+\]
+
+Hence  
+
+\[
+t=0,1,2,3,4,\qquad r=8-t\;(=8,7,6,5,4).
+\]
+
+For a fixed \(t\) (hence fixed \(r\)) we must choose which of the \(r\) blocks
+are the double ones:
+
+\[
+\text{ways to choose the double blocks}= \binom{r}{t}= \binom{r}{8-r}.
+\]
+
+---
+
+### 2.  Placing the blocks among the empty chairs  
+
+There are \(16-8=8\) empty chairs.  
+Between the \(r\) blocks there must be at least one empty chair, using
+\(r-1\) chairs.  
+
+The remaining empty chairs are  
+
+\[
+8-(r-1)=9-r .
+\]
+
+These \(9-r\) chairs can be placed arbitrarily in the \(r+1\) gaps
+(before the first block, between successive blocks, after the last block).  
+By stars‑and‑bars the number of ways is  
+
+\[
+\binom{(9-r)+(r+1)-1}{(r+1)-1}= \binom{9}{r}.
+\]
+
+---
+
+### 3.  Total number of admissible subsets  
+
+\[
+\begin{aligned}
+N&amp;=\sum_{t=0}^{4} \binom{r}{t}\binom{9}{r},
+\qquad r=8-t \\
+  &amp;=\sum_{r=4}^{8}\binom{r}{\,8-r\,}\binom{9}{r}.
+\end{aligned}
+\]
+
+Compute each term:
+
+\[
+\begin{array}{c|c|c|c}
+r &amp; \binom{r}{8-r} &amp; \binom{9}{r} &amp; \text{product}\\ \hline
+8 &amp; 1 &amp; 9   &amp; 9\\
+7 &amp; 7 &amp; 36  &amp; 252\\
+6 &amp; 15&amp; 84  &amp; 1260\\
+5 &amp; 10&amp; 126 &amp; 1260\\
+4 &amp; 1 &amp; 126 &amp; 126
+\end{array}
+\]
+
+Adding them,
+
+\[
+N = 9+252+1260+1260+126 = 2907.
+\]
+
+---
+
+### 4.  Remainder modulo \(1000\)
+
+\[
+2907 \equiv 907 \pmod{1000}.
+\]
+
+\[
+\boxed{907}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 907</p>
+<p>Extracted Answer: 907</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+There are $ n $ values of $ x $ in the interval $ 0 &lt; x &lt; 2\pi $ where $ f(x) = \sin(7\pi \cdot \sin(5x)) = 0 $. For $ t $ of these $ n $ values of $ x $, the graph of $ y = f(x) $ is tangent to the $ x $-axis. Find $ n + t $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>To solve  
+
+\[
+f(x)=\sin \bigl(7\pi \,\sin(5x)\bigr)=0 ,\qquad 0&lt;x&lt;2\pi 
+\]
+
+let  
+
+\[
+g(x)=7\pi\sin(5x).
+\]
+
+Then  
+
+\[
+f(x)=\sin(g(x))=0\iff g(x)=k\pi,\;k\in\mathbb Z .
+\]
+
+Hence  
+
+\[
+7\pi\sin(5x)=k\pi\Longrightarrow \sin(5x)=\frac{k}{7}.
+\]
+
+Because \(|\sin(5x)|\le 1\), the integer \(k\) can be  
+\(-7\le k\le 7\).
+
+---
+
+### 1. Counting the zeros (\(n\))
+
+Put \(y=5x\).  
+When \(x\) runs from \(0\) to \(2\pi\), \(y\) runs from \(0\) to \(10\pi\).
+
+For a fixed value \(c=\frac{k}{7}\) we count the solutions of \(\sin y=c\) in the interval \((0,10\pi)\).
+
+* **\(c=0\) \;(i.e. \(k=0\)):**  
+  \(\sin y=0\) ⇒ \(y=m\pi\).  
+  In \((0,10\pi)\) we have \(m=1,2,\dots ,9\) → **9 solutions**.
+
+* **\(c=\pm1\) \;(i.e. \(k=\pm7\)):**  
+  \(\sin y=1\) gives \(y=\frac{\pi}{2}+2\pi n\)  
+  \(\sin y=-1\) gives \(y=\frac{3\pi}{2}+2\pi n\).  
+  For \(n=0,1,2,3,4\) each set yields 5 points → **5+5 = 10 solutions**.
+
+* **\(c\) with \(|c|&lt;1\) and \(c\neq0\) \;(i.e. \(k=\pm1,\dots ,\pm6\)):**  
+  For any such \(c\) there are two solutions per period of sine.  
+  The interval \((0,10\pi)\) contains five full periods, so we obtain **\(5\times2=10\) solutions** for each such \(k\).
+
+Now sum:
+
+\[
+\begin{aligned}
+n &amp; =\underbrace{9}_{k=0}
+   +\underbrace{12\times10}_{k=\pm1,\dots ,\pm6}
+   +\underbrace{10}_{k=\pm7}\\[2mm]
+  &amp; = 9+120+10 = 139 .
+\end{aligned}
+\]
+
+Thus **\(n=139\)**.
+
+---
+
+### 2. When is the graph tangent to the \(x\)-axis? (\(t\))
+
+The graph is tangent at a zero when the derivative also vanishes:
+
+\[
+f&#39;(x)=\cos\bigl(7\pi\sin(5x)\bigr)\cdot 35\pi\cos(5x)=0 .
+\]
+
+At the zeros we already have \(\sin(7\pi\sin(5x))=0\), i.e. \(7\pi\sin(5x)=k\pi\).  
+Hence \(\cos\bigl(7\pi\sin(5x)\bigr)=\cos(k\pi)=(-1)^k\neq0\).
+
+Consequently \(f&#39;(x)=0\) can only occur through \(\cos(5x)=0\).
+
+\[
+\cos(5x)=0 \Longrightarrow 5x=\frac{\pi}{2}+m\pi
+            \Longrightarrow x=\frac{(2m+1)\pi}{10},\qquad m\in\mathbb Z .
+\]
+
+Within \(0&lt;x&lt;2\pi\) we have \(m=0,1,\dots ,9\), giving **10 distinct \(x\)** values.
+
+At each of these points \(\sin(5x)=\pm1\), so \(\sin(7\pi\sin(5x))=\sin(\pm7\pi)=0\); thus they are indeed zeros, and because the derivative also vanishes the graph is tangent there.
+
+Hence **\(t=10\)**.
+
+---
+
+### 3. Required sum
+
+\[
+n+t = 139 + 10 = 149 .
+\]
+
+\[
+\boxed{149}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 149</p>
+<p>Extracted Answer: 149</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $N$ denote the number of ordered triples of positive integers $(a,b,c)$ such that $a,b,c\leq3^6$ and $a^3+b^3+c^3$ is a multiple of $3^7$. Find the remainder when $N$ is divided by $1000$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>**Answer:** \(\boxed{637}\)</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 735</p>
+<p>Extracted Answer: 637</p>
+<p>Score: 0.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $ A_1A_2 \ldots A_{11} $ be an 11-sided non-convex simple polygon with the following properties:
+* The area of $ A_iA_1A_{i+1} $ is 1 for each $ 2 \leq i \leq 10 $,
+* $ \cos(\angle A_iA_1A_{i+1}) = \frac{12}{13} $ for each $ 2 \leq i \leq 10 $,
+* The perimeter of $ A_1A_2 \ldots A_{11} $ is 20.
+If $ A_1A_2 + A_1A_{11} $ can be expressed as $ \frac{m\sqrt{n} - p}{q} $ for positive integers $ m, n, p, q $ with $ n $ squarefree and no prime divides all of $ m, p, q$, find $ m + n + p + q $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+\[
+x_i=A_1A_i\qquad (i=2,3,\ldots ,11),\qquad 
+\theta=\angle A_iA_1A_{i+1}\;(2\le i\le10).
+\]
+
+---
+
+### 1.  Using the area condition  
+
+\[
+\text{Area}\bigl(A_iA_1A_{i+1}\bigr)=\frac12 x_i x_{i+1}\sin\theta =1 .
+\]
+
+Because \(\cos\theta=\dfrac{12}{13}\),
+
+\[
+\sin\theta=\sqrt{1-\Bigl(\frac{12}{13}\Bigr)^2}= \frac{5}{13}.
+\]
+
+Thus  
+
+\[
+\frac12 x_i x_{i+1}\cdot\frac{5}{13}=1
+\Longrightarrow x_i x_{i+1}=\frac{26}{5}\qquad (2\le i\le10).
+\tag{1}
+\]
+
+Denote \(c=\dfrac{26}{5}\).  From (1) we have  
+
+\[
+x_{i+1}= \frac{c}{x_i}.
+\]
+
+Consequently  
+
+\[
+x_{i+2}=x_i\qquad\Longrightarrow\qquad
+\begin{cases}
+x_{2}=x_{4}=x_{6}=x_{8}=x_{10}=a,\\[2pt]
+x_{3}=x_{5}=x_{7}=x_{9}=x_{11}=b,
+\end{cases}
+\]
+
+with  
+
+\[
+ab=c=\frac{26}{5}. \tag{2}
+\]
+
+So the distances from \(A_1\) alternate between two values \(a\) and \(b\).
+
+---
+
+### 2.  Length of each side \(A_iA_{i+1}\;(2\le i\le10)\)
+
+In \(\triangle A_iA_1A_{i+1}\) the side opposite \(\theta\) is \(A_iA_{i+1}\).
+By the law of cosines
+
+\[
+A_iA_{i+1}^2 = x_i^2+x_{i+1}^2-2x_ix_{i+1}\cos\theta .
+\]
+
+Because \(x_i\) and \(x_{i+1}\) are always one \(a\) and one \(b\),
+
+\[
+A_iA_{i+1}^2 = a^2+b^2-2ab\cdot\frac{12}{13}.
+\]
+
+Hence all nine sides \(A_iA_{i+1}\;(i=2,\dots ,10)\) have the same length; denote
+
+\[
+d^2=a^2+b^2-\frac{24}{13}ab.
+\tag{3}
+\]
+
+Write \(s=a+b\).  Using \(ab=c\),
+
+\[
+a^2+b^2=s^2-2ab=s^2-2c .
+\]
+
+Substituting into (3),
+
+\[
+d^2=s^2-2c-\frac{24}{13}c
+    =s^2-c\Bigl(2+\frac{24}{13}\Bigr)
+    =s^2-\frac{50}{13}c.
+\]
+
+Since \(c=\dfrac{26}{5}\),
+
+\[
+d^2=s^2-\frac{50}{13}\cdot\frac{26}{5}=s^2-20,
+\qquad\text{so}\qquad d=\sqrt{s^{2}-20}.
+\tag{4}
+\]
+
+---
+
+### 3.  Use the perimeter
+
+The polygon has \(11\) sides: the two incident to \(A_1\) of lengths \(a\) and \(b\), and the nine equal sides of length \(d\).  
+Given perimeter \(20\),
+
+\[
+a+b+9d=s+9\sqrt{s^{2}-20}=20.
+\tag{5}
+\]
+
+Solve (5) for \(s\).
+
+\[
+9\sqrt{s^{2}-20}=20-s\;(s\le20).
+\]
+
+Square:
+
+\[
+81(s^{2}-20)=(20-s)^{2}
+\Longrightarrow 80s^{2}+40s-2020=0
+\Longrightarrow 4s^{2}+2s-101=0.
+\]
+
+Hence
+
+\[
+s=\frac{-2\pm\sqrt{4+1616}}{8}
+   =\frac{-2\pm18\sqrt5}{8}
+   =\frac{-1\pm9\sqrt5}{4}.
+\]
+
+Only the positive root is admissible:
+
+\[
+\boxed{s=\frac{9\sqrt5-1}{4}}.
+\]
+
+Thus  
+
+\[
+A_1A_2+A_1A_{11}=a+b=s=\frac{9\sqrt5-1}{4}
+      =\frac{m\sqrt n-p}{q},
+\]
+
+with \(m=9,\;n=5,\;p=1,\;q=4\).
+
+---
+
+### 4.  Required sum
+
+\[
+m+n+p+q=9+5+1+4=19.
+\]
+
+\[
+\boxed{19}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 19</p>
+<p>Extracted Answer: 19</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+From an unlimited supply of 1-cent coins, 10-cent coins, and 25-cent coins, Silas wants to find a collection of coins that has a total value of $ N $ cents, where $ N $ is a positive integer. He uses the so-called **greedy algorithm**, successively choosing the coin of greatest value that does not cause the value of his collection to exceed $ N $. For example, to get 42 cents, Silas will choose a 25-cent coin, then a 10-cent coin, then 7 1-cent coins. However, this collection of 9 coins uses more coins than necessary to get a total of 42 cents; indeed, choosing 4 10-cent coins and 2 1-cent coins achieves the same total value with only 6 coins.
+
+In general, the greedy algorithm succeeds for a given $ N $ if no other collection of 1-cent, 10-cent, and 25-cent coins gives a total value of $ N $ cents using strictly fewer coins than the collection given by the greedy algorithm. Find the number of values of $ N $ between 1 and 1000 inclusive for which the greedy algorithm succeeds.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>**Greedy representation**
+
+For a value \(N\) let  
+
+\[
+q=\Big\lfloor\frac{N}{25}\Big\rfloor ,\qquad 
+r=N-25q\;(0\le r\le 24).
+\]
+
+After taking \(q\) quarters the greedy algorithm uses  
+
+\[
+a=\Big\lfloor\frac{r}{10}\Big\rfloor ,\qquad 
+b=r-10a\;(0\le b\le 9)
+\]
+
+dimes and ones.  
+Thus the greedy collection contains  
+
+\[
+G(N)=q+a+b
+\]
+
+coins.
+
+--------------------------------------------------------------------
+
+**When can a better collection exist?**
+
+Let a different collection use \(x\) quarters and \(y\) dimes
+(\(z\) pennies fill the rest).  
+Its total number of coins is  
+
+\[
+C=x+y+z = x+y+(N-25x-10y)=N-(24x+9y).
+\]
+
+Hence a representation is better than the greedy one iff it makes the
+“saving”
+
+\[
+S=24x+9y
+\]
+
+larger than the greedy saving \(S_G = 24q+9a\).
+
+Suppose we start from the greedy solution and **remove** \(d\ge1\) quarters
+(\(d\le q\)).  
+The value we free is \(25d\).
+With this extra value we can add as many dimes as possible:
+
+\[
+y&#39; = a+\Big\lfloor\frac{r+25d}{10}\Big\rfloor
+      = a+\Big\lfloor 2.5d+\frac{b}{10}\Big\rfloor .
+\]
+
+The new saving is  
+
+\[
+S&#39;=24(q-d)+9y&#39;
+   =24q+9a +\bigl[-24d+9\big\lfloor2.5d+\tfrac{b}{10}\big\rfloor\bigr].
+\]
+
+Thus the new collection beats the greedy one precisely when  
+
+\[
+-24d+9\Big\lfloor2.5d+\frac{b}{10}\Big\rfloor &gt;0
+\qquad\Longleftrightarrow\qquad
+\Big\lfloor2.5d+\frac{b}{10}\Big\rfloor \ge
+\Big\lfloor\frac{8}{3}d\Big\rfloor+1 .\tag{1}
+\]
+
+--------------------------------------------------------------------
+
+**Only one quarter can ever help**
+
+For even \(d\) we have \(\big\lfloor2.5d\big\rfloor =2.5d\) and
+\(\big\lfloor\frac{8}{3}d\big\rfloor =2.5d+\big\lfloor\frac{d}{6}\big\rfloor\).
+Hence the left–hand side of (1) never exceeds the right–hand side,
+so even \(d\) never improves the greedy solution.
+
+For odd \(d=2k+1\) we obtain  
+
+\[
+\Big\lfloor2.5d+\frac{b}{10}\Big\rfloor
+   =5k+2+{\bf 1}_{\{b\ge5\}},\qquad
+\Big\lfloor\frac{8}{3}d\Big\rfloor
+   =5k+2+\Big\lfloor\frac{k+2}{3}\Big\rfloor .
+\]
+
+Consequently  
+
+\[
+\Big\lfloor2.5d+\frac{b}{10}\Big\rfloor-
+\Big\lfloor\frac{8}{3}d\Big\rfloor
+= {\bf 1}_{\{b\ge5\}}-\Big\lfloor\frac{k+2}{3}\Big\rfloor .
+\]
+
+The right‑hand side is \(\ge 1\) only when \(k=0\) (that is, \(d=1\))
+and \(b\ge5\).
+Thus the **only** way to improve upon the greedy solution is to
+replace **exactly one** quarter and have \(b\ge5\).
+
+--------------------------------------------------------------------
+
+**What does \(b\ge5\) mean?**
+
+Recall \(b\) is the number of pennies left after taking all possible
+quarters and then all possible dimes.  Hence
+
+\[
+b = N-25q-10a\in\{0,1,\dots ,9\}.
+\]
+
+The condition \(b\ge5\) is equivalent to
+
+\[
+N-25q\equiv 5,6,7,8,9\pmod{10},
+\]
+
+or, more simply,
+
+\[
+N\equiv 5,6,7,8,9\pmod{25}.
+\]
+
+If \(q=0\) (i.e. \(N&lt;25\)) there is no quarter to replace, so the greedy
+algorithm is always optimal for \(1\le N\le24\).
+
+Hence **the greedy algorithm fails exactly for the numbers**
+
+\[
+N\ge 25 \quad\text{with}\quad N\equiv 5,6,7,8,9\pmod{25}.
+\]
+
+--------------------------------------------------------------------
+
+**Counting the successes**
+
+All integers \(1\le N\le1000\): 1000 of them.
+
+Numbers that cause failure:
+
+* The residues \(5,6,7,8,9\) each occur
+  \(\bigl\lfloor\frac{1000-r}{25}\bigr\rfloor+1 = 40\) times for
+  \(r=5,6,7,8,9\).
+  Hence \(5\times40=200\) such numbers in \([1,1000]\).
+
+* The five smallest ones, \(5,6,7,8,9\), are \(&lt;25\); they do **not**
+  cause failure because no quarter can be replaced.
+
+Thus the genuine failures are \(200-5 = 195\) numbers.
+
+Consequently the number of values for which the greedy algorithm
+succeeds is  
+
+\[
+1000-195 = 805.
+\]
+
+\[
+\boxed{805}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 610</p>
+<p>Extracted Answer: 805</p>
+<p>Score: 0.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $ S $ be the set of vertices of a regular 24-gon. Find the number of ways to draw 12 segments of equal lengths so that each vertex in $ S $ is an endpoint of exactly one of the 12 segments.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let the vertices of the regular \(24\)-gon be labelled  
+
+\[
+0,1,2,\dots ,23\qquad (\text{mod }24).
+\]
+
+If a segment connects vertex \(i\) to vertex \(j\) then its length is determined only by the
+step  
+
+\[
+k\equiv j-i\pmod{24},\qquad 1\le k\le 12 .
+\]
+
+All \(12\) segments must have the same length, therefore they all have the same step \(k\) (the
+step \(24-k\) gives the same length, so it is enough to consider \(k=1,2,\dots ,12\)).
+
+--------------------------------------------------------------------
+### 1.  The graph for a fixed step \(k\)
+
+For a fixed \(k\) join each vertex \(i\) with the two vertices
+\(i\pm k\).  The resulting graph \(G_k\) is a union of cycles:
+
+* Let \(d=\gcd(k,24)\).
+* Each cycle has length \(\displaystyle L=\frac{24}{d}\) and there are \(d\) such
+  cycles.
+
+Indeed the permutation \(i\mapsto i+k\) on \(\{0,\dots ,23\}\) consists of
+\(d\) cycles of length \(L\).
+
+--------------------------------------------------------------------
+### 2.  Perfect matchings of \(G_k\)
+
+A required drawing is a perfect matching of \(G_k\).
+
+* If a cycle has even length, it has exactly **2** perfect matchings
+  (alternating edges).
+* If a cycle has odd length, a perfect matching does **not** exist.
+* The only exceptional case is \(k=12\); then each vertex has only one
+  neighbour (its opposite) and the whole graph is already a perfect
+  matching.
+
+Thus, for \(k\neq 12\),
+
+\[
+\text{# matchings for }G_k=
+\begin{cases}
+2^{\,d} &amp; \text{if }L\text{ is even},\\[2mm]
+0       &amp; \text{if }L\text{ is odd}.
+\end{cases}
+\]
+
+Since \(L\) is odd exactly when \(L=3\), i.e. when \(d=8\) (the only such
+\(k\) is \(k=8\)), we have
+
+\[
+N(k)=
+\begin{cases}
+2^{\gcd(k,24)} &amp; \gcd(k,24)\neq 8,\;k\neq 12,\\[2mm]
+0 &amp; k=8,\\[2mm]
+1 &amp; k=12 .
+\end{cases}
+\]
+
+--------------------------------------------------------------------
+### 3.  Evaluate for \(k=1,\dots ,12\)
+
+\[
+\begin{array}{c|c|c|c}
+k &amp; \gcd(k,24) &amp; \text{cycles} &amp; N(k)\\ \hline
+1 &amp; 1 &amp; 1\ \text{cycle of length }24 &amp; 2\\
+2 &amp; 2 &amp; 2\ \text{cycles of length }12 &amp; 4\\
+3 &amp; 3 &amp; 3\ \text{cycles of length }8  &amp; 8\\
+4 &amp; 4 &amp; 4\ \text{cycles of length }6  &amp; 16\\
+5 &amp; 1 &amp; 1\ \text{cycle of length }24 &amp; 2\\
+6 &amp; 6 &amp; 6\ \text{cycles of length }4  &amp; 64\\
+7 &amp; 1 &amp; 1\ \text{cycle of length }24 &amp; 2\\
+8 &amp; 8 &amp; 8\ \text{cycles of length }3  &amp; 0\\
+9 &amp; 3 &amp; 3\ \text{cycles of length }8  &amp; 8\\
+10&amp; 2 &amp; 2\ \text{cycles of length }12 &amp; 4\\
+11&amp; 1 &amp; 1\ \text{cycle of length }24 &amp; 2\\
+12&amp;12 &amp; 12\ \text{edges (pairs)}       &amp; 1
+\end{array}
+\]
+
+--------------------------------------------------------------------
+### 4.  Sum over all possible lengths
+
+\[
+\begin{aligned}
+\sum_{k=1}^{12} N(k)
+&amp;=2+4+8+16+2+64+2+0+8+4+2+1\\
+&amp;=113 .
+\end{aligned}
+\]
+
+--------------------------------------------------------------------
+\[
+\boxed{113}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 113</p>
+<p>Extracted Answer: 113</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Find the sum of all integer bases $b&gt;9$ for which $17_{b}$ is a divisor of $97_{b}$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>For a base \(b&gt;9\),
+
+\[
+17_{b}=1\cdot b+7=b+7 ,\qquad   
+97_{b}=9\cdot b+7=9b+7 .
+\]
+
+We need  
+
+\[
+b+7 \mid 9b+7 .
+\]
+
+Let \(d=b+7\;(&gt;0)\). Then \(b=d-7\) and
+
+\[
+9b+7 = 9(d-7)+7 = 9d-56 .
+\]
+
+Hence  
+
+\[
+d \mid (9d-56) \Longrightarrow d\mid 56 .
+\]
+
+So \(d\) must be a positive divisor of \(56\).  
+Since \(b&gt;9\), we have \(d=b+7&gt;9+7=16\).  
+The divisors of \(56\) larger than \(16\) are
+
+\[
+d=28,\;56 .
+\]
+
+Corresponding bases are  
+
+\[
+b=d-7:
+\begin{cases}
+d=28 \Rightarrow b=21,\\[2mm]
+d=56 \Rightarrow b=49.
+\end{cases}
+\]
+
+Both satisfy \(b&gt;9\) and indeed  
+
+\[
+\frac{9b+7}{b+7}=7\;(b=21),\qquad 
+\frac{9b+7}{b+7}=8\;(b=49).
+\]
+
+Thus the integer bases are \(b=21\) and \(b=49\). Their sum is  
+
+\[
+21+49=70.
+\]
+
+\[
+\boxed{70}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 70</p>
+<p>Extracted Answer: 70</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Suppose $ \triangle ABC $ has angles $ \angle BAC = 84^\circ $, $ \angle ABC = 60^\circ $, and $ \angle ACB = 36^\circ $. Let $ D, E, $ and $ F $ be the midpoints of sides $ \overline{BC} $, $ \overline{AC} $, and $ \overline{AB} $, respectively. The circumcircle of $ \triangle DEF $ intersects $ \overline{BD} $, $ \overline{AE} $, and $ \overline{AF} $ at points $ G, H, $ and $ J $, respectively. The points $ G, D, E, H, J, $ and $ F $ divide the circumcircle of $ \triangle DEF $ into six minor arcs, as shown. Find $ \widehat{DE} + 2 \cdot \widehat{HJ} + 3 \cdot \widehat{FG} $, where the arcs are measured in degrees.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>**Solution Overview**
+
+The circle through the midpoints \(D,E,F\) of the sides of \(\triangle ABC\) is the **nine‑point circle** of \(\triangle ABC\).
+Hence  
+
+* \(D,E,F\) are the vertices of the medial triangle,
+* \(\angle D= \angle A=84^{\circ},\ \angle E= \angle B=60^{\circ},\ \angle F=\angle C=36^{\circ}\).
+
+Since the nine‑point circle is the circumcircle of \(\triangle DEF\),
+
+\[
+\widehat{DE}=2\angle F=2\cdot 36^{\circ}=72^{\circ}.
+\tag{1}
+\]
+
+We must also determine the arcs \(\widehat{FG}\) and \(\widehat{HJ}\).
+
+---------------------------------------------------------------------
+
+### 1.  The arc \(\widehat{FG}\)
+
+\(G\) is the second intersection of the median \(BD\) with the nine‑point circle.
+At point \(D\) the chord \(DG\) lies on the line \(BD\), while the chord \(DF\) is parallel to side \(AC\) (mid‑segment theorem).
+
+Therefore  
+
+\[
+\angle FDG=\angle(\text{line } DF,\text{line } DG)
+          =\angle(\,AC ,\,BD\,).
+\]
+
+The angle between side \(AC\) and the median from \(B\) can be read directly from the triangle:
+\( \angle(\,AC ,\,BD\,)=\angle C=36^{\circ}\).
+
+Consequently  
+
+\[
+\widehat{FG}=2\angle FDG=2\cdot36^{\circ}=72^{\circ}.
+\tag{2}
+\]
+
+---------------------------------------------------------------------
+
+### 2.  The arc \(\widehat{HJ}\)
+
+\(H\) and \(J\) are the second intersections of the sides \(AC\) and \(AB\) with the nine‑point circle.
+Thus the two secants through the exterior point \(A\) intersect the circle at the pairs \(\{F,J\}\) and \(\{E,H\}\).
+
+For an exterior point the angle formed by two secants equals half the **difference** of the intercepted arcs:
+
+\[
+\angle BAC=\frac12\bigl(\widehat{JH}-\widehat{FE}\bigr).
+\tag{3}
+\]
+
+We already know the arc \(\widehat{FE}\) of the nine‑point circle:
+\[
+\widehat{FE}=2\angle D =2\cdot 84^{\circ}=168^{\circ}.
+\tag{4}
+\]
+
+Plugging \(\angle BAC=84^{\circ}\) and (4) into (3) gives  
+
+\[
+84^{\circ}=\frac12\bigl(\widehat{JH}-168^{\circ}\bigr)
+\Longrightarrow \widehat{JH}=336^{\circ}.
+\]
+
+The **minor** arc \(HJ\) is the complement of \(336^{\circ}\) on the circle:
+
+\[
+\widehat{HJ}=360^{\circ}-336^{\circ}=24^{\circ}.
+\tag{5}
+\]
+
+---------------------------------------------------------------------
+
+### 3.  Computing the required sum
+
+From (1), (2) and (5)
+
+\[
+\begin{aligned}
+\widehat{DE}+2\widehat{HJ}+3\widehat{FG}
+&amp;=72^{\circ}+2\cdot24^{\circ}+3\cdot72^{\circ}  \\
+&amp;=72^{\circ}+48^{\circ}+216^{\circ}\\
+&amp;=336^{\circ}.
+\end{aligned}
+\]
+
+---------------------------------------------------------------------
+
+\[
+\boxed{336}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 336</p>
+<p>Extracted Answer: 336</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+The 9 members of a baseball team went to an ice cream parlor after their game. Each player had a singlescoop cone of chocolate, vanilla, or strawberry ice cream. At least one player chose each flavor, and the number of players who chose chocolate was greater than the number of players who chose vanilla, which was greater than the number of players who chose strawberry. Let $N$ be the number of different assignments of flavors to players that meet these conditions. Find the remainder when $N$ is divided by 1000.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>The nine players are distinct, so for a given triple \((c,v,s)\) (numbers of chocolate, vanilla, and strawberry cones) the number of assignments is  
+
+\[
+\frac{9!}{c!\,v!\,s!}.
+\]
+
+We must count all triples of positive integers satisfying  
+
+\[
+c+v+s = 9,\qquad c&gt;v&gt;s\ge 1 .
+\]
+
+---
+
+### Find the possible triples \((c,v,s)\)
+
+Because the three numbers are distinct and sum to 9, we list the partitions of 9 into three distinct positive parts:
+
+\[
+\begin{aligned}
+9 &amp;= 6+2+1,\\
+9 &amp;= 5+3+1,\\
+9 &amp;= 4+3+2 .
+\end{aligned}
+\]
+
+These are the only triples with strict descending order, so  
+
+\[
+(c,v,s) \in \{(6,2,1),\;(5,3,1),\;(4,3,2)\}.
+\]
+
+---
+
+### Count assignments for each triple
+
+\[
+\begin{aligned}
+(6,2,1):\quad &amp;\frac{9!}{6!\,2!\,1!}= \frac{362880}{720\cdot2}=252,\\[4pt]
+(5,3,1):\quad &amp;\frac{9!}{5!\,3!\,1!}= \frac{362880}{120\cdot6}=504,\\[4pt]
+(4,3,2):\quad &amp;\frac{9!}{4!\,3!\,2!}= \frac{362880}{24\cdot6\cdot2}=1260.
+\end{aligned}
+\]
+
+---
+
+### Total number of assignments
+
+\[
+N = 252 + 504 + 1260 = 2016.
+\]
+
+---
+
+### Remainder modulo \(1000\)
+
+\[
+2016 \equiv 16 \pmod{1000}.
+\]
+
+\[
+\boxed{16}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 16</p>
+<p>Extracted Answer: 16</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Alex divides a disk into four quadrants with two perpendicular diameters intersecting at the center of the disk. He draws 25 more line segments through the disk, drawing each segment by selecting two points at random on the perimeter of the disk in different quadrants and connecting those two points. Find the expected number of regions into which these 27 line segments divide the disk.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>**Step 1.  What determines the number of regions?**  
+
+If we draw line‑segments in a disc and no three of them meet in a common interior point, then each new segment splits one existing region for every interior intersection it makes, plus one more region for the segment itself.  
+Hence  
+
+\[
+\#\text{regions}=1+(\#\text{segments})+(\#\text{interior intersection points}).
+\]
+
+We have  
+
+* 2 diameters,
+* 25 random chords,
+* total segments \(=27\).
+
+So we need the **expected number of interior intersections**.
+
+---------------------------------------------------------------------
+
+**Step 2.  Intersections that are certain**
+
+The two diameters intersect at the centre ⇒ one interior intersection.
+
+---------------------------------------------------------------------
+
+**Step 3.  Intersections of a chord with the diameters**
+
+A chord is drawn by picking two points on the circle that lie in **different quadrants**.
+
+*If the two quadrants are adjacent* (e.g. quadrant I and II), the chord crosses **exactly one** diameter.  
+*If the two quadrants are opposite* (e.g. quadrant I and III), the chord crosses **both** diameters.
+
+The unordered pair of distinct quadrants is uniformly chosen among the \(\binom{4}{2}=6\) possibilities:
+
+* 4 adjacent pairs → probability \(4/6=2/3\);
+* 2 opposite pairs → probability \(2/6=1/3\).
+
+Hence for one random chord
+
+\[
+E[\hbox{diameter‑intersections}]
+  =\frac23\cdot1+\frac13\cdot2=\frac43 .
+\]
+
+For the 25 chords  
+
+\[
+E[I_{\text{chord–diameter}}]=25\cdot\frac43=\frac{100}{3}.
+\]
+
+---------------------------------------------------------------------
+
+**Step 4.  Intersections between two random chords**
+
+Let the two chords be \(AB\) and \(CD\).  
+Write \(L\) for the clockwise length of the arc from \(A\) to \(B\) (so \(0\le L\le2\pi\)).  
+Let \(L_i^{(1)}\) be the length of that arc inside quadrant \(i\) (\(i=1,\dots ,4\)), and
+\(L_i^{(2)}=\frac{\pi}{2}-L_i^{(1)}\) the length of the complementary arc inside the same quadrant.
+
+For a given chord \(AB\)
+
+* the probability that a random chord \(CD\) meets \(AB\) **and** has its endpoints in different quadrants is  
+
+\[
+p_{\text{int}}(A,B)=
+\frac{L(2\pi-L)-\displaystyle\sum_{i=1}^{4}L_i^{(1)}L_i^{(2)}}{2\pi^{2}} .
+\tag{1}
+\]
+
+(The numerator is the area of the product set
+\(\{(C,D):C\in\text{arc}_1,D\in\text{arc}_2\}\) minus the part where \(C\) and \(D\) fall in the same quadrant.)
+
+Define  
+
+\[
+Q(A,B)=L(2\pi-L)-\sum_{i=1}^{4}L_i^{(1)}L_i^{(2)} .
+\]
+
+Then \(p_{\text{int}}(A,B)=Q(A,B)/(2\pi^{2})\).
+
+---------------------------------------------------------------------
+
+**Step 5.  Averaging \(Q\)**  
+
+Put the circle’s total length as \(4d\) with a quadrant length \(d=\pi/2\).
+Write the clockwise length as a multiple of \(d\): \(t=L/d\in[0,4]\).
+
+For a fixed \(t\) and a uniformly random starting point of the arc,
+the expected value of \(\sum_i (L_i^{(1)})^{2}\) (the sum of squares of the pieces of the arc) is
+
+\[
+h(t)=
+\begin{cases}
+t^{2}-\dfrac{t^{3}}{3}, &amp; 0\le t\le 1,\\[4pt]
+t-\dfrac13,               &amp; 1\le t\le 4 .
+\end{cases}
+\]
+
+Consequently  
+
+\[
+E\!\left[\sum_i L_i^{(1)}L_i^{(2)}\right]
+      =\frac{\pi}{2}E[L]-E\!\left[\sum_i(L_i^{(1)})^{2}\right]
+      =\frac{\pi^{2}}{2}-\frac{27\pi^{2}}{64}
+      =\frac{5\pi^{2}}{64}.
+\]
+
+From this we obtain the unconditional expectation
+
+\[
+E[Q]=E\!\bigl[L(2\pi-L)\bigr]-E\!\Bigl[\sum_i L_i^{(1)}L_i^{(2)}\Bigr]
+      =\frac{2}{3}\pi^{2}-\frac{5}{64}\pi^{2}
+      =\frac{113}{192}\pi^{2}.
+\tag{2}
+\]
+
+---------------------------------------------------------------------
+
+**Step 6.  Conditioning on “different quadrants’’ for the first chord**
+
+If the first chord’s endpoints lie in the *same* quadrant (probability \(1/4\)),
+then \(Q\) simplifies to \(Q=\frac{3\pi}{2}L\).  
+Because the absolute difference of two points inside a quadrant has mean \(d/3=\pi/6\),
+
+\[
+E[Q\mid\text{same quadrant}]=\frac{3\pi}{2}\cdot\frac{\pi}{6}
+                              =\frac{\pi^{2}}{4}.
+\]
+
+Hence  
+
+\[
+E[Q\;{\bf 1}_{\text{different quadrants}}]
+   =E[Q]-\frac14\cdot\frac{\pi^{2}}{4}
+   =\frac{113}{192}\pi^{2}-\frac{\pi^{2}}{16}
+   =\frac{101}{192}\pi^{2}. \tag{3}
+\]
+
+---------------------------------------------------------------------
+
+**Step 7.  Probability that two *valid* chords intersect**
+
+From (1) and (3),
+
+\[
+\boxed{
+P(\text{intersection } \&amp;\; AB\text{ valid}\; \&amp;\; CD\text{ valid})
+    =\frac{E[Q\,{\bf 1}_{\text{different quadrants}}]}{2\pi^{2}}
+    =\frac{101}{384}.
+}
+\]
+
+The event “both chords are valid’’ occurs with probability \((3/4)^{2}=9/16\).  
+Therefore the conditional probability that two random valid chords intersect is
+
+\[
+P_{\text{int}}=
+\frac{101/384}{9/16}= \frac{101}{216}\approx0.4676.
+\tag{4}
+\]
+
+---------------------------------------------------------------------
+
+**Step 8.  Expected number of chord–chord intersections**
+
+\[
+E[I_{\text{chord–chord}}]
+   =\binom{25}{2}\;P_{\text{int}}
+   =300\cdot\frac{101}{216}
+   =\frac{2525}{18}.
+\]
+
+---------------------------------------------------------------------
+
+**Step 9.  Total expected interior intersections**
+
+\[
+\begin{aligned}
+E[I] &amp;=
+\underbrace{1}_{\text{diameters}}+
+\underbrace{\frac{100}{3}}_{\text{chord–diameter}}+
+\underbrace{\frac{2525}{18}}_{\text{chord–chord}} \\[4pt]
+&amp;= \frac{18+600+2525}{18}
+   =\frac{3143}{18}.
+\end{aligned}
+\]
+
+---------------------------------------------------------------------
+
+**Step 10.  Expected number of regions**
+
+\[
+\begin{aligned}
+E[\#\text{regions}]
+&amp;=1+(\#\text{segments})+E[I] \\
+&amp;=1+27+\frac{3143}{18}\\[4pt]
+&amp;=28+\frac{3143}{18}
+   =\frac{504+3143}{18}
+   =\boxed{\frac{3647}{18}}\; \approx 202.6 .
+\end{aligned}
+\]
+
+Thus, on average Alex’s 27 line segments partition the disk into \(\displaystyle \frac{3647}{18}\) regions.</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 204</p>
+<p>Extracted Answer: None</p>
+<p>Score: 0.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Find the number of ordered pairs $(x,y)$, where both $x$ and $y$ are integers between $-100$ and $100$, inclusive, such that $12x^{2}-xy-6y^{2}=0$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>\[
+12x^{2}-xy-6y^{2}=0
+\]
+
+---
+
+### 1.  Factor the quadratic  
+
+Look for integers \(a,b,c,d\) such that  
+
+\[
+(ax+by)(cx+dy)=12x^{2}-xy-6y^{2}.
+\]
+
+We need  
+
+\[
+ac=12,\qquad bd=-6,\qquad ad+bc=-1 .
+\]
+
+Taking \(a=4,\;c=3\) (since \(4\cdot 3=12\)) and trying \(b=-3,\;d=2\) gives  
+
+\[
+bd=(-3)(2)=-6,\qquad ad+bc=4\cdot2+3\cdot(-3)=8-9=-1.
+\]
+
+Hence  
+
+\[
+12x^{2}-xy-6y^{2}=(4x-3y)(3x+2y).
+\]
+
+So the original equation is equivalent to  
+
+\[
+(4x-3y)(3x+2y)=0.
+\]
+
+Thus any integer solution must satisfy one of the two linear equations  
+
+\[
+\boxed{4x-3y=0}\qquad\text{or}\qquad\boxed{3x+2y=0}.
+\]
+
+---
+
+### 2.  Solve each linear equation in integers  
+
+**(i) \(4x-3y=0\).**  
+
+\(4x=3y\Rightarrow y= \frac{4}{3}x\).  
+Since \(\gcd(4,3)=1\), write \(x=3k,\;y=4k\) for some integer \(k\).
+
+Both coordinates must satisfy \(-100\le x,y\le 100\):
+
+\[
+-100\le 3k\le 100 \Longrightarrow -\frac{100}{3}\le k\le \frac{100}{3},
+\qquad
+-100\le 4k\le 100 \Longrightarrow -25\le k\le 25.
+\]
+
+The tighter bound is \(-25\le k\le 25\).  
+Hence there are  
+
+\[
+25-(-25)+1 = 51
+\]
+
+solutions from this family.
+
+---
+
+**(ii) \(3x+2y=0\).**  
+
+\(3x=-2y\Rightarrow x=-\frac{2}{3}y\).  
+Again \(\gcd(3,2)=1\), so write \(y=3m,\;x=-2m\) for some integer \(m\).
+
+Bounds:
+
+\[
+-100\le -2m\le 100 \Longrightarrow -50\le m\le 50,
+\qquad
+-100\le 3m\le 100 \Longrightarrow -\frac{100}{3}\le m\le \frac{100}{3}
+\Longrightarrow -33\le m\le 33.
+\]
+
+Thus \(-33\le m\le 33\), giving  
+
+\[
+33-(-33)+1 = 67
+\]
+
+solutions from this family.
+
+---
+
+### 3.  Remove the double‑counted solution  
+
+The two families intersect only when both equations hold, i.e. when  
+
+\[
+4x-3y=0\;\text{and}\;3x+2y=0\Longrightarrow (x,y)=(0,0).
+\]
+
+So \((0,0)\) has been counted twice.  
+
+Total distinct ordered pairs:
+
+\[
+51+67-1 = 117.
+\]
+
+---
+
+\[
+\boxed{117}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 117</p>
+<p>Extracted Answer: 117</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $ \triangle ABC $ be a right triangle with $ \angle A = 90^\circ $ and $ BC = 38 $. There exist points $ K $ and $ L $ inside the triangle such that $ AK = AL = BK = CL = KL = 14. $ The area of the quadrilateral $ BKLC $ can be expressed as $ n \sqrt{3} $ for some positive integer $ n $. Find $ n $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+\[
+A=(0,0),\qquad B=(b,0),\qquad C=(0,c)
+\]
+
+with \(\angle A=90^{\circ}\) and \(BC=38\Rightarrow b^{2}+c^{2}=38^{2}=1444\).
+
+---
+
+### 1.  Locating \(K\) and \(L\)
+
+\(AK=BK=14\).  
+The circles \(\odot(A,14)\) and \(\odot(B,14)\) intersect at the interior point  
+
+\[
+K=\Bigl(\frac b2,\; \sqrt{196-\Bigl(\frac b2\Bigr)^2}\Bigr).
+\]
+
+Similarly \(AL=CL=14\) gives  
+
+\[
+L=\Bigl(\sqrt{196-\Bigl(\frac c2\Bigr)^2},\; \frac c2\Bigr).
+\]
+
+Since \(AK=AL=KL=14\), points \(A,K,L\) form an equilateral triangle.
+Put  
+
+\[
+K=(14\cos\theta,14\sin\theta),\qquad 
+L=(14\cos(\theta+60^\circ),14\sin(\theta+60^\circ)).
+\]
+
+Using \(BK=14\) and \(CL=14\),
+
+\[
+b=28\cos\theta,\qquad c=28\sin(\theta+60^\circ). \tag{1}
+\]
+
+---
+
+### 2.  Determining \(\theta\)
+
+From \(b^2+c^2=1444\),
+
+\[
+\cos^{2}\theta+\sin^{2}(\theta+60^\circ)=\frac{1444}{28^{2}}
+        =\frac{361}{196}=\Bigl(\frac{19}{14}\Bigr)^{2}.
+\]
+
+Using \(\cos^2x=\frac{1+\cos2x}{2},\ \sin^2x=\frac{1-\cos2x}{2}\),
+
+\[
+\frac{2+\cos2\theta-\cos(2\theta+120^\circ)}2
+      =\frac{361}{196}.
+\]
+
+Simplifying gives  
+
+\[
+\cos2\theta-\cos(2\theta+120^\circ)=\frac{165}{98}.
+\]
+
+Since \(\cos A-\cos B=-2\sin\frac{A+B}{2}\sin\frac{A-B}{2}\),
+
+\[
+\sqrt3\sin(2\theta+60^\circ)=\frac{165}{98}
+   \Longrightarrow \sin(2\theta+60^\circ)=\frac{55\sqrt3}{98}.
+\]
+
+Hence  
+
+\[
+\cos(2\theta+60^\circ)=\frac{23}{98},\qquad 
+\sin(2\theta+60^\circ)=\frac{55\sqrt3}{98}.
+\]
+
+Let \(\phi=2\theta+60^\circ\). Then
+
+\[
+\cos\phi=\frac{23}{98},\qquad \sin\phi=\frac{55\sqrt3}{98}.
+\]
+
+Compute \(\cos(\phi-60^\circ)\) and \(\cos(\phi+60^\circ)\):
+
+\[
+\cos(\phi-60^\circ)=\frac{47}{49},\qquad
+\cos(\phi+60^\circ)=-\frac{71}{98}.
+\]
+
+Now
+
+\[
+\cos\theta=\sqrt{\frac{1+\cos(\phi-60^\circ)}2}
+          =\sqrt{\frac{1+\frac{47}{49}}2}
+          =\sqrt{\frac{48}{49}}=\frac{4\sqrt3}{7},
+\]
+
+\[
+\sin(\theta+60^\circ)=\sqrt{\frac{1-\cos(\phi+60^\circ)}2}
+                     =\sqrt{\frac{1+\frac{71}{98}}2}
+                     =\sqrt{\frac{169}{196}}=\frac{13}{14}.
+\]
+
+Using (1),
+
+\[
+b=28\cos\theta=28\cdot\frac{4\sqrt3}{7}=16\sqrt3,
+\qquad
+c=28\sin(\theta+60^\circ)=28\cdot\frac{13}{14}=26.
+\]
+
+Thus  
+
+\[
+AB=16\sqrt3,\qquad AC=26,\qquad BC=38.
+\]
+
+Consequently  
+
+\[
+K=\Bigl(\frac{b}{2},\sqrt{196-\Bigl(\frac b2\Bigr)^2}\Bigr)
+  =\bigl(8\sqrt3,\;2\bigr),\qquad
+L=\Bigl(\sqrt{196-\Bigl(\frac c2\Bigr)^2},\frac c2\Bigr)
+  =\bigl(3\sqrt3,\;13\bigr).
+\]
+
+---
+
+### 3.  Area of \(BKLC\)
+
+Using the shoelace formula for vertices  
+
+\[
+B=(16\sqrt3,0),\; K=(8\sqrt3,2),\; L=(3\sqrt3,13),\; C=(0,26),
+\]
+
+\[
+\begin{aligned}
+\sum x_iy_{i+1}&amp;=16\sqrt3\cdot2+8\sqrt3\cdot13+3\sqrt3\cdot26+0\cdot0\\
+               &amp;=214\sqrt3,\\[2mm]
+\sum y_ix_{i+1}&amp;=0\cdot8\sqrt3+2\cdot3\sqrt3+13\cdot0+26\cdot16\sqrt3\\
+               &amp;=422\sqrt3.
+\end{aligned}
+\]
+
+Hence
+
+\[
+\text{Area}(BKLC)=\frac12|214\sqrt3-422\sqrt3|=104\sqrt3.
+\]
+
+---
+
+Thus the area of \(BKLC\) is \(104\sqrt3\), so  
+
+\[
+\boxed{104}.
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 104</p>
+<p>Extracted Answer: 104</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+An isosceles trapezoid has an inscribed circle tangent to each of its four sides. The radius of the circle is 3, and the area of the trapezoid is 72. Let the parallel sides of the trapezoid have lengths $r$ and $s$, with $r \neq s$. Find $r^{2}+s^{2}$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let the trapezoid have parallel sides (bases) \(r\) and \(s\) \((r\neq s)\), the equal legs \(L\), and height \(h\).
+
+---
+
+### 1.  Height from the incircle  
+
+The circle of radius \(3\) is tangent to the two parallel sides, so the distance between those sides equals the sum of the distances from the centre to each side:
+
+\[
+h = 3+3 = 6 .
+\]
+
+---
+
+### 2.  Sum of the bases from the area  
+
+\[
+\text{Area}= \frac{r+s}{2}\,h = 72
+\quad\Longrightarrow\quad
+\frac{r+s}{2}\cdot 6 = 72 \implies r+s = 24 .
+\]
+
+---
+
+### 3.  Relation of the legs (tangential quadrilateral)  
+
+A quadrilateral has an incircle iff the sums of opposite sides are equal.  
+For the trapezoid the opposite sides are the two bases and the two legs, so
+
+\[
+r+s = L+L \;\Longrightarrow\; L =\frac{r+s}{2}=12 .
+\]
+
+Thus each leg has length \(L=12\).
+
+---
+
+### 4.  Difference of the bases from the leg length  
+
+Because the trapezoid is isosceles, each leg together with the height forms a right triangle whose horizontal leg is \(\dfrac{|s-r|}{2}\):
+
+\[
+L^{2}=h^{2}+ \left(\frac{s-r}{2}\right)^{2}.
+\]
+
+Insert \(L=12,\;h=6\):
+
+\[
+12^{2}=6^{2}+ \left(\frac{s-r}{2}\right)^{2}
+\Longrightarrow 144-36 = \left(\frac{s-r}{2}\right)^{2}
+\Longrightarrow \left(\frac{s-r}{2}\right)^{2}=108.
+\]
+
+Hence  
+
+\[
+|s-r| = 2\sqrt{108}=12\sqrt3 .
+\]
+
+Assume \(s&gt;r\); then \(s-r=12\sqrt3\).
+
+---
+
+### 5.  Solve for \(r\) and \(s\)
+
+\[
+\begin{cases}
+r+s = 24,\\
+s-r = 12\sqrt3.
+\end{cases}
+\qquad\Longrightarrow\qquad
+\begin{aligned}
+s &amp;= 12+6\sqrt3,\\
+r &amp;= 12-6\sqrt3.
+\end{aligned}
+\]
+
+---
+
+### 6.  Compute \(r^{2}+s^{2}\)
+
+\[
+\begin{aligned}
+r^{2}+s^{2} &amp;= (12-6\sqrt3)^{2}+(12+6\sqrt3)^{2} \\
+&amp;= \bigl(144-144\sqrt3+108\bigr)+\bigl(144+144\sqrt3+108\bigr) \\
+&amp;= 252-144\sqrt3+252+144\sqrt3 \\
+&amp;= 504.
+\end{aligned}
+\]
+
+---
+
+\[
+\boxed{504}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 504</p>
+<p>Extracted Answer: 504</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+There are $8!=40320$ eight-digit positive integers that use each of the digits $1,2,3,4,5,6,7,8$ exactly once. Let $N$ be the number of these integers that are divisible by 22. Find the difference between $N$ and 2025.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>For an 8‑digit number using each of the digits \(1,2,\dots ,8\) exactly once  
+
+\[
+22=2\cdot11
+\]
+
+so the number must be divisible by \(2\) **and** by \(11\).
+
+---
+
+### 1.  Divisibility by \(2\)
+
+The units digit must be even, i.e. one of \(\{2,4,6,8\}\).
+
+---
+
+### 2.  Divisibility by \(11\)
+
+For an 8‑digit number \(a_1a_2\ldots a_8\),
+
+\[
+(a_1+a_3+a_5+a_7)-(a_2+a_4+a_6+a_8)\equiv 0\pmod{11}.
+\]
+
+Let  
+
+\[
+S_{\text{odd}}=a_1+a_3+a_5+a_7,\qquad 
+S_{\text{even}}=a_2+a_4+a_6+a_8 .
+\]
+
+Since the digits \(1\) through \(8\) sum to \(36\),
+
+\[
+S_{\text{odd}}+S_{\text{even}}=36\qquad\text{and}\qquad 
+S_{\text{odd}}-S_{\text{even}}\equiv0\pmod{11}.
+\]
+
+Thus  
+
+\[
+2S_{\text{odd}}\equiv36\equiv3\pmod{11}\Longrightarrow
+S_{\text{odd}}\equiv7\pmod{11}.
+\]
+
+The possible values of \(S_{\text{odd}}\) (sum of four distinct digits from \(1\)–\(8\)) lie between \(10\) and \(26\).  
+The only value in this interval congruent to \(7\pmod{11}\) is \(18\).
+
+Hence
+
+\[
+S_{\text{odd}}=S_{\text{even}}=18 .
+\]
+
+So the four digits placed in the odd positions must sum to \(18\).
+
+---
+
+### 3.  4‑digit subsets with sum \(18\)
+
+All 4‑element subsets of \(\{1,\dots ,8\}\) whose sum is \(18\) are  
+
+\[
+\begin{aligned}
+&amp;\{1,2,7,8\},\; \{1,3,6,8\},\; \{1,4,5,8\},\; \{1,4,6,7\},\\
+&amp;\{2,3,5,8\},\; \{2,3,6,7\},\; \{2,4,5,7\},\; \{3,4,5,6\}.
+\end{aligned}
+\]
+
+There are exactly \(8\) such subsets.  
+Each contains **exactly two even digits** (the even digits are \(2,4,6,8\)).
+
+---
+
+### 4.  Arranging the digits
+
+* Choose one of the 8 subsets for the odd positions.
+* Permute its four digits among the odd places \((1,3,5,7)\) – \(4! = 24\) ways.
+* The remaining four digits occupy the even places \((2,4,6,8)\).  
+
+  The units place (position 8) must be even.  
+  Since the complementary set also has exactly two even digits, we may
+  \[
+  \text{choose the even digit for position 8 in }2\text{ ways,}
+  \]
+  then arrange the other three digits in positions \(2,4,6\) in \(3! = 6\) ways.
+
+Hence for a given subset the number of valid permutations is  
+
+\[
+24 \times (2 \times 6)=24 \times 12 = 288 .
+\]
+
+With \(8\) possible subsets,
+
+\[
+N = 8 \times 288 = 2304 .
+\]
+
+---
+
+### 5.  Required difference
+
+\[
+N-2025 = 2304-2025 = 279 .
+\]
+
+\[
+\boxed{279}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 279</p>
+<p>Extracted Answer: 279</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $k$ be real numbers such that the system $|25+20i-z|=5$ and $|z-4-k|=|z-3i-k|$ has exactly one complex solution $z$. The sum of all possible values of $k$ can be written as $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$. Here $i=\sqrt{-1}$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>The first equation  
+
+\[
+|25+20i-z|=5
+\]
+
+describes the circle  
+
+\[
+\text{Center }C=(25,20),\qquad\text{radius }R=5 .
+\]
+
+The second equation  
+
+\[
+|z-4-k|=|z-3i-k|
+\]
+
+states that the distance from \(z\) to the point  
+
+\[
+A=4+k\;(=k+4+0i)
+\]
+
+equals its distance to the point  
+
+\[
+B=3i+k\;(=k+0i+3i).
+\]
+
+Hence the locus of points satisfying the second condition is the **perpendicular bisector** of the segment \(\overline{AB}\).
+
+---
+
+### 1.  Equation of the perpendicular bisector
+
+Coordinates:
+
+\[
+A=(k+4,0),\qquad B=(k,3).
+\]
+
+Midpoint  
+
+\[
+M=\Big(\frac{k+4+k}{2},\frac{0+3}{2}\Big)=\Big(k+2,\frac32\Big).
+\]
+
+Slope of \(\overline{AB}\):
+
+\[
+\frac{3-0}{k-(k+4)}=\frac{3}{-4}=-\frac34 .
+\]
+
+Therefore the slope of the perpendicular bisector is the negative reciprocal,
+
+\[
+m=\frac{4}{3}.
+\]
+
+Using point–slope form through \(M\):
+
+\[
+y-\frac32=\frac{4}{3}(x-(k+2)).
+\]
+
+Multiplying by \(6\),
+
+\[
+6y-9=8x-8k-16\qquad\Longrightarrow\qquad 8x-6y=8k+7.
+\]
+
+Thus the line is  
+
+\[
+L:\;8x-6y=8k+7 .
+\]
+
+---
+
+### 2.  Tangency condition
+
+The system has **exactly one** solution \(z\) when the line \(L\) is tangent to the circle.  
+The distance from the center \(C=(25,20)\) to \(L\) must equal the radius \(5\).
+
+For a line \(Ax+By+C=0\), the distance from \((x_0,y_0)\) is  
+
+\[
+d=\frac{|Ax_0+By_0+C|}{\sqrt{A^2+B^2}} .
+\]
+
+Write \(L\) as \(8x-6y-(8k+7)=0\). Then
+
+\[
+d=\frac{|8\cdot25-6\cdot20-(8k+7)|}{\sqrt{8^2+(-6)^2}}
+   =\frac{|200-120-8k-7|}{\sqrt{64+36}}
+   =\frac{|73-8k|}{10}.
+\]
+
+Set \(d=R=5\):
+
+\[
+\frac{|73-8k|}{10}=5 \;\Longrightarrow\; |73-8k|=50 .
+\]
+
+Hence  
+
+\[
+73-8k=50 \quad\text{or}\quad 73-8k=-50.
+\]
+
+Solving:
+
+\[
+\begin{aligned}
+73-8k=50 &amp;\Rightarrow 8k=23 \Rightarrow k=\frac{23}{8},\\[2mm]
+73-8k=-50 &amp;\Rightarrow 8k=123 \Rightarrow k=\frac{123}{8}.
+\end{aligned}
+\]
+
+Both values give a line tangent to the circle, so the system has exactly one complex solution for each.
+
+---
+
+### 3.  Sum of all possible \(k\)
+
+\[
+\frac{23}{8}+\frac{123}{8}=\frac{146}{8}=\frac{73}{4}.
+\]
+
+Write \(\frac{73}{4}\) as \(\frac{m}{n}\) with \(\gcd(m,n)=1\); here \(m=73,\;n=4\).
+
+\[
+m+n=73+4=77.
+\]
+
+\[
+\boxed{77}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 77</p>
+<p>Extracted Answer: 77</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let the sequence of rationals $ x_1, x_2, \ldots $ be defined such that $ x_1 = \frac{25}{11} $ and
+$ x_{k+1} = \frac{1}{3} \left( x_k + \frac{1}{x_k} - 1 \right). $
+$ x_{2025} $ can be expressed as $ \frac{m}{n} $ for relatively prime positive integers $ m $ and $ n $. Find the remainder when $ m + n $ is divided by 1000.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>The recurrence  
+
+\[
+x_{k+1}= \frac{1}{3}\Bigl(x_k+\frac{1}{x_k}-1\Bigr)
+\]
+
+can be rewritten as  
+
+\[
+x_{k+1}= \frac{x_k^2-x_k+1}{3x_k}.
+\]
+
+---
+
+### 1.  A convenient change of variables  
+
+Define  
+
+\[
+t_k=\frac{2x_k-1}{x_k+1}\qquad\Longleftrightarrow\qquad 
+x_k=\frac{b_k+a_k}{2b_k-a_k},
+\]
+
+where \(a_k,b_k\) are integers defined below.  
+
+From the definition  
+
+\[
+t_{k+1}=t_k\bigl(t_k-1\bigr),\qquad t_1=\frac{13}{12}.
+\]
+
+---
+
+### 2.  Integer sequences  
+
+Write \(t_k=\dfrac{a_k}{b_k}\) in lowest terms.  
+From \(t_{k+1}=t_k(t_k-1)\) we obtain  
+
+\[
+a_{k+1}=a_k\bigl(a_k-b_k\bigr),\qquad  
+b_{k+1}=b_k^2,\qquad a_1=13,\;b_1=12 .
+\]
+
+Thus  
+
+\[
+b_k=12^{\,2^{\,k-1}} .
+\]
+
+Because \(a_k\) is always odd and not a multiple of \(3\), \(\gcd(a_k,b_k)=1\) for all \(k\).
+
+---
+
+### 3.  Expressing \(x_k\)  
+
+Using \(x_k=\dfrac{b_k+a_k}{2b_k-a_k}\) we get  
+
+\[
+m_k=b_k+a_k,\qquad n_k=2b_k-a_k,
+\]
+so that  
+
+\[
+m_k+n_k = (b_k+a_k)+(2b_k-a_k)=3b_k .
+\]
+
+Hence for any \(k\),
+
+\[
+m_k+n_k = 3\cdot 12^{\,2^{\,k-1}} .
+\]
+
+---
+
+### 4.  The required term  
+
+For \(k=2025\),
+
+\[
+m+n = 3\cdot 12^{\,2^{\,2024}} .
+\]
+
+We need this number modulo \(1000\).
+
+---
+
+### 5.  Computing \(3\cdot12^{2^{2024}}\pmod{1000}\)
+
+Since \(1000=8\cdot125\), work modulo \(8\) and \(125\).
+
+*Modulo 8*: \(12\equiv4\pmod8\) and \(4^2\equiv0\pmod8\); with exponent \(2^{2024}&gt;1\),
+
+\[
+12^{2^{2024}}\equiv0\pmod8\Longrightarrow
+3\cdot12^{2^{2024}}\equiv0\pmod8 .
+\]
+
+*Modulo 125*: \(\gcd(12,125)=1\), \(\phi(125)=100\).  
+Reduce the exponent modulo 100:
+
+\[
+2^{2024}\equiv 2^{4}=16\pmod{100}
+\]
+(because \(2^{2024}\equiv16\pmod{100}\)).  
+Hence  
+
+\[
+12^{2^{2024}}\equiv12^{16}\pmod{125}.
+\]
+
+Compute:
+\[
+12^2\equiv19,\quad
+12^4\equiv19^2\equiv111,\quad
+12^8\equiv111^2\equiv71,\quad
+12^{16}\equiv71^2\equiv41\pmod{125}.
+\]
+
+Thus  
+
+\[
+3\cdot12^{2^{2024}}\equiv3\cdot41=123\pmod{125}.
+\]
+
+Now solve  
+
+\[
+R\equiv0\pmod8,\qquad R\equiv123\pmod{125}.
+\]
+
+Write \(R=125a+123\). Mod 8:
+
+\[
+125a+123\equiv5a+3\equiv0\pmod8\Longrightarrow5a\equiv5\pmod8
+\Longrightarrow a\equiv1\pmod8.
+\]
+
+Take \(a=1\); then \(R=125\cdot1+123=248\).
+
+Hence  
+
+\[
+m+n\equiv 248 \pmod{1000}.
+\]
+
+---
+
+\[
+\boxed{248}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 248</p>
+<p>Extracted Answer: 248</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+On $\triangle ABC$ points $A,D,E$, and $B$ lie that order on side $\overline{AB}$ with $AD=4, DE=16$, and $EB=8$. Points $A,F,G$, and $C$ lie in that order on side $\overline{AC}$ with $AF=13, FG=52$, and $GC=26$. Let $M$ be the reflection of $D$ through $F$, and let $N$ be the reflection of $G$ through $E$. Quadrilateral $DEGF$ has area 288. Find the area of heptagon $AFNBCEM$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+\[
+AD=4,\; DE=16,\; EB=8,\qquad AF=13,\; FG=52,\; GC=26 .
+\]
+
+Hence  
+
+\[
+AB=4+16+8=28,\qquad AC=13+52+26=91 .
+\]
+
+--------------------------------------------------------------------
+### 1.  Coordinates
+
+Place \(A=(0,0),\; B=(28,0)\) and let the height of \(\triangle ABC\) be \(h\).  
+Write \(C=(x,h)\) (the \(x\)‑coordinate is unknown).
+
+Points on the sides are then  
+
+\[
+\begin{aligned}
+D&amp;=(4,0),   &amp;E&amp;=(20,0), \\
+F&amp;=\Bigl(\frac{13}{91}x,\;\frac{13}{91}h\Bigr), &amp;
+G&amp;=\Bigl(\frac{65}{91}x,\;\frac{65}{91}h\Bigr).
+\end{aligned}
+\]
+
+Since \(M\) is the reflection of \(D\) about \(F\),
+
+\[
+M=2F-D=\Bigl(\frac{26}{91}x-4,\;\frac{26}{91}h\Bigr),
+\]
+
+and because \(N\) is the reflection of \(G\) about \(E\),
+
+\[
+N=2E-G=\Bigl(40-\frac{65}{91}x,\;-\frac{65}{91}h\Bigr).
+\]
+
+--------------------------------------------------------------------
+### 2.  Height from the given area
+
+Quadrilateral \(DEGF\) consists of triangles \(DEG\) and \(DFG\).  
+Its area is
+
+\[
+\begin{aligned}
+[DEGF]&amp;=\frac12\Bigl[\,DE\cdot G_y
+      +|\,\overrightarrow{DF}\times\overrightarrow{DG}\,|\,\Bigr]\\[2mm]
+     &amp;=\frac{h}{2\cdot91}\Bigl(16\cdot65+4\cdot52\Bigr)
+      =\frac{1248}{182}\,h
+      =\frac{624}{91}\,h .
+\end{aligned}
+\]
+
+Given \([DEGF]=288\),
+
+\[
+\frac{624}{91}\,h=288\quad\Longrightarrow\quad h=42 .
+\]
+
+--------------------------------------------------------------------
+### 3.  Area of \(\triangle ABC\)
+
+\[
+[ABC]=\frac12\cdot AB\cdot h
+      =\frac12\cdot28\cdot42
+      =588 .
+\]
+
+--------------------------------------------------------------------
+### 4.  Area of the heptagon \(AFNBCEM\)
+
+Use the shoelace formula with the vertices in the order  
+
+\[
+A,\;F,\;N,\;B,\;C,\;E,\;M .
+\]
+
+Because the \(x\)-coordinate \(x\) of \(C\) appears only in the
+terms \(x\,h\) and they cancel each other, the sum reduces to  
+
+\[
+\begin{aligned}
+S&amp;=2\bigl( -\tfrac{2\cdot13}{91} (4+16)h
+          + (4+16+8)h
+          + (4+16+8)h
+          - (4+16)h \bigr) \\
+  &amp;=2\cdot 28h .
+\end{aligned}
+\]
+
+Hence
+
+\[
+[AFNBCEM]=\frac12 S = \frac12\cdot28h = [ABC]=588 .
+\]
+
+--------------------------------------------------------------------
+\[
+\boxed{588}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 588</p>
+<p>Extracted Answer: 588</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+The parabola with equation $y=x^{2}-4$ is rotated $60^{\circ}$ counterclockwise around the origin. The unique point in the fourth quadrant where the original parabola and its image intersect has $y$-coordinate $\frac{a-\sqrt{b}}{c}$, where $a$, $b$, and $c$ are positive integers, and $a$ and $c$ are relatively prime. Find $a+b+c$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>The original parabola is  
+
+\[
+y=x^{2}-4 .
+\]
+
+Rotate it \(60^{\circ}\) counter‑clockwise about the origin.  
+If \((X,Y)\) is a point on the rotated parabola, then rotating it back
+\(60^{\circ}\) (clockwise) must put it on the original parabola:
+
+\[
+\begin{aligned}
+x &amp;= X\cos60^{\circ}+Y\sin60^{\circ},\\
+y &amp;=-X\sin60^{\circ}+Y\cos60^{\circ},
+\end{aligned}
+\qquad\text{with }\;y=x^{2}-4 .
+\]
+
+Using \(\cos60^{\circ}= \tfrac12,\; \sin60^{\circ}= \tfrac{\sqrt3}{2}\),
+
+\[
+-\,\frac{\sqrt3}{2}X+\frac12Y= \Bigl(\frac12X+\frac{\sqrt3}{2}Y\Bigr)^{2}-4 .
+\tag{1}
+\]
+
+The original parabola gives \(Y=X^{2}-4\). Substituting this into (1) and
+clearing denominators yields
+
+\[
+3X^{4}+2\sqrt3\,X^{3}-25X^{2}-6\sqrt3\,X+40=0 .
+\tag{2}
+\]
+
+The quartic factors over \(\mathbb{Q}(\sqrt3)\):
+
+\[
+\bigl(X^{2}+\sqrt3\,X-4\bigr)\bigl(3X^{2}-\sqrt3\,X-10\bigr)=0 .
+\]
+
+Hence the possible \(X\)-coordinates are the roots of the two quadratics.
+
+* From \(X^{2}+\sqrt3X-4=0\) :
+
+\[
+X=\frac{-\sqrt3\pm\sqrt{19}}{2}.
+\]
+
+The positive root is  
+
+\[
+X_{0}= \frac{-\sqrt3+\sqrt{19}}{2}\approx1.31,
+\]
+
+which satisfies \(0&lt;X&lt;2\); thus the point \((X_{0},Y_{0})\) lies in the
+fourth quadrant.
+
+* The other quadratic \(3X^{2}-\sqrt3X-10=0\) gives \(X\approx2.14\) or
+\(X\approx-1.56\), neither of which lies in the fourth quadrant.
+
+Therefore the unique fourth‑quadrant intersection comes from
+\(X_{0}\).  For this root we have from the quadratic
+
+\[
+X_{0}^{2}=4-\sqrt3 X_{0},
+\qquad\text{so}\qquad
+Y_{0}=X_{0}^{2}-4=-\sqrt3 X_{0}.
+\]
+
+Thus
+
+\[
+Y_{0}= -\sqrt3\left(\frac{-\sqrt3+\sqrt{19}}{2}\right)
+     =\frac{3-\sqrt{57}}{2}.
+\]
+
+The \(y\)-coordinate is \(\displaystyle\frac{a-\sqrt b}{c}\) with  
+
+\[
+a=3,\qquad b=57,\qquad c=2.
+\]
+
+Since \(\gcd(3,2)=1\), the conditions are satisfied.  
+
+\[
+a+b+c=3+57+2=62.
+\]
+
+\[
+\boxed{62}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 62</p>
+<p>Extracted Answer: 62</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+A piecewise linear periodic function is defined by $f(x)=\begin{cases}x&amp;\text{if }x\in[-1,1)\\2-x&amp;\text{if }x\in[1,3)\end{cases}$ and $f(x+4)=f(x)$ for all real numbers $x$. The graph of $f(x)$ has the sawtooth pattern. The parabola $x=34y^2$ intersects the graph of $f(x)$ at finitely many points. The sum of the $y$-coordinates of these intersection points can be expressed in the form $\frac{a+b\sqrt{c}}{d}$, where $a,b,c,$ and $d$ are positive integers, $a,b,$ and $d$ have greatest common divisor equal to 1, and $c$ is not divisible by the square of any prime. Find $a+b+c+d$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>The periodic function  
+
+\[
+f(x)=\begin{cases}
+x,&amp;x\in[-1,1)\\[2pt]
+2-x,&amp;x\in[1,3)
+\end{cases},
+\qquad f(x+4)=f(x)
+\]
+
+has period \(4\).  
+On each period write  
+
+\[
+x=4k+u,\qquad u\in[-1,3),\ k\in\mathbb Z .
+\]
+
+Then  
+
+\[
+f(x)=\begin{cases}
+u, &amp; u\in[-1,1)\\[2pt]
+2-u,&amp;u\in[1,3)
+\end{cases}.
+\]
+
+The parabola is \(x=34y^{2}\;(x\ge 0,\;|y|\le 1)\).  
+Set \(x=34y^{2}=4k+u\) with \(u\in[-1,3)\).  
+The integer \(k\) is uniquely determined by  
+
+\[
+\frac{34y^{2}-3}{4}&lt;k\le\frac{34y^{2}+1}{4},
+\]
+
+so for each \(y\) there is exactly one such \(k\).
+
+---
+
+### 1.  Rising part \((u\in[-1,1))\)
+
+Here \(y=u\).  Hence  
+
+\[
+y=34y^{2}-4k\Longrightarrow 34y^{2}-y-4k=0.
+\]
+
+For a fixed \(k\) the two roots are  
+
+\[
+y_{R,k}^{\pm}= \frac{1\pm\sqrt{1+544k}}{68},
+\qquad k=0,1,\dots ,8 .
+\]
+
+Both lie in \([-1,1]\) for all these \(k\).  
+Each pair sums to  
+
+\[
+y_{R,k}^{+}+y_{R,k}^{-}= \frac1{34}.
+\]
+
+Thus  
+
+\[
+\sum_{k=0}^{8}\bigl(y_{R,k}^{+}+y_{R,k}^{-}\bigr)=\frac{9}{34}.
+\]
+
+---
+
+### 2.  Falling part \((u\in[1,3))\)
+
+Here \(y=2-u\).  Hence  
+
+\[
+y=2-(34y^{2}-4k)\Longrightarrow 34y^{2}+y-(4k+2)=0.
+\]
+
+The roots are  
+
+\[
+y_{D,k}^{\pm}= \frac{-1\pm\sqrt{273+544k}}{68},
+\qquad k=0,1,\dots ,8 .
+\]
+
+For \(k=0,\dots ,7\) both roots lie in \([-1,1]\); for \(k=8\) the
+negative root is \(&lt;-1\) and must be discarded.
+Each admissible pair sums to  
+
+\[
+y_{D,k}^{+}+y_{D,k}^{-}= -\frac1{34},
+\]
+
+so for \(k=0,\dots ,7\)
+
+\[
+\sum_{k=0}^{7}\bigl(y_{D,k}^{+}+y_{D,k}^{-}\bigr)= -\frac{8}{34}
+= -\frac{4}{17}.
+\]
+
+The remaining root (the positive one for \(k=8\)) is  
+
+\[
+y_{D,8}^{+}= \frac{-1+ \sqrt{273+544\cdot8}}{68}
+          = \frac{-1+ \sqrt{4625}}{68}
+          = \frac{-1+5\sqrt{185}}{68}.
+\]
+
+---
+
+### 3.  Sum of all \(y\)-coordinates
+
+Adding the contributions,
+
+\[
+\begin{aligned}
+S &amp;=\frac{9}{34}-\frac{4}{17}+\frac{-1+5\sqrt{185}}{68}\\[2pt]
+  &amp;=\frac{9}{34}-\frac{8}{34}+\frac{-1}{68}+\frac{5\sqrt{185}}{68}\\[2pt]
+  &amp;=\frac{1}{34}-\frac{1}{68}+\frac{5\sqrt{185}}{68}\\[2pt]
+  &amp;=\frac{1+5\sqrt{185}}{68}.
+\end{aligned}
+\]
+
+Thus the sum can be written as \(\displaystyle\frac{a+b\sqrt{c}}{d}\) with  
+
+\[
+a=1,\qquad b=5,\qquad c=185,\qquad d=68,
+\]
+
+where \(\gcd(a,b,d)=1\) and \(c\) is square‑free.
+
+Finally  
+
+\[
+a+b+c+d=1+5+185+68=259.
+\]
+
+\[
+\boxed{259}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 259</p>
+<p>Extracted Answer: 259</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $ABCDE$ be a convex pentagon with $AB=14, BC=7, CD=24, DE=13, EA=26,$ and $\angle B=\angle E=60^\circ$. For each point $X$ in the plane, define $f(X)=AX+BX+CX+DX+EX$. The least possible value of $f(X)$ can be expressed as $m+n\sqrt{p}$, where $m$ and $n$ are positive integers and $p$ is not divisible by the square of any prime. Find $m+n+p$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>The required sum is  
+
+\[
+\min_{X\in \mathbb {R}^2}\bigl(AX+BX+CX+DX+EX\bigr)
+=38+19\sqrt{3}.
+\]
+
+Hence  
+
+\[
+m=38,\qquad n=19,\qquad p=3,
+\]
+
+and  
+
+\[
+m+n+p=38+19+3=60.
+\]
+
+\[
+\boxed{60}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 60</p>
+<p>Extracted Answer: 60</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+The 27 cells of a $3\times9$ grid are filled in using the numbers 1 through 9 so that each row contains 9 different numbers, and each of the three $3\times3$ blocks heavily outlined in the example below contains 9 different numbers, as in the first three rows of a Sudoku puzzle. 
+ | 4 | 2 | 8 | 9 | 6 | 3 | 1 | 7 | 5 | 
+ | 3 | 7 | 9 | 5 | 2 | 1 | 6 | 8 | 4 | 
+ | 5 | 6 | 1 | 8 | 4 | 7 | 9 | 2 | 3 | 
+ The number of different ways to fill such a grid can be written as $p^a\cdot q^b\cdot r^c\cdot s^d$, where $p,q,r,$ and $s$ are distinct prime numbers and $a,b,c,$ and $d$ are positive integers. Find $p\cdot a+q\cdot b+r\cdot c+s\cdot d$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let the rows be \(R_{1},R_{2},R_{3}\) and the three \(3\times3\) blocks be
+\(B_{1},B_{2},B_{3}\) (columns \(1\!-\!3,\;4\!-\!6,\;7\!-\!9\)).
+Each number \(x\in\{1,\dots ,9\}\) appears
+
+* once in each row,
+* once in each block.
+
+Hence for a fixed number \(x\) the three occurrences give a bijection  
+
+\[
+\sigma _x:\{R_1,R_2,R_3\}\longrightarrow \{B_1,B_2,B_3\},
+\qquad 
+\sigma_x(R_i)=\text{the block containing }x\text{ in row }R_i .
+\]
+
+Thus \(\sigma_x\) is a permutation of \(\{1,2,3\}\).  
+Conversely, any choice of a permutation \(\sigma_x\) for every \(x\) determines
+which block each occurrence of \(x\) occupies.
+
+--------------------------------------------------------------------
+### 1.  Counting the permutations \(\sigma_x\)
+
+Write a \(9\times3\) matrix whose rows are the six possible permutations of
+\(\{1,2,3\}\):
+
+\[
+\begin{array}{c}
+123\\ 213\\ 321\\ 132\\ 231\\ 312
+\end{array}
+\]
+
+If a number receives a given permutation, that row of the matrix is placed in
+the matrix of size \(9\times3\).  
+Denote by \(x_i\;(i=1,\dots ,6)\) the number of numbers that receive the
+\(i\)‑th permutation.  
+
+Row‑balance (each number uses each symbol once) is automatic; column‑balance
+(because each block must contain exactly three numbers in each row) gives
+
+\[
+\begin{aligned}
+x_1+x_4&amp;=3,\qquad x_2+x_5=3,\qquad x_3+x_6=3,\\
+x_2+x_6&amp;=3,\qquad x_1+x_3=3,\qquad x_4+x_5=3,
+\end{aligned}
+\]
+
+with \(\sum_{i=1}^6x_i=9\).
+Solving gives a one‑parameter family
+
+\[
+(x_1,x_2,x_3,x_4,x_5,x_6)=\bigl(3-t,\;t,\;t,\;t,\;3-t,\;3-t\bigr)
+\qquad(t=0,1,2,3).
+\]
+
+For a fixed \(t\) the numbers are assigned to the six permutation types in  
+
+\[
+\frac{9!}{(t!)^3\bigl((3-t)!\bigr)^3}
+\]
+
+ways.  Summing over the four possible values of \(t\),
+
+\[
+N_{\sigma}= \frac{9!}{(3!)^3}+\frac{9!}{(1!)^3(2!)^3}
+          +\frac{9!}{(2!)^3(1!)^3}+\frac{9!}{(3!)^3}
+          =94\,080 .
+\]
+
+--------------------------------------------------------------------
+### 2.  Placing the numbers inside the blocks
+
+Fix the block‑row distribution given by the \(\sigma_x\)’s.
+In each block, a row contains exactly three different numbers.
+These three numbers can be arranged in the three columns of the block in
+\(3! = 6\) ways, independently for the three rows.
+Hence each block offers \(6^{3}=216\) possibilities, and for the three blocks
+
+\[
+N_{\text{cols}} = 6^{9}=10\,077\,696 .
+\]
+
+--------------------------------------------------------------------
+### 3.  Total number of fillings
+
+\[
+N = N_{\sigma}\,N_{\text{cols}}
+   = 94\,080 \times 6^{9}
+   = 948\,109\,639\,680 .
+\]
+
+Prime factorising,
+
+\[
+N = 2^{16}\cdot 3^{10}\cdot 5^{1}\cdot 7^{2}.
+\]
+
+Thus we may take  
+
+\[
+p=2,\;a=16,\qquad q=3,\;b=10,\qquad r=5,\;c=1,\qquad s=7,\;d=2 .
+\]
+
+Finally,
+
+\[
+p a+ q b+ r c+ s d
+= 2\cdot16 + 3\cdot10 + 5\cdot1 + 7\cdot2
+= 32+30+5+14 = 81 .
+\]
+
+\[
+\boxed{81}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 81</p>
+<p>Extracted Answer: 81</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+The twelve letters $A,B,C,D,E,F,G,H,I,J,K$, and $L$ are randomly grouped into six pairs of letters. The two letters in each pair are placed next to each other in alphabetical order to form six two-letter words, and those six words are listed alphabetically. For example, a possible result is $AB,CJ,DG,EK,FL,HI$. The probability that the last word listed contains $G$ is $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+\[
+\{A,B,\dots ,L\}= \{1,2,\dots ,12\}
+\]
+
+and let a random pairing be a perfect matching of the 12 numbers.
+For each pair \(\{a,b\}\;(a&lt;b)\) we write the word \(ab\);  
+the six words are then listed in alphabetical order.  
+
+--------------------------------------------------------------------
+### 1.  What determines the last word?
+
+In each pair the smaller letter is written first, so the six words are
+
+\[
+\{\,\underbrace{\text{smaller}}_{\text{first letter}},\ \text{larger}\,\}.
+\]
+
+If we denote by  
+
+\[
+S=\{\,\min\{a,b\}\mid\{a,b\}\text{ a pair}\,\},
+\]
+
+then \(|S|=6\) and the last (lexicographically largest) word is the
+pair whose **smaller** element is the largest element of \(S\).
+
+Hence the last word contains \(G\) iff the smaller element of the
+pair containing \(G\) is the maximal element of \(S\).
+
+--------------------------------------------------------------------
+### 2.  Condition on the partner of \(G\)
+
+Let the partner of \(G\;(=7)\) be \(j\neq7\).
+
+*If \(j&gt;7\):* then the smaller element of the \(G\)–pair is \(7\).  
+We need that every other pair have its smaller element \(\le 6\); i.e.
+all the other five “smaller” letters must lie in \(\{1,\dots ,6\}\).
+
+*If \(j&lt;7\):* then the smaller element of the \(G\)–pair is \(j\).  
+We need that every other smaller element be \(&lt;j\); consequently all
+the remaining five smaller letters must be taken from \(\{1,\dots ,j-1\}\).
+
+--------------------------------------------------------------------
+### 3.  Counting matchings that satisfy the condition
+
+After fixing the partner \(j\) we have 10 letters left.
+Let  
+
+\[
+L=\{\text{remaining letters }&lt;j\},\qquad H=\{\text{remaining letters }\ge j\}.
+\]
+
+The condition “no other pair has a smaller element \(\ge j\)” is
+equivalent to **no pair joining two letters of \(H\)**; every element
+of \(H\) must be paired with a distinct element of \(L\).
+
+If \(|L|=l\) and \(|H|=h\) (\(l+h=10\)), the number of perfect matchings
+with no \(H\!-\!H\) pair is
+
+\[
+\binom{l}{h}h!\,(l-h-1)!!\;,
+\]
+
+where \((2k-1)!!=1\cdot3\cdots(2k-1)\).
+The total number of matchings on 10 letters is \((10-1)!!=945\).
+
+---
+
+* **\(j&gt;7\) (five possibilities)**  
+  Here \(j\in\{8,9,10,11,12\}\).  
+  We have \(L=\{1,\dots ,6\}\;(l=6),\ H=\) the four other numbers \(&gt;7\)
+  \((h=4)\).  
+
+  \[
+  \frac{\binom{6}{4}4!\,(6-4-1)!!}{945}
+  =\frac{15\cdot24\cdot1}{945}=\frac{8}{21}.
+  \]
+
+* **\(j=6\)**  
+  Then \(L=\{1,\dots ,5\},\ H=\{8,9,10,11,12\}\) (\(l=h=5\)).  
+
+  \[
+  \frac{\binom{5}{5}5!\,(5-5-1)!!}{945}
+  =\frac{5!}{945}=\frac{120}{945}=\frac{8}{63}.
+  \]
+
+* **\(j=1,2,3,4,5\)**  
+  In these cases \(h&gt;l\); it is impossible to avoid an \(H\!-\!H\) pair,
+  so the probability is \(0\).
+
+--------------------------------------------------------------------
+### 4.  Assemble the total probability
+
+Each of the 11 possible partners of \(G\) is equally likely (\(1/11\)).
+Therefore
+
+\[
+\begin{aligned}
+P(\text{last word contains }G)
+&amp;= \frac1{11}\Bigl(5\cdot\frac{8}{21}+\frac{8}{63}\Bigr)\\[2mm]
+&amp;= \frac1{11}\Bigl(\frac{120}{63}+\frac{8}{63}\Bigr)\\[2mm]
+&amp;= \frac{128}{693}.
+\end{aligned}
+\]
+
+The fraction \(\displaystyle\frac{128}{693}\) is already in lowest terms.
+Hence  
+
+\[
+m=128,\qquad n=693,\qquad m+n=821.
+\]
+
+--------------------------------------------------------------------
+\[
+\boxed{821}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 821</p>
+<p>Extracted Answer: 821</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Find the sum of all positive integers $ n $ such that $ n + 2 $ divides the product $ 3(n + 3)(n^2 + 9) $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+\[
+P(n)=3(n+3)(n^{2}+9).
+\]
+
+We need all positive integers \(n\) for which  
+
+\[
+n+2 \mid P(n).
+\]
+
+---
+
+### 1. Work modulo \(n+2\)
+
+Write \(n\equiv -2 \pmod{\,n+2\,}\).  
+Replace \(n\) by \(-2\) in the factors of \(P(n)\) (this gives the remainder of each factor modulo \(n+2\)):
+
+\[
+\begin{aligned}
+n+3 &amp;\equiv (-2)+3 = 1 \pmod{n+2},\\[2mm]
+n^{2}+9 &amp;\equiv (-2)^{2}+9 = 4+9 = 13 \pmod{n+2}.
+\end{aligned}
+\]
+
+Hence
+
+\[
+P(n)=3(n+3)(n^{2}+9)\equiv 3\cdot 1\cdot 13 = 39\pmod{n+2}.
+\]
+
+---
+
+### 2. Condition for divisibility
+
+The requirement \(n+2\mid P(n)\) is equivalent to  
+
+\[
+P(n)\equiv 0\pmod{n+2}\Longleftrightarrow 39\equiv 0\pmod{n+2}.
+\]
+
+Thus  
+
+\[
+n+2 \text{ must be a positive divisor of } 39.
+\]
+
+The positive divisors of \(39\) are  
+
+\[
+1,\;3,\;13,\;39.
+\]
+
+Since \(n\) is a **positive** integer, \(n+2\ge 3\).  
+Hence \(n+2\) can be only \(3,\;13,\;39\).
+
+---
+
+### 3. Corresponding values of \(n\)
+
+\[
+\begin{array}{c|c}
+n+2 &amp; n \\ \hline
+3   &amp; 1\\
+13  &amp; 11\\
+39  &amp; 37
+\end{array}
+\]
+
+All three satisfy the original condition (a quick check confirms divisibility).
+
+---
+
+### 4. Sum of all such \(n\)
+
+\[
+1+11+37 = 49.
+\]
+
+\[
+\boxed{49}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 49</p>
+<p>Extracted Answer: 49</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Six points $ A, B, C, D, E, $ and $ F $ lie in a straight line in that order. Suppose that $ G $ is a point not on the line and that $ AC = 26 $, $ BD = 22 $, $ CE = 31 $, $ DF = 33 $, $ AF = 73 $, $ CG = 40 $, and $ DG = 30 $. Find the area of $ \triangle BGE $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>We place the six collinear points on the \(x\)-axis.
+
+---
+
+### 1.  Determine the coordinates of \(A,B,C,D,E,F\)
+
+Let \(A=(0,0)\).  
+Write the distances in terms of the unknown coordinate \(AB=x\).
+
+\[
+\begin{aligned}
+C&amp;: AC=26 \quad\Longrightarrow\quad C=(26,0)\\
+B&amp;: AB=x \quad\Longrightarrow\quad B=(x,0)\\
+D&amp;: BD=22 \quad\Longrightarrow\quad D=(x+22,0)\\
+E&amp;: CE=31 \quad\Longrightarrow\quad E=(26+31,0)=(57,0)\\
+F&amp;: DF=33 \quad\Longrightarrow\quad F=(x+22+33,0)=(x+55,0)\\
+\text{and }AF&amp;=73 \Longrightarrow x+55=73 .
+\end{aligned}
+\]
+
+Hence \(x=18\). So  
+
+\[
+A=0,\; B=18,\; C=26,\; D=40,\; E=57,\; F=73 .
+\]
+
+These satisfy all given segment lengths.
+
+---
+
+### 2.  Locate point \(G\)
+
+Let \(G=(u,v)\) with \(v\neq 0\).  
+From the given distances
+
+\[
+\begin{cases}
+(u-26)^2+v^2 = 40^2 =1600,\\[2pt]
+(u-40)^2+v^2 = 30^2 = 900 .
+\end{cases}
+\]
+
+Subtract the second equation from the first:
+
+\[
+(u-26)^2-(u-40)^2 = 700 .
+\]
+
+Expanding,
+
+\[
+(-52u+676)-(-80u+1600)=28u-924=700
+\Longrightarrow 28u=1624\Longrightarrow u=58 .
+\]
+
+Now find \(v\):
+
+\[
+(58-26)^2+v^2=1600\Longrightarrow 32^2+v^2=1600
+\Longrightarrow v^2=1600-1024=576 .
+\]
+
+Thus \(|v|=24\).  Take \(v=24\) (the sign does not affect the area).  
+
+\[
+\boxed{G=(58,24)} .
+\]
+
+---
+
+### 3.  Area of \(\triangle BGE\)
+
+Points on the \(x\)-axis:
+
+\[
+B=(18,0),\qquad E=(57,0).
+\]
+
+The length of the base \(BE\) is
+
+\[
+BE = 57-18 = 39 .
+\]
+
+Since the line through \(B\) and \(E\) is the \(x\)-axis, the perpendicular distance from \(G\) to this line is \(|v|=24\).
+
+Hence
+
+\[
+[\triangle BGE]=\frac12\,(BE)\cdot(\text{height})
+               =\frac12\cdot 39\cdot 24
+               =\frac{936}{2}=468 .
+\]
+
+(Using the determinant formula also gives \(468\).)
+
+---
+
+\[
+\boxed{468}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 468</p>
+<p>Extracted Answer: 468</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+The set of points in 3-dimensional coordinate space that lie in the plane $x+y+z=75$ whose coordinates satisfy the inequalities $x-yz&lt;y-zx&lt;z-xy$ forms three disjoint convex regions. Exactly one of those regions has finite area. The area of this finite region can be expressed in the form $a\sqrt{b}$, where $a$ and $b$ are positive integers and $b$ is not divisible by the square of any prime. Find $a+b$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>The inequalities  
+
+\[
+x-yz&lt;y-zx&lt;z-xy
+\]
+
+can be rewritten by factoring:
+
+\[
+\begin{aligned}
+x-yz&lt;y-zx &amp;\iff (x-y)(1+z)&lt;0,\\[2pt]
+y-zx&lt;z-xy &amp;\iff (y-z)(1+x)&lt;0 .
+\end{aligned}
+\]
+
+Since the points lie on the plane  
+
+\[
+x+y+z=75\qquad\Longrightarrow\qquad z=75-x-y,
+\]
+
+the two conditions become inequalities in the variables \(x,y\):
+
+\[
+\begin{cases}
+(x-y)\bigl(76-x-y\bigr)&lt;0,\\[2pt]
+\bigl(x+2y-75\bigr)(1+x)&lt;0 .
+\end{cases}
+\tag{1}
+\]
+
+---
+
+### 1.  Geometry of the half‑planes
+
+From (1)
+
+* \((x-y)(76-x-y)&lt;0\) gives either  
+
+  \[
+  \begin{cases}
+  x&gt;y,\;x+y&gt;76 \quad\text{(region }A_1)\\
+  \text{or}\\
+  x&lt;y,\;x+y&lt;76 \quad\text{(region }A_2)
+  \end{cases}
+  \]
+
+* \((x+2y-75)(1+x)&lt;0\) gives either  
+
+  \[
+  \begin{cases}
+  x&lt;-1,\;x+2y&gt;75 \quad\text{(region }B_1)\\
+  \text{or}\\
+  x&gt;-1,\;x+2y&lt;75 \quad\text{(region }B_2)
+  \end{cases}
+  \]
+
+The set of points satisfying both inequalities is the intersection of one of the
+\(A_i\) with one of the \(B_j\).
+
+Checking the four possibilities:
+
+* \(A_1\cap B_1=\varnothing\) (impossible to have \(x&gt;y\) and \(x&lt;-1\) while
+  \(x+y&gt;76\)).
+* \(A_1\cap B_2\) is non‑empty and unbounded (e.g. \(x&gt;77\)).
+* \(A_2\cap B_1\) is non‑empty and unbounded (e.g. \(x&lt;-1\)).
+* \(A_2\cap B_2\) is bounded.
+
+Thus there are three convex components: two infinite ones and one finite one,
+the latter being \(A_2\cap B_2\).
+
+---
+
+### 2.  The finite region
+
+\(A_2\cap B_2\) is described by  
+
+\[
+\begin{cases}
+x&gt;-1,\\
+x&lt;y,\\
+x+2y&lt;75 .
+\end{cases}
+\]
+
+From \(x+2y&lt;75\) we have \(y&lt;(75-x)/2\).  
+Together with \(y&gt;x\) we obtain
+
+\[
+-1&lt;x&lt;25,\qquad x&lt;y&lt;\frac{75-x}{2}.
+\]
+
+The three bounding lines intersect at
+
+\[
+\begin{aligned}
+x=-1 \ \text{and}\ y=x&amp;\;&amp;\Rightarrow\;(-1,-1),\\
+x=-1 \ \text{and}\ x+2y=75&amp;\;&amp;\Rightarrow\;(-1,38),\\
+y=x \ \text{and}\ x+2y=75&amp;\;&amp;\Rightarrow\;(25,25).
+\end{aligned}
+\]
+
+Hence the finite region is the interior of the triangle with vertices  
+\((-1,-1),\;(-1,38),\;(25,25)\).
+
+Its area in the \(xy\)-plane is
+
+\[
+\text{Area}_{xy}
+=\frac12\cdot\text{base}\cdot\text{height}
+=\frac12\cdot 39\cdot 26 =507 .
+\]
+
+---
+
+### 3.  Area on the plane \(x+y+z=75\)
+
+The map \((x,y)\mapsto (x,y,75-x-y)\) sends the \(xy\)-plane onto the given
+plane.  The area is scaled by the factor
+
+\[
+\bigl|\partial_{x}(x,y,z)\times\partial_{y}(x,y,z)\bigr|
+=|(1,0,-1)\times(0,1,-1)|
+=|(1,1,1)|
+=\sqrt{3}.
+\]
+
+Thus the area of the finite region on the plane is
+
+\[
+\text{Area}= \sqrt{3}\times 507 = 507\sqrt{3}.
+\]
+
+---
+
+The required form is \(a\sqrt{b}\) with \(a=507,\;b=3\).  Hence
+
+\[
+a+b = 507+3 = 510.
+\]
+
+\[
+\boxed{510}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 510</p>
+<p>Extracted Answer: 510</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+The product $ \prod_{k=4}^{63} \frac{\log_k(5^{k^2-1})}{\log_{k+1}(5^{k^2-4})} = \frac{\log_4(5^{15})}{\log_5(5^{12})} \cdot \frac{\log_5(5^{24})}{\log_6(5^{21})} \cdot \frac{\log_6(5^{35})}{\log_7(5^{32})} \cdots \frac{\log_{63}(5^{3968})}{\log_{64}(5^{3965})} $ is equal to $ \frac{m}{n} $, where $ m $ and $ n $ are relatively prime positive integers. Find $ m + n $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>\[
+P=\prod_{k=4}^{63}\frac{\log_k\!\big(5^{\,k^2-1}\big)}{\log_{k+1}\!\big(5^{\,k^2-4}\big)}
+\]
+
+---
+
+### 1.  Change of base  
+
+\[
+\log_a b=\frac{\ln b}{\ln a}
+\]
+
+Hence  
+
+\[
+\begin{aligned}
+\log_k\!\big(5^{k^2-1}\big)&amp;=\frac{(k^2-1)\ln5}{\ln k},\\[2mm]
+\log_{k+1}\!\big(5^{k^2-4}\big)&amp;=\frac{(k^2-4)\ln5}{\ln(k+1)} .
+\end{aligned}
+\]
+
+Therefore each factor of the product is
+
+\[
+\frac{(k^2-1)\ln5/\ln k}{(k^2-4)\ln5/\ln(k+1)}
+= \frac{k^2-1}{k^2-4}\cdot\frac{\ln(k+1)}{\ln k}.
+\]
+
+Thus  
+
+\[
+P=\Bigg(\prod_{k=4}^{63}\frac{k^2-1}{k^2-4}\Bigg)
+   \Bigg(\prod_{k=4}^{63}\frac{\ln(k+1)}{\ln k}\Bigg).
+\]
+
+---
+
+### 2.  Telescoping the logarithmic part  
+
+\[
+\prod_{k=4}^{63}\frac{\ln(k+1)}{\ln k}
+ =\frac{\ln5}{\ln4}\cdot\frac{\ln6}{\ln5}\cdots\frac{\ln64}{\ln63}
+ =\frac{\ln64}{\ln4}
+ =\log_4 64 = 3 .
+\]
+
+---
+
+### 3.  Simplify the rational part  
+
+\[
+\frac{k^2-1}{k^2-4}
+ =\frac{(k-1)(k+1)}{(k-2)(k+2)}
+ =\frac{k-1}{k-2}\cdot\frac{k+1}{k+2}.
+\]
+
+Hence  
+
+\[
+\prod_{k=4}^{63}\frac{k^2-1}{k^2-4}
+ =\Bigg(\prod_{k=4}^{63}\frac{k-1}{k-2}\Bigg)
+  \Bigg(\prod_{k=4}^{63}\frac{k+1}{k+2}\Bigg).
+\]
+
+*First product*  
+
+\[
+\prod_{k=4}^{63}\frac{k-1}{k-2}
+ =\frac{3}{2}\cdot\frac{4}{3}\cdot\frac{5}{4}\cdots\frac{62}{61}
+ =\frac{62}{2}=31 .
+\]
+
+*Second product*  
+
+\[
+\prod_{k=4}^{63}\frac{k+1}{k+2}
+ =\frac{5}{6}\cdot\frac{6}{7}\cdot\frac{7}{8}\cdots\frac{64}{65}
+ =\frac{5}{65}= \frac{1}{13}.
+\]
+
+Thus the rational part equals  
+
+\[
+31\cdot\frac{1}{13}= \frac{31}{13}.
+\]
+
+---
+
+### 4.  Combine the two parts  
+
+\[
+P=\frac{31}{13}\times 3 = \frac{93}{13}.
+\]
+
+The fraction \(\frac{93}{13}\) is already in lowest terms, so  
+
+\[
+m=93,\qquad n=13,\qquad m+n=93+13=106.
+\]
+
+\[
+\boxed{106}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 106</p>
+<p>Extracted Answer: 106</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Four unit squares form a $2 \times 2$ grid. Each of the 12 unit line segments forming the sides of the squares is colored either red or blue in such a way that each unit square has 2 red sides and 2 blue sides. Find the number of such colorings.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+* \(a_{1},a_{2}\) be the two **vertical** interior unit segments (the left–right dividing line),  
+* \(b_{1},b_{2}\) be the two **horizontal** interior unit segments (the bottom–top dividing line).
+
+The eight outer–boundary unit segments belong to only one square, while each interior segment belongs to two squares.
+
+---
+
+### 1.  Equations for the four unit squares  
+
+Denote by \(L_1 ,D_1\) the left and bottom edges of the lower‑left square, etc.  
+Writing a red edge as \(1\) and a blue edge as \(0\), the condition “exactly two red sides’’ for each square gives  
+
+\[
+\begin{aligned}
+L_1 + D_1 + a_{1}+ b_{1} &amp;=2,\\
+D_2 + R_2 + a_{1}+ b_{2} &amp;=2,\\
+L_3 + T_3 + a_{2}+ b_{1} &amp;=2,\\
+R_4 + T_4 + a_{2}+ b_{2} &amp;=2,
+\end{aligned}
+\]
+
+where the eight variables \(L_1,D_1,D_2,R_2,L_3,T_3,R_4,T_4\) are the boundary edges and the
+four variables \(a_{1},a_{2},b_{1},b_{2}\) are the interior edges.
+
+For a fixed choice of the interior edges, each equation tells us the sum of the two
+boundary edges of that square:
+
+\[
+\begin{aligned}
+L_1+D_1 &amp;=2-(a_{1}+b_{1}),\\
+D_2+R_2 &amp;=2-(a_{1}+b_{2}),\\
+L_3+T_3 &amp;=2-(a_{2}+b_{1}),\\
+R_4+T_4 &amp;=2-(a_{2}+b_{2}).
+\end{aligned}
+\tag{1}
+\]
+
+The right‑hand side can be \(0,1,\) or \(2\).  
+
+* If it is \(0\) or \(2\) there is **exactly one** way to colour the two boundary
+edges (both blue or both red).  
+* If it is \(1\) there are **two** ways (one red, one blue).
+
+Thus for a given interior assignment the number of completions equals  
+
+\[
+\prod_{i=1}^{4}f\bigl(2-(a_{i}+b_{j})\bigr),
+\qquad
+f(0)=f(2)=1,\;f(1)=2 .
+\tag{2}
+\]
+
+The factor contributed by a square is \(2\) precisely when the sum of its two
+interior edges equals \(1\).
+
+---
+
+### 2.  How many squares have interior‑sum \(=1\)?
+
+Let  
+
+\[
+A = a_{1}+a_{2}\quad(\text{number of red vertical interiors}),\qquad
+B = b_{1}+b_{2}\quad(\text{number of red horizontal interiors}).
+\]
+
+For a square the two interior edges are one vertical and one horizontal, so the
+square’s interior sum is \(1\) exactly when the chosen vertical edge and horizontal
+edge have different colours.  Hence the number of squares with interior‑sum \(=1\) is  
+
+\[
+N = A(2-B)+(2-A)B = 2A+2B-2AB.
+\tag{3}
+\]
+
+Because \(A,B\in\{0,1,2\}\),
+
+\[
+N=
+\begin{cases}
+0 &amp; (A,B)=(0,0)\text{ or }(2,2),\\[2pt]
+2 &amp; \text{otherwise except the next case},\\[2pt]
+4 &amp; (A,B)=(0,2)\text{ or }(2,0).
+\end{cases}
+\]
+
+---
+
+### 3.  Counting all interior assignments  
+
+The numbers of interior assignments for each \((A,B)\) are
+
+\[
+\begin{array}{c|c|c}
+(A,B) &amp; \text{\# assignments} &amp; N \\ \hline
+(0,0) &amp; 1 &amp; 0\\
+(2,2) &amp; 1 &amp; 0\\
+(0,2) &amp; 1 &amp; 4\\
+(2,0) &amp; 1 &amp; 4\\
+(0,1) &amp; 2 &amp; 2\\
+(1,0) &amp; 2 &amp; 2\\
+(1,1) &amp; 4 &amp; 2\\
+(1,2) &amp; 2 &amp; 2\\
+(2,1) &amp; 2 &amp; 2
+\end{array}
+\]
+
+For a given interior assignment the number of ways to colour the boundary
+edges is \(2^{N}\) (by (2)).  Therefore
+
+\[
+\begin{aligned}
+\#\text{colorings}&amp;=
+1\cdot2^{0}+1\cdot2^{0}
++1\cdot2^{4}+1\cdot2^{4}
++ (2+2+4+2+2)\cdot2^{2} \\[4pt]
+&amp;=2\cdot1 + 2\cdot16 + 12\cdot4 \\[4pt]
+&amp;=2 + 32 + 48 \\[4pt]
+&amp;=82 .
+\end{aligned}
+\]
+
+---
+
+\[
+\boxed{82}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 82</p>
+<p>Extracted Answer: 82</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Circle $\omega_1$ with radius 6 centered at point $A$ is internally tangent at point $B$ to circle $\omega_2$ with radius 15. Points $C$ and $D$ lie on $\omega_2$ such that $\overline{BC}$ is a diameter of $\omega_2$ and $\overline{BC} \perp \overline{AD}$. The rectangle $EFGH$ is inscribed in $\omega_1$ such that $\overline{EF} \perp \overline{BC}$, $C$ is closer to $\overline{GH}$ than to $\overline{EF}$, and $D$ is closer to $\overline{FG}$ than to $\overline{EH}$, as shown. Triangles $\triangle DGF$ and $\triangle CHG$ have equal areas. The area of rectangle $EFGH$ is $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m + n$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+* \(O\) be the centre of \(\omega _2\) (radius \(15\)),
+* \(A\) the centre of \(\omega _1\) (radius \(6\)),
+* \(B\) the internal point of tangency of the two circles.
+
+Place the picture on a coordinate plane.
+
+---
+
+### 1.  Coordinates of the given points  
+
+Take \(O=(0,0)\).  
+Since \(OA=15-6=9\) and the circles are tangent internally, we may put  
+
+\[
+A=(9,0), \qquad B=(15,0).
+\]
+
+\(BC\) is a diameter of \(\omega _2\) through \(B\); hence  
+
+\[
+C=(-15,0).
+\]
+
+\(AD\perp BC\) forces \(AD\) to be the vertical line through \(A\); intersecting this line with
+\(\omega _2\) gives  
+
+\[
+D=(9,-12)\quad\text{or}\quad (9,12).
+\]
+
+The condition “\(D\) is closer to \(\overline{FG}\) than to \(\overline{EH}\)” (see below) makes
+\(D=(9,-12)\).
+
+---
+
+### 2.  The rectangle \(EFGH\)
+
+\(EFGH\) is inscribed in the circle \(\omega_1\), so its vertices lie on  
+
+\[
+(x-9)^2+y^2=6^2=36 .
+\]
+
+Since \(\overline{EF}\perp BC\) and \(BC\) is horizontal, \(\overline{EF}\) is vertical.
+Let  
+
+\[
+\begin{aligned}
+E&amp;=(9+w,\,h),\\
+F&amp;=(9+w,\,-h),\\
+G&amp;=(9-w,\,-h),\\
+H&amp;=(9-w,\,h),
+\end{aligned}
+\]
+
+where \(w&gt;0,\,h&gt;0\) are the half‑width and half‑height of the rectangle.
+
+All four vertices satisfy the circle equation, giving the single relation  
+
+\[
+w^{2}+h^{2}=36\tag{1}
+\]
+
+(the rectangle’s centre is the circle’s centre \(A\)).
+
+Because the point \(C=(-15,0)\) is farther to the right than to the left,
+the condition “\(C\) is closer to \(\overline{GH}\) than to \(\overline{EF}\)’’ forces
+\(\overline{GH}\) to be the **left** side (\(x=9-w\)), which is already the case.
+
+Since \(D=(9,-12)\) lies below the centre, “\(D\) is closer to \(\overline{FG}\) than to \(\overline{EH}\)’’ forces
+\(\overline{FG}\) to be the **bottom** side (\(y=-h\)).  This orientation matches the above labeling.
+
+---
+
+### 3.  Areas of the two triangles  
+
+*Triangle \(DGF\)*  
+
+The points are \(D(9,-12),\; G(9-w,-h),\; F(9+w,-h)\).
+Its base \(GF\) has length \(2w\) and its height (vertical distance from \(D\) to the base) is \(12-h\).  
+Hence  
+
+\[
+[\,DGF\,]=\tfrac12\,(2w)(12-h)=w(12-h).\tag{2}
+\]
+
+*Triangle \(CHG\)*  
+
+The points are \(C(-15,0),\; H(9-w,h),\; G(9-w,-h)\).
+Its base \(HG\) has length \(2h\) and its horizontal distance from \(C\) to the line \(x=9-w\) is
+\(|-15-(9-w)|=24-w\).  
+Thus  
+
+\[
+[\,CHG\,]=\tfrac12\,(2h)(24-w)=h(24-w).\tag{3}
+\]
+
+The problem states the two areas are equal, so
+
+\[
+w(12-h)=h(24-w).\tag{4}
+\]
+
+Expanding gives \(12w-wh=24h-wh\), whence  
+
+\[
+12w=24h \qquad\Longrightarrow\qquad w=2h.\tag{5}
+\]
+
+---
+
+### 4.  Solving for \(w\) and \(h\)
+
+Substituting \(w=2h\) into (1):
+
+\[
+(2h)^2+h^2=36 \;\Longrightarrow\;5h^{2}=36 \;\Longrightarrow\;
+h=\frac{6}{\sqrt5}=\frac{6\sqrt5}{5}.
+\]
+
+Hence  
+
+\[
+w=2h=\frac{12}{\sqrt5}=\frac{12\sqrt5}{5}.
+\]
+
+---
+
+### 5.  Area of the rectangle  
+
+The side lengths are \(2w\) and \(2h\).  Therefore  
+
+\[
+\text{Area}= (2w)(2h)=4wh.
+\]
+
+Using \(w=2h\),
+
+\[
+4wh = 4(2h)h = 8h^{2}=8\left(\frac{36}{5}\right)=\frac{288}{5}.
+\]
+
+Thus the area is \(\displaystyle\frac{288}{5}\); the numerator and denominator are coprime.
+
+\[
+m=288,\qquad n=5,\qquad m+n=288+5=293.
+\]
+
+\[
+\boxed{293}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 293</p>
+<p>Extracted Answer: 293</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $ A $ be the set of positive integer divisors of 2025. Let $ B $ be a randomly selected subset of $ A $. The probability that $ B $ is a nonempty set with the property that the least common multiple of its elements is 2025 is $ \frac{m}{n} $, where $ m $ and $ n $ are relatively prime positive integers. Find $ m + n $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>The divisors of \(2025\) are all numbers of the form  
+
+\[
+3^{a}5^{b},\qquad 0\le a\le 4,\;0\le b\le 2 .
+\]
+
+Hence  
+
+\[
+|A|=(4+1)(2+1)=15 .
+\]
+
+So there are \(2^{15}\) subsets of \(A\) (including the empty set).
+
+--------------------------------------------------------------------
+### When does a subset have lcm \(2025\)?
+
+The prime factorisation of \(2025\) is  
+
+\[
+2025 = 3^{4}\,5^{2}.
+\]
+
+For a subset \(B\subseteq A\),
+
+\[
+\operatorname{lcm}(B)=3^{\max a_i}\,5^{\max b_i},
+\]
+
+where \((a_i,b_i)\) are the exponents of the elements of \(B\).
+Thus \(\operatorname{lcm}(B)=2025\) iff  
+
+* at least one element has exponent \(a=4\) (i.e. contains \(3^4\));
+* at least one element has exponent \(b=2\) (i.e. contains \(5^2\)).
+
+--------------------------------------------------------------------
+### Sets that provide the required exponents  
+
+\[
+A_4=\{d\in A:3^4\mid d\}=\{3^4\! \cdot\! 5^0,\;3^4\! \cdot\!5^1,\;3^4\! \cdot\!5^2\}
+\]
+has \(|A_4|=3\) elements.
+
+\[
+B_2=\{d\in A:5^2\mid d\}=\{3^0\! \cdot\!5^2,\;3^1\! \cdot\!5^2,\;3^2\! \cdot\!5^2,
+\;3^3\! \cdot\!5^2,\;3^4\! \cdot\!5^2\}
+\]
+has \(|B_2|=5\) elements.
+
+Their intersection is the single divisor \(2025=3^4\! \cdot\!5^2\).
+
+--------------------------------------------------------------------
+### Counting the suitable subsets  
+
+A subset \(B\) works iff it contains **at least one** element of \(A_4\) **and** at least one element of \(B_2\).
+
+Using inclusion–exclusion on the \(2^{15}\) total subsets:
+
+\[
+\begin{aligned}
+N &amp;= 2^{15}
+     -\underbrace{2^{15-3}}_{\text{subsets missing }A_4}
+     -\underbrace{2^{15-5}}_{\text{subsets missing }B_2}
+     +\underbrace{2^{15-7}}_{\text{subsets missing both}} \\[4pt]
+  &amp;= 2^{15}-2^{12}-2^{10}+2^{8}\\
+  &amp;= 32768-4096-1024+256\\
+  &amp;= 27904 .
+\end{aligned}
+\]
+
+Thus the desired probability is  
+
+\[
+\frac{N}{2^{15}}=\frac{27904}{32768}
+          =\frac{109}{128}\qquad(\text{after cancelling }256).
+\]
+
+--------------------------------------------------------------------
+### Answer  
+
+\(m=109,\;n=128\), so  
+
+\[
+m+n=109+128=237 .
+\]
+
+\[
+\boxed{237}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 237</p>
+<p>Extracted Answer: 237</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Alex divides a disk into four quadrants with two perpendicular diameters intersecting at the center of the disk. He draws 25 more line segments through the disk, drawing each segment by selecting two points at random on the perimeter of the disk in different quadrants and connecting those two points. Find the expected number of regions into which these 27 line segments divide the disk.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>**Step 1 –  What we have to count**
+
+The two perpendicular diameters are two line segments that intersect once, so after they are drawn the disk is divided into  
+
+\[
+F_0=4\qquad\text{regions}.
+\]
+
+Every time we draw a new segment, it splits each region it meets into two pieces.  
+If the new segment meets \(k\) already‑drawn segments in interior points, it creates \(k+1\) new regions.  
+
+Hence  
+
+\[
+\boxed{\text{# of regions}=1+\#\text{segments}+ \#\text{intersection points}}
+\tag{1}
+\]
+
+(the “\(1\)” is the original whole disk).  
+We have \(27\) segments in total (the 2 diameters + the 25 random chords).  
+Thus we only have to find the **expected number of intersection points**.
+
+--------------------------------------------------------------------
+
+**Step 2 –  Intersections with the two diameters**
+
+For a random chord we must choose its two endpoints in *different* quadrants.
+The unordered pair of quadrants is equally likely among the  
+
+\[
+\binom{4}{2}=6
+\]
+
+possibilities.  
+
+* Adjacent quadrants (four choices) – the chord meets **one** diameter.  
+* Opposite quadrants (two choices) – the chord meets **both** diameters.
+
+Therefore for one random chord  
+
+\[
+E[\text{diameters met}]
+=\frac{4}{6}\cdot1+\frac{2}{6}\cdot2=\frac{4}{3}.
+\]
+
+With \(N=25\) random chords
+
+\[
+E[\text{intersections with the two diameters}]
+=N\cdot\frac{4}{3}= \frac{100}{3}.
+\tag{2}
+\]
+
+--------------------------------------------------------------------
+
+**Step 3 –  Intersection of two random chords**
+
+Let a chord be drawn.  
+Write its endpoints as angles measured from the positive \(x\)–axis.
+Because the two endpoints are in different quadrants, the unordered pair of
+quadrants is uniform among the six possibilities.
+
+*Probability that a second random chord meets the first.*
+
+Let the first chord be fixed.  
+Denote by \(I\) the clockwise arc of the circle from its first endpoint to its
+second endpoint; let \(|I|=L\).
+If a second chord has one endpoint in \(I\) and the other outside \(I\) the two
+chords intersect.  
+
+When the second chord is chosen, its first endpoint \(U\) is uniform on the whole
+circle, and its second endpoint \(V\) is uniform on the *three* quadrants that are
+different from the quadrant of \(U\).  
+A short calculation (integrating over the position of \(U\) inside \(I\))
+gives for a fixed chord
+
+\[
+\boxed{q=\frac{L}{\pi}-\frac{2L^{2}}{3\pi^{2}}
+      +\frac{2}{3\pi^{2}}\!\int_{I}\!|I\cap Q(\theta)|\,d\theta},
+\tag{3}
+\]
+where \(Q(\theta)\) is the quadrant containing \(\theta\).
+
+Now we average (3) over the possible positions of the first chord.
+
+*Adjac­ent quadrants.*  
+The arc \(I\) lies in exactly two quadrants; write its lengths in those
+quadrants as \(L_{1},L_{2}\) (\(L=L_{1}+L_{2}\)).  
+Then \(\int_{I}|I\cap Q|\,d\theta = L_{1}^{2}+L_{2}^{2}\).
+With \(L_{1},L_{2}\) independent and uniform on \([0,\pi/2]\),
+
+\[
+E[q\mid\text{adjacent}] = \frac{5}{12}.
+\]
+
+*Opposite quadrants.*  
+Now \(I\) occupies three quadrants; let the lengths in the three
+quadrants be \(u,\,\pi/2,\,v\) (\(u,v\) independent uniform on \([0,\pi/2]\)).  
+Then \(\int_{I}|I\cap Q|\,d\theta = u^{2}+(\pi/2)^{2}+v^{2}\).
+Averaging gives
+
+\[
+E[q\mid\text{opposite}] = \frac{7}{12}.
+\]
+
+The first chord is adjacent with probability \(\frac{2}{3}\) and opposite with
+probability \(\frac13\).  Hence the probability that two independently drawn
+random chords intersect is
+
+\[
+p=\frac{2}{3}\cdot\frac{5}{12}+\frac{1}{3}\cdot\frac{7}{12}
+    =\frac{17}{36}.
+\tag{4}
+\]
+
+--------------------------------------------------------------------
+
+**Step 4 –  Expected intersections among the 25 random chords**
+
+There are \(\binom{25}{2}=300\) unordered pairs of random chords, each
+intersecting with probability \(p\).  Thus
+
+\[
+E[\text{intersections among the 25 chords}]
+=300\cdot\frac{17}{36}= \frac{425}{3}.
+\tag{5}
+\]
+
+--------------------------------------------------------------------
+
+**Step 5 –  Total expected number of intersection points**
+
+Add all contributions:
+
+* one intersection of the two diameters,
+* intersections of random chords with the two diameters \(\displaystyle\frac{100}{3}\)   (from (2)),
+* intersections among the random chords \(\displaystyle\frac{425}{3}\)   (from (5)).
+
+\[
+E[\text{total intersections}]
+=1+\frac{100}{3}+\frac{425}{3}=1+\frac{525}{3}=176.
+\tag{6}
+\]
+
+--------------------------------------------------------------------
+
+**Step 6 –  Expected number of regions**
+
+Insert (6) into formula (1):
+
+\[
+E[\text{regions}]
+=1+\underbrace{27}_{\text{segments}}+\underbrace{176}_{\text{intersection points}}
+=204 .
+\]
+
+--------------------------------------------------------------------
+
+\[
+\boxed{204}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 204</p>
+<p>Extracted Answer: 204</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+There are $ n $ values of $ x $ in the interval $ 0 &lt; x &lt; 2\pi $ where $ f(x) = \sin(7\pi \cdot \sin(5x)) = 0 $. For $ t $ of these $ n $ values of $ x $, the graph of $ y = f(x) $ is tangent to the $ x $-axis. Find $ n + t $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>The zeros of  
+
+\[
+f(x)=\sin\bigl(7\pi\sin(5x)\bigr)
+\]
+
+satisfy  
+
+\[
+\sin\bigl(7\pi\sin(5x)\bigr)=0\Longrightarrow 7\pi\sin(5x)=k\pi,\qquad k\in\mathbb Z .
+\]
+
+Hence  
+
+\[
+\sin (5x)=\frac{k}{7},\qquad -7\le k\le 7 .
+\]
+
+---
+
+### 1.  Counting all zeros \(n\)
+
+Put \(\theta =5x\).  
+Because \(0&lt;x&lt;2\pi\), we have \(0&lt;\theta&lt;10\pi\).
+
+For each integer \(k\) we count the solutions of \(\sin\theta = k/7\) in \((0,10\pi)\).
+
+* **\(k=\pm7\) :** \(\sin\theta=\pm1\).  
+  Solutions are \(\theta =\frac{\pi}{2}+2\pi m\) (or \(\frac{3\pi}{2}+2\pi m\)).  
+  In a length \(10\pi\) there are \(5\) such values for each sign.  
+  → \(5+5=10\) solutions.
+
+* **\(k=0\) :** \(\sin\theta=0\).  
+  Solutions are \(\theta=n\pi\).  
+  With \(0&lt;\theta&lt;10\pi\) we have \(n=1,2,\dots ,9\): \(9\) solutions.
+
+* **\(k=\pm1,\pm2,\ldots,\pm6\) (12 values):** \(\sin\theta = k/7\) is a non‑extreme value.  
+  In each full period of length \(2\pi\) there are \(2\) solutions; we have five periods, so each such \(k\) yields \(10\) solutions.  
+  → \(12\cdot10=120\) solutions.
+
+Hence  
+
+\[
+n = 10\;(\text{from }k=\pm7)+9\;(\text{from }k=0)+120\;(\text{from }k=\pm1,\dots,\pm6)=139 .
+\]
+
+---
+
+### 2.  Tangential zeros \(t\)
+
+The derivative is  
+
+\[
+f&#39;(x)=\cos\bigl(7\pi\sin(5x)\bigr)\cdot 7\pi\cdot5\cos(5x)
+      =35\pi\cos\bigl(7\pi\sin(5x)\bigr)\cos(5x).
+\]
+
+At a zero of \(f\) we have \(\sin(5x)=k/7\) and thus  
+\(\cos(7\pi\sin(5x))=\cos(k\pi)=(-1)^{k}\).
+
+Therefore  
+
+\[
+f&#39;(x)=35\pi(-1)^{k}\cos(5x).
+\]
+
+For the graph to be tangent to the \(x\)-axis we need \(f&#39;(x)=0\); this occurs exactly when  
+
+\[
+\cos(5x)=0 \quad\Longleftrightarrow\quad \sin(5x)=\pm1.
+\]
+
+Thus the tangential zeros correspond to the case \(k=\pm7\).  
+We already counted those: \(5\) solutions for \(k=7\) and \(5\) for \(k=-7\).
+
+\[
+t = 5+5 = 10.
+\]
+
+---
+
+### 3.  Required sum
+
+\[
+n+t = 139+10 = 149.
+\]
+
+\[
+\boxed{149}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 149</p>
+<p>Extracted Answer: 149</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Sixteen chairs are arranged in a row. Eight people each select a chair in which to sit so that no person sits next to two other people. Let $ N $ be the number of subsets of 16 chairs that could be selected. Find the remainder when $ N $ is divided by 1000.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let the chairs be numbered \(1,2,\dots ,16\).
+Choosing the chairs for the eight people is equivalent to writing a binary
+string of length \(16\) with exactly eight \(1\)’s (occupied chairs) and
+seven \(0\)’s (empty chairs).
+
+The condition *“no person sits next to two other people’’* means that no
+occupied chair can have occupied neighbours on both sides; thus the binary
+string must contain **no substring \(111\)**.  
+Hence we must count binary strings of length \(16\) with weight \(8\) that avoid
+\(111\).
+
+---
+
+### 1.  Describing the strings
+
+The \(1\)’s can appear only in blocks of length \(1\) or \(2\) (a block of
+length \(3\) would give a forbidden \(111\)).  
+Suppose there are  
+
+* \(s\) blocks of length \(2\);
+* \(t-s\) blocks of length \(1\),
+
+so the total number of blocks of \(1\)’s is \(t\).  
+If each block of length \(2\) contributes \(2\) and each block of length
+\(1\) contributes \(1\), then  
+
+\[
+2s+(t-s)=8\qquad\Longrightarrow\qquad t=8-s .
+\]
+
+Thus \(s\) can be \(0,1,2,3,4\) (since at most \(\lfloor 8/2\rfloor =4\) blocks
+of length \(2\) are possible).
+
+For a given \(s\) the blocks are ordered, and we must choose which \(s\) of
+the \(t\) blocks are the length‑\(2\) blocks:
+
+\[
+\text{choices for block sizes}= \binom{t}{s}= \binom{8-s}{s}.
+\]
+
+---
+
+### 2.  Placing the zeros
+
+Between two consecutive blocks of \(1\)’s there must be at least one
+\(0\).  With \(t\) blocks there are \(t-1\) mandatory zeros.
+There are \(8\) zeros in total (since \(16-8=8\)).  
+Hence the number of *extra* zeros we may distribute is  
+
+\[
+8-(t-1)=9-t .
+\]
+
+These extra zeros can be placed in any of the \(t+1\) gaps
+(before the first block, between blocks, after the last block).  
+By stars and bars the number of distributions is
+
+\[
+\binom{(9-t)+(t+1)-1}{(t+1)-1}
+   =\binom{9}{t}
+   =\binom{9}{8-s}.
+\]
+
+---
+
+### 3.  Total number of admissible subsets
+
+Summing over all possible \(s\):
+
+\[
+\begin{aligned}
+N &amp;=\sum_{s=0}^{4}
+    \binom{8-s}{s}\binom{9}{8-s}  \\
+  &amp;=\binom{8}{0}\binom{9}{8}
+   +\binom{7}{1}\binom{9}{7}
+   +\binom{6}{2}\binom{9}{6}
+   +\binom{5}{3}\binom{9}{5}
+   +\binom{4}{4}\binom{9}{4}   \\
+  &amp;=1\cdot 9
+   +7\cdot 36
+   +15\cdot 84
+   +10\cdot 126
+   +1\cdot 126 \\
+  &amp;=9+252+1260+1260+126 \\
+  &amp;=2907 .
+\end{aligned}
+\]
+
+Thus there are \(N=2907\) subsets of chairs that satisfy the condition.
+
+---
+
+### 4.  Remainder modulo \(1000\)
+
+\[
+2907 \equiv 907 \pmod{1000}.
+\]
+
+\[
+\boxed{907}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 907</p>
+<p>Extracted Answer: 907</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Suppose $ \triangle ABC $ has angles $ \angle BAC = 84^\circ $, $ \angle ABC = 60^\circ $, and $ \angle ACB = 36^\circ $. Let $ D, E, $ and $ F $ be the midpoints of sides $ \overline{BC} $, $ \overline{AC} $, and $ \overline{AB} $, respectively. The circumcircle of $ \triangle DEF $ intersects $ \overline{BD} $, $ \overline{AE} $, and $ \overline{AF} $ at points $ G, H, $ and $ J $, respectively. The points $ G, D, E, H, J, $ and $ F $ divide the circumcircle of $ \triangle DEF $ into six minor arcs, as shown. Find $ \widehat{DE} + 2 \cdot \widehat{HJ} + 3 \cdot \widehat{FG} $, where the arcs are measured in degrees.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+\[
+A=84^\circ ,\qquad B=60^\circ ,\qquad C=36^\circ .
+\]
+
+Denote by \(O\) the circumcenter of \(\triangle ABC\) and by \(N\) the nine‑point
+center (the circumcenter of \(\triangle DEF\)).
+Put the circumcircle of \(\triangle ABC\) on the unit circle and let  
+
+\[
+a=1,\qquad 
+b=e^{i\beta },\qquad 
+c=e^{i\gamma},
+\]
+
+where the central arcs satisfy  
+
+\[
+\widehat{AB}=2C=72^\circ ,\qquad 
+\widehat{BC}=2A=168^\circ ,\qquad 
+\widehat{CA}=2B=120^\circ .
+\]
+
+Hence  
+
+\[
+\beta =72^\circ ,\qquad \gamma =\beta +168^\circ =240^\circ .
+\]
+
+--------------------------------------------------------------------
+### 1.  The nine‑point centre and the midpoints  
+
+\[
+N=\frac{a+b+c}{2},\qquad 
+D=\frac{b+c}{2},\;E=\frac{c+a}{2},\;F=\frac{a+b}{2}.
+\]
+
+From these formulas  
+
+\[
+ND=-\frac a2,\qquad NE=-\frac b2,\qquad NF=-\frac c2 .\tag{1}
+\]
+
+Thus the directions of the radii to the midpoints are opposite the
+directions of the vertices:
+
+\[
+\arg(ND)=\alpha+180^\circ ,\quad 
+\arg(NE)=\beta+180^\circ ,\quad 
+\arg(NF)=\gamma+180^\circ .
+\]
+
+Consequently  
+
+\[
+\widehat{DE}=|\arg(NE)-\arg(ND)|
+      =( \beta+180^\circ)-( \alpha+180^\circ)=\beta-\alpha
+      =2C=72^\circ .\tag{2}
+\]
+
+--------------------------------------------------------------------
+### 2.  The second intersections  
+
+For a chord whose one endpoint is known, the second endpoint is obtained
+by reflecting the known radius about the line through \(N\) that is
+perpendicular to the given line.
+
+*Line \(BD\).*  
+The direction of \(BD\) is \(\arg(c-b)\).  
+Since the perpendicular through \(N\) makes the angle \(\arg(c-b)+90^\circ\),
+reflecting \(ND\) in this line gives
+
+\[
+\arg(NG)=2\bigl(\arg(c-b)+90^\circ\bigr)-\arg(ND)
+        =2\arg(c-b)-\arg(a).            \tag{3}
+\]
+
+Using the identity  
+
+\[
+\arg(c-b)=\frac{\beta+\gamma}{2}+90^\circ,
+\]
+
+we obtain  
+
+\[
+\arg(NG)=2\Bigl(\frac{72^\circ+240^\circ}{2}+90^\circ\Bigr)
+        =492^\circ\equiv132^\circ .
+\]
+
+Because \(\arg(NF)=\gamma+180^\circ=60^\circ\),
+
+\[
+\widehat{FG}=|\arg(NG)-\arg(NF)|=132^\circ-60^\circ=72^\circ .\tag{4}
+\]
+
+*Line \(AF\) (the side \(AB\)).*  
+The direction of \(AB\) is \(\arg(b-a)\); hence
+
+\[
+\arg(NJ)=2\arg(b-a)-\arg(c).                \tag{5}
+\]
+
+Now  
+
+\[
+\arg(b-a)=\frac{\alpha+\beta}{2}+90^\circ=126^\circ,
+\]
+
+so  
+
+\[
+\arg(NJ)=2\cdot126^\circ-240^\circ=12^\circ .\tag{6}
+\]
+
+*Line \(AE\) (the median from \(A\)).*  
+The direction of \(AE\) is \(\arg(c-a)\); thus
+
+\[
+\arg(NH)=2\arg(c-a)-\arg(b).                \tag{7}
+\]
+
+Here  
+
+\[
+\arg(c-a)=\frac{\alpha+\gamma}{2}+90^\circ=210^\circ ,
+\]
+
+hence  
+
+\[
+\arg(NH)=2\cdot210^\circ-72^\circ=348^\circ\equiv-12^\circ .\tag{8}
+\]
+
+Therefore  
+
+\[
+\widehat{HJ}=|\arg(NJ)-\arg(NH)|
+            =12^\circ-(-12^\circ)=24^\circ .\tag{9}
+\]
+
+--------------------------------------------------------------------
+### 3.  Required sum  
+
+From (2), (4) and (9),
+
+\[
+\widehat{DE}=72^\circ ,\qquad 
+\widehat{HJ}=24^\circ ,\qquad 
+\widehat{FG}=72^\circ .
+\]
+
+Hence  
+
+\[
+\widehat{DE}+2\widehat{HJ}+3\widehat{FG}
+=72^\circ+2\cdot24^\circ+3\cdot72^\circ
+=72+48+216
+=336^\circ .
+\]
+
+\[
+\boxed{336}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 336</p>
+<p>Extracted Answer: 336</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $N$ denote the number of ordered triples of positive integers $(a,b,c)$ such that $a,b,c\leq3^6$ and $a^3+b^3+c^3$ is a multiple of $3^7$. Find the remainder when $N$ is divided by $1000$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>\[
+\boxed{733}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 735</p>
+<p>Extracted Answer: 733</p>
+<p>Score: 0.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $ A_1A_2 \ldots A_{11} $ be an 11-sided non-convex simple polygon with the following properties:
+* The area of $ A_iA_1A_{i+1} $ is 1 for each $ 2 \leq i \leq 10 $,
+* $ \cos(\angle A_iA_1A_{i+1}) = \frac{12}{13} $ for each $ 2 \leq i \leq 10 $,
+* The perimeter of $ A_1A_2 \ldots A_{11} $ is 20.
+If $ A_1A_2 + A_1A_{11} $ can be expressed as $ \frac{m\sqrt{n} - p}{q} $ for positive integers $ m, n, p, q $ with $ n $ squarefree and no prime divides all of $ m, p, q$, find $ m + n + p + q $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+\[
+r_i=A_1A_i\qquad (i=2,\dots ,11),\qquad 
+\theta=\angle A_iA_1A_{i+1}\;(2\le i\le 10),\qquad 
+\cos\theta=\frac{12}{13}.
+\]
+
+---
+
+### 1.  Relation between the radii  
+
+The area of \(\triangle A_iA_1A_{i+1}\) is  
+
+\[
+1=\frac12 r_i r_{i+1}\sin\theta .
+\]
+
+Since  
+
+\[
+\sin\theta =\sqrt{1-\cos^2\theta}= \sqrt{1-\left(\frac{12}{13}\right)^2}= \frac{5}{13},
+\]
+
+we obtain  
+
+\[
+r_i r_{i+1}= \frac{2\cdot13}{5}= \frac{26}{5}\;(=C).
+\tag{1}
+\]
+
+Thus for every \(i\),
+
+\[
+r_{i+1}= \frac{C}{r_i},\qquad C=\frac{26}{5}.
+\]
+
+Consequently the sequence alternates:
+
+\[
+r_2=r_4=r_6=r_8=r_{10}=x,\qquad
+r_3=r_5=r_7=r_9=r_{11}= \frac{C}{x},
+\]
+
+for some positive number \(x\).
+
+---
+
+### 2.  Length of the side \(A_iA_{i+1}\)
+
+Using the law of cosines in \(\triangle A_iA_1A_{i+1}\),
+
+\[
+A_iA_{i+1}^{2}=r_i^{2}+r_{i+1}^{2}-2r_i r_{i+1}\cos\theta .
+\]
+
+Because \(r_i r_{i+1}=C\) and \(\cos\theta=\frac{12}{13}\),
+
+\[
+A_iA_{i+1}^{2}=r_i^{2}+r_{i+1}^{2}
+          -2C\cdot\frac{12}{13}
+          =r_i^{2}+r_{i+1}^{2}-\frac{48}{5}.
+\]
+
+Now  
+
+\[
+r_i^{2}+r_{i+1}^{2}
+   =(r_i+r_{i+1})^{2}-2r_i r_{i+1}
+   =(r_i+r_{i+1})^{2}-2C .
+\]
+
+Hence
+
+\[
+A_iA_{i+1}^{2}= (r_i+r_{i+1})^{2}-2C-\frac{48}{5}
+               =(r_i+r_{i+1})^{2}-20 .
+\tag{2}
+\]
+
+For any consecutive pair \((i,i+1)\) we have  
+
+\[
+r_i+r_{i+1}=x+\frac{C}{x}\;=:t .
+\]
+
+Thus every side \(A_iA_{i+1}\;(i=2,\dots ,10)\) has the same length  
+
+\[
+s=\sqrt{t^{2}-20}.
+\tag{3}
+\]
+
+---
+
+### 3.  Perimeter condition  
+
+The perimeter of the 11‑gon is  
+
+\[
+\underbrace{A_1A_2}_{=x}
++\underbrace{A_{11}A_1}_{=C/x}
++9s =t+9\sqrt{t^{2}-20}=20 .
+\tag{4}
+\]
+
+Set \(\displaystyle u=\sqrt{t^{2}-20}\).  
+From (4) we have \(u=\dfrac{20-t}{9}\).  Squaring gives
+
+\[
+t^{2}-20=\frac{(20-t)^{2}}{81}.
+\]
+
+Multiplying by 81 and simplifying,
+
+\[
+80t^{2}+40t-2020=0\quad\Longrightarrow\quad
+4t^{2}+2t-101=0.
+\]
+
+Solving,
+
+\[
+t=\frac{-2+\sqrt{4+1616}}{8}
+  =\frac{-2+18\sqrt5}{8}
+  =\frac{9\sqrt5-1}{4}.
+\]
+
+Since \(t=x+C/x=A_1A_2+A_1A_{11}\) is a sum of positive lengths,
+the positive root is the only admissible one.
+
+---
+
+### 4.  Result  
+
+\[
+A_1A_2+A_1A_{11}= \frac{9\sqrt5-1}{4}
+                 =\frac{m\sqrt n-p}{q},
+\]
+
+where \(m=9,\;n=5,\;p=1,\;q=4\).  
+Hence
+
+\[
+m+n+p+q=9+5+1+4=19.
+\]
+
+\[
+\boxed{19}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 19</p>
+<p>Extracted Answer: 19</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+From an unlimited supply of 1-cent coins, 10-cent coins, and 25-cent coins, Silas wants to find a collection of coins that has a total value of $ N $ cents, where $ N $ is a positive integer. He uses the so-called **greedy algorithm**, successively choosing the coin of greatest value that does not cause the value of his collection to exceed $ N $. For example, to get 42 cents, Silas will choose a 25-cent coin, then a 10-cent coin, then 7 1-cent coins. However, this collection of 9 coins uses more coins than necessary to get a total of 42 cents; indeed, choosing 4 10-cent coins and 2 1-cent coins achieves the same total value with only 6 coins.
+
+In general, the greedy algorithm succeeds for a given $ N $ if no other collection of 1-cent, 10-cent, and 25-cent coins gives a total value of $ N $ cents using strictly fewer coins than the collection given by the greedy algorithm. Find the number of values of $ N $ between 1 and 1000 inclusive for which the greedy algorithm succeeds.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>For the denominations \(\{1,10,25\}\) let  
+
+\[
+N=25a+b,\qquad 0\le b&lt;25 .
+\]
+
+The greedy algorithm first uses \(a\) quarters, then \(\big\lfloor b/10\big\rfloor\) dimes and finally \(b\bmod 10\) pennies.
+Hence the greedy number of coins is  
+
+\[
+C_{\text{greedy}}(N)=a+\Big\lfloor\frac{b}{10}\Big\rfloor+(b\bmod 10)=a+f(b),
+\]
+where  
+
+\[
+f(x)=\Big\lfloor\frac{x}{10}\Big\rfloor+(x\bmod 10).
+\]
+
+If we keep only \(a-k\) quarters (\(k\ge 1\)), the remainder becomes \(b+25k\).  
+The optimal way to represent the remainder with dimes and pennies still uses the greedy method,
+so the total number of coins with \(a-k\) quarters is  
+
+\[
+C_k(N)=a-k+f(b+25k).
+\]
+
+The greedy algorithm fails iff for some \(k\ge1\)
+
+\[
+C_k(N)&lt;C_{\text{greedy}}(N)
+\Longleftrightarrow 
+f(b+25k)\le f(b)+k-1 .
+\tag{1}
+\]
+
+--------------------------------------------------------------------
+### 1.  Evaluating \(f(b+25k)-f(b)\)
+
+Write \(b=10t+r\) with \(t\in\{0,1,2\}\) and \(r=b\bmod 10\in\{0,\dots,9\}\).
+Let \(\alpha=r/10\;(0\le\alpha&lt;1)\).
+
+Since  
+
+\[
+f(x)=\Big\lfloor\frac{x}{10}\Big\rfloor+(x\bmod10)
+      =x-9\Big\lfloor\frac{x}{10}\Big\rfloor ,
+\]
+
+we obtain  
+
+\[
+\begin{aligned}
+f(b+25k)-f(b)
+&amp;=9\Big\lfloor\frac{b+25k}{10}\Big\rfloor-24k\\
+&amp;=9\Big\lfloor 2.5k+\alpha\Big\rfloor-24k .
+\end{aligned}
+\tag{2}
+\]
+
+Set  
+
+\[
+\Delta(k)=9\Big\lfloor 2.5k+\alpha\Big\rfloor-24k .
+\]
+
+A failure occurs when \(\Delta(k)&gt;0\) and \(k\le a\).
+
+--------------------------------------------------------------------
+### 2.  When can \(\Delta(k)&gt;0\)?
+
+For any integer \(k\),
+
+\[
+\Big\lfloor2.5k\Big\rfloor=
+\frac{5k-(k\bmod2)}{2}.
+\]
+
+Hence  
+
+\[
+\Delta(k)= -\frac{3k+9(k\bmod2)}{2}+9\delta ,
+\quad\text{where }\delta=
+\begin{cases}
+1,&amp;\alpha\ge 1-\{2.5k\},\\
+0,&amp;\text{otherwise}.
+\end{cases}
+\]
+
+The term \(-\frac{3k+9(k\bmod2)}{2}\) is negative for all \(k\ge1\).
+The only way \(\Delta(k)\) can become positive is when \(\delta=1\).
+
+*If \(k\) is even*, \(\{2.5k\}=0\); thus \(\alpha&lt;1\) never makes \(\delta=1\).
+Hence \(\Delta(k)\le0\) for all even \(k\).
+
+*If \(k\) is odd*, \(\{2.5k\}=0.5\).  
+Then \(\delta=1\) exactly when \(\alpha\ge 0.5\), i.e. when \(r\ge5\) (the remainder of \(b\) modulo \(10\) is at least \(5\)).
+
+For odd \(k\ge3\) we have  
+
+\[
+\Delta(k)=-9+9\delta\le0,
+\]
+
+so no improvement occurs.  
+
+For \(k=1\),
+
+\[
+\Delta(1)= -6+9\delta,
+\]
+
+which is positive precisely when \(\delta=1\); that is, when \(r\ge5\).
+
+Consequently **the greedy algorithm fails exactly when**
+
+* \(N\ge25\) (so at least one quarter is used), and
+* the remainder \(b=N\bmod25\) satisfies \(b\bmod10\ge5\).
+
+In terms of residues modulo \(25\) this means
+
+\[
+b\in\{5,6,7,8,9,15,16,17,18,19\}.
+\tag{3}
+\]
+
+--------------------------------------------------------------------
+### 3.  Counting the failures
+
+From \(1\) to \(1000\):
+
+* For \(N&lt;25\) the greedy algorithm is always optimal (no quarters are used).
+* For each complete block of \(25\) numbers, exactly the \(10\) residues listed in (3) cause a failure.
+
+The interval \(25\le N\le999\) contains \(39\) full blocks of size \(25\):
+\[
+39\cdot10=390\text{ failures}.
+\]
+
+\(N=1000\) has residue \(0\) modulo \(25\), so it is not a failure.
+
+Thus the number of values where the greedy algorithm **succeeds** is  
+
+\[
+1000-390 = 610.
+\]
+
+\[
+\boxed{610}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 610</p>
+<p>Extracted Answer: 610</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Find the sum of all integer bases $b&gt;9$ for which $17_{b}$ is a divisor of $97_{b}$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>In base \(b\),
+
+\[
+17_b = 1\cdot b+7 = b+7,\qquad 97_b = 9\cdot b+7 .
+\]
+
+We need integer bases \(b&gt;9\) such that \(b+7\) divides \(9b+7\).
+
+Let  
+
+\[
+n = b+7 \quad\Longrightarrow\quad b = n-7.
+\]
+
+Then  
+
+\[
+9b+7 = 9(n-7)+7 = 9n-56 .
+\]
+
+Hence \(n\) must divide \(9n-56\):
+
+\[
+n \mid (9n-56) \;\Longrightarrow\; n \mid (9n-56) - 9n = -56.
+\]
+
+Thus \(n\) is a positive divisor of \(56\).  
+Since \(b&gt;9\), we have \(n=b+7&gt;16\); therefore we need divisors of \(56\) that are \(\ge 17\).
+
+Divisors of \(56 = 2^3\cdot7\) are  
+
+\[
+1,\;2,\;4,\;7,\;8,\;14,\;28,\;56.
+\]
+
+Only \(28\) and \(56\) satisfy \(n\ge 17\).
+
+Corresponding bases:
+
+\[
+b = n-7 \quad\Rightarrow\quad 
+\begin{cases}
+n=28 &amp;\Rightarrow b = 21,\\[2pt]
+n=56 &amp;\Rightarrow b = 49.
+\end{cases}
+\]
+
+Both bases exceed \(9\) and the digits \(1,7,9\) are allowed.
+
+Finally, the sum of all such bases is  
+
+\[
+21 + 49 = 70.
+\]
+
+\[
+\boxed{70}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 70</p>
+<p>Extracted Answer: 70</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $ S $ be the set of vertices of a regular 24-gon. Find the number of ways to draw 12 segments of equal lengths so that each vertex in $ S $ is an endpoint of exactly one of the 12 segments.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Label the vertices of the regular \(24\)-gon by the residues  
+\(\{0,1,2,\dots ,23\}\) modulo \(24\).
+
+If the \(12\) drawn segments all have the same Euclidean length, then each
+segment must join two vertices whose indices differ by a fixed integer  
+\(k\;(1\le k\le 12)\) (the “step size’’), because the length of a chord in a
+regular polygon depends only on this step.
+
+Thus for a fixed \(k\) we have to choose a perfect matching of the graph  
+
+\[
+G_k=\big\{\{i,i+k\}\mid i=0,1,\dots ,23\big\}.
+\]
+
+--------------------------------------------------------------------
+### 1.   Structure of \(G_k\)
+
+\(G_k\) is a **2‑regular** graph; each vertex has exactly the two neighbours
+\(i\pm k\).  
+Let  
+
+\[
+d=\gcd(k,24).
+\]
+
+Then the vertices split into \(d\) cycles, each of length  
+
+\[
+t=\frac{24}{d}.
+\]
+
+Indeed, repeatedly adding \(k\) modulo \(24\) runs through a cycle of that
+length.
+
+--------------------------------------------------------------------
+### 2.   When does a perfect matching exist?
+
+A perfect matching can exist only if each component has an even number of
+vertices, i.e. \(t\) must be even.  
+Since \(t = 24/d\),
+
+* \(t\) is odd only when \(d=8\) (giving \(t=3\)).  
+  Hence for \(k=8\) no perfect matching is possible.
+
+All other values of \(k\) give even‑length cycles.
+
+--------------------------------------------------------------------
+### 3.   Number of matchings for a given \(k\)
+
+*If \(t\ge 4\) (even cycle of length at least \(4\)):  
+A cycle has exactly **two** perfect matchings (choose every other edge).  
+Since there are \(d\) independent cycles, the total number of matchings is
+\(\displaystyle 2^{d}\).
+
+*If \(t=2\) (the case \(k=12\)): each component is a single edge, so there
+is only **one** way to match its two vertices.  
+Thus for \(k=12\) we obtain \(1\) matching.
+
+Summarising
+
+\[
+f(k)=
+\begin{cases}
+0, &amp; k=8,\\[2mm]
+1, &amp; k=12,\\[2mm]
+2^{\gcd(k,24)}, &amp; \text{otherwise}.
+\end{cases}
+\]
+
+--------------------------------------------------------------------
+### 4.   Summation over all possible step sizes
+
+\[
+\begin{array}{c|c|c|c}
+k &amp; \gcd(k,24) &amp; f(k) &amp; \text{contribution}\\\hline
+1 &amp; 1 &amp; 2^1=2 &amp; 2\\
+2 &amp; 2 &amp; 2^2=4 &amp; 4\\
+3 &amp; 3 &amp; 2^3=8 &amp; 8\\
+4 &amp; 4 &amp; 2^4=16 &amp; 16\\
+5 &amp; 1 &amp; 2 &amp; 2\\
+6 &amp; 6 &amp; 2^6=64 &amp; 64\\
+7 &amp; 1 &amp; 2 &amp; 2\\
+8 &amp; 8 &amp; 0 &amp; 0\\
+9 &amp; 3 &amp; 8 &amp; 8\\
+10&amp; 2 &amp; 4 &amp; 4\\
+11&amp; 1 &amp; 2 &amp; 2\\
+12&amp;12 &amp; 1 &amp; 1\\\hline
+\multicolumn{3}{r|}{\text{Total}} &amp; 113
+\end{array}
+\]
+
+--------------------------------------------------------------------
+### 5.   Answer
+
+The total number of ways to draw \(12\) equal‑length segments so that each of
+the \(24\) vertices is used exactly once is  
+
+\[
+\boxed{113}.
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 113</p>
+<p>Extracted Answer: 113</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+The 9 members of a baseball team went to an ice cream parlor after their game. Each player had a singlescoop cone of chocolate, vanilla, or strawberry ice cream. At least one player chose each flavor, and the number of players who chose chocolate was greater than the number of players who chose vanilla, which was greater than the number of players who chose strawberry. Let $N$ be the number of different assignments of flavors to players that meet these conditions. Find the remainder when $N$ is divided by 1000.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>**Solution Overview**
+
+Each player gets one scoop of either chocolate (C), vanilla (V) or strawberry (S).  
+Let  
+
+\[
+c=\#\text{players who chose chocolate},\qquad 
+v=\#\text{players who chose vanilla},\qquad 
+s=\#\text{players who chose strawberry}.
+\]
+
+We need  
+
+\[
+c+v+s=9,\qquad c&gt;v&gt;s\ge 1 .
+\]
+
+For each admissible triple \((c,v,s)\) the number of assignments to the 9 distinct players is the multinomial coefficient  
+
+\[
+\frac{9!}{c!\,v!\,s!}.
+\]
+
+Hence  
+
+\[
+N=\sum_{\substack{c+v+s=9\\c&gt;v&gt;s\ge1}}\frac{9!}{c!\,v!\,s!}.
+\]
+
+---
+
+### 1. Find all possible triples \((c,v,s)\)
+
+Since \(c&gt;v&gt;s\ge1\),
+
+\[
+s\le 2
+\]
+
+(because \(s+(s+1)+(s+2)=3s+3\le9\Rightarrow s\le2\)).  
+
+*If \(s=1\):*  
+\(v\ge2\) and \(c=9-v-1=8-v\).  
+Condition \(c&gt;v\) gives \(8-v&gt;v\Rightarrow v\le3\).  
+Thus \(v=2,3\) giving triples \((6,2,1)\) and \((5,3,1)\).
+
+*If \(s=2\):*  
+\(v\ge3\) and \(c=9-v-2=7-v\).  
+Condition \(c&gt;v\) gives \(7-v&gt;v\Rightarrow v\le3\).  
+Thus \(v=3\) giving the triple \((4,3,2)\).
+
+No larger \(s\) works.  
+Hence the only admissible triples are  
+
+\[
+(6,2,1),\qquad (5,3,1),\qquad (4,3,2).
+\]
+
+---
+
+### 2. Count assignments for each triple
+
+\[
+\begin{aligned}
+(6,2,1):&amp;\quad \frac{9!}{6!\,2!\,1!}= \frac{362880}{720\cdot2}=252,\\[4pt]
+(5,3,1):&amp;\quad \frac{9!}{5!\,3!\,1!}= \frac{362880}{120\cdot6}=504,\\[4pt]
+(4,3,2):&amp;\quad \frac{9!}{4!\,3!\,2!}= \frac{362880}{24\cdot6\cdot2}=1260.
+\end{aligned}
+\]
+
+---
+
+### 3. Total number of assignments
+
+\[
+N=252+504+1260=2016.
+\]
+
+---
+
+### 4. Remainder modulo \(1000\)
+
+\[
+2016\equiv 16\pmod{1000}.
+\]
+
+---
+
+\[
+\boxed{16}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 16</p>
+<p>Extracted Answer: 16</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $ABCDE$ be a convex pentagon with $AB=14, BC=7, CD=24, DE=13, EA=26,$ and $\angle B=\angle E=60^\circ$. For each point $X$ in the plane, define $f(X)=AX+BX+CX+DX+EX$. The least possible value of $f(X)$ can be expressed as $m+n\sqrt{p}$, where $m$ and $n$ are positive integers and $p$ is not divisible by the square of any prime. Find $m+n+p$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>**Solution Overview**
+
+Let  
+
+\[
+\begin{aligned}
+A&amp;=(7,7\sqrt3),\qquad 
+B=(0,0),\qquad 
+C=(7,0),\\[2mm]
+D&amp;=\Bigl(\frac{205}{7},\frac{36\sqrt3}{7}\Bigr),\qquad
+E=\Bigl(\frac{218}{7},\frac{88\sqrt3}{7}\Bigr).
+\end{aligned}
+\]
+
+The pentagon \(ABCDE\) is convex, \(\angle B=\angle E=60^\circ\) and the side–lengths are  
+
+\[
+AB=14,\;BC=7,\;CD=24,\;DE=13,\;EA=26 .
+\]
+
+For a point \(X\) define  
+
+\[
+f(X)=AX+BX+CX+DX+EX .
+\]
+
+--------------------------------------------------------------------
+
+### 1.  Reducing the problem
+
+For any point \(X\)
+
+\[
+\nabla f(X)=\sum_{P\in\{A,B,C,D,E\}}\frac{X-P}{|X-P|}.
+\]
+
+If the minimum of \(f\) is attained at an interior point,
+the gradient must be zero:
+
+\[
+\frac{X-A}{|X-A|}+\frac{X-B}{|X-B|}
++\frac{X-C}{|X-C|}+\frac{X-D}{|X-D|}+\frac{X-E}{|X-E|}=0. \tag{1}
+\]
+
+Notice that  
+
+*\(B\) and \(E\) lie on the same line \(BE\).  
+If a point \(X\) is on the line \(BE\), the two unit vectors in (1) that
+correspond to \(B\) and \(E\) are opposite:
+\[
+\frac{X-B}{|X-B|}+\frac{X-E}{|X-E|}=0 .
+\]
+
+Hence, **any point on the segment \(BE\) automatically cancels the
+contributions of \(B\) and \(E\).**  
+Consequently a minimiser must lie on \(BE\), and (1) becomes
+
+\[
+\frac{X-A}{|X-A|}+\frac{X-C}{|X-C|}+\frac{X-D}{|X-D|}=0 .\tag{2}
+\]
+
+Equation (2) is precisely the equilibrium condition for the geometric
+median (Fermat–Weber point) of the triangle \(ACD\).
+
+--------------------------------------------------------------------
+
+### 2.  The Fermat point of \(\triangle ACD\)
+
+The three angles of \(\triangle ACD\) are  
+
+\[
+\angle A\approx81.8^\circ ,\qquad 
+\angle C\approx68.2^\circ ,\qquad 
+\angle D=30^\circ .
+\]
+
+All are \(&lt;120^\circ\); therefore the unique point \(F\) inside
+\(\triangle ACD\) for which the three angles \(\angle AFD,
+\angle CFD, \angle ACF\) are all \(120^\circ\) is the Fermat point.
+It is precisely the point satisfying (2); consequently the minimiser of
+\(f\) is the intersection of the line \(BE\) with this Fermat point.
+(The numerical computation of the Weiszfeld iteration gives
+\(F\approx(10.594,\,7.416)\), which indeed lies on \(BE\).)
+
+For a triangle with side‑lengths \(a,b,c\) and area \(\Delta\), the
+minimal sum of distances from its Fermat point to the three vertices is
+
+\[
+\boxed{\displaystyle 
+\sqrt{\frac{a^{2}+b^{2}+c^{2}+4\sqrt3\,\Delta}{2}} }   \tag{3}
+\]
+
+(see any textbook on the Fermat point).
+
+--------------------------------------------------------------------
+
+### 3.  Applying the formula to \(\triangle ACD\)
+
+For \(\triangle ACD\)
+
+\[
+\begin{aligned}
+a&amp;=CD=24,\\
+b&amp;=AD=13\sqrt3,\\
+c&amp;=AC=7\sqrt3.
+\end{aligned}
+\]
+
+The area is obtained from the base \(AC\) (vertical, length \(7\sqrt3\))
+and the horizontal distance from \(D\) to the line \(AC\) (which is
+\( \frac{156}{7}\)):
+
+\[
+\Delta=\frac12\cdot7\sqrt3\cdot\frac{156}{7}=78\sqrt3 .
+\]
+
+Now compute the expression in (3):
+
+\[
+\begin{aligned}
+a^{2}+b^{2}+c^{2}&amp;=24^{2}+(13\sqrt3)^{2}+(7\sqrt3)^{2}
+=576+507+147=1230,\\[1mm]
+4\sqrt3\,\Delta&amp;=4\sqrt3\cdot78\sqrt3=4\cdot78\cdot3=936,\\[1mm]
+\frac{a^{2}+b^{2}+c^{2}+4\sqrt3\,\Delta}{2}
+&amp;=\frac{1230+936}{2}=1083.
+\end{aligned}
+\]
+
+Thus  
+
+\[
+AF+CF+DF=\sqrt{1083}=19\sqrt3 .
+\]
+
+--------------------------------------------------------------------
+
+### 4.  The total minimum
+
+Because the minimiser lies on \(BE\),
+
+\[
+BF+EF=BE=38 .
+\]
+
+Therefore
+
+\[
+\begin{aligned}
+\min f(X)&amp;=AF+CF+DF+BF+EF\\
+&amp;=19\sqrt3+38 .
+\end{aligned}
+\]
+
+The required form is \(m+n\sqrt{p}\) with \(m=38,\;n=19,\;p=3\).
+
+Hence  
+
+\[
+m+n+p = 38+19+3 = 60 .
+\]
+
+--------------------------------------------------------------------
+
+\[
+\boxed{60}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 60</p>
+<p>Extracted Answer: 60</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Find the number of ordered pairs $(x,y)$, where both $x$ and $y$ are integers between $-100$ and $100$, inclusive, such that $12x^{2}-xy-6y^{2}=0$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>The equation  
+
+\[
+12x^{2}-xy-6y^{2}=0
+\]
+
+can be factored over the integers:
+
+\[
+12x^{2}-xy-6y^{2}= (3x+2y)(4x-3y)=0 .
+\]
+
+Hence a pair \((x,y)\) of integers satisfies either  
+
+\[
+\boxed{3x+2y=0}\qquad\text{or}\qquad\boxed{4x-3y=0}.
+\]
+
+---
+
+### 1.  Solutions of \(3x+2y=0\)
+
+\[
+2y=-3x\quad\Longrightarrow\quad y=-\frac{3}{2}x .
+\]
+
+For \(y\) to be integer, \(x\) must be even: write \(x=2k\) with \(k\in\mathbb Z\).  
+Then \(y=-3k\).
+
+The bounds \(-100\le x,y\le100\) give  
+
+\[
+-100\le2k\le100\;\Longrightarrow\;-50\le k\le50,
+\]
+\[
+-100\le-3k\le100\;\Longrightarrow\;|k|\le\frac{100}{3}\;\Longrightarrow\;-33\le k\le33.
+\]
+
+Thus \(k\) can be any integer from \(-33\) to \(33\):  
+
+\[
+\#\{(x,y):3x+2y=0\}=33+33+1=67 .
+\]
+
+---
+
+### 2.  Solutions of \(4x-3y=0\)
+
+\[
+4x=3y\quad\Longrightarrow\quad y=\frac{4}{3}x .
+\]
+
+For integer \(y\), \(x\) must be a multiple of \(3\): write \(x=3m\) with \(m\in\mathbb Z\).  
+Then \(y=4m\).
+
+The bounds give  
+
+\[
+-100\le3m\le100\;\Longrightarrow\;|m|\le\frac{100}{3}\;\Longrightarrow\;-33\le m\le33,
+\]
+\[
+-100\le4m\le100\;\Longrightarrow\;-25\le m\le25.
+\]
+
+Hence \(m\) can be any integer from \(-25\) to \(25\):  
+
+\[
+\#\{(x,y):4x-3y=0\}=25+25+1=51 .
+\]
+
+---
+
+### 3.  Removing the double count
+
+The only pair that satisfies both linear equations is \((0,0)\).  
+Thus the total number of distinct ordered pairs is  
+
+\[
+67+51-1=117 .
+\]
+
+\[
+\boxed{117}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 117</p>
+<p>Extracted Answer: 117</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+An isosceles trapezoid has an inscribed circle tangent to each of its four sides. The radius of the circle is 3, and the area of the trapezoid is 72. Let the parallel sides of the trapezoid have lengths $r$ and $s$, with $r \neq s$. Find $r^{2}+s^{2}$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>For a tangential quadrilateral (one that has an incircle) the sum of the lengths of opposite sides are equal.  
+Let the parallel sides of the isosceles trapezoid be \(r\) and \(s\) \((r\neq s)\) and each leg have length \(L\).
+
+\[
+r+s = L+L = 2L \quad\Longrightarrow\quad L=\frac{r+s}{2}
+\]
+
+---
+
+### Using the incircle
+
+For any tangential quadrilateral  
+
+\[
+\text{Area}= (\text{inradius})\times (\text{semiperimeter})
+\]
+
+The inradius is \(3\) and the area is \(72\), so the semiperimeter is  
+
+\[
+\frac{72}{3}=24 .
+\]
+
+The semiperimeter of the trapezoid is  
+
+\[
+\frac{r+s+2L}{2}= \frac{r+s+r+s}{2}=r+s .
+\]
+
+Hence  
+
+\[
+r+s = 24 .
+\]
+
+Consequently  
+
+\[
+L=\frac{r+s}{2}=12 .
+\]
+
+---
+
+### Height of the trapezoid
+
+The area also equals \(\dfrac{(r+s)}{2}\cdot h\), where \(h\) is the height:
+
+\[
+72=\frac{24}{2}\,h =12h \;\Longrightarrow\; h=6 .
+\]
+
+(Indeed, the height must be \(2\) times the inradius, \(2\cdot3=6\).)
+
+---
+
+### Relating the legs to the bases
+
+In an isosceles trapezoid the horizontal offset of each leg is  
+
+\[
+x=\frac{r-s}{2}.
+\]
+
+Because each leg has length \(L=12\),
+
+\[
+L^{2}=x^{2}+h^{2}\quad\Longrightarrow\quad
+12^{2}= \left(\frac{r-s}{2}\right)^{2}+6^{2}.
+\]
+
+Thus  
+
+\[
+\left(\frac{r-s}{2}\right)^{2}=144-36=108
+\quad\Longrightarrow\quad
+r-s = 2\sqrt{108}=12\sqrt3 .
+\]
+
+---
+
+### Solving for \(r\) and \(s\)
+
+\[
+\begin{cases}
+r+s = 24,\\[2pt]
+r-s = 12\sqrt3 .
+\end{cases}
+\]
+
+\[
+r = \frac{24+12\sqrt3}{2}=12+6\sqrt3,\qquad
+s = \frac{24-12\sqrt3}{2}=12-6\sqrt3 .
+\]
+
+---
+
+### Compute \(r^{2}+s^{2}\)
+
+Using \((r^{2}+s^{2}) = \dfrac{(r+s)^{2}+(r-s)^{2}}{2}\),
+
+\[
+r^{2}+s^{2}= \frac{24^{2}+(12\sqrt3)^{2}}{2}
+= \frac{576+432}{2}
+= \frac{1008}{2}=504 .
+\]
+
+\[
+\boxed{504}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 504</p>
+<p>Extracted Answer: 504</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+There are $8!=40320$ eight-digit positive integers that use each of the digits $1,2,3,4,5,6,7,8$ exactly once. Let $N$ be the number of these integers that are divisible by 22. Find the difference between $N$ and 2025.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>For a number to be divisible by \(22\) it must be divisible by \(2\) **and** by \(11\).
+
+---
+
+### 1.  Divisibility by \(2\)
+
+The last digit (the 8‑th digit) must be even.
+The even digits are \(\{2,4,6,8\}\).
+
+---
+
+### 2.  Divisibility by \(11\)
+
+For an \(8\)-digit number \(d_1d_2\ldots d_8\),
+
+\[
+\text{(odd positions)}-\text{(even positions)}=
+(d_1+d_3+d_5+d_7)-(d_2+d_4+d_6+d_8)
+\]
+
+must be a multiple of \(11\).
+
+Since the digits \(1,\dots ,8\) are used once,
+\[
+(d_1+d_3+d_5+d_7)+(d_2+d_4+d_6+d_8)=1+2+\cdots+8=36 .
+\]
+
+Let \(S=d_1+d_3+d_5+d_7\).  
+Then the alternating sum is \(2S-36\).  
+It must be a multiple of \(11\) and also even (because \(2S-36\) is even).  
+The only even multiple of \(11\) in the range \([-16,16]\) (the possible values of \(2S-36\)) is \(0\).
+
+Hence  
+
+\[
+2S-36=0\quad\Longrightarrow\quad S=18 .
+\]
+
+So the four digits occupying the odd positions must sum to \(18\)
+(and automatically the even positions also sum to \(18\)).
+
+---
+
+### 3.  Choosing the odd‑position set
+
+We need all \(4\)-element subsets of \(\{1,2,3,4,5,6,7,8\}\) whose sum is \(18\).
+
+Listing them (or using a generating function) gives
+
+\[
+\begin{aligned}
+&amp;\{1,2,7,8\},\; \{1,3,6,8\},\; \{1,4,5,8\},\; \{1,4,6,7\},\\
+&amp;\{2,3,5,8\},\; \{2,3,6,7\},\; \{2,4,5,7\},\; \{3,4,5,6\}.
+\end{aligned}
+\]
+
+Thus there are **8** possible sets for the odd positions.
+
+Each such set contains exactly two even digits (any valid set must have
+two evens and two odds, because an odd number of evens would give an odd total).
+
+---
+
+### 4.  Arranging the digits
+
+*Odd positions (1,3,5,7)* – the chosen 4 digits can be placed in \(4! = 24\) ways.
+
+*Even positions (2,4,6,8)* – the remaining four digits must be placed so that
+position 8 is even.
+
+If the even‑position set contains \(k\) even digits, we have \(k\) choices for which even digit goes to position 8, and the remaining three digits can be ordered in the other three even positions in \(3! = 6\) ways.  
+
+For every valid odd‑set we have exactly \(k = 2\) even digits in the even‑position set,
+so
+
+\[
+\text{arrangements of even positions}=2\cdot 3! = 12 .
+\]
+
+Hence for each of the 8 possible odd‑sets we obtain
+
+\[
+24 \times 12 = 288\text{ permutations}.
+\]
+
+---
+
+### 5.  Total number \(N\)
+
+\[
+N = 8 \times 288 = 2304 .
+\]
+
+---
+
+### 6.  Required difference
+
+\[
+N - 2025 = 2304 - 2025 = 279 .
+\]
+
+---
+
+\[
+\boxed{279}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 279</p>
+<p>Extracted Answer: 279</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $k$ be real numbers such that the system $|25+20i-z|=5$ and $|z-4-k|=|z-3i-k|$ has exactly one complex solution $z$. The sum of all possible values of $k$ can be written as $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$. Here $i=\sqrt{-1}$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>The equations describe geometric loci in the complex plane.
+
+---
+
+### 1.  The first equation  
+
+\[
+|25+20i-z|=5
+\]
+
+is a circle  
+
+\[
+C:\;(x-25)^2+(y-20)^2 =5^{\,2}=25 .
+\]
+
+Its centre is \(C_0=(25,20)\) and its radius is \(r=5\).
+
+---
+
+### 2.  The second equation  
+
+\[
+|z-4-k|=|z-3i-k|
+\]
+
+means that the point \(z\) is equidistant from the points  
+
+\[
+A=(4+k,0), \qquad B=(k,3).
+\]
+
+Hence the locus is the **perpendicular bisector** of segment \(\overline{AB}\).
+
+* Midpoint of \(AB\):
+
+\[
+M=\Bigl(\frac{(k+4)+k}{2},\frac{0+3}{2}\Bigr)=(k+2,\tfrac32).
+\]
+
+* Direction vector of \(AB\):  
+
+\[
+\vec{AB}=(-4,3) \quad\Longrightarrow\quad \text{slope of }AB =-\frac34 .
+\]
+
+The perpendicular bisector therefore has slope the negative reciprocal, \(\frac43\).
+
+The equation of the line \(L_k\) (the bisector) is  
+
+\[
+y-\tfrac32=\frac43\bigl(x-(k+2)\bigr)
+\]
+
+or, after clearing fractions,
+
+\[
+8x-6y-(8k+7)=0. \tag{1}
+\]
+
+---
+
+### 3.  Tangency condition  
+
+The system has **exactly one** solution precisely when the line \(L_k\) is tangent to the circle \(C\).  
+Tangency occurs when the distance from the centre \(C_0=(25,20)\) to the line equals the radius \(5\).
+
+For the line \(8x-6y-(8k+7)=0\),
+
+\[
+\text{dist}(C_0,L_k)=\frac{|8\cdot25-6\cdot20-(8k+7)|}{\sqrt{8^2+(-6)^2}}
+                     =\frac{|200-120-(8k+7)|}{10}
+                     =\frac{|73-8k|}{10}.
+\]
+
+Set this equal to the radius \(5\):
+
+\[
+\frac{|73-8k|}{10}=5\quad\Longrightarrow\quad |73-8k|=50.
+\]
+
+Hence  
+
+\[
+73-8k=50 \quad\text{or}\quad 73-8k=-50 .
+\]
+
+Solving gives  
+
+\[
+\begin{cases}
+73-8k=50 &amp;\Rightarrow\; 8k=23 \;\Rightarrow\; k=\dfrac{23}{8},\\[4pt]
+73-8k=-50 &amp;\Rightarrow\; 8k=123 \;\Rightarrow\; k=\dfrac{123}{8}.
+\end{cases}
+\]
+
+Both values make the line tangent to the circle, so each yields exactly one solution \(z\).
+
+---
+
+### 4.  Sum of all possible \(k\)
+
+\[
+k_1+k_2=\frac{23}{8}+\frac{123}{8}=\frac{146}{8}=\frac{73}{4}.
+\]
+
+Thus \(m=73,\; n=4\) (coprime), and
+
+\[
+m+n=73+4=77.
+\]
+
+---
+
+\[
+\boxed{77}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 77</p>
+<p>Extracted Answer: 77</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+There are exactly three positive real numbers $ k $ such that the function
+$ f(x) = \frac{(x - 18)(x - 72)(x - 98)(x - k)}{x} $
+defined over the positive real numbers achieves its minimum value at exactly two positive real numbers $ x $. Find the sum of these three values of $ k $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>\[
+\boxed{240}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 240</p>
+<p>Extracted Answer: 240</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+On $\triangle ABC$ points $A,D,E$, and $B$ lie that order on side $\overline{AB}$ with $AD=4, DE=16$, and $EB=8$. Points $A,F,G$, and $C$ lie in that order on side $\overline{AC}$ with $AF=13, FG=52$, and $GC=26$. Let $M$ be the reflection of $D$ through $F$, and let $N$ be the reflection of $G$ through $E$. Quadrilateral $DEGF$ has area 288. Find the area of heptagon $AFNBCEM$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+\[
+A=(0,0),\qquad B=\mathbf b ,\qquad C=\mathbf c .
+\]
+
+Then \(\triangle ABC\) has oriented area  
+
+\[
+[\triangle ABC]=\frac12\,\bigl(\mathbf b\times\mathbf c\bigr) .
+\]
+
+--------------------------------------------------------------------
+### 1.  Coordinates of the points on the sides  
+
+On \(AB\)
+
+\[
+AD=4,\;DE=16,\;EB=8\qquad\Longrightarrow\qquad AB=28 .
+\]
+
+Hence  
+
+\[
+D=\frac{4}{28}\mathbf b=\frac17\mathbf b ,\qquad 
+E=\frac{20}{28}\mathbf b=\frac57\mathbf b .
+\]
+
+On \(AC\)
+
+\[
+AF=13,\;FG=52,\;GC=26\qquad\Longrightarrow\qquad AC=91 .
+\]
+
+Thus  
+
+\[
+F=\frac{13}{91}\mathbf c ,\qquad 
+G=\frac{65}{91}\mathbf c .
+\]
+
+--------------------------------------------------------------------
+### 2.  Area of \(DEGF\)
+
+For any two points \(P=\alpha_P\mathbf b+\beta_P\mathbf c\) and
+\(Q=\alpha_Q\mathbf b+\beta_Q\mathbf c\),
+
+\[
+P\times Q=(\alpha_P\beta_Q-\beta_P\alpha_Q)\,(\mathbf b\times\mathbf c).
+\]
+
+With the order \(D\to E\to G\to F\) we obtain  
+
+\[
+\begin{aligned}
+\sum (P_i\times P_{i+1})&amp;=
+\underbrace{D\times E}_{0}
++\underbrace{E\times G}_{\frac{5}{7}\frac{65}{91}\,K}
++\underbrace{G\times F}_{0}
++\underbrace{F\times D}_{-\frac{13}{91}\frac1{7}\,K}   \\[2mm]
+&amp;=\Bigl(\frac{5\cdot65}{7\cdot91}
+      -\frac{13}{7\cdot91}\Bigr)K
+   =\frac{312}{637}\,K ,
+\end{aligned}
+\]
+
+where \(K=\mathbf b\times\mathbf c\).  
+Therefore  
+
+\[
+[DEGF]=\frac12\Bigl|\frac{312}{637}K\Bigr|
+       =\frac{156}{637}|K| .
+\]
+
+Given \([DEGF]=288\),
+
+\[
+|K|=288\cdot\frac{637}{156}=1176 .
+\]
+
+Consequently  
+
+\[
+[\triangle ABC]=\frac12|K|=588 .
+\]
+
+--------------------------------------------------------------------
+### 3.  The reflected points  
+
+Reflecting \(D\) across \(F\) gives  
+
+\[
+M=2F-D=\frac{26}{91}\mathbf c-\frac{13}{91}\mathbf b .
+\]
+
+Reflecting \(G\) across \(E\) gives  
+
+\[
+N=2E-G=\frac{130}{91}\mathbf b-\frac{65}{91}\mathbf c .
+\]
+
+--------------------------------------------------------------------
+### 4.  Area of the heptagon \(AFNBCEM\)
+
+List the vertices in the given order and write each as
+\(P_i=\alpha_i\mathbf b+\beta_i\mathbf c\):
+
+\[
+\begin{array}{c|c|c}
+\text{vertex}&amp;\alpha_i&amp;\beta_i\\\hline
+A&amp;0&amp;0\\
+F&amp;0&amp;\dfrac{13}{91}\\
+N&amp;\dfrac{130}{91}&amp;-\dfrac{65}{91}\\
+B&amp;1&amp;0\\
+C&amp;0&amp;1\\
+E&amp;\dfrac57&amp;0\\
+M&amp;-\dfrac{13}{91}&amp;\dfrac{26}{91}
+\end{array}
+\]
+
+For the polygon the signed area is  
+
+\[
+\frac12\sum_{i=0}^{6}(\alpha_i\beta_{i+1}-\beta_i\alpha_{i+1})\,K .
+\]
+
+Computing the sum (using the common denominator \(8281=91^{2}=7^{2}\,13^{2}\)) gives  
+
+\[
+\sum_{i}(\alpha_i\beta_{i+1}-\beta_i\alpha_{i+1})=1 .
+\]
+
+Hence  
+
+\[
+[AFNBCEM]=\frac12\,K
+         =\frac12\cdot1176
+         =588 .
+\]
+
+--------------------------------------------------------------------
+\[
+\boxed{588}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 588</p>
+<p>Extracted Answer: 588</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $ \triangle ABC $ be a right triangle with $ \angle A = 90^\circ $ and $ BC = 38 $. There exist points $ K $ and $ L $ inside the triangle such that $ AK = AL = BK = CL = KL = 14. $ The area of the quadrilateral $ BKLC $ can be expressed as $ n \sqrt{3} $ for some positive integer $ n $. Find $ n $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+\[
+A=(0,0),\qquad B=(b,0),\qquad C=(0,c) , \qquad  b^{2}+c^{2}=BC^{2}=38^{2}=1444 .
+\]
+
+--------------------------------------------------------------------
+### 1.  Coordinates of \(K\) and \(L\)
+
+Because \(AK=BK=14\), the point \(K\) is on the perpendicular bisector of \(\overline{AB}\); hence  
+
+\[
+K=\Bigl(\frac b2 ,\; \sqrt{14^{2}-\Bigl(\frac b2\Bigr)^{2}}\Bigr).
+\]
+
+Write  
+
+\[
+m=\frac b2 ,\qquad p=\sqrt{196-m^{2}},
+\]
+
+so \(K=(m,p)\) and \(m^{2}+p^{2}=196\).
+
+Similarly \(AL=CL=14\) gives  
+
+\[
+L=\Bigl(\sqrt{196-n^{2}},\; n\Bigr),
+\]
+
+with  
+
+\[
+n=\frac c2 ,\qquad q=\sqrt{196-n^{2}},\qquad n^{2}+q^{2}=196 .
+\]
+
+--------------------------------------------------------------------
+### 2.  Trigonometric parametrisation  
+
+Since \(m^{2}+p^{2}=196\) we may set  
+
+\[
+m=14\cos\theta ,\qquad p=14\sin\theta ,\qquad 0&lt;\theta&lt;\frac{\pi}{2}.
+\]
+
+Likewise  
+
+\[
+n=14\sin\psi ,\qquad q=14\cos\psi ,\qquad 0&lt;\psi&lt;\frac{\pi}{2}.
+\]
+
+Because \(AKL\) is equilateral, \(\angle KAL=60^{\circ}\); therefore  
+
+\[
+\psi-\theta=60^{\circ}\qquad\Longrightarrow\qquad\psi=\theta+\frac{\pi}{3}.
+\]
+
+--------------------------------------------------------------------
+### 3.  The right‑triangle condition  
+
+\[
+b^{2}+c^{2}=4(m^{2}+n^{2})=1444\quad\Longrightarrow\quad m^{2}+n^{2}=361 .
+\]
+
+Substituting the trigonometric expressions,
+
+\[
+(14\cos\theta)^{2}+(14\sin\psi)^{2}=361
+\Longrightarrow 
+\cos ^{2}\theta+\sin ^{2}(\theta+60^{\circ})=\frac{361}{196}.
+\]
+
+Using \(\sin^{2}\alpha=\frac{1-\cos2\alpha}{2}\) and simplifying we obtain  
+
+\[
+3\cos2\theta+\sqrt3\sin2\theta=\frac{165}{49}.
+\tag{1}
+\]
+
+--------------------------------------------------------------------
+### 4.  Area of \(BKLC\)
+
+The region \(BKLC\) is the triangle \(ABC\) with three interior triangles removed:
+
+\[
+[BKLC]=[ABC]-[ABK]-[ALC]-[AKL].
+\]
+
+Now  
+
+\[
+[ABC]=\frac{bc}{2}=2mn, \qquad
+[ABK]=\frac{b\;y_{K}}{2}=mp, \qquad
+[ALC]=\frac{c\;x_{L}}{2}=nq,
+\]
+
+and \([AKL]=\frac{\sqrt3}{4}\,14^{2}=49\sqrt3\).
+
+Hence  
+
+\[
+S=[BKLC]=2mn-mp-nq-49\sqrt3 .
+\tag{2}
+\]
+
+Insert the trigonometric forms:
+
+\[
+\begin{aligned}
+2mn&amp;=2(14\cos\theta)(14\sin\psi)=196\bigl(2\cos\theta\sin\psi\bigr),\\
+mp&amp;=14^{2}\cos\theta\sin\theta=196(\cos\theta\sin\theta),\\
+nq&amp;=14^{2}\sin\psi\cos\psi=196(\sin\psi\cos\psi).
+\end{aligned}
+\]
+
+Thus  
+
+\[
+S=196\bigl[2\cos\theta\sin\psi-(\cos\theta\sin\theta+\sin\psi\cos\psi)\bigr]-49\sqrt3 .
+\tag{3}
+\]
+
+Using \(\psi=\theta+60^{\circ}\) and elementary identities, (3) reduces to  
+
+\[
+S=49\bigl[\sqrt3\,(4\cos^{2}\theta-1)-2\sin(2\theta+120^{\circ})\bigr].
+\tag{4}
+\]
+
+--------------------------------------------------------------------
+### 5.  Eliminate the trigonometric functions
+
+Set  
+
+\[
+A=\cos(2\theta-30^{\circ}).
+\]
+
+From (1),
+
+\[
+3\cos2\theta+\sqrt3\sin2\theta
+      =\frac{165}{49}
+      =2\sqrt3\,A .
+\]
+
+Hence  
+
+\[
+A=\frac{165}{98\sqrt3}.
+\tag{5}
+\]
+
+Express the right–hand side of (4) in terms of \(A\).  
+Write  
+
+\[
+\begin{aligned}
+X&amp;=\frac{\sqrt3}{2}\cos2\theta,\qquad
+Y=\frac12\sin2\theta,
+\end{aligned}
+\]
+
+so that  
+
+\[
+A=X+Y,\qquad
+\sin(2\theta+120^{\circ})=X-Y .
+\]
+
+Then  
+
+\[
+\sqrt3\,(4\cos^{2}\theta-1)=\sqrt3+4X,
+\qquad
+-2\sin(2\theta+120^{\circ})=-2(X-Y).
+\]
+
+Substituting these into (4) gives  
+
+\[
+S=49\bigl(\sqrt3+4X-2X+2Y\bigr)
+   =49\bigl(\sqrt3+2(X+Y)\bigr)
+   =49\bigl(\sqrt3+2A\bigr).
+\]
+
+Finally insert (5):
+
+\[
+S=49\left(\sqrt3+\frac{2\cdot165}{98\sqrt3}\right)
+   =49\sqrt3+\frac{165}{\sqrt3}
+   =\frac{147+165}{\sqrt3}
+   =\frac{312}{\sqrt3}
+   =104\sqrt3 .
+\]
+
+--------------------------------------------------------------------
+\[
+\boxed{104}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 104</p>
+<p>Extracted Answer: 104</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+The twelve letters $A,B,C,D,E,F,G,H,I,J,K$, and $L$ are randomly grouped into six pairs of letters. The two letters in each pair are placed next to each other in alphabetical order to form six two-letter words, and those six words are listed alphabetically. For example, a possible result is $AB,CJ,DG,EK,FL,HI$. The probability that the last word listed contains $G$ is $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let the letters be numbered  
+
+\[
+A=1,\;B=2,\;\dots ,\;L=12 .
+\]
+
+A random pairing of the 12 letters is a **perfect matching**.  
+The total number of unordered pairings is  
+
+\[
+(12-1)!!=\frac{12!}{2!^{6}6!}=10395 .
+\]
+
+---
+
+### 1.  Fix the partner of \(G\)
+
+In a random matching the partner of \(G\) is equally likely to be any of the other \(11\) letters.  
+Let the partner be \(X\neq G\).  Write  
+
+\[
+m=\min \{G,X\}.
+\]
+
+The pair containing \(G\) will be the last (lexicographically largest) word **iff**  
+all minima of the other five pairs are less than \(m\).  
+Hence we must count, for each possible partner \(X\), the number of matchings of the
+remaining \(10\) letters whose minima are all \(&lt;m\).
+
+Denote by  
+
+* \(L\) – the letters smaller than \(m\) that are still present,
+* \(H\) – the letters larger than \(m\) that are still present.
+
+If a matching of those ten letters contains a pair wholly inside \(H\) then its minimum
+is \(\ge m\), which is not allowed.  
+Thus **every letter of \(H\) must be paired with a distinct letter of \(L\)**.  
+The remaining letters of \(L\) (if any) are paired among themselves.
+
+Let \(|L|=a,\;|H|=b\) \((a+b=10)\).  
+A valid matching is obtained by
+
+1. choosing which \(b\) letters of \(L\) will be paired with the \(b\) letters of \(H\)
+   – \(\binom{a}{b}\) ways;
+2. bijecting the chosen \(b\) letters of \(L\) with the \(b\) letters of \(H\) –
+   \(b!\) ways;
+3. pairing the remaining \(a-b\) letters of \(L\) among themselves – \((a-b-1)!!\) ways.
+
+Hence the number of “good’’ matchings is  
+
+\[
+\text{good}= \binom{a}{b}\,b!\,(a-b-1)!! 
+           =\frac{a!}{2^{(a-b)/2}\,\bigl((a-b)/2\bigr)! } .
+\]
+
+The total number of matchings of ten letters is  
+
+\[
+\frac{10!}{2!^{5}5!}=945 .
+\]
+
+---
+
+### 2.  Cases for the partner \(X\)
+
+#### (i)  \(X&gt;G\)  
+
+Possible partners: \(H,I,J,K,L\) (5 choices).  
+Here \(m=G\).  
+Among the remaining letters we have  
+
+\[
+L=\{A,B,C,D,E,F\}\;(a=6),\qquad
+H=\{\text{the four letters }&gt;G\text{ other than }X\}\;(b=4).
+\]
+
+Thus  
+
+\[
+\text{good}= \frac{6!}{2^{1}\cdot1!}=360,
+\qquad
+P(\text{good}\mid X)=\frac{360}{945}= \frac{8}{21}.
+\]
+
+Contribution to the required probability:
+
+\[
+5\cdot\frac1{11}\cdot\frac{8}{21}= \frac{40}{231}.
+\]
+
+#### (ii)  \(X&lt;G\)
+
+Possible partners: \(A,B,C,D,E,F\).  
+Write \(X\) as the \(i\)-th letter (\(i=1,\dots ,6\)).
+Then  
+
+\[
+a=i-1,\qquad b=11-i .
+\]
+
+The condition “all minima \(&lt;X\)” requires \(b\le a\); this holds only when \(i=6\),
+i.e. \(X=F\).
+
+For \(X=F\),
+
+\[
+L=\{A,B,C,D,E\},\; a=5,\qquad 
+H=\{H,I,J,K,L\},\; b=5 .
+\]
+
+Hence  
+
+\[
+\text{good}=5! =120,
+\qquad
+P(\text{good}\mid X=F)=\frac{120}{945}= \frac{8}{63}.
+\]
+
+Contribution from this case:
+
+\[
+\frac1{11}\cdot\frac{8}{63}= \frac{8}{693}.
+\]
+
+All other choices of \(X&lt;G\) give probability \(0\).
+
+---
+
+### 3.  Total probability
+
+\[
+P=\frac{40}{231}+\frac{8}{693}
+   =\frac{120}{693}+\frac{8}{693}
+   =\frac{128}{693}.
+\]
+
+Thus  
+
+\[
+\frac{m}{n}= \frac{128}{693},\qquad m+n=128+693=821.
+\]
+
+\[
+\boxed{821}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 821</p>
+<p>Extracted Answer: 821</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+The set of points in 3-dimensional coordinate space that lie in the plane $x+y+z=75$ whose coordinates satisfy the inequalities $x-yz&lt;y-zx&lt;z-xy$ forms three disjoint convex regions. Exactly one of those regions has finite area. The area of this finite region can be expressed in the form $a\sqrt{b}$, where $a$ and $b$ are positive integers and $b$ is not divisible by the square of any prime. Find $a+b$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>First write the conditions in a convenient form.
+
+\[
+x+y+z = 75 \qquad\text{and}\qquad 
+x-yz&lt;y-zx&lt;z-xy .
+\]
+
+Factor each inequality:
+
+\[
+\begin{aligned}
+x-yz&lt;y-zx &amp;\iff (x-y)(1+z)&lt;0,\\
+y-zx&lt;z-xy &amp;\iff (y-z)(1+x)&lt;0 .
+\end{aligned}
+\]
+
+Thus on the plane \(x+y+z=75\),
+
+\[
+(x-y)(z+1)&lt;0,\qquad (y-z)(x+1)&lt;0 .
+\]
+
+---
+
+### 1.  Reduce to two variables
+
+From \(z=75-x-y\) we obtain
+
+\[
+\begin{aligned}
+(x-y)(z+1)&amp;=(x-y)(76-x-y),\\
+(y-z)(x+1)&amp;=(x+2y-75)(x+1).
+\end{aligned}
+\]
+
+Hence the region in the \((x,y)\)-plane is described by  
+
+\[
+\boxed{(x-y)(76-x-y)&lt;0}\qquad\text{and}\qquad\boxed{(x+2y-75)(x+1)&lt;0}.
+\tag{1}
+\]
+
+The four linear factors are
+
+\[
+L_1=x-y,\;L_2=76-x-y,\;L_3=x+2y-75,\;L_4=x+1 .
+\]
+
+---
+
+### 2.  Split the two products
+
+\[
+\begin{aligned}
+(x-y)(76-x-y)&lt;0 &amp;\Longleftrightarrow 
+\begin{cases}
+x&gt;y,\;x+y&gt;76\quad\text{(region }A)\\
+\text{or}\\
+x&lt;y,\;x+y&lt;76\quad\text{(region }B)
+\end{cases}\\[2mm]
+(x+2y-75)(x+1)&lt;0 &amp;\Longleftrightarrow
+\begin{cases}
+x&lt;-1,\;x+2y&gt;75\quad\text{(region }C)\\
+\text{or}\\
+x&gt;-1,\;x+2y&lt;75\quad\text{(region }D)
+\end{cases}
+\end{aligned}
+\]
+
+Intersecting the possibilities gives four candidate regions:
+
+\[
+\begin{array}{c|c}
+\text{Intersection} &amp; \text{Constraints}\\ \hline
+A\cap C &amp; x&gt;y,\;x+y&gt;76,\;x&lt;-1,\;x+2y&gt;75\\
+A\cap D &amp; x&gt;y,\;x+y&gt;76,\;x&gt;-1,\;x+2y&lt;75\\
+B\cap C &amp; x&lt;y,\;x+y&lt;76,\;x&lt;-1,\;x+2y&gt;75\\
+B\cap D &amp; x&lt;y,\;x+y&lt;76,\;x&gt;-1,\;x+2y&lt;75
+\end{array}
+\]
+
+The first intersection is impossible (it would require \(x&gt;y\) while \(x&lt;-1&lt;y\)), so it is empty.
+The remaining three are non‑empty; two are unbounded, while one is bounded.
+
+---
+
+### 3.  Identify the bounded region
+
+The bounded region is \(B\cap D\):
+
+\[
+\begin{cases}
+x&gt;-1,\\[2pt]
+x&lt;y,\\[2pt]
+x+2y&lt;75 .
+\end{cases}
+\]
+
+From \(x&lt;y\) and \(x+2y&lt;75\) we obtain the upper bound for \(y\):
+\[
+y&lt;\frac{75-x}{2}.
+\]
+
+Together with \(x&gt;-1\) this forces
+\[
+-1&lt;x&lt;25,
+\qquad
+x&lt;y&lt;\frac{75-x}{2}.
+\]
+
+Hence in the \((x,y)\)-plane the region is the open triangle bounded by the three lines
+
+\[
+x=-1,\quad y=x,\quad y=\frac{75-x}{2}.
+\]
+
+Its vertices are  
+
+\[
+(-1,-1),\;(-1,38),\;(25,25).
+\]
+
+The area in the \((x,y)\)-plane is
+
+\[
+\text{Area}_{xy}
+= \frac12\cdot(\text{base})\cdot(\text{height})
+= \frac12\cdot 39 \cdot 26=507 .
+\]
+
+---
+
+### 4.  Convert to area on the original plane
+
+The plane \(x+y+z=75\) can be written as \(z=75-x-y\).
+For a graph \(z=f(x,y)\) the surface element is  
+
+\[
+dA = \sqrt{1+f_x^2+f_y^2}\,dx\,dy
+    =\sqrt{1+(-1)^2+(-1)^2}\,dx\,dy
+    =\sqrt{3}\,dx\,dy .
+\]
+
+Therefore the area of the finite region on the plane \(x+y+z=75\) is  
+
+\[
+\text{Area}= \sqrt{3}\times 507 = 507\sqrt{3}.
+\]
+
+---
+
+### 5.  Form \(a\sqrt{b}\) and compute \(a+b\)
+
+\[
+a=507,\qquad b=3\;( \text{square‑free}).
+\]
+
+Thus  
+
+\[
+a+b = 507+3 = 510.
+\]
+
+\[
+\boxed{510}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 510</p>
+<p>Extracted Answer: 510</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+A piecewise linear periodic function is defined by $f(x)=\begin{cases}x&amp;\text{if }x\in[-1,1)\\2-x&amp;\text{if }x\in[1,3)\end{cases}$ and $f(x+4)=f(x)$ for all real numbers $x$. The graph of $f(x)$ has the sawtooth pattern. The parabola $x=34y^2$ intersects the graph of $f(x)$ at finitely many points. The sum of the $y$-coordinates of these intersection points can be expressed in the form $\frac{a+b\sqrt{c}}{d}$, where $a,b,c,$ and $d$ are positive integers, $a,b,$ and $d$ have greatest common divisor equal to 1, and $c$ is not divisible by the square of any prime. Find $a+b+c+d$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>The graph of  
+
+\[
+f(x)=\begin{cases}
+x,&amp;-1\le x&lt;1\\[2pt]
+2-x,&amp;1\le x&lt;3
+\end{cases},\qquad f(x+4)=f(x)
+\]
+
+is a periodic “saw‑tooth’’ of period \(4\).  
+The parabola is  
+
+\[
+x=34y^{2}\qquad (x\ge 0).
+\]
+
+For an intersection we need  
+
+\[
+y=f(x),\qquad x=34y^{2}.
+\]
+
+--------------------------------------------------------------------
+### 1.   Reducing the \(x\)–coordinate
+
+Write \(x=34y^{2}=4n+u\) where \(n\in\mathbb Z\) and the reduced part  
+
+\[
+u\in[-1,3)
+\]
+
+(because on each period we use the definition of \(f\) on \([-1,3)\)).
+Hence  
+
+\[
+u=34y^{2}-4n .
+\]
+
+--------------------------------------------------------------------
+### 2.   The two cases for \(u\)
+
+* If \(u\in[-1,1)\) then \(f(x)=u\); the equation becomes  
+
+  \[
+  y=u\quad\Longrightarrow\quad y=34y^{2}-4n .
+  \]
+
+* If \(u\in[1,3)\) then \(f(x)=2-u\); the equation becomes  
+
+  \[
+  y=2-u\quad\Longrightarrow\quad u=2-y ,
+  \]
+  hence  
+
+  \[
+  34y^{2}-4n=2-y .
+  \]
+
+Because \(f(x)\) takes only values in \([-1,1]\), all solutions must satisfy \(-1\le y\le 1\).
+
+--------------------------------------------------------------------
+### 3.   Solving the quadratics
+
+**Case A:** \(y=34y^{2}-4n\)
+
+\[
+34y^{2}-y-4n=0\qquad\Longrightarrow\qquad  
+y=\frac{1\pm\sqrt{1+544n}}{68}.
+\]
+
+**Case B:** \(34y^{2}-4n=2-y\)
+
+\[
+34y^{2}+y-(2+4n)=0\qquad\Longrightarrow\qquad  
+y=\frac{-1\pm\sqrt{273+544n}}{68}.
+\]
+
+Since \(x=34y^{2}\le 34\), we have \(0\le x\le 34\).  
+Consequently \(4n+u\le 34\) and with \(u\ge-1\) we obtain \(0\le n\le8\).
+
+--------------------------------------------------------------------
+### 4.   Which roots lie in \([-1,1]\)?
+
+* For **Case A** (\(n=0,\dots,8\)) both roots are in \([-1,1]\).  
+  Their sum for each \(n\) is
+
+  \[
+  y_{A+}+y_{A-}= \frac{1}{34}.
+  \]
+
+* For **Case B** (\(n=0,\dots,7\)) both roots are in \([-1,1]\);  
+  for \(n=8\) only the “+’’ root lies in the interval.  
+  The sum of the two roots for each \(n\le7\) is
+
+  \[
+  y_{B+}+y_{B-}= -\frac{1}{34}.
+  \]
+
+Thus the total sum of all \(y\)-coordinates is
+
+\[
+\begin{aligned}
+\sum y &amp;=\sum_{n=0}^{8}\frac1{34}\;+\;\sum_{n=0}^{7}\!\Big(-\frac1{34}\Big)\;+\;y_{B+}(8)\\
+&amp;= \frac{9}{34}-\frac{8}{34}+y_{B+}(8)\\
+&amp;= \frac1{34}+ \frac{-1+\sqrt{273+544\cdot8}}{68}.
+\end{aligned}
+\]
+
+Since \(273+544\cdot8 = 4625 = 25\cdot185\),
+
+\[
+y_{B+}(8)=\frac{-1+5\sqrt{185}}{68},
+\qquad
+\frac1{34}= \frac{2}{68}.
+\]
+
+Hence
+
+\[
+\sum y =\frac{2-1+5\sqrt{185}}{68}= \frac{1+5\sqrt{185}}{68}.
+\]
+
+--------------------------------------------------------------------
+### 5.   Final form
+
+\[
+\frac{1+5\sqrt{185}}{68}= \frac{a+b\sqrt{c}}{d},
+\qquad 
+a=1,\;b=5,\;c=185,\;d=68 .
+\]
+
+All conditions are satisfied (\(\gcd(a,b,d)=1\) and \(185\) is square‑free).
+
+\[
+a+b+c+d = 1+5+185+68 = 259.
+\]
+
+\[
+\boxed{259}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 259</p>
+<p>Extracted Answer: 259</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+The 27 cells of a $3\times9$ grid are filled in using the numbers 1 through 9 so that each row contains 9 different numbers, and each of the three $3\times3$ blocks heavily outlined in the example below contains 9 different numbers, as in the first three rows of a Sudoku puzzle. 
+ | 4 | 2 | 8 | 9 | 6 | 3 | 1 | 7 | 5 | 
+ | 3 | 7 | 9 | 5 | 2 | 1 | 6 | 8 | 4 | 
+ | 5 | 6 | 1 | 8 | 4 | 7 | 9 | 2 | 3 | 
+ The number of different ways to fill such a grid can be written as $p^a\cdot q^b\cdot r^c\cdot s^d$, where $p,q,r,$ and $s$ are distinct prime numbers and $a,b,c,$ and $d$ are positive integers. Find $p\cdot a+q\cdot b+r\cdot c+s\cdot d$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let the three rows be \(R_{1},R_{2},R_{3}\) and the three \(3\times 3\) blocks be  
+
+\[
+B_{1}= \text{columns }1\!-\!3,\qquad   
+B_{2}= \text{columns }4\!-\!6,\qquad   
+B_{3}= \text{columns }7\!-\!9 .
+\]
+
+--------------------------------------------------------------------
+### 1.  Fix the first row  
+
+Since the rows are labelled, we may first choose any permutation of \(\{1,\dots ,9\}\) for \(R_{1}\).
+There are  
+
+\[
+9! = 2^{7}\cdot 3^{4}\cdot5\cdot7
+\]
+
+ways.
+
+--------------------------------------------------------------------
+### 2.  Which digits go to the second row in each block?  
+
+Assume \(R_{1}=1\,2\,3\;4\,5\,6\;7\,8\,9\) (the identity permutation).  
+Then  
+
+* In \(B_{1}\) the missing digits are \(\{4,5,6,7,8,9\}\);  
+* In \(B_{2}\) the missing digits are \(\{1,2,3,7,8,9\}\);  
+* In \(B_{3}\) the missing digits are \(\{1,2,3,4,5,6\}\).
+
+For the second row we must pick, from each block, three of its six missing digits.
+The three rows must each contain every digit exactly once, so each digit
+must appear **once** in \(R_{2}\) (and the remaining occurrence of that digit will be in \(R_{3}\)).
+Thus the choice of digits for \(R_{2}\) is a partition of the six–digit sets
+subject to the condition that each of the nine digits occurs in exactly one block of \(R_{2}\).
+
+Let  
+
+* \(x\) = number of digits \(\{1,2,3\}\) placed in \(B_{2}\) (the rest go to \(B_{3}\));
+* \(y\) = number of digits \(\{4,5,6\}\) placed in \(B_{1}\) (the rest go to \(B_{3}\));
+* \(z\) = number of digits \(\{7,8,9\}\) placed in \(B_{1}\) (the rest go to \(B_{2}\)).
+
+From the block‑size condition we obtain  
+
+\[
+\begin{cases}
+y+z=3,\\
+x+ (3-z)=3,\\
+(3-x)+(3-y)=3,
+\end{cases}\qquad\Longrightarrow\qquad
+x=z,\;x+y=3 .
+\]
+
+Hence \(x\) may be \(0,1,2,3\); then \(y=3-x\) and \(z=x\).
+For a given \(x\),
+
+* choose the \(x\) digits of \(\{1,2,3\}\) that go to \(B_{2}\): \(\binom{3}{x}\) ways;
+* choose the \(y=3-x\) digits of \(\{4,5,6\}\) that go to \(B_{1}\): \(\binom{3}{3-x}=\binom{3}{x}\) ways;
+* choose the \(z=x\) digits of \(\{7,8,9\}\) that go to \(B_{1}\): \(\binom{3}{x}\) ways.
+
+Thus for this \(x\) we have \(\bigl(\binom{3}{x}\bigr)^{3}\) possibilities.
+Summing over \(x=0,1,2,3\),
+
+\[
+\sum_{x=0}^{3}\binom{3}{x}^{3}=1+27+27+1=56 .
+\]
+
+So there are \(56\) ways to decide which three‑digit sets belong to the second row
+(and the third row is forced to receive the complementary sets).
+
+--------------------------------------------------------------------
+### 3.  Ordering the digits inside each block  
+
+Inside a block each row contains three distinct digits.
+For a fixed block, the three chosen digits of \(R_{2}\) can be placed in the
+three columns in \(3!\) ways, and independently the three digits of \(R_{3}\) can be placed in \(3!\) ways.
+Hence each block contributes \((3!)^{2}=36\) arrangements.
+
+With three blocks we obtain \((36)^{3}=36^{3}=46\,656\) column‑orderings.
+
+--------------------------------------------------------------------
+### 4.  Total number of grids  
+
+\[
+N = 9! \times 56 \times 36^{3}
+     = 2^{7}\!3^{4}\!5\!7\; \times 2^{3}\!7\; \times 2^{6}\!3^{6}
+     = 2^{16}\,3^{10}\,5^{1}\,7^{2}.
+\]
+
+Thus
+
+\[
+N = p^{a}\,q^{b}\,r^{c}\,s^{d}
+\quad\text{with}\quad
+(p,q,r,s)=(2,3,5,7),\;
+(a,b,c,d)=(16,10,1,2).
+\]
+
+--------------------------------------------------------------------
+### 5.  Required sum  
+
+\[
+p a + q b + r c + s d
+ = 2\cdot16 + 3\cdot10 + 5\cdot1 + 7\cdot2
+ = 32 + 30 + 5 + 14
+ = 81 .
+\]
+
+\[
+\boxed{81}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 81</p>
+<p>Extracted Answer: 81</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Six points $ A, B, C, D, E, $ and $ F $ lie in a straight line in that order. Suppose that $ G $ is a point not on the line and that $ AC = 26 $, $ BD = 22 $, $ CE = 31 $, $ DF = 33 $, $ AF = 73 $, $ CG = 40 $, and $ DG = 30 $. Find the area of $ \triangle BGE $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let the line containing the points be the \(x\)-axis.  
+Place \(A\) at the origin, \(A=(0,0)\), and write the coordinates of the other
+collinear points as
+
+\[
+B=(x_B,0),\;C=(x_C,0),\;D=(x_D,0),\;E=(x_E,0),\;F=(x_F,0).
+\]
+
+---
+
+### 1.  Find the positions of \(B,\;C,\;D,\;E,\;F\)
+
+The given distances are along the line, so
+
+\[
+\begin{aligned}
+AC&amp;=26 &amp;&amp;\Rightarrow x_C=26,\\[2pt]
+AF&amp;=73 &amp;&amp;\Rightarrow x_F=73,\\[2pt]
+CE&amp;=31 &amp;&amp;\Rightarrow x_E=x_C+31=57,\\[2pt]
+DF&amp;=33 &amp;&amp;\Rightarrow x_D=x_F-33=40,\\[2pt]
+BD&amp;=22 &amp;&amp;\Rightarrow x_B=x_D-22=18.
+\end{aligned}
+\]
+
+Thus  
+
+\[
+A=0,\; B=18,\; C=26,\; D=40,\; E=57,\; F=73 .
+\]
+
+---
+
+### 2.  Coordinates of \(G\)
+
+Let \(G=(x_G,h)\), where \(h&gt;0\) is the perpendicular distance from \(G\) to the line.
+
+The distances from \(G\) to \(C\) and \(D\) give
+
+\[
+\begin{cases}
+(x_G-26)^2+h^2 = 40^2 = 1600,\\[4pt]
+(x_G-40)^2+h^2 = 30^2 = 900 .
+\end{cases}
+\]
+
+Subtracting the second equation from the first:
+
+\[
+(x_G-26)^2-(x_G-40)^2 = 1600-900 = 700 .
+\]
+
+Compute the left side:
+
+\[
+(x_G^2-52x_G+26^2)-(x_G^2-80x_G+40^2)
+=28x_G-924 .
+\]
+
+Hence  
+
+\[
+28x_G-924 = 700 \quad\Longrightarrow\quad 28x_G = 1624
+\quad\Longrightarrow\quad x_G = 58 .
+\]
+
+Now find \(h\) using either distance equation; use the first:
+
+\[
+(58-26)^2 + h^2 = 1600
+\Longrightarrow 32^2 + h^2 = 1600
+\Longrightarrow h^2 = 1600-1024 = 576
+\Longrightarrow h = 24 .
+\]
+
+Thus \(G=(58,24)\). Its perpendicular projection onto the line is at \(x=58\), which lies between \(E\) and \(F\).
+
+---
+
+### 3.  Area of \(\triangle BGE\)
+
+The base \(BE\) lies on the \(x\)-axis:
+
+\[
+BE = x_E - x_B = 57-18 = 39 .
+\]
+
+The height from \(G\) to this base is the vertical distance \(h=24\).
+
+Therefore
+
+\[
+\text{Area} = \frac12 \times (\text{base}) \times (\text{height})
+= \frac12 \times 39 \times 24 = 39 \times 12 = 468 .
+\]
+
+---
+
+\[
+\boxed{468}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 468</p>
+<p>Extracted Answer: 468</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Find the sum of all positive integers $ n $ such that $ n + 2 $ divides the product $ 3(n + 3)(n^2 + 9) $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>\[
+\text{Find all }n\in\mathbb Z_{&gt;0}\text{ such that }(n+2)\mid 3(n+3)(n^2+9).
+\]
+
+---
+
+### 1.  Replace \(n+2\) by a new variable  
+
+Set  
+\[
+m=n+2\qquad (m\ge 3).
+\]
+
+Then  
+
+\[
+n=m-2,\qquad n+3=m+1,\qquad n^2+9=(m-2)^2+9=m^{2}-4m+13 .
+\]
+
+Hence the divisibility condition becomes  
+
+\[
+m\mid 3(m+1)(m^{2}-4m+13).
+\tag{1}
+\]
+
+---
+
+### 2.  Reduce the right–hand side modulo \(m\)
+
+Modulo \(m\),
+
+\[
+m+1\equiv 1,\qquad m^{2}-4m+13\equiv 13 .
+\]
+
+Therefore  
+
+\[
+3(m+1)(m^{2}-4m+13)\equiv 3\cdot1\cdot13=39 \pmod m .
+\]
+
+So (1) is equivalent to  
+
+\[
+m\mid 39 .
+\tag{2}
+\]
+
+Indeed, if \(m\mid 39\) then the right–hand side of (1) equals \(39+km\) for some integer \(k\), hence is divisible by \(m\); conversely, if \(m\mid 3(m+1)(m^{2}-4m+13)\) then \(m\mid 39\).
+
+---
+
+### 3.  List possible \(m\)
+
+The positive divisors of \(39\) are  
+
+\[
+1,\;3,\;13,\;39 .
+\]
+
+Since \(m=n+2\ge 3\) (because \(n\ge1\)), we keep  
+
+\[
+m\in\{3,\;13,\;39\}.
+\]
+
+---
+
+### 4.  Recover the corresponding \(n\)
+
+\[
+\begin{aligned}
+m=3 &amp;\;\Rightarrow\; n=m-2=1,\\[2pt]
+m=13 &amp;\;\Rightarrow\; n=11,\\[2pt]
+m=39 &amp;\;\Rightarrow\; n=37 .
+\end{aligned}
+\]
+
+All three indeed satisfy the original divisibility (quick check: the quotients are \(40,420,4240\) respectively).
+
+---
+
+### 5.  Sum of all such \(n\)
+
+\[
+1+11+37=49.
+\]
+
+\[
+\boxed{49}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 49</p>
+<p>Extracted Answer: 49</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+The parabola with equation $y=x^{2}-4$ is rotated $60^{\circ}$ counterclockwise around the origin. The unique point in the fourth quadrant where the original parabola and its image intersect has $y$-coordinate $\frac{a-\sqrt{b}}{c}$, where $a$, $b$, and $c$ are positive integers, and $a$ and $c$ are relatively prime. Find $a+b+c$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+\[
+P:\;y=x^{2}-4
+\]
+
+and rotate \(P\) \(60^{\circ}\) counter‑clockwise about the origin.  
+If \((u,v)\) is a point of \(P\) \((v=u^{2}-4)\), after the rotation we obtain  
+
+\[
+\begin{aligned}
+x &amp;=u\cos 60^{\circ}-v\sin 60^{\circ}
+      =\frac{u-\sqrt3\,(u^{2}-4)}2,\\[2mm]
+y &amp;=u\sin 60^{\circ}+v\cos 60^{\circ}
+      =\frac{\sqrt3\,u+u^{2}-4}2 .
+\end{aligned}
+\tag{1}
+\]
+
+A point \((x,y)\) that belongs to both the original parabola and its image
+must satisfy  
+
+\[
+y=x^{2}-4 \qquad\text{and}\qquad (x,y)=\bigl(x(u),y(u)\bigr)\text{ for some }u .
+\]
+
+Using (1) and substituting \(y=x^{2}-4\) we get an equation for the
+pre‑image coordinate \(u\):
+
+\[
+\Bigl(u-\sqrt3\,(u^{2}-4)\Bigr)^{2}=2u^{2}+2\sqrt3\,u+8 .
+\]
+
+Simplifying gives  
+
+\[
+3u^{4}-25u^{2}+40+2\sqrt3\,u\,(3-u^{2})=0 .
+\tag{2}
+\]
+
+Let \(t=u^{2}=x^{2}\;(t\ge0)\).  Equation (2) becomes  
+
+\[
+\bigl(3t^{2}-25t+40\bigr)^{2}=12t\,(3-t)^{2},
+\]
+
+or
+
+\[
+9t^{4}-162t^{3}+937t^{2}-2108t+1600=0 .
+\tag{3}
+\]
+
+The quartic factors over the integers:
+
+\[
+\begin{aligned}
+9t^{4}-162t^{3}+937t^{2}-2108t+1600
+  &amp;=\bigl(t^{2}-11t+16\bigr)\bigl(9t^{2}-63t+100\bigr).
+\end{aligned}
+\]
+
+Thus the possible values of \(t\) are
+
+\[
+t=\frac{11\pm\sqrt{57}}2,\qquad
+t=\frac{63\pm\sqrt{369}}{18}.
+\]
+
+Recall that \(t=x^{2}\) and that a genuine intersection must satisfy the
+original unsquared equation  
+
+\[
+3t^{2}-25t+40=2\sqrt3\,\sqrt t\,(3-t).
+\tag{4}
+\]
+
+Checking the sign of each side of (4) shows that only  
+
+\[
+t=\frac{11-\sqrt{57}}2\approx1.725
+\]
+
+satisfies (4) with \(x&gt;0\).  (The other three roots correspond to the
+case \(3t^{2}-25t+40= -2\sqrt3\,\sqrt t\,(3-t)\) or give \(y&gt;0\).)
+
+Since \(y=x^{2}-4=t-4\),
+
+\[
+y=\frac{11-\sqrt{57}}2-4=\frac{3-\sqrt{57}}2 .
+\]
+
+Hence the required numbers are  
+
+\[
+a=3,\qquad b=57,\qquad c=2,
+\]
+
+with \(\gcd(a,c)=1\).  Therefore
+
+\[
+a+b+c=3+57+2=62 .
+\]
+
+\[
+\boxed{62}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 62</p>
+<p>Extracted Answer: 62</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+The product $ \prod_{k=4}^{63} \frac{\log_k(5^{k^2-1})}{\log_{k+1}(5^{k^2-4})} = \frac{\log_4(5^{15})}{\log_5(5^{12})} \cdot \frac{\log_5(5^{24})}{\log_6(5^{21})} \cdot \frac{\log_6(5^{35})}{\log_7(5^{32})} \cdots \frac{\log_{63}(5^{3968})}{\log_{64}(5^{3965})} $ is equal to $ \frac{m}{n} $, where $ m $ and $ n $ are relatively prime positive integers. Find $ m + n $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>\[
+\prod_{k=4}^{63}\frac{\log_k(5^{k^2-1})}{\log_{k+1}(5^{k^2-4})}
+\]
+
+---
+
+### 1.  Rewrite each term using change of base  
+
+\[
+\log_a b=\frac{\ln b}{\ln a}
+\]
+
+Hence  
+
+\[
+\frac{\log_k(5^{k^2-1})}{\log_{k+1}(5^{k^2-4})}
+ =\frac{\displaystyle\frac{\ln\! \big(5^{\,k^2-1}\big)}{\ln k}}
+        {\displaystyle\frac{\ln\! \big(5^{\,k^2-4}\big)}{\ln (k+1)}}
+ =\frac{(k^2-1)\ln5}{\ln k}\cdot\frac{\ln (k+1)}{(k^2-4)\ln5}
+ =\frac{k^2-1}{k^2-4}\cdot\frac{\ln(k+1)}{\ln k}.
+\]
+
+Thus the whole product becomes  
+
+\[
+\Bigl[\prod_{k=4}^{63}\frac{k^2-1}{\,k^2-4}\Bigr]\,
+\Bigl[\prod_{k=4}^{63}\frac{\ln(k+1)}{\ln k}\Bigr].
+\]
+
+---
+
+### 2.  The logarithmic factor telescopes  
+
+\[
+\prod_{k=4}^{63}\frac{\ln(k+1)}{\ln k}
+= \frac{\ln5}{\ln4}\cdot\frac{\ln6}{\ln5}\cdots\frac{\ln64}{\ln63}
+= \frac{\ln64}{\ln4}
+= \frac{6\ln2}{2\ln2}=3.
+\]
+
+---
+
+### 3.  Simplify the rational factor  
+
+\[
+\frac{k^2-1}{k^2-4}= \frac{(k-1)(k+1)}{(k-2)(k+2)}.
+\]
+
+Hence  
+
+\[
+\prod_{k=4}^{63}\frac{k^2-1}{k^2-4}
+= \Bigl[\prod_{k=4}^{63}\frac{k-1}{k-2}\Bigr]
+  \Bigl[\prod_{k=4}^{63}\frac{k+1}{k+2}\Bigr].
+\]
+
+**First product**
+
+\[
+\prod_{k=4}^{63}\frac{k-1}{k-2}
+= \frac{3}{2}\cdot\frac{4}{3}\cdot\frac{5}{4}\cdots\frac{62}{61}
+= \frac{62}{2}=31.
+\]
+
+**Second product**
+
+\[
+\prod_{k=4}^{63}\frac{k+1}{k+2}
+= \frac{5}{6}\cdot\frac{6}{7}\cdot\frac{7}{8}\cdots\frac{64}{65}
+= \frac{5}{65}= \frac{1}{13}.
+\]
+
+Multiplying,
+
+\[
+\prod_{k=4}^{63}\frac{k^2-1}{k^2-4}=31\cdot\frac{1}{13}= \frac{31}{13}.
+\]
+
+---
+
+### 4.  Combine the two parts  
+
+\[
+\prod_{k=4}^{63}\frac{\log_k(5^{k^2-1})}{\log_{k+1}(5^{k^2-4})}
+= \frac{31}{13}\times 3 = \frac{93}{13}.
+\]
+
+The fraction \(\frac{93}{13}\) is already in lowest terms (\(\gcd(93,13)=1\)).  
+
+Thus \(m=93,\; n=13\) and  
+
+\[
+m+n = 93+13 = 106.
+\]
+
+\[
+\boxed{106}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 106</p>
+<p>Extracted Answer: 106</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $N$ denote the number of ordered triples of positive integers $(a,b,c)$ such that $a,b,c\leq3^6$ and $a^3+b^3+c^3$ is a multiple of $3^7$. Find the remainder when $N$ is divided by $1000$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>**Solution Sketch**
+
+Write every integer \(a\le 3^{6}=729\) in its base‑\(3\) expansion  
+
+\[
+a = a_{0}+a_{1}3+a_{2}3^{2}+a_{3}3^{3}+a_{4}3^{4}+a_{5}3^{5},
+\qquad a_{i}\in\{0,1,2\}.
+\]
+
+Let  
+
+\[
+A(x)=a_{0}+a_{1}x+a_{2}x^{2}+a_{3}x^{3}+a_{4}x^{4}+a_{5}x^{5}\in\mathbb{F}_{3}[x].
+\]
+
+Modulo \(3^{7}\) we have  
+
+\[
+a^{3}\equiv a_{0}^{3}+9a_{0}^{2}a_{1}+27\bigl(a_{0}a_{1}^{2}+a_{0}^{2}a_{2}\bigr)
+               +\; \cdots\;+3^{6}a_{2}^{3}\pmod{3^{7}} .
+\]
+
+Hence
+
+\[
+a^{3}+b^{3}+c^{3}\equiv 
+\sum_{i=0}^{2}3^{i}\bigl(a_{i}^{3}+b_{i}^{3}+c_{i}^{3}\bigr)\pmod{3^{7}} .
+\]
+
+Because \(x^{3}\equiv x\pmod 3\) for \(x\in\{0,1,2\}\), the condition
+\(a^{3}+b^{3}+c^{3}\equiv0\pmod{3^{7}}\) is equivalent to the three
+independent linear equations  
+
+\[
+a_{0}+b_{0}+c_{0}\equiv0,\qquad
+a_{1}+b_{1}+c_{1}\equiv0,\qquad
+a_{2}+b_{2}+c_{2}\equiv0\pmod 3 .
+\]
+
+For each digit‑position \(i=0,1,2\) the number of ordered triples
+\((a_{i},b_{i},c_{i})\) satisfying the linear condition is
+\(3^{2}=9\) (choose any two digits freely, the third one is forced).
+The remaining higher digits \(a_{3},a_{4},a_{5}\) are unrestricted; each
+has \(3^{3}=27\) possibilities (three choices for each of the three
+numbers).
+
+Therefore the total number of admissible triples \((a,b,c)\) is  
+
+\[
+N = 9^{3}\cdot 27^{3}=3^{15}=14\,348\,907 .
+\]
+
+Finally we need the remainder of \(N\) modulo \(1000\):
+
+\[
+14\,348\,907\equiv 907\pmod{1000}.
+\]
+
+\[
+\boxed{907}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 735</p>
+<p>Extracted Answer: 907</p>
+<p>Score: 0.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Four unit squares form a $2 \times 2$ grid. Each of the 12 unit line segments forming the sides of the squares is colored either red or blue in such a way that each unit square has 2 red sides and 2 blue sides. Find the number of such colorings.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+* \(a,b,c,d\) be the four interior edges (the two interior vertical and the two interior horizontal sides).  
+* The eight outer edges are the two edges that belong to each unit square but are on the boundary of the
+\(2\times2\) grid.
+
+For a particular unit square the number of its interior red sides is the number of red interior edges incident
+to it.  
+If a square has \(s\) interior red sides, then it needs exactly \(2-s\) red outer sides, because the total number
+of red sides must be \(2\).  
+
+For a given square
+
+\[
+\#\text{ ways to colour its two outer edges}= \binom{2}{\,2-s\,}=
+\begin{cases}
+1,&amp;s=0\text{ or }2,\\[2pt]
+2,&amp;s=1 .
+\end{cases}
+\]
+
+Thus, once the interior edges are fixed, the outer edges can be coloured independently for each square.
+If among the four squares exactly \(k\) of them have \(s=1\) (i.e. exactly one interior red edge incident to the
+square), the number of completions of the outer edges is \(2^{k}\).
+
+--------------------------------------------------------------------
+
+### Counting interior–edge configurations
+
+The interior edges form a 4‑cycle  
+
+\[
+A\;-\;B\;-\;D\;-\;C\;-\;A .
+\]
+
+We list all \(2^{4}=16\) subsets of these edges and, for each, count how many squares have one interior red
+edge.
+
+| # interior edges | type of selection | \# of squares with \(s=1\) | \# of such subsets | contributions |
+|------------------|-------------------|----------------------------|--------------------|---------------|
+| 0 | none | 0 | 1 | \(2^{0}=1\) |
+| 1 | any one edge | 2 (the two squares incident to the edge) | 4 | \(4\cdot2^{2}=16\) |
+| 2 | adjacent edges (share a vertex) | 2 (the two squares adjacent to the common vertex) | 4 | \(4\cdot2^{2}=16\) |
+| 2 | opposite edges (no common vertex) | 4 (each square gets one) | 2 | \(2\cdot2^{4}=32\) |
+| 3 | all but one edge | 2 (the two squares not incident to the missing edge) | 4 | \(4\cdot2^{2}=16\) |
+| 4 | all four edges | 0 | 1 | \(1\cdot2^{0}=1\) |
+
+Adding the contributions:
+
+\[
+1+16+16+32+16+1 = 82 .
+\]
+
+--------------------------------------------------------------------
+
+Therefore there are  
+
+\[
+\boxed{82}
+\]
+
+different ways to colour the 12 unit segments so that each of the four unit squares has exactly two red sides
+(and consequently two blue sides).</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 82</p>
+<p>Extracted Answer: 82</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $ A $ be the set of positive integer divisors of 2025. Let $ B $ be a randomly selected subset of $ A $. The probability that $ B $ is a nonempty set with the property that the least common multiple of its elements is 2025 is $ \frac{m}{n} $, where $ m $ and $ n $ are relatively prime positive integers. Find $ m + n $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>\(2025=3^{4}\cdot5^{2}\).
+
+Divisors of \(2025\) are of the form \(3^{a}5^{b}\) with  
+\(0\le a\le4,\;0\le b\le2\); therefore  
+
+\[
+|A|=(4+1)(2+1)=15 .
+\]
+
+--------------------------------------------------------------------
+### Condition for the LCM
+
+For a subset \(B\subseteq A\),
+
+\[
+\operatorname{lcm}(B)=3^{\max a}\,5^{\max b}.
+\]
+
+Thus \(\operatorname{lcm}(B)=2025=3^{4}5^{2}\) iff  
+
+* at least one element of \(B\) has exponent \(a=4\) (i.e. is divisible by \(3^{4}\)), and  
+* at least one element of \(B\) has exponent \(b=2\) (i.e. is divisible by \(5^{2}\)).
+
+--------------------------------------------------------------------
+### Relevant divisor families  
+
+\[
+X=\{d\in A\mid 3^{4}\mid d\}=\{81,405,2025\},\qquad |X|=3,
+\]
+
+\[
+Y=\{d\in A\mid 5^{2}\mid d\}=\{25,75,225,675,2025\},\qquad |Y|=5.
+\]
+
+\(X\cap Y=\{2025\}\), so \(|X\cup Y|=3+5-1=7\).
+
+--------------------------------------------------------------------
+### Counting subsets with the required property  
+
+A subset \(B\) works iff it meets both \(X\) and \(Y\).  
+Using inclusion–exclusion on all \(2^{15}\) subsets of \(A\):
+
+\[
+\begin{aligned}
+\#\{B:\ B\cap X\neq\varnothing,\ B\cap Y\neq\varnothing\}
+&amp;=2^{15}
+ -2^{12}\;(\text{subsets missing }X)
+ -2^{10}\;(\text{subsets missing }Y)\\
+&amp;\qquad +2^{8}\;(\text{subsets missing both }X\cup Y)\\[2mm]
+&amp;=32768-4096-1024+256\\
+&amp;=27904 .
+\end{aligned}
+\]
+
+All these subsets are non‑empty, so the numerator is \(27904\).
+
+--------------------------------------------------------------------
+### Probability
+
+\[
+P=\frac{27904}{2^{15}}=\frac{27904}{32768}.
+\]
+
+Both numbers are divisible by \(256\):
+
+\[
+\frac{27904}{32768}=\frac{27904/256}{32768/256}= \frac{109}{128}.
+\]
+
+The fraction \(\frac{109}{128}\) is already in lowest terms, so  
+\(m=109,\;n=128\).
+
+\[
+m+n=109+128=237.
+\]
+
+\[
+\boxed{237}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 237</p>
+<p>Extracted Answer: 237</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Alex divides a disk into four quadrants with two perpendicular diameters intersecting at the center of the disk. He draws 25 more line segments through the disk, drawing each segment by selecting two points at random on the perimeter of the disk in different quadrants and connecting those two points. Find the expected number of regions into which these 27 line segments divide the disk.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>**Step 1 –  How regions grow**
+
+When a new line segment is drawn in the disk, it either  
+*does not meet any previous segment* – it creates **one** new region, or  
+*meets \(k\) previous segments in interior points* – it creates **\(k+1\)** new regions  
+(the segment is cut into \(k+1\) pieces, each of which separates a region).
+
+Hence, if we start with one region (the whole disk),
+
+\[
+\#\text{regions}=1+\#\text{segments}+\#\text{interior intersections } .
+\tag{1}
+\]
+
+The two perpendicular diameters intersect once, giving the four initial
+quadrants.  After the 25 random chords are added we will have  
+
+\[
+27\text{ segments} = 2\text{ diameters}+25\text{ chords}.
+\]
+
+So we only have to find the **expected number of interior intersection points**.
+
+--------------------------------------------------------------------
+
+**Step 2 –  Intersections with the diameters**
+
+A random chord meets a fixed diameter iff its two endpoints lie on opposite
+sides of that diameter.  
+
+*Horizontal diameter* (\(y=0\)): the endpoints must belong to one of the
+four unordered quadrant pairs  
+
+\[
+\{Q_1,Q_3\},\{Q_1,Q_4\},\{Q_2,Q_3\},\{Q_2,Q_4\},
+\]
+
+i.e. 4 out of the 6 possible unordered pairs of different quadrants.
+Thus  
+
+\[
+P(\text{chord meets a given diameter})=\frac{4}{6}= \frac23 .
+\]
+
+The same probability holds for the vertical diameter.  
+Hence the expected number of chord‑diameter intersections is  
+
+\[
+25\;( \text{chords})\times 2\;( \text{diameters})\times \frac23
+  =\frac{100}{3}.
+\tag{2}
+\]
+
+--------------------------------------------------------------------
+
+**Step 3 –  Intersections between two random chords**
+
+Let a chord be represented by the unordered pair of quadrants that contain its
+end‑points.  
+There are  
+
+* 4 *adjacent* pairs  \(\{0,1\},\{1,2\},\{2,3\},\{3,0\}\);  
+* 2 *opposite* pairs   \(\{0,2\},\{1,3\}\).
+
+Thus the six possible chords are the six edges of the complete graph \(K_4\)
+on the four quadrants.
+
+Two chords may be:
+
+| Relation of the two edges | How many ordered pairs | Intersection probability |
+|---------------------------|-----------------------|--------------------------|
+| Same edge (both chords use the same pair) | 6 (4 adjacent + 2 opposite) | \(\frac12\) |
+| Share one vertex (adjacent edges) | 24 (8 both adjacent + 16 one adjacent–one opposite) | \(\frac12\) |
+| Disjoint edges, both adjacent (e.g. \{0,1\} &amp; \{2,3\}) | 4 | \(0\) |
+| Disjoint edges, both opposite ( \{0,2\} &amp; \{1,3\}) | 2 | \(1\) |
+
+*Why these probabilities?*  
+
+* Same edge – the two chords are independent copies inside the same two
+quadrants.  A short calculation (or a symmetry argument) gives a crossing
+probability of \(\frac12\).
+* Share a vertex – one endpoint of the second chord lies in the same quadrant
+as an endpoint of the first chord.  The second endpoint is always in a
+different quadrant, so the second chord meets the first exactly when the
+point that shares the vertex falls between the two endpoints of the first
+chord.  Averaging over the uniform positions gives \(\frac12\) again.
+* Disjoint adjacent edges lie completely on opposite sides of the
+horizontal (or vertical) diameter, so they can never meet ⇒ probability \(0\).
+* Disjoint opposite edges always cross the centre of the disk; any two such
+chords intersect ⇒ probability \(1\).
+
+Summing the contributions of the \(36\) ordered pairs of chords,
+
+\[
+S = 6\!\left(\frac12\right)+24\!\left(\frac12\right)+4\cdot0+2\cdot1 = 17 .
+\]
+
+Therefore the probability that two independently chosen random chords intersect is  
+
+\[
+p_{\text{chord–chord}} = \frac{S}{36}= \frac{17}{36}.
+\tag{3}
+\]
+
+--------------------------------------------------------------------
+
+**Step 4 –  Expected number of chord–chord intersections**
+
+There are \(\binom{25}{2}=300\) unordered pairs of the 25 random chords.  
+Using (3),
+
+\[
+E(\text{chord–chord intersections})=300\cdot\frac{17}{36}
+     =\frac{425}{3}=141\frac{2}{3}.
+\tag{4}
+\]
+
+--------------------------------------------------------------------
+
+**Step 5 –  Total expected interior intersections**
+
+\[
+\begin{aligned}
+E(\text{total interior intersections})
+&amp;= (\text{diameters intersect})\\
+&amp;\qquad +(\text{chord–diameter intersections})\\
+&amp;\qquad +(\text{chord–chord intersections})\\[2mm]
+&amp;= 1+\frac{100}{3}+ \frac{425}{3}= 176 .
+\end{aligned}
+\tag{5}
+\]
+
+--------------------------------------------------------------------
+
+**Step 6 –  Expected number of regions**
+
+Insert (5) into formula (1) with the total of \(27\) segments:
+
+\[
+E(\text{regions}) = 1 + 27 + 176 = 204 .
+\]
+
+--------------------------------------------------------------------
+
+\[
+\boxed{204}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 204</p>
+<p>Extracted Answer: 204</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Circle $\omega_1$ with radius 6 centered at point $A$ is internally tangent at point $B$ to circle $\omega_2$ with radius 15. Points $C$ and $D$ lie on $\omega_2$ such that $\overline{BC}$ is a diameter of $\omega_2$ and $\overline{BC} \perp \overline{AD}$. The rectangle $EFGH$ is inscribed in $\omega_1$ such that $\overline{EF} \perp \overline{BC}$, $C$ is closer to $\overline{GH}$ than to $\overline{EF}$, and $D$ is closer to $\overline{FG}$ than to $\overline{EH}$, as shown. Triangles $\triangle DGF$ and $\triangle CHG$ have equal areas. The area of rectangle $EFGH$ is $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m + n$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>**Solution Overview**
+
+Place the two circles on a coordinate plane, compute the positions of the relevant points, and write the
+rectangle’s vertices in terms of its side–lengths.  
+The conditions “\(C\) is closer to \(\overline{GH}\) than to \(\overline{EF}\)” and “\(D\) is closer to
+\(\overline{FG}\) than to \(\overline{EH}\)” fix the orientation of the rectangle.  
+Using the equality of the two triangle areas we obtain a simple relation between the rectangle’s width
+and height, which together with the fact that the rectangle is inscribed in the small circle yields the
+required dimensions and its area.
+
+--------------------------------------------------------------------
+
+### 1.  Coordinate set‑up  
+
+Let  
+
+* \(O\) be the centre of the large circle \(\omega_2\) (radius \(15\)).
+* \(A\) be the centre of the small circle \(\omega_1\) (radius \(6\)).
+* \(B\) the common point of tangency.
+
+Because the circles are internally tangent,
+\[
+OA = 15-6=9,
+\qquad AB=6,
+\qquad OB =15 .
+\]
+
+Choose the \(x\)–axis along \(\overline{BC}\).  
+Take  
+
+\[
+O=(0,0),\qquad B=(15,0).
+\]
+
+Then \(A\) lies on the same line, nine units left of \(B\):
+\[
+A=(9,0).
+\]
+
+Since \(BC\) is a diameter of \(\omega_2\), the opposite end of the diameter is
+\[
+C=(-15,0).
+\]
+
+The condition \(\overline{BC}\perp\overline{AD}\) makes \(AD\) vertical, so the points of
+\(\omega_2\) with \(x=9\) are
+\[
+D=(9,12)\quad\text{or}\quad D=(9,-12).
+\]
+Because later we need \(D\) to be nearer the top side of the rectangle, we take  
+
+\[
+\boxed{D=(9,12)} .
+\]
+
+--------------------------------------------------------------------
+
+### 2.  The rectangle \(EFGH\)
+
+\(EF\) is required to be perpendicular to \(\overline{BC}\); hence \(EF\) is a vertical side.
+Let the rectangle have
+
+* width \(w\) (the horizontal side \(\overline{FG}\)),
+* height \(h\) (the vertical side \(\overline{EF}= \overline{GH}\)).
+
+Since the rectangle is inscribed in \(\omega_1\), its centre coincides with the centre of \(\omega_1\),
+namely \(A=(9,0)\).  Consequently the vertices are
+
+\[
+\begin{aligned}
+E&amp;=\bigl(b,\,-\tfrac{h}{2}\bigr), &amp;
+F&amp;=\bigl(b, \tfrac{h}{2}\bigr),\\[2mm]
+G&amp;=\bigl(a, \tfrac{h}{2}\bigr), &amp;
+H&amp;=\bigl(a,\,-\tfrac{h}{2}\bigr),
+\end{aligned}
+\]
+where  
+
+\[
+a = 9-\frac{w}{2},\qquad b = 9+\frac{w}{2}.
+\]
+
+Because every vertex lies on \(\omega_1\) (radius \(6\) and centre \((9,0)\)),
+\[
+(a-9)^2+\Bigl(\frac{h}{2}\Bigr)^2 = (b-9)^2+\Bigl(\frac{h}{2}\Bigr)^2 = 6^{2}=36 .
+\]
+Both equations give the single relation  
+
+\[
+\boxed{w^{2}+h^{2}=144}\tag{1}
+\]
+(the rectangle’s diagonal is the diameter \(12\) of the small circle).
+
+--------------------------------------------------------------------
+
+### 3.  Interpreting the “closer‑to” conditions  
+
+The statement “\(C\) is closer to \(\overline{GH}\) than to \(\overline{EF}\)” forces \(\overline{GH}\) to be
+the left vertical side (smaller \(x\))-coordinate) and \(\overline{EF}\) the right vertical side.  
+Similarly “\(D\) is closer to \(\overline{FG}\) than to \(\overline{EH}\)” places \(\overline{FG}\) at the
+top (larger \(y\))-coordinate.
+
+Thus  
+
+\[
+\begin{aligned}
+\text{dist}(C,\overline{GH})&amp;=a-(-15)=a+15,\\
+\text{dist}(C,\overline{EF})&amp;=b+15,\\[1mm]
+\text{dist}(D,\overline{FG})&amp;=12-\frac{h}{2},\\
+\text{dist}(D,\overline{EH})&amp;=12+\frac{h}{2},
+\end{aligned}
+\]
+and the above inequalities are automatically satisfied for any feasible rectangle
+(\(a&lt;b\) and \(h/2&lt;12\)).
+
+--------------------------------------------------------------------
+
+### 4.  Equality of the two triangle areas  
+
+*Triangle \(DGF\).*  
+\(G\) and \(F\) are the top‑left and top‑right vertices, so \(\overline{GF}\) is horizontal,
+\(|GF| = w\).  The altitude from \(D\) to \(\overline{GF}\) is the vertical distance
+\(12-\frac{h}{2}\).  Hence  
+
+\[
+[ DGF ] = \frac12 \, w\!\left(12-\frac{h}{2}\right).
+\tag{2}
+\]
+
+*Triangle \(CHG\).*  
+\(G\) and \(H\) lie on the left side, \(|GH|=h\).  The altitude from \(C\) to this side is the
+horizontal distance \(a+15\).  Thus  
+
+\[
+[ CHG ] = \frac12 \, h\,(a+15).
+\tag{3}
+\]
+
+Given \([DGF]=[CHG]\) and using \(a=9-\dfrac w2\), we have  
+
+\[
+w\!\left(12-\frac{h}{2}\right)=
+h\!\Bigl(9-\frac{w}{2}+15\Bigr)
+= h\!\bigl(24-\frac{w}{2}\bigr).
+\]
+
+Expanding and cancelling the common term \(-\dfrac{wh}{2}\) yields  
+
+\[
+12w = 24h \quad\Longrightarrow\quad \boxed{w = 2h}. \tag{4}
+\]
+
+--------------------------------------------------------------------
+
+### 5.  Determining \(w\) and \(h\)
+
+Insert \(w=2h\) into (1):
+
+\[
+(2h)^{2}+h^{2}=144
+\;\Longrightarrow\;5h^{2}=144
+\;\Longrightarrow\;h^{2}=\frac{144}{5}.
+\]
+
+Hence  
+
+\[
+h = \frac{12}{\sqrt5}= \frac{12\sqrt5}{5},
+\qquad 
+w = 2h = \frac{24\sqrt5}{5}.
+\]
+
+--------------------------------------------------------------------
+
+### 6.  Area of the rectangle  
+
+\[
+[EFGH]=w\cdot h = 2h^{2}=2\cdot\frac{144}{5}= \frac{288}{5}.
+\]
+
+Thus the required area is \(\displaystyle \frac{288}{5}\); the fraction is already in lowest terms.
+So \(m=288,\; n=5\) and  
+
+\[
+m+n = 288+5 = 293 .
+\]
+
+--------------------------------------------------------------------
+
+\[
+\boxed{293}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 293</p>
+<p>Extracted Answer: 293</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let the sequence of rationals $ x_1, x_2, \ldots $ be defined such that $ x_1 = \frac{25}{11} $ and
+$ x_{k+1} = \frac{1}{3} \left( x_k + \frac{1}{x_k} - 1 \right). $
+$ x_{2025} $ can be expressed as $ \frac{m}{n} $ for relatively prime positive integers $ m $ and $ n $. Find the remainder when $ m + n $ is divided by 1000.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>\[
+x_{k+1}= \frac{x_k+\dfrac1{x_k}-1}{3}, \qquad x_1=\frac{25}{11}.
+\]
+
+--------------------------------------------------------------------
+### 1.  A convenient change of variable  
+
+Set  
+
+\[
+t_k=\frac{x_k-1}{x_k+1}\qquad\Longleftrightarrow\qquad 
+x_k=\frac{1+t_k}{1-t_k}.
+\]
+
+Then a short computation gives  
+
+\[
+t_{k+1}= \frac{3t_k^{2}-1}{2}. \tag{1}
+\]
+
+Thus the problem reduces to iterating the quadratic map  
+
+\[
+F(t)=\frac{3t^{2}-1}{2}
+\]
+
+starting from  
+
+\[
+t_1=\frac{x_1-1}{x_1+1}
+      =\frac{25/11-1}{25/11+1}
+      =\frac{7}{18}.
+\]
+
+--------------------------------------------------------------------
+### 2.  Working with the original rationals  
+
+Write \(t_k=p_k/q_k\) in lowest terms.   
+From (1)
+
+\[
+\frac{p_{k+1}}{q_{k+1}}=
+\frac{3p_k^{2}-3p_kq_k+3q_k^{2}}{2q_k^{2}}
+      =\frac{p_k^{2}-p_kq_k+q_k^{2}}{3}\;\Big/
+        \;\frac{p_kq_k}{1},
+\]
+
+hence (clearing the common factor \(3\))
+
+\[
+\boxed{\displaystyle 
+p_{k+1}= \frac{p_k^{2}-p_kq_k+q_k^{2}}{3},
+\qquad 
+q_{k+1}=p_kq_k } . \tag{2}
+\]
+
+For the initial pair  
+
+\[
+p_1=25,\qquad q_1=11 .
+\]
+
+Because \(p_1\equiv1,\; q_1\equiv2\pmod 3\) one checks from (2) that  
+\(p_k\equiv1,\; q_k\equiv2\pmod 3\) for every \(k\); consequently the
+division by \(3\) in (2) is always exact and the reduced fractions
+\(\dfrac{p_k}{q_k}=x_k\) stay in lowest terms.
+
+--------------------------------------------------------------------
+### 3.  Behaviour modulo \(8\)
+
+\(3\) is invertible modulo \(8\) (\(3^{-1}\equiv3\)).  
+From (2)
+
+\[
+p_{k+1}\equiv 3\bigl(p_k^{2}-p_kq_k+q_k^{2}\bigr)\pmod 8,
+\qquad 
+q_{k+1}\equiv p_kq_k\pmod 8 .
+\]
+
+Starting with \((p_1,q_1)\equiv(1,3)\pmod8\) one obtains
+
+\[
+(p_2,q_2)\equiv(5,3),\qquad
+(p_3,q_3)\equiv(1,7),
+\]
+
+and thereafter  
+
+\[
+p_k\equiv1,\quad q_k\equiv7\pmod8 \qquad(k\ge3).
+\]
+
+Hence for every \(k\ge3\)
+
+\[
+p_k+q_k\equiv0\pmod8. \tag{3}
+\]
+
+--------------------------------------------------------------------
+### 4.  Behaviour modulo \(125\)
+
+\(3^{-1}\equiv42\pmod{125}\).  Using (2),
+
+\[
+p_{k+1}\equiv42\bigl(p_k^{2}-p_kq_k+q_k^{2}\bigr)\pmod{125},
+\qquad 
+q_{k+1}\equiv p_kq_k\pmod{125}. \tag{4}
+\]
+
+Computating a few steps (mod 125) gives  
+
+\[
+\begin{array}{c|c|c}
+k &amp; p_k\pmod{125} &amp; q_k\pmod{125}\\ \hline
+1 &amp; 25 &amp; 11\\
+2 &amp; 32 &amp; 25\\
+3 &amp; 33 &amp; 50\\
+4 &amp; 63 &amp; 25\\
+5 &amp; 48 &amp; 75\\
+6 &amp; 68 &amp;100\\
+\vdots &amp;\vdots &amp;\vdots
+\end{array}
+\]
+
+From \(k=4\) onward the pair \((p_k,q_k)\) repeats with period 20:
+
+\[
+(p_{k+20},q_{k+20})\equiv(p_k,q_k)\pmod{125}\qquad(k\ge4).
+\]
+
+Since \(2025\equiv5\pmod{20}\) and \(2025\ge4\),
+
+\[
+p_{2025}\equiv p_5\equiv48,\qquad
+q_{2025}\equiv q_5\equiv75 \pmod{125}. \tag{5}
+\]
+
+Thus
+
+\[
+p_{2025}+q_{2025}\equiv48+75=123\pmod{125}. \tag{6}
+\]
+
+--------------------------------------------------------------------
+### 5.  Combination (Chinese Remainder)
+
+From (3) we have \(p_{2025}+q_{2025}\equiv0\pmod8\);   
+from (6) we have \(p_{2025}+q_{2025}\equiv123\pmod{125}\).
+
+Let \(S=p_{2025}+q_{2025}\).  
+Write \(S=8u\); then \(8u\equiv123\pmod{125}\).
+Since \(8^{-1}\equiv47\pmod{125}\),
+
+\[
+u\equiv47\cdot123\equiv31\pmod{125},
+\qquad
+S=8u\equiv8\cdot31=248\pmod{1000}.
+\]
+
+--------------------------------------------------------------------
+### 6.  Answer
+
+The required remainder is  
+
+\[
+\boxed{248}.
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 248</p>
+<p>Extracted Answer: 248</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+From an unlimited supply of 1-cent coins, 10-cent coins, and 25-cent coins, Silas wants to find a collection of coins that has a total value of $ N $ cents, where $ N $ is a positive integer. He uses the so-called **greedy algorithm**, successively choosing the coin of greatest value that does not cause the value of his collection to exceed $ N $. For example, to get 42 cents, Silas will choose a 25-cent coin, then a 10-cent coin, then 7 1-cent coins. However, this collection of 9 coins uses more coins than necessary to get a total of 42 cents; indeed, choosing 4 10-cent coins and 2 1-cent coins achieves the same total value with only 6 coins.
+
+In general, the greedy algorithm succeeds for a given $ N $ if no other collection of 1-cent, 10-cent, and 25-cent coins gives a total value of $ N $ cents using strictly fewer coins than the collection given by the greedy algorithm. Find the number of values of $ N $ between 1 and 1000 inclusive for which the greedy algorithm succeeds.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>**Step 1.  Greedy representation**
+
+For a value \(N\) write  
+
+\[
+N = 25q + r ,\qquad 0\le r&lt;25 .
+\]
+
+The greedy algorithm first uses \(q\) quarters, then as many dimes as possible from the remainder \(r\):
+\[
+r = 10d + e ,\qquad 0\le e&lt;10 .
+\]
+Hence the greedy collection has  
+
+\[
+\text{coins}_{\text{greedy}} = q+d+e .
+\tag{1}
+\]
+
+**Step 2.  When can we do better?**
+
+A collection using \(a\) quarters and \(b\) dimes (the pennies are forced) has  
+
+\[
+25a+10b\le N ,\qquad \text{pennies}=N-25a-10b .
+\]
+
+Its total number of coins is  
+
+\[
+a+b+(N-25a-10b)=N-(24a+9b).
+\]
+
+Because \(N\) is fixed, the collection is optimal iff the quantity  
+
+\[
+W=24a+9b
+\tag{2}
+\]
+
+is as large as possible under the constraint \(25a+10b\le N\).  
+
+**Step 3.  Compare the greedy choice with one fewer quarter**
+
+The greedy choice uses \(a=q\) and \(b=d\).  
+Consider reducing the number of quarters by one: take \(a&#39;=q-1\).  
+The value that must now be made with dimes and pennies is \(25+r\); the maximal possible number
+of dimes is
+
+\[
+b&#39;=\Big\lfloor\frac{25+r}{10}\Big\rfloor .
+\]
+
+Write \(r=10d+e\;(0\le e\le 9)\). Then  
+
+\[
+\frac{25+r}{10}=2+d+\frac{e+5}{10},
+\qquad
+b&#39;=d+2+f,
+\]
+where  
+
+\[
+f=\Big\lfloor\frac{e+5}{10}\Big\rfloor=
+\begin{cases}
+0,&amp;e\le4,\\[2pt]
+1,&amp;e\ge5 .
+\end{cases}
+\]
+
+The weight (2) for the greedy choice is  
+
+\[
+W_{\text{gr}}=24q+9d .
+\]
+
+For the alternative with one fewer quarter we have  
+
+\[
+W_{\text{alt}}=24(q-1)+9(d+2+f)=W_{\text{gr}}-24+18+9f
+      =W_{\text{gr}}+( -6+9f).
+\]
+
+Thus  
+
+\[
+W_{\text{alt}}-W_{\text{gr}}=
+\begin{cases}
+-6, &amp; e\le 4,\\[2pt]
++3, &amp; e\ge 5 .
+\end{cases}
+\]
+
+If \(e\ge5\) the alternative has **larger** weight, i.e. it uses **fewer** coins
+(three fewer, because the weight increases by 3).  
+If \(e\le4\) the alternative is worse.
+
+Consequently the greedy algorithm is **not optimal exactly when**
+\[
+e = r \bmod 10 \ge 5 .
+\tag{3}
+\]
+
+**Step 4.  Which remainders cause failure?**
+
+Since \(r\) ranges from \(0\) to \(24\), condition (3) means  
+
+\[
+r\in\{5,6,7,8,9,15,16,17,18,19\}.
+\tag{4}
+\]
+
+For \(N&lt;25\) we have \(q=0\); only 1‑cent and 10‑cent coins are usable, and the greedy
+choice (as many dimes as possible) is obviously optimal.  Hence failures occur only for
+\(N\ge25\) with remainder (4) upon division by \(25\).
+
+**Step 5.  Counting the failures between 1 and 1000**
+
+The numbers \(25\le N\le 1000\) form 39 complete blocks of 25 consecutive integers
+(\(25\)–\(999\)) and the single extra number \(1000\).
+
+- In each full block every residue modulo \(25\) appears once,
+  so each block contains exactly \(10\) failures (the residues in (4)).
+- Hence failures in the 39 blocks: \(39\times10=390\).
+
+The leftover number \(1000\) has residue \(0\) (not a failure).
+
+Thus the total number of failures is \(390\).
+
+**Step 6.  Successes**
+
+Out of the \(1000\) possible values of \(N\),
+
+\[
+\text{successful }N = 1000 - 390 = 610 .
+\]
+
+\[
+\boxed{610}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 610</p>
+<p>Extracted Answer: 610</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+There are $ n $ values of $ x $ in the interval $ 0 &lt; x &lt; 2\pi $ where $ f(x) = \sin(7\pi \cdot \sin(5x)) = 0 $. For $ t $ of these $ n $ values of $ x $, the graph of $ y = f(x) $ is tangent to the $ x $-axis. Find $ n + t $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>For  
+
+\[
+f(x)=\sin\bigl(7\pi\sin(5x)\bigr)
+\]
+
+we need the solutions of  
+
+\[
+\sin\bigl(7\pi\sin(5x)\bigr)=0\qquad(0&lt;x&lt;2\pi).
+\]
+
+---
+
+### 1.  Zeros of \(f\)
+
+\[
+\sin(A)=0\iff A=m\pi,\;m\in\mathbb Z .
+\]
+
+Hence  
+
+\[
+7\pi\sin(5x)=m\pi\Longrightarrow \sin(5x)=\frac{m}{7}.
+\]
+
+Because \(\sin(5x)\in[-1,1]\), the integer \(m\) must satisfy  
+
+\[
+-7\le m\le 7 .
+\]
+
+Let \(k=m\). For each integer \(k\) with \(-7\le k\le 7\) we solve  
+
+\[
+\sin(5x)=\frac{k}{7}.
+\]
+
+Put \(\theta =5x\). Then \(\theta\in(0,10\pi)\) and we need  
+
+\[
+\sin\theta = \frac{k}{7}.
+\]
+
+* **\(k=\pm7\)** (\(\sin\theta=\pm1\)).  
+  In each \(2\pi\)-period there is exactly one solution.  
+  Over the interval \((0,10\pi)\) (5 periods) we obtain \(5\) solutions for \(k=7\) and
+  \(5\) solutions for \(k=-7\).
+
+* **\(k=0\)** (\(\sin\theta=0\)).  
+  Solutions are \(\theta=n\pi\).  
+  With \(0&lt;\theta&lt;10\pi\) we have \(n=1,2,\dots ,9\): \(9\) solutions.
+
+* **\(k=\pm1,\pm2,\dots ,\pm6\)** (\(|k/7|&lt;1\) and \(\neq0\)).  
+  In each period there are two distinct solutions, so over \(5\) periods we get
+  \(2\cdot5=10\) solutions for each such \(k\).
+
+There are \(12\) values of \(k\) with \(|k|\le6\) and \(k\neq0\).
+
+Hence the total number of zeros is  
+
+\[
+n = 5+5+9+12\cdot10 = 139 .
+\]
+
+---
+
+### 2.  Tangent points
+
+Differentiate:
+
+\[
+f&#39;(x)=\cos\!\bigl(7\pi\sin(5x)\bigr)\cdot7\pi\cdot5\cos(5x)
+      =35\pi\cos(5x)\cos\!\bigl(7\pi\sin(5x)\bigr).
+\]
+
+At a zero of \(f\) we have \(\sin(5x)=k/7\), so  
+
+\[
+\cos\!\bigl(7\pi\sin(5x)\bigr)=\cos(k\pi)=(-1)^k\neq0 .
+\]
+
+Thus \(f&#39;(x)=0\) exactly when \(\cos(5x)=0\), i.e. when \(\sin(5x)=\pm1\).
+Those correspond precisely to the cases \(k=\pm7\).
+
+We already counted \(5\) solutions for \(k=7\) and \(5\) for \(k=-7\); all of them are
+tangency points. Hence  
+
+\[
+t = 5+5 = 10 .
+\]
+
+---
+
+### 3.  Required sum
+
+\[
+n+t = 139+10 = 149 .
+\]
+
+\[
+\boxed{149}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 149</p>
+<p>Extracted Answer: 149</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $ S $ be the set of vertices of a regular 24-gon. Find the number of ways to draw 12 segments of equal lengths so that each vertex in $ S $ is an endpoint of exactly one of the 12 segments.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Label the vertices of the regular \(24\)-gon by  
+
+\[
+0,1,2,\ldots ,23\qquad(\text{mod }24).
+\]
+
+If a segment connects vertices \(i\) and \(j\) then the chord length is determined by the
+shorter distance  
+
+\[
+k=\min\{|i-j|,\;24-|i-j|\},\qquad 1\le k\le 12 .
+\]
+
+All 12 drawn segments must have the same length, so every segment must join two vertices that
+are exactly \(k\) steps apart for one fixed \(k\in\{1,2,\ldots ,12\}\).
+
+---------------------------------------------------------------------
+
+### 1.  The graph for a fixed \(k\)
+
+For a given \(k\) consider the graph  
+
+\[
+G_k=\{\,\{i,i+k\}:i=0,1,\ldots ,23\}\ .
+\]
+
+Each vertex has degree \(2\) (edges to \(i+k\) and to \(i-k\)), so \(G_k\) is a disjoint union
+of cycles.  
+
+Let  
+
+\[
+g=\gcd(24,k).
+\]
+
+Then \(G_k\) consists of \(g\) cycles, each of length  
+
+\[
+L=\frac{24}{g}.
+\]
+
+---------------------------------------------------------------------
+
+### 2.  Perfect matchings of \(G_k\)
+
+A required drawing is exactly a perfect matching (1‑factor) of \(G_k\).
+
+* If \(L\) is odd, a perfect matching is impossible.  
+  This occurs only for \(k=8\) (\(g=8,\;L=3\)).
+
+* If \(L=2\) (the case \(k=12\)), each component is a single edge, so the matching is
+forced – exactly **one** way.
+
+* If \(L\) is even and \(\,L\ge4\), each even cycle has exactly two perfect matchings
+(alternating edges).  
+  Hence for such a \(k\) the number of matchings is  
+
+  \[
+  2^{\,\text{number of cycles}}=2^{g}.
+  \]
+
+---------------------------------------------------------------------
+
+### 3.  Count for each possible \(k\)
+
+\[
+\begin{array}{c|c|c|c}
+k &amp; g=\gcd(24,k) &amp; L=24/g &amp; \text{matchings }N(k)\\ \hline
+1 &amp; 1 &amp; 24 &amp; 2\\
+2 &amp; 2 &amp; 12 &amp; 4\\
+3 &amp; 3 &amp; 8  &amp; 8\\
+4 &amp; 4 &amp; 6  &amp; 16\\
+5 &amp; 1 &amp; 24 &amp; 2\\
+6 &amp; 6 &amp; 4  &amp; 64\\
+7 &amp; 1 &amp; 24 &amp; 2\\
+8 &amp; 8 &amp; 3  &amp; 0\\
+9 &amp; 3 &amp; 8  &amp; 8\\
+10&amp; 2 &amp; 12 &amp; 4\\
+11&amp; 1 &amp; 24 &amp; 2\\
+12&amp;12 &amp; 2  &amp; 1
+\end{array}
+\]
+
+---------------------------------------------------------------------
+
+### 4.  Total number of drawings
+
+\[
+\begin{aligned}
+\sum_{k=1}^{12} N(k)&amp;=
+2+4+8+16+2+64+2+0+8+4+2+1\\
+&amp;=113 .
+\end{aligned}
+\]
+
+---------------------------------------------------------------------
+
+Thus there are  
+
+\[
+\boxed{113}
+\]
+
+different ways to draw 12 equal‑length segments so that every vertex of the regular 24‑gon
+is an endpoint of exactly one segment.</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 113</p>
+<p>Extracted Answer: 113</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $ A_1A_2 \ldots A_{11} $ be an 11-sided non-convex simple polygon with the following properties:
+* The area of $ A_iA_1A_{i+1} $ is 1 for each $ 2 \leq i \leq 10 $,
+* $ \cos(\angle A_iA_1A_{i+1}) = \frac{12}{13} $ for each $ 2 \leq i \leq 10 $,
+* The perimeter of $ A_1A_2 \ldots A_{11} $ is 20.
+If $ A_1A_2 + A_1A_{11} $ can be expressed as $ \frac{m\sqrt{n} - p}{q} $ for positive integers $ m, n, p, q $ with $ n $ squarefree and no prime divides all of $ m, p, q$, find $ m + n + p + q $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+\[
+a_i=|A_iA_1|\qquad (i=2,\dots ,11),\qquad b_i=|A_iA_{i+1}|\;(i=2,\dots ,10)
+\]
+
+and let \(\theta =\angle A_iA_1A_{i+1}\) for \(2\le i\le10\).
+
+--------------------------------------------------------------------
+### 1.  The radii from \(A_1\)
+
+For each triangle \(A_iA_1A_{i+1}\)
+
+\[
+\text{area}=1,\qquad \cos\theta=\frac{12}{13}.
+\]
+
+Hence  
+
+\[
+\sin\theta =\sqrt{1-\cos^2\theta}
+          =\sqrt{1-\frac{144}{169}}
+          =\frac{5}{13}.
+\]
+
+The area formula gives  
+
+\[
+1=\frac12 a_i a_{i+1}\sin\theta
+   \Longrightarrow a_i a_{i+1}= \frac{2}{\sin\theta}
+   =\frac{2}{5/13}= \frac{26}{5}\qquad (1)
+\]
+
+for every \(i=2,\dots ,10\).
+
+Thus every adjacent pair of radii satisfies the same product.
+Consequently the lengths alternate:
+
+\[
+a_2=a_4=a_6=a_8=a_{10}=x,\qquad 
+a_3=a_5=a_7=a_9=a_{11}=y,
+\]
+
+with  
+
+\[
+xy=\frac{26}{5}. \tag{2}
+\]
+
+--------------------------------------------------------------------
+### 2.  Lengths of the polygon sides not incident with \(A_1\)
+
+In \(\triangle A_iA_1A_{i+1}\) the side \(b_i=|A_iA_{i+1}|\) satisfies the law of cosines:
+
+\[
+b_i^2 = a_i^2 + a_{i+1}^2 -2a_i a_{i+1}\cos\theta .
+\]
+
+Using \(\cos\theta=\frac{12}{13}\) and (1),
+
+\[
+b_i^2 = a_i^2 + a_{i+1}^2
+        - 2\!\left(\frac{26}{5}\right)\!\frac{12}{13}
+      = a_i^2 + a_{i+1}^2 - \frac{624}{65}
+      = a_i^2 + a_{i+1}^2 - 9.6 .
+\]
+
+Because each adjacent pair consists of one \(x\) and one \(y\), the quantity
+\(a_i^2+a_{i+1}^2\) is the same for all \(i\).  Hence all \(b_i\) are equal; denote this common length by \(b\).
+
+Let  
+
+\[
+S=x+y .
+\]
+
+Then \(x^2+y^2=S^2-2xy\).  Using (2) we obtain
+
+\[
+b^{2}=S^{2}-2xy-2xy\cos\theta
+      =S^{2}-2xy(1+\cos\theta).
+\]
+
+Since \(\cos\theta=\frac{12}{13}\),  
+
+\[
+1+\cos\theta = \frac{25}{13},\qquad
+2xy(1+\cos\theta)=2\!\left(\frac{26}{5}\right)\!\frac{25}{13}=20.
+\]
+
+Thus  
+
+\[
+b^{2}=S^{2}-20,\qquad b=\sqrt{S^{2}-20}. \tag{3}
+\]
+
+--------------------------------------------------------------------
+### 3.  Using the perimeter
+
+The perimeter of the 11‑gon is
+
+\[
+|A_1A_2|+|A_1A_{11}|+\sum_{i=2}^{10}|A_iA_{i+1}|
+= x + y + 9b = S + 9\sqrt{S^{2}-20}=20.
+\]
+
+Let \(t=\sqrt{S^{2}-20}\;(t\ge0)\).  Then  
+
+\[
+\sqrt{t^{2}+20}+9t=20\quad\Longrightarrow\quad 
+\sqrt{t^{2}+20}=20-9t.
+\]
+
+Squaring yields  
+
+\[
+t^{2}+20 = (20-9t)^{2}=400-360t+81t^{2},
+\]
+\[
+80t^{2}-360t+380=0\;\Longrightarrow\;
+4t^{2}-18t+19=0.
+\]
+
+The discriminant is \(D=18^{2}-4\cdot4\cdot19=324-304=20\), so
+
+\[
+t=\frac{18\pm\sqrt{20}}{8}
+   =\frac{9\pm\sqrt5}{4}.
+\]
+
+Since \(20-9t\ge0\), we take the minus sign:
+
+\[
+t=\frac{9-\sqrt5}{4}.
+\]
+
+Now \(S = 20-9t\):
+
+\[
+S = 20 - 9\!\left(\frac{9-\sqrt5}{4}\right)
+   = \frac{80-(81-9\sqrt5)}{4}
+   = \frac{9\sqrt5-1}{4}.
+\]
+
+Thus  
+
+\[
+|A_1A_2|+|A_1A_{11}| = S = \frac{9\sqrt5-1}{4}.
+\]
+
+--------------------------------------------------------------------
+### 4.  Putting it into the required form
+
+\[
+\frac{9\sqrt5-1}{4}=\frac{m\sqrt{n}-p}{q},
+\qquad m=9,\; n=5,\; p=1,\; q=4.
+\]
+
+These satisfy the given conditions ( \(n\) square‑free, no prime divides all of \(m,p,q\) ).
+
+Finally  
+
+\[
+m+n+p+q = 9+5+1+4 = 19.
+\]
+
+\[
+\boxed{19}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 19</p>
+<p>Extracted Answer: 19</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Sixteen chairs are arranged in a row. Eight people each select a chair in which to sit so that no person sits next to two other people. Let $ N $ be the number of subsets of 16 chairs that could be selected. Find the remainder when $ N $ is divided by 1000.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>**Solution Overview**
+
+Let the 16 chairs be numbered \(1,2,\dots ,16\).  
+A selection of 8 chairs corresponds to a binary string of length \(16\) with exactly eight \(1\)’s (occupied chairs) and eight \(0\)’s (empty chairs).
+
+A person “sits next to two other people’’ exactly when a chair is occupied **and** its two neighbours are also occupied.  
+Hence the forbidden pattern in the binary string is the block \(111\).  
+
+Thus we must count the binary strings of length \(16\) containing exactly eight \(1\)’s and **no** occurrence of \(111\).
+
+--------------------------------------------------------------------
+
+### 1.  Decomposing the 1‑blocks
+
+Because a block of three or more consecutive \(1\)’s is not allowed, every maximal block of 1’s is of length **1** or **2**.
+
+Suppose the string contains  
+
+* \(a\) blocks of length \(1\) and  
+* \(c\) blocks of length \(2\).
+
+Then  
+
+\[
+a+2c = 8\qquad(\text{total number of }1\text{&#39;s}),
+\]
+\[
+b = a+c = 8-c\qquad(\text{total number of blocks}).
+\]
+
+--------------------------------------------------------------------
+
+### 2.  Placing the blocks among the 0’s
+
+Between any two consecutive blocks we need at least one \(0\).  
+With \(b\) blocks we need at least \(b-1\) separating zeros.
+
+The total number of zeros is \(16-8 = 8\).  
+After reserving the mandatory \(b-1\) zeros, there remain  
+
+\[
+8-(b-1)=9-b
+\]
+
+extra zeros that may be placed arbitrarily in the \(b+1\) gaps
+(before the first block, between blocks, after the last block).
+
+The number of ways to distribute these extra zeros is a stars‑and‑bars count:
+
+\[
+\binom{(9-b)+(b+1)-1}{b}= \binom{9}{b}.
+\]
+
+--------------------------------------------------------------------
+
+### 3.  Ordering the blocks
+
+Among the \(b\) blocks, we must choose which \(c\) of them are the length‑2 blocks.
+That can be done in  
+
+\[
+\binom{b}{c}=\binom{8-c}{c}
+\]
+
+ways.
+
+--------------------------------------------------------------------
+
+### 4.  Summation
+
+Summing over all feasible values of \(c\) (from \(0\) to \(\lfloor 8/2\rfloor =4\)) we obtain
+
+\[
+\begin{aligned}
+N &amp;=\sum_{c=0}^{4}\binom{8-c}{c}\binom{9}{\,8-c\,} \\[2mm]
+  &amp;=\binom{8}{0}\binom{9}{8}
+    +\binom{7}{1}\binom{9}{7}
+    +\binom{6}{2}\binom{9}{6}
+    +\binom{5}{3}\binom{9}{5}
+    +\binom{4}{4}\binom{9}{4}\\[2mm]
+  &amp;=1\cdot9\;+\;7\cdot36\;+\;15\cdot84\;+\;10\cdot126\;+\;1\cdot126\\[2mm]
+  &amp;=9+252+1260+1260+126\\[2mm]
+  &amp;=2907.
+\end{aligned}
+\]
+
+Thus there are \(N=2907\) possible selections of 8 chairs satisfying the condition.
+
+--------------------------------------------------------------------
+
+### 5.  Required remainder
+
+\[
+N \bmod 1000 = 2907 \bmod 1000 = 907.
+\]
+
+--------------------------------------------------------------------
+
+\[
+\boxed{907}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 907</p>
+<p>Extracted Answer: 907</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Find the sum of all integer bases $b&gt;9$ for which $17_{b}$ is a divisor of $97_{b}$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>In base \(b\) the numbers  
+
+\[
+17_b = 1\cdot b + 7 = b+7 ,\qquad  
+97_b = 9\cdot b + 7 .
+\]
+
+We need bases \(b&gt;9\) (so that the digits \(7\) and \(9\) are allowed) such that  
+
+\[
+b+7 \mid 9b+7 .
+\]
+
+---
+
+### Reduce the divisibility condition
+
+If \(b+7\) divides \(9b+7\), then it also divides any integer linear combination of these two numbers.  
+Consider  
+
+\[
+9(b+7) - (9b+7) = 9b+63 - 9b - 7 = 56 .
+\]
+
+Hence  
+
+\[
+b+7 \mid 56 .
+\]
+
+Conversely, if \(b+7\) divides \(56\) then
+
+\[
+9b+7 = 9(b+7) - 56
+\]
+
+is also a multiple of \(b+7\). Thus the condition is equivalent to  
+
+\[
+b+7 \text{ is a positive divisor of } 56 .
+\]
+
+---
+
+### Find admissible divisors
+
+The positive divisors of \(56\) are  
+
+\[
+1,\;2,\;4,\;7,\;8,\;14,\;28,\;56 .
+\]
+
+Since \(b&gt;9\), we have \(b+7&gt;16\). The only divisors of \(56\) exceeding \(16\) are \(28\) and \(56\).
+
+\[
+\begin{aligned}
+b+7 &amp;= 28 &amp;\implies&amp;\; b = 21,\\[2mm]
+b+7 &amp;= 56 &amp;\implies&amp;\; b = 49 .
+\end{aligned}
+\]
+
+Both satisfy \(b&gt;9\) and the original divisibility:
+\[
+\begin{aligned}
+b=21:&amp;\quad 17_{21}=28,\; 97_{21}=196=28\cdot7;\\
+b=49:&amp;\quad 17_{49}=56,\; 97_{49}=448=56\cdot8.
+\end{aligned}
+\]
+
+No other bases work.
+
+---
+
+### Sum of all such bases
+
+\[
+21+49 = 70 .
+\]
+
+\[
+\boxed{70}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 70</p>
+<p>Extracted Answer: 70</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $ \triangle ABC $ be a right triangle with $ \angle A = 90^\circ $ and $ BC = 38 $. There exist points $ K $ and $ L $ inside the triangle such that $ AK = AL = BK = CL = KL = 14. $ The area of the quadrilateral $ BKLC $ can be expressed as $ n \sqrt{3} $ for some positive integer $ n $. Find $ n $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+\[
+A=(0,0),\qquad B=(b,0),\qquad C=(0,c),\qquad b^2+c^2=BC^2=38^2=1444 .
+\]
+
+Put  
+
+\[
+K=(x_k ,y_k),\qquad L=(x_l ,y_l).
+\]
+
+The given distances give  
+
+\[
+\begin{aligned}
+&amp;AK=AL=BK=CL=KL=14,\\
+&amp;x_k^2+y_k^2=196,\quad (x_k-b)^2+y_k^2=196,\\[2mm]
+&amp;x_l^2+y_l^2=196,\quad x_l^2+(y_l-c)^2=196,\\[2mm]
+&amp;(x_k-x_l)^2+(y_k-y_l)^2=196 .
+\end{aligned}
+\]
+
+From the first two equations  
+
+\[
+b=2x_k,\qquad y_k=\sqrt{196-x_k^2}.
+\]
+
+From the next two  
+
+\[
+c=2y_l,\qquad x_l=\sqrt{196-y_l^2}.
+\]
+
+Thus  
+
+\[
+K=(b/2,\;\sqrt{196-b^{2}/4}),\qquad 
+L=(\sqrt{196-c^{2}/4},\;c/2).
+\]
+
+Since \(AK=AL=KL=14\), the triangle \(AKL\) is equilateral; hence
+the angle \(\angle KAL=60^\circ\).  Write
+
+\[
+K=14(\cos\alpha,\sin\alpha),\qquad  
+L=14(\cos(\alpha+60^\circ),\sin(\alpha+60^\circ))
+\]
+
+for some \(\alpha\) with \(0^\circ&lt;\alpha&lt;30^\circ\).
+Comparing with the expressions for \(K\) and \(L\) gives  
+
+\[
+b=28\cos\alpha,\qquad c=28\sin(\alpha+60^\circ).
+\]
+
+The hypotenuse length yields
+
+\[
+b^{2}+c^{2}=28^{2}\bigl(\cos^{2}\alpha+\sin^{2}(\alpha+60^\circ)\bigr)=38^{2}=1444,
+\]
+
+so  
+
+\[
+\cos^{2}\alpha+\sin^{2}(\alpha+60^\circ)=\frac{361}{196}.
+\tag{1}
+\]
+
+From (1) we obtain, after using \(\sin^{2}\theta= \tfrac12(1-\cos2\theta)\),
+
+\[
+\sqrt3\sin(2\alpha+60^\circ)=\frac{165}{98},
+\qquad\Longrightarrow\qquad
+\sin(2\alpha+60^\circ)=\frac{165}{98\sqrt3}.
+\tag{2}
+\]
+
+Now compute the required area.
+
+*Area of \(\triangle ABC\)*  
+
+\[
+[ABC]=\tfrac12bc=\tfrac12\,(28\cos\alpha)(28\sin(\alpha+60^\circ))
+      =392\cos\alpha\sin(\alpha+60^\circ).
+\tag{3}
+\]
+
+*Area of \(\triangle AKB\)*  
+
+The altitude from \(K\) to \(AB\) is \(y_k=14\sin\alpha\), and \(AB=28\cos\alpha\); thus  
+
+\[
+[AKB]=\tfrac12\,(28\cos\alpha)(14\sin\alpha)=98\sin2\alpha .
+\tag{4}
+\]
+
+*Area of \(\triangle ALC\)*  
+
+Analogously  
+
+\[
+[ALC]=\tfrac12\,(28\sin(\alpha+60^\circ))(14\cos(\alpha+60^\circ))
+      =98\sin\bigl(2\alpha+120^\circ\bigr).
+\tag{5}
+\]
+
+*Area of the equilateral \(\triangle AKL\)*  
+
+\[
+[AKL]=\frac{\sqrt3}{4}\cdot14^{2}=49\sqrt3.
+\tag{6}
+\]
+
+Hence  
+
+\[
+\begin{aligned}
+[BKLC]&amp;=[ABC]-[AKB]-[ALC]-[AKL] \\[2mm]
+&amp;=392\cos\alpha\sin(\alpha+60^\circ)
+   -98\sin2\alpha-98\sin(2\alpha+120^\circ)-49\sqrt3 .
+\end{aligned}
+\]
+
+Using \(\sin(\alpha+60^\circ)=\tfrac12\sin\alpha+\tfrac{\sqrt3}{2}\cos\alpha\) and
+simplifying, the expression reduces to  
+
+\[
+[BKLC]=49\Bigl(\sin2\alpha+\sqrt3\bigl(1+\cos2\alpha\bigr)\Bigr).
+\tag{7}
+\]
+
+From (2),
+
+\[
+\sin2\alpha+\sqrt3\cos2\alpha
+    =2\sin(2\alpha+60^\circ)=\frac{165}{49\sqrt3}.
+\]
+
+Insert this into (7):
+
+\[
+\begin{aligned}
+[BKLC]&amp;=49\Bigl(\frac{165}{49\sqrt3}+\sqrt3\Bigr)
+       =\frac{165}{\sqrt3}+49\sqrt3\\[2mm]
+      &amp;=\frac{165\sqrt3}{3}+49\sqrt3
+       =55\sqrt3+49\sqrt3=104\sqrt3.
+\end{aligned}
+\]
+
+Thus the area of quadrilateral \(BKLC\) equals \(104\sqrt3\).
+
+\[
+\boxed{104}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 104</p>
+<p>Extracted Answer: 104</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Suppose $ \triangle ABC $ has angles $ \angle BAC = 84^\circ $, $ \angle ABC = 60^\circ $, and $ \angle ACB = 36^\circ $. Let $ D, E, $ and $ F $ be the midpoints of sides $ \overline{BC} $, $ \overline{AC} $, and $ \overline{AB} $, respectively. The circumcircle of $ \triangle DEF $ intersects $ \overline{BD} $, $ \overline{AE} $, and $ \overline{AF} $ at points $ G, H, $ and $ J $, respectively. The points $ G, D, E, H, J, $ and $ F $ divide the circumcircle of $ \triangle DEF $ into six minor arcs, as shown. Find $ \widehat{DE} + 2 \cdot \widehat{HJ} + 3 \cdot \widehat{FG} $, where the arcs are measured in degrees.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+* \(A,B,C\) be the vertices of the acute triangle with  
+\(\angle A=84^{\circ},\ \angle B=60^{\circ},\ \angle C=36^{\circ}\);
+* \(D,E,F\) the midpoints of \(BC,CA,AB\);
+* \(G,H,J\) the second intersections of the nine‑point circle with
+\(BC,CA,AB\) respectively.
+
+The circumcircle of \(\triangle DEF\) is the nine‑point circle of \(\triangle ABC\).
+Hence \(G,H,J\) are the three feet of the altitudes of \(\triangle ABC\);  
+they form the orthic triangle \(G\!H\!J\).
+
+--------------------------------------------------------------------
+### 1.  Arc \(\widehat{DE}\)
+
+On the nine‑point circle the vectors from its centre \(N\) to the
+midpoints are  
+
+\[
+ND=-\frac{\mathbf a}{2},\qquad NE=-\frac{\mathbf b}{2},
+\]
+
+where \(\mathbf a,\mathbf b,\mathbf c\) are the unit vectors of the
+circumcircle of \(\triangle ABC\).  Consequently
+
+\[
+\widehat{DE}= \angle(-\mathbf a,-\mathbf b)=\angle(\mathbf a,\mathbf b)
+          =2\angle ACB=2C = 2\cdot36^{\circ}=72^{\circ}.
+\tag{1}
+\]
+
+--------------------------------------------------------------------
+### 2.  Arc \(\widehat{HJ}\)
+
+\(H\) and \(J\) are the feet of the altitudes from \(B\) and \(C\);
+they are vertices of the orthic triangle \(G\!H\!J\).
+For an acute triangle the angles of its orthic triangle are  
+
+\[
+\angle G =180^{\circ}-2A,\qquad 
+\angle H =180^{\circ}-2B,\qquad 
+\angle J =180^{\circ}-2C .
+\]
+
+With \(A=84^{\circ},B=60^{\circ},C=36^{\circ}\),
+
+\[
+\angle G =12^{\circ},\quad
+\angle H =60^{\circ},\quad
+\angle J =108^{\circ}.
+\]
+
+Since the nine‑point circle is the circumcircle of
+\(\triangle G\!H\!J\), the central arc opposite a vertex equals twice the
+opposite interior angle.  Hence
+
+\[
+\widehat{HJ}= \widehat{B&#39;C&#39;} = 2\angle G
+            =2\bigl(180^{\circ}-2A\bigr)=360^{\circ}-4A
+            =360^{\circ}-4\cdot84^{\circ}=24^{\circ}.
+\tag{2}
+\]
+
+--------------------------------------------------------------------
+### 3.  Arc \(\widehat{FG}\)
+
+The points \(D,E,F\) are the midpoints of the sides; they satisfy  
+
+\[
+\angle N D F =\angle(-\mathbf a,-\mathbf c)=120^{\circ},
+\]
+
+so the minor arc \(\widehat{DF}\) of the nine‑point circle measures
+\(120^{\circ}\).  The arc \(\widehat{DF}\) is the sum of the two
+consecutive arcs \(\widehat{DG}\) and \(\widehat{GF}\).
+
+The central arc \(\widehat{DG}\) equals the angle between the
+vectors \(ND\) (direction \(-\mathbf a\)) and \(NG\) (direction of the
+foot from \(A\) onto \(BC\)).
+A short angle chase using the orthic triangle gives
+
+\[
+\widehat{DG}=48^{\circ}.
+\]
+
+Therefore
+
+\[
+\widehat{FG}= \widehat{DF}-\widehat{DG}=120^{\circ}-48^{\circ}=72^{\circ}.
+\tag{3}
+\]
+
+(One can also obtain \(\widehat{FG}=72^{\circ}\) directly from the fact
+that the chord \(FJ\) subtends the angle \(60^{\circ}\) at the centre,
+so the complementary chord \(FG\) subtends \(72^{\circ}\).)
+
+--------------------------------------------------------------------
+### 4.  Required sum
+
+From (1)–(3),
+
+\[
+\begin{aligned}
+\widehat{DE}+2\widehat{HJ}+3\widehat{FG}
+&amp;= 72^{\circ}+2\cdot24^{\circ}+3\cdot72^{\circ}\\[2mm]
+&amp;= 72^{\circ}+48^{\circ}+216^{\circ}\\
+&amp;= 336^{\circ}.
+\end{aligned}
+\]
+
+--------------------------------------------------------------------
+\[
+\boxed{336}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 336</p>
+<p>Extracted Answer: 336</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+The 9 members of a baseball team went to an ice cream parlor after their game. Each player had a singlescoop cone of chocolate, vanilla, or strawberry ice cream. At least one player chose each flavor, and the number of players who chose chocolate was greater than the number of players who chose vanilla, which was greater than the number of players who chose strawberry. Let $N$ be the number of different assignments of flavors to players that meet these conditions. Find the remainder when $N$ is divided by 1000.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>The players are distinct, so an assignment of flavors is a function from the nine players to the three flavors.  
+Let  
+
+\[
+c=\#\text{chocolate},\qquad v=\#\text{vanilla},\qquad s=\#\text{strawberry}.
+\]
+
+We need  
+
+\[
+c+v+s=9,\qquad c&gt;v&gt;s\ge 1 .
+\]
+
+---
+
+### 1.  Find all possible triples \((c,v,s)\).
+
+Write \(s=a\), \(v=a+d\), \(c=a+d+e\) with \(a,d,e\ge1\).  
+Then  
+
+\[
+a+(a+d)+(a+d+e)=9\Longrightarrow 3a+2d+e=9 .
+\]
+
+Searching integer solutions with \(a,d,e\ge1\) gives only three possibilities:
+
+* \(a=1,d=1,e=4\) → \((c,v,s)=(6,2,1)\)
+* \(a=1,d=2,e=2\) → \((c,v,s)=(5,3,1)\)
+* \(a=2,d=1,e=1\) → \((c,v,s)=(4,3,2)\)
+
+No other triples satisfy \(c&gt;v&gt;s\) and sum to 9.
+
+---
+
+### 2.  Count assignments for each triple.
+
+For a fixed triple \((c,v,s)\) the number of assignments equals the multinomial coefficient  
+
+\[
+\frac{9!}{c!\,v!\,s!}.
+\]
+
+\[
+\begin{aligned}
+(6,2,1)&amp;:\ \frac{9!}{6!\,2!\,1!}= \frac{362880}{720\cdot2}=252,\\[2mm]
+(5,3,1)&amp;:\ \frac{9!}{5!\,3!\,1!}= \frac{362880}{120\cdot6}=504,\\[2mm]
+(4,3,2)&amp;:\ \frac{9!}{4!\,3!\,2!}= \frac{362880}{24\cdot6\cdot2}=1260.
+\end{aligned}
+\]
+
+---
+
+### 3.  Total number of assignments.
+
+\[
+N=252+504+1260=2016.
+\]
+
+---
+
+### 4.  Remainder modulo \(1000\).
+
+\[
+2016\equiv 16 \pmod{1000}.
+\]
+
+---
+
+\[
+\boxed{16}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 16</p>
+<p>Extracted Answer: 16</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Find the number of ordered pairs $(x,y)$, where both $x$ and $y$ are integers between $-100$ and $100$, inclusive, such that $12x^{2}-xy-6y^{2}=0$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>First factor the quadratic form.
+
+\[
+12x^{2}-xy-6y^{2}= (4x-3y)(3x+2y)
+\]
+
+Hence  
+
+\[
+(4x-3y)(3x+2y)=0\Longrightarrow 
+\begin{cases}
+4x-3y=0\\[2mm]
+\text{or}\\[2mm]
+3x+2y=0
+\end{cases}
+\]
+
+---
+
+### 1.  Solutions of \(4x-3y=0\)
+
+\(4x=3y\Rightarrow y=\dfrac{4}{3}x\).  
+Since \(x,y\) are integers, \(x\) must be a multiple of \(3\): set \(x=3k\), then  
+
+\[
+y=4k,\qquad k\in\mathbb Z .
+\]
+
+Both coordinates must satisfy \(-100\le x,y\le100\):
+
+\[
+|3k|\le100,\qquad|4k|\le100\Longrightarrow |k|\le \Big\lfloor\frac{100}{4}\Big\rfloor =25 .
+\]
+
+Thus \(k=-25,-24,\dots ,25\):  \(51\) integer pairs.
+
+---
+
+### 2.  Solutions of \(3x+2y=0\)
+
+\(3x=-2y\Rightarrow y=-\dfrac{3}{2}x\).  
+For integers we need \(x\) even: write \(x=2m\), then  
+
+\[
+y=-3m,\qquad m\in\mathbb Z .
+\]
+
+Again \(-100\le x,y\le100\) gives  
+
+\[
+|2m|\le100,\qquad|3m|\le100\Longrightarrow |m|\le\Big\lfloor\frac{100}{3}\Big\rfloor =33 .
+\]
+
+Thus \(m=-33,-32,\dots ,33\):  \(67\) integer pairs.
+
+---
+
+### 3.  Remove double counting
+
+The two families intersect only at \((0,0)\) (when \(k=m=0\)).  
+Hence the total number of distinct ordered pairs is  
+
+\[
+51+67-1=117 .
+\]
+
+\[
+\boxed{117}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 117</p>
+<p>Extracted Answer: 117</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+There are exactly three positive real numbers $ k $ such that the function
+$ f(x) = \frac{(x - 18)(x - 72)(x - 98)(x - k)}{x} $
+defined over the positive real numbers achieves its minimum value at exactly two positive real numbers $ x $. Find the sum of these three values of $ k $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>The function  
+
+\[
+f(x)=\frac{(x-18)(x-72)(x-98)(x-k)}{x}\qquad (x&gt;0)
+\]
+
+has zeros at \(x=18,\;72,\;98,\;k\) and  
+\(\displaystyle \lim_{x\to0^+}f(x)=\lim_{x\to\infty}f(x)=+\infty\).
+Hence \(f\) is positive near the ends and negative on each of the two
+intervals bounded by the smallest two zeros and by the largest two zeros.
+Consequently \(f\) has exactly two local minima (one in each negative
+interval).
+
+Let the common minimal value be \(m&lt;0\).  At a minimum the graph of
+\(y=f(x)\) is tangent to the horizontal line \(y=m\); therefore the
+equation  
+
+\[
+f(x)=m\quad\Longleftrightarrow\quad (x-18)(x-72)(x-98)(x-k)-mx=0
+\]
+
+must have a **double root** at each minimum.  Thus the quartic polynomial
+must be a perfect square of a quadratic:
+
+\[
+(x-18)(x-72)(x-98)(x-k)-mx=(x^{2}-Sx+P)^{2},
+\]
+where \(S,P,m\) are constants.
+
+Expanding and equating coefficients with  
+
+\[
+N(x)-mx=x^{4}-(188+k)x^{3}+(10116+188k)x^{2}-(127008+10116k+m)x+127008k
+\]
+
+gives  
+
+\[
+\begin{cases}
+S=\dfrac{188+k}{2},\\[4pt]
+S^{2}+2P=10116+188k,\\[4pt]
+m=2SP-(127008+10116k),\\[4pt]
+P^{2}=127008\,k .
+\end{cases}
+\]
+
+From \(P^{2}=127008k\) set \(t=\sqrt{2k}&gt;0\); then  
+
+\[
+P=252t,\qquad k=\dfrac{t^{2}}{2},
+\quad S=\frac{188+k}{2}=94+\frac{t^{2}}{4}.
+\]
+
+Substituting these into \(S^{2}+2P=10116+188k\) yields an equation in
+\(t\):
+
+\[
+\frac{(188+k)^{2}}{4}+504\sqrt{2k}=10116+188k
+\Longrightarrow
+t^{4}-752t^{2}+8064t-20480=0 .
+\]
+
+Factoring,
+
+\[
+t^{4}-752t^{2}+8064t-20480=(t-4)(t-8)(t-20)(t+32)=0 .
+\]
+
+Since \(t&gt;0\), we obtain  
+
+\[
+t=4,\;8,\;20\quad\Longrightarrow\quad 
+k=\frac{t^{2}}{2}=8,\;32,\;200 .
+\]
+
+For each of these \(k\) one computes \(\Delta=S^{2}-4P&gt;0\), so the
+quadratic \(x^{2}-Sx+P\) has two distinct real roots.  They lie exactly in
+the two negative intervals, giving two distinct points where \(f\) attains
+the value \(m\).  Moreover \(m&lt;0\), while all zeros of \(f\) are at
+\(0\), so these are the global minima.  
+No other positive \(k\) satisfies the required condition.
+
+Hence the three admissible values of \(k\) are \(8,\;32,\;200\), and their
+sum is
+
+\[
+8+32+200 = 240.
+\]
+
+\[
+\boxed{240}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 240</p>
+<p>Extracted Answer: 240</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+An isosceles trapezoid has an inscribed circle tangent to each of its four sides. The radius of the circle is 3, and the area of the trapezoid is 72. Let the parallel sides of the trapezoid have lengths $r$ and $s$, with $r \neq s$. Find $r^{2}+s^{2}$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>For a quadrilateral that has an incircle (a **tangential quadrilateral**)  
+
+\[
+\text{area}=r_{\text{in}}\cdot\frac{\text{perimeter}}2 .
+\tag{1}
+\]
+
+---
+
+### 1.  Using the given area
+
+Let the parallel sides be \(r\) and \(s\) \((r\neq s)\) and the equal legs be \(\ell\).
+The incircle radius is \(r_{\text{in}}=3\) and the area is \(72\).
+
+From (1),
+
+\[
+72=3\cdot\frac{r+s+2\ell}{2}\Longrightarrow
+r+s+2\ell=48.
+\tag{2}
+\]
+
+---
+
+### 2.  Pitot’s theorem
+
+A tangential quadrilateral satisfies Pitot’s theorem: the sum of opposite sides are equal.  
+Thus for our isosceles trapezoid  
+
+\[
+r+s= \ell+\ell =2\ell \Longrightarrow \ell=\frac{r+s}{2}.
+\tag{3}
+\]
+
+Substituting (3) into (2),
+
+\[
+r+s+2\Bigl(\frac{r+s}{2}\Bigr)=48\Longrightarrow 2(r+s)=48
+\Longrightarrow r+s=24.
+\tag{4}
+\]
+
+Hence each leg is  
+
+\[
+\ell=\frac{r+s}{2}=12.
+\]
+
+---
+
+### 3.  Height of the trapezoid
+
+A circle tangent to two parallel lines must have its centre midway between them, so the distance (the height \(h\)) between the bases equals twice the radius:
+
+\[
+h=2\cdot3=6.
+\]
+
+The area of a trapezoid is also  
+
+\[
+\text{Area}= \frac{r+s}{2}\,h = \frac{24}{2}\cdot6 = 72,
+\]
+
+which checks with the given data.
+
+---
+
+### 4.  Relating the legs, height, and bases  
+
+In an isosceles trapezoid the leg \(\ell\) together with the height \(h\) and half the difference of the bases forms a right triangle:
+
+\[
+\ell^{2}=h^{2}+\Bigl(\frac{s-r}{2}\Bigr)^{2}.
+\]
+
+Plugging \(\ell=12\) and \(h=6\),
+
+\[
+12^{2}=6^{2}+\Bigl(\frac{s-r}{2}\Bigr)^{2}
+\Longrightarrow 144=36+\frac{(s-r)^{2}}{4}
+\Longrightarrow (s-r)^{2}=432.
+\]
+
+Thus  
+
+\[
+s-r= \sqrt{432}=12\sqrt3 .
+\tag{5}
+\]
+
+---
+
+### 5.  Solving for \(r\) and \(s\)
+
+From (4) and (5):
+
+\[
+\begin{cases}
+s+r = 24,\\[2pt]
+s-r = 12\sqrt3,
+\end{cases}
+\qquad\Longrightarrow\qquad
+s = 12+6\sqrt3,\;\; r = 12-6\sqrt3.
+\]
+
+---
+
+### 6.  Computing \(r^{2}+s^{2}\)
+
+\[
+r^{2}+s^{2}= (12-6\sqrt3)^{2}+(12+6\sqrt3)^{2}
+= (252-144\sqrt3)+(252+144\sqrt3)=504.
+\]
+
+(Alternatively, using \((r+s)^{2}=r^{2}+s^{2}+2rs\) and \(rs=36\) from \((s+r)^{2}-(s-r)^{2}=4rs\) also gives \(r^{2}+s^{2}=504\).)
+
+\[
+\boxed{504}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 504</p>
+<p>Extracted Answer: 504</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+There are exactly three positive real numbers $ k $ such that the function
+$ f(x) = \frac{(x - 18)(x - 72)(x - 98)(x - k)}{x} $
+defined over the positive real numbers achieves its minimum value at exactly two positive real numbers $ x $. Find the sum of these three values of $ k $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>\[
+\boxed{240}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 240</p>
+<p>Extracted Answer: 240</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+There are $8!=40320$ eight-digit positive integers that use each of the digits $1,2,3,4,5,6,7,8$ exactly once. Let $N$ be the number of these integers that are divisible by 22. Find the difference between $N$ and 2025.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>The number must be divisible by \(22=2\cdot 11\).
+
+---
+
+### 1.  Divisibility by \(2\)
+
+The last digit (the 8‑th digit) must be even, i.e. one of \(2,4,6,8\).
+
+---
+
+### 2.  Divisibility by \(11\)
+
+For an 8‑digit number \(d_1d_2\ldots d_8\)
+
+\[
+d_1-d_2+d_3-d_4+d_5-d_6+d_7-d_8\equiv0\pmod{11}.
+\]
+
+Let  
+
+\[
+S_{\text{odd}}=d_1+d_3+d_5+d_7,\qquad  
+S_{\text{even}}=d_2+d_4+d_6+d_8 .
+\]
+
+Then the condition becomes  
+
+\[
+S_{\text{odd}}-S_{\text{even}}\equiv0\pmod{11}.
+\]
+
+Since the digits \(1,2,\dots ,8\) are used exactly once,  
+
+\[
+S_{\text{odd}}+S_{\text{even}}=1+2+\cdots +8=36 .
+\]
+
+Hence  
+
+\[
+2S_{\text{even}}\equiv36\pmod{11}\Longrightarrow2S_{\text{even}}\equiv3\pmod{11}
+\]
+\[
+\Longrightarrow S_{\text{even}}\equiv3\cdot 6\equiv18\equiv7\pmod{11}.
+\]
+
+The possible values for a sum of four distinct digits from \(\{1,\ldots ,8\}\) lie between \(10\) and \(26\); the only value congruent to \(7\pmod{11}\) in this interval is \(18\).  
+Thus we must have  
+
+\[
+S_{\text{even}}=18\qquad\text{and}\qquad S_{\text{odd}}=18 .
+\]
+
+---
+
+### 3.  Choosing the four digits that go to even positions
+
+We need all 4‑element subsets of \(\{1,2,3,4,5,6,7,8\}\) whose sum is \(18\).
+
+Listing them:
+
+\[
+\begin{aligned}
+&amp;\{1,2,7,8\},\; \{1,3,6,8\},\; \{1,4,5,8\},\; \{1,4,6,7\},\\
+&amp;\{2,3,5,8\},\; \{2,3,6,7\},\; \{2,4,5,7\},\; \{3,4,5,6\}.
+\end{aligned}
+\]
+
+There are **8** such subsets.  
+Each of them contains exactly two even digits (the evens are \(2,4,6,8\)).
+
+---
+
+### 4.  Arranging the digits
+
+For a fixed subset \(S\) (the digits that occupy the even positions 2,4,6,8):
+
+* The last position (position 8) must be even.  
+  Since \(S\) has exactly two evens, we have \(2\) choices for the digit that goes to position 8.
+* The remaining three digits of \(S\) can be placed in positions 2,4,6 in any order: \(3! = 6\) ways.
+
+Hence the even positions can be filled in \(2\cdot6 = 12\) ways.
+
+The four digits not in \(S\) occupy the odd positions \(1,3,5,7\) and may be arranged arbitrarily:
+\(4! = 24\) ways.
+
+Thus each subset contributes  
+
+\[
+12 \times 24 = 288
+\]
+
+different 8‑digit numbers.
+
+With 8 admissible subsets, the total number of 8‑digit numbers divisible by 22 is  
+
+\[
+N = 8 \times 288 = 2304.
+\]
+
+---
+
+### 5.  Required difference
+
+\[
+N-2025 = 2304-2025 = 279.
+\]
+
+\[
+\boxed{279}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 279</p>
+<p>Extracted Answer: 279</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let the sequence of rationals $ x_1, x_2, \ldots $ be defined such that $ x_1 = \frac{25}{11} $ and
+$ x_{k+1} = \frac{1}{3} \left( x_k + \frac{1}{x_k} - 1 \right). $
+$ x_{2025} $ can be expressed as $ \frac{m}{n} $ for relatively prime positive integers $ m $ and $ n $. Find the remainder when $ m + n $ is divided by 1000.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>\[
+x_{k+1}=\frac{x_k+\dfrac1{x_k}-1}{3}
+      =\frac{x_k^2-x_k+1}{3x_k}\qquad (k\ge 1),\qquad 
+x_1=\frac{25}{11}.
+\]
+
+--------------------------------------------------------------------
+### 1.  A convenient change of variable  
+
+Put  
+
+\[
+y_k=\frac{x_k-1}{x_k+1}\qquad\Longleftrightarrow\qquad 
+x_k=\frac{1+y_k}{1-y_k}.
+\]
+
+Then  
+
+\[
+y_{k+1}= \frac{x_{k+1}-1}{x_{k+1}+1}
+        =\frac{3y_k^{2}-1}{2}.
+\tag{1}
+\]
+
+Indeed,
+\[
+\frac{x_k+1/x_k-1}{3}= \frac{1+y_k}{1-y_k}
+        \Longrightarrow
+y_{k+1}= \frac{3y_k^{2}-1}{2}.
+\]
+
+From \(x_1=25/11\) we obtain
+
+\[
+y_1=\frac{25/11-1}{25/11+1}= \frac{14/11}{36/11}= \frac{7}{18}.
+\]
+
+--------------------------------------------------------------------
+### 2.  Removing the common factor  
+
+Write \(y_k =\dfrac{a_k}{b_k}\) with \(\gcd(a_k,b_k)=1\).
+From (1)
+
+\[
+\frac{a_{k+1}}{b_{k+1}}=\frac{3a_k^{2}-b_k^{2}}{2b_k^{2}} .
+\]
+
+Because \(b_k\) is always a multiple of \(3\), the fraction can be reduced by the
+factor \(3\) and we obtain the **integer** recurrences
+
+\[
+\boxed{\;
+\begin{aligned}
+a_{k+1}&amp;=\frac{3a_k^{2}-b_k^{2}}{3},\\[2mm]
+b_{k+1}&amp;=\frac{2b_k^{2}}{3},
+\end{aligned}\qquad a_1=7,\;b_1=18.}
+\tag{2}
+\]
+
+--------------------------------------------------------------------
+### 3.  Closed form for \(b_k\)
+
+From the second line of (2)
+
+\[
+b_{k+1}=\frac{2}{3}b_k^{2}, \qquad b_1=18.
+\]
+
+Induction gives  
+
+\[
+\boxed{\,b_k=2^{\,2^{\,k}-1}\;3^{\,2^{\,k-1}+1}\,}\qquad(k\ge1).   \tag{3}
+\]
+
+Check: \(b_1=2^{2-1}3^{1+1}=2\cdot 9=18\).
+
+--------------------------------------------------------------------
+### 4.  The reduced form of \(x_k\)
+
+Since \(x_k=\dfrac{1+y_k}{1-y_k}\) and \(y_k=a_k/b_k\),
+
+\[
+x_k=\frac{a_k+b_k}{\,b_k-a_k\,}.
+\]
+
+Thus the reduced numerator and denominator are  
+
+\[
+m_k=a_k+b_k,\qquad n_k=b_k-a_k,
+\]
+
+and
+
+\[
+m_k+n_k=2b_k. \tag{4}
+\]
+
+Consequently we only need \(2b_{2025}\pmod{1000}\).
+
+--------------------------------------------------------------------
+### 5.  Computing \(2b_{2025}\pmod{1000}\)
+
+From (3)
+
+\[
+2b_{2025}=2\cdot
+2^{\,2^{2025}-1}\;3^{\,2^{2024}+1}
+=2^{\,2^{2025}}\;3^{\,2^{2024}+1}.
+\]
+
+Work modulo \(1000=8\cdot125\).
+
+*Modulo \(8\):*  
+\(2^{\,2^{2025}}\) is a multiple of \(8\) (the exponent is \(\ge3\)), so the product is
+\(0\pmod 8\).
+
+*Modulo \(125\):*  
+Both bases are invertible, so we may reduce the exponents modulo \(\varphi(125)=100\).
+
+\[
+\begin{aligned}
+2^{2025}\pmod{100}&amp;\equiv 32,\\
+2^{2024}\pmod{100}&amp;\equiv 16,
+\end{aligned}
+\qquad\Longrightarrow\qquad
+\begin{aligned}
+2^{\,2^{2025}} &amp;\equiv 2^{32}\pmod{125},\\
+3^{\,2^{2024}+1}&amp;\equiv 3^{17}\pmod{125}.
+\end{aligned}
+\]
+
+\[
+2^{32}\equiv46\pmod{125},\qquad 
+3^{17}\equiv38\pmod{125}.
+\]
+
+Hence  
+
+\[
+2^{\,2^{2025}}3^{\,2^{2024}+1}\equiv46\cdot38\equiv123\pmod{125}.
+\]
+
+*Chinese remainder:*  Find \(N\) with  
+
+\[
+N\equiv0\pmod8,\qquad N\equiv123\pmod{125}.
+\]
+
+Writing \(N=125a+123\) and testing \(a=0,\dots,7\) gives \(a=1\) as the solution,
+so \(N=125\cdot1+123=248\).
+
+Thus  
+
+\[
+2b_{2025}\equiv 248\pmod{1000}.
+\]
+
+By (4) this is exactly \((m+n)\pmod{1000}\).
+
+--------------------------------------------------------------------
+\[
+\boxed{248}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 248</p>
+<p>Extracted Answer: 248</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $k$ be real numbers such that the system $|25+20i-z|=5$ and $|z-4-k|=|z-3i-k|$ has exactly one complex solution $z$. The sum of all possible values of $k$ can be written as $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$. Here $i=\sqrt{-1}$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+\[
+z=x+yi .
+\]
+
+The first equation  
+
+\[
+|25+20i-z|=5
+\]
+
+represents the circle  
+
+\[
+(x-25)^2+(y-20)^2=5^2        \tag{1}
+\]
+
+centered at \(C=(25,20)\) with radius \(r=5\).
+
+---
+
+### Locus of the second equation  
+
+\[
+|z-4-k|=|z-3i-k|
+\]
+
+means that the distance from \(z\) to the point  
+
+\[
+A=(4+k,0)
+\]
+
+equals its distance to the point  
+
+\[
+B=(k,3).
+\]
+
+Hence the set of all such \(z\) is the **perpendicular bisector** of the segment \(AB\).
+
+- Midpoint of \(AB\):
+  \[
+  M=\Bigl(\frac{4+k+k}{2},\frac{0+3}{2}\Bigr)=(2+k,\tfrac32).
+  \]
+
+- Slope of \(AB\):
+  \[
+  m_{AB}= \frac{3-0}{k-(4+k)}=\frac{3}{-4}=-\frac34 .
+  \]
+
+- Slope of the perpendicular bisector:
+  \[
+  m_{L}= \frac{4}{3}.
+  \]
+
+Thus the line \(L_k\) (the perpendicular bisector) has equation  
+
+\[
+y-\frac32=\frac43\Bigl(x-(2+k)\Bigr).
+\]
+
+Writing it in the form \(Ax+By+C=0\),
+
+\[
+8x-6y-(8k+7)=0\qquad\Longleftrightarrow\qquad 8x-6y=8k+7. \tag{2}
+\]
+
+---
+
+### Tangency condition  
+
+The system has exactly one solution \(z\) iff the line \(L_k\) is **tangent** to the circle \((1)\); i.e. the distance from the centre \(C\) to the line equals the radius \(5\).
+
+Distance from \(C=(25,20)\) to line \((2)\):
+
+\[
+d=\frac{|\,8\cdot25-6\cdot20-(8k+7)\,|}{\sqrt{8^{2}+(-6)^{2}}}
+   =\frac{|200-120-8k-7|}{10}
+   =\frac{|73-8k|}{10}.
+\]
+
+Set \(d=5\):
+
+\[
+\frac{|73-8k|}{10}=5 \Longrightarrow |73-8k|=50.
+\]
+
+Hence  
+
+\[
+73-8k=50 \quad\text{or}\quad 73-8k=-50,
+\]
+
+which give  
+
+\[
+k=\frac{23}{8},\qquad k=\frac{123}{8}.
+\]
+
+Both values indeed make the line tangent (the discriminant of the combined equations becomes zero), so each yields exactly one complex solution \(z\).
+
+---
+
+### Sum of all possible \(k\)
+
+\[
+\frac{23}{8}+\frac{123}{8}= \frac{146}{8}= \frac{73}{4}.
+\]
+
+Write \(\frac{73}{4}\) as \(\frac{m}{n}\) with \(\gcd(m,n)=1\): \(m=73,\; n=4\).
+
+\[
+m+n=73+4=77.
+\]
+
+\[
+\boxed{77}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 77</p>
+<p>Extracted Answer: 77</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+The 27 cells of a $3\times9$ grid are filled in using the numbers 1 through 9 so that each row contains 9 different numbers, and each of the three $3\times3$ blocks heavily outlined in the example below contains 9 different numbers, as in the first three rows of a Sudoku puzzle. 
+ | 4 | 2 | 8 | 9 | 6 | 3 | 1 | 7 | 5 | 
+ | 3 | 7 | 9 | 5 | 2 | 1 | 6 | 8 | 4 | 
+ | 5 | 6 | 1 | 8 | 4 | 7 | 9 | 2 | 3 | 
+ The number of different ways to fill such a grid can be written as $p^a\cdot q^b\cdot r^c\cdot s^d$, where $p,q,r,$ and $s$ are distinct prime numbers and $a,b,c,$ and $d$ are positive integers. Find $p\cdot a+q\cdot b+r\cdot c+s\cdot d$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>The grid has three rows and three \(3\times3\) blocks.  
+Each row must contain the numbers \(1,\dots ,9\) once, and each block must also contain every number once.
+
+---
+
+### 1.  Fix the first row  
+
+Because the numbers are distinct, we may fix the first row to be  
+
+\[
+(1,2,3,4,5,6,7,8,9)
+\]
+
+and later multiply the count by the \(9!\) possible permutations of this row.
+
+---
+
+### 2.  What must the other two rows contain?
+
+* Block 1 (columns 1–3): row 1 already has \(\{1,2,3\}\); thus rows 2–3 must contain the six numbers \(\{4,5,6,7,8,9\}\).
+
+* Block 2 (columns 4–6): rows 2–3 must contain \(\{1,2,3,7,8,9\}\).
+
+* Block 3 (columns 7–9): rows 2–3 must contain \(\{1,2,3,4,5,6\}\).
+
+Each of rows 2 and 3 must be a permutation of \(\{1,\dots ,9\}\).
+
+Hence for each number \(m\) (which appears in two of the three blocks) we must decide in which of those two blocks it will be placed in row 2 (the other occurrence will go to row 3).  
+
+The numbers are grouped as
+
+\[
+\begin{aligned}
+&amp;\{1,2,3\}\ \text{appear in blocks }2\text{ and }3,\\
+&amp;\{4,5,6\}\ \text{appear in blocks }1\text{ and }3,\\
+&amp;\{7,8,9\}\ \text{appear in blocks }1\text{ and }2.
+\end{aligned}
+\]
+
+Let  
+
+* \(x\) = how many of \(\{1,2,3\}\) go to block 2 (the rest go to block 3);
+* \(y\) = how many of \(\{4,5,6\}\) go to block 1 (the rest go to block 3);
+* \(z\) = how many of \(\{7,8,9\}\) go to block 1 (the rest go to block 2).
+
+Because each block must receive exactly three numbers for row 2 we obtain  
+
+\[
+\begin{cases}
+y+z=3 &amp;(\text{block }1)\\
+x+(3-z)=3 &amp;(\text{block }2)\\
+(3-x)+(3-y)=3 &amp;(\text{block }3)
+\end{cases}
+\Longrightarrow x=z,\quad y=3-x .
+\]
+
+Thus \(x\) can be \(0,1,2,3\).  
+For a given \(x\),
+
+* choose \(x\) of the three numbers \(\{1,2,3\}\) to go to block 2: \(\binom{3}{x}\) ways;
+* choose \(y=3-x\) of \(\{4,5,6\}\) to go to block 1: \(\binom{3}{3-x}=\binom{3}{x}\) ways;
+* choose \(z=x\) of \(\{7,8,9\}\) to go to block 1: \(\binom{3}{x}\) ways.
+
+Hence the number of ways to decide **which numbers** belong to row 2 in each block is  
+
+\[
+\sum_{x=0}^{3}\binom{3}{x}^3=1^3+3^3+3^3+1^3=56 .
+\]
+
+---
+
+### 3.  Placing the chosen numbers in the cells  
+
+Within each block, row 2 has three cells and row 3 three cells.  
+The three numbers assigned to row 2 can be arranged in those three cells in \(3!\) ways, and similarly for row 3.  
+
+Thus for each block there are \(3!\times3! = 36\) placements, and for the three blocks
+
+\[
+36^3 = 46656
+\]
+
+placements.
+
+Consequently, with the first row fixed,
+
+\[
+\text{# grids} = 56 \times 36^3 = 56 \times 46656 = 2\,612\,736 .
+\]
+
+---
+
+### 4.  Restore the first row  
+
+The first row could be any permutation of the numbers \(1\)–\(9\); there are \(9! = 362880\) possibilities.
+
+\[
+N = 2\,612\,736 \times 362\,880 = 948\,109\,639\,680 .
+\]
+
+---
+
+### 5.  Prime factorisation  
+
+\[
+\begin{aligned}
+56 &amp;= 2^3 \cdot 7,\\[2pt]
+36^3 &amp;= (2^2 3^2)^3 = 2^6 \cdot 3^6,\\[2pt]
+9! &amp;= 2^7 \cdot 3^4 \cdot 5 \cdot 7 .
+\end{aligned}
+\]
+
+Multiplying:
+
+\[
+N = 2^{3+6+7}\, 3^{6+4}\, 5^{1}\, 7^{1+1}
+   = 2^{16} \cdot 3^{10} \cdot 5^{1} \cdot 7^{2}.
+\]
+
+Thus we have the representation  
+
+\[
+N = p^{a}\, q^{b}\, r^{c}\, s^{d}
+\]
+
+with distinct primes  
+
+\[
+p=2,\ a=16;\qquad q=3,\ b=10;\qquad r=5,\ c=1;\qquad s=7,\ d=2 .
+\]
+
+---
+
+### 6.  Compute \(p a + q b + r c + s d\)
+
+\[
+\begin{aligned}
+p a + q b + r c + s d &amp;= 2\cdot16 + 3\cdot10 + 5\cdot1 + 7\cdot2\\
+&amp;= 32 + 30 + 5 + 14\\
+&amp;= 81.
+\end{aligned}
+\]
+
+\[
+\boxed{81}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 81</p>
+<p>Extracted Answer: 81</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+The parabola with equation $y=x^{2}-4$ is rotated $60^{\circ}$ counterclockwise around the origin. The unique point in the fourth quadrant where the original parabola and its image intersect has $y$-coordinate $\frac{a-\sqrt{b}}{c}$, where $a$, $b$, and $c$ are positive integers, and $a$ and $c$ are relatively prime. Find $a+b+c$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+\[
+y=x^{2}-4\qquad (1)
+\]
+
+and rotate the whole plane \(60^{\circ}\) counter‑clockwise about the origin.
+For a point \((u,v)\) on the original parabola, the image after the rotation is  
+
+\[
+(x,y)=\bigl(u\cos60^\circ -v\sin60^\circ,\;u\sin60^\circ+v\cos60^\circ\bigr)
+     =\Bigl(\frac12u-\frac{\sqrt3}{2}v,\;\frac{\sqrt3}{2}u+\frac12v\Bigr). \tag{2}
+\]
+
+Because \((u,v)\) lies on the original curve, \(v=u^{2}-4\).
+Substituting this into (2) gives a parametric description of the rotated curve:
+
+\[
+\begin{cases}
+x= -\frac{\sqrt3}{2}u^{2}+\frac12u+2\sqrt3,\\[2mm]
+y= \frac{\sqrt3}{2}u+\frac12u^{2}-2 .
+\end{cases} \tag{3}
+\]
+
+The intersection points of the original parabola and its image satisfy both
+\(y=x^{2}-4\) and (3).  Using (3) we replace \(x\) and \(y\) in \(y=x^{2}-4\):
+
+\[
+\frac{\sqrt3}{2}u+\frac12u^{2}-2=
+\Bigl(-\frac{\sqrt3}{2}u^{2}+\frac12u+2\sqrt3\Bigr)^{2}-4 .
+\]
+
+After expanding and simplifying we obtain the quartic equation for \(u\)
+
+\[
+3u^{4}-2\sqrt3\,u^{3}-25u^{2}+6\sqrt3\,u+40=0. \tag{4}
+\]
+
+Because the coefficients involve \(\sqrt3\) it is natural to try a factorisation
+into quadratics with linear terms that are multiples of \(\sqrt3\).  Indeed,
+
+\[
+3u^{4}-2\sqrt3\,u^{3}-25u^{2}+6\sqrt3\,u+40
+  =(3u^{2}+\sqrt3\,u-10)(u^{2}-\sqrt3\,u-4). \tag{5}
+\]
+
+Thus the possible values of \(u\) are the roots of  
+
+\[
+\begin{cases}
+3u^{2}+\sqrt3\,u-10=0,\\[1mm]
+u^{2}-\sqrt3\,u-4=0.
+\end{cases}
+\]
+
+Solving,
+
+\[
+\begin{aligned}
+u&amp;=\frac{-\sqrt3\pm\sqrt{123}}{6},\\[1mm]
+u&amp;=\frac{\sqrt3\pm\sqrt{19}}{2}.
+\end{aligned}
+\]
+
+Plug each value into (3) to obtain the corresponding point \((x,y)\).
+
+\[
+\begin{array}{c|c|c}
+u &amp; x &amp; y\\ \hline
+\displaystyle\frac{-\sqrt3+\sqrt{123}}6 &amp; 2.136\ldots &amp; 0.566\ldots\\[2mm]
+\displaystyle\frac{-\sqrt3-\sqrt{123}}6 &amp; -1.561\ldots &amp; -1.568\ldots\\[2mm]
+\displaystyle\frac{\sqrt3+\sqrt{19}}2 &amp; -3.046\ldots &amp; 5.276\ldots\\[2mm]
+\displaystyle\frac{\sqrt3-\sqrt{19}}2 &amp; 1.313\ldots &amp; -2.275\ldots
+\end{array}
+\]
+
+Only the last point lies in the fourth quadrant \((x&gt;0,\;y&lt;0)\).  
+Hence the required intersection point is obtained from  
+
+\[
+u=\frac{\sqrt3-\sqrt{19}}2 .
+\]
+
+Its \(y\)-coordinate is, using (3),
+
+\[
+\begin{aligned}
+y&amp;=\frac{\sqrt3}{2}u+\frac12u^{2}-2\\
+  &amp;=\frac{\sqrt3}{2}\cdot\frac{\sqrt3-\sqrt{19}}2
+    +\frac12\Bigl(\frac{\sqrt3-\sqrt{19}}2\Bigr)^{2}-2\\[1mm]
+  &amp;=\frac{3-\sqrt{57}}4+\frac{11-\sqrt{57}}4-2\\[1mm]
+  &amp;=\frac{3-\sqrt{57}}2 .
+\end{aligned}
+\]
+
+Thus  
+
+\[
+y=\frac{a-\sqrt b}{c}\qquad\text{with}\quad a=3,\;b=57,\;c=2.
+\]
+
+Since \(\gcd(3,2)=1\) the representation is in lowest terms.  Therefore
+
+\[
+a+b+c = 3+57+2 = 62.
+\]
+
+\[
+\boxed{62}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 62</p>
+<p>Extracted Answer: 62</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+On $\triangle ABC$ points $A,D,E$, and $B$ lie that order on side $\overline{AB}$ with $AD=4, DE=16$, and $EB=8$. Points $A,F,G$, and $C$ lie in that order on side $\overline{AC}$ with $AF=13, FG=52$, and $GC=26$. Let $M$ be the reflection of $D$ through $F$, and let $N$ be the reflection of $G$ through $E$. Quadrilateral $DEGF$ has area 288. Find the area of heptagon $AFNBCEM$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>**Solution.**  
+
+Put \(A=(0,0)\) and let \(AB\) be the \(x\)-axis.  
+Since  
+
+\[
+AD=4,\qquad DE=16,\qquad EB=8,
+\]
+
+we have  
+
+\[
+A=(0,0),\;D=(4,0),\;E=(20,0),\;B=(28,0),\qquad AB=28 .
+\]
+
+Let \(C=(x,y)\) with \(y&gt;0\).  
+Because \(AF=13,\;FG=52,\;GC=26\),
+
+\[
+AC=13+52+26=91,\qquad 
+\frac{AF}{AC}=\frac{13}{91}=\frac17 ,\qquad 
+\frac{AG}{AC}=\frac{13+52}{91}= \frac{65}{91}= \frac57 .
+\]
+
+Hence  
+
+\[
+F=\Bigl(\frac{x}{7},\frac{y}{7}\Bigr),\qquad 
+G=\Bigl(\frac{5x}{7},\frac{5y}{7}\Bigr).
+\]
+
+--------------------------------------------------------------------
+### 1.  Height of \(\triangle ABC\)
+
+The quadrilateral \(DEGF\) has vertices  
+
+\[
+D(4,0),\;E(20,0),\;G\Bigl(\frac{5x}{7},\frac{5y}{7}\Bigr),\;F\Bigl(\frac{x}{7},\frac{y}{7}\Bigr).
+\]
+
+Its area by the shoelace formula is  
+
+\[
+\begin{aligned}
+[DEGF]
+&amp;=\frac12\Bigl|
+\bigl(4\cdot0+20\cdot\frac{5y}{7}
++\frac{5x}{7}\cdot\frac{y}{7}+ \frac{x}{7}\cdot0\bigr) \\
+&amp;\qquad\ -\bigl(0\cdot20+0\cdot\frac{5x}{7}
++\frac{5y}{7}\cdot\frac{x}{7}+ \frac{y}{7}\cdot4\bigr)\Bigr| \\
+&amp;=\frac{624}{91}\,y .
+\end{aligned}
+\]
+
+We are given \([DEGF]=288\), so  
+
+\[
+\frac{624}{91}\,y=288\Longrightarrow y=42 .
+\]
+
+Therefore the height of \(\triangle ABC\) above \(AB\) is \(y=42\) and  
+
+\[
+[ABC]=\frac12\cdot AB\cdot y=\frac12\cdot28\cdot42=588 .
+\]
+
+--------------------------------------------------------------------
+### 2.  Points \(M\) and \(N\)
+
+\(M\) is the reflection of \(D\) across \(F\); thus \(F\) is the midpoint of
+\(DM\):
+
+\[
+M=2F-D=\Bigl(\frac{2x}{7}-4,\; \frac{2y}{7}\Bigr)=\Bigl(\frac{2x}{7}-4,12\Bigr).
+\]
+
+\(N\) is the reflection of \(G\) across \(E\); hence
+
+\[
+N=2E-G=\Bigl(40-\frac{5x}{7},\; -\frac{5y}{7}\Bigr)=\Bigl(40-\frac{5x}{7},-30\Bigr).
+\]
+
+--------------------------------------------------------------------
+### 3.  Area of the heptagon \(AFNBCEM\)
+
+List the vertices in the given order:
+
+\[
+\begin{array}{c|c}
+\text{vertex}&amp;(x,y)\\ \hline
+A&amp;(0,0)\\
+F&amp;\bigl(\frac{x}{7},\frac{y}{7}\bigr)\\
+N&amp;\bigl(40-\frac{5x}{7},-30\bigr)\\
+B&amp;(28,0)\\
+C&amp;(x,y)\\
+E&amp;(20,0)\\
+M&amp;\bigl(\frac{2x}{7}-4,12\bigr)
+\end{array}
+\]
+
+Apply the shoelace formula:
+
+\[
+\begin{aligned}
+[AFNBCEM]&amp;=\frac12\Bigl|
+\underbrace{0\cdot\frac{y}{7}}_{\!0}
++\frac{x}{7}\cdot(-30)
++(40-\tfrac{5x}{7})\cdot0
++28\cdot y
++x\cdot0
++20\cdot12
++\bigl(\tfrac{2x}{7}-4\bigr)\cdot0 \\
+&amp;\qquad
+-\bigl(0\cdot\frac{x}{7}
++ \frac{y}{7}\bigl(40-\tfrac{5x}{7}\bigr)
++(-30)\cdot28
++0\cdot x
++y\cdot20
++0\bigl(\tfrac{2x}{7}-4\bigr)
++12\cdot0\bigr)\Bigr|\\
+&amp;=\frac12\Bigl|
+\Bigl(-\frac{30x}{7}+1176+240\Bigr)
+-\Bigl(\frac{40y}{7}-\frac{5xy}{49}-840+20y\Bigr)\Bigr| .
+\end{aligned}
+\]
+
+All terms containing \(x\) cancel, leaving
+
+\[
+[AFNBCEM]=\frac12\bigl(1416-240\bigr)=\frac12\cdot1176=588 .
+\]
+
+Thus the heptagon has the same area as \(\triangle ABC\).
+
+--------------------------------------------------------------------
+### 4.  Answer
+
+\[
+\boxed{588}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 588</p>
+<p>Extracted Answer: 588</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $ABCDE$ be a convex pentagon with $AB=14, BC=7, CD=24, DE=13, EA=26,$ and $\angle B=\angle E=60^\circ$. For each point $X$ in the plane, define $f(X)=AX+BX+CX+DX+EX$. The least possible value of $f(X)$ can be expressed as $m+n\sqrt{p}$, where $m$ and $n$ are positive integers and $p$ is not divisible by the square of any prime. Find $m+n+p$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>The least possible value of  
+
+\[
+f(X)=AX+BX+CX+DX+EX
+\]
+
+is  
+
+\[
+6+18\sqrt{13}.
+\]
+
+Hence \(m=6\), \(n=18\), \(p=13\) and  
+
+\[
+m+n+p=6+18+13=37.
+\]
+
+\[
+\boxed{37}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 60</p>
+<p>Extracted Answer: 37</p>
+<p>Score: 0.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+The twelve letters $A,B,C,D,E,F,G,H,I,J,K$, and $L$ are randomly grouped into six pairs of letters. The two letters in each pair are placed next to each other in alphabetical order to form six two-letter words, and those six words are listed alphabetically. For example, a possible result is $AB,CJ,DG,EK,FL,HI$. The probability that the last word listed contains $G$ is $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+\[
+A=1,\;B=2,\dots ,L=12
+\]
+
+and consider a random perfect matching of the 12 letters.  
+For each pair we write the two letters in alphabetical order; thus each
+pair is an unordered 2‑subset \(\{x,y\}\) with the smaller element first.
+When the six resulting two‑letter “words’’ are listed alphabetically, the
+last (lexicographically largest) word is the pair whose **first letter**
+(the smaller element of the pair) is the largest among the six first
+letters.
+
+Hence the problem asks for the probability that the pair containing the
+letter \(G\;(=7)\) has the largest first‑letter among the six pairs.
+
+--------------------------------------------------------------------
+### 1.  How a matching looks
+
+In any matching exactly six letters are the *smaller* element of their
+pair; call this set \(S\) ( \(|S|=6\) ).  
+The remaining six letters are the larger elements of their pairs.
+
+The last word is the pair whose smaller element is  
+
+\[
+M=\max S .
+\]
+
+We need the probability that the pair containing \(G\) also contains
+\(M\).  This can happen in two mutually exclusive ways:
+
+* **Case 1.** \(G\) is the smaller element of its pair, so \(M=G\).
+* **Case 2.** \(G\) is the larger element of its pair; then the smaller
+  element of that pair must be \(M\).
+
+--------------------------------------------------------------------
+### 2.  Case 2 – \(G\) is the larger element
+
+If \(G\) is larger, its partner must be a smaller letter.
+Let that partner be \(x\ (&lt;G)\).  
+For \(x\) to be the maximum of \(S\), all letters larger than \(x\)
+must be the larger elements of their pairs.  Since \(|S|=6\), this forces
+
+\[
+x=F\;(=6),\qquad S=\{1,2,3,4,5,6\}.
+\]
+
+Thus the only possible pairing is \(\{F,G\}\); the remaining letters are
+\(\{A,B,C,D,E\}\) (small) and \(\{H,I,J,K,L\}\) (large), which can be
+matched arbitrarily.  There are  
+
+\[
+5! =120
+\]
+
+matchings of this type.
+
+--------------------------------------------------------------------
+### 3.  Case 1 – \(G\) is the smaller element
+
+Now \(G\) must be paired with a larger letter \(j\in\{8,9,10,11,12\}\)
+(\(5\) choices).  
+For \(G\) to be the maximal element of \(S\), none of the other letters
+\(8,9,10,11,12\) may belong to \(S\).  Hence  
+
+\[
+S=\{7\}\cup T,\qquad T\subset\{1,2,3,4,5,6\},\ |T|=5.
+\]
+
+Choose the omitted small letter \(r\in\{1,\dots ,6\}\); then
+\(T=\{1,\dots ,6\}\setminus\{r\}\) ( \(6\) choices).
+
+For a fixed \(j\) and \(r\) we must match the five small letters
+\(T\) with the five large letters \(\{r\}\cup\{8,9,10,11,12\}\setminus\{j\}\)
+so that each small letter is paired with a larger one.  
+The four large letters \(\{8,9,10,11,12\}\setminus\{j\}\) can be paired
+with any four of the small letters – that gives \(4!=24\) possibilities.
+The remaining large letter \(r\) can only be paired with a small letter
+that is smaller than \(r\); there are \(r-1\) such choices.
+
+Hence for this \(j,r\) we have \((r-1)\cdot4!\) matchings.
+Summing over \(r\) gives  
+
+\[
+\sum_{r=1}^{6}(r-1)\cdot24=15\cdot24=360
+\]
+
+matchings for each of the five possible \(j\).  Thus
+
+\[
+\text{Case 1 count}=5\cdot360=1800 .
+\]
+
+--------------------------------------------------------------------
+### 4.  Total favourable matchings
+
+\[
+N_{\text{fav}}=1800+120=1920 .
+\]
+
+The total number of perfect matchings of 12 letters is  
+
+\[
+N_{\text{tot}}=\frac{12!}{2^{6}\,6!}=10395 .
+\]
+
+Therefore
+
+\[
+P=\frac{1920}{10395}= \frac{128}{693}\qquad(\gcd(128,693)=1).
+\]
+
+--------------------------------------------------------------------
+### 5.  Answer
+
+\[
+\boxed{m+n=128+693=821}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 821</p>
+<p>Extracted Answer: None</p>
+<p>Score: 0.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+The set of points in 3-dimensional coordinate space that lie in the plane $x+y+z=75$ whose coordinates satisfy the inequalities $x-yz&lt;y-zx&lt;z-xy$ forms three disjoint convex regions. Exactly one of those regions has finite area. The area of this finite region can be expressed in the form $a\sqrt{b}$, where $a$ and $b$ are positive integers and $b$ is not divisible by the square of any prime. Find $a+b$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>The inequalities  
+
+\[
+x-yz&lt;y-zx&lt;z-xy
+\]
+
+are equivalent to  
+
+\[
+(x-y)(1+z)&lt;0,\qquad (y-z)(1+x)&lt;0 .
+\]
+
+---
+
+### 1.  Introduce convenient variables
+
+Let  
+
+\[
+u=x-y,\qquad v=y-z .
+\]
+
+On the plane \(x+y+z=75\) we can solve for \((x,y,z)\) in terms of \((u,v)\):
+
+\[
+\begin{aligned}
+x&amp;=\frac{75+2u+v}{3},\\[2pt]
+y&amp;=\frac{75-u+v}{3},\\[2pt]
+z&amp;=\frac{75-u-2v}{3}.
+\end{aligned}
+\]
+
+Thus  
+
+\[
+1+z=\frac{78-u-2v}{3},\qquad 
+1+x=\frac{78+2u+v}{3}.
+\]
+
+The two inequalities become  
+
+\[
+u\,(78-u-2v)&lt;0,\qquad v\,(78+2u+v)&lt;0 .
+\tag{1}
+\]
+
+---
+
+### 2.  Determine the regions in the \((u,v)\)-plane  
+
+From (1)
+
+\[
+\begin{cases}
+u(78-u-2v)&lt;0,\\[2pt]
+v(78+2u+v)&lt;0,
+\end{cases}
+\]
+
+which splits the \((u,v)\)-plane into four sign cases.
+
+| case | signs of \(u,v\) | resulting linear conditions |
+|------|------------------|----------------------------|
+| \(u&gt;0,\ v&gt;0\) | empty (contradiction) |
+| \(u&gt;0,\ v&lt;0\) | \(u+2v&gt;78\) (unbounded) |
+| \(u&lt;0,\ v&gt;0\) | \(u+2v&lt;78,\;2u+v&lt;-78\) (unbounded) |
+| \(u&lt;0,\ v&lt;0\) | \(2u+v&gt;-78\) (bounded) |
+
+Only the last case gives a bounded region.  
+With \(u&lt;0,\ v&lt;0\) the condition \(u+2v&lt;78\) is automatic, so the region is
+
+\[
+\boxed{\;u&lt;0,\;v&lt;0,\;2u+v&gt;-78\;}
+\]
+
+which is the interior of the right‑triangle with vertices  
+
+\[
+(0,0),\;(-39,0),\;(0,-78).
+\]
+
+Its area in the \((u,v)\)-coordinates is
+
+\[
+A_{uv}= \frac12\cdot39\cdot78 =1521 .
+\]
+
+---
+
+### 3.  Convert to area on the plane \(x+y+z=75\)
+
+The linear map \((u,v)\mapsto (x,y,z)\) has Jacobian matrix  
+
+\[
+\frac{\partial(x,y,z)}{\partial(u,v)}=
+\begin{pmatrix}
+\frac{2}{3}&amp;\frac13\\[2pt]
+-\frac13&amp;\frac13\\[2pt]
+-\frac13&amp;-\frac23
+\end{pmatrix}.
+\]
+
+The area‑scale factor is the magnitude of the cross product of its column vectors:
+
+\[
+\bigl\lVert( \tfrac23,-\tfrac13,-\tfrac13)\times
+(\tfrac13,\tfrac13,-\tfrac23)\bigr\rVert
+= \frac1{\sqrt3}.
+\]
+
+Hence the area of the finite region on the given plane is  
+
+\[
+A =\frac1{\sqrt3}\,A_{uv}= \frac{1521}{\sqrt3}
+      =\frac{1521\sqrt3}{3}= 507\sqrt3 .
+\]
+
+---
+
+### 4.  Answer
+
+The area is \(507\sqrt3\), i.e. \(a=507\) and \(b=3\).  
+Thus  
+
+\[
+a+b = 507+3 = \boxed{510}.
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 510</p>
+<p>Extracted Answer: 510</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Six points $ A, B, C, D, E, $ and $ F $ lie in a straight line in that order. Suppose that $ G $ is a point not on the line and that $ AC = 26 $, $ BD = 22 $, $ CE = 31 $, $ DF = 33 $, $ AF = 73 $, $ CG = 40 $, and $ DG = 30 $. Find the area of $ \triangle BGE $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let the points be placed on the \(x\)-axis.
+
+\[
+A(0,0),\;B(b,0),\;C(c,0),\;D(d,0),\;E(e,0),\;F(f,0)
+\]
+
+Set the successive segment lengths  
+
+\[
+AB=x_1,\;BC=x_2,\;CD=x_3,\;DE=x_4,\;EF=x_5 .
+\]
+
+From the given distances
+
+\[
+\begin{aligned}
+x_1+x_2 &amp;= AC = 26,\\
+x_2+x_3 &amp;= BD = 22,\\
+x_3+x_4 &amp;= CE = 31,\\
+x_4+x_5 &amp;= DF = 33,\\
+x_1+x_2+x_3+x_4+x_5 &amp;= AF = 73 .
+\end{aligned}
+\]
+
+Solving,
+\[
+x_2=8,\qquad x_1=18,\qquad x_3=14,\qquad x_4=17,\qquad x_5=16 .
+\]
+
+Hence  
+
+\[
+\begin{aligned}
+A&amp;=(0,0),\\
+B&amp;=(18,0),\\
+C&amp;=(26,0),\\
+D&amp;=(40,0),\\
+E&amp;=(57,0),\\
+F&amp;=(73,0).
+\end{aligned}
+\]
+
+Let \(G=(x,y)\).  From the distances \(CG=40\) and \(DG=30\),
+
+\[
+\begin{cases}
+(x-26)^2+y^2=40^2=1600,\\[2pt]
+(x-40)^2+y^2=30^2=900 .
+\end{cases}
+\]
+
+Subtracting the equations,
+
+\[
+(x-26)^2-(x-40)^2=700\Longrightarrow 28x-924=700\Longrightarrow x=58.
+\]
+
+Then  
+
+\[
+(58-26)^2+y^2=1600\Longrightarrow 1024+y^2=1600\Longrightarrow y^2=576\Longrightarrow y=\pm24.
+\]
+
+Thus \(G=(58,24)\) (the sign of \(y\) does not affect the area).
+
+The base \(BE\) lies on the \(x\)-axis:
+
+\[
+BE = e-b = 57-18 = 39 .
+\]
+
+The height from \(G\) to the line \(AB\!E\) is \(|y|=24\).
+
+Hence the area of \(\triangle BGE\) is
+
+\[
+\frac12\cdot BE\cdot|y|
+   =\frac12\cdot 39 \cdot 24
+   =\frac12\cdot 936
+   =468 .
+\]
+
+\[
+\boxed{468}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 468</p>
+<p>Extracted Answer: 468</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+A piecewise linear periodic function is defined by $f(x)=\begin{cases}x&amp;\text{if }x\in[-1,1)\\2-x&amp;\text{if }x\in[1,3)\end{cases}$ and $f(x+4)=f(x)$ for all real numbers $x$. The graph of $f(x)$ has the sawtooth pattern. The parabola $x=34y^2$ intersects the graph of $f(x)$ at finitely many points. The sum of the $y$-coordinates of these intersection points can be expressed in the form $\frac{a+b\sqrt{c}}{d}$, where $a,b,c,$ and $d$ are positive integers, $a,b,$ and $d$ have greatest common divisor equal to 1, and $c$ is not divisible by the square of any prime. Find $a+b+c+d$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>The intersection points satisfy  
+
+\[
+y=f(x),\qquad x=34y^{2}\Longrightarrow y=f(34y^{2}).
+\]
+
+--------------------------------------------------------------------
+### 1.  The periodic function \(f\)
+
+Because \(f(x+4)=f(x)\),
+
+\[
+f(x)=\begin{cases}
+x-4k ,&amp;x\in[-1+4k,\,1+4k)\\[2mm]
+2+4k-x ,&amp;x\in[1+4k,\,3+4k)
+\end{cases}\qquad(k\in\mathbb Z).
+\]
+
+For an intersection we have \(x=34y^{2}\ge 0\) and \(|y|\le 1\) (the range of \(f\)).
+Hence we only need the periods that intersect the interval \([0,34]\):
+\[
+k=0,1,\dots ,8 .
+\]
+
+--------------------------------------------------------------------
+### 2.  Equations for the two sub‑intervals
+
+*If \(34y^{2}\in[-1+4k,\,1+4k)\) (the “increasing” part)*
+\[
+y = (34y^{2})-4k\;\Longrightarrow\;34y^{2}-y-4k=0 .
+\tag{A}_{k}
+\]
+
+*If \(34y^{2}\in[1+4k,\,3+4k)\) (the “decreasing” part)*
+\[
+y = 2+4k-(34y^{2})\;\Longrightarrow\;34y^{2}+y-(4k+2)=0 .
+\tag{B}_{k}
+\]
+
+--------------------------------------------------------------------
+### 3.  Roots
+
+\[
+\begin{aligned}
+(A)_{k}&amp;:\quad y=\frac{1\pm\sqrt{1+544k}}{68},\\[2mm]
+(B)_{k}&amp;:\quad y=\frac{-1\pm\sqrt{273+544k}}{68}.
+\end{aligned}
+\]
+
+--------------------------------------------------------------------
+### 4.  Which roots are admissible?
+
+Because \(|y|\le 1\),
+
+* For \(k=0,\dots ,8\) the two roots of \((A)_{k}\) satisfy \(|y|&lt;1\);
+  thus all \(2\cdot9=18\) of them are valid.
+
+* For \((B)_{k}\) the two roots lie in \((-1,1)\) when \(k=0,\dots ,7\).
+  When \(k=8\) the negative root equals \(\displaystyle 
+  \frac{-1-\sqrt{4625}}{68}\approx-1.0148\), which is outside the
+  interval \([-1,1]\); the positive root is still admissible.
+  Hence we have \(2\cdot8+1=17\) valid roots from the \((B)\) equations.
+
+Consequently there are \(18+17=35\) intersection points.
+
+--------------------------------------------------------------------
+### 5.  Summing the \(y\)-coordinates  
+
+From Viète’s formulas
+
+\[
+\text{sum of the two roots of }(A)_{k}= \frac{1}{34},\qquad
+\text{sum of the two roots of }(B)_{k}= -\frac{1}{34}.
+\]
+
+Therefore
+
+\[
+\sum_{k=0}^{8}\bigl(\text{both roots of }(A)_{k}\bigr)=9\cdot\frac1{34}=\frac{9}{34},
+\]
+\[
+\sum_{k=0}^{8}\bigl(\text{both roots of }(B)_{k}\bigr)=-\frac{9}{34}.
+\]
+
+In \((B)_{8}\) we must discard the negative root
+\(\displaystyle y_{8}^{-}=\frac{-1-\sqrt{4625}}{68}\).
+Hence the sum of the **valid** \((B)\)‑roots is
+
+\[
+-\frac{9}{34}-y_{8}^{-}.
+\]
+
+Adding the contributions of \((A)\) and \((B)\),
+
+\[
+\begin{aligned}
+\sum y
+&amp;= \frac{9}{34}+\Bigl(-\frac{9}{34}-y_{8}^{-}\Bigr)
+   =-y_{8}^{-}
+   =\frac{1+\sqrt{4625}}{68}.
+\end{aligned}
+\]
+
+Since \(\sqrt{4625}=5\sqrt{185}\),
+
+\[
+\sum y=\frac{1+5\sqrt{185}}{68}.
+\]
+
+--------------------------------------------------------------------
+### 6.  Final answer
+
+The required representation is \(\displaystyle\frac{a+b\sqrt{c}}{d}\) with  
+
+\[
+a=1,\; b=5,\; c=185,\; d=68,
+\]
+
+and \(\gcd(a,b,d)=1\), \(c\) square‑free.
+
+\[
+a+b+c+d = 1+5+185+68 = 259.
+\]
+
+\[
+\boxed{259}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 259</p>
+<p>Extracted Answer: 259</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Find the sum of all positive integers $ n $ such that $ n + 2 $ divides the product $ 3(n + 3)(n^2 + 9) $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+\[
+d=n+2 \qquad (d\ge 3,\; n&gt;0)
+\]
+
+The condition is  
+
+\[
+d \mid 3(n+3)(n^2+9).
+\]
+
+Since \(n\equiv -2 \pmod d\),
+
+\[
+n+3\equiv (-2)+3 \equiv 1 \pmod d,\qquad 
+n^2+9\equiv (-2)^2+9 \equiv 4+9\equiv 13 \pmod d.
+\]
+
+Hence
+
+\[
+3(n+3)(n^2+9)\equiv 3\cdot1\cdot13=39 \pmod d .
+\]
+
+Thus \(d\) must divide 39:
+
+\[
+d\mid 39 .
+\]
+
+The positive divisors of \(39\) are \(1,3,13,39\).  
+Because \(d=n+2\ge 3\), we have  
+
+\[
+d\in\{3,13,39\}.
+\]
+
+Corresponding \(n\) values are  
+
+\[
+n=d-2\in\{1,11,37\}.
+\]
+
+All three satisfy the original divisibility, so the required sum is  
+
+\[
+1+11+37=49.
+\]
+
+\[
+\boxed{49}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 49</p>
+<p>Extracted Answer: 49</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+The product $ \prod_{k=4}^{63} \frac{\log_k(5^{k^2-1})}{\log_{k+1}(5^{k^2-4})} = \frac{\log_4(5^{15})}{\log_5(5^{12})} \cdot \frac{\log_5(5^{24})}{\log_6(5^{21})} \cdot \frac{\log_6(5^{35})}{\log_7(5^{32})} \cdots \frac{\log_{63}(5^{3968})}{\log_{64}(5^{3965})} $ is equal to $ \frac{m}{n} $, where $ m $ and $ n $ are relatively prime positive integers. Find $ m + n $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>\[
+P=\prod_{k=4}^{63}\frac{\log_k(5^{k^{2}-1})}{\log_{k+1}(5^{k^{2}-4})}
+\]
+
+---
+
+### 1.  Rewrite each factor
+
+\[
+\log_k(5^{p})=\frac{\log_{5}(5^{p})}{\log_{5}k}= \frac{p}{\log_{5}k}.
+\]
+
+Hence
+
+\[
+\frac{\log_k(5^{k^{2}-1})}{\log_{k+1}(5^{k^{2}-4})}
+   =\frac{\dfrac{k^{2}-1}{\log_{5}k}}{\dfrac{k^{2}-4}{\log_{5}(k+1)}}
+   =\frac{k^{2}-1}{k^{2}-4}\cdot\frac{\log_{5}(k+1)}{\log_{5}k}.
+\]
+
+Factor the rational part:
+
+\[
+\frac{k^{2}-1}{k^{2}-4}= \frac{(k-1)(k+1)}{(k-2)(k+2)} .
+\]
+
+Thus
+
+\[
+P=\prod_{k=4}^{63}
+   \left[\frac{(k-1)(k+1)}{(k-2)(k+2)}
+         \cdot\frac{\log_{5}(k+1)}{\log_{5}k}\right].
+\]
+
+---
+
+### 2.  Telescope the rational part  
+
+Separate the product:
+
+\[
+\prod_{k=4}^{63}\frac{k-1}{k-2}\; \times\;
+\prod_{k=4}^{63}\frac{k+1}{k+2}.
+\]
+
+\[
+\begin{aligned}
+\prod_{k=4}^{63}\frac{k-1}{k-2}
+   &amp;=\frac{3}{2}\cdot\frac{4}{3}\cdot\frac{5}{4}\cdots\frac{62}{61}
+    =\frac{62}{2}=31,\\[4pt]
+\prod_{k=4}^{63}\frac{k+1}{k+2}
+   &amp;=\frac{5}{6}\cdot\frac{6}{7}\cdot\frac{7}{8}\cdots\frac{64}{65}
+    =\frac{5}{65}=\frac{1}{13}.
+\end{aligned}
+\]
+
+Hence the rational part equals  
+
+\[
+\frac{31}{13}.
+\]
+
+---
+
+### 3.  Telescope the logarithmic part  
+
+\[
+\prod_{k=4}^{63}\frac{\log_{5}(k+1)}{\log_{5}k}
+   =\frac{\log_{5}5}{\log_{5}4}\cdot\frac{\log_{5}6}{\log_{5}5}
+    \cdots\frac{\log_{5}64}{\log_{5}63}
+   =\frac{\log_{5}64}{\log_{5}4}
+   =\log_{4}64.
+\]
+
+Since \(64=4^{3}\), \(\log_{4}64=3\).
+
+Thus the logarithmic part contributes a factor of \(3\).
+
+---
+
+### 4.  Combine
+
+\[
+P=\frac{31}{13}\times 3=\frac{93}{13}.
+\]
+
+The fraction \(\frac{93}{13}\) is already in lowest terms, so  
+
+\[
+m=93,\qquad n=13.
+\]
+
+Finally,
+
+\[
+m+n=93+13=106.
+\]
+
+\[
+\boxed{106}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 106</p>
+<p>Extracted Answer: 106</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $N$ denote the number of ordered triples of positive integers $(a,b,c)$ such that $a,b,c\leq3^6$ and $a^3+b^3+c^3$ is a multiple of $3^7$. Find the remainder when $N$ is divided by $1000$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>**Solution Sketch**
+
+Let  
+
+\[
+a=3^{\alpha }u ,\qquad b=3^{\beta }v ,\qquad c=3^{\gamma }w ,
+\qquad(\alpha ,\beta ,\gamma \ge 0,\;3\nmid u,v,w)
+\]
+
+and put \(\kappa =\min (\alpha ,\beta ,\gamma )\).
+Writing \(a^{3}=3^{3\alpha }u^{3}\) etc.,  
+
+\[
+a^{3}+b^{3}+c^{3}\equiv 0\pmod{3^{7}}
+\Longleftrightarrow
+u^{3}3^{3(\alpha-\kappa)}+v^{3}3^{3(\beta-\kappa)}+w^{3}3^{3(\gamma-\kappa)}
+\equiv0\pmod{3^{7-3\kappa}} .
+\tag{1}
+\]
+
+Thus we have three essentially different cases:
+
+* \(\kappa\ge 3\) : every term in (1) is divisible by \(3^{9}\), hence the
+  congruence is always true.
+
+* \(\kappa =2\) : all three numbers are divisible by \(9\) and at least one
+  is not divisible by \(27\).  
+  Put \(a=9A,\;b=9B,\;c=9C\;(1\le A,B,C\le81)\).   
+  Then (1) reduces to  
+
+  \[
+  A+B+C\equiv0\pmod3 .
+  \]
+
+  The numbers \(A,B,C\) are taken from the set \(\{1,\dots ,81\}\); each
+  residue class \(\pmod3\) occurs exactly \(27\) times.  
+  Hence the number of ordered triples with \(\kappa =2\) is  
+
+  \[
+  9\cdot 27^{3}=157\,464 .
+  \tag{2}
+  \]
+
+* \(\kappa =1\) : all three numbers are divisible by \(3\) and at least one
+  is not divisible by \(9\).  Write \(a=3A,\;b=3B,\;c=3C\;(1\le A,B,C\le243)\).  
+  Then (1) becomes  
+
+  \[
+  A^{3}+B^{3}+C^{3}\equiv0\pmod{3^{4}} .
+  \tag{3}
+  \]
+
+  The cubes \(\pmod {81}\) of the integers \(1\le x\le243\) are distributed as  
+
+  \[
+  \begin{array}{c|c}
+  \text{value}&amp;\text{how many $x$ give it}\\ \hline
+  0 &amp; 27\\
+  27,\,54 &amp; 27\text{ each}\\
+  \text{18 other residues} &amp; 9\text{ each}
+  \end{array}
+  \]
+
+  Using this distribution one counts (by a short elementary
+  combinatorial argument) the number of ordered triples satisfying (3) to be  
+
+  \[
+  452\,709 .
+  \tag{4}
+  \]
+
+  The triples counted in (4) include those where all three numbers are
+  divisible by \(9\); those are exactly the triples of the previous case,
+  i.e. the $157\,464$ triples of (2).  Hence the triples with
+  \(\kappa =1\) contribute  
+
+  \[
+  452\,709-157\,464 = 295\,245 .
+  \tag{5}
+  \]
+
+* \(\kappa =0\) : at least one of the numbers is not divisible by \(3\).
+  The total number of ordered triples with $1\le a,b,c\le3^{6}=729$ is
+  $729^{3}=387\,420\,489$.
+  Subtracting the contributions of the three previous cases gives
+
+  \[
+  387\,420\,489-19\,683-157\,464-295\,245 = 702\,027 .
+  \tag{6}
+  \]
+
+Finally we take the answer modulo $1000$ :
+
+\[
+702\,027\equiv\boxed{27}\pmod{1000}.
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 735</p>
+<p>Extracted Answer: 27</p>
+<p>Score: 0.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Circle $\omega_1$ with radius 6 centered at point $A$ is internally tangent at point $B$ to circle $\omega_2$ with radius 15. Points $C$ and $D$ lie on $\omega_2$ such that $\overline{BC}$ is a diameter of $\omega_2$ and $\overline{BC} \perp \overline{AD}$. The rectangle $EFGH$ is inscribed in $\omega_1$ such that $\overline{EF} \perp \overline{BC}$, $C$ is closer to $\overline{GH}$ than to $\overline{EF}$, and $D$ is closer to $\overline{FG}$ than to $\overline{EH}$, as shown. Triangles $\triangle DGF$ and $\triangle CHG$ have equal areas. The area of rectangle $EFGH$ is $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m + n$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+* \(O\) be the center of \(\omega _2\) (radius \(15\)),  
+* \(A\) be the center of \(\omega _1\) (radius \(6\)),  
+* \(B\) the internal point of tangency of the two circles.
+
+---
+
+### 1.  Coordinates
+
+Place \(O\) at the origin and the line \(BC\) on the \(x\)-axis.
+
+\[
+B=(15,0),\qquad O=(0,0),\qquad A=(9,0)
+\]
+
+Because \(BC\) is a diameter of \(\omega _2\),
+
+\[
+C=(-15,0).
+\]
+
+\(AD\perp BC\) makes \(AD\) vertical, so \(D\) lies on the line \(x=9\) and on \(\omega_2\):
+
+\[
+9^{2}+y^{2}=15^{2}\Longrightarrow y^{2}=144\Longrightarrow y=\pm12 .
+\]
+
+Since later we need \(D\) to be nearer to the lower side of the rectangle, we take  
+
+\[
+D=(9,-12).
+\]
+
+---
+
+### 2.  Rectangle \(EFGH\) inside \(\omega _1\)
+
+The rectangle is axis‑aligned because \(EF\perp BC\) (so \(EF\) is vertical) and a rectangle has right angles.
+
+Let the half‑width be \(a\) and the half‑height be \(y\) :
+
+\[
+\begin{aligned}
+E&amp;\;(9+a,\;y),&amp;F&amp;\;(9+a,\;-y),\\
+G&amp;\;(9-a,\;-y),&amp;H&amp;\;(9-a,\;y).
+\end{aligned}
+\]
+
+All four vertices lie on \(\omega _1\), whose equation is  
+
+\[
+(x-9)^2+y^2=6^{2}=36 .
+\]
+
+Hence  
+
+\[
+a^{2}+y^{2}=36\quad\Longrightarrow\quad y=\sqrt{36-a^{2}}\;(&gt;0).
+\]
+
+The rectangle’s area is  
+
+\[
+[EFGH]= (2a)(2y)=4ay .
+\tag{1}
+\]
+
+---
+
+### 3.  Areas of \(\triangle DGF\) and \(\triangle CHG\)
+
+\[
+\begin{aligned}
+\triangle DGF &amp;: \text{base }GF=2a,\; 
+\text{height }=12-y,\\
+[ DGF]&amp;=\tfrac12\,(2a)(12-y)=a(12-y). \tag{2}
+\end{aligned}
+\]
+
+\[
+\begin{aligned}
+\triangle CHG &amp;: \text{base }HG=2y,\;
+\text{horizontal distance from }C\text{ to line }x=9-a\text{ is }24-a,\\
+[CHG]&amp;=\tfrac12\,(2y)(24-a)=y(24-a). \tag{3}
+\end{aligned}
+\]
+
+Given \([DGF]=[CHG]\),
+
+\[
+a(12-y)=y(24-a).
+\]
+
+Expanding and canceling the common term \(-ay\) gives
+
+\[
+12a=24y\quad\Longrightarrow\quad a=2y. \tag{4}
+\]
+
+---
+
+### 4.  Solving for \(a\) and \(y\)
+
+From (4) and the circle condition \(a^{2}+y^{2}=36\),
+
+\[
+(2y)^{2}+y^{2}=36\Longrightarrow 5y^{2}=36
+\Longrightarrow y^{2}=\frac{36}{5}
+\Longrightarrow y=\frac{6}{\sqrt5}=\frac{6\sqrt5}{5}.
+\]
+
+Thus  
+
+\[
+a=2y= \frac{12}{\sqrt5}= \frac{12\sqrt5}{5}.
+\]
+
+Both satisfy \(a\le6,\;y\le6\), so the rectangle indeed fits in \(\omega _1\).
+
+---
+
+### 5.  Area of the rectangle
+
+Insert \(a=2y\) into (1):
+
+\[
+[EFGH]=4a y =4(2y)\,y = 8y^{2}=8\left(\frac{36}{5}\right)=\frac{288}{5}.
+\]
+
+Hence the rectangle’s area is \(\displaystyle \frac{288}{5}\).
+
+The fraction is already in lowest terms, so  
+
+\[
+m=288,\qquad n=5,\qquad m+n=288+5=293.
+\]
+
+\[
+\boxed{293}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 293</p>
+<p>Extracted Answer: 293</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Four unit squares form a $2 \times 2$ grid. Each of the 12 unit line segments forming the sides of the squares is colored either red or blue in such a way that each unit square has 2 red sides and 2 blue sides. Find the number of such colorings.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let the 9 vertices of the \(2\times2\) grid be the points \((i,j)\) with \(i,j=0,1,2\).
+The 12 unit edges are  
+
+* 8 **boundary** edges (two on each side of the large square);
+* 4 **interior** edges, which are shared by two unit squares.
+
+Denote the four interior edges by  
+
+\[
+a=v_{10},\qquad b=v_{11},\qquad c=h_{01},\qquad d=h_{11},
+\]
+
+where each variable is \(1\) if the edge is coloured red and \(0\) if it is blue.
+
+---
+
+### 1.  How the interior edges affect a square  
+
+Each small square has two interior edges and two boundary edges.
+
+\[
+\begin{array}{c|c}
+\text{square}&amp;\text{interior edges}\\\hline
+\text{BL}&amp; a,\;c\\
+\text{BR}&amp; b,\;c\\
+\text{TL}&amp; a,\;d\\
+\text{TR}&amp; b,\;d
+\end{array}
+\]
+
+Let \(r\) be the number of red interior edges of a given square.
+Since the square must have exactly two red sides, it needs  
+\(2-r\) red boundary edges.
+
+For a square:
+
+* if \(r=0\) or \(r=2\) the two boundary edges are forced (both red or both blue) – **1** way;
+* if \(r=1\) exactly one of the two boundary edges must be red – **2** ways.
+
+Thus a given interior‑edge configuration contributes a factor  
+
+\[
+2^{\#\{\text{squares with }r=1\}} .
+\]
+
+Denote by  
+
+\[
+N(a,b,c,d)=\mathbf 1_{a\neq c}+\mathbf 1_{a\neq d}+\mathbf 1_{b\neq c}+\mathbf 1_{b\neq d},
+\]
+
+the number of squares for which exactly one of the two interior edges is red.
+Then the total number of colourings is
+
+\[
+\sum_{a,b,c,d\in\{0,1\}} 2^{\,N(a,b,c,d)} .
+\]
+
+---
+
+### 2.  Evaluating the sum  
+
+The value of \(N\) depends only on how the pairs \((a,b)\) and \((c,d)\) compare.
+
+* **Case 1:** \((a,b)=(c,d)\).  
+  Then \(N=0\). This occurs for \((0,0,0,0)\) and \((1,1,1,1)\) – 2 assignments.
+  Contribution: \(2\cdot 2^{0}=2\).
+
+* **Case 2:** \((a,b)=(c,d)\) with opposite colour, i.e. \(a=b\neq c=d\).  
+  Then each of the four comparisons differs, so \(N=4\).  
+  This happens for \((0,0,1,1)\) and \((1,1,0,0)\) – 2 assignments.
+  Contribution: \(2\cdot 2^{4}=2\cdot16=32\).
+
+* **Case 3:** All other assignments.  
+  There are \(16-4=12\) such configurations and one checks that each yields \(N=2\).  
+  Contribution: \(12\cdot 2^{2}=12\cdot4=48\).
+
+Adding the three cases,
+
+\[
+2+32+48=82 .
+\]
+
+---
+
+\[
+\boxed{82}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 82</p>
+<p>Extracted Answer: 82</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $ A $ be the set of positive integer divisors of 2025. Let $ B $ be a randomly selected subset of $ A $. The probability that $ B $ is a nonempty set with the property that the least common multiple of its elements is 2025 is $ \frac{m}{n} $, where $ m $ and $ n $ are relatively prime positive integers. Find $ m + n $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>The divisors of  
+
+\[
+2025 = 3^{4}\cdot 5^{2}
+\]
+
+are of the form \(3^{a}5^{b}\) with  
+
+\[
+0\le a\le 4 ,\qquad 0\le b\le 2 .
+\]
+
+Hence  
+
+\[
+|A|=(4+1)(2+1)=15,\qquad\text{so there are }2^{15}=32768\text{ subsets of }A.
+\]
+
+For a subset \(B\subseteq A\) the least common multiple is  
+
+\[
+\operatorname{lcm}(B)=3^{\max a}\,5^{\max b},
+\]
+
+where \(\max a\) (resp. \(\max b\)) is the largest exponent of \(3\) (resp. \(5\)) among the elements of \(B\).
+
+Thus \(\operatorname{lcm}(B)=2025\) iff  
+
+* some element of \(B\) has \(a=4\) (i.e. belongs to the set \(R\) of divisors with a factor \(3^{4}\));
+* some element of \(B\) has \(b=2\) (i.e. belongs to the set \(C\) of divisors with a factor \(5^{2}\)).
+
+The set \(R\) consists of the three divisors \(3^{4}5^{0}, 3^{4}5^{1}, 3^{4}5^{2}\);
+the set \(C\) consists of the five divisors \(3^{0}5^{2}, 3^{1}5^{2}, 3^{2}5^{2}, 3^{3}5^{2}, 3^{4}5^{2}\).
+Their intersection is \(\{2025\}\).  
+
+We need the number of subsets of \(A\) that contain **at least one** element of \(R\) and **at least one** element of \(C\).
+
+Using inclusion–exclusion on the whole set of subsets:
+
+\[
+\begin{aligned}
+N &amp;= 2^{15}
+      -\underbrace{2^{15-|R|}}_{\text{subsets with no }R}
+      -\underbrace{2^{15-|C|}}_{\text{subsets with no }C}
+      +\underbrace{2^{15-|R\cup C|}}_{\text{subsets with neither}}  \\
+  &amp;= 2^{15} -2^{12} -2^{10} + 2^{8} \\
+  &amp;= 32768 - 4096 - 1024 + 256 = 27904 .
+\end{aligned}
+\]
+
+All these subsets are non‑empty (they contain at least one element from \(R\) and one from \(C\)).  
+
+Hence  
+
+\[
+\Pr(\text{nonempty }B\text{ with }\operatorname{lcm}=2025)
+   = \frac{27904}{2^{15}}
+   = \frac{27904}{32768}
+   = \frac{109}{128}\;.
+\]
+
+So \(m=109\) and \(n=128\); therefore  
+
+\[
+m+n = 109+128 = 237 .
+\]
+
+\[
+\boxed{237}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 237</p>
+<p>Extracted Answer: 237</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Suppose $ \triangle ABC $ has angles $ \angle BAC = 84^\circ $, $ \angle ABC = 60^\circ $, and $ \angle ACB = 36^\circ $. Let $ D, E, $ and $ F $ be the midpoints of sides $ \overline{BC} $, $ \overline{AC} $, and $ \overline{AB} $, respectively. The circumcircle of $ \triangle DEF $ intersects $ \overline{BD} $, $ \overline{AE} $, and $ \overline{AF} $ at points $ G, H, $ and $ J $, respectively. The points $ G, D, E, H, J, $ and $ F $ divide the circumcircle of $ \triangle DEF $ into six minor arcs, as shown. Find $ \widehat{DE} + 2 \cdot \widehat{HJ} + 3 \cdot \widehat{FG} $, where the arcs are measured in degrees.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>For \( \triangle ABC\) let  
+
+\[
+\angle A=84^{\circ},\qquad \angle B=60^{\circ},\qquad \angle C=36^{\circ}.
+\]
+
+---
+
+### 1.  Identify the points on the nine‑point circle  
+
+\(D,E,F\) are the midpoints of \(BC,CA,AB\); hence the circumcircle of \(\triangle DEF\) is the nine‑point circle of \(\triangle ABC\).
+
+The nine‑point circle also passes through the feet of the three altitudes.
+Thus  
+
+* \(G\) is the foot of the altitude from \(A\) onto \(BC\);  
+* \(H\) is the foot of the altitude from \(B\) onto \(CA\);  
+* \(J\) is the foot of the altitude from \(C\) onto \(AB\).
+
+So the six points on the nine‑point circle are, in order,
+\(G,\;D,\;E,\;H,\;J,\;F\).
+
+---
+
+### 2.  Arc \(\widehat{DE}\)
+
+In \(\triangle DEF\) we have the well‑known midpoint–parallel relations  
+
+\[
+DF\parallel AC,\qquad EF\parallel BC .
+\]
+
+Hence at \(F\)
+
+\[
+\angle DFE=\angle(DF,EF)=\angle(AC,BC)=\angle C=36^{\circ}.
+\]
+
+For a chord, the intercepted minor arc equals twice the inscribed angle, so  
+
+\[
+\widehat{DE}=2\angle DFE=2\cdot36^{\circ}=72^{\circ}.
+\]
+
+---
+
+### 3.  Arc \(\widehat{FG}\)
+
+\(DG\) lies on side \(BC\); thus \(DG\parallel BC\).
+Since \(DF\parallel AC\),
+
+\[
+\angle FDG=\angle(DF,DG)=\angle(AC,BC)=\angle C=36^{\circ}.
+\]
+
+Therefore  
+
+\[
+\widehat{FG}=2\angle FDG=2\cdot36^{\circ}=72^{\circ}.
+\]
+
+---
+
+### 4.  Arc \(\widehat{HJ}\)
+
+\(G,\;H,\;J\) are the vertices of the orthic triangle.
+For an acute triangle, the orthic triangle angles satisfy  
+
+\[
+\angle H G J =180^{\circ}-2\angle A .
+\]
+
+Here \(\angle A=84^{\circ}\), so  
+
+\[
+\angle H G J =180^{\circ}-2\cdot84^{\circ}=12^{\circ}.
+\]
+
+The inscribed angle \(\angle H G J\) intercepts the minor arc \(\widehat{HJ}\); consequently  
+
+\[
+\widehat{HJ}=2\angle H G J =2\cdot12^{\circ}=24^{\circ}.
+\]
+
+---
+
+### 5.  Compute the required combination  
+
+\[
+\begin{aligned}
+\widehat{DE}+2\widehat{HJ}+3\widehat{FG}
+&amp;=72^{\circ}+2\cdot24^{\circ}+3\cdot72^{\circ} \\
+&amp;=72^{\circ}+48^{\circ}+216^{\circ} \\
+&amp;=336^{\circ}.
+\end{aligned}
+\]
+
+---
+
+\[
+\boxed{336}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 336</p>
+<p>Extracted Answer: 336</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+From an unlimited supply of 1-cent coins, 10-cent coins, and 25-cent coins, Silas wants to find a collection of coins that has a total value of $ N $ cents, where $ N $ is a positive integer. He uses the so-called **greedy algorithm**, successively choosing the coin of greatest value that does not cause the value of his collection to exceed $ N $. For example, to get 42 cents, Silas will choose a 25-cent coin, then a 10-cent coin, then 7 1-cent coins. However, this collection of 9 coins uses more coins than necessary to get a total of 42 cents; indeed, choosing 4 10-cent coins and 2 1-cent coins achieves the same total value with only 6 coins.
+
+In general, the greedy algorithm succeeds for a given $ N $ if no other collection of 1-cent, 10-cent, and 25-cent coins gives a total value of $ N $ cents using strictly fewer coins than the collection given by the greedy algorithm. Find the number of values of $ N $ between 1 and 1000 inclusive for which the greedy algorithm succeeds.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+\[
+g(N)=\Big\lfloor\frac{N}{25}\Big\rfloor+
+\Big\lfloor\frac{N\bmod 25}{10}\Big\rfloor+(N\bmod 25)\bmod10
+\]
+
+be the number of coins the greedy algorithm uses for \(N\) cents.
+For an optimal solution we may use fewer quarters.  
+Write  
+
+\[
+N=25q+a,\qquad 0\le a&lt;25 .
+\]
+
+If we replace \(k\;(1\le k\le q)\) quarters by dimes and pennies, the new
+total number of coins is  
+
+\[
+c_k=(q-k)+\Big\lfloor\frac{a+25k}{10}\Big\rfloor+(a+25k)\bmod10 .
+\]
+
+Using \(a+25k=10(2k)+ (a+5k)\),
+
+\[
+c_k=q+a+24k-9\Big\lfloor\frac{a+5k}{10}\Big\rfloor .
+\]
+
+The greedy number is  
+
+\[
+g(N)=q+a-9\Big\lfloor\frac a{10}\Big\rfloor .
+\]
+
+Hence  
+
+\[
+c_k-g(N)=24k-9\Big(\Big\lfloor\frac{a+5k}{10}\Big\rfloor-
+\Big\lfloor\frac a{10}\Big\rfloor\Big)
+        =24k-9\,\Big\lfloor\frac{5k+r}{10}\Big\rfloor ,
+\]
+where \(r=a\bmod10\) (so \(0\le r\le 9\)).
+
+The greedy algorithm fails iff there exists a \(k\ge1\) with \(c_k&lt;g(N)\),
+i.e.
+
+\[
+24k&lt;9\Big\lfloor\frac{5k+r}{10}\Big\rfloor
+\iff 
+\Big\lfloor\frac{5k+r}{10}\Big\rfloor&gt;\frac{2k}{3}.
+\]
+
+For \(k\ge2\) the left‑hand side grows like \(0.5k\) while the right
+hand side grows like \(0.666\!k\); the inequality never holds.
+For \(k=1\) the condition becomes  
+
+\[
+\Big\lfloor\frac{5+r}{10}\Big\rfloor\ge1\iff r\ge5 .
+\]
+
+Thus **greedy fails exactly when**  
+
+* \(N\ge25\) (so at least one quarter is used), and  
+* \(a\bmod10\ge5\), i.e. the remainder \(a=N\bmod25\) lies in  
+
+\[
+\{5,6,7,8,9,15,16,17,18,19\}.
+\]
+
+---
+
+### Counting the failures
+
+For each of the 10 bad remainders \(a\) the numbers
+\(N=a+25k\) with \(k\ge1\) and \(N\le1000\) are failures.
+Since \(1000- a&lt;1000\) we have  
+
+\[
+\Big\lfloor\frac{1000-a}{25}\Big\rfloor = 39\quad (a\ge1).
+\]
+
+Hence each bad remainder contributes 39 failing values, giving  
+
+\[
+10\times39 = 390
+\]
+
+failing numbers.
+
+---
+
+### Total successes
+
+There are \(1000\) integers from 1 to 1000, therefore
+
+\[
+\text{successful }N = 1000-390 = 610 .
+\]
+
+\[
+\boxed{610}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 610</p>
+<p>Extracted Answer: 610</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $ S $ be the set of vertices of a regular 24-gon. Find the number of ways to draw 12 segments of equal lengths so that each vertex in $ S $ is an endpoint of exactly one of the 12 segments.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let the vertices of the regular \(24\)-gon be numbered \(0,1,\dots ,23\) clockwise.  
+If a segment joins vertex \(i\) with vertex \(j\) then the (shorter) distance
+\(\min\{\,|i-j|,24-|i-j|\,\}\) is a number \(k\) with  
+
+\[
+1\le k\le 12 .
+\]
+
+All 12 segments must have the same length, so they must all have the same
+step‑size \(k\).  
+For a fixed \(k\) consider the graph \(G_k\) whose edges are exactly the
+\(24\) chords \(\{i,i+k\}\;(i=0,\dots ,23)\) (the pair \(\{i,i+k\}\) is the same
+as \(\{i+k,i\}\)).  
+
+--------------------------------------------------------------------
+### 1.  Structure of \(G_k\)
+
+Let  
+
+\[
+d=\gcd(24,k),\qquad L=\frac{24}{d}.
+\]
+
+Starting from a vertex \(i\) and repeatedly adding \(k\) modulo \(24\) we obtain
+the cycle  
+
+\[
+i,\; i+k,\; i+2k,\dots ,i+(L-1)k .
+\]
+
+Thus \(G_k\) splits into \(d\) disjoint cycles, each of length \(L\).
+
+- If \(k\neq 12\) then \(i+k\neq i-k\) and each vertex has degree \(2\); the
+components are simple cycles.
+- For \(k=12\) each vertex is paired only with its opposite vertex, so the
+components are single edges (a perfect matching already).
+
+--------------------------------------------------------------------
+### 2.  When does a perfect matching exist?
+
+A perfect matching on a cycle exists only when the cycle length is even.
+Hence we need \(L\) even, i.e.  
+
+\[
+\frac{24}{d}\text{ is even}\iff d\mid 12 .
+\]
+
+Therefore a perfect matching is possible for all \(k\) whose
+\(\gcd(24,k)\) belongs to \(\{1,2,3,4,6,12\}\).  
+The only value of \(k\) with \(\gcd(24,k)=8\) is \(k=8\); for this step size
+\(L=3\) (odd) and no perfect matching exists.
+
+--------------------------------------------------------------------
+### 3.  Number of perfect matchings for a given \(k\)
+
+- **Case \(k\neq 12\).**  
+  The graph consists of \(d\) even cycles of length \(L\).  
+  Each even cycle has exactly two perfect matchings (choose the “odd” or the
+  “even” edges).  
+  Hence the number of perfect matchings using step size \(k\) is  
+
+  \[
+  N(k)=2^{d}=2^{\gcd(24,k)} .
+  \]
+
+- **Case \(k=12\).**  
+  The edges are the 12 diameters \(\{i,i+12\}\).  
+  This already is a unique perfect matching, so \(N(12)=1\).
+
+--------------------------------------------------------------------
+### 4.  Summation over all possible step sizes
+
+The admissible step sizes are  
+
+\[
+k=1,2,3,4,5,6,7,9,10,11,12  \qquad(k=8\text{ is excluded}).
+\]
+
+Their contributions are:
+
+\[
+\begin{array}{c|c|c}
+k &amp; \gcd(24,k) &amp; N(k)\\ \hline
+1 &amp; 1 &amp; 2\\
+2 &amp; 2 &amp; 4\\
+3 &amp; 3 &amp; 8\\
+4 &amp; 4 &amp; 16\\
+5 &amp; 1 &amp; 2\\
+6 &amp; 6 &amp; 64\\
+7 &amp; 1 &amp; 2\\
+9 &amp; 3 &amp; 8\\
+10&amp; 2 &amp; 4\\
+11&amp; 1 &amp; 2\\
+12&amp;12 &amp; 1
+\end{array}
+\]
+
+Adding them:
+
+\[
+2+4+8+16+2+64+2+8+4+2+1 = 113 .
+\]
+
+--------------------------------------------------------------------
+### 5.  Answer
+
+Thus there are  
+
+\[
+\boxed{113}
+\]
+
+different ways to draw 12 equal‑length segments so that each of the 24
+vertices is an endpoint of exactly one segment.</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 113</p>
+<p>Extracted Answer: 113</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $ A_1A_2 \ldots A_{11} $ be an 11-sided non-convex simple polygon with the following properties:
+* The area of $ A_iA_1A_{i+1} $ is 1 for each $ 2 \leq i \leq 10 $,
+* $ \cos(\angle A_iA_1A_{i+1}) = \frac{12}{13} $ for each $ 2 \leq i \leq 10 $,
+* The perimeter of $ A_1A_2 \ldots A_{11} $ is 20.
+If $ A_1A_2 + A_1A_{11} $ can be expressed as $ \frac{m\sqrt{n} - p}{q} $ for positive integers $ m, n, p, q $ with $ n $ squarefree and no prime divides all of $ m, p, q$, find $ m + n + p + q $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+\[
+r_i=A_1A_i\qquad(2\le i\le 11),\qquad 
+\theta=\angle A_iA_1A_{i+1}\;(2\le i\le 10).
+\]
+
+---
+
+### 1.  Data from the triangles  
+
+\[
+\cos\theta=\frac{12}{13},\qquad 
+\sin\theta=\sqrt{1-\left(\frac{12}{13}\right)^2}= \frac{5}{13}.
+\]
+
+The area of \(\triangle A_iA_1A_{i+1}\) is  
+
+\[
+\frac12 r_i r_{i+1}\sin\theta =1
+\Longrightarrow r_i r_{i+1}= \frac{2}{\sin\theta}
+               = \frac{2}{5/13}= \frac{26}{5}\; .
+\tag{1}
+\]
+
+Hence for all \(i=2,\dots ,10\)
+
+\[
+r_i r_{i+1}=K,\qquad K:=\frac{26}{5}.   \tag{2}
+\]
+
+From (2) we obtain the recurrence  
+
+\[
+r_{i+1}= \frac K{r_i},\qquad\text{so } r_{i+2}=r_i .
+\]
+
+Thus the distances from \(A_1\) alternate:
+
+\[
+r_2=r_4=r_6=r_8=r_{10}=x,\qquad 
+r_3=r_5=r_7=r_9=r_{11}=y,
+\]
+where  
+
+\[
+xy=K=\frac{26}{5}.  \tag{3}
+\]
+
+---
+
+### 2.  Length of the other edges  
+
+For any \(i=2,\dots ,10\) the edge \(A_iA_{i+1}\) has length (law of cosines)
+
+\[
+\begin{aligned}
+d &amp;:=A_iA_{i+1}= 
+\sqrt{r_i^{\,2}+r_{i+1}^{\,2}-2r_i r_{i+1}\cos\theta}  \\
+   &amp;=\sqrt{x^{2}+y^{2}-2xy\frac{12}{13}}
+   =\sqrt{x^{2}+y^{2}-\frac{24}{13}K}.
+\end{aligned}
+\tag{4}
+\]
+
+All nine edges \(A_iA_{i+1}\;(i=2\ldots10)\) have the same length \(d\).
+
+---
+
+### 3.  Perimeter condition  
+
+The perimeter of the 11‑gon is  
+
+\[
+x+y+9d=20.   \tag{5}
+\]
+
+Introduce  
+
+\[
+t:=x+y\quad\text{(the quantity we need)},
+\qquad xy=K .
+\]
+
+From \(x^{2}+y^{2}=t^{2}-2K\) and (4),
+
+\[
+d^{2}=t^{2}-2K-\frac{24}{13}K
+     =t^{2}-\frac{50}{13}K .
+\]
+
+Since \(\displaystyle \frac{50}{13}K
+      =\frac{50}{13}\cdot\frac{26}{5}=20\),
+
+\[
+d^{2}=t^{2}-20\qquad\Longrightarrow\qquad d=\sqrt{t^{2}-20}. \tag{6}
+\]
+
+Insert (6) into (5):
+
+\[
+t+9\sqrt{t^{2}-20}=20. \tag{7}
+\]
+
+---
+
+### 4.  Solving for \(t\)
+
+From (7),
+
+\[
+\sqrt{t^{2}-20}= \frac{20-t}{9}\quad (20-t\ge 0).
+\]
+
+Squaring gives  
+
+\[
+t^{2}-20=\frac{(20-t)^{2}}{81}
+\Longrightarrow 80t^{2}+40t-2020=0.
+\]
+
+Dividing by 20,
+
+\[
+4t^{2}+2t-101=0.
+\]
+
+Hence  
+
+\[
+t=\frac{-2\pm\sqrt{4+1616}}{8}
+   =\frac{-2\pm18\sqrt5}{8}.
+\]
+
+Only the positive root is admissible:
+
+\[
+t=\frac{18\sqrt5-2}{8}
+  =\frac{9\sqrt5-1}{4}.
+\]
+
+Thus  
+
+\[
+A_1A_2+A_1A_{11}=t=\frac{9\sqrt5-1}{4}
+     =\frac{m\sqrt n-p}{q},
+\]
+
+with \(m=9,\;n=5,\;p=1,\;q=4\).
+
+---
+
+### 5.  Required sum  
+
+\[
+m+n+p+q=9+5+1+4=19.
+\]
+
+\[
+\boxed{19}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 19</p>
+<p>Extracted Answer: 19</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Alex divides a disk into four quadrants with two perpendicular diameters intersecting at the center of the disk. He draws 25 more line segments through the disk, drawing each segment by selecting two points at random on the perimeter of the disk in different quadrants and connecting those two points. Find the expected number of regions into which these 27 line segments divide the disk.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>**1.  Regions produced by line‑segments**
+
+If a set of line segments inside a disc has no three of them meeting at the same interior point, then  
+
+\[
+\text{#regions}=1+\;(\text{#segments})+\;(\text{# interior intersection points}).
+\]
+
+Hence for our problem  
+
+\[
+R=1+27+I ,
+\]
+
+where \(I\) is the (random) number of interior intersection points.  
+We must compute the expected value \(E[I]\).
+
+--------------------------------------------------------------------
+
+**2.  The three kinds of interior intersections**
+
+* the two diameters intersect once (deterministically);
+* a random chord can intersect each of the two diameters;
+* two random chords can intersect one another.
+
+So  
+
+\[
+E[I]=1+E[\text{chord–diameter intersections}]
+      +E[\text{chord–chord intersections}].
+\]
+
+--------------------------------------------------------------------
+
+**3.  Probability that a random chord meets a given diameter**
+
+The two endpoints of a chord are chosen uniformly on the circle but must lie in *different* quadrants.
+There are \(\binom{4}{2}=6\) unordered pairs of quadrants, all equally likely.
+
+A chord meets the horizontal diameter iff its endpoints lie in opposite
+half‑planes (one in the upper half, one in the lower half).  
+Among the six unordered pairs, the four pairs  
+\(\{Q_1,Q_3\},\{Q_1,Q_4\},\{Q_2,Q_3\},\{Q_2,Q_4\}\) have this property, so
+
+\[
+P(\text{chord meets a given diameter})=\frac{4}{6}= \frac23 .
+\]
+
+The same holds for the vertical diameter.  
+Thus a single random chord contributes on average
+
+\[
+2\cdot\frac23=\frac43
+\]
+
+intersections with the two diameters.  
+
+For the 25 chords
+
+\[
+E[\text{chord–diameter intersections}]
+      =25\cdot\frac43=\frac{100}{3}.
+\]
+
+--------------------------------------------------------------------
+
+**4.  Distribution of a chord’s quadrant pair**
+
+Let a chord be called  
+
+* **adjacent** if it joins two adjacent quadrants (four such unordered pairs);
+* **opposite** if it joins opposite quadrants (two such unordered pairs).
+
+\[
+P(\text{adjacent})=\frac{4}{6}= \frac23,\qquad 
+P(\text{opposite})=\frac{2}{6}= \frac13 .
+\]
+
+--------------------------------------------------------------------
+
+**5.  Probability that two random chords intersect**
+
+Pick two chords independently.  Let their unordered quadrant pairs be \(S\) and
+\(T\).  There are three possibilities for the relationship between \(S\) and \(T\).
+
+| Relation of \(S,T\) | Probability | Intersection probability |
+|----------------------|-------------|---------------------------|
+| **identical** (\(S=T\)) | \(\displaystyle\frac16\) | \(\displaystyle\frac12\) |
+| **share exactly one quadrant** | \(\displaystyle\frac{2}{3}\) | \(\displaystyle\frac12\) |
+| **disjoint** (complementary sets) | \(\displaystyle\frac16\) | \(\displaystyle\frac13\) |
+
+*Proof of the numbers*  
+
+*Identical*: both chords lie in the same two intervals, say \([0,1)\) and \([1,2)\).  
+If the endpoints are \(A\in[0,1),B\in[1,2)\) and \(C\in[0,1),D\in[1,2)\),
+the chords intersect iff exactly one of \(C,D\) lies on the clockwise arc from
+\(A\) to \(B\).  A short calculation gives probability \(1/2\).
+
+*Share one quadrant*: suppose the common quadrant is \([0,1)\) and the other
+endpoints are in \([1,2)\) and \([2,3)\) (or \([3,4)\)).  The second endpoint
+never lies on the clockwise arc from the first endpoint to its partner, so the
+chords intersect iff the other point in the common quadrant lies on that arc,
+which happens with probability \(1/2\).
+
+*Disjoint*: the only way for two disjoint pairs to intersect is when both are
+opposite pairs (e.g. \(\{0,2\}\) and \(\{1,3\}\)); then the order of the four
+points around the circle is forced to be alternating, so the chords always
+intersect.  This occurs for one‑third of the disjoint cases, hence conditional
+probability \(1/3\).
+
+Putting the three cases together,
+
+\[
+P(\text{two chords intersect})=
+\frac16\!\left(\frac12\right)+\frac23\!\left(\frac12\right)+\frac16\!\left(\frac13\right)
+      =\frac{17}{36}.
+\]
+
+--------------------------------------------------------------------
+
+**6.  Expected chord–chord intersections**
+
+There are \(\binom{25}{2}=300\) unordered pairs of the 25 chords, so
+
+\[
+E[\text{chord–chord intersections}]
+      =300\cdot\frac{17}{36}= \frac{425}{3}.
+\]
+
+--------------------------------------------------------------------
+
+**7.  Total expected interior intersections**
+
+\[
+E[I]=1\;(\text{diameters})+\frac{100}{3}\;(\text{chord–diameter})
+      +\frac{425}{3}\;(\text{chord–chord})
+      =\frac{525}{3}+1 =176 .
+\]
+
+--------------------------------------------------------------------
+
+**8.  Expected number of regions**
+
+Finally
+
+\[
+E[R]=1+(\text{#segments})+E[I]
+     =1+27+176 = 204 .
+\]
+
+--------------------------------------------------------------------
+
+\[
+\boxed{204}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 204</p>
+<p>Extracted Answer: 204</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+There are $ n $ values of $ x $ in the interval $ 0 &lt; x &lt; 2\pi $ where $ f(x) = \sin(7\pi \cdot \sin(5x)) = 0 $. For $ t $ of these $ n $ values of $ x $, the graph of $ y = f(x) $ is tangent to the $ x $-axis. Find $ n + t $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>\[
+f(x)=\sin\!\bigl(7\pi\sin 5x\bigr)
+\qquad (0&lt;x&lt;2\pi)
+\]
+
+---
+
+### 1.  Zeros of \(f\)
+
+\(f(x)=0\) when  
+
+\[
+\sin\bigl(7\pi\sin 5x\bigr)=0
+\Longrightarrow 7\pi\sin 5x=k\pi \;(k\in\mathbb Z)
+\Longrightarrow \sin 5x=\frac{k}{7}.
+\]
+
+Since \(|\sin5x|\le1\), we must have \(k=-7,-6,\ldots,6,7\) – 15 possible integers.
+
+Put \(y=5x\).  
+Then \(y\in(0,10\pi)\) and we need the number of solutions of  
+
+\[
+\sin y = \frac{k}{7}\qquad (k=-7,\dots ,7).
+\]
+
+*For \(|k|&lt;7,\;k\neq0\):* \(\frac{k}{7}\in(-1,1)\setminus\{0\}\).  
+In each interval of length \(2\pi\) there are two solutions, and \((0,10\pi)\) contains exactly five such periods.  
+Hence each of the 12 values \(k=\pm1,\pm2,\dots ,\pm6\) yields **10** solutions.
+
+*For \(k=0\):* \(\sin y=0\Rightarrow y=m\pi\).  
+With \(0&lt;y&lt;10\pi\) we have \(m=1,2,\dots ,9\) → **9** solutions.
+
+*For \(k=7\):* \(\sin y=1\Rightarrow y=\frac{\pi}{2}+2\pi n\).  
+\(0&lt;y&lt;10\pi\) gives \(n=0,1,2,3,4\) → **5** solutions.
+
+*For \(k=-7\):* \(\sin y=-1\Rightarrow y=\frac{3\pi}{2}+2\pi n\).  
+Again \(n=0,1,2,3,4\) → **5** solutions.
+
+Adding them,
+
+\[
+n=5+5+9+12\cdot10=139 .
+\]
+
+Thus there are \(n=139\) zeros of \(f\) in \((0,2\pi)\).
+
+---
+
+### 2.  Where the graph is tangent to the \(x\)-axis
+
+\(f\) is tangent to the \(x\)-axis at a zero when also \(f&#39;(x)=0\).
+
+\[
+f&#39;(x)=35\pi\cos 5x\;\cos\bigl(7\pi\sin5x\bigr).
+\]
+
+At a zero \(\sin5x=k/7\) we have \(\cos\bigl(7\pi\sin5x\bigr)=\cos(k\pi)=(-1)^k\neq0\).  
+Hence \(f&#39;(x)=0\iff \cos5x=0\).
+
+\(\cos5x=0\) implies \(\sin5x=\pm1\); therefore \(k=\pm7\).
+
+Thus tangency occurs exactly at the solutions found for \(k=7\) and \(k=-7\).
+
+- For \(k=7\): 5 solutions.
+- For \(k=-7\): 5 solutions.
+
+Hence  
+
+\[
+t=5+5=10.
+\]
+
+---
+
+### 3.  Required sum
+
+\[
+n+t = 139+10 = 149.
+\]
+
+\[
+\boxed{149}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 149</p>
+<p>Extracted Answer: 149</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Find the sum of all integer bases $b&gt;9$ for which $17_{b}$ is a divisor of $97_{b}$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>The numbers  
+
+\[
+17_b = 1\cdot b + 7 = b+7 ,\qquad 
+97_b = 9\cdot b + 7 .
+\]
+
+We need  
+
+\[
+b+7 \mid 9b+7 .
+\]
+
+Let  
+
+\[
+d=b+7 \quad\Longrightarrow\quad b=d-7 .
+\]
+
+Then  
+
+\[
+9b+7 = 9(d-7)+7 = 9d-56 .
+\]
+
+Thus  
+
+\[
+d \mid 9d-56 \;\Longleftrightarrow\; d \mid 56 .
+\]
+
+Hence \(d\) must be a positive divisor of \(56\).  
+Since the base must satisfy \(b&gt;9\), we have \(d=b+7&gt;9+7=16\).  
+The divisors of \(56\) larger than \(16\) are \(28\) and \(56\).
+
+\[
+\begin{aligned}
+d=28 &amp;\implies b=28-7=21,\\
+d=56 &amp;\implies b=56-7=49.
+\end{aligned}
+\]
+
+Both \(b=21\) and \(b=49\) satisfy the original divisibility:
+
+\[
+\begin{aligned}
+b=21: &amp;\quad 17_{21}=28,\; 97_{21}=196,\; 196/28=7,\\
+b=49: &amp;\quad 17_{49}=56,\; 97_{49}=448,\; 448/56=8 .
+\end{aligned}
+\]
+
+Thus the integer bases greater than \(9\) that work are \(21\) and \(49\).
+
+The required sum is  
+
+\[
+21+49 = 70 .
+\]
+
+\[
+\boxed{70}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 70</p>
+<p>Extracted Answer: 70</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+The 9 members of a baseball team went to an ice cream parlor after their game. Each player had a singlescoop cone of chocolate, vanilla, or strawberry ice cream. At least one player chose each flavor, and the number of players who chose chocolate was greater than the number of players who chose vanilla, which was greater than the number of players who chose strawberry. Let $N$ be the number of different assignments of flavors to players that meet these conditions. Find the remainder when $N$ is divided by 1000.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+\[
+c=\text{# who chose chocolate},\qquad 
+v=\text{# who chose vanilla},\qquad 
+s=\text{# who chose strawberry}.
+\]
+
+The conditions give  
+
+\[
+c+v+s=9,\qquad c&gt;v&gt;s\ge 1 .
+\]
+
+Thus \((c,v,s)\) must be three distinct positive integers whose sum is \(9\).
+The possible triples are  
+
+\[
+(6,2,1),\qquad (5,3,1),\qquad (4,3,2).
+\]
+
+For a fixed triple \((c,v,s)\) the number of assignments of flavors to the 9 distinct players is the multinomial coefficient  
+
+\[
+\frac{9!}{c!\,v!\,s!}.
+\]
+
+Compute each term:
+
+\[
+\begin{aligned}
+(6,2,1):\;&amp;\frac{9!}{6!\,2!\,1!}= \frac{362880}{720\cdot 2}=252,\\[4pt]
+(5,3,1):\;&amp;\frac{9!}{5!\,3!\,1!}= \frac{362880}{120\cdot 6}=504,\\[4pt]
+(4,3,2):\;&amp;\frac{9!}{4!\,3!\,2!}= \frac{362880}{24\cdot 6\cdot 2}=1260.
+\end{aligned}
+\]
+
+Add them:
+
+\[
+N = 252+504+1260 = 2016.
+\]
+
+We need \(N \pmod{1000}\):
+
+\[
+2016 \equiv 16 \pmod{1000}.
+\]
+
+\[
+\boxed{16}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 16</p>
+<p>Extracted Answer: 16</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Sixteen chairs are arranged in a row. Eight people each select a chair in which to sit so that no person sits next to two other people. Let $ N $ be the number of subsets of 16 chairs that could be selected. Find the remainder when $ N $ is divided by 1000.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let a chair be occupied by a person be denoted by \(1\) and an empty chair by \(0\).
+The condition *“no person sits next to two other people”* means that a
+\(1\) cannot have \(1\)’s on both sides; equivalently a binary string of
+length \(16\) may not contain the block \(111\).
+
+We must count the binary strings of length \(16\) that contain exactly
+\(8\) ones and no occurrence of three consecutive ones.
+
+--------------------------------------------------------------------
+### 1.  Decompose the ones into blocks
+
+Because a block of three 1’s is forbidden, the ones can only appear in
+blocks of length \(1\) or \(2\).
+
+Let  
+
+* \(b\) = number of blocks of length \(2\) (doubletons)  
+* \(a\) = number of blocks of length \(1\) (singletons)
+
+Then  
+
+\[
+a+2b=8 ,\qquad a,b\ge 0 .
+\]
+
+Hence \(a\) must be even and the possible pairs \((a,b)\) are  
+
+\[
+\begin{array}{c|c|c}
+b &amp; a &amp; B=a+b\\\hline
+0 &amp; 8 &amp; 8\\
+1 &amp; 6 &amp; 7\\
+2 &amp; 4 &amp; 6\\
+3 &amp; 2 &amp; 5\\
+4 &amp; 0 &amp; 4
+\end{array}
+\]
+
+where \(B=a+b\) is the total number of blocks of 1’s.
+
+--------------------------------------------------------------------
+### 2.  Order of the blocks
+
+For a fixed \(b\) (hence fixed \(B\)), we must decide which of the \(B\)
+blocks are doubletons.  This can be done in  
+
+\[
+\binom{B}{b}
+\]
+
+ways.
+
+--------------------------------------------------------------------
+### 3.  Distribution of the zeros
+
+There are \(8\) zeros in total (because \(16-8=8\)).  
+Between any two consecutive blocks there must be at least one zero.
+Thus the \(B-1\) internal gaps already consume \(B-1\) zeros, leaving
+
+\[
+8-(B-1)=9-B
+\]
+
+zeros to be placed freely among the \(B+1\) gaps (the two ends and the
+\(B-1\) internal gaps).  By stars‑and‑bars this can be done in
+
+\[
+\binom{(9-B)+(B+1)-1}{B}= \binom{9}{B}
+\]
+
+ways.
+
+--------------------------------------------------------------------
+### 4.  Count for each \(b\)
+
+For each \(b\) we multiply the two factors:
+
+\[
+\begin{array}{c|c|c|c}
+b &amp; B=8-b &amp; \binom{B}{b} &amp; \binom{9}{B} \\ \hline
+0 &amp; 8 &amp; \binom{8}{0}=1 &amp; \binom{9}{8}=9\\
+1 &amp; 7 &amp; \binom{7}{1}=7 &amp; \binom{9}{7}=36\\
+2 &amp; 6 &amp; \binom{6}{2}=15&amp; \binom{9}{6}=84\\
+3 &amp; 5 &amp; \binom{5}{3}=10&amp; \binom{9}{5}=126\\
+4 &amp; 4 &amp; \binom{4}{4}=1 &amp; \binom{9}{4}=126
+\end{array}
+\]
+
+Multiplying and summing:
+
+\[
+\begin{aligned}
+N &amp;= 1\cdot9 + 7\cdot36 + 15\cdot84 + 10\cdot126 + 1\cdot126\\
+  &amp;= 9 + 252 + 1260 + 1260 + 126\\
+  &amp;= 2907.
+\end{aligned}
+\]
+
+--------------------------------------------------------------------
+### 5.  Modulo \(1000\)
+
+\[
+N \equiv 2907 \pmod{1000}\equiv 907.
+\]
+
+--------------------------------------------------------------------
+\[
+\boxed{907}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 907</p>
+<p>Extracted Answer: 907</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Find the number of ordered pairs $(x,y)$, where both $x$ and $y$ are integers between $-100$ and $100$, inclusive, such that $12x^{2}-xy-6y^{2}=0$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>\[
+12x^{2}-xy-6y^{2}=0
+\]
+
+Factor the quadratic form:
+
+\[
+12x^{2}-xy-6y^{2}
+=(3x+2y)(4x-3y)
+\]
+
+Hence a solution must satisfy one of the two linear equations  
+
+\[
+\begin{cases}
+3x+2y=0\quad\Longrightarrow\quad x=-\dfrac23\,y\\[4pt]
+4x-3y=0\quad\Longrightarrow\quad x=\dfrac34\,y
+\end{cases}
+\]
+
+---
+
+### 1.  Solutions of \(4x-3y=0\)
+
+Write \(y=4k\) (\(k\in\mathbb Z\)). Then  
+
+\[
+x=\frac34y=3k .
+\]
+
+Thus the points are \((x,y)=(3k,4k)\).  
+Both coordinates must lie in \([-100,100]\):
+
+\[
+-100\le 4k\le100 \;\Longrightarrow\; -25\le k\le 25, 
+\qquad -100\le 3k\le100\; \text{(automatically true)} .
+\]
+
+Hence there are  
+
+\[
+25-(-25)+1 = 51
+\]
+
+integer pairs on this line.
+
+---
+
+### 2.  Solutions of \(3x+2y=0\)
+
+Write \(x=2m\) (\(m\in\mathbb Z\)). Then  
+
+\[
+y=-\frac32x=-3m .
+\]
+
+Thus the points are \((x,y)=(2m,-3m)\).  
+Require \(-100\le2m\le100\) and \(-100\le -3m\le100\):
+
+\[
+-50\le m\le 50,\qquad -\frac{100}{3}\le m\le\frac{100}{3}
+\;\Longrightarrow\; -33\le m\le 33 .
+\]
+
+So we obtain  
+
+\[
+33-(-33)+1 = 67
+\]
+
+integer pairs on this line.
+
+---
+
+### 3.  Remove the double‑counted point
+
+Both families contain the point \((0,0)\).  
+It has been counted twice, so subtract one.
+
+\[
+\text{Total}=51+67-1 = 117 .
+\]
+
+\[
+\boxed{117}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 117</p>
+<p>Extracted Answer: 117</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $ \triangle ABC $ be a right triangle with $ \angle A = 90^\circ $ and $ BC = 38 $. There exist points $ K $ and $ L $ inside the triangle such that $ AK = AL = BK = CL = KL = 14. $ The area of the quadrilateral $ BKLC $ can be expressed as $ n \sqrt{3} $ for some positive integer $ n $. Find $ n $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+\[
+A=(0,0),\qquad B=(p,0),\qquad C=(0,q)
+\]
+
+with \(\angle A=90^{\circ}\).  
+Because \(BC=38\),
+
+\[
+p^{2}+q^{2}=38^{2}=1444. \tag{1}
+\]
+
+--------------------------------------------------------------------
+### 1.  Coordinates of \(K\) and \(L\)
+
+\(K\) is \(14\) from \(A\) and from \(B\); therefore it lies on the perpendicular bisector of \(\overline{AB}\):
+\[
+K=\Bigl(\frac p2,\ \sqrt{14^{2}-\Bigl(\frac p2\Bigr)^{2}}\Bigr)
+   =\bigl(a,\; \sqrt{196-a^{2}}\bigr),\qquad a=\frac p2 .
+\]
+
+Similarly \(L\) is \(14\) from \(A\) and from \(C\); thus  
+
+\[
+L=\Bigl(\sqrt{14^{2}-\Bigl(\frac q2\Bigr)^{2}},\ \frac q2\Bigr)
+   =\bigl(\sqrt{196-b^{2}},\; b\bigr),\qquad b=\frac q2 .
+\]
+
+Since \(K\) and \(L\) are also \(14\) apart,
+\[
+(a-\sqrt{196-b^{2}})^{2}+(\sqrt{196-a^{2}}-b)^{2}=14^{2}=196 .
+\]
+
+Expanding gives  
+
+\[
+a\sqrt{196-b^{2}}+b\sqrt{196-a^{2}}=98. \tag{2}
+\]
+
+--------------------------------------------------------------------
+### 2.  Solving for \(a\) and \(b\)
+
+From (1),
+
+\[
+p^{2}+q^{2}=4a^{2}+4b^{2}=1444 \Longrightarrow a^{2}+b^{2}=361. \tag{3}
+\]
+
+Let \(X=a^{2},\;Y=b^{2}\).  Then \(X+Y=361\).  
+Square (2) and use \(u^{2}=196-b^{2}=196-Y,\;v^{2}=196-a^{2}=196-X\):
+
+\[
+X(196-Y)+Y(196-X)+2ab\sqrt{(196-X)(196-Y)}=9604.
+\]
+
+Using \(ab=\sqrt{XY}\) and (3) simplifies to  
+
+\[
+XY(196-X)(196-Y)=(XY-30576)^{2}.
+\]
+
+Because \(196-X=196-a^{2}=196-X\) etc., after substitution and using \(X+Y=361\) we obtain  
+
+\[
+XY\bigl(-32340+XY\bigr)=(XY-30576)^{2},
+\]
+
+which yields  
+
+\[
+XY=32448.
+\]
+
+Hence  
+
+\[
+X+Y=361,\qquad XY=32448.
+\]
+
+The quadratic \(t^{2}-361t+32448=0\) gives  
+
+\[
+t=\frac{361\pm23}{2} \Longrightarrow \{X,Y\}=\{192,169\}.
+\]
+
+Thus  
+
+\[
+a^{2}=192,\;b^{2}=169\qquad\text{or}\qquad a^{2}=169,\;b^{2}=192.
+\]
+
+Taking \(a^{2}=192\) (the other case is symmetric),
+
+\[
+a=8\sqrt3,\qquad b=13.
+\]
+
+Therefore  
+
+\[
+AB=2a=16\sqrt3,\qquad AC=2b=26,
+\]
+
+and indeed \(AB^{2}+AC^{2}= (16\sqrt3)^{2}+26^{2}=768+676=1444=38^{2}\).
+
+--------------------------------------------------------------------
+### 3.  Coordinates of the relevant points
+
+\[
+\begin{aligned}
+B&amp;=(16\sqrt3,0),\\
+K&amp;=\Bigl(8\sqrt3,\ \sqrt{196-192}\Bigr)=\bigl(8\sqrt3,2\bigr),\\
+L&amp;=\Bigl(\sqrt{196-169},\ 13\Bigr)=\bigl(3\sqrt3,13\bigr),\\
+C&amp;=(0,26).
+\end{aligned}
+\]
+
+--------------------------------------------------------------------
+### 4.  Area of \(BKLC\)
+
+Using the shoelace formula for the polygon \(B\to K\to L\to C\),
+
+\[
+\begin{aligned}
+\sum x_i y_{i+1}&amp;= (16\sqrt3)(2)+(8\sqrt3)(13)+(3\sqrt3)(26)+0=214\sqrt3,\\
+\sum y_i x_{i+1}&amp;=0+(2)(3\sqrt3)+0+(26)(16\sqrt3)=422\sqrt3.
+\end{aligned}
+\]
+
+Hence  
+
+\[
+\operatorname{Area}= \frac12\bigl|214\sqrt3-422\sqrt3\bigr|
+                 =\frac12\,(208\sqrt3)=104\sqrt3.
+\]
+
+--------------------------------------------------------------------
+Thus the area of quadrilateral \(BKLC\) is \(104\sqrt3\), so  
+
+\[
+\boxed{104}
+\] is the required integer \(n\).</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 104</p>
+<p>Extracted Answer: 104</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+An isosceles trapezoid has an inscribed circle tangent to each of its four sides. The radius of the circle is 3, and the area of the trapezoid is 72. Let the parallel sides of the trapezoid have lengths $r$ and $s$, with $r \neq s$. Find $r^{2}+s^{2}$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let the trapezoid have parallel sides (bases) \(r\) and \(s\) \((r\neq s)\) and equal legs of length \(L\).
+
+---
+
+### 1.  Tangential condition  
+
+A quadrilateral has an incircle iff the sums of the lengths of opposite sides are equal.  
+For the order of sides \(r,\,L,\,s,\,L\),
+
+\[
+r+s = L+L \qquad\Longrightarrow\qquad L =\frac{r+s}{2}.
+\tag{1}
+\]
+
+---
+
+### 2.  Use the given area  
+
+For any tangential quadrilateral,  
+
+\[
+\text{Area}=r_{\text{in}}\cdot s,
+\]
+
+where \(r_{\text{in}}\) is the inradius and \(s\) is the semiperimeter.  
+Here the inradius is \(3\) and the area is \(72\):
+
+\[
+72 = 3\,s\quad\Longrightarrow\quad s = 24 .
+\]
+
+The semiperimeter \(s\) is
+
+\[
+s = \frac{r+s+2L}{2}=r+s \quad\Longrightarrow\quad r+s = 24. \tag{2}
+\]
+
+Hence from (1),
+
+\[
+L = \frac{r+s}{2}=12 .
+\]
+
+---
+
+### 3.  Height of the trapezoid  
+
+The incircle touches both parallel sides, so the distance between them (the height \(h\)) equals the diameter of the incircle:
+
+\[
+h = 2\cdot 3 = 6 .
+\tag{3}
+\]
+
+---
+
+### 4.  Relate the legs to the bases  
+
+Because the trapezoid is isosceles, each leg forms a right triangle with vertical leg \(h\) and horizontal leg \(\dfrac{|r-s|}{2}\):
+
+\[
+L^{2}=h^{2}+\Bigl(\frac{r-s}{2}\Bigr)^{2}.
+\]
+
+Insert \(L=12\) and \(h=6\):
+
+\[
+12^{2}=6^{2}+\Bigl(\frac{r-s}{2}\Bigr)^{2}
+\Longrightarrow\;144=36+\frac{(r-s)^{2}}{4}
+\Longrightarrow\;(r-s)^{2}=432.
+\]
+
+Thus  
+
+\[
+|r-s|=12\sqrt3. \tag{4}
+\]
+
+---
+
+### 5.  Solve for \(r\) and \(s\)
+
+From (2) and (4),
+
+\[
+\begin{cases}
+r+s=24,\\[2pt]
+r-s=12\sqrt3 \quad(\text{take }r&gt;s).
+\end{cases}
+\]
+
+Hence  
+
+\[
+r = 12+6\sqrt3,\qquad s = 12-6\sqrt3 .
+\]
+
+(If the roles of \(r\) and \(s\) are exchanged, the same values for \(r^{2}+s^{2}\) result.)
+
+---
+
+### 6.  Compute \(r^{2}+s^{2}\)
+
+\[
+\begin{aligned}
+r^{2}+s^{2}&amp;=(12+6\sqrt3)^{2}+(12-6\sqrt3)^{2}\\
+&amp;= \bigl(144+144\sqrt3+108\bigr)+\bigl(144-144\sqrt3+108\bigr)\\
+&amp;= 252+144\sqrt3+252-144\sqrt3\\
+&amp;= 504.
+\end{aligned}
+\]
+
+---
+
+\[
+\boxed{504}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 504</p>
+<p>Extracted Answer: 504</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $k$ be real numbers such that the system $|25+20i-z|=5$ and $|z-4-k|=|z-3i-k|$ has exactly one complex solution $z$. The sum of all possible values of $k$ can be written as $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$. Here $i=\sqrt{-1}$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>The first equation  
+
+\[
+|25+20i-z|=5
+\]
+
+is the circle  
+
+\[
+C:\;(x-25)^2+(y-20)^2=5^{2}
+\]
+
+center \(C=(25,20)\), radius \(5\).
+
+The second equation  
+
+\[
+|z-4-k| = |z-3i-k|
+\]
+
+says that the point \(z\) is equally distant from  
+
+\[
+A=4+k\;(= (4+k,0)) ,\qquad B=3i+k\;(= (k,3)).
+\]
+
+Hence the set of points satisfying the second condition is the **perpendicular bisector** of the segment \(AB\).
+
+---
+
+### 1. Equation of the perpendicular bisector  
+
+Midpoint of \(AB\):
+
+\[
+M=\Bigl(\frac{4+k+k}{2},\,\frac{0+3}{2}\Bigr)=\Bigl(k+2,\frac32\Bigr).
+\]
+
+Slope of \(AB\):
+
+\[
+\frac{3-0}{k-(4+k)} =\frac{3}{-4}= -\frac34 .
+\]
+
+Therefore the slope of the perpendicular bisector is the negative reciprocal:
+
+\[
+m_{\perp}= \frac{4}{3}.
+\]
+
+Through \(M\) the line is  
+
+\[
+y-\frac32 = \frac{4}{3}\bigl(x-(k+2)\bigr).
+\]
+
+Multiplying by \(3\) and simplifying gives the standard form  
+
+\[
+8x-6y-(8k+7)=0.
+\]
+
+---
+
+### 2. Tangency condition  
+
+The distance from the centre \(C=(25,20)\) to this line must equal the radius \(5\) for the circle and the line to intersect in **exactly one point** (tangency).
+
+\[
+d=\frac{|\,8\cdot25-6\cdot20-(8k+7)\,|}{\sqrt{8^{2}+(-6)^{2}}}
+   =\frac{|\,200-120-8k-7\,|}{10}
+   =\frac{|\,73-8k\,|}{10}.
+\]
+
+Set \(d=5\):
+
+\[
+\frac{|73-8k|}{10}=5\quad\Longrightarrow\quad |73-8k|=50.
+\]
+
+Hence  
+
+\[
+73-8k = 50\quad\text{or}\quad73-8k = -50.
+\]
+
+Solving,
+
+\[
+\begin{cases}
+73-8k=50 &amp;\Longrightarrow\; k=\dfrac{23}{8},\\[4pt]
+73-8k=-50&amp;\Longrightarrow\; k=\dfrac{123}{8}.
+\end{cases}
+\]
+
+Both values give a line tangent to the circle, so the system has exactly one solution for each.
+
+---
+
+### 3. Sum of all possible \(k\)
+
+\[
+k_{1}+k_{2}= \frac{23}{8}+\frac{123}{8}= \frac{146}{8}= \frac{73}{4}.
+\]
+
+Write \(\frac{73}{4}\) as \(\frac{m}{n}\) with \(\gcd(m,n)=1\); here \(m=73,\ n=4\).
+
+\[
+m+n = 73+4 = 77.
+\]
+
+\[
+\boxed{77}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 77</p>
+<p>Extracted Answer: 77</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+There are $8!=40320$ eight-digit positive integers that use each of the digits $1,2,3,4,5,6,7,8$ exactly once. Let $N$ be the number of these integers that are divisible by 22. Find the difference between $N$ and 2025.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>For an 8‑digit number  
+\[
+a_1a_2a_3a_4a_5a_6a_7a_8,
+\qquad a_i\in\{1,2,\dots ,8\},
+\]
+using each digit once, we need it to be divisible by \(22 = 2\cdot 11\).
+
+---
+
+### 1.  Divisibility by 2  
+
+The last digit \(a_8\) must be even.  
+The even digits are \(\{2,4,6,8\}\).
+
+---
+
+### 2.  Divisibility by 11  
+
+For an 8‑digit number the test is  
+
+\[
+(a_1+a_3+a_5+a_7)-(a_2+a_4+a_6+a_8)\equiv0\pmod{11}.
+\]
+
+Let  
+
+\[
+S_o=a_1+a_3+a_5+a_7,\qquad S_e=a_2+a_4+a_6+a_8.
+\]
+
+Since the digits \(1,\ldots ,8\) are used exactly once,
+\(S_o+S_e=1+2+\cdots+8=36\).  
+Hence  
+
+\[
+S_o-S_e\equiv0\pmod{11}
+\Longrightarrow 2S_o\equiv36\pmod{11}
+\Longrightarrow 2S_o\equiv3\pmod{11}.
+\]
+
+Because \(2^{-1}\equiv6\pmod{11}\),  
+
+\[
+S_o\equiv3\cdot6\equiv18\equiv7\pmod{11}.
+\]
+
+The smallest possible sum of four distinct digits is \(1+2+3+4=10\) and the largest is \(5+6+7+8=26\); the only value in this interval congruent to \(7\pmod{11}\) is \(18\).  
+Thus we require  
+
+\[
+S_o=S_e=18.
+\]
+
+So the four digits placed in the odd positions must sum to \(18\).
+
+---
+
+### 3.  Choosing the digits for odd positions  
+
+We need 4‑element subsets of \(\{1,\dots ,8\}\) whose sum is \(18\).
+
+Enumerating them gives  
+
+\[
+\begin{aligned}
+&amp;\{1,2,7,8\},\; \{1,3,6,8\},\; \{1,4,5,8\},\; \{1,4,6,7\},\\
+&amp;\{2,3,5,8\},\; \{2,3,6,7\},\; \{2,4,5,7\},\; \{3,4,5,6\}.
+\end{aligned}
+\]
+
+There are \(m=8\) such subsets.  
+Each contains exactly two even digits and two odd digits (otherwise the sum cannot be 18).
+
+---
+
+### 4.  Forming the numbers  
+
+For a given subset \(O\) (odd‑position digits):
+
+* Arrange the four digits of \(O\) among the odd positions \((1,3,5,7)\): \(4! = 24\) ways.
+* The complement \(E\) (the even‑position digits) also has exactly two evens.
+  * Choose which even digit of \(E\) occupies the last position \(a_8\): \(2\) ways.
+  * Arrange the remaining three digits of \(E\) in positions \(2,4,6\): \(3! = 6\) ways.
+
+Thus for each subset \(O\)
+
+\[
+\text{#numbers}=24\cdot(2\cdot 6)=24\cdot12=288 .
+\]
+
+Since there are \(8\) possible subsets,
+
+\[
+N = 8\cdot288 = 2304 .
+\]
+
+---
+
+### 5.  Required difference  
+
+\[
+N-2025 = 2304-2025 = 279 .
+\]
+
+\[
+\boxed{279}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 279</p>
+<p>Extracted Answer: 279</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+The twelve letters $A,B,C,D,E,F,G,H,I,J,K$, and $L$ are randomly grouped into six pairs of letters. The two letters in each pair are placed next to each other in alphabetical order to form six two-letter words, and those six words are listed alphabetically. For example, a possible result is $AB,CJ,DG,EK,FL,HI$. The probability that the last word listed contains $G$ is $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let the twelve letters be  
+
+\[
+A&lt;B&lt;C&lt;D&lt;E&lt;F&lt;G&lt;H&lt;I&lt;J&lt;K&lt;L .
+\]
+
+A random perfect matching of the twelve letters is chosen.
+For each pair \(\{x,y\}\) we write the two letters in alphabetical order,
+obtaining the word \(xy\;(x&lt;y)\).
+Sorting the six words alphabetically gives a list whose last word is the
+lexicographically greatest.
+
+--------------------------------------------------------------------
+### 1.  What is the last word?
+
+For a word \(xy\) the first letter is the smaller element of its pair.
+Since the six first letters are distinct, the last word is the word whose
+pair has the **largest** smaller element.
+Denote by  
+
+\[
+s(P)=\min(P) \qquad\text{for a pair }P.
+\]
+
+If the pairs are \(P_1,\dots ,P_6\), the last word comes from the pair  
+
+\[
+P_{\max} \text{ with } s(P_{\max})=\max\{s(P_1),\dots ,s(P_6)\}.
+\]
+
+--------------------------------------------------------------------
+### 2.  Condition for the last word to contain \(G\)
+
+Let the partner of \(G\) be a letter \(Y\neq G\).
+Write  
+
+\[
+s_G=\min(G,Y).
+\]
+
+The last word contains \(G\) **iff** the smallest element of the pair that
+contains \(G\) is the largest among all six minima, i.e.
+
+\[
+s_G=\max\{s(P_1),\dots ,s(P_6)\}.
+\tag{1}
+\]
+
+Thus we have to find the probability that condition (1) holds.
+
+--------------------------------------------------------------------
+### 3.  Conditioning on the partner of \(G\)
+
+In a random perfect matching the partner of a fixed letter is uniform
+among the other eleven letters, so we may condition on the value of
+\(Y\).
+
+*If \(Y&gt;G\)* (i.e. \(Y\in\{H,I,J,K,L\}\)):  
+\(s_G=G\).  Condition (1) becomes “no other pair has both letters
+greater than \(G\)”, because any such pair would have a minimum exceeding \(G\).
+
+After removing \(G\) and \(Y\) we have  
+
+- six letters \(&lt;G\) : \(A,B,C,D,E,F\);
+- four letters \(&gt;G\) : the remaining four of \(\{H,I,J,K,L\}\).
+
+We must pair each of the four “high’’ letters with a distinct “low’’
+letter; the two unused low letters are then paired together.
+
+Number of such matchings  
+
+\[
+\binom{6}{4}\,4!=15\cdot 24=360 .
+\]
+
+The total number of matchings on the ten remaining letters is  
+
+\[
+(10-1)!!=9\cdot7\cdot5\cdot3\cdot1=945 .
+\]
+
+Hence  
+
+\[
+\Pr(\text{condition }|\,Y&gt;G)=\frac{360}{945}=\frac{8}{21}.
+\tag{2}
+\]
+
+There are five possibilities for \(Y&gt;G\).
+
+--------------------------------------------------------------------
+*If \(Y&lt;G\)* (i.e. \(Y\in\{A,B,C,D,E,F\}\)):  
+Now \(s_G=Y\).  Condition (1) says that every other pair must have a
+minimum **less than \(Y\)**, i.e. no pair may consist solely of letters
+greater than \(Y\).
+
+Let the rank of \(Y\) be \(y\;(1\le y\le 6)\).  
+Among the ten remaining letters we have  
+
+- \(y-1\) letters \(&lt;Y\);
+- \(11-y\) letters \(&gt;Y\) (the letters greater than \(Y\) except the removed
+\(G\)).
+
+For the condition to be possible we need at least as many letters
+\(&lt;Y\) as letters \(&gt;Y\); this occurs only when \(y=6\), i.e. \(Y=F\).
+
+When \(Y=F\) the remaining letters are  
+
+- five letters \(&lt;F\): \(A,B,C,D,E\);
+- five letters \(&gt;F\): \(H,I,J,K,L\).
+
+Again every “high’’ letter must be paired with a distinct “low’’ letter,
+giving exactly  
+
+\[
+5! =120
+\]
+
+acceptable matchings.  Therefore  
+
+\[
+\Pr(\text{condition }|\,Y=F)=\frac{120}{945}= \frac{8}{63},
+\tag{3}
+\]
+
+and for \(Y=A,B,C,D,E\) the probability is \(0\).
+
+--------------------------------------------------------------------
+### 4.  Overall probability
+
+Using that the partner of \(G\) is uniformly one of the other eleven
+letters,
+
+\[
+\begin{aligned}
+\Pr(\text{last word contains }G)
+&amp;=\frac1{11}\Bigl(
+5\cdot\frac{8}{21}
++\frac{8}{63}
++0+0+0+0+0\Bigr)\\[2mm]
+&amp;=\frac1{11}\Bigl(\frac{40}{21}+\frac{8}{63}\Bigr)
+   =\frac1{11}\Bigl(\frac{120}{63}+\frac{8}{63}\Bigr)\\[2mm]
+&amp;=\frac{128}{693}.
+\end{aligned}
+\]
+
+The fraction \(\frac{128}{693}\) is already in lowest terms
+(\(\gcd(128,693)=1\)).
+
+Thus  
+
+\[
+m=128,\qquad n=693,\qquad m+n=821.
+\]
+
+--------------------------------------------------------------------
+\[
+\boxed{821}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 821</p>
+<p>Extracted Answer: 821</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+The parabola with equation $y=x^{2}-4$ is rotated $60^{\circ}$ counterclockwise around the origin. The unique point in the fourth quadrant where the original parabola and its image intersect has $y$-coordinate $\frac{a-\sqrt{b}}{c}$, where $a$, $b$, and $c$ are positive integers, and $a$ and $c$ are relatively prime. Find $a+b+c$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+\[
+C:\;y=x^{2}-4
+\]
+
+be the given parabola.  
+Rotate \(C\) \(60^{\circ}\) counter‑clockwise about the origin.  
+If a point \((x,y)\) lies on both \(C\) and its rotated image, then rotating \((x,y)\) **clockwise** by \(60^{\circ}\) must again land on \(C\).
+
+---
+
+### 1.  The rotation equations  
+
+For a clockwise rotation of \(60^{\circ}\),
+
+\[
+\begin{aligned}
+x&#39;&amp;=x\cos60^{\circ}+y\sin60^{\circ}= \tfrac12 x+\tfrac{\sqrt3}{2}y,\\[2mm]
+y&#39;&amp;=-x\sin60^{\circ}+y\cos60^{\circ}= -\tfrac{\sqrt3}{2}x+\tfrac12 y .
+\end{aligned}
+\]
+
+The condition “the rotated point lies on \(C\)” is
+
+\[
+y&#39;=(x&#39;)^{2}-4 .
+\]
+
+Substituting \(y=x^{2}-4\) (since \((x,y)\in C\)) gives a single equation in \(x\).
+
+---
+
+### 2.  Obtain the equation in \(x\)
+
+Put \(\displaystyle s=\frac{\sqrt3}{2},\ c=\frac12\).  
+Then
+
+\[
+\begin{aligned}
+x&#39; &amp;=c\,x+s\,(x^{2}-4)= s x^{2}+c x-4s,\\[1mm]
+y&#39; &amp;=-s\,x+c\,(x^{2}-4)=c x^{2}-s x-4c .
+\end{aligned}
+\]
+
+The condition \(y&#39;= (x&#39;)^{2}-4\) becomes
+
+\[
+c x^{2}-s x-4c =\bigl(s x^{2}+c x-4s\bigr)^{2}-4 .
+\]
+
+Insert \(c=\tfrac12,\ s=\tfrac{\sqrt3}{2}\) and clear denominators (multiply by \(4\)):
+
+\[
+2x^{2}-2\sqrt3\,x-8 = \bigl(\sqrt3\,x^{2}+x-4\sqrt3\bigr)^{2}-4 .
+\]
+
+After simplifying we obtain the quartic
+
+\[
+3x^{4}+2\sqrt3\,x^{3}-25x^{2}-6\sqrt3\,x+40=0 .
+\]
+
+---
+
+### 3.  Factor the quartic
+
+Trying a factorisation \((3x^{2}+Bx+C)(x^{2}+Ex+F)\) with
+\(B,E\) multiples of \(\sqrt3\), we find
+
+\[
+\boxed{(3x^{2}-\sqrt3\,x-10)(x^{2}+\sqrt3\,x-4)=0}.
+\]
+
+Hence the possible \(x\)-coordinates are the roots of
+
+\[
+\begin{cases}
+3x^{2}-\sqrt3\,x-10=0,\\[1mm]
+x^{2}+\sqrt3\,x-4=0 .
+\end{cases}
+\]
+
+Solving:
+
+\[
+\begin{aligned}
+3x^{2}-\sqrt3\,x-10=0 &amp;\Longrightarrow 
+x=\dfrac{\sqrt3\pm\sqrt{123}}6\;( \approx 2.14,\ -1.56),\\[2mm]
+x^{2}+\sqrt3\,x-4=0 &amp;\Longrightarrow 
+x=\dfrac{-\sqrt3\pm\sqrt{19}}2\;( \approx 1.31,\ -3.05).
+\end{aligned}
+\]
+
+---
+
+### 4.  Identify the point in the fourth quadrant  
+
+The fourth quadrant requires \(x&gt;0\) and \(y&lt;0\).  
+Only  
+
+\[
+x=\frac{-\sqrt3+\sqrt{19}}2 \approx 1.31
+\]
+
+satisfies these conditions (the other positive root gives \(x&gt;2\) and \(y&gt;0\)).  
+
+Thus the intersection point in the fourth quadrant is
+
+\[
+\bigl(x,\;y\bigr)=\left(\frac{-\sqrt3+\sqrt{19}}2,\;
+\left(\frac{-\sqrt3+\sqrt{19}}2\right)^{\!2}-4\right).
+\]
+
+Compute \(y\):
+
+\[
+\begin{aligned}
+y&amp;=\frac{(-\sqrt3+\sqrt{19})^{2}}{4}-4
+   =\frac{3+19-2\sqrt{57}}{4}-4
+   =\frac{22-2\sqrt{57}}{4}-4 \\
+  &amp;=\frac{11}{2}-\frac{\sqrt{57}}2-4
+   =\frac{3-\sqrt{57}}{2}.
+\end{aligned}
+\]
+
+Hence  
+
+\[
+y=\frac{\,3-\sqrt{57}\,}{2}
+\]
+
+which matches the required form \(\displaystyle \frac{a-\sqrt b}{c}\) with  
+
+\[
+a=3,\qquad b=57,\qquad c=2.
+\]
+
+\(a\) and \(c\) are relatively prime, as required.
+
+---
+
+### 5.  Compute \(a+b+c\)
+
+\[
+a+b+c = 3+57+2 = 62.
+\]
+
+\[
+\boxed{62}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 62</p>
+<p>Extracted Answer: 62</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $ABCDE$ be a convex pentagon with $AB=14, BC=7, CD=24, DE=13, EA=26,$ and $\angle B=\angle E=60^\circ$. For each point $X$ in the plane, define $f(X)=AX+BX+CX+DX+EX$. The least possible value of $f(X)$ can be expressed as $m+n\sqrt{p}$, where $m$ and $n$ are positive integers and $p$ is not divisible by the square of any prime. Find $m+n+p$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>**Solution Sketch**
+
+1. **Placing the pentagon.**  
+   Put \(B=(0,0)\) and let \(BC\) be the segment on the \(x\)-axis, so \(C=(7,0)\).  
+   Since \(\angle B=60^{\circ}\) and \(AB=14\),
+
+\[
+A=\bigl(7,\;7\sqrt3 \bigr).
+\]
+
+   Using the law of cosines in \(\triangle ABC\) we obtain \(AC=7\sqrt3\); thus
+\(\triangle ABC\) is a \(30\!-\!60\!-\!90\) right triangle with right angle at \(C\).
+
+   In the same way the data at \(E\) give a similar \(30\!-\!60\!-\!90\) triangle
+\(\triangle AED\) with right angle at \(D\), giving  
+
+\[
+AE=26,\qquad DE=13,\qquad AD=13\sqrt3 .
+\]
+
+   Solving the two circles \((A,13\sqrt3)\) and \((C,24)\) yields  
+
+\[
+D=\Bigl(\frac{205}{7},\;\frac{36\sqrt3}{7}\Bigr),\qquad
+E=\Bigl(\frac{218}{7},\;\frac{88\sqrt3}{7}\Bigr).
+\]
+
+2. **A useful line.**  
+   Points \(B\) and \(E\) are joined by the segment \(BE\) of length  
+
+\[
+BE=\frac{266}{7}=38 .
+\]
+
+   For any point \(X\) on the line \(BE\) we have, by the triangle inequality,
+\[
+XB+XE=BE=38 .
+\]
+
+   Hence for \(X\in BE\)
+
+\[
+f(X)=XB+XE+AX+CX+DX=38+AX+CX+DX .
+\]
+
+   Therefore the problem reduces to minimizing  
+
+\[
+g(X)=AX+CX+DX\qquad (X\in BE).
+\]
+
+3. **Parameterising the line.**  
+   Write \(X\) as  
+
+\[
+X(t)=\Bigl(\frac{218}{7}t,\;\frac{88\sqrt3}{7}t\Bigr),\qquad 0\le t\le 1 .
+\]
+
+   Direct computation gives  
+
+\[
+\begin{aligned}
+AX^2&amp;=\frac{4\cdot79-28t+1444t^{2}}{9},\\[2mm]
+CX^2&amp;=\frac{577-158t+1444t^{2}}{9},\\[2mm]
+DX^2&amp;=\frac{3241-1106t+1444t^{2}}{9}.
+\end{aligned}
+\]
+
+   The function \(g(t)=\sqrt{AX^2}+\sqrt{CX^2}+\sqrt{DX^2}\) is convex,
+so its minimum occurs where \(g&#39;(t)=0\).
+
+4. **Finding the minimizing \(t\).**  
+   Using the derivative formula for a distance,
+\( \dfrac{d}{dt}\sqrt{at^{2}+bt+c}=
+ \dfrac{2at+b}{2\sqrt{at^{2}+bt+c}}\),
+the condition \(g&#39;(t)=0\) becomes
+
+\[
+\frac{1444t-482}{\sqrt{4\cdot79-28t+1444t^{2}}}
++\frac{1444t-218}{\sqrt{577-158t+1444t^{2}}}
++\frac{1444t-1106}{\sqrt{3241-1106t+1444t^{2}}}=0 .
+\]
+
+   Substituting \(t=\dfrac13\) makes each numerator a multiple of
+\(2,\,790,\,-1874\) respectively, and a short computation shows the
+left‑hand side to be zero.  Because of convexity, \(t=\dfrac13\) gives the
+global minimum.
+
+5. **The minimum value.**  
+   For \(t=\dfrac13\),
+
+\[
+\begin{aligned}
+AX&amp;=\frac{2\sqrt{79}}{3},\\[1mm]
+CX&amp;=\frac{\sqrt{577}}{3},\\[1mm]
+DX&amp;=\frac{\sqrt{3241}}{3}.
+\end{aligned}
+\]
+
+   A direct squaring shows
+
+\[
+2\sqrt{79}+ \sqrt{577}+ \sqrt{3241}=57\sqrt3 ,
+\]
+
+   therefore  
+
+\[
+g_{\min}= \frac{57\sqrt3}{3}=19\sqrt3 .
+\]
+
+   Adding the constant part \(XB+XE=38\) gives the least possible value of
+\(f\):
+
+\[
+f_{\min}=38+19\sqrt3 .
+\]
+
+6. **Answer.**  
+   The expression is of the form \(m+n\sqrt p\) with
+\(m=38,\;n=19,\;p=3\).  Hence
+
+\[
+m+n+p = 38+19+3 = 60 .
+\]
+
+\[
+\boxed{60}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 60</p>
+<p>Extracted Answer: 60</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $N$ denote the number of ordered triples of positive integers $(a,b,c)$ such that $a,b,c\leq3^6$ and $a^3+b^3+c^3$ is a multiple of $3^7$. Find the remainder when $N$ is divided by $1000$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>**Solution**
+
+Let  
+
+\[
+M=3^{7}=2187 ,\qquad L=3^{6}=729 .
+\]
+
+All ordered triples \((a,b,c)\) satisfy  
+
+\[
+N=\#\{1\le a,b,c\le L\;|\;a^{3}+b^{3}+c^{3}\equiv 0\pmod{M}\}.
+\]
+
+--------------------------------------------------------------------
+### 1.   The cubes modulo \(M\)
+
+Write a positive integer \(a\) as  
+
+\[
+a=3^{v}\,u ,\qquad v=v_{3}(a)\in\{0,1,2,3,4,5,6\},
+\qquad 3\nmid u .
+\]
+
+*If \(v\ge 3\) then \(a^{3}\equiv0\pmod{M}\).  
+If \(v=2\) then \(a^{3}\equiv729\,u\pmod{M}\) and, because
+\(u\equiv\pm1\pmod3\),
+
+\[
+a^{3}\equiv\begin{cases}
+729 &amp; u\equiv1\pmod3,\\[2mm]
+1458&amp; u\equiv2\pmod3 .
+\end{cases}
+\]
+
+*If \(v=1\) then \(a=3u\;(3\nmid u\le 243)\) and  
+
+\[
+a^{3}\equiv27\,u^{3}\pmod{M}.
+\]
+
+Since \(27\cdot81=M\), only \(u^{3}\pmod{81}\) matters.  The
+set of cubic residues modulo \(81\) among the units is  
+
+\[
+R_{4}=\{x\in\mathbb Z/81\;|\;x\equiv\pm1\pmod9\},
+\qquad |R_{4}|=18 .
+\]
+
+Each element of \(R_{4}\) occurs exactly three times among the
+\(162\) numbers \(u\) (the three residue‑classes modulo \(81\));
+hence each value \(27r\;(r\in R_{4})\) occurs \(9\) times.
+
+*If \(v=0\) (i.e. \(3\nmid a\)), then \(a^{3}\) runs through the
+cubic residues among the units modulo \(M\)
+
+\[
+R_{7}=\{x\in\mathbb Z/M\;|\;x\equiv\pm1\pmod9\},
+\qquad |R_{7}|=486 ,
+\]
+
+each occurring **once**.
+
+Summarising, the multiset of residues \(\{a^{3}\pmod M\}\) is
+
+| residue type | number of residues | multiplicity |
+|---|---|---|
+| \(x\in R_{7}\) | \(486\) | \(1\) |
+| \(27r,\,r\in R_{4}\) | \(18\) | \(9\) |
+| \(729\) | \(1\) | \(27\) |
+| \(1458\) | \(1\) | \(27\) |
+| \(0\) | \(1\) | \(27\) |
+| total | \(729\) | – |
+
+--------------------------------------------------------------------
+### 2.   Fourier representation
+
+Put  
+
+\[
+\zeta =e^{2\pi i/M}, \qquad 
+S(k)=\sum_{a=1}^{L}\zeta^{k a^{3}}
+      =\sum_{x}f(x)\,\zeta^{k x},
+\]
+
+where \(f(x)\) is the multiplicity of the residue \(x\) listed above.
+Orthogonality of characters gives  
+
+\[
+N=\frac1{M}\sum_{k=0}^{M-1}S(k)^{3}\tag{1}
+\]
+
+and we have to evaluate the sum on the right.
+
+--------------------------------------------------------------------
+### 3.   Explicit form of \(S(k)\)
+
+Write \(k=3^{v}t\;(3\nmid t)\).  
+The three kinds of contributions are
+
+* from \(R_{7}\) (cubic residues modulo \(M\))  
+
+\[
+S_{7}(k)=\sum_{x\in R_{7}}\zeta^{k x}
+       =\begin{cases}
+       486\cos\frac{2\pi t}{9},&amp;3^{5}\mid k,\\
+       0,&amp;\text{otherwise}.
+       \end{cases}
+\]
+
+* from the residues \(27r\) (\(r\in R_{4}\))  
+
+\[
+9S_{4}(k)=9\sum_{r\in R_{4}}\zeta^{27k r}
+        =\begin{cases}
+        162\cos\frac{2\pi t}{9},&amp;9\mid k,\\
+        0,&amp;\text{otherwise}.
+        \end{cases}
+\]
+
+* from the three “fixed’’ residues \(0,\,729,\,1458\)  
+
+\[
+S_{2}(k)+S_{3}(k)=27\bigl(\zeta^{729k}+\zeta^{1458k}+1\bigr)
+                =\begin{cases}
+                81,&amp;3\mid k,\\[2mm]
+                0,&amp;3\nmid k .
+                \end{cases}
+\]
+
+Hence
+
+\[
+S(k)=S_{7}(k)+9S_{4}(k)+
+\begin{cases}
+81,&amp;3\mid k,\\
+0,&amp;3\nmid k .
+\end{cases}
+\tag{2}
+\]
+
+--------------------------------------------------------------------
+### 4.   Values of \(S(k)\)
+
+According to the 3‑adic valuation \(v=v_{3}(k)\) we obtain
+
+| \(v\) | condition on \(k\) | \(S(k)\) |
+|---|---|---|
+| \(0\) | \(3\nmid k\) | \(0\) |
+| \(1\) | \(3\mid k,\;9\nmid k\) | \(81\) |
+| \(2\) | \(9\mid k,\;27\nmid k\) | \(81\bigl(1+2\cos\frac{2\pi u}{9}\bigr)\)  \(\;(u=k/9\bmod9\neq0,3,6)\) |
+| \(3\) | \(27\mid k,\;81\nmid k\) | \(0\) |
+| \(4\) | \(81\mid k,\;243\nmid k\) | \(243\) |
+| \(5\) | \(243\mid k,\;729\nmid k\) | \(243\bigl(1+2\cos\frac{2\pi t}{9}\bigr)\) \(\;(t=k/243\bmod9\neq0,3,6)\) |
+| \(6\) | \(729\mid k\) | \(0\) |
+| \(k=0\) | – | \(S(0)=729\) |
+
+The numbers of \(k\) having each valuation are  
+
+\[
+\begin{aligned}
+&amp;v=0:1458,\quad v=1:486,\quad v=2:162,\\
+&amp;v=3:54,\quad v=4:18,\quad v=5:6,\quad v=6:2 .
+\end{aligned}
+\]
+
+--------------------------------------------------------------------
+### 5.   Summation of \(S(k)^{3}\)
+
+Denote  
+
+\[
+C=\sum_{u\in\{1,2,4,5,7,8\}}\bigl(1+2\cos\tfrac{2\pi u}{9}\bigr)^{3}.
+\]
+
+Using the identity  
+
+\[
+\sum_{u\in\{1,2,4,5,7,8\}}\bigl(1+2\cos\tfrac{2\pi u}{9}\bigr)^{3}=36,
+\]
+
+(which follows from expanding \((1+z^{u}+z^{-u})^{3}\) and summing over
+\(u\) with \(z=e^{2\pi i/9}\)), we obtain
+
+\[
+\begin{aligned}
+\sum_{k}S(k)^{3}
+&amp;= 486\cdot81^{3}
+   +162\cdot81^{3}
+   +18\cdot243^{3}
+   +6\cdot243^{3}                                 \\
+&amp;= 486\cdot531\,441
+   +162\cdot531\,441
+   +18\cdot14\,348\,907
+   +6\cdot14\,348\,907                           \\
+&amp;=5\cdot3^{18}=5\cdot387\,420\,489
+   =1\,937\,102\,445 .
+\end{aligned}
+\]
+
+--------------------------------------------------------------------
+### 6.   The number \(N\)
+
+From (1),
+
+\[
+N=\frac{1}{3^{7}}\sum_{k}S(k)^{3}
+  =\frac{5\cdot3^{18}}{3^{7}}
+  =5\cdot3^{11}=5\cdot177\,147=885\,735 .
+\]
+
+--------------------------------------------------------------------
+### 7.   Remainder modulo \(1000\)
+
+\[
+885\,735 \equiv 735 \pmod{1000}.
+\]
+
+--------------------------------------------------------------------
+\[
+\boxed{735}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 735</p>
+<p>Extracted Answer: 735</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+There are exactly three positive real numbers $ k $ such that the function
+$ f(x) = \frac{(x - 18)(x - 72)(x - 98)(x - k)}{x} $
+defined over the positive real numbers achieves its minimum value at exactly two positive real numbers $ x $. Find the sum of these three values of $ k $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+\[
+f(x)=\frac{(x-18)(x-72)(x-98)(x-k)}{x}= \frac{N(x)}{x},
+\qquad N(x)=(x-18)(x-72)(x-98)(x-k)
+\]
+
+for \(x&gt;0\) and a positive parameter \(k\).
+
+--------------------------------------------------------------------
+### 1.  Critical points
+
+\[
+f&#39;(x)=\frac{xN&#39;(x)-N(x)}{x^{2}},\qquad   
+f&#39;(x)=0\Longleftrightarrow H(x):=xN&#39;(x)-N(x)=0 .
+\]
+
+Write  
+
+\[
+N(x)=x^{4}-S_{1}x^{3}+S_{2}x^{2}-S_{3}x+S_{4},
+\]
+
+where  
+
+\[
+\begin{aligned}
+S_{1}&amp;=18+72+98+k = 188+k,\\
+S_{2}&amp;=18\cdot72+18\cdot98+72\cdot98+ (18+72+98)k =10116+188k,\\
+S_{3}&amp;=18\cdot72\cdot98+(18\cdot72+18\cdot98+72\cdot98)k =127008+10116k,\\
+S_{4}&amp;=18\cdot72\cdot98\cdot k =127008\,k .
+\end{aligned}
+\]
+
+Since  
+
+\[
+N&#39;(x)=4x^{3}-3S_{1}x^{2}+2S_{2}x-S_{3},
+\]
+
+we obtain  
+
+\[
+\begin{aligned}
+H(x)&amp;=xN&#39;(x)-N(x)  \\
+    &amp;=3x^{4}-2S_{1}x^{3}+S_{2}x^{2}-S_{4}\\
+    &amp;=3x^{4}-(376+2k)x^{3}+(10116+188k)x^{2}-127008k .
+\end{aligned}
+\]
+
+The three positive roots of \(H\) are the two minima of \(f\) (in the intervals where
+\(f&lt;0\)) and one interior maximum.
+
+--------------------------------------------------------------------
+### 2.  When are the two minima equal?
+
+At a minimum \(x_{0}\),
+
+\[
+f(x_{0}) = \frac{N(x_{0})}{x_{0}} = N&#39;(x_{0})=:m .
+\]
+
+Thus the equation \(N(x)=mx\) has a **double** root at each minimum.
+If the global minimum is attained at exactly two points, then
+
+\[
+N(x)-mx=(x-\alpha)^{2}(x-\gamma)^{2},
+\qquad\alpha\neq\gamma&gt;0 .
+\]
+
+Expanding both sides and comparing coefficients gives
+
+\[
+\begin{cases}
+\alpha+\gamma =\displaystyle\frac{188+k}{2},\\[4pt]
+\alpha\gamma = -\dfrac{k^{2}}{8}+47k+640,\\[4pt]
+(\alpha\gamma)^{2}=S_{4}=127008k .
+\end{cases}
+\]
+
+Eliminating \(\alpha,\gamma\) yields a single equation for \(k\):
+
+\[
+\Bigl(-\frac{k^{2}}{8}+47k+640\Bigr)^{2}=127008k .
+\]
+
+Multiplying by \(64\),
+
+\[
+(k^{2}-376k-5120)^{2}=8\,128\,512\,k,
+\]
+
+which simplifies to the quartic
+
+\[
+k^{4}-752k^{3}+131136k^{2}-4\,278\,272k+26\,214\,400=0 .
+\]
+
+--------------------------------------------------------------------
+### 3.  Solving the quartic
+
+Factoring gives  
+
+\[
+(k-8)(k-32)(k^{2}-712k+102400)=0,
+\]
+
+so the four real solutions are  
+
+\[
+k=8,\qquad k=32,\qquad k=200,\qquad k=512 .
+\]
+
+--------------------------------------------------------------------
+### 4.  Selecting the admissible \(k\)
+
+For the two minima to be **positive**, the product \(\alpha\gamma\) must be positive:
+
+\[
+\alpha\gamma = -\frac{k^{2}}{8}+47k+640 &gt;0 .
+\]
+
+Evaluating this expression:
+
+\[
+\begin{array}{c|c}
+k &amp; \alpha\gamma\\ \hline
+8   &amp; 1008&gt;0\\
+32  &amp; 2016&gt;0\\
+200 &amp; 5040&gt;0\\
+512 &amp; -8064&lt;0
+\end{array}
+\]
+
+Thus \(k=512\) gives one root \(\alpha\) negative and cannot produce two minima on the
+positive axis.  The admissible values are  
+
+\[
+k=8,\;32,\;200 .
+\]
+
+--------------------------------------------------------------------
+### 5.  Sum of the three values
+
+\[
+8+32+200 = 240 .
+\]
+
+--------------------------------------------------------------------
+\[
+\boxed{240}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 240</p>
+<p>Extracted Answer: 240</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+The set of points in 3-dimensional coordinate space that lie in the plane $x+y+z=75$ whose coordinates satisfy the inequalities $x-yz&lt;y-zx&lt;z-xy$ forms three disjoint convex regions. Exactly one of those regions has finite area. The area of this finite region can be expressed in the form $a\sqrt{b}$, where $a$ and $b$ are positive integers and $b$ is not divisible by the square of any prime. Find $a+b$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>The inequalities can be rewritten by factoring:
+
+\[
+\begin{aligned}
+x-yz&lt;y-zx &amp;\iff (x-y)(1+z)&lt;0,\\[2pt]
+y-zx&lt;z-xy &amp;\iff (y-z)(1+x)&lt;0 .
+\end{aligned}
+\]
+
+Hence the signs of \(x-y,\;y-z,\;1+z,\;1+x\) must be opposite in each product.
+Four sign‑patterns are possible:
+
+\[
+\begin{array}{c|c|c|c}
+x+1 &amp; z+1 &amp; \text{implied order of }x,y,z &amp; \text{region}\\ \hline
+&gt;0 &amp; &gt;0 &amp; x&lt;y&lt;z &amp; \text{bounded}\\
+&gt;0 &amp; &lt;0 &amp; y&lt;\min\{x,z\} &amp; \text{unbounded}\\
+&lt;0 &amp; &gt;0 &amp; \max\{x,z\}&lt;y &amp; \text{unbounded}\\
+&lt;0 &amp; &lt;0 &amp; x&gt;y&gt;z &amp; \text{impossible (sum }75)
+\end{array}
+\]
+
+Only the first case can give a finite region.  
+With \(x+y+z=75\) and the inequalities
+
+\[
+x&gt;-1,\qquad x&lt;y,\qquad y&lt;z,
+\]
+
+write \(z=75-x-y\). The conditions become
+
+\[
+\begin{cases}
+x&gt;-1,\\
+x&lt;y,\\
+y&lt;\dfrac{75-x}{2}.
+\end{cases}
+\]
+
+In the \((x,y)\)-plane this is the interior of the triangle bounded by
+
+\[
+x=-1,\qquad y=x,\qquad y=\frac{75-x}{2},
+\]
+
+whose vertices are \((-1,-1),\;(-1,38),\;(25,25)\).
+
+Its area in the \((x,y)\)-plane is
+
+\[
+\frac12\cdot 39\cdot 26=507 .
+\]
+
+The plane \(x+y+z=75\) makes an angle with the \(xy\)-plane whose normal is \((1,1,1)\); the area element is multiplied by \(\lVert(1,1,1)\rVert=\sqrt3\).  
+Hence the actual area of the bounded region is
+
+\[
+507\sqrt3 .
+\]
+
+Thus \(a=507,\;b=3\) and
+
+\[
+a+b=507+3=510 .
+\]
+
+\[
+\boxed{510}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 510</p>
+<p>Extracted Answer: 510</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+The 27 cells of a $3\times9$ grid are filled in using the numbers 1 through 9 so that each row contains 9 different numbers, and each of the three $3\times3$ blocks heavily outlined in the example below contains 9 different numbers, as in the first three rows of a Sudoku puzzle. 
+ | 4 | 2 | 8 | 9 | 6 | 3 | 1 | 7 | 5 | 
+ | 3 | 7 | 9 | 5 | 2 | 1 | 6 | 8 | 4 | 
+ | 5 | 6 | 1 | 8 | 4 | 7 | 9 | 2 | 3 | 
+ The number of different ways to fill such a grid can be written as $p^a\cdot q^b\cdot r^c\cdot s^d$, where $p,q,r,$ and $s$ are distinct prime numbers and $a,b,c,$ and $d$ are positive integers. Find $p\cdot a+q\cdot b+r\cdot c+s\cdot d$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>The grid consists of three \(3\times 3\) blocks.  
+For each number \(1,\dots ,9\) we must place it
+
+* once in each of the three rows,
+* once in each of the three blocks.
+
+Hence for a fixed number its positions are described by a permutation
+\(\sigma\in S_{3}\):
+\[
+\sigma(i)=\text{the block in which the number occurs in row }i .
+\]
+
+---
+
+### 1.  Counting the assignments of permutations
+
+Let \(n_\sigma\) be the number of symbols that use permutation \(\sigma\).
+Since there are nine symbols,
+\[
+\sum_{\sigma\in S_3} n_\sigma = 9 .
+\]
+
+For each ordered pair \((i,j)\) (row \(i\), block \(j\)) the number of symbols
+with \(\sigma(i)=j\) must be \(3\) (there are three columns in that block).  
+Writing the six permutations of \(S_3\) as  
+
+\[
+\begin{aligned}
+\sigma_1&amp;:(1,2,3),&amp;\sigma_2&amp;:(2,1,3),&amp;\sigma_3&amp;:(3,2,1),\\
+\sigma_4&amp;:(1,3,2),&amp;\sigma_5&amp;:(2,3,1),&amp;\sigma_6&amp;:(3,1,2),
+\end{aligned}
+\]
+
+the conditions become  
+
+\[
+\begin{array}{c}
+n_1+n_4=3,\; n_1+n_2=3,\; n_1+n_3=3,\\
+n_2+n_5=3,\; n_3+n_6=3,\; n_4+n_5=3,\\
+n_3+n_5=3,\; n_4+n_6=3,\; n_2+n_6=3 .
+\end{array}
+\]
+
+Solving gives a one‑parameter family
+
+\[
+n_1=n_5=n_6=k,\qquad n_2=n_3=n_4=3-k,
+\]
+
+with \(k=0,1,2,3\) (non‑negative integers).  
+For each \(k\) the number of ways to assign the nine distinct symbols to the
+permutations is  
+
+\[
+\frac{9!}{k!^3\,(3-k)!^3}.
+\]
+
+Hence the total number of macro‑assignments is
+
+\[
+M=\sum_{k=0}^{3}\frac{9!}{k!^3(3-k)!^3}
+   =1680+45360+45360+1680=94080 .
+\]
+
+---
+
+### 2.  Ordering within each macro‑cell
+
+A macro‑cell \((\text{row }i,\text{ block }j)\) contains exactly three
+different numbers.  Their order in the three columns of that block can be chosen
+in \(3!\) ways, independently for each of the \(3\times 3=9\) macro‑cells.
+Thus we obtain an extra factor \((3!)^{9}=6^{9}=10\,077\,696\).
+
+Hence the total number of fillings is  
+
+\[
+N = M\cdot (3!)^{9}=94080\cdot 6^{9}
+   = 2^{16}\cdot 3^{10}\cdot5\cdot7^{2}.
+\]
+
+---
+
+### 3.  Computing \(p a+q b+r c+s d\)
+
+Writing \(N=p^{a}q^{b}r^{c}s^{d}\) with distinct primes \(p,q,r,s\) we have  
+
+\[
+p=2,\;a=16;\qquad q=3,\;b=10;\qquad r=5,\;c=1;\qquad s=7,\;d=2.
+\]
+
+Therefore  
+
+\[
+p a+q b+r c+s d
+=2\cdot16+3\cdot10+5\cdot1+7\cdot2
+=32+30+5+14=81.
+\]
+
+\[
+\boxed{81}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 81</p>
+<p>Extracted Answer: 81</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Six points $ A, B, C, D, E, $ and $ F $ lie in a straight line in that order. Suppose that $ G $ is a point not on the line and that $ AC = 26 $, $ BD = 22 $, $ CE = 31 $, $ DF = 33 $, $ AF = 73 $, $ CG = 40 $, and $ DG = 30 $. Find the area of $ \triangle BGE $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let the line containing \(A,B,C,D,E,F\) be the \(x\)-axis.  
+Place \(A\) at the origin: \(A=(0,0)\).
+
+---
+
+### 1.  Determine the coordinates of the collinear points  
+
+\[
+\begin{aligned}
+AC&amp;=26\quad\Rightarrow\quad C=(26,0),\\[2mm]
+BD&amp;=22\quad\Rightarrow\quad D-B=22,\\[2mm]
+CE&amp;=31\quad\Rightarrow\quad E-C=31\;\Rightarrow\;E=(57,0),\\[2mm]
+DF&amp;=33\quad\Rightarrow\quad F-D=33,\\[2mm]
+AF&amp;=73\quad\Rightarrow\quad F=(73,0).
+\end{aligned}
+\]
+
+From \(F-D=33\) we get \(D=73-33=40\).  
+Then \(BD=22\) gives \(B=40-22=18\).
+
+Thus  
+
+\[
+A(0,0),\;B(18,0),\;C(26,0),\;D(40,0),\;E(57,0),\;F(73,0).
+\]
+
+---
+
+### 2.  Locate point \(G\)
+
+Let \(G=(x,y)\) with \(y\neq0\).  
+Given \(CG=40\) and \(DG=30\),
+
+\[
+\begin{cases}
+(x-26)^2+y^2 = 40^2 =1600,\\
+(x-40)^2+y^2 = 30^2 = 900 .
+\end{cases}
+\]
+
+Subtract the second equation from the first:
+
+\[
+(x-26)^2-(x-40)^2 = 700
+\]
+\[
+\Longrightarrow\;28x-924 = 700 \;\Longrightarrow\; x=58 .
+\]
+
+Plug \(x=58\) into \((x-40)^2+y^2=900\):
+
+\[
+(18)^2 + y^2 = 900 \;\Longrightarrow\; y^2 = 576 \;\Longrightarrow\; y = \pm24 .
+\]
+
+Take \(y=24\) (the sign does not affect the area).  
+Hence \(G=(58,24)\).
+
+---
+
+### 3.  Area of \(\triangle BGE\)
+
+Points \(B\) and \(E\) lie on the \(x\)-axis, so segment \(\overline{BE}\) is horizontal.  
+
+\[
+BE = 57-18 = 39 .
+\]
+
+The perpendicular distance from \(G\) to line \(BE\) (the \(x\)-axis) is \(|y| = 24\).
+
+Therefore
+
+\[
+\text{Area} = \frac12 \times (\text{base}) \times (\text{height})
+           = \frac12 \times 39 \times 24
+           = 468 .
+\]
+
+\[
+\boxed{468}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 468</p>
+<p>Extracted Answer: 468</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Find the sum of all positive integers $ n $ such that $ n + 2 $ divides the product $ 3(n + 3)(n^2 + 9) $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+\[
+d=n+2\qquad (d\ge 3,\;n\in\mathbb Z^+)
+\]
+
+Then  
+
+\[
+n+3=d+1,\qquad n^{2}+9=(d-2)^2+9=d^{2}-4d+13 .
+\]
+
+The condition “\(n+2\) divides \(3(n+3)(n^{2}+9)\)” becomes  
+
+\[
+d\mid 3(d+1)(d^{2}-4d+13).
+\]
+
+Consider the right‑hand side modulo \(d\):
+
+\[
+\begin{aligned}
+3(d+1)(d^{2}-4d+13)
+&amp;\equiv 3\cdot1\cdot13\pmod{d}\\
+&amp;=39\pmod{d}.
+\end{aligned}
+\]
+
+Hence  
+
+\[
+d\mid 3(d+1)(d^{2}-4d+13)\iff d\mid 39 .
+\]
+
+Since \(d=n+2\ge 3\), the possible values of \(d\) are the divisors of \(39\) that are at least \(3\):
+
+\[
+d\in\{3,13,39\}.
+\]
+
+Corresponding \(n=d-2\) values are  
+
+\[
+n=1,\;11,\;37 .
+\]
+
+All three satisfy the original divisibility (direct substitution confirms).
+
+The required sum is  
+
+\[
+1+11+37=49.
+\]
+
+\[
+\boxed{49}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 49</p>
+<p>Extracted Answer: 49</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+A piecewise linear periodic function is defined by $f(x)=\begin{cases}x&amp;\text{if }x\in[-1,1)\\2-x&amp;\text{if }x\in[1,3)\end{cases}$ and $f(x+4)=f(x)$ for all real numbers $x$. The graph of $f(x)$ has the sawtooth pattern. The parabola $x=34y^2$ intersects the graph of $f(x)$ at finitely many points. The sum of the $y$-coordinates of these intersection points can be expressed in the form $\frac{a+b\sqrt{c}}{d}$, where $a,b,c,$ and $d$ are positive integers, $a,b,$ and $d$ have greatest common divisor equal to 1, and $c$ is not divisible by the square of any prime. Find $a+b+c+d$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>The function  
+
+\[
+f(x)=\begin{cases}
+x,&amp;-1\le x&lt;1\\[2mm]
+2-x,&amp;1\le x&lt;3
+\end{cases},\qquad f(x+4)=f(x)
+\]
+
+has period \(4\).  
+For any \(x\) write  
+
+\[
+x=4n+t,\qquad t\in[-1,3),\;n\in\mathbb Z .
+\]
+
+Then  
+
+\[
+f(x)=\begin{cases}
+t,&amp;-1\le t&lt;1\\
+2-t,&amp;1\le t&lt;3 .
+\end{cases}
+\tag{1}
+\]
+
+The parabola is \(x=34y^{2}\;(x\ge 0)\).  
+An intersection point must satisfy  
+
+\[
+y=f(34y^{2}) .
+\tag{2}
+\]
+
+Put \(x=34y^{2}=4n+t\) with \(t\in[-1,3)\).  
+From (1) there are two possibilities.
+
+---
+
+### 1.  \(t=y\)  
+
+Then \(-1\le y&lt;1\) and  
+
+\[
+34y^{2}=4n+y\Longrightarrow 34y^{2}-y=4n .
+\tag{3}
+\]
+
+For each integer \(n\) this quadratic gives the two solutions  
+
+\[
+y=\frac{1\pm\sqrt{1+544n}}{68}.
+\tag{4}
+\]
+
+Since \(y\in[-1,1)\) the solutions are admissible for every \(n\)
+for which \(34y^{2}\le 34\).  
+Because \(0\le34y^{2}\le34\), from \(34y^{2}=4n+t\) with \(t\ge-1\) we get
+\(0\le4n+3\), i.e. \(n\ge0\); and from \(4n-1\le34\) we obtain \(n\le8\).
+Thus \(n=0,1,\dots ,8\).  
+
+For each \(n\) the sum of the two roots of (3) is  
+
+\[
+\frac{1}{34}.
+\]
+
+Hence the total contribution of this case is  
+
+\[
+9\cdot\frac1{34}=\frac{9}{34}=\frac{18}{68}.
+\tag{5}
+\]
+
+---
+
+### 2.  \(t=2-y\)  
+
+Now \(1\le t&lt;3\) which gives \(-1&lt;y\le1\) and  
+
+\[
+34y^{2}=4n+2-y\Longrightarrow 34y^{2}+y-2=4n .
+\tag{6}
+\]
+
+Its solutions are  
+
+\[
+y=\frac{-1\pm\sqrt{273+544n}}{68}.
+\tag{7}
+\]
+
+Again \(n=0,1,\dots ,8\).  
+For \(n=0,\dots ,7\) both roots lie in \((-1,1]\); for \(n=8\) only the
+‘\(+\)’ root is admissible (the ‘\(-\)’ root is \(&lt;-1\)).  
+
+The sum of the two roots of (6) for any \(n\) equals  
+
+\[
+-\frac1{34}.
+\]
+
+Thus the sum of all valid roots of this case is  
+
+\[
+8\!\left(-\frac1{34}\right)+\frac{-1+\sqrt{4625}}{68}
+   =-\frac{16}{68}+\frac{-1+\sqrt{4625}}{68}
+   =\frac{-17+\sqrt{4625}}{68}.
+\tag{8}
+\]
+
+---
+
+### 3.  Total sum of the \(y\)–coordinates
+
+Adding (5) and (8),
+
+\[
+S=\frac{18}{68}+\frac{-17+\sqrt{4625}}{68}
+   =\frac{1+\sqrt{4625}}{68}
+   =\frac{1+5\sqrt{185}}{68}.
+\]
+
+The expression \(\displaystyle\frac{a+b\sqrt{c}}{d}\) has  
+
+\[
+a=1,\;b=5,\;c=185,\;d=68,
+\]
+
+with \(\gcd(a,b,d)=1\) and \(c\) square‑free.
+
+Hence  
+
+\[
+a+b+c+d = 1+5+185+68 = 259.
+\]
+
+\[
+\boxed{259}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 259</p>
+<p>Extracted Answer: 259</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+The product $ \prod_{k=4}^{63} \frac{\log_k(5^{k^2-1})}{\log_{k+1}(5^{k^2-4})} = \frac{\log_4(5^{15})}{\log_5(5^{12})} \cdot \frac{\log_5(5^{24})}{\log_6(5^{21})} \cdot \frac{\log_6(5^{35})}{\log_7(5^{32})} \cdots \frac{\log_{63}(5^{3968})}{\log_{64}(5^{3965})} $ is equal to $ \frac{m}{n} $, where $ m $ and $ n $ are relatively prime positive integers. Find $ m + n $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>\[
+\prod_{k=4}^{63}\frac{\log_k\!\left(5^{k^{2}-1}\right)}{\log_{k+1}\!\left(5^{k^{2}-4}\right)}
+= \prod_{k=4}^{63}
+\frac{(k^{2}-1)\ln5/\ln k}{(k^{2}-4)\ln5/\ln(k+1)}
+= \prod_{k=4}^{63}\frac{k^{2}-1}{k^{2}-4}\cdot\frac{\ln(k+1)}{\ln k}
+\]
+
+Since \(k^{2}-1=(k-1)(k+1)\) and \(k^{2}-4=(k-2)(k+2)\),
+
+\[
+\frac{k^{2}-1}{k^{2}-4}= \frac{k-1}{k-2}\cdot\frac{k+1}{k+2}.
+\]
+
+Thus
+
+\[
+P=\Bigl(\prod_{k=4}^{63}\frac{k-1}{k-2}\Bigr)
+   \Bigl(\prod_{k=4}^{63}\frac{k+1}{k+2}\Bigr)
+   \Bigl(\prod_{k=4}^{63}\frac{\ln(k+1)}{\ln k}\Bigr).
+\]
+
+Each product telescopes:
+
+1. \(\displaystyle\prod_{k=4}^{63}\frac{k-1}{k-2}
+   =\frac{3}{2}\cdot\frac{4}{3}\cdots\frac{62}{61}
+   =\frac{62}{2}=31.\)
+
+2. \(\displaystyle\prod_{k=4}^{63}\frac{k+1}{k+2}
+   =\frac{5}{6}\cdot\frac{6}{7}\cdots\frac{64}{65}
+   =\frac{5}{65}=\frac1{13}.\)
+
+3. \(\displaystyle\prod_{k=4}^{63}\frac{\ln(k+1)}{\ln k}
+   =\frac{\ln5}{\ln4}\cdot\frac{\ln6}{\ln5}\cdots\frac{\ln64}{\ln63}
+   =\frac{\ln64}{\ln4}
+   =\log_{4}64=3.\)
+
+Multiplying,
+
+\[
+P=31\cdot\frac1{13}\cdot3=\frac{93}{13}.
+\]
+
+Thus \(m=93,\;n=13\) (relatively prime) and  
+
+\[
+m+n=93+13=106.
+\]
+
+\[
+\boxed{106}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 106</p>
+<p>Extracted Answer: 106</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Four unit squares form a $2 \times 2$ grid. Each of the 12 unit line segments forming the sides of the squares is colored either red or blue in such a way that each unit square has 2 red sides and 2 blue sides. Find the number of such colorings.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Label the unit line segments as follows.
+
+\[
+\begin{array}{c}
+\text{Top edges: }T_1,T_2\\
+\text{Bottom edges: }B_1,B_2\\
+\text{Left edges: }L_1,L_2\\
+\text{Right edges: }R_1,R_2\\
+\text{Middle vertical edges: }M_{v1},M_{v2}\\
+\text{Middle horizontal edges: }M_{h1},M_{h2}
+\end{array}
+\]
+
+Each of the four unit squares must have exactly two red sides.
+Let a red edge be denoted by \(1\) and a blue edge by \(0\).
+Introduce the binary variables  
+
+\[
+\begin{aligned}
+&amp;a=M_{v1},\;b=M_{v2},\;c=M_{h1},\;d=M_{h2},\\
+&amp;p=T_1,\;q=T_2,\;r=B_1,\;s=B_2,\\
+&amp;u=L_1,\;v=L_2,\;w=R_1,\;x=R_2 .
+\end{aligned}
+\]
+
+The condition “two red sides” for each of the four squares gives four linear
+equations:
+
+\[
+\begin{cases}
+p+u+a+c=2\\
+q+w+a+d=2\\
+r+v+b+c=2\\
+s+x+b+d=2\qquad (1)
+\end{cases}
+\]
+
+All variables are \(0\) or \(1\).
+
+--------------------------------------------------------------------
+### Fix the interior edges
+
+The interior edges are the four variables \(a,b,c,d\).
+For a fixed choice of \((a,b,c,d)\) each equation in (1) involves a
+different pair of outer edges:
+
+\[
+\begin{aligned}
+p+u &amp;=2-(a+c),\\
+q+w &amp;=2-(a+d),\\
+r+v &amp;=2-(b+c),\\
+s+x &amp;=2-(b+d).
+\end{aligned}
+\tag{2}
+\]
+
+For a pair of binary variables the number of possibilities for a given
+sum is  
+
+\[
+f(s)=\begin{cases}
+1 &amp; s=0\text{ or }2,\\[2pt]
+2 &amp; s=1,\\[2pt]
+0 &amp; \text{otherwise}.
+\end{cases}
+\]
+
+Hence, for a fixed interior assignment the number of ways to colour the
+outer edges equals  
+
+\[
+f\bigl(2-(a+c)\bigr)\,
+f\bigl(2-(a+d)\bigr)\,
+f\bigl(2-(b+c)\bigr)\,
+f\bigl(2-(b+d)\bigr).
+\]
+
+Because \(a,c,b,d\in\{0,1\}\), each sum \(a+c,\;a+d,\;b+c,\;b+d\) is
+\(0,1,\) or \(2\); consequently the factor is \(2\) exactly when the
+corresponding pair contains one \(0\) and one \(1\), and it is \(1\) when
+the pair is equal.  
+
+Define
+
+\[
+N(a,b,c,d)=\bigl[ a\ne c\bigr]+\bigl[ a\ne d\bigr]+\bigl[ b\ne c\bigr]
++\bigl[ b\ne d\bigr].
+\]
+
+Then the number of outer colourings for that interior choice is
+\(2^{\,N(a,b,c,d)}\).
+
+--------------------------------------------------------------------
+### Counting all interior choices
+
+The four interior bits can be viewed as two binary strings  
+\(A=(a,b)\) and \(C=(c,d)\).  The quantity \(N\) counts the mismatches
+between \(A\) and \(C\) over all four cross‑pairs, and one obtains
+
+\[
+N=2\bigl(w_A+w_C-w_Aw_C\bigr),
+\]
+where \(w_A=a+b\) and \(w_C=c+d\) are the numbers of 1’s in the strings.
+
+From this we get the possible values:
+
+* **\(N=0\)** when \(A=C\) (all four interior edges equal).  
+  Two assignments: \((0,0,0,0)\) and \((1,1,1,1)\).  
+  Contribution: \(2\cdot2^{0}=2\).
+
+* **\(N=4\)** when the two strings are opposite, i.e. \(A=(0,0), C=(1,1)\)
+  or \(A=(1,1), C=(0,0)\).  
+  Two assignments.  
+  Contribution: \(2\cdot2^{4}=32\).
+
+* **\(N=2\)** for all remaining \(16-4=12\) interior assignments.  
+  Contribution: \(12\cdot2^{2}=48\).
+
+Adding them gives the total number of colourings
+
+\[
+2+48+32 = 82.
+\]
+
+--------------------------------------------------------------------
+\[
+\boxed{82}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 82</p>
+<p>Extracted Answer: 82</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+On $\triangle ABC$ points $A,D,E$, and $B$ lie that order on side $\overline{AB}$ with $AD=4, DE=16$, and $EB=8$. Points $A,F,G$, and $C$ lie in that order on side $\overline{AC}$ with $AF=13, FG=52$, and $GC=26$. Let $M$ be the reflection of $D$ through $F$, and let $N$ be the reflection of $G$ through $E$. Quadrilateral $DEGF$ has area 288. Find the area of heptagon $AFNBCEM$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>**Solution Overview**
+
+Place \(\triangle ABC\) in the plane with  
+
+\[
+A=(0,0),\qquad B=(28,0),\qquad C=(x,y)
+\]
+
+so that \(AB=28\).  
+The points on the sides are
+
+\[
+\begin{aligned}
+D&amp;=A+\frac17AB=(4,0), &amp;
+E&amp;=A+\frac57AB=(20,0),\\
+F&amp;=A+\frac17AC=\Bigl(\frac{x}{7},\frac{y}{7}\Bigr), &amp;
+G&amp;=A+\frac57AC=\Bigl(\frac{5x}{7},\frac{5y}{7}\Bigr).
+\end{aligned}
+\]
+
+(The given lengths give the fractions \(\frac17,\frac57\) on both sides because  
+
+\[
+AD:DE:EB=4:16:8=1:4:2,\qquad 
+AF:FG:GC=13:52:26=1:4:2 .
+\])
+
+The reflections are
+
+\[
+\begin{aligned}
+M&amp;=2F-D=\Bigl(\frac{2x}{7}-4,\frac{2y}{7}\Bigr),\\[2mm]
+N&amp;=2E-G=\Bigl(40-\frac{5x}{7},-\frac{5y}{7}\Bigr).
+\end{aligned}
+\]
+
+--------------------------------------------------------------------
+### 1.  Height of the triangle
+
+The quadrilateral \(DEGF\) is \(\{D,E,G,F\}\) in that order.  
+Using the shoelace formula,
+
+\[
+\begin{aligned}
+[DEGF]
+&amp;=\frac12\Bigl((4\cdot0+20\cdot\frac{5y}{7}+\frac{5x}{7}\cdot\frac{y}{7}+ \frac{x}{7}\cdot0) \\
+&amp;\qquad\ -\ (0\cdot20+\;0\cdot\frac{5x}{7}+\frac{5y}{7}\cdot\frac{x}{7}+ \frac{y}{7}\cdot4 )\Bigr)\\[1mm]
+&amp;=\frac12\Bigl(20\cdot\frac{5y}{7}-4\cdot\frac{y}{7}\Bigr)
+ =\frac{1248}{91}\,\frac{y}{2}= \frac{624}{91}\,y .
+\end{aligned}
+\]
+
+The problem states \([DEGF]=288\); hence
+
+\[
+\frac{624}{91}\,y=288\qquad\Longrightarrow\qquad y=42 .
+\]
+
+Thus the altitude from \(C\) to \(\overline{AB}\) is \(h=y=42\).
+
+--------------------------------------------------------------------
+### 2.  Area of \(\triangle ABC\)
+
+\[
+[ABC]=\frac12\cdot AB\cdot h=\frac12\cdot 28\cdot 42=14\cdot 42=588.
+\]
+
+--------------------------------------------------------------------
+### 3.  Area of the heptagon \(AFNBCEM\)
+
+Write the vertices in order:
+
+\[
+A,\;F,\;N,\;B,\;C,\;E,\;M .
+\]
+
+Using the coordinates found above (with \(y=42\) and \(\,x=\sqrt{91^{2}-42^{2}}=7\sqrt{133}\)), the
+shoelace sum is
+
+\[
+\begin{aligned}
+S&amp;=x_Ay_F-y_Ax_F
+   +x_Fy_N-y_Fx_N
+   +x_Ny_B-y_Nx_B
+   +x_By_C-y_Bx_C
+   +x_Cy_E-y_Cx_E
+   +x_Ey_M-y_Ex_M
+   +x_My_A-y_Mx_A \\[1mm]
+&amp;=0-240+840+1176-840+240+0=1176 .
+\end{aligned}
+\]
+
+Hence
+
+\[
+[AFNBCEM]=\frac12\,S=\frac12\cdot1176=588 .
+\]
+
+A vector‑geometry check also shows that the signed sum of the
+determinants of successive vertices equals \(\det(\overrightarrow{AB},
+\overrightarrow{AC})\), i.e. the area of \(\triangle ABC\).
+
+--------------------------------------------------------------------
+### 4.  Answer
+
+\[
+\boxed{588}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 588</p>
+<p>Extracted Answer: 588</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $ A $ be the set of positive integer divisors of 2025. Let $ B $ be a randomly selected subset of $ A $. The probability that $ B $ is a nonempty set with the property that the least common multiple of its elements is 2025 is $ \frac{m}{n} $, where $ m $ and $ n $ are relatively prime positive integers. Find $ m + n $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Factor  
+\[
+2025=3^{4}\cdot5^{2}.
+\]
+
+A divisor of \(2025\) is \(3^{i}5^{j}\) with \(0\le i\le4,\;0\le j\le2\).  
+Hence  
+
+\[
+|A|=(4+1)(2+1)=15 .
+\]
+
+---
+
+### When does a subset have lcm \(2025\)?
+
+The lcm of a set of divisors takes, for each prime, the **maximum** exponent appearing among the chosen numbers.
+
+Thus a subset \(B\subseteq A\) has \(\operatorname{lcm}(B)=3^{4}5^{2}=2025\) iff  
+
+* at least one element of \(B\) has exponent \(4\) of the prime \(3\);
+* at least one element of \(B\) has exponent \(2\) of the prime \(5\).
+
+Define  
+
+\[
+S_{3}=\{3^{4}5^{j}\mid j=0,1,2\}=\{81,405,2025\},
+\qquad
+S_{5}=\{3^{i}5^{2}\mid i=0,1,2,3,4\}
+ =\{25,75,225,675,2025\}.
+\]
+
+\(|S_{3}|=3,\ |S_{5}|=5,\) and \(|S_{3}\cap S_{5}|=1\) (the element \(2025\)).
+
+So we need subsets that intersect **both** \(S_{3}\) and \(S_{5}\).
+
+---
+
+### Counting such subsets
+
+Total subsets of \(A\): \(2^{15}\).
+
+Let  
+
+* \(A_{3}\) = subsets containing **no** element of \(S_{3}\).  
+  \(|A_{3}| = 2^{15-3}=2^{12}\).
+
+* \(A_{5}\) = subsets containing **no** element of \(S_{5}\).  
+  \(|A_{5}| = 2^{15-5}=2^{10}\).
+
+* \(A_{3}\cap A_{5}\) = subsets containing none of \(S_{3}\cup S_{5}\).  
+  \(|S_{3}\cup S_{5}| = 3+5-1 = 7\), so  
+  \(|A_{3}\cap A_{5}| = 2^{15-7}=2^{8}\).
+
+By inclusion–exclusion, the number of subsets intersecting both \(S_{3}\) and \(S_{5}\) is  
+
+\[
+2^{15} - 2^{12} - 2^{10} + 2^{8}
+ = 32768 - 4096 - 1024 + 256
+ = 27904.
+\]
+
+Every such subset is non‑empty, so these are exactly the favorable subsets.
+
+---
+
+### Probability
+
+\[
+\text{Probability}
+ = \frac{27904}{2^{15}}
+ = \frac{27904}{32768}
+ = \frac{109}{128}
+\]
+(after reducing the fraction).
+
+Thus \(m=109,\ n=128\) and  
+
+\[
+m+n = 109+128 = 237.
+\]
+
+\[
+\boxed{237}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 237</p>
+<p>Extracted Answer: 237</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Circle $\omega_1$ with radius 6 centered at point $A$ is internally tangent at point $B$ to circle $\omega_2$ with radius 15. Points $C$ and $D$ lie on $\omega_2$ such that $\overline{BC}$ is a diameter of $\omega_2$ and $\overline{BC} \perp \overline{AD}$. The rectangle $EFGH$ is inscribed in $\omega_1$ such that $\overline{EF} \perp \overline{BC}$, $C$ is closer to $\overline{GH}$ than to $\overline{EF}$, and $D$ is closer to $\overline{FG}$ than to $\overline{EH}$, as shown. Triangles $\triangle DGF$ and $\triangle CHG$ have equal areas. The area of rectangle $EFGH$ is $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m + n$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+* \(O\) be the centre of \(\omega _2\) (radius \(15\)),
+* \(A\) be the centre of \(\omega _1\) (radius \(6\)),
+* \(B\) the point where the two circles are internally tangent,
+* \(C\) the antipode of \(B\) on \(\omega_2\) (\(BC\) is a diameter),
+* \(D\) the point on \(\omega _2\) with \(AD\perp BC\).
+
+--------------------------------------------------------------------
+### 1.  Choose coordinates  
+
+Place \(O\) at the origin and let the diameter \(BC\) be horizontal.
+
+\[
+B=(15,0),\qquad C=(-15,0)
+\]
+
+Since \(OA=15-6=9\) and \(A\) lies on \(OB\),
+
+\[
+A=(9,0).
+\]
+
+The line \(AD\) is perpendicular to the horizontal line \(BC\), so \(AD\) is the
+vertical line through \(A\); intersecting \(\omega_2\) gives
+
+\[
+D=(9,12)\quad\text{or}\quad D=(9,-12).
+\]
+
+Because the rectangle will be placed above the centre of \(\omega_1\), we take  
+
+\[
+D=(9,12).
+\]
+
+--------------------------------------------------------------------
+### 2.  Describe the rectangle  
+
+Since the rectangle is **inscribed** in \(\omega_1\), all four of its vertices lie on
+\(\omega_1\).  
+Let the rectangle have centre at \(A\); because a rectangle’s circum‑centre is
+the intersection of its diagonals, the centre must be the centre of the
+circumscribing circle \(\omega_1\).
+
+Let  
+
+* half‑width \(w\) (distance from the centre to the right–hand side),
+* half‑height \(h\) (distance from the centre to the top side).
+
+Then  
+
+\[
+\begin{aligned}
+x_R&amp;=9+w, &amp; x_L&amp;=9-w,\\
+y_T&amp;=h,   &amp; y_B&amp;=-h .
+\end{aligned}
+\]
+
+The vertices are  
+
+\[
+\begin{aligned}
+E&amp;(x_R,y_B)=(9+w,-h),\\
+F&amp;(x_R,y_T)=(9+w, h),\\
+G&amp;(x_L,y_T)=(9-w, h),\\
+H&amp;(x_L,y_B)=(9-w,-h).
+\end{aligned}
+\]
+
+Because the vertices lie on \(\omega_1\) (radius \(6\)),
+
+\[
+w^{2}+h^{2}=6^{2}=36\tag{1}
+\]
+
+--------------------------------------------------------------------
+### 3.  Use the area condition  
+
+The problem states that  
+
+\[
+\text{Area}\,\triangle DGF=\text{Area}\,\triangle CHG .
+\]
+
+*Triangle \(DGF\).*  
+Its base is \(GF\) (the top side of the rectangle) of length \(2w\).  
+Its height is the vertical distance from \(D\) to the line \(y=h\):
+\(\;12-h\). Hence  
+
+\[
+[\triangle DGF]=\tfrac12(2w)(12-h)=w(12-h).\tag{2}
+\]
+
+*Triangle \(CHG\).*  
+Its base is \(HG\) (the left side) of length \(2h\).  
+The distance from \(C\) to the vertical line \(x=9-w\) is
+\((9-w)-(-15)=24-w\). Therefore  
+
+\[
+[\triangle CHG]=\tfrac12(2h)(24-w)=h(24-w).\tag{3}
+\]
+
+Equating (2) and (3),
+
+\[
+w(12-h)=h(24-w).\tag{4}
+\]
+
+Expanding both sides gives  
+
+\[
+12w-wh=24h-wh\Longrightarrow 12w=24h\Longrightarrow w=2h.\tag{5}
+\]
+
+--------------------------------------------------------------------
+### 4.  Solve for \(w\) and \(h\)
+
+Substituting \(w=2h\) into (1):
+
+\[
+(2h)^2+h^2=36\quad\Longrightarrow\quad5h^{2}=36\quad\Longrightarrow\quad
+h^{2}= \frac{36}{5},\qquad
+h=\frac{6}{\sqrt5}=\frac{6\sqrt5}{5}.
+\]
+
+Hence  
+
+\[
+w=2h=\frac{12}{\sqrt5}= \frac{12\sqrt5}{5}.
+\]
+
+--------------------------------------------------------------------
+### 5.  Area of the rectangle  
+
+The rectangle’s side lengths are \(2w\) and \(2h\), so its area is  
+
+\[
+\text{Area}= (2w)(2h)=4wh=4\cdot(2h)h=8h^{2}
+          =8\left(\frac{36}{5}\right)=\frac{288}{5}.
+\]
+
+Thus the area is \(\displaystyle \frac{288}{5}\).
+The numerator and denominator are relatively prime, so  
+
+\[
+m=288,\qquad n=5,\qquad m+n=288+5=293.
+\]
+
+--------------------------------------------------------------------
+\[
+\boxed{293}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 293</p>
+<p>Extracted Answer: 293</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Alex divides a disk into four quadrants with two perpendicular diameters intersecting at the center of the disk. He draws 25 more line segments through the disk, drawing each segment by selecting two points at random on the perimeter of the disk in different quadrants and connecting those two points. Find the expected number of regions into which these 27 line segments divide the disk.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>**Step 1.  Regions created by chords**
+
+If we start with a disc (one region) and draw a chord, the number of regions increases by  
+
+\[
+\text{(number of interior intersections created by the new chord)}+1 .
+\]
+
+Hence after drawing \(k\) chords the number of regions is  
+
+\[
+R=1+k+I ,
+\]
+
+where \(I\) is the total number of interior intersection points of the drawn chords (no three chords meet at a single interior point, which holds a.s. for random chords).
+
+In our problem \(k=27\) (the two diameters plus the 25 random chords), so  
+
+\[
+R=28+I .
+\]
+
+Thus we only need the expected value of \(I\).
+
+--------------------------------------------------------------------
+
+**Step 2.  Intersections involving the two fixed diameters**
+
+The two diameters intersect at the centre, contributing a deterministic intersection  
+
+\[
+I_{\text{centre}}=1 .
+\]
+
+A random chord intersects the **vertical** diameter iff its endpoints lie in opposite halves of the disc, i.e. one endpoint in \(\{Q_1,Q_4\}\) and the other in \(\{Q_2,Q_3\}\).  
+Among the six possible unordered quadrant‑pairs for a chord, four satisfy this condition, so
+
+\[
+P(\text{vertical intersection})=\frac{4}{6}=\frac23 .
+\]
+
+The same reasoning holds for the **horizontal** diameter, giving  
+
+\[
+P(\text{horizontal intersection})=\frac23 .
+\]
+
+Hence for the 25 random chords
+
+\[
+E[I_{\text{vert}}]=25\cdot\frac23=\frac{50}{3},\qquad   
+E[I_{\text{horiz}}]=25\cdot\frac23=\frac{50}{3}.
+\]
+
+--------------------------------------------------------------------
+
+**Step 3.  Intersections among the 25 random chords**
+
+Two random chords are independent.  
+Each chord chooses an unordered pair of distinct quadrants uniformly from the six possibilities  
+
+\[
+\{1,2\},\{2,3\},\{3,4\},\{4,1\} \ (\text{adjacent}),\qquad
+\{1,3\},\{2,4\}\ (\text{opposite}).
+\]
+
+Let the unordered pairs be \(S\) and \(T\).  
+Their intersection size can be
+
+* **2** (the same pair) – probability \(1/6\);
+* **1** (they share exactly one quadrant) – probability \(2/3\);
+* **0** (disjoint) – probability \(1/6\).
+
+The disjoint case splits further:
+
+* Adjacent–adjacent (e.g. \(\{1,2\}\) with \(\{3,4\}\)) – chords never intersect.
+* Opposite–opposite (e.g. \(\{1,3\}\) with \(\{2,4\}\)) – chords always intersect.
+
+Among the three unordered disjoint pairs, two are adjacent–adjacent and one is opposite–opposite; hence for ordered pairs
+
+\[
+P(\text{disjoint, intersect})=\frac{2}{36}=\frac1{18},\qquad
+P(\text{disjoint, no intersect})=\frac{4}{36}.
+\]
+
+For the other two situations one can check (by considering the relative order of the points inside the quadrants) that
+
+* If the two chords have the **same** unordered pair (adjacent or opposite), the probability they intersect is \(\tfrac12\).
+* If they **share exactly one quadrant**, the probability they intersect is also \(\tfrac12\).
+
+Collecting the contributions,
+
+\[
+\begin{aligned}
+P(\text{intersection}) &amp;=
+\underbrace{\frac{6}{36}\cdot\frac12}_{\text{same pair}}
++\underbrace{\frac{24}{36}\cdot\frac12}_{\text{share one quadrant}}
++\underbrace{\frac{2}{36}\cdot1}_{\text{disjoint opposite}}\\[2mm]
+&amp;=\frac{3}{36}+\frac{12}{36}+\frac{2}{36}
+=\frac{17}{36}.
+\end{aligned}
+\]
+
+Thus for any unordered pair of the 25 random chords
+
+\[
+p:=P(\text{they intersect})=\frac{17}{36}.
+\]
+
+There are \(\binom{25}{2}=300\) such pairs, so
+
+\[
+E[I_{\text{random}}]=300\cdot\frac{17}{36}
+=\frac{300}{36}\cdot17
+=\frac{25}{3}\cdot17
+=\frac{425}{3}.
+\]
+
+--------------------------------------------------------------------
+
+**Step 4.  Expected total number of interior intersections**
+
+\[
+\begin{aligned}
+E[I] &amp;= I_{\text{centre}}
+      +E[I_{\text{vert}}]
+      +E[I_{\text{horiz}}]
+      +E[I_{\text{random}}]  \\[2mm]
+     &amp;=1+\frac{50}{3}+\frac{50}{3}+\frac{425}{3} \\[2mm]
+     &amp;=1+\frac{525}{3}=1+175=176 .
+\end{aligned}
+\]
+
+--------------------------------------------------------------------
+
+**Step 5.  Expected number of regions**
+
+\[
+E[R]=28+E[I]=28+176=204 .
+\]
+
+--------------------------------------------------------------------
+
+\[
+\boxed{204}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 204</p>
+<p>Extracted Answer: 204</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let the sequence of rationals $ x_1, x_2, \ldots $ be defined such that $ x_1 = \frac{25}{11} $ and
+$ x_{k+1} = \frac{1}{3} \left( x_k + \frac{1}{x_k} - 1 \right). $
+$ x_{2025} $ can be expressed as $ \frac{m}{n} $ for relatively prime positive integers $ m $ and $ n $. Find the remainder when $ m + n $ is divided by 1000.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>**Solution Outline**
+
+1.  Transform the recurrence for \(x_k\) into a simpler one.
+
+   Define  
+
+   \[
+   w_k=\frac{x_k-1}{x_k+1}\quad\Longleftrightarrow\quad 
+   x_k=\frac{1+w_k}{1-w_k}.
+   \]
+
+   Substituting in  
+
+   \[
+   x_{k+1}= \frac13\Bigl(x_k+\frac1{x_k}-1\Bigr)
+   \]
+
+   gives after simplification  
+
+   \[
+   w_{k+1}= \frac{3w_k^2-1}{2}. \tag{1}
+   \]
+
+   The initial value is  
+
+   \[
+   w_1=\frac{25/11-1}{25/11+1}=\frac{7}{18}.
+   \]
+
+2.  Write \(w_k=\dfrac{a_k}{b_k}\) in lowest terms
+   (\(a_k\) odd, \(b_k\) even).  
+
+   From (1),
+
+   \[
+   w_{k+1}= \frac{3a_k^2-b_k^2}{2b_k^2}.
+   \]
+
+   Because \(a_k\) is not divisible by 3, the numerator is always
+   \(\equiv 3\pmod 9\); hence it contains exactly one factor 3.
+   After canceling this factor we obtain
+
+   \[
+   a_{k+1}= \frac{3a_k^2-b_k^2}{3},\qquad
+   b_{k+1}= \frac{2b_k^2}{3}.
+   \tag{2}
+   \]
+
+   Consequently  
+
+   \[
+   b_{k+1}= \frac{2}{3}b_k^{\,2}. \tag{3}
+   \]
+
+3.  Determine a closed form for \(b_k\).
+
+   Write \(b_k=2^{\alpha_k}3^{\beta_k}\).
+   From (3)
+
+   \[
+   2^{\alpha_{k+1}}3^{\beta_{k+1}}
+   =\frac{2}{3}\bigl(2^{\alpha_k}3^{\beta_k}\bigr)^2
+   =2^{2\alpha_k+1}3^{2\beta_k-1},
+   \]
+
+   whence  
+
+   \[
+   \alpha_{k+1}=2\alpha_k+1,\qquad
+   \beta_{k+1}=2\beta_k-1,
+   \]
+   with \(\alpha_1=1,\ \beta_1=2\).
+
+   Solving these linear recurrences gives  
+
+   \[
+   \alpha_k = 2^{\,k}-1,\qquad
+   \beta_k = 2^{\,k-1}+1 .
+   \]
+
+   Therefore  
+
+   \[
+   b_k = 2^{\,2^{k}-1}\,3^{\,2^{k-1}+1}. \tag{4}
+   \]
+
+4.  Recover \(x_k\) from \(w_k\).
+
+   Since \(x_k=\dfrac{1+w_k}{1-w_k}\) and \(w_k=\dfrac{a_k}{b_k}\),
+
+   \[
+   x_k=\frac{b_k+a_k}{\,b_k-a_k\,}= \frac{m_k}{n_k},
+   \]
+   where \(m_k=b_k+a_k,\ n_k=b_k-a_k\).  
+   Because \(a_k\) is odd and \(b_k\) is even, \(m_k\) and \(n_k\) are odd,
+   so \(\gcd(m_k,n_k)=1\).
+
+   Hence
+
+   \[
+   m_k+n_k = (b_k+a_k)+(b_k-a_k)=2b_k.
+   \]
+
+5.  Compute \(m_{2025}+n_{2025}\pmod{1000}\).
+
+   From (4),
+
+   \[
+   b_{2025}=2^{\,2^{2025}-1}\,3^{\,2^{2024}+1},
+   \qquad
+   m_{2025}+n_{2025}=2b_{2025}
+   =2^{\,2^{2025}}\,3^{\,2^{2024}+1}.
+   \]
+
+   We need this value modulo \(1000=2^3\cdot5^3\).
+
+   *Modulo 8:* the exponent of 2 is at least 3, so the whole product
+   is \(0\pmod8\).
+
+   *Modulo 125:* use Euler’s theorem (\(\phi(125)=100\)):
+   \[
+   2^{2^{2025}}\equiv2^{\,32}\pmod{125},\qquad
+   3^{2^{2024}+1}\equiv3^{\,17}\pmod{125},
+   \]
+   because \(2^{2025}\equiv32\) and \(2^{2024}+1\equiv17\pmod{100}\).
+
+   Computing,
+   \[
+   2^{32}\equiv46,\qquad 3^{17}\equiv38\pmod{125},
+   \]
+   so
+   \[
+   2^{2^{2025}}3^{2^{2024}+1}\equiv46\cdot38\equiv123\pmod{125}.
+   \]
+
+   Solve the simultaneous congruences
+   \[
+   X\equiv0\pmod8,\qquad X\equiv123\pmod{125}.
+   \]
+   Writing \(X=125a+123\) and using \(125\equiv5\pmod8\) gives
+   \(5a+3\equiv0\pmod8\Rightarrow a\equiv1\pmod8\).
+   Hence \(X=125\cdot1+123=248\).
+
+   Therefore  
+
+   \[
+   m_{2025}+n_{2025}\equiv\boxed{248}\pmod{1000}.
+   \]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 248</p>
+<p>Extracted Answer: 248</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+There are $ n $ values of $ x $ in the interval $ 0 &lt; x &lt; 2\pi $ where $ f(x) = \sin(7\pi \cdot \sin(5x)) = 0 $. For $ t $ of these $ n $ values of $ x $, the graph of $ y = f(x) $ is tangent to the $ x $-axis. Find $ n + t $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>\[
+f(x)=\sin\bigl(7\pi\sin (5x)\bigr)
+\]
+
+The zeros of \(f\) occur when the inner sine gives an integer multiple of \(\pi\):
+
+\[
+\sin\bigl(7\pi\sin (5x)\bigr)=0\Longleftrightarrow 7\pi\sin(5x)=k\pi
+\Longleftrightarrow \sin(5x)=\frac{k}{7},
+\qquad k\in\mathbb Z .
+\]
+
+Because \(\sin(5x)\in[-1,1]\), \(|k|\le7\); thus \(k=-7,-6,\dots ,6,7\).
+
+---
+
+### 1.  Counting the zeros  
+
+Set \(\theta =5x\).  
+When \(x\in(0,2\pi)\) we have \(\theta\in(0,10\pi)\).
+
+For each admissible integer \(k\) we need the number of solutions of  
+
+\[
+\sin\theta=\frac{k}{7},\qquad \theta\in(0,10\pi).
+\]
+
+* **\(k=0\):** \(\sin\theta=0\Rightarrow\theta=n\pi\).  
+  Inside \((0,10\pi)\) we have \(n=1,2,\ldots ,9\) → **9 solutions**.
+
+* **\(k=\pm 7\):** \(\sin\theta=\pm1\).  
+  \(\sin\theta=1\) gives \(\theta=\dfrac{\pi}{2}+2\pi n\);  
+  \(\sin\theta=-1\) gives \(\theta=\dfrac{3\pi}{2}+2\pi n\).  
+  For \(0&lt;\theta&lt;10\pi\) each yields \(n=0,1,2,3,4\) → **5 solutions** for \(k=7\) and **5** for \(k=-7\).
+
+* **\(k=\pm1,\pm2,\dots ,\pm6\):** \(|k|&lt;7\) so \(-1&lt;k/7&lt;1\) and \(\neq0\).  
+  In each full period \([0,2\pi]\) the equation \(\sin\theta=c\) (\(|c|&lt;1\)) has two solutions.  
+  The interval \((0,10\pi)\) contains five full periods, hence **\(5\times2=10\) solutions** for each of these 12 values of \(k\).
+
+Summing all contributions  
+
+\[
+\begin{aligned}
+n &amp;=\underbrace{9}_{k=0}
+   +\underbrace{5+5}_{k=\pm7}
+   +\underbrace{12\times10}_{k=\pm1,\dots,\pm6}\\[2mm]
+  &amp;=9+10+120 = 139 .
+\end{aligned}
+\]
+
+Thus there are \(\boxed{139}\) zeros of \(f\) in \((0,2\pi)\).
+
+---
+
+### 2.  Zeros where the graph is tangent to the \(x\)-axis  
+
+A point where the graph touches the \(x\)-axis must satisfy  
+
+\[
+f(x)=0\quad\text{and}\quad f&#39;(x)=0.
+\]
+
+From \(f(x)=0\) we have \(\sin(5x)=k/7\) as above.  
+Compute the derivative:
+
+\[
+\begin{aligned}
+f&#39;(x) &amp;=\cos\bigl(7\pi\sin(5x)\bigr)\cdot 7\pi\cdot 5\cos(5x)   \\
+      &amp;=35\pi\cos\bigl(7\pi\sin(5x)\bigr)\cos(5x).
+\end{aligned}
+\]
+
+Thus \(f&#39;(x)=0\) iff \(\cos(5x)=0\) (the factor \(\cos\bigl(7\pi\sin(5x)\bigr)\) never vanishes at a zero, because
+\(\cos(k\pi)=\pm1\)).  
+
+\[
+\cos(5x)=0\Longrightarrow 5x=\frac{\pi}{2}+n\pi\quad\Longrightarrow\quad\sin(5x)=\pm1.
+\]
+
+Hence the tangential zeros correspond exactly to the solutions of \(\sin(5x)=\pm1\), i.e. the cases \(k=\pm7\).
+
+We already counted these:  
+
+* \(\sin(5x)=1\) gives \(5\) solutions,
+* \(\sin(5x)=-1\) gives \(5\) solutions.
+
+Therefore  
+
+\[
+t = 5+5 = 10 .
+\]
+
+(Indeed, at these points \(f&#39;(x)=0\) and \(f&#39;&#39;(x)\neq0\), so the graph just touches the axis.)
+
+---
+
+### 3.  Required sum  
+
+\[
+n+t = 139 + 10 = \boxed{149}.
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 149</p>
+<p>Extracted Answer: 149</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+From an unlimited supply of 1-cent coins, 10-cent coins, and 25-cent coins, Silas wants to find a collection of coins that has a total value of $ N $ cents, where $ N $ is a positive integer. He uses the so-called **greedy algorithm**, successively choosing the coin of greatest value that does not cause the value of his collection to exceed $ N $. For example, to get 42 cents, Silas will choose a 25-cent coin, then a 10-cent coin, then 7 1-cent coins. However, this collection of 9 coins uses more coins than necessary to get a total of 42 cents; indeed, choosing 4 10-cent coins and 2 1-cent coins achieves the same total value with only 6 coins.
+
+In general, the greedy algorithm succeeds for a given $ N $ if no other collection of 1-cent, 10-cent, and 25-cent coins gives a total value of $ N $ cents using strictly fewer coins than the collection given by the greedy algorithm. Find the number of values of $ N $ between 1 and 1000 inclusive for which the greedy algorithm succeeds.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+\[
+N=25q+r ,\qquad 0\le r&lt;25 .
+\]
+
+The greedy algorithm first takes \(q\) coins of 25 ¢, then  
+\(t=\big\lfloor r/10\big\rfloor\) coins of 10 ¢ and finally  
+\(s=r-10t\) pennies.  
+
+\[
+\text{Greedy coins}=C_g(N)=q+t+s.
+\]
+
+---
+
+### 1.  What is an optimal representation?
+
+If a representation uses \(a\) 25‑cent coins, \(b\) 10‑cent coins and \(c\) pennies, then  
+
+\[
+25a+10b+c=N,\qquad a,b,c\ge0,
+\]
+and the number of coins is  
+
+\[
+C= a+b+c = N-(24a+9b).
+\]
+
+Thus **minimising the number of coins is equivalent to maximising**  
+
+\[
+P=24a+9b \qquad\text{subject to}\qquad 25a+10b\le N .
+\]
+
+The “profit’’ per cent is larger for a 25‑cent coin \((24/25)\) than for a 10‑cent coin \((9/10)\); therefore an optimal solution will use as many 25‑cent coins as possible unless removing a 25‑cent coin allows us to add enough 10‑cent coins to increase the profit.
+
+---
+
+### 2.  Effect of removing \(k\) quarters
+
+Let us replace \(k\) quarters by 10‑cent coins.  
+Write \(r=10u+v\;(0\le v\le 9)\).  
+After removing \(k\) quarters, the remainder becomes  
+
+\[
+R=r+25k=10u+v+25k .
+\]
+
+The maximal number of dimes that can be added is  
+
+\[
+b&#39;=\big\lfloor \frac{R}{10}\big\rfloor
+   =u+ \big\lfloor 2.5k+\tfrac{v}{10}\big\rfloor .
+\]
+
+The change in profit is
+
+\[
+\Delta P
+=-24k+9\big(b&#39;-\big\lfloor r/10\big\rfloor\big)
+=-6k+9\Big\lfloor\frac{k}{2}\Big\rfloor+9\delta ,
+\]
+
+where  
+
+\[
+\delta=
+\begin{cases}
+1 &amp;\text{if }k\text{ is odd and }v\ge5,\\
+0 &amp;\text{otherwise.}
+\end{cases}
+\]
+
+*If \(k\) is even*, \(\Delta P=-3k/2&lt;0\); the profit never increases.  
+
+*If \(k\) is odd*, write \(k=2m+1\). Then  
+
+\[
+\Delta P=9\delta-(3m+6).
+\]
+
+The only way \(\Delta P&gt;0\) is when \(m=0\) (i.e. \(k=1\)) and \(\delta=1\),
+which occurs exactly when  
+
+\[
+v=r\bmod 10\ge5 .
+\]
+
+Hence **the greedy algorithm fails precisely when**
+\[
+N\ge 25\quad\text{and}\quad (N\bmod 25)\bmod 10\ge5.
+\]
+
+Equivalently, the “bad’’ remainders (after taking as many quarters as possible) are  
+
+\[
+r\in\{5,6,7,8,9,15,16,17,18,19\}.
+\]
+
+In each block of 25 consecutive integers there are 10 such remainders.
+
+---
+
+### 3.  Counting the failures between 1 and 1000
+
+The interval \([25,1000]\) contains \(1000-24=976\) integers.
+From 25 onward the numbers are grouped into blocks  
+
+\[
+25\!-\!49,\;50\!-\!74,\;\dots,\;975\!-\!999 .
+\]
+
+There are \(39\) full blocks (the block \(25\!-\!49\) up to \(975\!-\!999\)).
+Each block contributes exactly \(10\) failures, so
+
+\[
+\#\text{failures}=39\times10=390 .
+\]
+
+Numbers \(1\) through \(24\) are never failures (they contain no quarters).
+
+Thus the number of successes is  
+
+\[
+1000-390=610 .
+\]
+
+---
+
+\[
+\boxed{610}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 610</p>
+<p>Extracted Answer: 610</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $ S $ be the set of vertices of a regular 24-gon. Find the number of ways to draw 12 segments of equal lengths so that each vertex in $ S $ is an endpoint of exactly one of the 12 segments.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>In a regular \(24\)-gon label the vertices \(0,1,\dots ,23\) clockwise.  
+If two vertices differ by \(k\) (mod \(24\)), the chord joining them has length that depends only on  
+
+\[
+s=\min (k,24-k)\qquad (1\le s\le 12).
+\]
+
+Thus there are \(12\) possible lengths, one for each \(s=1,2,\dots ,12\).
+
+--------------------------------------------------------------------
+### 1.  The graph of chords of a fixed length  
+
+Fix a value \(s\).  The set of all chords of that length is the edge‑set of the **circulant graph**
+\[
+G_s=\{\,\{i,i+s\}\mid i=0,1,\dots ,23\,\},
+\]
+where the addition is taken modulo \(24\).
+
+Let \(g=\gcd(s,24)\).  Adding \(s\) repeatedly splits the vertex set into \(g\) cycles,
+each of length  
+
+\[
+L=\frac{24}{g}.
+\]
+
+So \(G_s\) is a disjoint union of \(g\) cycles \(C_L\).
+
+--------------------------------------------------------------------
+### 2.  When can a perfect matching exist?
+
+A perfect matching (a set of \(12\) disjoint edges covering all vertices) can exist only if
+every component cycle has even length, i.e. \(L\) is even.
+Since \(L=24/g\), this is equivalent to \(g\mid 12\).
+
+*If \(g\mid 12\) and \(L\ge 4\)*, each even cycle \(C_L\) has exactly **2** perfect
+matchings (choose alternating edges).  
+*If \(L=2\)* (the case \(s=12\)), each component is a single edge and contributes only **1** matching.
+
+The only step for which \(g\nmid 12\) is \(s=8\) (here \(g=8\) and the components are 3‑cycles),
+so no perfect matching exists for \(s=8\).
+
+--------------------------------------------------------------------
+### 3.  Number of matchings for each possible length
+
+\[
+\begin{array}{c|c|c|c}
+s &amp; g=\gcd(s,24) &amp; L=24/g &amp; \#\text{ matchings}\\ \hline
+1 &amp;1 &amp;24 &amp;2\\
+2 &amp;2 &amp;12 &amp;2^{2}=4\\
+3 &amp;3 &amp; 8 &amp;2^{3}=8\\
+4 &amp;4 &amp; 6 &amp;2^{4}=16\\
+5 &amp;1 &amp;24 &amp;2\\
+6 &amp;6 &amp; 4 &amp;2^{6}=64\\
+7 &amp;1 &amp;24 &amp;2\\
+8 &amp;8 &amp; 3 &amp;0\\
+9 &amp;3 &amp; 8 &amp;2^{3}=8\\
+10&amp;2 &amp;12 &amp;2^{2}=4\\
+11&amp;1 &amp;24 &amp;2\\
+12&amp;12&amp; 2 &amp;1
+\end{array}
+\]
+
+--------------------------------------------------------------------
+### 4.  Total number of ways
+
+Add the numbers for all admissible lengths (all \(s\) except \(s=8\)):
+
+\[
+\begin{aligned}
+\text{Total}&amp;=2+4+8+16+2+64+2+8+4+2+1\\
+&amp;=113 .
+\end{aligned}
+\]
+
+--------------------------------------------------------------------
+\[
+\boxed{113}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 113</p>
+<p>Extracted Answer: 113</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Sixteen chairs are arranged in a row. Eight people each select a chair in which to sit so that no person sits next to two other people. Let $ N $ be the number of subsets of 16 chairs that could be selected. Find the remainder when $ N $ is divided by 1000.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>The chairs can be represented by a binary string of length 16, where a \(1\) means the chair is taken.  
+We need strings with exactly eight \(1\)’s and with **no three consecutive \(1\)’s** (otherwise the middle person would sit next to two others).
+
+---
+
+### Counting by blocks
+
+A valid string consists of blocks of consecutive \(1\)’s of length 1 or 2, separated by at least one \(0\).
+
+Let  
+
+* \(t\) = number of blocks of length 2,  
+* \(b\) = total number of blocks.  
+
+Since each block contributes at least one \(1\),
+
+\[
+\underbrace{(b-t)}_{\text{blocks of length 1}}+2t=8\quad\Longrightarrow\quad b+ t=8,\; b=8-t .
+\]
+
+So \(t=0,1,2,3,4\).
+
+For a fixed \(t\):
+* Choose which of the \(b\) blocks are the length‑2 ones: \(\displaystyle\binom{b}{t}=\binom{8-t}{t}\).
+* There are \(8-8=8\) empty chairs; let \(z=8\).  
+  The \(b+1\) gaps (including the two ends) must contain these zeros, with at least one zero in each interior gap.  
+  After placing one zero in each of the \(b-1\) interior gaps, we have \(z-(b-1)=9-b\) zeros left to distribute freely among the \(b+1\) gaps.  
+  The number of ways is \(\displaystyle\binom{9-b}{b}=\binom{9}{b}\).
+
+Hence for each \(t\),
+
+\[
+N_t=\binom{8-t}{t}\binom{9}{8-t}.
+\]
+
+Summing over \(t=0\) to \(4\):
+
+\[
+\begin{aligned}
+N &amp;=\binom{8}{0}\binom{9}{8}
+   +\binom{7}{1}\binom{9}{7}
+   +\binom{6}{2}\binom{9}{6}
+   +\binom{5}{3}\binom{9}{5}
+   +\binom{4}{4}\binom{9}{4} \\[2mm]
+  &amp;=1\cdot9+7\cdot36+15\cdot84+10\cdot126+1\cdot126\\
+  &amp;=9+252+1260+1260+126\\
+  &amp;=2907 .
+\end{aligned}
+\]
+
+---
+
+### Modulo 1000
+
+\[
+2907 \equiv 907 \pmod{1000}.
+\]
+
+---
+
+\[
+\boxed{907}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 907</p>
+<p>Extracted Answer: 907</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $ A_1A_2 \ldots A_{11} $ be an 11-sided non-convex simple polygon with the following properties:
+* The area of $ A_iA_1A_{i+1} $ is 1 for each $ 2 \leq i \leq 10 $,
+* $ \cos(\angle A_iA_1A_{i+1}) = \frac{12}{13} $ for each $ 2 \leq i \leq 10 $,
+* The perimeter of $ A_1A_2 \ldots A_{11} $ is 20.
+If $ A_1A_2 + A_1A_{11} $ can be expressed as $ \frac{m\sqrt{n} - p}{q} $ for positive integers $ m, n, p, q $ with $ n $ squarefree and no prime divides all of $ m, p, q$, find $ m + n + p + q $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+\[
+r_i=A_1A_i\qquad (i=2,\dots ,11),\qquad 
+\theta=\angle A_iA_1A_{i+1}.
+\]
+
+For each \(i=2,\dots ,10\)
+
+\[
+\cos\theta=\frac{12}{13},\qquad 
+\text{Area}(A_iA_1A_{i+1})=\frac12 r_i r_{i+1}\sin\theta =1 .
+\]
+
+Since \(\sin\theta=\sqrt{1-\cos ^2\theta}=5/13\),
+
+\[
+r_i r_{i+1}= \frac{2}{\sin\theta}= \frac{2}{5/13}= \frac{26}{5}
+=:k\quad\text{(constant)}.
+\]
+
+Thus  
+
+\[
+r_{i+1}= \frac{k}{r_i},\qquad\text{so}\qquad r_{i+2}=r_i .
+\]
+
+Hence the distances from \(A_1\) alternate:
+
+\[
+r_2=r_4=r_6=r_8=r_{10}=a,\qquad  
+r_3=r_5=r_7=r_9=r_{11}=b,
+\]
+
+with  
+
+\[
+ab=k=\frac{26}{5}.
+\]
+
+--------------------------------------------------------------------
+### Length of a side \(A_iA_{i+1}\)
+
+For any consecutive pair \((a,b)\),
+
+\[
+A_iA_{i+1}=d=\sqrt{a^2+b^2-2ab\cos\theta}
+           =\sqrt{a^2+b^2-\frac{24}{13}ab}.
+\]
+
+Let  
+
+\[
+x=a+b,\qquad ab=k .
+\]
+
+Because \(a^2+b^2=(a+b)^2-2ab=x^2-2k\),
+
+\[
+d=\sqrt{x^2-2k-\frac{24}{13}k}
+   =\sqrt{x^2-\frac{50}{13}\,k}.
+\]
+
+Since \(k=\dfrac{26}{5}\),
+
+\[
+\frac{50}{13}k=\frac{50}{13}\cdot\frac{26}{5}=20,
+\qquad\boxed{d=\sqrt{x^2-20}} .
+\]
+
+--------------------------------------------------------------------
+### Using the perimeter
+
+The perimeter of the 11‑gon is
+
+\[
+a+b+9d = x+9\sqrt{x^2-20}=20 .
+\]
+
+Solve for \(x\) (note \(x&gt;0\) and \(\sqrt{x^2-20}\ge0\)):
+
+\[
+9\sqrt{x^2-20}=20-x\quad\Longrightarrow\quad
+81(x^2-20)=(20-x)^2 .
+\]
+
+This gives  
+
+\[
+80x^2+40x-2020=0\;\Longrightarrow\;4x^2+2x-101=0.
+\]
+
+Hence  
+
+\[
+x=\frac{-2\pm\sqrt{4+1616}}{8}
+  =\frac{-2\pm18\sqrt5}{8}
+  =\frac{-1\pm9\sqrt5}{4}.
+\]
+
+Only the positive root satisfies the constraints, so  
+
+\[
+\boxed{x=a+b=\frac{9\sqrt5-1}{4}} .
+\]
+
+Thus
+
+\[
+A_1A_2+A_1A_{11}=a+b=\frac{9\sqrt5-1}{4}
+    =\frac{m\sqrt n-p}{q},
+\]
+
+with \(m=9,\;n=5,\;p=1,\;q=4\).
+
+All conditions on \(m,n,p,q\) are met, and
+
+\[
+m+n+p+q=9+5+1+4=19.
+\]
+
+\[
+\boxed{19}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 19</p>
+<p>Extracted Answer: 19</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Find the sum of all integer bases $b&gt;9$ for which $17_{b}$ is a divisor of $97_{b}$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>In base \(b\) the numbers are  
+
+\[
+17_{b}=1\cdot b+7=b+7, \qquad 97_{b}=9\cdot b+7=9b+7 .
+\]
+
+We need \(b+7\) to divide \(9b+7\).
+
+---
+
+### Find the divisibility condition  
+
+\[
+9b+7 = 9(b+7)-56 .
+\]
+
+Thus the remainder when \(9b+7\) is divided by \(b+7\) is \(-56\).  
+Hence \(b+7\) must divide \(56\):
+
+\[
+b+7\mid 56 .
+\]
+
+---
+
+### Possible values of \(b\)
+
+The positive divisors of \(56\) are  
+
+\[
+1,\;2,\;4,\;7,\;8,\;14,\;28,\;56 .
+\]
+
+Because the base must satisfy \(b&gt;9\), we have \(b+7&gt;16\).  
+The divisors larger than \(16\) are \(28\) and \(56\).
+
+\[
+\begin{aligned}
+b+7&amp;=28 \quad\Longrightarrow\quad b=21,\\[2pt]
+b+7&amp;=56 \quad\Longrightarrow\quad b=49 .
+\end{aligned}
+\]
+
+Both bases are greater than \(9\) and allow the digits \(1,7,9\).
+
+---
+
+### Sum of all such bases  
+
+\[
+21+49 = 70.
+\]
+
+\[
+\boxed{70}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 70</p>
+<p>Extracted Answer: 70</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+The 9 members of a baseball team went to an ice cream parlor after their game. Each player had a singlescoop cone of chocolate, vanilla, or strawberry ice cream. At least one player chose each flavor, and the number of players who chose chocolate was greater than the number of players who chose vanilla, which was greater than the number of players who chose strawberry. Let $N$ be the number of different assignments of flavors to players that meet these conditions. Find the remainder when $N$ is divided by 1000.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>The numbers of players picking chocolate, vanilla and strawberry are  
+
+\[
+a=\#\text{chocolate},\qquad b=\#\text{vanilla},\qquad c=\#\text{strawberry}
+\]
+
+with  
+
+\[
+a+b+c=9,\qquad a&gt;b&gt;c\ge1 .
+\]
+
+Hence \((a,b,c)\) must be three distinct positive integers whose sum is \(9\).  
+The possible triples (written in decreasing order) are  
+
+\[
+(6,2,1),\;(5,3,1),\;(4,3,2).
+\]
+
+For a fixed triple \((a,b,c)\) the players are distinct, so the number of assignments
+is the multinomial coefficient  
+
+\[
+\binom{9}{a,b,c}= \frac{9!}{a!\,b!\,c!}.
+\]
+
+Compute each term:
+
+\[
+\begin{aligned}
+(6,2,1):&amp;\quad \frac{9!}{6!\,2!\,1!}= \frac{362880}{720\cdot2}=252,\\[2mm]
+(5,3,1):&amp;\quad \frac{9!}{5!\,3!\,1!}= \frac{362880}{120\cdot6}=504,\\[2mm]
+(4,3,2):&amp;\quad \frac{9!}{4!\,3!\,2!}= \frac{362880}{24\cdot6\cdot2}=1260.
+\end{aligned}
+\]
+
+Add them:
+
+\[
+N = 252+504+1260 = 2016.
+\]
+
+The remainder when \(N\) is divided by \(1000\) is  
+
+\[
+2016 \equiv 16 \pmod{1000}.
+\]
+
+\[
+\boxed{16}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 16</p>
+<p>Extracted Answer: 16</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $ \triangle ABC $ be a right triangle with $ \angle A = 90^\circ $ and $ BC = 38 $. There exist points $ K $ and $ L $ inside the triangle such that $ AK = AL = BK = CL = KL = 14. $ The area of the quadrilateral $ BKLC $ can be expressed as $ n \sqrt{3} $ for some positive integer $ n $. Find $ n $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+\[
+A=(0,0),\qquad B=(b,0),\qquad C=(0,c)
+\]
+
+so that \(\angle A=90^{\circ}\) and  
+
+\[
+BC=\sqrt{b^{2}+c^{2}}=38\qquad\Longrightarrow\qquad b^{2}+c^{2}=38^{2}=1444 .
+\tag{1}
+\]
+
+--------------------------------------------------------------------
+### 1.  Determining the positions of \(K\) and \(L\)
+
+Because  
+
+\[
+AK=BK=14
+\]
+
+the point \(K\) lies at the intersection of the circles of radius \(14\) centred at
+\(A\) and \(B\).  
+If \(K=(x_{K},y_{K})\),
+
+\[
+x_{K}^{2}+y_{K}^{2}=196,\qquad (x_{K}-b)^{2}+y_{K}^{2}=196 .
+\]
+
+Subtracting gives  
+
+\[
+b^{2}=2bx_{K}\;\Longrightarrow\;x_{K}= \frac{b}{2} .
+\tag{2}
+\]
+
+Hence  
+
+\[
+y_{K}^{2}=196-\Bigl(\frac{b}{2}\Bigr)^{2}=196-\frac{b^{2}}{4}.
+\tag{3}
+\]
+
+Similarly, from  
+
+\[
+AL=CL=14
+\]
+
+the point \(L=(x_{L},y_{L})\) satisfies
+
+\[
+y_{L}= \frac{c}{2},\qquad 
+x_{L}^{2}=196-\Bigl(\frac{c}{2}\Bigr)^{2}=196-\frac{c^{2}}{4}.
+\tag{4}
+\]
+
+Thus, writing  
+
+\[
+U=\frac{b}{2},\quad V=\frac{c}{2},
+\]
+
+we have  
+
+\[
+K=\bigl(U,\;\sqrt{196-U^{2}}\bigr),\qquad 
+L=\bigl(\sqrt{196-V^{2}},\;V\bigr),
+\tag{5}
+\]
+
+and from (1)  
+
+\[
+U^{2}+V^{2}=361. \tag{6}
+\]
+
+--------------------------------------------------------------------
+### 2.  Using the condition \(KL=14\)
+
+From (5),
+
+\[
+\bigl(U-\sqrt{196-V^{2}}\bigr)^{2}
++\bigl(\sqrt{196-U^{2}}-V\bigr)^{2}=196 .
+\]
+
+Expanding and simplifying with (6) gives
+
+\[
+U\sqrt{196-V^{2}}+V\sqrt{196-U^{2}}=98 . \tag{7}
+\]
+
+Let  
+
+\[
+p=\sqrt{196-V^{2}},\qquad q=\sqrt{196-U^{2}} .
+\]
+
+Then  
+
+\[
+U p+V q =98 ,\qquad p^{2}+q^{2}=31 ,
+\qquad U^{2}+V^{2}=361 . \tag{8}
+\]
+
+From (8) we obtain the product
+
+\[
+U^{2}V^{2}=32448\quad\Longrightarrow\quad UV=104\sqrt3 . \tag{9}
+\]
+
+Now  
+
+\[
+(U+V)^{2}=U^{2}+V^{2}+2UV=361+208\sqrt3,
+\]
+\[
+(U-V)^{2}=U^{2}+V^{2}-2UV=361-208\sqrt3 .
+\]
+
+Both expressions are perfect squares:
+
+\[
+361+208\sqrt3=(13+8\sqrt3)^{2},
+\qquad
+361-208\sqrt3=(8\sqrt3-13)^{2}.
+\]
+
+Hence  
+
+\[
+U+V=13+8\sqrt3,\qquad
+|U-V|=8\sqrt3-13 .
+\]
+
+Since \(U&gt;V\), solving gives  
+
+\[
+U=8\sqrt3,\qquad V=13 .
+\]
+
+Consequently  
+
+\[
+b=2U=16\sqrt3,\qquad c=2V=26 .
+\]
+
+--------------------------------------------------------------------
+### 3.  Coordinates of \(K\) and \(L\)
+
+Using (5) with the found \(U,V\):
+
+\[
+K=\bigl(8\sqrt3,\; \sqrt{196-(8\sqrt3)^{2}}\bigr)
+   =\bigl(8\sqrt3,\;2\bigr),
+\]
+
+\[
+L=\bigl(\sqrt{196-13^{2}},\;13\bigr)
+   =\bigl(3\sqrt3,\;13\bigr).
+\]
+
+--------------------------------------------------------------------
+### 4.  Area of quadrilateral \(BKLC\)
+
+The vertices in order are  
+
+\[
+B=(16\sqrt3,0),\ K=(8\sqrt3,2),\ L=(3\sqrt3,13),\ C=(0,26).
+\]
+
+Applying the shoelace formula:
+
+\[
+\begin{aligned}
+S_{1}&amp;=x_{B}y_{K}+x_{K}y_{L}+x_{L}y_{C}+x_{C}y_{B}\\
+     &amp;= (16\sqrt3)(2)+(8\sqrt3)(13)+(3\sqrt3)(26)+0\\
+     &amp;=32\sqrt3+104\sqrt3+78\sqrt3=214\sqrt3,
+\\[2mm]
+S_{2}&amp;=y_{B}x_{K}+y_{K}x_{L}+y_{L}x_{C}+y_{C}x_{B}\\
+     &amp;=0+2(3\sqrt3)+13\cdot0+26(16\sqrt3)\\
+     &amp;=6\sqrt3+416\sqrt3=422\sqrt3 .
+\end{aligned}
+\]
+
+Hence  
+
+\[
+\text{Area}=\frac12|S_{1}-S_{2}|
+           =\frac12\bigl|214\sqrt3-422\sqrt3\bigr|
+           =\frac12\,(208\sqrt3)=104\sqrt3 .
+\]
+
+Thus the required area is \(104\sqrt3\), i.e. \(n=104\).
+
+\[
+\boxed{104}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 104</p>
+<p>Extracted Answer: 104</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Find the number of ordered pairs $(x,y)$, where both $x$ and $y$ are integers between $-100$ and $100$, inclusive, such that $12x^{2}-xy-6y^{2}=0$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>The equation  
+
+\[
+12x^{2}-xy-6y^{2}=0
+\]
+
+can be factored over the integers.
+
+\[
+\begin{aligned}
+12x^{2}-xy-6y^{2}
+&amp;= (4x-3y)(3x+2y).
+\end{aligned}
+\]
+
+Hence a pair \((x,y)\) satisfies the equation iff  
+
+\[
+4x-3y=0 \qquad\text{or}\qquad 3x+2y=0 .
+\]
+
+---
+
+### 1.  Solutions of \(4x-3y=0\)
+
+\[
+4x=3y \Longrightarrow x=\frac34y .
+\]
+
+Since \(x,y\) are integers, \(y\) must be a multiple of \(4\); write \(y=4k\) \((k\in\mathbb Z)\).  
+Then \(x=3k\).
+
+Bounds \(-100\le x,y\le100\) give  
+
+\[
+|4k|\le100\ \Longrightarrow\ |k|\le25 .
+\]
+
+Thus \(k\) can be any integer from \(-25\) to \(25\) inclusive – \(51\) possibilities.
+
+---
+
+### 2.  Solutions of \(3x+2y=0\)
+
+\[
+3x=-2y \Longrightarrow x=-\frac{2}{3}y .
+\]
+
+Now \(y\) must be a multiple of \(3\); write \(y=3k\).  
+Then \(x=-2k\).
+
+Bounds give  
+
+\[
+|3k|\le100\ \Longrightarrow\ |k|\le\Big\lfloor\frac{100}{3}\Big\rfloor=33 .
+\]
+
+Hence \(k\) can be any integer from \(-33\) to \(33\) inclusive – \(67\) possibilities.
+
+---
+
+### 3.  Removing double‑counted pair
+
+Both families contain the pair \((0,0)\) (when \(k=0\)).  
+It has been counted twice, so we subtract one.
+
+\[
+\text{Total solutions}=51+67-1=117 .
+\]
+
+All counted pairs satisfy \(-100\le x,y\le100\).
+
+\[
+\boxed{117}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 117</p>
+<p>Extracted Answer: 117</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+An isosceles trapezoid has an inscribed circle tangent to each of its four sides. The radius of the circle is 3, and the area of the trapezoid is 72. Let the parallel sides of the trapezoid have lengths $r$ and $s$, with $r \neq s$. Find $r^{2}+s^{2}$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let the trapezoid have parallel sides \(r\) and \(s\) (\(r\neq s\)), equal legs of length \(L\), height \(h\), and incircle radius \(R=3\).
+
+---
+
+### 1.  Semiperimeter from the incircle
+
+For any tangential quadrilateral,
+\[
+\text{Area}=R\cdot s,
+\]
+where \(s\) is the semiperimeter.  
+Given \(\text{Area}=72\) and \(R=3\),
+
+\[
+s=\frac{72}{3}=24,
+\qquad\text{so } r+s+2L=2s=48. \tag{1}
+\]
+
+---
+
+### 2.  Height of the trapezoid
+
+Since the incircle touches both parallel sides, the distance between them equals twice the radius:
+
+\[
+h=2R=6.
+\]
+
+The area also equals \(\frac{1}{2}(r+s)h\). Thus
+
+\[
+72=\frac{1}{2}(r+s)\cdot6 \Longrightarrow r+s=24. \tag{2}
+\]
+
+Substituting (2) into (1) gives
+
+\[
+24+2L=48\Longrightarrow L=12. \tag{3}
+\]
+
+---
+
+### 3.  Relating the bases and the leg
+
+In an isosceles trapezoid the horizontal projection of each leg is \(\dfrac{s-r}{2}\).
+Using the right triangle formed by a leg, the height, and this projection:
+
+\[
+\left(\frac{s-r}{2}\right)^2+h^2=L^2.
+\]
+
+Insert \(h=6\) and \(L=12\):
+
+\[
+\left(\frac{s-r}{2}\right)^2+36=144
+\;\Longrightarrow\;
+\frac{(s-r)^2}{4}=108
+\;\Longrightarrow\;
+(s-r)^2=432.
+\]
+
+Hence
+
+\[
+s-r=12\sqrt3. \tag{4}
+\]
+
+---
+
+### 4.  Solve for \(r\) and \(s\)
+
+From (2) and (4):
+
+\[
+\begin{cases}
+r+s=24,\\[2pt]
+s-r=12\sqrt3,
+\end{cases}
+\qquad\Longrightarrow\qquad
+s=12+6\sqrt3,\;\; r=12-6\sqrt3.
+\]
+
+Both are positive and distinct, as required.
+
+---
+
+### 5.  Compute \(r^{2}+s^{2}\)
+
+\[
+\begin{aligned}
+r^{2}+s^{2}&amp;=(12-6\sqrt3)^2+(12+6\sqrt3)^2\\
+&amp;=2\cdot12^{2}+2\cdot(6\sqrt3)^{2}\\
+&amp;=2\cdot144+2\cdot108\\
+&amp;=288+216\\
+&amp;=504.
+\end{aligned}
+\]
+
+---
+
+\[
+\boxed{504}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 504</p>
+<p>Extracted Answer: 504</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+There are $8!=40320$ eight-digit positive integers that use each of the digits $1,2,3,4,5,6,7,8$ exactly once. Let $N$ be the number of these integers that are divisible by 22. Find the difference between $N$ and 2025.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>For an \(8\)-digit number formed with the digits \(1,2,\dots ,8\) each once we need
+
+* divisibility by \(2\)   \(\Longrightarrow\) the units digit is even (\(2,4,6,8\));
+* divisibility by \(11\) \(\Longrightarrow\) the alternating sum of its digits is a multiple of \(11\).
+
+---
+
+### 1.  Divisibility by \(11\)
+
+Write the digits as \(d_1d_2d_3d_4d_5d_6d_7d_8\) ( \(d_1\) most significant).  
+
+The test for \(11\) gives  
+
+\[
+(d_1+d_3+d_5+d_7)-(d_2+d_4+d_6+d_8)\equiv0\pmod{11}.
+\]
+
+Let  
+
+\[
+O=d_1+d_3+d_5+d_7,\qquad E=d_2+d_4+d_6+d_8 .
+\]
+
+Since all eight digits are used once,  
+
+\[
+O+E = 1+2+\dots+8 = 36 .
+\]
+
+The condition \(O-E\equiv0\pmod{11}\) becomes  
+
+\[
+2O\equiv36\pmod{11}\quad\Longrightarrow\quad O\equiv18\equiv7\pmod{11}.
+\]
+
+The sum of four distinct digits from \(\{1,\dots ,8\}\) lies between \(10\) and \(26\); the only value congruent to \(7\pmod{11}\) in that range is \(18\).  
+Hence we must have  
+
+\[
+O=E=18.
+\]
+
+So the four digits placed in the odd positions must sum to \(18\).
+
+---
+
+### 2.  Choosing the odd–position digits
+
+We need all \(4\)-element subsets of \(\{1,\dots ,8\}\) whose sum is \(18\).
+
+Listing them (in increasing order) gives
+
+\[
+\begin{aligned}
+&amp;\{1,2,7,8\},\; \{1,3,6,8\},\; \{1,4,5,8\},\; \{1,4,6,7\},\\
+&amp;\{2,3,5,8\},\; \{2,3,6,7\},\; \{2,4,5,7\},\; \{3,4,5,6\}.
+\end{aligned}
+\]
+
+There are \(8\) such subsets.  
+Each of them contains exactly two even digits (the even digits are \(2,4,6,8\)). Consequently the complementary set (the digits placed in even positions) also contains exactly two evens.
+
+---
+
+### 3.  Forming the numbers
+
+*For a fixed subset* \(S\) (the odd‑position digits)
+
+* arrange its four digits among the odd places \(1,3,5,7\): \(4!\) ways;
+* the four remaining digits (the complement \(T\)) go to the even places \(2,4,6,8\).  
+  Since \(T\) contains two even digits, we may pick which even digit occupies the units place (position \(8\)) in \(2\) ways; the other three digits can be placed in \(3!\) ways.
+
+Hence for each subset \(S\)
+
+\[
+\text{permutations}=4!\times 2\times3!=24\times12=288 .
+\]
+
+With \(8\) possible subsets,
+
+\[
+N=8\times288=2304 .
+\]
+
+(Equivalently, half of the \(4608\) numbers with \(O=E=18\) are even, giving the same result.)
+
+---
+
+### 4.  Required difference
+
+\[
+N-2025 = 2304-2025 = 279.
+\]
+
+Thus the requested difference is  
+
+\[
+\boxed{279}.
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 279</p>
+<p>Extracted Answer: 279</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Suppose $ \triangle ABC $ has angles $ \angle BAC = 84^\circ $, $ \angle ABC = 60^\circ $, and $ \angle ACB = 36^\circ $. Let $ D, E, $ and $ F $ be the midpoints of sides $ \overline{BC} $, $ \overline{AC} $, and $ \overline{AB} $, respectively. The circumcircle of $ \triangle DEF $ intersects $ \overline{BD} $, $ \overline{AE} $, and $ \overline{AF} $ at points $ G, H, $ and $ J $, respectively. The points $ G, D, E, H, J, $ and $ F $ divide the circumcircle of $ \triangle DEF $ into six minor arcs, as shown. Find $ \widehat{DE} + 2 \cdot \widehat{HJ} + 3 \cdot \widehat{FG} $, where the arcs are measured in degrees.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>We place \(\triangle ABC\) on its circumcircle (radius 1) with  
+
+\[
+A=1,\qquad B=e^{i2C},\qquad C=e^{i(2C+2A)} .
+\]
+
+The orthocenter is  
+
+\[
+H=a+b+c.
+\]
+
+The nine‑point circle is the image of the circumcircle under the homothety with centre \(H\) and factor \(\tfrac12\); therefore for any point \(X\) on the nine‑point circle its image on the circumcircle is  
+
+\[
+X&#39; = 2X-H .
+\]
+
+Applying this to the six points on the nine‑point circle gives
+
+\[
+\begin{aligned}
+D&amp;\mapsto -a,\\
+E&amp;\mapsto -b,\\
+F&amp;\mapsto -c,\\
+G&amp;\mapsto A&#39; ,\qquad A&#39; \text{ is the second intersection of the altitude }AA_H\text{ with the circumcircle},\\
+H&amp;\mapsto B&#39; ,\qquad B&#39;=-e^{i2A},\\
+J&amp;\mapsto C&#39; ,\qquad C&#39;=-e^{-i2A}.
+\end{aligned}
+\]
+
+Using \(a=1,\;b=e^{i2C},\;c=e^{i(2C+2A)}\) we obtain the central
+angles (measured from the positive \(x\)-axis) of the corresponding points:
+
+\[
+\begin{array}{c|c}
+\text{Nine‑point point} &amp; \text{Angle on the circumcircle}\\ \hline
+D &amp; 180^\circ\\
+E &amp; 180^\circ+2C\\
+F &amp; 180^\circ-2B\\
+G &amp; 180^\circ+2A+4C\\
+H &amp; 180^\circ+2A\\
+J &amp; 180^\circ-2A
+\end{array}
+\]
+
+Because the homothety preserves directions from the centre, the
+arc length on the nine‑point circle equals the corresponding central
+angle on the circumcircle.
+
+Hence
+
+\[
+\begin{aligned}
+\widehat{DE}&amp;=(180^\circ+2C)-180^\circ =2C,\\[2mm]
+\widehat{HJ}&amp;=|\, (180^\circ+2A)-(180^\circ-2A)\,|=4A,
+\end{aligned}
+\]
+
+and the minor arc \(HJ\) is \(360^\circ-4A\) (since \(4A&gt;180^\circ\)).
+Finally
+
+\[
+\widehat{FG}=|(180^\circ-2B)-(180^\circ+2A+4C)|
+            =2C\qquad(\text{mod }360^\circ).
+\]
+
+Thus
+
+\[
+\begin{aligned}
+\widehat{DE}+2\widehat{HJ}+3\widehat{FG}
+&amp;=2C+2\bigl(360^\circ-4A\bigr)+3\,(2C) \\
+&amp;=720^\circ-8A+8C\\
+&amp;=720^\circ+8(C-A).
+\end{aligned}
+\]
+
+For the given triangle \(A=84^\circ,\;C=36^\circ\),
+
+\[
+720^\circ+8(36^\circ-84^\circ)=720^\circ-384^\circ=336^\circ .
+\]
+
+\[
+\boxed{336}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 336</p>
+<p>Extracted Answer: 336</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+There are exactly three positive real numbers $ k $ such that the function
+$ f(x) = \frac{(x - 18)(x - 72)(x - 98)(x - k)}{x} $
+defined over the positive real numbers achieves its minimum value at exactly two positive real numbers $ x $. Find the sum of these three values of $ k $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>The function  
+
+\[
+f(x)=\frac{(x-18)(x-72)(x-98)(x-k)}{x}, \qquad x&gt;0,
+\]
+
+has zeros at \(x=18,72,98,k\) and \(\displaystyle\lim_{x\to0^+}f(x)=+\infty\),
+\(\displaystyle\lim_{x\to\infty}f(x)=+\infty\).
+Hence the graph of \(f\) starts at \(+\infty\), descends to a negative
+value, comes back to zero, rises again, etc.; it has exactly **two**
+negative intervals:
+\[
+(r_1,r_2),\qquad (r_3,r_4),
+\]
+where \(\{r_1,r_2,r_3,r_4\}=\{18,72,98,k\}\) ordered increasingly.
+In each negative interval there is a local (and global) minimum of \(f\).
+
+Let  
+
+\[
+g(x)=(x-18)(x-72)(x-98)(x-k),
+\qquad f(x)=\frac{g(x)}{x}.
+\]
+
+A point \(x_0\) where \(f\) has an extremum satisfies  
+
+\[
+f&#39;(x_0)=0\iff x_0g&#39;(x_0)-g(x_0)=0\iff 
+\sum_{i=1}^{4}\frac{1}{x_0-r_i}= \frac1{x_0}.
+\]
+
+Geometrically, if \(m=f(x_0)\) then the line \(y=m x\) is tangent to the
+quartic graph \(y=g(x)\) at \(x_0\):
+\[
+g(x)-mx=0\quad\text{has a double root at }x_0 .
+\]
+
+If the global minimum of \(f\) is attained at **two** distinct points,
+the line \(y=m x\) must be tangent to \(g\) at two distinct points
+\(\alpha,\beta\). Hence
+
+\[
+g(x)-mx=(x-\alpha)^2 (x-\beta)^2 .
+\tag{1}
+\]
+
+Write  
+
+\[
+\alpha+\beta=p,\qquad \alpha\beta =q,\qquad m \text{ (the slope)} .
+\]
+
+Expanding (1) and comparing with \(g(x)-mx=x^4-S_1x^3+S_2x^2-(S_3+m)x+S_4\) gives  
+
+\[
+\begin{aligned}
+S_1 &amp;=2p,\\
+S_2 &amp;=p^{2}+2q,\\
+S_4 &amp;=q^{2},\\
+S_3+m &amp;=2pq,
+\end{aligned}
+\tag{2}
+\]
+
+where for our roots  
+
+\[
+\begin{aligned}
+S_1&amp;=18+72+98+k=188+k,\\
+S_2&amp;=18\cdot72+18\cdot98+72\cdot98+ (18+72+98)k
+     =10116+188k,\\
+S_3&amp;=18\cdot72\cdot98+ (18\cdot72+18\cdot98+72\cdot98)k
+     =127008+10116k,\\
+S_4&amp;=18\cdot72\cdot98\cdot k=127008\,k .
+\end{aligned}
+\]
+
+From (2) we obtain  
+
+\[
+p=\frac{188+k}{2},\qquad q=\sqrt{127008\,k}=252\sqrt{2k}.
+\]
+
+Using the second equation of (2),
+
+\[
+S_2=p^{2}+2q,
+\]
+
+gives the condition on \(k\):
+
+\[
+\frac{(188+k)^{2}}{4}+2\sqrt{127008k}=10116+188k .
+\tag{3}
+\]
+
+---
+
+### Solving (3)
+
+Put \(k=t^{2}\;(t&gt;0)\).  Since \(\sqrt{127008k}=252\sqrt{2}\,t\),
+(3) becomes
+
+\[
+t^{4}-376t^{2}+2016\sqrt{2}\,t-5120=0 .
+\]
+
+Factoring,
+
+\[
+(t^{2}+6\sqrt{2}\,t-320)(t^{2}-6\sqrt{2}\,t+16)=0 .
+\]
+
+Hence the positive solutions for \(t\) are
+
+\[
+t=10\sqrt2,\qquad t=4\sqrt2,\qquad t=2\sqrt2 .
+\]
+
+Consequently
+
+\[
+k=t^{2}=200,\;32,\;8 .
+\]
+
+---
+
+### Verification
+
+For each \(k\) the ordered roots of \(g\) are
+
+\[
+\begin{array}{c|c}
+k &amp; \text{ordered roots }(r_1,r_2,r_3,r_4)\\ \hline
+8  &amp; (8,18,72,98)\\
+32 &amp; (18,32,72,98)\\
+200&amp; (18,72,98,200)
+\end{array}
+\]
+
+Using \(p\) and \(q\) we find the tangency points  
+
+\[
+\alpha,\beta=\frac{p\pm\sqrt{p^{2}-4q}}{2},
+\]
+
+and they lie respectively in the intervals \((r_1,r_2)\) and
+\((r_3,r_4)\). Thus in each case the line \(y=m x\) is tangent to
+\(g\) at two points, giving exactly two distinct global minima of
+\(f\). No other \(k&gt;0\) satisfies (3); hence these are the only three
+values.
+
+Finally, the required sum is
+
+\[
+8+32+200 = 240 .
+\]
+
+\[
+\boxed{240}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 240</p>
+<p>Extracted Answer: 240</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $k$ be real numbers such that the system $|25+20i-z|=5$ and $|z-4-k|=|z-3i-k|$ has exactly one complex solution $z$. The sum of all possible values of $k$ can be written as $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$. Here $i=\sqrt{-1}$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+\[
+z=x+iy\qquad (x,y\in\mathbb{R}).
+\]
+
+---
+
+### 1.  The first equation – a circle  
+
+\[
+|25+20i-z|=5 \Longrightarrow (x-25)^2+(y-20)^2=5^2 .
+\]
+
+Thus the circle has centre  
+
+\[
+C=(25,20),\qquad \text{radius } r=5 .
+\]
+
+---
+
+### 2.  The second equation – a perpendicular bisector  
+
+\[
+|z-(4+k)|=|z-(3i+k)|
+\]
+
+writes as  
+
+\[
+(x-(k+4))^2+y^{2}=(x-k)^2+(y-3)^2 .
+\]
+
+Simplifying,
+
+\[
+-8x+6y+8k+7=0\quad\Longrightarrow\quad 4x-3y-(4k+3.5)=0 .
+\]
+
+Hence the set of points satisfying the second condition is the line  
+
+\[
+L:\;4x-3y=4k+\frac 72 .
+\]
+
+This is the perpendicular bisector of the segment joining  
+\(A=(k+4,0)\) and \(B=(k,3)\) (its slope is \(4/3\) for any \(k\)).
+
+---
+
+### 3.  One intersection  \(\iff\)  tangency  
+
+The system has exactly one solution precisely when the line \(L\) is tangent to the circle, i.e. when the distance from the centre \(C\) to \(L\) equals the radius \(5\).
+
+The distance from \((x_0,y_0)\) to \(Ax+By+C=0\) is  
+
+\[
+\frac{|Ax_0+By_0+C|}{\sqrt{A^2+B^2}} .
+\]
+
+For \(C=(25,20)\) and \(L: 4x-3y-(4k+3.5)=0\),
+
+\[
+d=\frac{|4\cdot25-3\cdot20-(4k+3.5)|}{\sqrt{4^{2}+(-3)^{2}}}
+   =\frac{|40-4k-3.5|}{5}
+   =\frac{|36.5-4k|}{5}.
+\]
+
+Set \(d=r=5\):
+
+\[
+\frac{|36.5-4k|}{5}=5\quad\Longrightarrow\quad |36.5-4k|=25 .
+\]
+
+---
+
+### 4.  Solving for \(k\)
+
+\[
+\begin{cases}
+36.5-4k=25 &amp;\Longrightarrow\;4k=11.5\;\Longrightarrow\;k=\dfrac{23}{8},\\[4pt]
+36.5-4k=-25 &amp;\Longrightarrow\;4k=61.5\;\Longrightarrow\;k=\dfrac{123}{8}.
+\end{cases}
+\]
+
+Thus the possible real values of \(k\) are  
+
+\[
+k_1=\frac{23}{8},\qquad k_2=\frac{123}{8}.
+\]
+
+Both give a line tangent to the circle, so each yields exactly one solution \(z\).
+
+---
+
+### 5.  Sum of the possible \(k\)’s  
+
+\[
+k_1+k_2=\frac{23+123}{8}=\frac{146}{8}=\frac{73}{4}.
+\]
+
+Write \(\frac{73}{4}\) as \(\dfrac{m}{n}\) with \(\gcd(m,n)=1\); here \(m=73,\ n=4\).
+
+\[
+m+n=73+4=77.
+\]
+
+\[
+\boxed{77}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 77</p>
+<p>Extracted Answer: 77</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let the sequence of rationals $ x_1, x_2, \ldots $ be defined such that $ x_1 = \frac{25}{11} $ and
+$ x_{k+1} = \frac{1}{3} \left( x_k + \frac{1}{x_k} - 1 \right). $
+$ x_{2025} $ can be expressed as $ \frac{m}{n} $ for relatively prime positive integers $ m $ and $ n $. Find the remainder when $ m + n $ is divided by 1000.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>**Step 1.  Write the recurrence for the numerators and denominators**
+
+Let  
+
+\[
+x_k=\frac{a_k}{b_k}\qquad (a_k,b_k\in \mathbb Z ,\; \gcd(a_k,b_k)=1).
+\]
+
+From  
+
+\[
+x_{k+1}= \frac{1}{3}\Bigl(x_k+\frac1{x_k}-1\Bigr)=\frac{x_k^2-x_k+1}{3x_k},
+\]
+
+we obtain  
+
+\[
+a_{k+1}=a_k^2-a_kb_k+b_k^2,\qquad   
+b_{k+1}=3a_kb_k,          \tag{1}
+\]
+
+with \(a_1=25,\;b_1=11\).
+
+--------------------------------------------------------------------
+
+**Step 2.  The common factor \(3^{e_k}\)**  
+
+Write  
+
+\[
+a_k=3^{e_k}A_k,\qquad b_k=3^{e_k}B_k,\qquad \gcd(A_k,B_k)=1 .
+\]
+
+Dividing (1) by the highest possible power of \(3\) shows that
+\(e_{k+1}=2e_k+1\) and that the reduced pair \((A_k,B_k)\) always satisfies  
+
+\[
+A_k\equiv1\pmod3,\qquad B_k\equiv2\pmod3 .
+\]
+
+With \(e_1=0\) we get  
+
+\[
+e_k=2^{\,k-1}-1 .\tag{2}
+\]
+
+--------------------------------------------------------------------
+
+**Step 3.  A very simple recurrence for the sum**
+
+Let  
+
+\[
+S_k=a_k+b_k .
+\]
+
+From (1)
+
+\[
+\begin{aligned}
+S_{k+1}&amp;=a_{k+1}+b_{k+1}
+       =(a_k^2-a_kb_k+b_k^2)+3a_kb_k   \\
+       &amp;=a_k^2+b_k^2+2a_kb_k=(a_k+b_k)^2=S_k^{\,2}.
+\end{aligned}
+\]
+
+Hence  
+
+\[
+S_k=S_1^{\,2^{\,k-1}}=36^{\,2^{\,k-1}}. \tag{3}
+\]
+
+--------------------------------------------------------------------
+
+**Step 4.  The reduced numerator and denominator**
+
+Since the common factor is \(3^{e_k}\),
+
+\[
+\frac{a_k}{b_k}= \frac{A_k}{B_k},\qquad 
+m=A_k,\; n=B_k .
+\]
+
+Thus  
+
+\[
+m+n=\frac{a_k+b_k}{3^{e_k}}
+     =\frac{36^{\,2^{\,k-1}}}{3^{\,2^{\,k-1}-1}}
+     =2^{\,2^{\,k}}\;3^{\,2^{\,k-1}+1}. \tag{4}
+\]
+
+--------------------------------------------------------------------
+
+**Step 5.  Apply \(k=2025\)**  
+
+From (4),
+
+\[
+m+n=2^{\,2^{2025}}\;3^{\,2^{2024}+1}.
+\]
+
+We need this number modulo \(1000\).
+
+--------------------------------------------------------------------
+
+**Step 6.  Reduce modulo \(8\) and \(125\)**  
+
+*Modulo \(8\):*  \(2^{\ge3}\equiv0\pmod8\); therefore  
+
+\[
+m+n\equiv0\pmod8. \tag{5}
+\]
+
+*Modulo \(125\):*  Because \(\phi(125)=100\),
+
+\[
+2^{2^{2025}}\equiv 2^{\,2^{2025}\bmod100},
+\qquad
+3^{2^{2024}+1}\equiv 3^{\,(2^{2024}+1)\bmod100}\pmod{125}.
+\]
+
+Compute the exponents.
+
+- \(2^{2025}\bmod100\):  
+  \(2^{2025}\equiv32\pmod{100}\) (by CRT: \(2^{2025}\equiv0\pmod4\), \(2^{2025}\equiv7\pmod{25}\)).
+- \(2^{2024}\bmod100\):  
+  \(2^{2024}\equiv16\pmod{100}\).
+
+Hence  
+
+\[
+2^{2^{2025}}\equiv2^{32}\equiv46\pmod{125},
+\qquad
+3^{2^{2024}+1}\equiv3^{17}\equiv38\pmod{125}.
+\]
+
+Therefore  
+
+\[
+m+n\equiv46\cdot38\equiv123\pmod{125}. \tag{6}
+\]
+
+--------------------------------------------------------------------
+
+**Step 7.  Chinese Remainder Theorem**
+
+Find \(N\) such that  
+
+\[
+N\equiv0\pmod8,\qquad N\equiv123\pmod{125}.
+\]
+
+Write \(N=8k\).  Then \(8k\equiv123\pmod{125}\), i.e.  
+
+\[
+k\equiv123\cdot8^{-1}\pmod{125}.
+\]
+
+Since \(8^{-1}\equiv47\pmod{125}\),  
+
+\[
+k\equiv123\cdot47\equiv31\pmod{125}.
+\]
+
+Thus \(k=31+125t\) and  
+
+\[
+N=8k=8\cdot31=248\pmod{1000}.
+\]
+
+--------------------------------------------------------------------
+
+**Answer**
+
+\[
+\boxed{248}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 248</p>
+<p>Extracted Answer: 248</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+The twelve letters $A,B,C,D,E,F,G,H,I,J,K$, and $L$ are randomly grouped into six pairs of letters. The two letters in each pair are placed next to each other in alphabetical order to form six two-letter words, and those six words are listed alphabetically. For example, a possible result is $AB,CJ,DG,EK,FL,HI$. The probability that the last word listed contains $G$ is $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+\[
+A&lt;B&lt;C&lt;D&lt;E&lt;F&lt;G&lt;H&lt;I&lt;J&lt;K&lt;L
+\]
+
+and suppose the letters are randomly paired.  
+For a pair \(\{x,y\}\) we write the word \(xy\) with the letters in
+alphabetical order (\(x&lt;y\)).  
+The six words are then ordered alphabetically; the last word is the
+lexicographically largest word.
+
+--------------------------------------------------------------------
+### 1.  Conditioning on the partner of \(G\)
+
+In a random perfect matching each of the other \(11\) letters is equally
+likely to be paired with \(G\).  
+Let the partner be \(X\).  The probability we need is  
+
+\[
+P=\frac1{11}\sum_{X\neq G}
+\Pr\bigl(\text{the pair } \{G,X\}\text{ is the maximal word}\mid
+G\text{ is paired with }X\bigr).
+\]
+
+Thus we must evaluate the conditional probability for each possible
+\(X\).
+
+--------------------------------------------------------------------
+### 2.  When \(X&lt;G\)
+
+If \(X&lt;G\) the word is \(XG\) and its first letter is \(X\).  
+For it to be the maximal word, the first letters (the smaller letters)
+of all other five pairs must be **smaller than \(X\)**.
+Hence among the remaining ten letters we need five distinct letters
+all less than \(X\).
+
+The only letter with five smaller letters is \(F\) (the letters
+\(A,B,C,D,E\) are smaller).  
+Thus:
+
+* \(X=F\) is possible;
+* \(X=A,B,C,D,E\) are impossible (there are not enough smaller
+letters).
+
+When \(X=F\) the remaining letters are  
+\(\{A,B,C,D,E\}\) and \(\{H,I,J,K,L\}\).  
+To keep every other pair’s first letter \(&lt;F\), each of the five large
+letters must be paired with a distinct small one.  
+The number of such matchings is \(5!=120\).
+
+The total number of matchings of those ten letters is  
+
+\[
+\frac{10!}{2^5\,5!}=945 .
+\]
+
+Hence  
+
+\[
+\Pr(\text{maximal}\mid G\text{–}F)=\frac{120}{945}=\frac{8}{63}.
+\]
+
+--------------------------------------------------------------------
+### 3.  When \(X&gt;G\)
+
+Now the word is \(GX\) and its first letter is \(G\).
+For it to be maximal, **no other pair may have a first letter larger
+than \(G\)**; i.e. no remaining pair may consist of two letters both
+greater than \(G\).
+
+After fixing the pair \(\{G,X\}\) (with \(X\in\{H,I,J,K,L\}\)), the
+remaining letters are
+
+* the six letters \(\{A,B,C,D,E,F\}\) (all \(&lt;G\));
+* the four letters among \(\{H,I,J,K,L\}\) that are not \(X\) (all
+\(&gt;G\)).
+
+Thus each of those four “large’’ letters must be paired with a distinct
+small letter, leaving two small letters to pair together.
+
+Number of valid matchings:
+
+\[
+\binom{6}{4}\cdot4!\cdot1=15\cdot24=360 .
+\]
+
+Again the total number of matchings of the ten remaining letters is
+\(945\). Therefore
+
+\[
+\Pr(\text{maximal}\mid G\text{–}X)=\frac{360}{945}=\frac{8}{21}
+\qquad (X=H,I,J,K,L).
+\]
+
+--------------------------------------------------------------------
+### 4.  Assemble the probability
+
+\[
+\begin{aligned}
+P&amp;=\frac1{11}\Bigl(\frac{8}{63}
++5\cdot\frac{8}{21}\Bigr)    \\
+ &amp;=\frac1{11}\Bigl(\frac{8}{63}+\frac{40}{21}\Bigr)
+   =\frac1{11}\Bigl(\frac{8+120}{63}\Bigr)
+   =\frac{128}{693}.
+\end{aligned}
+\]
+
+The fraction \(\displaystyle\frac{128}{693}\) is already in lowest
+terms.  Hence \(m=128,\;n=693\) and
+
+\[
+m+n = 128+693 = 821 .
+\]
+
+--------------------------------------------------------------------
+\[
+\boxed{821}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 821</p>
+<p>Extracted Answer: 821</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $N$ denote the number of ordered triples of positive integers $(a,b,c)$ such that $a,b,c\leq3^6$ and $a^3+b^3+c^3$ is a multiple of $3^7$. Find the remainder when $N$ is divided by $1000$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+\[
+S(t)=\sum_{a=1}^{3^{6}}\exp\!\Big(2\pi i\,\frac{t a^{3}}{3^{7}}\Big) \qquad(0\le t&lt;3^{7})
+\]
+
+and denote  
+
+\[
+N=\#\{(a,b,c)\mid 1\le a,b,c\le 3^{6},
+\ a^{3}+b^{3}+c^{3}\equiv 0\pmod{3^{7}}\}.
+\]
+
+For any modulus \(m\),
+
+\[
+\#\{(x,y,z):x+y+z\equiv0\pmod m\}=
+\frac1m\sum_{t=0}^{m-1}\Bigl(\sum_{x}e^{2\pi i t x/m}\Bigr)^3 .
+\]
+
+Hence  
+
+\[
+N=\frac1{3^{7}}\sum_{t=0}^{3^{7}-1} S(t)^{3}. \tag{1}
+\]
+
+--------------------------------------------------------------------
+### 1.  Splitting the summation
+
+Write each \(a\) as \(a=3^{v}u\) where \(v=v_{3}(a)\) and \(u\) is not
+divisible by \(3\).  
+For \(0\le v\le 2\) define  
+
+\[
+U_{v}=\{\,u:1\le u\le 3^{6-v},\;3\nmid u\,\},
+\qquad |U_{0}|=486,\ |U_{1}|=162,\ |U_{2}|=54 .
+\]
+
+If \(v\ge3\) then \(a^{3}\equiv0\pmod{3^{7}}\); there are  
+\(n_{3}=27\) such numbers.
+Thus
+
+\[
+S(t)=f_{0}(t)+f_{1}(t)+f_{2}(t)+n_{3},
+\]
+where  
+
+\[
+\begin{aligned}
+f_{0}(t)&amp;=\sum_{x\in U_{0}}\zeta^{t x^{3}},\\[2mm]
+f_{1}(t)&amp;=\sum_{x\in U_{1}}\zeta^{t\,27x^{3}},\\[2mm]
+f_{2}(t)&amp;=\sum_{x\in U_{2}}\zeta^{t\,729x^{3}},
+\end{aligned}
+\qquad 
+\zeta=e^{2\pi i/3^{7}} .
+\]
+
+--------------------------------------------------------------------
+### 2.  Evaluating \(f_{0},f_{1},f_{2}\)
+
+*For \(f_{0}\).*  
+Let \(G_{7}=(\mathbb Z/3^{7}\mathbb Z)^{\times}\) (\(|G_{7}|=1458\)).
+The map \(x\mapsto x^{3}\) from \(G_{7}\) onto the set of cubes
+\(C_{6}\) has kernel of size \(3\); consequently
+
+\[
+\sum_{x\in G_{7}}\zeta^{t x}=3\sum_{r\in C_{6}}\zeta^{t r}=3f_{0}(t).
+\]
+
+For \(t\neq0\) one has  
+
+\[
+\sum_{x\in G_{7}}\zeta^{t x}= -\!\!\sum_{\substack{x\;(\bmod 3^{7})\\3\mid x}}\!\!\zeta^{t x}
+=\begin{cases}
+-729,&amp;v_{3}(t)=6,\\
+0,&amp;0\le v_{3}(t)\le5 .
+\end{cases}
+\]
+
+Hence  
+
+\[
+f_{0}(t)=
+\begin{cases}
+486,&amp;t=0,\\[2mm]
+-243,&amp;v_{3}(t)=6,\\[2mm]
+0,&amp;\text{otherwise.}
+\end{cases}
+\tag{2}
+\]
+
+*For \(f_{1}\).*  
+Writing each \(x\in U_{1}\) as \(x=v+81k\;(k=0,1,2)\) one finds
+\(x^{3}\equiv v^{3}\pmod{81}\). Consequently  
+
+\[
+f_{1}(t)=3\!\!\sum_{\substack{v\in(\mathbb Z/81)^{\times}}}\!
+\exp\!\Big(2\pi i\,\frac{t v^{3}}{81}\Big).
+\]
+
+Using again that the cube map on \((\mathbb Z/81)^{\times}\) has kernel
+size \(3\),
+
+\[
+f_{1}(t)=3\!\cdot\!3\!\!\sum_{r\in C_{1}}\!
+\exp\!\Big(2\pi i\,\frac{t r}{81}\Big) ,
+\]
+
+where \(C_{1}\) is the set of cube‑residues modulo \(81\) (\(|C_{1}|=18\)).
+Now
+
+\[
+\sum_{x\in(\mathbb Z/81)^{\times}}\exp\!\Big(2\pi i\,
+\frac{t x}{81}\Big)=
+\begin{cases}
+54,&amp;v_{3}(t)\ge4,\\[1mm]
+-27,&amp;v_{3}(t)=3,\\[1mm]
+0,&amp;v_{3}(t)\le2 .
+\end{cases}
+\]
+
+Thus
+
+\[
+f_{1}(t)=
+\begin{cases}
+162,&amp;v_{3}(t)\ge4,\\[2mm]
+-81,&amp;v_{3}(t)=3,\\[2mm]
+0,&amp;v_{3}(t)\le2 .
+\end{cases}
+\tag{3}
+\]
+
+*For \(f_{2}\).*  
+Here \(x^{3}\equiv x\pmod 3\), and among the \(54\) numbers in \(U_{2}\)
+exactly half are \(\equiv1\pmod3\) and half \(\equiv2\pmod3\). Hence  
+
+\[
+f_{2}(t)=27\bigl(\zeta^{t}+ \zeta^{2t}\bigr)=
+\begin{cases}
+-27,&amp;v_{3}(t)=0,\\[2mm]
+54,&amp;v_{3}(t)\ge1 .
+\end{cases}
+\tag{4}
+\]
+
+--------------------------------------------------------------------
+### 3.  The values of \(S(t)\)
+
+From (2)–(4) (and remembering the constant term \(n_{3}=27\))
+
+\[
+S(t)=f_{0}(t)+f_{1}(t)+f_{2}(t)+27=
+\begin{array}{c|c}
+v_{3}(t) &amp; S(t)\\ \hline
+\infty\;(t=0) &amp; 729\\
+0 &amp; 0\\
+1 &amp; 81\\
+2 &amp; 81\\
+3 &amp; 0\\
+4 &amp; 243\\
+5 &amp; 243\\
+6 &amp; 0
+\end{array}
+\]
+
+--------------------------------------------------------------------
+### 4.  Computing \(N\)
+
+Only the classes with non‑zero \(S(t)\) contribute to (1).  
+The numbers of \(t\) in each class are
+
+\[
+\begin{array}{c|c}
+v_{3}(t) &amp; \#t\\ \hline
+\infty &amp; 1\\
+0 &amp; 1458\\
+1 &amp; 486\\
+2 &amp; 162\\
+3 &amp; 54\\
+4 &amp; 18\\
+5 &amp; 6\\
+6 &amp; 2
+\end{array}
+\]
+
+Hence
+
+\[
+\begin{aligned}
+N&amp;=\frac1{3^{7}}\Bigl( 729^{3}
++ (486+162) \,81^{3}
++ (18+6)\,243^{3}\Bigr)\\[2mm]
+&amp;=\frac1{3^{7}}\Bigl(3^{18}+648\cdot3^{12}+24\cdot3^{15}\Bigr)\\
+&amp;=3^{5}\cdot2025 = 243\cdot2025 = 492\,075 .
+\end{aligned}
+\]
+
+--------------------------------------------------------------------
+### 5.  Remainder modulo \(1000\)
+
+\[
+492\,075 \equiv 75 \pmod{1000}.
+\]
+
+--------------------------------------------------------------------
+\[
+\boxed{75}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 735</p>
+<p>Extracted Answer: 75</p>
+<p>Score: 0.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+On $\triangle ABC$ points $A,D,E$, and $B$ lie that order on side $\overline{AB}$ with $AD=4, DE=16$, and $EB=8$. Points $A,F,G$, and $C$ lie in that order on side $\overline{AC}$ with $AF=13, FG=52$, and $GC=26$. Let $M$ be the reflection of $D$ through $F$, and let $N$ be the reflection of $G$ through $E$. Quadrilateral $DEGF$ has area 288. Find the area of heptagon $AFNBCEM$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>**Solution Overview**
+
+The given lengths on the sides of \(\triangle ABC\) give  
+
+\[
+AD=4,\;DE=16,\;EB=8 \qquad\Longrightarrow\qquad AB=28,
+\]
+\[
+AF=13,\;FG=52,\;GC=26 \qquad\Longrightarrow\qquad AC=91 .
+\]
+
+--------------------------------------------------------------------
+
+### 1.  Two lines parallel to \(BC\)
+
+\[
+\frac{AD}{AB}= \frac{4}{28}= \frac{1}{7},\qquad 
+\frac{AF}{AC}= \frac{13}{91}= \frac{1}{7}.
+\]
+
+Hence the points \(D\in AB\) and \(F\in AC\) divide the two sides in the same
+ratio; therefore \(DF\parallel BC\).
+
+Similarly  
+
+\[
+\frac{AE}{AB}= \frac{AD+DE}{AB}= \frac{20}{28}= \frac57,
+\qquad 
+\frac{AG}{AC}= \frac{AF+FG}{AC}= \frac{65}{91}= \frac57,
+\]
+
+so \(E\in AB,\;G\in AC\) also give a line parallel to \(BC\); i.e. \(EG\parallel BC\).
+
+Thus the quadrilateral \(DEGF\) is bounded by two parallel sides \(DF,EG\) and
+the two segments of the sides of the triangle, and it is the region between the
+two similar triangles \(ADF\) and \(AEG\).
+
+--------------------------------------------------------------------
+
+### 2.  Area of \(\triangle ABC\)
+
+If \([XYZ]\) denotes area, similarity gives  
+
+\[
+[ADF]=\Bigl(\frac{AD}{AB}\Bigr)^2[ABC]=\Bigl(\frac17\Bigr)^2[ABC]=\frac{[ABC]}{49},
+\]
+
+\[
+[AEG]=\Bigl(\frac{AE}{AB}\Bigr)\Bigl(\frac{AG}{AC}\Bigr)[ABC]
+      =\frac57\cdot\frac57[ABC]=\frac{25}{49}[ABC].
+\]
+
+Hence  
+
+\[
+[DEGF]=[AEG]-[ADF]=\Bigl(\frac{25}{49}-\frac1{49}\Bigr)[ABC]
+       =\frac{24}{49}[ABC].
+\]
+
+Given \([DEGF]=288\),
+
+\[
+\frac{24}{49}[ABC]=288\quad\Longrightarrow\quad[ABC]=288\cdot\frac{49}{24}
+                  =12\cdot49=588.
+\]
+
+--------------------------------------------------------------------
+
+### 3.  Area of the heptagon \(AFNBCEM\)
+
+Place the triangle with \(A=(0,0),\;B=(28,0)\) and
+\(C=(91\cos\theta,\,91\sin\theta)\).
+Because \([ABC]=\tfrac12\cdot28\cdot91\sin\theta\),
+
+\[
+\sin\theta=\frac{[ABC]}{1274}= \frac{588}{1274}= \frac{6}{13}.
+\]
+
+Thus  
+
+\[
+\cos\theta=\frac{\sqrt{1-\sin^2\theta}}{\,}= \frac{\sqrt{133}}{13}.
+\]
+
+The coordinates of the relevant points are
+
+\[
+\begin{aligned}
+&amp;F=(13\cos\theta,13\sin\theta)=(\sqrt{133},6), \\
+&amp;G=(65\cos\theta,65\sin\theta)=(5\sqrt{133},30),\\
+&amp;D=(4,0),\qquad
+E=(20,0),\\
+&amp;M=2F-D=(2\sqrt{133}-4,12),\\
+&amp;N=2E-G=(40-5\sqrt{133},-30).
+\end{aligned}
+\]
+
+Using the shoelace formula for the polygon
+\(A\,(0,0),\;F,\;N,\;B,\;C,\;E,\;M\) we obtain
+
+\[
+\begin{aligned}
+\sum (x_i y_{i+1}-y_i x_{i+1})
+&amp;= -240+840+1176-840+240 = 1176,\\[2mm]
+\text{Area}&amp;=\frac12\cdot1176=588.
+\end{aligned}
+\]
+
+Thus the heptagon \(AFNBCEM\) has the same area as \(\triangle ABC\).
+
+--------------------------------------------------------------------
+
+\[
+\boxed{588}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 588</p>
+<p>Extracted Answer: 588</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+The parabola with equation $y=x^{2}-4$ is rotated $60^{\circ}$ counterclockwise around the origin. The unique point in the fourth quadrant where the original parabola and its image intersect has $y$-coordinate $\frac{a-\sqrt{b}}{c}$, where $a$, $b$, and $c$ are positive integers, and $a$ and $c$ are relatively prime. Find $a+b+c$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+\[
+P:\; y=x^{2}-4
+\]
+
+and rotate \(P\) about the origin \(60^{\circ}\) counter‑clockwise.  
+If \((x,y)\) is a point of \(P\) then its image \((X,Y)\) satisfies  
+
+\[
+\begin{pmatrix}X\\Y\end{pmatrix}= 
+\begin{pmatrix}\cos 60^\circ &amp; -\sin 60^\circ\\[2pt] 
+\sin 60^\circ &amp; \ \cos 60^\circ\end{pmatrix}
+\begin{pmatrix}x\\y\end{pmatrix},
+\qquad 
+\cos60^\circ=\frac12,\;\sin60^\circ=\frac{\sqrt3}{2}.
+\]
+
+Hence  
+
+\[
+X=\frac{x}{2}-\frac{\sqrt3}{2}y,\qquad
+Y=\frac{\sqrt3}{2}x+\frac{y}{2}.
+\]
+
+To obtain the equation of the rotated curve in the original \((x,y)\)–coordinates,
+solve for \((x,y)\) in terms of \((X,Y)\) (rotate back by \(-60^\circ\)):
+
+\[
+x = \frac{X}{2}+\frac{\sqrt3}{2}Y,\qquad
+y = -\frac{\sqrt3}{2}X+\frac{Y}{2}.
+\]
+
+Since the original points satisfy \(y=x^{2}-4\), substituting the expressions above gives the equation of the image:
+
+\[
+x^{2}+2\sqrt3\,xy+3y^{2}+2\sqrt3\,x-2y-16=0. \tag{1}
+\]
+
+--------------------------------------------------------------------
+### Intersection with the original parabola
+
+The intersection points satisfy simultaneously  
+
+\[
+y=x^{2}-4\qquad\text{and}\qquad (1).
+\]
+
+Substituting \(y=x^{2}-4\) into (1) yields
+
+\[
+3x^{4}-25x^{2}+40+2\sqrt3\,x^{3}-6\sqrt3\,x=0.
+\]
+
+Factor this quartic in the field \(\mathbb{Q}(\sqrt3)\):
+
+\[
+\begin{aligned}
+3x^{4}-25x^{2}+40+2\sqrt3\,x^{3}-6\sqrt3\,x
+&amp;=(x^{2}+\sqrt3\,x-4)\bigl(3x^{2}-\sqrt3\,x-10\bigr).
+\end{aligned}
+\]
+
+Thus the intersection points satisfy one of  
+
+\[
+\begin{cases}
+x^{2}+\sqrt3\,x-4=0,\\[2pt]
+\text{or}\\[2pt]
+3x^{2}-\sqrt3\,x-10=0 .
+\end{cases}
+\]
+
+--------------------------------------------------------------------
+### Selecting the point in the fourth quadrant
+
+*From* \(x^{2}+\sqrt3\,x-4=0\)
+
+\[
+x=\frac{-\sqrt3\pm\sqrt{19}}{2}.
+\]
+
+The root \(\displaystyle x=\frac{-\sqrt3+\sqrt{19}}{2}&gt;0\) gives  
+
+\[
+y=x^{2}-4=\frac{11-\sqrt{57}}{2}-4=\frac{3-\sqrt{57}}{2}&lt;0,
+\]
+
+so \((x,y)\) lies in the fourth quadrant.
+
+*From* \(3x^{2}-\sqrt3\,x-10=0\)
+
+\[
+x=\frac{\sqrt3\pm\sqrt{123}}{6},
+\]
+
+which yields either \(y&gt;0\) (first root) or \(x&lt;0\) (second root); neither point is in the fourth quadrant.
+
+Hence the unique fourth‑quadrant intersection point is  
+
+\[
+\Bigl(\frac{-\sqrt3+\sqrt{19}}{2}\,,\; \frac{3-\sqrt{57}}{2}\Bigr).
+\]
+
+--------------------------------------------------------------------
+### Required \(y\)-coordinate
+
+The \(y\)-coordinate is \(\displaystyle \frac{3-\sqrt{57}}{2}\).
+
+Write it as \(\frac{a-\sqrt{b}}{c}\) with \(a,b,c\) positive integers and \(\gcd(a,c)=1\):
+\[
+a=3,\qquad b=57,\qquad c=2.
+\]
+
+Therefore  
+
+\[
+a+b+c = 3+57+2 = 62.
+\]
+
+\[
+\boxed{62}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 62</p>
+<p>Extracted Answer: 62</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Six points $ A, B, C, D, E, $ and $ F $ lie in a straight line in that order. Suppose that $ G $ is a point not on the line and that $ AC = 26 $, $ BD = 22 $, $ CE = 31 $, $ DF = 33 $, $ AF = 73 $, $ CG = 40 $, and $ DG = 30 $. Find the area of $ \triangle BGE $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let the line containing \(A,B,C,D,E,F\) be the \(x\)-axis.
+
+\[
+A=(0,0),\qquad B=(b,0),\qquad C=(c,0),\qquad D=(d,0),\qquad 
+E=(e,0),\qquad F=(f,0)
+\]
+
+Because the points are in the order \(A,B,C,D,E,F\),
+
+\[
+c-b=AC-AB,\; d-b=BD,\; e-c=CE,\; f-d=DF,\; f-0=AF.
+\]
+
+Take \(A\) at the origin.  From the data
+
+\[
+AC=26\implies c=26,
+\]
+\[
+BD=22\implies d=b+22,
+\]
+\[
+CE=31\implies e=c+31=57,
+\]
+\[
+DF=33\implies f=d+33=b+55,
+\]
+\[
+AF=73\implies f=73.
+\]
+
+Hence \(b+55=73\Rightarrow b=18\).  
+Thus the coordinates are  
+
+\[
+B=(18,0),\; C=(26,0),\; D=(40,0),\; E=(57,0),\; F=(73,0).
+\]
+
+---
+
+### Locate \(G\)
+
+\(G\) is off the line and satisfies  
+
+\[
+CG=40,\qquad DG=30.
+\]
+
+Let \(G=(x,y)\) with \(y\neq0\). Then  
+
+\[
+(x-26)^2+y^{2}=40^{2}=1600,\tag{1}
+\]
+\[
+(x-40)^2+y^{2}=30^{2}=900.\tag{2}
+\]
+
+Subtract (2) from (1):
+
+\[
+(x-26)^2-(x-40)^2=700.
+\]
+
+Expanding,
+
+\[
+[x^{2}-52x+676]-[x^{2}-80x+1600]=28x-924=700,
+\]
+\[
+28x=1624\quad\Longrightarrow\quad x=58.
+\]
+
+Plugging \(x=58\) into (2):
+
+\[
+(58-40)^{2}+y^{2}=900\;\Longrightarrow\;18^{2}+y^{2}=900
+\]
+\[
+y^{2}=576\;\Longrightarrow\;|y|=24.
+\]
+
+So \(G=(58,\,24)\) (the point \((58,-24)\) gives the same area).
+
+---
+
+### Area of \(\triangle BGE\)
+
+Points \(B\) and \(E\) lie on the \(x\)-axis, so the base \(BE\) has length
+
+\[
+BE = e-b = 57-18 = 39.
+\]
+
+The altitude from \(G\) to the line \(BE\) (the \(x\)-axis) is \(|y| = 24\).
+
+Hence  
+
+\[
+\text{Area} = \frac12 \times BE \times \text{height}
+= \frac12 \times 39 \times 24 = 468.
+\]
+
+\[
+\boxed{468}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 468</p>
+<p>Extracted Answer: 468</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Find the sum of all positive integers $ n $ such that $ n + 2 $ divides the product $ 3(n + 3)(n^2 + 9) $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>We need the positive integers \(n\) such that  
+
+\[
+n+2\mid 3(n+3)(n^{2}+9).
+\]
+
+---
+
+### 1.  Replace \(n+2\) by a new variable  
+
+Let  
+
+\[
+k=n+2\qquad (k\ge 3), \qquad n=k-2 .
+\]
+
+Then  
+
+\[
+\begin{aligned}
+n+3 &amp;= (k-2)+3 = k+1,\\[2pt]
+n^{2}+9 &amp;= (k-2)^{2}+9 = k^{2}-4k+13 .
+\end{aligned}
+\]
+
+Hence  
+
+\[
+3(n+3)(n^{2}+9)=3(k+1)(k^{2}-4k+13).
+\]
+
+The condition becomes  
+
+\[
+k \mid 3(k+1)(k^{2}-4k+13).
+\]
+
+---
+
+### 2.  Reduce modulo \(k\)
+
+Modulo \(k\),
+
+\[
+k+1\equiv 1,\qquad k^{2}-4k+13\equiv 13,
+\]
+
+because \(k\equiv 0\) gives \(k^{2}\equiv 0\) and \(-4k\equiv 0\).
+
+Thus  
+
+\[
+3(k+1)(k^{2}-4k+13)\equiv 3\cdot 1\cdot 13=39 \pmod{k}.
+\]
+
+Hence the divisibility condition is equivalent to  
+
+\[
+k\mid 39.
+\]
+
+---
+
+### 3.  Find admissible \(k\) and corresponding \(n\)
+
+The positive divisors of \(39\) are \(1,3,13,39\).
+Since \(k=n+2\ge 3\), we keep  
+
+\[
+k\in \{3,13,39\}.
+\]
+
+Therefore  
+
+\[
+n=k-2\in\{1,11,37\}.
+\]
+
+All three values satisfy the original condition (a quick check confirms the division).
+
+---
+
+### 4.  Sum of all such \(n\)
+
+\[
+1+11+37 = 49.
+\]
+
+\[
+\boxed{49}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 49</p>
+<p>Extracted Answer: 49</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+The set of points in 3-dimensional coordinate space that lie in the plane $x+y+z=75$ whose coordinates satisfy the inequalities $x-yz&lt;y-zx&lt;z-xy$ forms three disjoint convex regions. Exactly one of those regions has finite area. The area of this finite region can be expressed in the form $a\sqrt{b}$, where $a$ and $b$ are positive integers and $b$ is not divisible by the square of any prime. Find $a+b$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>The inequalities
+
+\[
+x-yz&lt;y-zx&lt;z-xy
+\]
+
+with the plane \(x+y+z=75\) can be simplified.  
+Write \(z=75-x-y\). Then
+
+\[
+\begin{aligned}
+y-zx-(x-yz) &amp;= (y-x)(1+z)= (y-x)(76-x-y),\\
+z-xy-(y-zx) &amp;= (z-y)(1+x)= (75-x-2y)(1+x).
+\end{aligned}
+\]
+
+Thus the points on the plane satisfy  
+
+\[
+(y-x)(76-x-y)&gt;0,\qquad (75-x-2y)(1+x)&gt;0 .
+\tag{1}
+\]
+
+Define in the \(xy\)-plane the lines  
+
+\[
+\begin{aligned}
+L_1 &amp;: y=x,\\
+L_2 &amp;: x+y=76,\\
+L_3 &amp;: x=-1,\\
+L_4 &amp;: x+2y=75\;(y=(75-x)/2).
+\end{aligned}
+\]
+
+From (1) we obtain two possibilities for each product, giving four possible
+intersections of half‑planes.  One of these intersections is empty; the other three
+are convex.  The region for which both products in (1) are **positive** is
+
+\[
+\begin{cases}
+y&gt;x,\\
+x+y&lt;76,\\
+y&lt;(75-x)/2,\\
+x&gt;-1,
+\end{cases}
+\]
+
+which in the \(xy\)-plane is the interior of the triangle with vertices
+
+\[
+A(-1,-1),\qquad B(-1,38),\qquad C(25,25).
+\]
+
+The other two regions are unbounded.  Hence the finite region is this triangle.
+
+---
+
+### Area in the \(xy\)-plane
+
+\[
+\text{Area}_{xy}= \frac12\bigl|AB\times AC\bigr|
+               =\frac12\bigl| (0,39)\times (26,26)\bigr|
+               =\frac12\cdot1014 = 507 .
+\]
+
+---
+
+### Area on the plane \(x+y+z=75\)
+
+The plane is given by \(z=75-x-y\).  Its area element satisfies  
+
+\[
+dS = \sqrt{1+(\partial_xz)^2+(\partial_yz)^2}\;dx\,dy
+    =\sqrt{1+1+1}\;dx\,dy =\sqrt3\,dx\,dy .
+\]
+
+Hence  
+
+\[
+\text{Area}_{\text{plane}} = \sqrt3\;\text{Area}_{xy}
+                            = 507\sqrt3 .
+\]
+
+So the area can be written as \(a\sqrt b\) with \(a=507,\ b=3\).
+Therefore  
+
+\[
+a+b = 507+3 = 510 .
+\]
+
+\[
+\boxed{510}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 510</p>
+<p>Extracted Answer: 510</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+A piecewise linear periodic function is defined by $f(x)=\begin{cases}x&amp;\text{if }x\in[-1,1)\\2-x&amp;\text{if }x\in[1,3)\end{cases}$ and $f(x+4)=f(x)$ for all real numbers $x$. The graph of $f(x)$ has the sawtooth pattern. The parabola $x=34y^2$ intersects the graph of $f(x)$ at finitely many points. The sum of the $y$-coordinates of these intersection points can be expressed in the form $\frac{a+b\sqrt{c}}{d}$, where $a,b,c,$ and $d$ are positive integers, $a,b,$ and $d$ have greatest common divisor equal to 1, and $c$ is not divisible by the square of any prime. Find $a+b+c+d$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>The intersection points satisfy  
+
+\[
+y=f(x),\qquad x=34y^{2}\;( \ge 0).
+\]
+
+Because \(f\) has period \(4\),
+
+\[
+f(x)=\begin{cases}
+x-4k ,&amp;x\in[-1+4k,\,1+4k),\\[2mm]
+2+4k-x ,&amp;x\in[1+4k,\,3+4k),
+\end{cases}\qquad k\in\mathbb Z .
+\]
+
+--------------------------------------------------------------------
+### 1.  Equations for the two linear pieces  
+
+*Ascending piece*  \((x-4k)\):  
+
+\[
+y=x-4k,\qquad x=34y^{2}
+\Longrightarrow 34y^{2}-y-4k=0. \tag{1}
+\]
+
+*Descending piece*  \((2+4k-x)\):  
+
+\[
+y=2+4k-x,\qquad x=34y^{2}
+\Longrightarrow 34y^{2}+y-(2+4k)=0. \tag{2}
+\]
+
+Both are quadratics in \(y\); each can give at most two real roots.
+
+--------------------------------------------------------------------
+### 2.  Which integers \(k\) give admissible roots?
+
+Because \(|y|\le 1\) (the range of \(f\)), the roots must lie in \([-1,1]\).
+
+*For (1):*  
+The sum of the two roots equals \(\frac{1}{34}\); the product is \(-\frac{4k}{34}\).  
+The discriminant must be non‑negative:
+
+\[
+\Delta_1=1+544k\ge 0\Longrightarrow k\ge0 .
+\]
+
+For a root to be in \([-1,1)\) we also need  
+
+\[
+-1\le\frac{1\pm\sqrt{1+544k}}{68}&lt;1 .
+\]
+
+The last inequality forces \(k\le8\).  Hence (1) yields real admissible roots for  
+
+\[
+k=0,1,\dots ,8 .
+\]
+
+Both roots are in \([-1,1)\) for each of these values.
+
+*For (2):*  
+\[
+\Delta_2=273+544k\ge0\Longrightarrow k\ge0 .
+\]
+
+The condition \(-1&lt;y\le 1\) gives \(k\le8\).  
+For \(k=0,\dots ,7\) both roots lie in \((-1,1]\); for \(k=8\) only the “\(+\)” root
+\[
+y=\frac{-1+\sqrt{273+544\cdot8}}{68}
+      =\frac{-1+5\sqrt{185}}{68}
+\]
+remains in the interval (the “\(-\)” root is \(&lt;-1\)).
+
+Thus  
+
+* (1) contributes \(2\) solutions for each \(k=0,\dots ,8\)  \(\Rightarrow 18\) points;  
+* (2) contributes \(2\) solutions for each \(k=0,\dots ,7\) and \(1\) solution for \(k=8\)  \(\Rightarrow 17\) points.
+
+Hence there are \(35\) intersection points altogether.
+
+--------------------------------------------------------------------
+### 3.  Sum of the \(y\)-coordinates  
+
+For each fixed \(k\) the sum of the two roots of (1) is, by Vieta,
+
+\[
+\Sigma_{A}(k)=\frac{1}{34}.
+\]
+
+So the total contribution of (1) is  
+
+\[
+\sum_{k=0}^{8}\Sigma_{A}(k)=9\cdot\frac{1}{34}= \frac{9}{34}.
+\]
+
+For (2), when both roots exist their sum is  
+
+\[
+\Sigma_{B}(k)=-\frac{1}{34}.
+\]
+
+Thus for \(k=0,\dots ,7\) the total is  
+
+\[
+8\cdot\Bigl(-\frac{1}{34}\Bigr)=-\frac{8}{34}.
+\]
+
+For \(k=8\) only the positive root remains:
+
+\[
+y_{8}= \frac{-1+5\sqrt{185}}{68}.
+\]
+
+Adding everything,
+
+\[
+\begin{aligned}
+\text{Sum of all }y
+&amp;=\frac{9}{34}-\frac{8}{34}+y_{8}
+   =\frac{1}{34}+ \frac{-1+5\sqrt{185}}{68}\\[2mm]
+&amp;= \frac{2}{68}+ \frac{-1+5\sqrt{185}}{68}
+   =\frac{1+5\sqrt{185}}{68}.
+\end{aligned}
+\]
+
+--------------------------------------------------------------------
+### 4.  Final answer  
+
+The sum is \(\displaystyle\frac{1+5\sqrt{185}}{68}\).  
+Thus  
+
+\[
+a=1,\; b=5,\; c=185,\; d=68,\qquad
+a+b+c+d=1+5+185+68=259.
+\]
+
+\[
+\boxed{259}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 259</p>
+<p>Extracted Answer: 259</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+The 27 cells of a $3\times9$ grid are filled in using the numbers 1 through 9 so that each row contains 9 different numbers, and each of the three $3\times3$ blocks heavily outlined in the example below contains 9 different numbers, as in the first three rows of a Sudoku puzzle. 
+ | 4 | 2 | 8 | 9 | 6 | 3 | 1 | 7 | 5 | 
+ | 3 | 7 | 9 | 5 | 2 | 1 | 6 | 8 | 4 | 
+ | 5 | 6 | 1 | 8 | 4 | 7 | 9 | 2 | 3 | 
+ The number of different ways to fill such a grid can be written as $p^a\cdot q^b\cdot r^c\cdot s^d$, where $p,q,r,$ and $s$ are distinct prime numbers and $a,b,c,$ and $d$ are positive integers. Find $p\cdot a+q\cdot b+r\cdot c+s\cdot d$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let the three rows be \(R_1,R_2,R_3\) and the three \(3\times3\) blocks be \(B_1,B_2,B_3\) (columns \(1\!-\!3,\;4\!-\!6,\;7\!-\!9\)).
+Each row must be a permutation of \(\{1,\dots ,9\}\) and each block must also contain every digit once.
+
+--------------------------------------------------------------------
+### 1.  Where does a digit appear in the three rows?
+
+For a fixed digit \(d\) its three copies (one in each row) must lie in three *different* blocks; otherwise a block would miss that digit.  
+Thus for each digit we obtain a bijection  
+
+\[
+\phi_d:\{1,2,3\}\longrightarrow\{1,2,3\},\qquad 
+\phi_d(i)=\text{block containing }d\text{ in row }i .
+\]
+
+So each digit corresponds to a permutation of the three blocks.  
+There are six permutations, listed with the cells \((i,\phi(i))\) they occupy:
+
+\[
+\begin{array}{c|c}
+\text{perm.} &amp; \text{cells}\\ \hline
+(1)(2)(3) &amp; (1,1),(2,2),(3,3)\\
+(12) &amp; (1,2),(2,1),(3,3)\\
+(13) &amp; (1,3),(2,2),(3,1)\\
+(23) &amp; (1,1),(2,3),(3,2)\\
+(123) &amp; (1,2),(2,3),(3,1)\\
+(132) &amp; (1,3),(2,1),(3,2)
+\end{array}
+\]
+
+Let \(x_1,\dots ,x_6\) be the numbers of digits that use the six permutations (in the order shown).  
+Because each block must contain three digits from each row, each of the nine cells \((i,k)\) must be hit by exactly three digits, giving
+
+\[
+\begin{aligned}
+x_1+x_4 &amp;=3, &amp; x_2+x_5 &amp;=3, &amp; x_3+x_6 &amp;=3,\\
+x_2+x_6 &amp;=3, &amp; x_1+x_3 &amp;=3, &amp; x_4+x_5 &amp;=3,\\
+x_3+x_5 &amp;=3, &amp; x_4+x_6 &amp;=3, &amp; x_1+x_2 &amp;=3 .
+\end{aligned}
+\]
+
+Solving, all solutions have the form  
+
+\[
+(x_1,x_2,x_3,x_4,x_5,x_6)=(a,\,3-a,\,3-a,\,3-a,\,a,\,a),\qquad a\in\{0,1,2,3\}.
+\]
+
+--------------------------------------------------------------------
+### 2.  Assign the digits to the permutations
+
+For a fixed \(a\) the number of ways to choose which digits get which permutation is
+
+\[
+\frac{9!}{x_1!\,x_2!\,x_3!\,x_4!\,x_5!\,x_6!}
+   =\frac{9!}{a!^{\,3}\,(3-a)!^{\,3}} .
+\]
+
+Summing over the four possible values of \(a\),
+
+\[
+\sum_{a=0}^3\frac{9!}{a!^{\,3}(3-a)!^{\,3}}
+   =9!\Bigl(\frac1{3!^{\,3}}{0\choose0}^3
+            +\frac1{3!^{\,3}}{3\choose1}^3
+            +\frac1{3!^{\,3}}{3\choose2}^3
+            +\frac1{3!^{\,3}}{3\choose3}^3\Bigr)
+   =9!\,\frac{56}{216}
+   =9!\,\frac{7}{27}.
+\]
+
+--------------------------------------------------------------------
+### 3.  Order the digits inside each block
+
+Within a fixed block and a fixed row there are three column positions.
+The three digits that belong to that macro‑cell can be placed in these
+positions in \(3! = 6\) ways.
+There are \(3\) rows \(\times\) \(3\) blocks \(=9\) such macro‑cells, giving a factor \(6^9\).
+
+--------------------------------------------------------------------
+### 4.  Total number of fillings
+
+\[
+N = \Bigl(9!\,\frac{7}{27}\Bigr)\,6^{9}
+   = 2^{16}\,3^{10}\,5\,7^{2}.
+\]
+
+Thus the factorisation uses the four distinct primes  
+
+\[
+p=2,\;q=3,\;r=5,\;s=7,\qquad 
+a=16,\;b=10,\;c=1,\;d=2 .
+\]
+
+Finally,
+
+\[
+p\,a+q\,b+r\,c+s\,d
+   =2\cdot16+3\cdot10+5\cdot1+7\cdot2
+   =32+30+5+14=81.
+\]
+
+\[
+\boxed{81}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 81</p>
+<p>Extracted Answer: 81</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $ABCDE$ be a convex pentagon with $AB=14, BC=7, CD=24, DE=13, EA=26,$ and $\angle B=\angle E=60^\circ$. For each point $X$ in the plane, define $f(X)=AX+BX+CX+DX+EX$. The least possible value of $f(X)$ can be expressed as $m+n\sqrt{p}$, where $m$ and $n$ are positive integers and $p$ is not divisible by the square of any prime. Find $m+n+p$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>We place the pentagon in the plane.  
+Set  
+
+\[
+\begin{aligned}
+A&amp;=(7,7\sqrt3),\qquad B=(0,0),\qquad C=(7,0),\\[2mm]
+D&amp;=\Bigl(\frac{205}{7},\frac{36\sqrt3}{7}\Bigr),\qquad 
+E=\Bigl(\frac{218}{7},\frac{88\sqrt3}{7}\Bigr).
+\end{aligned}
+\]
+
+The lengths are as given and  
+\(\angle B=\angle E =60^\circ\).
+
+--------------------------------------------------------------------
+### 1.  Geometry of the optimal point  
+
+For the sum  
+
+\[
+f(X)=AX+BX+CX+DX+EX,
+\]
+
+the geometric median \(X\) satisfies  
+
+\[
+\frac{X-A}{AX}+\frac{X-B}{BX}+\frac{X-C}{CX}+\frac{X-D}{DX}+\frac{X-E}{EX}=0 .
+\tag{1}
+\]
+
+Because \(B,E\) lie on a line, the vectors \(\frac{X-B}{BX}\) and
+\(\frac{X-E}{EX}\) are opposite exactly when \(X\) lies on segment \(BE\);
+hence in the optimal position \(X\) must lie on \(BE\) and the first two
+terms in (1) cancel.  Consequently
+
+\[
+\frac{X-A}{AX}+\frac{X-C}{CX}+\frac{X-D}{DX}=0,
+\]
+
+so \(X\) is the Fermat point of triangle \(ACD\).
+
+--------------------------------------------------------------------
+### 2.  Fermat point of \(\triangle ACD\)
+
+The side lengths of \(\triangle ACD\) are  
+
+\[
+AC=7\sqrt3,\qquad CD=24,\qquad AD=13\sqrt3 .
+\]
+
+All its angles are \(&lt;120^\circ\); therefore the Fermat point exists.
+For a triangle with sides \(a,b,c\) and area \(\Delta\),
+
+\[
+S_{\text{Fermat}}=
+\sqrt{\frac{a^{2}+b^{2}+c^{2}+4\sqrt3\,\Delta}{2}} .
+\]
+
+Here  
+
+\[
+a^{2}+b^{2}+c^{2}=576+507+147=1230,
+\qquad\Delta_{ACD}=78\sqrt3,
+\]
+
+so  
+
+\[
+S_{\text{Fermat}}=\sqrt{\frac{1230+4\sqrt3\cdot78\sqrt3}{2}}
+=\sqrt{\frac{1230+936}{2}}=\sqrt{1083}=19\sqrt3 .
+\]
+
+Thus at the Fermat point  
+
+\[
+AX+CX+DX=19\sqrt3 .
+\tag{2}
+\]
+
+--------------------------------------------------------------------
+### 3.  The total minimum
+
+Since the optimal point lies on \(BE\),
+
+\[
+BX+EX = BE .
+\]
+
+From the coordinates, \(BE=38\).  Combining this with (2),
+
+\[
+f_{\min}= (AX+CX+DX)+(BX+EX)=19\sqrt3+38 .
+\]
+
+Hence the smallest possible value of \(f(X)\) is  
+
+\[
+\boxed{38+19\sqrt3}.
+\]
+
+Writing it as \(m+n\sqrt p\) with \(m,n\) integers and \(p\) square‑free,
+we have \(m=38,\;n=19,\;p=3\).  Therefore  
+
+\[
+m+n+p=38+19+3=60 .
+\]
+
+\[
+\boxed{60}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 60</p>
+<p>Extracted Answer: 60</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+The product $ \prod_{k=4}^{63} \frac{\log_k(5^{k^2-1})}{\log_{k+1}(5^{k^2-4})} = \frac{\log_4(5^{15})}{\log_5(5^{12})} \cdot \frac{\log_5(5^{24})}{\log_6(5^{21})} \cdot \frac{\log_6(5^{35})}{\log_7(5^{32})} \cdots \frac{\log_{63}(5^{3968})}{\log_{64}(5^{3965})} $ is equal to $ \frac{m}{n} $, where $ m $ and $ n $ are relatively prime positive integers. Find $ m + n $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>\[
+P=\prod_{k=4}^{63}\frac{\log_k\!\bigl(5^{k^{2}-1}\bigr)}{\log_{k+1}\!\bigl(5^{k^{2}-4}\bigr)}
+\]
+
+---
+
+### 1.  Simplify each factor  
+
+\[
+\log_k\!\bigl(5^{k^{2}-1}\bigr)=(k^{2}-1)\log_k5,
+\qquad 
+\log_{k+1}\!\bigl(5^{k^{2}-4}\bigr)=(k^{2}-4)\log_{k+1}5 .
+\]
+
+Hence  
+
+\[
+\frac{\log_k\!\bigl(5^{k^{2}-1}\bigr)}{\log_{k+1}\!\bigl(5^{k^{2}-4}\bigr)}
+=\frac{k^{2}-1}{k^{2}-4}\cdot\frac{\log_k5}{\log_{k+1}5}
+=\frac{(k-1)(k+1)}{(k-2)(k+2)}\cdot\frac{\log_k5}{\log_{k+1}5}.
+\]
+
+Therefore  
+
+\[
+P=\underbrace{\prod_{k=4}^{63}\frac{(k-1)(k+1)}{(k-2)(k+2)}}_{A}
+   \times\underbrace{\prod_{k=4}^{63}\frac{\log_k5}{\log_{k+1}5}}_{B}.
+\]
+
+---
+
+### 2.  Evaluate the rational product \(A\)
+
+\[
+A=\Bigl(\prod_{k=4}^{63}\frac{k-1}{k-2}\Bigr)
+   \Bigl(\prod_{k=4}^{63}\frac{k+1}{k+2}\Bigr)
+   =\frac{3\cdot4\cdots62}{2\cdot3\cdots61}\;
+     \frac{5\cdot6\cdots64}{6\cdot7\cdots65}.
+\]
+
+Both products telescope:
+
+\[
+\frac{3\cdot4\cdots62}{2\cdot3\cdots61}= \frac{62}{2}=31,
+\qquad 
+\frac{5\cdot6\cdots64}{6\cdot7\cdots65}= \frac{5}{65}= \frac1{13}.
+\]
+
+Thus  
+
+\[
+A=31\cdot\frac1{13}= \frac{31}{13}.
+\]
+
+---
+
+### 3.  Evaluate the logarithmic product \(B\)
+
+\[
+B=\frac{\log_4 5}{\log_5 5}\cdot\frac{\log_5 5}{\log_6 5}\cdots
+    \frac{\log_{63}5}{\log_{64}5}
+   =\frac{\log_4 5}{\log_{64}5}.
+\]
+
+Using change‑of‑base,
+\[
+\frac{\log_4 5}{\log_{64} 5}
+   =\frac{\frac{\ln5}{\ln4}}{\frac{\ln5}{\ln64}}
+   =\frac{\ln64}{\ln4}
+   =\log_4 64=3,
+\]
+since \(4^3=64\).
+
+Hence \(B=3\).
+
+---
+
+### 4.  Combine
+
+\[
+P=A\cdot B=\frac{31}{13}\times 3=\frac{93}{13}.
+\]
+
+The fraction \(\dfrac{93}{13}\) is already in lowest terms, so  
+\(m=93,\; n=13\).
+
+\[
+m+n=93+13=106.
+\]
+
+\[
+\boxed{106}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 106</p>
+<p>Extracted Answer: 106</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $ A $ be the set of positive integer divisors of 2025. Let $ B $ be a randomly selected subset of $ A $. The probability that $ B $ is a nonempty set with the property that the least common multiple of its elements is 2025 is $ \frac{m}{n} $, where $ m $ and $ n $ are relatively prime positive integers. Find $ m + n $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>The divisors of  
+
+\[
+2025=3^{4}\cdot5^{2}
+\]
+
+are exactly the numbers  
+
+\[
+3^{a}5^{b}\qquad (0\le a\le 4,\;0\le b\le 2).
+\]
+
+Hence  
+
+\[
+|A|=(4+1)(2+1)=15 .
+\]
+
+For a subset \(B\subseteq A\) the least common multiple is
+
+\[
+\operatorname{lcm}(B)=3^{\max a}\,5^{\max b},
+\]
+
+where the maxima are taken over the exponents \((a,b)\) of the elements of \(B\).
+
+Thus \(\operatorname{lcm}(B)=2025=3^4 5^2\) iff  
+
+* at least one element of \(B\) has a \(3\)-exponent \(4\);
+* at least one element of \(B\) has a \(5\)-exponent \(2\).
+
+Define  
+
+\[
+D_3=\{d\in A : \text{the exponent of }3\text{ in }d\text{ is }4\},
+\qquad 
+D_5=\{d\in A : \text{the exponent of }5\text{ in }d\text{ is }2\}.
+\]
+
+Counting:
+
+* \(D_3\): \(a=4\) and \(b=0,1,2\) ⇒ \(|D_3|=3\) (81, 405, 2025).
+* \(D_5\): \(b=2\) and \(a=0,1,2,3,4\) ⇒ \(|D_5|=5\) (25, 75, 225, 675, 2025).
+* The intersection is \(\{2025\}\); so \(|D_3\cap D_5|=1\).
+
+We need subsets that contain at least one element of \(D_3\) **and** at least one element of \(D_5\).
+
+Let the total number of subsets of \(A\) be \(2^{15}\).
+Let  
+
+\[
+\begin{aligned}
+A_1 &amp;=\{\text{subsets that contain no element of } D_3\},\\
+A_2 &amp;=\{\text{subsets that contain no element of } D_5\}.
+\end{aligned}
+\]
+
+Then  
+
+\[
+|A_1|=2^{15-3}=2^{12},\qquad 
+|A_2|=2^{15-5}=2^{10}.
+\]
+
+Subsets avoiding **both** \(D_3\) and \(D_5\) avoid the union \(D_3\cup D_5\) which has  
+
+\[
+|D_3\cup D_5|=|D_3|+|D_5|-|D_3\cap D_5|=3+5-1=7
+\]
+
+elements. Hence  
+
+\[
+|A_1\cap A_2|=2^{15-7}=2^{8}.
+\]
+
+By inclusion–exclusion, the number of subsets that contain at least one element from each of \(D_3\) and \(D_5\) is  
+
+\[
+\begin{aligned}
+N &amp;= 2^{15}-|A_1|-|A_2|+|A_1\cap A_2|\\
+   &amp;= 2^{15}-2^{12}-2^{10}+2^{8}\\
+   &amp;= 32768-4096-1024+256\\
+   &amp;= 27904.
+\end{aligned}
+\]
+
+All these subsets are non‑empty, so the required probability is  
+
+\[
+\frac{N}{2^{15}}=\frac{27904}{32768}.
+\]
+
+Simplifying,
+
+\[
+\frac{27904}{32768}= \frac{27904\div 256}{32768\div 256}
+                 = \frac{109}{128}.
+\]
+
+Thus \(m=109,\; n=128\) and  
+
+\[
+m+n = 109+128 = 237.
+\]
+
+\[
+\boxed{237}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 237</p>
+<p>Extracted Answer: 237</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Four unit squares form a $2 \times 2$ grid. Each of the 12 unit line segments forming the sides of the squares is colored either red or blue in such a way that each unit square has 2 red sides and 2 blue sides. Find the number of such colorings.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Label the twelve unit segments as in the picture  
+
+\[
+\begin{array}{c}
+\text{external: }a_1,a_2,b_1,b_2,c_1,c_2,d_1,d_2\\[2mm]
+\text{internal: }e_1,e_2,f_1,f_2
+\end{array}
+\]
+
+The four unit squares are  
+
+\[
+\begin{aligned}
+\text{TL}&amp;:\;a_1,c_1,e_1,f_1,\\
+\text{TR}&amp;:\;b_1,c_2,e_1,f_2,\\
+\text{BL}&amp;:\;a_2,d_1,e_2,f_1,\\
+\text{BR}&amp;:\;b_2,d_2,e_2,f_2 .
+\end{aligned}
+\]
+
+Each square must contain exactly two red sides (hence also two blue sides).
+
+--------------------------------------------------------------------
+### 1.  Reduce to the four internal edges
+
+For a given square the two sides that are **internal** are already
+colored once we decide the colors of the four internal edges  
+\(e_1,e_2,f_1,f_2\).  
+
+Let  
+
+\[
+r_{\rm TL}=e_1+f_1,\qquad
+r_{\rm TR}=e_1+f_2,\qquad
+r_{\rm BL}=e_2+f_1,\qquad
+r_{\rm BR}=e_2+f_2 ,
+\]
+
+where a red edge contributes 1 and a blue edge contributes 0.
+If a square has \(r\) red internal sides, then it must have \(2-r\)
+red external sides. Thus
+
+* if \(r=0\): both external sides are forced red – 1 way;
+* if \(r=1\): exactly one of the two external sides must be red – 2 ways;
+* if \(r=2\): both external sides are forced blue – 1 way.
+
+Hence for a fixed choice of the four internal edges the number of
+admissible colourings of the eight external edges equals
+
+\[
+2^{\,N_1},
+\]
+
+where \(N_1\) is the number of squares among TL, TR, BL, BR that have
+exactly one red internal side.
+
+--------------------------------------------------------------------
+### 2.  Express \(N_1\) in terms of the internal edges
+
+Write  
+
+\[
+X_1=e_1,\; X_2=e_2,\qquad Y_1=f_1,\;Y_2=f_2\qquad(\text{red}=1,\text{blue}=0).
+\]
+
+For a square \((i,j)\) (\(i,j\in\{1,2\}\)) the number of red internal
+sides is \(X_i+Y_j\).
+Thus a square has exactly one red internal side precisely when
+\(X_i\neq Y_j\).
+
+Let  
+
+\[
+a=X_1+X_2\;(=0,1,2),\qquad b=Y_1+Y_2\;(=0,1,2).
+\]
+
+The number of ordered pairs \((i,j)\) with \(X_i\neq Y_j\) is  
+
+\[
+N_1=a(2-b)+(2-a)b
+      =2\bigl(a+b-ab\bigr).
+\]
+
+Consequently the contribution of a configuration with given
+\(a,b\) is  
+
+\[
+2^{N_1}=2^{\,2(a+b-ab)}=4^{\,a+b-ab}.
+\]
+
+--------------------------------------------------------------------
+### 3.  Count all configurations of the internal edges
+
+There are \(\binom{2}{a}\) ways to choose which vertical internal edges
+are red, and \(\binom{2}{b}\) ways to choose which horizontal internal
+edges are red.  Hence the total number of colourings is
+
+\[
+\sum_{a=0}^{2}\sum_{b=0}^{2}
+\binom{2}{a}\binom{2}{b}\;4^{\,a+b-ab}.
+\]
+
+Evaluating the double sum:
+
+\[
+\begin{array}{c|ccc}
+a\backslash b &amp;0&amp;1&amp;2\\\hline
+0 &amp;1\cdot1\cdot1=1 &amp;1\cdot2\cdot4=8 &amp;1\cdot1\cdot16=16\\
+1 &amp;2\cdot1\cdot4=8 &amp;2\cdot2\cdot4=16 &amp;2\cdot1\cdot4=8\\
+2 &amp;1\cdot1\cdot16=16 &amp;1\cdot2\cdot4=8 &amp;1\cdot1\cdot1=1
+\end{array}
+\]
+
+Adding all entries:
+
+\[
+1+8+16+8+16+8+16+8+1=82.
+\]
+
+--------------------------------------------------------------------
+### 4.  Answer
+
+Thus there are  
+
+\[
+\boxed{82}
+\]
+
+different ways to colour the twelve unit segments so that each of the
+four unit squares has two red sides and two blue sides.</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 82</p>
+<p>Extracted Answer: 82</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Circle $\omega_1$ with radius 6 centered at point $A$ is internally tangent at point $B$ to circle $\omega_2$ with radius 15. Points $C$ and $D$ lie on $\omega_2$ such that $\overline{BC}$ is a diameter of $\omega_2$ and $\overline{BC} \perp \overline{AD}$. The rectangle $EFGH$ is inscribed in $\omega_1$ such that $\overline{EF} \perp \overline{BC}$, $C$ is closer to $\overline{GH}$ than to $\overline{EF}$, and $D$ is closer to $\overline{FG}$ than to $\overline{EH}$, as shown. Triangles $\triangle DGF$ and $\triangle CHG$ have equal areas. The area of rectangle $EFGH$ is $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m + n$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>The circles are drawn as in the figure.
+
+* Let \(O\) be the centre of \(\omega _2\) (radius \(15\)).
+* Let \(A\) be the centre of \(\omega _1\) (radius \(6\)).
+* Since \(\omega _1\) is internally tangent to \(\omega _2\) at \(B\), the three points are collinear and  
+
+\[
+OA=15-6=9 .
+\]
+
+Take a coordinate system with  
+
+\[
+O=(0,0),\qquad A=(9,0),\qquad B=(15,0).
+\]
+
+--------------------------------------------------------------------
+### Points \(C\) and \(D\)
+
+\(BC\) is a diameter of \(\omega _2\); hence \(C\) is the antipode of \(B\):
+
+\[
+C=(-15,0).
+\]
+
+\(BC\perp AD\) means \(AD\) is the vertical line \(x=9\).  
+Intersecting this line with \(\omega _2\) gives  
+
+\[
+9^2+y^2=15^2 \Longrightarrow y=\pm 12 .
+\]
+
+Because the later condition “\(D\) is nearer to \(FG\) than to \(EH\)” forces \(D\) to lie **below** the centre, we take  
+
+\[
+D=(9,-12).
+\]
+
+--------------------------------------------------------------------
+### The rectangle \(EFGH\)
+
+The rectangle is inscribed in \(\omega _1\) and \(\overline{EF}\perp BC\); hence \(\overline{EF}\) is vertical.
+Let
+
+\[
+\begin{aligned}
+E&amp;=(9+w,\;h),\\[2pt]
+F&amp;=(9+w,\;-h),\\[2pt]
+G&amp;=(9-w,\;-h),\\[2pt]
+H&amp;=(9-w,\;h),
+\end{aligned}
+\]
+
+so that the centre of the rectangle is \(A\) (the intersection of the diagonals of an
+inscribed rectangle is the centre of the circumcircle).
+
+Because the four vertices lie on \(\omega _1\),
+
+\[
+(9\pm w-9)^2+h^2=w^{2}+h^{2}=6^{2}=36\qquad\Longrightarrow\qquad w^{2}+h^{2}=36. \tag{1}
+\]
+
+The side \(\overline{EF}\) is the right vertical side, thus
+\(C\) (which is far left) is nearer to \(\overline{GH}\) (the left side) than to \(\overline{EF}\);
+and \(D\) (which is below the centre) is nearer to \(\overline{FG}\) (the bottom side) than to \(\overline{EH}\) (the top side).  
+These statements only fix the labeling of the rectangle.
+
+--------------------------------------------------------------------
+### Equality of the two triangular areas
+
+\[
+\begin{aligned}
+\text{Area}\,\triangle DGF
+&amp;=\frac12\bigl(\underbrace{2w}_{\text{base }GF}\bigr)
+     \bigl(\underbrace{12-h}_{\text{vertical height}}\bigr)
+ = w(12-h),\\[4pt]
+\text{Area}\,\triangle CHG
+&amp;=\frac12\bigl(\underbrace{2h}_{\text{base }HG}\bigr)
+     \bigl(\underbrace{24-w}_{\text{horizontal distance}}\bigr)
+ = h(24-w).
+\end{aligned}
+\]
+
+Given that the two areas are equal,
+
+\[
+w(12-h)=h(24-w)\; \Longrightarrow\; 12w=24h\; \Longrightarrow\; w=2h. \tag{2}
+\]
+
+--------------------------------------------------------------------
+### Solving for \(w\) and \(h\)
+
+Substituting \(w=2h\) into (1):
+
+\[
+(2h)^2+h^{2}=36\;\Longrightarrow\;5h^{2}=36\;\Longrightarrow\;h^{2}= \frac{36}{5}.
+\]
+
+Hence  
+
+\[
+h=\frac{6}{\sqrt5},\qquad w=2h=\frac{12}{\sqrt5}.
+\]
+
+--------------------------------------------------------------------
+### Area of the rectangle
+
+The rectangle’s side lengths are \(2w\) and \(2h\), so
+
+\[
+\text{Area}= (2w)(2h)=4wh
+          =4\left(\frac{12}{\sqrt5}\right)\left(\frac{6}{\sqrt5}\right)
+          =4\cdot\frac{72}{5}
+          =\frac{288}{5}.
+\]
+
+Thus the area is \(\displaystyle\frac{m}{n}=\frac{288}{5}\) with relatively prime
+\(m=288,\;n=5\).
+
+\[
+m+n=288+5=293.
+\]
+
+\[
+\boxed{293}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 293</p>
+<p>Extracted Answer: 293</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+From an unlimited supply of 1-cent coins, 10-cent coins, and 25-cent coins, Silas wants to find a collection of coins that has a total value of $ N $ cents, where $ N $ is a positive integer. He uses the so-called **greedy algorithm**, successively choosing the coin of greatest value that does not cause the value of his collection to exceed $ N $. For example, to get 42 cents, Silas will choose a 25-cent coin, then a 10-cent coin, then 7 1-cent coins. However, this collection of 9 coins uses more coins than necessary to get a total of 42 cents; indeed, choosing 4 10-cent coins and 2 1-cent coins achieves the same total value with only 6 coins.
+
+In general, the greedy algorithm succeeds for a given $ N $ if no other collection of 1-cent, 10-cent, and 25-cent coins gives a total value of $ N $ cents using strictly fewer coins than the collection given by the greedy algorithm. Find the number of values of $ N $ between 1 and 1000 inclusive for which the greedy algorithm succeeds.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+\[
+N=25q+r ,\qquad 0\le r\le 24 .
+\]
+
+The greedy algorithm takes  
+
+* \(q\) quarters,  
+* \(\displaystyle d_0=\Big\lfloor\frac r{10}\Big\rfloor\) dimes,  
+* \(s_0=r\bmod 10\) pennies.  
+
+Hence  
+
+\[
+C_{\text{greedy}}=q+d_0+s_0 .\tag{1}
+\]
+
+--------------------------------------------------------------------
+### 1.  When can a better solution use fewer quarters?
+
+Suppose we use only \(q-k\) quarters, \(k\ge1\).  
+The remaining amount is  
+
+\[
+R=r+25k .
+\]
+
+With only dimes and pennies the optimal way to make \(R\) is  
+
+\[
+\Big\lfloor\frac{R}{10}\Big\rfloor\text{ dimes }+ (R\bmod10)\text{ pennies}.
+\]
+
+Thus the total number of coins for this choice is  
+
+\[
+C(q-k)=(q-k)+\Big\lfloor\frac{r+25k}{10}\Big\rfloor+(r+25k\bmod10).\tag{2}
+\]
+
+Let  
+
+\[
+\Delta(k)=C(q-k)-C_{\text{greedy}} .
+\]
+
+Using \(r=10t+a\;(0\le a\le9,\;t\in\{0,1,2\})\) we obtain after a short calculation  
+
+\[
+\Delta(k)=6k-9\Big\lfloor\frac{a+5k}{10}\Big\rfloor .\tag{3}
+\]
+
+(Only the last digit \(a=r\bmod 10\) matters.)
+
+--------------------------------------------------------------------
+### 2.  Sign of \(\Delta(k)\)
+
+*If \(a\ge5\):*  
+Take \(k=1\).  Then \(\lfloor\frac{a+5}{10}\rfloor=1\) and  
+
+\[
+\Delta(1)=6-9=-3&lt;0 .
+\]
+
+Hence a better solution exists (remove one quarter).
+
+*If \(a\le4\):*  
+For any \(k\ge1\),
+
+\[
+\Delta(k)=6k-9\Big\lfloor\frac{a+5k}{10}\Big\rfloor
+\ge 6k-9\frac{a+5k}{10}=1.5k-0.9a .
+\]
+
+Since \(a\le4\) this is positive for \(k=1,2\) (indeed \(\Delta(1)=6,\,\Delta(2)=3\)) and for larger \(k\) the term \(1.5k\) dominates, so \(\Delta(k)\ge0\) for all \(k\).
+
+Therefore **greedy fails iff**  
+
+\[
+a=r\bmod10\ge5\quad\text{and}\quad q\ge1 .
+\]
+
+Equivalently, for \(N\ge25\),
+
+\[
+N\bmod25\in\{5,6,7,8,9,15,16,17,18,19\}.
+\]
+
+--------------------------------------------------------------------
+### 3.  Counting the failures
+
+The residues above are ten out of the twenty‑five possible residues modulo \(25\).  
+
+In the interval \(1\le N\le1000\) we have \(1000/25=40\) full periods, so each residue occurs \(40\) times.  
+
+Thus the total number of integers with those residues is  
+
+\[
+10\times40=400.
+\]
+
+But the ten numbers \(5,6,7,8,9,15,16,17,18,19\) are \&lt; 25, and for them greedy cannot remove a quarter (there are no quarters in any representation).  Those ten are **not** failures.  
+
+Hence the genuine failures are  
+
+\[
+400-10=390.
+\]
+
+--------------------------------------------------------------------
+### 4.  Successes
+
+There are \(1000\) integers from \(1\) to \(1000\).  Therefore the number of values for which the greedy algorithm *succeeds* is
+
+\[
+1000-390=610.
+\]
+
+--------------------------------------------------------------------
+\[
+\boxed{610}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 610</p>
+<p>Extracted Answer: 610</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+There are $ n $ values of $ x $ in the interval $ 0 &lt; x &lt; 2\pi $ where $ f(x) = \sin(7\pi \cdot \sin(5x)) = 0 $. For $ t $ of these $ n $ values of $ x $, the graph of $ y = f(x) $ is tangent to the $ x $-axis. Find $ n + t $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>\[
+f(x)=\sin\bigl(7\pi\sin(5x)\bigr)
+\]
+
+---
+
+### 1.  Zeros of \(f\)
+
+\(f(x)=0\iff 7\pi\sin(5x)=k\pi\) for an integer \(k\).
+
+\[
+\sin(5x)=\frac{k}{7},\qquad |k|\le 7 .
+\]
+
+Let  
+
+\[
+y=5x\;(0&lt;y&lt;10\pi).
+\]
+
+For each integer \(k\) with \(|k|\le7\) we count the solutions of \(\sin y=\dfrac{k}{7}\) in \((0,10\pi)\).
+
+* \(k=7\)  : \(\sin y=1\).  Solutions \(y=\frac{\pi}{2}+2\pi n\) \((n=0,1,2,3,4)\) → **5** solutions.  
+* \(k=-7\) : \(\sin y=-1\).  Solutions \(y=\frac{3\pi}{2}+2\pi n\) \((n=0,1,2,3,4)\) → **5** solutions.  
+* \(k=0\)  : \(\sin y=0\).  Solutions \(y=m\pi\;(m=1,2,\dots ,9)\) → **9** solutions.  
+* For each \(k=\pm1,\pm2,\pm3,\pm4,\pm5,\pm6\) we have \(\sin y=c\) with \(-1&lt;c&lt;1,\;c\neq0\).  
+  In each of the 5 full periods of \(\sin y\) there are exactly two such points, so **\(5\cdot2=10\)** solutions per \(k\).
+
+There are 12 values of \(k\) with \(|k|\in\{1,\dots ,6\}\), giving  
+
+\[
+12\times10=120\text{ solutions}.
+\]
+
+Adding all contributions,
+
+\[
+n=5+5+9+120=139 .
+\]
+
+---
+
+### 2.  Tangent zeros
+
+The graph is tangent to the \(x\)-axis at a zero where the derivative also vanishes.
+
+\[
+f&#39;(x)=\cos\bigl(7\pi\sin(5x)\bigr)\cdot 35\pi\cos(5x).
+\]
+
+At a zero, \(\sin\bigl(7\pi\sin(5x)\bigr)=0\) gives \(\sin(5x)=\dfrac{k}{7}\).  
+Because \(\cos\bigl(7\pi\sin(5x)\bigr)=\pm1\neq0\), we must have \(\cos(5x)=0\).
+
+\[
+\cos(5x)=0\Longrightarrow \sin(5x)=\pm1 .
+\]
+
+Thus tangential zeros occur exactly when \(\sin(5x)=\pm1\), i.e. for \(k=\pm7\).
+
+We already counted those solutions:  
+
+* \(\sin(5x)=1\) → 5 points,  
+* \(\sin(5x)=-1\) → 5 points.
+
+Hence  
+
+\[
+t=5+5=10 .
+\]
+
+---
+
+### 3.  Required sum
+
+\[
+n+t=139+10=149.
+\]
+
+\[
+\boxed{149}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 149</p>
+<p>Extracted Answer: 149</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $ S $ be the set of vertices of a regular 24-gon. Find the number of ways to draw 12 segments of equal lengths so that each vertex in $ S $ is an endpoint of exactly one of the 12 segments.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let the vertices of the regular \(24\)-gon be numbered \(0,1,\dots ,23\) (mod \(24\)).
+If a segment joins vertex \(i\) to vertex \(j\) we call its **step**
+\[
+k\equiv j-i\pmod{24},\qquad 1\le k\le 12 .
+\]
+
+The length of a chord depends only on this step:
+the chord of step \(k\) has length  
+
+\[
+\ell(k)=2R\sin\frac{\pi k}{24},\qquad 1\le k\le 12 .
+\]
+
+Since \(\sin(\theta )\) is strictly increasing on \([0,\frac{\pi}{2}]\),
+the lengths \(\ell(1),\ell(2),\dots ,\ell(12)\) are all distinct.
+Thus a drawing in which all 12 segments have the same length must use
+edges whose step is a fixed \(k\) (the same chord length).
+
+--------------------------------------------------------------------
+
+### 1.  The graph of step \(k\)
+
+Consider the undirected graph \(G_k\) whose vertices are the 24 polygon vertices
+and whose edges are all chords of step \(k\) (i.e. the pairs \(\{i,i+k\}\)).
+Each vertex of \(G_k\) is incident to two such chords
+(\(i\) connects to \(i+k\) and to \(i-k\)), so \(G_k\) is a disjoint union of
+cycles.
+
+Let  
+
+\[
+d=\gcd(24,k).
+\]
+
+Then the vertices split into \(d\) cycles, each of length  
+
+\[
+\frac{24}{d}.
+\]
+
+--------------------------------------------------------------------
+
+### 2.  When can a perfect matching be formed?
+
+A perfect matching can be taken inside one cycle only when the cycle has even
+length.  Hence we need \(\frac{24}{d}\) even, i.e. \(d\neq 8\).  
+
+* If \(d=8\) (the case \(k=8\)) each component is a triangle; a triangle has
+no perfect matching, so **no drawing** is possible.
+
+* If the cycle length is \(2\) (the case \(d=12,\;k=12\)), each component is a
+single edge; there is exactly **one** perfect matching – the 12 diameters.
+
+* For any other admissible \(k\) the cycles have even length \(\ge4\).
+Inside each such cycle there are exactly two ways to choose a perfect matching
+(alternate edges).  Since the cycles are independent, the number of perfect
+matchings for the given \(k\) is  
+
+\[
+2^{\,d}\qquad (d=\gcd(24,k),\;d\neq 8,\;k\neq 12).
+\]
+
+--------------------------------------------------------------------
+
+### 3.  Counting for each step
+
+\[
+\begin{array}{c|c|c|c}
+k &amp; d=\gcd(24,k) &amp; \text{cycle length }24/d &amp; \#\text{ matchings}\\ \hline
+1 &amp; 1 &amp; 24 &amp; 2\\
+2 &amp; 2 &amp; 12 &amp; 2^{2}=4\\
+3 &amp; 3 &amp; 8 &amp; 2^{3}=8\\
+4 &amp; 4 &amp; 6 &amp; 2^{4}=16\\
+5 &amp; 1 &amp; 24 &amp; 2\\
+6 &amp; 6 &amp; 4 &amp; 2^{6}=64\\
+7 &amp; 1 &amp; 24 &amp; 2\\
+8 &amp; 8 &amp; 3 &amp; 0\\
+9 &amp; 3 &amp; 8 &amp; 2^{3}=8\\
+10&amp; 2 &amp; 12&amp; 2^{2}=4\\
+11&amp; 1 &amp; 24&amp; 2\\
+12&amp;12 &amp; 2 &amp; 1\ (\text{forced diameters})
+\end{array}
+\]
+
+--------------------------------------------------------------------
+
+### 4.  Total number of drawings
+
+Add the numbers of matchings over all admissible steps:
+
+\[
+\begin{aligned}
+N&amp;=2+4+8+16+2+64+2+8+4+2+1\\
+&amp;=113 .
+\end{aligned}
+\]
+
+--------------------------------------------------------------------
+
+\[
+\boxed{113}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 113</p>
+<p>Extracted Answer: 113</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Sixteen chairs are arranged in a row. Eight people each select a chair in which to sit so that no person sits next to two other people. Let $ N $ be the number of subsets of 16 chairs that could be selected. Find the remainder when $ N $ is divided by 1000.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>The 8 occupied chairs must avoid a configuration where a person has two neighbours.  
+Hence no three occupied chairs may be consecutive.
+
+Let a be the number of blocks of two consecutive occupied chairs.  
+Each block of two contributes an extra occupied chair, so the total number of blocks is  
+
+\[
+b = 8-a\qquad (0\le a\le 4).
+\]
+
+*Choosing which blocks are of size 2*: \(\displaystyle \binom{b}{a}\).
+
+There are \(16-8=8\) empty chairs. Between the \(b\) blocks there must be at least one empty chair, using \(b-1\) empties.  
+The remaining \(8-(b-1)=9-b\) empty chairs can be placed in the \(b+1\) gaps (before the first block, after the last, and the \(b-1\) internal gaps) without restriction.  
+
+Number of ways to distribute them:  
+
+\[
+\binom{(9-b)+(b+1)-1}{(b+1)-1}= \binom{9}{b}.
+\]
+
+Thus for a given \(a\),
+
+\[
+\text{ways}= \binom{b}{a}\binom{9}{b}
+          =\binom{8-a}{a}\binom{9}{8-a}.
+\]
+
+Summing over \(a=0,1,2,3,4\),
+
+\[
+\begin{aligned}
+N &amp;=\binom{8}{0}\binom{9}{8} 
+   +\binom{7}{1}\binom{9}{7}
+   +\binom{6}{2}\binom{9}{6}
+   +\binom{5}{3}\binom{9}{5}
+   +\binom{4}{4}\binom{9}{4} \\[2mm]
+  &amp;= 1\cdot 9 + 7\cdot 36 + 15\cdot 84 + 10\cdot 126 + 1\cdot126\\
+  &amp;= 9+252+1260+1260+126 = 2907.
+\end{aligned}
+\]
+
+Therefore  
+
+\[
+N \equiv 2907 \pmod{1000}=907.
+\]
+
+\[
+\boxed{907}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 907</p>
+<p>Extracted Answer: 907</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $ A_1A_2 \ldots A_{11} $ be an 11-sided non-convex simple polygon with the following properties:
+* The area of $ A_iA_1A_{i+1} $ is 1 for each $ 2 \leq i \leq 10 $,
+* $ \cos(\angle A_iA_1A_{i+1}) = \frac{12}{13} $ for each $ 2 \leq i \leq 10 $,
+* The perimeter of $ A_1A_2 \ldots A_{11} $ is 20.
+If $ A_1A_2 + A_1A_{11} $ can be expressed as $ \frac{m\sqrt{n} - p}{q} $ for positive integers $ m, n, p, q $ with $ n $ squarefree and no prime divides all of $ m, p, q$, find $ m + n + p + q $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+\[
+r_i=|A_1A_i| \qquad (i=2,\dots ,11)
+\]
+
+and denote  
+
+\[
+\theta=\angle A_iA_1A_{i+1}\qquad (2\le i\le 10).
+\]
+
+Because  
+
+\[
+\cos\theta=\frac{12}{13}\;\Longrightarrow\;\sin\theta=\frac{5}{13},
+\]
+
+the area of \(\triangle A_iA_1A_{i+1}\) is  
+
+\[
+\frac12 r_i r_{i+1}\sin\theta
+   =\frac12 r_i r_{i+1}\frac{5}{13}=1 .
+\]
+
+Hence  
+
+\[
+r_i r_{i+1}= \frac{26}{5}=K\qquad (2\le i\le 10). \tag{1}
+\]
+
+From (1),
+
+\[
+r_{i+2}= \frac{K}{r_{i+1}}=r_i ,
+\]
+
+so the distances from \(A_1\) alternate:
+
+\[
+r_2=r_4=r_6=r_8=r_{10}=a,\qquad
+r_3=r_5=r_7=r_9=r_{11}=b,
+\]
+
+with  
+
+\[
+ab=K=\frac{26}{5}. \tag{2}
+\]
+
+--------------------------------------------------------------------
+### Lengths of the other sides
+
+For any \(i=2,\dots ,10\) the side \(A_iA_{i+1}\) (call it \(L\)) satisfies the law of cosines:
+
+\[
+L^2=a^{2}+b^{2}-2ab\cos\theta
+      =a^{2}+b^{2}-2ab\frac{12}{13}.
+\]
+
+Using (2),
+
+\[
+L^2=a^{2}+b^{2}-\frac{24}{13}\cdot\frac{26}{5}
+    =a^{2}+b^{2}-\frac{48}{5}.
+\]
+
+Since \(a^{2}+b^{2}=(a+b)^{2}-2ab\),
+
+\[
+L^2=(a+b)^{2}-2\frac{26}{5}-\frac{48}{5}
+     =(a+b)^{2}-20.
+\]
+
+Let  
+
+\[
+s=a+b.
+\]
+
+Then  
+
+\[
+L=\sqrt{s^{2}-20}. \tag{3}
+\]
+
+--------------------------------------------------------------------
+### Using the perimeter
+
+The perimeter of the 11‑gon is
+
+\[
+|A_1A_2|+|A_1A_{11}|+\sum_{i=2}^{10}|A_iA_{i+1}|
+= a+b+9L = s+9\sqrt{s^{2}-20}=20.
+\]
+
+Set \(t=\sqrt{s^{2}-20}&gt;0\). Then \(s=20-9t\) and
+
+\[
+t^{2}=s^{2}-20=(20-9t)^{2}-20.
+\]
+
+Solving,
+
+\[
+t^{2}=380-360t+81t^{2}
+\Longrightarrow 80t^{2}-360t+380=0
+\Longrightarrow 4t^{2}-18t+19=0.
+\]
+
+Hence  
+
+\[
+t=\frac{18\pm\sqrt{324-304}}{8}
+   =\frac{18\pm2\sqrt5}{8}
+   =\frac{9\pm\sqrt5}{4}.
+\]
+
+If the plus sign is taken, \(t&gt;\frac{20}{9}\) and \(s=20-9t&lt;0\), impossible.
+Thus  
+
+\[
+t=\frac{9-\sqrt5}{4},
+\qquad
+s=20-9t=\frac{9\sqrt5-1}{4}.
+\]
+
+Consequently  
+
+\[
+A_1A_2+A_1A_{11}=s=\frac{9\sqrt5-1}{4}.
+\]
+
+Written as \(\dfrac{m\sqrt n-p}{q}\) we have  
+
+\[
+m=9,\;n=5,\;p=1,\;q=4,
+\]
+
+so  
+
+\[
+m+n+p+q=9+5+1+4=19.
+\]
+
+\[
+\boxed{19}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 19</p>
+<p>Extracted Answer: 19</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Alex divides a disk into four quadrants with two perpendicular diameters intersecting at the center of the disk. He draws 25 more line segments through the disk, drawing each segment by selecting two points at random on the perimeter of the disk in different quadrants and connecting those two points. Find the expected number of regions into which these 27 line segments divide the disk.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>**Step 1.  Regions created by chords**
+
+If a circle already has \(k\) chords drawn in its interior, then a new chord
+adds one region for itself plus one extra region for every interior
+intersection it creates.  
+Thus for a set of \(n\) chords
+
+\[
+\text{# regions}=n+1+\text{# interior intersection points.}
+\]
+
+In our problem we have  
+
+* 2 fixed diameters (the two perpendicular ones),  
+* 25 random chords.
+
+Hence \(n=27\).  
+We only have to find the expected number \(I\) of interior intersection
+points.
+
+\[
+E[\text{regions}]=27+1+E[I]=28+E[I].
+\]
+
+--------------------------------------------------------------------
+
+**Step 2.  Intersections involving the two diameters**
+
+Let the horizontal diameter be the line that separates the *upper* quadrants
+\(Q_{1},Q_{2}\) from the *lower* quadrants \(Q_{3},Q_{4}\).
+
+A random chord has its two endpoints in different quadrants.
+The chord meets the horizontal diameter exactly when the endpoints lie in
+different half‑planes, i.e. one endpoint is in \(\{Q_{1},Q_{2}\}\) and the
+other in \(\{Q_{3},Q_{4}\}\).
+
+For the ordered pair of quadrants of a random chord there are  
+\(12\) equally likely possibilities (the \(4\cdot 3\) ordered pairs with
+different quadrants).  
+Exactly \(8\) of them have the endpoints in opposite half‑planes, hence
+
+\[
+p_d=\Pr(\text{a random chord meets a given diameter})=\frac{8}{12}=
+\frac{2}{3}.
+\]
+
+Therefore
+
+\[
+\boxed{\text{Expected intersections of the 25 chords with one diameter}=25\cdot\frac23}
+\]
+
+and with the two diameters together
+
+\[
+E[I_{\text{diameters}}]=2\cdot25\cdot\frac23=\frac{100}{3}.
+\]
+
+The two diameters intersect each other once, so add \(1\) more interior
+intersection.
+
+--------------------------------------------------------------------
+
+**Step 3.  Intersections of two random chords**
+
+Denote the four endpoints by  
+\(\alpha_1,\alpha_2\) (chord 1) and \(\beta_1,\beta_2\) (chord 2).  
+All four points are independent uniform on the circle.
+
+Let  
+
+\[
+A=\{\text{endpoints of chord 1 lie in different quadrants}\},\qquad 
+B=\{\text{endpoints of chord 2 lie in different quadrants}\}.
+\]
+
+\[
+P(A)=P(B)=\frac34 .
+\]
+
+Two chords intersect iff the endpoints are interleaved on the circle,
+i.e. exactly one of \(\beta_1,\beta_2\) lies on the clockwise arc from
+\(\alpha_1\) to \(\alpha_2\).
+
+Fix \(\alpha_1=x\) and \(\alpha_2=y\) (with \(x\neq y\)).
+Let \(I=(x,y)\) be the clockwise arc from \(x\) to \(y\) and let
+\(d=|I|\) be its length.  
+For independent uniform \(\beta_1,\beta_2\),
+
+* the probability that exactly one lies in \(I\) is \(2d(1-d)\);
+* the probability that the two \(\beta\)’s are in *different* quadrants
+  is \(\frac34\).
+
+Conditioning on the actual placement of the interval \(I\) with respect
+to the four quarter‑arcs yields (after a short computation)
+
+\[
+\Pr(\beta_1,\beta_2\text{ satisfy both conditions}\mid x,y)=
+2\Bigl[d\Bigl(\tfrac34-d\Bigr)+\sum_{q=0}^{3}a_q^{\,2}\Bigr],
+\tag{1}
+\]
+
+where \(a_q\) is the length of the part of \(I\) that lies in quadrant
+\(q\).
+
+Now average (1) over all ordered pairs \((x,y)\) that are in different
+quadrants.  By symmetry it suffices to place \(x\) in the first quadrant
+\([0,\tfrac14)\) and let \(y\) run in the three other quadrants.
+Carrying out the integration (splitting the three possible clockwise
+distances) gives
+
+\[
+\int\!\!\int_{x\in Q_0,\;y\in Q_m}
+2\Bigl[d\Bigl(\tfrac34-d\Bigr)+\sum a_q^{\,2}\Bigr]\,dy\,dx
+   =\frac{17}{64}\qquad(m=1,2,3\text{ summed}).
+\]
+
+Thus
+
+\[
+P(A\cap B\cap\{\text{the chords intersect}\})=\frac{17}{64}.
+\]
+
+Finally
+
+\[
+p_r=
+\Pr(\text{intersection}\mid A\cap B)=
+\frac{P(A\cap B\cap\text{intersect})}{P(A)P(B)}
+=\frac{17/64}{(3/4)^2}
+=\frac{16}{9}\cdot\frac{17}{64}
+=\frac{17}{36}.
+\]
+
+--------------------------------------------------------------------
+
+**Step 4.  Expected interior intersections**
+
+* Intersections of the two diameters: \(1\).
+* Intersections of the 25 random chords with the two diameters:
+  \(\displaystyle \frac{100}{3}\).
+* Intersections among the 25 random chords:
+  \(\displaystyle \binom{25}{2}\,p_r
+   =300\cdot\frac{17}{36}= \frac{425}{3}\).
+
+Hence
+
+\[
+E[I]=1+\frac{100}{3}+\frac{425}{3}
+     =1+\frac{525}{3}=1+175=176.
+\]
+
+--------------------------------------------------------------------
+
+**Step 5.  Expected number of regions**
+
+\[
+E[\text{regions}]=27+1+E[I]=28+176=204.
+\]
+
+--------------------------------------------------------------------
+
+\[
+\boxed{204}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 204</p>
+<p>Extracted Answer: 204</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Suppose $ \triangle ABC $ has angles $ \angle BAC = 84^\circ $, $ \angle ABC = 60^\circ $, and $ \angle ACB = 36^\circ $. Let $ D, E, $ and $ F $ be the midpoints of sides $ \overline{BC} $, $ \overline{AC} $, and $ \overline{AB} $, respectively. The circumcircle of $ \triangle DEF $ intersects $ \overline{BD} $, $ \overline{AE} $, and $ \overline{AF} $ at points $ G, H, $ and $ J $, respectively. The points $ G, D, E, H, J, $ and $ F $ divide the circumcircle of $ \triangle DEF $ into six minor arcs, as shown. Find $ \widehat{DE} + 2 \cdot \widehat{HJ} + 3 \cdot \widehat{FG} $, where the arcs are measured in degrees.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+\[
+\triangle ABC\qquad 
+\angle A=84^{\circ},\; \angle B=60^{\circ},\; \angle C=36^{\circ}.
+\]
+
+Denote  
+
+\[
+D,E,F \text{ – the midpoints of }BC,CA,AB,
+\]
+\[
+G,H,J \text{ – the second intersections of }BD,AE,AF\text{ with the circumcircle of } \triangle DEF .
+\]
+
+--------------------------------------------------------------------
+### 1.  The points \(G,H,J\) are the feet of the altitudes  
+
+The nine‑point circle of \(\triangle ABC\) passes through the three midpoints \(D,E,F\) **and** through the three feet of the altitudes.  
+Because  
+
+* \(BD\) lies on the side \(BC\),  
+* \(AE\) lies on the side \(CA\),  
+* \(AF\) lies on the side \(AB\),
+
+the second intersection of each of these sides with the nine‑point circle must be the corresponding foot of an altitude:
+
+\[
+\begin{aligned}
+G&amp;= \text{foot from }A\text{ onto }BC,\\[2mm]
+H&amp;= \text{foot from }B\text{ onto }CA,\\[2mm]
+J&amp;= \text{foot from }C\text{ onto }AB .
+\end{aligned}
+\]
+
+Thus \(G,H,J\) are the vertices of the orthic triangle.
+
+--------------------------------------------------------------------
+### 2.  Arc \(\widehat{DE}\)
+
+The medial triangle \(\triangle DEF\) is similar to \(\triangle ABC\) (ratio \(1\!:\!2\)).  
+Consequently  
+
+\[
+\angle DFE = \angle C = 36^{\circ}.
+\]
+
+For any inscribed angle, the intercepted minor arc is twice the angle; hence  
+
+\[
+\widehat{DE}=2\angle DFE = 2\cdot 36^{\circ}=72^{\circ}.
+\]
+
+--------------------------------------------------------------------
+### 3.  Arc \(\widehat{FG}\)
+
+Since \(D\) and \(G\) both lie on side \(BC\), the chord \(DG\) is a part of \(BC\).  
+The chord \(DF\) joins the midpoints of \(AB\) and \(BC\); by the Midpoint Theorem  
+
+\[
+DF \parallel AC .
+\]
+
+Therefore  
+
+\[
+\angle FDG =\angle (\text{line }DF,\text{ line }DG)
+        =\angle (AC,BC)=\angle C=36^{\circ}.
+\]
+
+Thus  
+
+\[
+\widehat{FG}=2\angle FDG = 2\cdot 36^{\circ}=72^{\circ}.
+\]
+
+--------------------------------------------------------------------
+### 4.  Arc \(\widehat{HJ}\)
+
+\(H,J,G\) are the vertices of the orthic triangle.  
+A standard fact about the orthic triangle is that its angles are  
+
+\[
+\angle HGJ = 180^{\circ}-2\angle A,\qquad
+\angle GJH = 180^{\circ}-2\angle B,\qquad
+\angle JHG = 180^{\circ}-2\angle C .
+\]
+
+(The fact follows from simple angle‑chasing with the right‑angles at the feet of the altitudes.)
+
+Hence the minor arc opposite \(G\) – that is, \(\widehat{HJ}\) – satisfies  
+
+\[
+\widehat{HJ}=2\angle HGJ =2\bigl(180^{\circ}-2A\bigr)
+               =360^{\circ}-4A.
+\]
+
+With \(\angle A =84^{\circ}\),
+
+\[
+\widehat{HJ}=360^{\circ}-4\cdot84^{\circ}=24^{\circ}.
+\]
+
+--------------------------------------------------------------------
+### 5.  Required sum
+
+\[
+\begin{aligned}
+\widehat{DE}+2\widehat{HJ}+3\widehat{FG}
+&amp;= 72^{\circ}+2\cdot24^{\circ}+3\cdot72^{\circ}\\
+&amp;= 72^{\circ}+48^{\circ}+216^{\circ}\\[2mm]
+&amp;= 336^{\circ}.
+\end{aligned}
+\]
+
+--------------------------------------------------------------------
+\[
+\boxed{336}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 336</p>
+<p>Extracted Answer: 336</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $ \triangle ABC $ be a right triangle with $ \angle A = 90^\circ $ and $ BC = 38 $. There exist points $ K $ and $ L $ inside the triangle such that $ AK = AL = BK = CL = KL = 14. $ The area of the quadrilateral $ BKLC $ can be expressed as $ n \sqrt{3} $ for some positive integer $ n $. Find $ n $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+\[
+\angle A =90^\circ ,\qquad BC =38 .
+\]
+
+Place  
+
+\[
+A=(0,0),\qquad B=(b,0),\qquad C=(0,c)
+\]
+
+so that the legs are  
+
+\[
+AB=b,\qquad AC=c,\qquad b^{2}+c^{2}=38^{2}=1444 .
+\tag{1}
+\]
+
+--------------------------------------------------------------------
+### 1.  Coordinates of \(K\) and \(L\)
+
+Because  
+
+\[
+AK=BK=14,
+\]
+
+\(K\) lies on the perpendicular bisector of \(\overline{AB}\); hence  
+
+\[
+K=\Bigl(\frac b2,\;\sqrt{14^{2}-\Bigl(\frac b2\Bigr)^{2}}\Bigr)
+   =\bigl( X,\;U\bigr)
+\]
+
+with  
+
+\[
+X=\frac b2,\qquad U=\sqrt{196-X^{2}} .\tag{2}
+\]
+
+Similarly  
+
+\[
+AL=CL=14\Longrightarrow 
+L=\Bigl(\sqrt{196-\Bigl(\frac c2\Bigr)^{2}},\;\frac c2\Bigr)
+   =(V,Y),\qquad 
+Y=\frac c2,\;V=\sqrt{196-Y^{2}} .\tag{3}
+\]
+
+Thus  
+
+\[
+X^{2}+Y^{2}= \frac{b^{2}+c^{2}}{4}
+           =\frac{1444}{4}=361 .\tag{4}
+\]
+
+--------------------------------------------------------------------
+### 2.  The equilateral triangle \(AKL\)
+
+All three sides of \(\triangle AKL\) equal \(14\), so \(\angle KAL=60^\circ\).
+Using the vectors \(\overrightarrow{AK}=(X,U)\) and \(\overrightarrow{AL}=(V,Y)\),
+
+\[
+\overrightarrow{AK}\cdot\overrightarrow{AL}=|AK||AL|\cos 60^\circ
+\Longrightarrow
+XV+YU=98 .\tag{5}
+\]
+
+From (2)–(5) we have the system
+
+\[
+\begin{cases}
+X^{2}+Y^{2}=361,\\[2pt]
+X\sqrt{196-Y^{2}}+Y\sqrt{196-X^{2}}=98 .
+\end{cases}
+\]
+
+--------------------------------------------------------------------
+### 3.  Solving the system
+
+Set  
+
+\[
+X=14\cos\alpha ,\qquad U=14\sin\alpha ,\qquad 
+Y=14\cos\beta ,\qquad V=14\sin\beta .
+\]
+
+Then (5) becomes  
+
+\[
+14^{2}\bigl(\cos\alpha\sin\beta+\cos\beta\sin\alpha\bigr)
+   =196\sin(\alpha+\beta)=98,
+\]
+
+hence  
+
+\[
+\sin(\alpha+\beta)=\frac12\Longrightarrow\alpha+\beta=\frac{\pi}{6}\;(30^\circ). \tag{6}
+\]
+
+From \(X^{2}+Y^{2}=361\),
+
+\[
+196\bigl(\cos^{2}\alpha+\cos^{2}\beta\bigr)=361
+\Longrightarrow
+\cos^{2}\alpha+\cos^{2}\beta= \frac{361}{196}=1+\frac{165}{196}.
+\]
+
+Using \(\cos^{2}\alpha+\cos^{2}\beta=
+1+\cos(\alpha+\beta)\cos(\alpha-\beta)\) gives  
+
+\[
+\cos\frac{\pi}{6}\,\cos(\alpha-\beta)=\frac{165}{196}
+\Longrightarrow
+\cos(\alpha-\beta)=\frac{165}{98\sqrt3}
+       =\frac{55\sqrt3}{98}.
+\]
+
+Hence  
+
+\[
+\sin(\alpha-\beta)=\sqrt{1-\Bigl(\frac{55\sqrt3}{98}\Bigr)^{2}}
+                 =\frac{23}{98}.
+\]
+
+Now compute \(\cos\alpha\) and \(\cos\beta\):
+\[
+\cos\alpha=\sqrt{\frac{1+\cos(\alpha+\beta)}{2}}
+          =\sqrt{\frac{1+\frac{71}{98}}{2}}
+          =\frac{13}{14},
+\qquad
+\cos\beta =\sqrt{\frac{1+\cos(\alpha-\beta)}{2}}
+          =\sqrt{\frac{1+\frac{47}{49}}{2}}
+          =\frac{4\sqrt3}{7}.
+\]
+
+Therefore  
+
+\[
+X=14\cos\alpha =13,\qquad 
+Y=14\cos\beta =8\sqrt3 .
+\]
+
+Consequently  
+
+\[
+b=2X=26,\qquad c=2Y=16\sqrt3 .
+\]
+
+One easily checks that \(b^{2}+c^{2}=26^{2}+ (16\sqrt3)^{2}=1444\), i.e. \(BC=38\).
+
+--------------------------------------------------------------------
+### 4.  Area of \(BKLC\)
+
+The right‑triangle \(ABC\) has area  
+
+\[
+[ABC]=\frac12\,b\,c
+      =\frac12\cdot26\cdot16\sqrt3
+      =208\sqrt3 .
+\]
+
+The three small triangles cut off by \(K\) and \(L\) have areas  
+
+\[
+\begin{aligned}
+[ABK]&amp;=\frac12\cdot b\cdot U
+      =\frac12\cdot26\cdot3\sqrt3=39\sqrt3,\\[2pt]
+[ALC]&amp;=\frac12\cdot c\cdot V
+      =\frac12\cdot16\sqrt3\cdot2=16\sqrt3,\\[2pt]
+[AKL]&amp;=\frac{\sqrt3}{4}\cdot14^{2}=49\sqrt3 .
+\end{aligned}
+\]
+
+Thus
+
+\[
+\begin{aligned}
+[BKLC] &amp;=[ABC]-[ABK]-[ALC]-[AKL]\\
+       &amp;=208\sqrt3-(39\sqrt3+16\sqrt3+49\sqrt3)\\
+       &amp;=104\sqrt3 .
+\end{aligned}
+\]
+
+Hence the area of \(BKLC\) is \(n\sqrt3\) with  
+
+\[
+\boxed{n=104}.
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 104</p>
+<p>Extracted Answer: None</p>
+<p>Score: 0.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let the sequence of rationals $ x_1, x_2, \ldots $ be defined such that $ x_1 = \frac{25}{11} $ and
+$ x_{k+1} = \frac{1}{3} \left( x_k + \frac{1}{x_k} - 1 \right). $
+$ x_{2025} $ can be expressed as $ \frac{m}{n} $ for relatively prime positive integers $ m $ and $ n $. Find the remainder when $ m + n $ is divided by 1000.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>**Solution**
+
+\[
+x_{k+1}= \frac13\Bigl(x_k+\frac1{x_k}-1\Bigr),\qquad 
+x_1=\frac{25}{11}
+\]
+
+Write each term as a reduced fraction  
+
+\[
+x_k=\frac{p_k}{q_k},\qquad \gcd(p_k,q_k)=1 .
+\]
+
+Then  
+
+\[
+x_{k+1}= \frac{p_k^2+q_k^2-p_kq_k}{3p_kq_k}
+      =\frac{p_{k+1}}{q_{k+1}}
+\]
+
+where  
+
+\[
+p_{k+1}= \frac{p_k^2+q_k^2-p_kq_k}{3},
+\qquad 
+q_{k+1}=p_kq_k . \tag{1}
+\]
+
+(The numerator is always divisible by \(3\); one checks that
+\(\gcd(p_{k+1},q_{k+1})=1\) for every \(k\).)
+
+--------------------------------------------------------------------
+### 1.  A simple recurrence for the sum  
+
+Let  
+
+\[
+s_k=p_k+q_k .
+\]
+
+Adding the two formulas in (1),
+
+\[
+\begin{aligned}
+s_{k+1}&amp;=p_{k+1}+q_{k+1}
+        =\frac{p_k^2+q_k^2-p_kq_k}{3}+p_kq_k  \\
+        &amp;=\frac{p_k^2+2p_kq_k+q_k^2}{3}
+        =\frac{(p_k+q_k)^2}{3}
+        =\frac{s_k^{\,2}}{3}.
+\end{aligned}
+\]
+
+Thus  
+
+\[
+s_{k+1}= \frac{s_k^{\,2}}{3},\qquad s_1=p_1+q_1=25+11=36.
+\tag{2}
+\]
+
+--------------------------------------------------------------------
+### 2.  Closed form
+
+Set \(t_k=s_k/3\).  From (2)
+
+\[
+t_{k+1}=t_k^{\,2},\qquad t_1=\frac{36}{3}=12 .
+\]
+
+Hence  
+
+\[
+t_k=12^{\,2^{\,k-1}},\qquad 
+s_k=3t_k=3\cdot 12^{\,2^{\,k-1}} . \tag{3}
+\]
+
+Therefore  
+
+\[
+p_{2025}+q_{2025}=s_{2025}=3\cdot 12^{\,2^{2024}} .
+\]
+
+--------------------------------------------------------------------
+### 3.  Computing the last three digits  
+
+We need  
+
+\[
+M=3\cdot 12^{\,2^{2024}}\pmod{1000}.
+\]
+
+Because \(1000=8\cdot125\) we compute the two residues separately.
+
+*Modulo \(8\)*  
+
+\(12\equiv4\pmod8\) and \(4^{2}=0\pmod8\).  
+Since the exponent \(2^{2024}\ge2\),
+
+\[
+12^{\,2^{2024}}\equiv0\pmod8 .
+\]
+
+Hence \(M\equiv0\pmod8\).
+
+*Modulo \(125\)*  
+
+\(\gcd(12,125)=1\) and \(\varphi(125)=100\), so  
+\(12^{100}\equiv1\pmod{125}\).  
+Thus only the exponent modulo \(100\) matters:
+
+\[
+e=2^{2024}\pmod{100}.
+\]
+
+For \(n\ge2\) the powers of \(2\) modulo \(100\) have period \(20\):
+\(2^{n+20}\equiv2^n\pmod{100}\).
+Since \(2024\equiv4\pmod{20}\),
+
+\[
+e\equiv2^{4}=16\pmod{100}.
+\]
+
+Now compute \(12^{16}\pmod{125}\):
+
+\[
+\begin{aligned}
+12^{2}&amp;\equiv144\equiv19,\\
+12^{4}&amp;\equiv19^{2}=361\equiv111,\\
+12^{8}&amp;\equiv111^{2}=12321\equiv71,\\
+12^{16}&amp;\equiv71^{2}=5041\equiv41\pmod{125}.
+\end{aligned}
+\]
+
+Hence  
+
+\[
+12^{\,2^{2024}}\equiv41\pmod{125}.
+\]
+
+*Chinese remainder theorem*  
+
+Find \(A\) such that  
+
+\[
+A\equiv0\pmod8,\qquad A\equiv41\pmod{125}.
+\]
+
+Write \(A=8k\).  Then \(8k\equiv41\pmod{125}\Rightarrow
+k\equiv41\cdot8^{-1}\pmod{125}\).
+Since \(8^{-1}\equiv47\pmod{125}\),
+
+\[
+k\equiv41\cdot47\equiv52\pmod{125},
+\]
+so \(k=52+125t\) and  
+
+\[
+A=8k=416+1000t\equiv416\pmod{1000}.
+\]
+
+Finally  
+
+\[
+M=3A\equiv3\cdot416=1248\equiv\boxed{248}\pmod{1000}.
+\]
+
+Thus the remainder of \(m+n\) when divided by \(1000\) is **248**.</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 248</p>
+<p>Extracted Answer: 248</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+There are exactly three positive real numbers $ k $ such that the function
+$ f(x) = \frac{(x - 18)(x - 72)(x - 98)(x - k)}{x} $
+defined over the positive real numbers achieves its minimum value at exactly two positive real numbers $ x $. Find the sum of these three values of $ k $.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>Let  
+
+\[
+f_k(x)=\frac{(x-18)(x-72)(x-98)(x-k)}{x}= \frac{N(x)}{x},\qquad x&gt;0 ,
+\]
+
+where  
+
+\[
+N(x)=(x-18)(x-72)(x-98)(x-k)
+      =x^{4}-(188+k)x^{3}+(10116+188k)x^{2}-(127008+10116k)x+127008k .
+\]
+
+--------------------------------------------------------------------
+### 1.  What does “the minimum is attained at exactly two points’’ mean?
+
+If the global minimum value is \(m\), then for every \(x&gt;0\)
+
+\[
+\frac{N(x)}{x}\ge m\qquad\Longleftrightarrow\qquad N(x)-mx\ge0 .
+\]
+
+Equality occurs exactly at the points where the minimum is attained.
+Since \(N(x)-mx\) is a quartic polynomial, the only way it can be
+non‑negative for all \(x\) and vanish at exactly two distinct points is
+
+\[
+N(x)-mx=(x-a)^{2}(x-b)^{2}\qquad(a\neq b,\;a,b&gt;0).
+\]
+
+Thus there are numbers \(a,b,m\) such that  
+
+\[
+\begin{cases}
+N(a)=ma,\quad N&#39;(a)=m,\\[2pt]
+N(b)=mb,\quad N&#39;(b)=m .
+\end{cases}
+\]
+
+--------------------------------------------------------------------
+### 2.  Coefficient comparison
+
+Write
+
+\[
+(x-a)^{2}(x-b)^{2}=(x^{2}-Sx+P)^{2},
+\qquad
+S=a+b,\;P=ab .
+\]
+
+Equating coefficients of \(N(x)-mx\) and \((x^{2}-Sx+P)^{2}\) yields  
+
+\[
+\begin{aligned}
+S&amp;=\frac{188+k}{2},\tag{1}\\[2pt]
+S^{2}+2P&amp;=10116+188k,\tag{2}\\[2pt]
+2SP&amp;=127008+10116k+m,\tag{3}\\[2pt]
+P^{2}&amp;=127008\,k.\tag{4}
+\end{aligned}
+\]
+
+From (1) and (4)
+
+\[
+S=\frac{188+k}{2},\qquad P=\sqrt{127008\,k}.
+\]
+
+Insert these in (2):
+
+\[
+\frac{(188+k)^{2}}{4}+2\sqrt{127008\,k}=10116+188k .
+\]
+
+Multiplying by \(4\) and using \(\sqrt{127008}=252\sqrt2\) gives  
+
+\[
+k^{2}-376k-5120+2016\sqrt{2k}=0. \tag{5}
+\]
+
+--------------------------------------------------------------------
+### 3.  Solving for \(k\)
+
+Set \(u=\sqrt{k}&gt;0\).  Then \(\sqrt{2k}=u\sqrt2\) and (5) becomes  
+
+\[
+u^{4}-376u^{2}+2016\sqrt2\,u-5120=0 .
+\]
+
+Write \(u=a\sqrt2\;(a&gt;0)\); the equation reduces to  
+
+\[
+a^{4}-188a^{2}+1008a-1280=0 .
+\]
+
+Factoring,
+
+\[
+(a^{2}-6a+8)(a^{2}+6a-160)=0,
+\]
+
+so  
+
+\[
+a=2,\;4,\;10\quad(\text{the root }a=-16\text{ gives }u&lt;0\text{ and is discarded}).
+\]
+
+Since \(k=u^{2}=2a^{2}\),
+
+\[
+k=2\cdot2^{2}=8,\qquad
+k=2\cdot4^{2}=32,\qquad
+k=2\cdot10^{2}=200 .
+\]
+
+For each of these values the discriminant  
+
+\[
+\Delta=S^{2}-4P&gt;0
+\]
+
+so the quadratic \(x^{2}-Sx+P\) has two distinct positive roots; consequently
+\(f_{k}(x)\) attains its global minimum at exactly those two points.
+
+--------------------------------------------------------------------
+### 4.  Sum of the admissible \(k\)
+
+\[
+8+32+200 = 240 .
+\]
+
+\[
+\boxed{240}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 240</p>
+<p>Extracted Answer: 240</p>
+<p>Score: 1.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $N$ denote the number of ordered triples of positive integers $(a,b,c)$ such that $a,b,c\leq3^6$ and $a^3+b^3+c^3$ is a multiple of $3^7$. Find the remainder when $N$ is divided by $1000$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>**Solution Outline**
+
+1.  Let \(M=3^{7}=2187\) and \(A=\{1,\ldots ,3^{6}\}= \{1,\dots ,729\}\).
+    For each \(a\in A\) put \(r(a)=a^{3}\pmod{M}\).
+    The required number  
+
+    \[
+    N=\#\{(a,b,c)\in A^{3}:r(a)+r(b)+r(c)\equiv0\pmod M\}
+    \]
+
+    is the weighted convolution of the distribution of the residues
+    \(r(a)\).
+
+2.  Write each \(a\) as \(a=3^{v}a&#39;\) with \(\gcd(a&#39;,3)=1\).
+
+| \(v\) | range of \(a\) | # of such \(a\) | residue \(a^{3}\) (mod \(M\)) | weight |
+|-------|----------------|-----------------|-------------------------------|--------|
+| 0 | not divisible by 3 | \(486\) | \(a^{\prime\,3}\) (unit cube) | \(1\) |
+| 1 | \(3\mid a,9\nmid a\) | \(162\) | \(27a^{\prime\,3}\) | \(9\) |
+| 2 | \(9\mid a,27\nmid a\) | \(54\) | \(729a^{\prime\,3}\) | \(27\) |
+| \(\ge3\) | \(27\mid a\) | \(27\) | \(0\) | \(27\)
+
+Hence the possible residues and their multiplicities are  
+
+* 0      weight \(27\);
+* the two residues \(729,\,1458\) weight \(27\) each;
+* 18 residues (the cubes of the unit group modulo \(81\)) weight \(9\) each;
+* 486 residues (the cubes of the unit group modulo \(3^{7}\)) weight \(1\) each.
+
+Denote by  
+
+* \(D\) the 486 unit‑cube residues (weight 1);
+* \(C\) the 18 residues \(27\cdot u\) with \(u\) a unit‑cube modulo \(81\) (weight 9);
+* \(B\) the two residues \(729,1458\) (weight 27);
+* \(0\) the zero residue (weight 27).
+
+3.  Split the count according to how many zero‑terms occur.
+    Let  
+
+    \[
+    w(x)=\text{weight of residue }x.
+    \]
+
+    For \(x\neq0\) put \(R&#39;=\{D\cup C\cup B\}\).  Then
+
+    \[
+    N=N_{0}+N_{1}+N_{2},
+    \]
+
+    where  
+
+    * \(N_{2}=w(0)^{3}=27^{3}=19683\)  (all three residues zero);
+    * \(N_{1}=3\,w(0)\displaystyle\sum_{\substack{y+z\equiv0\\y,z\in R&#39;}}
+            w(y)w(z) =3\cdot27\cdot3402=275\,562\);
+    * \(N_{0}\) counts triples with no zero term.
+
+    The sum in \(N_{1}\) is obtained easily:
+    each \(x\in D\) pairs with its inverse, giving \(486\) ordered pairs,
+    each \(x\in C\) gives \(18\) ordered pairs (weight \(9^{2}=81\)), and each
+    \(x\in B\) gives \(2\) ordered pairs (weight \(27^{2}=729\)).
+    Hence \(\displaystyle\sum_{y+z\equiv0}w(y)w(z)=486+1458+1458=3402\).
+
+4.  Compute \(N_{0}\).
+    After factoring the common factor \(27\) from the elements of \(C\cup B\),
+    the condition \(x+y+z\equiv0\pmod{M}\) becomes
+
+    \[
+    u+v+w\equiv0\pmod{81},
+    \]
+
+    where \(u,v,w\) belong to  
+
+    * the set \(S\) of the 18 unit‑cubes modulo \(81\) (weight 9);
+    * the two residues \(27,54\) (weight 27).
+
+    For the set \(S\) one has the simple description  
+
+    \[
+    S=\{x\pmod{81}:x\equiv\pm1\pmod9\}.
+    \]
+
+    Using this description we compute the additive convolution on \(\mathbb Z/81\).
+
+    * For any \(t\equiv0\pmod9\) we have \(\#\{(s_{1},s_{2})\in S^{2}:s_{1}+s_{2}\equiv t\}=18\).
+    * For any \(t\equiv\pm2\pmod9\) the count equals \(9\).
+    * For any other residue the count is \(0\).
+
+    Consequently
+
+    * there are no triples \(s_{1}+s_{2}+s_{3}\equiv0\) with all three from \(S\);
+    * ordered triples with exactly one element from \(\{27,54\}\) and two from \(S\) are possible.
+      For each of the two choices \(\{27,54\}\) there are
+      \((A*A)(27)=(A*A)(54)=18\) ordered pairs from \(S\);  
+      with three possible positions for the “\(B\)’’ element we obtain  
+
+      \[
+      2\cdot3\cdot18=108
+      \]
+
+      ordered triples.  Their weight is \(27\cdot9^{2}=2187\), giving a contribution  
+
+      \[
+      108\cdot2187=236\,196 .
+      \]
+
+    * triples consisting only of the two “\(B\)” residues satisfy the condition
+      only when all three are equal, giving two ordered triples,
+      each of weight \(27^{3}=19683\); contribution  
+
+      \[
+      2\cdot19683=39\,366 .
+      \]
+
+    Adding these contributions:
+
+    \[
+    N_{0}=236\,196+39\,366=275\,562 .
+    \]
+
+5.  Assemble all parts:
+
+    \[
+    N=N_{0}+N_{1}+N_{2}=275\,562+275\,562+19\,683=570\,807 .
+    \]
+
+6.  The required remainder is  
+
+    \[
+    N\bmod1000 = 570\,807\bmod1000 = \boxed{807}.
+    \]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 735</p>
+<p>Extracted Answer: 807</p>
+<p>Score: 0.0</p>
+    <hr>
+    
+    
+<h3>Prompt conversation</h3>
+
+
+<div class="message user">
+    <div class="role">
+    user
+    
+    </div>
+    <div class="content">
+    <pre>
+Let $ABCDE$ be a convex pentagon with $AB=14, BC=7, CD=24, DE=13, EA=26,$ and $\angle B=\angle E=60^\circ$. For each point $X$ in the plane, define $f(X)=AX+BX+CX+DX+EX$. The least possible value of $f(X)$ can be expressed as $m+n\sqrt{p}$, where $m$ and $n$ are positive integers and $p$ is not divisible by the square of any prime. Find $m+n+p$.
+Please reason step by step, and put your final answer within \boxed{}.
+</pre>
+    </div>
+</div>
+
+<h3>Sampled message</h3>
+
+<div class="message assistant">
+    <div class="role">
+    assistant
+    
+    </div>
+    <div class="content">
+    <pre>The minimum value of \(f(X)\) works out to be  
+
+\[
+f_{\min}=18+20\sqrt7 .
+\]
+
+Thus \(m=18,\; n=20,\; p=7\) and  
+
+\[
+m+n+p = 18+20+7 = 45 .
+\]
+
+\[
+\boxed{45}
+\]</pre>
+    </div>
+</div>
+<h3>Results</h3>
+<p>Correct Answer: 60</p>
+<p>Extracted Answer: 45</p>
+<p>Score: 0.0</p>
+    <hr>
+    
+    </body>
+</html>
\ No newline at end of file
diff --git a/benches/dgx-spark/aime25_openai__gpt-oss-120b-high_temp1.0_20251109_094547.json b/benches/dgx-spark/aime25_openai__gpt-oss-120b-high_temp1.0_20251109_094547.json
new file mode 100644
index 00000000000..7d4e54b4ce2
--- /dev/null
+++ b/benches/dgx-spark/aime25_openai__gpt-oss-120b-high_temp1.0_20251109_094547.json
@@ -0,0 +1,6 @@
+{
+  "chars": 2296.1916666666666,
+  "chars:std": 986.051306946325,
+  "score": 0.925,
+  "score:std": 0.26339134382131846
+}
\ No newline at end of file
diff --git a/benches/dgx-spark/aime25_openai__gpt-oss-120b-high_temp1.0_20251109_094547_allresults.json b/benches/dgx-spark/aime25_openai__gpt-oss-120b-high_temp1.0_20251109_094547_allresults.json
new file mode 100644
index 00000000000..4a85ce57c65
--- /dev/null
+++ b/benches/dgx-spark/aime25_openai__gpt-oss-120b-high_temp1.0_20251109_094547_allresults.json
@@ -0,0 +1,2896 @@
+{
+  "score": 0.925,
+  "metrics": {
+    "chars": 2296.1916666666666,
+    "chars:std": 986.051306946325,
+    "score:std": 0.26339134382131846
+  },
+  "htmls": [
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nFind the sum of all integer bases $b&gt;9$ for which $17_{b}$ is a divisor of $97_{b}$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>First write the two numbers in base\u201110.\n\n\\[\n17_{b}=1\\cdot b+7=b+7,\\qquad \n97_{b}=9\\cdot b+7=9b+7 .\n\\]\n\nWe need  \n\n\\[\nb+7 \\mid 9b+7 .\n\\]\n\nUse the Euclidean algorithm:\n\n\\[\n9b+7 = 9(b+7)-56 .\n\\]\n\nHence  \n\n\\[\nb+7 \\mid 9b+7 \\iff b+7 \\mid 56 .\n\\]\n\nSo \\(b+7\\) must be a positive divisor of \\(56\\).\n\nSince the base must satisfy \\(b&gt;9\\), we have \\(b+7&gt;16\\).  \nThe divisors of \\(56\\) exceeding \\(16\\) are \\(28\\) and \\(56\\).\n\n\\[\n\\begin{cases}\nb+7=28 \\ \\Rightarrow\\ b=21,\\\\[2pt]\nb+7=56 \\ \\Rightarrow\\ b=49.\n\\end{cases}\n\\]\n\nBoth bases indeed work:\n\n\\[\n\\frac{97_{21}}{17_{21}}=\\frac{196}{28}=7,\\qquad \n\\frac{97_{49}}{17_{49}}=\\frac{448}{56}=8 .\n\\]\n\nTherefore the required bases are \\(21\\) and \\(49\\), and their sum is  \n\n\\[\n21+49 = 70.\n\\]\n\n\\[\n\\boxed{70}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 70</p>\n<p>Extracted Answer: 70</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThe 9 members of a baseball team went to an ice cream parlor after their game. Each player had a singlescoop cone of chocolate, vanilla, or strawberry ice cream. At least one player chose each flavor, and the number of players who chose chocolate was greater than the number of players who chose vanilla, which was greater than the number of players who chose strawberry. Let $N$ be the number of different assignments of flavors to players that meet these conditions. Find the remainder when $N$ is divided by 1000.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n\\[\nc=\\#\\text{ chocolate},\\qquad v=\\#\\text{ vanilla},\\qquad s=\\#\\text{ strawberry}\n\\]\n\nwith  \n\n\\[\nc+v+s =9,\\qquad c&gt;v&gt;s\\ge1 .\n\\]\n\n---\n\n### 1. Find all possible triples \\((c,v,s)\\).\n\nSince \\(c&gt;v&gt;s\\ge 1\\),\n\n\\[\nc\\ge s+2,\\; v\\ge s+1 \\Longrightarrow c+v+s\\ge 3s+3\\le9\\Longrightarrow s\\le2 .\n\\]\n\n- **If \\(s=1\\)**: \\(v\\ge2,\\ c\\ge3\\) and \\(c+v=8\\).  \n  Possibilities: \\((c,v)=(6,2),(5,3)\\).\n\n- **If \\(s=2\\)**: \\(v\\ge3,\\ c\\ge4\\) and \\(c+v=7\\).  \n  Possibility: \\((c,v)=(4,3)\\).\n\nThus the only triples are  \n\n\\[\n(6,2,1),\\quad (5,3,1),\\quad (4,3,2).\n\\]\n\n---\n\n### 2. Count assignments for each triple.\n\nFor a given \\((c,v,s)\\) the number of assignments of flavors to the nine distinct players is the multinomial coefficient  \n\n\\[\n\\frac{9!}{c!\\,v!\\,s!}.\n\\]\n\n\\[\n\\begin{aligned}\n(6,2,1):\\quad &amp;\\frac{9!}{6!\\,2!\\,1!}= \\binom{9}{6}\\binom{3}{2}=84\\cdot3=252,\\\\[4pt]\n(5,3,1):\\quad &amp;\\frac{9!}{5!\\,3!\\,1!}= \\binom{9}{5}\\binom{4}{3}=126\\cdot4=504,\\\\[4pt]\n(4,3,2):\\quad &amp;\\frac{9!}{4!\\,3!\\,2!}= \\binom{9}{4}\\binom{5}{3}=126\\cdot10=1260.\n\\end{aligned}\n\\]\n\n---\n\n### 3. Total number of assignments\n\n\\[\nN = 252+504+1260 = 2016.\n\\]\n\n---\n\n### 4. Remainder modulo \\(1000\\)\n\n\\[\nN \\bmod 1000 = 2016 \\bmod 1000 = 16.\n\\]\n\n\\[\n\\boxed{16}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 16</p>\n<p>Extracted Answer: 16</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nAn isosceles trapezoid has an inscribed circle tangent to each of its four sides. The radius of the circle is 3, and the area of the trapezoid is 72. Let the parallel sides of the trapezoid have lengths $r$ and $s$, with $r \\neq s$. Find $r^{2}+s^{2}$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let the trapezoid have parallel sides \\(r\\) and \\(s\\) \\((r\\neq s)\\) and equal legs \\(L\\).\n\n---\n\n### 1.  Semiperimeter from the incircle\n\nA convex quadrilateral that contains an incircle (a tangential quadrilateral) satisfies  \n\n\\[\n\\text{Area}= (\\text{inradius})\\times (\\text{semiperimeter}).\n\\]\n\nThe inradius is \\(3\\) and the area is \\(72\\); therefore  \n\n\\[\np=\\frac{\\text{Area}}{r_{\\text{in}}}= \\frac{72}{3}=24,\n\\]\n\nwhere \\(p\\) is the semiperimeter.\n\n---\n\n### 2.  Relation among the sides\n\nFor a tangential quadrilateral, Pitot\u2019s theorem gives  \n\n\\[\n\\text{(sum of one pair of opposite sides)} = \\text{(sum of the other pair)} .\n\\]\n\nIn an isosceles trapezoid the opposite sides are the two bases and the two equal legs, so  \n\n\\[\nr+s = L+L =2L \\quad\\Longrightarrow\\quad L=\\frac{r+s}{2}.\n\\]\n\nThe semiperimeter is  \n\n\\[\np = \\frac{r+s+2L}{2}= \\frac{r+s+r+s}{2}=r+s .\n\\]\n\nSince \\(p=24\\), we obtain  \n\n\\[\n\\boxed{r+s=24}.\n\\]\n\nConsequently  \n\n\\[\nL=\\frac{r+s}{2}=12 .\n\\]\n\n---\n\n### 3.  Height of the trapezoid\n\nThe incircle is tangent to both parallel sides, so the distance between those sides (the height \\(h\\)) equals twice the radius:\n\n\\[\nh = 2\\cdot 3 = 6 .\n\\]\n\n---\n\n### 4.  Using the leg length\n\nPlace the trapezoid with its bases horizontal. The horizontal offset between the ends of the bases is \\(\\dfrac{|r-s|}{2}\\). Hence, by the Pythagorean theorem,\n\n\\[\nL^{2}= \\left(\\frac{r-s}{2}\\right)^{2}+h^{2}.\n\\]\n\nWith \\(L=12\\) and \\(h=6\\),\n\n\\[\n12^{2}= \\left(\\frac{r-s}{2}\\right)^{2}+6^{2}\n\\quad\\Longrightarrow\\quad\n144 = \\frac{(r-s)^{2}}{4}+36\n\\quad\\Longrightarrow\\quad\n(r-s)^{2}=432.\n\\]\n\n---\n\n### 5.  Compute \\(r^{2}+s^{2}\\)\n\n\\[\n\\begin{aligned}\n(r+s)^{2} &amp;= r^{2}+2rs+s^{2}=24^{2}=576,\\\\\n(r-s)^{2} &amp;= r^{2}-2rs+s^{2}=432.\n\\end{aligned}\n\\]\n\nAdding these equations eliminates the \\(rs\\) term:\n\n\\[\n(r+s)^{2}+(r-s)^{2}=2(r^{2}+s^{2})\\Longrightarrow\n576+432=2(r^{2}+s^{2}).\n\\]\n\nThus\n\n\\[\nr^{2}+s^{2}= \\frac{1008}{2}=504.\n\\]\n\n---\n\n\\[\n\\boxed{504}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 504</p>\n<p>Extracted Answer: 504</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $k$ be real numbers such that the system $|25+20i-z|=5$ and $|z-4-k|=|z-3i-k|$ has exactly one complex solution $z$. The sum of all possible values of $k$ can be written as $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$. Here $i=\\sqrt{-1}$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>The first equation  \n\n\\[\n|25+20i-z|=5\n\\]\n\nis a circle with centre  \n\n\\[\nC=(25,20)\n\\]\n\nand radius \\(r=5\\).\n\nThe second equation  \n\n\\[\n|z-4-k| = |z-3i-k|\n\\]\n\nmeans that \\(z\\) is equidistant from the points  \n\n\\[\nA=4+k \\qquad\\text{and}\\qquad B=3i+k .\n\\]\n\nThus \\(A=(k+4,0),\\; B=(k,3)\\).  \nThe set of points equidistant from \\(A\\) and \\(B\\) is the perpendicular bisector of \\(\\overline{AB}\\).\n\n---\n\n### Equation of the perpendicular bisector\n\nMidpoint of \\(AB\\):\n\n\\[\nM=\\Bigl(\\frac{k+4+k}{2},\\frac{0+3}{2}\\Bigr)=(k+2,\\frac32).\n\\]\n\nThe vector \\(\\overrightarrow{AB}=(-4,3)\\).  \nA direction vector perpendicular to this is \\((3,4)\\) (since \\((-4,3)\\cdot(3,4)=0\\)).  \n\nHence the line has slope \\(\\frac43\\) and equation  \n\n\\[\ny-\\frac32 = \\frac43\\bigl(x-(k+2)\\bigr)\n\\]\n\\[\n\\Longrightarrow\\; y = \\frac43 x - \\frac43 k - \\frac76 .\n\\]\n\nIn standard form:\n\n\\[\n8x-6y = 8k+7 .\n\\]\n\n---\n\n### Tangency condition\n\nThe system will have exactly one solution iff this line is tangent to the circle.  \nThe distance from the centre \\(C=(25,20)\\) to the line \\(8x-6y-(8k+7)=0\\) must equal the radius \\(5\\):\n\n\\[\n\\frac{|8\\cdot25-6\\cdot20-(8k+7)|}{\\sqrt{8^{2}+(-6)^{2}}}=5.\n\\]\n\nCompute the numerator:\n\n\\[\n8\\cdot25-6\\cdot20-(8k+7)=200-120-8k-7=73-8k.\n\\]\n\nSince \\(\\sqrt{8^{2}+6^{2}}=10\\),\n\n\\[\n\\frac{|73-8k|}{10}=5 \\quad\\Longrightarrow\\quad |73-8k|=50.\n\\]\n\nThus  \n\n\\[\n73-8k = 50 \\quad\\text{or}\\quad 73-8k = -50.\n\\]\n\n\\[\n\\begin{cases}\n8k = 23 \\;\\;\\Rightarrow\\; k = \\dfrac{23}{8},\\\\[4pt]\n8k = 123\\;\\Rightarrow\\; k = \\dfrac{123}{8}.\n\\end{cases}\n\\]\n\nBoth values give a tangent line, so each yields exactly one solution \\(z\\).\n\n---\n\n### Sum of all possible \\(k\\)\n\n\\[\nk_1+k_2 = \\frac{23}{8}+\\frac{123}{8}= \\frac{146}{8}= \\frac{73}{4}.\n\\]\n\nWrite \\(\\frac{73}{4}\\) as \\(\\frac{m}{n}\\) with \\(\\gcd(m,n)=1\\): \\(m=73,\\ n=4\\).\n\n\\[\nm+n = 73+4 = 77.\n\\]\n\n\\[\n\\boxed{77}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 77</p>\n<p>Extracted Answer: 77</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nFind the number of ordered pairs $(x,y)$, where both $x$ and $y$ are integers between $-100$ and $100$, inclusive, such that $12x^{2}-xy-6y^{2}=0$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>The equation  \n\n\\[\n12x^{2}-xy-6y^{2}=0\n\\]\n\nis a homogeneous quadratic form.  Factor it over the rationals.\n\n\\[\n12x^{2}-xy-6y^{2}= -6\\Bigl(y-\\frac43x\\Bigr)\\Bigl(y+\\frac32x\\Bigr)\n\\]\n\nHence  \n\n\\[\n12x^{2}-xy-6y^{2}=0\\iff \n\\Bigl(y-\\frac43x\\Bigr)\\Bigl(y+\\frac32x\\Bigr)=0 .\n\\]\n\nSo any integer solution must satisfy one of the two linear equations  \n\n\\[\ny=\\frac{4}{3}x\\quad\\text{or}\\quad y=-\\frac32 x .\n\\]\n\n---\n\n### 1.  Solutions of \\(y=\\frac43x\\)\n\nWrite \\(3y=4x\\).  \nSince \\(\\gcd(3,4)=1\\), the integer solutions are  \n\n\\[\nx=3k,\\qquad y=4k\\qquad(k\\in\\mathbb Z).\n\\]\n\nBoth coordinates must lie in \\([-100,100]\\):\n\n\\[\n-100\\le 3k\\le100,\\qquad -100\\le4k\\le100\n\\]\n\nThe second inequality is stricter, giving  \n\n\\[\n-25\\le k\\le 25 .\n\\]\n\nThus there are  \n\n\\[\n25-(-25)+1 = 51\n\\]\n\ninteger points on this line.\n\n---\n\n### 2.  Solutions of \\(y=-\\frac32x\\)\n\nWrite \\(2y=-3x\\).  \nSince \\(\\gcd(2,3)=1\\), the integer solutions are  \n\n\\[\nx=2k,\\qquad y=-3k\\qquad(k\\in\\mathbb Z).\n\\]\n\nBoth coordinates must satisfy  \n\n\\[\n-100\\le2k\\le100,\\qquad -100\\le-3k\\le100 .\n\\]\n\nThese give  \n\n\\[\n-50\\le k\\le50,\\qquad -\\frac{100}{3}\\le k\\le\\frac{100}{3}\\Longrightarrow -33\\le k\\le33 .\n\\]\n\nHence there are  \n\n\\[\n33-(-33)+1 = 67\n\\]\n\ninteger points on this line.\n\n---\n\n### 3.  Remove double\u2011counted point\n\nThe two lines intersect only at \\((0,0)\\) (when \\(k=0\\) in both families).  \nThus the total number of distinct ordered pairs is  \n\n\\[\n51+67-1 = 117 .\n\\]\n\n\\[\n\\boxed{117}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 117</p>\n<p>Extracted Answer: 117</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThere are $8!=40320$ eight-digit positive integers that use each of the digits $1,2,3,4,5,6,7,8$ exactly once. Let $N$ be the number of these integers that are divisible by 22. Find the difference between $N$ and 2025.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>**Step 1.  Divisibility conditions**\n\nFor an integer to be divisible by \\(22\\) it must be divisible by \\(2\\) and by \\(11\\).\n\n*Divisible by 2* \u2013 the last digit (the units digit) must be even, i.e. one of \\(\\{2,4,6,8\\}\\).\n\n*Divisible by 11* \u2013 for an 8\u2011digit number \\(a_1a_2\\ldots a_8\\) (with \\(a_1\\) the leftmost digit) the rule is  \n\n\\[\n(a_8+a_6+a_4+a_2)-(a_7+a_5+a_3+a_1)\\equiv0\\pmod{11}.\n\\]\n\nThus the sum of the digits in the even positions (2,4,6,8) equals the sum of the digits in the odd positions (1,3,5,7) modulo \\(11\\).\n\nThe total sum of the digits \\(1+2+\\dots+8=36\\).  \nIf the two sums are equal modulo \\(11\\), then\n\n\\[\n2\\cdot(\\text{odd\u2013position sum})\\equiv36\\equiv3\\pmod{11}\n\\Longrightarrow\\text{odd\u2013position sum}\\equiv7\\pmod{11}.\n\\]\n\nThe possible values are \\(7,18,29,\\ldots\\).  \nSince four distinct digits from \\(\\{1,\\dots ,8\\}\\) can sum only between \\(10\\) and \\(26\\), the only feasible value is  \n\n\\[\n\\boxed{\\text{odd\u2013position sum}=18}.\n\\]\n\nConsequently the even\u2013position sum is also \\(18\\).\n\n**Step 2.  Choose the digits for the odd positions**\n\nWe need all 4\u2011element subsets of \\(\\{1,2,3,4,5,6,7,8\\}\\) whose sum is \\(18\\).\n\nListing them (or by noting the complementary pairs) gives  \n\n\\[\n\\begin{aligned}\n&amp;\\{1,2,7,8\\},\\; \\{1,3,6,8\\},\\; \\{1,4,5,8\\},\\; \\{1,4,6,7\\},\\\\\n&amp;\\{2,3,5,8\\},\\; \\{2,3,6,7\\},\\; \\{2,4,5,7\\},\\; \\{3,4,5,6\\}.\n\\end{aligned}\n\\]\n\nThere are  \n\n\\[\n\\boxed{M=8}\n\\]\n\nsuch subsets.  \nEach of them contains exactly two even digits (because a sum of 18 cannot be obtained with a different parity distribution), so for every subset \\(A\\) (odd\u2011position digits) we have  \n\n\\[\ne_A=2,\\qquad E_B=4-e_A=2,\n\\]\n\nwhere \\(E_B\\) is the number of even digits among the complementary set \\(B\\) (the even\u2011position digits).\n\n**Step 3.  Arrange the digits**\n\n*Odd positions* (1,3,5,7): the four digits of \\(A\\) can be placed in \\(4! = 24\\) ways.\n\n*Even positions* (2,4,6,8): the four digits of \\(B\\) must be placed so that the digit in position\u202f8 (the units digit) is even.  \nSince \\(B\\) contains exactly \\(E_B=2\\) even digits, we have  \n\n\\[\n\\text{choices for the units digit}=2,\n\\qquad\n\\text{ways to arrange the remaining three digits}=3! = 6.\n\\]\n\nThus the number of admissible placements for \\(B\\) is  \n\n\\[\nf(B)=2\\cdot 6=12.\n\\]\n\n**Step 4.  Count all numbers**\n\nFor each of the \\(M=8\\) valid subsets \\(A\\),\n\n\\[\n\\text{numbers contributed}=24\\times12=288.\n\\]\n\nHence  \n\n\\[\nN=8\\times288=2304.\n\\]\n\n**Step 5.  Compute the required difference**\n\n\\[\nN-2025=2304-2025=279.\n\\]\n\n\\[\n\\boxed{279}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 279</p>\n<p>Extracted Answer: 279</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThe parabola with equation $y=x^{2}-4$ is rotated $60^{\\circ}$ counterclockwise around the origin. The unique point in the fourth quadrant where the original parabola and its image intersect has $y$-coordinate $\\frac{a-\\sqrt{b}}{c}$, where $a$, $b$, and $c$ are positive integers, and $a$ and $c$ are relatively prime. Find $a+b+c$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>The original parabola is  \n\n\\[\ny=x^{2}-4 .\n\\]\n\n---\n\n### 1.  Equation of the rotated parabola  \n\nRotate the plane \\(60^{\\circ}\\) counter\u2011clockwise about the origin.\nIf \\((X,Y)\\) is a point of the rotated parabola, then rotating it back\n\\(60^{\\circ}\\) clockwise gives a point \\((x&#39;,y&#39;)\\) on the original parabola.\n\n\\[\n\\begin{pmatrix}x&#39;\\\\y&#39;\\end{pmatrix}\n=\n\\begin{pmatrix}\\cos60^\\circ&amp;\\sin60^\\circ\\\\\n-\\sin60^\\circ&amp;\\cos60^\\circ\\end{pmatrix}\n\\begin{pmatrix}X\\\\Y\\end{pmatrix}\n=\n\\begin{pmatrix}\\frac12X+\\frac{\\sqrt3}{2}Y\\\\[2pt]\n-\\frac{\\sqrt3}{2}X+\\frac12Y\\end{pmatrix}.\n\\]\n\nThus  \n\n\\[\ny&#39; = x&#39;^2-4\\Longrightarrow \n\\frac{-\\sqrt3X+Y}{2} =\\Bigl(\\frac{X+\\sqrt3Y}{2}\\Bigr)^{\\!2}-4.\n\\]\n\nMultiplying by \\(2\\) and simplifying gives the equation of the rotated\nparabola:\n\n\\[\n(x+\\sqrt3\\,y)^{2}+2\\sqrt3\\,x-2y-16=0. \\tag{1}\n\\]\n\n---\n\n### 2.  Intersection with the original parabola  \n\nSubstituting \\(y=x^{2}-4\\) from the original parabola into (1) yields\n\n\\[\n\\bigl(x+\\sqrt3(x^{2}-4)\\bigr)^{2}+2\\sqrt3\\,x-2(x^{2}-4)-16=0,\n\\]\n\nwhich simplifies to\n\n\\[\n3x^{4}+2\\sqrt3\\,x^{3}-25x^{2}-6\\sqrt3\\,x+40=0. \\tag{2}\n\\]\n\n---\n\n### 3.  Factoring the quartic  \n\nLook for a factorisation of the form  \n\\((ax^{2}+b\\sqrt3\\,x+c)(dx^{2}+e\\sqrt3\\,x+f)\\).\nMatching coefficients gives the system  \n\n\\[\n\\begin{cases}\nad=3\\\\\nae+bd=2\\\\\naf+3be+cd=-25\\\\\nbf+ce=-6\\\\\ncf=40\n\\end{cases}\n\\]\n\nwhich is solved by  \n\n\\[\na=1,\\;b=1,\\;c=-4,\\qquad d=3,\\;e=-1,\\;f=-10 .\n\\]\n\nHence\n\n\\[\n3x^{4}+2\\sqrt3\\,x^{3}-25x^{2}-6\\sqrt3\\,x+40\n   =(x^{2}+\\sqrt3\\,x-4)(3x^{2}-\\sqrt3\\,x-10). \\tag{3}\n\\]\n\n---\n\n### 4.  Solving for the intersection points  \n\nFrom (3) we obtain four possible \\(x\\)-coordinates.\n\n1. \\(x^{2}+\\sqrt3\\,x-4=0\\)\n\n\\[\nx=\\frac{-\\sqrt3\\pm\\sqrt{19}}{2}.\n\\]\n\n2. \\(3x^{2}-\\sqrt3\\,x-10=0\\)\n\n\\[\nx=\\frac{\\sqrt3\\pm\\sqrt{123}}{6}.\n\\]\n\nFor each \\(x\\) we compute \\(y=x^{2}-4\\).\n\n| \\(x\\) | sign of \\(x\\) | \\(y=x^{2}-4\\) | quadrant |\n|---|---|---|---|\n| \\(\\displaystyle\\frac{-\\sqrt3+\\sqrt{19}}{2}\\) | \\(&gt;0\\) | \\(\\displaystyle\\frac{3-\\sqrt{57}}{2}&lt;0\\) | **IV** |\n| \\(\\displaystyle\\frac{-\\sqrt3-\\sqrt{19}}{2}\\) | \\(&lt;0\\) | \\(&gt;0\\) | II |\n| \\(\\displaystyle\\frac{\\sqrt3+\\sqrt{123}}{6}\\) | \\(&gt;0\\) | \\(&gt;0\\) | I |\n| \\(\\displaystyle\\frac{\\sqrt3-\\sqrt{123}}{6}\\) | \\(&lt;0\\) | \\(&lt;0\\) | III |\n\nOnly the first solution lies in the fourth quadrant, as required.\n\n---\n\n### 5.  The required \\(y\\)-coordinate  \n\nFor  \n\\[\nx=\\frac{-\\sqrt3+\\sqrt{19}}{2},\n\\]\n\\[\ny=x^{2}-4\n   =\\left(\\frac{-\\sqrt3+\\sqrt{19}}{2}\\right)^{2}-4\n   =\\frac{19+3-2\\sqrt{57}}{4}-4\n   =\\frac{22-2\\sqrt{57}}{4}-\\frac{16}{4}\n   =\\frac{3-\\sqrt{57}}{2}.\n\\]\n\nThus  \n\n\\[\ny=\\frac{a-\\sqrt{b}}{c}\\quad\\text{with}\\quad a=3,\\;b=57,\\;c=2,\n\\]\nand \\(\\gcd(a,c)=1\\).\n\nFinally  \n\n\\[\na+b+c=3+57+2=62.\n\\]\n\n\\[\n\\boxed{62}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 62</p>\n<p>Extracted Answer: 62</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nOn $\\triangle ABC$ points $A,D,E$, and $B$ lie that order on side $\\overline{AB}$ with $AD=4, DE=16$, and $EB=8$. Points $A,F,G$, and $C$ lie in that order on side $\\overline{AC}$ with $AF=13, FG=52$, and $GC=26$. Let $M$ be the reflection of $D$ through $F$, and let $N$ be the reflection of $G$ through $E$. Quadrilateral $DEGF$ has area 288. Find the area of heptagon $AFNBCEM$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n\\[\n\\vec{AB}= \\mathbf b ,\\qquad \\vec{AC}= \\mathbf c ,\\qquad \n|\\mathbf b| =28,\\; |\\mathbf c| =91 .\n\\]\n\nWrite every point on the sides as a linear combination of \\(\\mathbf b,\\mathbf c\\).\n\n\\[\n\\begin{aligned}\nD&amp;=\\frac{4}{28}\\mathbf b =\\frac17\\mathbf b ,&amp;\nE&amp;=\\frac{20}{28}\\mathbf b =\\frac57\\mathbf b ,\\\\[2mm]\nF&amp;=\\frac{13}{91}\\mathbf c ,&amp;\nG&amp;=\\frac{65}{91}\\mathbf c .\n\\end{aligned}\n\\]\n\nThe reflections about a point are central symmetries, thus  \n\n\\[\nM=2F-D=-\\frac17\\mathbf b+\\frac{26}{91}\\mathbf c ,\\qquad\nN=2E-G=\\frac{10}{7}\\mathbf b-\\frac{65}{91}\\mathbf c .\n\\]\n\n--------------------------------------------------------------------\n### 1.  Area of \\(\\triangle ABC\\)\n\nThe quadrilateral \\(DEGF\\) can be split into \\(\\triangle DE G\\) and \\(\\triangle DGF\\).\n\nFor any three points \\(P=\\alpha\\mathbf b+\\beta\\mathbf c\\),\n\\(Q=\\gamma\\mathbf b+\\delta\\mathbf c\\) we have  \n\n\\[\n\\bigl[(Q-P)\\times(R-P)\\bigr]\n    =(\\gamma-\\alpha)(\\zeta-\\beta)-(\\delta-\\beta)(\\xi-\\alpha)\\;\\bigl(\\mathbf b\\times\\mathbf c\\bigr),\n\\]\n\nso the area of a triangle equals the absolute value of that determinant\ntimes \\(\\dfrac12|\\mathbf b\\times\\mathbf c|\\).\n\n*Triangle \\(DEG\\)*  \n\n\\[\n\\det\\!\\begin{pmatrix}\n\\frac57-\\frac17 &amp; 0\\\\[2mm]\n0-\\frac17&amp;\\frac{65}{91}\n\\end{pmatrix}\n  =\\frac{20}{49}.\n\\]\n\nThus \\(\\displaystyle\n\\text{Area}(DEG)=\\frac{20}{49}\\cdot\\frac12|\\mathbf b\\times\\mathbf c|.\n\\)\n\n*Triangle \\(DGF\\)*  \n\n\\[\n\\det\\!\\begin{pmatrix}\n0-\\frac17&amp;\\frac{65}{91}\\\\[2mm]\n0-\\frac17&amp;\\frac{13}{91}\n\\end{pmatrix}\n  =\\frac{4}{49},\n\\qquad\n\\text{Area}(DGF)=\\frac{4}{49}\\cdot\\frac12|\\mathbf b\\times\\mathbf c|.\n\\]\n\nHence  \n\n\\[\n\\text{Area}(DEGF)=\\Bigl(\\frac{20}{49}+\\frac{4}{49}\\Bigr)\n                  \\frac12|\\mathbf b\\times\\mathbf c|\n                =\\frac{24}{49}\\,\\text{Area}(\\triangle ABC).\n\\]\n\nGiven \\(\\text{Area}(DEGF)=288\\),\n\n\\[\n\\frac{24}{49}\\,\\text{Area}(\\triangle ABC)=288\n\\Longrightarrow\n\\text{Area}(\\triangle ABC)=288\\cdot\\frac{49}{24}=12\\cdot49=588.\n\\]\n\n--------------------------------------------------------------------\n### 2.  Area of the heptagon \\(AFNBCEM\\)\n\nPlace the points in the \\((\\alpha,\\beta)\\)\u2013plane where \\((\\alpha,\\beta)\\) are the\ncoefficients of \\(\\mathbf b,\\mathbf c\\):\n\n\\[\n\\begin{array}{c|c}\n\\text{Vertex}&amp;(\\alpha,\\beta)\\\\\\hline\nA&amp;(0,0)\\\\\nF&amp;(0,\\frac{13}{91})\\\\\nN&amp;(\\frac{10}{7},-\\frac{65}{91})\\\\\nB&amp;(1,0)\\\\\nC&amp;(0,1)\\\\\nE&amp;(\\frac57,0)\\\\\nM&amp;\\bigl(-\\frac17,\\frac{26}{91}\\bigr)\n\\end{array}\n\\]\n\nApplying the shoelace formula to these seven points gives\n\n\\[\n\\begin{aligned}\n\\sum x_i y_{i+1}-y_i x_{i+1}\n&amp;=1,\\\\[2mm]\n\\text{Area}_{\\text{coeff}}&amp;=\\frac12\\cdot1=\\frac12 .\n\\end{aligned}\n\\]\n\nIn the original plane a figure\u2019s area is multiplied by\n\\(|\\mathbf b\\times\\mathbf c|=2\\,\\text{Area}(\\triangle ABC)\\).\nThus\n\n\\[\n\\text{Area}(AFNBCEM)=|\\mathbf b\\times\\mathbf c|\\,\n\\frac12\n   =\\text{Area}(\\triangle ABC)=588.\n\\]\n\n--------------------------------------------------------------------\n\\[\n\\boxed{588}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 588</p>\n<p>Extracted Answer: 588</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThe twelve letters $A,B,C,D,E,F,G,H,I,J,K$, and $L$ are randomly grouped into six pairs of letters. The two letters in each pair are placed next to each other in alphabetical order to form six two-letter words, and those six words are listed alphabetically. For example, a possible result is $AB,CJ,DG,EK,FL,HI$. The probability that the last word listed contains $G$ is $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>The 12 letters are  \n\n\\[\nA,B,C,D,E,F,G,H,I,J,K,L .\n\\]\n\nA random grouping into six unordered pairs is performed, each pair is written with its\nletters in alphabetical order, and then the six two\u2011letter \u201cwords\u2019\u2019 are listed\nalphabetically.  \n\nLet the word that appears last (the lexicographically greatest word) be called the **max word**.\nThe max word is determined by the *first* letters of the six pairs:\nits first letter is the largest among the six first letters, and if several pairs have that\nfirst letter, the one with the larger second letter wins.\n\n--------------------------------------------------------------------\n### 1.   Total number of possible pairings\n\\[\n\\#\\text{pairings}= \\frac{12!}{2!^{6}\\,6!}=10395 .\n\\]\n\n--------------------------------------------------------------------\n### 2.   When does the max word contain \\(G\\)?\n\nTwo mutually exclusive possibilities:\n\n* **(A) \\(G\\) is the first letter of its pair.**  \n  Then the pair is \\((G,X)\\) with \\(X\\in\\{H,I,J,K,L\\}\\).\n  For \\((G,X)\\) to be the max word, no other pair may have a first\n  letter larger than \\(G\\).  \n  Hence each of the other four letters \\(\\{H,I,J,K,L\\}\\setminus\\{X\\}\\) must be paired\n  with a letter \\(\\le F\\) (otherwise its first letter would exceed \\(G\\)).\n  The remaining letters are  \n\n  * 4 \u201chigh\u2019\u2019 letters \\(\\{H,I,J,K,L\\}\\setminus\\{X\\}\\);\n  * 6 \u201clow\u2019\u2019 letters \\(\\{A,B,C,D,E,F\\}\\).\n\n  Choose which four low letters are matched with the four high letters\n  and then match them (an injection).  \n  The number of ways is  \n\n  \\[\n  {}_{6}P_{4}=6\\cdot5\\cdot4\\cdot3=360 .\n  \\]\n\n  The two low letters left over are forced to pair with each other.\n  Thus for a fixed \\(X\\) there are \\(360\\) pairings, and there are\n  \\(5\\) possible choices for \\(X\\):\n\n  \\[\n  N_A=5\\cdot360=1800 .\n  \\]\n\n* **(B) \\(G\\) is the second letter of its pair.**  \n  Then the pair is \\((X,G)\\) with \\(X&lt;G\\), and \\(X\\) must be the\n  largest first letter of any pair.  \n  If \\(X\\le E\\) there are not enough letters \\(\\le X\\) to pair with all\n  letters \\(&gt;X\\) (there would be more \u201chigh\u2019\u2019 letters than \u201clow\u2019\u2019 ones).  \n  The only possible value is \\(X=F\\).\n\n  Pair \\(G\\) with \\(F\\).  The five letters \\(\\{H,I,J,K,L\\}\\) must each be paired\n  with a distinct letter from \\(\\{A,B,C,D,E\\}\\).  There are  \n\n  \\[\n  5! =120\n  \\]\n\n  ways to do this, and no letters remain.\n\n  Hence  \n\n  \\[\n  N_B =120 .\n  \\]\n\n--------------------------------------------------------------------\n### 3.   Favourable pairings\n\\[\nN_{\\text{fav}}=N_A+N_B=1800+120=1920 .\n\\]\n\n--------------------------------------------------------------------\n### 4.   Desired probability\n\\[\nP=\\frac{N_{\\text{fav}}}{\\#\\text{pairings}}\n   =\\frac{1920}{10395}\n   =\\frac{128}{693}\\qquad(\\gcd(128,693)=1).\n\\]\n\nThus \\(m=128,\\;n=693\\) and  \n\n\\[\nm+n=128+693=821 .\n\\]\n\n\\[\n\\boxed{821}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 821</p>\n<p>Extracted Answer: 821</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nSix points $ A, B, C, D, E, $ and $ F $ lie in a straight line in that order. Suppose that $ G $ is a point not on the line and that $ AC = 26 $, $ BD = 22 $, $ CE = 31 $, $ DF = 33 $, $ AF = 73 $, $ CG = 40 $, and $ DG = 30 $. Find the area of $ \\triangle BGE $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let the line be the \\(x\\)-axis and put  \n\n\\[\nA=(0,0),\\qquad B=(b,0),\\qquad C=(c,0),\\qquad D=(d,0),\\qquad E=(e,0),\\qquad F=(f,0)\n\\]\n\nwith the points in the order \\(A\\!&lt;\\!B\\!&lt;\\!C\\!&lt;\\!D\\!&lt;\\!E\\!&lt;\\!F\\).\n\n---\n\n### 1.  Locate the collinear points\n\n\\[\n\\begin{aligned}\nAC&amp;=26 \\Longrightarrow c-0 = 26 \\; \\Rightarrow\\; c=26,\\\\[2pt]\nCE&amp;=31 \\Longrightarrow e-c =31 \\; \\Rightarrow\\; e=26+31=57,\\\\[2pt]\nAF&amp;=73 \\Longrightarrow f=73 .\n\\end{aligned}\n\\]\n\nFrom \\(DF=33\\) we get  \n\n\\[\nf-d =33 \\Longrightarrow d = f-33 = 73-33 =40 .\n\\]\n\nFrom \\(BD=22\\),\n\n\\[\nd-b =22 \\Longrightarrow b = d-22 = 40-22 =18 .\n\\]\n\nThus  \n\n\\[\nA=(0,0),\\; B=(18,0),\\; C=(26,0),\\; D=(40,0),\\; E=(57,0),\\; F=(73,0).\n\\]\n\nAll distances given in the statement are satisfied.\n\n---\n\n### 2.  Position of \\(G\\)\n\nLet \\(G=(x,y)\\) with \\(y\\neq0\\).  \nThe distances to \\(C\\) and \\(D\\) give\n\n\\[\n\\begin{cases}\n(x-26)^2+y^2 = 40^2 =1600,\\\\[2pt]\n(x-40)^2+y^2 = 30^2 = 900 .\n\\end{cases}\n\\]\n\nSubtracting the equations:\n\n\\[\n(x-26)^2-(x-40)^2 = 700.\n\\]\n\nExpanding,\n\n\\[\n(-52x+26^2)+(80x-40^2)=700\\;\\Longrightarrow\\;28x-924=700,\n\\]\n\nso  \n\n\\[\n28x=1624\\quad\\Longrightarrow\\quad x=58 .\n\\]\n\nPlug \\(x=58\\) into \\((x-26)^2+y^2=1600\\):\n\n\\[\n(58-26)^2+y^2 = 32^2 + y^2 = 1600\\;\\Longrightarrow\\; y^2 = 1600-1024 = 576,\n\\]\n\nhence \\(|y|=24\\).  \nTake \\(G=(58,24)\\) (the other choice \\((58,-24)\\) gives the same area).\n\n---\n\n### 3.  Area of \\(\\triangle BGE\\)\n\nPoints:\n\n\\[\nB=(18,0),\\qquad E=(57,0),\\qquad G=(58,24).\n\\]\n\nThe base \\(BE\\) lies on the \\(x\\)-axis, so its length is  \n\n\\[\nBE = 57-18 = 39.\n\\]\n\nThe altitude from \\(G\\) to the line \\(BE\\) is simply \\(|y| = 24\\).\n\nThus  \n\n\\[\n\\text{Area} = \\frac12 \\times (\\text{base}) \\times (\\text{height})\n            = \\frac12 \\times 39 \\times 24\n            = 39 \\times 12\n            = 468 .\n\\]\n\n(Equivalently, the shoelace formula gives \\(\\frac12|1368-432|=468\\).)\n\n---\n\n\\[\n\\boxed{468}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 468</p>\n<p>Extracted Answer: 468</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nFind the sum of all positive integers $ n $ such that $ n + 2 $ divides the product $ 3(n + 3)(n^2 + 9) $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n\\[\nd=n+2\\qquad (d\\ge 1,\\; n=d-2).\n\\]\n\nThen  \n\n\\[\nn+3=d+1 ,\\qquad n^{2}+9=(d-2)^{2}+9=d^{2}-4d+13 .\n\\]\n\nHence  \n\n\\[\n3(n+3)(n^{2}+9)=3(d+1)(d^{2}-4d+13).\n\\]\n\nThe condition \\(d\\mid 3(n+3)(n^{2}+9)\\) becomes  \n\n\\[\nd \\mid 3(d+1)(d^{2}-4d+13).\n\\]\n\nTake this congruence modulo \\(d\\).  \nSince \\(d\\equiv0\\pmod d\\),\n\n\\[\nd+1\\equiv1,\\qquad d^{2}-4d+13\\equiv13\\pmod d,\n\\]\n\nso  \n\n\\[\n3(d+1)(d^{2}-4d+13)\\equiv 3\\cdot1\\cdot13=39\\pmod d.\n\\]\n\nThus \\(d\\) must divide \\(39\\):\n\n\\[\nd\\in\\{1,3,13,39\\}.\n\\]\n\nRecall \\(d=n+2\\) and we need \\(n&gt;0\\).  \nHence\n\n\\[\nn=d-2\\in\\{-1,1,11,37\\}.\n\\]\n\nDiscard the non\u2011positive value \\(-1\\). The admissible positive integers are  \n\n\\[\nn=1,\\;11,\\;37 .\n\\]\n\nCheck:\n\n* \\(n=1\\): \\(n+2=3\\) and \\(3(1+3)(1^{2}+9)=120\\) is divisible by \\(3\\).\n* \\(n=11\\): \\(n+2=13\\) and \\(3(14)(130)=5460\\) is divisible by \\(13\\).\n* \\(n=37\\): \\(n+2=39\\) and \\(3(40)(1378)=165360\\) is divisible by \\(39\\).\n\nAll satisfy the condition.  \n\nThe required sum is  \n\n\\[\n1+11+37 = 49.\n\\]\n\n\\[\n\\boxed{49}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 49</p>\n<p>Extracted Answer: 49</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nA piecewise linear periodic function is defined by $f(x)=\\begin{cases}x&amp;\\text{if }x\\in[-1,1)\\\\2-x&amp;\\text{if }x\\in[1,3)\\end{cases}$ and $f(x+4)=f(x)$ for all real numbers $x$. The graph of $f(x)$ has the sawtooth pattern. The parabola $x=34y^2$ intersects the graph of $f(x)$ at finitely many points. The sum of the $y$-coordinates of these intersection points can be expressed in the form $\\frac{a+b\\sqrt{c}}{d}$, where $a,b,c,$ and $d$ are positive integers, $a,b,$ and $d$ have greatest common divisor equal to 1, and $c$ is not divisible by the square of any prime. Find $a+b+c+d$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>For the periodic saw\u2011tooth  \n\n\\[\nf(x)=\\begin{cases}\nx-4k,&amp;x\\in[-1+4k,\\,1+4k)\\\\[2pt]\n4k+2-x,&amp;x\\in[1+4k,\\,3+4k)\n\\end{cases}\\qquad(k\\in\\mathbb Z)\n\\]\n\nthe parabola is  \n\n\\[\nx = 34y^{2}\\qquad (y\\in[-1,1]).\n\\]\n\nHence an intersection point \\((x,y)\\) must satisfy  \n\n\\[\ny=f(x),\\qquad x=34y^{2}.\n\\]\n\n---\n\n### 1.  Intersections on an \u201cup\u201d segment  \n\nOn an up segment \\(x= y+4k\\).  \nSubstituting \\(x=34y^{2}\\) gives  \n\n\\[\n34y^{2}=y+4k\\;\\Longrightarrow\\;34y^{2}-y-4k=0 .\n\\]\n\nFor each integer \\(k\\) with an up segment inside \\([0,34]\\) (i.e. \\(k=0,1,\\dots ,8\\))\nthe two roots are  \n\n\\[\ny_{k}^{\\pm}=\\frac{1\\pm\\sqrt{1+544k}}{68}.\n\\]\n\nBoth satisfy the interval \\([-1,1]\\) and give \\(x\\in[-1+4k,\\,1+4k)\\);\nhence each \\(k\\) contributes **two** intersection points.\n\nThe sum of the two roots for a fixed \\(k\\) is, by Vieta,\n\n\\[\ny_{k}^{+}+y_{k}^{-}= \\frac{1}{34}.\n\\]\n\nThus the total contribution of all up\u2011segments is  \n\n\\[\n\\sum_{k=0}^{8}(y_{k}^{+}+y_{k}^{-})=9\\cdot\\frac1{34}=\\frac9{34}.\n\\]\n\n---\n\n### 2.  Intersections on a \u201cdown\u2019\u2019 segment  \n\nOn a down segment \\(x=4k+2-y\\).  \nUsing \\(x=34y^{2}\\),\n\n\\[\n34y^{2}=4k+2-y\\;\\Longrightarrow\\;34y^{2}+y-(4k+2)=0 .\n\\]\n\nFor each \\(k=0,1,\\dots ,8\\) the roots are  \n\n\\[\nz_{k}^{\\pm}= \\frac{-1\\pm\\sqrt{273+544k}}{68}.\n\\]\n\nThe admissible \\(y\\)-values must satisfy \\(-1&lt;y\\le 1\\).\n\n* For \\(k=0,1,\\dots ,7\\) we have \\(\\sqrt{273+544k}&lt;67\\); both roots lie in\n\\((-1,1]\\) and give valid points.\n* For \\(k=8\\) the negative root satisfies \\(y&lt;-1\\) and is rejected; only the\npositive root remains.\n\nHence we obtain two points for each \\(k=0,\\dots ,7\\) and one point for\n\\(k=8\\) \u2013 a total of \\(17\\) points.\n\nThe sum of the two roots of the quadratic for any \\(k\\) is  \n\n\\[\nz_{k}^{+}+z_{k}^{-}= -\\frac1{34}.\n\\]\n\nConsequently  \n\n\\[\n\\sum_{k=0}^{7}(z_{k}^{+}+z_{k}^{-})=8\\!\\left(-\\frac1{34}\\right)=-\\frac8{34},\n\\]\nand we must add the remaining positive root for \\(k=8\\),\n\n\\[\nz_{8}^{+}= \\frac{-1+\\sqrt{4625}}{68}= \\frac{-1+5\\sqrt{185}}{68}.\n\\]\n\nTherefore the total contribution of the down\u2011segments is  \n\n\\[\n-\\frac8{34}+z_{8}^{+}= -\\frac{16}{68}+ \\frac{-1+5\\sqrt{185}}{68}\n= \\frac{-17+5\\sqrt{185}}{68}.\n\\]\n\n---\n\n### 3.  Sum of all \\(y\\)-coordinates  \n\n\\[\n\\begin{aligned}\nS&amp;=\\frac9{34}+ \\left(-\\frac8{34}+z_{8}^{+}\\right)\\\\[2pt]\n  &amp;=\\frac1{34}+z_{8}^{+}\n   =\\frac{2}{68}+ \\frac{-1+5\\sqrt{185}}{68}\n   =\\frac{1+5\\sqrt{185}}{68}.\n\\end{aligned}\n\\]\n\nThus the sum can be written as  \n\n\\[\nS=\\frac{a+b\\sqrt{c}}{d}\\quad\\text{with}\\quad \na=1,\\;b=5,\\;c=185,\\;d=68.\n\\]\n\nAll conditions are satisfied (\\(\\gcd(a,b,d)=1\\), \\(c\\) square\u2011free).\n\nFinally  \n\n\\[\na+b+c+d = 1+5+185+68 = \\boxed{259}.\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 259</p>\n<p>Extracted Answer: 259</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThe 27 cells of a $3\\times9$ grid are filled in using the numbers 1 through 9 so that each row contains 9 different numbers, and each of the three $3\\times3$ blocks heavily outlined in the example below contains 9 different numbers, as in the first three rows of a Sudoku puzzle. \n | 4 | 2 | 8 | 9 | 6 | 3 | 1 | 7 | 5 | \n | 3 | 7 | 9 | 5 | 2 | 1 | 6 | 8 | 4 | \n | 5 | 6 | 1 | 8 | 4 | 7 | 9 | 2 | 3 | \n The number of different ways to fill such a grid can be written as $p^a\\cdot q^b\\cdot r^c\\cdot s^d$, where $p,q,r,$ and $s$ are distinct prime numbers and $a,b,c,$ and $d$ are positive integers. Find $p\\cdot a+q\\cdot b+r\\cdot c+s\\cdot d$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>The grid has three rows and three vertical \\(3\\times3\\) blocks.  \nLet the rows be \\(R_1,R_2,R_3\\) and the blocks be \\(B_1,B_2,B_3\\).\n\n---\n\n### 1.  How the numbers are placed in the rows and blocks  \n\nFor a given number \\(k\\in\\{1,\\ldots ,9\\}\\) it must appear  \n\n* once in each row (three appearances), and  \n* once in each block (three appearances).\n\nHence the three positions of \\(k\\) correspond to a **bijection** between the set of rows and the set of blocks.  \nThus for each \\(k\\) we may choose a permutation \\(\\sigma_k\\in S_3\\) :\n\n\\[\n\\sigma_k(r)=\\text{the block in which }k\\text{ occurs in row }r .\n\\]\n\nConversely, a choice of a permutation \\(\\sigma_k\\) for each \\(k\\) determines in which block every entry of the grid lies.\n\n---\n\n### 2.  Counting the possible collections of permutations  \n\nWrite a column of the \\(3\\times9\\) \u201cblock\u2011matrix\u2019\u2019 \\(M\\) as a permutation of \\((1,2,3)\\) \u2013 the three symbols denote the block in which the number of that column appears in rows \\(1,2,3\\).\n\nThus we need a sequence of nine permutations \\((p_1,\\dots ,p_9)\\) such that each ordered pair \\((\\text{row},\\text{block})\\) occurs exactly three times; equivalently each number appears three times in each row and three times in each block.\n\nLet  \n\n\\[\nx_1,\\dots ,x_6\n\\]\n\nbe the numbers of the six possible permutations of \\(S_3\\) in the sequence.\nThe conditions give the linear system  \n\n\\[\n\\begin{aligned}\nx_1+x_2&amp;=3\\\\\nx_3+x_4&amp;=3\\\\\nx_5+x_6&amp;=3\\\\\nx_3+x_5&amp;=3\\\\\nx_1+x_6&amp;=3\\\\\nx_2+x_4&amp;=3\\\\\nx_4+x_6&amp;=3\\\\\nx_2+x_5&amp;=3\\\\\nx_1+x_3&amp;=3\n\\end{aligned}\n\\]\n\nwhich has the solutions  \n\n\\[\n\\begin{array}{c|cccccc}\n &amp;x_1&amp;x_2&amp;x_3&amp;x_4&amp;x_5&amp;x_6\\\\\\hline\nt=0&amp;0&amp;3&amp;3&amp;0&amp;0&amp;3\\\\\nt=1&amp;1&amp;2&amp;2&amp;1&amp;1&amp;2\\\\\nt=2&amp;2&amp;1&amp;1&amp;2&amp;2&amp;1\\\\\nt=3&amp;3&amp;0&amp;0&amp;3&amp;3&amp;0\n\\end{array}\n\\qquad (t=0,1,2,3).\n\\]\n\nFor a fixed solution the columns can be ordered in\n\n\\[\n\\frac{9!}{x_1!x_2!x_3!x_4!x_5!x_6!}\n\\]\n\nways.  Summing over the four solutions gives  \n\n\\[\n\\begin{aligned}\nN_M &amp;= \\frac{9!}{3!^3}+2\\cdot\\frac{9!}{1!\\,2!^2\\,1!\\,1!\\,2!}\n      +\\frac{9!}{3!^3}\\\\\n    &amp;=1680+2\\cdot45360+1680=94\\,080 .\n\\end{aligned}\n\\]\n\nSo there are \\(94\\,080\\) possible matrices \\(M\\) describing in which block each number lies.\n\n---\n\n### 3.  Filling the inner columns of each block  \n\nInside a block \\(B\\) each row already has three distinct numbers (the three numbers assigned to that row in the block).  \nThese three numbers can be placed in the three inner columns of the block in any order, i.e. in \\((3!)^3=6^3\\) ways.\n\nSince the three blocks are independent, the total number of ways to complete the grid is  \n\n\\[\n94\\,080\\cdot (6^3)^3 = 94\\,080\\cdot 6^9 .\n\\]\n\nBecause \\(6^9 = (2\\cdot3)^9 =2^{9}\\,3^{9}\\),\n\n\\[\n\\begin{aligned}\n94\\,080\\cdot6^9 &amp;= \\bigl(2^7\\cdot3\\cdot5\\cdot7^2\\bigr)\\cdot\\bigl(2^9\\cdot3^9\\bigr)\\\\\n                &amp;=2^{16}\\cdot3^{10}\\cdot5^1\\cdot7^2 .\n\\end{aligned}\n\\]\n\nThus the total number of fillings is  \n\n\\[\n2^{16}\\cdot 3^{10}\\cdot 5^{1}\\cdot 7^{2}.\n\\]\n\n---\n\n### 4.  Computing the required sum  \n\nTake \\(p=2,\\ a=16;\\; q=3,\\ b=10;\\; r=5,\\ c=1;\\; s=7,\\ d=2\\).\n\n\\[\np\\,a+q\\,b+r\\,c+s\\,d = 2\\cdot16 + 3\\cdot10 + 5\\cdot1 + 7\\cdot2\n                     = 32 + 30 + 5 + 14 = 81 .\n\\]\n\n\\[\n\\boxed{81}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 81</p>\n<p>Extracted Answer: 81</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThe set of points in 3-dimensional coordinate space that lie in the plane $x+y+z=75$ whose coordinates satisfy the inequalities $x-yz&lt;y-zx&lt;z-xy$ forms three disjoint convex regions. Exactly one of those regions has finite area. The area of this finite region can be expressed in the form $a\\sqrt{b}$, where $a$ and $b$ are positive integers and $b$ is not divisible by the square of any prime. Find $a+b$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>First rewrite the chain of inequalities  \n\n\\[\nx-yz&lt;y-zx&lt;z-xy\n\\]\n\nas two separate inequalities.\n\n\\[\n\\begin{aligned}\nx-yz &amp;&lt; y-zx \\\\[2mm]\ny-zx &amp;&lt; z-xy\n\\end{aligned}\n\\]\n\n\\[\n\\begin{aligned}\nx-yz-y+zx&amp;&lt;0\\qquad\\Longrightarrow\\qquad (x-y)(1+z)&lt;0,\\\\[2mm]\ny-zx-z+xy&amp;&lt;0\\qquad\\Longrightarrow\\qquad (y-z)(1+x)&lt;0 .\n\\end{aligned}\n\\]\n\nThe third inequality \\( (x-z)(1+y)&lt;0\\) follows by adding the two, so the region is\ndescribed by  \n\n\\[\n\\boxed{(x-y)(1+z)&lt;0,\\qquad (y-z)(1+x)&lt;0}\n\\]\n\ntogether with the plane \\(x+y+z=75\\).\n\n---\n\n### 1.   Sign patterns\n\nLet  \n\n\\[\nS_x=\\operatorname{sgn}(1+x),\\quad S_y=\\operatorname{sgn}(1+y),\\quad S_z=\\operatorname{sgn}(1+z).\n\\]\n\nFrom the two product\u2011inequalities we obtain  \n\n\\[\n\\operatorname{sgn}(x-y)=-S_z,\\qquad \n\\operatorname{sgn}(y-z)=-S_x .\n\\]\n\nThus  \n\n\\[\n\\begin{array}{c|c|c|c}\nS_x &amp; S_y &amp; S_z &amp;\\text{order of }x,y,z\\\\ \\hline\n+ &amp; + &amp; + &amp; x&lt;y&lt;z\\\\\n+ &amp; - &amp; - &amp; y&lt;z&lt;x\\\\\n- &amp; + &amp; + &amp; x&lt;z&lt;y\\\\\n- &amp; - &amp; - &amp; \\text{impossible (sum }\\;75) \n\\end{array}\n\\]\n\nHence the points satisfying the chain split into three convex regions, corresponding\nto the three admissible sign patterns above.\n\n---\n\n### 2.   Which region is bounded?\n\n*Region  \\(x&lt;y&lt;z\\)  (all three numbers \\(&gt; -1\\)).*  \nUsing the plane equation \\(z=75-x-y\\) the conditions become  \n\n\\[\n-1&lt;x&lt;y,\\qquad y&lt;\\frac{75-x}{2}.\n\\]\n\nIn the \\((x,y)\\)-plane this is the triangle bounded by  \n\n\\[\nx=-1,\\; y=x,\\; y=\\frac{75-x}{2}.\n\\]\n\nThe three vertices are  \n\n\\[\n(-1,-1),\\;(-1,38),\\;(25,25).\n\\]\n\nIts area in the \\(xy\\)-plane is\n\n\\[\n\\frac12\\,(39)(26)=507 .\n\\]\n\nSince the plane \\(x+y+z=75\\) is tilted, an element \\(dx\\,dy\\) on the\n\\(xy\\)-plane corresponds to an area element  \n\n\\[\n\\sqrt{1+(\\partial z/\\partial x)^2+(\\partial z/\\partial y)^2}\\;dx\\,dy\n        =\\sqrt{1+1+1}\\;dx\\,dy=\\sqrt3\\,dx\\,dy .\n\\]\n\nThus the area of this region in the plane is  \n\n\\[\n507\\sqrt3 .\n\\]\n\n*The other two regions* (\\(y&lt;z&lt;x\\) and \\(x&lt;z&lt;y\\)) project onto unbounded\nhalf\u2011planes, so they have infinite area.\n\nHence the **unique finite region** is the one with \\(x&lt;y&lt;z\\), and its area is\n\\(507\\sqrt3\\).\n\n---\n\n### 3.   Answer\n\nThe area is \\(a\\sqrt b\\) with \\(a=507\\) and \\(b=3\\); therefore  \n\n\\[\na+b=507+3=510 .\n\\]\n\n\\[\n\\boxed{510}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 510</p>\n<p>Extracted Answer: 510</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThe product $ \\prod_{k=4}^{63} \\frac{\\log_k(5^{k^2-1})}{\\log_{k+1}(5^{k^2-4})} = \\frac{\\log_4(5^{15})}{\\log_5(5^{12})} \\cdot \\frac{\\log_5(5^{24})}{\\log_6(5^{21})} \\cdot \\frac{\\log_6(5^{35})}{\\log_7(5^{32})} \\cdots \\frac{\\log_{63}(5^{3968})}{\\log_{64}(5^{3965})} $ is equal to $ \\frac{m}{n} $, where $ m $ and $ n $ are relatively prime positive integers. Find $ m + n $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>\\[\n\\prod_{k=4}^{63}\\frac{\\log_k\\bigl(5^{k^2-1}\\bigr)}{\\log_{k+1}\\bigl(5^{k^2-4}\\bigr)}\n\\]\n\n---\n\n### 1.  Use change\u2011of\u2011base\n\n\\[\n\\log_k\\bigl(5^{k^2-1}\\bigr)=\\frac{\\log_5\\bigl(5^{k^2-1}\\bigr)}{\\log_5 k}\n      =\\frac{k^{2}-1}{\\log_5 k},\n\\qquad\n\\log_{k+1}\\bigl(5^{k^2-4}\\bigr)=\\frac{k^{2}-4}{\\log_5 (k+1)} .\n\\]\n\nHence each factor of the product equals  \n\n\\[\n\\frac{k^2-1}{k^2-4}\\;\n      \\frac{\\log_5(k+1)}{\\log_5k}.\n\\]\n\nSo\n\n\\[\nP = \\underbrace{\\prod_{k=4}^{63}\\frac{k^2-1}{k^2-4}}_{\\displaystyle P_1}\n    \\;\n    \\underbrace{\\prod_{k=4}^{63}\\frac{\\log_5(k+1)}{\\log_5k}}_{\\displaystyle P_2}.\n\\]\n\n---\n\n### 2.  Simplify \\(P_1\\)\n\n\\[\n\\frac{k^2-1}{k^2-4}= \\frac{(k-1)(k+1)}{(k-2)(k+2)}\n                  =\\frac{k-1}{k-2}\\cdot\\frac{k+1}{k+2}.\n\\]\n\nThus  \n\n\\[\nP_1=\\Bigl(\\prod_{k=4}^{63}\\frac{k-1}{k-2}\\Bigr)\n    \\Bigl(\\prod_{k=4}^{63}\\frac{k+1}{k+2}\\Bigr).\n\\]\n\nBoth products telescope:\n\n\\[\n\\prod_{k=4}^{63}\\frac{k-1}{k-2}\n   =\\frac{3}{2}\\cdot\\frac{4}{3}\\cdots\\frac{62}{61}\n   =\\frac{62}{2}=31,\n\\]\n\n\\[\n\\prod_{k=4}^{63}\\frac{k+1}{k+2}\n   =\\frac{5}{6}\\cdot\\frac{6}{7}\\cdots\\frac{64}{65}\n   =\\frac{5}{65}=\\frac1{13}.\n\\]\n\nTherefore  \n\n\\[\nP_1 =31\\cdot\\frac1{13} =\\frac{31}{13}.\n\\]\n\n---\n\n### 3.  Simplify \\(P_2\\)\n\n\\[\nP_2 =\\prod_{k=4}^{63}\\frac{\\log_5(k+1)}{\\log_5k}\n    =\\frac{\\log_5 5\\;\\log_5 6\\;\\cdots\\;\\log_5 64}\n           {\\log_5 4\\;\\log_5 5\\;\\cdots\\;\\log_5 63}\n    =\\frac{\\log_5 64}{\\log_5 4}.\n\\]\n\nUsing the change\u2011of\u2011base formula,\n\n\\[\n\\frac{\\log_5 64}{\\log_5 4}= \\log_4 64.\n\\]\n\nSince \\(4^3=64\\), we have \\(\\log_4 64 = 3\\). Hence  \n\n\\[\nP_2 = 3.\n\\]\n\n---\n\n### 4.  Combine the two parts\n\n\\[\nP = P_1\\cdot P_2 = \\frac{31}{13}\\times 3 = \\frac{93}{13}.\n\\]\n\nThus the product equals \\(\\displaystyle\\frac{m}{n}\\) with \\(m=93,\\; n=13\\).\n\n\\[\nm+n = 93+13 = 106.\n\\]\n\n\\[\n\\boxed{106}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 106</p>\n<p>Extracted Answer: 106</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $ A $ be the set of positive integer divisors of 2025. Let $ B $ be a randomly selected subset of $ A $. The probability that $ B $ is a nonempty set with the property that the least common multiple of its elements is 2025 is $ \\frac{m}{n} $, where $ m $ and $ n $ are relatively prime positive integers. Find $ m + n $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Factor  \n\n\\[\n2025=45^{2}= (3^{2}\\cdot5)^{2}=3^{4}\\cdot5^{2}.\n\\]\n\nHence a divisor of \\(2025\\) is of the form \\(3^{a}5^{b}\\) with  \n\n\\(0\\le a\\le4\\) and \\(0\\le b\\le2\\).  \nThus  \n\n\\[\n|A|=(4+1)(2+1)=15 .\n\\]\n\nAll \\(2^{15}\\) subsets of \\(A\\) are equally likely.\n\n---\n\n### Divisors needed for the LCM\n\nFor a subset \\(B\\subseteq A\\),\n\n\\[\n\\operatorname{lcm}(B)=3^{\\max_{d\\in B}a_d}\\;5^{\\max_{d\\in B}b_d}.\n\\]\n\nTo obtain \\(\\operatorname{lcm}(B)=2025=3^{4}5^{2}\\) we must have  \n\n* at least one element whose exponent of \\(3\\) equals \\(4\\);\n* at least one element whose exponent of \\(5\\) equals \\(2\\).\n\nDefine  \n\n\\[\nD_3=\\{d\\in A:\\, \\text{the exponent of }3\\text{ in }d\\text{ is }4\\},\\qquad \nD_5=\\{d\\in A:\\, \\text{the exponent of }5\\text{ in }d\\text{ is }2\\}.\n\\]\n\nCounting these divisors:\n\n* \\(D_3 = \\{3^{4}5^{0}, 3^{4}5^{1}, 3^{4}5^{2}\\}\\) \u21d2 \\(|D_3|=3\\);\n* \\(D_5 = \\{3^{0}5^{2}, 3^{1}5^{2}, 3^{2}5^{2}, 3^{3}5^{2}, 3^{4}5^{2}\\}\\) \u21d2 \\(|D_5|=5\\);\n* The intersection \\(D_3\\cap D_5=\\{3^{4}5^{2}\\}= \\{2025\\}\\) \u21d2 \\(|D_3\\cap D_5|=1\\).\n\nThus a subset \\(B\\) has \\(\\operatorname{lcm}(B)=2025\\) iff it contains **at least one element of \\(D_3\\) and at least one element of \\(D_5\\)** (the same element may satisfy both conditions).\n\n---\n\n### Counting such subsets\n\nLet \\(U\\) be the set of all subsets of \\(A\\) (including the empty set).  \nUse inclusion\u2013exclusion.\n\n\\[\n\\begin{aligned}\n|U| &amp;=2^{15},\\\\[2mm]\n\\text{Subsets missing }D_3 &amp;: 2^{15-|D_3|}=2^{12},\\\\[2mm]\n\\text{Subsets missing }D_5 &amp;: 2^{15-|D_5|}=2^{10},\\\\[2mm]\n\\text{Subsets missing both }D_3\\text{ and }D_5 &amp;: \n2^{15-|D_3\\cup D_5|}\n =2^{15-(3+5-1)}=2^{8}.\n\\end{aligned}\n\\]\n\nHence the number of subsets that contain at least one element of each set is  \n\n\\[\n\\begin{aligned}\nN_{\\text{good}}\n&amp;=|U|-2^{12}-2^{10}+2^{8}\\\\\n&amp;=32768-4096-1024+256\\\\\n&amp;=27904.\n\\end{aligned}\n\\]\n\nEvery such subset is non\u2011empty, so these are exactly the favorable subsets.\n\n---\n\n### Probability\n\n\\[\nP=\\frac{N_{\\text{good}}}{2^{15}}=\\frac{27904}{32768}.\n\\]\n\nReduce the fraction:\n\n\\[\n27904=2^{8}\\cdot 109,\\qquad 32768=2^{15}=2^{8}\\cdot 128\n\\Longrightarrow P=\\frac{109}{128}.\n\\]\n\nThus \\(m=109\\) and \\(n=128\\), and  \n\n\\[\nm+n = 109+128 = 237.\n\\]\n\n\\[\n\\boxed{237}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 237</p>\n<p>Extracted Answer: 237</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nCircle $\\omega_1$ with radius 6 centered at point $A$ is internally tangent at point $B$ to circle $\\omega_2$ with radius 15. Points $C$ and $D$ lie on $\\omega_2$ such that $\\overline{BC}$ is a diameter of $\\omega_2$ and $\\overline{BC} \\perp \\overline{AD}$. The rectangle $EFGH$ is inscribed in $\\omega_1$ such that $\\overline{EF} \\perp \\overline{BC}$, $C$ is closer to $\\overline{GH}$ than to $\\overline{EF}$, and $D$ is closer to $\\overline{FG}$ than to $\\overline{EH}$, as shown. Triangles $\\triangle DGF$ and $\\triangle CHG$ have equal areas. The area of rectangle $EFGH$ is $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m + n$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n* \\(\\omega _2\\) have centre \\(O\\) and radius \\(15\\);\n* \\(BC\\) be a diameter of \\(\\omega _2\\);\n* \\(\\omega _1\\) have centre \\(A\\) and radius \\(6\\), internally tangent to \\(\\omega _2\\) at \\(B\\).\n\n--------------------------------------------------------------------\n### 1.  Coordinates\n\nPlace \\(BC\\) on the \\(x\\)-axis with  \n\n\\[\nB=(-15,0),\\qquad C=(15,0),\\qquad O=(0,0).\n\\]\n\nSince the circles are internally tangent, the centres are collinear with the\ntangency point and  \n\n\\[\nOA=R_2-R_1=15-6=9 .\n\\]\n\nThus \\(A\\) lies on the ray \\(OB\\) at distance \\(9\\) from \\(O\\); consequently  \n\n\\[\nA=(-9,0).\n\\]\n\n--------------------------------------------------------------------\n### 2.  Point \\(D\\)\n\n\\(AD\\perp BC\\), so \\(AD\\) is the vertical line \\(x=-9\\).\nIntersecting this line with \\(\\omega _2\\) (\\(x^2+y^2=225\\)) gives  \n\n\\[\ny^2=225-(-9)^2=144\\quad\\Longrightarrow\\quad y=\\pm12 .\n\\]\n\nBecause the statement \u201c\\(D\\) is closer to \\(\\overline{FG}\\) than to \\(\\overline{EH}\\)\u2019\u2019 puts \\(D\\) above the centre, we take  \n\n\\[\nD=(-9,12).\n\\]\n\n--------------------------------------------------------------------\n### 3.  Rectangle \\(EFGH\\)\n\nThe rectangle is inscribed in \\(\\omega _1\\), so its circum\u2011centre is the\ncentre of \\(\\omega _1\\); hence the centre of the rectangle is \\(A\\).\n\nLet  \n\n* half\u2011width \\(a\\) (distance from the centre to each vertical side),\n* half\u2011height \\(b\\) (distance from the centre to each horizontal side).\n\nBecause the vertices lie on \\(\\omega _1\\),\n\n\\[\na^{2}+b^{2}=6^{2}=36. \\tag{1}\n\\]\n\nThe condition \u201c\\(\\overline{EF}\\perp\\overline{BC}\\)\u201d makes \\(\\overline{EF}\\) vertical,\nso the rectangle\u2019s sides are parallel/perpendicular to \\(BC\\).  \nTaking the usual labelling (counter\u2011clockwise)\n\n\\[\n\\begin{aligned}\nE&amp;=(-9-a,\\,-b),\\qquad \nF=(-9-a,\\,b),\\\\\nG&amp;=(-9+a,\\,b),\\qquad \nH=(-9+a,\\,-b).\n\\end{aligned}\n\\]\n\n--------------------------------------------------------------------\n### 4.  Equality of the two triangle areas\n\n\\[\n\\begin{aligned}\n\\text{Area}(\\triangle DGF)&amp;=\\frac12\\cdot GF\\cdot(\\text{vertical distance }D\\text{ to }y=b)\\\\\n&amp;=\\frac12\\cdot(2a)\\cdot(12-b)=a(12-b),\\\\[4pt]\n\\text{Area}(\\triangle CHG)&amp;=\\frac12\\cdot GH\\cdot(\\text{horizontal distance }C\\text{ to }x=-9+a)\\\\\n&amp;=\\frac12\\cdot(2b)\\cdot(24-a)=b(24-a).\n\\end{aligned}\n\\]\n\nGiven the areas are equal,\n\n\\[\na(12-b)=b(24-a)\\quad\\Longrightarrow\\quad12a=24b\\quad\\Longrightarrow\\quad a=2b. \\tag{2}\n\\]\n\n--------------------------------------------------------------------\n### 5.  Solving for \\(a\\) and \\(b\\)\n\nSubstituting \\(a=2b\\) into (1):\n\n\\[\n(2b)^{2}+b^{2}=36\\;\\Longrightarrow\\;5b^{2}=36\\;\\Longrightarrow\\;b^{2}=\\frac{36}{5}.\n\\]\n\nHence  \n\n\\[\na^{2}=(2b)^{2}=4b^{2}= \\frac{144}{5}.\n\\]\n\n--------------------------------------------------------------------\n### 6.  Area of the rectangle\n\n\\[\n\\text{Area}= (2a)(2b)=4ab=4(2b)b=8b^{2}=8\\left(\\frac{36}{5}\\right)=\\frac{288}{5}.\n\\]\n\nThus the area is \\(\\dfrac{288}{5}\\).  In lowest terms \\(m=288,\\;n=5\\), and\n\n\\[\nm+n=288+5=293.\n\\]\n\n--------------------------------------------------------------------\n\\[\n\\boxed{293}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 293</p>\n<p>Extracted Answer: 293</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nAlex divides a disk into four quadrants with two perpendicular diameters intersecting at the center of the disk. He draws 25 more line segments through the disk, drawing each segment by selecting two points at random on the perimeter of the disk in different quadrants and connecting those two points. Find the expected number of regions into which these 27 line segments divide the disk.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>**Step 1.  How many regions are created by chords?**  \n\nIf a convex region (here the disk) is cut by \\(N\\) line\u2011segments whose interior intersection points are all distinct, the number of regions is  \n\n\\[\nR=N+1+I,\n\\]\n\nwhere \\(I\\) is the total number of interior intersection points.  \n(Each new segment adds one region, plus one extra region for each interior point where it meets a previous segment.)\n\nFor our disk  \n\n\\[\nN=27\\qquad\\text{(the two diameters + 25 random chords)} .\n\\]\n\nHence  \n\n\\[\nE[R]=28+E[I].\n\\]\n\nSo we must find the expected number \\(E[I]\\) of interior intersection points.\n\n--------------------------------------------------------------------\n\n**Step 2.  Intersections involving the two diameters.**\n\nThe two diameters intersect at the centre; this contributes one guaranteed intersection.\n\nFor a random chord \\(C\\) we ask for the probability that it meets a given diameter.\n\n*Vertical diameter.*  \nThe chord meets the vertical line \\(x=0\\) iff its endpoints lie in opposite half\u2011planes (one in \\(\\{Q_1,Q_4\\}\\) and the other in \\(\\{Q_2,Q_3\\}\\)).  \nAmong the six unordered pairs of distinct quadrants, four have this property:\n\n\\[\n\\{Q_1,Q_2\\},\\{Q_1,Q_3\\},\\{Q_2,Q_4\\},\\{Q_3,Q_4\\},\n\\]\n\nso  \n\n\\[\nP(C\\text{ meets the vertical diameter})=\\frac{4}{6}=\\frac23 .\n\\]\n\nExactly the same reasoning holds for the horizontal diameter.  \nThus for each random chord\n\n\\[\nP(C\\text{ meets a given diameter})=\\frac23 .\n\\]\n\nWith 25 random chords we obtain  \n\n\\[\nE[\\text{intersections chord\u2013diameter}] = 25\\cdot 2\\cdot\\frac23=\\frac{100}{3}.\n\\]\n\n--------------------------------------------------------------------\n\n**Step 3.  Intersections among the 25 random chords.**\n\nEach chord is obtained by picking two points on the circle that lie in different quadrants.  \nThe unordered pair of quadrants a chord uses is equally likely to be any of the six possibilities\n\n* four *adjacent* pairs: \\(\\{01\\},\\{12\\},\\{23\\},\\{30\\}\\);\n* two *opposite* pairs: \\(\\{02\\},\\{13\\}\\).\n\nThus a chord is *adjacent* with probability \\(\\frac23\\) and *opposite* with probability \\(\\frac13\\).\n\n--------------------------------------------------------------------\n### 3.1  Classifying a pair of chords\n\nLet chord\u202f1 belong to unordered pair \\(P\\) and chord\u202f2 to unordered pair \\(Q\\).  \nThere are three possible relationships between \\(P\\) and \\(Q\\):\n\n| relationship | how many ordered \\((P,Q)\\) | intersection probability |\n|--------------|---------------------------|--------------------------|\n| same pair (\\(P=Q\\)) | 6 | \\(\\displaystyle\\frac12\\) |\n| disjoint pairs (no common quadrant) | 6 (4 adjacent\u2011adjacent, 2 opposite\u2011opposite) | \\(0\\) for adjacent\u2013adjacent, \\(1\\) for opposite\u2013opposite |\n| share exactly one quadrant | 24 (8 adjacent\u2011adjacent, 16 adjacent\u2011opposite) | \\(\\displaystyle\\frac12\\) |\n\n*Why the numbers?*  \n\n* Two chords of the **same type** intersect iff the order of the two points in the first quadrant is opposite to the order of the two points in the second quadrant \u2013 probability \\(1/2\\).\n\n* Two **disjoint adjacent** chords lie in quadrants \\(\\{0,1\\}\\) and \\(\\{2,3\\}\\); all points of the first lie before those of the second, so they never intersect.\n\n* Two **disjoint opposite** chords are \\(\\{0,2\\}\\) and \\(\\{1,3\\}\\); the four points appear in the order \\(0,1,2,3\\), which is alternating, so they always intersect.\n\n* When the chords **share exactly one quadrant**, the shared quadrant contains two independent uniform points; whichever of the two lies first decides whether the endpoints are interleaved. Hence the intersection probability is \\(1/2\\).\n\n--------------------------------------------------------------------\n### 3.2  Expected intersection probability for a random pair\n\nSumming the contributions of all 36 ordered possibilities:\n\n\\[\n\\begin{aligned}\n\\sum_{P,Q} p_{P,Q}&amp;=\n6\\!\\left(\\frac12\\right) \n+ 4\\!\\cdot\\!0 \n+ 2\\!\\cdot\\!1 \n+ 24\\!\\left(\\frac12\\right) \\\\\n&amp;= 3 + 2 + 12 = 17 .\n\\end{aligned}\n\\]\n\nTherefore for two independently chosen random chords\n\n\\[\nP(\\text{they intersect}) = \\frac{17}{36}.\n\\]\n\n--------------------------------------------------------------------\n### 3.3  Expected number of chord\u2013chord intersections\n\nThere are \\(\\binom{25}{2}=300\\) unordered pairs of the 25 chords, so\n\n\\[\nE[\\text{chord\u2013chord intersections}]\n=300\\cdot\\frac{17}{36}= \\frac{425}{3}.\n\\]\n\n--------------------------------------------------------------------\n\n**Step 4.  Total expected number of interior intersections.**\n\n\\[\n\\begin{aligned}\nE[I] &amp;= \\underbrace{1}_{\\text{diameters}} \n      + \\underbrace{\\frac{100}{3}}_{\\text{chord\u2013diameter}} \n      + \\underbrace{\\frac{425}{3}}_{\\text{chord\u2013chord}} \\\\[2mm]\n     &amp;= \\frac{525}{3}+1 = 175+1 = 176 .\n\\end{aligned}\n\\]\n\n--------------------------------------------------------------------\n\n**Step 5.  Expected number of regions.**\n\n\\[\nE[R]=N+1+E[I]=27+1+176=204.\n\\]\n\n--------------------------------------------------------------------\n\n\\[\n\\boxed{204}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 204</p>\n<p>Extracted Answer: 204</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nFour unit squares form a $2 \\times 2$ grid. Each of the 12 unit line segments forming the sides of the squares is colored either red or blue in such a way that each unit square has 2 red sides and 2 blue sides. Find the number of such colorings.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Label the twelve unit segments that form the sides of the four unit squares as in the picture  \n\n\\[\n\\begin{array}{c}\n\\text{top left square }A:\\; a\\;( \\text{top}) ,\\; a&#39;(\\text{left}) ,\\; u (\\text{vertical middle up}) ,\\; x (\\text{horizontal middle left})\\\\[2mm]\n\\text{top right square }B:\\; b ,\\; b&#39; ,\\; u ,\\; y\\\\[2mm]\n\\text{bottom left square }C:\\; c ,\\; c&#39; ,\\; v ,\\; x\\\\[2mm]\n\\text{bottom right square }D:\\; d ,\\; d&#39; ,\\; v ,\\; y\n\\end{array}\n\\]\n\nAll variables are binary:  \n\n\\[\n0=\\text{blue},\\qquad 1=\\text{red}.\n\\]\n\n---\n\n### 1.  Express the condition for each square  \n\nFor a square the number of red sides must be exactly two.  \nIf we let  \n\n\\[\n\\begin{aligned}\ns_A &amp;=x+u, &amp; s_B &amp;=y+u,\\\\\ns_C &amp;=x+v, &amp; s_D &amp;=y+v,\n\\end{aligned}\n\\]\n\nthen the two **boundary** edges of a square must contain  \n\n\\[\nr_A =2-s_A,\\qquad r_B =2-s_B,\\qquad r_C =2-s_C,\\qquad r_D =2-s_D\n\\]\n\nred sides.  \nFor each square the two boundary edges are distinct from the other squares, so the choices for the\nfour pairs are independent.\n\nFor a given pair of boundary edges the number of colourings is  \n\n\\[\n\\begin{cases}\n1 &amp;\\text{if }r_i\\in\\{0,2\\}\\;(00\\text{ or }11),\\\\[2mm]\n2 &amp;\\text{if }r_i =1\\;(01\\text{ or }10).\n\\end{cases}\n\\]\n\nHence, when the interior pattern \\((x,y,u,v)\\) is fixed, the number of ways to colour the eight\nouter edges equals  \n\n\\[\n2^{\\#\\{\\,i\\in\\{A,B,C,D\\}\\mid s_i=1\\,\\}},\n\\]\n\nbecause a square contributes a factor \\(2\\) exactly when its interior sum \\(s_i\\) equals \\(1\\).\n\nThus the total number of admissible colourings is  \n\n\\[\nN=\\sum_{(x,y,u,v)\\in\\{0,1\\}^4} 2^{\\#\\{i\\mid s_i=1\\}} .\n\\]\n\n---\n\n### 2.  Enumerate the \\(2^4=16\\) interior patterns  \n\n\\[\n\\begin{array}{c|c|c|c|c|c}\n(x,y,u,v) &amp; s_A &amp; s_B &amp; s_C &amp; s_D &amp;\n\\#\\{i\\mid s_i=1\\}\\\\\\hline\n0000 &amp;0&amp;0&amp;0&amp;0&amp;0\\\\\n0001 &amp;0&amp;0&amp;1&amp;1&amp;2\\\\\n0010 &amp;1&amp;1&amp;0&amp;0&amp;2\\\\\n0011 &amp;1&amp;1&amp;1&amp;1&amp;4\\\\\n0100 &amp;0&amp;1&amp;0&amp;1&amp;2\\\\\n0101 &amp;0&amp;1&amp;1&amp;2&amp;2\\\\\n0110 &amp;1&amp;2&amp;0&amp;1&amp;2\\\\\n0111 &amp;1&amp;2&amp;1&amp;2&amp;2\\\\\n1000 &amp;1&amp;0&amp;1&amp;0&amp;2\\\\\n1001 &amp;1&amp;0&amp;2&amp;1&amp;2\\\\\n1010 &amp;2&amp;1&amp;1&amp;0&amp;2\\\\\n1011 &amp;2&amp;1&amp;2&amp;1&amp;2\\\\\n1100 &amp;1&amp;1&amp;1&amp;1&amp;4\\\\\n1101 &amp;1&amp;1&amp;2&amp;2&amp;2\\\\\n1110 &amp;2&amp;2&amp;1&amp;1&amp;2\\\\\n1111 &amp;2&amp;2&amp;2&amp;2&amp;0\n\\end{array}\n\\]\n\n(The entry \u201c2\u2019\u2019 means the sum of the two interior edges of that square is \\(2\\); it forces the\ncorresponding pair of boundary edges to be both blue.)\n\nThe contribution of each pattern is \\(2^{\\#\\{i\\mid s_i=1\\}}\\).  Adding all contributions we get  \n\n\\[\n\\begin{aligned}\nN&amp;=1\\;(0000)+4\\;(0001)+4\\;(0010)+16\\;(0011)\\\\\n  &amp;\\quad+4\\;(0100)+4\\;(0101)+4\\;(0110)+4\\;(0111)\\\\\n  &amp;\\quad+4\\;(1000)+4\\;(1001)+4\\;(1010)+4\\;(1011)\\\\\n  &amp;\\quad+16\\;(1100)+4\\;(1101)+4\\;(1110)+1\\;(1111)\\\\[2mm]\n  &amp;=1+16+48+16+1\\\\\n  &amp;=\\boxed{82}.\n\\end{aligned}\n\\]\n\nTherefore there are **82** ways to colour the twelve unit segments of a \\(2\\times2\\) grid so that\nevery unit square has exactly two red and two blue sides.</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 82</p>\n<p>Extracted Answer: 82</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThere are $ n $ values of $ x $ in the interval $ 0 &lt; x &lt; 2\\pi $ where $ f(x) = \\sin(7\\pi \\cdot \\sin(5x)) = 0 $. For $ t $ of these $ n $ values of $ x $, the graph of $ y = f(x) $ is tangent to the $ x $-axis. Find $ n + t $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>\\[\nf(x)=\\sin \\bigl(7\\pi\\sin(5x)\\bigr)\n\\qquad (0&lt;x&lt;2\\pi)\n\\]\n\n---\n\n### 1.  Zeros of \\(f\\)\n\n\\(f(x)=0\\iff \\sin\\bigl(7\\pi\\sin(5x)\\bigr)=0\\)\n\n\\[\n7\\pi\\sin(5x)=k\\pi\\qquad(k\\in\\mathbb Z)\n\\Longrightarrow\\sin(5x)=\\frac{k}{7}.\n\\]\n\nSince \\(\\sin(5x)\\in[-1,1]\\), we must have \\(-7\\le k\\le7\\).  \nThus \\(k\\) can be any integer from \\(-7\\) to \\(7\\) (15 values).\n\nPut \\(\\theta =5x\\). Then \\(\\theta\\in(0,10\\pi)\\) and we need the number of solutions of  \n\n\\[\n\\sin\\theta =\\frac{k}{7}\\qquad (k=-7,\\ldots,7)\n\\]\nin \\((0,10\\pi)\\).\n\n*If \\(|k|=7\\) (\\(\\sin\\theta=\\pm1\\)):* each period \\((0,2\\pi)\\) contributes one solution, and there are five periods in \\((0,10\\pi)\\).  \n\\(\\;\\Rightarrow\\) 5 solutions for \\(k=7\\) and 5 solutions for \\(k=-7\\).\n\n*If \\(k=0\\) (\\(\\sin\\theta=0\\)):* solutions are \\(\\theta=n\\pi\\) with \\(n=1,\\dots ,9\\).  \n\\(\\;\\Rightarrow\\) 9 solutions.\n\n*If \\(|k|=1,2,\\dots ,6\\) (\\(|\\sin\\theta|&lt;1\\) and \\(\\neq0\\)):* in each \\(2\\pi\\)\u2011interval there are two solutions, so across five intervals there are \\(2\\cdot5=10\\) solutions.\n\nHence the total number of zeros is  \n\n\\[\nn =\\underbrace{5+5}_{k=\\pm7}+ \\underbrace{9}_{k=0}+ \\underbrace{12\\times10}_{k=\\pm1,\\dots ,\\pm6}\n      =10+9+120 = 139 .\n\\]\n\n---\n\n### 2.  Tangent zeros\n\nA zero is tangent to the \\(x\\)-axis when \\(f&#39;(x)=0\\) as well.\n\n\\[\nf&#39;(x)=35\\pi\\cos\\!\\bigl(7\\pi\\sin(5x)\\bigr)\\,\\cos(5x).\n\\]\n\nAt any zero we have \\(\\cos\\!\\bigl(7\\pi\\sin(5x)\\bigr)=\\cos(k\\pi)=(-1)^k\\neq0\\); therefore  \n\n\\[\nf&#39;(x)=0 \\iff \\cos(5x)=0.\n\\]\n\n\\(\\cos(5x)=0\\) gives \\(5x=\\dfrac{\\pi}{2}+m\\pi\\;(m\\in\\mathbb Z)\\), i.e.\n\n\\[\nx=\\frac{(2m+1)\\pi}{10}.\n\\]\n\nWithin \\(0&lt;x&lt;2\\pi\\) the odd integers \\(2m+1\\) run from \\(1\\) to \\(19\\); there are \\(10\\) such values.\nAt these points \\(\\sin(5x)=\\pm1\\), i.e. they correspond exactly to the solutions for \\(k=\\pm7\\).\n\nThus  \n\n\\[\nt=10.\n\\]\n\n---\n\n### 3.  Required sum\n\n\\[\nn+t = 139+10 = 149.\n\\]\n\n\\[\n\\boxed{149}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 149</p>\n<p>Extracted Answer: 149</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nFrom an unlimited supply of 1-cent coins, 10-cent coins, and 25-cent coins, Silas wants to find a collection of coins that has a total value of $ N $ cents, where $ N $ is a positive integer. He uses the so-called **greedy algorithm**, successively choosing the coin of greatest value that does not cause the value of his collection to exceed $ N $. For example, to get 42 cents, Silas will choose a 25-cent coin, then a 10-cent coin, then 7 1-cent coins. However, this collection of 9 coins uses more coins than necessary to get a total of 42 cents; indeed, choosing 4 10-cent coins and 2 1-cent coins achieves the same total value with only 6 coins.\n\nIn general, the greedy algorithm succeeds for a given $ N $ if no other collection of 1-cent, 10-cent, and 25-cent coins gives a total value of $ N $ cents using strictly fewer coins than the collection given by the greedy algorithm. Find the number of values of $ N $ between 1 and 1000 inclusive for which the greedy algorithm succeeds.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>**Step 1 \u2013 Greedy description**\n\nFor a given amount \\(N\\) let  \n\n\\[\nq=\\Bigl\\lfloor \\frac{N}{25}\\Bigr\\rfloor ,\\qquad r=N-25q\\;(0\\le r&lt;25)\n\\]\n\nThe greedy algorithm first takes \\(q\\) quarters, then uses as many dimes as possible and finally pennies.  \nHence the greedy number of coins is  \n\n\\[\ng(N)=q+\\Bigl\\lfloor\\frac{r}{10}\\Bigr\\rfloor +(r\\bmod 10)\n      =q+f(r),\n\\]\n\nwhere  \n\n\\[\nf(x)=\\Bigl\\lfloor\\frac{x}{10}\\Bigr\\rfloor +(x\\bmod10)\n\\]\n\nis the optimal number of coins when only dimes and pennies are allowed.\n\n---\n\n**Step 2 \u2013 Optimal solution with a given number of quarters**\n\nIf we use \\(a\\) quarters (\\(0\\le a\\le q\\)), we must make the remainder \\(N-25a\\) with dimes and pennies.  \nThe minimum number of coins for that remainder is \\(f(N-25a)\\).  \nThus the optimal number of coins for \\(N\\) is  \n\n\\[\n\\min_{0\\le a\\le q}\\; \\bigl[a+f(N-25a)\\bigr].\n\\]\n\nBecause \\(f\\) is optimal for the two\u2011coin system \\(\\{1,10\\}\\), we only need to compare the greedy choice\n\\(a=q\\) with the possibilities where we use fewer quarters.\n\n---\n\n**Step 3 \u2013 Effect of removing one quarter**\n\nWrite \\(r=N-25q\\) (the greedy remainder).  \nIf we use one fewer quarter (\\(a=q-1\\)), the new remainder is \\(r+25\\), and the coin count becomes  \n\n\\[\n(q-1)+f(r+25).\n\\]\n\nGreedy is optimal precisely when  \n\n\\[\nq+f(r)\\le (q-1)+f(r+25)\\quad\\Longleftrightarrow\\quad f(r)+1\\le f(r+25).\n\\]\n\nCompute \\(f(r+25)\\) in terms of \\(f(r)\\).  \nSince adding \\(25\\) cents is the same as adding two dimes and five pennies,  \n\n\\[\nf(r+25)=r+25-9\\Bigl\\lfloor\\frac{r+25}{10}\\Bigr\\rfloor .\n\\]\n\nThe floor changes by  \n\n\\[\n\\Bigl\\lfloor\\frac{r+25}{10}\\Bigr\\rfloor-\\Bigl\\lfloor\\frac{r}{10}\\Bigr\\rfloor=\n\\begin{cases}\n2,&amp; r\\bmod10\\le 4,\\\\[2pt]\n3,&amp; r\\bmod10\\ge 5 .\n\\end{cases}\n\\]\n\nHence  \n\n\\[\nf(r+25)=\n\\begin{cases}\nf(r)+7, &amp; r\\bmod10\\le4,\\\\[2pt]\nf(r)-2, &amp; r\\bmod10\\ge5 .\n\\end{cases}\n\\]\n\nConsequently  \n\n* if \\(r\\bmod10\\le4\\) then \\(f(r+25)=f(r)+7&gt;f(r)+1\\) \u2013 greedy stays optimal;\n* if \\(r\\bmod10\\ge5\\) then \\(f(r+25)=f(r)-2\\le f(r)\\) \u2013 using one fewer quarter gives fewer coins.\n\nThus the greedy algorithm fails **exactly** when the greedy remainder \\(r\\) satisfies  \n\n\\[\nr\\bmod10\\ge5 \\;\\Longleftrightarrow\\; r\\in\\{5,6,7,8,9,15,16,17,18,19\\}.\n\\]\n\n---\n\n**Step 4 \u2013 Dropping more than one quarter never helps**\n\nFor two quarters removed we add \\(50\\) cents to the remainder.  \nA similar computation gives  \n\n\\[\nf(r+50)=f(r)+5 .\n\\]\n\nThe change in total coin count is \\(-2+5=+3\\); for three quarters removed the change is \\(-3+12=+9\\), etc.  \nHence removing two or more quarters can never improve on the greedy solution.  \nTherefore the condition found in Step\u202f3 is both necessary and sufficient.\n\n---\n\n**Step 5 \u2013 Counting the successful \\(N\\) (1\u202f\u2264\u202fN\u202f\u2264\u202f1000)**  \n\nThe greedy fails for those \\(N\\ge25\\) whose remainder modulo \\(25\\) lies in  \n\n\\[\nR=\\{5,6,7,8,9,15,16,17,18,19\\}.\n\\]\n\nFor a fixed residue \\(r\\in R\\),\n\n\\[\nN=r+25k\\qquad (k\\ge1,\\; N\\le1000).\n\\]\n\nThe largest possible \\(k\\) is \\(\\bigl\\lfloor\\frac{1000-r}{25}\\bigr\\rfloor =39\\)\n(because \\(1000-r\\) ranges from \\(981\\) to \\(995\\)).  \nThus each residue contributes \\(39\\) failing numbers.\n\n\\[\n\\#\\text{failures}=|R|\\times 39 = 10\\times39 = 390 .\n\\]\n\nAll other numbers (including the ten numbers \\(5,6,7,8,9,15,16,17,18,19\\) themselves, which are \\(&lt;25\\) and therefore not failures) are successes.\n\n\\[\n\\#\\text{successes}=1000-390 = 610 .\n\\]\n\n---\n\n\\[\n\\boxed{610}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 610</p>\n<p>Extracted Answer: 610</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nSixteen chairs are arranged in a row. Eight people each select a chair in which to sit so that no person sits next to two other people. Let $ N $ be the number of subsets of 16 chairs that could be selected. Find the remainder when $ N $ is divided by 1000.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n\\[\na_1a_2\\dots a_{16},\\qquad a_i\\in\\{0,1\\}\n\\]\n\nbe a binary string where \\(a_i=1\\) means the \\(i^{\\text{th}}\\) chair is occupied.\nThe condition *no person sits next to two other people* means that a\n\\(1\\) may not have a \\(1\\) on both sides; equivalently the string contains\nno three consecutive \\(1\\)\u2019s.  \nHence we must count the binary strings of length \\(16\\) that\n\n* have exactly eight \\(1\\)\u2019s,\n* contain no substring \\(111\\).\n\n---\n\n### 1.  Decompose the occupied chairs into blocks\n\nSince a block of consecutive \\(1\\)\u2019s can have length at most \\(2\\), the eight\n\\(1\\)\u2019s are split into blocks of length \\(1\\) or \\(2\\).\n\nLet  \n\n* \\(x\\) = number of blocks of length \\(1\\),\n* \\(y\\) = number of blocks of length \\(2\\),\n* \\(m=x+y\\) = total number of blocks.\n\nThen  \n\n\\[\nx+2y=8,\\qquad x+y=m\\Longrightarrow y=8-m,\\;x=2m-8 .\n\\]\n\nThus \\(m\\) can be any integer with \\(\\lceil 8/2\\rceil\\le m\\le 8\\); i.e.  \n\n\\[\nm=4,5,6,7,8 .\n\\]\n\nFor a given \\(m\\) the positions of the \\(y=8-m\\) blocks of length \\(2\\)\namong the \\(m\\) blocks can be chosen in  \n\n\\[\n\\binom{m}{\\,8-m\\,}\n\\]\n\nways.\n\n---\n\n### 2.  Insert the separating zeros\n\nBetween two consecutive blocks there must be at least one \\(0\\).\nWith \\(m\\) blocks there are \\(m-1\\) mandatory zeros.\nThere are \\(16-8=8\\) zeros altogether, so after placing the mandatory ones we\nstill have  \n\n\\[\n8-(m-1)=9-m\n\\]\n\nzeros left.  \n\nThese remaining zeros may be distributed freely among the \\(m+1\\) gaps\n(the two ends and the \\(m-1\\) interior gaps).  By stars\u2011and\u2011bars the number\nof ways is\n\n\\[\n\\binom{(9-m)+(m+1)-1}{(m+1)-1}\n   =\\binom{9}{m}.\n\\]\n\n---\n\n### 3.  Count all possibilities\n\nFor each admissible \\(m\\),\n\n\\[\n\\text{choices}(m)=\\binom{m}{8-m}\\binom{9}{m}.\n\\]\n\nHence  \n\n\\[\n\\begin{aligned}\nN&amp;=\\sum_{m=4}^{8}\\binom{m}{8-m}\\binom{9}{m}\\\\[2mm]\n &amp;=\\binom{4}{4}\\binom{9}{4}\n   +\\binom{5}{3}\\binom{9}{5}\n   +\\binom{6}{2}\\binom{9}{6}\n   +\\binom{7}{1}\\binom{9}{7}\n   +\\binom{8}{0}\\binom{9}{8}\\\\[2mm]\n &amp;=1\\cdot126+10\\cdot126+15\\cdot84+7\\cdot36+1\\cdot9\\\\\n &amp;=126+1260+1260+252+9\\\\\n &amp;=2907 .\n\\end{aligned}\n\\]\n\n---\n\n### 4.  Remainder modulo \\(1000\\)\n\n\\[\n2907\\equiv 907\\pmod{1000}.\n\\]\n\n\\[\n\\boxed{907}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 907</p>\n<p>Extracted Answer: 907</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nSuppose $ \\triangle ABC $ has angles $ \\angle BAC = 84^\\circ $, $ \\angle ABC = 60^\\circ $, and $ \\angle ACB = 36^\\circ $. Let $ D, E, $ and $ F $ be the midpoints of sides $ \\overline{BC} $, $ \\overline{AC} $, and $ \\overline{AB} $, respectively. The circumcircle of $ \\triangle DEF $ intersects $ \\overline{BD} $, $ \\overline{AE} $, and $ \\overline{AF} $ at points $ G, H, $ and $ J $, respectively. The points $ G, D, E, H, J, $ and $ F $ divide the circumcircle of $ \\triangle DEF $ into six minor arcs, as shown. Find $ \\widehat{DE} + 2 \\cdot \\widehat{HJ} + 3 \\cdot \\widehat{FG} $, where the arcs are measured in degrees.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n\\[\n\\angle A=84^{\\circ},\\qquad \\angle B=60^{\\circ},\\qquad \\angle C=36^{\\circ}.\n\\]\n\n--------------------------------------------------------------------\n### 1.  The nine\u2011point circle in complex form  \n\nPut the circumcircle of \\(\\triangle ABC\\) as the unit circle and let  \n\n\\[\na=1,\\qquad b=e^{i\\beta},\\qquad c=e^{i\\gamma},\n\\]\n\nwhere  \n\n\\[\n\\beta =72^{\\circ},\\qquad \\gamma =240^{\\circ}\n\\]\n\nbecause the central arcs are twice the opposite angles:\n\\(\\widehat{BC}=2A=168^{\\circ},\\;\\widehat{CA}=2B=120^{\\circ},\n\\;\\widehat{AB}=2C=72^{\\circ}\\).\n\nThe nine\u2011point centre is\n\n\\[\nN=\\frac{a+b+c}{2},\n\\]\n\nand its radius is \\(\\frac12\\) (since \\(|a|=|b|=|c|=1\\)).  \nThe three midpoints are  \n\n\\[\nD=\\frac{b+c}{2},\\qquad \nE=\\frac{c+a}{2},\\qquad \nF=\\frac{a+b}{2}.\n\\]\n\nNotice that\n\n\\[\nD-N=-\\frac{a}{2},\\qquad \nE-N=-\\frac{b}{2},\\qquad \nF-N=-\\frac{c}{2} .\n\\tag{1}\n\\]\n\nHence the central angle \\(\\widehat{DE}\\) equals the angle between vectors\n\\(-a\\) and \\(-b\\); it is the same as the angle between \\(a\\) and \\(b\\).\n\n\\[\n\\widehat{DE}= \\angle aOb = 2\\angle ACB = 2\\cdot36^{\\circ}=72^{\\circ}.\n\\tag{2}\n\\]\n\n--------------------------------------------------------------------\n### 2.  The other intersection points  \n\nThe nine\u2011point circle is the image of the circumcircle under the similarity\n\n\\[\nX\\longmapsto N-\\frac{X}{2},\n\\tag{3}\n\\]\n\ni.e. the homothety with centre the centroid (factor \\(-\\tfrac12\\)).\nConsequently, if a point \\(Y\\) of the nine\u2011point circle is the image of\n\\(X\\) on the circumcircle, then  \n\n\\[\nY = N-\\frac{X}{2}\\qquad\\Longleftrightarrow\\qquad X=2(N-Y).\n\\tag{4}\n\\]\n\n--------------------------------------------------------------------\n#### (a) Point \\(G\\)\n\n\\(G\\) lies on line \\(BD\\).  Since \\(D\\) is the image of \\(A\\) and\n\\(B\\) is the image of the point \\(X\\) with \\(X=b\\), the line \\(BD\\) is the\nimage of the line through \\(A\\) parallel to chord \\(BC\\).\nThus \\(G\\) corresponds to the second intersection of the line through\n\\(A\\;(=a)\\) parallel to \\(BC\\) with the circumcircle.\n\nFor a line through a point \\(e^{i\\alpha}\\) parallel to chord\n\\(e^{i\\beta}e^{i\\gamma}\\) the second intersection is\n\\(e^{i(\\beta+\\gamma-\\alpha)}\\).  \nHere \\(\\alpha=0,\\;\\beta=72^{\\circ},\\;\\gamma=240^{\\circ}\\); therefore\n\n\\[\nX_G = e^{i(\\beta+\\gamma)}=e^{i312^{\\circ}} .\n\\]\n\nFrom (3) the point on the nine\u2011point circle is  \n\n\\[\nG = N-\\frac{X_G}{2}.\n\\]\n\nHence the vector \\(NG=-\\frac{X_G}{2}\\) has direction \\(312^{\\circ}+180^{\\circ}=132^{\\circ}\\).\n\n--------------------------------------------------------------------\n#### (b) Point \\(H\\)\n\n\\(H\\) lies on line \\(AE\\).  This line is parallel to chord \\(CA\\); the\nstarting point on the circumcircle is \\(B\\,(=e^{i72^{\\circ}})\\).  Thus\n\n\\[\nX_H = e^{i(0+240^{\\circ}-72^{\\circ})}=e^{i168^{\\circ}} ,\n\\qquad\nH=N-\\frac{X_H}{2},\n\\]\n\nso the direction of \\(NH\\) is \\(168^{\\circ}+180^{\\circ}=348^{\\circ}\\).\n\n--------------------------------------------------------------------\n#### (c) Point \\(J\\)\n\n\\(J\\) lies on line \\(AF\\), which is parallel to chord \\(AB\\); it starts\nfrom \\(C\\,(=e^{i240^{\\circ}})\\).  Therefore\n\n\\[\nX_J = e^{i(0+72^{\\circ}-240^{\\circ})}=e^{i192^{\\circ}},\n\\qquad\nJ=N-\\frac{X_J}{2},\n\\]\n\nand the direction of \\(NJ\\) is \\(192^{\\circ}+180^{\\circ}=12^{\\circ}\\).\n\n--------------------------------------------------------------------\n### 3.  The required arcs on the nine\u2011point circle  \n\nFrom the directions obtained:\n\n\\[\n\\begin{aligned}\n&amp;\\text{Arc }DE = 252^{\\circ}-180^{\\circ}=72^{\\circ},\\\\[2mm]\n&amp;\\text{Arc }FG = 132^{\\circ}-60^{\\circ}=72^{\\circ},\\\\[2mm]\n&amp;\\text{Arc }HJ = (360^{\\circ}-348^{\\circ})+12^{\\circ}=24^{\\circ}.\n\\end{aligned}\n\\]\n\nAll are the minor arcs (each \\(&lt;180^{\\circ}\\)).\n\n--------------------------------------------------------------------\n### 4.  Computing the requested expression  \n\n\\[\n\\widehat{DE}+2\\widehat{HJ}+3\\widehat{FG}\n=72^{\\circ}+2\\!\\cdot\\!24^{\\circ}+3\\!\\cdot\\!72^{\\circ}\n=72+48+216=336^{\\circ}.\n\\]\n\n--------------------------------------------------------------------\n\\[\n\\boxed{336}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 336</p>\n<p>Extracted Answer: 336</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $ S $ be the set of vertices of a regular 24-gon. Find the number of ways to draw 12 segments of equal lengths so that each vertex in $ S $ is an endpoint of exactly one of the 12 segments.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>For a regular 24\u2011gon label the vertices \\(0,1,\\ldots ,23\\) in order.\nIf a segment joins vertex \\(i\\) to vertex \\(j\\) then the chord length depends only on  \n\n\\[\nk=\\min \\{\\,|i-j|\\;,\\;24-|i-j|\\,\\},\n\\qquad 1\\le k\\le 12 .\n\\]\n\nThus a configuration in which all 12 segments have the same length corresponds to a\nperfect matching in the graph whose edges are all chords of a fixed step \\(k\\).\n\n---\n\n### 1.  Structure of the step\u2011\\(k\\) graph  \n\nLet \\(d=\\gcd(24,k)\\).  \nThe vertices split into \\(d\\) disjoint cycles, each of length  \n\n\\[\nL=\\frac{24}{d}.\n\\]\n\nEvery vertex is incident with exactly the two edges of its cycle.  \nA perfect matching can exist only if each cycle has even length, i.e. \\(L\\) must be even.\n\\(L\\) is odd only when \\(d=8\\) (then \\(L=3\\)); this occurs for \\(k=8\\).  \nHence the step \\(k=8\\) gives **no** valid configuration.\n\nFor an even cycle of length \\(L\\ge4\\) there are exactly two perfect matchings\n(the two possible \u201calternating\u201d choices).  \nIf \\(L=2\\) (the case \\(k=12\\)), the matching is forced and there is only one.\n\nConsequently, for a permissible \\(k\\)\n\n\\[\n\\#\\text{ matchings for step }k=\n\\begin{cases}\n2^{d}, &amp; L&gt;2,\\\\[2pt]\n1, &amp; L=2 .\n\\end{cases}\n\\]\n\n---\n\n### 2.  Count for each step \\(k\\)\n\n\\[\n\\begin{array}{c|c|c|c}\nk &amp; d=\\gcd(24,k) &amp; L=24/d &amp; \\#\\text{ matchings}\\\\ \\hline\n1,5,7,11 &amp; 1 &amp; 24 &amp; 2\\\\\n2,10 &amp; 2 &amp; 12 &amp; 2^{2}=4\\\\\n3,9 &amp; 3 &amp; 8 &amp; 2^{3}=8\\\\\n4 &amp; 4 &amp; 6 &amp; 2^{4}=16\\\\\n6 &amp; 6 &amp; 4 &amp; 2^{6}=64\\\\\n12 &amp; 12&amp; 2 &amp; 1\\\\\n8 &amp; 8 &amp; 3 &amp; \\text{none}\n\\end{array}\n\\]\n\nNow sum over all admissible \\(k\\) ( \\(k=1,\\dots ,12\\) except \\(k=8\\) ):\n\n\\[\n\\begin{aligned}\n\\text{Total}&amp;=4\\cdot2\\;+\\;2\\cdot4\\;+\\;2\\cdot8\\;+\\;1\\cdot16\\;+\\;1\\cdot64\\;+\\;1\\cdot1\\\\\n&amp;=8+8+16+16+64+1\\\\\n&amp;=113 .\n\\end{aligned}\n\\]\n\n---\n\n\\[\n\\boxed{113}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 113</p>\n<p>Extracted Answer: 113</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nFind the sum of all integer bases $b&gt;9$ for which $17_{b}$ is a divisor of $97_{b}$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n\\[\n17_{b}=1\\cdot b+7=b+7,\\qquad \n97_{b}=9\\cdot b+7=9b+7 .\n\\]\n\nWe need  \n\n\\[\nb+7 \\mid 9b+7 .\n\\]\n\nWrite \\(9b+7\\) in terms of \\(b+7\\):\n\n\\[\n9b+7 = 9(b+7) - 56 .\n\\]\n\nHence the remainder upon division by \\(b+7\\) is \\(-56\\).  \nThus \\(b+7\\) must divide \\(56\\):\n\n\\[\nb+7 \\mid 56 .\n\\]\n\nList the positive divisors of \\(56\\):\n\n\\[\n1,\\;2,\\;4,\\;7,\\;8,\\;14,\\;28,\\;56 .\n\\]\n\nSince the base must satisfy \\(b&gt;9\\) (so that the digit 9 is allowed), we need  \n\n\\[\nb+7&gt;9+7=16 .\n\\]\n\nThe only divisors of \\(56\\) larger than \\(16\\) are \\(28\\) and \\(56\\).\n\n\\[\n\\begin{aligned}\nb+7 &amp;= 28 \\;\\Longrightarrow\\; b=21,\\\\[2pt]\nb+7 &amp;= 56 \\;\\Longrightarrow\\; b=49.\n\\end{aligned}\n\\]\n\nBoth bases exceed \\(9\\) and thus are admissible.\n\nThe sum of all such bases is\n\n\\[\n21+49 = 70 .\n\\]\n\n\\[\n\\boxed{70}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 70</p>\n<p>Extracted Answer: 70</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $ A_1A_2 \\ldots A_{11} $ be an 11-sided non-convex simple polygon with the following properties:\n* The area of $ A_iA_1A_{i+1} $ is 1 for each $ 2 \\leq i \\leq 10 $,\n* $ \\cos(\\angle A_iA_1A_{i+1}) = \\frac{12}{13} $ for each $ 2 \\leq i \\leq 10 $,\n* The perimeter of $ A_1A_2 \\ldots A_{11} $ is 20.\nIf $ A_1A_2 + A_1A_{11} $ can be expressed as $ \\frac{m\\sqrt{n} - p}{q} $ for positive integers $ m, n, p, q $ with $ n $ squarefree and no prime divides all of $ m, p, q$, find $ m + n + p + q $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n\\[\na_i=A_1A_i\\qquad (i=2,\\dots ,11),\\qquad s_i=A_iA_{i+1}\\qquad (i=2,\\dots ,10).\n\\]\n\nFor each triangle \\(A_iA_1A_{i+1}\\;(2\\le i\\le10)\\)\n\n* \\(\\displaystyle \\text{Area}=1\\),\n* \\(\\displaystyle\\cos\\angle A_iA_1A_{i+1}= \\frac{12}{13}\\).\n\n--------------------------------------------------------------------\n### 1.  Product of the two sides from \\(A_1\\)\n\nWith \\(\\theta=\\angle A_iA_1A_{i+1}\\) we have  \n\n\\[\n\\sin\\theta=\\sqrt{1-\\cos ^2\\theta}= \\frac{5}{13}.\n\\]\n\nThe area of \\(\\triangle A_iA_1A_{i+1}\\) is  \n\n\\[\n\\frac12 a_i a_{i+1}\\sin\\theta =1\n\\Longrightarrow a_i a_{i+1}= \\frac{2}{\\sin\\theta}= \\frac{2}{5/13}= \\frac{26}{5}\\equiv c .\n\\tag{1}\n\\]\n\nHence for all \\(i\\)\n\n\\[\na_i a_{i+1}=c=\\frac{26}{5}.\n\\]\n\n--------------------------------------------------------------------\n### 2.  Length of the side \\(A_iA_{i+1}\\)\n\nApply the law of cosines in \\(\\triangle A_iA_1A_{i+1}\\):\n\n\\[\ns_i^2=a_i^{\\,2}+a_{i+1}^{\\,2}-2a_i a_{i+1}\\cos\\theta\n      =a_i^{\\,2}+a_{i+1}^{\\,2}-2c\\Bigl(\\frac{12}{13}\\Bigr).\n\\]\n\nBecause \\(2c\\frac{12}{13}= \\frac{624}{65}= \\frac{48}{5}\\),\n\n\\[\ns_i^{\\,2}=a_i^{\\,2}+a_{i+1}^{\\,2}-\\frac{48}{5}. \\tag{2}\n\\]\n\n--------------------------------------------------------------------\n### 3.  The alternating pattern of the radii\n\nFrom (1) we have \\(a_{i+1}=c/a_i\\). Consequently  \n\n\\[\na_{i+2}=c/a_{i+1}=c/(c/a_i)=a_i .\n\\]\n\nThus  \n\n\\[\na_{2}=a_{4}=a_{6}=a_{8}=a_{10}\\equiv x, \\qquad \na_{3}=a_{5}=a_{7}=a_{9}=a_{11}\\equiv \\frac{c}{x}.\n\\]\n\nAll sides \\(s_i\\;(i=2,\\dots ,10)\\) are equal, because each uses the\npair \\((x,\\;c/x)\\) in (2).  Set  \n\n\\[\nS^2=x^{2}+\\Bigl(\\frac{c}{x}\\Bigr)^2-\\frac{48}{5}.\n\\tag{3}\n\\]\n\n--------------------------------------------------------------------\n### 4.  Express everything via \\(t=x+\\dfrac{c}{x}\\)\n\nDefine  \n\n\\[\nt=x+\\frac{c}{x}=a_2+a_{11}.\n\\]\n\nThen  \n\n\\[\nx^{2}+\\Bigl(\\frac{c}{x}\\Bigr)^2=t^{2}-2c .\n\\]\n\nInsert this into (3):\n\n\\[\nS^{2}=t^{2}-2c-\\frac{48}{5}=t^{2}-(2c+\\frac{48}{5}).\n\\]\n\nSince \\(c=\\dfrac{26}{5}\\),\n\n\\[\n2c+\\frac{48}{5}= \\frac{52}{5}+\\frac{48}{5}=20.\n\\]\n\nHence  \n\n\\[\nS^{2}=t^{2}-20,\\qquad S=\\sqrt{t^{2}-20}. \\tag{4}\n\\]\n\n--------------------------------------------------------------------\n### 5.  Use the perimeter\n\nThe perimeter of the 11\u2011gon is  \n\n\\[\na_2+a_{11}+ \\sum_{i=2}^{10}s_i = t+9S =20.\n\\]\n\nSubstituting (4):\n\n\\[\nt+9\\sqrt{t^{2}-20}=20.\n\\]\n\nIsolate the radical and square:\n\n\\[\n9\\sqrt{t^{2}-20}=20-t \\quad\\Longrightarrow\\quad \n81(t^{2}-20)=(20-t)^{2}.\n\\]\n\nSimplifying:\n\n\\[\n80t^{2}+40t-2020=0\n\\Longrightarrow 4t^{2}+2t-101=0.\n\\]\n\nSolve for \\(t\\):\n\n\\[\nt=\\frac{-2\\pm\\sqrt{4+1616}}{8}\n   =\\frac{-2\\pm 18\\sqrt5}{8}\n   =\\frac{-1\\pm 9\\sqrt5}{4}.\n\\]\n\nSince \\(t&gt;0\\), we take the plus sign:\n\n\\[\n\\boxed{t=\\frac{9\\sqrt5-1}{4}}.\n\\]\n\nThus  \n\n\\[\nA_1A_2+A_1A_{11}= \\frac{9\\sqrt5-1}{4}\n            =\\frac{m\\sqrt n-p}{q},\n\\]\nwith \\(m=9,\\;n=5,\\;p=1,\\;q=4\\).\n\n--------------------------------------------------------------------\n### 6.  Compute \\(m+n+p+q\\)\n\n\\[\nm+n+p+q = 9+5+1+4 = 19.\n\\]\n\n\\[\n\\boxed{19}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 19</p>\n<p>Extracted Answer: 19</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThe 9 members of a baseball team went to an ice cream parlor after their game. Each player had a singlescoop cone of chocolate, vanilla, or strawberry ice cream. At least one player chose each flavor, and the number of players who chose chocolate was greater than the number of players who chose vanilla, which was greater than the number of players who chose strawberry. Let $N$ be the number of different assignments of flavors to players that meet these conditions. Find the remainder when $N$ is divided by 1000.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>The nine players are distinct.  Let  \n\n\\[\nc=\\#\\text{chocolate},\\qquad v=\\#\\text{vanilla},\\qquad s=\\#\\text{strawberry}\n\\]\n\nwith  \n\n\\[\nc+v+s=9,\\qquad c&gt;v&gt;s\\ge 1 .\n\\]\n\n---\n\n### 1.  Find all possible triples \\((c,v,s)\\)\n\nSince \\(c&gt;v&gt;s\\),\n\n\\[\nc\\ge v+1,\\qquad v\\ge s+1.\n\\]\n\nWrite \\(v=s+d_2\\) and \\(c=v+d_1\\) where \\(d_1,d_2\\ge 1\\).  \nThen  \n\n\\[\nc+v+s=(s+d_2+d_1)+(s+d_2)+s=3s+2d_2+d_1=9 .\n\\]\n\nBecause \\(s\\ge1\\), we have \\(3s\\le 9\\Rightarrow s=1,2,3\\).\n\n* **\\(s=1\\):** \\(2d_2+d_1=6\\).  \n  \\(d_2=1\\Rightarrow d_1=4\\) \u2192 \\((c,v,s)=(6,2,1)\\).  \n  \\(d_2=2\\Rightarrow d_1=2\\) \u2192 \\((c,v,s)=(5,3,1)\\).\n\n* **\\(s=2\\):** \\(2d_2+d_1=3\\).  \n  \\(d_2=1\\Rightarrow d_1=1\\) \u2192 \\((c,v,s)=(4,3,2)\\).\n\n* **\\(s=3\\):** \\(2d_2+d_1=0\\) \u2013 impossible with \\(d_1,d_2\\ge1\\).\n\nThus the only feasible triples are  \n\n\\[\n(6,2,1),\\;(5,3,1),\\;(4,3,2).\n\\]\n\n---\n\n### 2.  Count assignments for each triple\n\nFor a given \\((c,v,s)\\) the number of ways to assign the flavors to the 9 distinct players is the multinomial coefficient  \n\n\\[\n\\frac{9!}{c!\\,v!\\,s!}.\n\\]\n\n\\[\n\\begin{aligned}\n(6,2,1):\\;&amp;\\frac{9!}{6!\\,2!\\,1!}= \\frac{362880}{720\\cdot2}=252,\\\\[2mm]\n(5,3,1):\\;&amp;\\frac{9!}{5!\\,3!\\,1!}= \\frac{362880}{120\\cdot6}=504,\\\\[2mm]\n(4,3,2):\\;&amp;\\frac{9!}{4!\\,3!\\,2!}= \\frac{362880}{24\\cdot6\\cdot2}=1260.\n\\end{aligned}\n\\]\n\n---\n\n### 3.  Total number of assignments\n\n\\[\nN = 252+504+1260 = 2016.\n\\]\n\n---\n\n### 4.  Remainder modulo \\(1000\\)\n\n\\[\n2016 \\equiv 16 \\pmod{1000}.\n\\]\n\n\\[\n\\boxed{16}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 16</p>\n<p>Extracted Answer: 16</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nFind the number of ordered pairs $(x,y)$, where both $x$ and $y$ are integers between $-100$ and $100$, inclusive, such that $12x^{2}-xy-6y^{2}=0$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>The equation  \n\n\\[\n12x^{2}-xy-6y^{2}=0\n\\]\n\nis a homogeneous quadratic form.  \nFactor it over the integers:\n\n\\[\n12x^{2}-xy-6y^{2}= (3x+2y)(4x-3y).\n\\]\n\nIndeed  \n\n\\[\n(3x+2y)(4x-3y)=12x^{2}-9xy+8xy-6y^{2}=12x^{2}-xy-6y^{2}.\n\\]\n\nHence a pair \\((x,y)\\) of integers satisfies the equation iff\n\n\\[\n3x+2y=0\\qquad\\text{or}\\qquad 4x-3y=0 .\n\\]\n\n---\n\n### 1. Solutions of \\(3x+2y=0\\)\n\n\\[\n3x+2y=0 \\;\\Longrightarrow\\; y=-\\frac{3}{2}x .\n\\]\n\nFor \\(y\\) to be an integer, \\(x\\) must be even: write \\(x=2k\\). Then  \n\n\\[\n(x,y)=(2k,-3k),\\qquad k\\in\\mathbb Z .\n\\]\n\nBoth coordinates must lie in \\([-100,100]\\):\n\n\\[\n-100\\le 2k\\le 100\\;\\Longrightarrow\\;-50\\le k\\le 50,\\\\\n-100\\le -3k\\le 100\\;\\Longrightarrow\\;-33\\le k\\le 33.\n\\]\n\nThus \\(k=-33,-32,\\dots ,33\\); there are  \n\n\\[\n33-(-33)+1 = 67\n\\]\n\ninteger solutions on this line.\n\n---\n\n### 2. Solutions of \\(4x-3y=0\\)\n\n\\[\n4x-3y=0 \\;\\Longrightarrow\\; y=\\frac{4}{3}x .\n\\]\n\nFor \\(y\\) to be an integer, \\(x\\) must be a multiple of \\(3\\): put \\(x=3t\\). Then  \n\n\\[\n(x,y)=(3t,4t),\\qquad t\\in\\mathbb Z .\n\\]\n\nAgain impose the bounds:\n\n\\[\n-100\\le 3t\\le 100\\;\\Longrightarrow\\;-33\\le t\\le 33,\\\\\n-100\\le 4t\\le 100\\;\\Longrightarrow\\;-25\\le t\\le 25.\n\\]\n\nThus \\(t=-25,-24,\\dots ,25\\); the number of solutions here is  \n\n\\[\n25-(-25)+1 = 51.\n\\]\n\n---\n\n### 3. Intersection of the two lines\n\nBoth equations hold simultaneously only at the origin:\n\n\\[\n3x+2y=0,\\;4x-3y=0 \\Longrightarrow (x,y)=(0,0).\n\\]\n\nThis point has been counted in both previous totals, so we subtract it once.\n\n---\n\n### 4. Total number of ordered pairs\n\n\\[\n\\#\\text{solutions}=67+51-1=117.\n\\]\n\n\\[\n\\boxed{117}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 117</p>\n<p>Extracted Answer: 117</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nAn isosceles trapezoid has an inscribed circle tangent to each of its four sides. The radius of the circle is 3, and the area of the trapezoid is 72. Let the parallel sides of the trapezoid have lengths $r$ and $s$, with $r \\neq s$. Find $r^{2}+s^{2}$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let the trapezoid be \\(ABCD\\) with \\(AB\\parallel CD\\) and  \n\n\\[\nAB=s ,\\qquad CD=r ,\\qquad AD=BC=L \\;( \\text{isosceles}).\n\\]\n\nThe incircle has radius \\(R=3\\) and the area is \\(72\\).\n\n---\n\n### 1.  Semiperimeter\n\nFor any tangential quadrilateral (one with an incircle)\n\n\\[\n\\text{Area}=R\\cdot(\\text{semiperimeter}).\n\\]\n\nHence  \n\n\\[\n72=3\\cdot s_{\\!p}\\quad\\Longrightarrow\\quad s_{\\!p}=24 .\n\\]\n\nThus the perimeter is  \n\n\\[\n2s_{\\!p}=48\\quad\\Longrightarrow\\quad r+s+2L=48. \\tag{1}\n\\]\n\n---\n\n### 2.  Tangential condition\n\nIn a tangential quadrilateral the sums of opposite sides are equal:\n\n\\[\nAB+CD = AD+BC\\quad\\Longrightarrow\\quad r+s = 2L. \\tag{2}\n\\]\n\nFrom (1) and (2),\n\n\\[\n2(r+s)=48 \\;\\Longrightarrow\\; r+s=24,\\qquad\n2L=r+s=24\\;\\Longrightarrow\\; L=12.\n\\]\n\n---\n\n### 3.  Height\n\nThe incircle touches both parallel sides, so the distance between the bases equals twice the radius:\n\n\\[\nh=2R=6.\n\\]\n\n(Alternatively, \\(\\displaystyle 72=\\tfrac12(r+s)h\\) with \\(r+s=24\\) also gives \\(h=6\\).)\n\n---\n\n### 4.  Relating the bases\n\nPlace the trapezoid with its symmetry axis on the \\(y\\)-axis; the bases are horizontal.\nThe horizontal half\u2011difference of the bases is \\(\\dfrac{s-r}{2}\\).\nHence the leg length satisfies\n\n\\[\nL^{2}= \\left(\\frac{s-r}{2}\\right)^{2}+h^{2}.\n\\]\n\nUsing \\(L=12,\\;h=6\\),\n\n\\[\n12^{2}= \\frac{(s-r)^{2}}{4}+6^{2}\n\\quad\\Longrightarrow\\quad\n\\frac{(s-r)^{2}}{4}=108\n\\quad\\Longrightarrow\\quad\ns-r=12\\sqrt3. \\tag{3}\n\\]\n\n---\n\n### 5.  Solving for \\(r\\) and \\(s\\)\n\n\\[\n\\begin{cases}\nr+s=24,\\\\[2pt]\ns-r=12\\sqrt3,\n\\end{cases}\n\\qquad\\Longrightarrow\\qquad\n\\begin{aligned}\ns&amp;=\\frac{24+12\\sqrt3}{2}=12+6\\sqrt3,\\\\\nr&amp;=\\frac{24-12\\sqrt3}{2}=12-6\\sqrt3.\n\\end{aligned}\n\\]\n\n---\n\n### 6.  Required sum of squares\n\n\\[\n\\begin{aligned}\nr^{2}+s^{2}\n&amp;=(12-6\\sqrt3)^{2}+(12+6\\sqrt3)^{2}\\\\\n&amp;= \\bigl(144-144\\sqrt3+108\\bigr)+\\bigl(144+144\\sqrt3+108\\bigr)\\\\\n&amp;= 504.\n\\end{aligned}\n\\]\n\n\\[\n\\boxed{504}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 504</p>\n<p>Extracted Answer: 504</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $ \\triangle ABC $ be a right triangle with $ \\angle A = 90^\\circ $ and $ BC = 38 $. There exist points $ K $ and $ L $ inside the triangle such that $ AK = AL = BK = CL = KL = 14. $ The area of the quadrilateral $ BKLC $ can be expressed as $ n \\sqrt{3} $ for some positive integer $ n $. Find $ n $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n* \\(A=(0,0)\\),  \n* \\(B=(u,0)\\) on the \\(x\\)-axis,  \n* \\(C=(0,v)\\) on the \\(y\\)-axis.  \n\nSince \\(\\angle A=90^{\\circ}\\), \\(BC=38\\) gives  \n\n\\[\nu^{2}+v^{2}=38^{2}=1444\\tag{1}\n\\]\n\n---\n\n### 1.  The equilateral triangle \\(AKL\\)\n\nThe conditions  \n\n\\[\nAK=AL=KL=14\n\\]\n\nshow that \\(\\triangle AKL\\) is equilateral.  \nLet the direction of \\(\\overrightarrow{AK}\\) form an angle \\(\\theta\\) with the\npositive \\(x\\)-axis. Then\n\n\\[\nK=(14\\cos\\theta,\\;14\\sin\\theta),\\qquad \nL=(14\\cos(\\theta+60^\\circ),\\;14\\sin(\\theta+60^\\circ)).\\tag{2}\n\\]\n\n---\n\n### 2.  Using \\(BK=14\\) and \\(CL=14\\)\n\n\\[\nBK^{2}= (u-14\\cos\\theta)^2+(14\\sin\\theta)^2=14^{2}\n\\]\n\n\\[\n\\Longrightarrow\\; u=28\\cos\\theta.\\tag{3}\n\\]\n\nSimilarly  \n\n\\[\nCL^{2}= (14\\cos(\\theta+60^\\circ))^{2}+(v-14\\sin(\\theta+60^\\circ))^{2}=14^{2}\n\\]\n\n\\[\n\\Longrightarrow\\; v=28\\sin(\\theta+60^\\circ).\\tag{4}\n\\]\n\n---\n\n### 3.  Determining \\(\\theta\\)\n\nInsert (3) and (4) into (1):\n\n\\[\n(28\\cos\\theta)^{2}+(28\\sin(\\theta+60^\\circ))^{2}=1444\n\\]\n\\[\n\\Longrightarrow\\;\\cos^{2}\\theta+\\sin^{2}(\\theta+60^\\circ)=\\frac{361}{196}.\n\\]\n\nUsing \\(\\sin(\\theta+60^\\circ)=\\tfrac12\\sin\\theta+\\tfrac{\\sqrt3}{2}\\cos\\theta\\),\nthe equation reduces to  \n\n\\[\n6\\cos^{2}\\theta+2\\sqrt3\\sin\\theta\\cos\\theta= \\frac{312}{49}.\n\\]\n\nSolving gives \\(\\cos\\theta=\\frac{13}{14}\\) (the other root gives the same\ntriangle with the legs interchanged).  \n\nHence  \n\n\\[\nu=28\\cos\\theta=28\\cdot\\frac{13}{14}=26,\\qquad\nv=28\\sin(\\theta+60^\\circ)=28\\cdot\\frac{4\\sqrt3}{7}=16\\sqrt3 .\n\\]\n\nThus  \n\n\\[\nAB=26,\\qquad AC=16\\sqrt3,\\qquad BC=38.\n\\]\n\nFrom (2) we obtain the coordinates of the interior points\n\n\\[\nK=(13,\\;3\\sqrt3),\\qquad L=(2,\\;8\\sqrt3).\n\\]\n\n---\n\n### 4.  Area of \\(BKLC\\)\n\nUse the shoelace formula for the polygon \\(B(26,0),K(13,3\\sqrt3),L(2,8\\sqrt3),C(0,16\\sqrt3)\\):\n\n\\[\n\\begin{aligned}\nS_1&amp;=26\\cdot3\\sqrt3+13\\cdot8\\sqrt3+2\\cdot16\\sqrt3+0\\cdot0=214\\sqrt3,\\\\\nS_2&amp;=0\\cdot13+3\\sqrt3\\cdot2+8\\sqrt3\\cdot0+16\\sqrt3\\cdot26=422\\sqrt3.\n\\end{aligned}\n\\]\n\n\\[\n\\text{Area}=\\frac12|S_2-S_1|\n          =\\frac12(422-214)\\sqrt3\n          =104\\sqrt3 .\n\\]\n\nTherefore the area can be written as \\(n\\sqrt3\\) with  \n\n\\[\n\\boxed{n=104}.\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 104</p>\n<p>Extracted Answer: None</p>\n<p>Score: 0.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThere are $8!=40320$ eight-digit positive integers that use each of the digits $1,2,3,4,5,6,7,8$ exactly once. Let $N$ be the number of these integers that are divisible by 22. Find the difference between $N$ and 2025.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>For an eight\u2011digit number formed by a permutation of  \n\n\\[\n\\{1,2,3,4,5,6,7,8\\}\n\\]\n\nlet  \n\n\\[\na_1a_2a_3a_4a_5a_6a_7a_8\n\\]\n\nbe its digits (left to right).  \nA number is divisible by \\(22\\iff\\) it is divisible by \\(2\\) and by \\(11\\).\n\n---\n\n### 1.  Divisibility by 2  \n\nThe last digit \\(a_8\\) must be even, so \\(a_8\\in\\{2,4,6,8\\}\\).\n\n---\n\n### 2.  Divisibility by 11  \n\nFor an 8\u2011digit number the rule for 11 is  \n\n\\[\n(a_1+a_3+a_5+a_7)-(a_2+a_4+a_6+a_8)\\equiv 0\\pmod{11}.\n\\]\n\nSince the total sum of the digits is  \n\n\\[\n1+2+\\cdots+8 = 36,\n\\]\n\nlet  \n\n\\[\nS_{\\text{odd}}=a_1+a_3+a_5+a_7,\\qquad \nS_{\\text{even}}=a_2+a_4+a_6+a_8 .\n\\]\n\nThen \\(S_{\\text{odd}}+S_{\\text{even}}=36\\) and the condition gives  \n\n\\[\nS_{\\text{odd}}-S_{\\text{even}}\\equiv0\\pmod{11}.\n\\]\n\nThe only possible values for \\(S_{\\text{odd}}-S_{\\text{even}}\\) are \\(-22,0,22\\);   \n\\(-22\\) would give \\(S_{\\text{odd}}=7\\) and \\(22\\) would give \\(S_{\\text{odd}}=29\\), both impossible because a sum of four distinct digits from \\(\\{1,\\dots ,8\\}\\) cannot be smaller than \\(10\\) nor larger than \\(26\\).  \nHence\n\n\\[\nS_{\\text{odd}} = S_{\\text{even}} = 18 .\n\\]\n\nThus the four digits in the odd positions must sum to \\(18\\); the same holds for the even positions.\n\n---\n\n### 3.  Choosing the four digits for the odd positions  \n\nWe need 4\u2011element subsets of \\(\\{1,\\dots ,8\\}\\) whose sum is \\(18\\).  \nA quick enumeration gives the eight subsets\n\n\\[\n\\begin{aligned}\n&amp;\\{1,2,7,8\\},\\{1,3,6,8\\},\\{1,4,5,8\\},\\{1,4,6,7\\},\\\\\n&amp;\\{2,3,5,8\\},\\{2,3,6,7\\},\\{2,4,5,7\\},\\{3,4,5,6\\}.\n\\end{aligned}\n\\]\n\nEach contains exactly two even digits (the set \\(\\{2,4,6,8\\}\\)) and two odd digits.  \nHence every admissible odd\u2011position set has **2 even digits**.\n\nLet a chosen subset be \\(S\\) (the odd\u2011position digits) and its complement \\(S^c\\) (the even\u2011position digits).\n\n---\n\n### 4.  Arranging the digits  \n\n* The four digits of \\(S\\) can be placed in the odd positions \\((1,3,5,7)\\) in \\(4! = 24\\) ways.  \n* The four digits of \\(S^c\\) must fill the even positions \\((2,4,6,8)\\) with the extra requirement that the last digit \\(a_8\\) be even.  \n  Since \\(S^c\\) contains exactly \\(2\\) even digits, we have  \n\n\\[\n\\text{choices for }a_8 = 2,\\qquad\n\\text{arrangements of the remaining three even\u2011position digits}=3! = 6 .\n\\]\n\nThus for each set \\(S\\)\n\n\\[\n\\#\\text{numbers}=4!\\times(2\\times3!) = 24\\times12 = 288.\n\\]\n\n---\n\n### 5.  Total number \\(N\\)\n\nThere are \\(8\\) possible subsets \\(S\\); consequently\n\n\\[\nN = 8 \\times 288 = 2304 .\n\\]\n\n---\n\n### 6.  Required difference\n\n\\[\nN-2025 = 2304-2025 = 279 .\n\\]\n\n\\[\n\\boxed{279}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 279</p>\n<p>Extracted Answer: 279</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $k$ be real numbers such that the system $|25+20i-z|=5$ and $|z-4-k|=|z-3i-k|$ has exactly one complex solution $z$. The sum of all possible values of $k$ can be written as $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$. Here $i=\\sqrt{-1}$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n\\[\nC=25+20i,\\qquad r=5 ,\n\\]\n\nso  \n\n\\[\n|C-z|=5\n\\]\n\nis the circle with centre \\(C\\) and radius \\(5\\).\n\nThe second condition  \n\n\\[\n|z-4-k|=|z-3i-k|\n\\]\n\nmeans that \\(z\\) is equally distant from the points  \n\n\\[\nP_1=4+k\\quad(\\text{on the real axis}), \\qquad   \nP_2=k+3i .\n\\]\n\nHence the locus of \\(z\\) is the perpendicular bisector of the segment \\(\\overline{P_1P_2}\\); this is a straight line.\n\n---\n\n### 1. Equation of the line\n\nWrite \\(z=x+yi\\).  \n\n\\[\n(x-(4+k))^2+y^2=(x-k)^2+(y-3)^2 .\n\\]\n\nExpanding and simplifying gives  \n\n\\[\n-8(x-k)+16=-6y+9,\n\\]\n\n\\[\n-8x+8k+6y+7=0 .\n\\]\n\nThus the line \\(L(k)\\) is  \n\n\\[\n-8x+6y+8k+7=0 \\qquad\\text{or}\\qquad 8x-6y=8k+7 .\n\\]\n\nAll such lines have slope \\(\\dfrac{4}{3}\\); they are a family of parallel lines depending on \\(k\\).\n\n---\n\n### 2. Tangency condition\n\nThe system has exactly one solution precisely when the line \\(L(k)\\) is tangent to the circle \\(|z-C|=5\\).  \n\nFor a line \\(Ax+By+C=0\\) the distance from a point \\((x_0,y_0)\\) is  \n\n\\[\nd=\\frac{|Ax_0+By_0+C|}{\\sqrt{A^2+B^2}} .\n\\]\n\nHere \\(A=-8,\\;B=6,\\;C=8k+7\\) and the centre of the circle is \\((25,20)\\). Hence\n\n\\[\nd(k)=\\frac{\\bigl|-8\\cdot25+6\\cdot20+(8k+7)\\bigr|}{\\sqrt{(-8)^2+6^2}}\n      =\\frac{|8k-73|}{10}.\n\\]\n\nTangency requires \\(d(k)=r=5\\):\n\n\\[\n\\frac{|8k-73|}{10}=5\\quad\\Longrightarrow\\quad|8k-73|=50 .\n\\]\n\nThus  \n\n\\[\n8k-73=50\\quad\\text{or}\\quad8k-73=-50,\n\\]\n\n\\[\nk=\\frac{123}{8},\\qquad k=\\frac{23}{8}.\n\\]\n\nBoth values make the line tangent, giving exactly one intersection point with the circle.\n\n---\n\n### 3. Sum of the possible \\(k\\)\n\n\\[\n\\frac{123}{8}+\\frac{23}{8}= \\frac{146}{8}= \\frac{73}{4}.\n\\]\n\nWrite \\(\\dfrac{73}{4}\\) as \\(\\dfrac{m}{n}\\) with \\(\\gcd(m,n)=1\\); then \\(m=73,\\;n=4\\).\n\n\\[\nm+n = 73+4 = 77.\n\\]\n\n\\[\n\\boxed{77}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 77</p>\n<p>Extracted Answer: 77</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThe twelve letters $A,B,C,D,E,F,G,H,I,J,K$, and $L$ are randomly grouped into six pairs of letters. The two letters in each pair are placed next to each other in alphabetical order to form six two-letter words, and those six words are listed alphabetically. For example, a possible result is $AB,CJ,DG,EK,FL,HI$. The probability that the last word listed contains $G$ is $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let the letters be  \n\n\\[\nA&lt;B&lt;C&lt;D&lt;E&lt;F&lt;G&lt;H&lt;I&lt;J&lt;K&lt;L .\n\\]\n\nIn a random pairing each pair is written with its smaller letter first, so a\npair \\(\\{x,y\\}\\;(x&lt;y)\\) becomes the word \\(xy\\).\nThe six words are then listed alphabetically; the last word is the\nlexicographically largest of the six two\u2011letter words.\n\nBecause the first letters of the six words are all different (each letter can\nappear as the smaller element of at most one pair), the largest word is the\npair whose **smaller** element is the largest among the six smaller elements.\nHence the last word contains \\(G\\) precisely when the pair containing \\(G\\)\nhas the largest smaller element.\n\n---\n\n### 1.  Choose the partner of \\(G\\)\n\n\\(G\\) can be paired with any of the other 11 letters, each with probability\n\\(\\frac1{11}\\).\n\n*If \\(G\\) is paired with a letter larger than \\(G\\)*  \n(let the partner be \\(X\\in\\{H,I,J,K,L\\}\\)).  \nThen the smaller element of the \\(G\\!-\\!X\\) pair is \\(G\\).\n\nThe remaining 10 letters consist of  \n\n- 6 letters \\(\\{A,B,C,D,E,F\\}\\) smaller than \\(G\\) (call them \u201clow\u201d),  \n- 4 letters among \\(\\{H,I,J,K,L\\}\\setminus\\{X\\}\\) larger than \\(G\\) (call them \u201chigh\u201d).\n\nFor the pair \\(G\\!-\\!X\\) to have the largest smaller element, no other pair\nmay have a smaller element \\(\\ge G\\); i.e. no \u201chigh\u201d letter may be the smaller\nletter of its pair.  Hence each high letter must be matched with a low\nletter.  \n\nNumber of matchings of the 10 remaining letters with no high\u2013high pair:\n\n\\[\n\\binom{6}{4}\\,4!\\;(=15\\cdot24)=360 .\n\\]\n\nTotal matchings of 10 letters: \\((10-1)!!=945\\).\nThus\n\n\\[\nP(\\text{lexicographically largest pair }|\\,G\\!-\\!X,\\;X&gt;G)=\\frac{360}{945}\n=\\frac{8}{21}.\n\\]\n\nSince there are 5 possible partners larger than \\(G\\),\n\n\\[\n\\sum_{X&gt;G}\\frac1{11}\\cdot\\frac{8}{21}=5\\cdot\\frac{1}{11}\\cdot\\frac{8}{21}\n=\\frac{40}{231}.\n\\]\n\n*If \\(G\\) is paired with a letter smaller than \\(G\\)*  \nthe only possible partner is \\(F\\); for any smaller partner there are fewer\nthan five letters below it, making it impossible for its pair to have the\nlargest smaller element.\n\nWhen \\(G\\) is paired with \\(F\\), the smaller element of the pair is \\(F\\).\nThe other 10 letters are  \n\n\\[\n\\{A,B,C,D,E\\}\\ (\\text{low})\\quad\\text{and}\\quad\\{H,I,J,K,L\\}\\ (\\text{high}).\n\\]\n\nAll five high letters must be paired with the five low letters; otherwise a\nhigh letter would become a smaller element.  The number of such matchings is\n\\(5!=120\\).  Hence\n\n\\[\nP(\\text{largest pair }|\\,G\\!-\\!F)=\\frac{120}{945}=\\frac{8}{63},\n\\]\nand the contribution is \\(\\displaystyle\\frac1{11}\\cdot\\frac{8}{63}\n= \\frac{8}{693}\\).\n\nNo other partner of \\(G\\) can work, so the total probability that the last\nword contains \\(G\\) is\n\n\\[\n\\frac{40}{231}+\\frac{8}{693}\n=\\frac{120}{693}+\\frac{8}{693}\n=\\frac{128}{693}.\n\\]\n\nThe fraction \\(\\frac{128}{693}\\) is already in lowest terms.  \nThus \\(m=128,\\ n=693\\) and\n\n\\[\nm+n = 128+693 = 821.\n\\]\n\n\\[\n\\boxed{821}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 821</p>\n<p>Extracted Answer: 821</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nOn $\\triangle ABC$ points $A,D,E$, and $B$ lie that order on side $\\overline{AB}$ with $AD=4, DE=16$, and $EB=8$. Points $A,F,G$, and $C$ lie in that order on side $\\overline{AC}$ with $AF=13, FG=52$, and $GC=26$. Let $M$ be the reflection of $D$ through $F$, and let $N$ be the reflection of $G$ through $E$. Quadrilateral $DEGF$ has area 288. Find the area of heptagon $AFNBCEM$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>**Solution**\n\n--------------------------------------------------------------------\n\n### 1.  The ratios on the two sides  \n\n\\[\nAB=AD+DE+EB=4+16+8=28,\\qquad \nAC=AF+FG+GC=13+52+26=91 .\n\\]\n\n\\[\n\\frac{AD}{AB}=\\frac{4}{28}=\\frac17,\\qquad \n\\frac{AF}{AC}= \\frac{13}{91}= \\frac17 .\n\\]\n\nHence  \n\n\\[\n\\frac{AD}{AB}= \\frac{AF}{AC}= \\frac17\\qquad\\Longrightarrow\\qquad \nDF\\parallel BC .\n\\]\n\nSimilarly  \n\n\\[\n\\frac{AE}{AB}= \\frac{20}{28}= \\frac57,\\qquad \n\\frac{AG}{AC}= \\frac{65}{91}= \\frac57 ,\n\\]\n\nso  \n\n\\[\n\\frac{AE}{AB}= \\frac{AG}{AC}= \\frac57\\qquad\\Longrightarrow\\qquad \nEG\\parallel BC .\n\\]\n\nLet  \n\n\\[\np=\\frac17,\\qquad q=\\frac57 .\n\\]\n\n--------------------------------------------------------------------\n\n### 2.  Area of \\(\\triangle ABC\\)\n\nBecause \\(DF\\parallel EG\\parallel BC\\), the quadrilateral \\(DEGF\\) is the\nregion of \\(\\triangle ABC\\) between the two lines through \\(D\\) and \\(E\\)\nparallel to \\(BC\\).  \n\nTriangles \\(ADF\\) and \\(AEG\\) are similar to \\(\\triangle ABC\\) with similarity\nratios \\(p\\) and \\(q\\) respectively, so\n\n\\[\n[ADF]=p^{2}[ABC],\\qquad[AEG]=q^{2}[ABC].\n\\]\n\nHence  \n\n\\[\n[DEGF]=[AEG]-[ADF]=(q^{2}-p^{2})[ABC]\n        =\\Bigl(\\frac{5^{2}}{7^{2}}-\\frac{1^{2}}{7^{2}}\\Bigr)[ABC]\n        =\\frac{24}{49}[ABC].\n\\]\n\nGiven \\([DEGF]=288\\),\n\n\\[\n[ABC]=288\\cdot\\frac{49}{24}=12\\cdot 49 =\\boxed{588}.\n\\]\n\n--------------------------------------------------------------------\n\n### 3.  Coordinates\n\nPlace  \n\n\\[\nA=(0,0),\\qquad B=(28,0),\\qquad C=(c,\\,42)\n\\]\n\n(the height is \\(42\\) because \\([ABC]=\\frac12\\cdot28\\cdot42=588\\)).  \nUsing the ratios \\(p,q\\),\n\n\\[\n\\begin{aligned}\nD &amp;=pB=(4,0),                   &amp;E&amp;=qB=(20,0),\\\\[2mm]\nF &amp;=pC=\\Bigl(\\frac{c}{7},6\\Bigr), &amp;\nG &amp;=qC=\\Bigl(\\frac{5c}{7},30\\Bigr).\n\\end{aligned}\n\\]\n\nReflections give  \n\n\\[\nM=2F-D=\\Bigl(\\frac{2c}{7}-4,\\;12\\Bigr),\\qquad \nN=2E-G=\\Bigl(40-\\frac{5c}{7},\\;-30\\Bigr).\n\\]\n\n--------------------------------------------------------------------\n\n### 4.  Area of the heptagon \\(AFNBCEM\\)\n\nList the vertices in order:\n\n\\[\n\\begin{array}{c|c}\n\\text{Vertex}&amp;(x,y)\\\\ \\hline\nA&amp;(0,0)\\\\\nF&amp;\\bigl(\\frac{c}{7},6\\bigr)\\\\\nN&amp;\\bigl(40-\\frac{5c}{7},-30\\bigr)\\\\\nB&amp;(28,0)\\\\\nC&amp;(c,42)\\\\\nE&amp;(20,0)\\\\\nM&amp;\\bigl(\\frac{2c}{7}-4,12\\bigr)\n\\end{array}\n\\]\n\nApply the Shoelace formula.  The sum  \n\n\\[\n\\sum_{i=1}^{7}\\bigl(x_i y_{i+1}-y_i x_{i+1}\\bigr)\n\\]  \n\n(with \\(x_8=x_1,\\;y_8=y_1\\)) simplifies dramatically:\n\n\\[\n\\begin{aligned}\n&amp;0\\\\\n&amp;\\;-\\;240\\\\\n&amp;\\;+\\;840\\\\\n&amp;\\;+\\;1176\\\\\n&amp;\\;-\\;840\\\\\n&amp;\\;+\\;240\\\\\n&amp;0\n\\end{aligned}\n\\qquad =\\;1176 .\n\\]\n\nThus\n\n\\[\n[AFNBCEM]=\\frac12\\cdot1176=588 .\n\\]\n\nThe result does **not** depend on the unknown coordinate \\(c\\); the\ncancellation occurs because the vectors \\(DF\\) and \\(EG\\) are parallel to\n\\(BC\\).\n\n--------------------------------------------------------------------\n\n### 5.  Answer\n\n\\[\n\\boxed{588}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 588</p>\n<p>Extracted Answer: 588</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThe parabola with equation $y=x^{2}-4$ is rotated $60^{\\circ}$ counterclockwise around the origin. The unique point in the fourth quadrant where the original parabola and its image intersect has $y$-coordinate $\\frac{a-\\sqrt{b}}{c}$, where $a$, $b$, and $c$ are positive integers, and $a$ and $c$ are relatively prime. Find $a+b+c$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n\\[\nP:\\;y=x^{2}-4\n\\]\n\nand rotate \\(P\\) \\(60^{\\circ}\\) counter\u2011clockwise about the origin.  \nIf \\((x,y)\\) lies on the rotated curve, then there is a point \\((u,v)\\) on\n\\(P\\) such that  \n\n\\[\n\\begin{pmatrix}x\\\\y\\end{pmatrix}=R\\begin{pmatrix}u\\\\v\\end{pmatrix},\n\\qquad \nR=\\begin{pmatrix}\\tfrac12&amp;-\\tfrac{\\sqrt3}{2}\\\\[2pt]\\tfrac{\\sqrt3}{2}&amp;\\tfrac12\\end{pmatrix}.\n\\]\n\nEquivalently, a point \\((x,y)\\) is on both curves iff\n\n\\[\ny=x^{2}-4 \\qquad\\text{and}\\qquad \nR^{T}\\!\\begin{pmatrix}x\\\\y\\end{pmatrix}\n   =\\begin{pmatrix}x&#39;\\\\y&#39;\\end{pmatrix}\n\\text{ satisfies }y&#39;=(x&#39;)^{2}-4,\n\\]\n\nwhere  \n\n\\[\nR^{T}= \\begin{pmatrix}\\tfrac12&amp;\\tfrac{\\sqrt3}{2}\\\\[2pt]-\\tfrac{\\sqrt3}{2}&amp;\\tfrac12\\end{pmatrix},\n\\quad \nx&#39;=\\frac{x}{2}+\\frac{\\sqrt3\\,y}{2},\\qquad\ny&#39;=-\\frac{\\sqrt3\\,x}{2}+\\frac{y}{2}.\n\\]\n\nUsing \\(y=x^{2}-4\\),\n\n\\[\nx&#39;=\\frac{\\sqrt3 x^{2}+x-4\\sqrt3}{2},\\qquad \ny&#39;=\\frac{x^{2}-\\sqrt3 x-4}{2}.\n\\]\n\nThe condition \\(y&#39;=(x&#39;)^{2}-4\\) yields  \n\n\\[\n\\frac{x^{2}-\\sqrt3 x-4}{2}\n   =\\Bigl(\\frac{\\sqrt3 x^{2}+x-4\\sqrt3}{2}\\Bigr)^{2}-4 .\n\\]\n\nMultiplying by \\(2\\) and simplifying gives the quartic\n\n\\[\n3x^{4}+2\\sqrt3\\,x^{3}-25x^{2}-6\\sqrt3\\,x+40=0.\n\\]\n\nFactor this over \\(\\mathbb{Q}(\\sqrt3)\\):\n\n\\[\n\\begin{aligned}\n3x^{4}+2\\sqrt3\\,x^{3}-25x^{2}-6\\sqrt3\\,x+40\n&amp;=(x^{2}+\\sqrt3\\,x-4)(3x^{2}-\\sqrt3\\,x-10).\n\\end{aligned}\n\\]\n\nHence the possible \\(x\\)-coordinates are the roots of the two quadratics.\n\n\\[\n\\begin{cases}\nx^{2}+\\sqrt3\\,x-4=0 &amp;\\Longrightarrow\n\\displaystyle x=\\frac{-\\sqrt3\\pm\\sqrt{19}}2,\\\\[6pt]\n3x^{2}-\\sqrt3\\,x-10=0 &amp;\\Longrightarrow\n\\displaystyle x=\\frac{\\sqrt3\\pm\\sqrt{123}}6 .\n\\end{cases}\n\\]\n\nWe need a point in the fourth quadrant, i.e. \\(x&gt;0\\) and \\(y=x^{2}-4&lt;0\\).\nOnly  \n\n\\[\nx=\\frac{-\\sqrt3+\\sqrt{19}}2\\;(&gt;0,\\;&lt;2)\n\\]\n\nsatisfies this.  Its \\(y\\)-coordinate is\n\n\\[\n\\begin{aligned}\ny&amp;=x^{2}-4\n   =\\frac{(-\\sqrt3+\\sqrt{19})^{2}}{4}-4\n   =\\frac{22-2\\sqrt{57}}4-4\\\\\n  &amp;=\\frac{11-\\sqrt{57}}2-4\n   =\\frac{3-\\sqrt{57}}2 .\n\\end{aligned}\n\\]\n\nThus  \n\n\\[\ny=\\frac{a-\\sqrt{b}}{c}\\quad\\text{with}\\quad a=3,\\;b=57,\\;c=2,\n\\]\n\nand \\(a\\) and \\(c\\) are relatively prime.  \n\nFinally\n\n\\[\na+b+c=3+57+2=62.\n\\]\n\n\\[\n\\boxed{62}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 62</p>\n<p>Extracted Answer: 62</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThe set of points in 3-dimensional coordinate space that lie in the plane $x+y+z=75$ whose coordinates satisfy the inequalities $x-yz&lt;y-zx&lt;z-xy$ forms three disjoint convex regions. Exactly one of those regions has finite area. The area of this finite region can be expressed in the form $a\\sqrt{b}$, where $a$ and $b$ are positive integers and $b$ is not divisible by the square of any prime. Find $a+b$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>\\[\n\\begin{aligned}\n&amp;x-yz&lt;y-zx&lt;z-xy \\\\\n\\Longleftrightarrow\\;&amp;x-yz&lt;y-zx\\quad\\text{and}\\quad y-zx&lt;z-xy  \\\\\n\\Longleftrightarrow\\;&amp;(x-y)(1+z)&lt;0\\quad\\text{and}\\quad (y-z)(1+x)&lt;0 .\n\\end{aligned}\n\\]\n\nHence  \n\n\\[\n\\begin{cases}\n(x-y)(1+z)&lt;0,\\\\[2pt]\n(y-z)(1+x)&lt;0 .\n\\end{cases}\n\\]\n\nEach product being negative means the two factors have opposite signs.  \nThus we have four possible sign\u2011combinations:\n\n\\[\n\\begin{array}{c|c|c}\n\\text{Case}&amp; (x-y,\\;1+z) &amp; (y-z,\\;1+x)\\\\ \\hline\n\\text{I}&amp; (+,\\; -) &amp; (+,\\; -)\\\\\n\\text{II}&amp; (+,\\; -) &amp; (-,\\; +)\\\\\n\\text{III}&amp; (-,\\; +) &amp; (+,\\; -)\\\\\n\\text{IV}&amp; (-,\\; +) &amp; (-,\\; +)\n\\end{array}\n\\]\n\nTranslating them into linear inequalities:\n\n\\[\n\\begin{aligned}\n\\text{I}&amp;:\\; x&gt;y,\\;z&lt;-1,\\;y&gt;z,\\;x&lt;-1 \\qquad\\text{(impossible since }x+y+z=75)\\\\\n\\text{II}&amp;:\\; x&gt;y,\\;z&lt;-1,\\;y&lt;z,\\;x&gt;-1 \\\\\n\\text{III}&amp;:\\; x&lt;y,\\;z&gt;-1,\\;y&gt;z,\\;x&lt;-1 \\\\\n\\text{IV}&amp;:\\; x&lt;y,\\;z&gt;-1,\\;y&lt;z,\\;x&gt;-1 .\n\\end{aligned}\n\\]\n\nThus three non\u2011empty convex regions arise from cases II,\u202fIII,\u202fIV.\nCases II and III are unbounded, while case\u202fIV gives a bounded region.\n\n---\n\n### Bounded region (case\u202fIV)\n\nCase\u202fIV is equivalent to  \n\n\\[\n-1&lt;x&lt;y&lt;z ,\\qquad x+y+z=75 .\n\\]\n\nThe boundary of this region in the plane \\(x+y+z=75\\) consists of the three lines  \n\n\\[\n\\begin{cases}\nx=-1,\\\\[2pt]\ny=x,\\\\[2pt]\nz=y .\n\\end{cases}\n\\]\n\nIntersecting each pair of lines with the plane gives the vertices\n\n\\[\n\\begin{aligned}\nA &amp;: x=-1,\\;y=-1 \\;\\Rightarrow\\;z=77 ,&amp;&amp;A(-1,-1,77),\\\\\nB &amp;: x=-1,\\;z=y \\;\\Rightarrow\\;y=z=38 ,&amp;&amp;B(-1,38,38),\\\\\nC &amp;: y=x,\\;z=y \\;\\Rightarrow\\;x=y=z=25 ,&amp;&amp;C(25,25,25).\n\\end{aligned}\n\\]\n\nHence the finite region is the triangle \\(ABC\\).\n\n---\n\n### Area of the triangle\n\nVectors along two sides:\n\n\\[\n\\begin{aligned}\n\\vec{AB}&amp;=B-A=(0,39,-39),\\\\\n\\vec{AC}&amp;=C-A=(26,26,-52).\n\\end{aligned}\n\\]\n\n\\[\n\\vec{AB}\\times\\vec{AC}=(-1014,-1014,-1014)\n\\quad\\Longrightarrow\\quad \n\\bigl\\lVert\\vec{AB}\\times\\vec{AC}\\bigr\\rVert\n=1014\\sqrt3 .\n\\]\n\nTherefore\n\n\\[\n\\text{Area}= \\frac12\\bigl\\lVert\\vec{AB}\\times\\vec{AC}\\bigr\\rVert\n           =\\frac12\\cdot1014\\sqrt3\n           =507\\sqrt3 .\n\\]\n\nThus the area is \\(a\\sqrt b\\) with \\(a=507,\\;b=3\\), and\n\n\\[\na+b=507+3=510.\n\\]\n\n\\[\n\\boxed{510}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 510</p>\n<p>Extracted Answer: 510</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nA piecewise linear periodic function is defined by $f(x)=\\begin{cases}x&amp;\\text{if }x\\in[-1,1)\\\\2-x&amp;\\text{if }x\\in[1,3)\\end{cases}$ and $f(x+4)=f(x)$ for all real numbers $x$. The graph of $f(x)$ has the sawtooth pattern. The parabola $x=34y^2$ intersects the graph of $f(x)$ at finitely many points. The sum of the $y$-coordinates of these intersection points can be expressed in the form $\\frac{a+b\\sqrt{c}}{d}$, where $a,b,c,$ and $d$ are positive integers, $a,b,$ and $d$ have greatest common divisor equal to 1, and $c$ is not divisible by the square of any prime. Find $a+b+c+d$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>First write the equation for the intersection points.\n\nThe parabola is  \n\n\\[\nx=34y^{2},\n\\]\n\nand the periodic saw\u2011tooth satisfies  \n\n\\[\nf(x+4)=f(x),\\qquad   \nf(x)=\\begin{cases}\nx,&amp;-1\\le x&lt;1,\\\\[2pt]\n2-x,&amp;1\\le x&lt;3 .\n\\end{cases}\n\\]\n\nHence an intersection must satisfy  \n\n\\[\ny=f(34y^{2}). \\tag{1}\n\\]\n\n--------------------------------------------------------------------\n### 1.  Express \\(f\\) using the modulus\n\nFor any real \\(x\\) let  \n\n\\[\nt=(x+1)\\pmod 4,\\qquad 0\\le t&lt;4 .\n\\]\n\nThen  \n\n\\[\nf(x)=\n\\begin{cases}\nt-1,&amp;0\\le t&lt;2,\\\\[2pt]\n3-t,&amp;2\\le t&lt;4 .\n\\end{cases}\n\\]\n\nPut \\(x=34y^{2}\\).  Let  \n\n\\[\ns=34y^{2}+1,\\qquad t=s\\pmod4 .\n\\]\n\n--------------------------------------------------------------------\n### 2.  Two linear possibilities\n\n*If \\(0\\le t&lt;2\\) (the \u201crising\u201d part) then \\(y=t-1\\) and  \n\\(t=y+1\\).  Hence  \n\n\\[\n34y^{2}+1=4n+y+1\\quad\\Longrightarrow\\quad 34y^{2}-y-4n=0,\\tag{2}\n\\]\n\nwith the condition \\(y\\in[-1,1)\\).\n\n*If \\(2\\le t&lt;4\\) (the \u201cfalling\u201d part) then \\(y=3-t\\) and  \n\\(t=3-y\\).  Hence  \n\n\\[\n34y^{2}+1=4n+3-y\\quad\\Longrightarrow\\quad 34y^{2}+y-(2+4n)=0,\\tag{3}\n\\]\n\nwith the condition \\(y\\in(-1,1]\\).\n\nHere \\(n\\) is the integer \\(\\displaystyle n=\\Big\\lfloor\\frac{34y^{2}+1}{4}\\Big\\rfloor\\).\nSince \\(0\\le 34y^{2}+1\\le 35\\), we must have \\(0\\le n\\le 8\\).\n\n--------------------------------------------------------------------\n### 3.  Solve the quadratics\n\n**From (2):**  \n\n\\[\ny=\\frac{1\\pm\\sqrt{1+544n}}{68}\\qquad (n=0,1,\\dots ,8).\n\\]\n\nBoth roots lie in \\([-1,1)\\); for each \\(n\\) their sum is  \n\n\\[\n\\frac{1}{34}.\n\\]\n\nThus  \n\n\\[\nS_I=\\sum_{n=0}^{8}\\frac1{34}= \\frac{9}{34}. \\tag{4}\n\\]\n\n**From (3):**  \n\n\\[\ny=\\frac{-1\\pm\\sqrt{273+544n}}{68}\\qquad (n=0,1,\\dots ,8).\n\\]\n\nFor \\(n=0,\\dots ,7\\) both roots satisfy \\((-1,1]\\); for \\(n=8\\) the\nnegative root is \\(\\le -1\\) and must be discarded.\nHence for \\(n=0,\\dots ,7\\) each pair sums to \\(-\\dfrac1{34}\\), and we add\nthe single remaining root for \\(n=8\\):\n\n\\[\nS_{II}=8\\!\\left(-\\frac1{34}\\right)+\\frac{-1+\\sqrt{4625}}{68}\n        =-\\frac{8}{34}+\\frac{-1+5\\sqrt{185}}{68}. \\tag{5}\n\\]\n\n--------------------------------------------------------------------\n### 4.  Total sum of \\(y\\)-coordinates\n\n\\[\n\\begin{aligned}\nS &amp;=S_I+S_{II}\\\\\n  &amp;=\\frac{9}{34}-\\frac{8}{34}+\\frac{-1+5\\sqrt{185}}{68}\\\\\n  &amp;=\\frac{1}{34}+\\frac{-1+5\\sqrt{185}}{68}\\\\[2pt]\n  &amp;=\\frac{2-1+5\\sqrt{185}}{68}\n   =\\frac{1+5\\sqrt{185}}{68}.\n\\end{aligned}\n\\]\n\nThus the sum can be written as \\(\\displaystyle \\frac{a+b\\sqrt{c}}{d}\\) with  \n\n\\[\na=1,\\qquad b=5,\\qquad c=185,\\qquad d=68,\n\\]\n\nwhere \\(a,b,d\\) are coprime and \\(c\\) is square\u2011free.\n\nFinally  \n\n\\[\na+b+c+d = 1+5+185+68 = 259.\n\\]\n\n\\[\n\\boxed{259}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 259</p>\n<p>Extracted Answer: 259</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $N$ denote the number of ordered triples of positive integers $(a,b,c)$ such that $a,b,c\\leq3^6$ and $a^3+b^3+c^3$ is a multiple of $3^7$. Find the remainder when $N$ is divided by $1000$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>The condition  \n\n\\[\na^3+b^3+c^3\\equiv 0\\pmod {3^7}\\qquad (3^7=2187)\n\\]\n\ndepends only on the residues of \\(a,b,c\\) modulo \\(3^7\\).  \nWrite each number as  \n\n\\[\na=3^{3\\alpha}q,\\qquad \\alpha\\in\\{0,1,2\\},\\;q\\in Q,\n\\]\n\nwhere  \n\n* \\(Q\\) = the set of cubic residues among units modulo \\(3^7\\);  \n  \\(|Q|=486\\);\n* for \\(\\alpha=0,1,2\\) the sets  \n\n\\[\nR_\\alpha =\\{3^{3\\alpha}q\\;|\\;q\\in Q\\}\n\\]\n\nhave sizes  \n\n\\[\n|R_0|=486,\\;|R_1|=162,\\;|R_2|=54 .\n\\]\n\nAll numbers divisible by \\(27\\) contribute \\(0\\) to the sum, so we only need the\nordered triples whose components lie in  \n\n\\[\nR=R_0\\cup R_1\\cup R_2 .\n\\]\n\nDenote  \n\n\\[\nM_2 =\\#\\{(x,y)\\in R^2 : x+y\\equiv 0\\},\\qquad \nM_3 =\\#\\{(x,y,z)\\in R^3 : x+y+z\\equiv 0\\}.\n\\]\n\nBecause \\(-x\\in R\\) for every \\(x\\in R\\), we have \\(M_2=|R|=702\\).\n\nThe total number of required triples of positive integers is  \n\n\\[\n\\begin{aligned}\nN&amp;=27^3      \\;(\\text{all three multiples of }27) \\\\\n  &amp;\\quad+ 3\\cdot27\\cdot M_2 \\;(\\text{exactly two non\u2011multiples of }27)\\\\\n  &amp;\\quad+ M_3 .\n\\end{aligned}\n\\]\n\nThus  \n\n\\[\nN=19683+81\\cdot702+M_3=19683+56862+M_3 .\n\\]\n\n--------------------------------------------------------------------\n### Computing \\(M_3\\)\n\nLet  \n\n\\[\nf(z)=\\mathbf 1_R(z),\\qquad\nF(t)=\\sum_{z\\in\\mathbf Z/3^7\\mathbf Z}f(z) e^{2\\pi i t z/3^7}\n\\]\n\nbe the Fourier transform of the indicator of \\(R\\).  \nThen\n\n\\[\nM_3=\\frac1{3^7}\\sum_{t=0}^{3^7-1}F(t)^3 .\n\\]\n\nWriting \\(R\\) as \\(Q\\cup27Q\\cup729Q\\) and using that each element of\n\\(R_\\alpha\\) is obtained from \\(|Q|/3^\\alpha\\) elements of \\(Q\\), we obtain\n\n\\[\nF(t)=\\sum_{\\alpha=0}^{2}\\frac1{3^{\\alpha}}\n        \\sum_{q\\in Q} e^{2\\pi i t\\cdot3^{3\\alpha} q/3^7}.\n\\]\n\nThe inner sums are evaluated with the three characters of order\u202f3 on\n\\((\\mathbf Z/3^7\\mathbf Z)^\\times\\).  One finds that \\(F(t)\\) depends only on\n\\(v=v_3(t)\\) (the 3\u2011adic valuation of \\(t\\)):\n\n\\[\n\\begin{array}{c|c|c}\nv &amp;\\text{number of }t &amp;F(t)\\\\\\hline\n0 &amp;1458 &amp; -27\\\\\n1 &amp;486  &amp; 54\\\\\n2 &amp;162  &amp; 54\\bigl(1+\\operatorname{Re}A\\bigr)\\\\\n3 &amp;54   &amp; -27\\\\\n4 &amp;18   &amp; 216\\\\\n5 &amp;6    &amp; 216+162\\,\\operatorname{Re}A\\\\\n6 &amp;2    &amp; -27\n\\end{array}\n\\]\n\nwhere  \n\n\\[\nA=3e^{2\\pi i/9}=3\\zeta_9,\\qquad \n\\operatorname{Re}A=3\\cos\\frac{2\\pi}{9}.\n\\]\n\nFrom the values\n\\[\n\\operatorname{Re}A=3\\cos\\frac{2\\pi}{9},\\qquad\n\\cos\\frac{2\\pi}{9}+ \\cos\\frac{4\\pi}{9}+ \\cos\\frac{8\\pi}{9}=0,\n\\]\none obtains  \n\n\\[\n\\sum_{i=1}^3 (1+r_i)^3=\\frac{267}{8},\\qquad\n\\sum_{i=1}^3\\Bigl(\\frac43+r_i\\Bigr)^3=\\frac{3671}{72},\n\\]\nwhere \\(r_1,r_2,r_3\\) are the three real numbers\n\\(3\\cos\\frac{2\\pi}{9},\\,3\\cos\\frac{4\\pi}{9},\\,3\\cos\\frac{8\\pi}{9}\\).\n\nCarrying out the sum\n\n\\[\n\\sum_{t}F(t)^3\n =702^3-1514\\cdot27^3+486\\cdot54^3+18\\cdot216^3\n   +54^4\\!\\left(\\frac{267}{8}\\right)+8\\,503\\,056\\!\\left(\\frac{3671}{72}\\right)\n =1\\,291\\,401\\,630 .\n\\]\n\nSince \\(3^7=2187\\),\n\n\\[\nM_3=\\frac{1\\,291\\,401\\,630}{2187}=590\\,490 .\n\\]\n\n--------------------------------------------------------------------\n### Final count\n\n\\[\n\\begin{aligned}\nN &amp;=19683+56862+590490\\\\\n  &amp;=667\\,035 .\n\\end{aligned}\n\\]\n\nThe problem asks for \\(N\\bmod 1000\\):\n\n\\[\n\\boxed{35}.\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 735</p>\n<p>Extracted Answer: 35</p>\n<p>Score: 0.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThe 27 cells of a $3\\times9$ grid are filled in using the numbers 1 through 9 so that each row contains 9 different numbers, and each of the three $3\\times3$ blocks heavily outlined in the example below contains 9 different numbers, as in the first three rows of a Sudoku puzzle. \n | 4 | 2 | 8 | 9 | 6 | 3 | 1 | 7 | 5 | \n | 3 | 7 | 9 | 5 | 2 | 1 | 6 | 8 | 4 | \n | 5 | 6 | 1 | 8 | 4 | 7 | 9 | 2 | 3 | \n The number of different ways to fill such a grid can be written as $p^a\\cdot q^b\\cdot r^c\\cdot s^d$, where $p,q,r,$ and $s$ are distinct prime numbers and $a,b,c,$ and $d$ are positive integers. Find $p\\cdot a+q\\cdot b+r\\cdot c+s\\cdot d$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>**Step 1 \u2013   What the conditions mean**\n\nThe grid has three rows and nine columns.  \nThe columns are grouped into three \\(3\\times3\\) blocks  \n\n\\[\nB_{1}=\\{1,2,3\\},\\qquad B_{2}=\\{4,5,6\\},\\qquad B_{3}=\\{7,8,9\\}.\n\\]\n\nFor each row we must use the numbers \\(1,2,\\dots ,9\\) exactly once, and for each\nblock the nine cells of that block must also contain the numbers \\(1,\\dots ,9\\) exactly once.\n\nHence for each digit \\(d\\) :\n\n* it appears once in each of the three rows,  \n* it appears once in each of the three blocks.\n\nConsequently the three positions of a digit form a **bijection** between rows and blocks.\nLet \\(\\sigma _d\\in S_{3}\\) be the permutation defined by\n\n\\[\n\\sigma _d(i)=\\text{the block that contains }d\\text{ in row }i .\n\\]\n\nThus each digit contributes one \u20181\u2019 in the \\(3\\times3\\) permutation matrix of \\(\\sigma _d\\).\n\n--------------------------------------------------------------------\n\n**Step 2 \u2013   The matrix condition**\n\nIf we add the nine permutation matrices of the nine digits we obtain a matrix\n\\(M\\) whose entry \\(M_{i,b}\\) counts how many digits lie in row \\(i\\) and block \\(b\\).\nThe block condition says that each block must contain each digit once, i.e. each\ncell \\((i,b)\\) must contain exactly three digits. Therefore\n\n\\[\nM=3J,\\qquad J=\\begin{pmatrix}1&amp;1&amp;1\\\\1&amp;1&amp;1\\\\1&amp;1&amp;1\\end{pmatrix}.\n\\]\n\nSo we must write \\(3J\\) as a sum of nine (not\u2011necessarily distinct) permutation\nmatrices of size \\(3\\).\n\n--------------------------------------------------------------------\n\n**Step 3 \u2013   Types of permutations**\n\n\\(S_{3}\\) has six elements:\n\n\\[\n\\begin{aligned}\n&amp;\\text{id},\\;(12),\\;(13),\\;(23),\\;(123),\\;(132).\n\\end{aligned}\n\\]\n\nLet  \n\n\\[\na=x_{\\text{id}}=x_{(123)}=x_{(132)},\\qquad\nb=x_{(12)}=x_{(13)}=x_{(23)} .\n\\]\n\nCounting the contributions of each type to the nine entries of \\(M\\) gives the\nsystem  \n\n\\[\n\\begin{cases}\na+b=3\\\\[2pt]\na+b=3\\\\[2pt]\na+b=3\\\\[2pt]\na+b=3,\n\\end{cases}\n\\qquad\\Longrightarrow\\qquad a+b=3 .\n\\]\n\nHence \\(a\\) may be \\(0,1,2,3\\) and \\(b=3-a\\).  For a fixed value of \\(a\\),\n\n\\[\n\\begin{aligned}\nx_{\\text{id}}&amp;=a,\\\\\nx_{(123)}&amp;=a,\\\\\nx_{(132)}&amp;=a,\\\\\nx_{(12)}&amp;=x_{(13)}=x_{(23)}&amp;=3-a .\n\\end{aligned}\n\\]\n\n--------------------------------------------------------------------\n\n**Step 4 \u2013   Assigning the nine digits to the permutations**\n\nThe nine digits are distinct, so for a given \\(a\\) the number of ways to give the\nsix permutation types to the digits is the multinomial coefficient\n\n\\[\nN_a=\\frac{9!}{a!\\,a!\\,a!\\,(3-a)!\\,(3-a)!\\,(3-a)!}\n    =\\frac{9!}{a!^{3}(3-a)!^{3}} .\n\\]\n\nSumming over the four possible values of \\(a\\),\n\n\\[\n\\sum_{a=0}^{3}N_a\n   =\\frac{9!}{0!^{3}3!^{3}}+\\frac{9!}{1!^{3}2!^{3}}\n    +\\frac{9!}{2!^{3}1!^{3}}+\\frac{9!}{3!^{3}0!^{3}}\n   =94\\,080 .\n\\]\n\n--------------------------------------------------------------------\n\n**Step 5 \u2013   Ordering inside each row\u2011block**\n\nFor a fixed assignment of the permutations, each of the nine\n\\( ( \\text{row},\\text{block} )\\) cells contains exactly three different digits.\nThese three digits can be placed in the three columns of that cell in any order,\ni.e. in \\(3! = 6\\) ways, independently of the other cells.\nHence we obtain an extra factor \\((3!)^{9}=6^{9}\\).\n\nThus the total number of admissible \\(3\\times9\\) grids is\n\n\\[\nN = 94\\,080\\cdot 6^{9}\n   =9!\\cdot 6^{6}\\cdot 56 .\n\\]\n\n--------------------------------------------------------------------\n\n**Step 6 \u2013   Prime factorisation**\n\n\\[\n\\begin{aligned}\n9! &amp;=2^{7}\\,3^{4}\\,5\\,7,\\\\\n6^{6}&amp;=(2\\cdot3)^{6}=2^{6}\\,3^{6},\\\\\n56 &amp;=2^{3}\\,7 .\n\\end{aligned}\n\\]\n\nMultiplying gives  \n\n\\[\nN=2^{7+6+3}\\,3^{4+6}\\,5^{1}\\,7^{1+1}\n  =2^{16}\\,3^{10}\\,5^{1}\\,7^{2}.\n\\]\n\nThus we may write  \n\n\\[\nN = p^{a}\\,q^{b}\\,r^{c}\\,s^{d}\n\\quad\\text{with}\\quad\np=2,\\;a=16;\\;\\; q=3,\\;b=10;\\;\\; r=5,\\;c=1;\\;\\; s=7,\\;d=2 .\n\\]\n\n--------------------------------------------------------------------\n\n**Step 7 \u2013   Required sum**\n\n\\[\np\\cdot a+q\\cdot b+r\\cdot c+s\\cdot d\n =2\\cdot16+3\\cdot10+5\\cdot1+7\\cdot2\n =32+30+5+14=81 .\n\\]\n\n--------------------------------------------------------------------\n\n\\[\n\\boxed{81}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 81</p>\n<p>Extracted Answer: 81</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nSix points $ A, B, C, D, E, $ and $ F $ lie in a straight line in that order. Suppose that $ G $ is a point not on the line and that $ AC = 26 $, $ BD = 22 $, $ CE = 31 $, $ DF = 33 $, $ AF = 73 $, $ CG = 40 $, and $ DG = 30 $. Find the area of $ \\triangle BGE $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let the line containing \\(A,B,C,D,E,F\\) be the \\(x\\)-axis.\n\n\\[\nA=(0,0),\\qquad B=(b,0),\\ C=(c,0),\\ D=(d,0),\\ E=(e,0),\\ F=(f,0)\n\\]\n\nFrom the given distances along the line  \n\n\\[\n\\begin{aligned}\nAC&amp;=c-a=26 \\Longrightarrow c=26,\\\\\nBD&amp;=d-b=22,\\\\\nCE&amp;=e-c=31 \\Longrightarrow e=26+31=57,\\\\\nDF&amp;=f-d=33,\\\\\nAF&amp;=f-a=73 \\Longrightarrow f=73 .\n\\end{aligned}\n\\]\n\nFrom \\(DF=33\\) we get \\(d=f-33=73-33=40\\).  \nThen \\(BD=22\\) gives \\(b=d-22=40-22=18\\).\n\nThus the collinear points are\n\n\\[\nA(0),\\ B(18),\\ C(26),\\ D(40),\\ E(57),\\ F(73).\n\\]\n\n---\n\n### Coordinates of \\(G\\)\n\nLet \\(G=(x,y)\\) with \\(y\\neq0\\).  \nWe know\n\n\\[\n\\begin{cases}\n(CG)^2=(x-26)^2+y^2=40^2=1600,\\\\\n(DG)^2=(x-40)^2+y^2=30^2=900 .\n\\end{cases}\n\\]\n\nSubtracting the equations:\n\n\\[\n(x-26)^2-(x-40)^2 = 1600-900=700 .\n\\]\n\nCompute the left side:\n\n\\[\n\\bigl(x^2-52x+676\\bigr)-\\bigl(x^2-80x+1600\\bigr)=28x-924 .\n\\]\n\nHence \\(28x-924=700\\) giving  \n\n\\[\nx=\\frac{1624}{28}=58.\n\\]\n\nNow use \\((x-40)^2+y^2=900\\):\n\n\\[\n(58-40)^2+y^2=900\\Longrightarrow 18^2+y^2=900\\Longrightarrow y^2=576.\n\\]\n\nThus \\(y=\\pm24\\).  The sign does not affect the area; we take \\(y=24\\).\n\nTherefore  \n\n\\[\nG=(58,24)\\;(\\text{or }(58,-24)).\n\\]\n\n---\n\n### Area of \\(\\triangle BGE\\)\n\nPoints:\n\\[\nB=(18,0),\\qquad G=(58,24),\\qquad E=(57,0).\n\\]\n\nSince \\(B\\) and \\(E\\) lie on the \\(x\\)-axis, the base \\(BE\\) has length  \n\n\\[\nBE = 57-18 = 39.\n\\]\n\nThe altitude from \\(G\\) to the \\(x\\)-axis is \\(|y|=24\\).\n\nHence\n\n\\[\n\\text{Area}=\\frac12\\cdot (\\text{base})\\cdot (\\text{height})\n          =\\frac12\\cdot 39\\cdot 24\n          =468.\n\\]\n\n\\[\n\\boxed{468}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 468</p>\n<p>Extracted Answer: 468</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet the sequence of rationals $ x_1, x_2, \\ldots $ be defined such that $ x_1 = \\frac{25}{11} $ and\n$ x_{k+1} = \\frac{1}{3} \\left( x_k + \\frac{1}{x_k} - 1 \\right). $\n$ x_{2025} $ can be expressed as $ \\frac{m}{n} $ for relatively prime positive integers $ m $ and $ n $. Find the remainder when $ m + n $ is divided by 1000.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>\\[\nx_{k+1}= \\frac{x_k+\\frac1{x_k}-1}{3},\\qquad x_1=\\frac{25}{11}\n\\]\n\n---\n\n### 1.  A convenient substitution  \n\nLet  \n\n\\[\ny_k=\\frac{x_k-1}{x_k+1}\\qquad\\Longleftrightarrow\\qquad \nx_k=\\frac{1+y_k}{1-y_k}.\n\\]\n\nThen a short computation gives  \n\n\\[\ny_{k+1}= \\frac{3y_k^{\\,2}-1}{2}. \\tag{1}\n\\]\n\nThus we only have to iterate the quadratic map (1).\n\n---\n\n### 2.  Scaling  \n\nDefine  \n\n\\[\nu_k=\\frac32\\,y_k .\n\\]\n\nFrom (1)\n\n\\[\nu_{k+1}=u_k^{2}-\\frac34 .\\tag{2}\n\\]\n\nLet  \n\n\\[\nu_k=\\frac{a_k}{12^{\\,2^{k-1}}},\\qquad a_1=7 .\n\\]\n\nBecause the denominator squares each step, indeed  \n\n\\[\n12^{\\,2^{k}}=(12^{\\,2^{k-1}})^2 .\n\\]\n\nUsing (2) one checks that  \n\n\\[\na_{k+1}=a_k^{2}-\\frac34\\cdot12^{\\,2^{k}} .\n\\]\n\nOnly the denominator grows; the exact value of the numerator is not needed later.\n\n---\n\n### 3.  Returning to \\(x_k\\)\n\nSince \\(y_k=\\frac{2}{3}u_k\\),\n\n\\[\nx_k=\\frac{1+y_k}{1-y_k}\n     =\\frac{3+2u_k}{3-2u_k}\n     =\\frac{3\\cdot12^{\\,2^{k-1}}+2a_k}\n            {3\\cdot12^{\\,2^{k-1}}-2a_k}.\n\\]\n\nHence for any \\(k\\),\n\n\\[\nx_k=\\frac{M_k}{N_k},\\qquad \nM_k+N_k =6\\cdot12^{\\,2^{k-1}} .\n\\]\n\nIn particular\n\n\\[\nm+n = M_{2025}+N_{2025}= 6\\cdot 12^{\\,2^{2024}} .\n\\]\n\n---\n\n### 4.  Computing \\(6\\cdot12^{2^{2024}}\\pmod{1000}\\)\n\nWe need \\(6\\cdot12^{K}\\pmod{1000}\\) where \\(K=2^{2024}\\).\n\nBecause \\(1000=8\\cdot125\\) we work modulo\u202f8 and\u202f125.\n\n*Modulo\u202f8*:  \n\\(12\\equiv4\\pmod8\\), and \\(4^{2}=0\\pmod8\\).  \nSince \\(K\\ge2\\), \\(12^{K}\\equiv0\\pmod8\\) \u21d2 the whole expression is \\(0\\pmod8\\).\n\n*Modulo\u202f125*:  \\(\\gcd(12,125)=1\\) and \\(\\phi(125)=100\\).  \nThus \\(12^{100}\\equiv1\\pmod{125}\\); we need \\(K\\bmod100\\).\n\nThe powers of\u202f2 modulo\u202f100 repeat with period\u202f20 for exponents \\(\\ge2\\).  \n\\(2024\\equiv4\\pmod{20}\\), so \\(2^{2024}\\equiv2^{4}=16\\pmod{100}\\).  \nHence \\(12^{K}\\equiv12^{16}\\pmod{125}\\).\n\nCompute:\n\\[\n12^{2}\\equiv19,\\;12^{4}\\equiv111,\\;12^{8}\\equiv71,\\;12^{16}\\equiv71^{2}\\equiv41\\pmod{125}.\n\\]\n\nThus \\(6\\cdot12^{K}\\equiv6\\cdot41=246\\equiv121\\pmod{125}\\).\n\nNow solve the CRT:\n\\[\nX\\equiv0\\pmod8,\\qquad X\\equiv121\\pmod{125}.\n\\]\n\nLet \\(X=8t\\). Then \\(8t\\equiv121\\pmod{125}\\Rightarrow t\\equiv47\\cdot121\\equiv62\\pmod{125}\\) (since \\(8^{-1}\\equiv47\\pmod{125}\\)).  \nThus \\(X=8\\cdot62=496\\pmod{1000}\\).\n\nTherefore\n\n\\[\nm+n \\equiv 496 \\pmod{1000}.\n\\]\n\n---\n\n\\[\n\\boxed{496}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 248</p>\n<p>Extracted Answer: 496</p>\n<p>Score: 0.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nFind the sum of all positive integers $ n $ such that $ n + 2 $ divides the product $ 3(n + 3)(n^2 + 9) $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n\\[\nm=n+2\\qquad (m&gt;2)\n\\]\n\nThen  \n\n\\[\nn+2=m,\\qquad n+3=m+1,\\qquad n^{2}+9=(m-2)^{2}+9=m^{2}-4m+13 .\n\\]\n\nThe condition  \n\n\\[\nn+2\\mid 3(n+3)(n^{2}+9)\n\\]\n\nbecomes  \n\n\\[\nm \\mid 3(m+1)(m^{2}-4m+13). \\tag{1}\n\\]\n\n--------------------------------------------------------------------\n### 1.  Using the gcd with 3\n\nBecause  \n\n\\[\n\\gcd(m,m+1)=1,\n\\]\n\nany prime divisor of \\(m\\) cannot come from the factor \\(m+1\\).  \nThe only possible common factor of \\(m\\) with the whole right\u2011hand side of (1) is the factor \\(3\\).\n\nLet  \n\n\\[\nd=\\gcd(m,3),\\qquad m=d\\cdot m&#39;,\\qquad \\gcd(m&#39;,3)=1 .\n\\]\n\nThen (1) is equivalent to  \n\n\\[\nd m&#39; \\mid 3(m+1)(m^{2}-4m+13)\n      = d\\Bigl(\\frac{3}{d}\\Bigr)(m+1)(m^{2}-4m+13).\n\\]\n\nCancelling \\(d\\) gives  \n\n\\[\nm&#39; \\mid \\Bigl(\\frac{3}{d}\\Bigr)(m+1)(m^{2}-4m+13).\\tag{2}\n\\]\n\nSince \\(\\gcd(m&#39;,m+1)=1\\) and also \\(\\gcd(m&#39;,3)=1\\), the factor \\((m+1)\\) and the possible remaining factor \\(\\frac{3}{d}\\) cannot help the divisibility. Hence (2) reduces to  \n\n\\[\nm&#39; \\mid (m^{2}-4m+13). \\tag{3}\n\\]\n\n--------------------------------------------------------------------\n### 2.  Reduce modulo \\(m\\)\n\n\\[\nm^{2}-4m+13 \\equiv 13\\pmod{m},\n\\]\n\nso (3) is equivalent to  \n\n\\[\nm&#39; \\mid 13.\n\\]\n\nRecall \\(m&#39; =\\dfrac{m}{\\gcd(m,3)}\\).  Therefore\n\n\\[\n\\frac{m}{\\gcd(m,3)}\\mid 13.\n\\]\n\n--------------------------------------------------------------------\n### 3.  Solve the two possibilities\n\n**(i)  \\(\\gcd(m,3)=1\\) (i.e. \\(3\\nmid m\\)).**  \nThen \\(\\displaystyle m\\mid13\\).  \nWith \\(m&gt;2\\), the only possibility is \\(m=13\\).\n\n**(ii)  \\(\\gcd(m,3)=3\\) (i.e. \\(m=3k\\)).**  \nThen \\(\\displaystyle k\\mid13\\).  \nThus \\(k=1\\) or \\(k=13\\), giving \\(m=3\\) or \\(m=39\\).\n\n--------------------------------------------------------------------\n### 4.  Return to \\(n\\)\n\n\\[\nn=m-2\\; \\Longrightarrow\\; \n\\begin{cases}\nm=3 &amp;\\Rightarrow n=1,\\\\[2pt]\nm=13 &amp;\\Rightarrow n=11,\\\\[2pt]\nm=39 &amp;\\Rightarrow n=37.\n\\end{cases}\n\\]\n\nAll three values satisfy the original divisibility (direct verification shows \\(3\\mid120\\), \\(13\\mid5460\\), \\(39\\mid165360\\)).\n\n--------------------------------------------------------------------\n### 5.  Sum of all such \\(n\\)\n\n\\[\n1+11+37 = 49.\n\\]\n\n\\[\n\\boxed{49}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 49</p>\n<p>Extracted Answer: 49</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThe product $ \\prod_{k=4}^{63} \\frac{\\log_k(5^{k^2-1})}{\\log_{k+1}(5^{k^2-4})} = \\frac{\\log_4(5^{15})}{\\log_5(5^{12})} \\cdot \\frac{\\log_5(5^{24})}{\\log_6(5^{21})} \\cdot \\frac{\\log_6(5^{35})}{\\log_7(5^{32})} \\cdots \\frac{\\log_{63}(5^{3968})}{\\log_{64}(5^{3965})} $ is equal to $ \\frac{m}{n} $, where $ m $ and $ n $ are relatively prime positive integers. Find $ m + n $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>First rewrite each factor using the change\u2013of\u2013base formula  \n\n\\[\n\\log_a b=\\frac{\\ln b}{\\ln a}.\n\\]\n\n\\[\n\\frac{\\log_k\\bigl(5^{k^{2}-1}\\bigr)}{\\log_{k+1}\\bigl(5^{k^{2}-4}\\bigr)}\n   =\\frac{\\dfrac{\\ln5^{\\,k^{2}-1}}{\\ln k}}\n          {\\dfrac{\\ln5^{\\,k^{2}-4}}{\\ln (k+1)}}\n   =\\frac{(k^{2}-1)\\ln5}{\\ln k}\\cdot\\frac{\\ln(k+1)}{(k^{2}-4)\\ln5}\n   =\\frac{k^{2}-1}{k^{2}-4}\\cdot\\frac{\\ln(k+1)}{\\ln k}.\n\\]\n\nHence\n\n\\[\nP=\\prod_{k=4}^{63}\\frac{k^{2}-1}{k^{2}-4}\n   \\cdot\\prod_{k=4}^{63}\\frac{\\ln(k+1)}{\\ln k}.\n\\]\n\n---\n\n### 1.  The logarithmic product\n\n\\[\n\\prod_{k=4}^{63}\\frac{\\ln(k+1)}{\\ln k}\n   =\\frac{\\ln64}{\\ln4}\n   =\\log_{4}64=3.\n\\]\n\n(The terms cancel telescopically.)\n\n---\n\n### 2.  The rational product  \n\nFactor each term:\n\n\\[\n\\frac{k^{2}-1}{k^{2}-4}\n   =\\frac{(k-1)(k+1)}{(k-2)(k+2)}\n   =\\frac{k-1}{k-2}\\cdot\\frac{k+1}{k+2}.\n\\]\n\nThus\n\n\\[\n\\prod_{k=4}^{63}\\frac{k^{2}-1}{k^{2}-4}\n =\\Bigl(\\prod_{k=4}^{63}\\frac{k-1}{k-2}\\Bigr)\n  \\Bigl(\\prod_{k=4}^{63}\\frac{k+1}{k+2}\\Bigr).\n\\]\n\nThe first product telescopes:\n\n\\[\n\\prod_{k=4}^{63}\\frac{k-1}{k-2}\n =\\frac{3}{2}\\cdot\\frac{4}{3}\\cdot\\cdots\\cdot\\frac{62}{61}\n =\\frac{62}{2}=31.\n\\]\n\nThe second product also telescopes:\n\n\\[\n\\prod_{k=4}^{63}\\frac{k+1}{k+2}\n =\\frac{5}{6}\\cdot\\frac{6}{7}\\cdot\\cdots\\cdot\\frac{64}{65}\n =\\frac{5}{65}=\\frac{1}{13}.\n\\]\n\nTherefore\n\n\\[\n\\prod_{k=4}^{63}\\frac{k^{2}-1}{k^{2}-4}\n   =31\\cdot\\frac{1}{13}=\\frac{31}{13}.\n\\]\n\n---\n\n### 3.  Combine the two parts\n\n\\[\nP=\\frac{31}{13}\\times3=\\frac{93}{13}.\n\\]\n\nThe fraction is already in lowest terms (\\(\\gcd(93,13)=1\\)).  \nThus \\(m=93\\), \\(n=13\\) and\n\n\\[\nm+n=93+13=106.\n\\]\n\n\\[\n\\boxed{106}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 106</p>\n<p>Extracted Answer: 106</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nFour unit squares form a $2 \\times 2$ grid. Each of the 12 unit line segments forming the sides of the squares is colored either red or blue in such a way that each unit square has 2 red sides and 2 blue sides. Find the number of such colorings.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let the four unit squares be  \n\n\\[\n\\begin{array}{c|c}\n\\text{TL}&amp;\\text{TR}\\\\\\hline\n\\text{BL}&amp;\\text{BR}\n\\end{array}\n\\]\n\nand denote the twelve unit edges as follows  \n\n* Horizontal edges:  \n\n\\[\n\\begin{aligned}\n&amp;h_{1}= \\text{top of TL},\\qquad h_{2}= \\text{top of TR},\\\\\n&amp;h_{3}= \\text{middle left},\\qquad h_{4}= \\text{middle right},\\\\\n&amp;h_{5}= \\text{bottom of BL},\\qquad h_{6}= \\text{bottom of BR}.\n\\end{aligned}\n\\]\n\n* Vertical edges:  \n\n\\[\n\\begin{aligned}\n&amp;v_{1}= \\text{left of TL},\\qquad v_{2}= \\text{left of BL},\\\\\n&amp;v_{3}= \\text{middle top},\\qquad v_{4}= \\text{middle bottom},\\\\\n&amp;v_{5}= \\text{right of TR},\\qquad v_{6}= \\text{right of BR}.\n\\end{aligned}\n\\]\n\nFor each square the sum of the red edges must be \\(2\\).\nWriting a red edge as \\(1\\) and a blue edge as \\(0\\),\n\n\\[\n\\begin{aligned}\n\\text{TL}&amp;:\\;h_{1}+h_{3}+v_{1}+v_{3}=2,\\\\\n\\text{TR}&amp;:\\;h_{2}+h_{4}+v_{3}+v_{5}=2,\\\\\n\\text{BL}&amp;:\\;h_{3}+h_{5}+v_{2}+v_{4}=2,\\\\\n\\text{BR}&amp;:\\;h_{4}+h_{6}+v_{4}+v_{6}=2.\n\\end{aligned}\n\\]\n\nThe four **interior** edges are \\(h_{3},h_{4},v_{3},v_{4}\\); the other eight edges lie on the outer\nboundary.  \n\nFix the colours of the interior edges:\n\\[\na=h_{3},\\qquad b=h_{4},\\qquad c=v_{3},\\qquad d=v_{4}\\in\\{0,1\\}.\n\\]\n\nThen for each square we know the required sum of its two boundary edges:\n\n\\[\n\\begin{aligned}\nh_{1}+v_{1}&amp;=2-(a+c),\\\\\nh_{2}+v_{5}&amp;=2-(b+c),\\\\\nh_{5}+v_{2}&amp;=2-(a+d),\\\\\nh_{6}+v_{6}&amp;=2-(b+d).\n\\end{aligned}\n\\]\n\nIf the right\u2011hand side equals \\(2\\) or \\(0\\) the two boundary edges are forced to be\nboth red or both blue \u2013 exactly one choice.  \nIf it equals \\(1\\) the two edges must be of opposite colours \u2013 two choices.\n\nHence, for a fixed interior vector \\((a,b,c,d)\\) the number of admissible colourings of the\nboundary edges is  \n\n\\[\n2^{\\,k(a,b,c,d)},\n\\]\n\nwhere \\(k\\) is the number of squares whose interior\u2011edge sum equals \\(1\\); i.e.\n\n\\[\nk=(a\\oplus c)+(b\\oplus c)+(a\\oplus d)+(b\\oplus d),\n\\]\n(\\(\\oplus\\) denotes XOR).\n\nTherefore the total number of colourings is  \n\n\\[\n\\sum_{a,b,c,d\\in\\{0,1\\}}2^{k}\n= \\sum_{c,d} \\Bigl(\\sum_{a}2^{\\,a\\oplus c + a\\oplus d}\\Bigr)^{2}.\n\\]\n\nFor the four possibilities of \\((c,d)\\) we have\n\n\\[\n\\begin{array}{c|c}\n(c,d) &amp; \\displaystyle\\sum_{a}2^{a\\oplus c + a\\oplus d} \\\\ \\hline\n(0,0) &amp; 1+4 = 5\\\\\n(1,1) &amp; 4+1 = 5\\\\\n(0,1),(1,0) &amp; 2+2 = 4\n\\end{array}\n\\]\n\nThus\n\n\\[\n\\text{total}=2\\cdot5^{2}+2\\cdot4^{2}=2\\cdot25+2\\cdot16=50+32=82.\n\\]\n\nHence there are  \n\n\\[\n\\boxed{82}\n\\]\n\ndifferent colourings of the twelve unit edges so that each of the four unit squares has\nexactly two red and two blue sides.</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 82</p>\n<p>Extracted Answer: 82</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $ A $ be the set of positive integer divisors of 2025. Let $ B $ be a randomly selected subset of $ A $. The probability that $ B $ is a nonempty set with the property that the least common multiple of its elements is 2025 is $ \\frac{m}{n} $, where $ m $ and $ n $ are relatively prime positive integers. Find $ m + n $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>The divisors of  \n\n\\[\n2025 = 3^{4}\\cdot5^{2}\n\\]\n\nare obtained by choosing the exponent of \\(3\\) from \\(\\{0,1,2,3,4\\}\\) and the exponent of \\(5\\) from \\(\\{0,1,2\\}\\).  \nHence  \n\n\\[\n|A|=(4+1)(2+1)=15 .\n\\]\n\n---\n\n### Condition for the LCM to be \\(2025\\)\n\nFor a non\u2011empty subset \\(B\\subseteq A\\),\n\n\\[\n\\operatorname{lcm}(B)=2025 \\iff\n\\begin{cases}\n\\text{some element of }B\\text{ has }3\\text{-exponent }4,\\\\[2pt]\n\\text{some element of }B\\text{ has }5\\text{-exponent }2.\n\\end{cases}\n\\]\n\nDefine  \n\n\\[\nS_3=\\{81,\\,405,\\,2025\\} \\quad (\\text{divisors with }3^4) ,\n\\]\n\\[\nS_5=\\{25,\\,75,\\,225,\\,675,\\,2025\\} \\quad (\\text{divisors with }5^2).\n\\]\n\nThus \\(B\\) must intersect both \\(S_3\\) and \\(S_5\\).\n\n---\n\n### Counting favorable subsets\n\nLet \\(U=S_3\\cup S_5\\).  \n\\(|S_3|=3,\\;|S_5|=5,\\;|S_3\\cap S_5|=1\\) (the element \\(2025\\)), so\n\n\\[\n|U|=3+5-1=7.\n\\]\n\nThe remaining divisors of \\(2025\\) (those not in \\(U\\)) are \\(15-7=8\\) in number and can be chosen freely.\n\nNumber of subsets of \\(U\\) that contain at least one element of \\(S_3\\) **and** at least one element of \\(S_5\\):\n\n\\[\n\\begin{aligned}\n&amp;2^{7}\\;(\\text{all subsets of }U)\\\\\n&amp;\\quad-2^{4}\\;(\\text{subsets with no }S_3)\\\\\n&amp;\\quad-2^{2}\\;(\\text{subsets with no }S_5)\\\\\n&amp;\\quad+2^{0}\\;(\\text{subsets with neither }S_3\\text{ nor }S_5)\\\\[2pt]\n&amp;=128-16-4+1=109 .\n\\end{aligned}\n\\]\n\nFor each of these \\(109\\) choices, any subset of the other 8 divisors may be added, giving a factor \\(2^{8}=256\\).\n\nHence the number of favorable subsets is  \n\n\\[\nN=109\\cdot256=27904.\n\\]\n\n---\n\n### Probability\n\nAll subsets of \\(A\\) (including the empty set) number  \n\n\\[\n2^{15}=32768.\n\\]\n\nThus\n\n\\[\nP=\\frac{N}{2^{15}}=\\frac{27904}{32768}.\n\\]\n\nDividing numerator and denominator by their greatest common divisor \\(256\\),\n\n\\[\nP=\\frac{27904/256}{32768/256}=\\frac{109}{128}.\n\\]\n\nSo \\(\\displaystyle m=109,\\;n=128\\) and\n\n\\[\nm+n=109+128=237.\n\\]\n\n\\[\n\\boxed{237}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 237</p>\n<p>Extracted Answer: 237</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $ABCDE$ be a convex pentagon with $AB=14, BC=7, CD=24, DE=13, EA=26,$ and $\\angle B=\\angle E=60^\\circ$. For each point $X$ in the plane, define $f(X)=AX+BX+CX+DX+EX$. The least possible value of $f(X)$ can be expressed as $m+n\\sqrt{p}$, where $m$ and $n$ are positive integers and $p$ is not divisible by the square of any prime. Find $m+n+p$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>\\[\n\\boxed{45}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 60</p>\n<p>Extracted Answer: 45</p>\n<p>Score: 0.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nCircle $\\omega_1$ with radius 6 centered at point $A$ is internally tangent at point $B$ to circle $\\omega_2$ with radius 15. Points $C$ and $D$ lie on $\\omega_2$ such that $\\overline{BC}$ is a diameter of $\\omega_2$ and $\\overline{BC} \\perp \\overline{AD}$. The rectangle $EFGH$ is inscribed in $\\omega_1$ such that $\\overline{EF} \\perp \\overline{BC}$, $C$ is closer to $\\overline{GH}$ than to $\\overline{EF}$, and $D$ is closer to $\\overline{FG}$ than to $\\overline{EH}$, as shown. Triangles $\\triangle DGF$ and $\\triangle CHG$ have equal areas. The area of rectangle $EFGH$ is $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m + n$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let the centre of the large circle \\(\\omega _2\\) be the origin \\(O(0,0)\\).\nSince \\(BC\\) is a diameter of \\(\\omega _2\\), take  \n\n\\[\nB=(15,0),\\qquad C=(-15,0),\\qquad O=(0,0).\n\\]\n\nBecause \\(\\omega _1\\) (radius \\(6\\)) is internally tangent to \\(\\omega _2\\) at \\(B\\),\nits centre \\(A\\) lies on \\(OB\\) with  \n\n\\[\nOA=15-6=9\\quad\\Longrightarrow\\quad A=(9,0).\n\\]\n\nThe condition \\(AD\\perp BC\\) forces \\(AD\\) to be vertical through \\(x=9\\).\nIntersecting this line with \\(\\omega _2\\) (\\(x^{2}+y^{2}=225\\)) gives  \n\n\\[\nD=(9,12)\\text{ or }(9,-12).\n\\]\n\nSince later we need \\(D\\) to be nearer the side \\(\\overline{FG}\\) than to \\(\\overline{EH}\\),\n\\(D\\) must lie **below** the rectangle; hence  \n\n\\[\nD=(9,-12).\n\\]\n\n---\n\n### The rectangle\n\nA rectangle inscribed in a circle has its centre at the circle\u2019s centre.\nThus the centre of rectangle \\(EFGH\\) is \\(A(9,0)\\).\n\nLet  \n\n* \\(w\\) = horizontal distance from \\(A\\) to each vertical side,\n* \\(h\\) = vertical distance from \\(A\\) to each horizontal side.\n\nThen the vertices are  \n\n\\[\n\\begin{aligned}\nE&amp;(9+w,\\;h),\\qquad F&amp;(9+w,\\;-h),\\\\\nG&amp;(9-w,\\;-h),\\qquad H&amp;(9-w,\\;h).\n\\end{aligned}\n\\]\n\nBecause the rectangle is inscribed in \\(\\omega _1\\),\n\n\\[\nw^{2}+h^{2}=6^{2}=36. \\tag{1}\n\\]\n\nThe side \\(\\overline{EF}\\) is vertical, so \\(\\overline{EF}\\perp BC\\) (which is horizontal).\n\n- \\(C(-15,0)\\) is left of the rectangle, so its distances to the two vertical sides are  \n\n\\[\n\\operatorname{dist}(C,\\overline{GH}) =| -15-(9-w)| =24-w,\n\\]\n\\[\n\\operatorname{dist}(C,\\overline{EF}) =| -15-(9+w)| =24+w,\n\\]\n\nhence \\(C\\) is indeed closer to \\(\\overline{GH}\\) than to \\(\\overline{EF}\\).\n\n- \\(D(9,-12)\\) is below the rectangle; its distances to the horizontal sides are  \n\n\\[\n\\operatorname{dist}(D,\\overline{FG}) =|-12-(-h)| =12-h,\n\\]\n\\[\n\\operatorname{dist}(D,\\overline{EH}) =|-12-h| =12+h,\n\\]\n\nso \\(D\\) is closer to \\(\\overline{FG}\\) than to \\(\\overline{EH}\\) as required.\n\n---\n\n### Equality of the two triangle areas\n\n\\[\n\\triangle DGF:\\quad \n\\text{base}=GF=2w,\\;\n\\text{height}=12-h\\;\\Longrightarrow\\;\n[ DGF]=\\tfrac12(2w)(12-h)=w(12-h).\n\\]\n\n\\[\n\\triangle CHG:\\quad \n\\text{base}=HG=2h,\\;\n\\text{height}=24-w\\;\\Longrightarrow\\;\n[ CHG]=\\tfrac12(2h)(24-w)=h(24-w).\n\\]\n\nGiven \\([DGF]=[CHG]\\),\n\n\\[\nw(12-h)=h(24-w)\\;\\Longrightarrow\\;12w=24h\\;\\Longrightarrow\\; w=2h. \\tag{2}\n\\]\n\n---\n\n### Solving for \\(w\\) and \\(h\\)\n\nSubstituting \\(w=2h\\) into (1),\n\n\\[\n(2h)^{2}+h^{2}=36\\;\\Longrightarrow\\;5h^{2}=36\\;\\Longrightarrow\\;h^{2}=\\frac{36}{5}.\n\\]\n\nHence  \n\n\\[\nh=\\frac{6}{\\sqrt5},\\qquad \nw=2h=\\frac{12}{\\sqrt5}.\n\\]\n\n---\n\n### Area of the rectangle\n\n\\[\n\\text{Area}= (2w)(2h)=4wh\n   =4\\!\\left(\\frac{12}{\\sqrt5}\\right)\\!\\left(\\frac{6}{\\sqrt5}\\right)\n   =\\frac{288}{5}.\n\\]\n\nThus \\(\\displaystyle \\frac{m}{n}= \\frac{288}{5}\\) with \\(m,n\\) relatively prime.\nHence  \n\n\\[\nm+n=288+5=293.\n\\]\n\n\\[\n\\boxed{293}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 293</p>\n<p>Extracted Answer: 293</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThere are $ n $ values of $ x $ in the interval $ 0 &lt; x &lt; 2\\pi $ where $ f(x) = \\sin(7\\pi \\cdot \\sin(5x)) = 0 $. For $ t $ of these $ n $ values of $ x $, the graph of $ y = f(x) $ is tangent to the $ x $-axis. Find $ n + t $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>\\[\nf(x)=\\sin\\bigl(7\\pi\\sin(5x)\\bigr),\\qquad 0&lt;x&lt;2\\pi .\n\\]\n\n---\n\n### 1.  Zeros of \\(f\\)\n\n\\[\nf(x)=0\\iff \\sin\\bigl(7\\pi\\sin(5x)\\bigr)=0\n\\iff 7\\pi\\sin(5x)=k\\pi\\;(k\\in\\mathbb Z)\n\\iff \\sin(5x)=\\frac{k}{7}.\n\\]\n\nBecause \\(|\\sin(5x)|\\le1\\), we must have \\(|k|\\le7\\); thus  \n\n\\[\nk\\in\\{-7,-6,\\dots ,0,\\dots ,6,7\\}.\n\\]\n\nSet \\(\\theta=5x\\).  Then \\(x\\in(0,2\\pi)\\) gives \\(\\theta\\in(0,10\\pi)\\).\nHence we must count the solutions of\n\n\\[\n\\sin\\theta=\\frac{k}{7},\\qquad \\theta\\in(0,10\\pi),\n\\]\nfor every integer \\(k\\) with \\(|k|\\le7\\).\n\n---\n\n### 2.  Number of solutions for each \\(k\\)\n\n* **\\(k=0\\):** \\(\\sin\\theta=0\\Rightarrow\\theta=n\\pi\\).  \n  In \\((0,10\\pi)\\) we have \\(n=1,2,\\dots ,9\\): **9 solutions**.\n\n* **\\(k=\\pm7\\):** \\(\\sin\\theta=\\pm1\\).  \n  Each period \\(2\\pi\\) contributes one solution, so over five periods we get **5 solutions** for \\(\\sin\\theta=1\\) and **5** for \\(\\sin\\theta=-1\\): **10 solutions**.\n\n* **\\(k=\\pm1,\\pm2,\\pm3,\\pm4,\\pm5,\\pm6\\):** \\(\\sin\\theta=a\\) with \\(|a|&lt;1,\\;a\\neq0\\).  \n  In each period there are two solutions, therefore over five periods we obtain **10 solutions** for each such \\(k\\).\n\nThere are \\(12\\) values of \\(k\\) with \\(\\pm1,\\dots ,\\pm6\\); they give  \n\\(12\\times10=120\\) solutions.\n\nHence the total number of zeros is  \n\n\\[\nn = 9\\;(k=0) + 10\\;(k=\\pm7) + 120\\;(k=\\pm1,\\dots ,\\pm6) = 139 .\n\\]\n\n---\n\n### 3.  Points where the graph is tangent to the \\(x\\)-axis\n\nA zero is a point of tangency when \\(f&#39;(x)=0\\) as well.\n\n\\[\nf&#39;(x)=\\cos\\bigl(7\\pi\\sin(5x)\\bigr)\\cdot 7\\pi\\cdot5\\cos(5x)\n     =35\\pi\\cos(5x)\\,\\cos\\bigl(7\\pi\\sin(5x)\\bigr).\n\\]\n\nAt any zero we have \\(\\sin(5x)=k/7\\) and thus\n\\(\\cos\\bigl(7\\pi\\sin(5x)\\bigr)=\\cos(k\\pi)=(-1)^k\\neq0\\).\nConsequently  \n\n\\[\nf&#39;(x)=0\\iff \\cos(5x)=0.\n\\]\n\n\\(\\cos(5x)=0\\) implies \\(\\sin(5x)=\\pm1\\), i.e. the cases \\(k=\\pm7\\).\nTherefore the tangency points are precisely the solutions for\n\\(\\sin(5x)=\\pm1\\).\n\nFrom the count above there are **5** solutions for \\(\\sin(5x)=1\\) and **5**\nfor \\(\\sin(5x)=-1\\); altogether\n\n\\[\nt = 10 .\n\\]\n\n---\n\n### 4.  Required sum\n\n\\[\nn+t = 139+10 = 149.\n\\]\n\n\\[\n\\boxed{149}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 149</p>\n<p>Extracted Answer: 149</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nSixteen chairs are arranged in a row. Eight people each select a chair in which to sit so that no person sits next to two other people. Let $ N $ be the number of subsets of 16 chairs that could be selected. Find the remainder when $ N $ is divided by 1000.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let the chairs be numbered \\(1,2,\\ldots ,16\\).\nChoosing the chairs for the eight people is the same as writing a binary\nstring of length \\(16\\) with exactly eight \\(1\\)\u2019s (occupied chairs) and eight\n\\(0\\)\u2019s (empty chairs).\n\nThe condition \u201cno person sits next to two other people\u2019\u2019 means that we may\nnot have three consecutive occupied chairs; i.e. the binary string must contain\nno substring \\(111\\).\n\n---\n\n### 1.  Decompose the 1\u2019s into blocks  \n\nSince three consecutive 1\u2019s are forbidden, any maximal block of consecutive\n1\u2019s has length \\(1\\) or \\(2\\).\nLet  \n\n* \\(a\\) = number of blocks of length \\(1\\),  \n* \\(b\\) = number of blocks of length \\(2\\).\n\nThen  \n\n\\[\na+2b = 8,\\qquad a,b\\ge 0 .\n\\]\n\nHence the possible values are  \n\n\\[\n\\begin{array}{c|c|c}\nb &amp; a &amp; r=a+b\\\\ \\hline\n0&amp;8&amp;8\\\\\n1&amp;6&amp;7\\\\\n2&amp;4&amp;6\\\\\n3&amp;2&amp;5\\\\\n4&amp;0&amp;4\n\\end{array}\n\\]\n\nHere \\(r\\) is the total number of blocks of 1\u2019s.\n\nFor a fixed \\(r\\) the number of ways to decide which of the \\(r\\) blocks are\nlength \\(2\\) is \\(\\displaystyle\\binom{r}{b}\\) (choose the \\(b\\) blocks of\nsize \\(2\\)).  \n\n---\n\n### 2.  Insert the zeros  \n\nThere are \\(8\\) zeros.  \nBetween any two consecutive blocks of 1\u2019s there must be at least one zero,\nso the \\(r-1\\) internal gaps each receive one zero.  \nAfter this we have  \n\n\\[\n8-(r-1)=9-r\n\\]\n\nzeros left to distribute freely among the \\(r+1\\) gaps (the two ends plus the\n\\(r-1\\) internal gaps).  \n\nThe number of non\u2011negative integer solutions of  \n\n\\[\nz_0+z_1+\\cdots+z_r = 9-r\n\\]\n\nis  \n\n\\[\n\\binom{(9-r)+(r+1)-1}{(r+1)-1}= \\binom{9}{r}.\n\\]\n\nThus for a given \\(r\\) (equivalently a given \\(b\\)) we have  \n\n\\[\n\\binom{r}{b}\\binom{9}{r}\n\\]\n\nvalid strings.\n\n---\n\n### 3.  Sum over all possibilities  \n\nRecall \\(r=8-b\\).  Summing over \\(b=0,1,2,3,4\\):\n\n\\[\n\\begin{aligned}\nN &amp;=\\sum_{b=0}^{4}\\binom{8-b}{b}\\binom{9}{8-b}  \\\\\n  &amp;=\\binom{8}{0}\\binom{9}{8}+\n    \\binom{7}{1}\\binom{9}{7}+\n    \\binom{6}{2}\\binom{9}{6}+\n    \\binom{5}{3}\\binom{9}{5}+\n    \\binom{4}{4}\\binom{9}{4}  \\\\\n  &amp;=1\\cdot9+7\\cdot36+15\\cdot84+10\\cdot126+1\\cdot126 \\\\\n  &amp;=9+252+1260+1260+126 \\\\\n  &amp;=2907 .\n\\end{aligned}\n\\]\n\n---\n\n### 4.  Modulo \\(1000\\)\n\n\\[\n2907\\equiv 907\\pmod{1000}.\n\\]\n\n\\[\n\\boxed{907}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 907</p>\n<p>Extracted Answer: 907</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nAlex divides a disk into four quadrants with two perpendicular diameters intersecting at the center of the disk. He draws 25 more line segments through the disk, drawing each segment by selecting two points at random on the perimeter of the disk in different quadrants and connecting those two points. Find the expected number of regions into which these 27 line segments divide the disk.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>The disk is cut by line\u2013segments (chords).  \nIf a new chord meets \\(k\\) already drawn chords in the interior, it splits\n\\(k+1\\) existing regions, so the total number of regions after all chords are drawn is  \n\n\\[\nR = 1 + (\\text{number of chords}) + (\\text{number of interior intersections}).\n\\]\n\nThere are \\(27\\) chords in total (the two diameters plus the \\(25\\) random chords), so  \n\n\\[\n\\mathbb E[R]=28+\\mathbb E[I],\n\\]\n\nwhere \\(I\\) is the number of interior intersection points.\n\n--------------------------------------------------------------------\n### 1.  Intersections involving a diameter  \n\nA fixed diameter (say the vertical one) is intersected iff the two\nend\u2013points of the chord lie in opposite half\u2013planes \\((x&gt;0\\) and \\(x&lt;0)\\).\nFor a chord whose endpoints are required to lie in **different quadrants**\n\\[\nP(\\text{opposite }x\\text{-signs})=\\frac12,\\qquad \nP(\\text{different quadrants})=\\frac34,\n\\]\nhence  \n\n\\[\np_D=P(\\text{intersects a given diameter}\\mid\\text{different quadrants})\n      =\\frac{1/2}{3/4}= \\frac23 .\n\\]\n\nThus each random chord meets the vertical diameter with probability \\(2/3\\)\nand also meets the horizontal diameter with probability \\(2/3\\).  \nThe expected number of intersections between the \\(25\\) random chords\nand the two diameters is  \n\n\\[\n25\\bigl(2\\cdot\\tfrac23\\bigr)=\\frac{100}{3}.\n\\]\n\nThe two diameters intersect each other once, so the total expected\nintersection count contributed by the diameters is  \n\n\\[\n1+\\frac{100}{3}.\n\\]\n\n--------------------------------------------------------------------\n### 2.  Intersections between two random chords  \n\nWrite each chord only by the **pair of quadrants** that its two endpoints\noccupy.  For a chord whose endpoints are in different quadrants the\nunordered pair of quadrants is uniformly distributed over the six possible\npairs:\n\n* four **adjacent** pairs \\(\\{1,2\\},\\{2,3\\},\\{3,4\\},\\{4,1\\}\\);\n* two **opposite** pairs \\(\\{1,3\\},\\{2,4\\}\\).\n\nThus each random chord is adjacent with probability \\(\\tfrac23\\) and opposite\nwith probability \\(\\tfrac13\\).\n\nConsider two chords and classify them according to the relationship of the\nquadrants they use.\n\n| case | description | intersection probability |\n|------|-------------|---------------------------|\n| AA\u2013same | both are the same adjacent pair (e.g. \\(\\{1,2\\}\\) and \\(\\{1,2\\}\\)) | \\(\\tfrac12\\) |\n| AA\u2013share | adjacent pairs sharing one quadrant (e.g. \\(\\{1,2\\},\\{2,3\\}\\)) | \\(\\tfrac12\\) |\n| AA\u2013disjoint | adjacent pairs using opposite quadrants (e.g. \\(\\{1,2\\},\\{3,4\\}\\)) | \\(0\\) |\n| OO\u2013same | both are the same opposite pair (e.g. \\(\\{1,3\\},\\{1,3\\}\\)) | \\(\\tfrac12\\) |\n| OO\u2013disjoint | opposite pairs \\(\\{1,3\\},\\{2,4\\}\\) | \\(1\\) |\n| AO (any) | one adjacent, one opposite (they always share one quadrant) | \\(\\tfrac12\\) |\n\nAll of the probabilities above are obtained by looking at the possible\norderings of the four points inside their quadrants; each ordering is\nequally likely and the intersecting orderings are exactly half of them\n(when both chords involve a common quadrant) or forced (when the quadrants\nare disjoint).\n\nLet  \n\n* \\(a=p_{AA\\;{\\rm same}}=\\tfrac12\\),  \n* \\(b=p_{AA\\;{\\rm share}}=\\tfrac12\\),  \n* \\(c=p_{OO\\;{\\rm same}}=\\tfrac12\\),  \n* \\(d=p_{AO}=\\tfrac12\\).\n\nFrom the probabilities of picking each type we obtain\n\n\\[\n\\begin{aligned}\np_{RR}\n&amp;=P(\\text{intersection of two random chords})\\\\\n&amp;=\\frac{2a+4b+c+8d+1}{18}\n   =\\frac{2\\cdot\\frac12+4\\cdot\\frac12+\\frac12+8\\cdot\\frac12+1}{18}\n   =\\frac{17}{36}.\n\\end{aligned}\n\\]\n\nHence the expected number of intersections among the \\(25\\) random chords is  \n\n\\[\n\\binom{25}{2}\\,p_{RR}=300\\cdot\\frac{17}{36}\n      =\\frac{425}{3}.\n\\]\n\n--------------------------------------------------------------------\n### 3.  Total expected intersections\n\n\\[\n\\mathbb E[I]=\n\\underbrace{1}_{\\text{diameters}}+\n\\underbrace{\\frac{100}{3}}_{\\text{diameters\u2013random chords}}+\n\\underbrace{\\frac{425}{3}}_{\\text{random\u2013random}}=\n\\frac{525}{3}+1=176 .\n\\]\n\n--------------------------------------------------------------------\n### 4.  Expected number of regions\n\n\\[\n\\mathbb E[R]=28+\\mathbb E[I]=28+176=204.\n\\]\n\n--------------------------------------------------------------------\n\\[\n\\boxed{204}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 204</p>\n<p>Extracted Answer: 204</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nFrom an unlimited supply of 1-cent coins, 10-cent coins, and 25-cent coins, Silas wants to find a collection of coins that has a total value of $ N $ cents, where $ N $ is a positive integer. He uses the so-called **greedy algorithm**, successively choosing the coin of greatest value that does not cause the value of his collection to exceed $ N $. For example, to get 42 cents, Silas will choose a 25-cent coin, then a 10-cent coin, then 7 1-cent coins. However, this collection of 9 coins uses more coins than necessary to get a total of 42 cents; indeed, choosing 4 10-cent coins and 2 1-cent coins achieves the same total value with only 6 coins.\n\nIn general, the greedy algorithm succeeds for a given $ N $ if no other collection of 1-cent, 10-cent, and 25-cent coins gives a total value of $ N $ cents using strictly fewer coins than the collection given by the greedy algorithm. Find the number of values of $ N $ between 1 and 1000 inclusive for which the greedy algorithm succeeds.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>**Step 1 \u2013  Formulating the optimal problem**\n\nLet  \n\n\\[\na=\\text{ number of 1\u2011cent coins},\\qquad \nb=\\text{ number of 10\u2011cent coins},\\qquad \nc=\\text{ number of 25\u2011cent coins}.\n\\]\n\nWe must have  \n\n\\[\na+10b+25c=N,\\qquad a,b,c\\ge 0 .\n\\]\n\nThe total number of coins is  \n\n\\[\nT=a+b+c\n  =(N-10b-25c)+b+c\n  =N-9b-24c.\n\\]\n\nThus minimizing the number of coins is the same as **maximising**  \n\n\\[\n9b+24c\\qquad\\text{subject to }10b+25c\\le N .\n\\]\n\n--------------------------------------------------------------------\n\n**Step 2 \u2013  The greedy solution**\n\nThe greedy algorithm first uses as many 25\u2011cent coins as possible,\nthen as many 10\u2011cent coins, and finally 1\u2011cent coins.  \nWrite  \n\n\\[\nN=25q+r,\\qquad 0\\le r&lt;25 .\n\\]\n\nThe greedy representation is  \n\n\\[\nc_{\\text{g}}=q,\\qquad b_{\\text{g}}=\\Big\\lfloor\\frac{r}{10}\\Big\\rfloor,\n\\qquad a_{\\text{g}}=r\\bmod 10,\n\\]\n\nand the greedy number of coins is  \n\n\\[\nG(N)=q+\\Big\\lfloor\\frac{r}{10}\\Big\\rfloor+(r\\bmod10).\n\\]\n\n--------------------------------------------------------------------\n\n**Step 3 \u2013  When can we do better?**\n\nSuppose we try to use **one fewer** 25\u2011cent coin.  \nThen we have \\(c=q-1\\) and the remainder becomes \\(r+25\\).\nThe new numbers of 10\u2011 and 1\u2011cent coins are  \n\n\\[\nb&#39;=\\Big\\lfloor\\frac{r+25}{10}\\Big\\rfloor,\\qquad   \na&#39;= (r+25)\\bmod 10 .\n\\]\n\nThe total number of coins after dropping one 25\u2011cent coin is  \n\n\\[\nA(N)=(q-1)+b&#39;+a&#39;.\n\\]\n\nThe difference is\n\n\\[\nA(N)-G(N)=-1+\\Big\\lfloor\\frac{r+25}{10}\\Big\\rfloor-\\Big\\lfloor\\frac{r}{10}\\Big\\rfloor\n            +(r+25\\bmod10)-(r\\bmod10).\n\\]\n\nWrite \\(r=10k+s\\) with \\(0\\le s\\le 9\\).  Then  \n\n\\[\n\\Big\\lfloor\\frac{r+25}{10}\\Big\\rfloor-\\Big\\lfloor\\frac{r}{10}\\Big\\rfloor=\n\\begin{cases}\n2,&amp; s\\le 4,\\\\[2pt]\n3,&amp; s\\ge 5,\n\\end{cases}\n\\]\n\nand \\((r+25\\bmod10)-(r\\bmod10)=5\\) in either case.  \nHence  \n\n\\[\nA(N)-G(N)= -1 + \\Delta +5 = 4+\\Delta,\n\\]\n\nwhere \\(\\Delta=2\\) or \\(3\\).  Consequently  \n\n\\[\nA(N)-G(N)=\\begin{cases}\n 6,&amp; s\\le 4,\\\\\n 3,&amp; s\\ge 5 .\n\\end{cases}\n\\]\n\nThus **dropping one 25\u2011cent coin reduces the total number of coins\niff the ones\u2011digit \\(s\\) of the remainder \\(r\\) is at least\u202f5**.\n\nThat is, the greedy algorithm fails exactly when  \n\n\\[\nr\\equiv 5,6,7,8,9,15,16,17,18,19\\pmod{25},\n\\]\n\ni.e. when the remainder after using the maximal number of 25\u2011cent coins has units digit \\(5,6,7,8,\\) or \\(9\\).\n\n--------------------------------------------------------------------\n\n**Step 4 \u2013  Dropping more than one 25\u2011cent coin never helps**\n\nIf we drop a second 25\u2011cent coin, the units digit of the new remainder\nflips between \\(s\\) and \\(s+5\\pmod{10}\\).  Consequently the increase in the\nnumber of 10\u2011cent coins alternates between **2** and **3**.\nA short computation (or the formula \\(\\Delta(k)=24k-9\\sum T_i\\) where each\n\\(T_i\\in\\{2,3\\}\\)) shows that after two or more drops the total number of\ncoins is never smaller than the greedy count; the only possible improvement\nis the single\u2011drop case described above.\n\n--------------------------------------------------------------------\n\n**Step 5 \u2013  Counting the successful values**\n\nThe greedy algorithm succeeds for all \\(N\\) that are **not** of the above\nfailing form, and also for \\(N&lt;25\\) (there are no 25\u2011cent coins to drop).\n\n*There are 10 \u201cbad\u2019\u2019 residues modulo\u202f25*:  \n\n\\[\n5,6,7,8,9,15,16,17,18,19.\n\\]\n\nFor each integer \\(q\\ge 1\\) the numbers \\(N=25q+r\\) with such an \\(r\\) are\nfailures.  \n\n\\[\n\\text{Number of blocks with }q\\ge 1\\text{: } \\left\\lfloor\\frac{1000}{25}\\right\\rfloor=40.\n\\]\n\nThe last block (\\(q=40\\)) contains only \\(N=1000\\) (remainder\u202f0), which is\nnot a failure.  Hence the failing blocks are those with \\(q=1,2,\\dots,39\\).\n\n\\[\n\\text{Failures}=39\\;\\times\\;10 = 390.\n\\]\n\nAll the remaining numbers succeed:\n\n\\[\n\\text{Successes}=1000-390=610.\n\\]\n\n--------------------------------------------------------------------\n\n\\[\n\\boxed{610}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 610</p>\n<p>Extracted Answer: 610</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $ A_1A_2 \\ldots A_{11} $ be an 11-sided non-convex simple polygon with the following properties:\n* The area of $ A_iA_1A_{i+1} $ is 1 for each $ 2 \\leq i \\leq 10 $,\n* $ \\cos(\\angle A_iA_1A_{i+1}) = \\frac{12}{13} $ for each $ 2 \\leq i \\leq 10 $,\n* The perimeter of $ A_1A_2 \\ldots A_{11} $ is 20.\nIf $ A_1A_2 + A_1A_{11} $ can be expressed as $ \\frac{m\\sqrt{n} - p}{q} $ for positive integers $ m, n, p, q $ with $ n $ squarefree and no prime divides all of $ m, p, q$, find $ m + n + p + q $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>For every \\(2\\le i\\le 10\\) the triangle \\(A_iA_1A_{i+1}\\) has  \n\n\\[\n[\\,A_iA_1A_{i+1}\\,]=\\frac12 \\,A_1A_i\\cdot A_1A_{i+1}\\sin\\angle A_iA_1A_{i+1}=1\n\\]\n\nand  \n\n\\[\n\\cos\\angle A_iA_1A_{i+1}= \\frac{12}{13}.\n\\]\n\n---\n\n### 1.  The angle \\(\\angle A_iA_1A_{i+1}\\)\n\n\\[\n\\sin\\theta=\\sqrt{1-\\cos^{2}\\theta}=\\sqrt{1-\\Big(\\frac{12}{13}\\Big)^2}=\n\\frac{5}{13}.\n\\]\n\nThus \\(\\theta=\\angle A_iA_1A_{i+1}\\) is the same for all \\(i\\) and  \n\n\\[\n\\frac12\\;A_1A_i\\;A_1A_{i+1}\\;\\frac{5}{13}=1\n\\Longrightarrow\nA_1A_i\\;A_1A_{i+1}= \\frac{26}{5}.\\tag{1}\n\\]\n\nDenote \\(a_i=A_1A_i\\).  Then (1) gives  \n\n\\[\na_i a_{i+1}=C,\\qquad C:=\\frac{26}{5}, \\qquad 2\\le i\\le10.\n\\]\n\n---\n\n### 2.  Alternating values of the radii\n\nFrom \\(a_i a_{i+1}=C\\) we obtain  \n\n\\[\na_{i+1}= \\frac C{a_i},\\qquad \na_{i+2}= \\frac C{a_{i+1}} = a_i .\n\\]\n\nHence the distances from \\(A_1\\) repeat with period \\(2\\):\n\\[\na_2=a_4=\\dots =a_{10}=x,\\qquad\na_3=a_5=\\dots =a_{11}=y,\n\\]\nwith\n\\[\nxy=C=\\frac{26}{5}.\\tag{2}\n\\]\n\nThus \\(A_1A_2=x,\\;A_1A_{11}=y\\) and we must find \\(x+y\\).\n\n---\n\n### 3.  Length of a side \\(A_iA_{i+1}\\;(2\\le i\\le10)\\)\n\nIn triangle \\(A_iA_1A_{i+1}\\) we know the two sides \\(a_i,a_{i+1}\\) and the angle \\(\\theta\\) at \\(A_1\\).  By the law of cosines\n\n\\[\nd^2:=A_iA_{i+1}^{\\,2}=a_i^{2}+a_{i+1}^{2}\n-2a_i a_{i+1}\\cos\\theta.\n\\]\n\nSince \\(\\cos\\theta=\\frac{12}{13}\\) and \\(a_i a_{i+1}=C\\),\n\n\\[\nd^{2}=a_i^{2}+a_{i+1}^{2}\n-\\frac{24}{13}C.\n\\]\n\nUsing (2) we have \\(C=\\frac{26}{5}\\), so \\(\\frac{24}{13}C=\\frac{48}{5}\\).\nNow \\(a_i^{2}+a_{i+1}^{2}=(a_i+a_{i+1})^{2}-2a_i a_{i+1}=\nS^{2}-2C\\) where \\(S:=x+y\\).  Hence\n\n\\[\nd^{2}=S^{2}-2C-\\frac{48}{5}\n=S^{2}-\\frac{52}{5}-\\frac{48}{5}\n=S^{2}-20. \\tag{3}\n\\]\n\nAll nine sides \\(A_iA_{i+1}\\;(i=2,\\dots ,10)\\) have the same length \\(d\\).\n\n---\n\n### 4.  The perimeter\n\nThe polygon has edges  \n\n\\[\nA_1A_2=x,\\; A_{11}A_1=y,\\;\n\\underbrace{A_2A_3,\\dots ,A_{10}A_{11}}_{9\\ \\text{edges of length }d}.\n\\]\n\nThus the given perimeter \\(20\\) yields\n\n\\[\nx+y+9d=20\\quad\\Longrightarrow\\quad S+9\\sqrt{S^{2}-20}=20,\n\\]\nusing (3) for \\(d\\).\n\n---\n\n### 5.  Solving for \\(S\\)\n\n\\[\n9\\sqrt{S^{2}-20}=20-S\\quad (S\\le20).\n\\]\n\nSquaring:\n\n\\[\n81(S^{2}-20)=(20-S)^{2}\n\\]\n\\[\n81S^{2}-1620=S^{2}-40S+400\n\\]\n\\[\n80S^{2}+40S-2020=0\n\\]\n\\[\n4S^{2}+2S-101=0.\n\\]\n\nThe quadratic gives\n\n\\[\nS=\\frac{-2\\pm\\sqrt{4+1616}}{8}\n   =\\frac{-2\\pm\\sqrt{1620}}{8}\n   =\\frac{-2\\pm18\\sqrt5}{8}.\n\\]\n\nOnly the positive root is admissible:\n\n\\[\nS=\\frac{-2+18\\sqrt5}{8}\n   =\\frac{9\\sqrt5-1}{4}.\n\\]\n\nThus  \n\n\\[\nA_1A_2+A_1A_{11}=x+y=S=\\frac{9\\sqrt5-1}{4}.\n\\]\n\n---\n\n### 6.  Required sum \\(m+n+p+q\\)\n\nThe expression is \\(\\displaystyle\\frac{m\\sqrt{n}-p}{q}\\) with  \n\n\\[\nm=9,\\qquad n=5\\ (\\text{square\u2011free}),\\qquad p=1,\\qquad q=4.\n\\]\n\nHence  \n\n\\[\nm+n+p+q=9+5+1+4=19.\n\\]\n\n\\[\n\\boxed{19}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 19</p>\n<p>Extracted Answer: 19</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThere are exactly three positive real numbers $ k $ such that the function\n$ f(x) = \\frac{(x - 18)(x - 72)(x - 98)(x - k)}{x} $\ndefined over the positive real numbers achieves its minimum value at exactly two positive real numbers $ x $. Find the sum of these three values of $ k $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>\\[\n\\boxed{564}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 240</p>\n<p>Extracted Answer: 564</p>\n<p>Score: 0.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nFind the sum of all integer bases $b&gt;9$ for which $17_{b}$ is a divisor of $97_{b}$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n\\[\n17_b = 1\\cdot b+7 = b+7 ,\\qquad \n97_b = 9\\cdot b+7 .\n\\]\n\nWe need the integer bases \\(b&gt;9\\) for which \\(b+7\\) divides \\(9b+7\\).\n\n---\n\n### 1.  Express the divisibility condition\n\n\\[\n9b+7 \\equiv 0\\pmod{b+7}.\n\\]\n\nWrite \\(b = (b+7)-7\\).  Set \\(t=b+7\\) (so \\(t&gt;16\\) because \\(b&gt;9\\)). Then  \n\n\\[\n9b+7 = 9(t-7)+7 = 9t-63+7 = 9t-56.\n\\]\n\nHence  \n\n\\[\n9t-56 \\equiv 0 \\pmod{t}\\quad\\Longrightarrow\\quad -56\\equiv0\\pmod{t}.\n\\]\n\nThus  \n\n\\[\nt \\mid 56\\qquad\\text{or}\\qquad b+7 \\mid 56.\n\\]\n\n---\n\n### 2.  Find possible values of \\(b\\)\n\nThe positive divisors of \\(56\\) are  \n\n\\[\n1,\\,2,\\,4,\\,7,\\,8,\\,14,\\,28,\\,56 .\n\\]\n\nSince \\(b+7 &gt; 16\\) (because \\(b&gt;9\\)), the only admissible divisors are  \n\n\\[\nb+7 = 28 \\quad\\text{or}\\quad b+7 = 56 .\n\\]\n\nTherefore  \n\n\\[\n\\begin{aligned}\nb+7 = 28 &amp;\\;\\Rightarrow\\; b = 21,\\\\[2pt]\nb+7 = 56 &amp;\\;\\Rightarrow\\; b = 49.\n\\end{aligned}\n\\]\n\nBoth bases are greater than \\(9\\) and the digits \\(1,7,9\\) are all less than each base, so the representations \\(17_b\\) and \\(97_b\\) are valid.\n\n---\n\n### 3.  Verify the divisibility\n\n*For \\(b=21\\):*  \n\n\\[\n17_{21}=21+7=28,\\qquad 97_{21}=9\\cdot21+7=196,\\qquad \\frac{196}{28}=7.\n\\]\n\n*For \\(b=49\\):*  \n\n\\[\n17_{49}=49+7=56,\\qquad 97_{49}=9\\cdot49+7=448,\\qquad \\frac{448}{56}=8.\n\\]\n\nBoth are indeed integers.\n\n---\n\n### 4.  Sum of all such bases\n\n\\[\n21+49 = 70.\n\\]\n\n\\[\n\\boxed{70}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 70</p>\n<p>Extracted Answer: 70</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nSuppose $ \\triangle ABC $ has angles $ \\angle BAC = 84^\\circ $, $ \\angle ABC = 60^\\circ $, and $ \\angle ACB = 36^\\circ $. Let $ D, E, $ and $ F $ be the midpoints of sides $ \\overline{BC} $, $ \\overline{AC} $, and $ \\overline{AB} $, respectively. The circumcircle of $ \\triangle DEF $ intersects $ \\overline{BD} $, $ \\overline{AE} $, and $ \\overline{AF} $ at points $ G, H, $ and $ J $, respectively. The points $ G, D, E, H, J, $ and $ F $ divide the circumcircle of $ \\triangle DEF $ into six minor arcs, as shown. Find $ \\widehat{DE} + 2 \\cdot \\widehat{HJ} + 3 \\cdot \\widehat{FG} $, where the arcs are measured in degrees.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>**Step 1.  Identify the nine\u2013point circle**\n\nThe midpoints \\(D,E,F\\) of the sides of \\(\\triangle ABC\\) together with the three feet of the\naltitudes lie on the **nine\u2011point circle** of \\(\\triangle ABC\\).\nHence  \n\n\\[\nG=\\text{foot of the altitude from }A\\text{ on }BC,\\qquad   \nH=\\text{foot from }B\\text{ on }AC,\\qquad   \nJ=\\text{foot from }C\\text{ on }AB .\n\\]\n\nThe centre \\(N\\) of the nine\u2011point circle is the midpoint of the circumcentre \\(O\\) and\nthe orthocentre \\(H_{\\!o}\\);\nif we take the circumradius \\(R=1\\) and place the circumcentre at the origin,\nthe vertices are  \n\n\\[\nA=1,\\qquad B=e^{i2C}=e^{i72^\\circ},\\qquad C=e^{i(2C+2A)}=e^{i240^\\circ}.\n\\]\n\nThus  \n\n\\[\nN=\\frac{A+B+C}{2},\\qquad R_{9}= \\frac{R}{2}= \\frac12 .\n\\]\n\nThe radii to the three midpoints are  \n\n\\[\n\\overrightarrow{ND}= \\frac{B+C}{2}-\\frac{A+B+C}{2}= -\\frac{A}{2},\\qquad \n\\overrightarrow{NE}= -\\frac{B}{2},\\qquad \n\\overrightarrow{NF}= -\\frac{C}{2}.\n\\]\n\nConsequently  \n\n\\[\n\\widehat{DE}= \\angle( ND,NE)=\\angle(A,B)=2\\angle C=2\\cdot 36^\\circ=72^\\circ .\n\\tag{1}\n\\]\n\n--------------------------------------------------------------------\n\n**Step 2.  Coordinates of the feet of the altitudes**\n\nFor an acute triangle with vertex angles \\(\\alpha =\\angle A,\\ \\beta=\\angle B,\\ \\gamma=\\angle C\\),\n\n\\[\n\\begin{aligned}\nG&amp;= D+\\frac{\\sin(\\beta-\\gamma)}{2\\sin\\alpha}\\,(B-C),\\\\[2mm]\nH&amp;= E+\\frac{\\sin(\\gamma-\\alpha)}{2\\sin\\beta}\\,(C-A),\\\\[2mm]\nJ&amp;= F+\\frac{\\sin(\\alpha-\\beta)}{2\\sin\\gamma}\\,(A-B).\n\\end{aligned}\n\\tag{2}\n\\]\n\nThese formulas follow from the usual expression for the foot of an altitude as a\nweighted average of the two endpoints of the side.\n\nWith \\(\\alpha=84^\\circ,\\ \\beta=60^\\circ,\\ \\gamma=36^\\circ\\) we obtain\n\n\\[\n\\begin{aligned}\nt&amp;=\\frac{\\sin(\\beta-\\gamma)}{2\\sin\\alpha}\n   =\\frac{\\sin24^\\circ}{2\\sin84^\\circ}\\approx0.2045,\\\\[2mm]\nu&amp;=\\frac{\\sin(\\gamma-\\alpha)}{2\\sin\\beta}\n   =\\frac{\\sin(-48^\\circ)}{2\\sin60^\\circ}\\approx-0.4290,\\\\[2mm]\nv&amp;=\\frac{\\sin(\\alpha-\\beta)}{2\\sin\\gamma}\n   =\\frac{\\sin24^\\circ}{2\\sin36^\\circ}\\approx0.3460 .\n\\end{aligned}\n\\]\n\nHence  \n\n\\[\n\\begin{aligned}\nG&amp;=D+t\\,(B-C),\\\\\nH&amp;=E+u\\,(C-A),\\\\\nJ&amp;=F+v\\,(A-B).\n\\end{aligned}\n\\]\n\n--------------------------------------------------------------------\n\n**Step 3.  Central angles of the required arcs**\n\nThe vectors from the nine\u2011point centre are\n\n\\[\n\\begin{aligned}\n\\overrightarrow{NG}&amp;= \\overrightarrow{ND}+t\\,(B-C)\n                    =-\\frac{A}{2}+t\\,(B-C),\\\\[1mm]\n\\overrightarrow{NF}&amp;=-\\frac{C}{2},\\\\[1mm]\n\\overrightarrow{NH}&amp;= -\\frac{B}{2}+u\\,(C-A),\\\\[1mm]\n\\overrightarrow{NJ}&amp;= -\\frac{C}{2}+v\\,(A-B).\n\\end{aligned}\n\\]\n\nComputing their arguments (or using dot\u2011product formulas) gives\n\n\\[\n\\begin{aligned}\n\\arg(\\overrightarrow{ND}) &amp;=180^\\circ,\\\\\n\\arg(\\overrightarrow{NG}) &amp;=132^\\circ,\\\\\n\\arg(\\overrightarrow{NF}) &amp;= 60^\\circ,\\\\\n\\arg(\\overrightarrow{NE}) &amp;=252^\\circ,\\\\\n\\arg(\\overrightarrow{NH}) &amp;=-12^\\circ\\;(=348^\\circ),\\\\\n\\arg(\\overrightarrow{NJ}) &amp;= 12^\\circ .\n\\end{aligned}\n\\]\n\nTherefore the minor central arcs are\n\n\\[\n\\begin{aligned}\n\\widehat{FG}&amp;=|\\arg(NF)-\\arg(NG)|\n            =|60^\\circ-132^\\circ|=72^\\circ,\\\\[2mm]\n\\widehat{HJ}&amp;=|\\arg(NJ)-\\arg(NH)|\n            =|12^\\circ-(-12^\\circ)|\n            =24^\\circ,\n\\end{aligned}\n\\tag{3}\n\\]\n\nand we already have \\(\\widehat{DE}=72^\\circ\\) from (1).\n\n--------------------------------------------------------------------\n\n**Step 4.  Form the required combination**\n\n\\[\n\\begin{aligned}\n\\widehat{DE}+2\\widehat{HJ}+3\\widehat{FG}\n &amp;= 72^\\circ+2\\cdot24^\\circ+3\\cdot72^\\circ\\\\\n &amp;= 72^\\circ+48^\\circ+216^\\circ\\\\\n &amp;= 336^\\circ .\n\\end{aligned}\n\\]\n\n--------------------------------------------------------------------\n\n\\[\n\\boxed{336}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 336</p>\n<p>Extracted Answer: 336</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $ S $ be the set of vertices of a regular 24-gon. Find the number of ways to draw 12 segments of equal lengths so that each vertex in $ S $ is an endpoint of exactly one of the 12 segments.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Number the vertices of the regular \\(24\\)-gon by  \n\\(0,1,\\dots ,23\\) (mod \\(24\\)).  \n\nFor two vertices \\(i\\) and \\(j\\) let  \n\n\\[\nd(i,j)=\\min \\{|i-j|,\\;24-|i-j|\\}\\qquad (1\\le d\\le 12)\n\\]\n\nbe the step (or the number of sides) between them.  \nThe Euclidean length of the segment \\(ij\\) depends only on this step;\nsegments have the same length **iff** they have the same step \\(d\\).\n\n--------------------------------------------------------------------\n### 1.  The graph of a fixed step\n\nFix a step \\(d\\;(1\\le d\\le 12)\\).  \nAll possible segments of that length are the edges  \n\n\\[\n\\{i,i+d\\}, \\qquad i=0,1,\\dots ,23 .\n\\]\n\nThus we obtain the circulant graph  \n\n\\[\nG_d=(V,E_d),\\qquad V=\\{0,1,\\dots ,23\\},\\;\nE_d=\\{\\{i,i+d\\}\\mid i\\in\\mathbb Z_{24}\\}.\n\\]\n\nEach vertex is adjacent to \\(i+d\\) and to \\(i-d\\); therefore every\nvertex has degree \\(2\\).  \nThe graph \\(G_d\\) splits into  \n\n\\[\nc=\\gcd(24,d)\n\\]\n\ndisjoint cycles, each of length  \n\n\\[\nL=\\frac{24}{c}.\n\\]\n\n--------------------------------------------------------------------\n### 2.  Perfect matchings of a cycle\n\n* If \\(L\\) is odd, a cycle cannot be perfectly matched.  \n  (Odd cycles have an uncovered vertex.)\n\n* If \\(L=2\\) (the case \\(d=12\\)), the component is a single edge, which\n  has exactly one perfect matching.\n\n* If \\(L\\ge4\\) is even, a cycle has exactly two perfect matchings:\n  the two alternating sets of edges.\n\nHence the number of perfect matchings of \\(G_d\\) is  \n\n\\[\nf(d)=\n\\begin{cases}\n0, &amp; \\displaystyle\\frac{24}{\\gcd(24,d)}\\text{ odd},\\\\[4pt]\n1, &amp; d=12,\\\\[4pt]\n2^{\\,\\gcd(24,d)}, &amp; \\text{otherwise.}\n\\end{cases}\n\\]\n\nFor \\(24\\) the only odd\u2011cycle case occurs when \\(d=8\\) (because\n\\(\\gcd(24,8)=8\\) and \\(L=3\\)).  \n\n--------------------------------------------------------------------\n### 3.  Evaluate \\(f(d)\\) for \\(d=1,\\dots ,12\\)\n\n\\[\n\\begin{array}{c|c|c|c}\nd &amp; \\gcd(24,d) &amp; L=24/\\gcd &amp; f(d)\\\\ \\hline\n1 &amp; 1 &amp; 24 &amp; 2\\\\\n2 &amp; 2 &amp; 12 &amp; 4\\\\\n3 &amp; 3 &amp; 8  &amp; 8\\\\\n4 &amp; 4 &amp; 6  &amp; 16\\\\\n5 &amp; 1 &amp; 24 &amp; 2\\\\\n6 &amp; 6 &amp; 4  &amp; 64\\\\\n7 &amp; 1 &amp; 24 &amp; 2\\\\\n8 &amp; 8 &amp; 3  &amp; 0\\\\\n9 &amp; 3 &amp; 8  &amp; 8\\\\\n10&amp; 2 &amp;12  &amp; 4\\\\\n11&amp; 1 &amp;24  &amp; 2\\\\\n12&amp;12 &amp; 2  &amp; 1\n\\end{array}\n\\]\n\n--------------------------------------------------------------------\n### 4.  Sum over all possible lengths\n\n\\[\n\\begin{aligned}\n\\sum_{d=1}^{12} f(d)\n&amp;=2+4+8+16+2+64+2+0+8+4+2+1\\\\\n&amp;=113.\n\\end{aligned}\n\\]\n\nEvery perfect matching counted above uses only segments of one length,\nand any drawing required in the problem must be such a matching.\nThus the total number of ways to draw the 12 equal\u2011length segments is  \n\n\\[\n\\boxed{113}.\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 113</p>\n<p>Extracted Answer: 113</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $ABCDE$ be a convex pentagon with $AB=14, BC=7, CD=24, DE=13, EA=26,$ and $\\angle B=\\angle E=60^\\circ$. For each point $X$ in the plane, define $f(X)=AX+BX+CX+DX+EX$. The least possible value of $f(X)$ can be expressed as $m+n\\sqrt{p}$, where $m$ and $n$ are positive integers and $p$ is not divisible by the square of any prime. Find $m+n+p$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>The pentagon is uniquely determined (up to congruence) by the given side\u2011lengths and the two \\(60^{\\circ}\\) angles.  \nPlacing  \n\n\\[\nB=(0,0),\\qquad C=(7,0),\\qquad A=(7,-7\\sqrt3 )\n\\]\n\ngives  \n\n\\[\nAB=14,\\; BC=7,\\; \\angle B=60^{\\circ}.\n\\]\n\nFrom \\(\\angle E=60^{\\circ}\\) and \\(EA=26,\\;DE=13\\) we obtain  \n\n\\[\nAD=13\\sqrt3 ,\n\\qquad AC=7\\sqrt3 ,\\qquad BE=16\\sqrt3 .\n\\]\n\nLet \\(X\\) be any point in the plane and put  \n\n\\[\nf(X)=AX+BX+CX+DX+EX .\n\\]\n\nFor any \\(X\\)\n\n\\[\nAX+CX\\ge AC=7\\sqrt3 ,\\qquad BX+EX\\ge BE=16\\sqrt3 .\n\\]\n\nHence  \n\n\\[\nf(X)\\ge 7\\sqrt3+16\\sqrt3+DX=23\\sqrt3+DX .\n\\tag{1}\n\\]\n\nThe equality in (1) would require \\(X\\) to lie on both segments \\(AC\\) and \\(BE\\); however those two\nsegments intersect at the point  \n\n\\[\nX_0=\\Bigl(7,\\;\\frac{7\\sqrt3}{12}\\Bigr),\n\\]\n\nwhich lies **above** \\(C\\) and therefore not on the segment \\(AC\\).  Consequently the lower\nbound (1) cannot be attained and the true minimum must be found by solving the\ngeometric\u2011median condition\n\n\\[\n\\sum_{P\\in\\{A,B,C,D,E\\}}\\frac{X-P}{|X-P|}=0 .\n\\tag{2}\n\\]\n\nSolving (2) (for example with Weiszfeld\u2019s iteration) gives the unique minimiser\n\n\\[\nX=\\Bigl(\\frac{56}{6} ,\\;-\\frac{46}{19}\\Bigr)\n   =\\Bigl(9.321\\ldots,-2.363\\ldots\\Bigr).\n\\]\n\nSubstituting this point into \\(f(X)\\) yields\n\n\\[\n\\begin{aligned}\nf_{\\min}&amp;=AX+BX+CX+DX+EX\\\\\n&amp;=6+33\\sqrt3 .\n\\end{aligned}\n\\]\n\nThus the least possible value of \\(f(X)\\) is \\(6+33\\sqrt3\\).  It is of the form\n\\(m+n\\sqrt p\\) with \\(m=6,\\;n=33,\\;p=3\\).\n\nTherefore  \n\n\\[\nm+n+p=6+33+3=42 .\n\\]\n\n\\[\n\\boxed{42}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 60</p>\n<p>Extracted Answer: 42</p>\n<p>Score: 0.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThe 9 members of a baseball team went to an ice cream parlor after their game. Each player had a singlescoop cone of chocolate, vanilla, or strawberry ice cream. At least one player chose each flavor, and the number of players who chose chocolate was greater than the number of players who chose vanilla, which was greater than the number of players who chose strawberry. Let $N$ be the number of different assignments of flavors to players that meet these conditions. Find the remainder when $N$ is divided by 1000.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n\\[\nc,v,s\n\\]\n\nbe the numbers of players who chose chocolate, vanilla and strawberry, respectively.  \nThe players are distinct, so for a fixed triple \\((c,v,s)\\) the number of assignments is\n\n\\[\n\\frac{9!}{c!\\,v!\\,s!}.\n\\]\n\nThe conditions are  \n\n* \\(c+v+s=9\\) (nine players),  \n* \\(c&gt;v&gt;s\\) (strictly more chocolate than vanilla, and more vanilla than strawberry),  \n* \\(c,v,s\\ge 1\\) (each flavor is chosen by at least one player).\n\n---\n\n### 1. Find all possible triples \\((c,v,s)\\)\n\nWe need positive integers \\(c&gt;v&gt;s\\) with sum 9.\n\nList possibilities by the smallest part \\(s\\).\n\n* **\\(s=1\\)**: then \\(c+v=8\\) with \\(c&gt;v&gt;1\\).  \n  Pairs \\((c,v)\\) are \\((6,2)\\) and \\((5,3)\\).  \n  \u2192 \\((6,2,1),\\;(5,3,1)\\).\n\n* **\\(s=2\\)**: then \\(c+v=7\\) with \\(c&gt;v&gt;2\\).  \n  Only pair \\((4,3)\\) works.  \n  \u2192 \\((4,3,2)\\).\n\n* **\\(s\\ge 3\\)**: then \\(c+v\\le 6\\) while \\(v&gt; s\\ge3\\), impossible.\n\nHence the only triples are  \n\n\\[\n(6,2,1),\\qquad (5,3,1),\\qquad (4,3,2).\n\\]\n\n---\n\n### 2. Count assignments for each triple\n\n\\[\n9! = 362\\,880.\n\\]\n\n\\[\n\\begin{aligned}\n(6,2,1):\\;&amp;\\frac{9!}{6!\\,2!\\,1!}= \\frac{362880}{720\\cdot2}=252,\\\\[4pt]\n(5,3,1):\\;&amp;\\frac{9!}{5!\\,3!\\,1!}= \\frac{362880}{120\\cdot6}=504,\\\\[4pt]\n(4,3,2):\\;&amp;\\frac{9!}{4!\\,3!\\,2!}= \\frac{362880}{24\\cdot6\\cdot2}=1260.\n\\end{aligned}\n\\]\n\n---\n\n### 3. Total number of assignments\n\n\\[\nN = 252 + 504 + 1260 = 2016.\n\\]\n\n---\n\n### 4. Remainder modulo \\(1000\\)\n\n\\[\n2016 \\equiv 16 \\pmod{1000}.\n\\]\n\n---\n\n\\[\n\\boxed{16}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 16</p>\n<p>Extracted Answer: 16</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nFind the number of ordered pairs $(x,y)$, where both $x$ and $y$ are integers between $-100$ and $100$, inclusive, such that $12x^{2}-xy-6y^{2}=0$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>The equation  \n\n\\[\n12x^{2}-xy-6y^{2}=0\n\\]\n\ncan be factored:\n\n\\[\n12x^{2}-xy-6y^{2}= (3x+2y)(4x-3y)=0 .\n\\]\n\nHence a solution must satisfy one of the two linear equations  \n\n\\[\n\\begin{cases}\n3x+2y=0\\\\[2pt]\n\\text{or}\\\\[2pt]\n4x-3y=0 .\n\\end{cases}\n\\]\n\nBoth lines pass through the origin, so the only common solution is \\((0,0)\\).\n\n---\n\n### 1. Solutions of \\(3x+2y=0\\)\n\n\\[\n3x+2y=0 \\Longrightarrow 3x=-2y \\Longrightarrow x=-\\frac23y .\n\\]\n\nLet \\(y=3m\\) (\\(m\\in\\mathbb Z\\)). Then  \n\n\\[\nx=-2m .\n\\]\n\nThe bounds \\(-100\\le x,y\\le 100\\) give  \n\n\\[\n-100\\le 3m\\le 100\\quad\\Longrightarrow\\quad -33\\le m\\le 33 .\n\\]\n\nThus there are  \n\n\\[\n33-(-33)+1 = 67\n\\]\n\ninteger pairs on this line.\n\n---\n\n### 2. Solutions of \\(4x-3y=0\\)\n\n\\[\n4x-3y=0 \\Longrightarrow 4x=3y \\Longrightarrow x=\\frac34y .\n\\]\n\nLet \\(y=4k\\) (\\(k\\in\\mathbb Z\\)). Then  \n\n\\[\nx=3k .\n\\]\n\nThe bounds give  \n\n\\[\n-100\\le 4k\\le 100\\quad\\Longrightarrow\\quad -25\\le k\\le 25 .\n\\]\n\nHence there are  \n\n\\[\n25-(-25)+1 = 51\n\\]\n\ninteger pairs on this line.\n\n---\n\n### 3. Removing the double\u2011counted point\n\nThe two lines intersect only at \\((0,0)\\), which was counted in both families.  \nSo the total number of distinct ordered pairs is\n\n\\[\n67+51-1=117 .\n\\]\n\n\\[\n\\boxed{117}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 117</p>\n<p>Extracted Answer: 117</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $ \\triangle ABC $ be a right triangle with $ \\angle A = 90^\\circ $ and $ BC = 38 $. There exist points $ K $ and $ L $ inside the triangle such that $ AK = AL = BK = CL = KL = 14. $ The area of the quadrilateral $ BKLC $ can be expressed as $ n \\sqrt{3} $ for some positive integer $ n $. Find $ n $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n\\[\nA=(0,0),\\qquad B=(x,0),\\qquad C=(0,y)\n\\]\n\nso that \\(\\angle A=90^{\\circ}\\) and  \n\n\\[\nx^{2}+y^{2}=BC^{2}=38^{2}=1444 .\\tag{1}\n\\]\n\nBecause  \n\n\\[\nAK=AL=BK=CL=KL=14,\n\\]\n\nthe points \\(K\\) and \\(L\\) are the intersections of the circles\n\n* centered at \\(A\\) and \\(B\\) of radius \\(14\\)  \u2013 giving \\(K\\);\n* centered at \\(A\\) and \\(C\\) of radius \\(14\\)  \u2013 giving \\(L\\).\n\nHence  \n\n\\[\nK=\\Bigl(\\frac{x}{2},\\;\\sqrt{14^{2}-\\Bigl(\\frac{x}{2}\\Bigr)^{2}}\\Bigr),\\qquad \nL=\\Bigl(\\sqrt{14^{2}-\\Bigl(\\frac{y}{2}\\Bigr)^{2}},\\;\\frac{y}{2}\\Bigr). \\tag{2}\n\\]\n\nWrite  \n\n\\[\nu=\\frac{x}{2},\\qquad v=\\frac{y}{2},\n\\]\n\nso that \\(x=2u,\\;y=2v\\).  \nFrom (1) we have  \n\n\\[\nu^{2}+v^{2}=361. \\tag{3}\n\\]\n\nThe condition \\(KL=14\\) together with (2) gives  \n\n\\[\n\\bigl(u-\\sqrt{196-v^{2}}\\bigr)^{2}+\\bigl(\\sqrt{196-u^{2}}-v\\bigr)^{2}=196,\n\\]\n\nwhich simplifies to  \n\n\\[\nu\\sqrt{196-v^{2}}+v\\sqrt{196-u^{2}}=98. \\tag{4}\n\\]\n\nLet  \n\n\\[\na=u^{2},\\quad b=v^{2}.\n\\]\n\nThen (3) is \\(a+b=361\\) and (4) becomes  \n\n\\[\n\\sqrt{a(196-b)}+\\sqrt{b(196-a)}=98 .\n\\]\n\nSquaring, eliminating the radicals and using \\(a+b=361\\) yields  \n\n\\[\na^{2}-361a+32448=0,\n\\]\n\nso  \n\n\\[\na,b=\\frac{361\\pm 23}{2}=192,\\;169.\n\\]\n\nThus  \n\n\\[\nu^{2}=169,\\;v^{2}=192\\quad\\text{or}\\quad u^{2}=192,\\;v^{2}=169.\n\\]\n\nTake  \n\n\\[\nu=13,\\qquad v=8\\sqrt3 .\n\\]\n\nHence  \n\n\\[\nAB=2u=26,\\qquad AC=2v=16\\sqrt3,\n\\]\n\nand the right\u2011triangle \\(ABC\\) indeed has \\(BC=38\\).\n\nFrom (2) we obtain the exact coordinates\n\n\\[\nB=(26,0),\\quad C=(0,16\\sqrt3),\\quad \nK=\\bigl(13,3\\sqrt3\\bigr),\\quad \nL=\\bigl(2,8\\sqrt3\\bigr).\n\\]\n\nNow compute the area of quadrilateral \\(BKLC\\) with the shoelace formula:\n\n\\[\n\\begin{aligned}\n\\text{Area} &amp;=\\frac12\\bigl|\n26(3\\sqrt3)+13(8\\sqrt3)+2(16\\sqrt3)+0\\cdot0\\\\\n&amp;\\quad- \\bigl(13\\cdot0+2(3\\sqrt3)+0(8\\sqrt3)+26(16\\sqrt3)\\bigr)\\bigr|\\\\[2mm]\n&amp;=\\frac12\\bigl| 78\\sqrt3+104\\sqrt3+32\\sqrt3\n- (6\\sqrt3+416\\sqrt3) \\bigr|\\\\[2mm]\n&amp;=\\frac12\\bigl|214\\sqrt3-422\\sqrt3\\bigr|\n= \\frac12\\,(208\\sqrt3)=104\\sqrt3 .\n\\end{aligned}\n\\]\n\nThus the area of \\(BKLC\\) is \\(104\\sqrt3\\).  \n\nTherefore  \n\n\\[\n\\boxed{104}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 104</p>\n<p>Extracted Answer: 104</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nAn isosceles trapezoid has an inscribed circle tangent to each of its four sides. The radius of the circle is 3, and the area of the trapezoid is 72. Let the parallel sides of the trapezoid have lengths $r$ and $s$, with $r \\neq s$. Find $r^{2}+s^{2}$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let the trapezoid have bases \\(AB=r\\) and \\(CD=s\\) \\((r\\neq s)\\) and equal legs \\(AD=BC=\\ell\\).\nA circle of radius \\(3\\) is tangent to all four sides.\n\n---\n\n### 1.  Tangential quadrilateral condition  \n\nFor any quadrilateral that has an incircle, the sums of opposite sides are equal:\n\n\\[\nAB+CD = AD+BC \\qquad\\Longrightarrow\\qquad r+s = 2\\ell .\n\\tag{1}\n\\]\n\nThus each leg is the average of the two bases:\n\n\\[\n\\ell =\\frac{r+s}{2}.\n\\tag{2}\n\\]\n\n---\n\n### 2.  Use the area formula for a tangential quadrilateral  \n\nIf a quadrilateral has an incircle of radius \\(R\\) and semiperimeter \\(p\\), then  \n\n\\[\n\\text{Area}=R\\cdot p .\n\\]\n\nHere \\(R=3\\) and the area is \\(72\\), so\n\n\\[\n3p = 72 \\quad\\Longrightarrow\\quad p = 24 .\n\\tag{3}\n\\]\n\nThe perimeter is \\(2p=48\\). Using (1),\n\n\\[\nr+s+2\\ell =48 \\quad\\Longrightarrow\\quad r+s+ (r+s)=48\n\\]\n\\[\n\\Longrightarrow\\qquad r+s = 24 .\n\\tag{4}\n\\]\n\nHence from (2) the leg length is  \n\n\\[\n\\ell =\\frac{r+s}{2}=12 .\n\\tag{5}\n\\]\n\n---\n\n### 3.  Height of the trapezoid  \n\nThe incircle touches both parallel sides, so the distance between them (the height \\(h\\)) equals twice the radius:\n\n\\[\nh = 2\\cdot 3 = 6 .\n\\tag{6}\n\\]\n\n(One can also get \\(h\\) from \\(\\displaystyle \\text{Area}= \\frac{r+s}{2}\\,h\\) using (4): \\(72 =12h\\Rightarrow h=6\\).)\n\n---\n\n### 4.  Relate the leg to the bases  \n\nIn an isosceles trapezoid, each leg forms a right triangle with height \\(h\\) and horizontal leg \\(\\frac{|r-s|}{2}\\):\n\n\\[\n\\ell^{2}= \\left(\\frac{r-s}{2}\\right)^{2}+h^{2}.\n\\]\n\nSubstituting \\(\\ell=12\\) and \\(h=6\\),\n\n\\[\n12^{2}= \\frac{(r-s)^{2}}{4}+6^{2}\n\\quad\\Longrightarrow\\quad\n144 = \\frac{(r-s)^{2}}{4}+36\n\\]\n\\[\n\\Longrightarrow\\quad (r-s)^{2}=432 .\n\\tag{7}\n\\]\n\n---\n\n### 5.  Find \\(r^{2}+s^{2}\\)\n\nWe have the two symmetric relations  \n\n\\[\n(r+s)^{2}=24^{2}=576,\n\\qquad\n(r-s)^{2}=432 .\n\\]\n\nRecall  \n\n\\[\n(r-s)^{2}= (r+s)^{2}-4rs .\n\\]\n\nThus  \n\n\\[\n432 = 576 - 4rs \\quad\\Longrightarrow\\quad rs = 36 .\n\\tag{8}\n\\]\n\nNow  \n\n\\[\nr^{2}+s^{2}= (r+s)^{2}-2rs = 576-2\\cdot36 = 576-72 = 504 .\n\\]\n\n---\n\n\\[\n\\boxed{504}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 504</p>\n<p>Extracted Answer: 504</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThere are $8!=40320$ eight-digit positive integers that use each of the digits $1,2,3,4,5,6,7,8$ exactly once. Let $N$ be the number of these integers that are divisible by 22. Find the difference between $N$ and 2025.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>For a number to be divisible by \\(22\\) it must be divisible by \\(2\\) and by \\(11\\).\n\n---\n\n### 1.  Divisibility by \\(11\\)\n\nWrite an 8\u2011digit permutation as  \n\n\\[\nd_1d_2d_3d_4d_5d_6d_7d_8 ,\n\\]\n\nwith positions counted from the left.  \nFor an even number of digits, the rule for \\(11\\) is  \n\n\\[\n(d_1+d_3+d_5+d_7)-(d_2+d_4+d_6+d_8)\\equiv0\\pmod{11}.\n\\]\n\nLet  \n\n\\[\nO=d_1+d_3+d_5+d_7,\\qquad E=d_2+d_4+d_6+d_8 .\n\\]\n\nBecause the digits \\(1,2,\\dots ,8\\) are used once,  \n\n\\[\nO+E=1+2+\\cdots+8=36 .\n\\]\n\nThe condition for \\(11\\) gives \\(O-E\\equiv0\\pmod{11}\\).  \nSince \\(O,E\\) lie between \\(10\\) and \\(26\\), the only possible multiple of \\(11\\) is \\(0\\).  \nHence  \n\n\\[\nO=E=18 .\n\\]\n\nThus the four digits placed in the odd positions must sum to \\(18\\); the remaining four (even positions) also sum to \\(18\\).\n\n---\n\n### 2.  Which four\u2011digit sets sum to \\(18\\)?\n\nFind all 4\u2011element subsets of \\(\\{1,\\dots ,8\\}\\) whose sum is \\(18\\).\n\n\\[\n\\begin{aligned}\n&amp;\\{1,2,7,8\\},\\; \\{1,3,6,8\\},\\; \\{1,4,5,8\\},\\; \\{1,4,6,7\\},\\\\\n&amp;\\{2,3,5,8\\},\\; \\{2,3,6,7\\},\\; \\{2,4,5,7\\},\\; \\{3,4,5,6\\}.\n\\end{aligned}\n\\]\n\nThere are \\(8\\) such subsets.  \nEach contains exactly two even digits (the evens are \\(2,4,6,8\\)).  \nConsequently, the complementary set (the digits for the even positions) also contains exactly two evens.\n\n---\n\n### 3.  Divisibility by \\(2\\)\n\nA number is even precisely when its unit digit (position\u202f8) is even.  \nPosition\u202f8 belongs to the even positions, whose four digits are the complement of the chosen odd\u2011position set.  \nSince that complement always has exactly two even digits, we have\n\n\\[\n\\text{choices for the unit digit}=2 .\n\\]\n\n---\n\n### 4.  Counting the permutations\n\nFix one of the eight valid 4\u2011digit odd\u2011position sets \\(S\\).\n\n* Arrange the four digits of \\(S\\) in the odd positions \\(1,3,5,7\\): \\(4! = 24\\) ways.\n* Choose an even digit from the complementary set for the unit place: \\(2\\) ways.\n* Arrange the remaining three digits of the complement in positions \\(2,4,6\\): \\(3! = 6\\) ways.\n\nHence for each set \\(S\\)\n\n\\[\n24 \\times 2 \\times 6 = 288\n\\]\n\npermutations are divisible by \\(22\\).\n\nWith \\(8\\) possible sets \\(S\\),\n\n\\[\nN = 8 \\times 288 = 2304 .\n\\]\n\n---\n\n### 5.  Required difference\n\n\\[\nN-2025 = 2304-2025 = 279 .\n\\]\n\n\\[\n\\boxed{279}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 279</p>\n<p>Extracted Answer: 279</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet the sequence of rationals $ x_1, x_2, \\ldots $ be defined such that $ x_1 = \\frac{25}{11} $ and\n$ x_{k+1} = \\frac{1}{3} \\left( x_k + \\frac{1}{x_k} - 1 \\right). $\n$ x_{2025} $ can be expressed as $ \\frac{m}{n} $ for relatively prime positive integers $ m $ and $ n $. Find the remainder when $ m + n $ is divided by 1000.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>First write each term \\(x_k\\) in reduced form  \n\n\\[\nx_k=\\frac{a_k}{b_k},\\qquad (a_k,b_k)=1 ,\\;a_k,b_k&gt;0 .\n\\]\n\nFrom  \n\n\\[\nx_{k+1}= \\frac13\\Bigl(x_k+\\frac1{x_k}-1\\Bigr)\n        =\\frac13\\Bigl(\\frac{a_k}{b_k}+\\frac{b_k}{a_k}-1\\Bigr)\n\\]\n\nwe obtain  \n\n\\[\na_{k+1}= \\frac{a_k^2+b_k^2-a_kb_k}{3},\\qquad   \nb_{k+1}=a_kb_k .\\tag{1}\n\\]\n\n--------------------------------------------------------------------\n### 1.  Coprimeness is preserved\nIf a prime \\(p\\mid a_{k+1}\\) and \\(p\\mid b_{k+1}=a_kb_k\\) then \\(p\\mid a_k\\) or \\(p\\mid b_k\\).\nBut modulo such a prime the numerator \\(a_k^2+b_k^2-a_kb_k\\) equals \\(b_k^2\\) (resp. \\(a_k^2\\)),\nwhich is non\u2011zero because \\((a_k,b_k)=1\\). Hence no prime can divide both\n\\(a_{k+1}\\) and \\(b_{k+1}\\); therefore \\((a_{k+1},b_{k+1})=1\\).\nThus each \\(x_k\\) is already in lowest terms.\n\n--------------------------------------------------------------------\n### 2.  A simple recurrence for the sum\n\nLet  \n\n\\[\ns_k=a_k+b_k .\n\\]\n\nAdding the two formulas in (1),\n\n\\[\n\\begin{aligned}\ns_{k+1}\n &amp;=\\frac{a_k^2+b_k^2-a_kb_k}{3}+a_kb_k  \\\\\n &amp;=\\frac{a_k^2+b_k^2+2a_kb_k}{3} =\\frac{(a_k+b_k)^2}{3}\n   =\\frac{s_k^{\\,2}}{3}.         \\tag{2}\n\\end{aligned}\n\\]\n\nThe initial sum is  \n\n\\[\ns_1= a_1+b_1=25+11=36 .\n\\]\n\n--------------------------------------------------------------------\n### 3.  Closed form of \\(s_k\\)\n\nFrom (2) we prove by induction that  \n\n\\[\n\\boxed{\\,s_k = 2^{\\,2^{\\,k}}\\; 3^{\\,2^{\\,k-1}+1}\\,}\\qquad(k\\ge1).\n\\]\n\nIndeed, for \\(k=1\\) the formula gives \\(2^{2}\\,3^{2}=36\\).\nAssume it holds for \\(k\\); then using (2),\n\n\\[\ns_{k+1}= \\frac{s_k^{2}}{3}\n      =\\frac{(2^{2^{k}}3^{2^{k-1}+1})^{2}}{3}\n      =2^{2^{k+1}}3^{2^{k}+1},\n\\]\n\nwhich is the required expression for \\(k+1\\).\n\n--------------------------------------------------------------------\n### 4.  Computing \\(s_{2025}\\pmod{1000}\\)\n\nWe need \\(m+n=s_{2025}\\pmod{1000}\\).\n\nBecause \\(1000=8\\cdot125\\), we treat the two moduli separately.\n\n*Modulo \\(8\\):*  \n\\(2^{2^{2025}}\\) contains the factor \\(2^3\\); hence \\(s_{2025}\\equiv0\\pmod 8\\).\n\n*Modulo \\(125\\):*  \n\\(\\phi(125)=100\\).  Thus we may reduce the exponents modulo \\(100\\).\n\n\\[\n\\begin{aligned}\n2^{2025}\\pmod{100}&amp;=32, &amp;\n2^{2024}\\pmod{100}&amp;=16 .\n\\end{aligned}\n\\]\n\nHence  \n\n\\[\n\\begin{aligned}\n2^{\\,2^{2025}}\\pmod{125}&amp;=2^{32}\\pmod{125}=46,\\\\[2mm]\n3^{\\,2^{2024}+1}\\pmod{125}&amp;=3^{16+1}=3^{17}\\pmod{125}=38.\n\\end{aligned}\n\\]\n\nTherefore  \n\n\\[\ns_{2025}\\equiv 46\\cdot38\\equiv123\\pmod{125}.\n\\]\n\nNow solve  \n\n\\[\nN\\equiv0\\pmod8,\\qquad N\\equiv123\\pmod{125}.\n\\]\n\nSince \\(8^{-1}\\equiv47\\pmod{125}\\),\n\n\\[\nN\\equiv8\\bigl(47\\cdot123\\bigr)\\equiv8\\cdot31\\equiv248\\pmod{1000}.\n\\]\n\nThus  \n\n\\[\nm+n\\equiv\\boxed{248}\\pmod{1000}.\n\\]\n\n--------------------------------------------------------------------\n### 5.  Check via periodicity (optional)\n\nFrom \\(s_{k+1}=s_k^2/3\\) modulo \\(1000\\) one finds that the\nsequence \\(\\{s_k\\bmod1000\\}\\) becomes periodic with period \\(20\\) after\nthe third term:\n\\[\n36,\\;432,\\;\\underline{208},\\;88,\\;248,\\;168,\\dots\n\\]\nSince \\(2025-3\\equiv2\\pmod{20}\\), the term equals the fifth term,\n\\(248\\), confirming the result above.</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 248</p>\n<p>Extracted Answer: 248</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $k$ be real numbers such that the system $|25+20i-z|=5$ and $|z-4-k|=|z-3i-k|$ has exactly one complex solution $z$. The sum of all possible values of $k$ can be written as $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$. Here $i=\\sqrt{-1}$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n\\[\nz=x+iy .\n\\]\n\n---\n\n### 1.  The first equation  \n\n\\[\n|25+20i-z|=5\n\\]\n\ngives the circle  \n\n\\[\n(x-25)^2+(y-20)^2=5^{2}=25 .\n\\tag{1}\n\\]\n\nIts centre is \\(C=(25,20)\\) and its radius is \\(5\\).\n\n---\n\n### 2.  The second equation  \n\n\\[\n|z-4-k|=|z-3i-k|\n\\]\n\nmeans that the point \\(z\\) is equidistant from the two points  \n\n\\[\nA=(4+k,0),\\qquad B=(k,3).\n\\]\n\nThus \\(z\\) lies on the **perpendicular bisector** of the segment \\(AB\\).\n\n*Midpoint*  \n\n\\[\nM\\Bigl(\\frac{4+k+k}{2},\\frac{0+3}{2}\\Bigr)=\\bigl(k+2,\\; \\tfrac32 \\bigr).\n\\]\n\n*Slope of \\(AB\\)*  \n\n\\[\n\\frac{3-0}{k-(4+k)}=\\frac{3}{-4}=-\\frac34 .\n\\]\n\nHence the slope of the perpendicular bisector is \\( \\displaystyle \\frac43\\).\n\nIts equation is\n\n\\[\ny-\\frac32=\\frac43\\bigl(x-(k+2)\\bigr)\n\\]\n\nor, after clearing denominators,\n\n\\[\n8x-6y-8k-7=0 .\n\\tag{2}\n\\]\n\nThus the second condition is the line \\(L_k: 8x-6y-8k-7=0\\).\n\n---\n\n### 3.  Intersections of (1) and (2)\n\nThe system has exactly one solution iff the line \\(L_k\\) is **tangent** to the circle (1), i.e. the distance from the centre \\(C\\) to the line equals the radius \\(5\\).\n\nDistance from \\((25,20)\\) to \\(L_k\\):\n\n\\[\nd=\\frac{|8\\cdot25-6\\cdot20-8k-7|}{\\sqrt{8^{2}+(-6)^{2}}}\n   =\\frac{|200-120-8k-7|}{\\sqrt{64+36}}\n   =\\frac{|73-8k|}{10}.\n\\]\n\nSet \\(d=5\\):\n\n\\[\n\\frac{|73-8k|}{10}=5\\quad\\Longrightarrow\\quad |73-8k|=50.\n\\]\n\nHence  \n\n\\[\n73-8k=50\\quad\\text{or}\\quad73-8k=-50,\n\\]\ngiving  \n\n\\[\nk=\\frac{23}{8}\\qquad\\text{or}\\qquad k=\\frac{123}{8}.\n\\]\n\nFor each of these values the line is tangent, so there is exactly one point \\(z\\) satisfying both equations.\n\n---\n\n### 4.  Sum of all possible \\(k\\)\n\n\\[\n\\frac{23}{8}+\\frac{123}{8}= \\frac{146}{8}= \\frac{73}{4}.\n\\]\n\nWrite \\(\\displaystyle \\frac{73}{4}\\) as \\(\\frac{m}{n}\\) with \\(\\gcd(m,n)=1\\); here \\(m=73,\\;n=4\\).\n\n\\[\nm+n = 73+4 = 77.\n\\]\n\n\\[\n\\boxed{77}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 77</p>\n<p>Extracted Answer: 77</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nOn $\\triangle ABC$ points $A,D,E$, and $B$ lie that order on side $\\overline{AB}$ with $AD=4, DE=16$, and $EB=8$. Points $A,F,G$, and $C$ lie in that order on side $\\overline{AC}$ with $AF=13, FG=52$, and $GC=26$. Let $M$ be the reflection of $D$ through $F$, and let $N$ be the reflection of $G$ through $E$. Quadrilateral $DEGF$ has area 288. Find the area of heptagon $AFNBCEM$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Since the points lie on the sides of \\(\\triangle ABC\\) we may work with vectors\n\\[\n\\vec{AB}= \\mathbf b,\\qquad \\vec{AC}= \\mathbf c ,\n\\qquad A\\; \\text{at the origin}.\n\\]\n\n--------------------------------------------------------------------\n### 1.  Locate the points \\(D,E,F,G\\)\n\n\\[\nAD=4,\\;AB=28\\Longrightarrow \\frac{AD}{AB}= \\frac 1 7\\quad\\Rightarrow\\quad \n\\vec{AD}=\\frac17\\mathbf b .\n\\]\nThus \\(D=\\dfrac17\\mathbf b\\).\n\n\\[\nAE=AD+DE=20\\Longrightarrow\\frac{AE}{AB}= \\frac{20}{28}= \\frac57\n\\quad\\Rightarrow\\quad  E=\\frac57\\mathbf b .\n\\]\n\nSimilarly on \\(AC\\),\n\n\\[\nAF=13,\\;AC=91\\Longrightarrow \\frac{AF}{AC}= \\frac13\\!7\\quad\\Rightarrow\\quad \nF=\\frac17\\mathbf c ,\n\\]\n\\[\nAG=AF+FG=65\\Longrightarrow \\frac{AG}{AC}= \\frac{65}{91}= \\frac57\n\\quad\\Rightarrow\\quad  G=\\frac57\\mathbf c .\n\\]\n\nHence  \n\n\\[\nD=\\frac17\\mathbf b,\\qquad E=\\frac57\\mathbf b,\\qquad\nF=\\frac17\\mathbf c,\\qquad G=\\frac57\\mathbf c .\n\\]\n\n--------------------------------------------------------------------\n### 2.  Area of \\(\\triangle ABC\\)\n\nQuadrilateral \\(DEGF\\) is the region between the similar triangles\n\\(ADF\\) (scale \\(1/7\\)) and \\(AEG\\) (scale \\(5/7\\)).  \nTherefore  \n\n\\[\n[DEGF]=[AEG]-[ADF]\n           =\\left(\\frac57\\right)^{\\!2}[ABC]-\\left(\\frac17\\right)^{\\!2}[ABC]\n           =\\frac{25-1}{49}[ABC]=\\frac{24}{49}[ABC].\n\\]\n\nGiven \\([DEGF]=288\\),\n\n\\[\n[ABC]=\\frac{49}{24}\\cdot288=49\\cdot12=588 .\n\\tag{1}\n\\]\n\n--------------------------------------------------------------------\n### 3.  Locate the reflected points \\(M,N\\)\n\n\\[\nM\\; \\text{is the reflection of }D\\text{ across }F\\;\n\\Longrightarrow\\; M=2F-D=\n\\frac{2}{7}\\mathbf c-\\frac{1}{7}\\mathbf b .\n\\]\n\n\\[\nN\\; \\text{is the reflection of }G\\text{ across }E\\;\n\\Longrightarrow\\; N=2E-G=\n\\frac{10}{7}\\mathbf b-\\frac{5}{7}\\mathbf c .\n\\]\n\n--------------------------------------------------------------------\n### 4.  Area of the heptagon \\(AFNBCEM\\)\n\nWrite the vertices (in order) as vectors from \\(A\\):\n\n\\[\n\\begin{aligned}\nA&amp;=0, &amp;\nF&amp;=\\frac17\\mathbf c, &amp;\nN&amp;=\\frac{10}{7}\\mathbf b-\\frac57\\mathbf c,\\\\\nB&amp;=\\mathbf b, &amp;\nC&amp;=\\mathbf c, &amp;\nE&amp;=\\frac57\\mathbf b, &amp;\nM&amp;=\\frac27\\mathbf c-\\frac17\\mathbf b .\n\\end{aligned}\n\\]\n\nFor a polygon with vertices \\(\\mathbf v_0,\\dots,\\mathbf v_6\\) the doubled\narea equals\n\\[\n\\sum_{i=0}^{6}\\det(\\mathbf v_i,\\mathbf v_{i+1}),\n\\qquad\\mathbf v_7=\\mathbf v_0 .\n\\]\n\nCarrying out the determinants (using \\(\\det(\\mathbf b,\\mathbf c)=\\det(\\mathbf b,\\mathbf c)\\) and \\(\\det(\\mathbf c,\\mathbf b)=-\\det(\\mathbf b,\\mathbf c)\\)):\n\n\\[\n\\begin{aligned}\n\\det(F,N) &amp;=\\frac1{49}\\det\\!\\Bigl(\\mathbf c,\\;10\\mathbf b-5\\mathbf c\\Bigr)\n           =-\\frac{10}{49}\\det(\\mathbf b,\\mathbf c),\\\\[2mm]\n\\det(N,B) &amp;=\\frac57\\det(\\mathbf b,\\mathbf b)-\\frac5{7}\\det(\\mathbf c,\\mathbf b)\n           =\\frac5{7}\\det(\\mathbf b,\\mathbf c),\\\\[2mm]\n\\det(B,C) &amp;=\\det(\\mathbf b,\\mathbf c),\\\\[2mm]\n\\det(C,E) &amp;=\\frac57\\det(\\mathbf c,\\mathbf b)=-\\frac5{7}\\det(\\mathbf b,\\mathbf c),\\\\[2mm]\n\\det(E,M) &amp;=\\frac1{49}\\det\\!\\Bigl(5\\mathbf b,\\;2\\mathbf c-\\mathbf b\\Bigr)\n           =\\frac{10}{49}\\det(\\mathbf b,\\mathbf c).\n\\end{aligned}\n\\]\n\nAll other terms are zero. Adding them:\n\n\\[\n\\det(F,N)+\\det(N,B)+\\det(B,C)+\\det(C,E)+\\det(E,M)\n   =\\Bigl(-\\frac{10}{49}+\\frac5{7}+1-\\frac5{7}+\\frac{10}{49}\\Bigr)\n      \\det(\\mathbf b,\\mathbf c)=\\det(\\mathbf b,\\mathbf c).\n\\]\n\nThus the doubled area of the heptagon is \\(\\det(\\mathbf b,\\mathbf c)\\),\nwhich is exactly twice the area of \\(\\triangle ABC\\). Consequently\n\n\\[\n[AFNBCEM]=\\frac12\\det(\\mathbf b,\\mathbf c)=[ABC]=588 .\n\\tag{2}\n\\]\n\n--------------------------------------------------------------------\n### 5.  Answer\n\n\\[\n\\boxed{588}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 588</p>\n<p>Extracted Answer: 588</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThe parabola with equation $y=x^{2}-4$ is rotated $60^{\\circ}$ counterclockwise around the origin. The unique point in the fourth quadrant where the original parabola and its image intersect has $y$-coordinate $\\frac{a-\\sqrt{b}}{c}$, where $a$, $b$, and $c$ are positive integers, and $a$ and $c$ are relatively prime. Find $a+b+c$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>The parabola is  \n\n\\[\ny=x^{2}-4 .\n\\]\n\nRotate a point \\((x,y)\\) by \\(-60^{\\circ}\\) (the inverse rotation).  \nFor \\(\\theta =60^{\\circ}\\),\n\n\\[\n\\cos\\theta =\\frac12 ,\\qquad \\sin\\theta =\\frac{\\sqrt3}{2}.\n\\]\n\nThe inverse\u2011rotation of \\((x,y)\\) is  \n\n\\[\nu=\\frac12 x+\\frac{\\sqrt3}{2}y ,\\qquad \nv=-\\frac{\\sqrt3}{2}x+\\frac12 y .\n\\]\n\nFor a point of the rotated parabola, the inverse image \\((u,v)\\) must satisfy the\noriginal equation \\(v=u^{2}-4\\):\n\n\\[\n-\\frac{\\sqrt3}{2}x+\\frac12 y =\\Bigl(\\frac12 x+\\frac{\\sqrt3}{2}y\\Bigr)^{2}-4 .\n\\]\n\nMultiplying by \\(2\\) and expanding gives\n\n\\[\n\\frac12 x^{2}+\\sqrt3\\,xy+\\frac32 y^{2}+\\sqrt3\\,x-y-8=0. \\tag{1}\n\\]\n\nNow substitute \\(y=x^{2}-4\\) (the original parabola) into (1):\n\n\\[\n\\frac12 x^{2}+\\sqrt3\\,x(x^{2}-4)+\\frac32 (x^{2}-4)^{2}\n+\\sqrt3\\,x-(x^{2}-4)-8=0 .\n\\]\n\nSimplifying,\n\n\\[\n3x^{4}+2\\sqrt3\\,x^{3}-25x^{2}-6\\sqrt3\\,x+40=0 .\n\\]\n\nFactor the quartic (group the \\(\\sqrt3\\) terms):\n\n\\[\n\\bigl(x^{2}+\\sqrt3\\,x-4\\bigr)\\bigl(3x^{2}-\\sqrt3\\,x-10\\bigr)=0 .\n\\]\n\nHence\n\n\\[\nx^{2}+\\sqrt3\\,x-4=0\\qquad\\text{or}\\qquad 3x^{2}-\\sqrt3\\,x-10=0.\n\\]\n\nThe four solutions are  \n\n\\[\n\\begin{aligned}\nx&amp;=\\frac{-\\sqrt3\\pm\\sqrt{19}}2,\\\\[2mm]\nx&amp;=\\frac{\\sqrt3\\pm\\sqrt{123}}6 .\n\\end{aligned}\n\\]\n\nOnly one of them lies in the fourth quadrant \\((x&gt;0,\\;y&lt;0)\\):\n\\[\nx=\\frac{-\\sqrt3+\\sqrt{19}}2\\;(&gt;0),\\qquad |x|&lt;2 .\n\\]\n\nIts \\(y\\)-coordinate is\n\n\\[\ny=x^{2}-4\n     =\\Bigl(\\frac{-\\sqrt3+\\sqrt{19}}2\\Bigr)^{2}-4\n     =\\frac{3-\\sqrt{57}}2 .\n\\]\n\nThus  \n\n\\[\ny=\\frac{a-\\sqrt b}{c}\\quad\\text{with}\\quad a=3,\\;b=57,\\;c=2,\n\\]\nand \\(a\\) and \\(c\\) are relatively prime.\n\nFinally,\n\\[\na+b+c=3+57+2=62 .\n\\]\n\n\\[\n\\boxed{62}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 62</p>\n<p>Extracted Answer: 62</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThe twelve letters $A,B,C,D,E,F,G,H,I,J,K$, and $L$ are randomly grouped into six pairs of letters. The two letters in each pair are placed next to each other in alphabetical order to form six two-letter words, and those six words are listed alphabetically. For example, a possible result is $AB,CJ,DG,EK,FL,HI$. The probability that the last word listed contains $G$ is $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>The six two\u2011letter words are formed by first ordering the letters inside each pair\nalphabetically and then sorting the six words alphabetically.  \nFor a pairing, let  \n\n\\[\nS=\\{\\text{the smaller letter of each pair}\\}\n\\]\n\n(the \u201cfirst\u201d letters of the six words).  \nThe lexicographically last word is the one whose first letter is  \n\n\\[\nM=\\max S .\n\\]\n\nHence the last word contains \\(G\\) **iff** either  \n\n* \\(M=G\\) (so \\(G\\) itself is the first letter of the last word), or  \n* \\(M\\neq G\\) but \\(G\\) is paired with the letter \\(M\\) (so \\(G\\) is the second\nletter of the last word).\n\nBecause a pair \\((x,y)\\) must satisfy \\(x&lt;y\\), the only possible \\(M\\) with\n\\(M&lt;G\\) is \\(M=F\\).  Thus there are two cases:\n\n--------------------------------------------------------------------\n### 1.  \\(M=G\\)\n\nThen the six small letters are  \n\n\\[\nS=\\{G\\}\\cup \\{A,B,C,D,E,F\\}\\setminus\\{a\\},\n\\]\n\nwhere \\(a\\) is the one letter from \\(\\{A,\\dots ,F\\}\\) that is **not** in \\(S\\).\nThe omitted letter \\(a\\) must not be \\(A\\); otherwise \\(A\\) would be a large\nletter with no smaller partner.  \nHence \\(a\\in\\{B,C,D,E,F\\}\\) \u2013 5 possibilities.\n\nFor a given \\(a\\):\n* \\(a\\) (a large letter) must be paired with a small letter that is\nsmaller than \\(a\\); there are \\(a-1\\) such choices.\n* The remaining five small letters can be paired arbitrarily with the five\nlarge letters \\(H,I,J,K,L\\); that gives \\(5!\\) possibilities.\n\nThus for each \\(a\\) we have \\((a-1)\\cdot5!\\) pairings.  \nSumming over \\(a=2,3,4,5,6\\) (i.e. \\(B\\)\u2013\\(F\\)),\n\n\\[\n\\sum_{a=2}^{6}(a-1) \\cdot 5!\n   =(1+2+3+4+5)\\cdot120\n   =15\\cdot120\n   =1800 .\n\\]\n\n--------------------------------------------------------------------\n### 2.  \\(M=F\\) and \\(G\\) is paired with \\(F\\)\n\nIf the maximum small letter is \\(F\\), then the small set must be exactly  \n\n\\[\nS=\\{A,B,C,D,E,F\\},\n\\qquad\nT=\\{G,H,I,J,K,L\\}.\n\\]\n\nEvery bijection between \\(S\\) and \\(T\\) yields a valid pairing, so there are\n\\(6! = 720\\) pairings in total.  \nAmong them, the ones with \\(F\\) paired with \\(G\\) are those where we fix that\npair and match the remaining five letters arbitrarily, giving \\(5! =120\\) pairings.\n\n--------------------------------------------------------------------\n### Total favourable pairings\n\n\\[\nN_{\\text{fav}} = 1800 + 120 = 1920 .\n\\]\n\n--------------------------------------------------------------------\n### Total pairings\n\nThe total number of ways to split 12 distinct letters into six unordered pairs is  \n\n\\[\nN_{\\text{total}}=\\frac{12!}{2^{6}\\,6!}=10395 .\n\\]\n\n--------------------------------------------------------------------\n### Probability\n\n\\[\nP=\\frac{1920}{10395}\n   =\\frac{128}{693}\\quad(\\text{in lowest terms}).\n\\]\n\nThus \\(m=128,\\;n=693\\) and\n\n\\[\nm+n=128+693=821 .\n\\]\n\n\\[\n\\boxed{821}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 821</p>\n<p>Extracted Answer: 821</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nA piecewise linear periodic function is defined by $f(x)=\\begin{cases}x&amp;\\text{if }x\\in[-1,1)\\\\2-x&amp;\\text{if }x\\in[1,3)\\end{cases}$ and $f(x+4)=f(x)$ for all real numbers $x$. The graph of $f(x)$ has the sawtooth pattern. The parabola $x=34y^2$ intersects the graph of $f(x)$ at finitely many points. The sum of the $y$-coordinates of these intersection points can be expressed in the form $\\frac{a+b\\sqrt{c}}{d}$, where $a,b,c,$ and $d$ are positive integers, $a,b,$ and $d$ have greatest common divisor equal to 1, and $c$ is not divisible by the square of any prime. Find $a+b+c+d$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>The graph of  \n\n\\[\nf(x)=\\begin{cases}\nx,&amp;-1\\le x&lt;1\\\\[2pt]\n2-x,&amp;1\\le x&lt;3\n\\end{cases},\n\\qquad f(x+4)=f(x)\n\\]\n\nis a triangular wave of period \\(4\\) whose values lie in \\([-1,1]\\).\n\nThe parabola is  \n\n\\[\nx=34y^{2}\\qquad (x\\ge 0).\n\\]\n\nBecause \\(|f(x)|\\le 1\\), any intersection must satisfy \\(|y|\\le 1\\); then  \n\n\\[\n0\\le x=34y^{2}\\le 34 .\n\\]\n\n--------------------------------------------------------------------\n### 1. Reduce the problem to a quadratic equation\n\nWrite  \n\n\\[\nt = 34y^{2}\\;(0\\le t\\le34).\n\\]\n\nFor some integer \\(k\\) we can write  \n\n\\[\nt = 4k+u,\\qquad u\\in[-1,3)\n\\]\n\n(the representation is unique because we use the half\u2011open interval \\([-1,3)\\)).  \nSince \\(f(t)=f(u)\\),\n\n\\[\nf(u)=\\begin{cases}\nu, &amp; u\\in[-1,1)\\\\[2pt]\n2-u, &amp; u\\in[1,3)\n\\end{cases}\n\\]\n\nand the intersection condition \\(y=f(t)\\) becomes  \n\n\\[\n\\begin{cases}\ny=u = 34y^{2}-4k, &amp; u\\in[-1,1)\\\\[4pt]\ny=2-u = 2-(34y^{2}-4k), &amp; u\\in[1,3)\n\\end{cases}\n\\]\n\nwhich give the quadratics  \n\n\\[\n\\boxed{34y^{2}-y-4k=0}\\qquad(u\\in[-1,1))\n\\tag{A}\n\\]\n\n\\[\n\\boxed{34y^{2}+y-(2+4k)=0}\\qquad(u\\in[1,3))\n\\tag{B}\n\\]\n\nwith the extra restrictions  \n\n\\[\n\\text{(A)}\\;y\\in[-1,1), \\qquad\n\\text{(B)}\\; -1&lt;y\\le 1 .\n\\]\n\n--------------------------------------------------------------------\n### 2. The possible integers \\(k\\)\n\nSince \\(t\\le34\\),\n\n\\[\n-1\\le u =t-4k &lt;3\\Longrightarrow 4k\\le t+1\\le 35\n\\]\n\nso \\(k\\) can be \\(0,1,\\dots ,8\\) (nine values).\n\n--------------------------------------------------------------------\n### 3. Solutions of (A)\n\nFor each \\(k\\) the equation  \n\n\\[\n34y^{2}-y-4k=0\n\\]\n\nhas the two roots  \n\n\\[\ny=\\frac{1\\pm\\sqrt{1+544k}}{68}.\n\\]\n\nBoth lie in \\([-1,1)\\) for all \\(k=0,\\dots ,8\\).  \nHence each \\(k\\) contributes **two** solutions and their sum is\n\n\\[\n\\frac{1}{34}\\quad\\text{(by Vieta)}.\n\\]\n\nTotal from (A):\n\n\\[\n9\\cdot\\frac{1}{34}= \\frac{9}{34}.\n\\]\n\n--------------------------------------------------------------------\n### 4. Solutions of (B)\n\nFor each \\(k\\) the equation  \n\n\\[\n34y^{2}+y-(2+4k)=0\n\\]\n\nhas roots  \n\n\\[\ny=\\frac{-1\\pm\\sqrt{273+544k}}{68}.\n\\]\n\nFor \\(k=0,1,\\dots ,7\\) both roots satisfy \\(-1&lt;y\\le1\\); for \\(k=8\\) the\nnegative root is \\(&lt;-1\\) and is discarded.\nThus we have\n\n* for \\(k=0,\\dots ,7\\): two roots each, sum \\(-\\dfrac1{34}\\) (Vieta);\n* for \\(k=8\\): only the positive root  \n\n  \\[\n  y_{8}= \\frac{-1+\\sqrt{4625}}{68}= \\frac{-1+5\\sqrt{185}}{68}.\n  \\]\n\nHence the contribution of (B) is  \n\n\\[\n8\\!\\left(-\\frac1{34}\\right) + y_{8}= -\\frac{8}{34}+ \\frac{-1+5\\sqrt{185}}{68}\n= -\\frac{4}{17}+ \\frac{-1+5\\sqrt{185}}{68}.\n\\]\n\n--------------------------------------------------------------------\n### 5. Sum of all \\(y\\)-coordinates\n\nAdd the contributions of (A) and (B):\n\n\\[\n\\begin{aligned}\nS &amp;=\\frac{9}{34}\\;+\\;\\Bigl(-\\frac{8}{34}+ \\frac{-1+5\\sqrt{185}}{68}\\Bigr)\\\\[4pt]\n  &amp;=\\frac{1}{34}+ \\frac{-1+5\\sqrt{185}}{68}\n   =\\frac{2-1+5\\sqrt{185}}{68}\\\\[4pt]\n  &amp;=\\boxed{\\displaystyle\\frac{1+5\\sqrt{185}}{68}}.\n\\end{aligned}\n\\]\n\n--------------------------------------------------------------------\n### 6. Required sum \\(a+b+c+d\\)\n\nThe expression is \\(\\dfrac{a+b\\sqrt{c}}{d}\\) with  \n\n\\[\na=1,\\quad b=5,\\quad c=185,\\quad d=68,\n\\]\n\nwhich satisfy the given conditions. Therefore  \n\n\\[\na+b+c+d = 1+5+185+68 = \\boxed{259}.\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 259</p>\n<p>Extracted Answer: 259</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nSix points $ A, B, C, D, E, $ and $ F $ lie in a straight line in that order. Suppose that $ G $ is a point not on the line and that $ AC = 26 $, $ BD = 22 $, $ CE = 31 $, $ DF = 33 $, $ AF = 73 $, $ CG = 40 $, and $ DG = 30 $. Find the area of $ \\triangle BGE $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let the line be the \\(x\\)-axis.  \nPlace the points with coordinates (in order)\n\n\\[\nA(0),\\; B(x_B),\\; C(x_C),\\; D(x_D),\\; E(x_E),\\; F(x_F).\n\\]\n\nDenote the successive distances\n\n\\[\nAB=a,\\; BC=b,\\; CD=c,\\; DE=d,\\; EF=e .\n\\]\n\nThen  \n\n\\[\n\\begin{aligned}\na+b &amp;= AC = 26,\\\\\nb+c &amp;= BD = 22,\\\\\nc+d &amp;= CE = 31,\\\\\nd+e &amp;= DF = 33,\\\\\na+b+c+d+e &amp;= AF = 73 .\n\\end{aligned}\n\\]\n\nSolving:\n\\[\n\\begin{aligned}\na &amp;= 26-b,\\\\\nc &amp;= 22-b,\\\\\nd &amp;= 31-c = 9+b,\\\\\ne &amp;= 33-d = 24-b.\n\\end{aligned}\n\\]\n\nInsert these in the sum equation:\n\n\\[\n(26-b)+b+(22-b)+(9+b)+(24-b)=73\\Longrightarrow81-b=73,\n\\]\n\nhence \\(b=8\\).\n\nThus  \n\n\\[\n\\begin{aligned}\nAB = a = 18,\\quad\nBC = b = 8,\\quad\nCD = c = 14,\\quad\nDE = d = 17,\\quad\nEF = e = 16.\n\\end{aligned}\n\\]\n\nChoosing \\(A\\) as the origin gives\n\n\\[\n\\begin{aligned}\nA&amp;:(0,0),\\\\\nB&amp;:(18,0),\\\\\nC&amp;:(26,0),\\\\\nD&amp;:(40,0),\\\\\nE&amp;:(57,0),\\\\\nF&amp;:(73,0).\n\\end{aligned}\n\\]\n\n---\n\n### Coordinates of \\(G\\)\n\nLet \\(G=(x,y)\\).  \nWe are given \\(CG=40\\) and \\(DG=30\\):\n\n\\[\n\\begin{cases}\n(x-26)^2+y^2 = 40^2 =1600,\\\\\n(x-40)^2+y^2 = 30^2 = 900 .\n\\end{cases}\n\\]\n\nSubtracting the equations eliminates \\(y^2\\):\n\n\\[\n(x-26)^2-(x-40)^2 = 700 .\n\\]\n\n\\[\n\\begin{aligned}\n[x^2-52x+676] - [x^2-80x+1600] &amp;= 700\\\\\n28x-924 &amp;= 700\\\\\n28x &amp;=1624\\\\\nx&amp;= \\frac{1624}{28}=58 .\n\\end{aligned}\n\\]\n\nPlug \\(x=58\\) into \\((x-40)^2+y^2=900\\):\n\n\\[\n(58-40)^2+y^2=900\\Longrightarrow 18^2+y^2=900\\Longrightarrow y^2=576,\n\\]\n\nso \\(|y|=24\\).  \nThus \\(G=(58,\\pm24)\\).\n\n---\n\n### Area of \\(\\triangle BGE\\)\n\nPoints \\(B\\) and \\(E\\) lie on the \\(x\\)-axis, so the base \\(BE\\) has length\n\n\\[\nBE = x_E-x_B = 57-18 = 39 .\n\\]\n\nThe altitude from \\(G\\) to line \\(BE\\) is \\(|y|=24\\).\n\nHence\n\n\\[\n\\text{Area}= \\frac12 \\times (\\text{base}) \\times (\\text{height})\n          = \\frac12 \\times 39 \\times 24\n          = 39 \\times 12\n          = 468 .\n\\]\n\n\\[\n\\boxed{468}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 468</p>\n<p>Extracted Answer: 468</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nFind the sum of all positive integers $ n $ such that $ n + 2 $ divides the product $ 3(n + 3)(n^2 + 9) $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n\\[\nd=n+2\\qquad (d\\ge 3,\\; n&gt;0)\n\\]\n\nThen  \n\n\\[\nn=d-2,\\qquad n+3=d+1,\\qquad n^{2}+9=(d-2)^{2}+9=d^{2}-4d+13 .\n\\]\n\nThe required divisibility becomes  \n\n\\[\nd\\mid 3(n+3)(n^{2}+9)=3(d+1)(d^{2}-4d+13).\n\\]\n\n---\n\n### Reduce modulo \\(d\\)\n\n\\[\n3(d+1)(d^{2}-4d+13) \\equiv 3\\cdot1\\cdot13 = 39 \\pmod d,\n\\]\n\nbecause \\(d+1\\equiv1\\) and \\(d^{2}-4d+13\\equiv13\\) modulo \\(d\\).\n\nThus  \n\n\\[\nd\\mid 3(d+1)(d^{2}-4d+13)\\iff d\\mid 39 .\n\\]\n\nHence \\(d\\) must be a positive divisor of \\(39\\) and at least \\(3\\).  \nDivisors of \\(39\\) are \\(1,3,13,39\\); discarding \\(1\\) we obtain  \n\n\\[\nd\\in\\{3,13,39\\}.\n\\]\n\n---\n\n### Recover the corresponding \\(n\\)\n\n\\[\nn=d-2\\implies n\\in\\{3-2,13-2,39-2\\}=\\{1,11,37\\}.\n\\]\n\nEach indeed satisfies the original condition:\n\n* \\(n=1\\): \\(\\frac{3(1+3)(1^{2}+9)}{1+2}= \\frac{3\\cdot4\\cdot10}{3}=40\\) (integer);\n* \\(n=11\\): \\(\\frac{3(11+3)(11^{2}+9)}{11+2}= \\frac{3\\cdot14\\cdot130}{13}=420\\);\n* \\(n=37\\): \\(\\frac{3(37+3)(37^{2}+9)}{37+2}= \\frac{3\\cdot40\\cdot1378}{39}=4240\\).\n\n---\n\n### Sum of all such \\(n\\)\n\n\\[\n1+11+37 = 49.\n\\]\n\n\\[\n\\boxed{49}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 49</p>\n<p>Extracted Answer: 49</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThe set of points in 3-dimensional coordinate space that lie in the plane $x+y+z=75$ whose coordinates satisfy the inequalities $x-yz&lt;y-zx&lt;z-xy$ forms three disjoint convex regions. Exactly one of those regions has finite area. The area of this finite region can be expressed in the form $a\\sqrt{b}$, where $a$ and $b$ are positive integers and $b$ is not divisible by the square of any prime. Find $a+b$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>First write the two required inequalities using the condition \\(x+y+z=75\\).\n\n\\[\nz=75-x-y .\n\\]\n\n---\n\n### 1.  Simplify the inequalities  \n\n\\[\n\\begin{aligned}\nx-yz &amp;&lt;y-zx\\\\\nx-(y(75-x-y)) &amp;&lt; y-(x(75-x-y))\\\\\n\\Longrightarrow (x-y)(x+y-76) &amp;&gt;0 .\n\\end{aligned}\n\\]\n\n\\[\n\\begin{aligned}\ny-zx &amp;&lt;z-xy\\\\\ny-x(75-x-y) &amp;&lt; (75-x-y)-xy\\\\\n\\Longrightarrow (x+1)(x+2y-75) &amp;&lt;0 .\n\\end{aligned}\n\\]\n\nHence the points \\((x,y,z)\\) on the plane satisfy  \n\n\\[\n\\boxed{(x-y)(x+y-76)&gt;0},\\qquad\\boxed{(x+1)(x+2y-75)&lt;0}.\n\\]\n\nBoth are products of two linear factors.\n\n---\n\n### 2.  Work in the \\((x,y)\\)-plane  \n\nThe plane \\(x+y+z=75\\) is a linear image of the \\((x,y)\\)-plane via  \n\n\\[\n(x,y)\\mapsto (x,\\;y,\\;75-x-y) .\n\\]\n\nThe Jacobian matrix has columns \\((1,0,-1)\\) and \\((0,1,-1)\\); its Gram determinant is  \n\n\\[\n\\det\\begin{pmatrix}2&amp;1\\\\1&amp;2\\end{pmatrix}=3 .\n\\]\n\nThus an area element in the plane equals \\(\\sqrt3\\) times the ordinary area\n\\(dx\\,dy\\) in the \\((x,y)\\)-plane.\n\n---\n\n### 3.  Region defined by the two products  \n\nLet  \n\n\\[\nL_1:\\;x=-1,\\qquad L_2:\\;x+2y=75,\n\\]\n\\[\nL_3:\\;x=y,\\qquad L_4:\\;x+y=76 .\n\\]\n\nThe inequalities become\n\n\\[\n\\begin{cases}\nx&gt;-1 \\;\\text{and}\\; y&lt;\\dfrac{75-x}{2}   &amp;\\text{or } x&lt;-1 \\;\\text{and}\\; y&gt;\\dfrac{75-x}{2},\\\\[4pt]\nx&gt;y \\;\\text{and}\\; x+y&gt;76               &amp;\\text{or } x&lt;y \\;\\text{and}\\; x+y&lt;76 .\n\\end{cases}\n\\]\n\nOnly three of the four possible combinations are non\u2011empty:\n\n* **Region\u202f\\(R_1\\)** \u2013 \\(x&gt;-1,\\;y&lt;\\frac{75-x}{2},\\;x&gt;y,\\;x+y&gt;76\\) (unbounded).\n* **Region\u202f\\(R_2\\)** \u2013 \\(x&gt;-1,\\;y&lt;\\frac{75-x}{2},\\;x&lt;y,\\;x+y&lt;76\\) (bounded).\n* **Region\u202f\\(R_3\\)** \u2013 \\(x&lt;-1,\\;y&gt;\\frac{75-x}{2},\\;x&lt;y,\\;x+y&lt;76\\) (unbounded).\n\nHence the set consists of three disjoint convex regions; only \\(R_2\\) has finite area.\n\n---\n\n### 4.  The bounded region  \n\nFrom the inequalities for \\(R_2\\)\n\n\\[\n\\begin{cases}\n-1&lt;x&lt;25,\\\\[2pt]\nx&lt;y&lt;\\dfrac{75-x}{2},\n\\end{cases}\n\\]\n\nso \\(R_2\\) is the open triangle bounded by the lines  \n\n\\[\nx=-1,\\qquad y=x,\\qquad y=\\dfrac{75-x}{2}.\n\\]\n\nIts vertices are  \n\n\\[\nA(-1,-1),\\quad B(-1,38),\\quad C(25,25).\n\\]\n\nThe ordinary (planar) area is\n\n\\[\n\\frac12\\cdot|AB|\\cdot|AC|_{\\perp}= \\frac12\\,(39)\\,(26)=507 .\n\\]\n\n---\n\n### 5.  Area on the plane \\(x+y+z=75\\)\n\nMultiplying by the factor \\(\\sqrt3\\),\n\n\\[\n\\text{area}=507\\sqrt3 .\n\\]\n\nThus \\(a=507,\\;b=3\\) and\n\n\\[\na+b=507+3=510 .\n\\]\n\n\\[\n\\boxed{510}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 510</p>\n<p>Extracted Answer: 510</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThe product $ \\prod_{k=4}^{63} \\frac{\\log_k(5^{k^2-1})}{\\log_{k+1}(5^{k^2-4})} = \\frac{\\log_4(5^{15})}{\\log_5(5^{12})} \\cdot \\frac{\\log_5(5^{24})}{\\log_6(5^{21})} \\cdot \\frac{\\log_6(5^{35})}{\\log_7(5^{32})} \\cdots \\frac{\\log_{63}(5^{3968})}{\\log_{64}(5^{3965})} $ is equal to $ \\frac{m}{n} $, where $ m $ and $ n $ are relatively prime positive integers. Find $ m + n $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>\\[\nP=\\prod_{k=4}^{63}\\frac{\\log_k(5^{k^2-1})}{\\log_{k+1}(5^{k^2-4})}\n\\]\n\n---\n\n### 1.  Simplify one factor  \n\n\\[\n\\log_k(5^{k^2-1})=\\frac{\\ln(5^{k^2-1})}{\\ln k}\n            =\\frac{(k^2-1)\\ln5}{\\ln k},\n\\qquad\n\\log_{k+1}(5^{k^2-4})=\\frac{(k^2-4)\\ln5}{\\ln(k+1)}.\n\\]\n\nHence\n\n\\[\n\\frac{\\log_k(5^{k^2-1})}{\\log_{k+1}(5^{k^2-4})}\n   =\\frac{k^2-1}{k^2-4}\\cdot\\frac{\\ln(k+1)}{\\ln k}.\n\\]\n\nSo\n\n\\[\nP=\\Bigl(\\prod_{k=4}^{63}\\frac{k^2-1}{k^2-4}\\Bigr)\n   \\Bigl(\\prod_{k=4}^{63}\\frac{\\ln(k+1)}{\\ln k}\\Bigr).\n\\]\n\n---\n\n### 2.  Telescoping the logarithm part  \n\n\\[\n\\prod_{k=4}^{63}\\frac{\\ln(k+1)}{\\ln k}\n =\\frac{\\ln5}{\\ln4}\\cdot\\frac{\\ln6}{\\ln5}\\cdots\\frac{\\ln64}{\\ln63}\n =\\frac{\\ln64}{\\ln4}\n =\\log_4 64 =3 .\n\\]\n\n---\n\n### 3.  Telescoping the rational part  \n\n\\[\n\\frac{k^2-1}{k^2-4}= \\frac{(k-1)(k+1)}{(k-2)(k+2)}\n   =\\frac{k-1}{k-2}\\cdot\\frac{k+1}{k+2}.\n\\]\n\nHence\n\n\\[\n\\prod_{k=4}^{63}\\frac{k^2-1}{k^2-4}\n =\\Bigl(\\prod_{k=4}^{63}\\frac{k-1}{k-2}\\Bigr)\n   \\Bigl(\\prod_{k=4}^{63}\\frac{k+1}{k+2}\\Bigr).\n\\]\n\n*First product*  \n\nLet \\(i=k-2\\). Then \\(i\\) runs from \\(2\\) to \\(61\\):\n\n\\[\n\\prod_{k=4}^{63}\\frac{k-1}{k-2}\n =\\prod_{i=2}^{61}\\frac{i+1}{i}\n =\\frac{3}{2}\\cdot\\frac{4}{3}\\cdots\\frac{62}{61}\n =\\frac{62}{2}=31 .\n\\]\n\n*Second product*  \n\nLet \\(j=k+1\\). Then \\(j\\) runs from \\(5\\) to \\(64\\):\n\n\\[\n\\prod_{k=4}^{63}\\frac{k+1}{k+2}\n =\\prod_{j=5}^{64}\\frac{j}{j+1}\n =\\frac{5}{6}\\cdot\\frac{6}{7}\\cdots\\frac{64}{65}\n =\\frac{5}{65}=\\frac1{13}.\n\\]\n\nThus\n\n\\[\n\\prod_{k=4}^{63}\\frac{k^2-1}{k^2-4}=31\\cdot\\frac1{13}=\\frac{31}{13}.\n\\]\n\n---\n\n### 4.  Combine the two parts  \n\n\\[\nP = 3\\cdot\\frac{31}{13}= \\frac{93}{13}.\n\\]\n\nThe fraction \\(\\frac{93}{13}\\) is already in lowest terms (\\(\\gcd(93,13)=1\\)).\nThus \\(m=93,\\; n=13\\) and\n\n\\[\nm+n = 93+13 = 106 .\n\\]\n\n\\[\n\\boxed{106}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 106</p>\n<p>Extracted Answer: 106</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThe 27 cells of a $3\\times9$ grid are filled in using the numbers 1 through 9 so that each row contains 9 different numbers, and each of the three $3\\times3$ blocks heavily outlined in the example below contains 9 different numbers, as in the first three rows of a Sudoku puzzle. \n | 4 | 2 | 8 | 9 | 6 | 3 | 1 | 7 | 5 | \n | 3 | 7 | 9 | 5 | 2 | 1 | 6 | 8 | 4 | \n | 5 | 6 | 1 | 8 | 4 | 7 | 9 | 2 | 3 | \n The number of different ways to fill such a grid can be written as $p^a\\cdot q^b\\cdot r^c\\cdot s^d$, where $p,q,r,$ and $s$ are distinct prime numbers and $a,b,c,$ and $d$ are positive integers. Find $p\\cdot a+q\\cdot b+r\\cdot c+s\\cdot d$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>**Step 1 \u2013  what the conditions mean**\n\nIn a \\(3\\times 9\\) grid  \n\n* each of the three rows must be a permutation of the numbers \\(1,\\ldots ,9\\);  \n* each of the three \\(3\\times3\\) blocks (columns \\(1\\!-\\!3,\\;4\\!-\\!6,\\;7\\!-\\!9\\)) must also contain the numbers \\(1,\\ldots ,9\\) exactly once.\n\nHence every digit appears\n\n* once in each row (3 times in total), and  \n* once in each block (also 3 times in total).\n\nSo for a fixed digit \\(d\\) the three positions where it occurs are determined by a\nbijection between the three rows and the three blocks; i.e. a permutation\n\\(\\sigma_d\\in S_{3}\\).\n\n--------------------------------------------------------------------\n\n**Step 2 \u2013  describing a filling by permutations**\n\nFor the nine digits we obtain nine permutations  \n\n\\[\n\\sigma_1,\\sigma_2,\\dots ,\\sigma_9\\in S_3 .\n\\]\n\nIf \\(\\sigma_d(i)=j\\) then digit \\(d\\) is placed in row \\(i\\) inside block \\(j\\).\nFor a fixed block\u2013row cell \\((i,j)\\) there are three rows of the grid, hence it\nmust contain **exactly three** digits. Consequently for every cell \\((i,j)\\)\n\n\\[\n\\#\\{d\\mid \\sigma_d(i)=j\\}=3 .\n\\tag{1}\n\\]\n\n--------------------------------------------------------------------\n\n**Step 3 \u2013  solving the integer system**\n\nLet  \n\n\\[\n\\begin{aligned}\nx_{\\mathrm{id}}&amp;=\\#\\{\\sigma_d=\\text{id}\\},&amp;\nx_{12}&amp;=\\#\\{\\sigma_d=(12)\\},\\\\\nx_{13}&amp;=\\#\\{\\sigma_d=(13)\\},&amp;\nx_{23}&amp;=\\#\\{\\sigma_d=(23)\\},\\\\\nx_{123}&amp;=\\#\\{\\sigma_d=(123)\\},&amp;\nx_{132}&amp;=\\#\\{\\sigma_d=(132)\\}.\n\\end{aligned}\n\\]\n\nEach permutation contributes a \u20181\u2019 to three different cells; each cell is covered\nby exactly two permutations. From (1) we obtain nine equations, e.g.\n\n\\[\nx_{\\mathrm{id}}+x_{23}=3,\\qquad\nx_{12}+x_{123}=3,\\qquad\\ldots\n\\]\n\nSolving them gives\n\n\\[\nx_{12}=x_{13}=x_{23}=k,\\qquad\nx_{\\mathrm{id}}=x_{123}=x_{132}=3-k,\n\\]\n\nwhere \\(k\\in\\{0,1,2,3\\}\\).\n\n--------------------------------------------------------------------\n\n**Step 4 \u2013  assigning the permutations to the nine distinct digits**\n\nFor a fixed \\(k\\) the number of ways to give the nine digits the required\nmultiplicities is the multinomial coefficient\n\n\\[\n\\frac{9!}{k!^{\\,3}\\,(3-k)!^{\\,3}} .\n\\]\n\nSumming over the four possible values of \\(k\\) gives\n\n\\[\nN=\\sum_{k=0}^{3}\\frac{9!}{k!^{\\,3}(3-k)!^{\\,3}}\n   =2\\cdot\\frac{9!}{3!^{\\,3}}+2\\cdot\\frac{9!}{1!^{\\,3}2!^{\\,3}}\n   =1680+45360+45360+1680=94\\,080 .\n\\]\n\nThus there are \\(94\\,080\\) ways to decide, for every digit, in which block of\neach row it will appear.\n\n--------------------------------------------------------------------\n\n**Step 5 \u2013  placing the digits inside the blocks**\n\nFix a block \\(j\\).  \nRow \\(i\\) contributes exactly three distinct digits to this block; they can be\narranged in the three columns of the block in \\(3! = 6\\) ways, independently for\nthe three rows. Hence a block can be filled in \\((3!)^{3}=6^{3}=216\\) ways.\n\nThe three blocks are independent, so the column\u2011ordering factor is\n\n\\[\n(3!)^{9}=6^{9}=10\\,077\\,696 .\n\\]\n\n--------------------------------------------------------------------\n\n**Step 6 \u2013  total number of fillings**\n\n\\[\n\\boxed{T = N\\cdot (3!)^{9}=94\\,080\\cdot 10\\,077\\,696\n      = 948\\,109\\,639\\,680 }.\n\\]\n\nFactorising,\n\n\\[\nT = 2^{16}\\cdot 3^{10}\\cdot 5\\cdot 7^{2}.\n\\]\n\n--------------------------------------------------------------------\n\n**Step 7 \u2013  computing the required sum**\n\nTake \\(p=2,\\;q=3,\\;r=5,\\;s=7\\) with exponents\n\\(a=16,\\;b=10,\\;c=1,\\;d=2\\). Then\n\n\\[\np\\!a+q\\!b+r\\!c+s\\!d\n=2\\cdot16+3\\cdot10+5\\cdot1+7\\cdot2\n=32+30+5+14=81 .\n\\]\n\n\\[\n\\boxed{81}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 81</p>\n<p>Extracted Answer: 81</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThere are exactly three positive real numbers $ k $ such that the function\n$ f(x) = \\frac{(x - 18)(x - 72)(x - 98)(x - k)}{x} $\ndefined over the positive real numbers achieves its minimum value at exactly two positive real numbers $ x $. Find the sum of these three values of $ k $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>**Solution Overview**\n\nFor  \n\n\\[\nf(x)=\\frac{(x-18)(x-72)(x-98)(x-k)}{x},\\qquad x&gt;0,\n\\]\n\nlet  \n\n\\[\nN(x)=(x-18)(x-72)(x-98)(x-k)=x^4-S_1x^3+S_2x^2-S_3x+S_4,\n\\]\n\nwhere  \n\n\\[\n\\begin{aligned}\nS_1&amp;=18+72+98+k=188+k,\\\\[2pt]\nS_2&amp;=18\\cdot72+18\\cdot98+72\\cdot98+ k(18+72+98)=10116+188k,\\\\[2pt]\nS_4&amp;=18\\cdot72\\cdot98\\cdot k=127008\\,k .\n\\end{aligned}\n\\]\n\nThen  \n\n\\[\nf(x)=\\frac{N(x)}{x}=x^{3}-S_1x^{2}+S_2x-S_3+\\frac{S_4}{x},\n\\]\n\nand  \n\n\\[\nf&#39;(x)=\\frac{3x^{4}-2S_1x^{3}+S_2x^{2}-S_4}{x^{2}} .\n\\]\n\nHence the critical points are the (positive) roots of  \n\n\\[\nP(x)=3x^{4}-2S_1x^{3}+S_2x^{2}-S_4=0\\tag{1}\n\\]\n\n(the denominator $x^{2}&gt;0$ for $x&gt;0$).\n\nBecause $f(x)\\to +\\infty$ as $x\\to0^{+}$ and as $x\\to\\infty$, the graph must\nfirst decrease, then increase, then decrease, and finally increase again.\nThus (1) has three positive roots:\n\n* $x_1$ \u2013 a local **minimum** in the first negative interval,\n* $x_2$ \u2013 a local **maximum** in the positive interval,\n* $x_3$ \u2013 a second local **minimum** in the last negative interval.\n\nThe global minimum is achieved at the lower of the two minima.\nFor the minimum to be attained **exactly at two points** we need  \n\n\\[\nf(x_1)=f(x_3)\\qquad(\\text{the two minima have the same value}).\n\\tag{2}\n\\]\n\n--------------------------------------------------------------------\n### 1.  Translating the condition\n\nAt a critical point $x$ we have $f&#39;(x)=0$, i.e. $P(x)=0$.\nFrom $f(x)=\\dfrac{N(x)}{x}$ and $P(x)=0$ it follows that  \n\n\\[\nf(x)=\\frac{N(x)}{x}=N&#39;(x)\\qquad\\text{for any critical point}.\n\\tag{3}\n\\]\n\nThus (2) is equivalent to  \n\n\\[\nN&#39;(x_1)=N&#39;(x_3).\\tag{4}\n\\]\n\nWriting $x_1+ x_3=s$ and $x_1x_3=p$, the two equations $P(x_1)=P(x_3)=0$\ngive after elimination  \n\n\\[\n\\begin{cases}\n4(s^{2}-p)-3S_1s+2S_2=0,\\\\[2pt]\n3(s^{3}-2ps)-2S_1(s^{2}-p)+S_2s=0.\n\\end{cases}\\tag{5}\n\\]\n\nEquation (5) yields  \n\n\\[\n(2s-S_1)\\Bigl(3s(s-S_1)+2S_2\\Bigr)=0 .\n\\]\n\nHence either  \n\n\\[\n\\boxed{s=\\dfrac{S_1}{2}} \\qquad\\text{or}\\qquad\n3s^{2}-3S_1s+2S_2=0. \\tag{6}\n\\]\n\n--------------------------------------------------------------------\n### 2.  The case $s=S_1/2$\n\nFrom the first possibility in (6) we obtain  \n\n\\[\np=\\frac{4S_2-S_1^{2}}{8}.\n\\]\n\nUsing $x_1x_2=p$ and $x_1+x_2=S_1/2$ the two minima are  \n\n\\[\nx_{1,3}= \\frac{S_1\\pm 2\\sqrt{\\,\\Delta\\,}}{4},\n\\qquad \n\\Delta=\\frac34k^{2}-94k+6276 .\n\\]\n\nNow we must also satisfy $P(x_1)=0$, which after substitution gives\n\n\\[\n(S_1^{2}-4S_2)^{2}=64S_4 .\n\\]\n\nWith the explicit expressions for $S_1,S_2,S_4$ this becomes\n\n\\[\n(k^{2}-376k-5120)^{2}=8128512\\,k,\n\\]\n\nor  \n\n\\[\nk^{4}-752k^{3}+131136k^{2}-4278272k+26214400=0.\n\\tag{7}\n\\]\n\nFactoring (7) gives  \n\n\\[\n(k-8)(k-32)(k-200)(k-512)=0 .\n\\]\n\nFor a root to be admissible we need the two minima to lie in the\ntwo negative intervals of $f$.  \nThe left minimum equals  \n\n\\[\nx_1=\\frac{k+188-2\\sqrt{\\Delta}}{4},\n\\]\n\nwhich is **positive** only when  \n\n\\[\nk^{2}-376k-5120&lt;0\\qquad\\Longleftrightarrow\\qquad k&lt;389\\ldots .\n\\]\n\nThus $k=512$ is rejected, while $k=8,\\,32,\\,200$ are valid.\n\n--------------------------------------------------------------------\n### 3.  The second possibility in (6)\n\nThe alternative equation $3s^{2}-3S_1s+2S_2=0$ together with the condition\n$P(x_1)=0$ leads, after a completely analogous elimination, to the same\nquartic (7).  Its admissible positive solutions are again $8,32,200$,\nso no new $k$ appear.\n\n--------------------------------------------------------------------\n### 4.  Conclusion\n\nThe function $f$ has its global minimum attained at exactly two positive\npoints precisely for  \n\n\\[\nk\\in\\{8,\\;32,\\;200\\}.\n\\]\n\nTherefore the required sum is  \n\n\\[\n8+32+200 = \\boxed{240}.\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 240</p>\n<p>Extracted Answer: 240</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nFour unit squares form a $2 \\times 2$ grid. Each of the 12 unit line segments forming the sides of the squares is colored either red or blue in such a way that each unit square has 2 red sides and 2 blue sides. Find the number of such colorings.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let the four unit squares be  \n\n\\[\n\\begin{array}{cc}\nA&amp; B\\\\\nC&amp; D\n\\end{array}\n\\]\n\nand denote by  \n\n* \\(a=h_{0,1}\\)   \u2013 the middle horizontal segment between \\(A\\) and \\(C\\);  \n* \\(b=h_{1,1}\\)   \u2013 the middle horizontal segment between \\(B\\) and \\(D\\);  \n* \\(c=v_{1,0}\\)   \u2013 the middle vertical segment between \\(A\\) and \\(B\\);  \n* \\(d=v_{1,1}\\)   \u2013 the middle vertical segment between \\(C\\) and \\(D\\).\n\nThe eight outer unit\u2011segments are written as  \n\n\\[\n\\begin{aligned}\n&amp;e_1=h_{0,0},\\qquad e_2=v_{0,0},\\\\\n&amp;e_3=v_{2,0},\\qquad e_4=h_{1,0},\\\\\n&amp;e_5=h_{0,2},\\qquad e_6=v_{0,1},\\\\\n&amp;e_7=v_{2,1},\\qquad e_8=h_{1,2}.\n\\end{aligned}\n\\]\n\nAll variables take the value 1 for a red side and 0 for a blue side.\n\n--------------------------------------------------------------------\n### 1.  Equations for the squares  \n\nEach unit square must have exactly two red sides, so we obtain\n\n\\[\n\\begin{aligned}\nA:&amp;\\;e_1+e_2+a+c=2, \\\\\nB:&amp;\\;e_3+e_4+b+c=2, \\\\\nC:&amp;\\;e_5+e_6+a+d=2, \\\\\nD:&amp;\\;e_7+e_8+b+d=2 .\\qquad (1)\n\\end{aligned}\n\\]\n\n--------------------------------------------------------------------\n### 2.  Fix the interior edges  \n\nThe four interior edges \\(a,b,c,d\\) are independent; there are \\(2^4=16\\) possible\nchoices.\nFor a fixed quadruple \\((a,b,c,d)\\) the right\u2011hand side of each equation in (1)\nbecomes  \n\n\\[\ns_A=2-(a+c),\\; s_B=2-(b+c),\\; s_C=2-(a+d),\\; s_D=2-(b+d).\n\\]\n\nThe numbers \\(s_A,s_B,s_C,s_D\\) are the required sums of the two\nouter edges belonging to each square.\n\n*If \\(s_i=0\\) or \\(s_i=2\\):* the two outer edges are forced to be\n\\((0,0)\\) or \\((1,1)\\) \u2013 exactly **one** possibility.\n\n*If \\(s_i=1\\):* the outer edges must be \\((0,1)\\) or \\((1,0)\\) \u2013 **two**\npossibilities.\n\nHence, for a given \\((a,b,c,d)\\) the number of admissible colourings of the\nouter edges equals  \n\n\\[\n2^{\\,N},\\qquad N=\\#\\{i\\in\\{A,B,C,D\\}:s_i=1\\}.\n\\]\n\nBut \\(s_i=1\\) occurs precisely when the two interior edges of that square sum to\n\\(1\\); i.e.\n\n\\[\nN=[a\\neq c]+[b\\neq c]+[a\\neq d]+[b\\neq d],\\tag{2}\n\\]\n\nwhere \\([P]=1\\) if the statement \\(P\\) is true and \\(0\\) otherwise.\n\n--------------------------------------------------------------------\n### 3.  Summing over the interior edges  \n\nWrite the sum we need as  \n\n\\[\n\\sum_{a,b,c,d\\in\\{0,1\\}} 2^{[a\\neq c]+[b\\neq c]+[a\\neq d]+[b\\neq d]}.\n\\]\n\nFor fixed \\(a,b\\) the contributions of \\(c\\) and \\(d\\) factor:\n\n\\[\n\\bigl(\\sum_{c\\in\\{0,1\\}}2^{[a\\neq c]+[b\\neq c]}\\bigr)^2 .\n\\]\n\nNow compute the inner sum.\n\n*If \\(a=b\\) (either \\((0,0)\\) or \\((1,1)\\)):  \n\n\\[\nc=0\\!:\\;[a\\neq c]+[b\\neq c]=0,\\qquad\nc=1\\!:\\;[a\\neq c]+[b\\neq c]=2,\n\\]\nso the sum equals \\(2^{0}+2^{2}=1+4=5\\).\n\n*If \\(a\\neq b\\) (either \\((0,1)\\) or \\((1,0)\\)):  \n\n\\[\nc=0\\!:\\;[a\\neq c]+[b\\neq c]=1,\\qquad\nc=1\\!:\\;[a\\neq c]+[b\\neq c]=1,\n\\]\nso the sum equals \\(2^{1}+2^{1}=2+2=4\\).\n\nThus\n\n\\[\n\\begin{aligned}\n\\text{total}&amp;=\n2\\bigl(5^2\\bigr)+2\\bigl(4^2\\bigr)        \\\\\n&amp;=2\\cdot25+2\\cdot16\\\\\n&amp;=50+32\\\\\n&amp;=82 .\n\\end{aligned}\n\\]\n\n--------------------------------------------------------------------\n### 4.  Answer  \n\nThere are  \n\n\\[\n\\boxed{82}\n\\]\n\ndifferent colourings of the twelve unit segments such that each of the four\nunit squares has exactly two red sides and two blue sides.</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 82</p>\n<p>Extracted Answer: 82</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nCircle $\\omega_1$ with radius 6 centered at point $A$ is internally tangent at point $B$ to circle $\\omega_2$ with radius 15. Points $C$ and $D$ lie on $\\omega_2$ such that $\\overline{BC}$ is a diameter of $\\omega_2$ and $\\overline{BC} \\perp \\overline{AD}$. The rectangle $EFGH$ is inscribed in $\\omega_1$ such that $\\overline{EF} \\perp \\overline{BC}$, $C$ is closer to $\\overline{GH}$ than to $\\overline{EF}$, and $D$ is closer to $\\overline{FG}$ than to $\\overline{EH}$, as shown. Triangles $\\triangle DGF$ and $\\triangle CHG$ have equal areas. The area of rectangle $EFGH$ is $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m + n$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n* \\(O\\) be the centre of \\(\\omega _2\\) (radius \\(15\\)),\n* \\(A\\) be the centre of \\(\\omega _1\\) (radius \\(6\\)),\n* \\(B\\) the internal point of tangency.\n\nPlace \\(O\\) at the origin and take the diameter \\(BC\\) on the \\(x\\)-axis.\n\n\\[\nO=(0,0),\\qquad B=(15,0)\n\\]\n\nBecause \\(\\omega_1\\) is tangent internally at \\(B\\),\n\n\\[\nOA=15-6=9\\qquad\\Longrightarrow\\qquad A=(9,0).\n\\]\n\nSince \\(BC\\) is a diameter of \\(\\omega _2\\),\n\n\\[\nC=(-15,0).\n\\]\n\n\\(AD\\perp BC\\) forces \\(AD\\) to be vertical through \\(A\\); intersecting this line with \\(\\omega _2\\),\n\n\\[\nx=9,\\qquad x^{2}+y^{2}=225\\Longrightarrow y=\\pm 12 .\n\\]\n\nBecause the problem states that \\(D\\) is nearer to the side \\(FG\\) than to \\(EH\\), we take the point above the \\(x\\)-axis:\n\n\\[\nD=(9,12).\n\\]\n\n---------------------------------------------------------------------\n\n### 1.  The rectangle \\(EFGH\\)\n\n\\(EF\\perp BC\\); with \\(BC\\) horizontal this makes \\(EF\\) vertical, so the rectangle is axis\u2011aligned.\nLet its half\u2013width be \\(d&gt;0\\) and its half\u2013height be \\(h&gt;0\\).  \nSince the rectangle is inscribed in \\(\\omega _1\\) (centre \\(A\\)), its centre must coincide with \\(A\\).  \nThus the vertices are  \n\n\\[\n\\begin{aligned}\nE&amp;=(9+d,\\,-h),  &amp;F&amp;=(9+d,\\,h),\\\\\nG&amp;=(9-d,\\,h),   &amp;H&amp;=(9-d,\\,-h).\n\\end{aligned}\n\\]\n\nEach vertex lies on \\(\\omega _1\\):  \n\n\\[\n(x-9)^2+y^2=6^2\\quad\\Longrightarrow\\quad d^{\\,2}+h^{\\,2}=36. \\tag{1}\n\\]\n\n---------------------------------------------------------------------\n\n### 2.  Equality of the two triangle areas\n\n*Triangle \\(DGF\\)*  \nIts base \\(GF\\) is horizontal with length \\(2d\\); the height is the vertical distance from \\(D\\) to the line \\(y=h\\):\n\\[\n[\\,DGF\\,]=\\frac12\\cdot (2d)\\bigl(12-h\\bigr)=d(12-h).\n\\]\n\n*Triangle \\(CHG\\)*  \nIts base \\(GH\\) is vertical with length \\(2h\\); the height is the horizontal distance from \\(C\\) to the line \\(x=9-d\\):\n\\[\n[\\,CHG\\,]=\\frac12\\cdot (2h)\\bigl( (9-d)-(-15)\\bigr)=h(24-d).\n\\]\n\nThe condition \\([DGF]=[CHG]\\) gives  \n\n\\[\nd(12-h)=h(24-d)\\;\\Longrightarrow\\;12d=24h\\;\\Longrightarrow\\;d=2h. \\tag{2}\n\\]\n\n---------------------------------------------------------------------\n\n### 3.  Solving for \\(d\\) and \\(h\\)\n\nSubstituting \\(d=2h\\) into (1):\n\n\\[\n(2h)^2+h^{2}=36\\quad\\Longrightarrow\\quad5h^{2}=36\n\\quad\\Longrightarrow\\quad h^{2}=\\frac{36}{5},\\qquad \nh=\\frac{6}{\\sqrt5},\\qquad d=2h=\\frac{12}{\\sqrt5}.\n\\]\n\n---------------------------------------------------------------------\n\n### 4.  Area of the rectangle\n\n\\[\n\\text{Area}= (2d)(2h)=4dh=4(2h)h=8h^{2}=8\\cdot\\frac{36}{5}\n=\\frac{288}{5}.\n\\]\n\nThus the area equals \\(\\dfrac{m}{n}\\) with \\(m=288,\\;n=5\\) (coprime).  \n\n\\[\nm+n=288+5=293.\n\\]\n\n\\[\n\\boxed{293}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 293</p>\n<p>Extracted Answer: 293</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $ A $ be the set of positive integer divisors of 2025. Let $ B $ be a randomly selected subset of $ A $. The probability that $ B $ is a nonempty set with the property that the least common multiple of its elements is 2025 is $ \\frac{m}{n} $, where $ m $ and $ n $ are relatively prime positive integers. Find $ m + n $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Factor  \n\n\\[\n2025=3^{4}\\cdot5^{2}.\n\\]\n\nA divisor of \\(2025\\) has the form \\(3^{a}5^{b}\\) with \\(0\\le a\\le4,\\ 0\\le b\\le2\\).  \nHence  \n\n\\[\n|A|=(4+1)(2+1)=15,\n\\qquad\\text{total subsets}=2^{15}=32768 .\n\\]\n\n---\n\n### When does a subset have lcm \\(=2025\\)?\n\nThe lcm of a set of divisors is \\(3^{\\max a}\\cdot5^{\\max b}\\).  \nThus the lcm equals \\(2025=3^{4}\\cdot5^{2}\\) **iff**\n\n* at least one element has exponent \\(a=4\\) (a divisor containing \\(3^{4}\\));\n* at least one element has exponent \\(b=2\\) (a divisor containing \\(5^{2}\\)).\n\n---\n\n### Counting the desired subsets  \n\nDivisors with \\(a=4\\): \\(3^{4}5^{b}\\ (b=0,1,2)\\) \u2013 3 of them.  \nDivisors with \\(b=2\\): \\(3^{a}5^{2}\\ (a=0,\\dots ,4)\\) \u2013 5 of them.  \n\nLet  \n\n* \\(X\\) = subsets containing **no** divisor with \\(a=4\\);  \n* \\(Y\\) = subsets containing **no** divisor with \\(b=2\\).\n\n\\[\n|X|=2^{12}\\quad (\\text{choose any of the other }12\\text{ divisors}),\\qquad\n|Y|=2^{10}\\quad (\\text{choose any of the other }10\\text{ divisors}).\n\\]\n\nDivisors lacking both \\(a=4\\) and \\(b=2\\) have \\(a\\le3,\\ b\\le1\\); there are \\(4\\cdot2=8\\) of them, so\n\n\\[\n|X\\cap Y|=2^{8}.\n\\]\n\nUsing inclusion\u2013exclusion, the number of subsets that contain **both** an \\(a=4\\) divisor and a \\(b=2\\) divisor is  \n\n\\[\nN = 2^{15} - 2^{12} - 2^{10} + 2^{8}\n    = 32768 - 4096 - 1024 + 256\n    = 27904 .\n\\]\n\nThese subsets are precisely the non\u2011empty subsets whose lcm equals \\(2025\\); the empty set is automatically excluded by the inclusion\u2013exclusion count.\n\n---\n\n### Probability\n\n\\[\n\\text{Probability} = \\frac{N}{2^{15}} = \\frac{27904}{32768}\n                     = \\frac{2^{8}\\cdot 109}{2^{15}}\n                     = \\frac{109}{128}.\n\\]\n\nThe fraction \\(\\frac{109}{128}\\) is already in lowest terms, so  \n\n\\[\nm=109,\\qquad n=128,\\qquad m+n=237.\n\\]\n\n\\[\n\\boxed{237}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 237</p>\n<p>Extracted Answer: 237</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nSixteen chairs are arranged in a row. Eight people each select a chair in which to sit so that no person sits next to two other people. Let $ N $ be the number of subsets of 16 chairs that could be selected. Find the remainder when $ N $ is divided by 1000.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n\\[\n\\text{chairs}=1,2,\\dots ,16,\\qquad 8\\ \\text{people sit in 8 of them.}\n\\]\n\nThe condition *no person sits next to two other people* means that no three\noccupied chairs are consecutive.  \nHence we must count binary strings of length \\(16\\) with exactly eight 1\u2019s\nand no substring \\(111\\).\n\n---\n\n### 1.  Blocks of occupied chairs  \n\nOccupied chairs appear in blocks of length \\(1\\) or \\(2\\) (a block of length\n\\(3\\) would give a person with two neighbours).  \n\nLet  \n\n* \\(t\\) = number of blocks of length \\(2\\);\n* \\(s\\) = number of blocks of length \\(1\\).\n\nThen  \n\n\\[\ns+2t=8,\\qquad r=s+t \\text{ (total number of blocks)} .\n\\]\n\nHence  \n\n\\[\nt=0,1,2,3,4,\\qquad r=8-t\\;(=8,7,6,5,4).\n\\]\n\nFor a fixed \\(t\\) (hence fixed \\(r\\)) we must choose which of the \\(r\\) blocks\nare the double ones:\n\n\\[\n\\text{ways to choose the double blocks}= \\binom{r}{t}= \\binom{r}{8-r}.\n\\]\n\n---\n\n### 2.  Placing the blocks among the empty chairs  \n\nThere are \\(16-8=8\\) empty chairs.  \nBetween the \\(r\\) blocks there must be at least one empty chair, using\n\\(r-1\\) chairs.  \n\nThe remaining empty chairs are  \n\n\\[\n8-(r-1)=9-r .\n\\]\n\nThese \\(9-r\\) chairs can be placed arbitrarily in the \\(r+1\\) gaps\n(before the first block, between successive blocks, after the last block).  \nBy stars\u2011and\u2011bars the number of ways is  \n\n\\[\n\\binom{(9-r)+(r+1)-1}{(r+1)-1}= \\binom{9}{r}.\n\\]\n\n---\n\n### 3.  Total number of admissible subsets  \n\n\\[\n\\begin{aligned}\nN&amp;=\\sum_{t=0}^{4} \\binom{r}{t}\\binom{9}{r},\n\\qquad r=8-t \\\\\n  &amp;=\\sum_{r=4}^{8}\\binom{r}{\\,8-r\\,}\\binom{9}{r}.\n\\end{aligned}\n\\]\n\nCompute each term:\n\n\\[\n\\begin{array}{c|c|c|c}\nr &amp; \\binom{r}{8-r} &amp; \\binom{9}{r} &amp; \\text{product}\\\\ \\hline\n8 &amp; 1 &amp; 9   &amp; 9\\\\\n7 &amp; 7 &amp; 36  &amp; 252\\\\\n6 &amp; 15&amp; 84  &amp; 1260\\\\\n5 &amp; 10&amp; 126 &amp; 1260\\\\\n4 &amp; 1 &amp; 126 &amp; 126\n\\end{array}\n\\]\n\nAdding them,\n\n\\[\nN = 9+252+1260+1260+126 = 2907.\n\\]\n\n---\n\n### 4.  Remainder modulo \\(1000\\)\n\n\\[\n2907 \\equiv 907 \\pmod{1000}.\n\\]\n\n\\[\n\\boxed{907}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 907</p>\n<p>Extracted Answer: 907</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThere are $ n $ values of $ x $ in the interval $ 0 &lt; x &lt; 2\\pi $ where $ f(x) = \\sin(7\\pi \\cdot \\sin(5x)) = 0 $. For $ t $ of these $ n $ values of $ x $, the graph of $ y = f(x) $ is tangent to the $ x $-axis. Find $ n + t $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>To solve  \n\n\\[\nf(x)=\\sin \\bigl(7\\pi \\,\\sin(5x)\\bigr)=0 ,\\qquad 0&lt;x&lt;2\\pi \n\\]\n\nlet  \n\n\\[\ng(x)=7\\pi\\sin(5x).\n\\]\n\nThen  \n\n\\[\nf(x)=\\sin(g(x))=0\\iff g(x)=k\\pi,\\;k\\in\\mathbb Z .\n\\]\n\nHence  \n\n\\[\n7\\pi\\sin(5x)=k\\pi\\Longrightarrow \\sin(5x)=\\frac{k}{7}.\n\\]\n\nBecause \\(|\\sin(5x)|\\le 1\\), the integer \\(k\\) can be  \n\\(-7\\le k\\le 7\\).\n\n---\n\n### 1. Counting the zeros (\\(n\\))\n\nPut \\(y=5x\\).  \nWhen \\(x\\) runs from \\(0\\) to \\(2\\pi\\), \\(y\\) runs from \\(0\\) to \\(10\\pi\\).\n\nFor a fixed value \\(c=\\frac{k}{7}\\) we count the solutions of \\(\\sin y=c\\) in the interval \\((0,10\\pi)\\).\n\n* **\\(c=0\\) \\;(i.e. \\(k=0\\)):**  \n  \\(\\sin y=0\\) \u21d2 \\(y=m\\pi\\).  \n  In \\((0,10\\pi)\\) we have \\(m=1,2,\\dots ,9\\) \u2192 **9 solutions**.\n\n* **\\(c=\\pm1\\) \\;(i.e. \\(k=\\pm7\\)):**  \n  \\(\\sin y=1\\) gives \\(y=\\frac{\\pi}{2}+2\\pi n\\)  \n  \\(\\sin y=-1\\) gives \\(y=\\frac{3\\pi}{2}+2\\pi n\\).  \n  For \\(n=0,1,2,3,4\\) each set yields 5 points \u2192 **5+5 = 10 solutions**.\n\n* **\\(c\\) with \\(|c|&lt;1\\) and \\(c\\neq0\\) \\;(i.e. \\(k=\\pm1,\\dots ,\\pm6\\)):**  \n  For any such \\(c\\) there are two solutions per period of sine.  \n  The interval \\((0,10\\pi)\\) contains five full periods, so we obtain **\\(5\\times2=10\\) solutions** for each such \\(k\\).\n\nNow sum:\n\n\\[\n\\begin{aligned}\nn &amp; =\\underbrace{9}_{k=0}\n   +\\underbrace{12\\times10}_{k=\\pm1,\\dots ,\\pm6}\n   +\\underbrace{10}_{k=\\pm7}\\\\[2mm]\n  &amp; = 9+120+10 = 139 .\n\\end{aligned}\n\\]\n\nThus **\\(n=139\\)**.\n\n---\n\n### 2. When is the graph tangent to the \\(x\\)-axis? (\\(t\\))\n\nThe graph is tangent at a zero when the derivative also vanishes:\n\n\\[\nf&#39;(x)=\\cos\\bigl(7\\pi\\sin(5x)\\bigr)\\cdot 35\\pi\\cos(5x)=0 .\n\\]\n\nAt the zeros we already have \\(\\sin(7\\pi\\sin(5x))=0\\), i.e. \\(7\\pi\\sin(5x)=k\\pi\\).  \nHence \\(\\cos\\bigl(7\\pi\\sin(5x)\\bigr)=\\cos(k\\pi)=(-1)^k\\neq0\\).\n\nConsequently \\(f&#39;(x)=0\\) can only occur through \\(\\cos(5x)=0\\).\n\n\\[\n\\cos(5x)=0 \\Longrightarrow 5x=\\frac{\\pi}{2}+m\\pi\n            \\Longrightarrow x=\\frac{(2m+1)\\pi}{10},\\qquad m\\in\\mathbb Z .\n\\]\n\nWithin \\(0&lt;x&lt;2\\pi\\) we have \\(m=0,1,\\dots ,9\\), giving **10 distinct \\(x\\)** values.\n\nAt each of these points \\(\\sin(5x)=\\pm1\\), so \\(\\sin(7\\pi\\sin(5x))=\\sin(\\pm7\\pi)=0\\); thus they are indeed zeros, and because the derivative also vanishes the graph is tangent there.\n\nHence **\\(t=10\\)**.\n\n---\n\n### 3. Required sum\n\n\\[\nn+t = 139 + 10 = 149 .\n\\]\n\n\\[\n\\boxed{149}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 149</p>\n<p>Extracted Answer: 149</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $N$ denote the number of ordered triples of positive integers $(a,b,c)$ such that $a,b,c\\leq3^6$ and $a^3+b^3+c^3$ is a multiple of $3^7$. Find the remainder when $N$ is divided by $1000$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>**Answer:** \\(\\boxed{637}\\)</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 735</p>\n<p>Extracted Answer: 637</p>\n<p>Score: 0.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $ A_1A_2 \\ldots A_{11} $ be an 11-sided non-convex simple polygon with the following properties:\n* The area of $ A_iA_1A_{i+1} $ is 1 for each $ 2 \\leq i \\leq 10 $,\n* $ \\cos(\\angle A_iA_1A_{i+1}) = \\frac{12}{13} $ for each $ 2 \\leq i \\leq 10 $,\n* The perimeter of $ A_1A_2 \\ldots A_{11} $ is 20.\nIf $ A_1A_2 + A_1A_{11} $ can be expressed as $ \\frac{m\\sqrt{n} - p}{q} $ for positive integers $ m, n, p, q $ with $ n $ squarefree and no prime divides all of $ m, p, q$, find $ m + n + p + q $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n\\[\nx_i=A_1A_i\\qquad (i=2,3,\\ldots ,11),\\qquad \n\\theta=\\angle A_iA_1A_{i+1}\\;(2\\le i\\le10).\n\\]\n\n---\n\n### 1.  Using the area condition  \n\n\\[\n\\text{Area}\\bigl(A_iA_1A_{i+1}\\bigr)=\\frac12 x_i x_{i+1}\\sin\\theta =1 .\n\\]\n\nBecause \\(\\cos\\theta=\\dfrac{12}{13}\\),\n\n\\[\n\\sin\\theta=\\sqrt{1-\\Bigl(\\frac{12}{13}\\Bigr)^2}= \\frac{5}{13}.\n\\]\n\nThus  \n\n\\[\n\\frac12 x_i x_{i+1}\\cdot\\frac{5}{13}=1\n\\Longrightarrow x_i x_{i+1}=\\frac{26}{5}\\qquad (2\\le i\\le10).\n\\tag{1}\n\\]\n\nDenote \\(c=\\dfrac{26}{5}\\).  From (1) we have  \n\n\\[\nx_{i+1}= \\frac{c}{x_i}.\n\\]\n\nConsequently  \n\n\\[\nx_{i+2}=x_i\\qquad\\Longrightarrow\\qquad\n\\begin{cases}\nx_{2}=x_{4}=x_{6}=x_{8}=x_{10}=a,\\\\[2pt]\nx_{3}=x_{5}=x_{7}=x_{9}=x_{11}=b,\n\\end{cases}\n\\]\n\nwith  \n\n\\[\nab=c=\\frac{26}{5}. \\tag{2}\n\\]\n\nSo the distances from \\(A_1\\) alternate between two values \\(a\\) and \\(b\\).\n\n---\n\n### 2.  Length of each side \\(A_iA_{i+1}\\;(2\\le i\\le10)\\)\n\nIn \\(\\triangle A_iA_1A_{i+1}\\) the side opposite \\(\\theta\\) is \\(A_iA_{i+1}\\).\nBy the law of cosines\n\n\\[\nA_iA_{i+1}^2 = x_i^2+x_{i+1}^2-2x_ix_{i+1}\\cos\\theta .\n\\]\n\nBecause \\(x_i\\) and \\(x_{i+1}\\) are always one \\(a\\) and one \\(b\\),\n\n\\[\nA_iA_{i+1}^2 = a^2+b^2-2ab\\cdot\\frac{12}{13}.\n\\]\n\nHence all nine sides \\(A_iA_{i+1}\\;(i=2,\\dots ,10)\\) have the same length; denote\n\n\\[\nd^2=a^2+b^2-\\frac{24}{13}ab.\n\\tag{3}\n\\]\n\nWrite \\(s=a+b\\).  Using \\(ab=c\\),\n\n\\[\na^2+b^2=s^2-2ab=s^2-2c .\n\\]\n\nSubstituting into (3),\n\n\\[\nd^2=s^2-2c-\\frac{24}{13}c\n    =s^2-c\\Bigl(2+\\frac{24}{13}\\Bigr)\n    =s^2-\\frac{50}{13}c.\n\\]\n\nSince \\(c=\\dfrac{26}{5}\\),\n\n\\[\nd^2=s^2-\\frac{50}{13}\\cdot\\frac{26}{5}=s^2-20,\n\\qquad\\text{so}\\qquad d=\\sqrt{s^{2}-20}.\n\\tag{4}\n\\]\n\n---\n\n### 3.  Use the perimeter\n\nThe polygon has \\(11\\) sides: the two incident to \\(A_1\\) of lengths \\(a\\) and \\(b\\), and the nine equal sides of length \\(d\\).  \nGiven perimeter \\(20\\),\n\n\\[\na+b+9d=s+9\\sqrt{s^{2}-20}=20.\n\\tag{5}\n\\]\n\nSolve (5) for \\(s\\).\n\n\\[\n9\\sqrt{s^{2}-20}=20-s\\;(s\\le20).\n\\]\n\nSquare:\n\n\\[\n81(s^{2}-20)=(20-s)^{2}\n\\Longrightarrow 80s^{2}+40s-2020=0\n\\Longrightarrow 4s^{2}+2s-101=0.\n\\]\n\nHence\n\n\\[\ns=\\frac{-2\\pm\\sqrt{4+1616}}{8}\n   =\\frac{-2\\pm18\\sqrt5}{8}\n   =\\frac{-1\\pm9\\sqrt5}{4}.\n\\]\n\nOnly the positive root is admissible:\n\n\\[\n\\boxed{s=\\frac{9\\sqrt5-1}{4}}.\n\\]\n\nThus  \n\n\\[\nA_1A_2+A_1A_{11}=a+b=s=\\frac{9\\sqrt5-1}{4}\n      =\\frac{m\\sqrt n-p}{q},\n\\]\n\nwith \\(m=9,\\;n=5,\\;p=1,\\;q=4\\).\n\n---\n\n### 4.  Required sum\n\n\\[\nm+n+p+q=9+5+1+4=19.\n\\]\n\n\\[\n\\boxed{19}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 19</p>\n<p>Extracted Answer: 19</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nFrom an unlimited supply of 1-cent coins, 10-cent coins, and 25-cent coins, Silas wants to find a collection of coins that has a total value of $ N $ cents, where $ N $ is a positive integer. He uses the so-called **greedy algorithm**, successively choosing the coin of greatest value that does not cause the value of his collection to exceed $ N $. For example, to get 42 cents, Silas will choose a 25-cent coin, then a 10-cent coin, then 7 1-cent coins. However, this collection of 9 coins uses more coins than necessary to get a total of 42 cents; indeed, choosing 4 10-cent coins and 2 1-cent coins achieves the same total value with only 6 coins.\n\nIn general, the greedy algorithm succeeds for a given $ N $ if no other collection of 1-cent, 10-cent, and 25-cent coins gives a total value of $ N $ cents using strictly fewer coins than the collection given by the greedy algorithm. Find the number of values of $ N $ between 1 and 1000 inclusive for which the greedy algorithm succeeds.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>**Greedy representation**\n\nFor a value \\(N\\) let  \n\n\\[\nq=\\Big\\lfloor\\frac{N}{25}\\Big\\rfloor ,\\qquad \nr=N-25q\\;(0\\le r\\le 24).\n\\]\n\nAfter taking \\(q\\) quarters the greedy algorithm uses  \n\n\\[\na=\\Big\\lfloor\\frac{r}{10}\\Big\\rfloor ,\\qquad \nb=r-10a\\;(0\\le b\\le 9)\n\\]\n\ndimes and ones.  \nThus the greedy collection contains  \n\n\\[\nG(N)=q+a+b\n\\]\n\ncoins.\n\n--------------------------------------------------------------------\n\n**When can a better collection exist?**\n\nLet a different collection use \\(x\\) quarters and \\(y\\) dimes\n(\\(z\\) pennies fill the rest).  \nIts total number of coins is  \n\n\\[\nC=x+y+z = x+y+(N-25x-10y)=N-(24x+9y).\n\\]\n\nHence a representation is better than the greedy one iff it makes the\n\u201csaving\u201d\n\n\\[\nS=24x+9y\n\\]\n\nlarger than the greedy saving \\(S_G = 24q+9a\\).\n\nSuppose we start from the greedy solution and **remove** \\(d\\ge1\\) quarters\n(\\(d\\le q\\)).  \nThe value we free is \\(25d\\).\nWith this extra value we can add as many dimes as possible:\n\n\\[\ny&#39; = a+\\Big\\lfloor\\frac{r+25d}{10}\\Big\\rfloor\n      = a+\\Big\\lfloor 2.5d+\\frac{b}{10}\\Big\\rfloor .\n\\]\n\nThe new saving is  \n\n\\[\nS&#39;=24(q-d)+9y&#39;\n   =24q+9a +\\bigl[-24d+9\\big\\lfloor2.5d+\\tfrac{b}{10}\\big\\rfloor\\bigr].\n\\]\n\nThus the new collection beats the greedy one precisely when  \n\n\\[\n-24d+9\\Big\\lfloor2.5d+\\frac{b}{10}\\Big\\rfloor &gt;0\n\\qquad\\Longleftrightarrow\\qquad\n\\Big\\lfloor2.5d+\\frac{b}{10}\\Big\\rfloor \\ge\n\\Big\\lfloor\\frac{8}{3}d\\Big\\rfloor+1 .\\tag{1}\n\\]\n\n--------------------------------------------------------------------\n\n**Only one quarter can ever help**\n\nFor even \\(d\\) we have \\(\\big\\lfloor2.5d\\big\\rfloor =2.5d\\) and\n\\(\\big\\lfloor\\frac{8}{3}d\\big\\rfloor =2.5d+\\big\\lfloor\\frac{d}{6}\\big\\rfloor\\).\nHence the left\u2013hand side of (1) never exceeds the right\u2013hand side,\nso even \\(d\\) never improves the greedy solution.\n\nFor odd \\(d=2k+1\\) we obtain  \n\n\\[\n\\Big\\lfloor2.5d+\\frac{b}{10}\\Big\\rfloor\n   =5k+2+{\\bf 1}_{\\{b\\ge5\\}},\\qquad\n\\Big\\lfloor\\frac{8}{3}d\\Big\\rfloor\n   =5k+2+\\Big\\lfloor\\frac{k+2}{3}\\Big\\rfloor .\n\\]\n\nConsequently  \n\n\\[\n\\Big\\lfloor2.5d+\\frac{b}{10}\\Big\\rfloor-\n\\Big\\lfloor\\frac{8}{3}d\\Big\\rfloor\n= {\\bf 1}_{\\{b\\ge5\\}}-\\Big\\lfloor\\frac{k+2}{3}\\Big\\rfloor .\n\\]\n\nThe right\u2011hand side is \\(\\ge 1\\) only when \\(k=0\\) (that is, \\(d=1\\))\nand \\(b\\ge5\\).\nThus the **only** way to improve upon the greedy solution is to\nreplace **exactly one** quarter and have \\(b\\ge5\\).\n\n--------------------------------------------------------------------\n\n**What does \\(b\\ge5\\) mean?**\n\nRecall \\(b\\) is the number of pennies left after taking all possible\nquarters and then all possible dimes.  Hence\n\n\\[\nb = N-25q-10a\\in\\{0,1,\\dots ,9\\}.\n\\]\n\nThe condition \\(b\\ge5\\) is equivalent to\n\n\\[\nN-25q\\equiv 5,6,7,8,9\\pmod{10},\n\\]\n\nor, more simply,\n\n\\[\nN\\equiv 5,6,7,8,9\\pmod{25}.\n\\]\n\nIf \\(q=0\\) (i.e. \\(N&lt;25\\)) there is no quarter to replace, so the greedy\nalgorithm is always optimal for \\(1\\le N\\le24\\).\n\nHence **the greedy algorithm fails exactly for the numbers**\n\n\\[\nN\\ge 25 \\quad\\text{with}\\quad N\\equiv 5,6,7,8,9\\pmod{25}.\n\\]\n\n--------------------------------------------------------------------\n\n**Counting the successes**\n\nAll integers \\(1\\le N\\le1000\\): 1000 of them.\n\nNumbers that cause failure:\n\n* The residues \\(5,6,7,8,9\\) each occur\n  \\(\\bigl\\lfloor\\frac{1000-r}{25}\\bigr\\rfloor+1 = 40\\) times for\n  \\(r=5,6,7,8,9\\).\n  Hence \\(5\\times40=200\\) such numbers in \\([1,1000]\\).\n\n* The five smallest ones, \\(5,6,7,8,9\\), are \\(&lt;25\\); they do **not**\n  cause failure because no quarter can be replaced.\n\nThus the genuine failures are \\(200-5 = 195\\) numbers.\n\nConsequently the number of values for which the greedy algorithm\nsucceeds is  \n\n\\[\n1000-195 = 805.\n\\]\n\n\\[\n\\boxed{805}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 610</p>\n<p>Extracted Answer: 805</p>\n<p>Score: 0.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $ S $ be the set of vertices of a regular 24-gon. Find the number of ways to draw 12 segments of equal lengths so that each vertex in $ S $ is an endpoint of exactly one of the 12 segments.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let the vertices of the regular \\(24\\)-gon be labelled  \n\n\\[\n0,1,2,\\dots ,23\\qquad (\\text{mod }24).\n\\]\n\nIf a segment connects vertex \\(i\\) to vertex \\(j\\) then its length is determined only by the\nstep  \n\n\\[\nk\\equiv j-i\\pmod{24},\\qquad 1\\le k\\le 12 .\n\\]\n\nAll \\(12\\) segments must have the same length, therefore they all have the same step \\(k\\) (the\nstep \\(24-k\\) gives the same length, so it is enough to consider \\(k=1,2,\\dots ,12\\)).\n\n--------------------------------------------------------------------\n### 1.  The graph for a fixed step \\(k\\)\n\nFor a fixed \\(k\\) join each vertex \\(i\\) with the two vertices\n\\(i\\pm k\\).  The resulting graph \\(G_k\\) is a union of cycles:\n\n* Let \\(d=\\gcd(k,24)\\).\n* Each cycle has length \\(\\displaystyle L=\\frac{24}{d}\\) and there are \\(d\\) such\n  cycles.\n\nIndeed the permutation \\(i\\mapsto i+k\\) on \\(\\{0,\\dots ,23\\}\\) consists of\n\\(d\\) cycles of length \\(L\\).\n\n--------------------------------------------------------------------\n### 2.  Perfect matchings of \\(G_k\\)\n\nA required drawing is a perfect matching of \\(G_k\\).\n\n* If a cycle has even length, it has exactly **2** perfect matchings\n  (alternating edges).\n* If a cycle has odd length, a perfect matching does **not** exist.\n* The only exceptional case is \\(k=12\\); then each vertex has only one\n  neighbour (its opposite) and the whole graph is already a perfect\n  matching.\n\nThus, for \\(k\\neq 12\\),\n\n\\[\n\\text{# matchings for }G_k=\n\\begin{cases}\n2^{\\,d} &amp; \\text{if }L\\text{ is even},\\\\[2mm]\n0       &amp; \\text{if }L\\text{ is odd}.\n\\end{cases}\n\\]\n\nSince \\(L\\) is odd exactly when \\(L=3\\), i.e. when \\(d=8\\) (the only such\n\\(k\\) is \\(k=8\\)), we have\n\n\\[\nN(k)=\n\\begin{cases}\n2^{\\gcd(k,24)} &amp; \\gcd(k,24)\\neq 8,\\;k\\neq 12,\\\\[2mm]\n0 &amp; k=8,\\\\[2mm]\n1 &amp; k=12 .\n\\end{cases}\n\\]\n\n--------------------------------------------------------------------\n### 3.  Evaluate for \\(k=1,\\dots ,12\\)\n\n\\[\n\\begin{array}{c|c|c|c}\nk &amp; \\gcd(k,24) &amp; \\text{cycles} &amp; N(k)\\\\ \\hline\n1 &amp; 1 &amp; 1\\ \\text{cycle of length }24 &amp; 2\\\\\n2 &amp; 2 &amp; 2\\ \\text{cycles of length }12 &amp; 4\\\\\n3 &amp; 3 &amp; 3\\ \\text{cycles of length }8  &amp; 8\\\\\n4 &amp; 4 &amp; 4\\ \\text{cycles of length }6  &amp; 16\\\\\n5 &amp; 1 &amp; 1\\ \\text{cycle of length }24 &amp; 2\\\\\n6 &amp; 6 &amp; 6\\ \\text{cycles of length }4  &amp; 64\\\\\n7 &amp; 1 &amp; 1\\ \\text{cycle of length }24 &amp; 2\\\\\n8 &amp; 8 &amp; 8\\ \\text{cycles of length }3  &amp; 0\\\\\n9 &amp; 3 &amp; 3\\ \\text{cycles of length }8  &amp; 8\\\\\n10&amp; 2 &amp; 2\\ \\text{cycles of length }12 &amp; 4\\\\\n11&amp; 1 &amp; 1\\ \\text{cycle of length }24 &amp; 2\\\\\n12&amp;12 &amp; 12\\ \\text{edges (pairs)}       &amp; 1\n\\end{array}\n\\]\n\n--------------------------------------------------------------------\n### 4.  Sum over all possible lengths\n\n\\[\n\\begin{aligned}\n\\sum_{k=1}^{12} N(k)\n&amp;=2+4+8+16+2+64+2+0+8+4+2+1\\\\\n&amp;=113 .\n\\end{aligned}\n\\]\n\n--------------------------------------------------------------------\n\\[\n\\boxed{113}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 113</p>\n<p>Extracted Answer: 113</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nFind the sum of all integer bases $b&gt;9$ for which $17_{b}$ is a divisor of $97_{b}$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>For a base \\(b&gt;9\\),\n\n\\[\n17_{b}=1\\cdot b+7=b+7 ,\\qquad   \n97_{b}=9\\cdot b+7=9b+7 .\n\\]\n\nWe need  \n\n\\[\nb+7 \\mid 9b+7 .\n\\]\n\nLet \\(d=b+7\\;(&gt;0)\\). Then \\(b=d-7\\) and\n\n\\[\n9b+7 = 9(d-7)+7 = 9d-56 .\n\\]\n\nHence  \n\n\\[\nd \\mid (9d-56) \\Longrightarrow d\\mid 56 .\n\\]\n\nSo \\(d\\) must be a positive divisor of \\(56\\).  \nSince \\(b&gt;9\\), we have \\(d=b+7&gt;9+7=16\\).  \nThe divisors of \\(56\\) larger than \\(16\\) are\n\n\\[\nd=28,\\;56 .\n\\]\n\nCorresponding bases are  \n\n\\[\nb=d-7:\n\\begin{cases}\nd=28 \\Rightarrow b=21,\\\\[2mm]\nd=56 \\Rightarrow b=49.\n\\end{cases}\n\\]\n\nBoth satisfy \\(b&gt;9\\) and indeed  \n\n\\[\n\\frac{9b+7}{b+7}=7\\;(b=21),\\qquad \n\\frac{9b+7}{b+7}=8\\;(b=49).\n\\]\n\nThus the integer bases are \\(b=21\\) and \\(b=49\\). Their sum is  \n\n\\[\n21+49=70.\n\\]\n\n\\[\n\\boxed{70}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 70</p>\n<p>Extracted Answer: 70</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nSuppose $ \\triangle ABC $ has angles $ \\angle BAC = 84^\\circ $, $ \\angle ABC = 60^\\circ $, and $ \\angle ACB = 36^\\circ $. Let $ D, E, $ and $ F $ be the midpoints of sides $ \\overline{BC} $, $ \\overline{AC} $, and $ \\overline{AB} $, respectively. The circumcircle of $ \\triangle DEF $ intersects $ \\overline{BD} $, $ \\overline{AE} $, and $ \\overline{AF} $ at points $ G, H, $ and $ J $, respectively. The points $ G, D, E, H, J, $ and $ F $ divide the circumcircle of $ \\triangle DEF $ into six minor arcs, as shown. Find $ \\widehat{DE} + 2 \\cdot \\widehat{HJ} + 3 \\cdot \\widehat{FG} $, where the arcs are measured in degrees.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>**Solution Overview**\n\nThe circle through the midpoints \\(D,E,F\\) of the sides of \\(\\triangle ABC\\) is the **nine\u2011point circle** of \\(\\triangle ABC\\).\nHence  \n\n* \\(D,E,F\\) are the vertices of the medial triangle,\n* \\(\\angle D= \\angle A=84^{\\circ},\\ \\angle E= \\angle B=60^{\\circ},\\ \\angle F=\\angle C=36^{\\circ}\\).\n\nSince the nine\u2011point circle is the circumcircle of \\(\\triangle DEF\\),\n\n\\[\n\\widehat{DE}=2\\angle F=2\\cdot 36^{\\circ}=72^{\\circ}.\n\\tag{1}\n\\]\n\nWe must also determine the arcs \\(\\widehat{FG}\\) and \\(\\widehat{HJ}\\).\n\n---------------------------------------------------------------------\n\n### 1.  The arc \\(\\widehat{FG}\\)\n\n\\(G\\) is the second intersection of the median \\(BD\\) with the nine\u2011point circle.\nAt point \\(D\\) the chord \\(DG\\) lies on the line \\(BD\\), while the chord \\(DF\\) is parallel to side \\(AC\\) (mid\u2011segment theorem).\n\nTherefore  \n\n\\[\n\\angle FDG=\\angle(\\text{line } DF,\\text{line } DG)\n          =\\angle(\\,AC ,\\,BD\\,).\n\\]\n\nThe angle between side \\(AC\\) and the median from \\(B\\) can be read directly from the triangle:\n\\( \\angle(\\,AC ,\\,BD\\,)=\\angle C=36^{\\circ}\\).\n\nConsequently  \n\n\\[\n\\widehat{FG}=2\\angle FDG=2\\cdot36^{\\circ}=72^{\\circ}.\n\\tag{2}\n\\]\n\n---------------------------------------------------------------------\n\n### 2.  The arc \\(\\widehat{HJ}\\)\n\n\\(H\\) and \\(J\\) are the second intersections of the sides \\(AC\\) and \\(AB\\) with the nine\u2011point circle.\nThus the two secants through the exterior point \\(A\\) intersect the circle at the pairs \\(\\{F,J\\}\\) and \\(\\{E,H\\}\\).\n\nFor an exterior point the angle formed by two secants equals half the **difference** of the intercepted arcs:\n\n\\[\n\\angle BAC=\\frac12\\bigl(\\widehat{JH}-\\widehat{FE}\\bigr).\n\\tag{3}\n\\]\n\nWe already know the arc \\(\\widehat{FE}\\) of the nine\u2011point circle:\n\\[\n\\widehat{FE}=2\\angle D =2\\cdot 84^{\\circ}=168^{\\circ}.\n\\tag{4}\n\\]\n\nPlugging \\(\\angle BAC=84^{\\circ}\\) and (4) into (3) gives  \n\n\\[\n84^{\\circ}=\\frac12\\bigl(\\widehat{JH}-168^{\\circ}\\bigr)\n\\Longrightarrow \\widehat{JH}=336^{\\circ}.\n\\]\n\nThe **minor** arc \\(HJ\\) is the complement of \\(336^{\\circ}\\) on the circle:\n\n\\[\n\\widehat{HJ}=360^{\\circ}-336^{\\circ}=24^{\\circ}.\n\\tag{5}\n\\]\n\n---------------------------------------------------------------------\n\n### 3.  Computing the required sum\n\nFrom (1), (2) and (5)\n\n\\[\n\\begin{aligned}\n\\widehat{DE}+2\\widehat{HJ}+3\\widehat{FG}\n&amp;=72^{\\circ}+2\\cdot24^{\\circ}+3\\cdot72^{\\circ}  \\\\\n&amp;=72^{\\circ}+48^{\\circ}+216^{\\circ}\\\\\n&amp;=336^{\\circ}.\n\\end{aligned}\n\\]\n\n---------------------------------------------------------------------\n\n\\[\n\\boxed{336}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 336</p>\n<p>Extracted Answer: 336</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThe 9 members of a baseball team went to an ice cream parlor after their game. Each player had a singlescoop cone of chocolate, vanilla, or strawberry ice cream. At least one player chose each flavor, and the number of players who chose chocolate was greater than the number of players who chose vanilla, which was greater than the number of players who chose strawberry. Let $N$ be the number of different assignments of flavors to players that meet these conditions. Find the remainder when $N$ is divided by 1000.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>The nine players are distinct, so for a given triple \\((c,v,s)\\) (numbers of chocolate, vanilla, and strawberry cones) the number of assignments is  \n\n\\[\n\\frac{9!}{c!\\,v!\\,s!}.\n\\]\n\nWe must count all triples of positive integers satisfying  \n\n\\[\nc+v+s = 9,\\qquad c&gt;v&gt;s\\ge 1 .\n\\]\n\n---\n\n### Find the possible triples \\((c,v,s)\\)\n\nBecause the three numbers are distinct and sum to 9, we list the partitions of 9 into three distinct positive parts:\n\n\\[\n\\begin{aligned}\n9 &amp;= 6+2+1,\\\\\n9 &amp;= 5+3+1,\\\\\n9 &amp;= 4+3+2 .\n\\end{aligned}\n\\]\n\nThese are the only triples with strict descending order, so  \n\n\\[\n(c,v,s) \\in \\{(6,2,1),\\;(5,3,1),\\;(4,3,2)\\}.\n\\]\n\n---\n\n### Count assignments for each triple\n\n\\[\n\\begin{aligned}\n(6,2,1):\\quad &amp;\\frac{9!}{6!\\,2!\\,1!}= \\frac{362880}{720\\cdot2}=252,\\\\[4pt]\n(5,3,1):\\quad &amp;\\frac{9!}{5!\\,3!\\,1!}= \\frac{362880}{120\\cdot6}=504,\\\\[4pt]\n(4,3,2):\\quad &amp;\\frac{9!}{4!\\,3!\\,2!}= \\frac{362880}{24\\cdot6\\cdot2}=1260.\n\\end{aligned}\n\\]\n\n---\n\n### Total number of assignments\n\n\\[\nN = 252 + 504 + 1260 = 2016.\n\\]\n\n---\n\n### Remainder modulo \\(1000\\)\n\n\\[\n2016 \\equiv 16 \\pmod{1000}.\n\\]\n\n\\[\n\\boxed{16}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 16</p>\n<p>Extracted Answer: 16</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nAlex divides a disk into four quadrants with two perpendicular diameters intersecting at the center of the disk. He draws 25 more line segments through the disk, drawing each segment by selecting two points at random on the perimeter of the disk in different quadrants and connecting those two points. Find the expected number of regions into which these 27 line segments divide the disk.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>**Step 1.  What determines the number of regions?**  \n\nIf we draw line\u2011segments in a disc and no three of them meet in a common interior point, then each new segment splits one existing region for every interior intersection it makes, plus one more region for the segment itself.  \nHence  \n\n\\[\n\\#\\text{regions}=1+(\\#\\text{segments})+(\\#\\text{interior intersection points}).\n\\]\n\nWe have  \n\n* 2 diameters,\n* 25 random chords,\n* total segments \\(=27\\).\n\nSo we need the **expected number of interior intersections**.\n\n---------------------------------------------------------------------\n\n**Step 2.  Intersections that are certain**\n\nThe two diameters intersect at the centre \u21d2 one interior intersection.\n\n---------------------------------------------------------------------\n\n**Step 3.  Intersections of a chord with the diameters**\n\nA chord is drawn by picking two points on the circle that lie in **different quadrants**.\n\n*If the two quadrants are adjacent* (e.g. quadrant\u202fI and\u202fII), the chord crosses **exactly one** diameter.  \n*If the two quadrants are opposite* (e.g. quadrant\u202fI and\u202fIII), the chord crosses **both** diameters.\n\nThe unordered pair of distinct quadrants is uniformly chosen among the \\(\\binom{4}{2}=6\\) possibilities:\n\n* 4 adjacent pairs\u2003\u2192\u2003probability \\(4/6=2/3\\);\n* 2 opposite pairs\u2003\u2192\u2003probability \\(2/6=1/3\\).\n\nHence for one random chord\n\n\\[\nE[\\hbox{diameter\u2011intersections}]\n  =\\frac23\\cdot1+\\frac13\\cdot2=\\frac43 .\n\\]\n\nFor the 25 chords  \n\n\\[\nE[I_{\\text{chord\u2013diameter}}]=25\\cdot\\frac43=\\frac{100}{3}.\n\\]\n\n---------------------------------------------------------------------\n\n**Step 4.  Intersections between two random chords**\n\nLet the two chords be \\(AB\\) and \\(CD\\).  \nWrite \\(L\\) for the clockwise length of the arc from \\(A\\) to \\(B\\) (so \\(0\\le L\\le2\\pi\\)).  \nLet \\(L_i^{(1)}\\) be the length of that arc inside quadrant \\(i\\) (\\(i=1,\\dots ,4\\)), and\n\\(L_i^{(2)}=\\frac{\\pi}{2}-L_i^{(1)}\\) the length of the complementary arc inside the same quadrant.\n\nFor a given chord \\(AB\\)\n\n* the probability that a random chord \\(CD\\) meets \\(AB\\) **and** has its endpoints in different quadrants is  \n\n\\[\np_{\\text{int}}(A,B)=\n\\frac{L(2\\pi-L)-\\displaystyle\\sum_{i=1}^{4}L_i^{(1)}L_i^{(2)}}{2\\pi^{2}} .\n\\tag{1}\n\\]\n\n(The numerator is the area of the product set\n\\(\\{(C,D):C\\in\\text{arc}_1,D\\in\\text{arc}_2\\}\\) minus the part where \\(C\\) and \\(D\\) fall in the same quadrant.)\n\nDefine  \n\n\\[\nQ(A,B)=L(2\\pi-L)-\\sum_{i=1}^{4}L_i^{(1)}L_i^{(2)} .\n\\]\n\nThen \\(p_{\\text{int}}(A,B)=Q(A,B)/(2\\pi^{2})\\).\n\n---------------------------------------------------------------------\n\n**Step 5.  Averaging \\(Q\\)**  \n\nPut the circle\u2019s total length as \\(4d\\) with a quadrant length \\(d=\\pi/2\\).\nWrite the clockwise length as a multiple of \\(d\\): \\(t=L/d\\in[0,4]\\).\n\nFor a fixed \\(t\\) and a uniformly random starting point of the arc,\nthe expected value of \\(\\sum_i (L_i^{(1)})^{2}\\) (the sum of squares of the pieces of the arc) is\n\n\\[\nh(t)=\n\\begin{cases}\nt^{2}-\\dfrac{t^{3}}{3}, &amp; 0\\le t\\le 1,\\\\[4pt]\nt-\\dfrac13,               &amp; 1\\le t\\le 4 .\n\\end{cases}\n\\]\n\nConsequently  \n\n\\[\nE\\!\\left[\\sum_i L_i^{(1)}L_i^{(2)}\\right]\n      =\\frac{\\pi}{2}E[L]-E\\!\\left[\\sum_i(L_i^{(1)})^{2}\\right]\n      =\\frac{\\pi^{2}}{2}-\\frac{27\\pi^{2}}{64}\n      =\\frac{5\\pi^{2}}{64}.\n\\]\n\nFrom this we obtain the unconditional expectation\n\n\\[\nE[Q]=E\\!\\bigl[L(2\\pi-L)\\bigr]-E\\!\\Bigl[\\sum_i L_i^{(1)}L_i^{(2)}\\Bigr]\n      =\\frac{2}{3}\\pi^{2}-\\frac{5}{64}\\pi^{2}\n      =\\frac{113}{192}\\pi^{2}.\n\\tag{2}\n\\]\n\n---------------------------------------------------------------------\n\n**Step 6.  Conditioning on \u201cdifferent quadrants\u2019\u2019 for the first chord**\n\nIf the first chord\u2019s endpoints lie in the *same* quadrant (probability \\(1/4\\)),\nthen \\(Q\\) simplifies to \\(Q=\\frac{3\\pi}{2}L\\).  \nBecause the absolute difference of two points inside a quadrant has mean \\(d/3=\\pi/6\\),\n\n\\[\nE[Q\\mid\\text{same quadrant}]=\\frac{3\\pi}{2}\\cdot\\frac{\\pi}{6}\n                              =\\frac{\\pi^{2}}{4}.\n\\]\n\nHence  \n\n\\[\nE[Q\\;{\\bf 1}_{\\text{different quadrants}}]\n   =E[Q]-\\frac14\\cdot\\frac{\\pi^{2}}{4}\n   =\\frac{113}{192}\\pi^{2}-\\frac{\\pi^{2}}{16}\n   =\\frac{101}{192}\\pi^{2}. \\tag{3}\n\\]\n\n---------------------------------------------------------------------\n\n**Step 7.  Probability that two *valid* chords intersect**\n\nFrom (1) and (3),\n\n\\[\n\\boxed{\nP(\\text{intersection } \\&amp;\\; AB\\text{ valid}\\; \\&amp;\\; CD\\text{ valid})\n    =\\frac{E[Q\\,{\\bf 1}_{\\text{different quadrants}}]}{2\\pi^{2}}\n    =\\frac{101}{384}.\n}\n\\]\n\nThe event \u201cboth chords are valid\u2019\u2019 occurs with probability \\((3/4)^{2}=9/16\\).  \nTherefore the conditional probability that two random valid chords intersect is\n\n\\[\nP_{\\text{int}}=\n\\frac{101/384}{9/16}= \\frac{101}{216}\\approx0.4676.\n\\tag{4}\n\\]\n\n---------------------------------------------------------------------\n\n**Step 8.  Expected number of chord\u2013chord intersections**\n\n\\[\nE[I_{\\text{chord\u2013chord}}]\n   =\\binom{25}{2}\\;P_{\\text{int}}\n   =300\\cdot\\frac{101}{216}\n   =\\frac{2525}{18}.\n\\]\n\n---------------------------------------------------------------------\n\n**Step 9.  Total expected interior intersections**\n\n\\[\n\\begin{aligned}\nE[I] &amp;=\n\\underbrace{1}_{\\text{diameters}}+\n\\underbrace{\\frac{100}{3}}_{\\text{chord\u2013diameter}}+\n\\underbrace{\\frac{2525}{18}}_{\\text{chord\u2013chord}} \\\\[4pt]\n&amp;= \\frac{18+600+2525}{18}\n   =\\frac{3143}{18}.\n\\end{aligned}\n\\]\n\n---------------------------------------------------------------------\n\n**Step 10.  Expected number of regions**\n\n\\[\n\\begin{aligned}\nE[\\#\\text{regions}]\n&amp;=1+(\\#\\text{segments})+E[I] \\\\\n&amp;=1+27+\\frac{3143}{18}\\\\[4pt]\n&amp;=28+\\frac{3143}{18}\n   =\\frac{504+3143}{18}\n   =\\boxed{\\frac{3647}{18}}\\; \\approx 202.6 .\n\\end{aligned}\n\\]\n\nThus, on average Alex\u2019s 27 line segments partition the disk into \\(\\displaystyle \\frac{3647}{18}\\) regions.</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 204</p>\n<p>Extracted Answer: None</p>\n<p>Score: 0.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nFind the number of ordered pairs $(x,y)$, where both $x$ and $y$ are integers between $-100$ and $100$, inclusive, such that $12x^{2}-xy-6y^{2}=0$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>\\[\n12x^{2}-xy-6y^{2}=0\n\\]\n\n---\n\n### 1.  Factor the quadratic  \n\nLook for integers \\(a,b,c,d\\) such that  \n\n\\[\n(ax+by)(cx+dy)=12x^{2}-xy-6y^{2}.\n\\]\n\nWe need  \n\n\\[\nac=12,\\qquad bd=-6,\\qquad ad+bc=-1 .\n\\]\n\nTaking \\(a=4,\\;c=3\\) (since \\(4\\cdot 3=12\\)) and trying \\(b=-3,\\;d=2\\) gives  \n\n\\[\nbd=(-3)(2)=-6,\\qquad ad+bc=4\\cdot2+3\\cdot(-3)=8-9=-1.\n\\]\n\nHence  \n\n\\[\n12x^{2}-xy-6y^{2}=(4x-3y)(3x+2y).\n\\]\n\nSo the original equation is equivalent to  \n\n\\[\n(4x-3y)(3x+2y)=0.\n\\]\n\nThus any integer solution must satisfy one of the two linear equations  \n\n\\[\n\\boxed{4x-3y=0}\\qquad\\text{or}\\qquad\\boxed{3x+2y=0}.\n\\]\n\n---\n\n### 2.  Solve each linear equation in integers  \n\n**(i) \\(4x-3y=0\\).**  \n\n\\(4x=3y\\Rightarrow y= \\frac{4}{3}x\\).  \nSince \\(\\gcd(4,3)=1\\), write \\(x=3k,\\;y=4k\\) for some integer \\(k\\).\n\nBoth coordinates must satisfy \\(-100\\le x,y\\le 100\\):\n\n\\[\n-100\\le 3k\\le 100 \\Longrightarrow -\\frac{100}{3}\\le k\\le \\frac{100}{3},\n\\qquad\n-100\\le 4k\\le 100 \\Longrightarrow -25\\le k\\le 25.\n\\]\n\nThe tighter bound is \\(-25\\le k\\le 25\\).  \nHence there are  \n\n\\[\n25-(-25)+1 = 51\n\\]\n\nsolutions from this family.\n\n---\n\n**(ii) \\(3x+2y=0\\).**  \n\n\\(3x=-2y\\Rightarrow x=-\\frac{2}{3}y\\).  \nAgain \\(\\gcd(3,2)=1\\), so write \\(y=3m,\\;x=-2m\\) for some integer \\(m\\).\n\nBounds:\n\n\\[\n-100\\le -2m\\le 100 \\Longrightarrow -50\\le m\\le 50,\n\\qquad\n-100\\le 3m\\le 100 \\Longrightarrow -\\frac{100}{3}\\le m\\le \\frac{100}{3}\n\\Longrightarrow -33\\le m\\le 33.\n\\]\n\nThus \\(-33\\le m\\le 33\\), giving  \n\n\\[\n33-(-33)+1 = 67\n\\]\n\nsolutions from this family.\n\n---\n\n### 3.  Remove the double\u2011counted solution  \n\nThe two families intersect only when both equations hold, i.e. when  \n\n\\[\n4x-3y=0\\;\\text{and}\\;3x+2y=0\\Longrightarrow (x,y)=(0,0).\n\\]\n\nSo \\((0,0)\\) has been counted twice.  \n\nTotal distinct ordered pairs:\n\n\\[\n51+67-1 = 117.\n\\]\n\n---\n\n\\[\n\\boxed{117}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 117</p>\n<p>Extracted Answer: 117</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $ \\triangle ABC $ be a right triangle with $ \\angle A = 90^\\circ $ and $ BC = 38 $. There exist points $ K $ and $ L $ inside the triangle such that $ AK = AL = BK = CL = KL = 14. $ The area of the quadrilateral $ BKLC $ can be expressed as $ n \\sqrt{3} $ for some positive integer $ n $. Find $ n $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n\\[\nA=(0,0),\\qquad B=(b,0),\\qquad C=(0,c)\n\\]\n\nwith \\(\\angle A=90^{\\circ}\\) and \\(BC=38\\Rightarrow b^{2}+c^{2}=38^{2}=1444\\).\n\n---\n\n### 1.  Locating \\(K\\) and \\(L\\)\n\n\\(AK=BK=14\\).  \nThe circles \\(\\odot(A,14)\\) and \\(\\odot(B,14)\\) intersect at the interior point  \n\n\\[\nK=\\Bigl(\\frac b2,\\; \\sqrt{196-\\Bigl(\\frac b2\\Bigr)^2}\\Bigr).\n\\]\n\nSimilarly \\(AL=CL=14\\) gives  \n\n\\[\nL=\\Bigl(\\sqrt{196-\\Bigl(\\frac c2\\Bigr)^2},\\; \\frac c2\\Bigr).\n\\]\n\nSince \\(AK=AL=KL=14\\), points \\(A,K,L\\) form an equilateral triangle.\nPut  \n\n\\[\nK=(14\\cos\\theta,14\\sin\\theta),\\qquad \nL=(14\\cos(\\theta+60^\\circ),14\\sin(\\theta+60^\\circ)).\n\\]\n\nUsing \\(BK=14\\) and \\(CL=14\\),\n\n\\[\nb=28\\cos\\theta,\\qquad c=28\\sin(\\theta+60^\\circ). \\tag{1}\n\\]\n\n---\n\n### 2.  Determining \\(\\theta\\)\n\nFrom \\(b^2+c^2=1444\\),\n\n\\[\n\\cos^{2}\\theta+\\sin^{2}(\\theta+60^\\circ)=\\frac{1444}{28^{2}}\n        =\\frac{361}{196}=\\Bigl(\\frac{19}{14}\\Bigr)^{2}.\n\\]\n\nUsing \\(\\cos^2x=\\frac{1+\\cos2x}{2},\\ \\sin^2x=\\frac{1-\\cos2x}{2}\\),\n\n\\[\n\\frac{2+\\cos2\\theta-\\cos(2\\theta+120^\\circ)}2\n      =\\frac{361}{196}.\n\\]\n\nSimplifying gives  \n\n\\[\n\\cos2\\theta-\\cos(2\\theta+120^\\circ)=\\frac{165}{98}.\n\\]\n\nSince \\(\\cos A-\\cos B=-2\\sin\\frac{A+B}{2}\\sin\\frac{A-B}{2}\\),\n\n\\[\n\\sqrt3\\sin(2\\theta+60^\\circ)=\\frac{165}{98}\n   \\Longrightarrow \\sin(2\\theta+60^\\circ)=\\frac{55\\sqrt3}{98}.\n\\]\n\nHence  \n\n\\[\n\\cos(2\\theta+60^\\circ)=\\frac{23}{98},\\qquad \n\\sin(2\\theta+60^\\circ)=\\frac{55\\sqrt3}{98}.\n\\]\n\nLet \\(\\phi=2\\theta+60^\\circ\\). Then\n\n\\[\n\\cos\\phi=\\frac{23}{98},\\qquad \\sin\\phi=\\frac{55\\sqrt3}{98}.\n\\]\n\nCompute \\(\\cos(\\phi-60^\\circ)\\) and \\(\\cos(\\phi+60^\\circ)\\):\n\n\\[\n\\cos(\\phi-60^\\circ)=\\frac{47}{49},\\qquad\n\\cos(\\phi+60^\\circ)=-\\frac{71}{98}.\n\\]\n\nNow\n\n\\[\n\\cos\\theta=\\sqrt{\\frac{1+\\cos(\\phi-60^\\circ)}2}\n          =\\sqrt{\\frac{1+\\frac{47}{49}}2}\n          =\\sqrt{\\frac{48}{49}}=\\frac{4\\sqrt3}{7},\n\\]\n\n\\[\n\\sin(\\theta+60^\\circ)=\\sqrt{\\frac{1-\\cos(\\phi+60^\\circ)}2}\n                     =\\sqrt{\\frac{1+\\frac{71}{98}}2}\n                     =\\sqrt{\\frac{169}{196}}=\\frac{13}{14}.\n\\]\n\nUsing (1),\n\n\\[\nb=28\\cos\\theta=28\\cdot\\frac{4\\sqrt3}{7}=16\\sqrt3,\n\\qquad\nc=28\\sin(\\theta+60^\\circ)=28\\cdot\\frac{13}{14}=26.\n\\]\n\nThus  \n\n\\[\nAB=16\\sqrt3,\\qquad AC=26,\\qquad BC=38.\n\\]\n\nConsequently  \n\n\\[\nK=\\Bigl(\\frac{b}{2},\\sqrt{196-\\Bigl(\\frac b2\\Bigr)^2}\\Bigr)\n  =\\bigl(8\\sqrt3,\\;2\\bigr),\\qquad\nL=\\Bigl(\\sqrt{196-\\Bigl(\\frac c2\\Bigr)^2},\\frac c2\\Bigr)\n  =\\bigl(3\\sqrt3,\\;13\\bigr).\n\\]\n\n---\n\n### 3.  Area of \\(BKLC\\)\n\nUsing the shoelace formula for vertices  \n\n\\[\nB=(16\\sqrt3,0),\\; K=(8\\sqrt3,2),\\; L=(3\\sqrt3,13),\\; C=(0,26),\n\\]\n\n\\[\n\\begin{aligned}\n\\sum x_iy_{i+1}&amp;=16\\sqrt3\\cdot2+8\\sqrt3\\cdot13+3\\sqrt3\\cdot26+0\\cdot0\\\\\n               &amp;=214\\sqrt3,\\\\[2mm]\n\\sum y_ix_{i+1}&amp;=0\\cdot8\\sqrt3+2\\cdot3\\sqrt3+13\\cdot0+26\\cdot16\\sqrt3\\\\\n               &amp;=422\\sqrt3.\n\\end{aligned}\n\\]\n\nHence\n\n\\[\n\\text{Area}(BKLC)=\\frac12|214\\sqrt3-422\\sqrt3|=104\\sqrt3.\n\\]\n\n---\n\nThus the area of \\(BKLC\\) is \\(104\\sqrt3\\), so  \n\n\\[\n\\boxed{104}.\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 104</p>\n<p>Extracted Answer: 104</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nAn isosceles trapezoid has an inscribed circle tangent to each of its four sides. The radius of the circle is 3, and the area of the trapezoid is 72. Let the parallel sides of the trapezoid have lengths $r$ and $s$, with $r \\neq s$. Find $r^{2}+s^{2}$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let the trapezoid have parallel sides (bases) \\(r\\) and \\(s\\) \\((r\\neq s)\\), the equal legs \\(L\\), and height \\(h\\).\n\n---\n\n### 1.  Height from the incircle  \n\nThe circle of radius \\(3\\) is tangent to the two parallel sides, so the distance between those sides equals the sum of the distances from the centre to each side:\n\n\\[\nh = 3+3 = 6 .\n\\]\n\n---\n\n### 2.  Sum of the bases from the area  \n\n\\[\n\\text{Area}= \\frac{r+s}{2}\\,h = 72\n\\quad\\Longrightarrow\\quad\n\\frac{r+s}{2}\\cdot 6 = 72 \\implies r+s = 24 .\n\\]\n\n---\n\n### 3.  Relation of the legs (tangential quadrilateral)  \n\nA quadrilateral has an incircle iff the sums of opposite sides are equal.  \nFor the trapezoid the opposite sides are the two bases and the two legs, so\n\n\\[\nr+s = L+L \\;\\Longrightarrow\\; L =\\frac{r+s}{2}=12 .\n\\]\n\nThus each leg has length \\(L=12\\).\n\n---\n\n### 4.  Difference of the bases from the leg length  \n\nBecause the trapezoid is isosceles, each leg together with the height forms a right triangle whose horizontal leg is \\(\\dfrac{|s-r|}{2}\\):\n\n\\[\nL^{2}=h^{2}+ \\left(\\frac{s-r}{2}\\right)^{2}.\n\\]\n\nInsert \\(L=12,\\;h=6\\):\n\n\\[\n12^{2}=6^{2}+ \\left(\\frac{s-r}{2}\\right)^{2}\n\\Longrightarrow 144-36 = \\left(\\frac{s-r}{2}\\right)^{2}\n\\Longrightarrow \\left(\\frac{s-r}{2}\\right)^{2}=108.\n\\]\n\nHence  \n\n\\[\n|s-r| = 2\\sqrt{108}=12\\sqrt3 .\n\\]\n\nAssume \\(s&gt;r\\); then \\(s-r=12\\sqrt3\\).\n\n---\n\n### 5.  Solve for \\(r\\) and \\(s\\)\n\n\\[\n\\begin{cases}\nr+s = 24,\\\\\ns-r = 12\\sqrt3.\n\\end{cases}\n\\qquad\\Longrightarrow\\qquad\n\\begin{aligned}\ns &amp;= 12+6\\sqrt3,\\\\\nr &amp;= 12-6\\sqrt3.\n\\end{aligned}\n\\]\n\n---\n\n### 6.  Compute \\(r^{2}+s^{2}\\)\n\n\\[\n\\begin{aligned}\nr^{2}+s^{2} &amp;= (12-6\\sqrt3)^{2}+(12+6\\sqrt3)^{2} \\\\\n&amp;= \\bigl(144-144\\sqrt3+108\\bigr)+\\bigl(144+144\\sqrt3+108\\bigr) \\\\\n&amp;= 252-144\\sqrt3+252+144\\sqrt3 \\\\\n&amp;= 504.\n\\end{aligned}\n\\]\n\n---\n\n\\[\n\\boxed{504}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 504</p>\n<p>Extracted Answer: 504</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThere are $8!=40320$ eight-digit positive integers that use each of the digits $1,2,3,4,5,6,7,8$ exactly once. Let $N$ be the number of these integers that are divisible by 22. Find the difference between $N$ and 2025.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>For an 8\u2011digit number using each of the digits \\(1,2,\\dots ,8\\) exactly once  \n\n\\[\n22=2\\cdot11\n\\]\n\nso the number must be divisible by \\(2\\) **and** by \\(11\\).\n\n---\n\n### 1.  Divisibility by \\(2\\)\n\nThe units digit must be even, i.e. one of \\(\\{2,4,6,8\\}\\).\n\n---\n\n### 2.  Divisibility by \\(11\\)\n\nFor an 8\u2011digit number \\(a_1a_2\\ldots a_8\\),\n\n\\[\n(a_1+a_3+a_5+a_7)-(a_2+a_4+a_6+a_8)\\equiv 0\\pmod{11}.\n\\]\n\nLet  \n\n\\[\nS_{\\text{odd}}=a_1+a_3+a_5+a_7,\\qquad \nS_{\\text{even}}=a_2+a_4+a_6+a_8 .\n\\]\n\nSince the digits \\(1\\) through \\(8\\) sum to \\(36\\),\n\n\\[\nS_{\\text{odd}}+S_{\\text{even}}=36\\qquad\\text{and}\\qquad \nS_{\\text{odd}}-S_{\\text{even}}\\equiv0\\pmod{11}.\n\\]\n\nThus  \n\n\\[\n2S_{\\text{odd}}\\equiv36\\equiv3\\pmod{11}\\Longrightarrow\nS_{\\text{odd}}\\equiv7\\pmod{11}.\n\\]\n\nThe possible values of \\(S_{\\text{odd}}\\) (sum of four distinct digits from \\(1\\)\u2013\\(8\\)) lie between \\(10\\) and \\(26\\).  \nThe only value in this interval congruent to \\(7\\pmod{11}\\) is \\(18\\).\n\nHence\n\n\\[\nS_{\\text{odd}}=S_{\\text{even}}=18 .\n\\]\n\nSo the four digits placed in the odd positions must sum to \\(18\\).\n\n---\n\n### 3.  4\u2011digit subsets with sum \\(18\\)\n\nAll 4\u2011element subsets of \\(\\{1,\\dots ,8\\}\\) whose sum is \\(18\\) are  \n\n\\[\n\\begin{aligned}\n&amp;\\{1,2,7,8\\},\\; \\{1,3,6,8\\},\\; \\{1,4,5,8\\},\\; \\{1,4,6,7\\},\\\\\n&amp;\\{2,3,5,8\\},\\; \\{2,3,6,7\\},\\; \\{2,4,5,7\\},\\; \\{3,4,5,6\\}.\n\\end{aligned}\n\\]\n\nThere are exactly \\(8\\) such subsets.  \nEach contains **exactly two even digits** (the even digits are \\(2,4,6,8\\)).\n\n---\n\n### 4.  Arranging the digits\n\n* Choose one of the 8 subsets for the odd positions.\n* Permute its four digits among the odd places \\((1,3,5,7)\\) \u2013 \\(4! = 24\\) ways.\n* The remaining four digits occupy the even places \\((2,4,6,8)\\).  \n\n  The units place (position\u202f8) must be even.  \n  Since the complementary set also has exactly two even digits, we may\n  \\[\n  \\text{choose the even digit for position\u202f8 in }2\\text{ ways,}\n  \\]\n  then arrange the other three digits in positions \\(2,4,6\\) in \\(3! = 6\\) ways.\n\nHence for a given subset the number of valid permutations is  \n\n\\[\n24 \\times (2 \\times 6)=24 \\times 12 = 288 .\n\\]\n\nWith \\(8\\) possible subsets,\n\n\\[\nN = 8 \\times 288 = 2304 .\n\\]\n\n---\n\n### 5.  Required difference\n\n\\[\nN-2025 = 2304-2025 = 279 .\n\\]\n\n\\[\n\\boxed{279}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 279</p>\n<p>Extracted Answer: 279</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $k$ be real numbers such that the system $|25+20i-z|=5$ and $|z-4-k|=|z-3i-k|$ has exactly one complex solution $z$. The sum of all possible values of $k$ can be written as $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$. Here $i=\\sqrt{-1}$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>The first equation  \n\n\\[\n|25+20i-z|=5\n\\]\n\ndescribes the circle  \n\n\\[\n\\text{Center }C=(25,20),\\qquad\\text{radius }R=5 .\n\\]\n\nThe second equation  \n\n\\[\n|z-4-k|=|z-3i-k|\n\\]\n\nstates that the distance from \\(z\\) to the point  \n\n\\[\nA=4+k\\;(=k+4+0i)\n\\]\n\nequals its distance to the point  \n\n\\[\nB=3i+k\\;(=k+0i+3i).\n\\]\n\nHence the locus of points satisfying the second condition is the **perpendicular bisector** of the segment \\(\\overline{AB}\\).\n\n---\n\n### 1.  Equation of the perpendicular bisector\n\nCoordinates:\n\n\\[\nA=(k+4,0),\\qquad B=(k,3).\n\\]\n\nMidpoint  \n\n\\[\nM=\\Big(\\frac{k+4+k}{2},\\frac{0+3}{2}\\Big)=\\Big(k+2,\\frac32\\Big).\n\\]\n\nSlope of \\(\\overline{AB}\\):\n\n\\[\n\\frac{3-0}{k-(k+4)}=\\frac{3}{-4}=-\\frac34 .\n\\]\n\nTherefore the slope of the perpendicular bisector is the negative reciprocal,\n\n\\[\nm=\\frac{4}{3}.\n\\]\n\nUsing point\u2013slope form through \\(M\\):\n\n\\[\ny-\\frac32=\\frac{4}{3}(x-(k+2)).\n\\]\n\nMultiplying by \\(6\\),\n\n\\[\n6y-9=8x-8k-16\\qquad\\Longrightarrow\\qquad 8x-6y=8k+7.\n\\]\n\nThus the line is  \n\n\\[\nL:\\;8x-6y=8k+7 .\n\\]\n\n---\n\n### 2.  Tangency condition\n\nThe system has **exactly one** solution \\(z\\) when the line \\(L\\) is tangent to the circle.  \nThe distance from the center \\(C=(25,20)\\) to \\(L\\) must equal the radius \\(5\\).\n\nFor a line \\(Ax+By+C=0\\), the distance from \\((x_0,y_0)\\) is  \n\n\\[\nd=\\frac{|Ax_0+By_0+C|}{\\sqrt{A^2+B^2}} .\n\\]\n\nWrite \\(L\\) as \\(8x-6y-(8k+7)=0\\). Then\n\n\\[\nd=\\frac{|8\\cdot25-6\\cdot20-(8k+7)|}{\\sqrt{8^2+(-6)^2}}\n   =\\frac{|200-120-8k-7|}{\\sqrt{64+36}}\n   =\\frac{|73-8k|}{10}.\n\\]\n\nSet \\(d=R=5\\):\n\n\\[\n\\frac{|73-8k|}{10}=5 \\;\\Longrightarrow\\; |73-8k|=50 .\n\\]\n\nHence  \n\n\\[\n73-8k=50 \\quad\\text{or}\\quad 73-8k=-50.\n\\]\n\nSolving:\n\n\\[\n\\begin{aligned}\n73-8k=50 &amp;\\Rightarrow 8k=23 \\Rightarrow k=\\frac{23}{8},\\\\[2mm]\n73-8k=-50 &amp;\\Rightarrow 8k=123 \\Rightarrow k=\\frac{123}{8}.\n\\end{aligned}\n\\]\n\nBoth values give a line tangent to the circle, so the system has exactly one complex solution for each.\n\n---\n\n### 3.  Sum of all possible \\(k\\)\n\n\\[\n\\frac{23}{8}+\\frac{123}{8}=\\frac{146}{8}=\\frac{73}{4}.\n\\]\n\nWrite \\(\\frac{73}{4}\\) as \\(\\frac{m}{n}\\) with \\(\\gcd(m,n)=1\\); here \\(m=73,\\;n=4\\).\n\n\\[\nm+n=73+4=77.\n\\]\n\n\\[\n\\boxed{77}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 77</p>\n<p>Extracted Answer: 77</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet the sequence of rationals $ x_1, x_2, \\ldots $ be defined such that $ x_1 = \\frac{25}{11} $ and\n$ x_{k+1} = \\frac{1}{3} \\left( x_k + \\frac{1}{x_k} - 1 \\right). $\n$ x_{2025} $ can be expressed as $ \\frac{m}{n} $ for relatively prime positive integers $ m $ and $ n $. Find the remainder when $ m + n $ is divided by 1000.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>The recurrence  \n\n\\[\nx_{k+1}= \\frac{1}{3}\\Bigl(x_k+\\frac{1}{x_k}-1\\Bigr)\n\\]\n\ncan be rewritten as  \n\n\\[\nx_{k+1}= \\frac{x_k^2-x_k+1}{3x_k}.\n\\]\n\n---\n\n### 1.  A convenient change of variables  \n\nDefine  \n\n\\[\nt_k=\\frac{2x_k-1}{x_k+1}\\qquad\\Longleftrightarrow\\qquad \nx_k=\\frac{b_k+a_k}{2b_k-a_k},\n\\]\n\nwhere \\(a_k,b_k\\) are integers defined below.  \n\nFrom the definition  \n\n\\[\nt_{k+1}=t_k\\bigl(t_k-1\\bigr),\\qquad t_1=\\frac{13}{12}.\n\\]\n\n---\n\n### 2.  Integer sequences  \n\nWrite \\(t_k=\\dfrac{a_k}{b_k}\\) in lowest terms.  \nFrom \\(t_{k+1}=t_k(t_k-1)\\) we obtain  \n\n\\[\na_{k+1}=a_k\\bigl(a_k-b_k\\bigr),\\qquad  \nb_{k+1}=b_k^2,\\qquad a_1=13,\\;b_1=12 .\n\\]\n\nThus  \n\n\\[\nb_k=12^{\\,2^{\\,k-1}} .\n\\]\n\nBecause \\(a_k\\) is always odd and not a multiple of \\(3\\), \\(\\gcd(a_k,b_k)=1\\) for all \\(k\\).\n\n---\n\n### 3.  Expressing \\(x_k\\)  \n\nUsing \\(x_k=\\dfrac{b_k+a_k}{2b_k-a_k}\\) we get  \n\n\\[\nm_k=b_k+a_k,\\qquad n_k=2b_k-a_k,\n\\]\nso that  \n\n\\[\nm_k+n_k = (b_k+a_k)+(2b_k-a_k)=3b_k .\n\\]\n\nHence for any \\(k\\),\n\n\\[\nm_k+n_k = 3\\cdot 12^{\\,2^{\\,k-1}} .\n\\]\n\n---\n\n### 4.  The required term  \n\nFor \\(k=2025\\),\n\n\\[\nm+n = 3\\cdot 12^{\\,2^{\\,2024}} .\n\\]\n\nWe need this number modulo \\(1000\\).\n\n---\n\n### 5.  Computing \\(3\\cdot12^{2^{2024}}\\pmod{1000}\\)\n\nSince \\(1000=8\\cdot125\\), work modulo \\(8\\) and \\(125\\).\n\n*Modulo\u202f8*:\u2003\\(12\\equiv4\\pmod8\\) and \\(4^2\\equiv0\\pmod8\\); with exponent \\(2^{2024}&gt;1\\),\n\n\\[\n12^{2^{2024}}\\equiv0\\pmod8\\Longrightarrow\n3\\cdot12^{2^{2024}}\\equiv0\\pmod8 .\n\\]\n\n*Modulo\u202f125*:\u2003\\(\\gcd(12,125)=1\\), \\(\\phi(125)=100\\).  \nReduce the exponent modulo\u202f100:\n\n\\[\n2^{2024}\\equiv 2^{4}=16\\pmod{100}\n\\]\n(because \\(2^{2024}\\equiv16\\pmod{100}\\)).  \nHence  \n\n\\[\n12^{2^{2024}}\\equiv12^{16}\\pmod{125}.\n\\]\n\nCompute:\n\\[\n12^2\\equiv19,\\quad\n12^4\\equiv19^2\\equiv111,\\quad\n12^8\\equiv111^2\\equiv71,\\quad\n12^{16}\\equiv71^2\\equiv41\\pmod{125}.\n\\]\n\nThus  \n\n\\[\n3\\cdot12^{2^{2024}}\\equiv3\\cdot41=123\\pmod{125}.\n\\]\n\nNow solve  \n\n\\[\nR\\equiv0\\pmod8,\\qquad R\\equiv123\\pmod{125}.\n\\]\n\nWrite \\(R=125a+123\\). Mod\u202f8:\n\n\\[\n125a+123\\equiv5a+3\\equiv0\\pmod8\\Longrightarrow5a\\equiv5\\pmod8\n\\Longrightarrow a\\equiv1\\pmod8.\n\\]\n\nTake \\(a=1\\); then \\(R=125\\cdot1+123=248\\).\n\nHence  \n\n\\[\nm+n\\equiv 248 \\pmod{1000}.\n\\]\n\n---\n\n\\[\n\\boxed{248}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 248</p>\n<p>Extracted Answer: 248</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nOn $\\triangle ABC$ points $A,D,E$, and $B$ lie that order on side $\\overline{AB}$ with $AD=4, DE=16$, and $EB=8$. Points $A,F,G$, and $C$ lie in that order on side $\\overline{AC}$ with $AF=13, FG=52$, and $GC=26$. Let $M$ be the reflection of $D$ through $F$, and let $N$ be the reflection of $G$ through $E$. Quadrilateral $DEGF$ has area 288. Find the area of heptagon $AFNBCEM$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n\\[\nAD=4,\\; DE=16,\\; EB=8,\\qquad AF=13,\\; FG=52,\\; GC=26 .\n\\]\n\nHence  \n\n\\[\nAB=4+16+8=28,\\qquad AC=13+52+26=91 .\n\\]\n\n--------------------------------------------------------------------\n### 1.  Coordinates\n\nPlace \\(A=(0,0),\\; B=(28,0)\\) and let the height of \\(\\triangle ABC\\) be \\(h\\).  \nWrite \\(C=(x,h)\\) (the \\(x\\)\u2011coordinate is unknown).\n\nPoints on the sides are then  \n\n\\[\n\\begin{aligned}\nD&amp;=(4,0),   &amp;E&amp;=(20,0), \\\\\nF&amp;=\\Bigl(\\frac{13}{91}x,\\;\\frac{13}{91}h\\Bigr), &amp;\nG&amp;=\\Bigl(\\frac{65}{91}x,\\;\\frac{65}{91}h\\Bigr).\n\\end{aligned}\n\\]\n\nSince \\(M\\) is the reflection of \\(D\\) about \\(F\\),\n\n\\[\nM=2F-D=\\Bigl(\\frac{26}{91}x-4,\\;\\frac{26}{91}h\\Bigr),\n\\]\n\nand because \\(N\\) is the reflection of \\(G\\) about \\(E\\),\n\n\\[\nN=2E-G=\\Bigl(40-\\frac{65}{91}x,\\;-\\frac{65}{91}h\\Bigr).\n\\]\n\n--------------------------------------------------------------------\n### 2.  Height from the given area\n\nQuadrilateral \\(DEGF\\) consists of triangles \\(DEG\\) and \\(DFG\\).  \nIts area is\n\n\\[\n\\begin{aligned}\n[DEGF]&amp;=\\frac12\\Bigl[\\,DE\\cdot G_y\n      +|\\,\\overrightarrow{DF}\\times\\overrightarrow{DG}\\,|\\,\\Bigr]\\\\[2mm]\n     &amp;=\\frac{h}{2\\cdot91}\\Bigl(16\\cdot65+4\\cdot52\\Bigr)\n      =\\frac{1248}{182}\\,h\n      =\\frac{624}{91}\\,h .\n\\end{aligned}\n\\]\n\nGiven \\([DEGF]=288\\),\n\n\\[\n\\frac{624}{91}\\,h=288\\quad\\Longrightarrow\\quad h=42 .\n\\]\n\n--------------------------------------------------------------------\n### 3.  Area of \\(\\triangle ABC\\)\n\n\\[\n[ABC]=\\frac12\\cdot AB\\cdot h\n      =\\frac12\\cdot28\\cdot42\n      =588 .\n\\]\n\n--------------------------------------------------------------------\n### 4.  Area of the heptagon \\(AFNBCEM\\)\n\nUse the shoelace formula with the vertices in the order  \n\n\\[\nA,\\;F,\\;N,\\;B,\\;C,\\;E,\\;M .\n\\]\n\nBecause the \\(x\\)-coordinate \\(x\\) of \\(C\\) appears only in the\nterms \\(x\\,h\\) and they cancel each other, the sum reduces to  \n\n\\[\n\\begin{aligned}\nS&amp;=2\\bigl( -\\tfrac{2\\cdot13}{91} (4+16)h\n          + (4+16+8)h\n          + (4+16+8)h\n          - (4+16)h \\bigr) \\\\\n  &amp;=2\\cdot 28h .\n\\end{aligned}\n\\]\n\nHence\n\n\\[\n[AFNBCEM]=\\frac12 S = \\frac12\\cdot28h = [ABC]=588 .\n\\]\n\n--------------------------------------------------------------------\n\\[\n\\boxed{588}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 588</p>\n<p>Extracted Answer: 588</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThe parabola with equation $y=x^{2}-4$ is rotated $60^{\\circ}$ counterclockwise around the origin. The unique point in the fourth quadrant where the original parabola and its image intersect has $y$-coordinate $\\frac{a-\\sqrt{b}}{c}$, where $a$, $b$, and $c$ are positive integers, and $a$ and $c$ are relatively prime. Find $a+b+c$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>The original parabola is  \n\n\\[\ny=x^{2}-4 .\n\\]\n\nRotate it \\(60^{\\circ}\\) counter\u2011clockwise about the origin.  \nIf \\((X,Y)\\) is a point on the rotated parabola, then rotating it back\n\\(60^{\\circ}\\) (clockwise) must put it on the original parabola:\n\n\\[\n\\begin{aligned}\nx &amp;= X\\cos60^{\\circ}+Y\\sin60^{\\circ},\\\\\ny &amp;=-X\\sin60^{\\circ}+Y\\cos60^{\\circ},\n\\end{aligned}\n\\qquad\\text{with }\\;y=x^{2}-4 .\n\\]\n\nUsing \\(\\cos60^{\\circ}= \\tfrac12,\\; \\sin60^{\\circ}= \\tfrac{\\sqrt3}{2}\\),\n\n\\[\n-\\,\\frac{\\sqrt3}{2}X+\\frac12Y= \\Bigl(\\frac12X+\\frac{\\sqrt3}{2}Y\\Bigr)^{2}-4 .\n\\tag{1}\n\\]\n\nThe original parabola gives \\(Y=X^{2}-4\\). Substituting this into (1) and\nclearing denominators yields\n\n\\[\n3X^{4}+2\\sqrt3\\,X^{3}-25X^{2}-6\\sqrt3\\,X+40=0 .\n\\tag{2}\n\\]\n\nThe quartic factors over \\(\\mathbb{Q}(\\sqrt3)\\):\n\n\\[\n\\bigl(X^{2}+\\sqrt3\\,X-4\\bigr)\\bigl(3X^{2}-\\sqrt3\\,X-10\\bigr)=0 .\n\\]\n\nHence the possible \\(X\\)-coordinates are the roots of the two quadratics.\n\n* From \\(X^{2}+\\sqrt3X-4=0\\) :\n\n\\[\nX=\\frac{-\\sqrt3\\pm\\sqrt{19}}{2}.\n\\]\n\nThe positive root is  \n\n\\[\nX_{0}= \\frac{-\\sqrt3+\\sqrt{19}}{2}\\approx1.31,\n\\]\n\nwhich satisfies \\(0&lt;X&lt;2\\); thus the point \\((X_{0},Y_{0})\\) lies in the\nfourth quadrant.\n\n* The other quadratic \\(3X^{2}-\\sqrt3X-10=0\\) gives \\(X\\approx2.14\\) or\n\\(X\\approx-1.56\\), neither of which lies in the fourth quadrant.\n\nTherefore the unique fourth\u2011quadrant intersection comes from\n\\(X_{0}\\).  For this root we have from the quadratic\n\n\\[\nX_{0}^{2}=4-\\sqrt3 X_{0},\n\\qquad\\text{so}\\qquad\nY_{0}=X_{0}^{2}-4=-\\sqrt3 X_{0}.\n\\]\n\nThus\n\n\\[\nY_{0}= -\\sqrt3\\left(\\frac{-\\sqrt3+\\sqrt{19}}{2}\\right)\n     =\\frac{3-\\sqrt{57}}{2}.\n\\]\n\nThe \\(y\\)-coordinate is \\(\\displaystyle\\frac{a-\\sqrt b}{c}\\) with  \n\n\\[\na=3,\\qquad b=57,\\qquad c=2.\n\\]\n\nSince \\(\\gcd(3,2)=1\\), the conditions are satisfied.  \n\n\\[\na+b+c=3+57+2=62.\n\\]\n\n\\[\n\\boxed{62}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 62</p>\n<p>Extracted Answer: 62</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nA piecewise linear periodic function is defined by $f(x)=\\begin{cases}x&amp;\\text{if }x\\in[-1,1)\\\\2-x&amp;\\text{if }x\\in[1,3)\\end{cases}$ and $f(x+4)=f(x)$ for all real numbers $x$. The graph of $f(x)$ has the sawtooth pattern. The parabola $x=34y^2$ intersects the graph of $f(x)$ at finitely many points. The sum of the $y$-coordinates of these intersection points can be expressed in the form $\\frac{a+b\\sqrt{c}}{d}$, where $a,b,c,$ and $d$ are positive integers, $a,b,$ and $d$ have greatest common divisor equal to 1, and $c$ is not divisible by the square of any prime. Find $a+b+c+d$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>The periodic function  \n\n\\[\nf(x)=\\begin{cases}\nx,&amp;x\\in[-1,1)\\\\[2pt]\n2-x,&amp;x\\in[1,3)\n\\end{cases},\n\\qquad f(x+4)=f(x)\n\\]\n\nhas period \\(4\\).  \nOn each period write  \n\n\\[\nx=4k+u,\\qquad u\\in[-1,3),\\ k\\in\\mathbb Z .\n\\]\n\nThen  \n\n\\[\nf(x)=\\begin{cases}\nu, &amp; u\\in[-1,1)\\\\[2pt]\n2-u,&amp;u\\in[1,3)\n\\end{cases}.\n\\]\n\nThe parabola is \\(x=34y^{2}\\;(x\\ge 0,\\;|y|\\le 1)\\).  \nSet \\(x=34y^{2}=4k+u\\) with \\(u\\in[-1,3)\\).  \nThe integer \\(k\\) is uniquely determined by  \n\n\\[\n\\frac{34y^{2}-3}{4}&lt;k\\le\\frac{34y^{2}+1}{4},\n\\]\n\nso for each \\(y\\) there is exactly one such \\(k\\).\n\n---\n\n### 1.  Rising part \\((u\\in[-1,1))\\)\n\nHere \\(y=u\\).  Hence  \n\n\\[\ny=34y^{2}-4k\\Longrightarrow 34y^{2}-y-4k=0.\n\\]\n\nFor a fixed \\(k\\) the two roots are  \n\n\\[\ny_{R,k}^{\\pm}= \\frac{1\\pm\\sqrt{1+544k}}{68},\n\\qquad k=0,1,\\dots ,8 .\n\\]\n\nBoth lie in \\([-1,1]\\) for all these \\(k\\).  \nEach pair sums to  \n\n\\[\ny_{R,k}^{+}+y_{R,k}^{-}= \\frac1{34}.\n\\]\n\nThus  \n\n\\[\n\\sum_{k=0}^{8}\\bigl(y_{R,k}^{+}+y_{R,k}^{-}\\bigr)=\\frac{9}{34}.\n\\]\n\n---\n\n### 2.  Falling part \\((u\\in[1,3))\\)\n\nHere \\(y=2-u\\).  Hence  \n\n\\[\ny=2-(34y^{2}-4k)\\Longrightarrow 34y^{2}+y-(4k+2)=0.\n\\]\n\nThe roots are  \n\n\\[\ny_{D,k}^{\\pm}= \\frac{-1\\pm\\sqrt{273+544k}}{68},\n\\qquad k=0,1,\\dots ,8 .\n\\]\n\nFor \\(k=0,\\dots ,7\\) both roots lie in \\([-1,1]\\); for \\(k=8\\) the\nnegative root is \\(&lt;-1\\) and must be discarded.\nEach admissible pair sums to  \n\n\\[\ny_{D,k}^{+}+y_{D,k}^{-}= -\\frac1{34},\n\\]\n\nso for \\(k=0,\\dots ,7\\)\n\n\\[\n\\sum_{k=0}^{7}\\bigl(y_{D,k}^{+}+y_{D,k}^{-}\\bigr)= -\\frac{8}{34}\n= -\\frac{4}{17}.\n\\]\n\nThe remaining root (the positive one for \\(k=8\\)) is  \n\n\\[\ny_{D,8}^{+}= \\frac{-1+ \\sqrt{273+544\\cdot8}}{68}\n          = \\frac{-1+ \\sqrt{4625}}{68}\n          = \\frac{-1+5\\sqrt{185}}{68}.\n\\]\n\n---\n\n### 3.  Sum of all \\(y\\)-coordinates\n\nAdding the contributions,\n\n\\[\n\\begin{aligned}\nS &amp;=\\frac{9}{34}-\\frac{4}{17}+\\frac{-1+5\\sqrt{185}}{68}\\\\[2pt]\n  &amp;=\\frac{9}{34}-\\frac{8}{34}+\\frac{-1}{68}+\\frac{5\\sqrt{185}}{68}\\\\[2pt]\n  &amp;=\\frac{1}{34}-\\frac{1}{68}+\\frac{5\\sqrt{185}}{68}\\\\[2pt]\n  &amp;=\\frac{1+5\\sqrt{185}}{68}.\n\\end{aligned}\n\\]\n\nThus the sum can be written as \\(\\displaystyle\\frac{a+b\\sqrt{c}}{d}\\) with  \n\n\\[\na=1,\\qquad b=5,\\qquad c=185,\\qquad d=68,\n\\]\n\nwhere \\(\\gcd(a,b,d)=1\\) and \\(c\\) is square\u2011free.\n\nFinally  \n\n\\[\na+b+c+d=1+5+185+68=259.\n\\]\n\n\\[\n\\boxed{259}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 259</p>\n<p>Extracted Answer: 259</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $ABCDE$ be a convex pentagon with $AB=14, BC=7, CD=24, DE=13, EA=26,$ and $\\angle B=\\angle E=60^\\circ$. For each point $X$ in the plane, define $f(X)=AX+BX+CX+DX+EX$. The least possible value of $f(X)$ can be expressed as $m+n\\sqrt{p}$, where $m$ and $n$ are positive integers and $p$ is not divisible by the square of any prime. Find $m+n+p$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>The required sum is  \n\n\\[\n\\min_{X\\in \\mathbb {R}^2}\\bigl(AX+BX+CX+DX+EX\\bigr)\n=38+19\\sqrt{3}.\n\\]\n\nHence  \n\n\\[\nm=38,\\qquad n=19,\\qquad p=3,\n\\]\n\nand  \n\n\\[\nm+n+p=38+19+3=60.\n\\]\n\n\\[\n\\boxed{60}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 60</p>\n<p>Extracted Answer: 60</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThe 27 cells of a $3\\times9$ grid are filled in using the numbers 1 through 9 so that each row contains 9 different numbers, and each of the three $3\\times3$ blocks heavily outlined in the example below contains 9 different numbers, as in the first three rows of a Sudoku puzzle. \n | 4 | 2 | 8 | 9 | 6 | 3 | 1 | 7 | 5 | \n | 3 | 7 | 9 | 5 | 2 | 1 | 6 | 8 | 4 | \n | 5 | 6 | 1 | 8 | 4 | 7 | 9 | 2 | 3 | \n The number of different ways to fill such a grid can be written as $p^a\\cdot q^b\\cdot r^c\\cdot s^d$, where $p,q,r,$ and $s$ are distinct prime numbers and $a,b,c,$ and $d$ are positive integers. Find $p\\cdot a+q\\cdot b+r\\cdot c+s\\cdot d$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let the rows be \\(R_{1},R_{2},R_{3}\\) and the three \\(3\\times3\\) blocks be\n\\(B_{1},B_{2},B_{3}\\) (columns \\(1\\!-\\!3,\\;4\\!-\\!6,\\;7\\!-\\!9\\)).\nEach number \\(x\\in\\{1,\\dots ,9\\}\\) appears\n\n* once in each row,\n* once in each block.\n\nHence for a fixed number \\(x\\) the three occurrences give a bijection  \n\n\\[\n\\sigma _x:\\{R_1,R_2,R_3\\}\\longrightarrow \\{B_1,B_2,B_3\\},\n\\qquad \n\\sigma_x(R_i)=\\text{the block containing }x\\text{ in row }R_i .\n\\]\n\nThus \\(\\sigma_x\\) is a permutation of \\(\\{1,2,3\\}\\).  \nConversely, any choice of a permutation \\(\\sigma_x\\) for every \\(x\\) determines\nwhich block each occurrence of \\(x\\) occupies.\n\n--------------------------------------------------------------------\n### 1.  Counting the permutations \\(\\sigma_x\\)\n\nWrite a \\(9\\times3\\) matrix whose rows are the six possible permutations of\n\\(\\{1,2,3\\}\\):\n\n\\[\n\\begin{array}{c}\n123\\\\ 213\\\\ 321\\\\ 132\\\\ 231\\\\ 312\n\\end{array}\n\\]\n\nIf a number receives a given permutation, that row of the matrix is placed in\nthe matrix of size \\(9\\times3\\).  \nDenote by \\(x_i\\;(i=1,\\dots ,6)\\) the number of numbers that receive the\n\\(i\\)\u2011th permutation.  \n\nRow\u2011balance (each number uses each symbol once) is automatic; column\u2011balance\n(because each block must contain exactly three numbers in each row) gives\n\n\\[\n\\begin{aligned}\nx_1+x_4&amp;=3,\\qquad x_2+x_5=3,\\qquad x_3+x_6=3,\\\\\nx_2+x_6&amp;=3,\\qquad x_1+x_3=3,\\qquad x_4+x_5=3,\n\\end{aligned}\n\\]\n\nwith \\(\\sum_{i=1}^6x_i=9\\).\nSolving gives a one\u2011parameter family\n\n\\[\n(x_1,x_2,x_3,x_4,x_5,x_6)=\\bigl(3-t,\\;t,\\;t,\\;t,\\;3-t,\\;3-t\\bigr)\n\\qquad(t=0,1,2,3).\n\\]\n\nFor a fixed \\(t\\) the numbers are assigned to the six permutation types in  \n\n\\[\n\\frac{9!}{(t!)^3\\bigl((3-t)!\\bigr)^3}\n\\]\n\nways.  Summing over the four possible values of \\(t\\),\n\n\\[\nN_{\\sigma}= \\frac{9!}{(3!)^3}+\\frac{9!}{(1!)^3(2!)^3}\n          +\\frac{9!}{(2!)^3(1!)^3}+\\frac{9!}{(3!)^3}\n          =94\\,080 .\n\\]\n\n--------------------------------------------------------------------\n### 2.  Placing the numbers inside the blocks\n\nFix the block\u2011row distribution given by the \\(\\sigma_x\\)\u2019s.\nIn each block, a row contains exactly three different numbers.\nThese three numbers can be arranged in the three columns of the block in\n\\(3! = 6\\) ways, independently for the three rows.\nHence each block offers \\(6^{3}=216\\) possibilities, and for the three blocks\n\n\\[\nN_{\\text{cols}} = 6^{9}=10\\,077\\,696 .\n\\]\n\n--------------------------------------------------------------------\n### 3.  Total number of fillings\n\n\\[\nN = N_{\\sigma}\\,N_{\\text{cols}}\n   = 94\\,080 \\times 6^{9}\n   = 948\\,109\\,639\\,680 .\n\\]\n\nPrime factorising,\n\n\\[\nN = 2^{16}\\cdot 3^{10}\\cdot 5^{1}\\cdot 7^{2}.\n\\]\n\nThus we may take  \n\n\\[\np=2,\\;a=16,\\qquad q=3,\\;b=10,\\qquad r=5,\\;c=1,\\qquad s=7,\\;d=2 .\n\\]\n\nFinally,\n\n\\[\np a+ q b+ r c+ s d\n= 2\\cdot16 + 3\\cdot10 + 5\\cdot1 + 7\\cdot2\n= 32+30+5+14 = 81 .\n\\]\n\n\\[\n\\boxed{81}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 81</p>\n<p>Extracted Answer: 81</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThe twelve letters $A,B,C,D,E,F,G,H,I,J,K$, and $L$ are randomly grouped into six pairs of letters. The two letters in each pair are placed next to each other in alphabetical order to form six two-letter words, and those six words are listed alphabetically. For example, a possible result is $AB,CJ,DG,EK,FL,HI$. The probability that the last word listed contains $G$ is $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n\\[\n\\{A,B,\\dots ,L\\}= \\{1,2,\\dots ,12\\}\n\\]\n\nand let a random pairing be a perfect matching of the 12 numbers.\nFor each pair \\(\\{a,b\\}\\;(a&lt;b)\\) we write the word \\(ab\\);  \nthe six words are then listed in alphabetical order.  \n\n--------------------------------------------------------------------\n### 1.  What determines the last word?\n\nIn each pair the smaller letter is written first, so the six words are\n\n\\[\n\\{\\,\\underbrace{\\text{smaller}}_{\\text{first letter}},\\ \\text{larger}\\,\\}.\n\\]\n\nIf we denote by  \n\n\\[\nS=\\{\\,\\min\\{a,b\\}\\mid\\{a,b\\}\\text{ a pair}\\,\\},\n\\]\n\nthen \\(|S|=6\\) and the last (lexicographically largest) word is the\npair whose **smaller** element is the largest element of \\(S\\).\n\nHence the last word contains \\(G\\) iff the smaller element of the\npair containing \\(G\\) is the maximal element of \\(S\\).\n\n--------------------------------------------------------------------\n### 2.  Condition on the partner of \\(G\\)\n\nLet the partner of \\(G\\;(=7)\\) be \\(j\\neq7\\).\n\n*If \\(j&gt;7\\):* then the smaller element of the \\(G\\)\u2013pair is \\(7\\).  \nWe need that every other pair have its smaller element \\(\\le 6\\); i.e.\nall the other five \u201csmaller\u201d letters must lie in \\(\\{1,\\dots ,6\\}\\).\n\n*If \\(j&lt;7\\):* then the smaller element of the \\(G\\)\u2013pair is \\(j\\).  \nWe need that every other smaller element be \\(&lt;j\\); consequently all\nthe remaining five smaller letters must be taken from \\(\\{1,\\dots ,j-1\\}\\).\n\n--------------------------------------------------------------------\n### 3.  Counting matchings that satisfy the condition\n\nAfter fixing the partner \\(j\\) we have 10 letters left.\nLet  \n\n\\[\nL=\\{\\text{remaining letters }&lt;j\\},\\qquad H=\\{\\text{remaining letters }\\ge j\\}.\n\\]\n\nThe condition \u201cno other pair has a smaller element \\(\\ge j\\)\u201d is\nequivalent to **no pair joining two letters of \\(H\\)**; every element\nof \\(H\\) must be paired with a distinct element of \\(L\\).\n\nIf \\(|L|=l\\) and \\(|H|=h\\) (\\(l+h=10\\)), the number of perfect matchings\nwith no \\(H\\!-\\!H\\) pair is\n\n\\[\n\\binom{l}{h}h!\\,(l-h-1)!!\\;,\n\\]\n\nwhere \\((2k-1)!!=1\\cdot3\\cdots(2k-1)\\).\nThe total number of matchings on 10 letters is \\((10-1)!!=945\\).\n\n---\n\n* **\\(j&gt;7\\) (five possibilities)**  \n  Here \\(j\\in\\{8,9,10,11,12\\}\\).  \n  We have \\(L=\\{1,\\dots ,6\\}\\;(l=6),\\ H=\\) the four other numbers \\(&gt;7\\)\n  \\((h=4)\\).  \n\n  \\[\n  \\frac{\\binom{6}{4}4!\\,(6-4-1)!!}{945}\n  =\\frac{15\\cdot24\\cdot1}{945}=\\frac{8}{21}.\n  \\]\n\n* **\\(j=6\\)**  \n  Then \\(L=\\{1,\\dots ,5\\},\\ H=\\{8,9,10,11,12\\}\\) (\\(l=h=5\\)).  \n\n  \\[\n  \\frac{\\binom{5}{5}5!\\,(5-5-1)!!}{945}\n  =\\frac{5!}{945}=\\frac{120}{945}=\\frac{8}{63}.\n  \\]\n\n* **\\(j=1,2,3,4,5\\)**  \n  In these cases \\(h&gt;l\\); it is impossible to avoid an \\(H\\!-\\!H\\) pair,\n  so the probability is \\(0\\).\n\n--------------------------------------------------------------------\n### 4.  Assemble the total probability\n\nEach of the 11 possible partners of \\(G\\) is equally likely (\\(1/11\\)).\nTherefore\n\n\\[\n\\begin{aligned}\nP(\\text{last word contains }G)\n&amp;= \\frac1{11}\\Bigl(5\\cdot\\frac{8}{21}+\\frac{8}{63}\\Bigr)\\\\[2mm]\n&amp;= \\frac1{11}\\Bigl(\\frac{120}{63}+\\frac{8}{63}\\Bigr)\\\\[2mm]\n&amp;= \\frac{128}{693}.\n\\end{aligned}\n\\]\n\nThe fraction \\(\\displaystyle\\frac{128}{693}\\) is already in lowest terms.\nHence  \n\n\\[\nm=128,\\qquad n=693,\\qquad m+n=821.\n\\]\n\n--------------------------------------------------------------------\n\\[\n\\boxed{821}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 821</p>\n<p>Extracted Answer: 821</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nFind the sum of all positive integers $ n $ such that $ n + 2 $ divides the product $ 3(n + 3)(n^2 + 9) $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n\\[\nP(n)=3(n+3)(n^{2}+9).\n\\]\n\nWe need all positive integers \\(n\\) for which  \n\n\\[\nn+2 \\mid P(n).\n\\]\n\n---\n\n### 1. Work modulo \\(n+2\\)\n\nWrite \\(n\\equiv -2 \\pmod{\\,n+2\\,}\\).  \nReplace \\(n\\) by \\(-2\\) in the factors of \\(P(n)\\) (this gives the remainder of each factor modulo \\(n+2\\)):\n\n\\[\n\\begin{aligned}\nn+3 &amp;\\equiv (-2)+3 = 1 \\pmod{n+2},\\\\[2mm]\nn^{2}+9 &amp;\\equiv (-2)^{2}+9 = 4+9 = 13 \\pmod{n+2}.\n\\end{aligned}\n\\]\n\nHence\n\n\\[\nP(n)=3(n+3)(n^{2}+9)\\equiv 3\\cdot 1\\cdot 13 = 39\\pmod{n+2}.\n\\]\n\n---\n\n### 2. Condition for divisibility\n\nThe requirement \\(n+2\\mid P(n)\\) is equivalent to  \n\n\\[\nP(n)\\equiv 0\\pmod{n+2}\\Longleftrightarrow 39\\equiv 0\\pmod{n+2}.\n\\]\n\nThus  \n\n\\[\nn+2 \\text{ must be a positive divisor of } 39.\n\\]\n\nThe positive divisors of \\(39\\) are  \n\n\\[\n1,\\;3,\\;13,\\;39.\n\\]\n\nSince \\(n\\) is a **positive** integer, \\(n+2\\ge 3\\).  \nHence \\(n+2\\) can be only \\(3,\\;13,\\;39\\).\n\n---\n\n### 3. Corresponding values of \\(n\\)\n\n\\[\n\\begin{array}{c|c}\nn+2 &amp; n \\\\ \\hline\n3   &amp; 1\\\\\n13  &amp; 11\\\\\n39  &amp; 37\n\\end{array}\n\\]\n\nAll three satisfy the original condition (a quick check confirms divisibility).\n\n---\n\n### 4. Sum of all such \\(n\\)\n\n\\[\n1+11+37 = 49.\n\\]\n\n\\[\n\\boxed{49}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 49</p>\n<p>Extracted Answer: 49</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nSix points $ A, B, C, D, E, $ and $ F $ lie in a straight line in that order. Suppose that $ G $ is a point not on the line and that $ AC = 26 $, $ BD = 22 $, $ CE = 31 $, $ DF = 33 $, $ AF = 73 $, $ CG = 40 $, and $ DG = 30 $. Find the area of $ \\triangle BGE $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>We place the six collinear points on the \\(x\\)-axis.\n\n---\n\n### 1.  Determine the coordinates of \\(A,B,C,D,E,F\\)\n\nLet \\(A=(0,0)\\).  \nWrite the distances in terms of the unknown coordinate \\(AB=x\\).\n\n\\[\n\\begin{aligned}\nC&amp;: AC=26 \\quad\\Longrightarrow\\quad C=(26,0)\\\\\nB&amp;: AB=x \\quad\\Longrightarrow\\quad B=(x,0)\\\\\nD&amp;: BD=22 \\quad\\Longrightarrow\\quad D=(x+22,0)\\\\\nE&amp;: CE=31 \\quad\\Longrightarrow\\quad E=(26+31,0)=(57,0)\\\\\nF&amp;: DF=33 \\quad\\Longrightarrow\\quad F=(x+22+33,0)=(x+55,0)\\\\\n\\text{and }AF&amp;=73 \\Longrightarrow x+55=73 .\n\\end{aligned}\n\\]\n\nHence \\(x=18\\). So  \n\n\\[\nA=0,\\; B=18,\\; C=26,\\; D=40,\\; E=57,\\; F=73 .\n\\]\n\nThese satisfy all given segment lengths.\n\n---\n\n### 2.  Locate point \\(G\\)\n\nLet \\(G=(u,v)\\) with \\(v\\neq 0\\).  \nFrom the given distances\n\n\\[\n\\begin{cases}\n(u-26)^2+v^2 = 40^2 =1600,\\\\[2pt]\n(u-40)^2+v^2 = 30^2 = 900 .\n\\end{cases}\n\\]\n\nSubtract the second equation from the first:\n\n\\[\n(u-26)^2-(u-40)^2 = 700 .\n\\]\n\nExpanding,\n\n\\[\n(-52u+676)-(-80u+1600)=28u-924=700\n\\Longrightarrow 28u=1624\\Longrightarrow u=58 .\n\\]\n\nNow find \\(v\\):\n\n\\[\n(58-26)^2+v^2=1600\\Longrightarrow 32^2+v^2=1600\n\\Longrightarrow v^2=1600-1024=576 .\n\\]\n\nThus \\(|v|=24\\).  Take \\(v=24\\) (the sign does not affect the area).  \n\n\\[\n\\boxed{G=(58,24)} .\n\\]\n\n---\n\n### 3.  Area of \\(\\triangle BGE\\)\n\nPoints on the \\(x\\)-axis:\n\n\\[\nB=(18,0),\\qquad E=(57,0).\n\\]\n\nThe length of the base \\(BE\\) is\n\n\\[\nBE = 57-18 = 39 .\n\\]\n\nSince the line through \\(B\\) and \\(E\\) is the \\(x\\)-axis, the perpendicular distance from \\(G\\) to this line is \\(|v|=24\\).\n\nHence\n\n\\[\n[\\triangle BGE]=\\frac12\\,(BE)\\cdot(\\text{height})\n               =\\frac12\\cdot 39\\cdot 24\n               =\\frac{936}{2}=468 .\n\\]\n\n(Using the determinant formula also gives \\(468\\).)\n\n---\n\n\\[\n\\boxed{468}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 468</p>\n<p>Extracted Answer: 468</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThe set of points in 3-dimensional coordinate space that lie in the plane $x+y+z=75$ whose coordinates satisfy the inequalities $x-yz&lt;y-zx&lt;z-xy$ forms three disjoint convex regions. Exactly one of those regions has finite area. The area of this finite region can be expressed in the form $a\\sqrt{b}$, where $a$ and $b$ are positive integers and $b$ is not divisible by the square of any prime. Find $a+b$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>The inequalities  \n\n\\[\nx-yz&lt;y-zx&lt;z-xy\n\\]\n\ncan be rewritten by factoring:\n\n\\[\n\\begin{aligned}\nx-yz&lt;y-zx &amp;\\iff (x-y)(1+z)&lt;0,\\\\[2pt]\ny-zx&lt;z-xy &amp;\\iff (y-z)(1+x)&lt;0 .\n\\end{aligned}\n\\]\n\nSince the points lie on the plane  \n\n\\[\nx+y+z=75\\qquad\\Longrightarrow\\qquad z=75-x-y,\n\\]\n\nthe two conditions become inequalities in the variables \\(x,y\\):\n\n\\[\n\\begin{cases}\n(x-y)\\bigl(76-x-y\\bigr)&lt;0,\\\\[2pt]\n\\bigl(x+2y-75\\bigr)(1+x)&lt;0 .\n\\end{cases}\n\\tag{1}\n\\]\n\n---\n\n### 1.  Geometry of the half\u2011planes\n\nFrom (1)\n\n* \\((x-y)(76-x-y)&lt;0\\) gives either  \n\n  \\[\n  \\begin{cases}\n  x&gt;y,\\;x+y&gt;76 \\quad\\text{(region }A_1)\\\\\n  \\text{or}\\\\\n  x&lt;y,\\;x+y&lt;76 \\quad\\text{(region }A_2)\n  \\end{cases}\n  \\]\n\n* \\((x+2y-75)(1+x)&lt;0\\) gives either  \n\n  \\[\n  \\begin{cases}\n  x&lt;-1,\\;x+2y&gt;75 \\quad\\text{(region }B_1)\\\\\n  \\text{or}\\\\\n  x&gt;-1,\\;x+2y&lt;75 \\quad\\text{(region }B_2)\n  \\end{cases}\n  \\]\n\nThe set of points satisfying both inequalities is the intersection of one of the\n\\(A_i\\) with one of the \\(B_j\\).\n\nChecking the four possibilities:\n\n* \\(A_1\\cap B_1=\\varnothing\\) (impossible to have \\(x&gt;y\\) and \\(x&lt;-1\\) while\n  \\(x+y&gt;76\\)).\n* \\(A_1\\cap B_2\\) is non\u2011empty and unbounded (e.g. \\(x&gt;77\\)).\n* \\(A_2\\cap B_1\\) is non\u2011empty and unbounded (e.g. \\(x&lt;-1\\)).\n* \\(A_2\\cap B_2\\) is bounded.\n\nThus there are three convex components: two infinite ones and one finite one,\nthe latter being \\(A_2\\cap B_2\\).\n\n---\n\n### 2.  The finite region\n\n\\(A_2\\cap B_2\\) is described by  \n\n\\[\n\\begin{cases}\nx&gt;-1,\\\\\nx&lt;y,\\\\\nx+2y&lt;75 .\n\\end{cases}\n\\]\n\nFrom \\(x+2y&lt;75\\) we have \\(y&lt;(75-x)/2\\).  \nTogether with \\(y&gt;x\\) we obtain\n\n\\[\n-1&lt;x&lt;25,\\qquad x&lt;y&lt;\\frac{75-x}{2}.\n\\]\n\nThe three bounding lines intersect at\n\n\\[\n\\begin{aligned}\nx=-1 \\ \\text{and}\\ y=x&amp;\\;&amp;\\Rightarrow\\;(-1,-1),\\\\\nx=-1 \\ \\text{and}\\ x+2y=75&amp;\\;&amp;\\Rightarrow\\;(-1,38),\\\\\ny=x \\ \\text{and}\\ x+2y=75&amp;\\;&amp;\\Rightarrow\\;(25,25).\n\\end{aligned}\n\\]\n\nHence the finite region is the interior of the triangle with vertices  \n\\((-1,-1),\\;(-1,38),\\;(25,25)\\).\n\nIts area in the \\(xy\\)-plane is\n\n\\[\n\\text{Area}_{xy}\n=\\frac12\\cdot\\text{base}\\cdot\\text{height}\n=\\frac12\\cdot 39\\cdot 26 =507 .\n\\]\n\n---\n\n### 3.  Area on the plane \\(x+y+z=75\\)\n\nThe map \\((x,y)\\mapsto (x,y,75-x-y)\\) sends the \\(xy\\)-plane onto the given\nplane.  The area is scaled by the factor\n\n\\[\n\\bigl|\\partial_{x}(x,y,z)\\times\\partial_{y}(x,y,z)\\bigr|\n=|(1,0,-1)\\times(0,1,-1)|\n=|(1,1,1)|\n=\\sqrt{3}.\n\\]\n\nThus the area of the finite region on the plane is\n\n\\[\n\\text{Area}= \\sqrt{3}\\times 507 = 507\\sqrt{3}.\n\\]\n\n---\n\nThe required form is \\(a\\sqrt{b}\\) with \\(a=507,\\;b=3\\).  Hence\n\n\\[\na+b = 507+3 = 510.\n\\]\n\n\\[\n\\boxed{510}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 510</p>\n<p>Extracted Answer: 510</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThe product $ \\prod_{k=4}^{63} \\frac{\\log_k(5^{k^2-1})}{\\log_{k+1}(5^{k^2-4})} = \\frac{\\log_4(5^{15})}{\\log_5(5^{12})} \\cdot \\frac{\\log_5(5^{24})}{\\log_6(5^{21})} \\cdot \\frac{\\log_6(5^{35})}{\\log_7(5^{32})} \\cdots \\frac{\\log_{63}(5^{3968})}{\\log_{64}(5^{3965})} $ is equal to $ \\frac{m}{n} $, where $ m $ and $ n $ are relatively prime positive integers. Find $ m + n $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>\\[\nP=\\prod_{k=4}^{63}\\frac{\\log_k\\!\\big(5^{\\,k^2-1}\\big)}{\\log_{k+1}\\!\\big(5^{\\,k^2-4}\\big)}\n\\]\n\n---\n\n### 1.  Change of base  \n\n\\[\n\\log_a b=\\frac{\\ln b}{\\ln a}\n\\]\n\nHence  \n\n\\[\n\\begin{aligned}\n\\log_k\\!\\big(5^{k^2-1}\\big)&amp;=\\frac{(k^2-1)\\ln5}{\\ln k},\\\\[2mm]\n\\log_{k+1}\\!\\big(5^{k^2-4}\\big)&amp;=\\frac{(k^2-4)\\ln5}{\\ln(k+1)} .\n\\end{aligned}\n\\]\n\nTherefore each factor of the product is\n\n\\[\n\\frac{(k^2-1)\\ln5/\\ln k}{(k^2-4)\\ln5/\\ln(k+1)}\n= \\frac{k^2-1}{k^2-4}\\cdot\\frac{\\ln(k+1)}{\\ln k}.\n\\]\n\nThus  \n\n\\[\nP=\\Bigg(\\prod_{k=4}^{63}\\frac{k^2-1}{k^2-4}\\Bigg)\n   \\Bigg(\\prod_{k=4}^{63}\\frac{\\ln(k+1)}{\\ln k}\\Bigg).\n\\]\n\n---\n\n### 2.  Telescoping the logarithmic part  \n\n\\[\n\\prod_{k=4}^{63}\\frac{\\ln(k+1)}{\\ln k}\n =\\frac{\\ln5}{\\ln4}\\cdot\\frac{\\ln6}{\\ln5}\\cdots\\frac{\\ln64}{\\ln63}\n =\\frac{\\ln64}{\\ln4}\n =\\log_4 64 = 3 .\n\\]\n\n---\n\n### 3.  Simplify the rational part  \n\n\\[\n\\frac{k^2-1}{k^2-4}\n =\\frac{(k-1)(k+1)}{(k-2)(k+2)}\n =\\frac{k-1}{k-2}\\cdot\\frac{k+1}{k+2}.\n\\]\n\nHence  \n\n\\[\n\\prod_{k=4}^{63}\\frac{k^2-1}{k^2-4}\n =\\Bigg(\\prod_{k=4}^{63}\\frac{k-1}{k-2}\\Bigg)\n  \\Bigg(\\prod_{k=4}^{63}\\frac{k+1}{k+2}\\Bigg).\n\\]\n\n*First product*  \n\n\\[\n\\prod_{k=4}^{63}\\frac{k-1}{k-2}\n =\\frac{3}{2}\\cdot\\frac{4}{3}\\cdot\\frac{5}{4}\\cdots\\frac{62}{61}\n =\\frac{62}{2}=31 .\n\\]\n\n*Second product*  \n\n\\[\n\\prod_{k=4}^{63}\\frac{k+1}{k+2}\n =\\frac{5}{6}\\cdot\\frac{6}{7}\\cdot\\frac{7}{8}\\cdots\\frac{64}{65}\n =\\frac{5}{65}= \\frac{1}{13}.\n\\]\n\nThus the rational part equals  \n\n\\[\n31\\cdot\\frac{1}{13}= \\frac{31}{13}.\n\\]\n\n---\n\n### 4.  Combine the two parts  \n\n\\[\nP=\\frac{31}{13}\\times 3 = \\frac{93}{13}.\n\\]\n\nThe fraction \\(\\frac{93}{13}\\) is already in lowest terms, so  \n\n\\[\nm=93,\\qquad n=13,\\qquad m+n=93+13=106.\n\\]\n\n\\[\n\\boxed{106}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 106</p>\n<p>Extracted Answer: 106</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nFour unit squares form a $2 \\times 2$ grid. Each of the 12 unit line segments forming the sides of the squares is colored either red or blue in such a way that each unit square has 2 red sides and 2 blue sides. Find the number of such colorings.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n* \\(a_{1},a_{2}\\) be the two **vertical** interior unit segments (the left\u2013right dividing line),  \n* \\(b_{1},b_{2}\\) be the two **horizontal** interior unit segments (the bottom\u2013top dividing line).\n\nThe eight outer\u2013boundary unit segments belong to only one square, while each interior segment belongs to two squares.\n\n---\n\n### 1.  Equations for the four unit squares  \n\nDenote by \\(L_1 ,D_1\\) the left and bottom edges of the lower\u2011left square, etc.  \nWriting a red edge as \\(1\\) and a blue edge as \\(0\\), the condition \u201cexactly two red sides\u2019\u2019 for each square gives  \n\n\\[\n\\begin{aligned}\nL_1 + D_1 + a_{1}+ b_{1} &amp;=2,\\\\\nD_2 + R_2 + a_{1}+ b_{2} &amp;=2,\\\\\nL_3 + T_3 + a_{2}+ b_{1} &amp;=2,\\\\\nR_4 + T_4 + a_{2}+ b_{2} &amp;=2,\n\\end{aligned}\n\\]\n\nwhere the eight variables \\(L_1,D_1,D_2,R_2,L_3,T_3,R_4,T_4\\) are the boundary edges and the\nfour variables \\(a_{1},a_{2},b_{1},b_{2}\\) are the interior edges.\n\nFor a fixed choice of the interior edges, each equation tells us the sum of the two\nboundary edges of that square:\n\n\\[\n\\begin{aligned}\nL_1+D_1 &amp;=2-(a_{1}+b_{1}),\\\\\nD_2+R_2 &amp;=2-(a_{1}+b_{2}),\\\\\nL_3+T_3 &amp;=2-(a_{2}+b_{1}),\\\\\nR_4+T_4 &amp;=2-(a_{2}+b_{2}).\n\\end{aligned}\n\\tag{1}\n\\]\n\nThe right\u2011hand side can be \\(0,1,\\) or \\(2\\).  \n\n* If it is \\(0\\) or \\(2\\) there is **exactly one** way to colour the two boundary\nedges (both blue or both red).  \n* If it is \\(1\\) there are **two** ways (one red, one blue).\n\nThus for a given interior assignment the number of completions equals  \n\n\\[\n\\prod_{i=1}^{4}f\\bigl(2-(a_{i}+b_{j})\\bigr),\n\\qquad\nf(0)=f(2)=1,\\;f(1)=2 .\n\\tag{2}\n\\]\n\nThe factor contributed by a square is \\(2\\) precisely when the sum of its two\ninterior edges equals \\(1\\).\n\n---\n\n### 2.  How many squares have interior\u2011sum \\(=1\\)?\n\nLet  \n\n\\[\nA = a_{1}+a_{2}\\quad(\\text{number of red vertical interiors}),\\qquad\nB = b_{1}+b_{2}\\quad(\\text{number of red horizontal interiors}).\n\\]\n\nFor a square the two interior edges are one vertical and one horizontal, so the\nsquare\u2019s interior sum is \\(1\\) exactly when the chosen vertical edge and horizontal\nedge have different colours.  Hence the number of squares with interior\u2011sum \\(=1\\) is  \n\n\\[\nN = A(2-B)+(2-A)B = 2A+2B-2AB.\n\\tag{3}\n\\]\n\nBecause \\(A,B\\in\\{0,1,2\\}\\),\n\n\\[\nN=\n\\begin{cases}\n0 &amp; (A,B)=(0,0)\\text{ or }(2,2),\\\\[2pt]\n2 &amp; \\text{otherwise except the next case},\\\\[2pt]\n4 &amp; (A,B)=(0,2)\\text{ or }(2,0).\n\\end{cases}\n\\]\n\n---\n\n### 3.  Counting all interior assignments  \n\nThe numbers of interior assignments for each \\((A,B)\\) are\n\n\\[\n\\begin{array}{c|c|c}\n(A,B) &amp; \\text{\\# assignments} &amp; N \\\\ \\hline\n(0,0) &amp; 1 &amp; 0\\\\\n(2,2) &amp; 1 &amp; 0\\\\\n(0,2) &amp; 1 &amp; 4\\\\\n(2,0) &amp; 1 &amp; 4\\\\\n(0,1) &amp; 2 &amp; 2\\\\\n(1,0) &amp; 2 &amp; 2\\\\\n(1,1) &amp; 4 &amp; 2\\\\\n(1,2) &amp; 2 &amp; 2\\\\\n(2,1) &amp; 2 &amp; 2\n\\end{array}\n\\]\n\nFor a given interior assignment the number of ways to colour the boundary\nedges is \\(2^{N}\\) (by (2)).  Therefore\n\n\\[\n\\begin{aligned}\n\\#\\text{colorings}&amp;=\n1\\cdot2^{0}+1\\cdot2^{0}\n+1\\cdot2^{4}+1\\cdot2^{4}\n+ (2+2+4+2+2)\\cdot2^{2} \\\\[4pt]\n&amp;=2\\cdot1 + 2\\cdot16 + 12\\cdot4 \\\\[4pt]\n&amp;=2 + 32 + 48 \\\\[4pt]\n&amp;=82 .\n\\end{aligned}\n\\]\n\n---\n\n\\[\n\\boxed{82}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 82</p>\n<p>Extracted Answer: 82</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nCircle $\\omega_1$ with radius 6 centered at point $A$ is internally tangent at point $B$ to circle $\\omega_2$ with radius 15. Points $C$ and $D$ lie on $\\omega_2$ such that $\\overline{BC}$ is a diameter of $\\omega_2$ and $\\overline{BC} \\perp \\overline{AD}$. The rectangle $EFGH$ is inscribed in $\\omega_1$ such that $\\overline{EF} \\perp \\overline{BC}$, $C$ is closer to $\\overline{GH}$ than to $\\overline{EF}$, and $D$ is closer to $\\overline{FG}$ than to $\\overline{EH}$, as shown. Triangles $\\triangle DGF$ and $\\triangle CHG$ have equal areas. The area of rectangle $EFGH$ is $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m + n$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n* \\(O\\) be the centre of \\(\\omega _2\\) (radius \\(15\\)),\n* \\(A\\) the centre of \\(\\omega _1\\) (radius \\(6\\)),\n* \\(B\\) the internal point of tangency of the two circles.\n\nPlace the picture on a coordinate plane.\n\n---\n\n### 1.  Coordinates of the given points  \n\nTake \\(O=(0,0)\\).  \nSince \\(OA=15-6=9\\) and the circles are tangent internally, we may put  \n\n\\[\nA=(9,0), \\qquad B=(15,0).\n\\]\n\n\\(BC\\) is a diameter of \\(\\omega _2\\) through \\(B\\); hence  \n\n\\[\nC=(-15,0).\n\\]\n\n\\(AD\\perp BC\\) forces \\(AD\\) to be the vertical line through \\(A\\); intersecting this line with\n\\(\\omega _2\\) gives  \n\n\\[\nD=(9,-12)\\quad\\text{or}\\quad (9,12).\n\\]\n\nThe condition \u201c\\(D\\) is closer to \\(\\overline{FG}\\) than to \\(\\overline{EH}\\)\u201d (see below) makes\n\\(D=(9,-12)\\).\n\n---\n\n### 2.  The rectangle \\(EFGH\\)\n\n\\(EFGH\\) is inscribed in the circle \\(\\omega_1\\), so its vertices lie on  \n\n\\[\n(x-9)^2+y^2=6^2=36 .\n\\]\n\nSince \\(\\overline{EF}\\perp BC\\) and \\(BC\\) is horizontal, \\(\\overline{EF}\\) is vertical.\nLet  \n\n\\[\n\\begin{aligned}\nE&amp;=(9+w,\\,h),\\\\\nF&amp;=(9+w,\\,-h),\\\\\nG&amp;=(9-w,\\,-h),\\\\\nH&amp;=(9-w,\\,h),\n\\end{aligned}\n\\]\n\nwhere \\(w&gt;0,\\,h&gt;0\\) are the half\u2011width and half\u2011height of the rectangle.\n\nAll four vertices satisfy the circle equation, giving the single relation  \n\n\\[\nw^{2}+h^{2}=36\\tag{1}\n\\]\n\n(the rectangle\u2019s centre is the circle\u2019s centre \\(A\\)).\n\nBecause the point \\(C=(-15,0)\\) is farther to the right than to the left,\nthe condition \u201c\\(C\\) is closer to \\(\\overline{GH}\\) than to \\(\\overline{EF}\\)\u2019\u2019 forces\n\\(\\overline{GH}\\) to be the **left** side (\\(x=9-w\\)), which is already the case.\n\nSince \\(D=(9,-12)\\) lies below the centre, \u201c\\(D\\) is closer to \\(\\overline{FG}\\) than to \\(\\overline{EH}\\)\u2019\u2019 forces\n\\(\\overline{FG}\\) to be the **bottom** side (\\(y=-h\\)).  This orientation matches the above labeling.\n\n---\n\n### 3.  Areas of the two triangles  \n\n*Triangle \\(DGF\\)*  \n\nThe points are \\(D(9,-12),\\; G(9-w,-h),\\; F(9+w,-h)\\).\nIts base \\(GF\\) has length \\(2w\\) and its height (vertical distance from \\(D\\) to the base) is \\(12-h\\).  \nHence  \n\n\\[\n[\\,DGF\\,]=\\tfrac12\\,(2w)(12-h)=w(12-h).\\tag{2}\n\\]\n\n*Triangle \\(CHG\\)*  \n\nThe points are \\(C(-15,0),\\; H(9-w,h),\\; G(9-w,-h)\\).\nIts base \\(HG\\) has length \\(2h\\) and its horizontal distance from \\(C\\) to the line \\(x=9-w\\) is\n\\(|-15-(9-w)|=24-w\\).  \nThus  \n\n\\[\n[\\,CHG\\,]=\\tfrac12\\,(2h)(24-w)=h(24-w).\\tag{3}\n\\]\n\nThe problem states the two areas are equal, so\n\n\\[\nw(12-h)=h(24-w).\\tag{4}\n\\]\n\nExpanding gives \\(12w-wh=24h-wh\\), whence  \n\n\\[\n12w=24h \\qquad\\Longrightarrow\\qquad w=2h.\\tag{5}\n\\]\n\n---\n\n### 4.  Solving for \\(w\\) and \\(h\\)\n\nSubstituting \\(w=2h\\) into (1):\n\n\\[\n(2h)^2+h^2=36 \\;\\Longrightarrow\\;5h^{2}=36 \\;\\Longrightarrow\\;\nh=\\frac{6}{\\sqrt5}=\\frac{6\\sqrt5}{5}.\n\\]\n\nHence  \n\n\\[\nw=2h=\\frac{12}{\\sqrt5}=\\frac{12\\sqrt5}{5}.\n\\]\n\n---\n\n### 5.  Area of the rectangle  \n\nThe side lengths are \\(2w\\) and \\(2h\\).  Therefore  \n\n\\[\n\\text{Area}= (2w)(2h)=4wh.\n\\]\n\nUsing \\(w=2h\\),\n\n\\[\n4wh = 4(2h)h = 8h^{2}=8\\left(\\frac{36}{5}\\right)=\\frac{288}{5}.\n\\]\n\nThus the area is \\(\\displaystyle\\frac{288}{5}\\); the numerator and denominator are coprime.\n\n\\[\nm=288,\\qquad n=5,\\qquad m+n=288+5=293.\n\\]\n\n\\[\n\\boxed{293}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 293</p>\n<p>Extracted Answer: 293</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $ A $ be the set of positive integer divisors of 2025. Let $ B $ be a randomly selected subset of $ A $. The probability that $ B $ is a nonempty set with the property that the least common multiple of its elements is 2025 is $ \\frac{m}{n} $, where $ m $ and $ n $ are relatively prime positive integers. Find $ m + n $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>The divisors of \\(2025\\) are all numbers of the form  \n\n\\[\n3^{a}5^{b},\\qquad 0\\le a\\le 4,\\;0\\le b\\le 2 .\n\\]\n\nHence  \n\n\\[\n|A|=(4+1)(2+1)=15 .\n\\]\n\nSo there are \\(2^{15}\\) subsets of \\(A\\) (including the empty set).\n\n--------------------------------------------------------------------\n### When does a subset have lcm \\(2025\\)?\n\nThe prime factorisation of \\(2025\\) is  \n\n\\[\n2025 = 3^{4}\\,5^{2}.\n\\]\n\nFor a subset \\(B\\subseteq A\\),\n\n\\[\n\\operatorname{lcm}(B)=3^{\\max a_i}\\,5^{\\max b_i},\n\\]\n\nwhere \\((a_i,b_i)\\) are the exponents of the elements of \\(B\\).\nThus \\(\\operatorname{lcm}(B)=2025\\) iff  \n\n* at least one element has exponent \\(a=4\\) (i.e. contains \\(3^4\\));\n* at least one element has exponent \\(b=2\\) (i.e. contains \\(5^2\\)).\n\n--------------------------------------------------------------------\n### Sets that provide the required exponents  \n\n\\[\nA_4=\\{d\\in A:3^4\\mid d\\}=\\{3^4\\! \\cdot\\! 5^0,\\;3^4\\! \\cdot\\!5^1,\\;3^4\\! \\cdot\\!5^2\\}\n\\]\nhas \\(|A_4|=3\\) elements.\n\n\\[\nB_2=\\{d\\in A:5^2\\mid d\\}=\\{3^0\\! \\cdot\\!5^2,\\;3^1\\! \\cdot\\!5^2,\\;3^2\\! \\cdot\\!5^2,\n\\;3^3\\! \\cdot\\!5^2,\\;3^4\\! \\cdot\\!5^2\\}\n\\]\nhas \\(|B_2|=5\\) elements.\n\nTheir intersection is the single divisor \\(2025=3^4\\! \\cdot\\!5^2\\).\n\n--------------------------------------------------------------------\n### Counting the suitable subsets  \n\nA subset \\(B\\) works iff it contains **at least one** element of \\(A_4\\) **and** at least one element of \\(B_2\\).\n\nUsing inclusion\u2013exclusion on the \\(2^{15}\\) total subsets:\n\n\\[\n\\begin{aligned}\nN &amp;= 2^{15}\n     -\\underbrace{2^{15-3}}_{\\text{subsets missing }A_4}\n     -\\underbrace{2^{15-5}}_{\\text{subsets missing }B_2}\n     +\\underbrace{2^{15-7}}_{\\text{subsets missing both}} \\\\[4pt]\n  &amp;= 2^{15}-2^{12}-2^{10}+2^{8}\\\\\n  &amp;= 32768-4096-1024+256\\\\\n  &amp;= 27904 .\n\\end{aligned}\n\\]\n\nThus the desired probability is  \n\n\\[\n\\frac{N}{2^{15}}=\\frac{27904}{32768}\n          =\\frac{109}{128}\\qquad(\\text{after cancelling }256).\n\\]\n\n--------------------------------------------------------------------\n### Answer  \n\n\\(m=109,\\;n=128\\), so  \n\n\\[\nm+n=109+128=237 .\n\\]\n\n\\[\n\\boxed{237}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 237</p>\n<p>Extracted Answer: 237</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nAlex divides a disk into four quadrants with two perpendicular diameters intersecting at the center of the disk. He draws 25 more line segments through the disk, drawing each segment by selecting two points at random on the perimeter of the disk in different quadrants and connecting those two points. Find the expected number of regions into which these 27 line segments divide the disk.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>**Step 1 \u2013  What we have to count**\n\nThe two perpendicular diameters are two line segments that intersect once, so after they are drawn the disk is divided into  \n\n\\[\nF_0=4\\qquad\\text{regions}.\n\\]\n\nEvery time we draw a new segment, it splits each region it meets into two pieces.  \nIf the new segment meets \\(k\\) already\u2011drawn segments in interior points, it creates \\(k+1\\) new regions.  \n\nHence  \n\n\\[\n\\boxed{\\text{# of regions}=1+\\#\\text{segments}+ \\#\\text{intersection points}}\n\\tag{1}\n\\]\n\n(the \u201c\\(1\\)\u201d is the original whole disk).  \nWe have \\(27\\) segments in total (the 2 diameters + the 25 random chords).  \nThus we only have to find the **expected number of intersection points**.\n\n--------------------------------------------------------------------\n\n**Step 2 \u2013  Intersections with the two diameters**\n\nFor a random chord we must choose its two endpoints in *different* quadrants.\nThe unordered pair of quadrants is equally likely among the  \n\n\\[\n\\binom{4}{2}=6\n\\]\n\npossibilities.  \n\n* Adjacent quadrants (four choices) \u2013 the chord meets **one** diameter.  \n* Opposite quadrants (two choices) \u2013 the chord meets **both** diameters.\n\nTherefore for one random chord  \n\n\\[\nE[\\text{diameters met}]\n=\\frac{4}{6}\\cdot1+\\frac{2}{6}\\cdot2=\\frac{4}{3}.\n\\]\n\nWith \\(N=25\\) random chords\n\n\\[\nE[\\text{intersections with the two diameters}]\n=N\\cdot\\frac{4}{3}= \\frac{100}{3}.\n\\tag{2}\n\\]\n\n--------------------------------------------------------------------\n\n**Step 3 \u2013  Intersection of two random chords**\n\nLet a chord be drawn.  \nWrite its endpoints as angles measured from the positive \\(x\\)\u2013axis.\nBecause the two endpoints are in different quadrants, the unordered pair of\nquadrants is uniform among the six possibilities.\n\n*Probability that a second random chord meets the first.*\n\nLet the first chord be fixed.  \nDenote by \\(I\\) the clockwise arc of the circle from its first endpoint to its\nsecond endpoint; let \\(|I|=L\\).\nIf a second chord has one endpoint in \\(I\\) and the other outside \\(I\\) the two\nchords intersect.  \n\nWhen the second chord is chosen, its first endpoint \\(U\\) is uniform on the whole\ncircle, and its second endpoint \\(V\\) is uniform on the *three* quadrants that are\ndifferent from the quadrant of \\(U\\).  \nA short calculation (integrating over the position of \\(U\\) inside \\(I\\))\ngives for a fixed chord\n\n\\[\n\\boxed{q=\\frac{L}{\\pi}-\\frac{2L^{2}}{3\\pi^{2}}\n      +\\frac{2}{3\\pi^{2}}\\!\\int_{I}\\!|I\\cap Q(\\theta)|\\,d\\theta},\n\\tag{3}\n\\]\nwhere \\(Q(\\theta)\\) is the quadrant containing \\(\\theta\\).\n\nNow we average (3) over the possible positions of the first chord.\n\n*Adjac\u00adent quadrants.*  \nThe arc \\(I\\) lies in exactly two quadrants; write its lengths in those\nquadrants as \\(L_{1},L_{2}\\) (\\(L=L_{1}+L_{2}\\)).  \nThen \\(\\int_{I}|I\\cap Q|\\,d\\theta = L_{1}^{2}+L_{2}^{2}\\).\nWith \\(L_{1},L_{2}\\) independent and uniform on \\([0,\\pi/2]\\),\n\n\\[\nE[q\\mid\\text{adjacent}] = \\frac{5}{12}.\n\\]\n\n*Opposite quadrants.*  \nNow \\(I\\) occupies three quadrants; let the lengths in the three\nquadrants be \\(u,\\,\\pi/2,\\,v\\) (\\(u,v\\) independent uniform on \\([0,\\pi/2]\\)).  \nThen \\(\\int_{I}|I\\cap Q|\\,d\\theta = u^{2}+(\\pi/2)^{2}+v^{2}\\).\nAveraging gives\n\n\\[\nE[q\\mid\\text{opposite}] = \\frac{7}{12}.\n\\]\n\nThe first chord is adjacent with probability \\(\\frac{2}{3}\\) and opposite with\nprobability \\(\\frac13\\).  Hence the probability that two independently drawn\nrandom chords intersect is\n\n\\[\np=\\frac{2}{3}\\cdot\\frac{5}{12}+\\frac{1}{3}\\cdot\\frac{7}{12}\n    =\\frac{17}{36}.\n\\tag{4}\n\\]\n\n--------------------------------------------------------------------\n\n**Step 4 \u2013  Expected intersections among the 25 random chords**\n\nThere are \\(\\binom{25}{2}=300\\) unordered pairs of random chords, each\nintersecting with probability \\(p\\).  Thus\n\n\\[\nE[\\text{intersections among the 25 chords}]\n=300\\cdot\\frac{17}{36}= \\frac{425}{3}.\n\\tag{5}\n\\]\n\n--------------------------------------------------------------------\n\n**Step 5 \u2013  Total expected number of intersection points**\n\nAdd all contributions:\n\n* one intersection of the two diameters,\n* intersections of random chords with the two diameters \\(\\displaystyle\\frac{100}{3}\\)   (from (2)),\n* intersections among the random chords \\(\\displaystyle\\frac{425}{3}\\)   (from (5)).\n\n\\[\nE[\\text{total intersections}]\n=1+\\frac{100}{3}+\\frac{425}{3}=1+\\frac{525}{3}=176.\n\\tag{6}\n\\]\n\n--------------------------------------------------------------------\n\n**Step 6 \u2013  Expected number of regions**\n\nInsert (6) into formula (1):\n\n\\[\nE[\\text{regions}]\n=1+\\underbrace{27}_{\\text{segments}}+\\underbrace{176}_{\\text{intersection points}}\n=204 .\n\\]\n\n--------------------------------------------------------------------\n\n\\[\n\\boxed{204}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 204</p>\n<p>Extracted Answer: 204</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThere are $ n $ values of $ x $ in the interval $ 0 &lt; x &lt; 2\\pi $ where $ f(x) = \\sin(7\\pi \\cdot \\sin(5x)) = 0 $. For $ t $ of these $ n $ values of $ x $, the graph of $ y = f(x) $ is tangent to the $ x $-axis. Find $ n + t $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>The zeros of  \n\n\\[\nf(x)=\\sin\\bigl(7\\pi\\sin(5x)\\bigr)\n\\]\n\nsatisfy  \n\n\\[\n\\sin\\bigl(7\\pi\\sin(5x)\\bigr)=0\\Longrightarrow 7\\pi\\sin(5x)=k\\pi,\\qquad k\\in\\mathbb Z .\n\\]\n\nHence  \n\n\\[\n\\sin (5x)=\\frac{k}{7},\\qquad -7\\le k\\le 7 .\n\\]\n\n---\n\n### 1.  Counting all zeros \\(n\\)\n\nPut \\(\\theta =5x\\).  \nBecause \\(0&lt;x&lt;2\\pi\\), we have \\(0&lt;\\theta&lt;10\\pi\\).\n\nFor each integer \\(k\\) we count the solutions of \\(\\sin\\theta = k/7\\) in \\((0,10\\pi)\\).\n\n* **\\(k=\\pm7\\) :** \\(\\sin\\theta=\\pm1\\).  \n  Solutions are \\(\\theta =\\frac{\\pi}{2}+2\\pi m\\) (or \\(\\frac{3\\pi}{2}+2\\pi m\\)).  \n  In a length \\(10\\pi\\) there are \\(5\\) such values for each sign.  \n  \u2192 \\(5+5=10\\) solutions.\n\n* **\\(k=0\\) :** \\(\\sin\\theta=0\\).  \n  Solutions are \\(\\theta=n\\pi\\).  \n  With \\(0&lt;\\theta&lt;10\\pi\\) we have \\(n=1,2,\\dots ,9\\): \\(9\\) solutions.\n\n* **\\(k=\\pm1,\\pm2,\\ldots,\\pm6\\) (12 values):** \\(\\sin\\theta = k/7\\) is a non\u2011extreme value.  \n  In each full period of length \\(2\\pi\\) there are \\(2\\) solutions; we have five periods, so each such \\(k\\) yields \\(10\\) solutions.  \n  \u2192 \\(12\\cdot10=120\\) solutions.\n\nHence  \n\n\\[\nn = 10\\;(\\text{from }k=\\pm7)+9\\;(\\text{from }k=0)+120\\;(\\text{from }k=\\pm1,\\dots,\\pm6)=139 .\n\\]\n\n---\n\n### 2.  Tangential zeros \\(t\\)\n\nThe derivative is  \n\n\\[\nf&#39;(x)=\\cos\\bigl(7\\pi\\sin(5x)\\bigr)\\cdot 7\\pi\\cdot5\\cos(5x)\n      =35\\pi\\cos\\bigl(7\\pi\\sin(5x)\\bigr)\\cos(5x).\n\\]\n\nAt a zero of \\(f\\) we have \\(\\sin(5x)=k/7\\) and thus  \n\\(\\cos(7\\pi\\sin(5x))=\\cos(k\\pi)=(-1)^{k}\\).\n\nTherefore  \n\n\\[\nf&#39;(x)=35\\pi(-1)^{k}\\cos(5x).\n\\]\n\nFor the graph to be tangent to the \\(x\\)-axis we need \\(f&#39;(x)=0\\); this occurs exactly when  \n\n\\[\n\\cos(5x)=0 \\quad\\Longleftrightarrow\\quad \\sin(5x)=\\pm1.\n\\]\n\nThus the tangential zeros correspond to the case \\(k=\\pm7\\).  \nWe already counted those: \\(5\\) solutions for \\(k=7\\) and \\(5\\) for \\(k=-7\\).\n\n\\[\nt = 5+5 = 10.\n\\]\n\n---\n\n### 3.  Required sum\n\n\\[\nn+t = 139+10 = 149.\n\\]\n\n\\[\n\\boxed{149}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 149</p>\n<p>Extracted Answer: 149</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nSixteen chairs are arranged in a row. Eight people each select a chair in which to sit so that no person sits next to two other people. Let $ N $ be the number of subsets of 16 chairs that could be selected. Find the remainder when $ N $ is divided by 1000.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let the chairs be numbered \\(1,2,\\dots ,16\\).\nChoosing the chairs for the eight people is equivalent to writing a binary\nstring of length \\(16\\) with exactly eight \\(1\\)\u2019s (occupied chairs) and\nseven \\(0\\)\u2019s (empty chairs).\n\nThe condition *\u201cno person sits next to two other people\u2019\u2019* means that no\noccupied chair can have occupied neighbours on both sides; thus the binary\nstring must contain **no substring \\(111\\)**.  \nHence we must count binary strings of length \\(16\\) with weight \\(8\\) that avoid\n\\(111\\).\n\n---\n\n### 1.  Describing the strings\n\nThe \\(1\\)\u2019s can appear only in blocks of length \\(1\\) or \\(2\\) (a block of\nlength \\(3\\) would give a forbidden \\(111\\)).  \nSuppose there are  \n\n* \\(s\\) blocks of length \\(2\\);\n* \\(t-s\\) blocks of length \\(1\\),\n\nso the total number of blocks of \\(1\\)\u2019s is \\(t\\).  \nIf each block of length \\(2\\) contributes \\(2\\) and each block of length\n\\(1\\) contributes \\(1\\), then  \n\n\\[\n2s+(t-s)=8\\qquad\\Longrightarrow\\qquad t=8-s .\n\\]\n\nThus \\(s\\) can be \\(0,1,2,3,4\\) (since at most \\(\\lfloor 8/2\\rfloor =4\\) blocks\nof length \\(2\\) are possible).\n\nFor a given \\(s\\) the blocks are ordered, and we must choose which \\(s\\) of\nthe \\(t\\) blocks are the length\u2011\\(2\\) blocks:\n\n\\[\n\\text{choices for block sizes}= \\binom{t}{s}= \\binom{8-s}{s}.\n\\]\n\n---\n\n### 2.  Placing the zeros\n\nBetween two consecutive blocks of \\(1\\)\u2019s there must be at least one\n\\(0\\).  With \\(t\\) blocks there are \\(t-1\\) mandatory zeros.\nThere are \\(8\\) zeros in total (since \\(16-8=8\\)).  \nHence the number of *extra* zeros we may distribute is  \n\n\\[\n8-(t-1)=9-t .\n\\]\n\nThese extra zeros can be placed in any of the \\(t+1\\) gaps\n(before the first block, between blocks, after the last block).  \nBy stars and bars the number of distributions is\n\n\\[\n\\binom{(9-t)+(t+1)-1}{(t+1)-1}\n   =\\binom{9}{t}\n   =\\binom{9}{8-s}.\n\\]\n\n---\n\n### 3.  Total number of admissible subsets\n\nSumming over all possible \\(s\\):\n\n\\[\n\\begin{aligned}\nN &amp;=\\sum_{s=0}^{4}\n    \\binom{8-s}{s}\\binom{9}{8-s}  \\\\\n  &amp;=\\binom{8}{0}\\binom{9}{8}\n   +\\binom{7}{1}\\binom{9}{7}\n   +\\binom{6}{2}\\binom{9}{6}\n   +\\binom{5}{3}\\binom{9}{5}\n   +\\binom{4}{4}\\binom{9}{4}   \\\\\n  &amp;=1\\cdot 9\n   +7\\cdot 36\n   +15\\cdot 84\n   +10\\cdot 126\n   +1\\cdot 126 \\\\\n  &amp;=9+252+1260+1260+126 \\\\\n  &amp;=2907 .\n\\end{aligned}\n\\]\n\nThus there are \\(N=2907\\) subsets of chairs that satisfy the condition.\n\n---\n\n### 4.  Remainder modulo \\(1000\\)\n\n\\[\n2907 \\equiv 907 \\pmod{1000}.\n\\]\n\n\\[\n\\boxed{907}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 907</p>\n<p>Extracted Answer: 907</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nSuppose $ \\triangle ABC $ has angles $ \\angle BAC = 84^\\circ $, $ \\angle ABC = 60^\\circ $, and $ \\angle ACB = 36^\\circ $. Let $ D, E, $ and $ F $ be the midpoints of sides $ \\overline{BC} $, $ \\overline{AC} $, and $ \\overline{AB} $, respectively. The circumcircle of $ \\triangle DEF $ intersects $ \\overline{BD} $, $ \\overline{AE} $, and $ \\overline{AF} $ at points $ G, H, $ and $ J $, respectively. The points $ G, D, E, H, J, $ and $ F $ divide the circumcircle of $ \\triangle DEF $ into six minor arcs, as shown. Find $ \\widehat{DE} + 2 \\cdot \\widehat{HJ} + 3 \\cdot \\widehat{FG} $, where the arcs are measured in degrees.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n\\[\nA=84^\\circ ,\\qquad B=60^\\circ ,\\qquad C=36^\\circ .\n\\]\n\nDenote by \\(O\\) the circumcenter of \\(\\triangle ABC\\) and by \\(N\\) the nine\u2011point\ncenter (the circumcenter of \\(\\triangle DEF\\)).\nPut the circumcircle of \\(\\triangle ABC\\) on the unit circle and let  \n\n\\[\na=1,\\qquad \nb=e^{i\\beta },\\qquad \nc=e^{i\\gamma},\n\\]\n\nwhere the central arcs satisfy  \n\n\\[\n\\widehat{AB}=2C=72^\\circ ,\\qquad \n\\widehat{BC}=2A=168^\\circ ,\\qquad \n\\widehat{CA}=2B=120^\\circ .\n\\]\n\nHence  \n\n\\[\n\\beta =72^\\circ ,\\qquad \\gamma =\\beta +168^\\circ =240^\\circ .\n\\]\n\n--------------------------------------------------------------------\n### 1.  The nine\u2011point centre and the midpoints  \n\n\\[\nN=\\frac{a+b+c}{2},\\qquad \nD=\\frac{b+c}{2},\\;E=\\frac{c+a}{2},\\;F=\\frac{a+b}{2}.\n\\]\n\nFrom these formulas  \n\n\\[\nND=-\\frac a2,\\qquad NE=-\\frac b2,\\qquad NF=-\\frac c2 .\\tag{1}\n\\]\n\nThus the directions of the radii to the midpoints are opposite the\ndirections of the vertices:\n\n\\[\n\\arg(ND)=\\alpha+180^\\circ ,\\quad \n\\arg(NE)=\\beta+180^\\circ ,\\quad \n\\arg(NF)=\\gamma+180^\\circ .\n\\]\n\nConsequently  \n\n\\[\n\\widehat{DE}=|\\arg(NE)-\\arg(ND)|\n      =( \\beta+180^\\circ)-( \\alpha+180^\\circ)=\\beta-\\alpha\n      =2C=72^\\circ .\\tag{2}\n\\]\n\n--------------------------------------------------------------------\n### 2.  The second intersections  \n\nFor a chord whose one endpoint is known, the second endpoint is obtained\nby reflecting the known radius about the line through \\(N\\) that is\nperpendicular to the given line.\n\n*Line \\(BD\\).*  \nThe direction of \\(BD\\) is \\(\\arg(c-b)\\).  \nSince the perpendicular through \\(N\\) makes the angle \\(\\arg(c-b)+90^\\circ\\),\nreflecting \\(ND\\) in this line gives\n\n\\[\n\\arg(NG)=2\\bigl(\\arg(c-b)+90^\\circ\\bigr)-\\arg(ND)\n        =2\\arg(c-b)-\\arg(a).            \\tag{3}\n\\]\n\nUsing the identity  \n\n\\[\n\\arg(c-b)=\\frac{\\beta+\\gamma}{2}+90^\\circ,\n\\]\n\nwe obtain  \n\n\\[\n\\arg(NG)=2\\Bigl(\\frac{72^\\circ+240^\\circ}{2}+90^\\circ\\Bigr)\n        =492^\\circ\\equiv132^\\circ .\n\\]\n\nBecause \\(\\arg(NF)=\\gamma+180^\\circ=60^\\circ\\),\n\n\\[\n\\widehat{FG}=|\\arg(NG)-\\arg(NF)|=132^\\circ-60^\\circ=72^\\circ .\\tag{4}\n\\]\n\n*Line \\(AF\\) (the side \\(AB\\)).*  \nThe direction of \\(AB\\) is \\(\\arg(b-a)\\); hence\n\n\\[\n\\arg(NJ)=2\\arg(b-a)-\\arg(c).                \\tag{5}\n\\]\n\nNow  \n\n\\[\n\\arg(b-a)=\\frac{\\alpha+\\beta}{2}+90^\\circ=126^\\circ,\n\\]\n\nso  \n\n\\[\n\\arg(NJ)=2\\cdot126^\\circ-240^\\circ=12^\\circ .\\tag{6}\n\\]\n\n*Line \\(AE\\) (the median from \\(A\\)).*  \nThe direction of \\(AE\\) is \\(\\arg(c-a)\\); thus\n\n\\[\n\\arg(NH)=2\\arg(c-a)-\\arg(b).                \\tag{7}\n\\]\n\nHere  \n\n\\[\n\\arg(c-a)=\\frac{\\alpha+\\gamma}{2}+90^\\circ=210^\\circ ,\n\\]\n\nhence  \n\n\\[\n\\arg(NH)=2\\cdot210^\\circ-72^\\circ=348^\\circ\\equiv-12^\\circ .\\tag{8}\n\\]\n\nTherefore  \n\n\\[\n\\widehat{HJ}=|\\arg(NJ)-\\arg(NH)|\n            =12^\\circ-(-12^\\circ)=24^\\circ .\\tag{9}\n\\]\n\n--------------------------------------------------------------------\n### 3.  Required sum  \n\nFrom (2), (4) and (9),\n\n\\[\n\\widehat{DE}=72^\\circ ,\\qquad \n\\widehat{HJ}=24^\\circ ,\\qquad \n\\widehat{FG}=72^\\circ .\n\\]\n\nHence  \n\n\\[\n\\widehat{DE}+2\\widehat{HJ}+3\\widehat{FG}\n=72^\\circ+2\\cdot24^\\circ+3\\cdot72^\\circ\n=72+48+216\n=336^\\circ .\n\\]\n\n\\[\n\\boxed{336}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 336</p>\n<p>Extracted Answer: 336</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $N$ denote the number of ordered triples of positive integers $(a,b,c)$ such that $a,b,c\\leq3^6$ and $a^3+b^3+c^3$ is a multiple of $3^7$. Find the remainder when $N$ is divided by $1000$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>\\[\n\\boxed{733}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 735</p>\n<p>Extracted Answer: 733</p>\n<p>Score: 0.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $ A_1A_2 \\ldots A_{11} $ be an 11-sided non-convex simple polygon with the following properties:\n* The area of $ A_iA_1A_{i+1} $ is 1 for each $ 2 \\leq i \\leq 10 $,\n* $ \\cos(\\angle A_iA_1A_{i+1}) = \\frac{12}{13} $ for each $ 2 \\leq i \\leq 10 $,\n* The perimeter of $ A_1A_2 \\ldots A_{11} $ is 20.\nIf $ A_1A_2 + A_1A_{11} $ can be expressed as $ \\frac{m\\sqrt{n} - p}{q} $ for positive integers $ m, n, p, q $ with $ n $ squarefree and no prime divides all of $ m, p, q$, find $ m + n + p + q $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n\\[\nr_i=A_1A_i\\qquad (i=2,\\dots ,11),\\qquad \n\\theta=\\angle A_iA_1A_{i+1}\\;(2\\le i\\le 10),\\qquad \n\\cos\\theta=\\frac{12}{13}.\n\\]\n\n---\n\n### 1.  Relation between the radii  \n\nThe area of \\(\\triangle A_iA_1A_{i+1}\\) is  \n\n\\[\n1=\\frac12 r_i r_{i+1}\\sin\\theta .\n\\]\n\nSince  \n\n\\[\n\\sin\\theta =\\sqrt{1-\\cos^2\\theta}= \\sqrt{1-\\left(\\frac{12}{13}\\right)^2}= \\frac{5}{13},\n\\]\n\nwe obtain  \n\n\\[\nr_i r_{i+1}= \\frac{2\\cdot13}{5}= \\frac{26}{5}\\;(=C).\n\\tag{1}\n\\]\n\nThus for every \\(i\\),\n\n\\[\nr_{i+1}= \\frac{C}{r_i},\\qquad C=\\frac{26}{5}.\n\\]\n\nConsequently the sequence alternates:\n\n\\[\nr_2=r_4=r_6=r_8=r_{10}=x,\\qquad\nr_3=r_5=r_7=r_9=r_{11}= \\frac{C}{x},\n\\]\n\nfor some positive number \\(x\\).\n\n---\n\n### 2.  Length of the side \\(A_iA_{i+1}\\)\n\nUsing the law of cosines in \\(\\triangle A_iA_1A_{i+1}\\),\n\n\\[\nA_iA_{i+1}^{2}=r_i^{2}+r_{i+1}^{2}-2r_i r_{i+1}\\cos\\theta .\n\\]\n\nBecause \\(r_i r_{i+1}=C\\) and \\(\\cos\\theta=\\frac{12}{13}\\),\n\n\\[\nA_iA_{i+1}^{2}=r_i^{2}+r_{i+1}^{2}\n          -2C\\cdot\\frac{12}{13}\n          =r_i^{2}+r_{i+1}^{2}-\\frac{48}{5}.\n\\]\n\nNow  \n\n\\[\nr_i^{2}+r_{i+1}^{2}\n   =(r_i+r_{i+1})^{2}-2r_i r_{i+1}\n   =(r_i+r_{i+1})^{2}-2C .\n\\]\n\nHence\n\n\\[\nA_iA_{i+1}^{2}= (r_i+r_{i+1})^{2}-2C-\\frac{48}{5}\n               =(r_i+r_{i+1})^{2}-20 .\n\\tag{2}\n\\]\n\nFor any consecutive pair \\((i,i+1)\\) we have  \n\n\\[\nr_i+r_{i+1}=x+\\frac{C}{x}\\;=:t .\n\\]\n\nThus every side \\(A_iA_{i+1}\\;(i=2,\\dots ,10)\\) has the same length  \n\n\\[\ns=\\sqrt{t^{2}-20}.\n\\tag{3}\n\\]\n\n---\n\n### 3.  Perimeter condition  \n\nThe perimeter of the 11\u2011gon is  \n\n\\[\n\\underbrace{A_1A_2}_{=x}\n+\\underbrace{A_{11}A_1}_{=C/x}\n+9s =t+9\\sqrt{t^{2}-20}=20 .\n\\tag{4}\n\\]\n\nSet \\(\\displaystyle u=\\sqrt{t^{2}-20}\\).  \nFrom (4) we have \\(u=\\dfrac{20-t}{9}\\).  Squaring gives\n\n\\[\nt^{2}-20=\\frac{(20-t)^{2}}{81}.\n\\]\n\nMultiplying by 81 and simplifying,\n\n\\[\n80t^{2}+40t-2020=0\\quad\\Longrightarrow\\quad\n4t^{2}+2t-101=0.\n\\]\n\nSolving,\n\n\\[\nt=\\frac{-2+\\sqrt{4+1616}}{8}\n  =\\frac{-2+18\\sqrt5}{8}\n  =\\frac{9\\sqrt5-1}{4}.\n\\]\n\nSince \\(t=x+C/x=A_1A_2+A_1A_{11}\\) is a sum of positive lengths,\nthe positive root is the only admissible one.\n\n---\n\n### 4.  Result  \n\n\\[\nA_1A_2+A_1A_{11}= \\frac{9\\sqrt5-1}{4}\n                 =\\frac{m\\sqrt n-p}{q},\n\\]\n\nwhere \\(m=9,\\;n=5,\\;p=1,\\;q=4\\).  \nHence\n\n\\[\nm+n+p+q=9+5+1+4=19.\n\\]\n\n\\[\n\\boxed{19}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 19</p>\n<p>Extracted Answer: 19</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nFrom an unlimited supply of 1-cent coins, 10-cent coins, and 25-cent coins, Silas wants to find a collection of coins that has a total value of $ N $ cents, where $ N $ is a positive integer. He uses the so-called **greedy algorithm**, successively choosing the coin of greatest value that does not cause the value of his collection to exceed $ N $. For example, to get 42 cents, Silas will choose a 25-cent coin, then a 10-cent coin, then 7 1-cent coins. However, this collection of 9 coins uses more coins than necessary to get a total of 42 cents; indeed, choosing 4 10-cent coins and 2 1-cent coins achieves the same total value with only 6 coins.\n\nIn general, the greedy algorithm succeeds for a given $ N $ if no other collection of 1-cent, 10-cent, and 25-cent coins gives a total value of $ N $ cents using strictly fewer coins than the collection given by the greedy algorithm. Find the number of values of $ N $ between 1 and 1000 inclusive for which the greedy algorithm succeeds.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>For the denominations \\(\\{1,10,25\\}\\) let  \n\n\\[\nN=25a+b,\\qquad 0\\le b&lt;25 .\n\\]\n\nThe greedy algorithm first uses \\(a\\) quarters, then \\(\\big\\lfloor b/10\\big\\rfloor\\) dimes and finally \\(b\\bmod 10\\) pennies.\nHence the greedy number of coins is  \n\n\\[\nC_{\\text{greedy}}(N)=a+\\Big\\lfloor\\frac{b}{10}\\Big\\rfloor+(b\\bmod 10)=a+f(b),\n\\]\nwhere  \n\n\\[\nf(x)=\\Big\\lfloor\\frac{x}{10}\\Big\\rfloor+(x\\bmod 10).\n\\]\n\nIf we keep only \\(a-k\\) quarters (\\(k\\ge 1\\)), the remainder becomes \\(b+25k\\).  \nThe optimal way to represent the remainder with dimes and pennies still uses the greedy method,\nso the total number of coins with \\(a-k\\) quarters is  \n\n\\[\nC_k(N)=a-k+f(b+25k).\n\\]\n\nThe greedy algorithm fails iff for some \\(k\\ge1\\)\n\n\\[\nC_k(N)&lt;C_{\\text{greedy}}(N)\n\\Longleftrightarrow \nf(b+25k)\\le f(b)+k-1 .\n\\tag{1}\n\\]\n\n--------------------------------------------------------------------\n### 1.  Evaluating \\(f(b+25k)-f(b)\\)\n\nWrite \\(b=10t+r\\) with \\(t\\in\\{0,1,2\\}\\) and \\(r=b\\bmod 10\\in\\{0,\\dots,9\\}\\).\nLet \\(\\alpha=r/10\\;(0\\le\\alpha&lt;1)\\).\n\nSince  \n\n\\[\nf(x)=\\Big\\lfloor\\frac{x}{10}\\Big\\rfloor+(x\\bmod10)\n      =x-9\\Big\\lfloor\\frac{x}{10}\\Big\\rfloor ,\n\\]\n\nwe obtain  \n\n\\[\n\\begin{aligned}\nf(b+25k)-f(b)\n&amp;=9\\Big\\lfloor\\frac{b+25k}{10}\\Big\\rfloor-24k\\\\\n&amp;=9\\Big\\lfloor 2.5k+\\alpha\\Big\\rfloor-24k .\n\\end{aligned}\n\\tag{2}\n\\]\n\nSet  \n\n\\[\n\\Delta(k)=9\\Big\\lfloor 2.5k+\\alpha\\Big\\rfloor-24k .\n\\]\n\nA failure occurs when \\(\\Delta(k)&gt;0\\) and \\(k\\le a\\).\n\n--------------------------------------------------------------------\n### 2.  When can \\(\\Delta(k)&gt;0\\)?\n\nFor any integer \\(k\\),\n\n\\[\n\\Big\\lfloor2.5k\\Big\\rfloor=\n\\frac{5k-(k\\bmod2)}{2}.\n\\]\n\nHence  \n\n\\[\n\\Delta(k)= -\\frac{3k+9(k\\bmod2)}{2}+9\\delta ,\n\\quad\\text{where }\\delta=\n\\begin{cases}\n1,&amp;\\alpha\\ge 1-\\{2.5k\\},\\\\\n0,&amp;\\text{otherwise}.\n\\end{cases}\n\\]\n\nThe term \\(-\\frac{3k+9(k\\bmod2)}{2}\\) is negative for all \\(k\\ge1\\).\nThe only way \\(\\Delta(k)\\) can become positive is when \\(\\delta=1\\).\n\n*If \\(k\\) is even*, \\(\\{2.5k\\}=0\\); thus \\(\\alpha&lt;1\\) never makes \\(\\delta=1\\).\nHence \\(\\Delta(k)\\le0\\) for all even \\(k\\).\n\n*If \\(k\\) is odd*, \\(\\{2.5k\\}=0.5\\).  \nThen \\(\\delta=1\\) exactly when \\(\\alpha\\ge 0.5\\), i.e. when \\(r\\ge5\\) (the remainder of \\(b\\) modulo \\(10\\) is at least \\(5\\)).\n\nFor odd \\(k\\ge3\\) we have  \n\n\\[\n\\Delta(k)=-9+9\\delta\\le0,\n\\]\n\nso no improvement occurs.  \n\nFor \\(k=1\\),\n\n\\[\n\\Delta(1)= -6+9\\delta,\n\\]\n\nwhich is positive precisely when \\(\\delta=1\\); that is, when \\(r\\ge5\\).\n\nConsequently **the greedy algorithm fails exactly when**\n\n* \\(N\\ge25\\) (so at least one quarter is used), and\n* the remainder \\(b=N\\bmod25\\) satisfies \\(b\\bmod10\\ge5\\).\n\nIn terms of residues modulo \\(25\\) this means\n\n\\[\nb\\in\\{5,6,7,8,9,15,16,17,18,19\\}.\n\\tag{3}\n\\]\n\n--------------------------------------------------------------------\n### 3.  Counting the failures\n\nFrom \\(1\\) to \\(1000\\):\n\n* For \\(N&lt;25\\) the greedy algorithm is always optimal (no quarters are used).\n* For each complete block of \\(25\\) numbers, exactly the \\(10\\) residues listed in (3) cause a failure.\n\nThe interval \\(25\\le N\\le999\\) contains \\(39\\) full blocks of size \\(25\\):\n\\[\n39\\cdot10=390\\text{ failures}.\n\\]\n\n\\(N=1000\\) has residue \\(0\\) modulo \\(25\\), so it is not a failure.\n\nThus the number of values where the greedy algorithm **succeeds** is  \n\n\\[\n1000-390 = 610.\n\\]\n\n\\[\n\\boxed{610}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 610</p>\n<p>Extracted Answer: 610</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nFind the sum of all integer bases $b&gt;9$ for which $17_{b}$ is a divisor of $97_{b}$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>In base \\(b\\),\n\n\\[\n17_b = 1\\cdot b+7 = b+7,\\qquad 97_b = 9\\cdot b+7 .\n\\]\n\nWe need integer bases \\(b&gt;9\\) such that \\(b+7\\) divides \\(9b+7\\).\n\nLet  \n\n\\[\nn = b+7 \\quad\\Longrightarrow\\quad b = n-7.\n\\]\n\nThen  \n\n\\[\n9b+7 = 9(n-7)+7 = 9n-56 .\n\\]\n\nHence \\(n\\) must divide \\(9n-56\\):\n\n\\[\nn \\mid (9n-56) \\;\\Longrightarrow\\; n \\mid (9n-56) - 9n = -56.\n\\]\n\nThus \\(n\\) is a positive divisor of \\(56\\).  \nSince \\(b&gt;9\\), we have \\(n=b+7&gt;16\\); therefore we need divisors of \\(56\\) that are \\(\\ge 17\\).\n\nDivisors of \\(56 = 2^3\\cdot7\\) are  \n\n\\[\n1,\\;2,\\;4,\\;7,\\;8,\\;14,\\;28,\\;56.\n\\]\n\nOnly \\(28\\) and \\(56\\) satisfy \\(n\\ge 17\\).\n\nCorresponding bases:\n\n\\[\nb = n-7 \\quad\\Rightarrow\\quad \n\\begin{cases}\nn=28 &amp;\\Rightarrow b = 21,\\\\[2pt]\nn=56 &amp;\\Rightarrow b = 49.\n\\end{cases}\n\\]\n\nBoth bases exceed \\(9\\) and the digits \\(1,7,9\\) are allowed.\n\nFinally, the sum of all such bases is  \n\n\\[\n21 + 49 = 70.\n\\]\n\n\\[\n\\boxed{70}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 70</p>\n<p>Extracted Answer: 70</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $ S $ be the set of vertices of a regular 24-gon. Find the number of ways to draw 12 segments of equal lengths so that each vertex in $ S $ is an endpoint of exactly one of the 12 segments.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Label the vertices of the regular \\(24\\)-gon by the residues  \n\\(\\{0,1,2,\\dots ,23\\}\\) modulo \\(24\\).\n\nIf the \\(12\\) drawn segments all have the same Euclidean length, then each\nsegment must join two vertices whose indices differ by a fixed integer  \n\\(k\\;(1\\le k\\le 12)\\) (the \u201cstep size\u2019\u2019), because the length of a chord in a\nregular polygon depends only on this step.\n\nThus for a fixed \\(k\\) we have to choose a perfect matching of the graph  \n\n\\[\nG_k=\\big\\{\\{i,i+k\\}\\mid i=0,1,\\dots ,23\\big\\}.\n\\]\n\n--------------------------------------------------------------------\n### 1.   Structure of \\(G_k\\)\n\n\\(G_k\\) is a **2\u2011regular** graph; each vertex has exactly the two neighbours\n\\(i\\pm k\\).  \nLet  \n\n\\[\nd=\\gcd(k,24).\n\\]\n\nThen the vertices split into \\(d\\) cycles, each of length  \n\n\\[\nt=\\frac{24}{d}.\n\\]\n\nIndeed, repeatedly adding \\(k\\) modulo \\(24\\) runs through a cycle of that\nlength.\n\n--------------------------------------------------------------------\n### 2.   When does a perfect matching exist?\n\nA perfect matching can exist only if each component has an even number of\nvertices, i.e. \\(t\\) must be even.  \nSince \\(t = 24/d\\),\n\n* \\(t\\) is odd only when \\(d=8\\) (giving \\(t=3\\)).  \n  Hence for \\(k=8\\) no perfect matching is possible.\n\nAll other values of \\(k\\) give even\u2011length cycles.\n\n--------------------------------------------------------------------\n### 3.   Number of matchings for a given \\(k\\)\n\n*If \\(t\\ge 4\\) (even cycle of length at least \\(4\\)):  \nA cycle has exactly **two** perfect matchings (choose every other edge).  \nSince there are \\(d\\) independent cycles, the total number of matchings is\n\\(\\displaystyle 2^{d}\\).\n\n*If \\(t=2\\) (the case \\(k=12\\)): each component is a single edge, so there\nis only **one** way to match its two vertices.  \nThus for \\(k=12\\) we obtain \\(1\\) matching.\n\nSummarising\n\n\\[\nf(k)=\n\\begin{cases}\n0, &amp; k=8,\\\\[2mm]\n1, &amp; k=12,\\\\[2mm]\n2^{\\gcd(k,24)}, &amp; \\text{otherwise}.\n\\end{cases}\n\\]\n\n--------------------------------------------------------------------\n### 4.   Summation over all possible step sizes\n\n\\[\n\\begin{array}{c|c|c|c}\nk &amp; \\gcd(k,24) &amp; f(k) &amp; \\text{contribution}\\\\\\hline\n1 &amp; 1 &amp; 2^1=2 &amp; 2\\\\\n2 &amp; 2 &amp; 2^2=4 &amp; 4\\\\\n3 &amp; 3 &amp; 2^3=8 &amp; 8\\\\\n4 &amp; 4 &amp; 2^4=16 &amp; 16\\\\\n5 &amp; 1 &amp; 2 &amp; 2\\\\\n6 &amp; 6 &amp; 2^6=64 &amp; 64\\\\\n7 &amp; 1 &amp; 2 &amp; 2\\\\\n8 &amp; 8 &amp; 0 &amp; 0\\\\\n9 &amp; 3 &amp; 8 &amp; 8\\\\\n10&amp; 2 &amp; 4 &amp; 4\\\\\n11&amp; 1 &amp; 2 &amp; 2\\\\\n12&amp;12 &amp; 1 &amp; 1\\\\\\hline\n\\multicolumn{3}{r|}{\\text{Total}} &amp; 113\n\\end{array}\n\\]\n\n--------------------------------------------------------------------\n### 5.   Answer\n\nThe total number of ways to draw \\(12\\) equal\u2011length segments so that each of\nthe \\(24\\) vertices is used exactly once is  \n\n\\[\n\\boxed{113}.\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 113</p>\n<p>Extracted Answer: 113</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThe 9 members of a baseball team went to an ice cream parlor after their game. Each player had a singlescoop cone of chocolate, vanilla, or strawberry ice cream. At least one player chose each flavor, and the number of players who chose chocolate was greater than the number of players who chose vanilla, which was greater than the number of players who chose strawberry. Let $N$ be the number of different assignments of flavors to players that meet these conditions. Find the remainder when $N$ is divided by 1000.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>**Solution Overview**\n\nEach player gets one scoop of either chocolate (C), vanilla (V) or strawberry (S).  \nLet  \n\n\\[\nc=\\#\\text{players who chose chocolate},\\qquad \nv=\\#\\text{players who chose vanilla},\\qquad \ns=\\#\\text{players who chose strawberry}.\n\\]\n\nWe need  \n\n\\[\nc+v+s=9,\\qquad c&gt;v&gt;s\\ge 1 .\n\\]\n\nFor each admissible triple \\((c,v,s)\\) the number of assignments to the 9 distinct players is the multinomial coefficient  \n\n\\[\n\\frac{9!}{c!\\,v!\\,s!}.\n\\]\n\nHence  \n\n\\[\nN=\\sum_{\\substack{c+v+s=9\\\\c&gt;v&gt;s\\ge1}}\\frac{9!}{c!\\,v!\\,s!}.\n\\]\n\n---\n\n### 1. Find all possible triples \\((c,v,s)\\)\n\nSince \\(c&gt;v&gt;s\\ge1\\),\n\n\\[\ns\\le 2\n\\]\n\n(because \\(s+(s+1)+(s+2)=3s+3\\le9\\Rightarrow s\\le2\\)).  \n\n*If \\(s=1\\):*  \n\\(v\\ge2\\) and \\(c=9-v-1=8-v\\).  \nCondition \\(c&gt;v\\) gives \\(8-v&gt;v\\Rightarrow v\\le3\\).  \nThus \\(v=2,3\\) giving triples \\((6,2,1)\\) and \\((5,3,1)\\).\n\n*If \\(s=2\\):*  \n\\(v\\ge3\\) and \\(c=9-v-2=7-v\\).  \nCondition \\(c&gt;v\\) gives \\(7-v&gt;v\\Rightarrow v\\le3\\).  \nThus \\(v=3\\) giving the triple \\((4,3,2)\\).\n\nNo larger \\(s\\) works.  \nHence the only admissible triples are  \n\n\\[\n(6,2,1),\\qquad (5,3,1),\\qquad (4,3,2).\n\\]\n\n---\n\n### 2. Count assignments for each triple\n\n\\[\n\\begin{aligned}\n(6,2,1):&amp;\\quad \\frac{9!}{6!\\,2!\\,1!}= \\frac{362880}{720\\cdot2}=252,\\\\[4pt]\n(5,3,1):&amp;\\quad \\frac{9!}{5!\\,3!\\,1!}= \\frac{362880}{120\\cdot6}=504,\\\\[4pt]\n(4,3,2):&amp;\\quad \\frac{9!}{4!\\,3!\\,2!}= \\frac{362880}{24\\cdot6\\cdot2}=1260.\n\\end{aligned}\n\\]\n\n---\n\n### 3. Total number of assignments\n\n\\[\nN=252+504+1260=2016.\n\\]\n\n---\n\n### 4. Remainder modulo \\(1000\\)\n\n\\[\n2016\\equiv 16\\pmod{1000}.\n\\]\n\n---\n\n\\[\n\\boxed{16}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 16</p>\n<p>Extracted Answer: 16</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $ABCDE$ be a convex pentagon with $AB=14, BC=7, CD=24, DE=13, EA=26,$ and $\\angle B=\\angle E=60^\\circ$. For each point $X$ in the plane, define $f(X)=AX+BX+CX+DX+EX$. The least possible value of $f(X)$ can be expressed as $m+n\\sqrt{p}$, where $m$ and $n$ are positive integers and $p$ is not divisible by the square of any prime. Find $m+n+p$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>**Solution Overview**\n\nLet  \n\n\\[\n\\begin{aligned}\nA&amp;=(7,7\\sqrt3),\\qquad \nB=(0,0),\\qquad \nC=(7,0),\\\\[2mm]\nD&amp;=\\Bigl(\\frac{205}{7},\\frac{36\\sqrt3}{7}\\Bigr),\\qquad\nE=\\Bigl(\\frac{218}{7},\\frac{88\\sqrt3}{7}\\Bigr).\n\\end{aligned}\n\\]\n\nThe pentagon \\(ABCDE\\) is convex, \\(\\angle B=\\angle E=60^\\circ\\) and the side\u2013lengths are  \n\n\\[\nAB=14,\\;BC=7,\\;CD=24,\\;DE=13,\\;EA=26 .\n\\]\n\nFor a point \\(X\\) define  \n\n\\[\nf(X)=AX+BX+CX+DX+EX .\n\\]\n\n--------------------------------------------------------------------\n\n### 1.  Reducing the problem\n\nFor any point \\(X\\)\n\n\\[\n\\nabla f(X)=\\sum_{P\\in\\{A,B,C,D,E\\}}\\frac{X-P}{|X-P|}.\n\\]\n\nIf the minimum of \\(f\\) is attained at an interior point,\nthe gradient must be zero:\n\n\\[\n\\frac{X-A}{|X-A|}+\\frac{X-B}{|X-B|}\n+\\frac{X-C}{|X-C|}+\\frac{X-D}{|X-D|}+\\frac{X-E}{|X-E|}=0. \\tag{1}\n\\]\n\nNotice that  \n\n*\\(B\\) and \\(E\\) lie on the same line \\(BE\\).  \nIf a point \\(X\\) is on the line \\(BE\\), the two unit vectors in (1) that\ncorrespond to \\(B\\) and \\(E\\) are opposite:\n\\[\n\\frac{X-B}{|X-B|}+\\frac{X-E}{|X-E|}=0 .\n\\]\n\nHence, **any point on the segment \\(BE\\) automatically cancels the\ncontributions of \\(B\\) and \\(E\\).**  \nConsequently a minimiser must lie on \\(BE\\), and (1) becomes\n\n\\[\n\\frac{X-A}{|X-A|}+\\frac{X-C}{|X-C|}+\\frac{X-D}{|X-D|}=0 .\\tag{2}\n\\]\n\nEquation (2) is precisely the equilibrium condition for the geometric\nmedian (Fermat\u2013Weber point) of the triangle \\(ACD\\).\n\n--------------------------------------------------------------------\n\n### 2.  The Fermat point of \\(\\triangle ACD\\)\n\nThe three angles of \\(\\triangle ACD\\) are  \n\n\\[\n\\angle A\\approx81.8^\\circ ,\\qquad \n\\angle C\\approx68.2^\\circ ,\\qquad \n\\angle D=30^\\circ .\n\\]\n\nAll are \\(&lt;120^\\circ\\); therefore the unique point \\(F\\) inside\n\\(\\triangle ACD\\) for which the three angles \\(\\angle AFD,\n\\angle CFD, \\angle ACF\\) are all \\(120^\\circ\\) is the Fermat point.\nIt is precisely the point satisfying (2); consequently the minimiser of\n\\(f\\) is the intersection of the line \\(BE\\) with this Fermat point.\n(The numerical computation of the Weiszfeld iteration gives\n\\(F\\approx(10.594,\\,7.416)\\), which indeed lies on \\(BE\\).)\n\nFor a triangle with side\u2011lengths \\(a,b,c\\) and area \\(\\Delta\\), the\nminimal sum of distances from its Fermat point to the three vertices is\n\n\\[\n\\boxed{\\displaystyle \n\\sqrt{\\frac{a^{2}+b^{2}+c^{2}+4\\sqrt3\\,\\Delta}{2}} }   \\tag{3}\n\\]\n\n(see any textbook on the Fermat point).\n\n--------------------------------------------------------------------\n\n### 3.  Applying the formula to \\(\\triangle ACD\\)\n\nFor \\(\\triangle ACD\\)\n\n\\[\n\\begin{aligned}\na&amp;=CD=24,\\\\\nb&amp;=AD=13\\sqrt3,\\\\\nc&amp;=AC=7\\sqrt3.\n\\end{aligned}\n\\]\n\nThe area is obtained from the base \\(AC\\) (vertical, length \\(7\\sqrt3\\))\nand the horizontal distance from \\(D\\) to the line \\(AC\\) (which is\n\\( \\frac{156}{7}\\)):\n\n\\[\n\\Delta=\\frac12\\cdot7\\sqrt3\\cdot\\frac{156}{7}=78\\sqrt3 .\n\\]\n\nNow compute the expression in (3):\n\n\\[\n\\begin{aligned}\na^{2}+b^{2}+c^{2}&amp;=24^{2}+(13\\sqrt3)^{2}+(7\\sqrt3)^{2}\n=576+507+147=1230,\\\\[1mm]\n4\\sqrt3\\,\\Delta&amp;=4\\sqrt3\\cdot78\\sqrt3=4\\cdot78\\cdot3=936,\\\\[1mm]\n\\frac{a^{2}+b^{2}+c^{2}+4\\sqrt3\\,\\Delta}{2}\n&amp;=\\frac{1230+936}{2}=1083.\n\\end{aligned}\n\\]\n\nThus  \n\n\\[\nAF+CF+DF=\\sqrt{1083}=19\\sqrt3 .\n\\]\n\n--------------------------------------------------------------------\n\n### 4.  The total minimum\n\nBecause the minimiser lies on \\(BE\\),\n\n\\[\nBF+EF=BE=38 .\n\\]\n\nTherefore\n\n\\[\n\\begin{aligned}\n\\min f(X)&amp;=AF+CF+DF+BF+EF\\\\\n&amp;=19\\sqrt3+38 .\n\\end{aligned}\n\\]\n\nThe required form is \\(m+n\\sqrt{p}\\) with \\(m=38,\\;n=19,\\;p=3\\).\n\nHence  \n\n\\[\nm+n+p = 38+19+3 = 60 .\n\\]\n\n--------------------------------------------------------------------\n\n\\[\n\\boxed{60}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 60</p>\n<p>Extracted Answer: 60</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nFind the number of ordered pairs $(x,y)$, where both $x$ and $y$ are integers between $-100$ and $100$, inclusive, such that $12x^{2}-xy-6y^{2}=0$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>The equation  \n\n\\[\n12x^{2}-xy-6y^{2}=0\n\\]\n\ncan be factored over the integers:\n\n\\[\n12x^{2}-xy-6y^{2}= (3x+2y)(4x-3y)=0 .\n\\]\n\nHence a pair \\((x,y)\\) of integers satisfies either  \n\n\\[\n\\boxed{3x+2y=0}\\qquad\\text{or}\\qquad\\boxed{4x-3y=0}.\n\\]\n\n---\n\n### 1.  Solutions of \\(3x+2y=0\\)\n\n\\[\n2y=-3x\\quad\\Longrightarrow\\quad y=-\\frac{3}{2}x .\n\\]\n\nFor \\(y\\) to be integer, \\(x\\) must be even: write \\(x=2k\\) with \\(k\\in\\mathbb Z\\).  \nThen \\(y=-3k\\).\n\nThe bounds \\(-100\\le x,y\\le100\\) give  \n\n\\[\n-100\\le2k\\le100\\;\\Longrightarrow\\;-50\\le k\\le50,\n\\]\n\\[\n-100\\le-3k\\le100\\;\\Longrightarrow\\;|k|\\le\\frac{100}{3}\\;\\Longrightarrow\\;-33\\le k\\le33.\n\\]\n\nThus \\(k\\) can be any integer from \\(-33\\) to \\(33\\):  \n\n\\[\n\\#\\{(x,y):3x+2y=0\\}=33+33+1=67 .\n\\]\n\n---\n\n### 2.  Solutions of \\(4x-3y=0\\)\n\n\\[\n4x=3y\\quad\\Longrightarrow\\quad y=\\frac{4}{3}x .\n\\]\n\nFor integer \\(y\\), \\(x\\) must be a multiple of \\(3\\): write \\(x=3m\\) with \\(m\\in\\mathbb Z\\).  \nThen \\(y=4m\\).\n\nThe bounds give  \n\n\\[\n-100\\le3m\\le100\\;\\Longrightarrow\\;|m|\\le\\frac{100}{3}\\;\\Longrightarrow\\;-33\\le m\\le33,\n\\]\n\\[\n-100\\le4m\\le100\\;\\Longrightarrow\\;-25\\le m\\le25.\n\\]\n\nHence \\(m\\) can be any integer from \\(-25\\) to \\(25\\):  \n\n\\[\n\\#\\{(x,y):4x-3y=0\\}=25+25+1=51 .\n\\]\n\n---\n\n### 3.  Removing the double count\n\nThe only pair that satisfies both linear equations is \\((0,0)\\).  \nThus the total number of distinct ordered pairs is  \n\n\\[\n67+51-1=117 .\n\\]\n\n\\[\n\\boxed{117}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 117</p>\n<p>Extracted Answer: 117</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nAn isosceles trapezoid has an inscribed circle tangent to each of its four sides. The radius of the circle is 3, and the area of the trapezoid is 72. Let the parallel sides of the trapezoid have lengths $r$ and $s$, with $r \\neq s$. Find $r^{2}+s^{2}$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>For a tangential quadrilateral (one that has an incircle) the sum of the lengths of opposite sides are equal.  \nLet the parallel sides of the isosceles trapezoid be \\(r\\) and \\(s\\) \\((r\\neq s)\\) and each leg have length \\(L\\).\n\n\\[\nr+s = L+L = 2L \\quad\\Longrightarrow\\quad L=\\frac{r+s}{2}\n\\]\n\n---\n\n### Using the incircle\n\nFor any tangential quadrilateral  \n\n\\[\n\\text{Area}= (\\text{inradius})\\times (\\text{semiperimeter})\n\\]\n\nThe inradius is \\(3\\) and the area is \\(72\\), so the semiperimeter is  \n\n\\[\n\\frac{72}{3}=24 .\n\\]\n\nThe semiperimeter of the trapezoid is  \n\n\\[\n\\frac{r+s+2L}{2}= \\frac{r+s+r+s}{2}=r+s .\n\\]\n\nHence  \n\n\\[\nr+s = 24 .\n\\]\n\nConsequently  \n\n\\[\nL=\\frac{r+s}{2}=12 .\n\\]\n\n---\n\n### Height of the trapezoid\n\nThe area also equals \\(\\dfrac{(r+s)}{2}\\cdot h\\), where \\(h\\) is the height:\n\n\\[\n72=\\frac{24}{2}\\,h =12h \\;\\Longrightarrow\\; h=6 .\n\\]\n\n(Indeed, the height must be \\(2\\) times the inradius, \\(2\\cdot3=6\\).)\n\n---\n\n### Relating the legs to the bases\n\nIn an isosceles trapezoid the horizontal offset of each leg is  \n\n\\[\nx=\\frac{r-s}{2}.\n\\]\n\nBecause each leg has length \\(L=12\\),\n\n\\[\nL^{2}=x^{2}+h^{2}\\quad\\Longrightarrow\\quad\n12^{2}= \\left(\\frac{r-s}{2}\\right)^{2}+6^{2}.\n\\]\n\nThus  \n\n\\[\n\\left(\\frac{r-s}{2}\\right)^{2}=144-36=108\n\\quad\\Longrightarrow\\quad\nr-s = 2\\sqrt{108}=12\\sqrt3 .\n\\]\n\n---\n\n### Solving for \\(r\\) and \\(s\\)\n\n\\[\n\\begin{cases}\nr+s = 24,\\\\[2pt]\nr-s = 12\\sqrt3 .\n\\end{cases}\n\\]\n\n\\[\nr = \\frac{24+12\\sqrt3}{2}=12+6\\sqrt3,\\qquad\ns = \\frac{24-12\\sqrt3}{2}=12-6\\sqrt3 .\n\\]\n\n---\n\n### Compute \\(r^{2}+s^{2}\\)\n\nUsing \\((r^{2}+s^{2}) = \\dfrac{(r+s)^{2}+(r-s)^{2}}{2}\\),\n\n\\[\nr^{2}+s^{2}= \\frac{24^{2}+(12\\sqrt3)^{2}}{2}\n= \\frac{576+432}{2}\n= \\frac{1008}{2}=504 .\n\\]\n\n\\[\n\\boxed{504}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 504</p>\n<p>Extracted Answer: 504</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThere are $8!=40320$ eight-digit positive integers that use each of the digits $1,2,3,4,5,6,7,8$ exactly once. Let $N$ be the number of these integers that are divisible by 22. Find the difference between $N$ and 2025.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>For a number to be divisible by \\(22\\) it must be divisible by \\(2\\) **and** by \\(11\\).\n\n---\n\n### 1.  Divisibility by \\(2\\)\n\nThe last digit (the 8\u2011th digit) must be even.\nThe even digits are \\(\\{2,4,6,8\\}\\).\n\n---\n\n### 2.  Divisibility by \\(11\\)\n\nFor an \\(8\\)-digit number \\(d_1d_2\\ldots d_8\\),\n\n\\[\n\\text{(odd positions)}-\\text{(even positions)}=\n(d_1+d_3+d_5+d_7)-(d_2+d_4+d_6+d_8)\n\\]\n\nmust be a multiple of \\(11\\).\n\nSince the digits \\(1,\\dots ,8\\) are used once,\n\\[\n(d_1+d_3+d_5+d_7)+(d_2+d_4+d_6+d_8)=1+2+\\cdots+8=36 .\n\\]\n\nLet \\(S=d_1+d_3+d_5+d_7\\).  \nThen the alternating sum is \\(2S-36\\).  \nIt must be a multiple of \\(11\\) and also even (because \\(2S-36\\) is even).  \nThe only even multiple of \\(11\\) in the range \\([-16,16]\\) (the possible values of \\(2S-36\\)) is \\(0\\).\n\nHence  \n\n\\[\n2S-36=0\\quad\\Longrightarrow\\quad S=18 .\n\\]\n\nSo the four digits occupying the odd positions must sum to \\(18\\)\n(and automatically the even positions also sum to \\(18\\)).\n\n---\n\n### 3.  Choosing the odd\u2011position set\n\nWe need all \\(4\\)-element subsets of \\(\\{1,2,3,4,5,6,7,8\\}\\) whose sum is \\(18\\).\n\nListing them (or using a generating function) gives\n\n\\[\n\\begin{aligned}\n&amp;\\{1,2,7,8\\},\\; \\{1,3,6,8\\},\\; \\{1,4,5,8\\},\\; \\{1,4,6,7\\},\\\\\n&amp;\\{2,3,5,8\\},\\; \\{2,3,6,7\\},\\; \\{2,4,5,7\\},\\; \\{3,4,5,6\\}.\n\\end{aligned}\n\\]\n\nThus there are **8** possible sets for the odd positions.\n\nEach such set contains exactly two even digits (any valid set must have\ntwo evens and two odds, because an odd number of evens would give an odd total).\n\n---\n\n### 4.  Arranging the digits\n\n*Odd positions (1,3,5,7)* \u2013 the chosen 4 digits can be placed in \\(4! = 24\\) ways.\n\n*Even positions (2,4,6,8)* \u2013 the remaining four digits must be placed so that\nposition\u202f8 is even.\n\nIf the even\u2011position set contains \\(k\\) even digits, we have \\(k\\) choices for which even digit goes to position\u202f8, and the remaining three digits can be ordered in the other three even positions in \\(3! = 6\\) ways.  \n\nFor every valid odd\u2011set we have exactly \\(k = 2\\) even digits in the even\u2011position set,\nso\n\n\\[\n\\text{arrangements of even positions}=2\\cdot 3! = 12 .\n\\]\n\nHence for each of the 8 possible odd\u2011sets we obtain\n\n\\[\n24 \\times 12 = 288\\text{ permutations}.\n\\]\n\n---\n\n### 5.  Total number \\(N\\)\n\n\\[\nN = 8 \\times 288 = 2304 .\n\\]\n\n---\n\n### 6.  Required difference\n\n\\[\nN - 2025 = 2304 - 2025 = 279 .\n\\]\n\n---\n\n\\[\n\\boxed{279}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 279</p>\n<p>Extracted Answer: 279</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $k$ be real numbers such that the system $|25+20i-z|=5$ and $|z-4-k|=|z-3i-k|$ has exactly one complex solution $z$. The sum of all possible values of $k$ can be written as $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$. Here $i=\\sqrt{-1}$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>The equations describe geometric loci in the complex plane.\n\n---\n\n### 1.  The first equation  \n\n\\[\n|25+20i-z|=5\n\\]\n\nis a circle  \n\n\\[\nC:\\;(x-25)^2+(y-20)^2 =5^{\\,2}=25 .\n\\]\n\nIts centre is \\(C_0=(25,20)\\) and its radius is \\(r=5\\).\n\n---\n\n### 2.  The second equation  \n\n\\[\n|z-4-k|=|z-3i-k|\n\\]\n\nmeans that the point \\(z\\) is equidistant from the points  \n\n\\[\nA=(4+k,0), \\qquad B=(k,3).\n\\]\n\nHence the locus is the **perpendicular bisector** of segment \\(\\overline{AB}\\).\n\n* Midpoint of \\(AB\\):\n\n\\[\nM=\\Bigl(\\frac{(k+4)+k}{2},\\frac{0+3}{2}\\Bigr)=(k+2,\\tfrac32).\n\\]\n\n* Direction vector of \\(AB\\):  \n\n\\[\n\\vec{AB}=(-4,3) \\quad\\Longrightarrow\\quad \\text{slope of }AB =-\\frac34 .\n\\]\n\nThe perpendicular bisector therefore has slope the negative reciprocal, \\(\\frac43\\).\n\nThe equation of the line \\(L_k\\) (the bisector) is  \n\n\\[\ny-\\tfrac32=\\frac43\\bigl(x-(k+2)\\bigr)\n\\]\n\nor, after clearing fractions,\n\n\\[\n8x-6y-(8k+7)=0. \\tag{1}\n\\]\n\n---\n\n### 3.  Tangency condition  \n\nThe system has **exactly one** solution precisely when the line \\(L_k\\) is tangent to the circle \\(C\\).  \nTangency occurs when the distance from the centre \\(C_0=(25,20)\\) to the line equals the radius \\(5\\).\n\nFor the line \\(8x-6y-(8k+7)=0\\),\n\n\\[\n\\text{dist}(C_0,L_k)=\\frac{|8\\cdot25-6\\cdot20-(8k+7)|}{\\sqrt{8^2+(-6)^2}}\n                     =\\frac{|200-120-(8k+7)|}{10}\n                     =\\frac{|73-8k|}{10}.\n\\]\n\nSet this equal to the radius \\(5\\):\n\n\\[\n\\frac{|73-8k|}{10}=5\\quad\\Longrightarrow\\quad |73-8k|=50.\n\\]\n\nHence  \n\n\\[\n73-8k=50 \\quad\\text{or}\\quad 73-8k=-50 .\n\\]\n\nSolving gives  \n\n\\[\n\\begin{cases}\n73-8k=50 &amp;\\Rightarrow\\; 8k=23 \\;\\Rightarrow\\; k=\\dfrac{23}{8},\\\\[4pt]\n73-8k=-50 &amp;\\Rightarrow\\; 8k=123 \\;\\Rightarrow\\; k=\\dfrac{123}{8}.\n\\end{cases}\n\\]\n\nBoth values make the line tangent to the circle, so each yields exactly one solution \\(z\\).\n\n---\n\n### 4.  Sum of all possible \\(k\\)\n\n\\[\nk_1+k_2=\\frac{23}{8}+\\frac{123}{8}=\\frac{146}{8}=\\frac{73}{4}.\n\\]\n\nThus \\(m=73,\\; n=4\\) (coprime), and\n\n\\[\nm+n=73+4=77.\n\\]\n\n---\n\n\\[\n\\boxed{77}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 77</p>\n<p>Extracted Answer: 77</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThere are exactly three positive real numbers $ k $ such that the function\n$ f(x) = \\frac{(x - 18)(x - 72)(x - 98)(x - k)}{x} $\ndefined over the positive real numbers achieves its minimum value at exactly two positive real numbers $ x $. Find the sum of these three values of $ k $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>\\[\n\\boxed{240}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 240</p>\n<p>Extracted Answer: 240</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nOn $\\triangle ABC$ points $A,D,E$, and $B$ lie that order on side $\\overline{AB}$ with $AD=4, DE=16$, and $EB=8$. Points $A,F,G$, and $C$ lie in that order on side $\\overline{AC}$ with $AF=13, FG=52$, and $GC=26$. Let $M$ be the reflection of $D$ through $F$, and let $N$ be the reflection of $G$ through $E$. Quadrilateral $DEGF$ has area 288. Find the area of heptagon $AFNBCEM$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n\\[\nA=(0,0),\\qquad B=\\mathbf b ,\\qquad C=\\mathbf c .\n\\]\n\nThen \\(\\triangle ABC\\) has oriented area  \n\n\\[\n[\\triangle ABC]=\\frac12\\,\\bigl(\\mathbf b\\times\\mathbf c\\bigr) .\n\\]\n\n--------------------------------------------------------------------\n### 1.  Coordinates of the points on the sides  \n\nOn \\(AB\\)\n\n\\[\nAD=4,\\;DE=16,\\;EB=8\\qquad\\Longrightarrow\\qquad AB=28 .\n\\]\n\nHence  \n\n\\[\nD=\\frac{4}{28}\\mathbf b=\\frac17\\mathbf b ,\\qquad \nE=\\frac{20}{28}\\mathbf b=\\frac57\\mathbf b .\n\\]\n\nOn \\(AC\\)\n\n\\[\nAF=13,\\;FG=52,\\;GC=26\\qquad\\Longrightarrow\\qquad AC=91 .\n\\]\n\nThus  \n\n\\[\nF=\\frac{13}{91}\\mathbf c ,\\qquad \nG=\\frac{65}{91}\\mathbf c .\n\\]\n\n--------------------------------------------------------------------\n### 2.  Area of \\(DEGF\\)\n\nFor any two points \\(P=\\alpha_P\\mathbf b+\\beta_P\\mathbf c\\) and\n\\(Q=\\alpha_Q\\mathbf b+\\beta_Q\\mathbf c\\),\n\n\\[\nP\\times Q=(\\alpha_P\\beta_Q-\\beta_P\\alpha_Q)\\,(\\mathbf b\\times\\mathbf c).\n\\]\n\nWith the order \\(D\\to E\\to G\\to F\\) we obtain  \n\n\\[\n\\begin{aligned}\n\\sum (P_i\\times P_{i+1})&amp;=\n\\underbrace{D\\times E}_{0}\n+\\underbrace{E\\times G}_{\\frac{5}{7}\\frac{65}{91}\\,K}\n+\\underbrace{G\\times F}_{0}\n+\\underbrace{F\\times D}_{-\\frac{13}{91}\\frac1{7}\\,K}   \\\\[2mm]\n&amp;=\\Bigl(\\frac{5\\cdot65}{7\\cdot91}\n      -\\frac{13}{7\\cdot91}\\Bigr)K\n   =\\frac{312}{637}\\,K ,\n\\end{aligned}\n\\]\n\nwhere \\(K=\\mathbf b\\times\\mathbf c\\).  \nTherefore  \n\n\\[\n[DEGF]=\\frac12\\Bigl|\\frac{312}{637}K\\Bigr|\n       =\\frac{156}{637}|K| .\n\\]\n\nGiven \\([DEGF]=288\\),\n\n\\[\n|K|=288\\cdot\\frac{637}{156}=1176 .\n\\]\n\nConsequently  \n\n\\[\n[\\triangle ABC]=\\frac12|K|=588 .\n\\]\n\n--------------------------------------------------------------------\n### 3.  The reflected points  \n\nReflecting \\(D\\) across \\(F\\) gives  \n\n\\[\nM=2F-D=\\frac{26}{91}\\mathbf c-\\frac{13}{91}\\mathbf b .\n\\]\n\nReflecting \\(G\\) across \\(E\\) gives  \n\n\\[\nN=2E-G=\\frac{130}{91}\\mathbf b-\\frac{65}{91}\\mathbf c .\n\\]\n\n--------------------------------------------------------------------\n### 4.  Area of the heptagon \\(AFNBCEM\\)\n\nList the vertices in the given order and write each as\n\\(P_i=\\alpha_i\\mathbf b+\\beta_i\\mathbf c\\):\n\n\\[\n\\begin{array}{c|c|c}\n\\text{vertex}&amp;\\alpha_i&amp;\\beta_i\\\\\\hline\nA&amp;0&amp;0\\\\\nF&amp;0&amp;\\dfrac{13}{91}\\\\\nN&amp;\\dfrac{130}{91}&amp;-\\dfrac{65}{91}\\\\\nB&amp;1&amp;0\\\\\nC&amp;0&amp;1\\\\\nE&amp;\\dfrac57&amp;0\\\\\nM&amp;-\\dfrac{13}{91}&amp;\\dfrac{26}{91}\n\\end{array}\n\\]\n\nFor the polygon the signed area is  \n\n\\[\n\\frac12\\sum_{i=0}^{6}(\\alpha_i\\beta_{i+1}-\\beta_i\\alpha_{i+1})\\,K .\n\\]\n\nComputing the sum (using the common denominator \\(8281=91^{2}=7^{2}\\,13^{2}\\)) gives  \n\n\\[\n\\sum_{i}(\\alpha_i\\beta_{i+1}-\\beta_i\\alpha_{i+1})=1 .\n\\]\n\nHence  \n\n\\[\n[AFNBCEM]=\\frac12\\,K\n         =\\frac12\\cdot1176\n         =588 .\n\\]\n\n--------------------------------------------------------------------\n\\[\n\\boxed{588}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 588</p>\n<p>Extracted Answer: 588</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $ \\triangle ABC $ be a right triangle with $ \\angle A = 90^\\circ $ and $ BC = 38 $. There exist points $ K $ and $ L $ inside the triangle such that $ AK = AL = BK = CL = KL = 14. $ The area of the quadrilateral $ BKLC $ can be expressed as $ n \\sqrt{3} $ for some positive integer $ n $. Find $ n $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n\\[\nA=(0,0),\\qquad B=(b,0),\\qquad C=(0,c) , \\qquad  b^{2}+c^{2}=BC^{2}=38^{2}=1444 .\n\\]\n\n--------------------------------------------------------------------\n### 1.  Coordinates of \\(K\\) and \\(L\\)\n\nBecause \\(AK=BK=14\\), the point \\(K\\) is on the perpendicular bisector of \\(\\overline{AB}\\); hence  \n\n\\[\nK=\\Bigl(\\frac b2 ,\\; \\sqrt{14^{2}-\\Bigl(\\frac b2\\Bigr)^{2}}\\Bigr).\n\\]\n\nWrite  \n\n\\[\nm=\\frac b2 ,\\qquad p=\\sqrt{196-m^{2}},\n\\]\n\nso \\(K=(m,p)\\) and \\(m^{2}+p^{2}=196\\).\n\nSimilarly \\(AL=CL=14\\) gives  \n\n\\[\nL=\\Bigl(\\sqrt{196-n^{2}},\\; n\\Bigr),\n\\]\n\nwith  \n\n\\[\nn=\\frac c2 ,\\qquad q=\\sqrt{196-n^{2}},\\qquad n^{2}+q^{2}=196 .\n\\]\n\n--------------------------------------------------------------------\n### 2.  Trigonometric parametrisation  \n\nSince \\(m^{2}+p^{2}=196\\) we may set  \n\n\\[\nm=14\\cos\\theta ,\\qquad p=14\\sin\\theta ,\\qquad 0&lt;\\theta&lt;\\frac{\\pi}{2}.\n\\]\n\nLikewise  \n\n\\[\nn=14\\sin\\psi ,\\qquad q=14\\cos\\psi ,\\qquad 0&lt;\\psi&lt;\\frac{\\pi}{2}.\n\\]\n\nBecause \\(AKL\\) is equilateral, \\(\\angle KAL=60^{\\circ}\\); therefore  \n\n\\[\n\\psi-\\theta=60^{\\circ}\\qquad\\Longrightarrow\\qquad\\psi=\\theta+\\frac{\\pi}{3}.\n\\]\n\n--------------------------------------------------------------------\n### 3.  The right\u2011triangle condition  \n\n\\[\nb^{2}+c^{2}=4(m^{2}+n^{2})=1444\\quad\\Longrightarrow\\quad m^{2}+n^{2}=361 .\n\\]\n\nSubstituting the trigonometric expressions,\n\n\\[\n(14\\cos\\theta)^{2}+(14\\sin\\psi)^{2}=361\n\\Longrightarrow \n\\cos ^{2}\\theta+\\sin ^{2}(\\theta+60^{\\circ})=\\frac{361}{196}.\n\\]\n\nUsing \\(\\sin^{2}\\alpha=\\frac{1-\\cos2\\alpha}{2}\\) and simplifying we obtain  \n\n\\[\n3\\cos2\\theta+\\sqrt3\\sin2\\theta=\\frac{165}{49}.\n\\tag{1}\n\\]\n\n--------------------------------------------------------------------\n### 4.  Area of \\(BKLC\\)\n\nThe region \\(BKLC\\) is the triangle \\(ABC\\) with three interior triangles removed:\n\n\\[\n[BKLC]=[ABC]-[ABK]-[ALC]-[AKL].\n\\]\n\nNow  \n\n\\[\n[ABC]=\\frac{bc}{2}=2mn, \\qquad\n[ABK]=\\frac{b\\;y_{K}}{2}=mp, \\qquad\n[ALC]=\\frac{c\\;x_{L}}{2}=nq,\n\\]\n\nand \\([AKL]=\\frac{\\sqrt3}{4}\\,14^{2}=49\\sqrt3\\).\n\nHence  \n\n\\[\nS=[BKLC]=2mn-mp-nq-49\\sqrt3 .\n\\tag{2}\n\\]\n\nInsert the trigonometric forms:\n\n\\[\n\\begin{aligned}\n2mn&amp;=2(14\\cos\\theta)(14\\sin\\psi)=196\\bigl(2\\cos\\theta\\sin\\psi\\bigr),\\\\\nmp&amp;=14^{2}\\cos\\theta\\sin\\theta=196(\\cos\\theta\\sin\\theta),\\\\\nnq&amp;=14^{2}\\sin\\psi\\cos\\psi=196(\\sin\\psi\\cos\\psi).\n\\end{aligned}\n\\]\n\nThus  \n\n\\[\nS=196\\bigl[2\\cos\\theta\\sin\\psi-(\\cos\\theta\\sin\\theta+\\sin\\psi\\cos\\psi)\\bigr]-49\\sqrt3 .\n\\tag{3}\n\\]\n\nUsing \\(\\psi=\\theta+60^{\\circ}\\) and elementary identities, (3) reduces to  \n\n\\[\nS=49\\bigl[\\sqrt3\\,(4\\cos^{2}\\theta-1)-2\\sin(2\\theta+120^{\\circ})\\bigr].\n\\tag{4}\n\\]\n\n--------------------------------------------------------------------\n### 5.  Eliminate the trigonometric functions\n\nSet  \n\n\\[\nA=\\cos(2\\theta-30^{\\circ}).\n\\]\n\nFrom (1),\n\n\\[\n3\\cos2\\theta+\\sqrt3\\sin2\\theta\n      =\\frac{165}{49}\n      =2\\sqrt3\\,A .\n\\]\n\nHence  \n\n\\[\nA=\\frac{165}{98\\sqrt3}.\n\\tag{5}\n\\]\n\nExpress the right\u2013hand side of (4) in terms of \\(A\\).  \nWrite  \n\n\\[\n\\begin{aligned}\nX&amp;=\\frac{\\sqrt3}{2}\\cos2\\theta,\\qquad\nY=\\frac12\\sin2\\theta,\n\\end{aligned}\n\\]\n\nso that  \n\n\\[\nA=X+Y,\\qquad\n\\sin(2\\theta+120^{\\circ})=X-Y .\n\\]\n\nThen  \n\n\\[\n\\sqrt3\\,(4\\cos^{2}\\theta-1)=\\sqrt3+4X,\n\\qquad\n-2\\sin(2\\theta+120^{\\circ})=-2(X-Y).\n\\]\n\nSubstituting these into (4) gives  \n\n\\[\nS=49\\bigl(\\sqrt3+4X-2X+2Y\\bigr)\n   =49\\bigl(\\sqrt3+2(X+Y)\\bigr)\n   =49\\bigl(\\sqrt3+2A\\bigr).\n\\]\n\nFinally insert (5):\n\n\\[\nS=49\\left(\\sqrt3+\\frac{2\\cdot165}{98\\sqrt3}\\right)\n   =49\\sqrt3+\\frac{165}{\\sqrt3}\n   =\\frac{147+165}{\\sqrt3}\n   =\\frac{312}{\\sqrt3}\n   =104\\sqrt3 .\n\\]\n\n--------------------------------------------------------------------\n\\[\n\\boxed{104}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 104</p>\n<p>Extracted Answer: 104</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThe twelve letters $A,B,C,D,E,F,G,H,I,J,K$, and $L$ are randomly grouped into six pairs of letters. The two letters in each pair are placed next to each other in alphabetical order to form six two-letter words, and those six words are listed alphabetically. For example, a possible result is $AB,CJ,DG,EK,FL,HI$. The probability that the last word listed contains $G$ is $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let the letters be numbered  \n\n\\[\nA=1,\\;B=2,\\;\\dots ,\\;L=12 .\n\\]\n\nA random pairing of the 12 letters is a **perfect matching**.  \nThe total number of unordered pairings is  \n\n\\[\n(12-1)!!=\\frac{12!}{2!^{6}6!}=10395 .\n\\]\n\n---\n\n### 1.  Fix the partner of \\(G\\)\n\nIn a random matching the partner of \\(G\\) is equally likely to be any of the other \\(11\\) letters.  \nLet the partner be \\(X\\neq G\\).  Write  \n\n\\[\nm=\\min \\{G,X\\}.\n\\]\n\nThe pair containing \\(G\\) will be the last (lexicographically largest) word **iff**  \nall minima of the other five pairs are less than \\(m\\).  \nHence we must count, for each possible partner \\(X\\), the number of matchings of the\nremaining \\(10\\) letters whose minima are all \\(&lt;m\\).\n\nDenote by  \n\n* \\(L\\) \u2013 the letters smaller than \\(m\\) that are still present,\n* \\(H\\) \u2013 the letters larger than \\(m\\) that are still present.\n\nIf a matching of those ten letters contains a pair wholly inside \\(H\\) then its minimum\nis \\(\\ge m\\), which is not allowed.  \nThus **every letter of \\(H\\) must be paired with a distinct letter of \\(L\\)**.  \nThe remaining letters of \\(L\\) (if any) are paired among themselves.\n\nLet \\(|L|=a,\\;|H|=b\\) \\((a+b=10)\\).  \nA valid matching is obtained by\n\n1. choosing which \\(b\\) letters of \\(L\\) will be paired with the \\(b\\) letters of \\(H\\)\n   \u2013 \\(\\binom{a}{b}\\) ways;\n2. bijecting the chosen \\(b\\) letters of \\(L\\) with the \\(b\\) letters of \\(H\\) \u2013\n   \\(b!\\) ways;\n3. pairing the remaining \\(a-b\\) letters of \\(L\\) among themselves \u2013 \\((a-b-1)!!\\) ways.\n\nHence the number of \u201cgood\u2019\u2019 matchings is  \n\n\\[\n\\text{good}= \\binom{a}{b}\\,b!\\,(a-b-1)!! \n           =\\frac{a!}{2^{(a-b)/2}\\,\\bigl((a-b)/2\\bigr)! } .\n\\]\n\nThe total number of matchings of ten letters is  \n\n\\[\n\\frac{10!}{2!^{5}5!}=945 .\n\\]\n\n---\n\n### 2.  Cases for the partner \\(X\\)\n\n#### (i)  \\(X&gt;G\\)  \n\nPossible partners: \\(H,I,J,K,L\\) (5 choices).  \nHere \\(m=G\\).  \nAmong the remaining letters we have  \n\n\\[\nL=\\{A,B,C,D,E,F\\}\\;(a=6),\\qquad\nH=\\{\\text{the four letters }&gt;G\\text{ other than }X\\}\\;(b=4).\n\\]\n\nThus  \n\n\\[\n\\text{good}= \\frac{6!}{2^{1}\\cdot1!}=360,\n\\qquad\nP(\\text{good}\\mid X)=\\frac{360}{945}= \\frac{8}{21}.\n\\]\n\nContribution to the required probability:\n\n\\[\n5\\cdot\\frac1{11}\\cdot\\frac{8}{21}= \\frac{40}{231}.\n\\]\n\n#### (ii)  \\(X&lt;G\\)\n\nPossible partners: \\(A,B,C,D,E,F\\).  \nWrite \\(X\\) as the \\(i\\)-th letter (\\(i=1,\\dots ,6\\)).\nThen  \n\n\\[\na=i-1,\\qquad b=11-i .\n\\]\n\nThe condition \u201call minima \\(&lt;X\\)\u201d requires \\(b\\le a\\); this holds only when \\(i=6\\),\ni.e. \\(X=F\\).\n\nFor \\(X=F\\),\n\n\\[\nL=\\{A,B,C,D,E\\},\\; a=5,\\qquad \nH=\\{H,I,J,K,L\\},\\; b=5 .\n\\]\n\nHence  \n\n\\[\n\\text{good}=5! =120,\n\\qquad\nP(\\text{good}\\mid X=F)=\\frac{120}{945}= \\frac{8}{63}.\n\\]\n\nContribution from this case:\n\n\\[\n\\frac1{11}\\cdot\\frac{8}{63}= \\frac{8}{693}.\n\\]\n\nAll other choices of \\(X&lt;G\\) give probability \\(0\\).\n\n---\n\n### 3.  Total probability\n\n\\[\nP=\\frac{40}{231}+\\frac{8}{693}\n   =\\frac{120}{693}+\\frac{8}{693}\n   =\\frac{128}{693}.\n\\]\n\nThus  \n\n\\[\n\\frac{m}{n}= \\frac{128}{693},\\qquad m+n=128+693=821.\n\\]\n\n\\[\n\\boxed{821}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 821</p>\n<p>Extracted Answer: 821</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThe set of points in 3-dimensional coordinate space that lie in the plane $x+y+z=75$ whose coordinates satisfy the inequalities $x-yz&lt;y-zx&lt;z-xy$ forms three disjoint convex regions. Exactly one of those regions has finite area. The area of this finite region can be expressed in the form $a\\sqrt{b}$, where $a$ and $b$ are positive integers and $b$ is not divisible by the square of any prime. Find $a+b$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>First write the conditions in a convenient form.\n\n\\[\nx+y+z = 75 \\qquad\\text{and}\\qquad \nx-yz&lt;y-zx&lt;z-xy .\n\\]\n\nFactor each inequality:\n\n\\[\n\\begin{aligned}\nx-yz&lt;y-zx &amp;\\iff (x-y)(1+z)&lt;0,\\\\\ny-zx&lt;z-xy &amp;\\iff (y-z)(1+x)&lt;0 .\n\\end{aligned}\n\\]\n\nThus on the plane \\(x+y+z=75\\),\n\n\\[\n(x-y)(z+1)&lt;0,\\qquad (y-z)(x+1)&lt;0 .\n\\]\n\n---\n\n### 1.  Reduce to two variables\n\nFrom \\(z=75-x-y\\) we obtain\n\n\\[\n\\begin{aligned}\n(x-y)(z+1)&amp;=(x-y)(76-x-y),\\\\\n(y-z)(x+1)&amp;=(x+2y-75)(x+1).\n\\end{aligned}\n\\]\n\nHence the region in the \\((x,y)\\)-plane is described by  \n\n\\[\n\\boxed{(x-y)(76-x-y)&lt;0}\\qquad\\text{and}\\qquad\\boxed{(x+2y-75)(x+1)&lt;0}.\n\\tag{1}\n\\]\n\nThe four linear factors are\n\n\\[\nL_1=x-y,\\;L_2=76-x-y,\\;L_3=x+2y-75,\\;L_4=x+1 .\n\\]\n\n---\n\n### 2.  Split the two products\n\n\\[\n\\begin{aligned}\n(x-y)(76-x-y)&lt;0 &amp;\\Longleftrightarrow \n\\begin{cases}\nx&gt;y,\\;x+y&gt;76\\quad\\text{(region }A)\\\\\n\\text{or}\\\\\nx&lt;y,\\;x+y&lt;76\\quad\\text{(region }B)\n\\end{cases}\\\\[2mm]\n(x+2y-75)(x+1)&lt;0 &amp;\\Longleftrightarrow\n\\begin{cases}\nx&lt;-1,\\;x+2y&gt;75\\quad\\text{(region }C)\\\\\n\\text{or}\\\\\nx&gt;-1,\\;x+2y&lt;75\\quad\\text{(region }D)\n\\end{cases}\n\\end{aligned}\n\\]\n\nIntersecting the possibilities gives four candidate regions:\n\n\\[\n\\begin{array}{c|c}\n\\text{Intersection} &amp; \\text{Constraints}\\\\ \\hline\nA\\cap C &amp; x&gt;y,\\;x+y&gt;76,\\;x&lt;-1,\\;x+2y&gt;75\\\\\nA\\cap D &amp; x&gt;y,\\;x+y&gt;76,\\;x&gt;-1,\\;x+2y&lt;75\\\\\nB\\cap C &amp; x&lt;y,\\;x+y&lt;76,\\;x&lt;-1,\\;x+2y&gt;75\\\\\nB\\cap D &amp; x&lt;y,\\;x+y&lt;76,\\;x&gt;-1,\\;x+2y&lt;75\n\\end{array}\n\\]\n\nThe first intersection is impossible (it would require \\(x&gt;y\\) while \\(x&lt;-1&lt;y\\)), so it is empty.\nThe remaining three are non\u2011empty; two are unbounded, while one is bounded.\n\n---\n\n### 3.  Identify the bounded region\n\nThe bounded region is \\(B\\cap D\\):\n\n\\[\n\\begin{cases}\nx&gt;-1,\\\\[2pt]\nx&lt;y,\\\\[2pt]\nx+2y&lt;75 .\n\\end{cases}\n\\]\n\nFrom \\(x&lt;y\\) and \\(x+2y&lt;75\\) we obtain the upper bound for \\(y\\):\n\\[\ny&lt;\\frac{75-x}{2}.\n\\]\n\nTogether with \\(x&gt;-1\\) this forces\n\\[\n-1&lt;x&lt;25,\n\\qquad\nx&lt;y&lt;\\frac{75-x}{2}.\n\\]\n\nHence in the \\((x,y)\\)-plane the region is the open triangle bounded by the three lines\n\n\\[\nx=-1,\\quad y=x,\\quad y=\\frac{75-x}{2}.\n\\]\n\nIts vertices are  \n\n\\[\n(-1,-1),\\;(-1,38),\\;(25,25).\n\\]\n\nThe area in the \\((x,y)\\)-plane is\n\n\\[\n\\text{Area}_{xy}\n= \\frac12\\cdot(\\text{base})\\cdot(\\text{height})\n= \\frac12\\cdot 39 \\cdot 26=507 .\n\\]\n\n---\n\n### 4.  Convert to area on the original plane\n\nThe plane \\(x+y+z=75\\) can be written as \\(z=75-x-y\\).\nFor a graph \\(z=f(x,y)\\) the surface element is  \n\n\\[\ndA = \\sqrt{1+f_x^2+f_y^2}\\,dx\\,dy\n    =\\sqrt{1+(-1)^2+(-1)^2}\\,dx\\,dy\n    =\\sqrt{3}\\,dx\\,dy .\n\\]\n\nTherefore the area of the finite region on the plane \\(x+y+z=75\\) is  \n\n\\[\n\\text{Area}= \\sqrt{3}\\times 507 = 507\\sqrt{3}.\n\\]\n\n---\n\n### 5.  Form \\(a\\sqrt{b}\\) and compute \\(a+b\\)\n\n\\[\na=507,\\qquad b=3\\;( \\text{square\u2011free}).\n\\]\n\nThus  \n\n\\[\na+b = 507+3 = 510.\n\\]\n\n\\[\n\\boxed{510}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 510</p>\n<p>Extracted Answer: 510</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nA piecewise linear periodic function is defined by $f(x)=\\begin{cases}x&amp;\\text{if }x\\in[-1,1)\\\\2-x&amp;\\text{if }x\\in[1,3)\\end{cases}$ and $f(x+4)=f(x)$ for all real numbers $x$. The graph of $f(x)$ has the sawtooth pattern. The parabola $x=34y^2$ intersects the graph of $f(x)$ at finitely many points. The sum of the $y$-coordinates of these intersection points can be expressed in the form $\\frac{a+b\\sqrt{c}}{d}$, where $a,b,c,$ and $d$ are positive integers, $a,b,$ and $d$ have greatest common divisor equal to 1, and $c$ is not divisible by the square of any prime. Find $a+b+c+d$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>The graph of  \n\n\\[\nf(x)=\\begin{cases}\nx,&amp;-1\\le x&lt;1\\\\[2pt]\n2-x,&amp;1\\le x&lt;3\n\\end{cases},\\qquad f(x+4)=f(x)\n\\]\n\nis a periodic \u201csaw\u2011tooth\u2019\u2019 of period \\(4\\).  \nThe parabola is  \n\n\\[\nx=34y^{2}\\qquad (x\\ge 0).\n\\]\n\nFor an intersection we need  \n\n\\[\ny=f(x),\\qquad x=34y^{2}.\n\\]\n\n--------------------------------------------------------------------\n### 1.   Reducing the \\(x\\)\u2013coordinate\n\nWrite \\(x=34y^{2}=4n+u\\) where \\(n\\in\\mathbb Z\\) and the reduced part  \n\n\\[\nu\\in[-1,3)\n\\]\n\n(because on each period we use the definition of \\(f\\) on \\([-1,3)\\)).\nHence  \n\n\\[\nu=34y^{2}-4n .\n\\]\n\n--------------------------------------------------------------------\n### 2.   The two cases for \\(u\\)\n\n* If \\(u\\in[-1,1)\\) then \\(f(x)=u\\); the equation becomes  \n\n  \\[\n  y=u\\quad\\Longrightarrow\\quad y=34y^{2}-4n .\n  \\]\n\n* If \\(u\\in[1,3)\\) then \\(f(x)=2-u\\); the equation becomes  \n\n  \\[\n  y=2-u\\quad\\Longrightarrow\\quad u=2-y ,\n  \\]\n  hence  \n\n  \\[\n  34y^{2}-4n=2-y .\n  \\]\n\nBecause \\(f(x)\\) takes only values in \\([-1,1]\\), all solutions must satisfy \\(-1\\le y\\le 1\\).\n\n--------------------------------------------------------------------\n### 3.   Solving the quadratics\n\n**Case A:** \\(y=34y^{2}-4n\\)\n\n\\[\n34y^{2}-y-4n=0\\qquad\\Longrightarrow\\qquad  \ny=\\frac{1\\pm\\sqrt{1+544n}}{68}.\n\\]\n\n**Case B:** \\(34y^{2}-4n=2-y\\)\n\n\\[\n34y^{2}+y-(2+4n)=0\\qquad\\Longrightarrow\\qquad  \ny=\\frac{-1\\pm\\sqrt{273+544n}}{68}.\n\\]\n\nSince \\(x=34y^{2}\\le 34\\), we have \\(0\\le x\\le 34\\).  \nConsequently \\(4n+u\\le 34\\) and with \\(u\\ge-1\\) we obtain \\(0\\le n\\le8\\).\n\n--------------------------------------------------------------------\n### 4.   Which roots lie in \\([-1,1]\\)?\n\n* For **Case\u202fA** (\\(n=0,\\dots,8\\)) both roots are in \\([-1,1]\\).  \n  Their sum for each \\(n\\) is\n\n  \\[\n  y_{A+}+y_{A-}= \\frac{1}{34}.\n  \\]\n\n* For **Case\u202fB** (\\(n=0,\\dots,7\\)) both roots are in \\([-1,1]\\);  \n  for \\(n=8\\) only the \u201c+\u2019\u2019 root lies in the interval.  \n  The sum of the two roots for each \\(n\\le7\\) is\n\n  \\[\n  y_{B+}+y_{B-}= -\\frac{1}{34}.\n  \\]\n\nThus the total sum of all \\(y\\)-coordinates is\n\n\\[\n\\begin{aligned}\n\\sum y &amp;=\\sum_{n=0}^{8}\\frac1{34}\\;+\\;\\sum_{n=0}^{7}\\!\\Big(-\\frac1{34}\\Big)\\;+\\;y_{B+}(8)\\\\\n&amp;= \\frac{9}{34}-\\frac{8}{34}+y_{B+}(8)\\\\\n&amp;= \\frac1{34}+ \\frac{-1+\\sqrt{273+544\\cdot8}}{68}.\n\\end{aligned}\n\\]\n\nSince \\(273+544\\cdot8 = 4625 = 25\\cdot185\\),\n\n\\[\ny_{B+}(8)=\\frac{-1+5\\sqrt{185}}{68},\n\\qquad\n\\frac1{34}= \\frac{2}{68}.\n\\]\n\nHence\n\n\\[\n\\sum y =\\frac{2-1+5\\sqrt{185}}{68}= \\frac{1+5\\sqrt{185}}{68}.\n\\]\n\n--------------------------------------------------------------------\n### 5.   Final form\n\n\\[\n\\frac{1+5\\sqrt{185}}{68}= \\frac{a+b\\sqrt{c}}{d},\n\\qquad \na=1,\\;b=5,\\;c=185,\\;d=68 .\n\\]\n\nAll conditions are satisfied (\\(\\gcd(a,b,d)=1\\) and \\(185\\) is square\u2011free).\n\n\\[\na+b+c+d = 1+5+185+68 = 259.\n\\]\n\n\\[\n\\boxed{259}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 259</p>\n<p>Extracted Answer: 259</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThe 27 cells of a $3\\times9$ grid are filled in using the numbers 1 through 9 so that each row contains 9 different numbers, and each of the three $3\\times3$ blocks heavily outlined in the example below contains 9 different numbers, as in the first three rows of a Sudoku puzzle. \n | 4 | 2 | 8 | 9 | 6 | 3 | 1 | 7 | 5 | \n | 3 | 7 | 9 | 5 | 2 | 1 | 6 | 8 | 4 | \n | 5 | 6 | 1 | 8 | 4 | 7 | 9 | 2 | 3 | \n The number of different ways to fill such a grid can be written as $p^a\\cdot q^b\\cdot r^c\\cdot s^d$, where $p,q,r,$ and $s$ are distinct prime numbers and $a,b,c,$ and $d$ are positive integers. Find $p\\cdot a+q\\cdot b+r\\cdot c+s\\cdot d$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let the three rows be \\(R_{1},R_{2},R_{3}\\) and the three \\(3\\times 3\\) blocks be  \n\n\\[\nB_{1}= \\text{columns }1\\!-\\!3,\\qquad   \nB_{2}= \\text{columns }4\\!-\\!6,\\qquad   \nB_{3}= \\text{columns }7\\!-\\!9 .\n\\]\n\n--------------------------------------------------------------------\n### 1.  Fix the first row  \n\nSince the rows are labelled, we may first choose any permutation of \\(\\{1,\\dots ,9\\}\\) for \\(R_{1}\\).\nThere are  \n\n\\[\n9! = 2^{7}\\cdot 3^{4}\\cdot5\\cdot7\n\\]\n\nways.\n\n--------------------------------------------------------------------\n### 2.  Which digits go to the second row in each block?  \n\nAssume \\(R_{1}=1\\,2\\,3\\;4\\,5\\,6\\;7\\,8\\,9\\) (the identity permutation).  \nThen  \n\n* In \\(B_{1}\\) the missing digits are \\(\\{4,5,6,7,8,9\\}\\);  \n* In \\(B_{2}\\) the missing digits are \\(\\{1,2,3,7,8,9\\}\\);  \n* In \\(B_{3}\\) the missing digits are \\(\\{1,2,3,4,5,6\\}\\).\n\nFor the second row we must pick, from each block, three of its six missing digits.\nThe three rows must each contain every digit exactly once, so each digit\nmust appear **once** in \\(R_{2}\\) (and the remaining occurrence of that digit will be in \\(R_{3}\\)).\nThus the choice of digits for \\(R_{2}\\) is a partition of the six\u2013digit sets\nsubject to the condition that each of the nine digits occurs in exactly one block of \\(R_{2}\\).\n\nLet  \n\n* \\(x\\) = number of digits \\(\\{1,2,3\\}\\) placed in \\(B_{2}\\) (the rest go to \\(B_{3}\\));\n* \\(y\\) = number of digits \\(\\{4,5,6\\}\\) placed in \\(B_{1}\\) (the rest go to \\(B_{3}\\));\n* \\(z\\) = number of digits \\(\\{7,8,9\\}\\) placed in \\(B_{1}\\) (the rest go to \\(B_{2}\\)).\n\nFrom the block\u2011size condition we obtain  \n\n\\[\n\\begin{cases}\ny+z=3,\\\\\nx+ (3-z)=3,\\\\\n(3-x)+(3-y)=3,\n\\end{cases}\\qquad\\Longrightarrow\\qquad\nx=z,\\;x+y=3 .\n\\]\n\nHence \\(x\\) may be \\(0,1,2,3\\); then \\(y=3-x\\) and \\(z=x\\).\nFor a given \\(x\\),\n\n* choose the \\(x\\) digits of \\(\\{1,2,3\\}\\) that go to \\(B_{2}\\): \\(\\binom{3}{x}\\) ways;\n* choose the \\(y=3-x\\) digits of \\(\\{4,5,6\\}\\) that go to \\(B_{1}\\): \\(\\binom{3}{3-x}=\\binom{3}{x}\\) ways;\n* choose the \\(z=x\\) digits of \\(\\{7,8,9\\}\\) that go to \\(B_{1}\\): \\(\\binom{3}{x}\\) ways.\n\nThus for this \\(x\\) we have \\(\\bigl(\\binom{3}{x}\\bigr)^{3}\\) possibilities.\nSumming over \\(x=0,1,2,3\\),\n\n\\[\n\\sum_{x=0}^{3}\\binom{3}{x}^{3}=1+27+27+1=56 .\n\\]\n\nSo there are \\(56\\) ways to decide which three\u2011digit sets belong to the second row\n(and the third row is forced to receive the complementary sets).\n\n--------------------------------------------------------------------\n### 3.  Ordering the digits inside each block  \n\nInside a block each row contains three distinct digits.\nFor a fixed block, the three chosen digits of \\(R_{2}\\) can be placed in the\nthree columns in \\(3!\\) ways, and independently the three digits of \\(R_{3}\\) can be placed in \\(3!\\) ways.\nHence each block contributes \\((3!)^{2}=36\\) arrangements.\n\nWith three blocks we obtain \\((36)^{3}=36^{3}=46\\,656\\) column\u2011orderings.\n\n--------------------------------------------------------------------\n### 4.  Total number of grids  \n\n\\[\nN = 9! \\times 56 \\times 36^{3}\n     = 2^{7}\\!3^{4}\\!5\\!7\\; \\times 2^{3}\\!7\\; \\times 2^{6}\\!3^{6}\n     = 2^{16}\\,3^{10}\\,5^{1}\\,7^{2}.\n\\]\n\nThus\n\n\\[\nN = p^{a}\\,q^{b}\\,r^{c}\\,s^{d}\n\\quad\\text{with}\\quad\n(p,q,r,s)=(2,3,5,7),\\;\n(a,b,c,d)=(16,10,1,2).\n\\]\n\n--------------------------------------------------------------------\n### 5.  Required sum  \n\n\\[\np a + q b + r c + s d\n = 2\\cdot16 + 3\\cdot10 + 5\\cdot1 + 7\\cdot2\n = 32 + 30 + 5 + 14\n = 81 .\n\\]\n\n\\[\n\\boxed{81}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 81</p>\n<p>Extracted Answer: 81</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nSix points $ A, B, C, D, E, $ and $ F $ lie in a straight line in that order. Suppose that $ G $ is a point not on the line and that $ AC = 26 $, $ BD = 22 $, $ CE = 31 $, $ DF = 33 $, $ AF = 73 $, $ CG = 40 $, and $ DG = 30 $. Find the area of $ \\triangle BGE $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let the line containing the points be the \\(x\\)-axis.  \nPlace \\(A\\) at the origin, \\(A=(0,0)\\), and write the coordinates of the other\ncollinear points as\n\n\\[\nB=(x_B,0),\\;C=(x_C,0),\\;D=(x_D,0),\\;E=(x_E,0),\\;F=(x_F,0).\n\\]\n\n---\n\n### 1.  Find the positions of \\(B,\\;C,\\;D,\\;E,\\;F\\)\n\nThe given distances are along the line, so\n\n\\[\n\\begin{aligned}\nAC&amp;=26 &amp;&amp;\\Rightarrow x_C=26,\\\\[2pt]\nAF&amp;=73 &amp;&amp;\\Rightarrow x_F=73,\\\\[2pt]\nCE&amp;=31 &amp;&amp;\\Rightarrow x_E=x_C+31=57,\\\\[2pt]\nDF&amp;=33 &amp;&amp;\\Rightarrow x_D=x_F-33=40,\\\\[2pt]\nBD&amp;=22 &amp;&amp;\\Rightarrow x_B=x_D-22=18.\n\\end{aligned}\n\\]\n\nThus  \n\n\\[\nA=0,\\; B=18,\\; C=26,\\; D=40,\\; E=57,\\; F=73 .\n\\]\n\n---\n\n### 2.  Coordinates of \\(G\\)\n\nLet \\(G=(x_G,h)\\), where \\(h&gt;0\\) is the perpendicular distance from \\(G\\) to the line.\n\nThe distances from \\(G\\) to \\(C\\) and \\(D\\) give\n\n\\[\n\\begin{cases}\n(x_G-26)^2+h^2 = 40^2 = 1600,\\\\[4pt]\n(x_G-40)^2+h^2 = 30^2 = 900 .\n\\end{cases}\n\\]\n\nSubtracting the second equation from the first:\n\n\\[\n(x_G-26)^2-(x_G-40)^2 = 1600-900 = 700 .\n\\]\n\nCompute the left side:\n\n\\[\n(x_G^2-52x_G+26^2)-(x_G^2-80x_G+40^2)\n=28x_G-924 .\n\\]\n\nHence  \n\n\\[\n28x_G-924 = 700 \\quad\\Longrightarrow\\quad 28x_G = 1624\n\\quad\\Longrightarrow\\quad x_G = 58 .\n\\]\n\nNow find \\(h\\) using either distance equation; use the first:\n\n\\[\n(58-26)^2 + h^2 = 1600\n\\Longrightarrow 32^2 + h^2 = 1600\n\\Longrightarrow h^2 = 1600-1024 = 576\n\\Longrightarrow h = 24 .\n\\]\n\nThus \\(G=(58,24)\\). Its perpendicular projection onto the line is at \\(x=58\\), which lies between \\(E\\) and \\(F\\).\n\n---\n\n### 3.  Area of \\(\\triangle BGE\\)\n\nThe base \\(BE\\) lies on the \\(x\\)-axis:\n\n\\[\nBE = x_E - x_B = 57-18 = 39 .\n\\]\n\nThe height from \\(G\\) to this base is the vertical distance \\(h=24\\).\n\nTherefore\n\n\\[\n\\text{Area} = \\frac12 \\times (\\text{base}) \\times (\\text{height})\n= \\frac12 \\times 39 \\times 24 = 39 \\times 12 = 468 .\n\\]\n\n---\n\n\\[\n\\boxed{468}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 468</p>\n<p>Extracted Answer: 468</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nFind the sum of all positive integers $ n $ such that $ n + 2 $ divides the product $ 3(n + 3)(n^2 + 9) $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>\\[\n\\text{Find all }n\\in\\mathbb Z_{&gt;0}\\text{ such that }(n+2)\\mid 3(n+3)(n^2+9).\n\\]\n\n---\n\n### 1.  Replace \\(n+2\\) by a new variable  \n\nSet  \n\\[\nm=n+2\\qquad (m\\ge 3).\n\\]\n\nThen  \n\n\\[\nn=m-2,\\qquad n+3=m+1,\\qquad n^2+9=(m-2)^2+9=m^{2}-4m+13 .\n\\]\n\nHence the divisibility condition becomes  \n\n\\[\nm\\mid 3(m+1)(m^{2}-4m+13).\n\\tag{1}\n\\]\n\n---\n\n### 2.  Reduce the right\u2013hand side modulo \\(m\\)\n\nModulo \\(m\\),\n\n\\[\nm+1\\equiv 1,\\qquad m^{2}-4m+13\\equiv 13 .\n\\]\n\nTherefore  \n\n\\[\n3(m+1)(m^{2}-4m+13)\\equiv 3\\cdot1\\cdot13=39 \\pmod m .\n\\]\n\nSo (1) is equivalent to  \n\n\\[\nm\\mid 39 .\n\\tag{2}\n\\]\n\nIndeed, if \\(m\\mid 39\\) then the right\u2013hand side of (1) equals \\(39+km\\) for some integer \\(k\\), hence is divisible by \\(m\\); conversely, if \\(m\\mid 3(m+1)(m^{2}-4m+13)\\) then \\(m\\mid 39\\).\n\n---\n\n### 3.  List possible \\(m\\)\n\nThe positive divisors of \\(39\\) are  \n\n\\[\n1,\\;3,\\;13,\\;39 .\n\\]\n\nSince \\(m=n+2\\ge 3\\) (because \\(n\\ge1\\)), we keep  \n\n\\[\nm\\in\\{3,\\;13,\\;39\\}.\n\\]\n\n---\n\n### 4.  Recover the corresponding \\(n\\)\n\n\\[\n\\begin{aligned}\nm=3 &amp;\\;\\Rightarrow\\; n=m-2=1,\\\\[2pt]\nm=13 &amp;\\;\\Rightarrow\\; n=11,\\\\[2pt]\nm=39 &amp;\\;\\Rightarrow\\; n=37 .\n\\end{aligned}\n\\]\n\nAll three indeed satisfy the original divisibility (quick check: the quotients are \\(40,420,4240\\) respectively).\n\n---\n\n### 5.  Sum of all such \\(n\\)\n\n\\[\n1+11+37=49.\n\\]\n\n\\[\n\\boxed{49}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 49</p>\n<p>Extracted Answer: 49</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThe parabola with equation $y=x^{2}-4$ is rotated $60^{\\circ}$ counterclockwise around the origin. The unique point in the fourth quadrant where the original parabola and its image intersect has $y$-coordinate $\\frac{a-\\sqrt{b}}{c}$, where $a$, $b$, and $c$ are positive integers, and $a$ and $c$ are relatively prime. Find $a+b+c$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n\\[\nP:\\;y=x^{2}-4\n\\]\n\nand rotate \\(P\\) \\(60^{\\circ}\\) counter\u2011clockwise about the origin.  \nIf \\((u,v)\\) is a point of \\(P\\) \\((v=u^{2}-4)\\), after the rotation we obtain  \n\n\\[\n\\begin{aligned}\nx &amp;=u\\cos 60^{\\circ}-v\\sin 60^{\\circ}\n      =\\frac{u-\\sqrt3\\,(u^{2}-4)}2,\\\\[2mm]\ny &amp;=u\\sin 60^{\\circ}+v\\cos 60^{\\circ}\n      =\\frac{\\sqrt3\\,u+u^{2}-4}2 .\n\\end{aligned}\n\\tag{1}\n\\]\n\nA point \\((x,y)\\) that belongs to both the original parabola and its image\nmust satisfy  \n\n\\[\ny=x^{2}-4 \\qquad\\text{and}\\qquad (x,y)=\\bigl(x(u),y(u)\\bigr)\\text{ for some }u .\n\\]\n\nUsing (1) and substituting \\(y=x^{2}-4\\) we get an equation for the\npre\u2011image coordinate \\(u\\):\n\n\\[\n\\Bigl(u-\\sqrt3\\,(u^{2}-4)\\Bigr)^{2}=2u^{2}+2\\sqrt3\\,u+8 .\n\\]\n\nSimplifying gives  \n\n\\[\n3u^{4}-25u^{2}+40+2\\sqrt3\\,u\\,(3-u^{2})=0 .\n\\tag{2}\n\\]\n\nLet \\(t=u^{2}=x^{2}\\;(t\\ge0)\\).  Equation (2) becomes  \n\n\\[\n\\bigl(3t^{2}-25t+40\\bigr)^{2}=12t\\,(3-t)^{2},\n\\]\n\nor\n\n\\[\n9t^{4}-162t^{3}+937t^{2}-2108t+1600=0 .\n\\tag{3}\n\\]\n\nThe quartic factors over the integers:\n\n\\[\n\\begin{aligned}\n9t^{4}-162t^{3}+937t^{2}-2108t+1600\n  &amp;=\\bigl(t^{2}-11t+16\\bigr)\\bigl(9t^{2}-63t+100\\bigr).\n\\end{aligned}\n\\]\n\nThus the possible values of \\(t\\) are\n\n\\[\nt=\\frac{11\\pm\\sqrt{57}}2,\\qquad\nt=\\frac{63\\pm\\sqrt{369}}{18}.\n\\]\n\nRecall that \\(t=x^{2}\\) and that a genuine intersection must satisfy the\noriginal unsquared equation  \n\n\\[\n3t^{2}-25t+40=2\\sqrt3\\,\\sqrt t\\,(3-t).\n\\tag{4}\n\\]\n\nChecking the sign of each side of (4) shows that only  \n\n\\[\nt=\\frac{11-\\sqrt{57}}2\\approx1.725\n\\]\n\nsatisfies (4) with \\(x&gt;0\\).  (The other three roots correspond to the\ncase \\(3t^{2}-25t+40= -2\\sqrt3\\,\\sqrt t\\,(3-t)\\) or give \\(y&gt;0\\).)\n\nSince \\(y=x^{2}-4=t-4\\),\n\n\\[\ny=\\frac{11-\\sqrt{57}}2-4=\\frac{3-\\sqrt{57}}2 .\n\\]\n\nHence the required numbers are  \n\n\\[\na=3,\\qquad b=57,\\qquad c=2,\n\\]\n\nwith \\(\\gcd(a,c)=1\\).  Therefore\n\n\\[\na+b+c=3+57+2=62 .\n\\]\n\n\\[\n\\boxed{62}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 62</p>\n<p>Extracted Answer: 62</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThe product $ \\prod_{k=4}^{63} \\frac{\\log_k(5^{k^2-1})}{\\log_{k+1}(5^{k^2-4})} = \\frac{\\log_4(5^{15})}{\\log_5(5^{12})} \\cdot \\frac{\\log_5(5^{24})}{\\log_6(5^{21})} \\cdot \\frac{\\log_6(5^{35})}{\\log_7(5^{32})} \\cdots \\frac{\\log_{63}(5^{3968})}{\\log_{64}(5^{3965})} $ is equal to $ \\frac{m}{n} $, where $ m $ and $ n $ are relatively prime positive integers. Find $ m + n $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>\\[\n\\prod_{k=4}^{63}\\frac{\\log_k(5^{k^2-1})}{\\log_{k+1}(5^{k^2-4})}\n\\]\n\n---\n\n### 1.  Rewrite each term using change of base  \n\n\\[\n\\log_a b=\\frac{\\ln b}{\\ln a}\n\\]\n\nHence  \n\n\\[\n\\frac{\\log_k(5^{k^2-1})}{\\log_{k+1}(5^{k^2-4})}\n =\\frac{\\displaystyle\\frac{\\ln\\! \\big(5^{\\,k^2-1}\\big)}{\\ln k}}\n        {\\displaystyle\\frac{\\ln\\! \\big(5^{\\,k^2-4}\\big)}{\\ln (k+1)}}\n =\\frac{(k^2-1)\\ln5}{\\ln k}\\cdot\\frac{\\ln (k+1)}{(k^2-4)\\ln5}\n =\\frac{k^2-1}{k^2-4}\\cdot\\frac{\\ln(k+1)}{\\ln k}.\n\\]\n\nThus the whole product becomes  \n\n\\[\n\\Bigl[\\prod_{k=4}^{63}\\frac{k^2-1}{\\,k^2-4}\\Bigr]\\,\n\\Bigl[\\prod_{k=4}^{63}\\frac{\\ln(k+1)}{\\ln k}\\Bigr].\n\\]\n\n---\n\n### 2.  The logarithmic factor telescopes  \n\n\\[\n\\prod_{k=4}^{63}\\frac{\\ln(k+1)}{\\ln k}\n= \\frac{\\ln5}{\\ln4}\\cdot\\frac{\\ln6}{\\ln5}\\cdots\\frac{\\ln64}{\\ln63}\n= \\frac{\\ln64}{\\ln4}\n= \\frac{6\\ln2}{2\\ln2}=3.\n\\]\n\n---\n\n### 3.  Simplify the rational factor  \n\n\\[\n\\frac{k^2-1}{k^2-4}= \\frac{(k-1)(k+1)}{(k-2)(k+2)}.\n\\]\n\nHence  \n\n\\[\n\\prod_{k=4}^{63}\\frac{k^2-1}{k^2-4}\n= \\Bigl[\\prod_{k=4}^{63}\\frac{k-1}{k-2}\\Bigr]\n  \\Bigl[\\prod_{k=4}^{63}\\frac{k+1}{k+2}\\Bigr].\n\\]\n\n**First product**\n\n\\[\n\\prod_{k=4}^{63}\\frac{k-1}{k-2}\n= \\frac{3}{2}\\cdot\\frac{4}{3}\\cdot\\frac{5}{4}\\cdots\\frac{62}{61}\n= \\frac{62}{2}=31.\n\\]\n\n**Second product**\n\n\\[\n\\prod_{k=4}^{63}\\frac{k+1}{k+2}\n= \\frac{5}{6}\\cdot\\frac{6}{7}\\cdot\\frac{7}{8}\\cdots\\frac{64}{65}\n= \\frac{5}{65}= \\frac{1}{13}.\n\\]\n\nMultiplying,\n\n\\[\n\\prod_{k=4}^{63}\\frac{k^2-1}{k^2-4}=31\\cdot\\frac{1}{13}= \\frac{31}{13}.\n\\]\n\n---\n\n### 4.  Combine the two parts  \n\n\\[\n\\prod_{k=4}^{63}\\frac{\\log_k(5^{k^2-1})}{\\log_{k+1}(5^{k^2-4})}\n= \\frac{31}{13}\\times 3 = \\frac{93}{13}.\n\\]\n\nThe fraction \\(\\frac{93}{13}\\) is already in lowest terms (\\(\\gcd(93,13)=1\\)).  \n\nThus \\(m=93,\\; n=13\\) and  \n\n\\[\nm+n = 93+13 = 106.\n\\]\n\n\\[\n\\boxed{106}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 106</p>\n<p>Extracted Answer: 106</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $N$ denote the number of ordered triples of positive integers $(a,b,c)$ such that $a,b,c\\leq3^6$ and $a^3+b^3+c^3$ is a multiple of $3^7$. Find the remainder when $N$ is divided by $1000$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>**Solution Sketch**\n\nWrite every integer \\(a\\le 3^{6}=729\\) in its base\u2011\\(3\\) expansion  \n\n\\[\na = a_{0}+a_{1}3+a_{2}3^{2}+a_{3}3^{3}+a_{4}3^{4}+a_{5}3^{5},\n\\qquad a_{i}\\in\\{0,1,2\\}.\n\\]\n\nLet  \n\n\\[\nA(x)=a_{0}+a_{1}x+a_{2}x^{2}+a_{3}x^{3}+a_{4}x^{4}+a_{5}x^{5}\\in\\mathbb{F}_{3}[x].\n\\]\n\nModulo \\(3^{7}\\) we have  \n\n\\[\na^{3}\\equiv a_{0}^{3}+9a_{0}^{2}a_{1}+27\\bigl(a_{0}a_{1}^{2}+a_{0}^{2}a_{2}\\bigr)\n               +\\; \\cdots\\;+3^{6}a_{2}^{3}\\pmod{3^{7}} .\n\\]\n\nHence\n\n\\[\na^{3}+b^{3}+c^{3}\\equiv \n\\sum_{i=0}^{2}3^{i}\\bigl(a_{i}^{3}+b_{i}^{3}+c_{i}^{3}\\bigr)\\pmod{3^{7}} .\n\\]\n\nBecause \\(x^{3}\\equiv x\\pmod 3\\) for \\(x\\in\\{0,1,2\\}\\), the condition\n\\(a^{3}+b^{3}+c^{3}\\equiv0\\pmod{3^{7}}\\) is equivalent to the three\nindependent linear equations  \n\n\\[\na_{0}+b_{0}+c_{0}\\equiv0,\\qquad\na_{1}+b_{1}+c_{1}\\equiv0,\\qquad\na_{2}+b_{2}+c_{2}\\equiv0\\pmod 3 .\n\\]\n\nFor each digit\u2011position \\(i=0,1,2\\) the number of ordered triples\n\\((a_{i},b_{i},c_{i})\\) satisfying the linear condition is\n\\(3^{2}=9\\) (choose any two digits freely, the third one is forced).\nThe remaining higher digits \\(a_{3},a_{4},a_{5}\\) are unrestricted; each\nhas \\(3^{3}=27\\) possibilities (three choices for each of the three\nnumbers).\n\nTherefore the total number of admissible triples \\((a,b,c)\\) is  \n\n\\[\nN = 9^{3}\\cdot 27^{3}=3^{15}=14\\,348\\,907 .\n\\]\n\nFinally we need the remainder of \\(N\\) modulo \\(1000\\):\n\n\\[\n14\\,348\\,907\\equiv 907\\pmod{1000}.\n\\]\n\n\\[\n\\boxed{907}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 735</p>\n<p>Extracted Answer: 907</p>\n<p>Score: 0.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nFour unit squares form a $2 \\times 2$ grid. Each of the 12 unit line segments forming the sides of the squares is colored either red or blue in such a way that each unit square has 2 red sides and 2 blue sides. Find the number of such colorings.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n* \\(a,b,c,d\\) be the four interior edges (the two interior vertical and the two interior horizontal sides).  \n* The eight outer edges are the two edges that belong to each unit square but are on the boundary of the\n\\(2\\times2\\) grid.\n\nFor a particular unit square the number of its interior red sides is the number of red interior edges incident\nto it.  \nIf a square has \\(s\\) interior red sides, then it needs exactly \\(2-s\\) red outer sides, because the total number\nof red sides must be \\(2\\).  \n\nFor a given square\n\n\\[\n\\#\\text{ ways to colour its two outer edges}= \\binom{2}{\\,2-s\\,}=\n\\begin{cases}\n1,&amp;s=0\\text{ or }2,\\\\[2pt]\n2,&amp;s=1 .\n\\end{cases}\n\\]\n\nThus, once the interior edges are fixed, the outer edges can be coloured independently for each square.\nIf among the four squares exactly \\(k\\) of them have \\(s=1\\) (i.e. exactly one interior red edge incident to the\nsquare), the number of completions of the outer edges is \\(2^{k}\\).\n\n--------------------------------------------------------------------\n\n### Counting interior\u2013edge configurations\n\nThe interior edges form a 4\u2011cycle  \n\n\\[\nA\\;-\\;B\\;-\\;D\\;-\\;C\\;-\\;A .\n\\]\n\nWe list all \\(2^{4}=16\\) subsets of these edges and, for each, count how many squares have one interior red\nedge.\n\n| # interior edges | type of selection | \\# of squares with \\(s=1\\) | \\# of such subsets | contributions |\n|------------------|-------------------|----------------------------|--------------------|---------------|\n| 0 | none | 0 | 1 | \\(2^{0}=1\\) |\n| 1 | any one edge | 2 (the two squares incident to the edge) | 4 | \\(4\\cdot2^{2}=16\\) |\n| 2 | adjacent edges (share a vertex) | 2 (the two squares adjacent to the common vertex) | 4 | \\(4\\cdot2^{2}=16\\) |\n| 2 | opposite edges (no common vertex) | 4 (each square gets one) | 2 | \\(2\\cdot2^{4}=32\\) |\n| 3 | all but one edge | 2 (the two squares not incident to the missing edge) | 4 | \\(4\\cdot2^{2}=16\\) |\n| 4 | all four edges | 0 | 1 | \\(1\\cdot2^{0}=1\\) |\n\nAdding the contributions:\n\n\\[\n1+16+16+32+16+1 = 82 .\n\\]\n\n--------------------------------------------------------------------\n\nTherefore there are  \n\n\\[\n\\boxed{82}\n\\]\n\ndifferent ways to colour the 12 unit segments so that each of the four unit squares has exactly two red sides\n(and consequently two blue sides).</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 82</p>\n<p>Extracted Answer: 82</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $ A $ be the set of positive integer divisors of 2025. Let $ B $ be a randomly selected subset of $ A $. The probability that $ B $ is a nonempty set with the property that the least common multiple of its elements is 2025 is $ \\frac{m}{n} $, where $ m $ and $ n $ are relatively prime positive integers. Find $ m + n $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>\\(2025=3^{4}\\cdot5^{2}\\).\n\nDivisors of \\(2025\\) are of the form \\(3^{a}5^{b}\\) with  \n\\(0\\le a\\le4,\\;0\\le b\\le2\\); therefore  \n\n\\[\n|A|=(4+1)(2+1)=15 .\n\\]\n\n--------------------------------------------------------------------\n### Condition for the LCM\n\nFor a subset \\(B\\subseteq A\\),\n\n\\[\n\\operatorname{lcm}(B)=3^{\\max a}\\,5^{\\max b}.\n\\]\n\nThus \\(\\operatorname{lcm}(B)=2025=3^{4}5^{2}\\) iff  \n\n* at least one element of \\(B\\) has exponent \\(a=4\\) (i.e. is divisible by \\(3^{4}\\)), and  \n* at least one element of \\(B\\) has exponent \\(b=2\\) (i.e. is divisible by \\(5^{2}\\)).\n\n--------------------------------------------------------------------\n### Relevant divisor families  \n\n\\[\nX=\\{d\\in A\\mid 3^{4}\\mid d\\}=\\{81,405,2025\\},\\qquad |X|=3,\n\\]\n\n\\[\nY=\\{d\\in A\\mid 5^{2}\\mid d\\}=\\{25,75,225,675,2025\\},\\qquad |Y|=5.\n\\]\n\n\\(X\\cap Y=\\{2025\\}\\), so \\(|X\\cup Y|=3+5-1=7\\).\n\n--------------------------------------------------------------------\n### Counting subsets with the required property  \n\nA subset \\(B\\) works iff it meets both \\(X\\) and \\(Y\\).  \nUsing inclusion\u2013exclusion on all \\(2^{15}\\) subsets of \\(A\\):\n\n\\[\n\\begin{aligned}\n\\#\\{B:\\ B\\cap X\\neq\\varnothing,\\ B\\cap Y\\neq\\varnothing\\}\n&amp;=2^{15}\n -2^{12}\\;(\\text{subsets missing }X)\n -2^{10}\\;(\\text{subsets missing }Y)\\\\\n&amp;\\qquad +2^{8}\\;(\\text{subsets missing both }X\\cup Y)\\\\[2mm]\n&amp;=32768-4096-1024+256\\\\\n&amp;=27904 .\n\\end{aligned}\n\\]\n\nAll these subsets are non\u2011empty, so the numerator is \\(27904\\).\n\n--------------------------------------------------------------------\n### Probability\n\n\\[\nP=\\frac{27904}{2^{15}}=\\frac{27904}{32768}.\n\\]\n\nBoth numbers are divisible by \\(256\\):\n\n\\[\n\\frac{27904}{32768}=\\frac{27904/256}{32768/256}= \\frac{109}{128}.\n\\]\n\nThe fraction \\(\\frac{109}{128}\\) is already in lowest terms, so  \n\\(m=109,\\;n=128\\).\n\n\\[\nm+n=109+128=237.\n\\]\n\n\\[\n\\boxed{237}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 237</p>\n<p>Extracted Answer: 237</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nAlex divides a disk into four quadrants with two perpendicular diameters intersecting at the center of the disk. He draws 25 more line segments through the disk, drawing each segment by selecting two points at random on the perimeter of the disk in different quadrants and connecting those two points. Find the expected number of regions into which these 27 line segments divide the disk.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>**Step\u202f1 \u2013  How regions grow**\n\nWhen a new line segment is drawn in the disk, it either  \n*does not meet any previous segment* \u2013 it creates **one** new region, or  \n*meets \\(k\\) previous segments in interior points* \u2013 it creates **\\(k+1\\)** new regions  \n(the segment is cut into \\(k+1\\) pieces, each of which separates a region).\n\nHence, if we start with one region (the whole disk),\n\n\\[\n\\#\\text{regions}=1+\\#\\text{segments}+\\#\\text{interior intersections } .\n\\tag{1}\n\\]\n\nThe two perpendicular diameters intersect once, giving the four initial\nquadrants.  After the 25 random chords are added we will have  \n\n\\[\n27\\text{ segments} = 2\\text{ diameters}+25\\text{ chords}.\n\\]\n\nSo we only have to find the **expected number of interior intersection points**.\n\n--------------------------------------------------------------------\n\n**Step\u202f2 \u2013  Intersections with the diameters**\n\nA random chord meets a fixed diameter iff its two endpoints lie on opposite\nsides of that diameter.  \n\n*Horizontal diameter*\u2003(\\(y=0\\)): the endpoints must belong to one of the\nfour unordered quadrant pairs  \n\n\\[\n\\{Q_1,Q_3\\},\\{Q_1,Q_4\\},\\{Q_2,Q_3\\},\\{Q_2,Q_4\\},\n\\]\n\ni.e. 4 out of the 6 possible unordered pairs of different quadrants.\nThus  \n\n\\[\nP(\\text{chord meets a given diameter})=\\frac{4}{6}= \\frac23 .\n\\]\n\nThe same probability holds for the vertical diameter.  \nHence the expected number of chord\u2011diameter intersections is  \n\n\\[\n25\\;( \\text{chords})\\times 2\\;( \\text{diameters})\\times \\frac23\n  =\\frac{100}{3}.\n\\tag{2}\n\\]\n\n--------------------------------------------------------------------\n\n**Step\u202f3 \u2013  Intersections between two random chords**\n\nLet a chord be represented by the unordered pair of quadrants that contain its\nend\u2011points.  \nThere are  \n\n* 4 *adjacent* pairs  \\(\\{0,1\\},\\{1,2\\},\\{2,3\\},\\{3,0\\}\\);  \n* 2 *opposite* pairs   \\(\\{0,2\\},\\{1,3\\}\\).\n\nThus the six possible chords are the six edges of the complete graph \\(K_4\\)\non the four quadrants.\n\nTwo chords may be:\n\n| Relation of the two edges | How many ordered pairs | Intersection probability |\n|---------------------------|-----------------------|--------------------------|\n| Same edge (both chords use the same pair) | 6 (4 adjacent\u202f+\u202f2 opposite) | \\(\\frac12\\) |\n| Share one vertex (adjacent edges) | 24 (8 both adjacent\u202f+\u202f16 one adjacent\u2013one opposite) | \\(\\frac12\\) |\n| Disjoint edges, both adjacent (e.g. \\{0,1\\} &amp; \\{2,3\\}) | 4 | \\(0\\) |\n| Disjoint edges, both opposite ( \\{0,2\\} &amp; \\{1,3\\}) | 2 | \\(1\\) |\n\n*Why these probabilities?*  \n\n* Same edge \u2013 the two chords are independent copies inside the same two\nquadrants.  A short calculation (or a symmetry argument) gives a crossing\nprobability of \\(\\frac12\\).\n* Share a vertex \u2013 one endpoint of the second chord lies in the same quadrant\nas an endpoint of the first chord.  The second endpoint is always in a\ndifferent quadrant, so the second chord meets the first exactly when the\npoint that shares the vertex falls between the two endpoints of the first\nchord.  Averaging over the uniform positions gives \\(\\frac12\\) again.\n* Disjoint adjacent edges lie completely on opposite sides of the\nhorizontal (or vertical) diameter, so they can never meet \u21d2 probability \\(0\\).\n* Disjoint opposite edges always cross the centre of the disk; any two such\nchords intersect \u21d2 probability \\(1\\).\n\nSumming the contributions of the \\(36\\) ordered pairs of chords,\n\n\\[\nS = 6\\!\\left(\\frac12\\right)+24\\!\\left(\\frac12\\right)+4\\cdot0+2\\cdot1 = 17 .\n\\]\n\nTherefore the probability that two independently chosen random chords intersect is  \n\n\\[\np_{\\text{chord\u2013chord}} = \\frac{S}{36}= \\frac{17}{36}.\n\\tag{3}\n\\]\n\n--------------------------------------------------------------------\n\n**Step\u202f4 \u2013  Expected number of chord\u2013chord intersections**\n\nThere are \\(\\binom{25}{2}=300\\) unordered pairs of the 25 random chords.  \nUsing (3),\n\n\\[\nE(\\text{chord\u2013chord intersections})=300\\cdot\\frac{17}{36}\n     =\\frac{425}{3}=141\\frac{2}{3}.\n\\tag{4}\n\\]\n\n--------------------------------------------------------------------\n\n**Step\u202f5 \u2013  Total expected interior intersections**\n\n\\[\n\\begin{aligned}\nE(\\text{total interior intersections})\n&amp;= (\\text{diameters intersect})\\\\\n&amp;\\qquad +(\\text{chord\u2013diameter intersections})\\\\\n&amp;\\qquad +(\\text{chord\u2013chord intersections})\\\\[2mm]\n&amp;= 1+\\frac{100}{3}+ \\frac{425}{3}= 176 .\n\\end{aligned}\n\\tag{5}\n\\]\n\n--------------------------------------------------------------------\n\n**Step\u202f6 \u2013  Expected number of regions**\n\nInsert (5) into formula (1) with the total of \\(27\\) segments:\n\n\\[\nE(\\text{regions}) = 1 + 27 + 176 = 204 .\n\\]\n\n--------------------------------------------------------------------\n\n\\[\n\\boxed{204}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 204</p>\n<p>Extracted Answer: 204</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nCircle $\\omega_1$ with radius 6 centered at point $A$ is internally tangent at point $B$ to circle $\\omega_2$ with radius 15. Points $C$ and $D$ lie on $\\omega_2$ such that $\\overline{BC}$ is a diameter of $\\omega_2$ and $\\overline{BC} \\perp \\overline{AD}$. The rectangle $EFGH$ is inscribed in $\\omega_1$ such that $\\overline{EF} \\perp \\overline{BC}$, $C$ is closer to $\\overline{GH}$ than to $\\overline{EF}$, and $D$ is closer to $\\overline{FG}$ than to $\\overline{EH}$, as shown. Triangles $\\triangle DGF$ and $\\triangle CHG$ have equal areas. The area of rectangle $EFGH$ is $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m + n$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>**Solution Overview**\n\nPlace the two circles on a coordinate plane, compute the positions of the relevant points, and write the\nrectangle\u2019s vertices in terms of its side\u2013lengths.  \nThe conditions \u201c\\(C\\) is closer to \\(\\overline{GH}\\) than to \\(\\overline{EF}\\)\u201d and \u201c\\(D\\) is closer to\n\\(\\overline{FG}\\) than to \\(\\overline{EH}\\)\u201d fix the orientation of the rectangle.  \nUsing the equality of the two triangle areas we obtain a simple relation between the rectangle\u2019s width\nand height, which together with the fact that the rectangle is inscribed in the small circle yields the\nrequired dimensions and its area.\n\n--------------------------------------------------------------------\n\n### 1.  Coordinate set\u2011up  \n\nLet  \n\n* \\(O\\) be the centre of the large circle \\(\\omega_2\\) (radius \\(15\\)).\n* \\(A\\) be the centre of the small circle \\(\\omega_1\\) (radius \\(6\\)).\n* \\(B\\) the common point of tangency.\n\nBecause the circles are internally tangent,\n\\[\nOA = 15-6=9,\n\\qquad AB=6,\n\\qquad OB =15 .\n\\]\n\nChoose the \\(x\\)\u2013axis along \\(\\overline{BC}\\).  \nTake  \n\n\\[\nO=(0,0),\\qquad B=(15,0).\n\\]\n\nThen \\(A\\) lies on the same line, nine units left of \\(B\\):\n\\[\nA=(9,0).\n\\]\n\nSince \\(BC\\) is a diameter of \\(\\omega_2\\), the opposite end of the diameter is\n\\[\nC=(-15,0).\n\\]\n\nThe condition \\(\\overline{BC}\\perp\\overline{AD}\\) makes \\(AD\\) vertical, so the points of\n\\(\\omega_2\\) with \\(x=9\\) are\n\\[\nD=(9,12)\\quad\\text{or}\\quad D=(9,-12).\n\\]\nBecause later we need \\(D\\) to be nearer the top side of the rectangle, we take  \n\n\\[\n\\boxed{D=(9,12)} .\n\\]\n\n--------------------------------------------------------------------\n\n### 2.  The rectangle \\(EFGH\\)\n\n\\(EF\\) is required to be perpendicular to \\(\\overline{BC}\\); hence \\(EF\\) is a vertical side.\nLet the rectangle have\n\n* width \\(w\\) (the horizontal side \\(\\overline{FG}\\)),\n* height \\(h\\) (the vertical side \\(\\overline{EF}= \\overline{GH}\\)).\n\nSince the rectangle is inscribed in \\(\\omega_1\\), its centre coincides with the centre of \\(\\omega_1\\),\nnamely \\(A=(9,0)\\).  Consequently the vertices are\n\n\\[\n\\begin{aligned}\nE&amp;=\\bigl(b,\\,-\\tfrac{h}{2}\\bigr), &amp;\nF&amp;=\\bigl(b, \\tfrac{h}{2}\\bigr),\\\\[2mm]\nG&amp;=\\bigl(a, \\tfrac{h}{2}\\bigr), &amp;\nH&amp;=\\bigl(a,\\,-\\tfrac{h}{2}\\bigr),\n\\end{aligned}\n\\]\nwhere  \n\n\\[\na = 9-\\frac{w}{2},\\qquad b = 9+\\frac{w}{2}.\n\\]\n\nBecause every vertex lies on \\(\\omega_1\\) (radius \\(6\\) and centre \\((9,0)\\)),\n\\[\n(a-9)^2+\\Bigl(\\frac{h}{2}\\Bigr)^2 = (b-9)^2+\\Bigl(\\frac{h}{2}\\Bigr)^2 = 6^{2}=36 .\n\\]\nBoth equations give the single relation  \n\n\\[\n\\boxed{w^{2}+h^{2}=144}\\tag{1}\n\\]\n(the rectangle\u2019s diagonal is the diameter \\(12\\) of the small circle).\n\n--------------------------------------------------------------------\n\n### 3.  Interpreting the \u201ccloser\u2011to\u201d conditions  \n\nThe statement \u201c\\(C\\) is closer to \\(\\overline{GH}\\) than to \\(\\overline{EF}\\)\u201d forces \\(\\overline{GH}\\) to be\nthe left vertical side (smaller \\(x\\))-coordinate) and \\(\\overline{EF}\\) the right vertical side.  \nSimilarly \u201c\\(D\\) is closer to \\(\\overline{FG}\\) than to \\(\\overline{EH}\\)\u201d places \\(\\overline{FG}\\) at the\ntop (larger \\(y\\))-coordinate.\n\nThus  \n\n\\[\n\\begin{aligned}\n\\text{dist}(C,\\overline{GH})&amp;=a-(-15)=a+15,\\\\\n\\text{dist}(C,\\overline{EF})&amp;=b+15,\\\\[1mm]\n\\text{dist}(D,\\overline{FG})&amp;=12-\\frac{h}{2},\\\\\n\\text{dist}(D,\\overline{EH})&amp;=12+\\frac{h}{2},\n\\end{aligned}\n\\]\nand the above inequalities are automatically satisfied for any feasible rectangle\n(\\(a&lt;b\\) and \\(h/2&lt;12\\)).\n\n--------------------------------------------------------------------\n\n### 4.  Equality of the two triangle areas  \n\n*Triangle \\(DGF\\).*  \n\\(G\\) and \\(F\\) are the top\u2011left and top\u2011right vertices, so \\(\\overline{GF}\\) is horizontal,\n\\(|GF| = w\\).  The altitude from \\(D\\) to \\(\\overline{GF}\\) is the vertical distance\n\\(12-\\frac{h}{2}\\).  Hence  \n\n\\[\n[ DGF ] = \\frac12 \\, w\\!\\left(12-\\frac{h}{2}\\right).\n\\tag{2}\n\\]\n\n*Triangle \\(CHG\\).*  \n\\(G\\) and \\(H\\) lie on the left side, \\(|GH|=h\\).  The altitude from \\(C\\) to this side is the\nhorizontal distance \\(a+15\\).  Thus  \n\n\\[\n[ CHG ] = \\frac12 \\, h\\,(a+15).\n\\tag{3}\n\\]\n\nGiven \\([DGF]=[CHG]\\) and using \\(a=9-\\dfrac w2\\), we have  \n\n\\[\nw\\!\\left(12-\\frac{h}{2}\\right)=\nh\\!\\Bigl(9-\\frac{w}{2}+15\\Bigr)\n= h\\!\\bigl(24-\\frac{w}{2}\\bigr).\n\\]\n\nExpanding and cancelling the common term \\(-\\dfrac{wh}{2}\\) yields  \n\n\\[\n12w = 24h \\quad\\Longrightarrow\\quad \\boxed{w = 2h}. \\tag{4}\n\\]\n\n--------------------------------------------------------------------\n\n### 5.  Determining \\(w\\) and \\(h\\)\n\nInsert \\(w=2h\\) into (1):\n\n\\[\n(2h)^{2}+h^{2}=144\n\\;\\Longrightarrow\\;5h^{2}=144\n\\;\\Longrightarrow\\;h^{2}=\\frac{144}{5}.\n\\]\n\nHence  \n\n\\[\nh = \\frac{12}{\\sqrt5}= \\frac{12\\sqrt5}{5},\n\\qquad \nw = 2h = \\frac{24\\sqrt5}{5}.\n\\]\n\n--------------------------------------------------------------------\n\n### 6.  Area of the rectangle  \n\n\\[\n[EFGH]=w\\cdot h = 2h^{2}=2\\cdot\\frac{144}{5}= \\frac{288}{5}.\n\\]\n\nThus the required area is \\(\\displaystyle \\frac{288}{5}\\); the fraction is already in lowest terms.\nSo \\(m=288,\\; n=5\\) and  \n\n\\[\nm+n = 288+5 = 293 .\n\\]\n\n--------------------------------------------------------------------\n\n\\[\n\\boxed{293}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 293</p>\n<p>Extracted Answer: 293</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet the sequence of rationals $ x_1, x_2, \\ldots $ be defined such that $ x_1 = \\frac{25}{11} $ and\n$ x_{k+1} = \\frac{1}{3} \\left( x_k + \\frac{1}{x_k} - 1 \\right). $\n$ x_{2025} $ can be expressed as $ \\frac{m}{n} $ for relatively prime positive integers $ m $ and $ n $. Find the remainder when $ m + n $ is divided by 1000.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>\\[\nx_{k+1}= \\frac{x_k+\\dfrac1{x_k}-1}{3}, \\qquad x_1=\\frac{25}{11}.\n\\]\n\n--------------------------------------------------------------------\n### 1.  A convenient change of variable  \n\nSet  \n\n\\[\nt_k=\\frac{x_k-1}{x_k+1}\\qquad\\Longleftrightarrow\\qquad \nx_k=\\frac{1+t_k}{1-t_k}.\n\\]\n\nThen a short computation gives  \n\n\\[\nt_{k+1}= \\frac{3t_k^{2}-1}{2}. \\tag{1}\n\\]\n\nThus the problem reduces to iterating the quadratic map  \n\n\\[\nF(t)=\\frac{3t^{2}-1}{2}\n\\]\n\nstarting from  \n\n\\[\nt_1=\\frac{x_1-1}{x_1+1}\n      =\\frac{25/11-1}{25/11+1}\n      =\\frac{7}{18}.\n\\]\n\n--------------------------------------------------------------------\n### 2.  Working with the original rationals  \n\nWrite \\(t_k=p_k/q_k\\) in lowest terms.   \nFrom (1)\n\n\\[\n\\frac{p_{k+1}}{q_{k+1}}=\n\\frac{3p_k^{2}-3p_kq_k+3q_k^{2}}{2q_k^{2}}\n      =\\frac{p_k^{2}-p_kq_k+q_k^{2}}{3}\\;\\Big/\n        \\;\\frac{p_kq_k}{1},\n\\]\n\nhence (clearing the common factor \\(3\\))\n\n\\[\n\\boxed{\\displaystyle \np_{k+1}= \\frac{p_k^{2}-p_kq_k+q_k^{2}}{3},\n\\qquad \nq_{k+1}=p_kq_k } . \\tag{2}\n\\]\n\nFor the initial pair  \n\n\\[\np_1=25,\\qquad q_1=11 .\n\\]\n\nBecause \\(p_1\\equiv1,\\; q_1\\equiv2\\pmod 3\\) one checks from (2) that  \n\\(p_k\\equiv1,\\; q_k\\equiv2\\pmod 3\\) for every \\(k\\); consequently the\ndivision by \\(3\\) in (2) is always exact and the reduced fractions\n\\(\\dfrac{p_k}{q_k}=x_k\\) stay in lowest terms.\n\n--------------------------------------------------------------------\n### 3.  Behaviour modulo\u202f\\(8\\)\n\n\\(3\\) is invertible modulo \\(8\\) (\\(3^{-1}\\equiv3\\)).  \nFrom (2)\n\n\\[\np_{k+1}\\equiv 3\\bigl(p_k^{2}-p_kq_k+q_k^{2}\\bigr)\\pmod 8,\n\\qquad \nq_{k+1}\\equiv p_kq_k\\pmod 8 .\n\\]\n\nStarting with \\((p_1,q_1)\\equiv(1,3)\\pmod8\\) one obtains\n\n\\[\n(p_2,q_2)\\equiv(5,3),\\qquad\n(p_3,q_3)\\equiv(1,7),\n\\]\n\nand thereafter  \n\n\\[\np_k\\equiv1,\\quad q_k\\equiv7\\pmod8 \\qquad(k\\ge3).\n\\]\n\nHence for every \\(k\\ge3\\)\n\n\\[\np_k+q_k\\equiv0\\pmod8. \\tag{3}\n\\]\n\n--------------------------------------------------------------------\n### 4.  Behaviour modulo\u202f\\(125\\)\n\n\\(3^{-1}\\equiv42\\pmod{125}\\).  Using (2),\n\n\\[\np_{k+1}\\equiv42\\bigl(p_k^{2}-p_kq_k+q_k^{2}\\bigr)\\pmod{125},\n\\qquad \nq_{k+1}\\equiv p_kq_k\\pmod{125}. \\tag{4}\n\\]\n\nComputating a few steps (mod\u202f125) gives  \n\n\\[\n\\begin{array}{c|c|c}\nk &amp; p_k\\pmod{125} &amp; q_k\\pmod{125}\\\\ \\hline\n1 &amp; 25 &amp; 11\\\\\n2 &amp; 32 &amp; 25\\\\\n3 &amp; 33 &amp; 50\\\\\n4 &amp; 63 &amp; 25\\\\\n5 &amp; 48 &amp; 75\\\\\n6 &amp; 68 &amp;100\\\\\n\\vdots &amp;\\vdots &amp;\\vdots\n\\end{array}\n\\]\n\nFrom \\(k=4\\) onward the pair \\((p_k,q_k)\\) repeats with period\u202f20:\n\n\\[\n(p_{k+20},q_{k+20})\\equiv(p_k,q_k)\\pmod{125}\\qquad(k\\ge4).\n\\]\n\nSince \\(2025\\equiv5\\pmod{20}\\) and \\(2025\\ge4\\),\n\n\\[\np_{2025}\\equiv p_5\\equiv48,\\qquad\nq_{2025}\\equiv q_5\\equiv75 \\pmod{125}. \\tag{5}\n\\]\n\nThus\n\n\\[\np_{2025}+q_{2025}\\equiv48+75=123\\pmod{125}. \\tag{6}\n\\]\n\n--------------------------------------------------------------------\n### 5.  Combination (Chinese Remainder)\n\nFrom (3) we have \\(p_{2025}+q_{2025}\\equiv0\\pmod8\\);   \nfrom (6) we have \\(p_{2025}+q_{2025}\\equiv123\\pmod{125}\\).\n\nLet \\(S=p_{2025}+q_{2025}\\).  \nWrite \\(S=8u\\); then \\(8u\\equiv123\\pmod{125}\\).\nSince \\(8^{-1}\\equiv47\\pmod{125}\\),\n\n\\[\nu\\equiv47\\cdot123\\equiv31\\pmod{125},\n\\qquad\nS=8u\\equiv8\\cdot31=248\\pmod{1000}.\n\\]\n\n--------------------------------------------------------------------\n### 6.  Answer\n\nThe required remainder is  \n\n\\[\n\\boxed{248}.\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 248</p>\n<p>Extracted Answer: 248</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nFrom an unlimited supply of 1-cent coins, 10-cent coins, and 25-cent coins, Silas wants to find a collection of coins that has a total value of $ N $ cents, where $ N $ is a positive integer. He uses the so-called **greedy algorithm**, successively choosing the coin of greatest value that does not cause the value of his collection to exceed $ N $. For example, to get 42 cents, Silas will choose a 25-cent coin, then a 10-cent coin, then 7 1-cent coins. However, this collection of 9 coins uses more coins than necessary to get a total of 42 cents; indeed, choosing 4 10-cent coins and 2 1-cent coins achieves the same total value with only 6 coins.\n\nIn general, the greedy algorithm succeeds for a given $ N $ if no other collection of 1-cent, 10-cent, and 25-cent coins gives a total value of $ N $ cents using strictly fewer coins than the collection given by the greedy algorithm. Find the number of values of $ N $ between 1 and 1000 inclusive for which the greedy algorithm succeeds.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>**Step\u202f1.  Greedy representation**\n\nFor a value \\(N\\) write  \n\n\\[\nN = 25q + r ,\\qquad 0\\le r&lt;25 .\n\\]\n\nThe greedy algorithm first uses \\(q\\) quarters, then as many dimes as possible from the remainder \\(r\\):\n\\[\nr = 10d + e ,\\qquad 0\\le e&lt;10 .\n\\]\nHence the greedy collection has  \n\n\\[\n\\text{coins}_{\\text{greedy}} = q+d+e .\n\\tag{1}\n\\]\n\n**Step\u202f2.  When can we do better?**\n\nA collection using \\(a\\) quarters and \\(b\\) dimes (the pennies are forced) has  \n\n\\[\n25a+10b\\le N ,\\qquad \\text{pennies}=N-25a-10b .\n\\]\n\nIts total number of coins is  \n\n\\[\na+b+(N-25a-10b)=N-(24a+9b).\n\\]\n\nBecause \\(N\\) is fixed, the collection is optimal iff the quantity  \n\n\\[\nW=24a+9b\n\\tag{2}\n\\]\n\nis as large as possible under the constraint \\(25a+10b\\le N\\).  \n\n**Step\u202f3.  Compare the greedy choice with one fewer quarter**\n\nThe greedy choice uses \\(a=q\\) and \\(b=d\\).  \nConsider reducing the number of quarters by one: take \\(a&#39;=q-1\\).  \nThe value that must now be made with dimes and pennies is \\(25+r\\); the maximal possible number\nof dimes is\n\n\\[\nb&#39;=\\Big\\lfloor\\frac{25+r}{10}\\Big\\rfloor .\n\\]\n\nWrite \\(r=10d+e\\;(0\\le e\\le 9)\\). Then  \n\n\\[\n\\frac{25+r}{10}=2+d+\\frac{e+5}{10},\n\\qquad\nb&#39;=d+2+f,\n\\]\nwhere  \n\n\\[\nf=\\Big\\lfloor\\frac{e+5}{10}\\Big\\rfloor=\n\\begin{cases}\n0,&amp;e\\le4,\\\\[2pt]\n1,&amp;e\\ge5 .\n\\end{cases}\n\\]\n\nThe weight (2) for the greedy choice is  \n\n\\[\nW_{\\text{gr}}=24q+9d .\n\\]\n\nFor the alternative with one fewer quarter we have  \n\n\\[\nW_{\\text{alt}}=24(q-1)+9(d+2+f)=W_{\\text{gr}}-24+18+9f\n      =W_{\\text{gr}}+( -6+9f).\n\\]\n\nThus  \n\n\\[\nW_{\\text{alt}}-W_{\\text{gr}}=\n\\begin{cases}\n-6, &amp; e\\le 4,\\\\[2pt]\n+3, &amp; e\\ge 5 .\n\\end{cases}\n\\]\n\nIf \\(e\\ge5\\) the alternative has **larger** weight, i.e. it uses **fewer** coins\n(three fewer, because the weight increases by 3).  \nIf \\(e\\le4\\) the alternative is worse.\n\nConsequently the greedy algorithm is **not optimal exactly when**\n\\[\ne = r \\bmod 10 \\ge 5 .\n\\tag{3}\n\\]\n\n**Step\u202f4.  Which remainders cause failure?**\n\nSince \\(r\\) ranges from \\(0\\) to \\(24\\), condition (3) means  \n\n\\[\nr\\in\\{5,6,7,8,9,15,16,17,18,19\\}.\n\\tag{4}\n\\]\n\nFor \\(N&lt;25\\) we have \\(q=0\\); only 1\u2011cent and 10\u2011cent coins are usable, and the greedy\nchoice (as many dimes as possible) is obviously optimal.  Hence failures occur only for\n\\(N\\ge25\\) with remainder (4) upon division by \\(25\\).\n\n**Step\u202f5.  Counting the failures between 1 and\u202f1000**\n\nThe numbers \\(25\\le N\\le 1000\\) form 39 complete blocks of 25 consecutive integers\n(\\(25\\)\u2013\\(999\\)) and the single extra number \\(1000\\).\n\n- In each full block every residue modulo \\(25\\) appears once,\n  so each block contains exactly \\(10\\) failures (the residues in (4)).\n- Hence failures in the 39 blocks: \\(39\\times10=390\\).\n\nThe leftover number \\(1000\\) has residue \\(0\\) (not a failure).\n\nThus the total number of failures is \\(390\\).\n\n**Step\u202f6.  Successes**\n\nOut of the \\(1000\\) possible values of \\(N\\),\n\n\\[\n\\text{successful }N = 1000 - 390 = 610 .\n\\]\n\n\\[\n\\boxed{610}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 610</p>\n<p>Extracted Answer: 610</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThere are $ n $ values of $ x $ in the interval $ 0 &lt; x &lt; 2\\pi $ where $ f(x) = \\sin(7\\pi \\cdot \\sin(5x)) = 0 $. For $ t $ of these $ n $ values of $ x $, the graph of $ y = f(x) $ is tangent to the $ x $-axis. Find $ n + t $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>For  \n\n\\[\nf(x)=\\sin\\bigl(7\\pi\\sin(5x)\\bigr)\n\\]\n\nwe need the solutions of  \n\n\\[\n\\sin\\bigl(7\\pi\\sin(5x)\\bigr)=0\\qquad(0&lt;x&lt;2\\pi).\n\\]\n\n---\n\n### 1.  Zeros of \\(f\\)\n\n\\[\n\\sin(A)=0\\iff A=m\\pi,\\;m\\in\\mathbb Z .\n\\]\n\nHence  \n\n\\[\n7\\pi\\sin(5x)=m\\pi\\Longrightarrow \\sin(5x)=\\frac{m}{7}.\n\\]\n\nBecause \\(\\sin(5x)\\in[-1,1]\\), the integer \\(m\\) must satisfy  \n\n\\[\n-7\\le m\\le 7 .\n\\]\n\nLet \\(k=m\\). For each integer \\(k\\) with \\(-7\\le k\\le 7\\) we solve  \n\n\\[\n\\sin(5x)=\\frac{k}{7}.\n\\]\n\nPut \\(\\theta =5x\\). Then \\(\\theta\\in(0,10\\pi)\\) and we need  \n\n\\[\n\\sin\\theta = \\frac{k}{7}.\n\\]\n\n* **\\(k=\\pm7\\)** (\\(\\sin\\theta=\\pm1\\)).  \n  In each \\(2\\pi\\)-period there is exactly one solution.  \n  Over the interval \\((0,10\\pi)\\) (5 periods) we obtain \\(5\\) solutions for \\(k=7\\) and\n  \\(5\\) solutions for \\(k=-7\\).\n\n* **\\(k=0\\)** (\\(\\sin\\theta=0\\)).  \n  Solutions are \\(\\theta=n\\pi\\).  \n  With \\(0&lt;\\theta&lt;10\\pi\\) we have \\(n=1,2,\\dots ,9\\): \\(9\\) solutions.\n\n* **\\(k=\\pm1,\\pm2,\\dots ,\\pm6\\)** (\\(|k/7|&lt;1\\) and \\(\\neq0\\)).  \n  In each period there are two distinct solutions, so over \\(5\\) periods we get\n  \\(2\\cdot5=10\\) solutions for each such \\(k\\).\n\nThere are \\(12\\) values of \\(k\\) with \\(|k|\\le6\\) and \\(k\\neq0\\).\n\nHence the total number of zeros is  \n\n\\[\nn = 5+5+9+12\\cdot10 = 139 .\n\\]\n\n---\n\n### 2.  Tangent points\n\nDifferentiate:\n\n\\[\nf&#39;(x)=\\cos\\!\\bigl(7\\pi\\sin(5x)\\bigr)\\cdot7\\pi\\cdot5\\cos(5x)\n      =35\\pi\\cos(5x)\\cos\\!\\bigl(7\\pi\\sin(5x)\\bigr).\n\\]\n\nAt a zero of \\(f\\) we have \\(\\sin(5x)=k/7\\), so  \n\n\\[\n\\cos\\!\\bigl(7\\pi\\sin(5x)\\bigr)=\\cos(k\\pi)=(-1)^k\\neq0 .\n\\]\n\nThus \\(f&#39;(x)=0\\) exactly when \\(\\cos(5x)=0\\), i.e. when \\(\\sin(5x)=\\pm1\\).\nThose correspond precisely to the cases \\(k=\\pm7\\).\n\nWe already counted \\(5\\) solutions for \\(k=7\\) and \\(5\\) for \\(k=-7\\); all of them are\ntangency points. Hence  \n\n\\[\nt = 5+5 = 10 .\n\\]\n\n---\n\n### 3.  Required sum\n\n\\[\nn+t = 139+10 = 149 .\n\\]\n\n\\[\n\\boxed{149}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 149</p>\n<p>Extracted Answer: 149</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $ S $ be the set of vertices of a regular 24-gon. Find the number of ways to draw 12 segments of equal lengths so that each vertex in $ S $ is an endpoint of exactly one of the 12 segments.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Label the vertices of the regular \\(24\\)-gon by  \n\n\\[\n0,1,2,\\ldots ,23\\qquad(\\text{mod }24).\n\\]\n\nIf a segment connects vertices \\(i\\) and \\(j\\) then the chord length is determined by the\nshorter distance  \n\n\\[\nk=\\min\\{|i-j|,\\;24-|i-j|\\},\\qquad 1\\le k\\le 12 .\n\\]\n\nAll 12 drawn segments must have the same length, so every segment must join two vertices that\nare exactly \\(k\\) steps apart for one fixed \\(k\\in\\{1,2,\\ldots ,12\\}\\).\n\n---------------------------------------------------------------------\n\n### 1.  The graph for a fixed \\(k\\)\n\nFor a given \\(k\\) consider the graph  \n\n\\[\nG_k=\\{\\,\\{i,i+k\\}:i=0,1,\\ldots ,23\\}\\ .\n\\]\n\nEach vertex has degree \\(2\\) (edges to \\(i+k\\) and to \\(i-k\\)), so \\(G_k\\) is a disjoint union\nof cycles.  \n\nLet  \n\n\\[\ng=\\gcd(24,k).\n\\]\n\nThen \\(G_k\\) consists of \\(g\\) cycles, each of length  \n\n\\[\nL=\\frac{24}{g}.\n\\]\n\n---------------------------------------------------------------------\n\n### 2.  Perfect matchings of \\(G_k\\)\n\nA required drawing is exactly a perfect matching (1\u2011factor) of \\(G_k\\).\n\n* If \\(L\\) is odd, a perfect matching is impossible.  \n  This occurs only for \\(k=8\\) (\\(g=8,\\;L=3\\)).\n\n* If \\(L=2\\) (the case \\(k=12\\)), each component is a single edge, so the matching is\nforced \u2013 exactly **one** way.\n\n* If \\(L\\) is even and \\(\\,L\\ge4\\), each even cycle has exactly two perfect matchings\n(alternating edges).  \n  Hence for such a \\(k\\) the number of matchings is  \n\n  \\[\n  2^{\\,\\text{number of cycles}}=2^{g}.\n  \\]\n\n---------------------------------------------------------------------\n\n### 3.  Count for each possible \\(k\\)\n\n\\[\n\\begin{array}{c|c|c|c}\nk &amp; g=\\gcd(24,k) &amp; L=24/g &amp; \\text{matchings }N(k)\\\\ \\hline\n1 &amp; 1 &amp; 24 &amp; 2\\\\\n2 &amp; 2 &amp; 12 &amp; 4\\\\\n3 &amp; 3 &amp; 8  &amp; 8\\\\\n4 &amp; 4 &amp; 6  &amp; 16\\\\\n5 &amp; 1 &amp; 24 &amp; 2\\\\\n6 &amp; 6 &amp; 4  &amp; 64\\\\\n7 &amp; 1 &amp; 24 &amp; 2\\\\\n8 &amp; 8 &amp; 3  &amp; 0\\\\\n9 &amp; 3 &amp; 8  &amp; 8\\\\\n10&amp; 2 &amp; 12 &amp; 4\\\\\n11&amp; 1 &amp; 24 &amp; 2\\\\\n12&amp;12 &amp; 2  &amp; 1\n\\end{array}\n\\]\n\n---------------------------------------------------------------------\n\n### 4.  Total number of drawings\n\n\\[\n\\begin{aligned}\n\\sum_{k=1}^{12} N(k)&amp;=\n2+4+8+16+2+64+2+0+8+4+2+1\\\\\n&amp;=113 .\n\\end{aligned}\n\\]\n\n---------------------------------------------------------------------\n\nThus there are  \n\n\\[\n\\boxed{113}\n\\]\n\ndifferent ways to draw 12 equal\u2011length segments so that every vertex of the regular 24\u2011gon\nis an endpoint of exactly one segment.</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 113</p>\n<p>Extracted Answer: 113</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $ A_1A_2 \\ldots A_{11} $ be an 11-sided non-convex simple polygon with the following properties:\n* The area of $ A_iA_1A_{i+1} $ is 1 for each $ 2 \\leq i \\leq 10 $,\n* $ \\cos(\\angle A_iA_1A_{i+1}) = \\frac{12}{13} $ for each $ 2 \\leq i \\leq 10 $,\n* The perimeter of $ A_1A_2 \\ldots A_{11} $ is 20.\nIf $ A_1A_2 + A_1A_{11} $ can be expressed as $ \\frac{m\\sqrt{n} - p}{q} $ for positive integers $ m, n, p, q $ with $ n $ squarefree and no prime divides all of $ m, p, q$, find $ m + n + p + q $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n\\[\na_i=|A_iA_1|\\qquad (i=2,\\dots ,11),\\qquad b_i=|A_iA_{i+1}|\\;(i=2,\\dots ,10)\n\\]\n\nand let \\(\\theta =\\angle A_iA_1A_{i+1}\\) for \\(2\\le i\\le10\\).\n\n--------------------------------------------------------------------\n### 1.  The radii from \\(A_1\\)\n\nFor each triangle \\(A_iA_1A_{i+1}\\)\n\n\\[\n\\text{area}=1,\\qquad \\cos\\theta=\\frac{12}{13}.\n\\]\n\nHence  \n\n\\[\n\\sin\\theta =\\sqrt{1-\\cos^2\\theta}\n          =\\sqrt{1-\\frac{144}{169}}\n          =\\frac{5}{13}.\n\\]\n\nThe area formula gives  \n\n\\[\n1=\\frac12 a_i a_{i+1}\\sin\\theta\n   \\Longrightarrow a_i a_{i+1}= \\frac{2}{\\sin\\theta}\n   =\\frac{2}{5/13}= \\frac{26}{5}\\qquad (1)\n\\]\n\nfor every \\(i=2,\\dots ,10\\).\n\nThus every adjacent pair of radii satisfies the same product.\nConsequently the lengths alternate:\n\n\\[\na_2=a_4=a_6=a_8=a_{10}=x,\\qquad \na_3=a_5=a_7=a_9=a_{11}=y,\n\\]\n\nwith  \n\n\\[\nxy=\\frac{26}{5}. \\tag{2}\n\\]\n\n--------------------------------------------------------------------\n### 2.  Lengths of the polygon sides not incident with \\(A_1\\)\n\nIn \\(\\triangle A_iA_1A_{i+1}\\) the side \\(b_i=|A_iA_{i+1}|\\) satisfies the law of cosines:\n\n\\[\nb_i^2 = a_i^2 + a_{i+1}^2 -2a_i a_{i+1}\\cos\\theta .\n\\]\n\nUsing \\(\\cos\\theta=\\frac{12}{13}\\) and (1),\n\n\\[\nb_i^2 = a_i^2 + a_{i+1}^2\n        - 2\\!\\left(\\frac{26}{5}\\right)\\!\\frac{12}{13}\n      = a_i^2 + a_{i+1}^2 - \\frac{624}{65}\n      = a_i^2 + a_{i+1}^2 - 9.6 .\n\\]\n\nBecause each adjacent pair consists of one \\(x\\) and one \\(y\\), the quantity\n\\(a_i^2+a_{i+1}^2\\) is the same for all \\(i\\).  Hence all \\(b_i\\) are equal; denote this common length by \\(b\\).\n\nLet  \n\n\\[\nS=x+y .\n\\]\n\nThen \\(x^2+y^2=S^2-2xy\\).  Using (2) we obtain\n\n\\[\nb^{2}=S^{2}-2xy-2xy\\cos\\theta\n      =S^{2}-2xy(1+\\cos\\theta).\n\\]\n\nSince \\(\\cos\\theta=\\frac{12}{13}\\),  \n\n\\[\n1+\\cos\\theta = \\frac{25}{13},\\qquad\n2xy(1+\\cos\\theta)=2\\!\\left(\\frac{26}{5}\\right)\\!\\frac{25}{13}=20.\n\\]\n\nThus  \n\n\\[\nb^{2}=S^{2}-20,\\qquad b=\\sqrt{S^{2}-20}. \\tag{3}\n\\]\n\n--------------------------------------------------------------------\n### 3.  Using the perimeter\n\nThe perimeter of the 11\u2011gon is\n\n\\[\n|A_1A_2|+|A_1A_{11}|+\\sum_{i=2}^{10}|A_iA_{i+1}|\n= x + y + 9b = S + 9\\sqrt{S^{2}-20}=20.\n\\]\n\nLet \\(t=\\sqrt{S^{2}-20}\\;(t\\ge0)\\).  Then  \n\n\\[\n\\sqrt{t^{2}+20}+9t=20\\quad\\Longrightarrow\\quad \n\\sqrt{t^{2}+20}=20-9t.\n\\]\n\nSquaring yields  \n\n\\[\nt^{2}+20 = (20-9t)^{2}=400-360t+81t^{2},\n\\]\n\\[\n80t^{2}-360t+380=0\\;\\Longrightarrow\\;\n4t^{2}-18t+19=0.\n\\]\n\nThe discriminant is \\(D=18^{2}-4\\cdot4\\cdot19=324-304=20\\), so\n\n\\[\nt=\\frac{18\\pm\\sqrt{20}}{8}\n   =\\frac{9\\pm\\sqrt5}{4}.\n\\]\n\nSince \\(20-9t\\ge0\\), we take the minus sign:\n\n\\[\nt=\\frac{9-\\sqrt5}{4}.\n\\]\n\nNow \\(S = 20-9t\\):\n\n\\[\nS = 20 - 9\\!\\left(\\frac{9-\\sqrt5}{4}\\right)\n   = \\frac{80-(81-9\\sqrt5)}{4}\n   = \\frac{9\\sqrt5-1}{4}.\n\\]\n\nThus  \n\n\\[\n|A_1A_2|+|A_1A_{11}| = S = \\frac{9\\sqrt5-1}{4}.\n\\]\n\n--------------------------------------------------------------------\n### 4.  Putting it into the required form\n\n\\[\n\\frac{9\\sqrt5-1}{4}=\\frac{m\\sqrt{n}-p}{q},\n\\qquad m=9,\\; n=5,\\; p=1,\\; q=4.\n\\]\n\nThese satisfy the given conditions ( \\(n\\) square\u2011free, no prime divides all of \\(m,p,q\\) ).\n\nFinally  \n\n\\[\nm+n+p+q = 9+5+1+4 = 19.\n\\]\n\n\\[\n\\boxed{19}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 19</p>\n<p>Extracted Answer: 19</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nSixteen chairs are arranged in a row. Eight people each select a chair in which to sit so that no person sits next to two other people. Let $ N $ be the number of subsets of 16 chairs that could be selected. Find the remainder when $ N $ is divided by 1000.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>**Solution Overview**\n\nLet the 16 chairs be numbered \\(1,2,\\dots ,16\\).  \nA selection of 8 chairs corresponds to a binary string of length \\(16\\) with exactly eight \\(1\\)\u2019s (occupied chairs) and eight \\(0\\)\u2019s (empty chairs).\n\nA person \u201csits next to two other people\u2019\u2019 exactly when a chair is occupied **and** its two neighbours are also occupied.  \nHence the forbidden pattern in the binary string is the block \\(111\\).  \n\nThus we must count the binary strings of length \\(16\\) containing exactly eight \\(1\\)\u2019s and **no** occurrence of \\(111\\).\n\n--------------------------------------------------------------------\n\n### 1.  Decomposing the 1\u2011blocks\n\nBecause a block of three or more consecutive \\(1\\)\u2019s is not allowed, every maximal block of 1\u2019s is of length **1** or **2**.\n\nSuppose the string contains  \n\n* \\(a\\) blocks of length \\(1\\) and  \n* \\(c\\) blocks of length \\(2\\).\n\nThen  \n\n\\[\na+2c = 8\\qquad(\\text{total number of }1\\text{&#39;s}),\n\\]\n\\[\nb = a+c = 8-c\\qquad(\\text{total number of blocks}).\n\\]\n\n--------------------------------------------------------------------\n\n### 2.  Placing the blocks among the 0\u2019s\n\nBetween any two consecutive blocks we need at least one \\(0\\).  \nWith \\(b\\) blocks we need at least \\(b-1\\) separating zeros.\n\nThe total number of zeros is \\(16-8 = 8\\).  \nAfter reserving the mandatory \\(b-1\\) zeros, there remain  \n\n\\[\n8-(b-1)=9-b\n\\]\n\nextra zeros that may be placed arbitrarily in the \\(b+1\\) gaps\n(before the first block, between blocks, after the last block).\n\nThe number of ways to distribute these extra zeros is a stars\u2011and\u2011bars count:\n\n\\[\n\\binom{(9-b)+(b+1)-1}{b}= \\binom{9}{b}.\n\\]\n\n--------------------------------------------------------------------\n\n### 3.  Ordering the blocks\n\nAmong the \\(b\\) blocks, we must choose which \\(c\\) of them are the length\u20112 blocks.\nThat can be done in  \n\n\\[\n\\binom{b}{c}=\\binom{8-c}{c}\n\\]\n\nways.\n\n--------------------------------------------------------------------\n\n### 4.  Summation\n\nSumming over all feasible values of \\(c\\) (from \\(0\\) to \\(\\lfloor 8/2\\rfloor =4\\)) we obtain\n\n\\[\n\\begin{aligned}\nN &amp;=\\sum_{c=0}^{4}\\binom{8-c}{c}\\binom{9}{\\,8-c\\,} \\\\[2mm]\n  &amp;=\\binom{8}{0}\\binom{9}{8}\n    +\\binom{7}{1}\\binom{9}{7}\n    +\\binom{6}{2}\\binom{9}{6}\n    +\\binom{5}{3}\\binom{9}{5}\n    +\\binom{4}{4}\\binom{9}{4}\\\\[2mm]\n  &amp;=1\\cdot9\\;+\\;7\\cdot36\\;+\\;15\\cdot84\\;+\\;10\\cdot126\\;+\\;1\\cdot126\\\\[2mm]\n  &amp;=9+252+1260+1260+126\\\\[2mm]\n  &amp;=2907.\n\\end{aligned}\n\\]\n\nThus there are \\(N=2907\\) possible selections of 8 chairs satisfying the condition.\n\n--------------------------------------------------------------------\n\n### 5.  Required remainder\n\n\\[\nN \\bmod 1000 = 2907 \\bmod 1000 = 907.\n\\]\n\n--------------------------------------------------------------------\n\n\\[\n\\boxed{907}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 907</p>\n<p>Extracted Answer: 907</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nFind the sum of all integer bases $b&gt;9$ for which $17_{b}$ is a divisor of $97_{b}$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>In base \\(b\\) the numbers  \n\n\\[\n17_b = 1\\cdot b + 7 = b+7 ,\\qquad  \n97_b = 9\\cdot b + 7 .\n\\]\n\nWe need bases \\(b&gt;9\\) (so that the digits \\(7\\) and \\(9\\) are allowed) such that  \n\n\\[\nb+7 \\mid 9b+7 .\n\\]\n\n---\n\n### Reduce the divisibility condition\n\nIf \\(b+7\\) divides \\(9b+7\\), then it also divides any integer linear combination of these two numbers.  \nConsider  \n\n\\[\n9(b+7) - (9b+7) = 9b+63 - 9b - 7 = 56 .\n\\]\n\nHence  \n\n\\[\nb+7 \\mid 56 .\n\\]\n\nConversely, if \\(b+7\\) divides \\(56\\) then\n\n\\[\n9b+7 = 9(b+7) - 56\n\\]\n\nis also a multiple of \\(b+7\\). Thus the condition is equivalent to  \n\n\\[\nb+7 \\text{ is a positive divisor of } 56 .\n\\]\n\n---\n\n### Find admissible divisors\n\nThe positive divisors of \\(56\\) are  \n\n\\[\n1,\\;2,\\;4,\\;7,\\;8,\\;14,\\;28,\\;56 .\n\\]\n\nSince \\(b&gt;9\\), we have \\(b+7&gt;16\\). The only divisors of \\(56\\) exceeding \\(16\\) are \\(28\\) and \\(56\\).\n\n\\[\n\\begin{aligned}\nb+7 &amp;= 28 &amp;\\implies&amp;\\; b = 21,\\\\[2mm]\nb+7 &amp;= 56 &amp;\\implies&amp;\\; b = 49 .\n\\end{aligned}\n\\]\n\nBoth satisfy \\(b&gt;9\\) and the original divisibility:\n\\[\n\\begin{aligned}\nb=21:&amp;\\quad 17_{21}=28,\\; 97_{21}=196=28\\cdot7;\\\\\nb=49:&amp;\\quad 17_{49}=56,\\; 97_{49}=448=56\\cdot8.\n\\end{aligned}\n\\]\n\nNo other bases work.\n\n---\n\n### Sum of all such bases\n\n\\[\n21+49 = 70 .\n\\]\n\n\\[\n\\boxed{70}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 70</p>\n<p>Extracted Answer: 70</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $ \\triangle ABC $ be a right triangle with $ \\angle A = 90^\\circ $ and $ BC = 38 $. There exist points $ K $ and $ L $ inside the triangle such that $ AK = AL = BK = CL = KL = 14. $ The area of the quadrilateral $ BKLC $ can be expressed as $ n \\sqrt{3} $ for some positive integer $ n $. Find $ n $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n\\[\nA=(0,0),\\qquad B=(b,0),\\qquad C=(0,c),\\qquad b^2+c^2=BC^2=38^2=1444 .\n\\]\n\nPut  \n\n\\[\nK=(x_k ,y_k),\\qquad L=(x_l ,y_l).\n\\]\n\nThe given distances give  \n\n\\[\n\\begin{aligned}\n&amp;AK=AL=BK=CL=KL=14,\\\\\n&amp;x_k^2+y_k^2=196,\\quad (x_k-b)^2+y_k^2=196,\\\\[2mm]\n&amp;x_l^2+y_l^2=196,\\quad x_l^2+(y_l-c)^2=196,\\\\[2mm]\n&amp;(x_k-x_l)^2+(y_k-y_l)^2=196 .\n\\end{aligned}\n\\]\n\nFrom the first two equations  \n\n\\[\nb=2x_k,\\qquad y_k=\\sqrt{196-x_k^2}.\n\\]\n\nFrom the next two  \n\n\\[\nc=2y_l,\\qquad x_l=\\sqrt{196-y_l^2}.\n\\]\n\nThus  \n\n\\[\nK=(b/2,\\;\\sqrt{196-b^{2}/4}),\\qquad \nL=(\\sqrt{196-c^{2}/4},\\;c/2).\n\\]\n\nSince \\(AK=AL=KL=14\\), the triangle \\(AKL\\) is equilateral; hence\nthe angle \\(\\angle KAL=60^\\circ\\).  Write\n\n\\[\nK=14(\\cos\\alpha,\\sin\\alpha),\\qquad  \nL=14(\\cos(\\alpha+60^\\circ),\\sin(\\alpha+60^\\circ))\n\\]\n\nfor some \\(\\alpha\\) with \\(0^\\circ&lt;\\alpha&lt;30^\\circ\\).\nComparing with the expressions for \\(K\\) and \\(L\\) gives  \n\n\\[\nb=28\\cos\\alpha,\\qquad c=28\\sin(\\alpha+60^\\circ).\n\\]\n\nThe hypotenuse length yields\n\n\\[\nb^{2}+c^{2}=28^{2}\\bigl(\\cos^{2}\\alpha+\\sin^{2}(\\alpha+60^\\circ)\\bigr)=38^{2}=1444,\n\\]\n\nso  \n\n\\[\n\\cos^{2}\\alpha+\\sin^{2}(\\alpha+60^\\circ)=\\frac{361}{196}.\n\\tag{1}\n\\]\n\nFrom (1) we obtain, after using \\(\\sin^{2}\\theta= \\tfrac12(1-\\cos2\\theta)\\),\n\n\\[\n\\sqrt3\\sin(2\\alpha+60^\\circ)=\\frac{165}{98},\n\\qquad\\Longrightarrow\\qquad\n\\sin(2\\alpha+60^\\circ)=\\frac{165}{98\\sqrt3}.\n\\tag{2}\n\\]\n\nNow compute the required area.\n\n*Area of \\(\\triangle ABC\\)*  \n\n\\[\n[ABC]=\\tfrac12bc=\\tfrac12\\,(28\\cos\\alpha)(28\\sin(\\alpha+60^\\circ))\n      =392\\cos\\alpha\\sin(\\alpha+60^\\circ).\n\\tag{3}\n\\]\n\n*Area of \\(\\triangle AKB\\)*  \n\nThe altitude from \\(K\\) to \\(AB\\) is \\(y_k=14\\sin\\alpha\\), and \\(AB=28\\cos\\alpha\\); thus  \n\n\\[\n[AKB]=\\tfrac12\\,(28\\cos\\alpha)(14\\sin\\alpha)=98\\sin2\\alpha .\n\\tag{4}\n\\]\n\n*Area of \\(\\triangle ALC\\)*  \n\nAnalogously  \n\n\\[\n[ALC]=\\tfrac12\\,(28\\sin(\\alpha+60^\\circ))(14\\cos(\\alpha+60^\\circ))\n      =98\\sin\\bigl(2\\alpha+120^\\circ\\bigr).\n\\tag{5}\n\\]\n\n*Area of the equilateral \\(\\triangle AKL\\)*  \n\n\\[\n[AKL]=\\frac{\\sqrt3}{4}\\cdot14^{2}=49\\sqrt3.\n\\tag{6}\n\\]\n\nHence  \n\n\\[\n\\begin{aligned}\n[BKLC]&amp;=[ABC]-[AKB]-[ALC]-[AKL] \\\\[2mm]\n&amp;=392\\cos\\alpha\\sin(\\alpha+60^\\circ)\n   -98\\sin2\\alpha-98\\sin(2\\alpha+120^\\circ)-49\\sqrt3 .\n\\end{aligned}\n\\]\n\nUsing \\(\\sin(\\alpha+60^\\circ)=\\tfrac12\\sin\\alpha+\\tfrac{\\sqrt3}{2}\\cos\\alpha\\) and\nsimplifying, the expression reduces to  \n\n\\[\n[BKLC]=49\\Bigl(\\sin2\\alpha+\\sqrt3\\bigl(1+\\cos2\\alpha\\bigr)\\Bigr).\n\\tag{7}\n\\]\n\nFrom (2),\n\n\\[\n\\sin2\\alpha+\\sqrt3\\cos2\\alpha\n    =2\\sin(2\\alpha+60^\\circ)=\\frac{165}{49\\sqrt3}.\n\\]\n\nInsert this into (7):\n\n\\[\n\\begin{aligned}\n[BKLC]&amp;=49\\Bigl(\\frac{165}{49\\sqrt3}+\\sqrt3\\Bigr)\n       =\\frac{165}{\\sqrt3}+49\\sqrt3\\\\[2mm]\n      &amp;=\\frac{165\\sqrt3}{3}+49\\sqrt3\n       =55\\sqrt3+49\\sqrt3=104\\sqrt3.\n\\end{aligned}\n\\]\n\nThus the area of quadrilateral \\(BKLC\\) equals \\(104\\sqrt3\\).\n\n\\[\n\\boxed{104}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 104</p>\n<p>Extracted Answer: 104</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nSuppose $ \\triangle ABC $ has angles $ \\angle BAC = 84^\\circ $, $ \\angle ABC = 60^\\circ $, and $ \\angle ACB = 36^\\circ $. Let $ D, E, $ and $ F $ be the midpoints of sides $ \\overline{BC} $, $ \\overline{AC} $, and $ \\overline{AB} $, respectively. The circumcircle of $ \\triangle DEF $ intersects $ \\overline{BD} $, $ \\overline{AE} $, and $ \\overline{AF} $ at points $ G, H, $ and $ J $, respectively. The points $ G, D, E, H, J, $ and $ F $ divide the circumcircle of $ \\triangle DEF $ into six minor arcs, as shown. Find $ \\widehat{DE} + 2 \\cdot \\widehat{HJ} + 3 \\cdot \\widehat{FG} $, where the arcs are measured in degrees.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n* \\(A,B,C\\) be the vertices of the acute triangle with  \n\\(\\angle A=84^{\\circ},\\ \\angle B=60^{\\circ},\\ \\angle C=36^{\\circ}\\);\n* \\(D,E,F\\) the midpoints of \\(BC,CA,AB\\);\n* \\(G,H,J\\) the second intersections of the nine\u2011point circle with\n\\(BC,CA,AB\\) respectively.\n\nThe circumcircle of \\(\\triangle DEF\\) is the nine\u2011point circle of \\(\\triangle ABC\\).\nHence \\(G,H,J\\) are the three feet of the altitudes of \\(\\triangle ABC\\);  \nthey form the orthic triangle \\(G\\!H\\!J\\).\n\n--------------------------------------------------------------------\n### 1.  Arc \\(\\widehat{DE}\\)\n\nOn the nine\u2011point circle the vectors from its centre \\(N\\) to the\nmidpoints are  \n\n\\[\nND=-\\frac{\\mathbf a}{2},\\qquad NE=-\\frac{\\mathbf b}{2},\n\\]\n\nwhere \\(\\mathbf a,\\mathbf b,\\mathbf c\\) are the unit vectors of the\ncircumcircle of \\(\\triangle ABC\\).  Consequently\n\n\\[\n\\widehat{DE}= \\angle(-\\mathbf a,-\\mathbf b)=\\angle(\\mathbf a,\\mathbf b)\n          =2\\angle ACB=2C = 2\\cdot36^{\\circ}=72^{\\circ}.\n\\tag{1}\n\\]\n\n--------------------------------------------------------------------\n### 2.  Arc \\(\\widehat{HJ}\\)\n\n\\(H\\) and \\(J\\) are the feet of the altitudes from \\(B\\) and \\(C\\);\nthey are vertices of the orthic triangle \\(G\\!H\\!J\\).\nFor an acute triangle the angles of its orthic triangle are  \n\n\\[\n\\angle G =180^{\\circ}-2A,\\qquad \n\\angle H =180^{\\circ}-2B,\\qquad \n\\angle J =180^{\\circ}-2C .\n\\]\n\nWith \\(A=84^{\\circ},B=60^{\\circ},C=36^{\\circ}\\),\n\n\\[\n\\angle G =12^{\\circ},\\quad\n\\angle H =60^{\\circ},\\quad\n\\angle J =108^{\\circ}.\n\\]\n\nSince the nine\u2011point circle is the circumcircle of\n\\(\\triangle G\\!H\\!J\\), the central arc opposite a vertex equals twice the\nopposite interior angle.  Hence\n\n\\[\n\\widehat{HJ}= \\widehat{B&#39;C&#39;} = 2\\angle G\n            =2\\bigl(180^{\\circ}-2A\\bigr)=360^{\\circ}-4A\n            =360^{\\circ}-4\\cdot84^{\\circ}=24^{\\circ}.\n\\tag{2}\n\\]\n\n--------------------------------------------------------------------\n### 3.  Arc \\(\\widehat{FG}\\)\n\nThe points \\(D,E,F\\) are the midpoints of the sides; they satisfy  \n\n\\[\n\\angle N D F =\\angle(-\\mathbf a,-\\mathbf c)=120^{\\circ},\n\\]\n\nso the minor arc \\(\\widehat{DF}\\) of the nine\u2011point circle measures\n\\(120^{\\circ}\\).  The arc \\(\\widehat{DF}\\) is the sum of the two\nconsecutive arcs \\(\\widehat{DG}\\) and \\(\\widehat{GF}\\).\n\nThe central arc \\(\\widehat{DG}\\) equals the angle between the\nvectors \\(ND\\) (direction \\(-\\mathbf a\\)) and \\(NG\\) (direction of the\nfoot from \\(A\\) onto \\(BC\\)).\nA short angle chase using the orthic triangle gives\n\n\\[\n\\widehat{DG}=48^{\\circ}.\n\\]\n\nTherefore\n\n\\[\n\\widehat{FG}= \\widehat{DF}-\\widehat{DG}=120^{\\circ}-48^{\\circ}=72^{\\circ}.\n\\tag{3}\n\\]\n\n(One can also obtain \\(\\widehat{FG}=72^{\\circ}\\) directly from the fact\nthat the chord \\(FJ\\) subtends the angle \\(60^{\\circ}\\) at the centre,\nso the complementary chord \\(FG\\) subtends \\(72^{\\circ}\\).)\n\n--------------------------------------------------------------------\n### 4.  Required sum\n\nFrom (1)\u2013(3),\n\n\\[\n\\begin{aligned}\n\\widehat{DE}+2\\widehat{HJ}+3\\widehat{FG}\n&amp;= 72^{\\circ}+2\\cdot24^{\\circ}+3\\cdot72^{\\circ}\\\\[2mm]\n&amp;= 72^{\\circ}+48^{\\circ}+216^{\\circ}\\\\\n&amp;= 336^{\\circ}.\n\\end{aligned}\n\\]\n\n--------------------------------------------------------------------\n\\[\n\\boxed{336}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 336</p>\n<p>Extracted Answer: 336</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThe 9 members of a baseball team went to an ice cream parlor after their game. Each player had a singlescoop cone of chocolate, vanilla, or strawberry ice cream. At least one player chose each flavor, and the number of players who chose chocolate was greater than the number of players who chose vanilla, which was greater than the number of players who chose strawberry. Let $N$ be the number of different assignments of flavors to players that meet these conditions. Find the remainder when $N$ is divided by 1000.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>The players are distinct, so an assignment of flavors is a function from the nine players to the three flavors.  \nLet  \n\n\\[\nc=\\#\\text{chocolate},\\qquad v=\\#\\text{vanilla},\\qquad s=\\#\\text{strawberry}.\n\\]\n\nWe need  \n\n\\[\nc+v+s=9,\\qquad c&gt;v&gt;s\\ge 1 .\n\\]\n\n---\n\n### 1.  Find all possible triples \\((c,v,s)\\).\n\nWrite \\(s=a\\), \\(v=a+d\\), \\(c=a+d+e\\) with \\(a,d,e\\ge1\\).  \nThen  \n\n\\[\na+(a+d)+(a+d+e)=9\\Longrightarrow 3a+2d+e=9 .\n\\]\n\nSearching integer solutions with \\(a,d,e\\ge1\\) gives only three possibilities:\n\n* \\(a=1,d=1,e=4\\)\u2003\u2192 \\((c,v,s)=(6,2,1)\\)\n* \\(a=1,d=2,e=2\\)\u2003\u2192 \\((c,v,s)=(5,3,1)\\)\n* \\(a=2,d=1,e=1\\)\u2003\u2192 \\((c,v,s)=(4,3,2)\\)\n\nNo other triples satisfy \\(c&gt;v&gt;s\\) and sum to 9.\n\n---\n\n### 2.  Count assignments for each triple.\n\nFor a fixed triple \\((c,v,s)\\) the number of assignments equals the multinomial coefficient  \n\n\\[\n\\frac{9!}{c!\\,v!\\,s!}.\n\\]\n\n\\[\n\\begin{aligned}\n(6,2,1)&amp;:\\ \\frac{9!}{6!\\,2!\\,1!}= \\frac{362880}{720\\cdot2}=252,\\\\[2mm]\n(5,3,1)&amp;:\\ \\frac{9!}{5!\\,3!\\,1!}= \\frac{362880}{120\\cdot6}=504,\\\\[2mm]\n(4,3,2)&amp;:\\ \\frac{9!}{4!\\,3!\\,2!}= \\frac{362880}{24\\cdot6\\cdot2}=1260.\n\\end{aligned}\n\\]\n\n---\n\n### 3.  Total number of assignments.\n\n\\[\nN=252+504+1260=2016.\n\\]\n\n---\n\n### 4.  Remainder modulo \\(1000\\).\n\n\\[\n2016\\equiv 16 \\pmod{1000}.\n\\]\n\n---\n\n\\[\n\\boxed{16}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 16</p>\n<p>Extracted Answer: 16</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nFind the number of ordered pairs $(x,y)$, where both $x$ and $y$ are integers between $-100$ and $100$, inclusive, such that $12x^{2}-xy-6y^{2}=0$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>First factor the quadratic form.\n\n\\[\n12x^{2}-xy-6y^{2}= (4x-3y)(3x+2y)\n\\]\n\nHence  \n\n\\[\n(4x-3y)(3x+2y)=0\\Longrightarrow \n\\begin{cases}\n4x-3y=0\\\\[2mm]\n\\text{or}\\\\[2mm]\n3x+2y=0\n\\end{cases}\n\\]\n\n---\n\n### 1.  Solutions of \\(4x-3y=0\\)\n\n\\(4x=3y\\Rightarrow y=\\dfrac{4}{3}x\\).  \nSince \\(x,y\\) are integers, \\(x\\) must be a multiple of \\(3\\): set \\(x=3k\\), then  \n\n\\[\ny=4k,\\qquad k\\in\\mathbb Z .\n\\]\n\nBoth coordinates must satisfy \\(-100\\le x,y\\le100\\):\n\n\\[\n|3k|\\le100,\\qquad|4k|\\le100\\Longrightarrow |k|\\le \\Big\\lfloor\\frac{100}{4}\\Big\\rfloor =25 .\n\\]\n\nThus \\(k=-25,-24,\\dots ,25\\):  \\(51\\) integer pairs.\n\n---\n\n### 2.  Solutions of \\(3x+2y=0\\)\n\n\\(3x=-2y\\Rightarrow y=-\\dfrac{3}{2}x\\).  \nFor integers we need \\(x\\) even: write \\(x=2m\\), then  \n\n\\[\ny=-3m,\\qquad m\\in\\mathbb Z .\n\\]\n\nAgain \\(-100\\le x,y\\le100\\) gives  \n\n\\[\n|2m|\\le100,\\qquad|3m|\\le100\\Longrightarrow |m|\\le\\Big\\lfloor\\frac{100}{3}\\Big\\rfloor =33 .\n\\]\n\nThus \\(m=-33,-32,\\dots ,33\\):  \\(67\\) integer pairs.\n\n---\n\n### 3.  Remove double counting\n\nThe two families intersect only at \\((0,0)\\) (when \\(k=m=0\\)).  \nHence the total number of distinct ordered pairs is  \n\n\\[\n51+67-1=117 .\n\\]\n\n\\[\n\\boxed{117}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 117</p>\n<p>Extracted Answer: 117</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThere are exactly three positive real numbers $ k $ such that the function\n$ f(x) = \\frac{(x - 18)(x - 72)(x - 98)(x - k)}{x} $\ndefined over the positive real numbers achieves its minimum value at exactly two positive real numbers $ x $. Find the sum of these three values of $ k $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>The function  \n\n\\[\nf(x)=\\frac{(x-18)(x-72)(x-98)(x-k)}{x}\\qquad (x&gt;0)\n\\]\n\nhas zeros at \\(x=18,\\;72,\\;98,\\;k\\) and  \n\\(\\displaystyle \\lim_{x\\to0^+}f(x)=\\lim_{x\\to\\infty}f(x)=+\\infty\\).\nHence \\(f\\) is positive near the ends and negative on each of the two\nintervals bounded by the smallest two zeros and by the largest two zeros.\nConsequently \\(f\\) has exactly two local minima (one in each negative\ninterval).\n\nLet the common minimal value be \\(m&lt;0\\).  At a minimum the graph of\n\\(y=f(x)\\) is tangent to the horizontal line \\(y=m\\); therefore the\nequation  \n\n\\[\nf(x)=m\\quad\\Longleftrightarrow\\quad (x-18)(x-72)(x-98)(x-k)-mx=0\n\\]\n\nmust have a **double root** at each minimum.  Thus the quartic polynomial\nmust be a perfect square of a quadratic:\n\n\\[\n(x-18)(x-72)(x-98)(x-k)-mx=(x^{2}-Sx+P)^{2},\n\\]\nwhere \\(S,P,m\\) are constants.\n\nExpanding and equating coefficients with  \n\n\\[\nN(x)-mx=x^{4}-(188+k)x^{3}+(10116+188k)x^{2}-(127008+10116k+m)x+127008k\n\\]\n\ngives  \n\n\\[\n\\begin{cases}\nS=\\dfrac{188+k}{2},\\\\[4pt]\nS^{2}+2P=10116+188k,\\\\[4pt]\nm=2SP-(127008+10116k),\\\\[4pt]\nP^{2}=127008\\,k .\n\\end{cases}\n\\]\n\nFrom \\(P^{2}=127008k\\) set \\(t=\\sqrt{2k}&gt;0\\); then  \n\n\\[\nP=252t,\\qquad k=\\dfrac{t^{2}}{2},\n\\quad S=\\frac{188+k}{2}=94+\\frac{t^{2}}{4}.\n\\]\n\nSubstituting these into \\(S^{2}+2P=10116+188k\\) yields an equation in\n\\(t\\):\n\n\\[\n\\frac{(188+k)^{2}}{4}+504\\sqrt{2k}=10116+188k\n\\Longrightarrow\nt^{4}-752t^{2}+8064t-20480=0 .\n\\]\n\nFactoring,\n\n\\[\nt^{4}-752t^{2}+8064t-20480=(t-4)(t-8)(t-20)(t+32)=0 .\n\\]\n\nSince \\(t&gt;0\\), we obtain  \n\n\\[\nt=4,\\;8,\\;20\\quad\\Longrightarrow\\quad \nk=\\frac{t^{2}}{2}=8,\\;32,\\;200 .\n\\]\n\nFor each of these \\(k\\) one computes \\(\\Delta=S^{2}-4P&gt;0\\), so the\nquadratic \\(x^{2}-Sx+P\\) has two distinct real roots.  They lie exactly in\nthe two negative intervals, giving two distinct points where \\(f\\) attains\nthe value \\(m\\).  Moreover \\(m&lt;0\\), while all zeros of \\(f\\) are at\n\\(0\\), so these are the global minima.  \nNo other positive \\(k\\) satisfies the required condition.\n\nHence the three admissible values of \\(k\\) are \\(8,\\;32,\\;200\\), and their\nsum is\n\n\\[\n8+32+200 = 240.\n\\]\n\n\\[\n\\boxed{240}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 240</p>\n<p>Extracted Answer: 240</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nAn isosceles trapezoid has an inscribed circle tangent to each of its four sides. The radius of the circle is 3, and the area of the trapezoid is 72. Let the parallel sides of the trapezoid have lengths $r$ and $s$, with $r \\neq s$. Find $r^{2}+s^{2}$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>For a quadrilateral that has an incircle (a **tangential quadrilateral**)  \n\n\\[\n\\text{area}=r_{\\text{in}}\\cdot\\frac{\\text{perimeter}}2 .\n\\tag{1}\n\\]\n\n---\n\n### 1.  Using the given area\n\nLet the parallel sides be \\(r\\) and \\(s\\) \\((r\\neq s)\\) and the equal legs be \\(\\ell\\).\nThe incircle radius is \\(r_{\\text{in}}=3\\) and the area is \\(72\\).\n\nFrom (1),\n\n\\[\n72=3\\cdot\\frac{r+s+2\\ell}{2}\\Longrightarrow\nr+s+2\\ell=48.\n\\tag{2}\n\\]\n\n---\n\n### 2.  Pitot\u2019s theorem\n\nA tangential quadrilateral satisfies Pitot\u2019s theorem: the sum of opposite sides are equal.  \nThus for our isosceles trapezoid  \n\n\\[\nr+s= \\ell+\\ell =2\\ell \\Longrightarrow \\ell=\\frac{r+s}{2}.\n\\tag{3}\n\\]\n\nSubstituting (3) into (2),\n\n\\[\nr+s+2\\Bigl(\\frac{r+s}{2}\\Bigr)=48\\Longrightarrow 2(r+s)=48\n\\Longrightarrow r+s=24.\n\\tag{4}\n\\]\n\nHence each leg is  \n\n\\[\n\\ell=\\frac{r+s}{2}=12.\n\\]\n\n---\n\n### 3.  Height of the trapezoid\n\nA circle tangent to two parallel lines must have its centre midway between them, so the distance (the height \\(h\\)) between the bases equals twice the radius:\n\n\\[\nh=2\\cdot3=6.\n\\]\n\nThe area of a trapezoid is also  \n\n\\[\n\\text{Area}= \\frac{r+s}{2}\\,h = \\frac{24}{2}\\cdot6 = 72,\n\\]\n\nwhich checks with the given data.\n\n---\n\n### 4.  Relating the legs, height, and bases  \n\nIn an isosceles trapezoid the leg \\(\\ell\\) together with the height \\(h\\) and half the difference of the bases forms a right triangle:\n\n\\[\n\\ell^{2}=h^{2}+\\Bigl(\\frac{s-r}{2}\\Bigr)^{2}.\n\\]\n\nPlugging \\(\\ell=12\\) and \\(h=6\\),\n\n\\[\n12^{2}=6^{2}+\\Bigl(\\frac{s-r}{2}\\Bigr)^{2}\n\\Longrightarrow 144=36+\\frac{(s-r)^{2}}{4}\n\\Longrightarrow (s-r)^{2}=432.\n\\]\n\nThus  \n\n\\[\ns-r= \\sqrt{432}=12\\sqrt3 .\n\\tag{5}\n\\]\n\n---\n\n### 5.  Solving for \\(r\\) and \\(s\\)\n\nFrom (4) and (5):\n\n\\[\n\\begin{cases}\ns+r = 24,\\\\[2pt]\ns-r = 12\\sqrt3,\n\\end{cases}\n\\qquad\\Longrightarrow\\qquad\ns = 12+6\\sqrt3,\\;\\; r = 12-6\\sqrt3.\n\\]\n\n---\n\n### 6.  Computing \\(r^{2}+s^{2}\\)\n\n\\[\nr^{2}+s^{2}= (12-6\\sqrt3)^{2}+(12+6\\sqrt3)^{2}\n= (252-144\\sqrt3)+(252+144\\sqrt3)=504.\n\\]\n\n(Alternatively, using \\((r+s)^{2}=r^{2}+s^{2}+2rs\\) and \\(rs=36\\) from \\((s+r)^{2}-(s-r)^{2}=4rs\\) also gives \\(r^{2}+s^{2}=504\\).)\n\n\\[\n\\boxed{504}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 504</p>\n<p>Extracted Answer: 504</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThere are exactly three positive real numbers $ k $ such that the function\n$ f(x) = \\frac{(x - 18)(x - 72)(x - 98)(x - k)}{x} $\ndefined over the positive real numbers achieves its minimum value at exactly two positive real numbers $ x $. Find the sum of these three values of $ k $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>\\[\n\\boxed{240}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 240</p>\n<p>Extracted Answer: 240</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThere are $8!=40320$ eight-digit positive integers that use each of the digits $1,2,3,4,5,6,7,8$ exactly once. Let $N$ be the number of these integers that are divisible by 22. Find the difference between $N$ and 2025.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>The number must be divisible by \\(22=2\\cdot 11\\).\n\n---\n\n### 1.  Divisibility by \\(2\\)\n\nThe last digit (the 8\u2011th digit) must be even, i.e. one of \\(2,4,6,8\\).\n\n---\n\n### 2.  Divisibility by \\(11\\)\n\nFor an 8\u2011digit number \\(d_1d_2\\ldots d_8\\)\n\n\\[\nd_1-d_2+d_3-d_4+d_5-d_6+d_7-d_8\\equiv0\\pmod{11}.\n\\]\n\nLet  \n\n\\[\nS_{\\text{odd}}=d_1+d_3+d_5+d_7,\\qquad  \nS_{\\text{even}}=d_2+d_4+d_6+d_8 .\n\\]\n\nThen the condition becomes  \n\n\\[\nS_{\\text{odd}}-S_{\\text{even}}\\equiv0\\pmod{11}.\n\\]\n\nSince the digits \\(1,2,\\dots ,8\\) are used exactly once,  \n\n\\[\nS_{\\text{odd}}+S_{\\text{even}}=1+2+\\cdots +8=36 .\n\\]\n\nHence  \n\n\\[\n2S_{\\text{even}}\\equiv36\\pmod{11}\\Longrightarrow2S_{\\text{even}}\\equiv3\\pmod{11}\n\\]\n\\[\n\\Longrightarrow S_{\\text{even}}\\equiv3\\cdot 6\\equiv18\\equiv7\\pmod{11}.\n\\]\n\nThe possible values for a sum of four distinct digits from \\(\\{1,\\ldots ,8\\}\\) lie between \\(10\\) and \\(26\\); the only value congruent to \\(7\\pmod{11}\\) in this interval is \\(18\\).  \nThus we must have  \n\n\\[\nS_{\\text{even}}=18\\qquad\\text{and}\\qquad S_{\\text{odd}}=18 .\n\\]\n\n---\n\n### 3.  Choosing the four digits that go to even positions\n\nWe need all 4\u2011element subsets of \\(\\{1,2,3,4,5,6,7,8\\}\\) whose sum is \\(18\\).\n\nListing them:\n\n\\[\n\\begin{aligned}\n&amp;\\{1,2,7,8\\},\\; \\{1,3,6,8\\},\\; \\{1,4,5,8\\},\\; \\{1,4,6,7\\},\\\\\n&amp;\\{2,3,5,8\\},\\; \\{2,3,6,7\\},\\; \\{2,4,5,7\\},\\; \\{3,4,5,6\\}.\n\\end{aligned}\n\\]\n\nThere are **8** such subsets.  \nEach of them contains exactly two even digits (the evens are \\(2,4,6,8\\)).\n\n---\n\n### 4.  Arranging the digits\n\nFor a fixed subset \\(S\\) (the digits that occupy the even positions 2,4,6,8):\n\n* The last position (position 8) must be even.  \n  Since \\(S\\) has exactly two evens, we have \\(2\\) choices for the digit that goes to position\u202f8.\n* The remaining three digits of \\(S\\) can be placed in positions 2,4,6 in any order: \\(3! = 6\\) ways.\n\nHence the even positions can be filled in \\(2\\cdot6 = 12\\) ways.\n\nThe four digits not in \\(S\\) occupy the odd positions \\(1,3,5,7\\) and may be arranged arbitrarily:\n\\(4! = 24\\) ways.\n\nThus each subset contributes  \n\n\\[\n12 \\times 24 = 288\n\\]\n\ndifferent 8\u2011digit numbers.\n\nWith 8 admissible subsets, the total number of 8\u2011digit numbers divisible by 22 is  \n\n\\[\nN = 8 \\times 288 = 2304.\n\\]\n\n---\n\n### 5.  Required difference\n\n\\[\nN-2025 = 2304-2025 = 279.\n\\]\n\n\\[\n\\boxed{279}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 279</p>\n<p>Extracted Answer: 279</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet the sequence of rationals $ x_1, x_2, \\ldots $ be defined such that $ x_1 = \\frac{25}{11} $ and\n$ x_{k+1} = \\frac{1}{3} \\left( x_k + \\frac{1}{x_k} - 1 \\right). $\n$ x_{2025} $ can be expressed as $ \\frac{m}{n} $ for relatively prime positive integers $ m $ and $ n $. Find the remainder when $ m + n $ is divided by 1000.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>\\[\nx_{k+1}=\\frac{x_k+\\dfrac1{x_k}-1}{3}\n      =\\frac{x_k^2-x_k+1}{3x_k}\\qquad (k\\ge 1),\\qquad \nx_1=\\frac{25}{11}.\n\\]\n\n--------------------------------------------------------------------\n### 1.  A convenient change of variable  \n\nPut  \n\n\\[\ny_k=\\frac{x_k-1}{x_k+1}\\qquad\\Longleftrightarrow\\qquad \nx_k=\\frac{1+y_k}{1-y_k}.\n\\]\n\nThen  \n\n\\[\ny_{k+1}= \\frac{x_{k+1}-1}{x_{k+1}+1}\n        =\\frac{3y_k^{2}-1}{2}.\n\\tag{1}\n\\]\n\nIndeed,\n\\[\n\\frac{x_k+1/x_k-1}{3}= \\frac{1+y_k}{1-y_k}\n        \\Longrightarrow\ny_{k+1}= \\frac{3y_k^{2}-1}{2}.\n\\]\n\nFrom \\(x_1=25/11\\) we obtain\n\n\\[\ny_1=\\frac{25/11-1}{25/11+1}= \\frac{14/11}{36/11}= \\frac{7}{18}.\n\\]\n\n--------------------------------------------------------------------\n### 2.  Removing the common factor  \n\nWrite \\(y_k =\\dfrac{a_k}{b_k}\\) with \\(\\gcd(a_k,b_k)=1\\).\nFrom (1)\n\n\\[\n\\frac{a_{k+1}}{b_{k+1}}=\\frac{3a_k^{2}-b_k^{2}}{2b_k^{2}} .\n\\]\n\nBecause \\(b_k\\) is always a multiple of \\(3\\), the fraction can be reduced by the\nfactor \\(3\\) and we obtain the **integer** recurrences\n\n\\[\n\\boxed{\\;\n\\begin{aligned}\na_{k+1}&amp;=\\frac{3a_k^{2}-b_k^{2}}{3},\\\\[2mm]\nb_{k+1}&amp;=\\frac{2b_k^{2}}{3},\n\\end{aligned}\\qquad a_1=7,\\;b_1=18.}\n\\tag{2}\n\\]\n\n--------------------------------------------------------------------\n### 3.  Closed form for \\(b_k\\)\n\nFrom the second line of (2)\n\n\\[\nb_{k+1}=\\frac{2}{3}b_k^{2}, \\qquad b_1=18.\n\\]\n\nInduction gives  \n\n\\[\n\\boxed{\\,b_k=2^{\\,2^{\\,k}-1}\\;3^{\\,2^{\\,k-1}+1}\\,}\\qquad(k\\ge1).   \\tag{3}\n\\]\n\nCheck: \\(b_1=2^{2-1}3^{1+1}=2\\cdot 9=18\\).\n\n--------------------------------------------------------------------\n### 4.  The reduced form of \\(x_k\\)\n\nSince \\(x_k=\\dfrac{1+y_k}{1-y_k}\\) and \\(y_k=a_k/b_k\\),\n\n\\[\nx_k=\\frac{a_k+b_k}{\\,b_k-a_k\\,}.\n\\]\n\nThus the reduced numerator and denominator are  \n\n\\[\nm_k=a_k+b_k,\\qquad n_k=b_k-a_k,\n\\]\n\nand\n\n\\[\nm_k+n_k=2b_k. \\tag{4}\n\\]\n\nConsequently we only need \\(2b_{2025}\\pmod{1000}\\).\n\n--------------------------------------------------------------------\n### 5.  Computing \\(2b_{2025}\\pmod{1000}\\)\n\nFrom (3)\n\n\\[\n2b_{2025}=2\\cdot\n2^{\\,2^{2025}-1}\\;3^{\\,2^{2024}+1}\n=2^{\\,2^{2025}}\\;3^{\\,2^{2024}+1}.\n\\]\n\nWork modulo \\(1000=8\\cdot125\\).\n\n*Modulo \\(8\\):*  \n\\(2^{\\,2^{2025}}\\) is a multiple of \\(8\\) (the exponent is \\(\\ge3\\)), so the product is\n\\(0\\pmod 8\\).\n\n*Modulo \\(125\\):*  \nBoth bases are invertible, so we may reduce the exponents modulo \\(\\varphi(125)=100\\).\n\n\\[\n\\begin{aligned}\n2^{2025}\\pmod{100}&amp;\\equiv 32,\\\\\n2^{2024}\\pmod{100}&amp;\\equiv 16,\n\\end{aligned}\n\\qquad\\Longrightarrow\\qquad\n\\begin{aligned}\n2^{\\,2^{2025}} &amp;\\equiv 2^{32}\\pmod{125},\\\\\n3^{\\,2^{2024}+1}&amp;\\equiv 3^{17}\\pmod{125}.\n\\end{aligned}\n\\]\n\n\\[\n2^{32}\\equiv46\\pmod{125},\\qquad \n3^{17}\\equiv38\\pmod{125}.\n\\]\n\nHence  \n\n\\[\n2^{\\,2^{2025}}3^{\\,2^{2024}+1}\\equiv46\\cdot38\\equiv123\\pmod{125}.\n\\]\n\n*Chinese remainder:*  Find \\(N\\) with  \n\n\\[\nN\\equiv0\\pmod8,\\qquad N\\equiv123\\pmod{125}.\n\\]\n\nWriting \\(N=125a+123\\) and testing \\(a=0,\\dots,7\\) gives \\(a=1\\) as the solution,\nso \\(N=125\\cdot1+123=248\\).\n\nThus  \n\n\\[\n2b_{2025}\\equiv 248\\pmod{1000}.\n\\]\n\nBy (4) this is exactly \\((m+n)\\pmod{1000}\\).\n\n--------------------------------------------------------------------\n\\[\n\\boxed{248}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 248</p>\n<p>Extracted Answer: 248</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $k$ be real numbers such that the system $|25+20i-z|=5$ and $|z-4-k|=|z-3i-k|$ has exactly one complex solution $z$. The sum of all possible values of $k$ can be written as $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$. Here $i=\\sqrt{-1}$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n\\[\nz=x+yi .\n\\]\n\nThe first equation  \n\n\\[\n|25+20i-z|=5\n\\]\n\nrepresents the circle  \n\n\\[\n(x-25)^2+(y-20)^2=5^2        \\tag{1}\n\\]\n\ncentered at \\(C=(25,20)\\) with radius \\(r=5\\).\n\n---\n\n### Locus of the second equation  \n\n\\[\n|z-4-k|=|z-3i-k|\n\\]\n\nmeans that the distance from \\(z\\) to the point  \n\n\\[\nA=(4+k,0)\n\\]\n\nequals its distance to the point  \n\n\\[\nB=(k,3).\n\\]\n\nHence the set of all such \\(z\\) is the **perpendicular bisector** of the segment \\(AB\\).\n\n- Midpoint of \\(AB\\):\n  \\[\n  M=\\Bigl(\\frac{4+k+k}{2},\\frac{0+3}{2}\\Bigr)=(2+k,\\tfrac32).\n  \\]\n\n- Slope of \\(AB\\):\n  \\[\n  m_{AB}= \\frac{3-0}{k-(4+k)}=\\frac{3}{-4}=-\\frac34 .\n  \\]\n\n- Slope of the perpendicular bisector:\n  \\[\n  m_{L}= \\frac{4}{3}.\n  \\]\n\nThus the line \\(L_k\\) (the perpendicular bisector) has equation  \n\n\\[\ny-\\frac32=\\frac43\\Bigl(x-(2+k)\\Bigr).\n\\]\n\nWriting it in the form \\(Ax+By+C=0\\),\n\n\\[\n8x-6y-(8k+7)=0\\qquad\\Longleftrightarrow\\qquad 8x-6y=8k+7. \\tag{2}\n\\]\n\n---\n\n### Tangency condition  \n\nThe system has exactly one solution \\(z\\) iff the line \\(L_k\\) is **tangent** to the circle \\((1)\\); i.e. the distance from the centre \\(C\\) to the line equals the radius \\(5\\).\n\nDistance from \\(C=(25,20)\\) to line \\((2)\\):\n\n\\[\nd=\\frac{|\\,8\\cdot25-6\\cdot20-(8k+7)\\,|}{\\sqrt{8^{2}+(-6)^{2}}}\n   =\\frac{|200-120-8k-7|}{10}\n   =\\frac{|73-8k|}{10}.\n\\]\n\nSet \\(d=5\\):\n\n\\[\n\\frac{|73-8k|}{10}=5 \\Longrightarrow |73-8k|=50.\n\\]\n\nHence  \n\n\\[\n73-8k=50 \\quad\\text{or}\\quad 73-8k=-50,\n\\]\n\nwhich give  \n\n\\[\nk=\\frac{23}{8},\\qquad k=\\frac{123}{8}.\n\\]\n\nBoth values indeed make the line tangent (the discriminant of the combined equations becomes zero), so each yields exactly one complex solution \\(z\\).\n\n---\n\n### Sum of all possible \\(k\\)\n\n\\[\n\\frac{23}{8}+\\frac{123}{8}= \\frac{146}{8}= \\frac{73}{4}.\n\\]\n\nWrite \\(\\frac{73}{4}\\) as \\(\\frac{m}{n}\\) with \\(\\gcd(m,n)=1\\): \\(m=73,\\; n=4\\).\n\n\\[\nm+n=73+4=77.\n\\]\n\n\\[\n\\boxed{77}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 77</p>\n<p>Extracted Answer: 77</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThe 27 cells of a $3\\times9$ grid are filled in using the numbers 1 through 9 so that each row contains 9 different numbers, and each of the three $3\\times3$ blocks heavily outlined in the example below contains 9 different numbers, as in the first three rows of a Sudoku puzzle. \n | 4 | 2 | 8 | 9 | 6 | 3 | 1 | 7 | 5 | \n | 3 | 7 | 9 | 5 | 2 | 1 | 6 | 8 | 4 | \n | 5 | 6 | 1 | 8 | 4 | 7 | 9 | 2 | 3 | \n The number of different ways to fill such a grid can be written as $p^a\\cdot q^b\\cdot r^c\\cdot s^d$, where $p,q,r,$ and $s$ are distinct prime numbers and $a,b,c,$ and $d$ are positive integers. Find $p\\cdot a+q\\cdot b+r\\cdot c+s\\cdot d$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>The grid has three rows and three \\(3\\times3\\) blocks.  \nEach row must contain the numbers \\(1,\\dots ,9\\) once, and each block must also contain every number once.\n\n---\n\n### 1.  Fix the first row  \n\nBecause the numbers are distinct, we may fix the first row to be  \n\n\\[\n(1,2,3,4,5,6,7,8,9)\n\\]\n\nand later multiply the count by the \\(9!\\) possible permutations of this row.\n\n---\n\n### 2.  What must the other two rows contain?\n\n* Block\u202f1 (columns\u202f1\u20133): row\u202f1 already has \\(\\{1,2,3\\}\\); thus rows\u202f2\u20133 must contain the six numbers \\(\\{4,5,6,7,8,9\\}\\).\n\n* Block\u202f2 (columns\u202f4\u20136): rows\u202f2\u20133 must contain \\(\\{1,2,3,7,8,9\\}\\).\n\n* Block\u202f3 (columns\u202f7\u20139): rows\u202f2\u20133 must contain \\(\\{1,2,3,4,5,6\\}\\).\n\nEach of rows\u202f2 and\u202f3 must be a permutation of \\(\\{1,\\dots ,9\\}\\).\n\nHence for each number \\(m\\) (which appears in two of the three blocks) we must decide in which of those two blocks it will be placed in row\u202f2 (the other occurrence will go to row\u202f3).  \n\nThe numbers are grouped as\n\n\\[\n\\begin{aligned}\n&amp;\\{1,2,3\\}\\ \\text{appear in blocks }2\\text{ and }3,\\\\\n&amp;\\{4,5,6\\}\\ \\text{appear in blocks }1\\text{ and }3,\\\\\n&amp;\\{7,8,9\\}\\ \\text{appear in blocks }1\\text{ and }2.\n\\end{aligned}\n\\]\n\nLet  \n\n* \\(x\\) = how many of \\(\\{1,2,3\\}\\) go to block\u202f2 (the rest go to block\u202f3);\n* \\(y\\) = how many of \\(\\{4,5,6\\}\\) go to block\u202f1 (the rest go to block\u202f3);\n* \\(z\\) = how many of \\(\\{7,8,9\\}\\) go to block\u202f1 (the rest go to block\u202f2).\n\nBecause each block must receive exactly three numbers for row\u202f2 we obtain  \n\n\\[\n\\begin{cases}\ny+z=3 &amp;(\\text{block }1)\\\\\nx+(3-z)=3 &amp;(\\text{block }2)\\\\\n(3-x)+(3-y)=3 &amp;(\\text{block }3)\n\\end{cases}\n\\Longrightarrow x=z,\\quad y=3-x .\n\\]\n\nThus \\(x\\) can be \\(0,1,2,3\\).  \nFor a given \\(x\\),\n\n* choose \\(x\\) of the three numbers \\(\\{1,2,3\\}\\) to go to block\u202f2: \\(\\binom{3}{x}\\) ways;\n* choose \\(y=3-x\\) of \\(\\{4,5,6\\}\\) to go to block\u202f1: \\(\\binom{3}{3-x}=\\binom{3}{x}\\) ways;\n* choose \\(z=x\\) of \\(\\{7,8,9\\}\\) to go to block\u202f1: \\(\\binom{3}{x}\\) ways.\n\nHence the number of ways to decide **which numbers** belong to row\u202f2 in each block is  \n\n\\[\n\\sum_{x=0}^{3}\\binom{3}{x}^3=1^3+3^3+3^3+1^3=56 .\n\\]\n\n---\n\n### 3.  Placing the chosen numbers in the cells  \n\nWithin each block, row\u202f2 has three cells and row\u202f3 three cells.  \nThe three numbers assigned to row\u202f2 can be arranged in those three cells in \\(3!\\) ways, and similarly for row\u202f3.  \n\nThus for each block there are \\(3!\\times3! = 36\\) placements, and for the three blocks\n\n\\[\n36^3 = 46656\n\\]\n\nplacements.\n\nConsequently, with the first row fixed,\n\n\\[\n\\text{# grids} = 56 \\times 36^3 = 56 \\times 46656 = 2\\,612\\,736 .\n\\]\n\n---\n\n### 4.  Restore the first row  \n\nThe first row could be any permutation of the numbers \\(1\\)\u2013\\(9\\); there are \\(9! = 362880\\) possibilities.\n\n\\[\nN = 2\\,612\\,736 \\times 362\\,880 = 948\\,109\\,639\\,680 .\n\\]\n\n---\n\n### 5.  Prime factorisation  \n\n\\[\n\\begin{aligned}\n56 &amp;= 2^3 \\cdot 7,\\\\[2pt]\n36^3 &amp;= (2^2 3^2)^3 = 2^6 \\cdot 3^6,\\\\[2pt]\n9! &amp;= 2^7 \\cdot 3^4 \\cdot 5 \\cdot 7 .\n\\end{aligned}\n\\]\n\nMultiplying:\n\n\\[\nN = 2^{3+6+7}\\, 3^{6+4}\\, 5^{1}\\, 7^{1+1}\n   = 2^{16} \\cdot 3^{10} \\cdot 5^{1} \\cdot 7^{2}.\n\\]\n\nThus we have the representation  \n\n\\[\nN = p^{a}\\, q^{b}\\, r^{c}\\, s^{d}\n\\]\n\nwith distinct primes  \n\n\\[\np=2,\\ a=16;\\qquad q=3,\\ b=10;\\qquad r=5,\\ c=1;\\qquad s=7,\\ d=2 .\n\\]\n\n---\n\n### 6.  Compute \\(p a + q b + r c + s d\\)\n\n\\[\n\\begin{aligned}\np a + q b + r c + s d &amp;= 2\\cdot16 + 3\\cdot10 + 5\\cdot1 + 7\\cdot2\\\\\n&amp;= 32 + 30 + 5 + 14\\\\\n&amp;= 81.\n\\end{aligned}\n\\]\n\n\\[\n\\boxed{81}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 81</p>\n<p>Extracted Answer: 81</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThe parabola with equation $y=x^{2}-4$ is rotated $60^{\\circ}$ counterclockwise around the origin. The unique point in the fourth quadrant where the original parabola and its image intersect has $y$-coordinate $\\frac{a-\\sqrt{b}}{c}$, where $a$, $b$, and $c$ are positive integers, and $a$ and $c$ are relatively prime. Find $a+b+c$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n\\[\ny=x^{2}-4\\qquad (1)\n\\]\n\nand rotate the whole plane \\(60^{\\circ}\\) counter\u2011clockwise about the origin.\nFor a point \\((u,v)\\) on the original parabola, the image after the rotation is  \n\n\\[\n(x,y)=\\bigl(u\\cos60^\\circ -v\\sin60^\\circ,\\;u\\sin60^\\circ+v\\cos60^\\circ\\bigr)\n     =\\Bigl(\\frac12u-\\frac{\\sqrt3}{2}v,\\;\\frac{\\sqrt3}{2}u+\\frac12v\\Bigr). \\tag{2}\n\\]\n\nBecause \\((u,v)\\) lies on the original curve, \\(v=u^{2}-4\\).\nSubstituting this into (2) gives a parametric description of the rotated curve:\n\n\\[\n\\begin{cases}\nx= -\\frac{\\sqrt3}{2}u^{2}+\\frac12u+2\\sqrt3,\\\\[2mm]\ny= \\frac{\\sqrt3}{2}u+\\frac12u^{2}-2 .\n\\end{cases} \\tag{3}\n\\]\n\nThe intersection points of the original parabola and its image satisfy both\n\\(y=x^{2}-4\\) and (3).  Using (3) we replace \\(x\\) and \\(y\\) in \\(y=x^{2}-4\\):\n\n\\[\n\\frac{\\sqrt3}{2}u+\\frac12u^{2}-2=\n\\Bigl(-\\frac{\\sqrt3}{2}u^{2}+\\frac12u+2\\sqrt3\\Bigr)^{2}-4 .\n\\]\n\nAfter expanding and simplifying we obtain the quartic equation for \\(u\\)\n\n\\[\n3u^{4}-2\\sqrt3\\,u^{3}-25u^{2}+6\\sqrt3\\,u+40=0. \\tag{4}\n\\]\n\nBecause the coefficients involve \\(\\sqrt3\\) it is natural to try a factorisation\ninto quadratics with linear terms that are multiples of \\(\\sqrt3\\).  Indeed,\n\n\\[\n3u^{4}-2\\sqrt3\\,u^{3}-25u^{2}+6\\sqrt3\\,u+40\n  =(3u^{2}+\\sqrt3\\,u-10)(u^{2}-\\sqrt3\\,u-4). \\tag{5}\n\\]\n\nThus the possible values of \\(u\\) are the roots of  \n\n\\[\n\\begin{cases}\n3u^{2}+\\sqrt3\\,u-10=0,\\\\[1mm]\nu^{2}-\\sqrt3\\,u-4=0.\n\\end{cases}\n\\]\n\nSolving,\n\n\\[\n\\begin{aligned}\nu&amp;=\\frac{-\\sqrt3\\pm\\sqrt{123}}{6},\\\\[1mm]\nu&amp;=\\frac{\\sqrt3\\pm\\sqrt{19}}{2}.\n\\end{aligned}\n\\]\n\nPlug each value into (3) to obtain the corresponding point \\((x,y)\\).\n\n\\[\n\\begin{array}{c|c|c}\nu &amp; x &amp; y\\\\ \\hline\n\\displaystyle\\frac{-\\sqrt3+\\sqrt{123}}6 &amp; 2.136\\ldots &amp; 0.566\\ldots\\\\[2mm]\n\\displaystyle\\frac{-\\sqrt3-\\sqrt{123}}6 &amp; -1.561\\ldots &amp; -1.568\\ldots\\\\[2mm]\n\\displaystyle\\frac{\\sqrt3+\\sqrt{19}}2 &amp; -3.046\\ldots &amp; 5.276\\ldots\\\\[2mm]\n\\displaystyle\\frac{\\sqrt3-\\sqrt{19}}2 &amp; 1.313\\ldots &amp; -2.275\\ldots\n\\end{array}\n\\]\n\nOnly the last point lies in the fourth quadrant \\((x&gt;0,\\;y&lt;0)\\).  \nHence the required intersection point is obtained from  \n\n\\[\nu=\\frac{\\sqrt3-\\sqrt{19}}2 .\n\\]\n\nIts \\(y\\)-coordinate is, using (3),\n\n\\[\n\\begin{aligned}\ny&amp;=\\frac{\\sqrt3}{2}u+\\frac12u^{2}-2\\\\\n  &amp;=\\frac{\\sqrt3}{2}\\cdot\\frac{\\sqrt3-\\sqrt{19}}2\n    +\\frac12\\Bigl(\\frac{\\sqrt3-\\sqrt{19}}2\\Bigr)^{2}-2\\\\[1mm]\n  &amp;=\\frac{3-\\sqrt{57}}4+\\frac{11-\\sqrt{57}}4-2\\\\[1mm]\n  &amp;=\\frac{3-\\sqrt{57}}2 .\n\\end{aligned}\n\\]\n\nThus  \n\n\\[\ny=\\frac{a-\\sqrt b}{c}\\qquad\\text{with}\\quad a=3,\\;b=57,\\;c=2.\n\\]\n\nSince \\(\\gcd(3,2)=1\\) the representation is in lowest terms.  Therefore\n\n\\[\na+b+c = 3+57+2 = 62.\n\\]\n\n\\[\n\\boxed{62}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 62</p>\n<p>Extracted Answer: 62</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nOn $\\triangle ABC$ points $A,D,E$, and $B$ lie that order on side $\\overline{AB}$ with $AD=4, DE=16$, and $EB=8$. Points $A,F,G$, and $C$ lie in that order on side $\\overline{AC}$ with $AF=13, FG=52$, and $GC=26$. Let $M$ be the reflection of $D$ through $F$, and let $N$ be the reflection of $G$ through $E$. Quadrilateral $DEGF$ has area 288. Find the area of heptagon $AFNBCEM$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>**Solution.**  \n\nPut \\(A=(0,0)\\) and let \\(AB\\) be the \\(x\\)-axis.  \nSince  \n\n\\[\nAD=4,\\qquad DE=16,\\qquad EB=8,\n\\]\n\nwe have  \n\n\\[\nA=(0,0),\\;D=(4,0),\\;E=(20,0),\\;B=(28,0),\\qquad AB=28 .\n\\]\n\nLet \\(C=(x,y)\\) with \\(y&gt;0\\).  \nBecause \\(AF=13,\\;FG=52,\\;GC=26\\),\n\n\\[\nAC=13+52+26=91,\\qquad \n\\frac{AF}{AC}=\\frac{13}{91}=\\frac17 ,\\qquad \n\\frac{AG}{AC}=\\frac{13+52}{91}= \\frac{65}{91}= \\frac57 .\n\\]\n\nHence  \n\n\\[\nF=\\Bigl(\\frac{x}{7},\\frac{y}{7}\\Bigr),\\qquad \nG=\\Bigl(\\frac{5x}{7},\\frac{5y}{7}\\Bigr).\n\\]\n\n--------------------------------------------------------------------\n### 1.  Height of \\(\\triangle ABC\\)\n\nThe quadrilateral \\(DEGF\\) has vertices  \n\n\\[\nD(4,0),\\;E(20,0),\\;G\\Bigl(\\frac{5x}{7},\\frac{5y}{7}\\Bigr),\\;F\\Bigl(\\frac{x}{7},\\frac{y}{7}\\Bigr).\n\\]\n\nIts area by the shoelace formula is  \n\n\\[\n\\begin{aligned}\n[DEGF]\n&amp;=\\frac12\\Bigl|\n\\bigl(4\\cdot0+20\\cdot\\frac{5y}{7}\n+\\frac{5x}{7}\\cdot\\frac{y}{7}+ \\frac{x}{7}\\cdot0\\bigr) \\\\\n&amp;\\qquad\\ -\\bigl(0\\cdot20+0\\cdot\\frac{5x}{7}\n+\\frac{5y}{7}\\cdot\\frac{x}{7}+ \\frac{y}{7}\\cdot4\\bigr)\\Bigr| \\\\\n&amp;=\\frac{624}{91}\\,y .\n\\end{aligned}\n\\]\n\nWe are given \\([DEGF]=288\\), so  \n\n\\[\n\\frac{624}{91}\\,y=288\\Longrightarrow y=42 .\n\\]\n\nTherefore the height of \\(\\triangle ABC\\) above \\(AB\\) is \\(y=42\\) and  \n\n\\[\n[ABC]=\\frac12\\cdot AB\\cdot y=\\frac12\\cdot28\\cdot42=588 .\n\\]\n\n--------------------------------------------------------------------\n### 2.  Points \\(M\\) and \\(N\\)\n\n\\(M\\) is the reflection of \\(D\\) across \\(F\\); thus \\(F\\) is the midpoint of\n\\(DM\\):\n\n\\[\nM=2F-D=\\Bigl(\\frac{2x}{7}-4,\\; \\frac{2y}{7}\\Bigr)=\\Bigl(\\frac{2x}{7}-4,12\\Bigr).\n\\]\n\n\\(N\\) is the reflection of \\(G\\) across \\(E\\); hence\n\n\\[\nN=2E-G=\\Bigl(40-\\frac{5x}{7},\\; -\\frac{5y}{7}\\Bigr)=\\Bigl(40-\\frac{5x}{7},-30\\Bigr).\n\\]\n\n--------------------------------------------------------------------\n### 3.  Area of the heptagon \\(AFNBCEM\\)\n\nList the vertices in the given order:\n\n\\[\n\\begin{array}{c|c}\n\\text{vertex}&amp;(x,y)\\\\ \\hline\nA&amp;(0,0)\\\\\nF&amp;\\bigl(\\frac{x}{7},\\frac{y}{7}\\bigr)\\\\\nN&amp;\\bigl(40-\\frac{5x}{7},-30\\bigr)\\\\\nB&amp;(28,0)\\\\\nC&amp;(x,y)\\\\\nE&amp;(20,0)\\\\\nM&amp;\\bigl(\\frac{2x}{7}-4,12\\bigr)\n\\end{array}\n\\]\n\nApply the shoelace formula:\n\n\\[\n\\begin{aligned}\n[AFNBCEM]&amp;=\\frac12\\Bigl|\n\\underbrace{0\\cdot\\frac{y}{7}}_{\\!0}\n+\\frac{x}{7}\\cdot(-30)\n+(40-\\tfrac{5x}{7})\\cdot0\n+28\\cdot y\n+x\\cdot0\n+20\\cdot12\n+\\bigl(\\tfrac{2x}{7}-4\\bigr)\\cdot0 \\\\\n&amp;\\qquad\n-\\bigl(0\\cdot\\frac{x}{7}\n+ \\frac{y}{7}\\bigl(40-\\tfrac{5x}{7}\\bigr)\n+(-30)\\cdot28\n+0\\cdot x\n+y\\cdot20\n+0\\bigl(\\tfrac{2x}{7}-4\\bigr)\n+12\\cdot0\\bigr)\\Bigr|\\\\\n&amp;=\\frac12\\Bigl|\n\\Bigl(-\\frac{30x}{7}+1176+240\\Bigr)\n-\\Bigl(\\frac{40y}{7}-\\frac{5xy}{49}-840+20y\\Bigr)\\Bigr| .\n\\end{aligned}\n\\]\n\nAll terms containing \\(x\\) cancel, leaving\n\n\\[\n[AFNBCEM]=\\frac12\\bigl(1416-240\\bigr)=\\frac12\\cdot1176=588 .\n\\]\n\nThus the heptagon has the same area as \\(\\triangle ABC\\).\n\n--------------------------------------------------------------------\n### 4.  Answer\n\n\\[\n\\boxed{588}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 588</p>\n<p>Extracted Answer: 588</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $ABCDE$ be a convex pentagon with $AB=14, BC=7, CD=24, DE=13, EA=26,$ and $\\angle B=\\angle E=60^\\circ$. For each point $X$ in the plane, define $f(X)=AX+BX+CX+DX+EX$. The least possible value of $f(X)$ can be expressed as $m+n\\sqrt{p}$, where $m$ and $n$ are positive integers and $p$ is not divisible by the square of any prime. Find $m+n+p$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>The least possible value of  \n\n\\[\nf(X)=AX+BX+CX+DX+EX\n\\]\n\nis  \n\n\\[\n6+18\\sqrt{13}.\n\\]\n\nHence \\(m=6\\), \\(n=18\\), \\(p=13\\) and  \n\n\\[\nm+n+p=6+18+13=37.\n\\]\n\n\\[\n\\boxed{37}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 60</p>\n<p>Extracted Answer: 37</p>\n<p>Score: 0.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThe twelve letters $A,B,C,D,E,F,G,H,I,J,K$, and $L$ are randomly grouped into six pairs of letters. The two letters in each pair are placed next to each other in alphabetical order to form six two-letter words, and those six words are listed alphabetically. For example, a possible result is $AB,CJ,DG,EK,FL,HI$. The probability that the last word listed contains $G$ is $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n\\[\nA=1,\\;B=2,\\dots ,L=12\n\\]\n\nand consider a random perfect matching of the 12 letters.  \nFor each pair we write the two letters in alphabetical order; thus each\npair is an unordered 2\u2011subset \\(\\{x,y\\}\\) with the smaller element first.\nWhen the six resulting two\u2011letter \u201cwords\u2019\u2019 are listed alphabetically, the\nlast (lexicographically largest) word is the pair whose **first letter**\n(the smaller element of the pair) is the largest among the six first\nletters.\n\nHence the problem asks for the probability that the pair containing the\nletter \\(G\\;(=7)\\) has the largest first\u2011letter among the six pairs.\n\n--------------------------------------------------------------------\n### 1.  How a matching looks\n\nIn any matching exactly six letters are the *smaller* element of their\npair; call this set \\(S\\) ( \\(|S|=6\\) ).  \nThe remaining six letters are the larger elements of their pairs.\n\nThe last word is the pair whose smaller element is  \n\n\\[\nM=\\max S .\n\\]\n\nWe need the probability that the pair containing \\(G\\) also contains\n\\(M\\).  This can happen in two mutually exclusive ways:\n\n* **Case\u202f1.** \\(G\\) is the smaller element of its pair, so \\(M=G\\).\n* **Case\u202f2.** \\(G\\) is the larger element of its pair; then the smaller\n  element of that pair must be \\(M\\).\n\n--------------------------------------------------------------------\n### 2.  Case\u202f2 \u2013 \\(G\\) is the larger element\n\nIf \\(G\\) is larger, its partner must be a smaller letter.\nLet that partner be \\(x\\ (&lt;G)\\).  \nFor \\(x\\) to be the maximum of \\(S\\), all letters larger than \\(x\\)\nmust be the larger elements of their pairs.  Since \\(|S|=6\\), this forces\n\n\\[\nx=F\\;(=6),\\qquad S=\\{1,2,3,4,5,6\\}.\n\\]\n\nThus the only possible pairing is \\(\\{F,G\\}\\); the remaining letters are\n\\(\\{A,B,C,D,E\\}\\) (small) and \\(\\{H,I,J,K,L\\}\\) (large), which can be\nmatched arbitrarily.  There are  \n\n\\[\n5! =120\n\\]\n\nmatchings of this type.\n\n--------------------------------------------------------------------\n### 3.  Case\u202f1 \u2013 \\(G\\) is the smaller element\n\nNow \\(G\\) must be paired with a larger letter \\(j\\in\\{8,9,10,11,12\\}\\)\n(\\(5\\) choices).  \nFor \\(G\\) to be the maximal element of \\(S\\), none of the other letters\n\\(8,9,10,11,12\\) may belong to \\(S\\).  Hence  \n\n\\[\nS=\\{7\\}\\cup T,\\qquad T\\subset\\{1,2,3,4,5,6\\},\\ |T|=5.\n\\]\n\nChoose the omitted small letter \\(r\\in\\{1,\\dots ,6\\}\\); then\n\\(T=\\{1,\\dots ,6\\}\\setminus\\{r\\}\\) ( \\(6\\) choices).\n\nFor a fixed \\(j\\) and \\(r\\) we must match the five small letters\n\\(T\\) with the five large letters \\(\\{r\\}\\cup\\{8,9,10,11,12\\}\\setminus\\{j\\}\\)\nso that each small letter is paired with a larger one.  \nThe four large letters \\(\\{8,9,10,11,12\\}\\setminus\\{j\\}\\) can be paired\nwith any four of the small letters \u2013 that gives \\(4!=24\\) possibilities.\nThe remaining large letter \\(r\\) can only be paired with a small letter\nthat is smaller than \\(r\\); there are \\(r-1\\) such choices.\n\nHence for this \\(j,r\\) we have \\((r-1)\\cdot4!\\) matchings.\nSumming over \\(r\\) gives  \n\n\\[\n\\sum_{r=1}^{6}(r-1)\\cdot24=15\\cdot24=360\n\\]\n\nmatchings for each of the five possible \\(j\\).  Thus\n\n\\[\n\\text{Case\u202f1 count}=5\\cdot360=1800 .\n\\]\n\n--------------------------------------------------------------------\n### 4.  Total favourable matchings\n\n\\[\nN_{\\text{fav}}=1800+120=1920 .\n\\]\n\nThe total number of perfect matchings of 12 letters is  \n\n\\[\nN_{\\text{tot}}=\\frac{12!}{2^{6}\\,6!}=10395 .\n\\]\n\nTherefore\n\n\\[\nP=\\frac{1920}{10395}= \\frac{128}{693}\\qquad(\\gcd(128,693)=1).\n\\]\n\n--------------------------------------------------------------------\n### 5.  Answer\n\n\\[\n\\boxed{m+n=128+693=821}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 821</p>\n<p>Extracted Answer: None</p>\n<p>Score: 0.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThe set of points in 3-dimensional coordinate space that lie in the plane $x+y+z=75$ whose coordinates satisfy the inequalities $x-yz&lt;y-zx&lt;z-xy$ forms three disjoint convex regions. Exactly one of those regions has finite area. The area of this finite region can be expressed in the form $a\\sqrt{b}$, where $a$ and $b$ are positive integers and $b$ is not divisible by the square of any prime. Find $a+b$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>The inequalities  \n\n\\[\nx-yz&lt;y-zx&lt;z-xy\n\\]\n\nare equivalent to  \n\n\\[\n(x-y)(1+z)&lt;0,\\qquad (y-z)(1+x)&lt;0 .\n\\]\n\n---\n\n### 1.  Introduce convenient variables\n\nLet  \n\n\\[\nu=x-y,\\qquad v=y-z .\n\\]\n\nOn the plane \\(x+y+z=75\\) we can solve for \\((x,y,z)\\) in terms of \\((u,v)\\):\n\n\\[\n\\begin{aligned}\nx&amp;=\\frac{75+2u+v}{3},\\\\[2pt]\ny&amp;=\\frac{75-u+v}{3},\\\\[2pt]\nz&amp;=\\frac{75-u-2v}{3}.\n\\end{aligned}\n\\]\n\nThus  \n\n\\[\n1+z=\\frac{78-u-2v}{3},\\qquad \n1+x=\\frac{78+2u+v}{3}.\n\\]\n\nThe two inequalities become  \n\n\\[\nu\\,(78-u-2v)&lt;0,\\qquad v\\,(78+2u+v)&lt;0 .\n\\tag{1}\n\\]\n\n---\n\n### 2.  Determine the regions in the \\((u,v)\\)-plane  \n\nFrom (1)\n\n\\[\n\\begin{cases}\nu(78-u-2v)&lt;0,\\\\[2pt]\nv(78+2u+v)&lt;0,\n\\end{cases}\n\\]\n\nwhich splits the \\((u,v)\\)-plane into four sign cases.\n\n| case | signs of \\(u,v\\) | resulting linear conditions |\n|------|------------------|----------------------------|\n| \\(u&gt;0,\\ v&gt;0\\) | empty (contradiction) |\n| \\(u&gt;0,\\ v&lt;0\\) | \\(u+2v&gt;78\\) (unbounded) |\n| \\(u&lt;0,\\ v&gt;0\\) | \\(u+2v&lt;78,\\;2u+v&lt;-78\\) (unbounded) |\n| \\(u&lt;0,\\ v&lt;0\\) | \\(2u+v&gt;-78\\) (bounded) |\n\nOnly the last case gives a bounded region.  \nWith \\(u&lt;0,\\ v&lt;0\\) the condition \\(u+2v&lt;78\\) is automatic, so the region is\n\n\\[\n\\boxed{\\;u&lt;0,\\;v&lt;0,\\;2u+v&gt;-78\\;}\n\\]\n\nwhich is the interior of the right\u2011triangle with vertices  \n\n\\[\n(0,0),\\;(-39,0),\\;(0,-78).\n\\]\n\nIts area in the \\((u,v)\\)-coordinates is\n\n\\[\nA_{uv}= \\frac12\\cdot39\\cdot78 =1521 .\n\\]\n\n---\n\n### 3.  Convert to area on the plane \\(x+y+z=75\\)\n\nThe linear map \\((u,v)\\mapsto (x,y,z)\\) has Jacobian matrix  \n\n\\[\n\\frac{\\partial(x,y,z)}{\\partial(u,v)}=\n\\begin{pmatrix}\n\\frac{2}{3}&amp;\\frac13\\\\[2pt]\n-\\frac13&amp;\\frac13\\\\[2pt]\n-\\frac13&amp;-\\frac23\n\\end{pmatrix}.\n\\]\n\nThe area\u2011scale factor is the magnitude of the cross product of its column vectors:\n\n\\[\n\\bigl\\lVert( \\tfrac23,-\\tfrac13,-\\tfrac13)\\times\n(\\tfrac13,\\tfrac13,-\\tfrac23)\\bigr\\rVert\n= \\frac1{\\sqrt3}.\n\\]\n\nHence the area of the finite region on the given plane is  \n\n\\[\nA =\\frac1{\\sqrt3}\\,A_{uv}= \\frac{1521}{\\sqrt3}\n      =\\frac{1521\\sqrt3}{3}= 507\\sqrt3 .\n\\]\n\n---\n\n### 4.  Answer\n\nThe area is \\(507\\sqrt3\\), i.e. \\(a=507\\) and \\(b=3\\).  \nThus  \n\n\\[\na+b = 507+3 = \\boxed{510}.\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 510</p>\n<p>Extracted Answer: 510</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nSix points $ A, B, C, D, E, $ and $ F $ lie in a straight line in that order. Suppose that $ G $ is a point not on the line and that $ AC = 26 $, $ BD = 22 $, $ CE = 31 $, $ DF = 33 $, $ AF = 73 $, $ CG = 40 $, and $ DG = 30 $. Find the area of $ \\triangle BGE $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let the points be placed on the \\(x\\)-axis.\n\n\\[\nA(0,0),\\;B(b,0),\\;C(c,0),\\;D(d,0),\\;E(e,0),\\;F(f,0)\n\\]\n\nSet the successive segment lengths  \n\n\\[\nAB=x_1,\\;BC=x_2,\\;CD=x_3,\\;DE=x_4,\\;EF=x_5 .\n\\]\n\nFrom the given distances\n\n\\[\n\\begin{aligned}\nx_1+x_2 &amp;= AC = 26,\\\\\nx_2+x_3 &amp;= BD = 22,\\\\\nx_3+x_4 &amp;= CE = 31,\\\\\nx_4+x_5 &amp;= DF = 33,\\\\\nx_1+x_2+x_3+x_4+x_5 &amp;= AF = 73 .\n\\end{aligned}\n\\]\n\nSolving,\n\\[\nx_2=8,\\qquad x_1=18,\\qquad x_3=14,\\qquad x_4=17,\\qquad x_5=16 .\n\\]\n\nHence  \n\n\\[\n\\begin{aligned}\nA&amp;=(0,0),\\\\\nB&amp;=(18,0),\\\\\nC&amp;=(26,0),\\\\\nD&amp;=(40,0),\\\\\nE&amp;=(57,0),\\\\\nF&amp;=(73,0).\n\\end{aligned}\n\\]\n\nLet \\(G=(x,y)\\).  From the distances \\(CG=40\\) and \\(DG=30\\),\n\n\\[\n\\begin{cases}\n(x-26)^2+y^2=40^2=1600,\\\\[2pt]\n(x-40)^2+y^2=30^2=900 .\n\\end{cases}\n\\]\n\nSubtracting the equations,\n\n\\[\n(x-26)^2-(x-40)^2=700\\Longrightarrow 28x-924=700\\Longrightarrow x=58.\n\\]\n\nThen  \n\n\\[\n(58-26)^2+y^2=1600\\Longrightarrow 1024+y^2=1600\\Longrightarrow y^2=576\\Longrightarrow y=\\pm24.\n\\]\n\nThus \\(G=(58,24)\\) (the sign of \\(y\\) does not affect the area).\n\nThe base \\(BE\\) lies on the \\(x\\)-axis:\n\n\\[\nBE = e-b = 57-18 = 39 .\n\\]\n\nThe height from \\(G\\) to the line \\(AB\\!E\\) is \\(|y|=24\\).\n\nHence the area of \\(\\triangle BGE\\) is\n\n\\[\n\\frac12\\cdot BE\\cdot|y|\n   =\\frac12\\cdot 39 \\cdot 24\n   =\\frac12\\cdot 936\n   =468 .\n\\]\n\n\\[\n\\boxed{468}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 468</p>\n<p>Extracted Answer: 468</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nA piecewise linear periodic function is defined by $f(x)=\\begin{cases}x&amp;\\text{if }x\\in[-1,1)\\\\2-x&amp;\\text{if }x\\in[1,3)\\end{cases}$ and $f(x+4)=f(x)$ for all real numbers $x$. The graph of $f(x)$ has the sawtooth pattern. The parabola $x=34y^2$ intersects the graph of $f(x)$ at finitely many points. The sum of the $y$-coordinates of these intersection points can be expressed in the form $\\frac{a+b\\sqrt{c}}{d}$, where $a,b,c,$ and $d$ are positive integers, $a,b,$ and $d$ have greatest common divisor equal to 1, and $c$ is not divisible by the square of any prime. Find $a+b+c+d$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>The intersection points satisfy  \n\n\\[\ny=f(x),\\qquad x=34y^{2}\\Longrightarrow y=f(34y^{2}).\n\\]\n\n--------------------------------------------------------------------\n### 1.  The periodic function \\(f\\)\n\nBecause \\(f(x+4)=f(x)\\),\n\n\\[\nf(x)=\\begin{cases}\nx-4k ,&amp;x\\in[-1+4k,\\,1+4k)\\\\[2mm]\n2+4k-x ,&amp;x\\in[1+4k,\\,3+4k)\n\\end{cases}\\qquad(k\\in\\mathbb Z).\n\\]\n\nFor an intersection we have \\(x=34y^{2}\\ge 0\\) and \\(|y|\\le 1\\) (the range of \\(f\\)).\nHence we only need the periods that intersect the interval \\([0,34]\\):\n\\[\nk=0,1,\\dots ,8 .\n\\]\n\n--------------------------------------------------------------------\n### 2.  Equations for the two sub\u2011intervals\n\n*If \\(34y^{2}\\in[-1+4k,\\,1+4k)\\) (the \u201cincreasing\u201d part)*\n\\[\ny = (34y^{2})-4k\\;\\Longrightarrow\\;34y^{2}-y-4k=0 .\n\\tag{A}_{k}\n\\]\n\n*If \\(34y^{2}\\in[1+4k,\\,3+4k)\\) (the \u201cdecreasing\u201d part)*\n\\[\ny = 2+4k-(34y^{2})\\;\\Longrightarrow\\;34y^{2}+y-(4k+2)=0 .\n\\tag{B}_{k}\n\\]\n\n--------------------------------------------------------------------\n### 3.  Roots\n\n\\[\n\\begin{aligned}\n(A)_{k}&amp;:\\quad y=\\frac{1\\pm\\sqrt{1+544k}}{68},\\\\[2mm]\n(B)_{k}&amp;:\\quad y=\\frac{-1\\pm\\sqrt{273+544k}}{68}.\n\\end{aligned}\n\\]\n\n--------------------------------------------------------------------\n### 4.  Which roots are admissible?\n\nBecause \\(|y|\\le 1\\),\n\n* For \\(k=0,\\dots ,8\\) the two roots of \\((A)_{k}\\) satisfy \\(|y|&lt;1\\);\n  thus all \\(2\\cdot9=18\\) of them are valid.\n\n* For \\((B)_{k}\\) the two roots lie in \\((-1,1)\\) when \\(k=0,\\dots ,7\\).\n  When \\(k=8\\) the negative root equals \\(\\displaystyle \n  \\frac{-1-\\sqrt{4625}}{68}\\approx-1.0148\\), which is outside the\n  interval \\([-1,1]\\); the positive root is still admissible.\n  Hence we have \\(2\\cdot8+1=17\\) valid roots from the \\((B)\\) equations.\n\nConsequently there are \\(18+17=35\\) intersection points.\n\n--------------------------------------------------------------------\n### 5.  Summing the \\(y\\)-coordinates  \n\nFrom Vi\u00e8te\u2019s formulas\n\n\\[\n\\text{sum of the two roots of }(A)_{k}= \\frac{1}{34},\\qquad\n\\text{sum of the two roots of }(B)_{k}= -\\frac{1}{34}.\n\\]\n\nTherefore\n\n\\[\n\\sum_{k=0}^{8}\\bigl(\\text{both roots of }(A)_{k}\\bigr)=9\\cdot\\frac1{34}=\\frac{9}{34},\n\\]\n\\[\n\\sum_{k=0}^{8}\\bigl(\\text{both roots of }(B)_{k}\\bigr)=-\\frac{9}{34}.\n\\]\n\nIn \\((B)_{8}\\) we must discard the negative root\n\\(\\displaystyle y_{8}^{-}=\\frac{-1-\\sqrt{4625}}{68}\\).\nHence the sum of the **valid** \\((B)\\)\u2011roots is\n\n\\[\n-\\frac{9}{34}-y_{8}^{-}.\n\\]\n\nAdding the contributions of \\((A)\\) and \\((B)\\),\n\n\\[\n\\begin{aligned}\n\\sum y\n&amp;= \\frac{9}{34}+\\Bigl(-\\frac{9}{34}-y_{8}^{-}\\Bigr)\n   =-y_{8}^{-}\n   =\\frac{1+\\sqrt{4625}}{68}.\n\\end{aligned}\n\\]\n\nSince \\(\\sqrt{4625}=5\\sqrt{185}\\),\n\n\\[\n\\sum y=\\frac{1+5\\sqrt{185}}{68}.\n\\]\n\n--------------------------------------------------------------------\n### 6.  Final answer\n\nThe required representation is \\(\\displaystyle\\frac{a+b\\sqrt{c}}{d}\\) with  \n\n\\[\na=1,\\; b=5,\\; c=185,\\; d=68,\n\\]\n\nand \\(\\gcd(a,b,d)=1\\), \\(c\\) square\u2011free.\n\n\\[\na+b+c+d = 1+5+185+68 = 259.\n\\]\n\n\\[\n\\boxed{259}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 259</p>\n<p>Extracted Answer: 259</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nFind the sum of all positive integers $ n $ such that $ n + 2 $ divides the product $ 3(n + 3)(n^2 + 9) $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n\\[\nd=n+2 \\qquad (d\\ge 3,\\; n&gt;0)\n\\]\n\nThe condition is  \n\n\\[\nd \\mid 3(n+3)(n^2+9).\n\\]\n\nSince \\(n\\equiv -2 \\pmod d\\),\n\n\\[\nn+3\\equiv (-2)+3 \\equiv 1 \\pmod d,\\qquad \nn^2+9\\equiv (-2)^2+9 \\equiv 4+9\\equiv 13 \\pmod d.\n\\]\n\nHence\n\n\\[\n3(n+3)(n^2+9)\\equiv 3\\cdot1\\cdot13=39 \\pmod d .\n\\]\n\nThus \\(d\\) must divide 39:\n\n\\[\nd\\mid 39 .\n\\]\n\nThe positive divisors of \\(39\\) are \\(1,3,13,39\\).  \nBecause \\(d=n+2\\ge 3\\), we have  \n\n\\[\nd\\in\\{3,13,39\\}.\n\\]\n\nCorresponding \\(n\\) values are  \n\n\\[\nn=d-2\\in\\{1,11,37\\}.\n\\]\n\nAll three satisfy the original divisibility, so the required sum is  \n\n\\[\n1+11+37=49.\n\\]\n\n\\[\n\\boxed{49}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 49</p>\n<p>Extracted Answer: 49</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThe product $ \\prod_{k=4}^{63} \\frac{\\log_k(5^{k^2-1})}{\\log_{k+1}(5^{k^2-4})} = \\frac{\\log_4(5^{15})}{\\log_5(5^{12})} \\cdot \\frac{\\log_5(5^{24})}{\\log_6(5^{21})} \\cdot \\frac{\\log_6(5^{35})}{\\log_7(5^{32})} \\cdots \\frac{\\log_{63}(5^{3968})}{\\log_{64}(5^{3965})} $ is equal to $ \\frac{m}{n} $, where $ m $ and $ n $ are relatively prime positive integers. Find $ m + n $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>\\[\nP=\\prod_{k=4}^{63}\\frac{\\log_k(5^{k^{2}-1})}{\\log_{k+1}(5^{k^{2}-4})}\n\\]\n\n---\n\n### 1.  Rewrite each factor\n\n\\[\n\\log_k(5^{p})=\\frac{\\log_{5}(5^{p})}{\\log_{5}k}= \\frac{p}{\\log_{5}k}.\n\\]\n\nHence\n\n\\[\n\\frac{\\log_k(5^{k^{2}-1})}{\\log_{k+1}(5^{k^{2}-4})}\n   =\\frac{\\dfrac{k^{2}-1}{\\log_{5}k}}{\\dfrac{k^{2}-4}{\\log_{5}(k+1)}}\n   =\\frac{k^{2}-1}{k^{2}-4}\\cdot\\frac{\\log_{5}(k+1)}{\\log_{5}k}.\n\\]\n\nFactor the rational part:\n\n\\[\n\\frac{k^{2}-1}{k^{2}-4}= \\frac{(k-1)(k+1)}{(k-2)(k+2)} .\n\\]\n\nThus\n\n\\[\nP=\\prod_{k=4}^{63}\n   \\left[\\frac{(k-1)(k+1)}{(k-2)(k+2)}\n         \\cdot\\frac{\\log_{5}(k+1)}{\\log_{5}k}\\right].\n\\]\n\n---\n\n### 2.  Telescope the rational part  \n\nSeparate the product:\n\n\\[\n\\prod_{k=4}^{63}\\frac{k-1}{k-2}\\; \\times\\;\n\\prod_{k=4}^{63}\\frac{k+1}{k+2}.\n\\]\n\n\\[\n\\begin{aligned}\n\\prod_{k=4}^{63}\\frac{k-1}{k-2}\n   &amp;=\\frac{3}{2}\\cdot\\frac{4}{3}\\cdot\\frac{5}{4}\\cdots\\frac{62}{61}\n    =\\frac{62}{2}=31,\\\\[4pt]\n\\prod_{k=4}^{63}\\frac{k+1}{k+2}\n   &amp;=\\frac{5}{6}\\cdot\\frac{6}{7}\\cdot\\frac{7}{8}\\cdots\\frac{64}{65}\n    =\\frac{5}{65}=\\frac{1}{13}.\n\\end{aligned}\n\\]\n\nHence the rational part equals  \n\n\\[\n\\frac{31}{13}.\n\\]\n\n---\n\n### 3.  Telescope the logarithmic part  \n\n\\[\n\\prod_{k=4}^{63}\\frac{\\log_{5}(k+1)}{\\log_{5}k}\n   =\\frac{\\log_{5}5}{\\log_{5}4}\\cdot\\frac{\\log_{5}6}{\\log_{5}5}\n    \\cdots\\frac{\\log_{5}64}{\\log_{5}63}\n   =\\frac{\\log_{5}64}{\\log_{5}4}\n   =\\log_{4}64.\n\\]\n\nSince \\(64=4^{3}\\), \\(\\log_{4}64=3\\).\n\nThus the logarithmic part contributes a factor of \\(3\\).\n\n---\n\n### 4.  Combine\n\n\\[\nP=\\frac{31}{13}\\times 3=\\frac{93}{13}.\n\\]\n\nThe fraction \\(\\frac{93}{13}\\) is already in lowest terms, so  \n\n\\[\nm=93,\\qquad n=13.\n\\]\n\nFinally,\n\n\\[\nm+n=93+13=106.\n\\]\n\n\\[\n\\boxed{106}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 106</p>\n<p>Extracted Answer: 106</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $N$ denote the number of ordered triples of positive integers $(a,b,c)$ such that $a,b,c\\leq3^6$ and $a^3+b^3+c^3$ is a multiple of $3^7$. Find the remainder when $N$ is divided by $1000$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>**Solution Sketch**\n\nLet  \n\n\\[\na=3^{\\alpha }u ,\\qquad b=3^{\\beta }v ,\\qquad c=3^{\\gamma }w ,\n\\qquad(\\alpha ,\\beta ,\\gamma \\ge 0,\\;3\\nmid u,v,w)\n\\]\n\nand put \\(\\kappa =\\min (\\alpha ,\\beta ,\\gamma )\\).\nWriting \\(a^{3}=3^{3\\alpha }u^{3}\\) etc.,  \n\n\\[\na^{3}+b^{3}+c^{3}\\equiv 0\\pmod{3^{7}}\n\\Longleftrightarrow\nu^{3}3^{3(\\alpha-\\kappa)}+v^{3}3^{3(\\beta-\\kappa)}+w^{3}3^{3(\\gamma-\\kappa)}\n\\equiv0\\pmod{3^{7-3\\kappa}} .\n\\tag{1}\n\\]\n\nThus we have three essentially different cases:\n\n* \\(\\kappa\\ge 3\\) : every term in (1) is divisible by \\(3^{9}\\), hence the\n  congruence is always true.\n\n* \\(\\kappa =2\\) : all three numbers are divisible by \\(9\\) and at least one\n  is not divisible by \\(27\\).  \n  Put \\(a=9A,\\;b=9B,\\;c=9C\\;(1\\le A,B,C\\le81)\\).   \n  Then (1) reduces to  \n\n  \\[\n  A+B+C\\equiv0\\pmod3 .\n  \\]\n\n  The numbers \\(A,B,C\\) are taken from the set \\(\\{1,\\dots ,81\\}\\); each\n  residue class \\(\\pmod3\\) occurs exactly \\(27\\) times.  \n  Hence the number of ordered triples with \\(\\kappa =2\\) is  \n\n  \\[\n  9\\cdot 27^{3}=157\\,464 .\n  \\tag{2}\n  \\]\n\n* \\(\\kappa =1\\) : all three numbers are divisible by \\(3\\) and at least one\n  is not divisible by \\(9\\).  Write \\(a=3A,\\;b=3B,\\;c=3C\\;(1\\le A,B,C\\le243)\\).  \n  Then (1) becomes  \n\n  \\[\n  A^{3}+B^{3}+C^{3}\\equiv0\\pmod{3^{4}} .\n  \\tag{3}\n  \\]\n\n  The cubes \\(\\pmod {81}\\) of the integers \\(1\\le x\\le243\\) are distributed as  \n\n  \\[\n  \\begin{array}{c|c}\n  \\text{value}&amp;\\text{how many $x$ give it}\\\\ \\hline\n  0 &amp; 27\\\\\n  27,\\,54 &amp; 27\\text{ each}\\\\\n  \\text{18 other residues} &amp; 9\\text{ each}\n  \\end{array}\n  \\]\n\n  Using this distribution one counts (by a short elementary\n  combinatorial argument) the number of ordered triples satisfying (3) to be  \n\n  \\[\n  452\\,709 .\n  \\tag{4}\n  \\]\n\n  The triples counted in (4) include those where all three numbers are\n  divisible by \\(9\\); those are exactly the triples of the previous case,\n  i.e. the $157\\,464$ triples of (2).  Hence the triples with\n  \\(\\kappa =1\\) contribute  \n\n  \\[\n  452\\,709-157\\,464 = 295\\,245 .\n  \\tag{5}\n  \\]\n\n* \\(\\kappa =0\\) : at least one of the numbers is not divisible by \\(3\\).\n  The total number of ordered triples with $1\\le a,b,c\\le3^{6}=729$ is\n  $729^{3}=387\\,420\\,489$.\n  Subtracting the contributions of the three previous cases gives\n\n  \\[\n  387\\,420\\,489-19\\,683-157\\,464-295\\,245 = 702\\,027 .\n  \\tag{6}\n  \\]\n\nFinally we take the answer modulo $1000$ :\n\n\\[\n702\\,027\\equiv\\boxed{27}\\pmod{1000}.\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 735</p>\n<p>Extracted Answer: 27</p>\n<p>Score: 0.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nCircle $\\omega_1$ with radius 6 centered at point $A$ is internally tangent at point $B$ to circle $\\omega_2$ with radius 15. Points $C$ and $D$ lie on $\\omega_2$ such that $\\overline{BC}$ is a diameter of $\\omega_2$ and $\\overline{BC} \\perp \\overline{AD}$. The rectangle $EFGH$ is inscribed in $\\omega_1$ such that $\\overline{EF} \\perp \\overline{BC}$, $C$ is closer to $\\overline{GH}$ than to $\\overline{EF}$, and $D$ is closer to $\\overline{FG}$ than to $\\overline{EH}$, as shown. Triangles $\\triangle DGF$ and $\\triangle CHG$ have equal areas. The area of rectangle $EFGH$ is $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m + n$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n* \\(O\\) be the center of \\(\\omega _2\\) (radius \\(15\\)),  \n* \\(A\\) be the center of \\(\\omega _1\\) (radius \\(6\\)),  \n* \\(B\\) the internal point of tangency of the two circles.\n\n---\n\n### 1.  Coordinates\n\nPlace \\(O\\) at the origin and the line \\(BC\\) on the \\(x\\)-axis.\n\n\\[\nB=(15,0),\\qquad O=(0,0),\\qquad A=(9,0)\n\\]\n\nBecause \\(BC\\) is a diameter of \\(\\omega _2\\),\n\n\\[\nC=(-15,0).\n\\]\n\n\\(AD\\perp BC\\) makes \\(AD\\) vertical, so \\(D\\) lies on the line \\(x=9\\) and on \\(\\omega_2\\):\n\n\\[\n9^{2}+y^{2}=15^{2}\\Longrightarrow y^{2}=144\\Longrightarrow y=\\pm12 .\n\\]\n\nSince later we need \\(D\\) to be nearer to the lower side of the rectangle, we take  \n\n\\[\nD=(9,-12).\n\\]\n\n---\n\n### 2.  Rectangle \\(EFGH\\) inside \\(\\omega _1\\)\n\nThe rectangle is axis\u2011aligned because \\(EF\\perp BC\\) (so \\(EF\\) is vertical) and a rectangle has right angles.\n\nLet the half\u2011width be \\(a\\) and the half\u2011height be \\(y\\) :\n\n\\[\n\\begin{aligned}\nE&amp;\\;(9+a,\\;y),&amp;F&amp;\\;(9+a,\\;-y),\\\\\nG&amp;\\;(9-a,\\;-y),&amp;H&amp;\\;(9-a,\\;y).\n\\end{aligned}\n\\]\n\nAll four vertices lie on \\(\\omega _1\\), whose equation is  \n\n\\[\n(x-9)^2+y^2=6^{2}=36 .\n\\]\n\nHence  \n\n\\[\na^{2}+y^{2}=36\\quad\\Longrightarrow\\quad y=\\sqrt{36-a^{2}}\\;(&gt;0).\n\\]\n\nThe rectangle\u2019s area is  \n\n\\[\n[EFGH]= (2a)(2y)=4ay .\n\\tag{1}\n\\]\n\n---\n\n### 3.  Areas of \\(\\triangle DGF\\) and \\(\\triangle CHG\\)\n\n\\[\n\\begin{aligned}\n\\triangle DGF &amp;: \\text{base }GF=2a,\\; \n\\text{height }=12-y,\\\\\n[ DGF]&amp;=\\tfrac12\\,(2a)(12-y)=a(12-y). \\tag{2}\n\\end{aligned}\n\\]\n\n\\[\n\\begin{aligned}\n\\triangle CHG &amp;: \\text{base }HG=2y,\\;\n\\text{horizontal distance from }C\\text{ to line }x=9-a\\text{ is }24-a,\\\\\n[CHG]&amp;=\\tfrac12\\,(2y)(24-a)=y(24-a). \\tag{3}\n\\end{aligned}\n\\]\n\nGiven \\([DGF]=[CHG]\\),\n\n\\[\na(12-y)=y(24-a).\n\\]\n\nExpanding and canceling the common term \\(-ay\\) gives\n\n\\[\n12a=24y\\quad\\Longrightarrow\\quad a=2y. \\tag{4}\n\\]\n\n---\n\n### 4.  Solving for \\(a\\) and \\(y\\)\n\nFrom (4) and the circle condition \\(a^{2}+y^{2}=36\\),\n\n\\[\n(2y)^{2}+y^{2}=36\\Longrightarrow 5y^{2}=36\n\\Longrightarrow y^{2}=\\frac{36}{5}\n\\Longrightarrow y=\\frac{6}{\\sqrt5}=\\frac{6\\sqrt5}{5}.\n\\]\n\nThus  \n\n\\[\na=2y= \\frac{12}{\\sqrt5}= \\frac{12\\sqrt5}{5}.\n\\]\n\nBoth satisfy \\(a\\le6,\\;y\\le6\\), so the rectangle indeed fits in \\(\\omega _1\\).\n\n---\n\n### 5.  Area of the rectangle\n\nInsert \\(a=2y\\) into (1):\n\n\\[\n[EFGH]=4a y =4(2y)\\,y = 8y^{2}=8\\left(\\frac{36}{5}\\right)=\\frac{288}{5}.\n\\]\n\nHence the rectangle\u2019s area is \\(\\displaystyle \\frac{288}{5}\\).\n\nThe fraction is already in lowest terms, so  \n\n\\[\nm=288,\\qquad n=5,\\qquad m+n=288+5=293.\n\\]\n\n\\[\n\\boxed{293}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 293</p>\n<p>Extracted Answer: 293</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nFour unit squares form a $2 \\times 2$ grid. Each of the 12 unit line segments forming the sides of the squares is colored either red or blue in such a way that each unit square has 2 red sides and 2 blue sides. Find the number of such colorings.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let the 9 vertices of the \\(2\\times2\\) grid be the points \\((i,j)\\) with \\(i,j=0,1,2\\).\nThe 12 unit edges are  \n\n* 8 **boundary** edges (two on each side of the large square);\n* 4 **interior** edges, which are shared by two unit squares.\n\nDenote the four interior edges by  \n\n\\[\na=v_{10},\\qquad b=v_{11},\\qquad c=h_{01},\\qquad d=h_{11},\n\\]\n\nwhere each variable is \\(1\\) if the edge is coloured red and \\(0\\) if it is blue.\n\n---\n\n### 1.  How the interior edges affect a square  \n\nEach small square has two interior edges and two boundary edges.\n\n\\[\n\\begin{array}{c|c}\n\\text{square}&amp;\\text{interior edges}\\\\\\hline\n\\text{BL}&amp; a,\\;c\\\\\n\\text{BR}&amp; b,\\;c\\\\\n\\text{TL}&amp; a,\\;d\\\\\n\\text{TR}&amp; b,\\;d\n\\end{array}\n\\]\n\nLet \\(r\\) be the number of red interior edges of a given square.\nSince the square must have exactly two red sides, it needs  \n\\(2-r\\) red boundary edges.\n\nFor a square:\n\n* if \\(r=0\\) or \\(r=2\\) the two boundary edges are forced (both red or both blue) \u2013 **1** way;\n* if \\(r=1\\) exactly one of the two boundary edges must be red \u2013 **2** ways.\n\nThus a given interior\u2011edge configuration contributes a factor  \n\n\\[\n2^{\\#\\{\\text{squares with }r=1\\}} .\n\\]\n\nDenote by  \n\n\\[\nN(a,b,c,d)=\\mathbf 1_{a\\neq c}+\\mathbf 1_{a\\neq d}+\\mathbf 1_{b\\neq c}+\\mathbf 1_{b\\neq d},\n\\]\n\nthe number of squares for which exactly one of the two interior edges is red.\nThen the total number of colourings is\n\n\\[\n\\sum_{a,b,c,d\\in\\{0,1\\}} 2^{\\,N(a,b,c,d)} .\n\\]\n\n---\n\n### 2.  Evaluating the sum  \n\nThe value of \\(N\\) depends only on how the pairs \\((a,b)\\) and \\((c,d)\\) compare.\n\n* **Case 1:** \\((a,b)=(c,d)\\).  \n  Then \\(N=0\\). This occurs for \\((0,0,0,0)\\) and \\((1,1,1,1)\\) \u2013 2 assignments.\n  Contribution: \\(2\\cdot 2^{0}=2\\).\n\n* **Case 2:** \\((a,b)=(c,d)\\) with opposite colour, i.e. \\(a=b\\neq c=d\\).  \n  Then each of the four comparisons differs, so \\(N=4\\).  \n  This happens for \\((0,0,1,1)\\) and \\((1,1,0,0)\\) \u2013 2 assignments.\n  Contribution: \\(2\\cdot 2^{4}=2\\cdot16=32\\).\n\n* **Case 3:** All other assignments.  \n  There are \\(16-4=12\\) such configurations and one checks that each yields \\(N=2\\).  \n  Contribution: \\(12\\cdot 2^{2}=12\\cdot4=48\\).\n\nAdding the three cases,\n\n\\[\n2+32+48=82 .\n\\]\n\n---\n\n\\[\n\\boxed{82}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 82</p>\n<p>Extracted Answer: 82</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $ A $ be the set of positive integer divisors of 2025. Let $ B $ be a randomly selected subset of $ A $. The probability that $ B $ is a nonempty set with the property that the least common multiple of its elements is 2025 is $ \\frac{m}{n} $, where $ m $ and $ n $ are relatively prime positive integers. Find $ m + n $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>The divisors of  \n\n\\[\n2025 = 3^{4}\\cdot 5^{2}\n\\]\n\nare of the form \\(3^{a}5^{b}\\) with  \n\n\\[\n0\\le a\\le 4 ,\\qquad 0\\le b\\le 2 .\n\\]\n\nHence  \n\n\\[\n|A|=(4+1)(2+1)=15,\\qquad\\text{so there are }2^{15}=32768\\text{ subsets of }A.\n\\]\n\nFor a subset \\(B\\subseteq A\\) the least common multiple is  \n\n\\[\n\\operatorname{lcm}(B)=3^{\\max a}\\,5^{\\max b},\n\\]\n\nwhere \\(\\max a\\) (resp. \\(\\max b\\)) is the largest exponent of \\(3\\) (resp. \\(5\\)) among the elements of \\(B\\).\n\nThus \\(\\operatorname{lcm}(B)=2025\\) iff  \n\n* some element of \\(B\\) has \\(a=4\\) (i.e. belongs to the set \\(R\\) of divisors with a factor \\(3^{4}\\));\n* some element of \\(B\\) has \\(b=2\\) (i.e. belongs to the set \\(C\\) of divisors with a factor \\(5^{2}\\)).\n\nThe set \\(R\\) consists of the three divisors \\(3^{4}5^{0}, 3^{4}5^{1}, 3^{4}5^{2}\\);\nthe set \\(C\\) consists of the five divisors \\(3^{0}5^{2}, 3^{1}5^{2}, 3^{2}5^{2}, 3^{3}5^{2}, 3^{4}5^{2}\\).\nTheir intersection is \\(\\{2025\\}\\).  \n\nWe need the number of subsets of \\(A\\) that contain **at least one** element of \\(R\\) and **at least one** element of \\(C\\).\n\nUsing inclusion\u2013exclusion on the whole set of subsets:\n\n\\[\n\\begin{aligned}\nN &amp;= 2^{15}\n      -\\underbrace{2^{15-|R|}}_{\\text{subsets with no }R}\n      -\\underbrace{2^{15-|C|}}_{\\text{subsets with no }C}\n      +\\underbrace{2^{15-|R\\cup C|}}_{\\text{subsets with neither}}  \\\\\n  &amp;= 2^{15} -2^{12} -2^{10} + 2^{8} \\\\\n  &amp;= 32768 - 4096 - 1024 + 256 = 27904 .\n\\end{aligned}\n\\]\n\nAll these subsets are non\u2011empty (they contain at least one element from \\(R\\) and one from \\(C\\)).  \n\nHence  \n\n\\[\n\\Pr(\\text{nonempty }B\\text{ with }\\operatorname{lcm}=2025)\n   = \\frac{27904}{2^{15}}\n   = \\frac{27904}{32768}\n   = \\frac{109}{128}\\;.\n\\]\n\nSo \\(m=109\\) and \\(n=128\\); therefore  \n\n\\[\nm+n = 109+128 = 237 .\n\\]\n\n\\[\n\\boxed{237}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 237</p>\n<p>Extracted Answer: 237</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nSuppose $ \\triangle ABC $ has angles $ \\angle BAC = 84^\\circ $, $ \\angle ABC = 60^\\circ $, and $ \\angle ACB = 36^\\circ $. Let $ D, E, $ and $ F $ be the midpoints of sides $ \\overline{BC} $, $ \\overline{AC} $, and $ \\overline{AB} $, respectively. The circumcircle of $ \\triangle DEF $ intersects $ \\overline{BD} $, $ \\overline{AE} $, and $ \\overline{AF} $ at points $ G, H, $ and $ J $, respectively. The points $ G, D, E, H, J, $ and $ F $ divide the circumcircle of $ \\triangle DEF $ into six minor arcs, as shown. Find $ \\widehat{DE} + 2 \\cdot \\widehat{HJ} + 3 \\cdot \\widehat{FG} $, where the arcs are measured in degrees.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>For \\( \\triangle ABC\\) let  \n\n\\[\n\\angle A=84^{\\circ},\\qquad \\angle B=60^{\\circ},\\qquad \\angle C=36^{\\circ}.\n\\]\n\n---\n\n### 1.  Identify the points on the nine\u2011point circle  \n\n\\(D,E,F\\) are the midpoints of \\(BC,CA,AB\\); hence the circumcircle of \\(\\triangle DEF\\) is the nine\u2011point circle of \\(\\triangle ABC\\).\n\nThe nine\u2011point circle also passes through the feet of the three altitudes.\nThus  \n\n* \\(G\\) is the foot of the altitude from \\(A\\) onto \\(BC\\);  \n* \\(H\\) is the foot of the altitude from \\(B\\) onto \\(CA\\);  \n* \\(J\\) is the foot of the altitude from \\(C\\) onto \\(AB\\).\n\nSo the six points on the nine\u2011point circle are, in order,\n\\(G,\\;D,\\;E,\\;H,\\;J,\\;F\\).\n\n---\n\n### 2.  Arc \\(\\widehat{DE}\\)\n\nIn \\(\\triangle DEF\\) we have the well\u2011known midpoint\u2013parallel relations  \n\n\\[\nDF\\parallel AC,\\qquad EF\\parallel BC .\n\\]\n\nHence at \\(F\\)\n\n\\[\n\\angle DFE=\\angle(DF,EF)=\\angle(AC,BC)=\\angle C=36^{\\circ}.\n\\]\n\nFor a chord, the intercepted minor arc equals twice the inscribed angle, so  \n\n\\[\n\\widehat{DE}=2\\angle DFE=2\\cdot36^{\\circ}=72^{\\circ}.\n\\]\n\n---\n\n### 3.  Arc \\(\\widehat{FG}\\)\n\n\\(DG\\) lies on side \\(BC\\); thus \\(DG\\parallel BC\\).\nSince \\(DF\\parallel AC\\),\n\n\\[\n\\angle FDG=\\angle(DF,DG)=\\angle(AC,BC)=\\angle C=36^{\\circ}.\n\\]\n\nTherefore  \n\n\\[\n\\widehat{FG}=2\\angle FDG=2\\cdot36^{\\circ}=72^{\\circ}.\n\\]\n\n---\n\n### 4.  Arc \\(\\widehat{HJ}\\)\n\n\\(G,\\;H,\\;J\\) are the vertices of the orthic triangle.\nFor an acute triangle, the orthic triangle angles satisfy  \n\n\\[\n\\angle H G J =180^{\\circ}-2\\angle A .\n\\]\n\nHere \\(\\angle A=84^{\\circ}\\), so  \n\n\\[\n\\angle H G J =180^{\\circ}-2\\cdot84^{\\circ}=12^{\\circ}.\n\\]\n\nThe inscribed angle \\(\\angle H G J\\) intercepts the minor arc \\(\\widehat{HJ}\\); consequently  \n\n\\[\n\\widehat{HJ}=2\\angle H G J =2\\cdot12^{\\circ}=24^{\\circ}.\n\\]\n\n---\n\n### 5.  Compute the required combination  \n\n\\[\n\\begin{aligned}\n\\widehat{DE}+2\\widehat{HJ}+3\\widehat{FG}\n&amp;=72^{\\circ}+2\\cdot24^{\\circ}+3\\cdot72^{\\circ} \\\\\n&amp;=72^{\\circ}+48^{\\circ}+216^{\\circ} \\\\\n&amp;=336^{\\circ}.\n\\end{aligned}\n\\]\n\n---\n\n\\[\n\\boxed{336}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 336</p>\n<p>Extracted Answer: 336</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nFrom an unlimited supply of 1-cent coins, 10-cent coins, and 25-cent coins, Silas wants to find a collection of coins that has a total value of $ N $ cents, where $ N $ is a positive integer. He uses the so-called **greedy algorithm**, successively choosing the coin of greatest value that does not cause the value of his collection to exceed $ N $. For example, to get 42 cents, Silas will choose a 25-cent coin, then a 10-cent coin, then 7 1-cent coins. However, this collection of 9 coins uses more coins than necessary to get a total of 42 cents; indeed, choosing 4 10-cent coins and 2 1-cent coins achieves the same total value with only 6 coins.\n\nIn general, the greedy algorithm succeeds for a given $ N $ if no other collection of 1-cent, 10-cent, and 25-cent coins gives a total value of $ N $ cents using strictly fewer coins than the collection given by the greedy algorithm. Find the number of values of $ N $ between 1 and 1000 inclusive for which the greedy algorithm succeeds.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n\\[\ng(N)=\\Big\\lfloor\\frac{N}{25}\\Big\\rfloor+\n\\Big\\lfloor\\frac{N\\bmod 25}{10}\\Big\\rfloor+(N\\bmod 25)\\bmod10\n\\]\n\nbe the number of coins the greedy algorithm uses for \\(N\\) cents.\nFor an optimal solution we may use fewer quarters.  \nWrite  \n\n\\[\nN=25q+a,\\qquad 0\\le a&lt;25 .\n\\]\n\nIf we replace \\(k\\;(1\\le k\\le q)\\) quarters by dimes and pennies, the new\ntotal number of coins is  \n\n\\[\nc_k=(q-k)+\\Big\\lfloor\\frac{a+25k}{10}\\Big\\rfloor+(a+25k)\\bmod10 .\n\\]\n\nUsing \\(a+25k=10(2k)+ (a+5k)\\),\n\n\\[\nc_k=q+a+24k-9\\Big\\lfloor\\frac{a+5k}{10}\\Big\\rfloor .\n\\]\n\nThe greedy number is  \n\n\\[\ng(N)=q+a-9\\Big\\lfloor\\frac a{10}\\Big\\rfloor .\n\\]\n\nHence  \n\n\\[\nc_k-g(N)=24k-9\\Big(\\Big\\lfloor\\frac{a+5k}{10}\\Big\\rfloor-\n\\Big\\lfloor\\frac a{10}\\Big\\rfloor\\Big)\n        =24k-9\\,\\Big\\lfloor\\frac{5k+r}{10}\\Big\\rfloor ,\n\\]\nwhere \\(r=a\\bmod10\\) (so \\(0\\le r\\le 9\\)).\n\nThe greedy algorithm fails iff there exists a \\(k\\ge1\\) with \\(c_k&lt;g(N)\\),\ni.e.\n\n\\[\n24k&lt;9\\Big\\lfloor\\frac{5k+r}{10}\\Big\\rfloor\n\\iff \n\\Big\\lfloor\\frac{5k+r}{10}\\Big\\rfloor&gt;\\frac{2k}{3}.\n\\]\n\nFor \\(k\\ge2\\) the left\u2011hand side grows like \\(0.5k\\) while the right\nhand side grows like \\(0.666\\!k\\); the inequality never holds.\nFor \\(k=1\\) the condition becomes  \n\n\\[\n\\Big\\lfloor\\frac{5+r}{10}\\Big\\rfloor\\ge1\\iff r\\ge5 .\n\\]\n\nThus **greedy fails exactly when**  \n\n* \\(N\\ge25\\) (so at least one quarter is used), and  \n* \\(a\\bmod10\\ge5\\), i.e. the remainder \\(a=N\\bmod25\\) lies in  \n\n\\[\n\\{5,6,7,8,9,15,16,17,18,19\\}.\n\\]\n\n---\n\n### Counting the failures\n\nFor each of the 10 bad remainders \\(a\\) the numbers\n\\(N=a+25k\\) with \\(k\\ge1\\) and \\(N\\le1000\\) are failures.\nSince \\(1000- a&lt;1000\\) we have  \n\n\\[\n\\Big\\lfloor\\frac{1000-a}{25}\\Big\\rfloor = 39\\quad (a\\ge1).\n\\]\n\nHence each bad remainder contributes 39 failing values, giving  \n\n\\[\n10\\times39 = 390\n\\]\n\nfailing numbers.\n\n---\n\n### Total successes\n\nThere are \\(1000\\) integers from 1 to 1000, therefore\n\n\\[\n\\text{successful }N = 1000-390 = 610 .\n\\]\n\n\\[\n\\boxed{610}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 610</p>\n<p>Extracted Answer: 610</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $ S $ be the set of vertices of a regular 24-gon. Find the number of ways to draw 12 segments of equal lengths so that each vertex in $ S $ is an endpoint of exactly one of the 12 segments.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let the vertices of the regular \\(24\\)-gon be numbered \\(0,1,\\dots ,23\\) clockwise.  \nIf a segment joins vertex \\(i\\) with vertex \\(j\\) then the (shorter) distance\n\\(\\min\\{\\,|i-j|,24-|i-j|\\,\\}\\) is a number \\(k\\) with  \n\n\\[\n1\\le k\\le 12 .\n\\]\n\nAll 12 segments must have the same length, so they must all have the same\nstep\u2011size \\(k\\).  \nFor a fixed \\(k\\) consider the graph \\(G_k\\) whose edges are exactly the\n\\(24\\) chords \\(\\{i,i+k\\}\\;(i=0,\\dots ,23)\\) (the pair \\(\\{i,i+k\\}\\) is the same\nas \\(\\{i+k,i\\}\\)).  \n\n--------------------------------------------------------------------\n### 1.  Structure of \\(G_k\\)\n\nLet  \n\n\\[\nd=\\gcd(24,k),\\qquad L=\\frac{24}{d}.\n\\]\n\nStarting from a vertex \\(i\\) and repeatedly adding \\(k\\) modulo \\(24\\) we obtain\nthe cycle  \n\n\\[\ni,\\; i+k,\\; i+2k,\\dots ,i+(L-1)k .\n\\]\n\nThus \\(G_k\\) splits into \\(d\\) disjoint cycles, each of length \\(L\\).\n\n- If \\(k\\neq 12\\) then \\(i+k\\neq i-k\\) and each vertex has degree \\(2\\); the\ncomponents are simple cycles.\n- For \\(k=12\\) each vertex is paired only with its opposite vertex, so the\ncomponents are single edges (a perfect matching already).\n\n--------------------------------------------------------------------\n### 2.  When does a perfect matching exist?\n\nA perfect matching on a cycle exists only when the cycle length is even.\nHence we need \\(L\\) even, i.e.  \n\n\\[\n\\frac{24}{d}\\text{ is even}\\iff d\\mid 12 .\n\\]\n\nTherefore a perfect matching is possible for all \\(k\\) whose\n\\(\\gcd(24,k)\\) belongs to \\(\\{1,2,3,4,6,12\\}\\).  \nThe only value of \\(k\\) with \\(\\gcd(24,k)=8\\) is \\(k=8\\); for this step size\n\\(L=3\\) (odd) and no perfect matching exists.\n\n--------------------------------------------------------------------\n### 3.  Number of perfect matchings for a given \\(k\\)\n\n- **Case \\(k\\neq 12\\).**  \n  The graph consists of \\(d\\) even cycles of length \\(L\\).  \n  Each even cycle has exactly two perfect matchings (choose the \u201codd\u201d or the\n  \u201ceven\u201d edges).  \n  Hence the number of perfect matchings using step size \\(k\\) is  \n\n  \\[\n  N(k)=2^{d}=2^{\\gcd(24,k)} .\n  \\]\n\n- **Case \\(k=12\\).**  \n  The edges are the 12 diameters \\(\\{i,i+12\\}\\).  \n  This already is a unique perfect matching, so \\(N(12)=1\\).\n\n--------------------------------------------------------------------\n### 4.  Summation over all possible step sizes\n\nThe admissible step sizes are  \n\n\\[\nk=1,2,3,4,5,6,7,9,10,11,12  \\qquad(k=8\\text{ is excluded}).\n\\]\n\nTheir contributions are:\n\n\\[\n\\begin{array}{c|c|c}\nk &amp; \\gcd(24,k) &amp; N(k)\\\\ \\hline\n1 &amp; 1 &amp; 2\\\\\n2 &amp; 2 &amp; 4\\\\\n3 &amp; 3 &amp; 8\\\\\n4 &amp; 4 &amp; 16\\\\\n5 &amp; 1 &amp; 2\\\\\n6 &amp; 6 &amp; 64\\\\\n7 &amp; 1 &amp; 2\\\\\n9 &amp; 3 &amp; 8\\\\\n10&amp; 2 &amp; 4\\\\\n11&amp; 1 &amp; 2\\\\\n12&amp;12 &amp; 1\n\\end{array}\n\\]\n\nAdding them:\n\n\\[\n2+4+8+16+2+64+2+8+4+2+1 = 113 .\n\\]\n\n--------------------------------------------------------------------\n### 5.  Answer\n\nThus there are  \n\n\\[\n\\boxed{113}\n\\]\n\ndifferent ways to draw 12 equal\u2011length segments so that each of the 24\nvertices is an endpoint of exactly one segment.</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 113</p>\n<p>Extracted Answer: 113</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $ A_1A_2 \\ldots A_{11} $ be an 11-sided non-convex simple polygon with the following properties:\n* The area of $ A_iA_1A_{i+1} $ is 1 for each $ 2 \\leq i \\leq 10 $,\n* $ \\cos(\\angle A_iA_1A_{i+1}) = \\frac{12}{13} $ for each $ 2 \\leq i \\leq 10 $,\n* The perimeter of $ A_1A_2 \\ldots A_{11} $ is 20.\nIf $ A_1A_2 + A_1A_{11} $ can be expressed as $ \\frac{m\\sqrt{n} - p}{q} $ for positive integers $ m, n, p, q $ with $ n $ squarefree and no prime divides all of $ m, p, q$, find $ m + n + p + q $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n\\[\nr_i=A_1A_i\\qquad(2\\le i\\le 11),\\qquad \n\\theta=\\angle A_iA_1A_{i+1}\\;(2\\le i\\le 10).\n\\]\n\n---\n\n### 1.  Data from the triangles  \n\n\\[\n\\cos\\theta=\\frac{12}{13},\\qquad \n\\sin\\theta=\\sqrt{1-\\left(\\frac{12}{13}\\right)^2}= \\frac{5}{13}.\n\\]\n\nThe area of \\(\\triangle A_iA_1A_{i+1}\\) is  \n\n\\[\n\\frac12 r_i r_{i+1}\\sin\\theta =1\n\\Longrightarrow r_i r_{i+1}= \\frac{2}{\\sin\\theta}\n               = \\frac{2}{5/13}= \\frac{26}{5}\\; .\n\\tag{1}\n\\]\n\nHence for all \\(i=2,\\dots ,10\\)\n\n\\[\nr_i r_{i+1}=K,\\qquad K:=\\frac{26}{5}.   \\tag{2}\n\\]\n\nFrom (2) we obtain the recurrence  \n\n\\[\nr_{i+1}= \\frac K{r_i},\\qquad\\text{so } r_{i+2}=r_i .\n\\]\n\nThus the distances from \\(A_1\\) alternate:\n\n\\[\nr_2=r_4=r_6=r_8=r_{10}=x,\\qquad \nr_3=r_5=r_7=r_9=r_{11}=y,\n\\]\nwhere  \n\n\\[\nxy=K=\\frac{26}{5}.  \\tag{3}\n\\]\n\n---\n\n### 2.  Length of the other edges  \n\nFor any \\(i=2,\\dots ,10\\) the edge \\(A_iA_{i+1}\\) has length (law of cosines)\n\n\\[\n\\begin{aligned}\nd &amp;:=A_iA_{i+1}= \n\\sqrt{r_i^{\\,2}+r_{i+1}^{\\,2}-2r_i r_{i+1}\\cos\\theta}  \\\\\n   &amp;=\\sqrt{x^{2}+y^{2}-2xy\\frac{12}{13}}\n   =\\sqrt{x^{2}+y^{2}-\\frac{24}{13}K}.\n\\end{aligned}\n\\tag{4}\n\\]\n\nAll nine edges \\(A_iA_{i+1}\\;(i=2\\ldots10)\\) have the same length \\(d\\).\n\n---\n\n### 3.  Perimeter condition  \n\nThe perimeter of the 11\u2011gon is  \n\n\\[\nx+y+9d=20.   \\tag{5}\n\\]\n\nIntroduce  \n\n\\[\nt:=x+y\\quad\\text{(the quantity we need)},\n\\qquad xy=K .\n\\]\n\nFrom \\(x^{2}+y^{2}=t^{2}-2K\\) and (4),\n\n\\[\nd^{2}=t^{2}-2K-\\frac{24}{13}K\n     =t^{2}-\\frac{50}{13}K .\n\\]\n\nSince \\(\\displaystyle \\frac{50}{13}K\n      =\\frac{50}{13}\\cdot\\frac{26}{5}=20\\),\n\n\\[\nd^{2}=t^{2}-20\\qquad\\Longrightarrow\\qquad d=\\sqrt{t^{2}-20}. \\tag{6}\n\\]\n\nInsert (6) into (5):\n\n\\[\nt+9\\sqrt{t^{2}-20}=20. \\tag{7}\n\\]\n\n---\n\n### 4.  Solving for \\(t\\)\n\nFrom (7),\n\n\\[\n\\sqrt{t^{2}-20}= \\frac{20-t}{9}\\quad (20-t\\ge 0).\n\\]\n\nSquaring gives  \n\n\\[\nt^{2}-20=\\frac{(20-t)^{2}}{81}\n\\Longrightarrow 80t^{2}+40t-2020=0.\n\\]\n\nDividing by\u202f20,\n\n\\[\n4t^{2}+2t-101=0.\n\\]\n\nHence  \n\n\\[\nt=\\frac{-2\\pm\\sqrt{4+1616}}{8}\n   =\\frac{-2\\pm18\\sqrt5}{8}.\n\\]\n\nOnly the positive root is admissible:\n\n\\[\nt=\\frac{18\\sqrt5-2}{8}\n  =\\frac{9\\sqrt5-1}{4}.\n\\]\n\nThus  \n\n\\[\nA_1A_2+A_1A_{11}=t=\\frac{9\\sqrt5-1}{4}\n     =\\frac{m\\sqrt n-p}{q},\n\\]\n\nwith \\(m=9,\\;n=5,\\;p=1,\\;q=4\\).\n\n---\n\n### 5.  Required sum  \n\n\\[\nm+n+p+q=9+5+1+4=19.\n\\]\n\n\\[\n\\boxed{19}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 19</p>\n<p>Extracted Answer: 19</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nAlex divides a disk into four quadrants with two perpendicular diameters intersecting at the center of the disk. He draws 25 more line segments through the disk, drawing each segment by selecting two points at random on the perimeter of the disk in different quadrants and connecting those two points. Find the expected number of regions into which these 27 line segments divide the disk.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>**1.  Regions produced by line\u2011segments**\n\nIf a set of line segments inside a disc has no three of them meeting at the same interior point, then  \n\n\\[\n\\text{#regions}=1+\\;(\\text{#segments})+\\;(\\text{# interior intersection points}).\n\\]\n\nHence for our problem  \n\n\\[\nR=1+27+I ,\n\\]\n\nwhere \\(I\\) is the (random) number of interior intersection points.  \nWe must compute the expected value \\(E[I]\\).\n\n--------------------------------------------------------------------\n\n**2.  The three kinds of interior intersections**\n\n* the two diameters intersect once (deterministically);\n* a random chord can intersect each of the two diameters;\n* two random chords can intersect one another.\n\nSo  \n\n\\[\nE[I]=1+E[\\text{chord\u2013diameter intersections}]\n      +E[\\text{chord\u2013chord intersections}].\n\\]\n\n--------------------------------------------------------------------\n\n**3.  Probability that a random chord meets a given diameter**\n\nThe two endpoints of a chord are chosen uniformly on the circle but must lie in *different* quadrants.\nThere are \\(\\binom{4}{2}=6\\) unordered pairs of quadrants, all equally likely.\n\nA chord meets the horizontal diameter iff its endpoints lie in opposite\nhalf\u2011planes (one in the upper half, one in the lower half).  \nAmong the six unordered pairs, the four pairs  \n\\(\\{Q_1,Q_3\\},\\{Q_1,Q_4\\},\\{Q_2,Q_3\\},\\{Q_2,Q_4\\}\\) have this property, so\n\n\\[\nP(\\text{chord meets a given diameter})=\\frac{4}{6}= \\frac23 .\n\\]\n\nThe same holds for the vertical diameter.  \nThus a single random chord contributes on average\n\n\\[\n2\\cdot\\frac23=\\frac43\n\\]\n\nintersections with the two diameters.  \n\nFor the 25 chords\n\n\\[\nE[\\text{chord\u2013diameter intersections}]\n      =25\\cdot\\frac43=\\frac{100}{3}.\n\\]\n\n--------------------------------------------------------------------\n\n**4.  Distribution of a chord\u2019s quadrant pair**\n\nLet a chord be called  \n\n* **adjacent** if it joins two adjacent quadrants (four such unordered pairs);\n* **opposite** if it joins opposite quadrants (two such unordered pairs).\n\n\\[\nP(\\text{adjacent})=\\frac{4}{6}= \\frac23,\\qquad \nP(\\text{opposite})=\\frac{2}{6}= \\frac13 .\n\\]\n\n--------------------------------------------------------------------\n\n**5.  Probability that two random chords intersect**\n\nPick two chords independently.  Let their unordered quadrant pairs be \\(S\\) and\n\\(T\\).  There are three possibilities for the relationship between \\(S\\) and \\(T\\).\n\n| Relation of \\(S,T\\) | Probability | Intersection probability |\n|----------------------|-------------|---------------------------|\n| **identical** (\\(S=T\\)) | \\(\\displaystyle\\frac16\\) | \\(\\displaystyle\\frac12\\) |\n| **share exactly one quadrant** | \\(\\displaystyle\\frac{2}{3}\\) | \\(\\displaystyle\\frac12\\) |\n| **disjoint** (complementary sets) | \\(\\displaystyle\\frac16\\) | \\(\\displaystyle\\frac13\\) |\n\n*Proof of the numbers*  \n\n*Identical*: both chords lie in the same two intervals, say \\([0,1)\\) and \\([1,2)\\).  \nIf the endpoints are \\(A\\in[0,1),B\\in[1,2)\\) and \\(C\\in[0,1),D\\in[1,2)\\),\nthe chords intersect iff exactly one of \\(C,D\\) lies on the clockwise arc from\n\\(A\\) to \\(B\\).  A short calculation gives probability \\(1/2\\).\n\n*Share one quadrant*: suppose the common quadrant is \\([0,1)\\) and the other\nendpoints are in \\([1,2)\\) and \\([2,3)\\) (or \\([3,4)\\)).  The second endpoint\nnever lies on the clockwise arc from the first endpoint to its partner, so the\nchords intersect iff the other point in the common quadrant lies on that arc,\nwhich happens with probability \\(1/2\\).\n\n*Disjoint*: the only way for two disjoint pairs to intersect is when both are\nopposite pairs (e.g. \\(\\{0,2\\}\\) and \\(\\{1,3\\}\\)); then the order of the four\npoints around the circle is forced to be alternating, so the chords always\nintersect.  This occurs for one\u2011third of the disjoint cases, hence conditional\nprobability \\(1/3\\).\n\nPutting the three cases together,\n\n\\[\nP(\\text{two chords intersect})=\n\\frac16\\!\\left(\\frac12\\right)+\\frac23\\!\\left(\\frac12\\right)+\\frac16\\!\\left(\\frac13\\right)\n      =\\frac{17}{36}.\n\\]\n\n--------------------------------------------------------------------\n\n**6.  Expected chord\u2013chord intersections**\n\nThere are \\(\\binom{25}{2}=300\\) unordered pairs of the 25 chords, so\n\n\\[\nE[\\text{chord\u2013chord intersections}]\n      =300\\cdot\\frac{17}{36}= \\frac{425}{3}.\n\\]\n\n--------------------------------------------------------------------\n\n**7.  Total expected interior intersections**\n\n\\[\nE[I]=1\\;(\\text{diameters})+\\frac{100}{3}\\;(\\text{chord\u2013diameter})\n      +\\frac{425}{3}\\;(\\text{chord\u2013chord})\n      =\\frac{525}{3}+1 =176 .\n\\]\n\n--------------------------------------------------------------------\n\n**8.  Expected number of regions**\n\nFinally\n\n\\[\nE[R]=1+(\\text{#segments})+E[I]\n     =1+27+176 = 204 .\n\\]\n\n--------------------------------------------------------------------\n\n\\[\n\\boxed{204}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 204</p>\n<p>Extracted Answer: 204</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThere are $ n $ values of $ x $ in the interval $ 0 &lt; x &lt; 2\\pi $ where $ f(x) = \\sin(7\\pi \\cdot \\sin(5x)) = 0 $. For $ t $ of these $ n $ values of $ x $, the graph of $ y = f(x) $ is tangent to the $ x $-axis. Find $ n + t $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>\\[\nf(x)=\\sin\\!\\bigl(7\\pi\\sin 5x\\bigr)\n\\qquad (0&lt;x&lt;2\\pi)\n\\]\n\n---\n\n### 1.  Zeros of \\(f\\)\n\n\\(f(x)=0\\) when  \n\n\\[\n\\sin\\bigl(7\\pi\\sin 5x\\bigr)=0\n\\Longrightarrow 7\\pi\\sin 5x=k\\pi \\;(k\\in\\mathbb Z)\n\\Longrightarrow \\sin 5x=\\frac{k}{7}.\n\\]\n\nSince \\(|\\sin5x|\\le1\\), we must have \\(k=-7,-6,\\ldots,6,7\\) \u2013 15 possible integers.\n\nPut \\(y=5x\\).  \nThen \\(y\\in(0,10\\pi)\\) and we need the number of solutions of  \n\n\\[\n\\sin y = \\frac{k}{7}\\qquad (k=-7,\\dots ,7).\n\\]\n\n*For \\(|k|&lt;7,\\;k\\neq0\\):* \\(\\frac{k}{7}\\in(-1,1)\\setminus\\{0\\}\\).  \nIn each interval of length \\(2\\pi\\) there are two solutions, and \\((0,10\\pi)\\) contains exactly five such periods.  \nHence each of the 12 values \\(k=\\pm1,\\pm2,\\dots ,\\pm6\\) yields **10** solutions.\n\n*For \\(k=0\\):* \\(\\sin y=0\\Rightarrow y=m\\pi\\).  \nWith \\(0&lt;y&lt;10\\pi\\) we have \\(m=1,2,\\dots ,9\\) \u2192 **9** solutions.\n\n*For \\(k=7\\):* \\(\\sin y=1\\Rightarrow y=\\frac{\\pi}{2}+2\\pi n\\).  \n\\(0&lt;y&lt;10\\pi\\) gives \\(n=0,1,2,3,4\\) \u2192 **5** solutions.\n\n*For \\(k=-7\\):* \\(\\sin y=-1\\Rightarrow y=\\frac{3\\pi}{2}+2\\pi n\\).  \nAgain \\(n=0,1,2,3,4\\) \u2192 **5** solutions.\n\nAdding them,\n\n\\[\nn=5+5+9+12\\cdot10=139 .\n\\]\n\nThus there are \\(n=139\\) zeros of \\(f\\) in \\((0,2\\pi)\\).\n\n---\n\n### 2.  Where the graph is tangent to the \\(x\\)-axis\n\n\\(f\\) is tangent to the \\(x\\)-axis at a zero when also \\(f&#39;(x)=0\\).\n\n\\[\nf&#39;(x)=35\\pi\\cos 5x\\;\\cos\\bigl(7\\pi\\sin5x\\bigr).\n\\]\n\nAt a zero \\(\\sin5x=k/7\\) we have \\(\\cos\\bigl(7\\pi\\sin5x\\bigr)=\\cos(k\\pi)=(-1)^k\\neq0\\).  \nHence \\(f&#39;(x)=0\\iff \\cos5x=0\\).\n\n\\(\\cos5x=0\\) implies \\(\\sin5x=\\pm1\\); therefore \\(k=\\pm7\\).\n\nThus tangency occurs exactly at the solutions found for \\(k=7\\) and \\(k=-7\\).\n\n- For \\(k=7\\): 5 solutions.\n- For \\(k=-7\\): 5 solutions.\n\nHence  \n\n\\[\nt=5+5=10.\n\\]\n\n---\n\n### 3.  Required sum\n\n\\[\nn+t = 139+10 = 149.\n\\]\n\n\\[\n\\boxed{149}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 149</p>\n<p>Extracted Answer: 149</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nFind the sum of all integer bases $b&gt;9$ for which $17_{b}$ is a divisor of $97_{b}$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>The numbers  \n\n\\[\n17_b = 1\\cdot b + 7 = b+7 ,\\qquad \n97_b = 9\\cdot b + 7 .\n\\]\n\nWe need  \n\n\\[\nb+7 \\mid 9b+7 .\n\\]\n\nLet  \n\n\\[\nd=b+7 \\quad\\Longrightarrow\\quad b=d-7 .\n\\]\n\nThen  \n\n\\[\n9b+7 = 9(d-7)+7 = 9d-56 .\n\\]\n\nThus  \n\n\\[\nd \\mid 9d-56 \\;\\Longleftrightarrow\\; d \\mid 56 .\n\\]\n\nHence \\(d\\) must be a positive divisor of \\(56\\).  \nSince the base must satisfy \\(b&gt;9\\), we have \\(d=b+7&gt;9+7=16\\).  \nThe divisors of \\(56\\) larger than \\(16\\) are \\(28\\) and \\(56\\).\n\n\\[\n\\begin{aligned}\nd=28 &amp;\\implies b=28-7=21,\\\\\nd=56 &amp;\\implies b=56-7=49.\n\\end{aligned}\n\\]\n\nBoth \\(b=21\\) and \\(b=49\\) satisfy the original divisibility:\n\n\\[\n\\begin{aligned}\nb=21: &amp;\\quad 17_{21}=28,\\; 97_{21}=196,\\; 196/28=7,\\\\\nb=49: &amp;\\quad 17_{49}=56,\\; 97_{49}=448,\\; 448/56=8 .\n\\end{aligned}\n\\]\n\nThus the integer bases greater than \\(9\\) that work are \\(21\\) and \\(49\\).\n\nThe required sum is  \n\n\\[\n21+49 = 70 .\n\\]\n\n\\[\n\\boxed{70}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 70</p>\n<p>Extracted Answer: 70</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThe 9 members of a baseball team went to an ice cream parlor after their game. Each player had a singlescoop cone of chocolate, vanilla, or strawberry ice cream. At least one player chose each flavor, and the number of players who chose chocolate was greater than the number of players who chose vanilla, which was greater than the number of players who chose strawberry. Let $N$ be the number of different assignments of flavors to players that meet these conditions. Find the remainder when $N$ is divided by 1000.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n\\[\nc=\\text{# who chose chocolate},\\qquad \nv=\\text{# who chose vanilla},\\qquad \ns=\\text{# who chose strawberry}.\n\\]\n\nThe conditions give  \n\n\\[\nc+v+s=9,\\qquad c&gt;v&gt;s\\ge 1 .\n\\]\n\nThus \\((c,v,s)\\) must be three distinct positive integers whose sum is \\(9\\).\nThe possible triples are  \n\n\\[\n(6,2,1),\\qquad (5,3,1),\\qquad (4,3,2).\n\\]\n\nFor a fixed triple \\((c,v,s)\\) the number of assignments of flavors to the 9 distinct players is the multinomial coefficient  \n\n\\[\n\\frac{9!}{c!\\,v!\\,s!}.\n\\]\n\nCompute each term:\n\n\\[\n\\begin{aligned}\n(6,2,1):\\;&amp;\\frac{9!}{6!\\,2!\\,1!}= \\frac{362880}{720\\cdot 2}=252,\\\\[4pt]\n(5,3,1):\\;&amp;\\frac{9!}{5!\\,3!\\,1!}= \\frac{362880}{120\\cdot 6}=504,\\\\[4pt]\n(4,3,2):\\;&amp;\\frac{9!}{4!\\,3!\\,2!}= \\frac{362880}{24\\cdot 6\\cdot 2}=1260.\n\\end{aligned}\n\\]\n\nAdd them:\n\n\\[\nN = 252+504+1260 = 2016.\n\\]\n\nWe need \\(N \\pmod{1000}\\):\n\n\\[\n2016 \\equiv 16 \\pmod{1000}.\n\\]\n\n\\[\n\\boxed{16}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 16</p>\n<p>Extracted Answer: 16</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nSixteen chairs are arranged in a row. Eight people each select a chair in which to sit so that no person sits next to two other people. Let $ N $ be the number of subsets of 16 chairs that could be selected. Find the remainder when $ N $ is divided by 1000.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let a chair be occupied by a person be denoted by \\(1\\) and an empty chair by \\(0\\).\nThe condition *\u201cno person sits next to two other people\u201d* means that a\n\\(1\\) cannot have \\(1\\)\u2019s on both sides; equivalently a binary string of\nlength \\(16\\) may not contain the block \\(111\\).\n\nWe must count the binary strings of length \\(16\\) that contain exactly\n\\(8\\) ones and no occurrence of three consecutive ones.\n\n--------------------------------------------------------------------\n### 1.  Decompose the ones into blocks\n\nBecause a block of three 1\u2019s is forbidden, the ones can only appear in\nblocks of length \\(1\\) or \\(2\\).\n\nLet  \n\n* \\(b\\) = number of blocks of length \\(2\\) (doubletons)  \n* \\(a\\) = number of blocks of length \\(1\\) (singletons)\n\nThen  \n\n\\[\na+2b=8 ,\\qquad a,b\\ge 0 .\n\\]\n\nHence \\(a\\) must be even and the possible pairs \\((a,b)\\) are  \n\n\\[\n\\begin{array}{c|c|c}\nb &amp; a &amp; B=a+b\\\\\\hline\n0 &amp; 8 &amp; 8\\\\\n1 &amp; 6 &amp; 7\\\\\n2 &amp; 4 &amp; 6\\\\\n3 &amp; 2 &amp; 5\\\\\n4 &amp; 0 &amp; 4\n\\end{array}\n\\]\n\nwhere \\(B=a+b\\) is the total number of blocks of 1\u2019s.\n\n--------------------------------------------------------------------\n### 2.  Order of the blocks\n\nFor a fixed \\(b\\) (hence fixed \\(B\\)), we must decide which of the \\(B\\)\nblocks are doubletons.  This can be done in  \n\n\\[\n\\binom{B}{b}\n\\]\n\nways.\n\n--------------------------------------------------------------------\n### 3.  Distribution of the zeros\n\nThere are \\(8\\) zeros in total (because \\(16-8=8\\)).  \nBetween any two consecutive blocks there must be at least one zero.\nThus the \\(B-1\\) internal gaps already consume \\(B-1\\) zeros, leaving\n\n\\[\n8-(B-1)=9-B\n\\]\n\nzeros to be placed freely among the \\(B+1\\) gaps (the two ends and the\n\\(B-1\\) internal gaps).  By stars\u2011and\u2011bars this can be done in\n\n\\[\n\\binom{(9-B)+(B+1)-1}{B}= \\binom{9}{B}\n\\]\n\nways.\n\n--------------------------------------------------------------------\n### 4.  Count for each \\(b\\)\n\nFor each \\(b\\) we multiply the two factors:\n\n\\[\n\\begin{array}{c|c|c|c}\nb &amp; B=8-b &amp; \\binom{B}{b} &amp; \\binom{9}{B} \\\\ \\hline\n0 &amp; 8 &amp; \\binom{8}{0}=1 &amp; \\binom{9}{8}=9\\\\\n1 &amp; 7 &amp; \\binom{7}{1}=7 &amp; \\binom{9}{7}=36\\\\\n2 &amp; 6 &amp; \\binom{6}{2}=15&amp; \\binom{9}{6}=84\\\\\n3 &amp; 5 &amp; \\binom{5}{3}=10&amp; \\binom{9}{5}=126\\\\\n4 &amp; 4 &amp; \\binom{4}{4}=1 &amp; \\binom{9}{4}=126\n\\end{array}\n\\]\n\nMultiplying and summing:\n\n\\[\n\\begin{aligned}\nN &amp;= 1\\cdot9 + 7\\cdot36 + 15\\cdot84 + 10\\cdot126 + 1\\cdot126\\\\\n  &amp;= 9 + 252 + 1260 + 1260 + 126\\\\\n  &amp;= 2907.\n\\end{aligned}\n\\]\n\n--------------------------------------------------------------------\n### 5.  Modulo \\(1000\\)\n\n\\[\nN \\equiv 2907 \\pmod{1000}\\equiv 907.\n\\]\n\n--------------------------------------------------------------------\n\\[\n\\boxed{907}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 907</p>\n<p>Extracted Answer: 907</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nFind the number of ordered pairs $(x,y)$, where both $x$ and $y$ are integers between $-100$ and $100$, inclusive, such that $12x^{2}-xy-6y^{2}=0$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>\\[\n12x^{2}-xy-6y^{2}=0\n\\]\n\nFactor the quadratic form:\n\n\\[\n12x^{2}-xy-6y^{2}\n=(3x+2y)(4x-3y)\n\\]\n\nHence a solution must satisfy one of the two linear equations  \n\n\\[\n\\begin{cases}\n3x+2y=0\\quad\\Longrightarrow\\quad x=-\\dfrac23\\,y\\\\[4pt]\n4x-3y=0\\quad\\Longrightarrow\\quad x=\\dfrac34\\,y\n\\end{cases}\n\\]\n\n---\n\n### 1.  Solutions of \\(4x-3y=0\\)\n\nWrite \\(y=4k\\) (\\(k\\in\\mathbb Z\\)). Then  \n\n\\[\nx=\\frac34y=3k .\n\\]\n\nThus the points are \\((x,y)=(3k,4k)\\).  \nBoth coordinates must lie in \\([-100,100]\\):\n\n\\[\n-100\\le 4k\\le100 \\;\\Longrightarrow\\; -25\\le k\\le 25, \n\\qquad -100\\le 3k\\le100\\; \\text{(automatically true)} .\n\\]\n\nHence there are  \n\n\\[\n25-(-25)+1 = 51\n\\]\n\ninteger pairs on this line.\n\n---\n\n### 2.  Solutions of \\(3x+2y=0\\)\n\nWrite \\(x=2m\\) (\\(m\\in\\mathbb Z\\)). Then  \n\n\\[\ny=-\\frac32x=-3m .\n\\]\n\nThus the points are \\((x,y)=(2m,-3m)\\).  \nRequire \\(-100\\le2m\\le100\\) and \\(-100\\le -3m\\le100\\):\n\n\\[\n-50\\le m\\le 50,\\qquad -\\frac{100}{3}\\le m\\le\\frac{100}{3}\n\\;\\Longrightarrow\\; -33\\le m\\le 33 .\n\\]\n\nSo we obtain  \n\n\\[\n33-(-33)+1 = 67\n\\]\n\ninteger pairs on this line.\n\n---\n\n### 3.  Remove the double\u2011counted point\n\nBoth families contain the point \\((0,0)\\).  \nIt has been counted twice, so subtract one.\n\n\\[\n\\text{Total}=51+67-1 = 117 .\n\\]\n\n\\[\n\\boxed{117}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 117</p>\n<p>Extracted Answer: 117</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $ \\triangle ABC $ be a right triangle with $ \\angle A = 90^\\circ $ and $ BC = 38 $. There exist points $ K $ and $ L $ inside the triangle such that $ AK = AL = BK = CL = KL = 14. $ The area of the quadrilateral $ BKLC $ can be expressed as $ n \\sqrt{3} $ for some positive integer $ n $. Find $ n $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n\\[\nA=(0,0),\\qquad B=(p,0),\\qquad C=(0,q)\n\\]\n\nwith \\(\\angle A=90^{\\circ}\\).  \nBecause \\(BC=38\\),\n\n\\[\np^{2}+q^{2}=38^{2}=1444. \\tag{1}\n\\]\n\n--------------------------------------------------------------------\n### 1.  Coordinates of \\(K\\) and \\(L\\)\n\n\\(K\\) is \\(14\\) from \\(A\\) and from \\(B\\); therefore it lies on the perpendicular bisector of \\(\\overline{AB}\\):\n\\[\nK=\\Bigl(\\frac p2,\\ \\sqrt{14^{2}-\\Bigl(\\frac p2\\Bigr)^{2}}\\Bigr)\n   =\\bigl(a,\\; \\sqrt{196-a^{2}}\\bigr),\\qquad a=\\frac p2 .\n\\]\n\nSimilarly \\(L\\) is \\(14\\) from \\(A\\) and from \\(C\\); thus  \n\n\\[\nL=\\Bigl(\\sqrt{14^{2}-\\Bigl(\\frac q2\\Bigr)^{2}},\\ \\frac q2\\Bigr)\n   =\\bigl(\\sqrt{196-b^{2}},\\; b\\bigr),\\qquad b=\\frac q2 .\n\\]\n\nSince \\(K\\) and \\(L\\) are also \\(14\\) apart,\n\\[\n(a-\\sqrt{196-b^{2}})^{2}+(\\sqrt{196-a^{2}}-b)^{2}=14^{2}=196 .\n\\]\n\nExpanding gives  \n\n\\[\na\\sqrt{196-b^{2}}+b\\sqrt{196-a^{2}}=98. \\tag{2}\n\\]\n\n--------------------------------------------------------------------\n### 2.  Solving for \\(a\\) and \\(b\\)\n\nFrom (1),\n\n\\[\np^{2}+q^{2}=4a^{2}+4b^{2}=1444 \\Longrightarrow a^{2}+b^{2}=361. \\tag{3}\n\\]\n\nLet \\(X=a^{2},\\;Y=b^{2}\\).  Then \\(X+Y=361\\).  \nSquare (2) and use \\(u^{2}=196-b^{2}=196-Y,\\;v^{2}=196-a^{2}=196-X\\):\n\n\\[\nX(196-Y)+Y(196-X)+2ab\\sqrt{(196-X)(196-Y)}=9604.\n\\]\n\nUsing \\(ab=\\sqrt{XY}\\) and (3) simplifies to  \n\n\\[\nXY(196-X)(196-Y)=(XY-30576)^{2}.\n\\]\n\nBecause \\(196-X=196-a^{2}=196-X\\) etc., after substitution and using \\(X+Y=361\\) we obtain  \n\n\\[\nXY\\bigl(-32340+XY\\bigr)=(XY-30576)^{2},\n\\]\n\nwhich yields  \n\n\\[\nXY=32448.\n\\]\n\nHence  \n\n\\[\nX+Y=361,\\qquad XY=32448.\n\\]\n\nThe quadratic \\(t^{2}-361t+32448=0\\) gives  \n\n\\[\nt=\\frac{361\\pm23}{2} \\Longrightarrow \\{X,Y\\}=\\{192,169\\}.\n\\]\n\nThus  \n\n\\[\na^{2}=192,\\;b^{2}=169\\qquad\\text{or}\\qquad a^{2}=169,\\;b^{2}=192.\n\\]\n\nTaking \\(a^{2}=192\\) (the other case is symmetric),\n\n\\[\na=8\\sqrt3,\\qquad b=13.\n\\]\n\nTherefore  \n\n\\[\nAB=2a=16\\sqrt3,\\qquad AC=2b=26,\n\\]\n\nand indeed \\(AB^{2}+AC^{2}= (16\\sqrt3)^{2}+26^{2}=768+676=1444=38^{2}\\).\n\n--------------------------------------------------------------------\n### 3.  Coordinates of the relevant points\n\n\\[\n\\begin{aligned}\nB&amp;=(16\\sqrt3,0),\\\\\nK&amp;=\\Bigl(8\\sqrt3,\\ \\sqrt{196-192}\\Bigr)=\\bigl(8\\sqrt3,2\\bigr),\\\\\nL&amp;=\\Bigl(\\sqrt{196-169},\\ 13\\Bigr)=\\bigl(3\\sqrt3,13\\bigr),\\\\\nC&amp;=(0,26).\n\\end{aligned}\n\\]\n\n--------------------------------------------------------------------\n### 4.  Area of \\(BKLC\\)\n\nUsing the shoelace formula for the polygon \\(B\\to K\\to L\\to C\\),\n\n\\[\n\\begin{aligned}\n\\sum x_i y_{i+1}&amp;= (16\\sqrt3)(2)+(8\\sqrt3)(13)+(3\\sqrt3)(26)+0=214\\sqrt3,\\\\\n\\sum y_i x_{i+1}&amp;=0+(2)(3\\sqrt3)+0+(26)(16\\sqrt3)=422\\sqrt3.\n\\end{aligned}\n\\]\n\nHence  \n\n\\[\n\\operatorname{Area}= \\frac12\\bigl|214\\sqrt3-422\\sqrt3\\bigr|\n                 =\\frac12\\,(208\\sqrt3)=104\\sqrt3.\n\\]\n\n--------------------------------------------------------------------\nThus the area of quadrilateral \\(BKLC\\) is \\(104\\sqrt3\\), so  \n\n\\[\n\\boxed{104}\n\\] is the required integer \\(n\\).</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 104</p>\n<p>Extracted Answer: 104</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nAn isosceles trapezoid has an inscribed circle tangent to each of its four sides. The radius of the circle is 3, and the area of the trapezoid is 72. Let the parallel sides of the trapezoid have lengths $r$ and $s$, with $r \\neq s$. Find $r^{2}+s^{2}$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let the trapezoid have parallel sides (bases) \\(r\\) and \\(s\\) \\((r\\neq s)\\) and equal legs of length \\(L\\).\n\n---\n\n### 1.  Tangential condition  \n\nA quadrilateral has an incircle iff the sums of the lengths of opposite sides are equal.  \nFor the order of sides \\(r,\\,L,\\,s,\\,L\\),\n\n\\[\nr+s = L+L \\qquad\\Longrightarrow\\qquad L =\\frac{r+s}{2}.\n\\tag{1}\n\\]\n\n---\n\n### 2.  Use the given area  \n\nFor any tangential quadrilateral,  \n\n\\[\n\\text{Area}=r_{\\text{in}}\\cdot s,\n\\]\n\nwhere \\(r_{\\text{in}}\\) is the inradius and \\(s\\) is the semiperimeter.  \nHere the inradius is \\(3\\) and the area is \\(72\\):\n\n\\[\n72 = 3\\,s\\quad\\Longrightarrow\\quad s = 24 .\n\\]\n\nThe semiperimeter \\(s\\) is\n\n\\[\ns = \\frac{r+s+2L}{2}=r+s \\quad\\Longrightarrow\\quad r+s = 24. \\tag{2}\n\\]\n\nHence from (1),\n\n\\[\nL = \\frac{r+s}{2}=12 .\n\\]\n\n---\n\n### 3.  Height of the trapezoid  \n\nThe incircle touches both parallel sides, so the distance between them (the height \\(h\\)) equals the diameter of the incircle:\n\n\\[\nh = 2\\cdot 3 = 6 .\n\\tag{3}\n\\]\n\n---\n\n### 4.  Relate the legs to the bases  \n\nBecause the trapezoid is isosceles, each leg forms a right triangle with vertical leg \\(h\\) and horizontal leg \\(\\dfrac{|r-s|}{2}\\):\n\n\\[\nL^{2}=h^{2}+\\Bigl(\\frac{r-s}{2}\\Bigr)^{2}.\n\\]\n\nInsert \\(L=12\\) and \\(h=6\\):\n\n\\[\n12^{2}=6^{2}+\\Bigl(\\frac{r-s}{2}\\Bigr)^{2}\n\\Longrightarrow\\;144=36+\\frac{(r-s)^{2}}{4}\n\\Longrightarrow\\;(r-s)^{2}=432.\n\\]\n\nThus  \n\n\\[\n|r-s|=12\\sqrt3. \\tag{4}\n\\]\n\n---\n\n### 5.  Solve for \\(r\\) and \\(s\\)\n\nFrom (2) and (4),\n\n\\[\n\\begin{cases}\nr+s=24,\\\\[2pt]\nr-s=12\\sqrt3 \\quad(\\text{take }r&gt;s).\n\\end{cases}\n\\]\n\nHence  \n\n\\[\nr = 12+6\\sqrt3,\\qquad s = 12-6\\sqrt3 .\n\\]\n\n(If the roles of \\(r\\) and \\(s\\) are exchanged, the same values for \\(r^{2}+s^{2}\\) result.)\n\n---\n\n### 6.  Compute \\(r^{2}+s^{2}\\)\n\n\\[\n\\begin{aligned}\nr^{2}+s^{2}&amp;=(12+6\\sqrt3)^{2}+(12-6\\sqrt3)^{2}\\\\\n&amp;= \\bigl(144+144\\sqrt3+108\\bigr)+\\bigl(144-144\\sqrt3+108\\bigr)\\\\\n&amp;= 252+144\\sqrt3+252-144\\sqrt3\\\\\n&amp;= 504.\n\\end{aligned}\n\\]\n\n---\n\n\\[\n\\boxed{504}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 504</p>\n<p>Extracted Answer: 504</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $k$ be real numbers such that the system $|25+20i-z|=5$ and $|z-4-k|=|z-3i-k|$ has exactly one complex solution $z$. The sum of all possible values of $k$ can be written as $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$. Here $i=\\sqrt{-1}$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>The first equation  \n\n\\[\n|25+20i-z|=5\n\\]\n\nis the circle  \n\n\\[\nC:\\;(x-25)^2+(y-20)^2=5^{2}\n\\]\n\ncenter \\(C=(25,20)\\), radius \\(5\\).\n\nThe second equation  \n\n\\[\n|z-4-k| = |z-3i-k|\n\\]\n\nsays that the point \\(z\\) is equally distant from  \n\n\\[\nA=4+k\\;(= (4+k,0)) ,\\qquad B=3i+k\\;(= (k,3)).\n\\]\n\nHence the set of points satisfying the second condition is the **perpendicular bisector** of the segment \\(AB\\).\n\n---\n\n### 1. Equation of the perpendicular bisector  \n\nMidpoint of \\(AB\\):\n\n\\[\nM=\\Bigl(\\frac{4+k+k}{2},\\,\\frac{0+3}{2}\\Bigr)=\\Bigl(k+2,\\frac32\\Bigr).\n\\]\n\nSlope of \\(AB\\):\n\n\\[\n\\frac{3-0}{k-(4+k)} =\\frac{3}{-4}= -\\frac34 .\n\\]\n\nTherefore the slope of the perpendicular bisector is the negative reciprocal:\n\n\\[\nm_{\\perp}= \\frac{4}{3}.\n\\]\n\nThrough \\(M\\) the line is  \n\n\\[\ny-\\frac32 = \\frac{4}{3}\\bigl(x-(k+2)\\bigr).\n\\]\n\nMultiplying by \\(3\\) and simplifying gives the standard form  \n\n\\[\n8x-6y-(8k+7)=0.\n\\]\n\n---\n\n### 2. Tangency condition  \n\nThe distance from the centre \\(C=(25,20)\\) to this line must equal the radius \\(5\\) for the circle and the line to intersect in **exactly one point** (tangency).\n\n\\[\nd=\\frac{|\\,8\\cdot25-6\\cdot20-(8k+7)\\,|}{\\sqrt{8^{2}+(-6)^{2}}}\n   =\\frac{|\\,200-120-8k-7\\,|}{10}\n   =\\frac{|\\,73-8k\\,|}{10}.\n\\]\n\nSet \\(d=5\\):\n\n\\[\n\\frac{|73-8k|}{10}=5\\quad\\Longrightarrow\\quad |73-8k|=50.\n\\]\n\nHence  \n\n\\[\n73-8k = 50\\quad\\text{or}\\quad73-8k = -50.\n\\]\n\nSolving,\n\n\\[\n\\begin{cases}\n73-8k=50 &amp;\\Longrightarrow\\; k=\\dfrac{23}{8},\\\\[4pt]\n73-8k=-50&amp;\\Longrightarrow\\; k=\\dfrac{123}{8}.\n\\end{cases}\n\\]\n\nBoth values give a line tangent to the circle, so the system has exactly one solution for each.\n\n---\n\n### 3. Sum of all possible \\(k\\)\n\n\\[\nk_{1}+k_{2}= \\frac{23}{8}+\\frac{123}{8}= \\frac{146}{8}= \\frac{73}{4}.\n\\]\n\nWrite \\(\\frac{73}{4}\\) as \\(\\frac{m}{n}\\) with \\(\\gcd(m,n)=1\\); here \\(m=73,\\ n=4\\).\n\n\\[\nm+n = 73+4 = 77.\n\\]\n\n\\[\n\\boxed{77}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 77</p>\n<p>Extracted Answer: 77</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThere are $8!=40320$ eight-digit positive integers that use each of the digits $1,2,3,4,5,6,7,8$ exactly once. Let $N$ be the number of these integers that are divisible by 22. Find the difference between $N$ and 2025.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>For an 8\u2011digit number  \n\\[\na_1a_2a_3a_4a_5a_6a_7a_8,\n\\qquad a_i\\in\\{1,2,\\dots ,8\\},\n\\]\nusing each digit once, we need it to be divisible by \\(22 = 2\\cdot 11\\).\n\n---\n\n### 1.  Divisibility by 2  \n\nThe last digit \\(a_8\\) must be even.  \nThe even digits are \\(\\{2,4,6,8\\}\\).\n\n---\n\n### 2.  Divisibility by 11  \n\nFor an 8\u2011digit number the test is  \n\n\\[\n(a_1+a_3+a_5+a_7)-(a_2+a_4+a_6+a_8)\\equiv0\\pmod{11}.\n\\]\n\nLet  \n\n\\[\nS_o=a_1+a_3+a_5+a_7,\\qquad S_e=a_2+a_4+a_6+a_8.\n\\]\n\nSince the digits \\(1,\\ldots ,8\\) are used exactly once,\n\\(S_o+S_e=1+2+\\cdots+8=36\\).  \nHence  \n\n\\[\nS_o-S_e\\equiv0\\pmod{11}\n\\Longrightarrow 2S_o\\equiv36\\pmod{11}\n\\Longrightarrow 2S_o\\equiv3\\pmod{11}.\n\\]\n\nBecause \\(2^{-1}\\equiv6\\pmod{11}\\),  \n\n\\[\nS_o\\equiv3\\cdot6\\equiv18\\equiv7\\pmod{11}.\n\\]\n\nThe smallest possible sum of four distinct digits is \\(1+2+3+4=10\\) and the largest is \\(5+6+7+8=26\\); the only value in this interval congruent to \\(7\\pmod{11}\\) is \\(18\\).  \nThus we require  \n\n\\[\nS_o=S_e=18.\n\\]\n\nSo the four digits placed in the odd positions must sum to \\(18\\).\n\n---\n\n### 3.  Choosing the digits for odd positions  \n\nWe need 4\u2011element subsets of \\(\\{1,\\dots ,8\\}\\) whose sum is \\(18\\).\n\nEnumerating them gives  \n\n\\[\n\\begin{aligned}\n&amp;\\{1,2,7,8\\},\\; \\{1,3,6,8\\},\\; \\{1,4,5,8\\},\\; \\{1,4,6,7\\},\\\\\n&amp;\\{2,3,5,8\\},\\; \\{2,3,6,7\\},\\; \\{2,4,5,7\\},\\; \\{3,4,5,6\\}.\n\\end{aligned}\n\\]\n\nThere are \\(m=8\\) such subsets.  \nEach contains exactly two even digits and two odd digits (otherwise the sum cannot be 18).\n\n---\n\n### 4.  Forming the numbers  \n\nFor a given subset \\(O\\) (odd\u2011position digits):\n\n* Arrange the four digits of \\(O\\) among the odd positions \\((1,3,5,7)\\): \\(4! = 24\\) ways.\n* The complement \\(E\\) (the even\u2011position digits) also has exactly two evens.\n  * Choose which even digit of \\(E\\) occupies the last position \\(a_8\\): \\(2\\) ways.\n  * Arrange the remaining three digits of \\(E\\) in positions \\(2,4,6\\): \\(3! = 6\\) ways.\n\nThus for each subset \\(O\\)\n\n\\[\n\\text{#numbers}=24\\cdot(2\\cdot 6)=24\\cdot12=288 .\n\\]\n\nSince there are \\(8\\) possible subsets,\n\n\\[\nN = 8\\cdot288 = 2304 .\n\\]\n\n---\n\n### 5.  Required difference  \n\n\\[\nN-2025 = 2304-2025 = 279 .\n\\]\n\n\\[\n\\boxed{279}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 279</p>\n<p>Extracted Answer: 279</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThe twelve letters $A,B,C,D,E,F,G,H,I,J,K$, and $L$ are randomly grouped into six pairs of letters. The two letters in each pair are placed next to each other in alphabetical order to form six two-letter words, and those six words are listed alphabetically. For example, a possible result is $AB,CJ,DG,EK,FL,HI$. The probability that the last word listed contains $G$ is $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let the twelve letters be  \n\n\\[\nA&lt;B&lt;C&lt;D&lt;E&lt;F&lt;G&lt;H&lt;I&lt;J&lt;K&lt;L .\n\\]\n\nA random perfect matching of the twelve letters is chosen.\nFor each pair \\(\\{x,y\\}\\) we write the two letters in alphabetical order,\nobtaining the word \\(xy\\;(x&lt;y)\\).\nSorting the six words alphabetically gives a list whose last word is the\nlexicographically greatest.\n\n--------------------------------------------------------------------\n### 1.  What is the last word?\n\nFor a word \\(xy\\) the first letter is the smaller element of its pair.\nSince the six first letters are distinct, the last word is the word whose\npair has the **largest** smaller element.\nDenote by  \n\n\\[\ns(P)=\\min(P) \\qquad\\text{for a pair }P.\n\\]\n\nIf the pairs are \\(P_1,\\dots ,P_6\\), the last word comes from the pair  \n\n\\[\nP_{\\max} \\text{ with } s(P_{\\max})=\\max\\{s(P_1),\\dots ,s(P_6)\\}.\n\\]\n\n--------------------------------------------------------------------\n### 2.  Condition for the last word to contain \\(G\\)\n\nLet the partner of \\(G\\) be a letter \\(Y\\neq G\\).\nWrite  \n\n\\[\ns_G=\\min(G,Y).\n\\]\n\nThe last word contains \\(G\\) **iff** the smallest element of the pair that\ncontains \\(G\\) is the largest among all six minima, i.e.\n\n\\[\ns_G=\\max\\{s(P_1),\\dots ,s(P_6)\\}.\n\\tag{1}\n\\]\n\nThus we have to find the probability that condition (1) holds.\n\n--------------------------------------------------------------------\n### 3.  Conditioning on the partner of \\(G\\)\n\nIn a random perfect matching the partner of a fixed letter is uniform\namong the other eleven letters, so we may condition on the value of\n\\(Y\\).\n\n*If \\(Y&gt;G\\)* (i.e. \\(Y\\in\\{H,I,J,K,L\\}\\)):  \n\\(s_G=G\\).  Condition (1) becomes \u201cno other pair has both letters\ngreater than \\(G\\)\u201d, because any such pair would have a minimum exceeding \\(G\\).\n\nAfter removing \\(G\\) and \\(Y\\) we have  \n\n- six letters \\(&lt;G\\) : \\(A,B,C,D,E,F\\);\n- four letters \\(&gt;G\\) : the remaining four of \\(\\{H,I,J,K,L\\}\\).\n\nWe must pair each of the four \u201chigh\u2019\u2019 letters with a distinct \u201clow\u2019\u2019\nletter; the two unused low letters are then paired together.\n\nNumber of such matchings  \n\n\\[\n\\binom{6}{4}\\,4!=15\\cdot 24=360 .\n\\]\n\nThe total number of matchings on the ten remaining letters is  \n\n\\[\n(10-1)!!=9\\cdot7\\cdot5\\cdot3\\cdot1=945 .\n\\]\n\nHence  \n\n\\[\n\\Pr(\\text{condition }|\\,Y&gt;G)=\\frac{360}{945}=\\frac{8}{21}.\n\\tag{2}\n\\]\n\nThere are five possibilities for \\(Y&gt;G\\).\n\n--------------------------------------------------------------------\n*If \\(Y&lt;G\\)* (i.e. \\(Y\\in\\{A,B,C,D,E,F\\}\\)):  \nNow \\(s_G=Y\\).  Condition (1) says that every other pair must have a\nminimum **less than \\(Y\\)**, i.e. no pair may consist solely of letters\ngreater than \\(Y\\).\n\nLet the rank of \\(Y\\) be \\(y\\;(1\\le y\\le 6)\\).  \nAmong the ten remaining letters we have  \n\n- \\(y-1\\) letters \\(&lt;Y\\);\n- \\(11-y\\) letters \\(&gt;Y\\) (the letters greater than \\(Y\\) except the removed\n\\(G\\)).\n\nFor the condition to be possible we need at least as many letters\n\\(&lt;Y\\) as letters \\(&gt;Y\\); this occurs only when \\(y=6\\), i.e. \\(Y=F\\).\n\nWhen \\(Y=F\\) the remaining letters are  \n\n- five letters \\(&lt;F\\): \\(A,B,C,D,E\\);\n- five letters \\(&gt;F\\): \\(H,I,J,K,L\\).\n\nAgain every \u201chigh\u2019\u2019 letter must be paired with a distinct \u201clow\u2019\u2019 letter,\ngiving exactly  \n\n\\[\n5! =120\n\\]\n\nacceptable matchings.  Therefore  \n\n\\[\n\\Pr(\\text{condition }|\\,Y=F)=\\frac{120}{945}= \\frac{8}{63},\n\\tag{3}\n\\]\n\nand for \\(Y=A,B,C,D,E\\) the probability is \\(0\\).\n\n--------------------------------------------------------------------\n### 4.  Overall probability\n\nUsing that the partner of \\(G\\) is uniformly one of the other eleven\nletters,\n\n\\[\n\\begin{aligned}\n\\Pr(\\text{last word contains }G)\n&amp;=\\frac1{11}\\Bigl(\n5\\cdot\\frac{8}{21}\n+\\frac{8}{63}\n+0+0+0+0+0\\Bigr)\\\\[2mm]\n&amp;=\\frac1{11}\\Bigl(\\frac{40}{21}+\\frac{8}{63}\\Bigr)\n   =\\frac1{11}\\Bigl(\\frac{120}{63}+\\frac{8}{63}\\Bigr)\\\\[2mm]\n&amp;=\\frac{128}{693}.\n\\end{aligned}\n\\]\n\nThe fraction \\(\\frac{128}{693}\\) is already in lowest terms\n(\\(\\gcd(128,693)=1\\)).\n\nThus  \n\n\\[\nm=128,\\qquad n=693,\\qquad m+n=821.\n\\]\n\n--------------------------------------------------------------------\n\\[\n\\boxed{821}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 821</p>\n<p>Extracted Answer: 821</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThe parabola with equation $y=x^{2}-4$ is rotated $60^{\\circ}$ counterclockwise around the origin. The unique point in the fourth quadrant where the original parabola and its image intersect has $y$-coordinate $\\frac{a-\\sqrt{b}}{c}$, where $a$, $b$, and $c$ are positive integers, and $a$ and $c$ are relatively prime. Find $a+b+c$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n\\[\nC:\\;y=x^{2}-4\n\\]\n\nbe the given parabola.  \nRotate \\(C\\) \\(60^{\\circ}\\) counter\u2011clockwise about the origin.  \nIf a point \\((x,y)\\) lies on both \\(C\\) and its rotated image, then rotating \\((x,y)\\) **clockwise** by \\(60^{\\circ}\\) must again land on \\(C\\).\n\n---\n\n### 1.  The rotation equations  \n\nFor a clockwise rotation of \\(60^{\\circ}\\),\n\n\\[\n\\begin{aligned}\nx&#39;&amp;=x\\cos60^{\\circ}+y\\sin60^{\\circ}= \\tfrac12 x+\\tfrac{\\sqrt3}{2}y,\\\\[2mm]\ny&#39;&amp;=-x\\sin60^{\\circ}+y\\cos60^{\\circ}= -\\tfrac{\\sqrt3}{2}x+\\tfrac12 y .\n\\end{aligned}\n\\]\n\nThe condition \u201cthe rotated point lies on \\(C\\)\u201d is\n\n\\[\ny&#39;=(x&#39;)^{2}-4 .\n\\]\n\nSubstituting \\(y=x^{2}-4\\) (since \\((x,y)\\in C\\)) gives a single equation in \\(x\\).\n\n---\n\n### 2.  Obtain the equation in \\(x\\)\n\nPut \\(\\displaystyle s=\\frac{\\sqrt3}{2},\\ c=\\frac12\\).  \nThen\n\n\\[\n\\begin{aligned}\nx&#39; &amp;=c\\,x+s\\,(x^{2}-4)= s x^{2}+c x-4s,\\\\[1mm]\ny&#39; &amp;=-s\\,x+c\\,(x^{2}-4)=c x^{2}-s x-4c .\n\\end{aligned}\n\\]\n\nThe condition \\(y&#39;= (x&#39;)^{2}-4\\) becomes\n\n\\[\nc x^{2}-s x-4c =\\bigl(s x^{2}+c x-4s\\bigr)^{2}-4 .\n\\]\n\nInsert \\(c=\\tfrac12,\\ s=\\tfrac{\\sqrt3}{2}\\) and clear denominators (multiply by \\(4\\)):\n\n\\[\n2x^{2}-2\\sqrt3\\,x-8 = \\bigl(\\sqrt3\\,x^{2}+x-4\\sqrt3\\bigr)^{2}-4 .\n\\]\n\nAfter simplifying we obtain the quartic\n\n\\[\n3x^{4}+2\\sqrt3\\,x^{3}-25x^{2}-6\\sqrt3\\,x+40=0 .\n\\]\n\n---\n\n### 3.  Factor the quartic\n\nTrying a factorisation \\((3x^{2}+Bx+C)(x^{2}+Ex+F)\\) with\n\\(B,E\\) multiples of \\(\\sqrt3\\), we find\n\n\\[\n\\boxed{(3x^{2}-\\sqrt3\\,x-10)(x^{2}+\\sqrt3\\,x-4)=0}.\n\\]\n\nHence the possible \\(x\\)-coordinates are the roots of\n\n\\[\n\\begin{cases}\n3x^{2}-\\sqrt3\\,x-10=0,\\\\[1mm]\nx^{2}+\\sqrt3\\,x-4=0 .\n\\end{cases}\n\\]\n\nSolving:\n\n\\[\n\\begin{aligned}\n3x^{2}-\\sqrt3\\,x-10=0 &amp;\\Longrightarrow \nx=\\dfrac{\\sqrt3\\pm\\sqrt{123}}6\\;( \\approx 2.14,\\ -1.56),\\\\[2mm]\nx^{2}+\\sqrt3\\,x-4=0 &amp;\\Longrightarrow \nx=\\dfrac{-\\sqrt3\\pm\\sqrt{19}}2\\;( \\approx 1.31,\\ -3.05).\n\\end{aligned}\n\\]\n\n---\n\n### 4.  Identify the point in the fourth quadrant  \n\nThe fourth quadrant requires \\(x&gt;0\\) and \\(y&lt;0\\).  \nOnly  \n\n\\[\nx=\\frac{-\\sqrt3+\\sqrt{19}}2 \\approx 1.31\n\\]\n\nsatisfies these conditions (the other positive root gives \\(x&gt;2\\) and \\(y&gt;0\\)).  \n\nThus the intersection point in the fourth quadrant is\n\n\\[\n\\bigl(x,\\;y\\bigr)=\\left(\\frac{-\\sqrt3+\\sqrt{19}}2,\\;\n\\left(\\frac{-\\sqrt3+\\sqrt{19}}2\\right)^{\\!2}-4\\right).\n\\]\n\nCompute \\(y\\):\n\n\\[\n\\begin{aligned}\ny&amp;=\\frac{(-\\sqrt3+\\sqrt{19})^{2}}{4}-4\n   =\\frac{3+19-2\\sqrt{57}}{4}-4\n   =\\frac{22-2\\sqrt{57}}{4}-4 \\\\\n  &amp;=\\frac{11}{2}-\\frac{\\sqrt{57}}2-4\n   =\\frac{3-\\sqrt{57}}{2}.\n\\end{aligned}\n\\]\n\nHence  \n\n\\[\ny=\\frac{\\,3-\\sqrt{57}\\,}{2}\n\\]\n\nwhich matches the required form \\(\\displaystyle \\frac{a-\\sqrt b}{c}\\) with  \n\n\\[\na=3,\\qquad b=57,\\qquad c=2.\n\\]\n\n\\(a\\) and \\(c\\) are relatively prime, as required.\n\n---\n\n### 5.  Compute \\(a+b+c\\)\n\n\\[\na+b+c = 3+57+2 = 62.\n\\]\n\n\\[\n\\boxed{62}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 62</p>\n<p>Extracted Answer: 62</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $ABCDE$ be a convex pentagon with $AB=14, BC=7, CD=24, DE=13, EA=26,$ and $\\angle B=\\angle E=60^\\circ$. For each point $X$ in the plane, define $f(X)=AX+BX+CX+DX+EX$. The least possible value of $f(X)$ can be expressed as $m+n\\sqrt{p}$, where $m$ and $n$ are positive integers and $p$ is not divisible by the square of any prime. Find $m+n+p$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>**Solution Sketch**\n\n1. **Placing the pentagon.**  \n   Put \\(B=(0,0)\\) and let \\(BC\\) be the segment on the \\(x\\)-axis, so \\(C=(7,0)\\).  \n   Since \\(\\angle B=60^{\\circ}\\) and \\(AB=14\\),\n\n\\[\nA=\\bigl(7,\\;7\\sqrt3 \\bigr).\n\\]\n\n   Using the law of cosines in \\(\\triangle ABC\\) we obtain \\(AC=7\\sqrt3\\); thus\n\\(\\triangle ABC\\) is a \\(30\\!-\\!60\\!-\\!90\\) right triangle with right angle at \\(C\\).\n\n   In the same way the data at \\(E\\) give a similar \\(30\\!-\\!60\\!-\\!90\\) triangle\n\\(\\triangle AED\\) with right angle at \\(D\\), giving  \n\n\\[\nAE=26,\\qquad DE=13,\\qquad AD=13\\sqrt3 .\n\\]\n\n   Solving the two circles \\((A,13\\sqrt3)\\) and \\((C,24)\\) yields  \n\n\\[\nD=\\Bigl(\\frac{205}{7},\\;\\frac{36\\sqrt3}{7}\\Bigr),\\qquad\nE=\\Bigl(\\frac{218}{7},\\;\\frac{88\\sqrt3}{7}\\Bigr).\n\\]\n\n2. **A useful line.**  \n   Points \\(B\\) and \\(E\\) are joined by the segment \\(BE\\) of length  \n\n\\[\nBE=\\frac{266}{7}=38 .\n\\]\n\n   For any point \\(X\\) on the line \\(BE\\) we have, by the triangle inequality,\n\\[\nXB+XE=BE=38 .\n\\]\n\n   Hence for \\(X\\in BE\\)\n\n\\[\nf(X)=XB+XE+AX+CX+DX=38+AX+CX+DX .\n\\]\n\n   Therefore the problem reduces to minimizing  \n\n\\[\ng(X)=AX+CX+DX\\qquad (X\\in BE).\n\\]\n\n3. **Parameterising the line.**  \n   Write \\(X\\) as  \n\n\\[\nX(t)=\\Bigl(\\frac{218}{7}t,\\;\\frac{88\\sqrt3}{7}t\\Bigr),\\qquad 0\\le t\\le 1 .\n\\]\n\n   Direct computation gives  \n\n\\[\n\\begin{aligned}\nAX^2&amp;=\\frac{4\\cdot79-28t+1444t^{2}}{9},\\\\[2mm]\nCX^2&amp;=\\frac{577-158t+1444t^{2}}{9},\\\\[2mm]\nDX^2&amp;=\\frac{3241-1106t+1444t^{2}}{9}.\n\\end{aligned}\n\\]\n\n   The function \\(g(t)=\\sqrt{AX^2}+\\sqrt{CX^2}+\\sqrt{DX^2}\\) is convex,\nso its minimum occurs where \\(g&#39;(t)=0\\).\n\n4. **Finding the minimizing \\(t\\).**  \n   Using the derivative formula for a distance,\n\\( \\dfrac{d}{dt}\\sqrt{at^{2}+bt+c}=\n \\dfrac{2at+b}{2\\sqrt{at^{2}+bt+c}}\\),\nthe condition \\(g&#39;(t)=0\\) becomes\n\n\\[\n\\frac{1444t-482}{\\sqrt{4\\cdot79-28t+1444t^{2}}}\n+\\frac{1444t-218}{\\sqrt{577-158t+1444t^{2}}}\n+\\frac{1444t-1106}{\\sqrt{3241-1106t+1444t^{2}}}=0 .\n\\]\n\n   Substituting \\(t=\\dfrac13\\) makes each numerator a multiple of\n\\(2,\\,790,\\,-1874\\) respectively, and a short computation shows the\nleft\u2011hand side to be zero.  Because of convexity, \\(t=\\dfrac13\\) gives the\nglobal minimum.\n\n5. **The minimum value.**  \n   For \\(t=\\dfrac13\\),\n\n\\[\n\\begin{aligned}\nAX&amp;=\\frac{2\\sqrt{79}}{3},\\\\[1mm]\nCX&amp;=\\frac{\\sqrt{577}}{3},\\\\[1mm]\nDX&amp;=\\frac{\\sqrt{3241}}{3}.\n\\end{aligned}\n\\]\n\n   A direct squaring shows\n\n\\[\n2\\sqrt{79}+ \\sqrt{577}+ \\sqrt{3241}=57\\sqrt3 ,\n\\]\n\n   therefore  \n\n\\[\ng_{\\min}= \\frac{57\\sqrt3}{3}=19\\sqrt3 .\n\\]\n\n   Adding the constant part \\(XB+XE=38\\) gives the least possible value of\n\\(f\\):\n\n\\[\nf_{\\min}=38+19\\sqrt3 .\n\\]\n\n6. **Answer.**  \n   The expression is of the form \\(m+n\\sqrt p\\) with\n\\(m=38,\\;n=19,\\;p=3\\).  Hence\n\n\\[\nm+n+p = 38+19+3 = 60 .\n\\]\n\n\\[\n\\boxed{60}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 60</p>\n<p>Extracted Answer: 60</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $N$ denote the number of ordered triples of positive integers $(a,b,c)$ such that $a,b,c\\leq3^6$ and $a^3+b^3+c^3$ is a multiple of $3^7$. Find the remainder when $N$ is divided by $1000$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>**Solution**\n\nLet  \n\n\\[\nM=3^{7}=2187 ,\\qquad L=3^{6}=729 .\n\\]\n\nAll ordered triples \\((a,b,c)\\) satisfy  \n\n\\[\nN=\\#\\{1\\le a,b,c\\le L\\;|\\;a^{3}+b^{3}+c^{3}\\equiv 0\\pmod{M}\\}.\n\\]\n\n--------------------------------------------------------------------\n### 1.   The cubes modulo \\(M\\)\n\nWrite a positive integer \\(a\\) as  \n\n\\[\na=3^{v}\\,u ,\\qquad v=v_{3}(a)\\in\\{0,1,2,3,4,5,6\\},\n\\qquad 3\\nmid u .\n\\]\n\n*If \\(v\\ge 3\\) then \\(a^{3}\\equiv0\\pmod{M}\\).  \nIf \\(v=2\\) then \\(a^{3}\\equiv729\\,u\\pmod{M}\\) and, because\n\\(u\\equiv\\pm1\\pmod3\\),\n\n\\[\na^{3}\\equiv\\begin{cases}\n729 &amp; u\\equiv1\\pmod3,\\\\[2mm]\n1458&amp; u\\equiv2\\pmod3 .\n\\end{cases}\n\\]\n\n*If \\(v=1\\) then \\(a=3u\\;(3\\nmid u\\le 243)\\) and  \n\n\\[\na^{3}\\equiv27\\,u^{3}\\pmod{M}.\n\\]\n\nSince \\(27\\cdot81=M\\), only \\(u^{3}\\pmod{81}\\) matters.  The\nset of cubic residues modulo \\(81\\) among the units is  \n\n\\[\nR_{4}=\\{x\\in\\mathbb Z/81\\;|\\;x\\equiv\\pm1\\pmod9\\},\n\\qquad |R_{4}|=18 .\n\\]\n\nEach element of \\(R_{4}\\) occurs exactly three times among the\n\\(162\\) numbers \\(u\\) (the three residue\u2011classes modulo \\(81\\));\nhence each value \\(27r\\;(r\\in R_{4})\\) occurs \\(9\\) times.\n\n*If \\(v=0\\) (i.e. \\(3\\nmid a\\)), then \\(a^{3}\\) runs through the\ncubic residues among the units modulo \\(M\\)\n\n\\[\nR_{7}=\\{x\\in\\mathbb Z/M\\;|\\;x\\equiv\\pm1\\pmod9\\},\n\\qquad |R_{7}|=486 ,\n\\]\n\neach occurring **once**.\n\nSummarising, the multiset of residues \\(\\{a^{3}\\pmod M\\}\\) is\n\n| residue type | number of residues | multiplicity |\n|---|---|---|\n| \\(x\\in R_{7}\\) | \\(486\\) | \\(1\\) |\n| \\(27r,\\,r\\in R_{4}\\) | \\(18\\) | \\(9\\) |\n| \\(729\\) | \\(1\\) | \\(27\\) |\n| \\(1458\\) | \\(1\\) | \\(27\\) |\n| \\(0\\) | \\(1\\) | \\(27\\) |\n| total | \\(729\\) | \u2013 |\n\n--------------------------------------------------------------------\n### 2.   Fourier representation\n\nPut  \n\n\\[\n\\zeta =e^{2\\pi i/M}, \\qquad \nS(k)=\\sum_{a=1}^{L}\\zeta^{k a^{3}}\n      =\\sum_{x}f(x)\\,\\zeta^{k x},\n\\]\n\nwhere \\(f(x)\\) is the multiplicity of the residue \\(x\\) listed above.\nOrthogonality of characters gives  \n\n\\[\nN=\\frac1{M}\\sum_{k=0}^{M-1}S(k)^{3}\\tag{1}\n\\]\n\nand we have to evaluate the sum on the right.\n\n--------------------------------------------------------------------\n### 3.   Explicit form of \\(S(k)\\)\n\nWrite \\(k=3^{v}t\\;(3\\nmid t)\\).  \nThe three kinds of contributions are\n\n* from \\(R_{7}\\) (cubic residues modulo \\(M\\))  \n\n\\[\nS_{7}(k)=\\sum_{x\\in R_{7}}\\zeta^{k x}\n       =\\begin{cases}\n       486\\cos\\frac{2\\pi t}{9},&amp;3^{5}\\mid k,\\\\\n       0,&amp;\\text{otherwise}.\n       \\end{cases}\n\\]\n\n* from the residues \\(27r\\) (\\(r\\in R_{4}\\))  \n\n\\[\n9S_{4}(k)=9\\sum_{r\\in R_{4}}\\zeta^{27k r}\n        =\\begin{cases}\n        162\\cos\\frac{2\\pi t}{9},&amp;9\\mid k,\\\\\n        0,&amp;\\text{otherwise}.\n        \\end{cases}\n\\]\n\n* from the three \u201cfixed\u2019\u2019 residues \\(0,\\,729,\\,1458\\)  \n\n\\[\nS_{2}(k)+S_{3}(k)=27\\bigl(\\zeta^{729k}+\\zeta^{1458k}+1\\bigr)\n                =\\begin{cases}\n                81,&amp;3\\mid k,\\\\[2mm]\n                0,&amp;3\\nmid k .\n                \\end{cases}\n\\]\n\nHence\n\n\\[\nS(k)=S_{7}(k)+9S_{4}(k)+\n\\begin{cases}\n81,&amp;3\\mid k,\\\\\n0,&amp;3\\nmid k .\n\\end{cases}\n\\tag{2}\n\\]\n\n--------------------------------------------------------------------\n### 4.   Values of \\(S(k)\\)\n\nAccording to the 3\u2011adic valuation \\(v=v_{3}(k)\\) we obtain\n\n| \\(v\\) | condition on \\(k\\) | \\(S(k)\\) |\n|---|---|---|\n| \\(0\\) | \\(3\\nmid k\\) | \\(0\\) |\n| \\(1\\) | \\(3\\mid k,\\;9\\nmid k\\) | \\(81\\) |\n| \\(2\\) | \\(9\\mid k,\\;27\\nmid k\\) | \\(81\\bigl(1+2\\cos\\frac{2\\pi u}{9}\\bigr)\\)  \\(\\;(u=k/9\\bmod9\\neq0,3,6)\\) |\n| \\(3\\) | \\(27\\mid k,\\;81\\nmid k\\) | \\(0\\) |\n| \\(4\\) | \\(81\\mid k,\\;243\\nmid k\\) | \\(243\\) |\n| \\(5\\) | \\(243\\mid k,\\;729\\nmid k\\) | \\(243\\bigl(1+2\\cos\\frac{2\\pi t}{9}\\bigr)\\) \\(\\;(t=k/243\\bmod9\\neq0,3,6)\\) |\n| \\(6\\) | \\(729\\mid k\\) | \\(0\\) |\n| \\(k=0\\) | \u2013 | \\(S(0)=729\\) |\n\nThe numbers of \\(k\\) having each valuation are  \n\n\\[\n\\begin{aligned}\n&amp;v=0:1458,\\quad v=1:486,\\quad v=2:162,\\\\\n&amp;v=3:54,\\quad v=4:18,\\quad v=5:6,\\quad v=6:2 .\n\\end{aligned}\n\\]\n\n--------------------------------------------------------------------\n### 5.   Summation of \\(S(k)^{3}\\)\n\nDenote  \n\n\\[\nC=\\sum_{u\\in\\{1,2,4,5,7,8\\}}\\bigl(1+2\\cos\\tfrac{2\\pi u}{9}\\bigr)^{3}.\n\\]\n\nUsing the identity  \n\n\\[\n\\sum_{u\\in\\{1,2,4,5,7,8\\}}\\bigl(1+2\\cos\\tfrac{2\\pi u}{9}\\bigr)^{3}=36,\n\\]\n\n(which follows from expanding \\((1+z^{u}+z^{-u})^{3}\\) and summing over\n\\(u\\) with \\(z=e^{2\\pi i/9}\\)), we obtain\n\n\\[\n\\begin{aligned}\n\\sum_{k}S(k)^{3}\n&amp;= 486\\cdot81^{3}\n   +162\\cdot81^{3}\n   +18\\cdot243^{3}\n   +6\\cdot243^{3}                                 \\\\\n&amp;= 486\\cdot531\\,441\n   +162\\cdot531\\,441\n   +18\\cdot14\\,348\\,907\n   +6\\cdot14\\,348\\,907                           \\\\\n&amp;=5\\cdot3^{18}=5\\cdot387\\,420\\,489\n   =1\\,937\\,102\\,445 .\n\\end{aligned}\n\\]\n\n--------------------------------------------------------------------\n### 6.   The number \\(N\\)\n\nFrom (1),\n\n\\[\nN=\\frac{1}{3^{7}}\\sum_{k}S(k)^{3}\n  =\\frac{5\\cdot3^{18}}{3^{7}}\n  =5\\cdot3^{11}=5\\cdot177\\,147=885\\,735 .\n\\]\n\n--------------------------------------------------------------------\n### 7.   Remainder modulo \\(1000\\)\n\n\\[\n885\\,735 \\equiv 735 \\pmod{1000}.\n\\]\n\n--------------------------------------------------------------------\n\\[\n\\boxed{735}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 735</p>\n<p>Extracted Answer: 735</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThere are exactly three positive real numbers $ k $ such that the function\n$ f(x) = \\frac{(x - 18)(x - 72)(x - 98)(x - k)}{x} $\ndefined over the positive real numbers achieves its minimum value at exactly two positive real numbers $ x $. Find the sum of these three values of $ k $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n\\[\nf(x)=\\frac{(x-18)(x-72)(x-98)(x-k)}{x}= \\frac{N(x)}{x},\n\\qquad N(x)=(x-18)(x-72)(x-98)(x-k)\n\\]\n\nfor \\(x&gt;0\\) and a positive parameter \\(k\\).\n\n--------------------------------------------------------------------\n### 1.  Critical points\n\n\\[\nf&#39;(x)=\\frac{xN&#39;(x)-N(x)}{x^{2}},\\qquad   \nf&#39;(x)=0\\Longleftrightarrow H(x):=xN&#39;(x)-N(x)=0 .\n\\]\n\nWrite  \n\n\\[\nN(x)=x^{4}-S_{1}x^{3}+S_{2}x^{2}-S_{3}x+S_{4},\n\\]\n\nwhere  \n\n\\[\n\\begin{aligned}\nS_{1}&amp;=18+72+98+k = 188+k,\\\\\nS_{2}&amp;=18\\cdot72+18\\cdot98+72\\cdot98+ (18+72+98)k =10116+188k,\\\\\nS_{3}&amp;=18\\cdot72\\cdot98+(18\\cdot72+18\\cdot98+72\\cdot98)k =127008+10116k,\\\\\nS_{4}&amp;=18\\cdot72\\cdot98\\cdot k =127008\\,k .\n\\end{aligned}\n\\]\n\nSince  \n\n\\[\nN&#39;(x)=4x^{3}-3S_{1}x^{2}+2S_{2}x-S_{3},\n\\]\n\nwe obtain  \n\n\\[\n\\begin{aligned}\nH(x)&amp;=xN&#39;(x)-N(x)  \\\\\n    &amp;=3x^{4}-2S_{1}x^{3}+S_{2}x^{2}-S_{4}\\\\\n    &amp;=3x^{4}-(376+2k)x^{3}+(10116+188k)x^{2}-127008k .\n\\end{aligned}\n\\]\n\nThe three positive roots of \\(H\\) are the two minima of \\(f\\) (in the intervals where\n\\(f&lt;0\\)) and one interior maximum.\n\n--------------------------------------------------------------------\n### 2.  When are the two minima equal?\n\nAt a minimum \\(x_{0}\\),\n\n\\[\nf(x_{0}) = \\frac{N(x_{0})}{x_{0}} = N&#39;(x_{0})=:m .\n\\]\n\nThus the equation \\(N(x)=mx\\) has a **double** root at each minimum.\nIf the global minimum is attained at exactly two points, then\n\n\\[\nN(x)-mx=(x-\\alpha)^{2}(x-\\gamma)^{2},\n\\qquad\\alpha\\neq\\gamma&gt;0 .\n\\]\n\nExpanding both sides and comparing coefficients gives\n\n\\[\n\\begin{cases}\n\\alpha+\\gamma =\\displaystyle\\frac{188+k}{2},\\\\[4pt]\n\\alpha\\gamma = -\\dfrac{k^{2}}{8}+47k+640,\\\\[4pt]\n(\\alpha\\gamma)^{2}=S_{4}=127008k .\n\\end{cases}\n\\]\n\nEliminating \\(\\alpha,\\gamma\\) yields a single equation for \\(k\\):\n\n\\[\n\\Bigl(-\\frac{k^{2}}{8}+47k+640\\Bigr)^{2}=127008k .\n\\]\n\nMultiplying by \\(64\\),\n\n\\[\n(k^{2}-376k-5120)^{2}=8\\,128\\,512\\,k,\n\\]\n\nwhich simplifies to the quartic\n\n\\[\nk^{4}-752k^{3}+131136k^{2}-4\\,278\\,272k+26\\,214\\,400=0 .\n\\]\n\n--------------------------------------------------------------------\n### 3.  Solving the quartic\n\nFactoring gives  \n\n\\[\n(k-8)(k-32)(k^{2}-712k+102400)=0,\n\\]\n\nso the four real solutions are  \n\n\\[\nk=8,\\qquad k=32,\\qquad k=200,\\qquad k=512 .\n\\]\n\n--------------------------------------------------------------------\n### 4.  Selecting the admissible \\(k\\)\n\nFor the two minima to be **positive**, the product \\(\\alpha\\gamma\\) must be positive:\n\n\\[\n\\alpha\\gamma = -\\frac{k^{2}}{8}+47k+640 &gt;0 .\n\\]\n\nEvaluating this expression:\n\n\\[\n\\begin{array}{c|c}\nk &amp; \\alpha\\gamma\\\\ \\hline\n8   &amp; 1008&gt;0\\\\\n32  &amp; 2016&gt;0\\\\\n200 &amp; 5040&gt;0\\\\\n512 &amp; -8064&lt;0\n\\end{array}\n\\]\n\nThus \\(k=512\\) gives one root \\(\\alpha\\) negative and cannot produce two minima on the\npositive axis.  The admissible values are  \n\n\\[\nk=8,\\;32,\\;200 .\n\\]\n\n--------------------------------------------------------------------\n### 5.  Sum of the three values\n\n\\[\n8+32+200 = 240 .\n\\]\n\n--------------------------------------------------------------------\n\\[\n\\boxed{240}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 240</p>\n<p>Extracted Answer: 240</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThe set of points in 3-dimensional coordinate space that lie in the plane $x+y+z=75$ whose coordinates satisfy the inequalities $x-yz&lt;y-zx&lt;z-xy$ forms three disjoint convex regions. Exactly one of those regions has finite area. The area of this finite region can be expressed in the form $a\\sqrt{b}$, where $a$ and $b$ are positive integers and $b$ is not divisible by the square of any prime. Find $a+b$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>The inequalities can be rewritten by factoring:\n\n\\[\n\\begin{aligned}\nx-yz&lt;y-zx &amp;\\iff (x-y)(1+z)&lt;0,\\\\[2pt]\ny-zx&lt;z-xy &amp;\\iff (y-z)(1+x)&lt;0 .\n\\end{aligned}\n\\]\n\nHence the signs of \\(x-y,\\;y-z,\\;1+z,\\;1+x\\) must be opposite in each product.\nFour sign\u2011patterns are possible:\n\n\\[\n\\begin{array}{c|c|c|c}\nx+1 &amp; z+1 &amp; \\text{implied order of }x,y,z &amp; \\text{region}\\\\ \\hline\n&gt;0 &amp; &gt;0 &amp; x&lt;y&lt;z &amp; \\text{bounded}\\\\\n&gt;0 &amp; &lt;0 &amp; y&lt;\\min\\{x,z\\} &amp; \\text{unbounded}\\\\\n&lt;0 &amp; &gt;0 &amp; \\max\\{x,z\\}&lt;y &amp; \\text{unbounded}\\\\\n&lt;0 &amp; &lt;0 &amp; x&gt;y&gt;z &amp; \\text{impossible (sum }75)\n\\end{array}\n\\]\n\nOnly the first case can give a finite region.  \nWith \\(x+y+z=75\\) and the inequalities\n\n\\[\nx&gt;-1,\\qquad x&lt;y,\\qquad y&lt;z,\n\\]\n\nwrite \\(z=75-x-y\\). The conditions become\n\n\\[\n\\begin{cases}\nx&gt;-1,\\\\\nx&lt;y,\\\\\ny&lt;\\dfrac{75-x}{2}.\n\\end{cases}\n\\]\n\nIn the \\((x,y)\\)-plane this is the interior of the triangle bounded by\n\n\\[\nx=-1,\\qquad y=x,\\qquad y=\\frac{75-x}{2},\n\\]\n\nwhose vertices are \\((-1,-1),\\;(-1,38),\\;(25,25)\\).\n\nIts area in the \\((x,y)\\)-plane is\n\n\\[\n\\frac12\\cdot 39\\cdot 26=507 .\n\\]\n\nThe plane \\(x+y+z=75\\) makes an angle with the \\(xy\\)-plane whose normal is \\((1,1,1)\\); the area element is multiplied by \\(\\lVert(1,1,1)\\rVert=\\sqrt3\\).  \nHence the actual area of the bounded region is\n\n\\[\n507\\sqrt3 .\n\\]\n\nThus \\(a=507,\\;b=3\\) and\n\n\\[\na+b=507+3=510 .\n\\]\n\n\\[\n\\boxed{510}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 510</p>\n<p>Extracted Answer: 510</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThe 27 cells of a $3\\times9$ grid are filled in using the numbers 1 through 9 so that each row contains 9 different numbers, and each of the three $3\\times3$ blocks heavily outlined in the example below contains 9 different numbers, as in the first three rows of a Sudoku puzzle. \n | 4 | 2 | 8 | 9 | 6 | 3 | 1 | 7 | 5 | \n | 3 | 7 | 9 | 5 | 2 | 1 | 6 | 8 | 4 | \n | 5 | 6 | 1 | 8 | 4 | 7 | 9 | 2 | 3 | \n The number of different ways to fill such a grid can be written as $p^a\\cdot q^b\\cdot r^c\\cdot s^d$, where $p,q,r,$ and $s$ are distinct prime numbers and $a,b,c,$ and $d$ are positive integers. Find $p\\cdot a+q\\cdot b+r\\cdot c+s\\cdot d$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>The grid consists of three \\(3\\times 3\\) blocks.  \nFor each number \\(1,\\dots ,9\\) we must place it\n\n* once in each of the three rows,\n* once in each of the three blocks.\n\nHence for a fixed number its positions are described by a permutation\n\\(\\sigma\\in S_{3}\\):\n\\[\n\\sigma(i)=\\text{the block in which the number occurs in row }i .\n\\]\n\n---\n\n### 1.  Counting the assignments of permutations\n\nLet \\(n_\\sigma\\) be the number of symbols that use permutation \\(\\sigma\\).\nSince there are nine symbols,\n\\[\n\\sum_{\\sigma\\in S_3} n_\\sigma = 9 .\n\\]\n\nFor each ordered pair \\((i,j)\\) (row \\(i\\), block \\(j\\)) the number of symbols\nwith \\(\\sigma(i)=j\\) must be \\(3\\) (there are three columns in that block).  \nWriting the six permutations of \\(S_3\\) as  \n\n\\[\n\\begin{aligned}\n\\sigma_1&amp;:(1,2,3),&amp;\\sigma_2&amp;:(2,1,3),&amp;\\sigma_3&amp;:(3,2,1),\\\\\n\\sigma_4&amp;:(1,3,2),&amp;\\sigma_5&amp;:(2,3,1),&amp;\\sigma_6&amp;:(3,1,2),\n\\end{aligned}\n\\]\n\nthe conditions become  \n\n\\[\n\\begin{array}{c}\nn_1+n_4=3,\\; n_1+n_2=3,\\; n_1+n_3=3,\\\\\nn_2+n_5=3,\\; n_3+n_6=3,\\; n_4+n_5=3,\\\\\nn_3+n_5=3,\\; n_4+n_6=3,\\; n_2+n_6=3 .\n\\end{array}\n\\]\n\nSolving gives a one\u2011parameter family\n\n\\[\nn_1=n_5=n_6=k,\\qquad n_2=n_3=n_4=3-k,\n\\]\n\nwith \\(k=0,1,2,3\\) (non\u2011negative integers).  \nFor each \\(k\\) the number of ways to assign the nine distinct symbols to the\npermutations is  \n\n\\[\n\\frac{9!}{k!^3\\,(3-k)!^3}.\n\\]\n\nHence the total number of macro\u2011assignments is\n\n\\[\nM=\\sum_{k=0}^{3}\\frac{9!}{k!^3(3-k)!^3}\n   =1680+45360+45360+1680=94080 .\n\\]\n\n---\n\n### 2.  Ordering within each macro\u2011cell\n\nA macro\u2011cell \\((\\text{row }i,\\text{ block }j)\\) contains exactly three\ndifferent numbers.  Their order in the three columns of that block can be chosen\nin \\(3!\\) ways, independently for each of the \\(3\\times 3=9\\) macro\u2011cells.\nThus we obtain an extra factor \\((3!)^{9}=6^{9}=10\\,077\\,696\\).\n\nHence the total number of fillings is  \n\n\\[\nN = M\\cdot (3!)^{9}=94080\\cdot 6^{9}\n   = 2^{16}\\cdot 3^{10}\\cdot5\\cdot7^{2}.\n\\]\n\n---\n\n### 3.  Computing \\(p a+q b+r c+s d\\)\n\nWriting \\(N=p^{a}q^{b}r^{c}s^{d}\\) with distinct primes \\(p,q,r,s\\) we have  \n\n\\[\np=2,\\;a=16;\\qquad q=3,\\;b=10;\\qquad r=5,\\;c=1;\\qquad s=7,\\;d=2.\n\\]\n\nTherefore  \n\n\\[\np a+q b+r c+s d\n=2\\cdot16+3\\cdot10+5\\cdot1+7\\cdot2\n=32+30+5+14=81.\n\\]\n\n\\[\n\\boxed{81}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 81</p>\n<p>Extracted Answer: 81</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nSix points $ A, B, C, D, E, $ and $ F $ lie in a straight line in that order. Suppose that $ G $ is a point not on the line and that $ AC = 26 $, $ BD = 22 $, $ CE = 31 $, $ DF = 33 $, $ AF = 73 $, $ CG = 40 $, and $ DG = 30 $. Find the area of $ \\triangle BGE $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let the line containing \\(A,B,C,D,E,F\\) be the \\(x\\)-axis.  \nPlace \\(A\\) at the origin: \\(A=(0,0)\\).\n\n---\n\n### 1.  Determine the coordinates of the collinear points  \n\n\\[\n\\begin{aligned}\nAC&amp;=26\\quad\\Rightarrow\\quad C=(26,0),\\\\[2mm]\nBD&amp;=22\\quad\\Rightarrow\\quad D-B=22,\\\\[2mm]\nCE&amp;=31\\quad\\Rightarrow\\quad E-C=31\\;\\Rightarrow\\;E=(57,0),\\\\[2mm]\nDF&amp;=33\\quad\\Rightarrow\\quad F-D=33,\\\\[2mm]\nAF&amp;=73\\quad\\Rightarrow\\quad F=(73,0).\n\\end{aligned}\n\\]\n\nFrom \\(F-D=33\\) we get \\(D=73-33=40\\).  \nThen \\(BD=22\\) gives \\(B=40-22=18\\).\n\nThus  \n\n\\[\nA(0,0),\\;B(18,0),\\;C(26,0),\\;D(40,0),\\;E(57,0),\\;F(73,0).\n\\]\n\n---\n\n### 2.  Locate point \\(G\\)\n\nLet \\(G=(x,y)\\) with \\(y\\neq0\\).  \nGiven \\(CG=40\\) and \\(DG=30\\),\n\n\\[\n\\begin{cases}\n(x-26)^2+y^2 = 40^2 =1600,\\\\\n(x-40)^2+y^2 = 30^2 = 900 .\n\\end{cases}\n\\]\n\nSubtract the second equation from the first:\n\n\\[\n(x-26)^2-(x-40)^2 = 700\n\\]\n\\[\n\\Longrightarrow\\;28x-924 = 700 \\;\\Longrightarrow\\; x=58 .\n\\]\n\nPlug \\(x=58\\) into \\((x-40)^2+y^2=900\\):\n\n\\[\n(18)^2 + y^2 = 900 \\;\\Longrightarrow\\; y^2 = 576 \\;\\Longrightarrow\\; y = \\pm24 .\n\\]\n\nTake \\(y=24\\) (the sign does not affect the area).  \nHence \\(G=(58,24)\\).\n\n---\n\n### 3.  Area of \\(\\triangle BGE\\)\n\nPoints \\(B\\) and \\(E\\) lie on the \\(x\\)-axis, so segment \\(\\overline{BE}\\) is horizontal.  \n\n\\[\nBE = 57-18 = 39 .\n\\]\n\nThe perpendicular distance from \\(G\\) to line \\(BE\\) (the \\(x\\)-axis) is \\(|y| = 24\\).\n\nTherefore\n\n\\[\n\\text{Area} = \\frac12 \\times (\\text{base}) \\times (\\text{height})\n           = \\frac12 \\times 39 \\times 24\n           = 468 .\n\\]\n\n\\[\n\\boxed{468}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 468</p>\n<p>Extracted Answer: 468</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nFind the sum of all positive integers $ n $ such that $ n + 2 $ divides the product $ 3(n + 3)(n^2 + 9) $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n\\[\nd=n+2\\qquad (d\\ge 3,\\;n\\in\\mathbb Z^+)\n\\]\n\nThen  \n\n\\[\nn+3=d+1,\\qquad n^{2}+9=(d-2)^2+9=d^{2}-4d+13 .\n\\]\n\nThe condition \u201c\\(n+2\\) divides \\(3(n+3)(n^{2}+9)\\)\u201d becomes  \n\n\\[\nd\\mid 3(d+1)(d^{2}-4d+13).\n\\]\n\nConsider the right\u2011hand side modulo \\(d\\):\n\n\\[\n\\begin{aligned}\n3(d+1)(d^{2}-4d+13)\n&amp;\\equiv 3\\cdot1\\cdot13\\pmod{d}\\\\\n&amp;=39\\pmod{d}.\n\\end{aligned}\n\\]\n\nHence  \n\n\\[\nd\\mid 3(d+1)(d^{2}-4d+13)\\iff d\\mid 39 .\n\\]\n\nSince \\(d=n+2\\ge 3\\), the possible values of \\(d\\) are the divisors of \\(39\\) that are at least \\(3\\):\n\n\\[\nd\\in\\{3,13,39\\}.\n\\]\n\nCorresponding \\(n=d-2\\) values are  \n\n\\[\nn=1,\\;11,\\;37 .\n\\]\n\nAll three satisfy the original divisibility (direct substitution confirms).\n\nThe required sum is  \n\n\\[\n1+11+37=49.\n\\]\n\n\\[\n\\boxed{49}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 49</p>\n<p>Extracted Answer: 49</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nA piecewise linear periodic function is defined by $f(x)=\\begin{cases}x&amp;\\text{if }x\\in[-1,1)\\\\2-x&amp;\\text{if }x\\in[1,3)\\end{cases}$ and $f(x+4)=f(x)$ for all real numbers $x$. The graph of $f(x)$ has the sawtooth pattern. The parabola $x=34y^2$ intersects the graph of $f(x)$ at finitely many points. The sum of the $y$-coordinates of these intersection points can be expressed in the form $\\frac{a+b\\sqrt{c}}{d}$, where $a,b,c,$ and $d$ are positive integers, $a,b,$ and $d$ have greatest common divisor equal to 1, and $c$ is not divisible by the square of any prime. Find $a+b+c+d$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>The function  \n\n\\[\nf(x)=\\begin{cases}\nx,&amp;-1\\le x&lt;1\\\\[2mm]\n2-x,&amp;1\\le x&lt;3\n\\end{cases},\\qquad f(x+4)=f(x)\n\\]\n\nhas period \\(4\\).  \nFor any \\(x\\) write  \n\n\\[\nx=4n+t,\\qquad t\\in[-1,3),\\;n\\in\\mathbb Z .\n\\]\n\nThen  \n\n\\[\nf(x)=\\begin{cases}\nt,&amp;-1\\le t&lt;1\\\\\n2-t,&amp;1\\le t&lt;3 .\n\\end{cases}\n\\tag{1}\n\\]\n\nThe parabola is \\(x=34y^{2}\\;(x\\ge 0)\\).  \nAn intersection point must satisfy  \n\n\\[\ny=f(34y^{2}) .\n\\tag{2}\n\\]\n\nPut \\(x=34y^{2}=4n+t\\) with \\(t\\in[-1,3)\\).  \nFrom (1) there are two possibilities.\n\n---\n\n### 1.  \\(t=y\\)  \n\nThen \\(-1\\le y&lt;1\\) and  \n\n\\[\n34y^{2}=4n+y\\Longrightarrow 34y^{2}-y=4n .\n\\tag{3}\n\\]\n\nFor each integer \\(n\\) this quadratic gives the two solutions  \n\n\\[\ny=\\frac{1\\pm\\sqrt{1+544n}}{68}.\n\\tag{4}\n\\]\n\nSince \\(y\\in[-1,1)\\) the solutions are admissible for every \\(n\\)\nfor which \\(34y^{2}\\le 34\\).  \nBecause \\(0\\le34y^{2}\\le34\\), from \\(34y^{2}=4n+t\\) with \\(t\\ge-1\\) we get\n\\(0\\le4n+3\\), i.e. \\(n\\ge0\\); and from \\(4n-1\\le34\\) we obtain \\(n\\le8\\).\nThus \\(n=0,1,\\dots ,8\\).  \n\nFor each \\(n\\) the sum of the two roots of (3) is  \n\n\\[\n\\frac{1}{34}.\n\\]\n\nHence the total contribution of this case is  \n\n\\[\n9\\cdot\\frac1{34}=\\frac{9}{34}=\\frac{18}{68}.\n\\tag{5}\n\\]\n\n---\n\n### 2.  \\(t=2-y\\)  \n\nNow \\(1\\le t&lt;3\\) which gives \\(-1&lt;y\\le1\\) and  \n\n\\[\n34y^{2}=4n+2-y\\Longrightarrow 34y^{2}+y-2=4n .\n\\tag{6}\n\\]\n\nIts solutions are  \n\n\\[\ny=\\frac{-1\\pm\\sqrt{273+544n}}{68}.\n\\tag{7}\n\\]\n\nAgain \\(n=0,1,\\dots ,8\\).  \nFor \\(n=0,\\dots ,7\\) both roots lie in \\((-1,1]\\); for \\(n=8\\) only the\n\u2018\\(+\\)\u2019 root is admissible (the \u2018\\(-\\)\u2019 root is \\(&lt;-1\\)).  \n\nThe sum of the two roots of (6) for any \\(n\\) equals  \n\n\\[\n-\\frac1{34}.\n\\]\n\nThus the sum of all valid roots of this case is  \n\n\\[\n8\\!\\left(-\\frac1{34}\\right)+\\frac{-1+\\sqrt{4625}}{68}\n   =-\\frac{16}{68}+\\frac{-1+\\sqrt{4625}}{68}\n   =\\frac{-17+\\sqrt{4625}}{68}.\n\\tag{8}\n\\]\n\n---\n\n### 3.  Total sum of the \\(y\\)\u2013coordinates\n\nAdding (5) and (8),\n\n\\[\nS=\\frac{18}{68}+\\frac{-17+\\sqrt{4625}}{68}\n   =\\frac{1+\\sqrt{4625}}{68}\n   =\\frac{1+5\\sqrt{185}}{68}.\n\\]\n\nThe expression \\(\\displaystyle\\frac{a+b\\sqrt{c}}{d}\\) has  \n\n\\[\na=1,\\;b=5,\\;c=185,\\;d=68,\n\\]\n\nwith \\(\\gcd(a,b,d)=1\\) and \\(c\\) square\u2011free.\n\nHence  \n\n\\[\na+b+c+d = 1+5+185+68 = 259.\n\\]\n\n\\[\n\\boxed{259}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 259</p>\n<p>Extracted Answer: 259</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThe product $ \\prod_{k=4}^{63} \\frac{\\log_k(5^{k^2-1})}{\\log_{k+1}(5^{k^2-4})} = \\frac{\\log_4(5^{15})}{\\log_5(5^{12})} \\cdot \\frac{\\log_5(5^{24})}{\\log_6(5^{21})} \\cdot \\frac{\\log_6(5^{35})}{\\log_7(5^{32})} \\cdots \\frac{\\log_{63}(5^{3968})}{\\log_{64}(5^{3965})} $ is equal to $ \\frac{m}{n} $, where $ m $ and $ n $ are relatively prime positive integers. Find $ m + n $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>\\[\n\\prod_{k=4}^{63}\\frac{\\log_k\\!\\left(5^{k^{2}-1}\\right)}{\\log_{k+1}\\!\\left(5^{k^{2}-4}\\right)}\n= \\prod_{k=4}^{63}\n\\frac{(k^{2}-1)\\ln5/\\ln k}{(k^{2}-4)\\ln5/\\ln(k+1)}\n= \\prod_{k=4}^{63}\\frac{k^{2}-1}{k^{2}-4}\\cdot\\frac{\\ln(k+1)}{\\ln k}\n\\]\n\nSince \\(k^{2}-1=(k-1)(k+1)\\) and \\(k^{2}-4=(k-2)(k+2)\\),\n\n\\[\n\\frac{k^{2}-1}{k^{2}-4}= \\frac{k-1}{k-2}\\cdot\\frac{k+1}{k+2}.\n\\]\n\nThus\n\n\\[\nP=\\Bigl(\\prod_{k=4}^{63}\\frac{k-1}{k-2}\\Bigr)\n   \\Bigl(\\prod_{k=4}^{63}\\frac{k+1}{k+2}\\Bigr)\n   \\Bigl(\\prod_{k=4}^{63}\\frac{\\ln(k+1)}{\\ln k}\\Bigr).\n\\]\n\nEach product telescopes:\n\n1. \\(\\displaystyle\\prod_{k=4}^{63}\\frac{k-1}{k-2}\n   =\\frac{3}{2}\\cdot\\frac{4}{3}\\cdots\\frac{62}{61}\n   =\\frac{62}{2}=31.\\)\n\n2. \\(\\displaystyle\\prod_{k=4}^{63}\\frac{k+1}{k+2}\n   =\\frac{5}{6}\\cdot\\frac{6}{7}\\cdots\\frac{64}{65}\n   =\\frac{5}{65}=\\frac1{13}.\\)\n\n3. \\(\\displaystyle\\prod_{k=4}^{63}\\frac{\\ln(k+1)}{\\ln k}\n   =\\frac{\\ln5}{\\ln4}\\cdot\\frac{\\ln6}{\\ln5}\\cdots\\frac{\\ln64}{\\ln63}\n   =\\frac{\\ln64}{\\ln4}\n   =\\log_{4}64=3.\\)\n\nMultiplying,\n\n\\[\nP=31\\cdot\\frac1{13}\\cdot3=\\frac{93}{13}.\n\\]\n\nThus \\(m=93,\\;n=13\\) (relatively prime) and  \n\n\\[\nm+n=93+13=106.\n\\]\n\n\\[\n\\boxed{106}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 106</p>\n<p>Extracted Answer: 106</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nFour unit squares form a $2 \\times 2$ grid. Each of the 12 unit line segments forming the sides of the squares is colored either red or blue in such a way that each unit square has 2 red sides and 2 blue sides. Find the number of such colorings.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Label the unit line segments as follows.\n\n\\[\n\\begin{array}{c}\n\\text{Top edges: }T_1,T_2\\\\\n\\text{Bottom edges: }B_1,B_2\\\\\n\\text{Left edges: }L_1,L_2\\\\\n\\text{Right edges: }R_1,R_2\\\\\n\\text{Middle vertical edges: }M_{v1},M_{v2}\\\\\n\\text{Middle horizontal edges: }M_{h1},M_{h2}\n\\end{array}\n\\]\n\nEach of the four unit squares must have exactly two red sides.\nLet a red edge be denoted by \\(1\\) and a blue edge by \\(0\\).\nIntroduce the binary variables  \n\n\\[\n\\begin{aligned}\n&amp;a=M_{v1},\\;b=M_{v2},\\;c=M_{h1},\\;d=M_{h2},\\\\\n&amp;p=T_1,\\;q=T_2,\\;r=B_1,\\;s=B_2,\\\\\n&amp;u=L_1,\\;v=L_2,\\;w=R_1,\\;x=R_2 .\n\\end{aligned}\n\\]\n\nThe condition \u201ctwo red sides\u201d for each of the four squares gives four linear\nequations:\n\n\\[\n\\begin{cases}\np+u+a+c=2\\\\\nq+w+a+d=2\\\\\nr+v+b+c=2\\\\\ns+x+b+d=2\\qquad (1)\n\\end{cases}\n\\]\n\nAll variables are \\(0\\) or \\(1\\).\n\n--------------------------------------------------------------------\n### Fix the interior edges\n\nThe interior edges are the four variables \\(a,b,c,d\\).\nFor a fixed choice of \\((a,b,c,d)\\) each equation in (1) involves a\ndifferent pair of outer edges:\n\n\\[\n\\begin{aligned}\np+u &amp;=2-(a+c),\\\\\nq+w &amp;=2-(a+d),\\\\\nr+v &amp;=2-(b+c),\\\\\ns+x &amp;=2-(b+d).\n\\end{aligned}\n\\tag{2}\n\\]\n\nFor a pair of binary variables the number of possibilities for a given\nsum is  \n\n\\[\nf(s)=\\begin{cases}\n1 &amp; s=0\\text{ or }2,\\\\[2pt]\n2 &amp; s=1,\\\\[2pt]\n0 &amp; \\text{otherwise}.\n\\end{cases}\n\\]\n\nHence, for a fixed interior assignment the number of ways to colour the\nouter edges equals  \n\n\\[\nf\\bigl(2-(a+c)\\bigr)\\,\nf\\bigl(2-(a+d)\\bigr)\\,\nf\\bigl(2-(b+c)\\bigr)\\,\nf\\bigl(2-(b+d)\\bigr).\n\\]\n\nBecause \\(a,c,b,d\\in\\{0,1\\}\\), each sum \\(a+c,\\;a+d,\\;b+c,\\;b+d\\) is\n\\(0,1,\\) or \\(2\\); consequently the factor is \\(2\\) exactly when the\ncorresponding pair contains one \\(0\\) and one \\(1\\), and it is \\(1\\) when\nthe pair is equal.  \n\nDefine\n\n\\[\nN(a,b,c,d)=\\bigl[ a\\ne c\\bigr]+\\bigl[ a\\ne d\\bigr]+\\bigl[ b\\ne c\\bigr]\n+\\bigl[ b\\ne d\\bigr].\n\\]\n\nThen the number of outer colourings for that interior choice is\n\\(2^{\\,N(a,b,c,d)}\\).\n\n--------------------------------------------------------------------\n### Counting all interior choices\n\nThe four interior bits can be viewed as two binary strings  \n\\(A=(a,b)\\) and \\(C=(c,d)\\).  The quantity \\(N\\) counts the mismatches\nbetween \\(A\\) and \\(C\\) over all four cross\u2011pairs, and one obtains\n\n\\[\nN=2\\bigl(w_A+w_C-w_Aw_C\\bigr),\n\\]\nwhere \\(w_A=a+b\\) and \\(w_C=c+d\\) are the numbers of 1\u2019s in the strings.\n\nFrom this we get the possible values:\n\n* **\\(N=0\\)** when \\(A=C\\) (all four interior edges equal).  \n  Two assignments: \\((0,0,0,0)\\) and \\((1,1,1,1)\\).  \n  Contribution: \\(2\\cdot2^{0}=2\\).\n\n* **\\(N=4\\)** when the two strings are opposite, i.e. \\(A=(0,0), C=(1,1)\\)\n  or \\(A=(1,1), C=(0,0)\\).  \n  Two assignments.  \n  Contribution: \\(2\\cdot2^{4}=32\\).\n\n* **\\(N=2\\)** for all remaining \\(16-4=12\\) interior assignments.  \n  Contribution: \\(12\\cdot2^{2}=48\\).\n\nAdding them gives the total number of colourings\n\n\\[\n2+48+32 = 82.\n\\]\n\n--------------------------------------------------------------------\n\\[\n\\boxed{82}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 82</p>\n<p>Extracted Answer: 82</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nOn $\\triangle ABC$ points $A,D,E$, and $B$ lie that order on side $\\overline{AB}$ with $AD=4, DE=16$, and $EB=8$. Points $A,F,G$, and $C$ lie in that order on side $\\overline{AC}$ with $AF=13, FG=52$, and $GC=26$. Let $M$ be the reflection of $D$ through $F$, and let $N$ be the reflection of $G$ through $E$. Quadrilateral $DEGF$ has area 288. Find the area of heptagon $AFNBCEM$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>**Solution Overview**\n\nPlace \\(\\triangle ABC\\) in the plane with  \n\n\\[\nA=(0,0),\\qquad B=(28,0),\\qquad C=(x,y)\n\\]\n\nso that \\(AB=28\\).  \nThe points on the sides are\n\n\\[\n\\begin{aligned}\nD&amp;=A+\\frac17AB=(4,0), &amp;\nE&amp;=A+\\frac57AB=(20,0),\\\\\nF&amp;=A+\\frac17AC=\\Bigl(\\frac{x}{7},\\frac{y}{7}\\Bigr), &amp;\nG&amp;=A+\\frac57AC=\\Bigl(\\frac{5x}{7},\\frac{5y}{7}\\Bigr).\n\\end{aligned}\n\\]\n\n(The given lengths give the fractions \\(\\frac17,\\frac57\\) on both sides because  \n\n\\[\nAD:DE:EB=4:16:8=1:4:2,\\qquad \nAF:FG:GC=13:52:26=1:4:2 .\n\\])\n\nThe reflections are\n\n\\[\n\\begin{aligned}\nM&amp;=2F-D=\\Bigl(\\frac{2x}{7}-4,\\frac{2y}{7}\\Bigr),\\\\[2mm]\nN&amp;=2E-G=\\Bigl(40-\\frac{5x}{7},-\\frac{5y}{7}\\Bigr).\n\\end{aligned}\n\\]\n\n--------------------------------------------------------------------\n### 1.  Height of the triangle\n\nThe quadrilateral \\(DEGF\\) is \\(\\{D,E,G,F\\}\\) in that order.  \nUsing the shoelace formula,\n\n\\[\n\\begin{aligned}\n[DEGF]\n&amp;=\\frac12\\Bigl((4\\cdot0+20\\cdot\\frac{5y}{7}+\\frac{5x}{7}\\cdot\\frac{y}{7}+ \\frac{x}{7}\\cdot0) \\\\\n&amp;\\qquad\\ -\\ (0\\cdot20+\\;0\\cdot\\frac{5x}{7}+\\frac{5y}{7}\\cdot\\frac{x}{7}+ \\frac{y}{7}\\cdot4 )\\Bigr)\\\\[1mm]\n&amp;=\\frac12\\Bigl(20\\cdot\\frac{5y}{7}-4\\cdot\\frac{y}{7}\\Bigr)\n =\\frac{1248}{91}\\,\\frac{y}{2}= \\frac{624}{91}\\,y .\n\\end{aligned}\n\\]\n\nThe problem states \\([DEGF]=288\\); hence\n\n\\[\n\\frac{624}{91}\\,y=288\\qquad\\Longrightarrow\\qquad y=42 .\n\\]\n\nThus the altitude from \\(C\\) to \\(\\overline{AB}\\) is \\(h=y=42\\).\n\n--------------------------------------------------------------------\n### 2.  Area of \\(\\triangle ABC\\)\n\n\\[\n[ABC]=\\frac12\\cdot AB\\cdot h=\\frac12\\cdot 28\\cdot 42=14\\cdot 42=588.\n\\]\n\n--------------------------------------------------------------------\n### 3.  Area of the heptagon \\(AFNBCEM\\)\n\nWrite the vertices in order:\n\n\\[\nA,\\;F,\\;N,\\;B,\\;C,\\;E,\\;M .\n\\]\n\nUsing the coordinates found above (with \\(y=42\\) and \\(\\,x=\\sqrt{91^{2}-42^{2}}=7\\sqrt{133}\\)), the\nshoelace sum is\n\n\\[\n\\begin{aligned}\nS&amp;=x_Ay_F-y_Ax_F\n   +x_Fy_N-y_Fx_N\n   +x_Ny_B-y_Nx_B\n   +x_By_C-y_Bx_C\n   +x_Cy_E-y_Cx_E\n   +x_Ey_M-y_Ex_M\n   +x_My_A-y_Mx_A \\\\[1mm]\n&amp;=0-240+840+1176-840+240+0=1176 .\n\\end{aligned}\n\\]\n\nHence\n\n\\[\n[AFNBCEM]=\\frac12\\,S=\\frac12\\cdot1176=588 .\n\\]\n\nA vector\u2011geometry check also shows that the signed sum of the\ndeterminants of successive vertices equals \\(\\det(\\overrightarrow{AB},\n\\overrightarrow{AC})\\), i.e. the area of \\(\\triangle ABC\\).\n\n--------------------------------------------------------------------\n### 4.  Answer\n\n\\[\n\\boxed{588}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 588</p>\n<p>Extracted Answer: 588</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $ A $ be the set of positive integer divisors of 2025. Let $ B $ be a randomly selected subset of $ A $. The probability that $ B $ is a nonempty set with the property that the least common multiple of its elements is 2025 is $ \\frac{m}{n} $, where $ m $ and $ n $ are relatively prime positive integers. Find $ m + n $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Factor  \n\\[\n2025=3^{4}\\cdot5^{2}.\n\\]\n\nA divisor of \\(2025\\) is \\(3^{i}5^{j}\\) with \\(0\\le i\\le4,\\;0\\le j\\le2\\).  \nHence  \n\n\\[\n|A|=(4+1)(2+1)=15 .\n\\]\n\n---\n\n### When does a subset have lcm \\(2025\\)?\n\nThe lcm of a set of divisors takes, for each prime, the **maximum** exponent appearing among the chosen numbers.\n\nThus a subset \\(B\\subseteq A\\) has \\(\\operatorname{lcm}(B)=3^{4}5^{2}=2025\\) iff  \n\n* at least one element of \\(B\\) has exponent \\(4\\) of the prime \\(3\\);\n* at least one element of \\(B\\) has exponent \\(2\\) of the prime \\(5\\).\n\nDefine  \n\n\\[\nS_{3}=\\{3^{4}5^{j}\\mid j=0,1,2\\}=\\{81,405,2025\\},\n\\qquad\nS_{5}=\\{3^{i}5^{2}\\mid i=0,1,2,3,4\\}\n =\\{25,75,225,675,2025\\}.\n\\]\n\n\\(|S_{3}|=3,\\ |S_{5}|=5,\\) and \\(|S_{3}\\cap S_{5}|=1\\) (the element \\(2025\\)).\n\nSo we need subsets that intersect **both** \\(S_{3}\\) and \\(S_{5}\\).\n\n---\n\n### Counting such subsets\n\nTotal subsets of \\(A\\): \\(2^{15}\\).\n\nLet  \n\n* \\(A_{3}\\) = subsets containing **no** element of \\(S_{3}\\).  \n  \\(|A_{3}| = 2^{15-3}=2^{12}\\).\n\n* \\(A_{5}\\) = subsets containing **no** element of \\(S_{5}\\).  \n  \\(|A_{5}| = 2^{15-5}=2^{10}\\).\n\n* \\(A_{3}\\cap A_{5}\\) = subsets containing none of \\(S_{3}\\cup S_{5}\\).  \n  \\(|S_{3}\\cup S_{5}| = 3+5-1 = 7\\), so  \n  \\(|A_{3}\\cap A_{5}| = 2^{15-7}=2^{8}\\).\n\nBy inclusion\u2013exclusion, the number of subsets intersecting both \\(S_{3}\\) and \\(S_{5}\\) is  \n\n\\[\n2^{15} - 2^{12} - 2^{10} + 2^{8}\n = 32768 - 4096 - 1024 + 256\n = 27904.\n\\]\n\nEvery such subset is non\u2011empty, so these are exactly the favorable subsets.\n\n---\n\n### Probability\n\n\\[\n\\text{Probability}\n = \\frac{27904}{2^{15}}\n = \\frac{27904}{32768}\n = \\frac{109}{128}\n\\]\n(after reducing the fraction).\n\nThus \\(m=109,\\ n=128\\) and  \n\n\\[\nm+n = 109+128 = 237.\n\\]\n\n\\[\n\\boxed{237}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 237</p>\n<p>Extracted Answer: 237</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nCircle $\\omega_1$ with radius 6 centered at point $A$ is internally tangent at point $B$ to circle $\\omega_2$ with radius 15. Points $C$ and $D$ lie on $\\omega_2$ such that $\\overline{BC}$ is a diameter of $\\omega_2$ and $\\overline{BC} \\perp \\overline{AD}$. The rectangle $EFGH$ is inscribed in $\\omega_1$ such that $\\overline{EF} \\perp \\overline{BC}$, $C$ is closer to $\\overline{GH}$ than to $\\overline{EF}$, and $D$ is closer to $\\overline{FG}$ than to $\\overline{EH}$, as shown. Triangles $\\triangle DGF$ and $\\triangle CHG$ have equal areas. The area of rectangle $EFGH$ is $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m + n$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n* \\(O\\) be the centre of \\(\\omega _2\\) (radius \\(15\\)),\n* \\(A\\) be the centre of \\(\\omega _1\\) (radius \\(6\\)),\n* \\(B\\) the point where the two circles are internally tangent,\n* \\(C\\) the antipode of \\(B\\) on \\(\\omega_2\\) (\\(BC\\) is a diameter),\n* \\(D\\) the point on \\(\\omega _2\\) with \\(AD\\perp BC\\).\n\n--------------------------------------------------------------------\n### 1.  Choose coordinates  \n\nPlace \\(O\\) at the origin and let the diameter \\(BC\\) be horizontal.\n\n\\[\nB=(15,0),\\qquad C=(-15,0)\n\\]\n\nSince \\(OA=15-6=9\\) and \\(A\\) lies on \\(OB\\),\n\n\\[\nA=(9,0).\n\\]\n\nThe line \\(AD\\) is perpendicular to the horizontal line \\(BC\\), so \\(AD\\) is the\nvertical line through \\(A\\); intersecting \\(\\omega_2\\) gives\n\n\\[\nD=(9,12)\\quad\\text{or}\\quad D=(9,-12).\n\\]\n\nBecause the rectangle will be placed above the centre of \\(\\omega_1\\), we take  \n\n\\[\nD=(9,12).\n\\]\n\n--------------------------------------------------------------------\n### 2.  Describe the rectangle  \n\nSince the rectangle is **inscribed** in \\(\\omega_1\\), all four of its vertices lie on\n\\(\\omega_1\\).  \nLet the rectangle have centre at \\(A\\); because a rectangle\u2019s circum\u2011centre is\nthe intersection of its diagonals, the centre must be the centre of the\ncircumscribing circle \\(\\omega_1\\).\n\nLet  \n\n* half\u2011width \\(w\\) (distance from the centre to the right\u2013hand side),\n* half\u2011height \\(h\\) (distance from the centre to the top side).\n\nThen  \n\n\\[\n\\begin{aligned}\nx_R&amp;=9+w, &amp; x_L&amp;=9-w,\\\\\ny_T&amp;=h,   &amp; y_B&amp;=-h .\n\\end{aligned}\n\\]\n\nThe vertices are  \n\n\\[\n\\begin{aligned}\nE&amp;(x_R,y_B)=(9+w,-h),\\\\\nF&amp;(x_R,y_T)=(9+w, h),\\\\\nG&amp;(x_L,y_T)=(9-w, h),\\\\\nH&amp;(x_L,y_B)=(9-w,-h).\n\\end{aligned}\n\\]\n\nBecause the vertices lie on \\(\\omega_1\\) (radius \\(6\\)),\n\n\\[\nw^{2}+h^{2}=6^{2}=36\\tag{1}\n\\]\n\n--------------------------------------------------------------------\n### 3.  Use the area condition  \n\nThe problem states that  \n\n\\[\n\\text{Area}\\,\\triangle DGF=\\text{Area}\\,\\triangle CHG .\n\\]\n\n*Triangle \\(DGF\\).*  \nIts base is \\(GF\\) (the top side of the rectangle) of length \\(2w\\).  \nIts height is the vertical distance from \\(D\\) to the line \\(y=h\\):\n\\(\\;12-h\\). Hence  \n\n\\[\n[\\triangle DGF]=\\tfrac12(2w)(12-h)=w(12-h).\\tag{2}\n\\]\n\n*Triangle \\(CHG\\).*  \nIts base is \\(HG\\) (the left side) of length \\(2h\\).  \nThe distance from \\(C\\) to the vertical line \\(x=9-w\\) is\n\\((9-w)-(-15)=24-w\\). Therefore  \n\n\\[\n[\\triangle CHG]=\\tfrac12(2h)(24-w)=h(24-w).\\tag{3}\n\\]\n\nEquating (2) and (3),\n\n\\[\nw(12-h)=h(24-w).\\tag{4}\n\\]\n\nExpanding both sides gives  \n\n\\[\n12w-wh=24h-wh\\Longrightarrow 12w=24h\\Longrightarrow w=2h.\\tag{5}\n\\]\n\n--------------------------------------------------------------------\n### 4.  Solve for \\(w\\) and \\(h\\)\n\nSubstituting \\(w=2h\\) into (1):\n\n\\[\n(2h)^2+h^2=36\\quad\\Longrightarrow\\quad5h^{2}=36\\quad\\Longrightarrow\\quad\nh^{2}= \\frac{36}{5},\\qquad\nh=\\frac{6}{\\sqrt5}=\\frac{6\\sqrt5}{5}.\n\\]\n\nHence  \n\n\\[\nw=2h=\\frac{12}{\\sqrt5}= \\frac{12\\sqrt5}{5}.\n\\]\n\n--------------------------------------------------------------------\n### 5.  Area of the rectangle  \n\nThe rectangle\u2019s side lengths are \\(2w\\) and \\(2h\\), so its area is  \n\n\\[\n\\text{Area}= (2w)(2h)=4wh=4\\cdot(2h)h=8h^{2}\n          =8\\left(\\frac{36}{5}\\right)=\\frac{288}{5}.\n\\]\n\nThus the area is \\(\\displaystyle \\frac{288}{5}\\).\nThe numerator and denominator are relatively prime, so  \n\n\\[\nm=288,\\qquad n=5,\\qquad m+n=288+5=293.\n\\]\n\n--------------------------------------------------------------------\n\\[\n\\boxed{293}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 293</p>\n<p>Extracted Answer: 293</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nAlex divides a disk into four quadrants with two perpendicular diameters intersecting at the center of the disk. He draws 25 more line segments through the disk, drawing each segment by selecting two points at random on the perimeter of the disk in different quadrants and connecting those two points. Find the expected number of regions into which these 27 line segments divide the disk.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>**Step 1.  Regions created by chords**\n\nIf we start with a disc (one region) and draw a chord, the number of regions increases by  \n\n\\[\n\\text{(number of interior intersections created by the new chord)}+1 .\n\\]\n\nHence after drawing \\(k\\) chords the number of regions is  \n\n\\[\nR=1+k+I ,\n\\]\n\nwhere \\(I\\) is the total number of interior intersection points of the drawn chords (no three chords meet at a single interior point, which holds a.s. for random chords).\n\nIn our problem \\(k=27\\) (the two diameters plus the 25 random chords), so  \n\n\\[\nR=28+I .\n\\]\n\nThus we only need the expected value of \\(I\\).\n\n--------------------------------------------------------------------\n\n**Step 2.  Intersections involving the two fixed diameters**\n\nThe two diameters intersect at the centre, contributing a deterministic intersection  \n\n\\[\nI_{\\text{centre}}=1 .\n\\]\n\nA random chord intersects the **vertical** diameter iff its endpoints lie in opposite halves of the disc, i.e. one endpoint in \\(\\{Q_1,Q_4\\}\\) and the other in \\(\\{Q_2,Q_3\\}\\).  \nAmong the six possible unordered quadrant\u2011pairs for a chord, four satisfy this condition, so\n\n\\[\nP(\\text{vertical intersection})=\\frac{4}{6}=\\frac23 .\n\\]\n\nThe same reasoning holds for the **horizontal** diameter, giving  \n\n\\[\nP(\\text{horizontal intersection})=\\frac23 .\n\\]\n\nHence for the 25 random chords\n\n\\[\nE[I_{\\text{vert}}]=25\\cdot\\frac23=\\frac{50}{3},\\qquad   \nE[I_{\\text{horiz}}]=25\\cdot\\frac23=\\frac{50}{3}.\n\\]\n\n--------------------------------------------------------------------\n\n**Step 3.  Intersections among the 25 random chords**\n\nTwo random chords are independent.  \nEach chord chooses an unordered pair of distinct quadrants uniformly from the six possibilities  \n\n\\[\n\\{1,2\\},\\{2,3\\},\\{3,4\\},\\{4,1\\} \\ (\\text{adjacent}),\\qquad\n\\{1,3\\},\\{2,4\\}\\ (\\text{opposite}).\n\\]\n\nLet the unordered pairs be \\(S\\) and \\(T\\).  \nTheir intersection size can be\n\n* **2** (the same pair) \u2013 probability \\(1/6\\);\n* **1** (they share exactly one quadrant) \u2013 probability \\(2/3\\);\n* **0** (disjoint) \u2013 probability \\(1/6\\).\n\nThe disjoint case splits further:\n\n* Adjacent\u2013adjacent (e.g. \\(\\{1,2\\}\\) with \\(\\{3,4\\}\\)) \u2013 chords never intersect.\n* Opposite\u2013opposite (e.g. \\(\\{1,3\\}\\) with \\(\\{2,4\\}\\)) \u2013 chords always intersect.\n\nAmong the three unordered disjoint pairs, two are adjacent\u2013adjacent and one is opposite\u2013opposite; hence for ordered pairs\n\n\\[\nP(\\text{disjoint, intersect})=\\frac{2}{36}=\\frac1{18},\\qquad\nP(\\text{disjoint, no intersect})=\\frac{4}{36}.\n\\]\n\nFor the other two situations one can check (by considering the relative order of the points inside the quadrants) that\n\n* If the two chords have the **same** unordered pair (adjacent or opposite), the probability they intersect is \\(\\tfrac12\\).\n* If they **share exactly one quadrant**, the probability they intersect is also \\(\\tfrac12\\).\n\nCollecting the contributions,\n\n\\[\n\\begin{aligned}\nP(\\text{intersection}) &amp;=\n\\underbrace{\\frac{6}{36}\\cdot\\frac12}_{\\text{same pair}}\n+\\underbrace{\\frac{24}{36}\\cdot\\frac12}_{\\text{share one quadrant}}\n+\\underbrace{\\frac{2}{36}\\cdot1}_{\\text{disjoint opposite}}\\\\[2mm]\n&amp;=\\frac{3}{36}+\\frac{12}{36}+\\frac{2}{36}\n=\\frac{17}{36}.\n\\end{aligned}\n\\]\n\nThus for any unordered pair of the 25 random chords\n\n\\[\np:=P(\\text{they intersect})=\\frac{17}{36}.\n\\]\n\nThere are \\(\\binom{25}{2}=300\\) such pairs, so\n\n\\[\nE[I_{\\text{random}}]=300\\cdot\\frac{17}{36}\n=\\frac{300}{36}\\cdot17\n=\\frac{25}{3}\\cdot17\n=\\frac{425}{3}.\n\\]\n\n--------------------------------------------------------------------\n\n**Step 4.  Expected total number of interior intersections**\n\n\\[\n\\begin{aligned}\nE[I] &amp;= I_{\\text{centre}}\n      +E[I_{\\text{vert}}]\n      +E[I_{\\text{horiz}}]\n      +E[I_{\\text{random}}]  \\\\[2mm]\n     &amp;=1+\\frac{50}{3}+\\frac{50}{3}+\\frac{425}{3} \\\\[2mm]\n     &amp;=1+\\frac{525}{3}=1+175=176 .\n\\end{aligned}\n\\]\n\n--------------------------------------------------------------------\n\n**Step 5.  Expected number of regions**\n\n\\[\nE[R]=28+E[I]=28+176=204 .\n\\]\n\n--------------------------------------------------------------------\n\n\\[\n\\boxed{204}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 204</p>\n<p>Extracted Answer: 204</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet the sequence of rationals $ x_1, x_2, \\ldots $ be defined such that $ x_1 = \\frac{25}{11} $ and\n$ x_{k+1} = \\frac{1}{3} \\left( x_k + \\frac{1}{x_k} - 1 \\right). $\n$ x_{2025} $ can be expressed as $ \\frac{m}{n} $ for relatively prime positive integers $ m $ and $ n $. Find the remainder when $ m + n $ is divided by 1000.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>**Solution Outline**\n\n1.  Transform the recurrence for \\(x_k\\) into a simpler one.\n\n   Define  \n\n   \\[\n   w_k=\\frac{x_k-1}{x_k+1}\\quad\\Longleftrightarrow\\quad \n   x_k=\\frac{1+w_k}{1-w_k}.\n   \\]\n\n   Substituting in  \n\n   \\[\n   x_{k+1}= \\frac13\\Bigl(x_k+\\frac1{x_k}-1\\Bigr)\n   \\]\n\n   gives after simplification  \n\n   \\[\n   w_{k+1}= \\frac{3w_k^2-1}{2}. \\tag{1}\n   \\]\n\n   The initial value is  \n\n   \\[\n   w_1=\\frac{25/11-1}{25/11+1}=\\frac{7}{18}.\n   \\]\n\n2.  Write \\(w_k=\\dfrac{a_k}{b_k}\\) in lowest terms\n   (\\(a_k\\) odd, \\(b_k\\) even).  \n\n   From (1),\n\n   \\[\n   w_{k+1}= \\frac{3a_k^2-b_k^2}{2b_k^2}.\n   \\]\n\n   Because \\(a_k\\) is not divisible by\u202f3, the numerator is always\n   \\(\\equiv 3\\pmod 9\\); hence it contains exactly one factor\u202f3.\n   After canceling this factor we obtain\n\n   \\[\n   a_{k+1}= \\frac{3a_k^2-b_k^2}{3},\\qquad\n   b_{k+1}= \\frac{2b_k^2}{3}.\n   \\tag{2}\n   \\]\n\n   Consequently  \n\n   \\[\n   b_{k+1}= \\frac{2}{3}b_k^{\\,2}. \\tag{3}\n   \\]\n\n3.  Determine a closed form for \\(b_k\\).\n\n   Write \\(b_k=2^{\\alpha_k}3^{\\beta_k}\\).\n   From (3)\n\n   \\[\n   2^{\\alpha_{k+1}}3^{\\beta_{k+1}}\n   =\\frac{2}{3}\\bigl(2^{\\alpha_k}3^{\\beta_k}\\bigr)^2\n   =2^{2\\alpha_k+1}3^{2\\beta_k-1},\n   \\]\n\n   whence  \n\n   \\[\n   \\alpha_{k+1}=2\\alpha_k+1,\\qquad\n   \\beta_{k+1}=2\\beta_k-1,\n   \\]\n   with \\(\\alpha_1=1,\\ \\beta_1=2\\).\n\n   Solving these linear recurrences gives  \n\n   \\[\n   \\alpha_k = 2^{\\,k}-1,\\qquad\n   \\beta_k = 2^{\\,k-1}+1 .\n   \\]\n\n   Therefore  \n\n   \\[\n   b_k = 2^{\\,2^{k}-1}\\,3^{\\,2^{k-1}+1}. \\tag{4}\n   \\]\n\n4.  Recover \\(x_k\\) from \\(w_k\\).\n\n   Since \\(x_k=\\dfrac{1+w_k}{1-w_k}\\) and \\(w_k=\\dfrac{a_k}{b_k}\\),\n\n   \\[\n   x_k=\\frac{b_k+a_k}{\\,b_k-a_k\\,}= \\frac{m_k}{n_k},\n   \\]\n   where \\(m_k=b_k+a_k,\\ n_k=b_k-a_k\\).  \n   Because \\(a_k\\) is odd and \\(b_k\\) is even, \\(m_k\\) and \\(n_k\\) are odd,\n   so \\(\\gcd(m_k,n_k)=1\\).\n\n   Hence\n\n   \\[\n   m_k+n_k = (b_k+a_k)+(b_k-a_k)=2b_k.\n   \\]\n\n5.  Compute \\(m_{2025}+n_{2025}\\pmod{1000}\\).\n\n   From (4),\n\n   \\[\n   b_{2025}=2^{\\,2^{2025}-1}\\,3^{\\,2^{2024}+1},\n   \\qquad\n   m_{2025}+n_{2025}=2b_{2025}\n   =2^{\\,2^{2025}}\\,3^{\\,2^{2024}+1}.\n   \\]\n\n   We need this value modulo \\(1000=2^3\\cdot5^3\\).\n\n   *Modulo\u202f8:* the exponent of\u202f2 is at least\u202f3, so the whole product\n   is \\(0\\pmod8\\).\n\n   *Modulo\u202f125:* use Euler\u2019s theorem (\\(\\phi(125)=100\\)):\n   \\[\n   2^{2^{2025}}\\equiv2^{\\,32}\\pmod{125},\\qquad\n   3^{2^{2024}+1}\\equiv3^{\\,17}\\pmod{125},\n   \\]\n   because \\(2^{2025}\\equiv32\\) and \\(2^{2024}+1\\equiv17\\pmod{100}\\).\n\n   Computing,\n   \\[\n   2^{32}\\equiv46,\\qquad 3^{17}\\equiv38\\pmod{125},\n   \\]\n   so\n   \\[\n   2^{2^{2025}}3^{2^{2024}+1}\\equiv46\\cdot38\\equiv123\\pmod{125}.\n   \\]\n\n   Solve the simultaneous congruences\n   \\[\n   X\\equiv0\\pmod8,\\qquad X\\equiv123\\pmod{125}.\n   \\]\n   Writing \\(X=125a+123\\) and using \\(125\\equiv5\\pmod8\\) gives\n   \\(5a+3\\equiv0\\pmod8\\Rightarrow a\\equiv1\\pmod8\\).\n   Hence \\(X=125\\cdot1+123=248\\).\n\n   Therefore  \n\n   \\[\n   m_{2025}+n_{2025}\\equiv\\boxed{248}\\pmod{1000}.\n   \\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 248</p>\n<p>Extracted Answer: 248</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThere are $ n $ values of $ x $ in the interval $ 0 &lt; x &lt; 2\\pi $ where $ f(x) = \\sin(7\\pi \\cdot \\sin(5x)) = 0 $. For $ t $ of these $ n $ values of $ x $, the graph of $ y = f(x) $ is tangent to the $ x $-axis. Find $ n + t $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>\\[\nf(x)=\\sin\\bigl(7\\pi\\sin (5x)\\bigr)\n\\]\n\nThe zeros of \\(f\\) occur when the inner sine gives an integer multiple of \\(\\pi\\):\n\n\\[\n\\sin\\bigl(7\\pi\\sin (5x)\\bigr)=0\\Longleftrightarrow 7\\pi\\sin(5x)=k\\pi\n\\Longleftrightarrow \\sin(5x)=\\frac{k}{7},\n\\qquad k\\in\\mathbb Z .\n\\]\n\nBecause \\(\\sin(5x)\\in[-1,1]\\), \\(|k|\\le7\\); thus \\(k=-7,-6,\\dots ,6,7\\).\n\n---\n\n### 1.  Counting the zeros  \n\nSet \\(\\theta =5x\\).  \nWhen \\(x\\in(0,2\\pi)\\) we have \\(\\theta\\in(0,10\\pi)\\).\n\nFor each admissible integer \\(k\\) we need the number of solutions of  \n\n\\[\n\\sin\\theta=\\frac{k}{7},\\qquad \\theta\\in(0,10\\pi).\n\\]\n\n* **\\(k=0\\):** \\(\\sin\\theta=0\\Rightarrow\\theta=n\\pi\\).  \n  Inside \\((0,10\\pi)\\) we have \\(n=1,2,\\ldots ,9\\) \u2192 **9 solutions**.\n\n* **\\(k=\\pm 7\\):** \\(\\sin\\theta=\\pm1\\).  \n  \\(\\sin\\theta=1\\) gives \\(\\theta=\\dfrac{\\pi}{2}+2\\pi n\\);  \n  \\(\\sin\\theta=-1\\) gives \\(\\theta=\\dfrac{3\\pi}{2}+2\\pi n\\).  \n  For \\(0&lt;\\theta&lt;10\\pi\\) each yields \\(n=0,1,2,3,4\\) \u2192 **5 solutions** for \\(k=7\\) and **5** for \\(k=-7\\).\n\n* **\\(k=\\pm1,\\pm2,\\dots ,\\pm6\\):** \\(|k|&lt;7\\) so \\(-1&lt;k/7&lt;1\\) and \\(\\neq0\\).  \n  In each full period \\([0,2\\pi]\\) the equation \\(\\sin\\theta=c\\) (\\(|c|&lt;1\\)) has two solutions.  \n  The interval \\((0,10\\pi)\\) contains five full periods, hence **\\(5\\times2=10\\) solutions** for each of these 12 values of \\(k\\).\n\nSumming all contributions  \n\n\\[\n\\begin{aligned}\nn &amp;=\\underbrace{9}_{k=0}\n   +\\underbrace{5+5}_{k=\\pm7}\n   +\\underbrace{12\\times10}_{k=\\pm1,\\dots,\\pm6}\\\\[2mm]\n  &amp;=9+10+120 = 139 .\n\\end{aligned}\n\\]\n\nThus there are \\(\\boxed{139}\\) zeros of \\(f\\) in \\((0,2\\pi)\\).\n\n---\n\n### 2.  Zeros where the graph is tangent to the \\(x\\)-axis  \n\nA point where the graph touches the \\(x\\)-axis must satisfy  \n\n\\[\nf(x)=0\\quad\\text{and}\\quad f&#39;(x)=0.\n\\]\n\nFrom \\(f(x)=0\\) we have \\(\\sin(5x)=k/7\\) as above.  \nCompute the derivative:\n\n\\[\n\\begin{aligned}\nf&#39;(x) &amp;=\\cos\\bigl(7\\pi\\sin(5x)\\bigr)\\cdot 7\\pi\\cdot 5\\cos(5x)   \\\\\n      &amp;=35\\pi\\cos\\bigl(7\\pi\\sin(5x)\\bigr)\\cos(5x).\n\\end{aligned}\n\\]\n\nThus \\(f&#39;(x)=0\\) iff \\(\\cos(5x)=0\\) (the factor \\(\\cos\\bigl(7\\pi\\sin(5x)\\bigr)\\) never vanishes at a zero, because\n\\(\\cos(k\\pi)=\\pm1\\)).  \n\n\\[\n\\cos(5x)=0\\Longrightarrow 5x=\\frac{\\pi}{2}+n\\pi\\quad\\Longrightarrow\\quad\\sin(5x)=\\pm1.\n\\]\n\nHence the tangential zeros correspond exactly to the solutions of \\(\\sin(5x)=\\pm1\\), i.e. the cases \\(k=\\pm7\\).\n\nWe already counted these:  \n\n* \\(\\sin(5x)=1\\) gives \\(5\\) solutions,\n* \\(\\sin(5x)=-1\\) gives \\(5\\) solutions.\n\nTherefore  \n\n\\[\nt = 5+5 = 10 .\n\\]\n\n(Indeed, at these points \\(f&#39;(x)=0\\) and \\(f&#39;&#39;(x)\\neq0\\), so the graph just touches the axis.)\n\n---\n\n### 3.  Required sum  \n\n\\[\nn+t = 139 + 10 = \\boxed{149}.\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 149</p>\n<p>Extracted Answer: 149</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nFrom an unlimited supply of 1-cent coins, 10-cent coins, and 25-cent coins, Silas wants to find a collection of coins that has a total value of $ N $ cents, where $ N $ is a positive integer. He uses the so-called **greedy algorithm**, successively choosing the coin of greatest value that does not cause the value of his collection to exceed $ N $. For example, to get 42 cents, Silas will choose a 25-cent coin, then a 10-cent coin, then 7 1-cent coins. However, this collection of 9 coins uses more coins than necessary to get a total of 42 cents; indeed, choosing 4 10-cent coins and 2 1-cent coins achieves the same total value with only 6 coins.\n\nIn general, the greedy algorithm succeeds for a given $ N $ if no other collection of 1-cent, 10-cent, and 25-cent coins gives a total value of $ N $ cents using strictly fewer coins than the collection given by the greedy algorithm. Find the number of values of $ N $ between 1 and 1000 inclusive for which the greedy algorithm succeeds.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n\\[\nN=25q+r ,\\qquad 0\\le r&lt;25 .\n\\]\n\nThe greedy algorithm first takes \\(q\\) coins of 25\u202f\u00a2, then  \n\\(t=\\big\\lfloor r/10\\big\\rfloor\\) coins of 10\u202f\u00a2 and finally  \n\\(s=r-10t\\) pennies.  \n\n\\[\n\\text{Greedy coins}=C_g(N)=q+t+s.\n\\]\n\n---\n\n### 1.  What is an optimal representation?\n\nIf a representation uses \\(a\\) 25\u2011cent coins, \\(b\\) 10\u2011cent coins and \\(c\\) pennies, then  \n\n\\[\n25a+10b+c=N,\\qquad a,b,c\\ge0,\n\\]\nand the number of coins is  \n\n\\[\nC= a+b+c = N-(24a+9b).\n\\]\n\nThus **minimising the number of coins is equivalent to maximising**  \n\n\\[\nP=24a+9b \\qquad\\text{subject to}\\qquad 25a+10b\\le N .\n\\]\n\nThe \u201cprofit\u2019\u2019 per cent is larger for a 25\u2011cent coin \\((24/25)\\) than for a 10\u2011cent coin \\((9/10)\\); therefore an optimal solution will use as many 25\u2011cent coins as possible unless removing a 25\u2011cent coin allows us to add enough 10\u2011cent coins to increase the profit.\n\n---\n\n### 2.  Effect of removing \\(k\\) quarters\n\nLet us replace \\(k\\) quarters by 10\u2011cent coins.  \nWrite \\(r=10u+v\\;(0\\le v\\le 9)\\).  \nAfter removing \\(k\\) quarters, the remainder becomes  \n\n\\[\nR=r+25k=10u+v+25k .\n\\]\n\nThe maximal number of dimes that can be added is  \n\n\\[\nb&#39;=\\big\\lfloor \\frac{R}{10}\\big\\rfloor\n   =u+ \\big\\lfloor 2.5k+\\tfrac{v}{10}\\big\\rfloor .\n\\]\n\nThe change in profit is\n\n\\[\n\\Delta P\n=-24k+9\\big(b&#39;-\\big\\lfloor r/10\\big\\rfloor\\big)\n=-6k+9\\Big\\lfloor\\frac{k}{2}\\Big\\rfloor+9\\delta ,\n\\]\n\nwhere  \n\n\\[\n\\delta=\n\\begin{cases}\n1 &amp;\\text{if }k\\text{ is odd and }v\\ge5,\\\\\n0 &amp;\\text{otherwise.}\n\\end{cases}\n\\]\n\n*If \\(k\\) is even*, \\(\\Delta P=-3k/2&lt;0\\); the profit never increases.  \n\n*If \\(k\\) is odd*, write \\(k=2m+1\\). Then  \n\n\\[\n\\Delta P=9\\delta-(3m+6).\n\\]\n\nThe only way \\(\\Delta P&gt;0\\) is when \\(m=0\\) (i.e. \\(k=1\\)) and \\(\\delta=1\\),\nwhich occurs exactly when  \n\n\\[\nv=r\\bmod 10\\ge5 .\n\\]\n\nHence **the greedy algorithm fails precisely when**\n\\[\nN\\ge 25\\quad\\text{and}\\quad (N\\bmod 25)\\bmod 10\\ge5.\n\\]\n\nEquivalently, the \u201cbad\u2019\u2019 remainders (after taking as many quarters as possible) are  \n\n\\[\nr\\in\\{5,6,7,8,9,15,16,17,18,19\\}.\n\\]\n\nIn each block of 25 consecutive integers there are 10 such remainders.\n\n---\n\n### 3.  Counting the failures between 1 and 1000\n\nThe interval \\([25,1000]\\) contains \\(1000-24=976\\) integers.\nFrom 25 onward the numbers are grouped into blocks  \n\n\\[\n25\\!-\\!49,\\;50\\!-\\!74,\\;\\dots,\\;975\\!-\\!999 .\n\\]\n\nThere are \\(39\\) full blocks (the block \\(25\\!-\\!49\\) up to \\(975\\!-\\!999\\)).\nEach block contributes exactly \\(10\\) failures, so\n\n\\[\n\\#\\text{failures}=39\\times10=390 .\n\\]\n\nNumbers \\(1\\) through \\(24\\) are never failures (they contain no quarters).\n\nThus the number of successes is  \n\n\\[\n1000-390=610 .\n\\]\n\n---\n\n\\[\n\\boxed{610}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 610</p>\n<p>Extracted Answer: 610</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $ S $ be the set of vertices of a regular 24-gon. Find the number of ways to draw 12 segments of equal lengths so that each vertex in $ S $ is an endpoint of exactly one of the 12 segments.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>In a regular \\(24\\)-gon label the vertices \\(0,1,\\dots ,23\\) clockwise.  \nIf two vertices differ by \\(k\\) (mod \\(24\\)), the chord joining them has length that depends only on  \n\n\\[\ns=\\min (k,24-k)\\qquad (1\\le s\\le 12).\n\\]\n\nThus there are \\(12\\) possible lengths, one for each \\(s=1,2,\\dots ,12\\).\n\n--------------------------------------------------------------------\n### 1.  The graph of chords of a fixed length  \n\nFix a value \\(s\\).  The set of all chords of that length is the edge\u2011set of the **circulant graph**\n\\[\nG_s=\\{\\,\\{i,i+s\\}\\mid i=0,1,\\dots ,23\\,\\},\n\\]\nwhere the addition is taken modulo \\(24\\).\n\nLet \\(g=\\gcd(s,24)\\).  Adding \\(s\\) repeatedly splits the vertex set into \\(g\\) cycles,\neach of length  \n\n\\[\nL=\\frac{24}{g}.\n\\]\n\nSo \\(G_s\\) is a disjoint union of \\(g\\) cycles \\(C_L\\).\n\n--------------------------------------------------------------------\n### 2.  When can a perfect matching exist?\n\nA perfect matching (a set of \\(12\\) disjoint edges covering all vertices) can exist only if\nevery component cycle has even length, i.e. \\(L\\) is even.\nSince \\(L=24/g\\), this is equivalent to \\(g\\mid 12\\).\n\n*If \\(g\\mid 12\\) and \\(L\\ge 4\\)*, each even cycle \\(C_L\\) has exactly **2** perfect\nmatchings (choose alternating edges).  \n*If \\(L=2\\)* (the case \\(s=12\\)), each component is a single edge and contributes only **1** matching.\n\nThe only step for which \\(g\\nmid 12\\) is \\(s=8\\) (here \\(g=8\\) and the components are 3\u2011cycles),\nso no perfect matching exists for \\(s=8\\).\n\n--------------------------------------------------------------------\n### 3.  Number of matchings for each possible length\n\n\\[\n\\begin{array}{c|c|c|c}\ns &amp; g=\\gcd(s,24) &amp; L=24/g &amp; \\#\\text{ matchings}\\\\ \\hline\n1 &amp;1 &amp;24 &amp;2\\\\\n2 &amp;2 &amp;12 &amp;2^{2}=4\\\\\n3 &amp;3 &amp; 8 &amp;2^{3}=8\\\\\n4 &amp;4 &amp; 6 &amp;2^{4}=16\\\\\n5 &amp;1 &amp;24 &amp;2\\\\\n6 &amp;6 &amp; 4 &amp;2^{6}=64\\\\\n7 &amp;1 &amp;24 &amp;2\\\\\n8 &amp;8 &amp; 3 &amp;0\\\\\n9 &amp;3 &amp; 8 &amp;2^{3}=8\\\\\n10&amp;2 &amp;12 &amp;2^{2}=4\\\\\n11&amp;1 &amp;24 &amp;2\\\\\n12&amp;12&amp; 2 &amp;1\n\\end{array}\n\\]\n\n--------------------------------------------------------------------\n### 4.  Total number of ways\n\nAdd the numbers for all admissible lengths (all \\(s\\) except \\(s=8\\)):\n\n\\[\n\\begin{aligned}\n\\text{Total}&amp;=2+4+8+16+2+64+2+8+4+2+1\\\\\n&amp;=113 .\n\\end{aligned}\n\\]\n\n--------------------------------------------------------------------\n\\[\n\\boxed{113}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 113</p>\n<p>Extracted Answer: 113</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nSixteen chairs are arranged in a row. Eight people each select a chair in which to sit so that no person sits next to two other people. Let $ N $ be the number of subsets of 16 chairs that could be selected. Find the remainder when $ N $ is divided by 1000.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>The chairs can be represented by a binary string of length\u202f16, where a \\(1\\) means the chair is taken.  \nWe need strings with exactly eight\u202f\\(1\\)\u2019s and with **no three consecutive \\(1\\)\u2019s** (otherwise the middle person would sit next to two others).\n\n---\n\n### Counting by blocks\n\nA valid string consists of blocks of consecutive \\(1\\)\u2019s of length\u202f1 or\u202f2, separated by at least one \\(0\\).\n\nLet  \n\n* \\(t\\) = number of blocks of length\u202f2,  \n* \\(b\\) = total number of blocks.  \n\nSince each block contributes at least one \\(1\\),\n\n\\[\n\\underbrace{(b-t)}_{\\text{blocks of length 1}}+2t=8\\quad\\Longrightarrow\\quad b+ t=8,\\; b=8-t .\n\\]\n\nSo \\(t=0,1,2,3,4\\).\n\nFor a fixed \\(t\\):\n* Choose which of the \\(b\\) blocks are the length\u20112 ones: \\(\\displaystyle\\binom{b}{t}=\\binom{8-t}{t}\\).\n* There are \\(8-8=8\\) empty chairs; let \\(z=8\\).  \n  The \\(b+1\\) gaps (including the two ends) must contain these zeros, with at least one zero in each interior gap.  \n  After placing one zero in each of the \\(b-1\\) interior gaps, we have \\(z-(b-1)=9-b\\) zeros left to distribute freely among the \\(b+1\\) gaps.  \n  The number of ways is \\(\\displaystyle\\binom{9-b}{b}=\\binom{9}{b}\\).\n\nHence for each \\(t\\),\n\n\\[\nN_t=\\binom{8-t}{t}\\binom{9}{8-t}.\n\\]\n\nSumming over \\(t=0\\) to \\(4\\):\n\n\\[\n\\begin{aligned}\nN &amp;=\\binom{8}{0}\\binom{9}{8}\n   +\\binom{7}{1}\\binom{9}{7}\n   +\\binom{6}{2}\\binom{9}{6}\n   +\\binom{5}{3}\\binom{9}{5}\n   +\\binom{4}{4}\\binom{9}{4} \\\\[2mm]\n  &amp;=1\\cdot9+7\\cdot36+15\\cdot84+10\\cdot126+1\\cdot126\\\\\n  &amp;=9+252+1260+1260+126\\\\\n  &amp;=2907 .\n\\end{aligned}\n\\]\n\n---\n\n### Modulo\u202f1000\n\n\\[\n2907 \\equiv 907 \\pmod{1000}.\n\\]\n\n---\n\n\\[\n\\boxed{907}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 907</p>\n<p>Extracted Answer: 907</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $ A_1A_2 \\ldots A_{11} $ be an 11-sided non-convex simple polygon with the following properties:\n* The area of $ A_iA_1A_{i+1} $ is 1 for each $ 2 \\leq i \\leq 10 $,\n* $ \\cos(\\angle A_iA_1A_{i+1}) = \\frac{12}{13} $ for each $ 2 \\leq i \\leq 10 $,\n* The perimeter of $ A_1A_2 \\ldots A_{11} $ is 20.\nIf $ A_1A_2 + A_1A_{11} $ can be expressed as $ \\frac{m\\sqrt{n} - p}{q} $ for positive integers $ m, n, p, q $ with $ n $ squarefree and no prime divides all of $ m, p, q$, find $ m + n + p + q $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n\\[\nr_i=A_1A_i\\qquad (i=2,\\dots ,11),\\qquad \n\\theta=\\angle A_iA_1A_{i+1}.\n\\]\n\nFor each \\(i=2,\\dots ,10\\)\n\n\\[\n\\cos\\theta=\\frac{12}{13},\\qquad \n\\text{Area}(A_iA_1A_{i+1})=\\frac12 r_i r_{i+1}\\sin\\theta =1 .\n\\]\n\nSince \\(\\sin\\theta=\\sqrt{1-\\cos ^2\\theta}=5/13\\),\n\n\\[\nr_i r_{i+1}= \\frac{2}{\\sin\\theta}= \\frac{2}{5/13}= \\frac{26}{5}\n=:k\\quad\\text{(constant)}.\n\\]\n\nThus  \n\n\\[\nr_{i+1}= \\frac{k}{r_i},\\qquad\\text{so}\\qquad r_{i+2}=r_i .\n\\]\n\nHence the distances from \\(A_1\\) alternate:\n\n\\[\nr_2=r_4=r_6=r_8=r_{10}=a,\\qquad  \nr_3=r_5=r_7=r_9=r_{11}=b,\n\\]\n\nwith  \n\n\\[\nab=k=\\frac{26}{5}.\n\\]\n\n--------------------------------------------------------------------\n### Length of a side \\(A_iA_{i+1}\\)\n\nFor any consecutive pair \\((a,b)\\),\n\n\\[\nA_iA_{i+1}=d=\\sqrt{a^2+b^2-2ab\\cos\\theta}\n           =\\sqrt{a^2+b^2-\\frac{24}{13}ab}.\n\\]\n\nLet  \n\n\\[\nx=a+b,\\qquad ab=k .\n\\]\n\nBecause \\(a^2+b^2=(a+b)^2-2ab=x^2-2k\\),\n\n\\[\nd=\\sqrt{x^2-2k-\\frac{24}{13}k}\n   =\\sqrt{x^2-\\frac{50}{13}\\,k}.\n\\]\n\nSince \\(k=\\dfrac{26}{5}\\),\n\n\\[\n\\frac{50}{13}k=\\frac{50}{13}\\cdot\\frac{26}{5}=20,\n\\qquad\\boxed{d=\\sqrt{x^2-20}} .\n\\]\n\n--------------------------------------------------------------------\n### Using the perimeter\n\nThe perimeter of the 11\u2011gon is\n\n\\[\na+b+9d = x+9\\sqrt{x^2-20}=20 .\n\\]\n\nSolve for \\(x\\) (note \\(x&gt;0\\) and \\(\\sqrt{x^2-20}\\ge0\\)):\n\n\\[\n9\\sqrt{x^2-20}=20-x\\quad\\Longrightarrow\\quad\n81(x^2-20)=(20-x)^2 .\n\\]\n\nThis gives  \n\n\\[\n80x^2+40x-2020=0\\;\\Longrightarrow\\;4x^2+2x-101=0.\n\\]\n\nHence  \n\n\\[\nx=\\frac{-2\\pm\\sqrt{4+1616}}{8}\n  =\\frac{-2\\pm18\\sqrt5}{8}\n  =\\frac{-1\\pm9\\sqrt5}{4}.\n\\]\n\nOnly the positive root satisfies the constraints, so  \n\n\\[\n\\boxed{x=a+b=\\frac{9\\sqrt5-1}{4}} .\n\\]\n\nThus\n\n\\[\nA_1A_2+A_1A_{11}=a+b=\\frac{9\\sqrt5-1}{4}\n    =\\frac{m\\sqrt n-p}{q},\n\\]\n\nwith \\(m=9,\\;n=5,\\;p=1,\\;q=4\\).\n\nAll conditions on \\(m,n,p,q\\) are met, and\n\n\\[\nm+n+p+q=9+5+1+4=19.\n\\]\n\n\\[\n\\boxed{19}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 19</p>\n<p>Extracted Answer: 19</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nFind the sum of all integer bases $b&gt;9$ for which $17_{b}$ is a divisor of $97_{b}$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>In base \\(b\\) the numbers are  \n\n\\[\n17_{b}=1\\cdot b+7=b+7, \\qquad 97_{b}=9\\cdot b+7=9b+7 .\n\\]\n\nWe need \\(b+7\\) to divide \\(9b+7\\).\n\n---\n\n### Find the divisibility condition  \n\n\\[\n9b+7 = 9(b+7)-56 .\n\\]\n\nThus the remainder when \\(9b+7\\) is divided by \\(b+7\\) is \\(-56\\).  \nHence \\(b+7\\) must divide \\(56\\):\n\n\\[\nb+7\\mid 56 .\n\\]\n\n---\n\n### Possible values of \\(b\\)\n\nThe positive divisors of \\(56\\) are  \n\n\\[\n1,\\;2,\\;4,\\;7,\\;8,\\;14,\\;28,\\;56 .\n\\]\n\nBecause the base must satisfy \\(b&gt;9\\), we have \\(b+7&gt;16\\).  \nThe divisors larger than \\(16\\) are \\(28\\) and \\(56\\).\n\n\\[\n\\begin{aligned}\nb+7&amp;=28 \\quad\\Longrightarrow\\quad b=21,\\\\[2pt]\nb+7&amp;=56 \\quad\\Longrightarrow\\quad b=49 .\n\\end{aligned}\n\\]\n\nBoth bases are greater than \\(9\\) and allow the digits \\(1,7,9\\).\n\n---\n\n### Sum of all such bases  \n\n\\[\n21+49 = 70.\n\\]\n\n\\[\n\\boxed{70}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 70</p>\n<p>Extracted Answer: 70</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThe 9 members of a baseball team went to an ice cream parlor after their game. Each player had a singlescoop cone of chocolate, vanilla, or strawberry ice cream. At least one player chose each flavor, and the number of players who chose chocolate was greater than the number of players who chose vanilla, which was greater than the number of players who chose strawberry. Let $N$ be the number of different assignments of flavors to players that meet these conditions. Find the remainder when $N$ is divided by 1000.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>The numbers of players picking chocolate, vanilla and strawberry are  \n\n\\[\na=\\#\\text{chocolate},\\qquad b=\\#\\text{vanilla},\\qquad c=\\#\\text{strawberry}\n\\]\n\nwith  \n\n\\[\na+b+c=9,\\qquad a&gt;b&gt;c\\ge1 .\n\\]\n\nHence \\((a,b,c)\\) must be three distinct positive integers whose sum is \\(9\\).  \nThe possible triples (written in decreasing order) are  \n\n\\[\n(6,2,1),\\;(5,3,1),\\;(4,3,2).\n\\]\n\nFor a fixed triple \\((a,b,c)\\) the players are distinct, so the number of assignments\nis the multinomial coefficient  \n\n\\[\n\\binom{9}{a,b,c}= \\frac{9!}{a!\\,b!\\,c!}.\n\\]\n\nCompute each term:\n\n\\[\n\\begin{aligned}\n(6,2,1):&amp;\\quad \\frac{9!}{6!\\,2!\\,1!}= \\frac{362880}{720\\cdot2}=252,\\\\[2mm]\n(5,3,1):&amp;\\quad \\frac{9!}{5!\\,3!\\,1!}= \\frac{362880}{120\\cdot6}=504,\\\\[2mm]\n(4,3,2):&amp;\\quad \\frac{9!}{4!\\,3!\\,2!}= \\frac{362880}{24\\cdot6\\cdot2}=1260.\n\\end{aligned}\n\\]\n\nAdd them:\n\n\\[\nN = 252+504+1260 = 2016.\n\\]\n\nThe remainder when \\(N\\) is divided by \\(1000\\) is  \n\n\\[\n2016 \\equiv 16 \\pmod{1000}.\n\\]\n\n\\[\n\\boxed{16}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 16</p>\n<p>Extracted Answer: 16</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $ \\triangle ABC $ be a right triangle with $ \\angle A = 90^\\circ $ and $ BC = 38 $. There exist points $ K $ and $ L $ inside the triangle such that $ AK = AL = BK = CL = KL = 14. $ The area of the quadrilateral $ BKLC $ can be expressed as $ n \\sqrt{3} $ for some positive integer $ n $. Find $ n $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n\\[\nA=(0,0),\\qquad B=(b,0),\\qquad C=(0,c)\n\\]\n\nso that \\(\\angle A=90^{\\circ}\\) and  \n\n\\[\nBC=\\sqrt{b^{2}+c^{2}}=38\\qquad\\Longrightarrow\\qquad b^{2}+c^{2}=38^{2}=1444 .\n\\tag{1}\n\\]\n\n--------------------------------------------------------------------\n### 1.  Determining the positions of \\(K\\) and \\(L\\)\n\nBecause  \n\n\\[\nAK=BK=14\n\\]\n\nthe point \\(K\\) lies at the intersection of the circles of radius \\(14\\) centred at\n\\(A\\) and \\(B\\).  \nIf \\(K=(x_{K},y_{K})\\),\n\n\\[\nx_{K}^{2}+y_{K}^{2}=196,\\qquad (x_{K}-b)^{2}+y_{K}^{2}=196 .\n\\]\n\nSubtracting gives  \n\n\\[\nb^{2}=2bx_{K}\\;\\Longrightarrow\\;x_{K}= \\frac{b}{2} .\n\\tag{2}\n\\]\n\nHence  \n\n\\[\ny_{K}^{2}=196-\\Bigl(\\frac{b}{2}\\Bigr)^{2}=196-\\frac{b^{2}}{4}.\n\\tag{3}\n\\]\n\nSimilarly, from  \n\n\\[\nAL=CL=14\n\\]\n\nthe point \\(L=(x_{L},y_{L})\\) satisfies\n\n\\[\ny_{L}= \\frac{c}{2},\\qquad \nx_{L}^{2}=196-\\Bigl(\\frac{c}{2}\\Bigr)^{2}=196-\\frac{c^{2}}{4}.\n\\tag{4}\n\\]\n\nThus, writing  \n\n\\[\nU=\\frac{b}{2},\\quad V=\\frac{c}{2},\n\\]\n\nwe have  \n\n\\[\nK=\\bigl(U,\\;\\sqrt{196-U^{2}}\\bigr),\\qquad \nL=\\bigl(\\sqrt{196-V^{2}},\\;V\\bigr),\n\\tag{5}\n\\]\n\nand from (1)  \n\n\\[\nU^{2}+V^{2}=361. \\tag{6}\n\\]\n\n--------------------------------------------------------------------\n### 2.  Using the condition \\(KL=14\\)\n\nFrom (5),\n\n\\[\n\\bigl(U-\\sqrt{196-V^{2}}\\bigr)^{2}\n+\\bigl(\\sqrt{196-U^{2}}-V\\bigr)^{2}=196 .\n\\]\n\nExpanding and simplifying with (6) gives\n\n\\[\nU\\sqrt{196-V^{2}}+V\\sqrt{196-U^{2}}=98 . \\tag{7}\n\\]\n\nLet  \n\n\\[\np=\\sqrt{196-V^{2}},\\qquad q=\\sqrt{196-U^{2}} .\n\\]\n\nThen  \n\n\\[\nU p+V q =98 ,\\qquad p^{2}+q^{2}=31 ,\n\\qquad U^{2}+V^{2}=361 . \\tag{8}\n\\]\n\nFrom (8) we obtain the product\n\n\\[\nU^{2}V^{2}=32448\\quad\\Longrightarrow\\quad UV=104\\sqrt3 . \\tag{9}\n\\]\n\nNow  \n\n\\[\n(U+V)^{2}=U^{2}+V^{2}+2UV=361+208\\sqrt3,\n\\]\n\\[\n(U-V)^{2}=U^{2}+V^{2}-2UV=361-208\\sqrt3 .\n\\]\n\nBoth expressions are perfect squares:\n\n\\[\n361+208\\sqrt3=(13+8\\sqrt3)^{2},\n\\qquad\n361-208\\sqrt3=(8\\sqrt3-13)^{2}.\n\\]\n\nHence  \n\n\\[\nU+V=13+8\\sqrt3,\\qquad\n|U-V|=8\\sqrt3-13 .\n\\]\n\nSince \\(U&gt;V\\), solving gives  \n\n\\[\nU=8\\sqrt3,\\qquad V=13 .\n\\]\n\nConsequently  \n\n\\[\nb=2U=16\\sqrt3,\\qquad c=2V=26 .\n\\]\n\n--------------------------------------------------------------------\n### 3.  Coordinates of \\(K\\) and \\(L\\)\n\nUsing (5) with the found \\(U,V\\):\n\n\\[\nK=\\bigl(8\\sqrt3,\\; \\sqrt{196-(8\\sqrt3)^{2}}\\bigr)\n   =\\bigl(8\\sqrt3,\\;2\\bigr),\n\\]\n\n\\[\nL=\\bigl(\\sqrt{196-13^{2}},\\;13\\bigr)\n   =\\bigl(3\\sqrt3,\\;13\\bigr).\n\\]\n\n--------------------------------------------------------------------\n### 4.  Area of quadrilateral \\(BKLC\\)\n\nThe vertices in order are  \n\n\\[\nB=(16\\sqrt3,0),\\ K=(8\\sqrt3,2),\\ L=(3\\sqrt3,13),\\ C=(0,26).\n\\]\n\nApplying the shoelace formula:\n\n\\[\n\\begin{aligned}\nS_{1}&amp;=x_{B}y_{K}+x_{K}y_{L}+x_{L}y_{C}+x_{C}y_{B}\\\\\n     &amp;= (16\\sqrt3)(2)+(8\\sqrt3)(13)+(3\\sqrt3)(26)+0\\\\\n     &amp;=32\\sqrt3+104\\sqrt3+78\\sqrt3=214\\sqrt3,\n\\\\[2mm]\nS_{2}&amp;=y_{B}x_{K}+y_{K}x_{L}+y_{L}x_{C}+y_{C}x_{B}\\\\\n     &amp;=0+2(3\\sqrt3)+13\\cdot0+26(16\\sqrt3)\\\\\n     &amp;=6\\sqrt3+416\\sqrt3=422\\sqrt3 .\n\\end{aligned}\n\\]\n\nHence  \n\n\\[\n\\text{Area}=\\frac12|S_{1}-S_{2}|\n           =\\frac12\\bigl|214\\sqrt3-422\\sqrt3\\bigr|\n           =\\frac12\\,(208\\sqrt3)=104\\sqrt3 .\n\\]\n\nThus the required area is \\(104\\sqrt3\\), i.e. \\(n=104\\).\n\n\\[\n\\boxed{104}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 104</p>\n<p>Extracted Answer: 104</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nFind the number of ordered pairs $(x,y)$, where both $x$ and $y$ are integers between $-100$ and $100$, inclusive, such that $12x^{2}-xy-6y^{2}=0$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>The equation  \n\n\\[\n12x^{2}-xy-6y^{2}=0\n\\]\n\ncan be factored over the integers.\n\n\\[\n\\begin{aligned}\n12x^{2}-xy-6y^{2}\n&amp;= (4x-3y)(3x+2y).\n\\end{aligned}\n\\]\n\nHence a pair \\((x,y)\\) satisfies the equation iff  \n\n\\[\n4x-3y=0 \\qquad\\text{or}\\qquad 3x+2y=0 .\n\\]\n\n---\n\n### 1.  Solutions of \\(4x-3y=0\\)\n\n\\[\n4x=3y \\Longrightarrow x=\\frac34y .\n\\]\n\nSince \\(x,y\\) are integers, \\(y\\) must be a multiple of \\(4\\); write \\(y=4k\\) \\((k\\in\\mathbb Z)\\).  \nThen \\(x=3k\\).\n\nBounds \\(-100\\le x,y\\le100\\) give  \n\n\\[\n|4k|\\le100\\ \\Longrightarrow\\ |k|\\le25 .\n\\]\n\nThus \\(k\\) can be any integer from \\(-25\\) to \\(25\\) inclusive \u2013 \\(51\\) possibilities.\n\n---\n\n### 2.  Solutions of \\(3x+2y=0\\)\n\n\\[\n3x=-2y \\Longrightarrow x=-\\frac{2}{3}y .\n\\]\n\nNow \\(y\\) must be a multiple of \\(3\\); write \\(y=3k\\).  \nThen \\(x=-2k\\).\n\nBounds give  \n\n\\[\n|3k|\\le100\\ \\Longrightarrow\\ |k|\\le\\Big\\lfloor\\frac{100}{3}\\Big\\rfloor=33 .\n\\]\n\nHence \\(k\\) can be any integer from \\(-33\\) to \\(33\\) inclusive \u2013 \\(67\\) possibilities.\n\n---\n\n### 3.  Removing double\u2011counted pair\n\nBoth families contain the pair \\((0,0)\\) (when \\(k=0\\)).  \nIt has been counted twice, so we subtract one.\n\n\\[\n\\text{Total solutions}=51+67-1=117 .\n\\]\n\nAll counted pairs satisfy \\(-100\\le x,y\\le100\\).\n\n\\[\n\\boxed{117}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 117</p>\n<p>Extracted Answer: 117</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nAn isosceles trapezoid has an inscribed circle tangent to each of its four sides. The radius of the circle is 3, and the area of the trapezoid is 72. Let the parallel sides of the trapezoid have lengths $r$ and $s$, with $r \\neq s$. Find $r^{2}+s^{2}$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let the trapezoid have parallel sides \\(r\\) and \\(s\\) (\\(r\\neq s\\)), equal legs of length \\(L\\), height \\(h\\), and incircle radius \\(R=3\\).\n\n---\n\n### 1.  Semiperimeter from the incircle\n\nFor any tangential quadrilateral,\n\\[\n\\text{Area}=R\\cdot s,\n\\]\nwhere \\(s\\) is the semiperimeter.  \nGiven \\(\\text{Area}=72\\) and \\(R=3\\),\n\n\\[\ns=\\frac{72}{3}=24,\n\\qquad\\text{so } r+s+2L=2s=48. \\tag{1}\n\\]\n\n---\n\n### 2.  Height of the trapezoid\n\nSince the incircle touches both parallel sides, the distance between them equals twice the radius:\n\n\\[\nh=2R=6.\n\\]\n\nThe area also equals \\(\\frac{1}{2}(r+s)h\\). Thus\n\n\\[\n72=\\frac{1}{2}(r+s)\\cdot6 \\Longrightarrow r+s=24. \\tag{2}\n\\]\n\nSubstituting (2) into (1) gives\n\n\\[\n24+2L=48\\Longrightarrow L=12. \\tag{3}\n\\]\n\n---\n\n### 3.  Relating the bases and the leg\n\nIn an isosceles trapezoid the horizontal projection of each leg is \\(\\dfrac{s-r}{2}\\).\nUsing the right triangle formed by a leg, the height, and this projection:\n\n\\[\n\\left(\\frac{s-r}{2}\\right)^2+h^2=L^2.\n\\]\n\nInsert \\(h=6\\) and \\(L=12\\):\n\n\\[\n\\left(\\frac{s-r}{2}\\right)^2+36=144\n\\;\\Longrightarrow\\;\n\\frac{(s-r)^2}{4}=108\n\\;\\Longrightarrow\\;\n(s-r)^2=432.\n\\]\n\nHence\n\n\\[\ns-r=12\\sqrt3. \\tag{4}\n\\]\n\n---\n\n### 4.  Solve for \\(r\\) and \\(s\\)\n\nFrom (2) and (4):\n\n\\[\n\\begin{cases}\nr+s=24,\\\\[2pt]\ns-r=12\\sqrt3,\n\\end{cases}\n\\qquad\\Longrightarrow\\qquad\ns=12+6\\sqrt3,\\;\\; r=12-6\\sqrt3.\n\\]\n\nBoth are positive and distinct, as required.\n\n---\n\n### 5.  Compute \\(r^{2}+s^{2}\\)\n\n\\[\n\\begin{aligned}\nr^{2}+s^{2}&amp;=(12-6\\sqrt3)^2+(12+6\\sqrt3)^2\\\\\n&amp;=2\\cdot12^{2}+2\\cdot(6\\sqrt3)^{2}\\\\\n&amp;=2\\cdot144+2\\cdot108\\\\\n&amp;=288+216\\\\\n&amp;=504.\n\\end{aligned}\n\\]\n\n---\n\n\\[\n\\boxed{504}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 504</p>\n<p>Extracted Answer: 504</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThere are $8!=40320$ eight-digit positive integers that use each of the digits $1,2,3,4,5,6,7,8$ exactly once. Let $N$ be the number of these integers that are divisible by 22. Find the difference between $N$ and 2025.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>For an \\(8\\)-digit number formed with the digits \\(1,2,\\dots ,8\\) each once we need\n\n* divisibility by \\(2\\)   \\(\\Longrightarrow\\) the units digit is even (\\(2,4,6,8\\));\n* divisibility by \\(11\\) \\(\\Longrightarrow\\) the alternating sum of its digits is a multiple of \\(11\\).\n\n---\n\n### 1.  Divisibility by \\(11\\)\n\nWrite the digits as \\(d_1d_2d_3d_4d_5d_6d_7d_8\\) ( \\(d_1\\) most significant).  \n\nThe test for \\(11\\) gives  \n\n\\[\n(d_1+d_3+d_5+d_7)-(d_2+d_4+d_6+d_8)\\equiv0\\pmod{11}.\n\\]\n\nLet  \n\n\\[\nO=d_1+d_3+d_5+d_7,\\qquad E=d_2+d_4+d_6+d_8 .\n\\]\n\nSince all eight digits are used once,  \n\n\\[\nO+E = 1+2+\\dots+8 = 36 .\n\\]\n\nThe condition \\(O-E\\equiv0\\pmod{11}\\) becomes  \n\n\\[\n2O\\equiv36\\pmod{11}\\quad\\Longrightarrow\\quad O\\equiv18\\equiv7\\pmod{11}.\n\\]\n\nThe sum of four distinct digits from \\(\\{1,\\dots ,8\\}\\) lies between \\(10\\) and \\(26\\); the only value congruent to \\(7\\pmod{11}\\) in that range is \\(18\\).  \nHence we must have  \n\n\\[\nO=E=18.\n\\]\n\nSo the four digits placed in the odd positions must sum to \\(18\\).\n\n---\n\n### 2.  Choosing the odd\u2013position digits\n\nWe need all \\(4\\)-element subsets of \\(\\{1,\\dots ,8\\}\\) whose sum is \\(18\\).\n\nListing them (in increasing order) gives\n\n\\[\n\\begin{aligned}\n&amp;\\{1,2,7,8\\},\\; \\{1,3,6,8\\},\\; \\{1,4,5,8\\},\\; \\{1,4,6,7\\},\\\\\n&amp;\\{2,3,5,8\\},\\; \\{2,3,6,7\\},\\; \\{2,4,5,7\\},\\; \\{3,4,5,6\\}.\n\\end{aligned}\n\\]\n\nThere are \\(8\\) such subsets.  \nEach of them contains exactly two even digits (the even digits are \\(2,4,6,8\\)). Consequently the complementary set (the digits placed in even positions) also contains exactly two evens.\n\n---\n\n### 3.  Forming the numbers\n\n*For a fixed subset* \\(S\\) (the odd\u2011position digits)\n\n* arrange its four digits among the odd places \\(1,3,5,7\\): \\(4!\\) ways;\n* the four remaining digits (the complement \\(T\\)) go to the even places \\(2,4,6,8\\).  \n  Since \\(T\\) contains two even digits, we may pick which even digit occupies the units place (position \\(8\\)) in \\(2\\) ways; the other three digits can be placed in \\(3!\\) ways.\n\nHence for each subset \\(S\\)\n\n\\[\n\\text{permutations}=4!\\times 2\\times3!=24\\times12=288 .\n\\]\n\nWith \\(8\\) possible subsets,\n\n\\[\nN=8\\times288=2304 .\n\\]\n\n(Equivalently, half of the \\(4608\\) numbers with \\(O=E=18\\) are even, giving the same result.)\n\n---\n\n### 4.  Required difference\n\n\\[\nN-2025 = 2304-2025 = 279.\n\\]\n\nThus the requested difference is  \n\n\\[\n\\boxed{279}.\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 279</p>\n<p>Extracted Answer: 279</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nSuppose $ \\triangle ABC $ has angles $ \\angle BAC = 84^\\circ $, $ \\angle ABC = 60^\\circ $, and $ \\angle ACB = 36^\\circ $. Let $ D, E, $ and $ F $ be the midpoints of sides $ \\overline{BC} $, $ \\overline{AC} $, and $ \\overline{AB} $, respectively. The circumcircle of $ \\triangle DEF $ intersects $ \\overline{BD} $, $ \\overline{AE} $, and $ \\overline{AF} $ at points $ G, H, $ and $ J $, respectively. The points $ G, D, E, H, J, $ and $ F $ divide the circumcircle of $ \\triangle DEF $ into six minor arcs, as shown. Find $ \\widehat{DE} + 2 \\cdot \\widehat{HJ} + 3 \\cdot \\widehat{FG} $, where the arcs are measured in degrees.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>We place \\(\\triangle ABC\\) on its circumcircle (radius\u00a01) with  \n\n\\[\nA=1,\\qquad B=e^{i2C},\\qquad C=e^{i(2C+2A)} .\n\\]\n\nThe orthocenter is  \n\n\\[\nH=a+b+c.\n\\]\n\nThe nine\u2011point circle is the image of the circumcircle under the homothety with centre \\(H\\) and factor \\(\\tfrac12\\); therefore for any point \\(X\\) on the nine\u2011point circle its image on the circumcircle is  \n\n\\[\nX&#39; = 2X-H .\n\\]\n\nApplying this to the six points on the nine\u2011point circle gives\n\n\\[\n\\begin{aligned}\nD&amp;\\mapsto -a,\\\\\nE&amp;\\mapsto -b,\\\\\nF&amp;\\mapsto -c,\\\\\nG&amp;\\mapsto A&#39; ,\\qquad A&#39; \\text{ is the second intersection of the altitude }AA_H\\text{ with the circumcircle},\\\\\nH&amp;\\mapsto B&#39; ,\\qquad B&#39;=-e^{i2A},\\\\\nJ&amp;\\mapsto C&#39; ,\\qquad C&#39;=-e^{-i2A}.\n\\end{aligned}\n\\]\n\nUsing \\(a=1,\\;b=e^{i2C},\\;c=e^{i(2C+2A)}\\) we obtain the central\nangles (measured from the positive \\(x\\)-axis) of the corresponding points:\n\n\\[\n\\begin{array}{c|c}\n\\text{Nine\u2011point point} &amp; \\text{Angle on the circumcircle}\\\\ \\hline\nD &amp; 180^\\circ\\\\\nE &amp; 180^\\circ+2C\\\\\nF &amp; 180^\\circ-2B\\\\\nG &amp; 180^\\circ+2A+4C\\\\\nH &amp; 180^\\circ+2A\\\\\nJ &amp; 180^\\circ-2A\n\\end{array}\n\\]\n\nBecause the homothety preserves directions from the centre, the\narc length on the nine\u2011point circle equals the corresponding central\nangle on the circumcircle.\n\nHence\n\n\\[\n\\begin{aligned}\n\\widehat{DE}&amp;=(180^\\circ+2C)-180^\\circ =2C,\\\\[2mm]\n\\widehat{HJ}&amp;=|\\, (180^\\circ+2A)-(180^\\circ-2A)\\,|=4A,\n\\end{aligned}\n\\]\n\nand the minor arc \\(HJ\\) is \\(360^\\circ-4A\\) (since \\(4A&gt;180^\\circ\\)).\nFinally\n\n\\[\n\\widehat{FG}=|(180^\\circ-2B)-(180^\\circ+2A+4C)|\n            =2C\\qquad(\\text{mod }360^\\circ).\n\\]\n\nThus\n\n\\[\n\\begin{aligned}\n\\widehat{DE}+2\\widehat{HJ}+3\\widehat{FG}\n&amp;=2C+2\\bigl(360^\\circ-4A\\bigr)+3\\,(2C) \\\\\n&amp;=720^\\circ-8A+8C\\\\\n&amp;=720^\\circ+8(C-A).\n\\end{aligned}\n\\]\n\nFor the given triangle \\(A=84^\\circ,\\;C=36^\\circ\\),\n\n\\[\n720^\\circ+8(36^\\circ-84^\\circ)=720^\\circ-384^\\circ=336^\\circ .\n\\]\n\n\\[\n\\boxed{336}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 336</p>\n<p>Extracted Answer: 336</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThere are exactly three positive real numbers $ k $ such that the function\n$ f(x) = \\frac{(x - 18)(x - 72)(x - 98)(x - k)}{x} $\ndefined over the positive real numbers achieves its minimum value at exactly two positive real numbers $ x $. Find the sum of these three values of $ k $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>The function  \n\n\\[\nf(x)=\\frac{(x-18)(x-72)(x-98)(x-k)}{x}, \\qquad x&gt;0,\n\\]\n\nhas zeros at \\(x=18,72,98,k\\) and \\(\\displaystyle\\lim_{x\\to0^+}f(x)=+\\infty\\),\n\\(\\displaystyle\\lim_{x\\to\\infty}f(x)=+\\infty\\).\nHence the graph of \\(f\\) starts at \\(+\\infty\\), descends to a negative\nvalue, comes back to zero, rises again, etc.; it has exactly **two**\nnegative intervals:\n\\[\n(r_1,r_2),\\qquad (r_3,r_4),\n\\]\nwhere \\(\\{r_1,r_2,r_3,r_4\\}=\\{18,72,98,k\\}\\) ordered increasingly.\nIn each negative interval there is a local (and global) minimum of \\(f\\).\n\nLet  \n\n\\[\ng(x)=(x-18)(x-72)(x-98)(x-k),\n\\qquad f(x)=\\frac{g(x)}{x}.\n\\]\n\nA point \\(x_0\\) where \\(f\\) has an extremum satisfies  \n\n\\[\nf&#39;(x_0)=0\\iff x_0g&#39;(x_0)-g(x_0)=0\\iff \n\\sum_{i=1}^{4}\\frac{1}{x_0-r_i}= \\frac1{x_0}.\n\\]\n\nGeometrically, if \\(m=f(x_0)\\) then the line \\(y=m x\\) is tangent to the\nquartic graph \\(y=g(x)\\) at \\(x_0\\):\n\\[\ng(x)-mx=0\\quad\\text{has a double root at }x_0 .\n\\]\n\nIf the global minimum of \\(f\\) is attained at **two** distinct points,\nthe line \\(y=m x\\) must be tangent to \\(g\\) at two distinct points\n\\(\\alpha,\\beta\\). Hence\n\n\\[\ng(x)-mx=(x-\\alpha)^2 (x-\\beta)^2 .\n\\tag{1}\n\\]\n\nWrite  \n\n\\[\n\\alpha+\\beta=p,\\qquad \\alpha\\beta =q,\\qquad m \\text{ (the slope)} .\n\\]\n\nExpanding (1) and comparing with \\(g(x)-mx=x^4-S_1x^3+S_2x^2-(S_3+m)x+S_4\\) gives  \n\n\\[\n\\begin{aligned}\nS_1 &amp;=2p,\\\\\nS_2 &amp;=p^{2}+2q,\\\\\nS_4 &amp;=q^{2},\\\\\nS_3+m &amp;=2pq,\n\\end{aligned}\n\\tag{2}\n\\]\n\nwhere for our roots  \n\n\\[\n\\begin{aligned}\nS_1&amp;=18+72+98+k=188+k,\\\\\nS_2&amp;=18\\cdot72+18\\cdot98+72\\cdot98+ (18+72+98)k\n     =10116+188k,\\\\\nS_3&amp;=18\\cdot72\\cdot98+ (18\\cdot72+18\\cdot98+72\\cdot98)k\n     =127008+10116k,\\\\\nS_4&amp;=18\\cdot72\\cdot98\\cdot k=127008\\,k .\n\\end{aligned}\n\\]\n\nFrom (2) we obtain  \n\n\\[\np=\\frac{188+k}{2},\\qquad q=\\sqrt{127008\\,k}=252\\sqrt{2k}.\n\\]\n\nUsing the second equation of (2),\n\n\\[\nS_2=p^{2}+2q,\n\\]\n\ngives the condition on \\(k\\):\n\n\\[\n\\frac{(188+k)^{2}}{4}+2\\sqrt{127008k}=10116+188k .\n\\tag{3}\n\\]\n\n---\n\n### Solving (3)\n\nPut \\(k=t^{2}\\;(t&gt;0)\\).  Since \\(\\sqrt{127008k}=252\\sqrt{2}\\,t\\),\n(3) becomes\n\n\\[\nt^{4}-376t^{2}+2016\\sqrt{2}\\,t-5120=0 .\n\\]\n\nFactoring,\n\n\\[\n(t^{2}+6\\sqrt{2}\\,t-320)(t^{2}-6\\sqrt{2}\\,t+16)=0 .\n\\]\n\nHence the positive solutions for \\(t\\) are\n\n\\[\nt=10\\sqrt2,\\qquad t=4\\sqrt2,\\qquad t=2\\sqrt2 .\n\\]\n\nConsequently\n\n\\[\nk=t^{2}=200,\\;32,\\;8 .\n\\]\n\n---\n\n### Verification\n\nFor each \\(k\\) the ordered roots of \\(g\\) are\n\n\\[\n\\begin{array}{c|c}\nk &amp; \\text{ordered roots }(r_1,r_2,r_3,r_4)\\\\ \\hline\n8  &amp; (8,18,72,98)\\\\\n32 &amp; (18,32,72,98)\\\\\n200&amp; (18,72,98,200)\n\\end{array}\n\\]\n\nUsing \\(p\\) and \\(q\\) we find the tangency points  \n\n\\[\n\\alpha,\\beta=\\frac{p\\pm\\sqrt{p^{2}-4q}}{2},\n\\]\n\nand they lie respectively in the intervals \\((r_1,r_2)\\) and\n\\((r_3,r_4)\\). Thus in each case the line \\(y=m x\\) is tangent to\n\\(g\\) at two points, giving exactly two distinct global minima of\n\\(f\\). No other \\(k&gt;0\\) satisfies (3); hence these are the only three\nvalues.\n\nFinally, the required sum is\n\n\\[\n8+32+200 = 240 .\n\\]\n\n\\[\n\\boxed{240}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 240</p>\n<p>Extracted Answer: 240</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $k$ be real numbers such that the system $|25+20i-z|=5$ and $|z-4-k|=|z-3i-k|$ has exactly one complex solution $z$. The sum of all possible values of $k$ can be written as $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$. Here $i=\\sqrt{-1}$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n\\[\nz=x+iy\\qquad (x,y\\in\\mathbb{R}).\n\\]\n\n---\n\n### 1.  The first equation \u2013 a circle  \n\n\\[\n|25+20i-z|=5 \\Longrightarrow (x-25)^2+(y-20)^2=5^2 .\n\\]\n\nThus the circle has centre  \n\n\\[\nC=(25,20),\\qquad \\text{radius } r=5 .\n\\]\n\n---\n\n### 2.  The second equation \u2013 a perpendicular bisector  \n\n\\[\n|z-(4+k)|=|z-(3i+k)|\n\\]\n\nwrites as  \n\n\\[\n(x-(k+4))^2+y^{2}=(x-k)^2+(y-3)^2 .\n\\]\n\nSimplifying,\n\n\\[\n-8x+6y+8k+7=0\\quad\\Longrightarrow\\quad 4x-3y-(4k+3.5)=0 .\n\\]\n\nHence the set of points satisfying the second condition is the line  \n\n\\[\nL:\\;4x-3y=4k+\\frac 72 .\n\\]\n\nThis is the perpendicular bisector of the segment joining  \n\\(A=(k+4,0)\\) and \\(B=(k,3)\\) (its slope is \\(4/3\\) for any \\(k\\)).\n\n---\n\n### 3.  One intersection  \\(\\iff\\)  tangency  \n\nThe system has exactly one solution precisely when the line \\(L\\) is tangent to the circle, i.e. when the distance from the centre \\(C\\) to \\(L\\) equals the radius \\(5\\).\n\nThe distance from \\((x_0,y_0)\\) to \\(Ax+By+C=0\\) is  \n\n\\[\n\\frac{|Ax_0+By_0+C|}{\\sqrt{A^2+B^2}} .\n\\]\n\nFor \\(C=(25,20)\\) and \\(L: 4x-3y-(4k+3.5)=0\\),\n\n\\[\nd=\\frac{|4\\cdot25-3\\cdot20-(4k+3.5)|}{\\sqrt{4^{2}+(-3)^{2}}}\n   =\\frac{|40-4k-3.5|}{5}\n   =\\frac{|36.5-4k|}{5}.\n\\]\n\nSet \\(d=r=5\\):\n\n\\[\n\\frac{|36.5-4k|}{5}=5\\quad\\Longrightarrow\\quad |36.5-4k|=25 .\n\\]\n\n---\n\n### 4.  Solving for \\(k\\)\n\n\\[\n\\begin{cases}\n36.5-4k=25 &amp;\\Longrightarrow\\;4k=11.5\\;\\Longrightarrow\\;k=\\dfrac{23}{8},\\\\[4pt]\n36.5-4k=-25 &amp;\\Longrightarrow\\;4k=61.5\\;\\Longrightarrow\\;k=\\dfrac{123}{8}.\n\\end{cases}\n\\]\n\nThus the possible real values of \\(k\\) are  \n\n\\[\nk_1=\\frac{23}{8},\\qquad k_2=\\frac{123}{8}.\n\\]\n\nBoth give a line tangent to the circle, so each yields exactly one solution \\(z\\).\n\n---\n\n### 5.  Sum of the possible \\(k\\)\u2019s  \n\n\\[\nk_1+k_2=\\frac{23+123}{8}=\\frac{146}{8}=\\frac{73}{4}.\n\\]\n\nWrite \\(\\frac{73}{4}\\) as \\(\\dfrac{m}{n}\\) with \\(\\gcd(m,n)=1\\); here \\(m=73,\\ n=4\\).\n\n\\[\nm+n=73+4=77.\n\\]\n\n\\[\n\\boxed{77}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 77</p>\n<p>Extracted Answer: 77</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet the sequence of rationals $ x_1, x_2, \\ldots $ be defined such that $ x_1 = \\frac{25}{11} $ and\n$ x_{k+1} = \\frac{1}{3} \\left( x_k + \\frac{1}{x_k} - 1 \\right). $\n$ x_{2025} $ can be expressed as $ \\frac{m}{n} $ for relatively prime positive integers $ m $ and $ n $. Find the remainder when $ m + n $ is divided by 1000.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>**Step 1.  Write the recurrence for the numerators and denominators**\n\nLet  \n\n\\[\nx_k=\\frac{a_k}{b_k}\\qquad (a_k,b_k\\in \\mathbb Z ,\\; \\gcd(a_k,b_k)=1).\n\\]\n\nFrom  \n\n\\[\nx_{k+1}= \\frac{1}{3}\\Bigl(x_k+\\frac1{x_k}-1\\Bigr)=\\frac{x_k^2-x_k+1}{3x_k},\n\\]\n\nwe obtain  \n\n\\[\na_{k+1}=a_k^2-a_kb_k+b_k^2,\\qquad   \nb_{k+1}=3a_kb_k,          \\tag{1}\n\\]\n\nwith \\(a_1=25,\\;b_1=11\\).\n\n--------------------------------------------------------------------\n\n**Step 2.  The common factor \\(3^{e_k}\\)**  \n\nWrite  \n\n\\[\na_k=3^{e_k}A_k,\\qquad b_k=3^{e_k}B_k,\\qquad \\gcd(A_k,B_k)=1 .\n\\]\n\nDividing (1) by the highest possible power of \\(3\\) shows that\n\\(e_{k+1}=2e_k+1\\) and that the reduced pair \\((A_k,B_k)\\) always satisfies  \n\n\\[\nA_k\\equiv1\\pmod3,\\qquad B_k\\equiv2\\pmod3 .\n\\]\n\nWith \\(e_1=0\\) we get  \n\n\\[\ne_k=2^{\\,k-1}-1 .\\tag{2}\n\\]\n\n--------------------------------------------------------------------\n\n**Step 3.  A very simple recurrence for the sum**\n\nLet  \n\n\\[\nS_k=a_k+b_k .\n\\]\n\nFrom (1)\n\n\\[\n\\begin{aligned}\nS_{k+1}&amp;=a_{k+1}+b_{k+1}\n       =(a_k^2-a_kb_k+b_k^2)+3a_kb_k   \\\\\n       &amp;=a_k^2+b_k^2+2a_kb_k=(a_k+b_k)^2=S_k^{\\,2}.\n\\end{aligned}\n\\]\n\nHence  \n\n\\[\nS_k=S_1^{\\,2^{\\,k-1}}=36^{\\,2^{\\,k-1}}. \\tag{3}\n\\]\n\n--------------------------------------------------------------------\n\n**Step 4.  The reduced numerator and denominator**\n\nSince the common factor is \\(3^{e_k}\\),\n\n\\[\n\\frac{a_k}{b_k}= \\frac{A_k}{B_k},\\qquad \nm=A_k,\\; n=B_k .\n\\]\n\nThus  \n\n\\[\nm+n=\\frac{a_k+b_k}{3^{e_k}}\n     =\\frac{36^{\\,2^{\\,k-1}}}{3^{\\,2^{\\,k-1}-1}}\n     =2^{\\,2^{\\,k}}\\;3^{\\,2^{\\,k-1}+1}. \\tag{4}\n\\]\n\n--------------------------------------------------------------------\n\n**Step 5.  Apply \\(k=2025\\)**  \n\nFrom (4),\n\n\\[\nm+n=2^{\\,2^{2025}}\\;3^{\\,2^{2024}+1}.\n\\]\n\nWe need this number modulo \\(1000\\).\n\n--------------------------------------------------------------------\n\n**Step 6.  Reduce modulo \\(8\\) and \\(125\\)**  \n\n*Modulo \\(8\\):*  \\(2^{\\ge3}\\equiv0\\pmod8\\); therefore  \n\n\\[\nm+n\\equiv0\\pmod8. \\tag{5}\n\\]\n\n*Modulo \\(125\\):*  Because \\(\\phi(125)=100\\),\n\n\\[\n2^{2^{2025}}\\equiv 2^{\\,2^{2025}\\bmod100},\n\\qquad\n3^{2^{2024}+1}\\equiv 3^{\\,(2^{2024}+1)\\bmod100}\\pmod{125}.\n\\]\n\nCompute the exponents.\n\n- \\(2^{2025}\\bmod100\\):  \n  \\(2^{2025}\\equiv32\\pmod{100}\\) (by CRT: \\(2^{2025}\\equiv0\\pmod4\\), \\(2^{2025}\\equiv7\\pmod{25}\\)).\n- \\(2^{2024}\\bmod100\\):  \n  \\(2^{2024}\\equiv16\\pmod{100}\\).\n\nHence  \n\n\\[\n2^{2^{2025}}\\equiv2^{32}\\equiv46\\pmod{125},\n\\qquad\n3^{2^{2024}+1}\\equiv3^{17}\\equiv38\\pmod{125}.\n\\]\n\nTherefore  \n\n\\[\nm+n\\equiv46\\cdot38\\equiv123\\pmod{125}. \\tag{6}\n\\]\n\n--------------------------------------------------------------------\n\n**Step 7.  Chinese Remainder Theorem**\n\nFind \\(N\\) such that  \n\n\\[\nN\\equiv0\\pmod8,\\qquad N\\equiv123\\pmod{125}.\n\\]\n\nWrite \\(N=8k\\).  Then \\(8k\\equiv123\\pmod{125}\\), i.e.  \n\n\\[\nk\\equiv123\\cdot8^{-1}\\pmod{125}.\n\\]\n\nSince \\(8^{-1}\\equiv47\\pmod{125}\\),  \n\n\\[\nk\\equiv123\\cdot47\\equiv31\\pmod{125}.\n\\]\n\nThus \\(k=31+125t\\) and  \n\n\\[\nN=8k=8\\cdot31=248\\pmod{1000}.\n\\]\n\n--------------------------------------------------------------------\n\n**Answer**\n\n\\[\n\\boxed{248}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 248</p>\n<p>Extracted Answer: 248</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThe twelve letters $A,B,C,D,E,F,G,H,I,J,K$, and $L$ are randomly grouped into six pairs of letters. The two letters in each pair are placed next to each other in alphabetical order to form six two-letter words, and those six words are listed alphabetically. For example, a possible result is $AB,CJ,DG,EK,FL,HI$. The probability that the last word listed contains $G$ is $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n\\[\nA&lt;B&lt;C&lt;D&lt;E&lt;F&lt;G&lt;H&lt;I&lt;J&lt;K&lt;L\n\\]\n\nand suppose the letters are randomly paired.  \nFor a pair \\(\\{x,y\\}\\) we write the word \\(xy\\) with the letters in\nalphabetical order (\\(x&lt;y\\)).  \nThe six words are then ordered alphabetically; the last word is the\nlexicographically largest word.\n\n--------------------------------------------------------------------\n### 1.  Conditioning on the partner of \\(G\\)\n\nIn a random perfect matching each of the other \\(11\\) letters is equally\nlikely to be paired with \\(G\\).  \nLet the partner be \\(X\\).  The probability we need is  \n\n\\[\nP=\\frac1{11}\\sum_{X\\neq G}\n\\Pr\\bigl(\\text{the pair } \\{G,X\\}\\text{ is the maximal word}\\mid\nG\\text{ is paired with }X\\bigr).\n\\]\n\nThus we must evaluate the conditional probability for each possible\n\\(X\\).\n\n--------------------------------------------------------------------\n### 2.  When \\(X&lt;G\\)\n\nIf \\(X&lt;G\\) the word is \\(XG\\) and its first letter is \\(X\\).  \nFor it to be the maximal word, the first letters (the smaller letters)\nof all other five pairs must be **smaller than \\(X\\)**.\nHence among the remaining ten letters we need five distinct letters\nall less than \\(X\\).\n\nThe only letter with five smaller letters is \\(F\\) (the letters\n\\(A,B,C,D,E\\) are smaller).  \nThus:\n\n* \\(X=F\\) is possible;\n* \\(X=A,B,C,D,E\\) are impossible (there are not enough smaller\nletters).\n\nWhen \\(X=F\\) the remaining letters are  \n\\(\\{A,B,C,D,E\\}\\) and \\(\\{H,I,J,K,L\\}\\).  \nTo keep every other pair\u2019s first letter \\(&lt;F\\), each of the five large\nletters must be paired with a distinct small one.  \nThe number of such matchings is \\(5!=120\\).\n\nThe total number of matchings of those ten letters is  \n\n\\[\n\\frac{10!}{2^5\\,5!}=945 .\n\\]\n\nHence  \n\n\\[\n\\Pr(\\text{maximal}\\mid G\\text{\u2013}F)=\\frac{120}{945}=\\frac{8}{63}.\n\\]\n\n--------------------------------------------------------------------\n### 3.  When \\(X&gt;G\\)\n\nNow the word is \\(GX\\) and its first letter is \\(G\\).\nFor it to be maximal, **no other pair may have a first letter larger\nthan \\(G\\)**; i.e. no remaining pair may consist of two letters both\ngreater than \\(G\\).\n\nAfter fixing the pair \\(\\{G,X\\}\\) (with \\(X\\in\\{H,I,J,K,L\\}\\)), the\nremaining letters are\n\n* the six letters \\(\\{A,B,C,D,E,F\\}\\) (all \\(&lt;G\\));\n* the four letters among \\(\\{H,I,J,K,L\\}\\) that are not \\(X\\) (all\n\\(&gt;G\\)).\n\nThus each of those four \u201clarge\u2019\u2019 letters must be paired with a distinct\nsmall letter, leaving two small letters to pair together.\n\nNumber of valid matchings:\n\n\\[\n\\binom{6}{4}\\cdot4!\\cdot1=15\\cdot24=360 .\n\\]\n\nAgain the total number of matchings of the ten remaining letters is\n\\(945\\). Therefore\n\n\\[\n\\Pr(\\text{maximal}\\mid G\\text{\u2013}X)=\\frac{360}{945}=\\frac{8}{21}\n\\qquad (X=H,I,J,K,L).\n\\]\n\n--------------------------------------------------------------------\n### 4.  Assemble the probability\n\n\\[\n\\begin{aligned}\nP&amp;=\\frac1{11}\\Bigl(\\frac{8}{63}\n+5\\cdot\\frac{8}{21}\\Bigr)    \\\\\n &amp;=\\frac1{11}\\Bigl(\\frac{8}{63}+\\frac{40}{21}\\Bigr)\n   =\\frac1{11}\\Bigl(\\frac{8+120}{63}\\Bigr)\n   =\\frac{128}{693}.\n\\end{aligned}\n\\]\n\nThe fraction \\(\\displaystyle\\frac{128}{693}\\) is already in lowest\nterms.  Hence \\(m=128,\\;n=693\\) and\n\n\\[\nm+n = 128+693 = 821 .\n\\]\n\n--------------------------------------------------------------------\n\\[\n\\boxed{821}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 821</p>\n<p>Extracted Answer: 821</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $N$ denote the number of ordered triples of positive integers $(a,b,c)$ such that $a,b,c\\leq3^6$ and $a^3+b^3+c^3$ is a multiple of $3^7$. Find the remainder when $N$ is divided by $1000$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n\\[\nS(t)=\\sum_{a=1}^{3^{6}}\\exp\\!\\Big(2\\pi i\\,\\frac{t a^{3}}{3^{7}}\\Big) \\qquad(0\\le t&lt;3^{7})\n\\]\n\nand denote  \n\n\\[\nN=\\#\\{(a,b,c)\\mid 1\\le a,b,c\\le 3^{6},\n\\ a^{3}+b^{3}+c^{3}\\equiv 0\\pmod{3^{7}}\\}.\n\\]\n\nFor any modulus \\(m\\),\n\n\\[\n\\#\\{(x,y,z):x+y+z\\equiv0\\pmod m\\}=\n\\frac1m\\sum_{t=0}^{m-1}\\Bigl(\\sum_{x}e^{2\\pi i t x/m}\\Bigr)^3 .\n\\]\n\nHence  \n\n\\[\nN=\\frac1{3^{7}}\\sum_{t=0}^{3^{7}-1} S(t)^{3}. \\tag{1}\n\\]\n\n--------------------------------------------------------------------\n### 1.  Splitting the summation\n\nWrite each \\(a\\) as \\(a=3^{v}u\\) where \\(v=v_{3}(a)\\) and \\(u\\) is not\ndivisible by \\(3\\).  \nFor \\(0\\le v\\le 2\\) define  \n\n\\[\nU_{v}=\\{\\,u:1\\le u\\le 3^{6-v},\\;3\\nmid u\\,\\},\n\\qquad |U_{0}|=486,\\ |U_{1}|=162,\\ |U_{2}|=54 .\n\\]\n\nIf \\(v\\ge3\\) then \\(a^{3}\\equiv0\\pmod{3^{7}}\\); there are  \n\\(n_{3}=27\\) such numbers.\nThus\n\n\\[\nS(t)=f_{0}(t)+f_{1}(t)+f_{2}(t)+n_{3},\n\\]\nwhere  \n\n\\[\n\\begin{aligned}\nf_{0}(t)&amp;=\\sum_{x\\in U_{0}}\\zeta^{t x^{3}},\\\\[2mm]\nf_{1}(t)&amp;=\\sum_{x\\in U_{1}}\\zeta^{t\\,27x^{3}},\\\\[2mm]\nf_{2}(t)&amp;=\\sum_{x\\in U_{2}}\\zeta^{t\\,729x^{3}},\n\\end{aligned}\n\\qquad \n\\zeta=e^{2\\pi i/3^{7}} .\n\\]\n\n--------------------------------------------------------------------\n### 2.  Evaluating \\(f_{0},f_{1},f_{2}\\)\n\n*For \\(f_{0}\\).*  \nLet \\(G_{7}=(\\mathbb Z/3^{7}\\mathbb Z)^{\\times}\\) (\\(|G_{7}|=1458\\)).\nThe map \\(x\\mapsto x^{3}\\) from \\(G_{7}\\) onto the set of cubes\n\\(C_{6}\\) has kernel of size \\(3\\); consequently\n\n\\[\n\\sum_{x\\in G_{7}}\\zeta^{t x}=3\\sum_{r\\in C_{6}}\\zeta^{t r}=3f_{0}(t).\n\\]\n\nFor \\(t\\neq0\\) one has  \n\n\\[\n\\sum_{x\\in G_{7}}\\zeta^{t x}= -\\!\\!\\sum_{\\substack{x\\;(\\bmod 3^{7})\\\\3\\mid x}}\\!\\!\\zeta^{t x}\n=\\begin{cases}\n-729,&amp;v_{3}(t)=6,\\\\\n0,&amp;0\\le v_{3}(t)\\le5 .\n\\end{cases}\n\\]\n\nHence  \n\n\\[\nf_{0}(t)=\n\\begin{cases}\n486,&amp;t=0,\\\\[2mm]\n-243,&amp;v_{3}(t)=6,\\\\[2mm]\n0,&amp;\\text{otherwise.}\n\\end{cases}\n\\tag{2}\n\\]\n\n*For \\(f_{1}\\).*  \nWriting each \\(x\\in U_{1}\\) as \\(x=v+81k\\;(k=0,1,2)\\) one finds\n\\(x^{3}\\equiv v^{3}\\pmod{81}\\). Consequently  \n\n\\[\nf_{1}(t)=3\\!\\!\\sum_{\\substack{v\\in(\\mathbb Z/81)^{\\times}}}\\!\n\\exp\\!\\Big(2\\pi i\\,\\frac{t v^{3}}{81}\\Big).\n\\]\n\nUsing again that the cube map on \\((\\mathbb Z/81)^{\\times}\\) has kernel\nsize \\(3\\),\n\n\\[\nf_{1}(t)=3\\!\\cdot\\!3\\!\\!\\sum_{r\\in C_{1}}\\!\n\\exp\\!\\Big(2\\pi i\\,\\frac{t r}{81}\\Big) ,\n\\]\n\nwhere \\(C_{1}\\) is the set of cube\u2011residues modulo \\(81\\) (\\(|C_{1}|=18\\)).\nNow\n\n\\[\n\\sum_{x\\in(\\mathbb Z/81)^{\\times}}\\exp\\!\\Big(2\\pi i\\,\n\\frac{t x}{81}\\Big)=\n\\begin{cases}\n54,&amp;v_{3}(t)\\ge4,\\\\[1mm]\n-27,&amp;v_{3}(t)=3,\\\\[1mm]\n0,&amp;v_{3}(t)\\le2 .\n\\end{cases}\n\\]\n\nThus\n\n\\[\nf_{1}(t)=\n\\begin{cases}\n162,&amp;v_{3}(t)\\ge4,\\\\[2mm]\n-81,&amp;v_{3}(t)=3,\\\\[2mm]\n0,&amp;v_{3}(t)\\le2 .\n\\end{cases}\n\\tag{3}\n\\]\n\n*For \\(f_{2}\\).*  \nHere \\(x^{3}\\equiv x\\pmod 3\\), and among the \\(54\\) numbers in \\(U_{2}\\)\nexactly half are \\(\\equiv1\\pmod3\\) and half \\(\\equiv2\\pmod3\\). Hence  \n\n\\[\nf_{2}(t)=27\\bigl(\\zeta^{t}+ \\zeta^{2t}\\bigr)=\n\\begin{cases}\n-27,&amp;v_{3}(t)=0,\\\\[2mm]\n54,&amp;v_{3}(t)\\ge1 .\n\\end{cases}\n\\tag{4}\n\\]\n\n--------------------------------------------------------------------\n### 3.  The values of \\(S(t)\\)\n\nFrom (2)\u2013(4) (and remembering the constant term \\(n_{3}=27\\))\n\n\\[\nS(t)=f_{0}(t)+f_{1}(t)+f_{2}(t)+27=\n\\begin{array}{c|c}\nv_{3}(t) &amp; S(t)\\\\ \\hline\n\\infty\\;(t=0) &amp; 729\\\\\n0 &amp; 0\\\\\n1 &amp; 81\\\\\n2 &amp; 81\\\\\n3 &amp; 0\\\\\n4 &amp; 243\\\\\n5 &amp; 243\\\\\n6 &amp; 0\n\\end{array}\n\\]\n\n--------------------------------------------------------------------\n### 4.  Computing \\(N\\)\n\nOnly the classes with non\u2011zero \\(S(t)\\) contribute to (1).  \nThe numbers of \\(t\\) in each class are\n\n\\[\n\\begin{array}{c|c}\nv_{3}(t) &amp; \\#t\\\\ \\hline\n\\infty &amp; 1\\\\\n0 &amp; 1458\\\\\n1 &amp; 486\\\\\n2 &amp; 162\\\\\n3 &amp; 54\\\\\n4 &amp; 18\\\\\n5 &amp; 6\\\\\n6 &amp; 2\n\\end{array}\n\\]\n\nHence\n\n\\[\n\\begin{aligned}\nN&amp;=\\frac1{3^{7}}\\Bigl( 729^{3}\n+ (486+162) \\,81^{3}\n+ (18+6)\\,243^{3}\\Bigr)\\\\[2mm]\n&amp;=\\frac1{3^{7}}\\Bigl(3^{18}+648\\cdot3^{12}+24\\cdot3^{15}\\Bigr)\\\\\n&amp;=3^{5}\\cdot2025 = 243\\cdot2025 = 492\\,075 .\n\\end{aligned}\n\\]\n\n--------------------------------------------------------------------\n### 5.  Remainder modulo \\(1000\\)\n\n\\[\n492\\,075 \\equiv 75 \\pmod{1000}.\n\\]\n\n--------------------------------------------------------------------\n\\[\n\\boxed{75}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 735</p>\n<p>Extracted Answer: 75</p>\n<p>Score: 0.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nOn $\\triangle ABC$ points $A,D,E$, and $B$ lie that order on side $\\overline{AB}$ with $AD=4, DE=16$, and $EB=8$. Points $A,F,G$, and $C$ lie in that order on side $\\overline{AC}$ with $AF=13, FG=52$, and $GC=26$. Let $M$ be the reflection of $D$ through $F$, and let $N$ be the reflection of $G$ through $E$. Quadrilateral $DEGF$ has area 288. Find the area of heptagon $AFNBCEM$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>**Solution Overview**\n\nThe given lengths on the sides of \\(\\triangle ABC\\) give  \n\n\\[\nAD=4,\\;DE=16,\\;EB=8 \\qquad\\Longrightarrow\\qquad AB=28,\n\\]\n\\[\nAF=13,\\;FG=52,\\;GC=26 \\qquad\\Longrightarrow\\qquad AC=91 .\n\\]\n\n--------------------------------------------------------------------\n\n### 1.  Two lines parallel to \\(BC\\)\n\n\\[\n\\frac{AD}{AB}= \\frac{4}{28}= \\frac{1}{7},\\qquad \n\\frac{AF}{AC}= \\frac{13}{91}= \\frac{1}{7}.\n\\]\n\nHence the points \\(D\\in AB\\) and \\(F\\in AC\\) divide the two sides in the same\nratio; therefore \\(DF\\parallel BC\\).\n\nSimilarly  \n\n\\[\n\\frac{AE}{AB}= \\frac{AD+DE}{AB}= \\frac{20}{28}= \\frac57,\n\\qquad \n\\frac{AG}{AC}= \\frac{AF+FG}{AC}= \\frac{65}{91}= \\frac57,\n\\]\n\nso \\(E\\in AB,\\;G\\in AC\\) also give a line parallel to \\(BC\\); i.e. \\(EG\\parallel BC\\).\n\nThus the quadrilateral \\(DEGF\\) is bounded by two parallel sides \\(DF,EG\\) and\nthe two segments of the sides of the triangle, and it is the region between the\ntwo similar triangles \\(ADF\\) and \\(AEG\\).\n\n--------------------------------------------------------------------\n\n### 2.  Area of \\(\\triangle ABC\\)\n\nIf \\([XYZ]\\) denotes area, similarity gives  \n\n\\[\n[ADF]=\\Bigl(\\frac{AD}{AB}\\Bigr)^2[ABC]=\\Bigl(\\frac17\\Bigr)^2[ABC]=\\frac{[ABC]}{49},\n\\]\n\n\\[\n[AEG]=\\Bigl(\\frac{AE}{AB}\\Bigr)\\Bigl(\\frac{AG}{AC}\\Bigr)[ABC]\n      =\\frac57\\cdot\\frac57[ABC]=\\frac{25}{49}[ABC].\n\\]\n\nHence  \n\n\\[\n[DEGF]=[AEG]-[ADF]=\\Bigl(\\frac{25}{49}-\\frac1{49}\\Bigr)[ABC]\n       =\\frac{24}{49}[ABC].\n\\]\n\nGiven \\([DEGF]=288\\),\n\n\\[\n\\frac{24}{49}[ABC]=288\\quad\\Longrightarrow\\quad[ABC]=288\\cdot\\frac{49}{24}\n                  =12\\cdot49=588.\n\\]\n\n--------------------------------------------------------------------\n\n### 3.  Area of the heptagon \\(AFNBCEM\\)\n\nPlace the triangle with \\(A=(0,0),\\;B=(28,0)\\) and\n\\(C=(91\\cos\\theta,\\,91\\sin\\theta)\\).\nBecause \\([ABC]=\\tfrac12\\cdot28\\cdot91\\sin\\theta\\),\n\n\\[\n\\sin\\theta=\\frac{[ABC]}{1274}= \\frac{588}{1274}= \\frac{6}{13}.\n\\]\n\nThus  \n\n\\[\n\\cos\\theta=\\frac{\\sqrt{1-\\sin^2\\theta}}{\\,}= \\frac{\\sqrt{133}}{13}.\n\\]\n\nThe coordinates of the relevant points are\n\n\\[\n\\begin{aligned}\n&amp;F=(13\\cos\\theta,13\\sin\\theta)=(\\sqrt{133},6), \\\\\n&amp;G=(65\\cos\\theta,65\\sin\\theta)=(5\\sqrt{133},30),\\\\\n&amp;D=(4,0),\\qquad\nE=(20,0),\\\\\n&amp;M=2F-D=(2\\sqrt{133}-4,12),\\\\\n&amp;N=2E-G=(40-5\\sqrt{133},-30).\n\\end{aligned}\n\\]\n\nUsing the shoelace formula for the polygon\n\\(A\\,(0,0),\\;F,\\;N,\\;B,\\;C,\\;E,\\;M\\) we obtain\n\n\\[\n\\begin{aligned}\n\\sum (x_i y_{i+1}-y_i x_{i+1})\n&amp;= -240+840+1176-840+240 = 1176,\\\\[2mm]\n\\text{Area}&amp;=\\frac12\\cdot1176=588.\n\\end{aligned}\n\\]\n\nThus the heptagon \\(AFNBCEM\\) has the same area as \\(\\triangle ABC\\).\n\n--------------------------------------------------------------------\n\n\\[\n\\boxed{588}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 588</p>\n<p>Extracted Answer: 588</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThe parabola with equation $y=x^{2}-4$ is rotated $60^{\\circ}$ counterclockwise around the origin. The unique point in the fourth quadrant where the original parabola and its image intersect has $y$-coordinate $\\frac{a-\\sqrt{b}}{c}$, where $a$, $b$, and $c$ are positive integers, and $a$ and $c$ are relatively prime. Find $a+b+c$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n\\[\nP:\\; y=x^{2}-4\n\\]\n\nand rotate \\(P\\) about the origin \\(60^{\\circ}\\) counter\u2011clockwise.  \nIf \\((x,y)\\) is a point of \\(P\\) then its image \\((X,Y)\\) satisfies  \n\n\\[\n\\begin{pmatrix}X\\\\Y\\end{pmatrix}= \n\\begin{pmatrix}\\cos 60^\\circ &amp; -\\sin 60^\\circ\\\\[2pt] \n\\sin 60^\\circ &amp; \\ \\cos 60^\\circ\\end{pmatrix}\n\\begin{pmatrix}x\\\\y\\end{pmatrix},\n\\qquad \n\\cos60^\\circ=\\frac12,\\;\\sin60^\\circ=\\frac{\\sqrt3}{2}.\n\\]\n\nHence  \n\n\\[\nX=\\frac{x}{2}-\\frac{\\sqrt3}{2}y,\\qquad\nY=\\frac{\\sqrt3}{2}x+\\frac{y}{2}.\n\\]\n\nTo obtain the equation of the rotated curve in the original \\((x,y)\\)\u2013coordinates,\nsolve for \\((x,y)\\) in terms of \\((X,Y)\\) (rotate back by \\(-60^\\circ\\)):\n\n\\[\nx = \\frac{X}{2}+\\frac{\\sqrt3}{2}Y,\\qquad\ny = -\\frac{\\sqrt3}{2}X+\\frac{Y}{2}.\n\\]\n\nSince the original points satisfy \\(y=x^{2}-4\\), substituting the expressions above gives the equation of the image:\n\n\\[\nx^{2}+2\\sqrt3\\,xy+3y^{2}+2\\sqrt3\\,x-2y-16=0. \\tag{1}\n\\]\n\n--------------------------------------------------------------------\n### Intersection with the original parabola\n\nThe intersection points satisfy simultaneously  \n\n\\[\ny=x^{2}-4\\qquad\\text{and}\\qquad (1).\n\\]\n\nSubstituting \\(y=x^{2}-4\\) into (1) yields\n\n\\[\n3x^{4}-25x^{2}+40+2\\sqrt3\\,x^{3}-6\\sqrt3\\,x=0.\n\\]\n\nFactor this quartic in the field \\(\\mathbb{Q}(\\sqrt3)\\):\n\n\\[\n\\begin{aligned}\n3x^{4}-25x^{2}+40+2\\sqrt3\\,x^{3}-6\\sqrt3\\,x\n&amp;=(x^{2}+\\sqrt3\\,x-4)\\bigl(3x^{2}-\\sqrt3\\,x-10\\bigr).\n\\end{aligned}\n\\]\n\nThus the intersection points satisfy one of  \n\n\\[\n\\begin{cases}\nx^{2}+\\sqrt3\\,x-4=0,\\\\[2pt]\n\\text{or}\\\\[2pt]\n3x^{2}-\\sqrt3\\,x-10=0 .\n\\end{cases}\n\\]\n\n--------------------------------------------------------------------\n### Selecting the point in the fourth quadrant\n\n*From* \\(x^{2}+\\sqrt3\\,x-4=0\\)\n\n\\[\nx=\\frac{-\\sqrt3\\pm\\sqrt{19}}{2}.\n\\]\n\nThe root \\(\\displaystyle x=\\frac{-\\sqrt3+\\sqrt{19}}{2}&gt;0\\) gives  \n\n\\[\ny=x^{2}-4=\\frac{11-\\sqrt{57}}{2}-4=\\frac{3-\\sqrt{57}}{2}&lt;0,\n\\]\n\nso \\((x,y)\\) lies in the fourth quadrant.\n\n*From* \\(3x^{2}-\\sqrt3\\,x-10=0\\)\n\n\\[\nx=\\frac{\\sqrt3\\pm\\sqrt{123}}{6},\n\\]\n\nwhich yields either \\(y&gt;0\\) (first root) or \\(x&lt;0\\) (second root); neither point is in the fourth quadrant.\n\nHence the unique fourth\u2011quadrant intersection point is  \n\n\\[\n\\Bigl(\\frac{-\\sqrt3+\\sqrt{19}}{2}\\,,\\; \\frac{3-\\sqrt{57}}{2}\\Bigr).\n\\]\n\n--------------------------------------------------------------------\n### Required \\(y\\)-coordinate\n\nThe \\(y\\)-coordinate is \\(\\displaystyle \\frac{3-\\sqrt{57}}{2}\\).\n\nWrite it as \\(\\frac{a-\\sqrt{b}}{c}\\) with \\(a,b,c\\) positive integers and \\(\\gcd(a,c)=1\\):\n\\[\na=3,\\qquad b=57,\\qquad c=2.\n\\]\n\nTherefore  \n\n\\[\na+b+c = 3+57+2 = 62.\n\\]\n\n\\[\n\\boxed{62}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 62</p>\n<p>Extracted Answer: 62</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nSix points $ A, B, C, D, E, $ and $ F $ lie in a straight line in that order. Suppose that $ G $ is a point not on the line and that $ AC = 26 $, $ BD = 22 $, $ CE = 31 $, $ DF = 33 $, $ AF = 73 $, $ CG = 40 $, and $ DG = 30 $. Find the area of $ \\triangle BGE $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let the line containing \\(A,B,C,D,E,F\\) be the \\(x\\)-axis.\n\n\\[\nA=(0,0),\\qquad B=(b,0),\\qquad C=(c,0),\\qquad D=(d,0),\\qquad \nE=(e,0),\\qquad F=(f,0)\n\\]\n\nBecause the points are in the order \\(A,B,C,D,E,F\\),\n\n\\[\nc-b=AC-AB,\\; d-b=BD,\\; e-c=CE,\\; f-d=DF,\\; f-0=AF.\n\\]\n\nTake \\(A\\) at the origin.  From the data\n\n\\[\nAC=26\\implies c=26,\n\\]\n\\[\nBD=22\\implies d=b+22,\n\\]\n\\[\nCE=31\\implies e=c+31=57,\n\\]\n\\[\nDF=33\\implies f=d+33=b+55,\n\\]\n\\[\nAF=73\\implies f=73.\n\\]\n\nHence \\(b+55=73\\Rightarrow b=18\\).  \nThus the coordinates are  \n\n\\[\nB=(18,0),\\; C=(26,0),\\; D=(40,0),\\; E=(57,0),\\; F=(73,0).\n\\]\n\n---\n\n### Locate \\(G\\)\n\n\\(G\\) is off the line and satisfies  \n\n\\[\nCG=40,\\qquad DG=30.\n\\]\n\nLet \\(G=(x,y)\\) with \\(y\\neq0\\). Then  \n\n\\[\n(x-26)^2+y^{2}=40^{2}=1600,\\tag{1}\n\\]\n\\[\n(x-40)^2+y^{2}=30^{2}=900.\\tag{2}\n\\]\n\nSubtract (2) from (1):\n\n\\[\n(x-26)^2-(x-40)^2=700.\n\\]\n\nExpanding,\n\n\\[\n[x^{2}-52x+676]-[x^{2}-80x+1600]=28x-924=700,\n\\]\n\\[\n28x=1624\\quad\\Longrightarrow\\quad x=58.\n\\]\n\nPlugging \\(x=58\\) into (2):\n\n\\[\n(58-40)^{2}+y^{2}=900\\;\\Longrightarrow\\;18^{2}+y^{2}=900\n\\]\n\\[\ny^{2}=576\\;\\Longrightarrow\\;|y|=24.\n\\]\n\nSo \\(G=(58,\\,24)\\) (the point \\((58,-24)\\) gives the same area).\n\n---\n\n### Area of \\(\\triangle BGE\\)\n\nPoints \\(B\\) and \\(E\\) lie on the \\(x\\)-axis, so the base \\(BE\\) has length\n\n\\[\nBE = e-b = 57-18 = 39.\n\\]\n\nThe altitude from \\(G\\) to the line \\(BE\\) (the \\(x\\)-axis) is \\(|y| = 24\\).\n\nHence  \n\n\\[\n\\text{Area} = \\frac12 \\times BE \\times \\text{height}\n= \\frac12 \\times 39 \\times 24 = 468.\n\\]\n\n\\[\n\\boxed{468}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 468</p>\n<p>Extracted Answer: 468</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nFind the sum of all positive integers $ n $ such that $ n + 2 $ divides the product $ 3(n + 3)(n^2 + 9) $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>We need the positive integers \\(n\\) such that  \n\n\\[\nn+2\\mid 3(n+3)(n^{2}+9).\n\\]\n\n---\n\n### 1.  Replace \\(n+2\\) by a new variable  \n\nLet  \n\n\\[\nk=n+2\\qquad (k\\ge 3), \\qquad n=k-2 .\n\\]\n\nThen  \n\n\\[\n\\begin{aligned}\nn+3 &amp;= (k-2)+3 = k+1,\\\\[2pt]\nn^{2}+9 &amp;= (k-2)^{2}+9 = k^{2}-4k+13 .\n\\end{aligned}\n\\]\n\nHence  \n\n\\[\n3(n+3)(n^{2}+9)=3(k+1)(k^{2}-4k+13).\n\\]\n\nThe condition becomes  \n\n\\[\nk \\mid 3(k+1)(k^{2}-4k+13).\n\\]\n\n---\n\n### 2.  Reduce modulo \\(k\\)\n\nModulo \\(k\\),\n\n\\[\nk+1\\equiv 1,\\qquad k^{2}-4k+13\\equiv 13,\n\\]\n\nbecause \\(k\\equiv 0\\) gives \\(k^{2}\\equiv 0\\) and \\(-4k\\equiv 0\\).\n\nThus  \n\n\\[\n3(k+1)(k^{2}-4k+13)\\equiv 3\\cdot 1\\cdot 13=39 \\pmod{k}.\n\\]\n\nHence the divisibility condition is equivalent to  \n\n\\[\nk\\mid 39.\n\\]\n\n---\n\n### 3.  Find admissible \\(k\\) and corresponding \\(n\\)\n\nThe positive divisors of \\(39\\) are \\(1,3,13,39\\).\nSince \\(k=n+2\\ge 3\\), we keep  \n\n\\[\nk\\in \\{3,13,39\\}.\n\\]\n\nTherefore  \n\n\\[\nn=k-2\\in\\{1,11,37\\}.\n\\]\n\nAll three values satisfy the original condition (a quick check confirms the division).\n\n---\n\n### 4.  Sum of all such \\(n\\)\n\n\\[\n1+11+37 = 49.\n\\]\n\n\\[\n\\boxed{49}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 49</p>\n<p>Extracted Answer: 49</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThe set of points in 3-dimensional coordinate space that lie in the plane $x+y+z=75$ whose coordinates satisfy the inequalities $x-yz&lt;y-zx&lt;z-xy$ forms three disjoint convex regions. Exactly one of those regions has finite area. The area of this finite region can be expressed in the form $a\\sqrt{b}$, where $a$ and $b$ are positive integers and $b$ is not divisible by the square of any prime. Find $a+b$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>The inequalities\n\n\\[\nx-yz&lt;y-zx&lt;z-xy\n\\]\n\nwith the plane \\(x+y+z=75\\) can be simplified.  \nWrite \\(z=75-x-y\\). Then\n\n\\[\n\\begin{aligned}\ny-zx-(x-yz) &amp;= (y-x)(1+z)= (y-x)(76-x-y),\\\\\nz-xy-(y-zx) &amp;= (z-y)(1+x)= (75-x-2y)(1+x).\n\\end{aligned}\n\\]\n\nThus the points on the plane satisfy  \n\n\\[\n(y-x)(76-x-y)&gt;0,\\qquad (75-x-2y)(1+x)&gt;0 .\n\\tag{1}\n\\]\n\nDefine in the \\(xy\\)-plane the lines  \n\n\\[\n\\begin{aligned}\nL_1 &amp;: y=x,\\\\\nL_2 &amp;: x+y=76,\\\\\nL_3 &amp;: x=-1,\\\\\nL_4 &amp;: x+2y=75\\;(y=(75-x)/2).\n\\end{aligned}\n\\]\n\nFrom (1) we obtain two possibilities for each product, giving four possible\nintersections of half\u2011planes.  One of these intersections is empty; the other three\nare convex.  The region for which both products in (1) are **positive** is\n\n\\[\n\\begin{cases}\ny&gt;x,\\\\\nx+y&lt;76,\\\\\ny&lt;(75-x)/2,\\\\\nx&gt;-1,\n\\end{cases}\n\\]\n\nwhich in the \\(xy\\)-plane is the interior of the triangle with vertices\n\n\\[\nA(-1,-1),\\qquad B(-1,38),\\qquad C(25,25).\n\\]\n\nThe other two regions are unbounded.  Hence the finite region is this triangle.\n\n---\n\n### Area in the \\(xy\\)-plane\n\n\\[\n\\text{Area}_{xy}= \\frac12\\bigl|AB\\times AC\\bigr|\n               =\\frac12\\bigl| (0,39)\\times (26,26)\\bigr|\n               =\\frac12\\cdot1014 = 507 .\n\\]\n\n---\n\n### Area on the plane \\(x+y+z=75\\)\n\nThe plane is given by \\(z=75-x-y\\).  Its area element satisfies  \n\n\\[\ndS = \\sqrt{1+(\\partial_xz)^2+(\\partial_yz)^2}\\;dx\\,dy\n    =\\sqrt{1+1+1}\\;dx\\,dy =\\sqrt3\\,dx\\,dy .\n\\]\n\nHence  \n\n\\[\n\\text{Area}_{\\text{plane}} = \\sqrt3\\;\\text{Area}_{xy}\n                            = 507\\sqrt3 .\n\\]\n\nSo the area can be written as \\(a\\sqrt b\\) with \\(a=507,\\ b=3\\).\nTherefore  \n\n\\[\na+b = 507+3 = 510 .\n\\]\n\n\\[\n\\boxed{510}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 510</p>\n<p>Extracted Answer: 510</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nA piecewise linear periodic function is defined by $f(x)=\\begin{cases}x&amp;\\text{if }x\\in[-1,1)\\\\2-x&amp;\\text{if }x\\in[1,3)\\end{cases}$ and $f(x+4)=f(x)$ for all real numbers $x$. The graph of $f(x)$ has the sawtooth pattern. The parabola $x=34y^2$ intersects the graph of $f(x)$ at finitely many points. The sum of the $y$-coordinates of these intersection points can be expressed in the form $\\frac{a+b\\sqrt{c}}{d}$, where $a,b,c,$ and $d$ are positive integers, $a,b,$ and $d$ have greatest common divisor equal to 1, and $c$ is not divisible by the square of any prime. Find $a+b+c+d$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>The intersection points satisfy  \n\n\\[\ny=f(x),\\qquad x=34y^{2}\\;( \\ge 0).\n\\]\n\nBecause \\(f\\) has period \\(4\\),\n\n\\[\nf(x)=\\begin{cases}\nx-4k ,&amp;x\\in[-1+4k,\\,1+4k),\\\\[2mm]\n2+4k-x ,&amp;x\\in[1+4k,\\,3+4k),\n\\end{cases}\\qquad k\\in\\mathbb Z .\n\\]\n\n--------------------------------------------------------------------\n### 1.  Equations for the two linear pieces  \n\n*Ascending piece*  \\((x-4k)\\):  \n\n\\[\ny=x-4k,\\qquad x=34y^{2}\n\\Longrightarrow 34y^{2}-y-4k=0. \\tag{1}\n\\]\n\n*Descending piece*  \\((2+4k-x)\\):  \n\n\\[\ny=2+4k-x,\\qquad x=34y^{2}\n\\Longrightarrow 34y^{2}+y-(2+4k)=0. \\tag{2}\n\\]\n\nBoth are quadratics in \\(y\\); each can give at most two real roots.\n\n--------------------------------------------------------------------\n### 2.  Which integers \\(k\\) give admissible roots?\n\nBecause \\(|y|\\le 1\\) (the range of \\(f\\)), the roots must lie in \\([-1,1]\\).\n\n*For (1):*  \nThe sum of the two roots equals \\(\\frac{1}{34}\\); the product is \\(-\\frac{4k}{34}\\).  \nThe discriminant must be non\u2011negative:\n\n\\[\n\\Delta_1=1+544k\\ge 0\\Longrightarrow k\\ge0 .\n\\]\n\nFor a root to be in \\([-1,1)\\) we also need  \n\n\\[\n-1\\le\\frac{1\\pm\\sqrt{1+544k}}{68}&lt;1 .\n\\]\n\nThe last inequality forces \\(k\\le8\\).  Hence (1) yields real admissible roots for  \n\n\\[\nk=0,1,\\dots ,8 .\n\\]\n\nBoth roots are in \\([-1,1)\\) for each of these values.\n\n*For (2):*  \n\\[\n\\Delta_2=273+544k\\ge0\\Longrightarrow k\\ge0 .\n\\]\n\nThe condition \\(-1&lt;y\\le 1\\) gives \\(k\\le8\\).  \nFor \\(k=0,\\dots ,7\\) both roots lie in \\((-1,1]\\); for \\(k=8\\) only the \u201c\\(+\\)\u201d root\n\\[\ny=\\frac{-1+\\sqrt{273+544\\cdot8}}{68}\n      =\\frac{-1+5\\sqrt{185}}{68}\n\\]\nremains in the interval (the \u201c\\(-\\)\u201d root is \\(&lt;-1\\)).\n\nThus  \n\n* (1) contributes \\(2\\) solutions for each \\(k=0,\\dots ,8\\)  \\(\\Rightarrow 18\\) points;  \n* (2) contributes \\(2\\) solutions for each \\(k=0,\\dots ,7\\) and \\(1\\) solution for \\(k=8\\)  \\(\\Rightarrow 17\\) points.\n\nHence there are \\(35\\) intersection points altogether.\n\n--------------------------------------------------------------------\n### 3.  Sum of the \\(y\\)-coordinates  \n\nFor each fixed \\(k\\) the sum of the two roots of (1) is, by Vieta,\n\n\\[\n\\Sigma_{A}(k)=\\frac{1}{34}.\n\\]\n\nSo the total contribution of (1) is  \n\n\\[\n\\sum_{k=0}^{8}\\Sigma_{A}(k)=9\\cdot\\frac{1}{34}= \\frac{9}{34}.\n\\]\n\nFor (2), when both roots exist their sum is  \n\n\\[\n\\Sigma_{B}(k)=-\\frac{1}{34}.\n\\]\n\nThus for \\(k=0,\\dots ,7\\) the total is  \n\n\\[\n8\\cdot\\Bigl(-\\frac{1}{34}\\Bigr)=-\\frac{8}{34}.\n\\]\n\nFor \\(k=8\\) only the positive root remains:\n\n\\[\ny_{8}= \\frac{-1+5\\sqrt{185}}{68}.\n\\]\n\nAdding everything,\n\n\\[\n\\begin{aligned}\n\\text{Sum of all }y\n&amp;=\\frac{9}{34}-\\frac{8}{34}+y_{8}\n   =\\frac{1}{34}+ \\frac{-1+5\\sqrt{185}}{68}\\\\[2mm]\n&amp;= \\frac{2}{68}+ \\frac{-1+5\\sqrt{185}}{68}\n   =\\frac{1+5\\sqrt{185}}{68}.\n\\end{aligned}\n\\]\n\n--------------------------------------------------------------------\n### 4.  Final answer  \n\nThe sum is \\(\\displaystyle\\frac{1+5\\sqrt{185}}{68}\\).  \nThus  \n\n\\[\na=1,\\; b=5,\\; c=185,\\; d=68,\\qquad\na+b+c+d=1+5+185+68=259.\n\\]\n\n\\[\n\\boxed{259}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 259</p>\n<p>Extracted Answer: 259</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThe 27 cells of a $3\\times9$ grid are filled in using the numbers 1 through 9 so that each row contains 9 different numbers, and each of the three $3\\times3$ blocks heavily outlined in the example below contains 9 different numbers, as in the first three rows of a Sudoku puzzle. \n | 4 | 2 | 8 | 9 | 6 | 3 | 1 | 7 | 5 | \n | 3 | 7 | 9 | 5 | 2 | 1 | 6 | 8 | 4 | \n | 5 | 6 | 1 | 8 | 4 | 7 | 9 | 2 | 3 | \n The number of different ways to fill such a grid can be written as $p^a\\cdot q^b\\cdot r^c\\cdot s^d$, where $p,q,r,$ and $s$ are distinct prime numbers and $a,b,c,$ and $d$ are positive integers. Find $p\\cdot a+q\\cdot b+r\\cdot c+s\\cdot d$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let the three rows be \\(R_1,R_2,R_3\\) and the three \\(3\\times3\\) blocks be \\(B_1,B_2,B_3\\) (columns \\(1\\!-\\!3,\\;4\\!-\\!6,\\;7\\!-\\!9\\)).\nEach row must be a permutation of \\(\\{1,\\dots ,9\\}\\) and each block must also contain every digit once.\n\n--------------------------------------------------------------------\n### 1.  Where does a digit appear in the three rows?\n\nFor a fixed digit \\(d\\) its three copies (one in each row) must lie in three *different* blocks; otherwise a block would miss that digit.  \nThus for each digit we obtain a bijection  \n\n\\[\n\\phi_d:\\{1,2,3\\}\\longrightarrow\\{1,2,3\\},\\qquad \n\\phi_d(i)=\\text{block containing }d\\text{ in row }i .\n\\]\n\nSo each digit corresponds to a permutation of the three blocks.  \nThere are six permutations, listed with the cells \\((i,\\phi(i))\\) they occupy:\n\n\\[\n\\begin{array}{c|c}\n\\text{perm.} &amp; \\text{cells}\\\\ \\hline\n(1)(2)(3) &amp; (1,1),(2,2),(3,3)\\\\\n(12) &amp; (1,2),(2,1),(3,3)\\\\\n(13) &amp; (1,3),(2,2),(3,1)\\\\\n(23) &amp; (1,1),(2,3),(3,2)\\\\\n(123) &amp; (1,2),(2,3),(3,1)\\\\\n(132) &amp; (1,3),(2,1),(3,2)\n\\end{array}\n\\]\n\nLet \\(x_1,\\dots ,x_6\\) be the numbers of digits that use the six permutations (in the order shown).  \nBecause each block must contain three digits from each row, each of the nine cells \\((i,k)\\) must be hit by exactly three digits, giving\n\n\\[\n\\begin{aligned}\nx_1+x_4 &amp;=3, &amp; x_2+x_5 &amp;=3, &amp; x_3+x_6 &amp;=3,\\\\\nx_2+x_6 &amp;=3, &amp; x_1+x_3 &amp;=3, &amp; x_4+x_5 &amp;=3,\\\\\nx_3+x_5 &amp;=3, &amp; x_4+x_6 &amp;=3, &amp; x_1+x_2 &amp;=3 .\n\\end{aligned}\n\\]\n\nSolving, all solutions have the form  \n\n\\[\n(x_1,x_2,x_3,x_4,x_5,x_6)=(a,\\,3-a,\\,3-a,\\,3-a,\\,a,\\,a),\\qquad a\\in\\{0,1,2,3\\}.\n\\]\n\n--------------------------------------------------------------------\n### 2.  Assign the digits to the permutations\n\nFor a fixed \\(a\\) the number of ways to choose which digits get which permutation is\n\n\\[\n\\frac{9!}{x_1!\\,x_2!\\,x_3!\\,x_4!\\,x_5!\\,x_6!}\n   =\\frac{9!}{a!^{\\,3}\\,(3-a)!^{\\,3}} .\n\\]\n\nSumming over the four possible values of \\(a\\),\n\n\\[\n\\sum_{a=0}^3\\frac{9!}{a!^{\\,3}(3-a)!^{\\,3}}\n   =9!\\Bigl(\\frac1{3!^{\\,3}}{0\\choose0}^3\n            +\\frac1{3!^{\\,3}}{3\\choose1}^3\n            +\\frac1{3!^{\\,3}}{3\\choose2}^3\n            +\\frac1{3!^{\\,3}}{3\\choose3}^3\\Bigr)\n   =9!\\,\\frac{56}{216}\n   =9!\\,\\frac{7}{27}.\n\\]\n\n--------------------------------------------------------------------\n### 3.  Order the digits inside each block\n\nWithin a fixed block and a fixed row there are three column positions.\nThe three digits that belong to that macro\u2011cell can be placed in these\npositions in \\(3! = 6\\) ways.\nThere are \\(3\\) rows \\(\\times\\) \\(3\\) blocks \\(=9\\) such macro\u2011cells, giving a factor \\(6^9\\).\n\n--------------------------------------------------------------------\n### 4.  Total number of fillings\n\n\\[\nN = \\Bigl(9!\\,\\frac{7}{27}\\Bigr)\\,6^{9}\n   = 2^{16}\\,3^{10}\\,5\\,7^{2}.\n\\]\n\nThus the factorisation uses the four distinct primes  \n\n\\[\np=2,\\;q=3,\\;r=5,\\;s=7,\\qquad \na=16,\\;b=10,\\;c=1,\\;d=2 .\n\\]\n\nFinally,\n\n\\[\np\\,a+q\\,b+r\\,c+s\\,d\n   =2\\cdot16+3\\cdot10+5\\cdot1+7\\cdot2\n   =32+30+5+14=81.\n\\]\n\n\\[\n\\boxed{81}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 81</p>\n<p>Extracted Answer: 81</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $ABCDE$ be a convex pentagon with $AB=14, BC=7, CD=24, DE=13, EA=26,$ and $\\angle B=\\angle E=60^\\circ$. For each point $X$ in the plane, define $f(X)=AX+BX+CX+DX+EX$. The least possible value of $f(X)$ can be expressed as $m+n\\sqrt{p}$, where $m$ and $n$ are positive integers and $p$ is not divisible by the square of any prime. Find $m+n+p$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>We place the pentagon in the plane.  \nSet  \n\n\\[\n\\begin{aligned}\nA&amp;=(7,7\\sqrt3),\\qquad B=(0,0),\\qquad C=(7,0),\\\\[2mm]\nD&amp;=\\Bigl(\\frac{205}{7},\\frac{36\\sqrt3}{7}\\Bigr),\\qquad \nE=\\Bigl(\\frac{218}{7},\\frac{88\\sqrt3}{7}\\Bigr).\n\\end{aligned}\n\\]\n\nThe lengths are as given and  \n\\(\\angle B=\\angle E =60^\\circ\\).\n\n--------------------------------------------------------------------\n### 1.  Geometry of the optimal point  \n\nFor the sum  \n\n\\[\nf(X)=AX+BX+CX+DX+EX,\n\\]\n\nthe geometric median \\(X\\) satisfies  \n\n\\[\n\\frac{X-A}{AX}+\\frac{X-B}{BX}+\\frac{X-C}{CX}+\\frac{X-D}{DX}+\\frac{X-E}{EX}=0 .\n\\tag{1}\n\\]\n\nBecause \\(B,E\\) lie on a line, the vectors \\(\\frac{X-B}{BX}\\) and\n\\(\\frac{X-E}{EX}\\) are opposite exactly when \\(X\\) lies on segment \\(BE\\);\nhence in the optimal position \\(X\\) must lie on \\(BE\\) and the first two\nterms in (1) cancel.  Consequently\n\n\\[\n\\frac{X-A}{AX}+\\frac{X-C}{CX}+\\frac{X-D}{DX}=0,\n\\]\n\nso \\(X\\) is the Fermat point of triangle \\(ACD\\).\n\n--------------------------------------------------------------------\n### 2.  Fermat point of \\(\\triangle ACD\\)\n\nThe side lengths of \\(\\triangle ACD\\) are  \n\n\\[\nAC=7\\sqrt3,\\qquad CD=24,\\qquad AD=13\\sqrt3 .\n\\]\n\nAll its angles are \\(&lt;120^\\circ\\); therefore the Fermat point exists.\nFor a triangle with sides \\(a,b,c\\) and area \\(\\Delta\\),\n\n\\[\nS_{\\text{Fermat}}=\n\\sqrt{\\frac{a^{2}+b^{2}+c^{2}+4\\sqrt3\\,\\Delta}{2}} .\n\\]\n\nHere  \n\n\\[\na^{2}+b^{2}+c^{2}=576+507+147=1230,\n\\qquad\\Delta_{ACD}=78\\sqrt3,\n\\]\n\nso  \n\n\\[\nS_{\\text{Fermat}}=\\sqrt{\\frac{1230+4\\sqrt3\\cdot78\\sqrt3}{2}}\n=\\sqrt{\\frac{1230+936}{2}}=\\sqrt{1083}=19\\sqrt3 .\n\\]\n\nThus at the Fermat point  \n\n\\[\nAX+CX+DX=19\\sqrt3 .\n\\tag{2}\n\\]\n\n--------------------------------------------------------------------\n### 3.  The total minimum\n\nSince the optimal point lies on \\(BE\\),\n\n\\[\nBX+EX = BE .\n\\]\n\nFrom the coordinates, \\(BE=38\\).  Combining this with (2),\n\n\\[\nf_{\\min}= (AX+CX+DX)+(BX+EX)=19\\sqrt3+38 .\n\\]\n\nHence the smallest possible value of \\(f(X)\\) is  \n\n\\[\n\\boxed{38+19\\sqrt3}.\n\\]\n\nWriting it as \\(m+n\\sqrt p\\) with \\(m,n\\) integers and \\(p\\) square\u2011free,\nwe have \\(m=38,\\;n=19,\\;p=3\\).  Therefore  \n\n\\[\nm+n+p=38+19+3=60 .\n\\]\n\n\\[\n\\boxed{60}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 60</p>\n<p>Extracted Answer: 60</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThe product $ \\prod_{k=4}^{63} \\frac{\\log_k(5^{k^2-1})}{\\log_{k+1}(5^{k^2-4})} = \\frac{\\log_4(5^{15})}{\\log_5(5^{12})} \\cdot \\frac{\\log_5(5^{24})}{\\log_6(5^{21})} \\cdot \\frac{\\log_6(5^{35})}{\\log_7(5^{32})} \\cdots \\frac{\\log_{63}(5^{3968})}{\\log_{64}(5^{3965})} $ is equal to $ \\frac{m}{n} $, where $ m $ and $ n $ are relatively prime positive integers. Find $ m + n $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>\\[\nP=\\prod_{k=4}^{63}\\frac{\\log_k\\!\\bigl(5^{k^{2}-1}\\bigr)}{\\log_{k+1}\\!\\bigl(5^{k^{2}-4}\\bigr)}\n\\]\n\n---\n\n### 1.  Simplify each factor  \n\n\\[\n\\log_k\\!\\bigl(5^{k^{2}-1}\\bigr)=(k^{2}-1)\\log_k5,\n\\qquad \n\\log_{k+1}\\!\\bigl(5^{k^{2}-4}\\bigr)=(k^{2}-4)\\log_{k+1}5 .\n\\]\n\nHence  \n\n\\[\n\\frac{\\log_k\\!\\bigl(5^{k^{2}-1}\\bigr)}{\\log_{k+1}\\!\\bigl(5^{k^{2}-4}\\bigr)}\n=\\frac{k^{2}-1}{k^{2}-4}\\cdot\\frac{\\log_k5}{\\log_{k+1}5}\n=\\frac{(k-1)(k+1)}{(k-2)(k+2)}\\cdot\\frac{\\log_k5}{\\log_{k+1}5}.\n\\]\n\nTherefore  \n\n\\[\nP=\\underbrace{\\prod_{k=4}^{63}\\frac{(k-1)(k+1)}{(k-2)(k+2)}}_{A}\n   \\times\\underbrace{\\prod_{k=4}^{63}\\frac{\\log_k5}{\\log_{k+1}5}}_{B}.\n\\]\n\n---\n\n### 2.  Evaluate the rational product \\(A\\)\n\n\\[\nA=\\Bigl(\\prod_{k=4}^{63}\\frac{k-1}{k-2}\\Bigr)\n   \\Bigl(\\prod_{k=4}^{63}\\frac{k+1}{k+2}\\Bigr)\n   =\\frac{3\\cdot4\\cdots62}{2\\cdot3\\cdots61}\\;\n     \\frac{5\\cdot6\\cdots64}{6\\cdot7\\cdots65}.\n\\]\n\nBoth products telescope:\n\n\\[\n\\frac{3\\cdot4\\cdots62}{2\\cdot3\\cdots61}= \\frac{62}{2}=31,\n\\qquad \n\\frac{5\\cdot6\\cdots64}{6\\cdot7\\cdots65}= \\frac{5}{65}= \\frac1{13}.\n\\]\n\nThus  \n\n\\[\nA=31\\cdot\\frac1{13}= \\frac{31}{13}.\n\\]\n\n---\n\n### 3.  Evaluate the logarithmic product \\(B\\)\n\n\\[\nB=\\frac{\\log_4 5}{\\log_5 5}\\cdot\\frac{\\log_5 5}{\\log_6 5}\\cdots\n    \\frac{\\log_{63}5}{\\log_{64}5}\n   =\\frac{\\log_4 5}{\\log_{64}5}.\n\\]\n\nUsing change\u2011of\u2011base,\n\\[\n\\frac{\\log_4 5}{\\log_{64} 5}\n   =\\frac{\\frac{\\ln5}{\\ln4}}{\\frac{\\ln5}{\\ln64}}\n   =\\frac{\\ln64}{\\ln4}\n   =\\log_4 64=3,\n\\]\nsince \\(4^3=64\\).\n\nHence \\(B=3\\).\n\n---\n\n### 4.  Combine\n\n\\[\nP=A\\cdot B=\\frac{31}{13}\\times 3=\\frac{93}{13}.\n\\]\n\nThe fraction \\(\\dfrac{93}{13}\\) is already in lowest terms, so  \n\\(m=93,\\; n=13\\).\n\n\\[\nm+n=93+13=106.\n\\]\n\n\\[\n\\boxed{106}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 106</p>\n<p>Extracted Answer: 106</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $ A $ be the set of positive integer divisors of 2025. Let $ B $ be a randomly selected subset of $ A $. The probability that $ B $ is a nonempty set with the property that the least common multiple of its elements is 2025 is $ \\frac{m}{n} $, where $ m $ and $ n $ are relatively prime positive integers. Find $ m + n $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>The divisors of  \n\n\\[\n2025=3^{4}\\cdot5^{2}\n\\]\n\nare exactly the numbers  \n\n\\[\n3^{a}5^{b}\\qquad (0\\le a\\le 4,\\;0\\le b\\le 2).\n\\]\n\nHence  \n\n\\[\n|A|=(4+1)(2+1)=15 .\n\\]\n\nFor a subset \\(B\\subseteq A\\) the least common multiple is\n\n\\[\n\\operatorname{lcm}(B)=3^{\\max a}\\,5^{\\max b},\n\\]\n\nwhere the maxima are taken over the exponents \\((a,b)\\) of the elements of \\(B\\).\n\nThus \\(\\operatorname{lcm}(B)=2025=3^4 5^2\\) iff  \n\n* at least one element of \\(B\\) has a \\(3\\)-exponent \\(4\\);\n* at least one element of \\(B\\) has a \\(5\\)-exponent \\(2\\).\n\nDefine  \n\n\\[\nD_3=\\{d\\in A : \\text{the exponent of }3\\text{ in }d\\text{ is }4\\},\n\\qquad \nD_5=\\{d\\in A : \\text{the exponent of }5\\text{ in }d\\text{ is }2\\}.\n\\]\n\nCounting:\n\n* \\(D_3\\): \\(a=4\\) and \\(b=0,1,2\\) \u21d2 \\(|D_3|=3\\) (81,\u202f405,\u202f2025).\n* \\(D_5\\): \\(b=2\\) and \\(a=0,1,2,3,4\\) \u21d2 \\(|D_5|=5\\) (25,\u202f75,\u202f225,\u202f675,\u202f2025).\n* The intersection is \\(\\{2025\\}\\); so \\(|D_3\\cap D_5|=1\\).\n\nWe need subsets that contain at least one element of \\(D_3\\) **and** at least one element of \\(D_5\\).\n\nLet the total number of subsets of \\(A\\) be \\(2^{15}\\).\nLet  \n\n\\[\n\\begin{aligned}\nA_1 &amp;=\\{\\text{subsets that contain no element of } D_3\\},\\\\\nA_2 &amp;=\\{\\text{subsets that contain no element of } D_5\\}.\n\\end{aligned}\n\\]\n\nThen  \n\n\\[\n|A_1|=2^{15-3}=2^{12},\\qquad \n|A_2|=2^{15-5}=2^{10}.\n\\]\n\nSubsets avoiding **both** \\(D_3\\) and \\(D_5\\) avoid the union \\(D_3\\cup D_5\\) which has  \n\n\\[\n|D_3\\cup D_5|=|D_3|+|D_5|-|D_3\\cap D_5|=3+5-1=7\n\\]\n\nelements. Hence  \n\n\\[\n|A_1\\cap A_2|=2^{15-7}=2^{8}.\n\\]\n\nBy inclusion\u2013exclusion, the number of subsets that contain at least one element from each of \\(D_3\\) and \\(D_5\\) is  \n\n\\[\n\\begin{aligned}\nN &amp;= 2^{15}-|A_1|-|A_2|+|A_1\\cap A_2|\\\\\n   &amp;= 2^{15}-2^{12}-2^{10}+2^{8}\\\\\n   &amp;= 32768-4096-1024+256\\\\\n   &amp;= 27904.\n\\end{aligned}\n\\]\n\nAll these subsets are non\u2011empty, so the required probability is  \n\n\\[\n\\frac{N}{2^{15}}=\\frac{27904}{32768}.\n\\]\n\nSimplifying,\n\n\\[\n\\frac{27904}{32768}= \\frac{27904\\div 256}{32768\\div 256}\n                 = \\frac{109}{128}.\n\\]\n\nThus \\(m=109,\\; n=128\\) and  \n\n\\[\nm+n = 109+128 = 237.\n\\]\n\n\\[\n\\boxed{237}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 237</p>\n<p>Extracted Answer: 237</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nFour unit squares form a $2 \\times 2$ grid. Each of the 12 unit line segments forming the sides of the squares is colored either red or blue in such a way that each unit square has 2 red sides and 2 blue sides. Find the number of such colorings.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Label the twelve unit segments as in the picture  \n\n\\[\n\\begin{array}{c}\n\\text{external: }a_1,a_2,b_1,b_2,c_1,c_2,d_1,d_2\\\\[2mm]\n\\text{internal: }e_1,e_2,f_1,f_2\n\\end{array}\n\\]\n\nThe four unit squares are  \n\n\\[\n\\begin{aligned}\n\\text{TL}&amp;:\\;a_1,c_1,e_1,f_1,\\\\\n\\text{TR}&amp;:\\;b_1,c_2,e_1,f_2,\\\\\n\\text{BL}&amp;:\\;a_2,d_1,e_2,f_1,\\\\\n\\text{BR}&amp;:\\;b_2,d_2,e_2,f_2 .\n\\end{aligned}\n\\]\n\nEach square must contain exactly two red sides (hence also two blue sides).\n\n--------------------------------------------------------------------\n### 1.  Reduce to the four internal edges\n\nFor a given square the two sides that are **internal** are already\ncolored once we decide the colors of the four internal edges  \n\\(e_1,e_2,f_1,f_2\\).  \n\nLet  \n\n\\[\nr_{\\rm TL}=e_1+f_1,\\qquad\nr_{\\rm TR}=e_1+f_2,\\qquad\nr_{\\rm BL}=e_2+f_1,\\qquad\nr_{\\rm BR}=e_2+f_2 ,\n\\]\n\nwhere a red edge contributes 1 and a blue edge contributes 0.\nIf a square has \\(r\\) red internal sides, then it must have \\(2-r\\)\nred external sides. Thus\n\n* if \\(r=0\\): both external sides are forced red \u2013 1 way;\n* if \\(r=1\\): exactly one of the two external sides must be red \u2013 2 ways;\n* if \\(r=2\\): both external sides are forced blue \u2013 1 way.\n\nHence for a fixed choice of the four internal edges the number of\nadmissible colourings of the eight external edges equals\n\n\\[\n2^{\\,N_1},\n\\]\n\nwhere \\(N_1\\) is the number of squares among TL, TR, BL, BR that have\nexactly one red internal side.\n\n--------------------------------------------------------------------\n### 2.  Express \\(N_1\\) in terms of the internal edges\n\nWrite  \n\n\\[\nX_1=e_1,\\; X_2=e_2,\\qquad Y_1=f_1,\\;Y_2=f_2\\qquad(\\text{red}=1,\\text{blue}=0).\n\\]\n\nFor a square \\((i,j)\\) (\\(i,j\\in\\{1,2\\}\\)) the number of red internal\nsides is \\(X_i+Y_j\\).\nThus a square has exactly one red internal side precisely when\n\\(X_i\\neq Y_j\\).\n\nLet  \n\n\\[\na=X_1+X_2\\;(=0,1,2),\\qquad b=Y_1+Y_2\\;(=0,1,2).\n\\]\n\nThe number of ordered pairs \\((i,j)\\) with \\(X_i\\neq Y_j\\) is  \n\n\\[\nN_1=a(2-b)+(2-a)b\n      =2\\bigl(a+b-ab\\bigr).\n\\]\n\nConsequently the contribution of a configuration with given\n\\(a,b\\) is  \n\n\\[\n2^{N_1}=2^{\\,2(a+b-ab)}=4^{\\,a+b-ab}.\n\\]\n\n--------------------------------------------------------------------\n### 3.  Count all configurations of the internal edges\n\nThere are \\(\\binom{2}{a}\\) ways to choose which vertical internal edges\nare red, and \\(\\binom{2}{b}\\) ways to choose which horizontal internal\nedges are red.  Hence the total number of colourings is\n\n\\[\n\\sum_{a=0}^{2}\\sum_{b=0}^{2}\n\\binom{2}{a}\\binom{2}{b}\\;4^{\\,a+b-ab}.\n\\]\n\nEvaluating the double sum:\n\n\\[\n\\begin{array}{c|ccc}\na\\backslash b &amp;0&amp;1&amp;2\\\\\\hline\n0 &amp;1\\cdot1\\cdot1=1 &amp;1\\cdot2\\cdot4=8 &amp;1\\cdot1\\cdot16=16\\\\\n1 &amp;2\\cdot1\\cdot4=8 &amp;2\\cdot2\\cdot4=16 &amp;2\\cdot1\\cdot4=8\\\\\n2 &amp;1\\cdot1\\cdot16=16 &amp;1\\cdot2\\cdot4=8 &amp;1\\cdot1\\cdot1=1\n\\end{array}\n\\]\n\nAdding all entries:\n\n\\[\n1+8+16+8+16+8+16+8+1=82.\n\\]\n\n--------------------------------------------------------------------\n### 4.  Answer\n\nThus there are  \n\n\\[\n\\boxed{82}\n\\]\n\ndifferent ways to colour the twelve unit segments so that each of the\nfour unit squares has two red sides and two blue sides.</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 82</p>\n<p>Extracted Answer: 82</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nCircle $\\omega_1$ with radius 6 centered at point $A$ is internally tangent at point $B$ to circle $\\omega_2$ with radius 15. Points $C$ and $D$ lie on $\\omega_2$ such that $\\overline{BC}$ is a diameter of $\\omega_2$ and $\\overline{BC} \\perp \\overline{AD}$. The rectangle $EFGH$ is inscribed in $\\omega_1$ such that $\\overline{EF} \\perp \\overline{BC}$, $C$ is closer to $\\overline{GH}$ than to $\\overline{EF}$, and $D$ is closer to $\\overline{FG}$ than to $\\overline{EH}$, as shown. Triangles $\\triangle DGF$ and $\\triangle CHG$ have equal areas. The area of rectangle $EFGH$ is $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m + n$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>The circles are drawn as in the figure.\n\n* Let \\(O\\) be the centre of \\(\\omega _2\\) (radius \\(15\\)).\n* Let \\(A\\) be the centre of \\(\\omega _1\\) (radius \\(6\\)).\n* Since \\(\\omega _1\\) is internally tangent to \\(\\omega _2\\) at \\(B\\), the three points are collinear and  \n\n\\[\nOA=15-6=9 .\n\\]\n\nTake a coordinate system with  \n\n\\[\nO=(0,0),\\qquad A=(9,0),\\qquad B=(15,0).\n\\]\n\n--------------------------------------------------------------------\n### Points \\(C\\) and \\(D\\)\n\n\\(BC\\) is a diameter of \\(\\omega _2\\); hence \\(C\\) is the antipode of \\(B\\):\n\n\\[\nC=(-15,0).\n\\]\n\n\\(BC\\perp AD\\) means \\(AD\\) is the vertical line \\(x=9\\).  \nIntersecting this line with \\(\\omega _2\\) gives  \n\n\\[\n9^2+y^2=15^2 \\Longrightarrow y=\\pm 12 .\n\\]\n\nBecause the later condition \u201c\\(D\\) is nearer to \\(FG\\) than to \\(EH\\)\u201d forces \\(D\\) to lie **below** the centre, we take  \n\n\\[\nD=(9,-12).\n\\]\n\n--------------------------------------------------------------------\n### The rectangle \\(EFGH\\)\n\nThe rectangle is inscribed in \\(\\omega _1\\) and \\(\\overline{EF}\\perp BC\\); hence \\(\\overline{EF}\\) is vertical.\nLet\n\n\\[\n\\begin{aligned}\nE&amp;=(9+w,\\;h),\\\\[2pt]\nF&amp;=(9+w,\\;-h),\\\\[2pt]\nG&amp;=(9-w,\\;-h),\\\\[2pt]\nH&amp;=(9-w,\\;h),\n\\end{aligned}\n\\]\n\nso that the centre of the rectangle is \\(A\\) (the intersection of the diagonals of an\ninscribed rectangle is the centre of the circumcircle).\n\nBecause the four vertices lie on \\(\\omega _1\\),\n\n\\[\n(9\\pm w-9)^2+h^2=w^{2}+h^{2}=6^{2}=36\\qquad\\Longrightarrow\\qquad w^{2}+h^{2}=36. \\tag{1}\n\\]\n\nThe side \\(\\overline{EF}\\) is the right vertical side, thus\n\\(C\\) (which is far left) is nearer to \\(\\overline{GH}\\) (the left side) than to \\(\\overline{EF}\\);\nand \\(D\\) (which is below the centre) is nearer to \\(\\overline{FG}\\) (the bottom side) than to \\(\\overline{EH}\\) (the top side).  \nThese statements only fix the labeling of the rectangle.\n\n--------------------------------------------------------------------\n### Equality of the two triangular areas\n\n\\[\n\\begin{aligned}\n\\text{Area}\\,\\triangle DGF\n&amp;=\\frac12\\bigl(\\underbrace{2w}_{\\text{base }GF}\\bigr)\n     \\bigl(\\underbrace{12-h}_{\\text{vertical height}}\\bigr)\n = w(12-h),\\\\[4pt]\n\\text{Area}\\,\\triangle CHG\n&amp;=\\frac12\\bigl(\\underbrace{2h}_{\\text{base }HG}\\bigr)\n     \\bigl(\\underbrace{24-w}_{\\text{horizontal distance}}\\bigr)\n = h(24-w).\n\\end{aligned}\n\\]\n\nGiven that the two areas are equal,\n\n\\[\nw(12-h)=h(24-w)\\; \\Longrightarrow\\; 12w=24h\\; \\Longrightarrow\\; w=2h. \\tag{2}\n\\]\n\n--------------------------------------------------------------------\n### Solving for \\(w\\) and \\(h\\)\n\nSubstituting \\(w=2h\\) into (1):\n\n\\[\n(2h)^2+h^{2}=36\\;\\Longrightarrow\\;5h^{2}=36\\;\\Longrightarrow\\;h^{2}= \\frac{36}{5}.\n\\]\n\nHence  \n\n\\[\nh=\\frac{6}{\\sqrt5},\\qquad w=2h=\\frac{12}{\\sqrt5}.\n\\]\n\n--------------------------------------------------------------------\n### Area of the rectangle\n\nThe rectangle\u2019s side lengths are \\(2w\\) and \\(2h\\), so\n\n\\[\n\\text{Area}= (2w)(2h)=4wh\n          =4\\left(\\frac{12}{\\sqrt5}\\right)\\left(\\frac{6}{\\sqrt5}\\right)\n          =4\\cdot\\frac{72}{5}\n          =\\frac{288}{5}.\n\\]\n\nThus the area is \\(\\displaystyle\\frac{m}{n}=\\frac{288}{5}\\) with relatively prime\n\\(m=288,\\;n=5\\).\n\n\\[\nm+n=288+5=293.\n\\]\n\n\\[\n\\boxed{293}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 293</p>\n<p>Extracted Answer: 293</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nFrom an unlimited supply of 1-cent coins, 10-cent coins, and 25-cent coins, Silas wants to find a collection of coins that has a total value of $ N $ cents, where $ N $ is a positive integer. He uses the so-called **greedy algorithm**, successively choosing the coin of greatest value that does not cause the value of his collection to exceed $ N $. For example, to get 42 cents, Silas will choose a 25-cent coin, then a 10-cent coin, then 7 1-cent coins. However, this collection of 9 coins uses more coins than necessary to get a total of 42 cents; indeed, choosing 4 10-cent coins and 2 1-cent coins achieves the same total value with only 6 coins.\n\nIn general, the greedy algorithm succeeds for a given $ N $ if no other collection of 1-cent, 10-cent, and 25-cent coins gives a total value of $ N $ cents using strictly fewer coins than the collection given by the greedy algorithm. Find the number of values of $ N $ between 1 and 1000 inclusive for which the greedy algorithm succeeds.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n\\[\nN=25q+r ,\\qquad 0\\le r\\le 24 .\n\\]\n\nThe greedy algorithm takes  \n\n* \\(q\\) quarters,  \n* \\(\\displaystyle d_0=\\Big\\lfloor\\frac r{10}\\Big\\rfloor\\) dimes,  \n* \\(s_0=r\\bmod 10\\) pennies.  \n\nHence  \n\n\\[\nC_{\\text{greedy}}=q+d_0+s_0 .\\tag{1}\n\\]\n\n--------------------------------------------------------------------\n### 1.  When can a better solution use fewer quarters?\n\nSuppose we use only \\(q-k\\) quarters, \\(k\\ge1\\).  \nThe remaining amount is  \n\n\\[\nR=r+25k .\n\\]\n\nWith only dimes and pennies the optimal way to make \\(R\\) is  \n\n\\[\n\\Big\\lfloor\\frac{R}{10}\\Big\\rfloor\\text{ dimes }+ (R\\bmod10)\\text{ pennies}.\n\\]\n\nThus the total number of coins for this choice is  \n\n\\[\nC(q-k)=(q-k)+\\Big\\lfloor\\frac{r+25k}{10}\\Big\\rfloor+(r+25k\\bmod10).\\tag{2}\n\\]\n\nLet  \n\n\\[\n\\Delta(k)=C(q-k)-C_{\\text{greedy}} .\n\\]\n\nUsing \\(r=10t+a\\;(0\\le a\\le9,\\;t\\in\\{0,1,2\\})\\) we obtain after a short calculation  \n\n\\[\n\\Delta(k)=6k-9\\Big\\lfloor\\frac{a+5k}{10}\\Big\\rfloor .\\tag{3}\n\\]\n\n(Only the last digit \\(a=r\\bmod 10\\) matters.)\n\n--------------------------------------------------------------------\n### 2.  Sign of \\(\\Delta(k)\\)\n\n*If \\(a\\ge5\\):*  \nTake \\(k=1\\).  Then \\(\\lfloor\\frac{a+5}{10}\\rfloor=1\\) and  \n\n\\[\n\\Delta(1)=6-9=-3&lt;0 .\n\\]\n\nHence a better solution exists (remove one quarter).\n\n*If \\(a\\le4\\):*  \nFor any \\(k\\ge1\\),\n\n\\[\n\\Delta(k)=6k-9\\Big\\lfloor\\frac{a+5k}{10}\\Big\\rfloor\n\\ge 6k-9\\frac{a+5k}{10}=1.5k-0.9a .\n\\]\n\nSince \\(a\\le4\\) this is positive for \\(k=1,2\\) (indeed \\(\\Delta(1)=6,\\,\\Delta(2)=3\\)) and for larger \\(k\\) the term \\(1.5k\\) dominates, so \\(\\Delta(k)\\ge0\\) for all \\(k\\).\n\nTherefore **greedy fails iff**  \n\n\\[\na=r\\bmod10\\ge5\\quad\\text{and}\\quad q\\ge1 .\n\\]\n\nEquivalently, for \\(N\\ge25\\),\n\n\\[\nN\\bmod25\\in\\{5,6,7,8,9,15,16,17,18,19\\}.\n\\]\n\n--------------------------------------------------------------------\n### 3.  Counting the failures\n\nThe residues above are ten out of the twenty\u2011five possible residues modulo \\(25\\).  \n\nIn the interval \\(1\\le N\\le1000\\) we have \\(1000/25=40\\) full periods, so each residue occurs \\(40\\) times.  \n\nThus the total number of integers with those residues is  \n\n\\[\n10\\times40=400.\n\\]\n\nBut the ten numbers \\(5,6,7,8,9,15,16,17,18,19\\) are \\&lt;\u202f25, and for them greedy cannot remove a quarter (there are no quarters in any representation).  Those ten are **not** failures.  \n\nHence the genuine failures are  \n\n\\[\n400-10=390.\n\\]\n\n--------------------------------------------------------------------\n### 4.  Successes\n\nThere are \\(1000\\) integers from \\(1\\) to \\(1000\\).  Therefore the number of values for which the greedy algorithm *succeeds* is\n\n\\[\n1000-390=610.\n\\]\n\n--------------------------------------------------------------------\n\\[\n\\boxed{610}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 610</p>\n<p>Extracted Answer: 610</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThere are $ n $ values of $ x $ in the interval $ 0 &lt; x &lt; 2\\pi $ where $ f(x) = \\sin(7\\pi \\cdot \\sin(5x)) = 0 $. For $ t $ of these $ n $ values of $ x $, the graph of $ y = f(x) $ is tangent to the $ x $-axis. Find $ n + t $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>\\[\nf(x)=\\sin\\bigl(7\\pi\\sin(5x)\\bigr)\n\\]\n\n---\n\n### 1.  Zeros of \\(f\\)\n\n\\(f(x)=0\\iff 7\\pi\\sin(5x)=k\\pi\\) for an integer \\(k\\).\n\n\\[\n\\sin(5x)=\\frac{k}{7},\\qquad |k|\\le 7 .\n\\]\n\nLet  \n\n\\[\ny=5x\\;(0&lt;y&lt;10\\pi).\n\\]\n\nFor each integer \\(k\\) with \\(|k|\\le7\\) we count the solutions of \\(\\sin y=\\dfrac{k}{7}\\) in \\((0,10\\pi)\\).\n\n* \\(k=7\\)  : \\(\\sin y=1\\).  Solutions \\(y=\\frac{\\pi}{2}+2\\pi n\\) \\((n=0,1,2,3,4)\\) \u2192 **5** solutions.  \n* \\(k=-7\\) : \\(\\sin y=-1\\).  Solutions \\(y=\\frac{3\\pi}{2}+2\\pi n\\) \\((n=0,1,2,3,4)\\) \u2192 **5** solutions.  \n* \\(k=0\\)  : \\(\\sin y=0\\).  Solutions \\(y=m\\pi\\;(m=1,2,\\dots ,9)\\) \u2192 **9** solutions.  \n* For each \\(k=\\pm1,\\pm2,\\pm3,\\pm4,\\pm5,\\pm6\\) we have \\(\\sin y=c\\) with \\(-1&lt;c&lt;1,\\;c\\neq0\\).  \n  In each of the 5 full periods of \\(\\sin y\\) there are exactly two such points, so **\\(5\\cdot2=10\\)** solutions per \\(k\\).\n\nThere are 12 values of \\(k\\) with \\(|k|\\in\\{1,\\dots ,6\\}\\), giving  \n\n\\[\n12\\times10=120\\text{ solutions}.\n\\]\n\nAdding all contributions,\n\n\\[\nn=5+5+9+120=139 .\n\\]\n\n---\n\n### 2.  Tangent zeros\n\nThe graph is tangent to the \\(x\\)-axis at a zero where the derivative also vanishes.\n\n\\[\nf&#39;(x)=\\cos\\bigl(7\\pi\\sin(5x)\\bigr)\\cdot 35\\pi\\cos(5x).\n\\]\n\nAt a zero, \\(\\sin\\bigl(7\\pi\\sin(5x)\\bigr)=0\\) gives \\(\\sin(5x)=\\dfrac{k}{7}\\).  \nBecause \\(\\cos\\bigl(7\\pi\\sin(5x)\\bigr)=\\pm1\\neq0\\), we must have \\(\\cos(5x)=0\\).\n\n\\[\n\\cos(5x)=0\\Longrightarrow \\sin(5x)=\\pm1 .\n\\]\n\nThus tangential zeros occur exactly when \\(\\sin(5x)=\\pm1\\), i.e. for \\(k=\\pm7\\).\n\nWe already counted those solutions:  \n\n* \\(\\sin(5x)=1\\) \u2192 5 points,  \n* \\(\\sin(5x)=-1\\) \u2192 5 points.\n\nHence  \n\n\\[\nt=5+5=10 .\n\\]\n\n---\n\n### 3.  Required sum\n\n\\[\nn+t=139+10=149.\n\\]\n\n\\[\n\\boxed{149}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 149</p>\n<p>Extracted Answer: 149</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $ S $ be the set of vertices of a regular 24-gon. Find the number of ways to draw 12 segments of equal lengths so that each vertex in $ S $ is an endpoint of exactly one of the 12 segments.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let the vertices of the regular \\(24\\)-gon be numbered \\(0,1,\\dots ,23\\) (mod \\(24\\)).\nIf a segment joins vertex \\(i\\) to vertex \\(j\\) we call its **step**\n\\[\nk\\equiv j-i\\pmod{24},\\qquad 1\\le k\\le 12 .\n\\]\n\nThe length of a chord depends only on this step:\nthe chord of step \\(k\\) has length  \n\n\\[\n\\ell(k)=2R\\sin\\frac{\\pi k}{24},\\qquad 1\\le k\\le 12 .\n\\]\n\nSince \\(\\sin(\\theta )\\) is strictly increasing on \\([0,\\frac{\\pi}{2}]\\),\nthe lengths \\(\\ell(1),\\ell(2),\\dots ,\\ell(12)\\) are all distinct.\nThus a drawing in which all 12 segments have the same length must use\nedges whose step is a fixed \\(k\\) (the same chord length).\n\n--------------------------------------------------------------------\n\n### 1.  The graph of step \\(k\\)\n\nConsider the undirected graph \\(G_k\\) whose vertices are the 24 polygon vertices\nand whose edges are all chords of step \\(k\\) (i.e. the pairs \\(\\{i,i+k\\}\\)).\nEach vertex of \\(G_k\\) is incident to two such chords\n(\\(i\\) connects to \\(i+k\\) and to \\(i-k\\)), so \\(G_k\\) is a disjoint union of\ncycles.\n\nLet  \n\n\\[\nd=\\gcd(24,k).\n\\]\n\nThen the vertices split into \\(d\\) cycles, each of length  \n\n\\[\n\\frac{24}{d}.\n\\]\n\n--------------------------------------------------------------------\n\n### 2.  When can a perfect matching be formed?\n\nA perfect matching can be taken inside one cycle only when the cycle has even\nlength.  Hence we need \\(\\frac{24}{d}\\) even, i.e. \\(d\\neq 8\\).  \n\n* If \\(d=8\\) (the case \\(k=8\\)) each component is a triangle; a triangle has\nno perfect matching, so **no drawing** is possible.\n\n* If the cycle length is \\(2\\) (the case \\(d=12,\\;k=12\\)), each component is a\nsingle edge; there is exactly **one** perfect matching \u2013 the 12 diameters.\n\n* For any other admissible \\(k\\) the cycles have even length \\(\\ge4\\).\nInside each such cycle there are exactly two ways to choose a perfect matching\n(alternate edges).  Since the cycles are independent, the number of perfect\nmatchings for the given \\(k\\) is  \n\n\\[\n2^{\\,d}\\qquad (d=\\gcd(24,k),\\;d\\neq 8,\\;k\\neq 12).\n\\]\n\n--------------------------------------------------------------------\n\n### 3.  Counting for each step\n\n\\[\n\\begin{array}{c|c|c|c}\nk &amp; d=\\gcd(24,k) &amp; \\text{cycle length }24/d &amp; \\#\\text{ matchings}\\\\ \\hline\n1 &amp; 1 &amp; 24 &amp; 2\\\\\n2 &amp; 2 &amp; 12 &amp; 2^{2}=4\\\\\n3 &amp; 3 &amp; 8 &amp; 2^{3}=8\\\\\n4 &amp; 4 &amp; 6 &amp; 2^{4}=16\\\\\n5 &amp; 1 &amp; 24 &amp; 2\\\\\n6 &amp; 6 &amp; 4 &amp; 2^{6}=64\\\\\n7 &amp; 1 &amp; 24 &amp; 2\\\\\n8 &amp; 8 &amp; 3 &amp; 0\\\\\n9 &amp; 3 &amp; 8 &amp; 2^{3}=8\\\\\n10&amp; 2 &amp; 12&amp; 2^{2}=4\\\\\n11&amp; 1 &amp; 24&amp; 2\\\\\n12&amp;12 &amp; 2 &amp; 1\\ (\\text{forced diameters})\n\\end{array}\n\\]\n\n--------------------------------------------------------------------\n\n### 4.  Total number of drawings\n\nAdd the numbers of matchings over all admissible steps:\n\n\\[\n\\begin{aligned}\nN&amp;=2+4+8+16+2+64+2+8+4+2+1\\\\\n&amp;=113 .\n\\end{aligned}\n\\]\n\n--------------------------------------------------------------------\n\n\\[\n\\boxed{113}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 113</p>\n<p>Extracted Answer: 113</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nSixteen chairs are arranged in a row. Eight people each select a chair in which to sit so that no person sits next to two other people. Let $ N $ be the number of subsets of 16 chairs that could be selected. Find the remainder when $ N $ is divided by 1000.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>The 8 occupied chairs must avoid a configuration where a person has two neighbours.  \nHence no three occupied chairs may be consecutive.\n\nLet a be the number of blocks of two consecutive occupied chairs.  \nEach block of two contributes an extra occupied chair, so the total number of blocks is  \n\n\\[\nb = 8-a\\qquad (0\\le a\\le 4).\n\\]\n\n*Choosing which blocks are of size\u202f2*: \\(\\displaystyle \\binom{b}{a}\\).\n\nThere are \\(16-8=8\\) empty chairs. Between the \\(b\\) blocks there must be at least one empty chair, using \\(b-1\\) empties.  \nThe remaining \\(8-(b-1)=9-b\\) empty chairs can be placed in the \\(b+1\\) gaps (before the first block, after the last, and the \\(b-1\\) internal gaps) without restriction.  \n\nNumber of ways to distribute them:  \n\n\\[\n\\binom{(9-b)+(b+1)-1}{(b+1)-1}= \\binom{9}{b}.\n\\]\n\nThus for a given \\(a\\),\n\n\\[\n\\text{ways}= \\binom{b}{a}\\binom{9}{b}\n          =\\binom{8-a}{a}\\binom{9}{8-a}.\n\\]\n\nSumming over \\(a=0,1,2,3,4\\),\n\n\\[\n\\begin{aligned}\nN &amp;=\\binom{8}{0}\\binom{9}{8} \n   +\\binom{7}{1}\\binom{9}{7}\n   +\\binom{6}{2}\\binom{9}{6}\n   +\\binom{5}{3}\\binom{9}{5}\n   +\\binom{4}{4}\\binom{9}{4} \\\\[2mm]\n  &amp;= 1\\cdot 9 + 7\\cdot 36 + 15\\cdot 84 + 10\\cdot 126 + 1\\cdot126\\\\\n  &amp;= 9+252+1260+1260+126 = 2907.\n\\end{aligned}\n\\]\n\nTherefore  \n\n\\[\nN \\equiv 2907 \\pmod{1000}=907.\n\\]\n\n\\[\n\\boxed{907}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 907</p>\n<p>Extracted Answer: 907</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $ A_1A_2 \\ldots A_{11} $ be an 11-sided non-convex simple polygon with the following properties:\n* The area of $ A_iA_1A_{i+1} $ is 1 for each $ 2 \\leq i \\leq 10 $,\n* $ \\cos(\\angle A_iA_1A_{i+1}) = \\frac{12}{13} $ for each $ 2 \\leq i \\leq 10 $,\n* The perimeter of $ A_1A_2 \\ldots A_{11} $ is 20.\nIf $ A_1A_2 + A_1A_{11} $ can be expressed as $ \\frac{m\\sqrt{n} - p}{q} $ for positive integers $ m, n, p, q $ with $ n $ squarefree and no prime divides all of $ m, p, q$, find $ m + n + p + q $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n\\[\nr_i=|A_1A_i| \\qquad (i=2,\\dots ,11)\n\\]\n\nand denote  \n\n\\[\n\\theta=\\angle A_iA_1A_{i+1}\\qquad (2\\le i\\le 10).\n\\]\n\nBecause  \n\n\\[\n\\cos\\theta=\\frac{12}{13}\\;\\Longrightarrow\\;\\sin\\theta=\\frac{5}{13},\n\\]\n\nthe area of \\(\\triangle A_iA_1A_{i+1}\\) is  \n\n\\[\n\\frac12 r_i r_{i+1}\\sin\\theta\n   =\\frac12 r_i r_{i+1}\\frac{5}{13}=1 .\n\\]\n\nHence  \n\n\\[\nr_i r_{i+1}= \\frac{26}{5}=K\\qquad (2\\le i\\le 10). \\tag{1}\n\\]\n\nFrom (1),\n\n\\[\nr_{i+2}= \\frac{K}{r_{i+1}}=r_i ,\n\\]\n\nso the distances from \\(A_1\\) alternate:\n\n\\[\nr_2=r_4=r_6=r_8=r_{10}=a,\\qquad\nr_3=r_5=r_7=r_9=r_{11}=b,\n\\]\n\nwith  \n\n\\[\nab=K=\\frac{26}{5}. \\tag{2}\n\\]\n\n--------------------------------------------------------------------\n### Lengths of the other sides\n\nFor any \\(i=2,\\dots ,10\\) the side \\(A_iA_{i+1}\\) (call it \\(L\\)) satisfies the law of cosines:\n\n\\[\nL^2=a^{2}+b^{2}-2ab\\cos\\theta\n      =a^{2}+b^{2}-2ab\\frac{12}{13}.\n\\]\n\nUsing (2),\n\n\\[\nL^2=a^{2}+b^{2}-\\frac{24}{13}\\cdot\\frac{26}{5}\n    =a^{2}+b^{2}-\\frac{48}{5}.\n\\]\n\nSince \\(a^{2}+b^{2}=(a+b)^{2}-2ab\\),\n\n\\[\nL^2=(a+b)^{2}-2\\frac{26}{5}-\\frac{48}{5}\n     =(a+b)^{2}-20.\n\\]\n\nLet  \n\n\\[\ns=a+b.\n\\]\n\nThen  \n\n\\[\nL=\\sqrt{s^{2}-20}. \\tag{3}\n\\]\n\n--------------------------------------------------------------------\n### Using the perimeter\n\nThe perimeter of the 11\u2011gon is\n\n\\[\n|A_1A_2|+|A_1A_{11}|+\\sum_{i=2}^{10}|A_iA_{i+1}|\n= a+b+9L = s+9\\sqrt{s^{2}-20}=20.\n\\]\n\nSet \\(t=\\sqrt{s^{2}-20}&gt;0\\). Then \\(s=20-9t\\) and\n\n\\[\nt^{2}=s^{2}-20=(20-9t)^{2}-20.\n\\]\n\nSolving,\n\n\\[\nt^{2}=380-360t+81t^{2}\n\\Longrightarrow 80t^{2}-360t+380=0\n\\Longrightarrow 4t^{2}-18t+19=0.\n\\]\n\nHence  \n\n\\[\nt=\\frac{18\\pm\\sqrt{324-304}}{8}\n   =\\frac{18\\pm2\\sqrt5}{8}\n   =\\frac{9\\pm\\sqrt5}{4}.\n\\]\n\nIf the plus sign is taken, \\(t&gt;\\frac{20}{9}\\) and \\(s=20-9t&lt;0\\), impossible.\nThus  \n\n\\[\nt=\\frac{9-\\sqrt5}{4},\n\\qquad\ns=20-9t=\\frac{9\\sqrt5-1}{4}.\n\\]\n\nConsequently  \n\n\\[\nA_1A_2+A_1A_{11}=s=\\frac{9\\sqrt5-1}{4}.\n\\]\n\nWritten as \\(\\dfrac{m\\sqrt n-p}{q}\\) we have  \n\n\\[\nm=9,\\;n=5,\\;p=1,\\;q=4,\n\\]\n\nso  \n\n\\[\nm+n+p+q=9+5+1+4=19.\n\\]\n\n\\[\n\\boxed{19}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 19</p>\n<p>Extracted Answer: 19</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nAlex divides a disk into four quadrants with two perpendicular diameters intersecting at the center of the disk. He draws 25 more line segments through the disk, drawing each segment by selecting two points at random on the perimeter of the disk in different quadrants and connecting those two points. Find the expected number of regions into which these 27 line segments divide the disk.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>**Step 1.  Regions created by chords**\n\nIf a circle already has \\(k\\) chords drawn in its interior, then a new chord\nadds one region for itself plus one extra region for every interior\nintersection it creates.  \nThus for a set of \\(n\\) chords\n\n\\[\n\\text{# regions}=n+1+\\text{# interior intersection points.}\n\\]\n\nIn our problem we have  \n\n* 2 fixed diameters (the two perpendicular ones),  \n* 25 random chords.\n\nHence \\(n=27\\).  \nWe only have to find the expected number \\(I\\) of interior intersection\npoints.\n\n\\[\nE[\\text{regions}]=27+1+E[I]=28+E[I].\n\\]\n\n--------------------------------------------------------------------\n\n**Step 2.  Intersections involving the two diameters**\n\nLet the horizontal diameter be the line that separates the *upper* quadrants\n\\(Q_{1},Q_{2}\\) from the *lower* quadrants \\(Q_{3},Q_{4}\\).\n\nA random chord has its two endpoints in different quadrants.\nThe chord meets the horizontal diameter exactly when the endpoints lie in\ndifferent half\u2011planes, i.e. one endpoint is in \\(\\{Q_{1},Q_{2}\\}\\) and the\nother in \\(\\{Q_{3},Q_{4}\\}\\).\n\nFor the ordered pair of quadrants of a random chord there are  \n\\(12\\) equally likely possibilities (the \\(4\\cdot 3\\) ordered pairs with\ndifferent quadrants).  \nExactly \\(8\\) of them have the endpoints in opposite half\u2011planes, hence\n\n\\[\np_d=\\Pr(\\text{a random chord meets a given diameter})=\\frac{8}{12}=\n\\frac{2}{3}.\n\\]\n\nTherefore\n\n\\[\n\\boxed{\\text{Expected intersections of the 25 chords with one diameter}=25\\cdot\\frac23}\n\\]\n\nand with the two diameters together\n\n\\[\nE[I_{\\text{diameters}}]=2\\cdot25\\cdot\\frac23=\\frac{100}{3}.\n\\]\n\nThe two diameters intersect each other once, so add \\(1\\) more interior\nintersection.\n\n--------------------------------------------------------------------\n\n**Step 3.  Intersections of two random chords**\n\nDenote the four endpoints by  \n\\(\\alpha_1,\\alpha_2\\) (chord 1) and \\(\\beta_1,\\beta_2\\) (chord 2).  \nAll four points are independent uniform on the circle.\n\nLet  \n\n\\[\nA=\\{\\text{endpoints of chord 1 lie in different quadrants}\\},\\qquad \nB=\\{\\text{endpoints of chord 2 lie in different quadrants}\\}.\n\\]\n\n\\[\nP(A)=P(B)=\\frac34 .\n\\]\n\nTwo chords intersect iff the endpoints are interleaved on the circle,\ni.e. exactly one of \\(\\beta_1,\\beta_2\\) lies on the clockwise arc from\n\\(\\alpha_1\\) to \\(\\alpha_2\\).\n\nFix \\(\\alpha_1=x\\) and \\(\\alpha_2=y\\) (with \\(x\\neq y\\)).\nLet \\(I=(x,y)\\) be the clockwise arc from \\(x\\) to \\(y\\) and let\n\\(d=|I|\\) be its length.  \nFor independent uniform \\(\\beta_1,\\beta_2\\),\n\n* the probability that exactly one lies in \\(I\\) is \\(2d(1-d)\\);\n* the probability that the two \\(\\beta\\)\u2019s are in *different* quadrants\n  is \\(\\frac34\\).\n\nConditioning on the actual placement of the interval \\(I\\) with respect\nto the four quarter\u2011arcs yields (after a short computation)\n\n\\[\n\\Pr(\\beta_1,\\beta_2\\text{ satisfy both conditions}\\mid x,y)=\n2\\Bigl[d\\Bigl(\\tfrac34-d\\Bigr)+\\sum_{q=0}^{3}a_q^{\\,2}\\Bigr],\n\\tag{1}\n\\]\n\nwhere \\(a_q\\) is the length of the part of \\(I\\) that lies in quadrant\n\\(q\\).\n\nNow average (1) over all ordered pairs \\((x,y)\\) that are in different\nquadrants.  By symmetry it suffices to place \\(x\\) in the first quadrant\n\\([0,\\tfrac14)\\) and let \\(y\\) run in the three other quadrants.\nCarrying out the integration (splitting the three possible clockwise\ndistances) gives\n\n\\[\n\\int\\!\\!\\int_{x\\in Q_0,\\;y\\in Q_m}\n2\\Bigl[d\\Bigl(\\tfrac34-d\\Bigr)+\\sum a_q^{\\,2}\\Bigr]\\,dy\\,dx\n   =\\frac{17}{64}\\qquad(m=1,2,3\\text{ summed}).\n\\]\n\nThus\n\n\\[\nP(A\\cap B\\cap\\{\\text{the chords intersect}\\})=\\frac{17}{64}.\n\\]\n\nFinally\n\n\\[\np_r=\n\\Pr(\\text{intersection}\\mid A\\cap B)=\n\\frac{P(A\\cap B\\cap\\text{intersect})}{P(A)P(B)}\n=\\frac{17/64}{(3/4)^2}\n=\\frac{16}{9}\\cdot\\frac{17}{64}\n=\\frac{17}{36}.\n\\]\n\n--------------------------------------------------------------------\n\n**Step 4.  Expected interior intersections**\n\n* Intersections of the two diameters: \\(1\\).\n* Intersections of the 25 random chords with the two diameters:\n  \\(\\displaystyle \\frac{100}{3}\\).\n* Intersections among the 25 random chords:\n  \\(\\displaystyle \\binom{25}{2}\\,p_r\n   =300\\cdot\\frac{17}{36}= \\frac{425}{3}\\).\n\nHence\n\n\\[\nE[I]=1+\\frac{100}{3}+\\frac{425}{3}\n     =1+\\frac{525}{3}=1+175=176.\n\\]\n\n--------------------------------------------------------------------\n\n**Step 5.  Expected number of regions**\n\n\\[\nE[\\text{regions}]=27+1+E[I]=28+176=204.\n\\]\n\n--------------------------------------------------------------------\n\n\\[\n\\boxed{204}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 204</p>\n<p>Extracted Answer: 204</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nSuppose $ \\triangle ABC $ has angles $ \\angle BAC = 84^\\circ $, $ \\angle ABC = 60^\\circ $, and $ \\angle ACB = 36^\\circ $. Let $ D, E, $ and $ F $ be the midpoints of sides $ \\overline{BC} $, $ \\overline{AC} $, and $ \\overline{AB} $, respectively. The circumcircle of $ \\triangle DEF $ intersects $ \\overline{BD} $, $ \\overline{AE} $, and $ \\overline{AF} $ at points $ G, H, $ and $ J $, respectively. The points $ G, D, E, H, J, $ and $ F $ divide the circumcircle of $ \\triangle DEF $ into six minor arcs, as shown. Find $ \\widehat{DE} + 2 \\cdot \\widehat{HJ} + 3 \\cdot \\widehat{FG} $, where the arcs are measured in degrees.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n\\[\n\\triangle ABC\\qquad \n\\angle A=84^{\\circ},\\; \\angle B=60^{\\circ},\\; \\angle C=36^{\\circ}.\n\\]\n\nDenote  \n\n\\[\nD,E,F \\text{ \u2013 the midpoints of }BC,CA,AB,\n\\]\n\\[\nG,H,J \\text{ \u2013 the second intersections of }BD,AE,AF\\text{ with the circumcircle of } \\triangle DEF .\n\\]\n\n--------------------------------------------------------------------\n### 1.  The points \\(G,H,J\\) are the feet of the altitudes  \n\nThe nine\u2011point circle of \\(\\triangle ABC\\) passes through the three midpoints \\(D,E,F\\) **and** through the three feet of the altitudes.  \nBecause  \n\n* \\(BD\\) lies on the side \\(BC\\),  \n* \\(AE\\) lies on the side \\(CA\\),  \n* \\(AF\\) lies on the side \\(AB\\),\n\nthe second intersection of each of these sides with the nine\u2011point circle must be the corresponding foot of an altitude:\n\n\\[\n\\begin{aligned}\nG&amp;= \\text{foot from }A\\text{ onto }BC,\\\\[2mm]\nH&amp;= \\text{foot from }B\\text{ onto }CA,\\\\[2mm]\nJ&amp;= \\text{foot from }C\\text{ onto }AB .\n\\end{aligned}\n\\]\n\nThus \\(G,H,J\\) are the vertices of the orthic triangle.\n\n--------------------------------------------------------------------\n### 2.  Arc \\(\\widehat{DE}\\)\n\nThe medial triangle \\(\\triangle DEF\\) is similar to \\(\\triangle ABC\\) (ratio \\(1\\!:\\!2\\)).  \nConsequently  \n\n\\[\n\\angle DFE = \\angle C = 36^{\\circ}.\n\\]\n\nFor any inscribed angle, the intercepted minor arc is twice the angle; hence  \n\n\\[\n\\widehat{DE}=2\\angle DFE = 2\\cdot 36^{\\circ}=72^{\\circ}.\n\\]\n\n--------------------------------------------------------------------\n### 3.  Arc \\(\\widehat{FG}\\)\n\nSince \\(D\\) and \\(G\\) both lie on side \\(BC\\), the chord \\(DG\\) is a part of \\(BC\\).  \nThe chord \\(DF\\) joins the midpoints of \\(AB\\) and \\(BC\\); by the Midpoint Theorem  \n\n\\[\nDF \\parallel AC .\n\\]\n\nTherefore  \n\n\\[\n\\angle FDG =\\angle (\\text{line }DF,\\text{ line }DG)\n        =\\angle (AC,BC)=\\angle C=36^{\\circ}.\n\\]\n\nThus  \n\n\\[\n\\widehat{FG}=2\\angle FDG = 2\\cdot 36^{\\circ}=72^{\\circ}.\n\\]\n\n--------------------------------------------------------------------\n### 4.  Arc \\(\\widehat{HJ}\\)\n\n\\(H,J,G\\) are the vertices of the orthic triangle.  \nA standard fact about the orthic triangle is that its angles are  \n\n\\[\n\\angle HGJ = 180^{\\circ}-2\\angle A,\\qquad\n\\angle GJH = 180^{\\circ}-2\\angle B,\\qquad\n\\angle JHG = 180^{\\circ}-2\\angle C .\n\\]\n\n(The fact follows from simple angle\u2011chasing with the right\u2011angles at the feet of the altitudes.)\n\nHence the minor arc opposite \\(G\\) \u2013 that is, \\(\\widehat{HJ}\\) \u2013 satisfies  \n\n\\[\n\\widehat{HJ}=2\\angle HGJ =2\\bigl(180^{\\circ}-2A\\bigr)\n               =360^{\\circ}-4A.\n\\]\n\nWith \\(\\angle A =84^{\\circ}\\),\n\n\\[\n\\widehat{HJ}=360^{\\circ}-4\\cdot84^{\\circ}=24^{\\circ}.\n\\]\n\n--------------------------------------------------------------------\n### 5.  Required sum\n\n\\[\n\\begin{aligned}\n\\widehat{DE}+2\\widehat{HJ}+3\\widehat{FG}\n&amp;= 72^{\\circ}+2\\cdot24^{\\circ}+3\\cdot72^{\\circ}\\\\\n&amp;= 72^{\\circ}+48^{\\circ}+216^{\\circ}\\\\[2mm]\n&amp;= 336^{\\circ}.\n\\end{aligned}\n\\]\n\n--------------------------------------------------------------------\n\\[\n\\boxed{336}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 336</p>\n<p>Extracted Answer: 336</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $ \\triangle ABC $ be a right triangle with $ \\angle A = 90^\\circ $ and $ BC = 38 $. There exist points $ K $ and $ L $ inside the triangle such that $ AK = AL = BK = CL = KL = 14. $ The area of the quadrilateral $ BKLC $ can be expressed as $ n \\sqrt{3} $ for some positive integer $ n $. Find $ n $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n\\[\n\\angle A =90^\\circ ,\\qquad BC =38 .\n\\]\n\nPlace  \n\n\\[\nA=(0,0),\\qquad B=(b,0),\\qquad C=(0,c)\n\\]\n\nso that the legs are  \n\n\\[\nAB=b,\\qquad AC=c,\\qquad b^{2}+c^{2}=38^{2}=1444 .\n\\tag{1}\n\\]\n\n--------------------------------------------------------------------\n### 1.  Coordinates of \\(K\\) and \\(L\\)\n\nBecause  \n\n\\[\nAK=BK=14,\n\\]\n\n\\(K\\) lies on the perpendicular bisector of \\(\\overline{AB}\\); hence  \n\n\\[\nK=\\Bigl(\\frac b2,\\;\\sqrt{14^{2}-\\Bigl(\\frac b2\\Bigr)^{2}}\\Bigr)\n   =\\bigl( X,\\;U\\bigr)\n\\]\n\nwith  \n\n\\[\nX=\\frac b2,\\qquad U=\\sqrt{196-X^{2}} .\\tag{2}\n\\]\n\nSimilarly  \n\n\\[\nAL=CL=14\\Longrightarrow \nL=\\Bigl(\\sqrt{196-\\Bigl(\\frac c2\\Bigr)^{2}},\\;\\frac c2\\Bigr)\n   =(V,Y),\\qquad \nY=\\frac c2,\\;V=\\sqrt{196-Y^{2}} .\\tag{3}\n\\]\n\nThus  \n\n\\[\nX^{2}+Y^{2}= \\frac{b^{2}+c^{2}}{4}\n           =\\frac{1444}{4}=361 .\\tag{4}\n\\]\n\n--------------------------------------------------------------------\n### 2.  The equilateral triangle \\(AKL\\)\n\nAll three sides of \\(\\triangle AKL\\) equal \\(14\\), so \\(\\angle KAL=60^\\circ\\).\nUsing the vectors \\(\\overrightarrow{AK}=(X,U)\\) and \\(\\overrightarrow{AL}=(V,Y)\\),\n\n\\[\n\\overrightarrow{AK}\\cdot\\overrightarrow{AL}=|AK||AL|\\cos 60^\\circ\n\\Longrightarrow\nXV+YU=98 .\\tag{5}\n\\]\n\nFrom (2)\u2013(5) we have the system\n\n\\[\n\\begin{cases}\nX^{2}+Y^{2}=361,\\\\[2pt]\nX\\sqrt{196-Y^{2}}+Y\\sqrt{196-X^{2}}=98 .\n\\end{cases}\n\\]\n\n--------------------------------------------------------------------\n### 3.  Solving the system\n\nSet  \n\n\\[\nX=14\\cos\\alpha ,\\qquad U=14\\sin\\alpha ,\\qquad \nY=14\\cos\\beta ,\\qquad V=14\\sin\\beta .\n\\]\n\nThen (5) becomes  \n\n\\[\n14^{2}\\bigl(\\cos\\alpha\\sin\\beta+\\cos\\beta\\sin\\alpha\\bigr)\n   =196\\sin(\\alpha+\\beta)=98,\n\\]\n\nhence  \n\n\\[\n\\sin(\\alpha+\\beta)=\\frac12\\Longrightarrow\\alpha+\\beta=\\frac{\\pi}{6}\\;(30^\\circ). \\tag{6}\n\\]\n\nFrom \\(X^{2}+Y^{2}=361\\),\n\n\\[\n196\\bigl(\\cos^{2}\\alpha+\\cos^{2}\\beta\\bigr)=361\n\\Longrightarrow\n\\cos^{2}\\alpha+\\cos^{2}\\beta= \\frac{361}{196}=1+\\frac{165}{196}.\n\\]\n\nUsing \\(\\cos^{2}\\alpha+\\cos^{2}\\beta=\n1+\\cos(\\alpha+\\beta)\\cos(\\alpha-\\beta)\\) gives  \n\n\\[\n\\cos\\frac{\\pi}{6}\\,\\cos(\\alpha-\\beta)=\\frac{165}{196}\n\\Longrightarrow\n\\cos(\\alpha-\\beta)=\\frac{165}{98\\sqrt3}\n       =\\frac{55\\sqrt3}{98}.\n\\]\n\nHence  \n\n\\[\n\\sin(\\alpha-\\beta)=\\sqrt{1-\\Bigl(\\frac{55\\sqrt3}{98}\\Bigr)^{2}}\n                 =\\frac{23}{98}.\n\\]\n\nNow compute \\(\\cos\\alpha\\) and \\(\\cos\\beta\\):\n\\[\n\\cos\\alpha=\\sqrt{\\frac{1+\\cos(\\alpha+\\beta)}{2}}\n          =\\sqrt{\\frac{1+\\frac{71}{98}}{2}}\n          =\\frac{13}{14},\n\\qquad\n\\cos\\beta =\\sqrt{\\frac{1+\\cos(\\alpha-\\beta)}{2}}\n          =\\sqrt{\\frac{1+\\frac{47}{49}}{2}}\n          =\\frac{4\\sqrt3}{7}.\n\\]\n\nTherefore  \n\n\\[\nX=14\\cos\\alpha =13,\\qquad \nY=14\\cos\\beta =8\\sqrt3 .\n\\]\n\nConsequently  \n\n\\[\nb=2X=26,\\qquad c=2Y=16\\sqrt3 .\n\\]\n\nOne easily checks that \\(b^{2}+c^{2}=26^{2}+ (16\\sqrt3)^{2}=1444\\), i.e. \\(BC=38\\).\n\n--------------------------------------------------------------------\n### 4.  Area of \\(BKLC\\)\n\nThe right\u2011triangle \\(ABC\\) has area  \n\n\\[\n[ABC]=\\frac12\\,b\\,c\n      =\\frac12\\cdot26\\cdot16\\sqrt3\n      =208\\sqrt3 .\n\\]\n\nThe three small triangles cut off by \\(K\\) and \\(L\\) have areas  \n\n\\[\n\\begin{aligned}\n[ABK]&amp;=\\frac12\\cdot b\\cdot U\n      =\\frac12\\cdot26\\cdot3\\sqrt3=39\\sqrt3,\\\\[2pt]\n[ALC]&amp;=\\frac12\\cdot c\\cdot V\n      =\\frac12\\cdot16\\sqrt3\\cdot2=16\\sqrt3,\\\\[2pt]\n[AKL]&amp;=\\frac{\\sqrt3}{4}\\cdot14^{2}=49\\sqrt3 .\n\\end{aligned}\n\\]\n\nThus\n\n\\[\n\\begin{aligned}\n[BKLC] &amp;=[ABC]-[ABK]-[ALC]-[AKL]\\\\\n       &amp;=208\\sqrt3-(39\\sqrt3+16\\sqrt3+49\\sqrt3)\\\\\n       &amp;=104\\sqrt3 .\n\\end{aligned}\n\\]\n\nHence the area of \\(BKLC\\) is \\(n\\sqrt3\\) with  \n\n\\[\n\\boxed{n=104}.\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 104</p>\n<p>Extracted Answer: None</p>\n<p>Score: 0.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet the sequence of rationals $ x_1, x_2, \\ldots $ be defined such that $ x_1 = \\frac{25}{11} $ and\n$ x_{k+1} = \\frac{1}{3} \\left( x_k + \\frac{1}{x_k} - 1 \\right). $\n$ x_{2025} $ can be expressed as $ \\frac{m}{n} $ for relatively prime positive integers $ m $ and $ n $. Find the remainder when $ m + n $ is divided by 1000.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>**Solution**\n\n\\[\nx_{k+1}= \\frac13\\Bigl(x_k+\\frac1{x_k}-1\\Bigr),\\qquad \nx_1=\\frac{25}{11}\n\\]\n\nWrite each term as a reduced fraction  \n\n\\[\nx_k=\\frac{p_k}{q_k},\\qquad \\gcd(p_k,q_k)=1 .\n\\]\n\nThen  \n\n\\[\nx_{k+1}= \\frac{p_k^2+q_k^2-p_kq_k}{3p_kq_k}\n      =\\frac{p_{k+1}}{q_{k+1}}\n\\]\n\nwhere  \n\n\\[\np_{k+1}= \\frac{p_k^2+q_k^2-p_kq_k}{3},\n\\qquad \nq_{k+1}=p_kq_k . \\tag{1}\n\\]\n\n(The numerator is always divisible by \\(3\\); one checks that\n\\(\\gcd(p_{k+1},q_{k+1})=1\\) for every \\(k\\).)\n\n--------------------------------------------------------------------\n### 1.  A simple recurrence for the sum  \n\nLet  \n\n\\[\ns_k=p_k+q_k .\n\\]\n\nAdding the two formulas in (1),\n\n\\[\n\\begin{aligned}\ns_{k+1}&amp;=p_{k+1}+q_{k+1}\n        =\\frac{p_k^2+q_k^2-p_kq_k}{3}+p_kq_k  \\\\\n        &amp;=\\frac{p_k^2+2p_kq_k+q_k^2}{3}\n        =\\frac{(p_k+q_k)^2}{3}\n        =\\frac{s_k^{\\,2}}{3}.\n\\end{aligned}\n\\]\n\nThus  \n\n\\[\ns_{k+1}= \\frac{s_k^{\\,2}}{3},\\qquad s_1=p_1+q_1=25+11=36.\n\\tag{2}\n\\]\n\n--------------------------------------------------------------------\n### 2.  Closed form\n\nSet \\(t_k=s_k/3\\).  From (2)\n\n\\[\nt_{k+1}=t_k^{\\,2},\\qquad t_1=\\frac{36}{3}=12 .\n\\]\n\nHence  \n\n\\[\nt_k=12^{\\,2^{\\,k-1}},\\qquad \ns_k=3t_k=3\\cdot 12^{\\,2^{\\,k-1}} . \\tag{3}\n\\]\n\nTherefore  \n\n\\[\np_{2025}+q_{2025}=s_{2025}=3\\cdot 12^{\\,2^{2024}} .\n\\]\n\n--------------------------------------------------------------------\n### 3.  Computing the last three digits  \n\nWe need  \n\n\\[\nM=3\\cdot 12^{\\,2^{2024}}\\pmod{1000}.\n\\]\n\nBecause \\(1000=8\\cdot125\\) we compute the two residues separately.\n\n*Modulo \\(8\\)*  \n\n\\(12\\equiv4\\pmod8\\) and \\(4^{2}=0\\pmod8\\).  \nSince the exponent \\(2^{2024}\\ge2\\),\n\n\\[\n12^{\\,2^{2024}}\\equiv0\\pmod8 .\n\\]\n\nHence \\(M\\equiv0\\pmod8\\).\n\n*Modulo \\(125\\)*  \n\n\\(\\gcd(12,125)=1\\) and \\(\\varphi(125)=100\\), so  \n\\(12^{100}\\equiv1\\pmod{125}\\).  \nThus only the exponent modulo \\(100\\) matters:\n\n\\[\ne=2^{2024}\\pmod{100}.\n\\]\n\nFor \\(n\\ge2\\) the powers of \\(2\\) modulo \\(100\\) have period \\(20\\):\n\\(2^{n+20}\\equiv2^n\\pmod{100}\\).\nSince \\(2024\\equiv4\\pmod{20}\\),\n\n\\[\ne\\equiv2^{4}=16\\pmod{100}.\n\\]\n\nNow compute \\(12^{16}\\pmod{125}\\):\n\n\\[\n\\begin{aligned}\n12^{2}&amp;\\equiv144\\equiv19,\\\\\n12^{4}&amp;\\equiv19^{2}=361\\equiv111,\\\\\n12^{8}&amp;\\equiv111^{2}=12321\\equiv71,\\\\\n12^{16}&amp;\\equiv71^{2}=5041\\equiv41\\pmod{125}.\n\\end{aligned}\n\\]\n\nHence  \n\n\\[\n12^{\\,2^{2024}}\\equiv41\\pmod{125}.\n\\]\n\n*Chinese remainder theorem*  \n\nFind \\(A\\) such that  \n\n\\[\nA\\equiv0\\pmod8,\\qquad A\\equiv41\\pmod{125}.\n\\]\n\nWrite \\(A=8k\\).  Then \\(8k\\equiv41\\pmod{125}\\Rightarrow\nk\\equiv41\\cdot8^{-1}\\pmod{125}\\).\nSince \\(8^{-1}\\equiv47\\pmod{125}\\),\n\n\\[\nk\\equiv41\\cdot47\\equiv52\\pmod{125},\n\\]\nso \\(k=52+125t\\) and  \n\n\\[\nA=8k=416+1000t\\equiv416\\pmod{1000}.\n\\]\n\nFinally  \n\n\\[\nM=3A\\equiv3\\cdot416=1248\\equiv\\boxed{248}\\pmod{1000}.\n\\]\n\nThus the remainder of \\(m+n\\) when divided by \\(1000\\) is **248**.</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 248</p>\n<p>Extracted Answer: 248</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nThere are exactly three positive real numbers $ k $ such that the function\n$ f(x) = \\frac{(x - 18)(x - 72)(x - 98)(x - k)}{x} $\ndefined over the positive real numbers achieves its minimum value at exactly two positive real numbers $ x $. Find the sum of these three values of $ k $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>Let  \n\n\\[\nf_k(x)=\\frac{(x-18)(x-72)(x-98)(x-k)}{x}= \\frac{N(x)}{x},\\qquad x&gt;0 ,\n\\]\n\nwhere  \n\n\\[\nN(x)=(x-18)(x-72)(x-98)(x-k)\n      =x^{4}-(188+k)x^{3}+(10116+188k)x^{2}-(127008+10116k)x+127008k .\n\\]\n\n--------------------------------------------------------------------\n### 1.  What does \u201cthe minimum is attained at exactly two points\u2019\u2019 mean?\n\nIf the global minimum value is \\(m\\), then for every \\(x&gt;0\\)\n\n\\[\n\\frac{N(x)}{x}\\ge m\\qquad\\Longleftrightarrow\\qquad N(x)-mx\\ge0 .\n\\]\n\nEquality occurs exactly at the points where the minimum is attained.\nSince \\(N(x)-mx\\) is a quartic polynomial, the only way it can be\nnon\u2011negative for all \\(x\\) and vanish at exactly two distinct points is\n\n\\[\nN(x)-mx=(x-a)^{2}(x-b)^{2}\\qquad(a\\neq b,\\;a,b&gt;0).\n\\]\n\nThus there are numbers \\(a,b,m\\) such that  \n\n\\[\n\\begin{cases}\nN(a)=ma,\\quad N&#39;(a)=m,\\\\[2pt]\nN(b)=mb,\\quad N&#39;(b)=m .\n\\end{cases}\n\\]\n\n--------------------------------------------------------------------\n### 2.  Coefficient comparison\n\nWrite\n\n\\[\n(x-a)^{2}(x-b)^{2}=(x^{2}-Sx+P)^{2},\n\\qquad\nS=a+b,\\;P=ab .\n\\]\n\nEquating coefficients of \\(N(x)-mx\\) and \\((x^{2}-Sx+P)^{2}\\) yields  \n\n\\[\n\\begin{aligned}\nS&amp;=\\frac{188+k}{2},\\tag{1}\\\\[2pt]\nS^{2}+2P&amp;=10116+188k,\\tag{2}\\\\[2pt]\n2SP&amp;=127008+10116k+m,\\tag{3}\\\\[2pt]\nP^{2}&amp;=127008\\,k.\\tag{4}\n\\end{aligned}\n\\]\n\nFrom (1) and (4)\n\n\\[\nS=\\frac{188+k}{2},\\qquad P=\\sqrt{127008\\,k}.\n\\]\n\nInsert these in (2):\n\n\\[\n\\frac{(188+k)^{2}}{4}+2\\sqrt{127008\\,k}=10116+188k .\n\\]\n\nMultiplying by \\(4\\) and using \\(\\sqrt{127008}=252\\sqrt2\\) gives  \n\n\\[\nk^{2}-376k-5120+2016\\sqrt{2k}=0. \\tag{5}\n\\]\n\n--------------------------------------------------------------------\n### 3.  Solving for \\(k\\)\n\nSet \\(u=\\sqrt{k}&gt;0\\).  Then \\(\\sqrt{2k}=u\\sqrt2\\) and (5) becomes  \n\n\\[\nu^{4}-376u^{2}+2016\\sqrt2\\,u-5120=0 .\n\\]\n\nWrite \\(u=a\\sqrt2\\;(a&gt;0)\\); the equation reduces to  \n\n\\[\na^{4}-188a^{2}+1008a-1280=0 .\n\\]\n\nFactoring,\n\n\\[\n(a^{2}-6a+8)(a^{2}+6a-160)=0,\n\\]\n\nso  \n\n\\[\na=2,\\;4,\\;10\\quad(\\text{the root }a=-16\\text{ gives }u&lt;0\\text{ and is discarded}).\n\\]\n\nSince \\(k=u^{2}=2a^{2}\\),\n\n\\[\nk=2\\cdot2^{2}=8,\\qquad\nk=2\\cdot4^{2}=32,\\qquad\nk=2\\cdot10^{2}=200 .\n\\]\n\nFor each of these values the discriminant  \n\n\\[\n\\Delta=S^{2}-4P&gt;0\n\\]\n\nso the quadratic \\(x^{2}-Sx+P\\) has two distinct positive roots; consequently\n\\(f_{k}(x)\\) attains its global minimum at exactly those two points.\n\n--------------------------------------------------------------------\n### 4.  Sum of the admissible \\(k\\)\n\n\\[\n8+32+200 = 240 .\n\\]\n\n\\[\n\\boxed{240}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 240</p>\n<p>Extracted Answer: 240</p>\n<p>Score: 1.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $N$ denote the number of ordered triples of positive integers $(a,b,c)$ such that $a,b,c\\leq3^6$ and $a^3+b^3+c^3$ is a multiple of $3^7$. Find the remainder when $N$ is divided by $1000$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>**Solution Outline**\n\n1.  Let \\(M=3^{7}=2187\\) and \\(A=\\{1,\\ldots ,3^{6}\\}= \\{1,\\dots ,729\\}\\).\n    For each \\(a\\in A\\) put \\(r(a)=a^{3}\\pmod{M}\\).\n    The required number  \n\n    \\[\n    N=\\#\\{(a,b,c)\\in A^{3}:r(a)+r(b)+r(c)\\equiv0\\pmod M\\}\n    \\]\n\n    is the weighted convolution of the distribution of the residues\n    \\(r(a)\\).\n\n2.  Write each \\(a\\) as \\(a=3^{v}a&#39;\\) with \\(\\gcd(a&#39;,3)=1\\).\n\n| \\(v\\) | range of \\(a\\) | # of such \\(a\\) | residue \\(a^{3}\\) (mod\u202f\\(M\\)) | weight |\n|-------|----------------|-----------------|-------------------------------|--------|\n| 0 | not divisible by 3 | \\(486\\) | \\(a^{\\prime\\,3}\\) (unit cube) | \\(1\\) |\n| 1 | \\(3\\mid a,9\\nmid a\\) | \\(162\\) | \\(27a^{\\prime\\,3}\\) | \\(9\\) |\n| 2 | \\(9\\mid a,27\\nmid a\\) | \\(54\\) | \\(729a^{\\prime\\,3}\\) | \\(27\\) |\n| \\(\\ge3\\) | \\(27\\mid a\\) | \\(27\\) | \\(0\\) | \\(27\\)\n\nHence the possible residues and their multiplicities are  \n\n* 0\u2003\u2003\u2003\u2003\u2003\u2003weight\u202f\\(27\\);\n* the two residues \\(729,\\,1458\\)\u2003weight\u202f\\(27\\) each;\n* 18 residues (the cubes of the unit group modulo\u202f\\(81\\))\u2003weight\u202f\\(9\\) each;\n* 486 residues (the cubes of the unit group modulo\u202f\\(3^{7}\\))\u2003weight\u202f\\(1\\) each.\n\nDenote by  \n\n* \\(D\\) the 486 unit\u2011cube residues (weight\u202f1);\n* \\(C\\) the 18 residues \\(27\\cdot u\\) with \\(u\\) a unit\u2011cube modulo\u202f\\(81\\) (weight\u202f9);\n* \\(B\\) the two residues \\(729,1458\\) (weight\u202f27);\n* \\(0\\) the zero residue (weight\u202f27).\n\n3.  Split the count according to how many zero\u2011terms occur.\n    Let  \n\n    \\[\n    w(x)=\\text{weight of residue }x.\n    \\]\n\n    For \\(x\\neq0\\) put \\(R&#39;=\\{D\\cup C\\cup B\\}\\).  Then\n\n    \\[\n    N=N_{0}+N_{1}+N_{2},\n    \\]\n\n    where  \n\n    * \\(N_{2}=w(0)^{3}=27^{3}=19683\\)  (all three residues zero);\n    * \\(N_{1}=3\\,w(0)\\displaystyle\\sum_{\\substack{y+z\\equiv0\\\\y,z\\in R&#39;}}\n            w(y)w(z) =3\\cdot27\\cdot3402=275\\,562\\);\n    * \\(N_{0}\\) counts triples with no zero term.\n\n    The sum in \\(N_{1}\\) is obtained easily:\n    each \\(x\\in D\\) pairs with its inverse, giving \\(486\\) ordered pairs,\n    each \\(x\\in C\\) gives \\(18\\) ordered pairs (weight \\(9^{2}=81\\)), and each\n    \\(x\\in B\\) gives \\(2\\) ordered pairs (weight \\(27^{2}=729\\)).\n    Hence \\(\\displaystyle\\sum_{y+z\\equiv0}w(y)w(z)=486+1458+1458=3402\\).\n\n4.  Compute \\(N_{0}\\).\n    After factoring the common factor \\(27\\) from the elements of \\(C\\cup B\\),\n    the condition \\(x+y+z\\equiv0\\pmod{M}\\) becomes\n\n    \\[\n    u+v+w\\equiv0\\pmod{81},\n    \\]\n\n    where \\(u,v,w\\) belong to  \n\n    * the set \\(S\\) of the 18 unit\u2011cubes modulo\u202f\\(81\\) (weight\u202f9);\n    * the two residues \\(27,54\\) (weight\u202f27).\n\n    For the set \\(S\\) one has the simple description  \n\n    \\[\n    S=\\{x\\pmod{81}:x\\equiv\\pm1\\pmod9\\}.\n    \\]\n\n    Using this description we compute the additive convolution on \\(\\mathbb Z/81\\).\n\n    * For any \\(t\\equiv0\\pmod9\\) we have \\(\\#\\{(s_{1},s_{2})\\in S^{2}:s_{1}+s_{2}\\equiv t\\}=18\\).\n    * For any \\(t\\equiv\\pm2\\pmod9\\) the count equals \\(9\\).\n    * For any other residue the count is \\(0\\).\n\n    Consequently\n\n    * there are no triples \\(s_{1}+s_{2}+s_{3}\\equiv0\\) with all three from \\(S\\);\n    * ordered triples with exactly one element from \\(\\{27,54\\}\\) and two from \\(S\\) are possible.\n      For each of the two choices \\(\\{27,54\\}\\) there are\n      \\((A*A)(27)=(A*A)(54)=18\\) ordered pairs from \\(S\\);  \n      with three possible positions for the \u201c\\(B\\)\u2019\u2019 element we obtain  \n\n      \\[\n      2\\cdot3\\cdot18=108\n      \\]\n\n      ordered triples.  Their weight is \\(27\\cdot9^{2}=2187\\), giving a contribution  \n\n      \\[\n      108\\cdot2187=236\\,196 .\n      \\]\n\n    * triples consisting only of the two \u201c\\(B\\)\u201d residues satisfy the condition\n      only when all three are equal, giving two ordered triples,\n      each of weight \\(27^{3}=19683\\); contribution  \n\n      \\[\n      2\\cdot19683=39\\,366 .\n      \\]\n\n    Adding these contributions:\n\n    \\[\n    N_{0}=236\\,196+39\\,366=275\\,562 .\n    \\]\n\n5.  Assemble all parts:\n\n    \\[\n    N=N_{0}+N_{1}+N_{2}=275\\,562+275\\,562+19\\,683=570\\,807 .\n    \\]\n\n6.  The required remainder is  \n\n    \\[\n    N\\bmod1000 = 570\\,807\\bmod1000 = \\boxed{807}.\n    \\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 735</p>\n<p>Extracted Answer: 807</p>\n<p>Score: 0.0</p>",
+    "\n<h3>Prompt conversation</h3>\n\n\n<div class=\"message user\">\n    <div class=\"role\">\n    user\n    \n    </div>\n    <div class=\"content\">\n    <pre>\nLet $ABCDE$ be a convex pentagon with $AB=14, BC=7, CD=24, DE=13, EA=26,$ and $\\angle B=\\angle E=60^\\circ$. For each point $X$ in the plane, define $f(X)=AX+BX+CX+DX+EX$. The least possible value of $f(X)$ can be expressed as $m+n\\sqrt{p}$, where $m$ and $n$ are positive integers and $p$ is not divisible by the square of any prime. Find $m+n+p$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n</pre>\n    </div>\n</div>\n\n<h3>Sampled message</h3>\n\n<div class=\"message assistant\">\n    <div class=\"role\">\n    assistant\n    \n    </div>\n    <div class=\"content\">\n    <pre>The minimum value of \\(f(X)\\) works out to be  \n\n\\[\nf_{\\min}=18+20\\sqrt7 .\n\\]\n\nThus \\(m=18,\\; n=20,\\; p=7\\) and  \n\n\\[\nm+n+p = 18+20+7 = 45 .\n\\]\n\n\\[\n\\boxed{45}\n\\]</pre>\n    </div>\n</div>\n<h3>Results</h3>\n<p>Correct Answer: 60</p>\n<p>Extracted Answer: 45</p>\n<p>Score: 0.0</p>"
+  ],
+  "convos": [
+    [
+      {
+        "role": "user",
+        "content": "\nFind the sum of all integer bases $b>9$ for which $17_{b}$ is a divisor of $97_{b}$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "First write the two numbers in base\u201110.\n\n\\[\n17_{b}=1\\cdot b+7=b+7,\\qquad \n97_{b}=9\\cdot b+7=9b+7 .\n\\]\n\nWe need  \n\n\\[\nb+7 \\mid 9b+7 .\n\\]\n\nUse the Euclidean algorithm:\n\n\\[\n9b+7 = 9(b+7)-56 .\n\\]\n\nHence  \n\n\\[\nb+7 \\mid 9b+7 \\iff b+7 \\mid 56 .\n\\]\n\nSo \\(b+7\\) must be a positive divisor of \\(56\\).\n\nSince the base must satisfy \\(b>9\\), we have \\(b+7>16\\).  \nThe divisors of \\(56\\) exceeding \\(16\\) are \\(28\\) and \\(56\\).\n\n\\[\n\\begin{cases}\nb+7=28 \\ \\Rightarrow\\ b=21,\\\\[2pt]\nb+7=56 \\ \\Rightarrow\\ b=49.\n\\end{cases}\n\\]\n\nBoth bases indeed work:\n\n\\[\n\\frac{97_{21}}{17_{21}}=\\frac{196}{28}=7,\\qquad \n\\frac{97_{49}}{17_{49}}=\\frac{448}{56}=8 .\n\\]\n\nTherefore the required bases are \\(21\\) and \\(49\\), and their sum is  \n\n\\[\n21+49 = 70.\n\\]\n\n\\[\n\\boxed{70}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nThe 9 members of a baseball team went to an ice cream parlor after their game. Each player had a singlescoop cone of chocolate, vanilla, or strawberry ice cream. At least one player chose each flavor, and the number of players who chose chocolate was greater than the number of players who chose vanilla, which was greater than the number of players who chose strawberry. Let $N$ be the number of different assignments of flavors to players that meet these conditions. Find the remainder when $N$ is divided by 1000.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n\\[\nc=\\#\\text{ chocolate},\\qquad v=\\#\\text{ vanilla},\\qquad s=\\#\\text{ strawberry}\n\\]\n\nwith  \n\n\\[\nc+v+s =9,\\qquad c>v>s\\ge1 .\n\\]\n\n---\n\n### 1. Find all possible triples \\((c,v,s)\\).\n\nSince \\(c>v>s\\ge 1\\),\n\n\\[\nc\\ge s+2,\\; v\\ge s+1 \\Longrightarrow c+v+s\\ge 3s+3\\le9\\Longrightarrow s\\le2 .\n\\]\n\n- **If \\(s=1\\)**: \\(v\\ge2,\\ c\\ge3\\) and \\(c+v=8\\).  \n  Possibilities: \\((c,v)=(6,2),(5,3)\\).\n\n- **If \\(s=2\\)**: \\(v\\ge3,\\ c\\ge4\\) and \\(c+v=7\\).  \n  Possibility: \\((c,v)=(4,3)\\).\n\nThus the only triples are  \n\n\\[\n(6,2,1),\\quad (5,3,1),\\quad (4,3,2).\n\\]\n\n---\n\n### 2. Count assignments for each triple.\n\nFor a given \\((c,v,s)\\) the number of assignments of flavors to the nine distinct players is the multinomial coefficient  \n\n\\[\n\\frac{9!}{c!\\,v!\\,s!}.\n\\]\n\n\\[\n\\begin{aligned}\n(6,2,1):\\quad &\\frac{9!}{6!\\,2!\\,1!}= \\binom{9}{6}\\binom{3}{2}=84\\cdot3=252,\\\\[4pt]\n(5,3,1):\\quad &\\frac{9!}{5!\\,3!\\,1!}= \\binom{9}{5}\\binom{4}{3}=126\\cdot4=504,\\\\[4pt]\n(4,3,2):\\quad &\\frac{9!}{4!\\,3!\\,2!}= \\binom{9}{4}\\binom{5}{3}=126\\cdot10=1260.\n\\end{aligned}\n\\]\n\n---\n\n### 3. Total number of assignments\n\n\\[\nN = 252+504+1260 = 2016.\n\\]\n\n---\n\n### 4. Remainder modulo \\(1000\\)\n\n\\[\nN \\bmod 1000 = 2016 \\bmod 1000 = 16.\n\\]\n\n\\[\n\\boxed{16}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nAn isosceles trapezoid has an inscribed circle tangent to each of its four sides. The radius of the circle is 3, and the area of the trapezoid is 72. Let the parallel sides of the trapezoid have lengths $r$ and $s$, with $r \\neq s$. Find $r^{2}+s^{2}$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let the trapezoid have parallel sides \\(r\\) and \\(s\\) \\((r\\neq s)\\) and equal legs \\(L\\).\n\n---\n\n### 1.  Semiperimeter from the incircle\n\nA convex quadrilateral that contains an incircle (a tangential quadrilateral) satisfies  \n\n\\[\n\\text{Area}= (\\text{inradius})\\times (\\text{semiperimeter}).\n\\]\n\nThe inradius is \\(3\\) and the area is \\(72\\); therefore  \n\n\\[\np=\\frac{\\text{Area}}{r_{\\text{in}}}= \\frac{72}{3}=24,\n\\]\n\nwhere \\(p\\) is the semiperimeter.\n\n---\n\n### 2.  Relation among the sides\n\nFor a tangential quadrilateral, Pitot\u2019s theorem gives  \n\n\\[\n\\text{(sum of one pair of opposite sides)} = \\text{(sum of the other pair)} .\n\\]\n\nIn an isosceles trapezoid the opposite sides are the two bases and the two equal legs, so  \n\n\\[\nr+s = L+L =2L \\quad\\Longrightarrow\\quad L=\\frac{r+s}{2}.\n\\]\n\nThe semiperimeter is  \n\n\\[\np = \\frac{r+s+2L}{2}= \\frac{r+s+r+s}{2}=r+s .\n\\]\n\nSince \\(p=24\\), we obtain  \n\n\\[\n\\boxed{r+s=24}.\n\\]\n\nConsequently  \n\n\\[\nL=\\frac{r+s}{2}=12 .\n\\]\n\n---\n\n### 3.  Height of the trapezoid\n\nThe incircle is tangent to both parallel sides, so the distance between those sides (the height \\(h\\)) equals twice the radius:\n\n\\[\nh = 2\\cdot 3 = 6 .\n\\]\n\n---\n\n### 4.  Using the leg length\n\nPlace the trapezoid with its bases horizontal. The horizontal offset between the ends of the bases is \\(\\dfrac{|r-s|}{2}\\). Hence, by the Pythagorean theorem,\n\n\\[\nL^{2}= \\left(\\frac{r-s}{2}\\right)^{2}+h^{2}.\n\\]\n\nWith \\(L=12\\) and \\(h=6\\),\n\n\\[\n12^{2}= \\left(\\frac{r-s}{2}\\right)^{2}+6^{2}\n\\quad\\Longrightarrow\\quad\n144 = \\frac{(r-s)^{2}}{4}+36\n\\quad\\Longrightarrow\\quad\n(r-s)^{2}=432.\n\\]\n\n---\n\n### 5.  Compute \\(r^{2}+s^{2}\\)\n\n\\[\n\\begin{aligned}\n(r+s)^{2} &= r^{2}+2rs+s^{2}=24^{2}=576,\\\\\n(r-s)^{2} &= r^{2}-2rs+s^{2}=432.\n\\end{aligned}\n\\]\n\nAdding these equations eliminates the \\(rs\\) term:\n\n\\[\n(r+s)^{2}+(r-s)^{2}=2(r^{2}+s^{2})\\Longrightarrow\n576+432=2(r^{2}+s^{2}).\n\\]\n\nThus\n\n\\[\nr^{2}+s^{2}= \\frac{1008}{2}=504.\n\\]\n\n---\n\n\\[\n\\boxed{504}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nLet $k$ be real numbers such that the system $|25+20i-z|=5$ and $|z-4-k|=|z-3i-k|$ has exactly one complex solution $z$. The sum of all possible values of $k$ can be written as $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$. Here $i=\\sqrt{-1}$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "The first equation  \n\n\\[\n|25+20i-z|=5\n\\]\n\nis a circle with centre  \n\n\\[\nC=(25,20)\n\\]\n\nand radius \\(r=5\\).\n\nThe second equation  \n\n\\[\n|z-4-k| = |z-3i-k|\n\\]\n\nmeans that \\(z\\) is equidistant from the points  \n\n\\[\nA=4+k \\qquad\\text{and}\\qquad B=3i+k .\n\\]\n\nThus \\(A=(k+4,0),\\; B=(k,3)\\).  \nThe set of points equidistant from \\(A\\) and \\(B\\) is the perpendicular bisector of \\(\\overline{AB}\\).\n\n---\n\n### Equation of the perpendicular bisector\n\nMidpoint of \\(AB\\):\n\n\\[\nM=\\Bigl(\\frac{k+4+k}{2},\\frac{0+3}{2}\\Bigr)=(k+2,\\frac32).\n\\]\n\nThe vector \\(\\overrightarrow{AB}=(-4,3)\\).  \nA direction vector perpendicular to this is \\((3,4)\\) (since \\((-4,3)\\cdot(3,4)=0\\)).  \n\nHence the line has slope \\(\\frac43\\) and equation  \n\n\\[\ny-\\frac32 = \\frac43\\bigl(x-(k+2)\\bigr)\n\\]\n\\[\n\\Longrightarrow\\; y = \\frac43 x - \\frac43 k - \\frac76 .\n\\]\n\nIn standard form:\n\n\\[\n8x-6y = 8k+7 .\n\\]\n\n---\n\n### Tangency condition\n\nThe system will have exactly one solution iff this line is tangent to the circle.  \nThe distance from the centre \\(C=(25,20)\\) to the line \\(8x-6y-(8k+7)=0\\) must equal the radius \\(5\\):\n\n\\[\n\\frac{|8\\cdot25-6\\cdot20-(8k+7)|}{\\sqrt{8^{2}+(-6)^{2}}}=5.\n\\]\n\nCompute the numerator:\n\n\\[\n8\\cdot25-6\\cdot20-(8k+7)=200-120-8k-7=73-8k.\n\\]\n\nSince \\(\\sqrt{8^{2}+6^{2}}=10\\),\n\n\\[\n\\frac{|73-8k|}{10}=5 \\quad\\Longrightarrow\\quad |73-8k|=50.\n\\]\n\nThus  \n\n\\[\n73-8k = 50 \\quad\\text{or}\\quad 73-8k = -50.\n\\]\n\n\\[\n\\begin{cases}\n8k = 23 \\;\\;\\Rightarrow\\; k = \\dfrac{23}{8},\\\\[4pt]\n8k = 123\\;\\Rightarrow\\; k = \\dfrac{123}{8}.\n\\end{cases}\n\\]\n\nBoth values give a tangent line, so each yields exactly one solution \\(z\\).\n\n---\n\n### Sum of all possible \\(k\\)\n\n\\[\nk_1+k_2 = \\frac{23}{8}+\\frac{123}{8}= \\frac{146}{8}= \\frac{73}{4}.\n\\]\n\nWrite \\(\\frac{73}{4}\\) as \\(\\frac{m}{n}\\) with \\(\\gcd(m,n)=1\\): \\(m=73,\\ n=4\\).\n\n\\[\nm+n = 73+4 = 77.\n\\]\n\n\\[\n\\boxed{77}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nFind the number of ordered pairs $(x,y)$, where both $x$ and $y$ are integers between $-100$ and $100$, inclusive, such that $12x^{2}-xy-6y^{2}=0$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "The equation  \n\n\\[\n12x^{2}-xy-6y^{2}=0\n\\]\n\nis a homogeneous quadratic form.  Factor it over the rationals.\n\n\\[\n12x^{2}-xy-6y^{2}= -6\\Bigl(y-\\frac43x\\Bigr)\\Bigl(y+\\frac32x\\Bigr)\n\\]\n\nHence  \n\n\\[\n12x^{2}-xy-6y^{2}=0\\iff \n\\Bigl(y-\\frac43x\\Bigr)\\Bigl(y+\\frac32x\\Bigr)=0 .\n\\]\n\nSo any integer solution must satisfy one of the two linear equations  \n\n\\[\ny=\\frac{4}{3}x\\quad\\text{or}\\quad y=-\\frac32 x .\n\\]\n\n---\n\n### 1.  Solutions of \\(y=\\frac43x\\)\n\nWrite \\(3y=4x\\).  \nSince \\(\\gcd(3,4)=1\\), the integer solutions are  \n\n\\[\nx=3k,\\qquad y=4k\\qquad(k\\in\\mathbb Z).\n\\]\n\nBoth coordinates must lie in \\([-100,100]\\):\n\n\\[\n-100\\le 3k\\le100,\\qquad -100\\le4k\\le100\n\\]\n\nThe second inequality is stricter, giving  \n\n\\[\n-25\\le k\\le 25 .\n\\]\n\nThus there are  \n\n\\[\n25-(-25)+1 = 51\n\\]\n\ninteger points on this line.\n\n---\n\n### 2.  Solutions of \\(y=-\\frac32x\\)\n\nWrite \\(2y=-3x\\).  \nSince \\(\\gcd(2,3)=1\\), the integer solutions are  \n\n\\[\nx=2k,\\qquad y=-3k\\qquad(k\\in\\mathbb Z).\n\\]\n\nBoth coordinates must satisfy  \n\n\\[\n-100\\le2k\\le100,\\qquad -100\\le-3k\\le100 .\n\\]\n\nThese give  \n\n\\[\n-50\\le k\\le50,\\qquad -\\frac{100}{3}\\le k\\le\\frac{100}{3}\\Longrightarrow -33\\le k\\le33 .\n\\]\n\nHence there are  \n\n\\[\n33-(-33)+1 = 67\n\\]\n\ninteger points on this line.\n\n---\n\n### 3.  Remove double\u2011counted point\n\nThe two lines intersect only at \\((0,0)\\) (when \\(k=0\\) in both families).  \nThus the total number of distinct ordered pairs is  \n\n\\[\n51+67-1 = 117 .\n\\]\n\n\\[\n\\boxed{117}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nThere are $8!=40320$ eight-digit positive integers that use each of the digits $1,2,3,4,5,6,7,8$ exactly once. Let $N$ be the number of these integers that are divisible by 22. Find the difference between $N$ and 2025.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "**Step 1.  Divisibility conditions**\n\nFor an integer to be divisible by \\(22\\) it must be divisible by \\(2\\) and by \\(11\\).\n\n*Divisible by 2* \u2013 the last digit (the units digit) must be even, i.e. one of \\(\\{2,4,6,8\\}\\).\n\n*Divisible by 11* \u2013 for an 8\u2011digit number \\(a_1a_2\\ldots a_8\\) (with \\(a_1\\) the leftmost digit) the rule is  \n\n\\[\n(a_8+a_6+a_4+a_2)-(a_7+a_5+a_3+a_1)\\equiv0\\pmod{11}.\n\\]\n\nThus the sum of the digits in the even positions (2,4,6,8) equals the sum of the digits in the odd positions (1,3,5,7) modulo \\(11\\).\n\nThe total sum of the digits \\(1+2+\\dots+8=36\\).  \nIf the two sums are equal modulo \\(11\\), then\n\n\\[\n2\\cdot(\\text{odd\u2013position sum})\\equiv36\\equiv3\\pmod{11}\n\\Longrightarrow\\text{odd\u2013position sum}\\equiv7\\pmod{11}.\n\\]\n\nThe possible values are \\(7,18,29,\\ldots\\).  \nSince four distinct digits from \\(\\{1,\\dots ,8\\}\\) can sum only between \\(10\\) and \\(26\\), the only feasible value is  \n\n\\[\n\\boxed{\\text{odd\u2013position sum}=18}.\n\\]\n\nConsequently the even\u2013position sum is also \\(18\\).\n\n**Step 2.  Choose the digits for the odd positions**\n\nWe need all 4\u2011element subsets of \\(\\{1,2,3,4,5,6,7,8\\}\\) whose sum is \\(18\\).\n\nListing them (or by noting the complementary pairs) gives  \n\n\\[\n\\begin{aligned}\n&\\{1,2,7,8\\},\\; \\{1,3,6,8\\},\\; \\{1,4,5,8\\},\\; \\{1,4,6,7\\},\\\\\n&\\{2,3,5,8\\},\\; \\{2,3,6,7\\},\\; \\{2,4,5,7\\},\\; \\{3,4,5,6\\}.\n\\end{aligned}\n\\]\n\nThere are  \n\n\\[\n\\boxed{M=8}\n\\]\n\nsuch subsets.  \nEach of them contains exactly two even digits (because a sum of 18 cannot be obtained with a different parity distribution), so for every subset \\(A\\) (odd\u2011position digits) we have  \n\n\\[\ne_A=2,\\qquad E_B=4-e_A=2,\n\\]\n\nwhere \\(E_B\\) is the number of even digits among the complementary set \\(B\\) (the even\u2011position digits).\n\n**Step 3.  Arrange the digits**\n\n*Odd positions* (1,3,5,7): the four digits of \\(A\\) can be placed in \\(4! = 24\\) ways.\n\n*Even positions* (2,4,6,8): the four digits of \\(B\\) must be placed so that the digit in position\u202f8 (the units digit) is even.  \nSince \\(B\\) contains exactly \\(E_B=2\\) even digits, we have  \n\n\\[\n\\text{choices for the units digit}=2,\n\\qquad\n\\text{ways to arrange the remaining three digits}=3! = 6.\n\\]\n\nThus the number of admissible placements for \\(B\\) is  \n\n\\[\nf(B)=2\\cdot 6=12.\n\\]\n\n**Step 4.  Count all numbers**\n\nFor each of the \\(M=8\\) valid subsets \\(A\\),\n\n\\[\n\\text{numbers contributed}=24\\times12=288.\n\\]\n\nHence  \n\n\\[\nN=8\\times288=2304.\n\\]\n\n**Step 5.  Compute the required difference**\n\n\\[\nN-2025=2304-2025=279.\n\\]\n\n\\[\n\\boxed{279}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nThe parabola with equation $y=x^{2}-4$ is rotated $60^{\\circ}$ counterclockwise around the origin. The unique point in the fourth quadrant where the original parabola and its image intersect has $y$-coordinate $\\frac{a-\\sqrt{b}}{c}$, where $a$, $b$, and $c$ are positive integers, and $a$ and $c$ are relatively prime. Find $a+b+c$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "The original parabola is  \n\n\\[\ny=x^{2}-4 .\n\\]\n\n---\n\n### 1.  Equation of the rotated parabola  \n\nRotate the plane \\(60^{\\circ}\\) counter\u2011clockwise about the origin.\nIf \\((X,Y)\\) is a point of the rotated parabola, then rotating it back\n\\(60^{\\circ}\\) clockwise gives a point \\((x',y')\\) on the original parabola.\n\n\\[\n\\begin{pmatrix}x'\\\\y'\\end{pmatrix}\n=\n\\begin{pmatrix}\\cos60^\\circ&\\sin60^\\circ\\\\\n-\\sin60^\\circ&\\cos60^\\circ\\end{pmatrix}\n\\begin{pmatrix}X\\\\Y\\end{pmatrix}\n=\n\\begin{pmatrix}\\frac12X+\\frac{\\sqrt3}{2}Y\\\\[2pt]\n-\\frac{\\sqrt3}{2}X+\\frac12Y\\end{pmatrix}.\n\\]\n\nThus  \n\n\\[\ny' = x'^2-4\\Longrightarrow \n\\frac{-\\sqrt3X+Y}{2} =\\Bigl(\\frac{X+\\sqrt3Y}{2}\\Bigr)^{\\!2}-4.\n\\]\n\nMultiplying by \\(2\\) and simplifying gives the equation of the rotated\nparabola:\n\n\\[\n(x+\\sqrt3\\,y)^{2}+2\\sqrt3\\,x-2y-16=0. \\tag{1}\n\\]\n\n---\n\n### 2.  Intersection with the original parabola  \n\nSubstituting \\(y=x^{2}-4\\) from the original parabola into (1) yields\n\n\\[\n\\bigl(x+\\sqrt3(x^{2}-4)\\bigr)^{2}+2\\sqrt3\\,x-2(x^{2}-4)-16=0,\n\\]\n\nwhich simplifies to\n\n\\[\n3x^{4}+2\\sqrt3\\,x^{3}-25x^{2}-6\\sqrt3\\,x+40=0. \\tag{2}\n\\]\n\n---\n\n### 3.  Factoring the quartic  \n\nLook for a factorisation of the form  \n\\((ax^{2}+b\\sqrt3\\,x+c)(dx^{2}+e\\sqrt3\\,x+f)\\).\nMatching coefficients gives the system  \n\n\\[\n\\begin{cases}\nad=3\\\\\nae+bd=2\\\\\naf+3be+cd=-25\\\\\nbf+ce=-6\\\\\ncf=40\n\\end{cases}\n\\]\n\nwhich is solved by  \n\n\\[\na=1,\\;b=1,\\;c=-4,\\qquad d=3,\\;e=-1,\\;f=-10 .\n\\]\n\nHence\n\n\\[\n3x^{4}+2\\sqrt3\\,x^{3}-25x^{2}-6\\sqrt3\\,x+40\n   =(x^{2}+\\sqrt3\\,x-4)(3x^{2}-\\sqrt3\\,x-10). \\tag{3}\n\\]\n\n---\n\n### 4.  Solving for the intersection points  \n\nFrom (3) we obtain four possible \\(x\\)-coordinates.\n\n1. \\(x^{2}+\\sqrt3\\,x-4=0\\)\n\n\\[\nx=\\frac{-\\sqrt3\\pm\\sqrt{19}}{2}.\n\\]\n\n2. \\(3x^{2}-\\sqrt3\\,x-10=0\\)\n\n\\[\nx=\\frac{\\sqrt3\\pm\\sqrt{123}}{6}.\n\\]\n\nFor each \\(x\\) we compute \\(y=x^{2}-4\\).\n\n| \\(x\\) | sign of \\(x\\) | \\(y=x^{2}-4\\) | quadrant |\n|---|---|---|---|\n| \\(\\displaystyle\\frac{-\\sqrt3+\\sqrt{19}}{2}\\) | \\(>0\\) | \\(\\displaystyle\\frac{3-\\sqrt{57}}{2}<0\\) | **IV** |\n| \\(\\displaystyle\\frac{-\\sqrt3-\\sqrt{19}}{2}\\) | \\(<0\\) | \\(>0\\) | II |\n| \\(\\displaystyle\\frac{\\sqrt3+\\sqrt{123}}{6}\\) | \\(>0\\) | \\(>0\\) | I |\n| \\(\\displaystyle\\frac{\\sqrt3-\\sqrt{123}}{6}\\) | \\(<0\\) | \\(<0\\) | III |\n\nOnly the first solution lies in the fourth quadrant, as required.\n\n---\n\n### 5.  The required \\(y\\)-coordinate  \n\nFor  \n\\[\nx=\\frac{-\\sqrt3+\\sqrt{19}}{2},\n\\]\n\\[\ny=x^{2}-4\n   =\\left(\\frac{-\\sqrt3+\\sqrt{19}}{2}\\right)^{2}-4\n   =\\frac{19+3-2\\sqrt{57}}{4}-4\n   =\\frac{22-2\\sqrt{57}}{4}-\\frac{16}{4}\n   =\\frac{3-\\sqrt{57}}{2}.\n\\]\n\nThus  \n\n\\[\ny=\\frac{a-\\sqrt{b}}{c}\\quad\\text{with}\\quad a=3,\\;b=57,\\;c=2,\n\\]\nand \\(\\gcd(a,c)=1\\).\n\nFinally  \n\n\\[\na+b+c=3+57+2=62.\n\\]\n\n\\[\n\\boxed{62}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nOn $\\triangle ABC$ points $A,D,E$, and $B$ lie that order on side $\\overline{AB}$ with $AD=4, DE=16$, and $EB=8$. Points $A,F,G$, and $C$ lie in that order on side $\\overline{AC}$ with $AF=13, FG=52$, and $GC=26$. Let $M$ be the reflection of $D$ through $F$, and let $N$ be the reflection of $G$ through $E$. Quadrilateral $DEGF$ has area 288. Find the area of heptagon $AFNBCEM$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n\\[\n\\vec{AB}= \\mathbf b ,\\qquad \\vec{AC}= \\mathbf c ,\\qquad \n|\\mathbf b| =28,\\; |\\mathbf c| =91 .\n\\]\n\nWrite every point on the sides as a linear combination of \\(\\mathbf b,\\mathbf c\\).\n\n\\[\n\\begin{aligned}\nD&=\\frac{4}{28}\\mathbf b =\\frac17\\mathbf b ,&\nE&=\\frac{20}{28}\\mathbf b =\\frac57\\mathbf b ,\\\\[2mm]\nF&=\\frac{13}{91}\\mathbf c ,&\nG&=\\frac{65}{91}\\mathbf c .\n\\end{aligned}\n\\]\n\nThe reflections about a point are central symmetries, thus  \n\n\\[\nM=2F-D=-\\frac17\\mathbf b+\\frac{26}{91}\\mathbf c ,\\qquad\nN=2E-G=\\frac{10}{7}\\mathbf b-\\frac{65}{91}\\mathbf c .\n\\]\n\n--------------------------------------------------------------------\n### 1.  Area of \\(\\triangle ABC\\)\n\nThe quadrilateral \\(DEGF\\) can be split into \\(\\triangle DE G\\) and \\(\\triangle DGF\\).\n\nFor any three points \\(P=\\alpha\\mathbf b+\\beta\\mathbf c\\),\n\\(Q=\\gamma\\mathbf b+\\delta\\mathbf c\\) we have  \n\n\\[\n\\bigl[(Q-P)\\times(R-P)\\bigr]\n    =(\\gamma-\\alpha)(\\zeta-\\beta)-(\\delta-\\beta)(\\xi-\\alpha)\\;\\bigl(\\mathbf b\\times\\mathbf c\\bigr),\n\\]\n\nso the area of a triangle equals the absolute value of that determinant\ntimes \\(\\dfrac12|\\mathbf b\\times\\mathbf c|\\).\n\n*Triangle \\(DEG\\)*  \n\n\\[\n\\det\\!\\begin{pmatrix}\n\\frac57-\\frac17 & 0\\\\[2mm]\n0-\\frac17&\\frac{65}{91}\n\\end{pmatrix}\n  =\\frac{20}{49}.\n\\]\n\nThus \\(\\displaystyle\n\\text{Area}(DEG)=\\frac{20}{49}\\cdot\\frac12|\\mathbf b\\times\\mathbf c|.\n\\)\n\n*Triangle \\(DGF\\)*  \n\n\\[\n\\det\\!\\begin{pmatrix}\n0-\\frac17&\\frac{65}{91}\\\\[2mm]\n0-\\frac17&\\frac{13}{91}\n\\end{pmatrix}\n  =\\frac{4}{49},\n\\qquad\n\\text{Area}(DGF)=\\frac{4}{49}\\cdot\\frac12|\\mathbf b\\times\\mathbf c|.\n\\]\n\nHence  \n\n\\[\n\\text{Area}(DEGF)=\\Bigl(\\frac{20}{49}+\\frac{4}{49}\\Bigr)\n                  \\frac12|\\mathbf b\\times\\mathbf c|\n                =\\frac{24}{49}\\,\\text{Area}(\\triangle ABC).\n\\]\n\nGiven \\(\\text{Area}(DEGF)=288\\),\n\n\\[\n\\frac{24}{49}\\,\\text{Area}(\\triangle ABC)=288\n\\Longrightarrow\n\\text{Area}(\\triangle ABC)=288\\cdot\\frac{49}{24}=12\\cdot49=588.\n\\]\n\n--------------------------------------------------------------------\n### 2.  Area of the heptagon \\(AFNBCEM\\)\n\nPlace the points in the \\((\\alpha,\\beta)\\)\u2013plane where \\((\\alpha,\\beta)\\) are the\ncoefficients of \\(\\mathbf b,\\mathbf c\\):\n\n\\[\n\\begin{array}{c|c}\n\\text{Vertex}&(\\alpha,\\beta)\\\\\\hline\nA&(0,0)\\\\\nF&(0,\\frac{13}{91})\\\\\nN&(\\frac{10}{7},-\\frac{65}{91})\\\\\nB&(1,0)\\\\\nC&(0,1)\\\\\nE&(\\frac57,0)\\\\\nM&\\bigl(-\\frac17,\\frac{26}{91}\\bigr)\n\\end{array}\n\\]\n\nApplying the shoelace formula to these seven points gives\n\n\\[\n\\begin{aligned}\n\\sum x_i y_{i+1}-y_i x_{i+1}\n&=1,\\\\[2mm]\n\\text{Area}_{\\text{coeff}}&=\\frac12\\cdot1=\\frac12 .\n\\end{aligned}\n\\]\n\nIn the original plane a figure\u2019s area is multiplied by\n\\(|\\mathbf b\\times\\mathbf c|=2\\,\\text{Area}(\\triangle ABC)\\).\nThus\n\n\\[\n\\text{Area}(AFNBCEM)=|\\mathbf b\\times\\mathbf c|\\,\n\\frac12\n   =\\text{Area}(\\triangle ABC)=588.\n\\]\n\n--------------------------------------------------------------------\n\\[\n\\boxed{588}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nThe twelve letters $A,B,C,D,E,F,G,H,I,J,K$, and $L$ are randomly grouped into six pairs of letters. The two letters in each pair are placed next to each other in alphabetical order to form six two-letter words, and those six words are listed alphabetically. For example, a possible result is $AB,CJ,DG,EK,FL,HI$. The probability that the last word listed contains $G$ is $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "The 12 letters are  \n\n\\[\nA,B,C,D,E,F,G,H,I,J,K,L .\n\\]\n\nA random grouping into six unordered pairs is performed, each pair is written with its\nletters in alphabetical order, and then the six two\u2011letter \u201cwords\u2019\u2019 are listed\nalphabetically.  \n\nLet the word that appears last (the lexicographically greatest word) be called the **max word**.\nThe max word is determined by the *first* letters of the six pairs:\nits first letter is the largest among the six first letters, and if several pairs have that\nfirst letter, the one with the larger second letter wins.\n\n--------------------------------------------------------------------\n### 1.   Total number of possible pairings\n\\[\n\\#\\text{pairings}= \\frac{12!}{2!^{6}\\,6!}=10395 .\n\\]\n\n--------------------------------------------------------------------\n### 2.   When does the max word contain \\(G\\)?\n\nTwo mutually exclusive possibilities:\n\n* **(A) \\(G\\) is the first letter of its pair.**  \n  Then the pair is \\((G,X)\\) with \\(X\\in\\{H,I,J,K,L\\}\\).\n  For \\((G,X)\\) to be the max word, no other pair may have a first\n  letter larger than \\(G\\).  \n  Hence each of the other four letters \\(\\{H,I,J,K,L\\}\\setminus\\{X\\}\\) must be paired\n  with a letter \\(\\le F\\) (otherwise its first letter would exceed \\(G\\)).\n  The remaining letters are  \n\n  * 4 \u201chigh\u2019\u2019 letters \\(\\{H,I,J,K,L\\}\\setminus\\{X\\}\\);\n  * 6 \u201clow\u2019\u2019 letters \\(\\{A,B,C,D,E,F\\}\\).\n\n  Choose which four low letters are matched with the four high letters\n  and then match them (an injection).  \n  The number of ways is  \n\n  \\[\n  {}_{6}P_{4}=6\\cdot5\\cdot4\\cdot3=360 .\n  \\]\n\n  The two low letters left over are forced to pair with each other.\n  Thus for a fixed \\(X\\) there are \\(360\\) pairings, and there are\n  \\(5\\) possible choices for \\(X\\):\n\n  \\[\n  N_A=5\\cdot360=1800 .\n  \\]\n\n* **(B) \\(G\\) is the second letter of its pair.**  \n  Then the pair is \\((X,G)\\) with \\(X<G\\), and \\(X\\) must be the\n  largest first letter of any pair.  \n  If \\(X\\le E\\) there are not enough letters \\(\\le X\\) to pair with all\n  letters \\(>X\\) (there would be more \u201chigh\u2019\u2019 letters than \u201clow\u2019\u2019 ones).  \n  The only possible value is \\(X=F\\).\n\n  Pair \\(G\\) with \\(F\\).  The five letters \\(\\{H,I,J,K,L\\}\\) must each be paired\n  with a distinct letter from \\(\\{A,B,C,D,E\\}\\).  There are  \n\n  \\[\n  5! =120\n  \\]\n\n  ways to do this, and no letters remain.\n\n  Hence  \n\n  \\[\n  N_B =120 .\n  \\]\n\n--------------------------------------------------------------------\n### 3.   Favourable pairings\n\\[\nN_{\\text{fav}}=N_A+N_B=1800+120=1920 .\n\\]\n\n--------------------------------------------------------------------\n### 4.   Desired probability\n\\[\nP=\\frac{N_{\\text{fav}}}{\\#\\text{pairings}}\n   =\\frac{1920}{10395}\n   =\\frac{128}{693}\\qquad(\\gcd(128,693)=1).\n\\]\n\nThus \\(m=128,\\;n=693\\) and  \n\n\\[\nm+n=128+693=821 .\n\\]\n\n\\[\n\\boxed{821}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nSix points $ A, B, C, D, E, $ and $ F $ lie in a straight line in that order. Suppose that $ G $ is a point not on the line and that $ AC = 26 $, $ BD = 22 $, $ CE = 31 $, $ DF = 33 $, $ AF = 73 $, $ CG = 40 $, and $ DG = 30 $. Find the area of $ \\triangle BGE $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let the line be the \\(x\\)-axis and put  \n\n\\[\nA=(0,0),\\qquad B=(b,0),\\qquad C=(c,0),\\qquad D=(d,0),\\qquad E=(e,0),\\qquad F=(f,0)\n\\]\n\nwith the points in the order \\(A\\!<\\!B\\!<\\!C\\!<\\!D\\!<\\!E\\!<\\!F\\).\n\n---\n\n### 1.  Locate the collinear points\n\n\\[\n\\begin{aligned}\nAC&=26 \\Longrightarrow c-0 = 26 \\; \\Rightarrow\\; c=26,\\\\[2pt]\nCE&=31 \\Longrightarrow e-c =31 \\; \\Rightarrow\\; e=26+31=57,\\\\[2pt]\nAF&=73 \\Longrightarrow f=73 .\n\\end{aligned}\n\\]\n\nFrom \\(DF=33\\) we get  \n\n\\[\nf-d =33 \\Longrightarrow d = f-33 = 73-33 =40 .\n\\]\n\nFrom \\(BD=22\\),\n\n\\[\nd-b =22 \\Longrightarrow b = d-22 = 40-22 =18 .\n\\]\n\nThus  \n\n\\[\nA=(0,0),\\; B=(18,0),\\; C=(26,0),\\; D=(40,0),\\; E=(57,0),\\; F=(73,0).\n\\]\n\nAll distances given in the statement are satisfied.\n\n---\n\n### 2.  Position of \\(G\\)\n\nLet \\(G=(x,y)\\) with \\(y\\neq0\\).  \nThe distances to \\(C\\) and \\(D\\) give\n\n\\[\n\\begin{cases}\n(x-26)^2+y^2 = 40^2 =1600,\\\\[2pt]\n(x-40)^2+y^2 = 30^2 = 900 .\n\\end{cases}\n\\]\n\nSubtracting the equations:\n\n\\[\n(x-26)^2-(x-40)^2 = 700.\n\\]\n\nExpanding,\n\n\\[\n(-52x+26^2)+(80x-40^2)=700\\;\\Longrightarrow\\;28x-924=700,\n\\]\n\nso  \n\n\\[\n28x=1624\\quad\\Longrightarrow\\quad x=58 .\n\\]\n\nPlug \\(x=58\\) into \\((x-26)^2+y^2=1600\\):\n\n\\[\n(58-26)^2+y^2 = 32^2 + y^2 = 1600\\;\\Longrightarrow\\; y^2 = 1600-1024 = 576,\n\\]\n\nhence \\(|y|=24\\).  \nTake \\(G=(58,24)\\) (the other choice \\((58,-24)\\) gives the same area).\n\n---\n\n### 3.  Area of \\(\\triangle BGE\\)\n\nPoints:\n\n\\[\nB=(18,0),\\qquad E=(57,0),\\qquad G=(58,24).\n\\]\n\nThe base \\(BE\\) lies on the \\(x\\)-axis, so its length is  \n\n\\[\nBE = 57-18 = 39.\n\\]\n\nThe altitude from \\(G\\) to the line \\(BE\\) is simply \\(|y| = 24\\).\n\nThus  \n\n\\[\n\\text{Area} = \\frac12 \\times (\\text{base}) \\times (\\text{height})\n            = \\frac12 \\times 39 \\times 24\n            = 39 \\times 12\n            = 468 .\n\\]\n\n(Equivalently, the shoelace formula gives \\(\\frac12|1368-432|=468\\).)\n\n---\n\n\\[\n\\boxed{468}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nFind the sum of all positive integers $ n $ such that $ n + 2 $ divides the product $ 3(n + 3)(n^2 + 9) $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n\\[\nd=n+2\\qquad (d\\ge 1,\\; n=d-2).\n\\]\n\nThen  \n\n\\[\nn+3=d+1 ,\\qquad n^{2}+9=(d-2)^{2}+9=d^{2}-4d+13 .\n\\]\n\nHence  \n\n\\[\n3(n+3)(n^{2}+9)=3(d+1)(d^{2}-4d+13).\n\\]\n\nThe condition \\(d\\mid 3(n+3)(n^{2}+9)\\) becomes  \n\n\\[\nd \\mid 3(d+1)(d^{2}-4d+13).\n\\]\n\nTake this congruence modulo \\(d\\).  \nSince \\(d\\equiv0\\pmod d\\),\n\n\\[\nd+1\\equiv1,\\qquad d^{2}-4d+13\\equiv13\\pmod d,\n\\]\n\nso  \n\n\\[\n3(d+1)(d^{2}-4d+13)\\equiv 3\\cdot1\\cdot13=39\\pmod d.\n\\]\n\nThus \\(d\\) must divide \\(39\\):\n\n\\[\nd\\in\\{1,3,13,39\\}.\n\\]\n\nRecall \\(d=n+2\\) and we need \\(n>0\\).  \nHence\n\n\\[\nn=d-2\\in\\{-1,1,11,37\\}.\n\\]\n\nDiscard the non\u2011positive value \\(-1\\). The admissible positive integers are  \n\n\\[\nn=1,\\;11,\\;37 .\n\\]\n\nCheck:\n\n* \\(n=1\\): \\(n+2=3\\) and \\(3(1+3)(1^{2}+9)=120\\) is divisible by \\(3\\).\n* \\(n=11\\): \\(n+2=13\\) and \\(3(14)(130)=5460\\) is divisible by \\(13\\).\n* \\(n=37\\): \\(n+2=39\\) and \\(3(40)(1378)=165360\\) is divisible by \\(39\\).\n\nAll satisfy the condition.  \n\nThe required sum is  \n\n\\[\n1+11+37 = 49.\n\\]\n\n\\[\n\\boxed{49}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nA piecewise linear periodic function is defined by $f(x)=\\begin{cases}x&\\text{if }x\\in[-1,1)\\\\2-x&\\text{if }x\\in[1,3)\\end{cases}$ and $f(x+4)=f(x)$ for all real numbers $x$. The graph of $f(x)$ has the sawtooth pattern. The parabola $x=34y^2$ intersects the graph of $f(x)$ at finitely many points. The sum of the $y$-coordinates of these intersection points can be expressed in the form $\\frac{a+b\\sqrt{c}}{d}$, where $a,b,c,$ and $d$ are positive integers, $a,b,$ and $d$ have greatest common divisor equal to 1, and $c$ is not divisible by the square of any prime. Find $a+b+c+d$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "For the periodic saw\u2011tooth  \n\n\\[\nf(x)=\\begin{cases}\nx-4k,&x\\in[-1+4k,\\,1+4k)\\\\[2pt]\n4k+2-x,&x\\in[1+4k,\\,3+4k)\n\\end{cases}\\qquad(k\\in\\mathbb Z)\n\\]\n\nthe parabola is  \n\n\\[\nx = 34y^{2}\\qquad (y\\in[-1,1]).\n\\]\n\nHence an intersection point \\((x,y)\\) must satisfy  \n\n\\[\ny=f(x),\\qquad x=34y^{2}.\n\\]\n\n---\n\n### 1.  Intersections on an \u201cup\u201d segment  \n\nOn an up segment \\(x= y+4k\\).  \nSubstituting \\(x=34y^{2}\\) gives  \n\n\\[\n34y^{2}=y+4k\\;\\Longrightarrow\\;34y^{2}-y-4k=0 .\n\\]\n\nFor each integer \\(k\\) with an up segment inside \\([0,34]\\) (i.e. \\(k=0,1,\\dots ,8\\))\nthe two roots are  \n\n\\[\ny_{k}^{\\pm}=\\frac{1\\pm\\sqrt{1+544k}}{68}.\n\\]\n\nBoth satisfy the interval \\([-1,1]\\) and give \\(x\\in[-1+4k,\\,1+4k)\\);\nhence each \\(k\\) contributes **two** intersection points.\n\nThe sum of the two roots for a fixed \\(k\\) is, by Vieta,\n\n\\[\ny_{k}^{+}+y_{k}^{-}= \\frac{1}{34}.\n\\]\n\nThus the total contribution of all up\u2011segments is  \n\n\\[\n\\sum_{k=0}^{8}(y_{k}^{+}+y_{k}^{-})=9\\cdot\\frac1{34}=\\frac9{34}.\n\\]\n\n---\n\n### 2.  Intersections on a \u201cdown\u2019\u2019 segment  \n\nOn a down segment \\(x=4k+2-y\\).  \nUsing \\(x=34y^{2}\\),\n\n\\[\n34y^{2}=4k+2-y\\;\\Longrightarrow\\;34y^{2}+y-(4k+2)=0 .\n\\]\n\nFor each \\(k=0,1,\\dots ,8\\) the roots are  \n\n\\[\nz_{k}^{\\pm}= \\frac{-1\\pm\\sqrt{273+544k}}{68}.\n\\]\n\nThe admissible \\(y\\)-values must satisfy \\(-1<y\\le 1\\).\n\n* For \\(k=0,1,\\dots ,7\\) we have \\(\\sqrt{273+544k}<67\\); both roots lie in\n\\((-1,1]\\) and give valid points.\n* For \\(k=8\\) the negative root satisfies \\(y<-1\\) and is rejected; only the\npositive root remains.\n\nHence we obtain two points for each \\(k=0,\\dots ,7\\) and one point for\n\\(k=8\\) \u2013 a total of \\(17\\) points.\n\nThe sum of the two roots of the quadratic for any \\(k\\) is  \n\n\\[\nz_{k}^{+}+z_{k}^{-}= -\\frac1{34}.\n\\]\n\nConsequently  \n\n\\[\n\\sum_{k=0}^{7}(z_{k}^{+}+z_{k}^{-})=8\\!\\left(-\\frac1{34}\\right)=-\\frac8{34},\n\\]\nand we must add the remaining positive root for \\(k=8\\),\n\n\\[\nz_{8}^{+}= \\frac{-1+\\sqrt{4625}}{68}= \\frac{-1+5\\sqrt{185}}{68}.\n\\]\n\nTherefore the total contribution of the down\u2011segments is  \n\n\\[\n-\\frac8{34}+z_{8}^{+}= -\\frac{16}{68}+ \\frac{-1+5\\sqrt{185}}{68}\n= \\frac{-17+5\\sqrt{185}}{68}.\n\\]\n\n---\n\n### 3.  Sum of all \\(y\\)-coordinates  \n\n\\[\n\\begin{aligned}\nS&=\\frac9{34}+ \\left(-\\frac8{34}+z_{8}^{+}\\right)\\\\[2pt]\n  &=\\frac1{34}+z_{8}^{+}\n   =\\frac{2}{68}+ \\frac{-1+5\\sqrt{185}}{68}\n   =\\frac{1+5\\sqrt{185}}{68}.\n\\end{aligned}\n\\]\n\nThus the sum can be written as  \n\n\\[\nS=\\frac{a+b\\sqrt{c}}{d}\\quad\\text{with}\\quad \na=1,\\;b=5,\\;c=185,\\;d=68.\n\\]\n\nAll conditions are satisfied (\\(\\gcd(a,b,d)=1\\), \\(c\\) square\u2011free).\n\nFinally  \n\n\\[\na+b+c+d = 1+5+185+68 = \\boxed{259}.\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nThe 27 cells of a $3\\times9$ grid are filled in using the numbers 1 through 9 so that each row contains 9 different numbers, and each of the three $3\\times3$ blocks heavily outlined in the example below contains 9 different numbers, as in the first three rows of a Sudoku puzzle. \n | 4 | 2 | 8 | 9 | 6 | 3 | 1 | 7 | 5 | \n | 3 | 7 | 9 | 5 | 2 | 1 | 6 | 8 | 4 | \n | 5 | 6 | 1 | 8 | 4 | 7 | 9 | 2 | 3 | \n The number of different ways to fill such a grid can be written as $p^a\\cdot q^b\\cdot r^c\\cdot s^d$, where $p,q,r,$ and $s$ are distinct prime numbers and $a,b,c,$ and $d$ are positive integers. Find $p\\cdot a+q\\cdot b+r\\cdot c+s\\cdot d$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "The grid has three rows and three vertical \\(3\\times3\\) blocks.  \nLet the rows be \\(R_1,R_2,R_3\\) and the blocks be \\(B_1,B_2,B_3\\).\n\n---\n\n### 1.  How the numbers are placed in the rows and blocks  \n\nFor a given number \\(k\\in\\{1,\\ldots ,9\\}\\) it must appear  \n\n* once in each row (three appearances), and  \n* once in each block (three appearances).\n\nHence the three positions of \\(k\\) correspond to a **bijection** between the set of rows and the set of blocks.  \nThus for each \\(k\\) we may choose a permutation \\(\\sigma_k\\in S_3\\) :\n\n\\[\n\\sigma_k(r)=\\text{the block in which }k\\text{ occurs in row }r .\n\\]\n\nConversely, a choice of a permutation \\(\\sigma_k\\) for each \\(k\\) determines in which block every entry of the grid lies.\n\n---\n\n### 2.  Counting the possible collections of permutations  \n\nWrite a column of the \\(3\\times9\\) \u201cblock\u2011matrix\u2019\u2019 \\(M\\) as a permutation of \\((1,2,3)\\) \u2013 the three symbols denote the block in which the number of that column appears in rows \\(1,2,3\\).\n\nThus we need a sequence of nine permutations \\((p_1,\\dots ,p_9)\\) such that each ordered pair \\((\\text{row},\\text{block})\\) occurs exactly three times; equivalently each number appears three times in each row and three times in each block.\n\nLet  \n\n\\[\nx_1,\\dots ,x_6\n\\]\n\nbe the numbers of the six possible permutations of \\(S_3\\) in the sequence.\nThe conditions give the linear system  \n\n\\[\n\\begin{aligned}\nx_1+x_2&=3\\\\\nx_3+x_4&=3\\\\\nx_5+x_6&=3\\\\\nx_3+x_5&=3\\\\\nx_1+x_6&=3\\\\\nx_2+x_4&=3\\\\\nx_4+x_6&=3\\\\\nx_2+x_5&=3\\\\\nx_1+x_3&=3\n\\end{aligned}\n\\]\n\nwhich has the solutions  \n\n\\[\n\\begin{array}{c|cccccc}\n &x_1&x_2&x_3&x_4&x_5&x_6\\\\\\hline\nt=0&0&3&3&0&0&3\\\\\nt=1&1&2&2&1&1&2\\\\\nt=2&2&1&1&2&2&1\\\\\nt=3&3&0&0&3&3&0\n\\end{array}\n\\qquad (t=0,1,2,3).\n\\]\n\nFor a fixed solution the columns can be ordered in\n\n\\[\n\\frac{9!}{x_1!x_2!x_3!x_4!x_5!x_6!}\n\\]\n\nways.  Summing over the four solutions gives  \n\n\\[\n\\begin{aligned}\nN_M &= \\frac{9!}{3!^3}+2\\cdot\\frac{9!}{1!\\,2!^2\\,1!\\,1!\\,2!}\n      +\\frac{9!}{3!^3}\\\\\n    &=1680+2\\cdot45360+1680=94\\,080 .\n\\end{aligned}\n\\]\n\nSo there are \\(94\\,080\\) possible matrices \\(M\\) describing in which block each number lies.\n\n---\n\n### 3.  Filling the inner columns of each block  \n\nInside a block \\(B\\) each row already has three distinct numbers (the three numbers assigned to that row in the block).  \nThese three numbers can be placed in the three inner columns of the block in any order, i.e. in \\((3!)^3=6^3\\) ways.\n\nSince the three blocks are independent, the total number of ways to complete the grid is  \n\n\\[\n94\\,080\\cdot (6^3)^3 = 94\\,080\\cdot 6^9 .\n\\]\n\nBecause \\(6^9 = (2\\cdot3)^9 =2^{9}\\,3^{9}\\),\n\n\\[\n\\begin{aligned}\n94\\,080\\cdot6^9 &= \\bigl(2^7\\cdot3\\cdot5\\cdot7^2\\bigr)\\cdot\\bigl(2^9\\cdot3^9\\bigr)\\\\\n                &=2^{16}\\cdot3^{10}\\cdot5^1\\cdot7^2 .\n\\end{aligned}\n\\]\n\nThus the total number of fillings is  \n\n\\[\n2^{16}\\cdot 3^{10}\\cdot 5^{1}\\cdot 7^{2}.\n\\]\n\n---\n\n### 4.  Computing the required sum  \n\nTake \\(p=2,\\ a=16;\\; q=3,\\ b=10;\\; r=5,\\ c=1;\\; s=7,\\ d=2\\).\n\n\\[\np\\,a+q\\,b+r\\,c+s\\,d = 2\\cdot16 + 3\\cdot10 + 5\\cdot1 + 7\\cdot2\n                     = 32 + 30 + 5 + 14 = 81 .\n\\]\n\n\\[\n\\boxed{81}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nThe set of points in 3-dimensional coordinate space that lie in the plane $x+y+z=75$ whose coordinates satisfy the inequalities $x-yz<y-zx<z-xy$ forms three disjoint convex regions. Exactly one of those regions has finite area. The area of this finite region can be expressed in the form $a\\sqrt{b}$, where $a$ and $b$ are positive integers and $b$ is not divisible by the square of any prime. Find $a+b$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "First rewrite the chain of inequalities  \n\n\\[\nx-yz<y-zx<z-xy\n\\]\n\nas two separate inequalities.\n\n\\[\n\\begin{aligned}\nx-yz &< y-zx \\\\[2mm]\ny-zx &< z-xy\n\\end{aligned}\n\\]\n\n\\[\n\\begin{aligned}\nx-yz-y+zx&<0\\qquad\\Longrightarrow\\qquad (x-y)(1+z)<0,\\\\[2mm]\ny-zx-z+xy&<0\\qquad\\Longrightarrow\\qquad (y-z)(1+x)<0 .\n\\end{aligned}\n\\]\n\nThe third inequality \\( (x-z)(1+y)<0\\) follows by adding the two, so the region is\ndescribed by  \n\n\\[\n\\boxed{(x-y)(1+z)<0,\\qquad (y-z)(1+x)<0}\n\\]\n\ntogether with the plane \\(x+y+z=75\\).\n\n---\n\n### 1.   Sign patterns\n\nLet  \n\n\\[\nS_x=\\operatorname{sgn}(1+x),\\quad S_y=\\operatorname{sgn}(1+y),\\quad S_z=\\operatorname{sgn}(1+z).\n\\]\n\nFrom the two product\u2011inequalities we obtain  \n\n\\[\n\\operatorname{sgn}(x-y)=-S_z,\\qquad \n\\operatorname{sgn}(y-z)=-S_x .\n\\]\n\nThus  \n\n\\[\n\\begin{array}{c|c|c|c}\nS_x & S_y & S_z &\\text{order of }x,y,z\\\\ \\hline\n+ & + & + & x<y<z\\\\\n+ & - & - & y<z<x\\\\\n- & + & + & x<z<y\\\\\n- & - & - & \\text{impossible (sum }\\;75) \n\\end{array}\n\\]\n\nHence the points satisfying the chain split into three convex regions, corresponding\nto the three admissible sign patterns above.\n\n---\n\n### 2.   Which region is bounded?\n\n*Region  \\(x<y<z\\)  (all three numbers \\(> -1\\)).*  \nUsing the plane equation \\(z=75-x-y\\) the conditions become  \n\n\\[\n-1<x<y,\\qquad y<\\frac{75-x}{2}.\n\\]\n\nIn the \\((x,y)\\)-plane this is the triangle bounded by  \n\n\\[\nx=-1,\\; y=x,\\; y=\\frac{75-x}{2}.\n\\]\n\nThe three vertices are  \n\n\\[\n(-1,-1),\\;(-1,38),\\;(25,25).\n\\]\n\nIts area in the \\(xy\\)-plane is\n\n\\[\n\\frac12\\,(39)(26)=507 .\n\\]\n\nSince the plane \\(x+y+z=75\\) is tilted, an element \\(dx\\,dy\\) on the\n\\(xy\\)-plane corresponds to an area element  \n\n\\[\n\\sqrt{1+(\\partial z/\\partial x)^2+(\\partial z/\\partial y)^2}\\;dx\\,dy\n        =\\sqrt{1+1+1}\\;dx\\,dy=\\sqrt3\\,dx\\,dy .\n\\]\n\nThus the area of this region in the plane is  \n\n\\[\n507\\sqrt3 .\n\\]\n\n*The other two regions* (\\(y<z<x\\) and \\(x<z<y\\)) project onto unbounded\nhalf\u2011planes, so they have infinite area.\n\nHence the **unique finite region** is the one with \\(x<y<z\\), and its area is\n\\(507\\sqrt3\\).\n\n---\n\n### 3.   Answer\n\nThe area is \\(a\\sqrt b\\) with \\(a=507\\) and \\(b=3\\); therefore  \n\n\\[\na+b=507+3=510 .\n\\]\n\n\\[\n\\boxed{510}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nThe product $ \\prod_{k=4}^{63} \\frac{\\log_k(5^{k^2-1})}{\\log_{k+1}(5^{k^2-4})} = \\frac{\\log_4(5^{15})}{\\log_5(5^{12})} \\cdot \\frac{\\log_5(5^{24})}{\\log_6(5^{21})} \\cdot \\frac{\\log_6(5^{35})}{\\log_7(5^{32})} \\cdots \\frac{\\log_{63}(5^{3968})}{\\log_{64}(5^{3965})} $ is equal to $ \\frac{m}{n} $, where $ m $ and $ n $ are relatively prime positive integers. Find $ m + n $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "\\[\n\\prod_{k=4}^{63}\\frac{\\log_k\\bigl(5^{k^2-1}\\bigr)}{\\log_{k+1}\\bigl(5^{k^2-4}\\bigr)}\n\\]\n\n---\n\n### 1.  Use change\u2011of\u2011base\n\n\\[\n\\log_k\\bigl(5^{k^2-1}\\bigr)=\\frac{\\log_5\\bigl(5^{k^2-1}\\bigr)}{\\log_5 k}\n      =\\frac{k^{2}-1}{\\log_5 k},\n\\qquad\n\\log_{k+1}\\bigl(5^{k^2-4}\\bigr)=\\frac{k^{2}-4}{\\log_5 (k+1)} .\n\\]\n\nHence each factor of the product equals  \n\n\\[\n\\frac{k^2-1}{k^2-4}\\;\n      \\frac{\\log_5(k+1)}{\\log_5k}.\n\\]\n\nSo\n\n\\[\nP = \\underbrace{\\prod_{k=4}^{63}\\frac{k^2-1}{k^2-4}}_{\\displaystyle P_1}\n    \\;\n    \\underbrace{\\prod_{k=4}^{63}\\frac{\\log_5(k+1)}{\\log_5k}}_{\\displaystyle P_2}.\n\\]\n\n---\n\n### 2.  Simplify \\(P_1\\)\n\n\\[\n\\frac{k^2-1}{k^2-4}= \\frac{(k-1)(k+1)}{(k-2)(k+2)}\n                  =\\frac{k-1}{k-2}\\cdot\\frac{k+1}{k+2}.\n\\]\n\nThus  \n\n\\[\nP_1=\\Bigl(\\prod_{k=4}^{63}\\frac{k-1}{k-2}\\Bigr)\n    \\Bigl(\\prod_{k=4}^{63}\\frac{k+1}{k+2}\\Bigr).\n\\]\n\nBoth products telescope:\n\n\\[\n\\prod_{k=4}^{63}\\frac{k-1}{k-2}\n   =\\frac{3}{2}\\cdot\\frac{4}{3}\\cdots\\frac{62}{61}\n   =\\frac{62}{2}=31,\n\\]\n\n\\[\n\\prod_{k=4}^{63}\\frac{k+1}{k+2}\n   =\\frac{5}{6}\\cdot\\frac{6}{7}\\cdots\\frac{64}{65}\n   =\\frac{5}{65}=\\frac1{13}.\n\\]\n\nTherefore  \n\n\\[\nP_1 =31\\cdot\\frac1{13} =\\frac{31}{13}.\n\\]\n\n---\n\n### 3.  Simplify \\(P_2\\)\n\n\\[\nP_2 =\\prod_{k=4}^{63}\\frac{\\log_5(k+1)}{\\log_5k}\n    =\\frac{\\log_5 5\\;\\log_5 6\\;\\cdots\\;\\log_5 64}\n           {\\log_5 4\\;\\log_5 5\\;\\cdots\\;\\log_5 63}\n    =\\frac{\\log_5 64}{\\log_5 4}.\n\\]\n\nUsing the change\u2011of\u2011base formula,\n\n\\[\n\\frac{\\log_5 64}{\\log_5 4}= \\log_4 64.\n\\]\n\nSince \\(4^3=64\\), we have \\(\\log_4 64 = 3\\). Hence  \n\n\\[\nP_2 = 3.\n\\]\n\n---\n\n### 4.  Combine the two parts\n\n\\[\nP = P_1\\cdot P_2 = \\frac{31}{13}\\times 3 = \\frac{93}{13}.\n\\]\n\nThus the product equals \\(\\displaystyle\\frac{m}{n}\\) with \\(m=93,\\; n=13\\).\n\n\\[\nm+n = 93+13 = 106.\n\\]\n\n\\[\n\\boxed{106}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nLet $ A $ be the set of positive integer divisors of 2025. Let $ B $ be a randomly selected subset of $ A $. The probability that $ B $ is a nonempty set with the property that the least common multiple of its elements is 2025 is $ \\frac{m}{n} $, where $ m $ and $ n $ are relatively prime positive integers. Find $ m + n $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Factor  \n\n\\[\n2025=45^{2}= (3^{2}\\cdot5)^{2}=3^{4}\\cdot5^{2}.\n\\]\n\nHence a divisor of \\(2025\\) is of the form \\(3^{a}5^{b}\\) with  \n\n\\(0\\le a\\le4\\) and \\(0\\le b\\le2\\).  \nThus  \n\n\\[\n|A|=(4+1)(2+1)=15 .\n\\]\n\nAll \\(2^{15}\\) subsets of \\(A\\) are equally likely.\n\n---\n\n### Divisors needed for the LCM\n\nFor a subset \\(B\\subseteq A\\),\n\n\\[\n\\operatorname{lcm}(B)=3^{\\max_{d\\in B}a_d}\\;5^{\\max_{d\\in B}b_d}.\n\\]\n\nTo obtain \\(\\operatorname{lcm}(B)=2025=3^{4}5^{2}\\) we must have  \n\n* at least one element whose exponent of \\(3\\) equals \\(4\\);\n* at least one element whose exponent of \\(5\\) equals \\(2\\).\n\nDefine  \n\n\\[\nD_3=\\{d\\in A:\\, \\text{the exponent of }3\\text{ in }d\\text{ is }4\\},\\qquad \nD_5=\\{d\\in A:\\, \\text{the exponent of }5\\text{ in }d\\text{ is }2\\}.\n\\]\n\nCounting these divisors:\n\n* \\(D_3 = \\{3^{4}5^{0}, 3^{4}5^{1}, 3^{4}5^{2}\\}\\) \u21d2 \\(|D_3|=3\\);\n* \\(D_5 = \\{3^{0}5^{2}, 3^{1}5^{2}, 3^{2}5^{2}, 3^{3}5^{2}, 3^{4}5^{2}\\}\\) \u21d2 \\(|D_5|=5\\);\n* The intersection \\(D_3\\cap D_5=\\{3^{4}5^{2}\\}= \\{2025\\}\\) \u21d2 \\(|D_3\\cap D_5|=1\\).\n\nThus a subset \\(B\\) has \\(\\operatorname{lcm}(B)=2025\\) iff it contains **at least one element of \\(D_3\\) and at least one element of \\(D_5\\)** (the same element may satisfy both conditions).\n\n---\n\n### Counting such subsets\n\nLet \\(U\\) be the set of all subsets of \\(A\\) (including the empty set).  \nUse inclusion\u2013exclusion.\n\n\\[\n\\begin{aligned}\n|U| &=2^{15},\\\\[2mm]\n\\text{Subsets missing }D_3 &: 2^{15-|D_3|}=2^{12},\\\\[2mm]\n\\text{Subsets missing }D_5 &: 2^{15-|D_5|}=2^{10},\\\\[2mm]\n\\text{Subsets missing both }D_3\\text{ and }D_5 &: \n2^{15-|D_3\\cup D_5|}\n =2^{15-(3+5-1)}=2^{8}.\n\\end{aligned}\n\\]\n\nHence the number of subsets that contain at least one element of each set is  \n\n\\[\n\\begin{aligned}\nN_{\\text{good}}\n&=|U|-2^{12}-2^{10}+2^{8}\\\\\n&=32768-4096-1024+256\\\\\n&=27904.\n\\end{aligned}\n\\]\n\nEvery such subset is non\u2011empty, so these are exactly the favorable subsets.\n\n---\n\n### Probability\n\n\\[\nP=\\frac{N_{\\text{good}}}{2^{15}}=\\frac{27904}{32768}.\n\\]\n\nReduce the fraction:\n\n\\[\n27904=2^{8}\\cdot 109,\\qquad 32768=2^{15}=2^{8}\\cdot 128\n\\Longrightarrow P=\\frac{109}{128}.\n\\]\n\nThus \\(m=109\\) and \\(n=128\\), and  \n\n\\[\nm+n = 109+128 = 237.\n\\]\n\n\\[\n\\boxed{237}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nCircle $\\omega_1$ with radius 6 centered at point $A$ is internally tangent at point $B$ to circle $\\omega_2$ with radius 15. Points $C$ and $D$ lie on $\\omega_2$ such that $\\overline{BC}$ is a diameter of $\\omega_2$ and $\\overline{BC} \\perp \\overline{AD}$. The rectangle $EFGH$ is inscribed in $\\omega_1$ such that $\\overline{EF} \\perp \\overline{BC}$, $C$ is closer to $\\overline{GH}$ than to $\\overline{EF}$, and $D$ is closer to $\\overline{FG}$ than to $\\overline{EH}$, as shown. Triangles $\\triangle DGF$ and $\\triangle CHG$ have equal areas. The area of rectangle $EFGH$ is $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m + n$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n* \\(\\omega _2\\) have centre \\(O\\) and radius \\(15\\);\n* \\(BC\\) be a diameter of \\(\\omega _2\\);\n* \\(\\omega _1\\) have centre \\(A\\) and radius \\(6\\), internally tangent to \\(\\omega _2\\) at \\(B\\).\n\n--------------------------------------------------------------------\n### 1.  Coordinates\n\nPlace \\(BC\\) on the \\(x\\)-axis with  \n\n\\[\nB=(-15,0),\\qquad C=(15,0),\\qquad O=(0,0).\n\\]\n\nSince the circles are internally tangent, the centres are collinear with the\ntangency point and  \n\n\\[\nOA=R_2-R_1=15-6=9 .\n\\]\n\nThus \\(A\\) lies on the ray \\(OB\\) at distance \\(9\\) from \\(O\\); consequently  \n\n\\[\nA=(-9,0).\n\\]\n\n--------------------------------------------------------------------\n### 2.  Point \\(D\\)\n\n\\(AD\\perp BC\\), so \\(AD\\) is the vertical line \\(x=-9\\).\nIntersecting this line with \\(\\omega _2\\) (\\(x^2+y^2=225\\)) gives  \n\n\\[\ny^2=225-(-9)^2=144\\quad\\Longrightarrow\\quad y=\\pm12 .\n\\]\n\nBecause the statement \u201c\\(D\\) is closer to \\(\\overline{FG}\\) than to \\(\\overline{EH}\\)\u2019\u2019 puts \\(D\\) above the centre, we take  \n\n\\[\nD=(-9,12).\n\\]\n\n--------------------------------------------------------------------\n### 3.  Rectangle \\(EFGH\\)\n\nThe rectangle is inscribed in \\(\\omega _1\\), so its circum\u2011centre is the\ncentre of \\(\\omega _1\\); hence the centre of the rectangle is \\(A\\).\n\nLet  \n\n* half\u2011width \\(a\\) (distance from the centre to each vertical side),\n* half\u2011height \\(b\\) (distance from the centre to each horizontal side).\n\nBecause the vertices lie on \\(\\omega _1\\),\n\n\\[\na^{2}+b^{2}=6^{2}=36. \\tag{1}\n\\]\n\nThe condition \u201c\\(\\overline{EF}\\perp\\overline{BC}\\)\u201d makes \\(\\overline{EF}\\) vertical,\nso the rectangle\u2019s sides are parallel/perpendicular to \\(BC\\).  \nTaking the usual labelling (counter\u2011clockwise)\n\n\\[\n\\begin{aligned}\nE&=(-9-a,\\,-b),\\qquad \nF=(-9-a,\\,b),\\\\\nG&=(-9+a,\\,b),\\qquad \nH=(-9+a,\\,-b).\n\\end{aligned}\n\\]\n\n--------------------------------------------------------------------\n### 4.  Equality of the two triangle areas\n\n\\[\n\\begin{aligned}\n\\text{Area}(\\triangle DGF)&=\\frac12\\cdot GF\\cdot(\\text{vertical distance }D\\text{ to }y=b)\\\\\n&=\\frac12\\cdot(2a)\\cdot(12-b)=a(12-b),\\\\[4pt]\n\\text{Area}(\\triangle CHG)&=\\frac12\\cdot GH\\cdot(\\text{horizontal distance }C\\text{ to }x=-9+a)\\\\\n&=\\frac12\\cdot(2b)\\cdot(24-a)=b(24-a).\n\\end{aligned}\n\\]\n\nGiven the areas are equal,\n\n\\[\na(12-b)=b(24-a)\\quad\\Longrightarrow\\quad12a=24b\\quad\\Longrightarrow\\quad a=2b. \\tag{2}\n\\]\n\n--------------------------------------------------------------------\n### 5.  Solving for \\(a\\) and \\(b\\)\n\nSubstituting \\(a=2b\\) into (1):\n\n\\[\n(2b)^{2}+b^{2}=36\\;\\Longrightarrow\\;5b^{2}=36\\;\\Longrightarrow\\;b^{2}=\\frac{36}{5}.\n\\]\n\nHence  \n\n\\[\na^{2}=(2b)^{2}=4b^{2}= \\frac{144}{5}.\n\\]\n\n--------------------------------------------------------------------\n### 6.  Area of the rectangle\n\n\\[\n\\text{Area}= (2a)(2b)=4ab=4(2b)b=8b^{2}=8\\left(\\frac{36}{5}\\right)=\\frac{288}{5}.\n\\]\n\nThus the area is \\(\\dfrac{288}{5}\\).  In lowest terms \\(m=288,\\;n=5\\), and\n\n\\[\nm+n=288+5=293.\n\\]\n\n--------------------------------------------------------------------\n\\[\n\\boxed{293}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nAlex divides a disk into four quadrants with two perpendicular diameters intersecting at the center of the disk. He draws 25 more line segments through the disk, drawing each segment by selecting two points at random on the perimeter of the disk in different quadrants and connecting those two points. Find the expected number of regions into which these 27 line segments divide the disk.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "**Step 1.  How many regions are created by chords?**  \n\nIf a convex region (here the disk) is cut by \\(N\\) line\u2011segments whose interior intersection points are all distinct, the number of regions is  \n\n\\[\nR=N+1+I,\n\\]\n\nwhere \\(I\\) is the total number of interior intersection points.  \n(Each new segment adds one region, plus one extra region for each interior point where it meets a previous segment.)\n\nFor our disk  \n\n\\[\nN=27\\qquad\\text{(the two diameters + 25 random chords)} .\n\\]\n\nHence  \n\n\\[\nE[R]=28+E[I].\n\\]\n\nSo we must find the expected number \\(E[I]\\) of interior intersection points.\n\n--------------------------------------------------------------------\n\n**Step 2.  Intersections involving the two diameters.**\n\nThe two diameters intersect at the centre; this contributes one guaranteed intersection.\n\nFor a random chord \\(C\\) we ask for the probability that it meets a given diameter.\n\n*Vertical diameter.*  \nThe chord meets the vertical line \\(x=0\\) iff its endpoints lie in opposite half\u2011planes (one in \\(\\{Q_1,Q_4\\}\\) and the other in \\(\\{Q_2,Q_3\\}\\)).  \nAmong the six unordered pairs of distinct quadrants, four have this property:\n\n\\[\n\\{Q_1,Q_2\\},\\{Q_1,Q_3\\},\\{Q_2,Q_4\\},\\{Q_3,Q_4\\},\n\\]\n\nso  \n\n\\[\nP(C\\text{ meets the vertical diameter})=\\frac{4}{6}=\\frac23 .\n\\]\n\nExactly the same reasoning holds for the horizontal diameter.  \nThus for each random chord\n\n\\[\nP(C\\text{ meets a given diameter})=\\frac23 .\n\\]\n\nWith 25 random chords we obtain  \n\n\\[\nE[\\text{intersections chord\u2013diameter}] = 25\\cdot 2\\cdot\\frac23=\\frac{100}{3}.\n\\]\n\n--------------------------------------------------------------------\n\n**Step 3.  Intersections among the 25 random chords.**\n\nEach chord is obtained by picking two points on the circle that lie in different quadrants.  \nThe unordered pair of quadrants a chord uses is equally likely to be any of the six possibilities\n\n* four *adjacent* pairs: \\(\\{01\\},\\{12\\},\\{23\\},\\{30\\}\\);\n* two *opposite* pairs: \\(\\{02\\},\\{13\\}\\).\n\nThus a chord is *adjacent* with probability \\(\\frac23\\) and *opposite* with probability \\(\\frac13\\).\n\n--------------------------------------------------------------------\n### 3.1  Classifying a pair of chords\n\nLet chord\u202f1 belong to unordered pair \\(P\\) and chord\u202f2 to unordered pair \\(Q\\).  \nThere are three possible relationships between \\(P\\) and \\(Q\\):\n\n| relationship | how many ordered \\((P,Q)\\) | intersection probability |\n|--------------|---------------------------|--------------------------|\n| same pair (\\(P=Q\\)) | 6 | \\(\\displaystyle\\frac12\\) |\n| disjoint pairs (no common quadrant) | 6 (4 adjacent\u2011adjacent, 2 opposite\u2011opposite) | \\(0\\) for adjacent\u2013adjacent, \\(1\\) for opposite\u2013opposite |\n| share exactly one quadrant | 24 (8 adjacent\u2011adjacent, 16 adjacent\u2011opposite) | \\(\\displaystyle\\frac12\\) |\n\n*Why the numbers?*  \n\n* Two chords of the **same type** intersect iff the order of the two points in the first quadrant is opposite to the order of the two points in the second quadrant \u2013 probability \\(1/2\\).\n\n* Two **disjoint adjacent** chords lie in quadrants \\(\\{0,1\\}\\) and \\(\\{2,3\\}\\); all points of the first lie before those of the second, so they never intersect.\n\n* Two **disjoint opposite** chords are \\(\\{0,2\\}\\) and \\(\\{1,3\\}\\); the four points appear in the order \\(0,1,2,3\\), which is alternating, so they always intersect.\n\n* When the chords **share exactly one quadrant**, the shared quadrant contains two independent uniform points; whichever of the two lies first decides whether the endpoints are interleaved. Hence the intersection probability is \\(1/2\\).\n\n--------------------------------------------------------------------\n### 3.2  Expected intersection probability for a random pair\n\nSumming the contributions of all 36 ordered possibilities:\n\n\\[\n\\begin{aligned}\n\\sum_{P,Q} p_{P,Q}&=\n6\\!\\left(\\frac12\\right) \n+ 4\\!\\cdot\\!0 \n+ 2\\!\\cdot\\!1 \n+ 24\\!\\left(\\frac12\\right) \\\\\n&= 3 + 2 + 12 = 17 .\n\\end{aligned}\n\\]\n\nTherefore for two independently chosen random chords\n\n\\[\nP(\\text{they intersect}) = \\frac{17}{36}.\n\\]\n\n--------------------------------------------------------------------\n### 3.3  Expected number of chord\u2013chord intersections\n\nThere are \\(\\binom{25}{2}=300\\) unordered pairs of the 25 chords, so\n\n\\[\nE[\\text{chord\u2013chord intersections}]\n=300\\cdot\\frac{17}{36}= \\frac{425}{3}.\n\\]\n\n--------------------------------------------------------------------\n\n**Step 4.  Total expected number of interior intersections.**\n\n\\[\n\\begin{aligned}\nE[I] &= \\underbrace{1}_{\\text{diameters}} \n      + \\underbrace{\\frac{100}{3}}_{\\text{chord\u2013diameter}} \n      + \\underbrace{\\frac{425}{3}}_{\\text{chord\u2013chord}} \\\\[2mm]\n     &= \\frac{525}{3}+1 = 175+1 = 176 .\n\\end{aligned}\n\\]\n\n--------------------------------------------------------------------\n\n**Step 5.  Expected number of regions.**\n\n\\[\nE[R]=N+1+E[I]=27+1+176=204.\n\\]\n\n--------------------------------------------------------------------\n\n\\[\n\\boxed{204}\n\\]",
+        "role": "assistant"
+      }
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+        "role": "user",
+        "content": "\nFour unit squares form a $2 \\times 2$ grid. Each of the 12 unit line segments forming the sides of the squares is colored either red or blue in such a way that each unit square has 2 red sides and 2 blue sides. Find the number of such colorings.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Label the twelve unit segments that form the sides of the four unit squares as in the picture  \n\n\\[\n\\begin{array}{c}\n\\text{top left square }A:\\; a\\;( \\text{top}) ,\\; a'(\\text{left}) ,\\; u (\\text{vertical middle up}) ,\\; x (\\text{horizontal middle left})\\\\[2mm]\n\\text{top right square }B:\\; b ,\\; b' ,\\; u ,\\; y\\\\[2mm]\n\\text{bottom left square }C:\\; c ,\\; c' ,\\; v ,\\; x\\\\[2mm]\n\\text{bottom right square }D:\\; d ,\\; d' ,\\; v ,\\; y\n\\end{array}\n\\]\n\nAll variables are binary:  \n\n\\[\n0=\\text{blue},\\qquad 1=\\text{red}.\n\\]\n\n---\n\n### 1.  Express the condition for each square  \n\nFor a square the number of red sides must be exactly two.  \nIf we let  \n\n\\[\n\\begin{aligned}\ns_A &=x+u, & s_B &=y+u,\\\\\ns_C &=x+v, & s_D &=y+v,\n\\end{aligned}\n\\]\n\nthen the two **boundary** edges of a square must contain  \n\n\\[\nr_A =2-s_A,\\qquad r_B =2-s_B,\\qquad r_C =2-s_C,\\qquad r_D =2-s_D\n\\]\n\nred sides.  \nFor each square the two boundary edges are distinct from the other squares, so the choices for the\nfour pairs are independent.\n\nFor a given pair of boundary edges the number of colourings is  \n\n\\[\n\\begin{cases}\n1 &\\text{if }r_i\\in\\{0,2\\}\\;(00\\text{ or }11),\\\\[2mm]\n2 &\\text{if }r_i =1\\;(01\\text{ or }10).\n\\end{cases}\n\\]\n\nHence, when the interior pattern \\((x,y,u,v)\\) is fixed, the number of ways to colour the eight\nouter edges equals  \n\n\\[\n2^{\\#\\{\\,i\\in\\{A,B,C,D\\}\\mid s_i=1\\,\\}},\n\\]\n\nbecause a square contributes a factor \\(2\\) exactly when its interior sum \\(s_i\\) equals \\(1\\).\n\nThus the total number of admissible colourings is  \n\n\\[\nN=\\sum_{(x,y,u,v)\\in\\{0,1\\}^4} 2^{\\#\\{i\\mid s_i=1\\}} .\n\\]\n\n---\n\n### 2.  Enumerate the \\(2^4=16\\) interior patterns  \n\n\\[\n\\begin{array}{c|c|c|c|c|c}\n(x,y,u,v) & s_A & s_B & s_C & s_D &\n\\#\\{i\\mid s_i=1\\}\\\\\\hline\n0000 &0&0&0&0&0\\\\\n0001 &0&0&1&1&2\\\\\n0010 &1&1&0&0&2\\\\\n0011 &1&1&1&1&4\\\\\n0100 &0&1&0&1&2\\\\\n0101 &0&1&1&2&2\\\\\n0110 &1&2&0&1&2\\\\\n0111 &1&2&1&2&2\\\\\n1000 &1&0&1&0&2\\\\\n1001 &1&0&2&1&2\\\\\n1010 &2&1&1&0&2\\\\\n1011 &2&1&2&1&2\\\\\n1100 &1&1&1&1&4\\\\\n1101 &1&1&2&2&2\\\\\n1110 &2&2&1&1&2\\\\\n1111 &2&2&2&2&0\n\\end{array}\n\\]\n\n(The entry \u201c2\u2019\u2019 means the sum of the two interior edges of that square is \\(2\\); it forces the\ncorresponding pair of boundary edges to be both blue.)\n\nThe contribution of each pattern is \\(2^{\\#\\{i\\mid s_i=1\\}}\\).  Adding all contributions we get  \n\n\\[\n\\begin{aligned}\nN&=1\\;(0000)+4\\;(0001)+4\\;(0010)+16\\;(0011)\\\\\n  &\\quad+4\\;(0100)+4\\;(0101)+4\\;(0110)+4\\;(0111)\\\\\n  &\\quad+4\\;(1000)+4\\;(1001)+4\\;(1010)+4\\;(1011)\\\\\n  &\\quad+16\\;(1100)+4\\;(1101)+4\\;(1110)+1\\;(1111)\\\\[2mm]\n  &=1+16+48+16+1\\\\\n  &=\\boxed{82}.\n\\end{aligned}\n\\]\n\nTherefore there are **82** ways to colour the twelve unit segments of a \\(2\\times2\\) grid so that\nevery unit square has exactly two red and two blue sides.",
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+        "role": "user",
+        "content": "\nThere are $ n $ values of $ x $ in the interval $ 0 < x < 2\\pi $ where $ f(x) = \\sin(7\\pi \\cdot \\sin(5x)) = 0 $. For $ t $ of these $ n $ values of $ x $, the graph of $ y = f(x) $ is tangent to the $ x $-axis. Find $ n + t $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "\\[\nf(x)=\\sin \\bigl(7\\pi\\sin(5x)\\bigr)\n\\qquad (0<x<2\\pi)\n\\]\n\n---\n\n### 1.  Zeros of \\(f\\)\n\n\\(f(x)=0\\iff \\sin\\bigl(7\\pi\\sin(5x)\\bigr)=0\\)\n\n\\[\n7\\pi\\sin(5x)=k\\pi\\qquad(k\\in\\mathbb Z)\n\\Longrightarrow\\sin(5x)=\\frac{k}{7}.\n\\]\n\nSince \\(\\sin(5x)\\in[-1,1]\\), we must have \\(-7\\le k\\le7\\).  \nThus \\(k\\) can be any integer from \\(-7\\) to \\(7\\) (15 values).\n\nPut \\(\\theta =5x\\). Then \\(\\theta\\in(0,10\\pi)\\) and we need the number of solutions of  \n\n\\[\n\\sin\\theta =\\frac{k}{7}\\qquad (k=-7,\\ldots,7)\n\\]\nin \\((0,10\\pi)\\).\n\n*If \\(|k|=7\\) (\\(\\sin\\theta=\\pm1\\)):* each period \\((0,2\\pi)\\) contributes one solution, and there are five periods in \\((0,10\\pi)\\).  \n\\(\\;\\Rightarrow\\) 5 solutions for \\(k=7\\) and 5 solutions for \\(k=-7\\).\n\n*If \\(k=0\\) (\\(\\sin\\theta=0\\)):* solutions are \\(\\theta=n\\pi\\) with \\(n=1,\\dots ,9\\).  \n\\(\\;\\Rightarrow\\) 9 solutions.\n\n*If \\(|k|=1,2,\\dots ,6\\) (\\(|\\sin\\theta|<1\\) and \\(\\neq0\\)):* in each \\(2\\pi\\)\u2011interval there are two solutions, so across five intervals there are \\(2\\cdot5=10\\) solutions.\n\nHence the total number of zeros is  \n\n\\[\nn =\\underbrace{5+5}_{k=\\pm7}+ \\underbrace{9}_{k=0}+ \\underbrace{12\\times10}_{k=\\pm1,\\dots ,\\pm6}\n      =10+9+120 = 139 .\n\\]\n\n---\n\n### 2.  Tangent zeros\n\nA zero is tangent to the \\(x\\)-axis when \\(f'(x)=0\\) as well.\n\n\\[\nf'(x)=35\\pi\\cos\\!\\bigl(7\\pi\\sin(5x)\\bigr)\\,\\cos(5x).\n\\]\n\nAt any zero we have \\(\\cos\\!\\bigl(7\\pi\\sin(5x)\\bigr)=\\cos(k\\pi)=(-1)^k\\neq0\\); therefore  \n\n\\[\nf'(x)=0 \\iff \\cos(5x)=0.\n\\]\n\n\\(\\cos(5x)=0\\) gives \\(5x=\\dfrac{\\pi}{2}+m\\pi\\;(m\\in\\mathbb Z)\\), i.e.\n\n\\[\nx=\\frac{(2m+1)\\pi}{10}.\n\\]\n\nWithin \\(0<x<2\\pi\\) the odd integers \\(2m+1\\) run from \\(1\\) to \\(19\\); there are \\(10\\) such values.\nAt these points \\(\\sin(5x)=\\pm1\\), i.e. they correspond exactly to the solutions for \\(k=\\pm7\\).\n\nThus  \n\n\\[\nt=10.\n\\]\n\n---\n\n### 3.  Required sum\n\n\\[\nn+t = 139+10 = 149.\n\\]\n\n\\[\n\\boxed{149}\n\\]",
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+        "role": "user",
+        "content": "\nFrom an unlimited supply of 1-cent coins, 10-cent coins, and 25-cent coins, Silas wants to find a collection of coins that has a total value of $ N $ cents, where $ N $ is a positive integer. He uses the so-called **greedy algorithm**, successively choosing the coin of greatest value that does not cause the value of his collection to exceed $ N $. For example, to get 42 cents, Silas will choose a 25-cent coin, then a 10-cent coin, then 7 1-cent coins. However, this collection of 9 coins uses more coins than necessary to get a total of 42 cents; indeed, choosing 4 10-cent coins and 2 1-cent coins achieves the same total value with only 6 coins.\n\nIn general, the greedy algorithm succeeds for a given $ N $ if no other collection of 1-cent, 10-cent, and 25-cent coins gives a total value of $ N $ cents using strictly fewer coins than the collection given by the greedy algorithm. Find the number of values of $ N $ between 1 and 1000 inclusive for which the greedy algorithm succeeds.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "**Step 1 \u2013 Greedy description**\n\nFor a given amount \\(N\\) let  \n\n\\[\nq=\\Bigl\\lfloor \\frac{N}{25}\\Bigr\\rfloor ,\\qquad r=N-25q\\;(0\\le r<25)\n\\]\n\nThe greedy algorithm first takes \\(q\\) quarters, then uses as many dimes as possible and finally pennies.  \nHence the greedy number of coins is  \n\n\\[\ng(N)=q+\\Bigl\\lfloor\\frac{r}{10}\\Bigr\\rfloor +(r\\bmod 10)\n      =q+f(r),\n\\]\n\nwhere  \n\n\\[\nf(x)=\\Bigl\\lfloor\\frac{x}{10}\\Bigr\\rfloor +(x\\bmod10)\n\\]\n\nis the optimal number of coins when only dimes and pennies are allowed.\n\n---\n\n**Step 2 \u2013 Optimal solution with a given number of quarters**\n\nIf we use \\(a\\) quarters (\\(0\\le a\\le q\\)), we must make the remainder \\(N-25a\\) with dimes and pennies.  \nThe minimum number of coins for that remainder is \\(f(N-25a)\\).  \nThus the optimal number of coins for \\(N\\) is  \n\n\\[\n\\min_{0\\le a\\le q}\\; \\bigl[a+f(N-25a)\\bigr].\n\\]\n\nBecause \\(f\\) is optimal for the two\u2011coin system \\(\\{1,10\\}\\), we only need to compare the greedy choice\n\\(a=q\\) with the possibilities where we use fewer quarters.\n\n---\n\n**Step 3 \u2013 Effect of removing one quarter**\n\nWrite \\(r=N-25q\\) (the greedy remainder).  \nIf we use one fewer quarter (\\(a=q-1\\)), the new remainder is \\(r+25\\), and the coin count becomes  \n\n\\[\n(q-1)+f(r+25).\n\\]\n\nGreedy is optimal precisely when  \n\n\\[\nq+f(r)\\le (q-1)+f(r+25)\\quad\\Longleftrightarrow\\quad f(r)+1\\le f(r+25).\n\\]\n\nCompute \\(f(r+25)\\) in terms of \\(f(r)\\).  \nSince adding \\(25\\) cents is the same as adding two dimes and five pennies,  \n\n\\[\nf(r+25)=r+25-9\\Bigl\\lfloor\\frac{r+25}{10}\\Bigr\\rfloor .\n\\]\n\nThe floor changes by  \n\n\\[\n\\Bigl\\lfloor\\frac{r+25}{10}\\Bigr\\rfloor-\\Bigl\\lfloor\\frac{r}{10}\\Bigr\\rfloor=\n\\begin{cases}\n2,& r\\bmod10\\le 4,\\\\[2pt]\n3,& r\\bmod10\\ge 5 .\n\\end{cases}\n\\]\n\nHence  \n\n\\[\nf(r+25)=\n\\begin{cases}\nf(r)+7, & r\\bmod10\\le4,\\\\[2pt]\nf(r)-2, & r\\bmod10\\ge5 .\n\\end{cases}\n\\]\n\nConsequently  \n\n* if \\(r\\bmod10\\le4\\) then \\(f(r+25)=f(r)+7>f(r)+1\\) \u2013 greedy stays optimal;\n* if \\(r\\bmod10\\ge5\\) then \\(f(r+25)=f(r)-2\\le f(r)\\) \u2013 using one fewer quarter gives fewer coins.\n\nThus the greedy algorithm fails **exactly** when the greedy remainder \\(r\\) satisfies  \n\n\\[\nr\\bmod10\\ge5 \\;\\Longleftrightarrow\\; r\\in\\{5,6,7,8,9,15,16,17,18,19\\}.\n\\]\n\n---\n\n**Step 4 \u2013 Dropping more than one quarter never helps**\n\nFor two quarters removed we add \\(50\\) cents to the remainder.  \nA similar computation gives  \n\n\\[\nf(r+50)=f(r)+5 .\n\\]\n\nThe change in total coin count is \\(-2+5=+3\\); for three quarters removed the change is \\(-3+12=+9\\), etc.  \nHence removing two or more quarters can never improve on the greedy solution.  \nTherefore the condition found in Step\u202f3 is both necessary and sufficient.\n\n---\n\n**Step 5 \u2013 Counting the successful \\(N\\) (1\u202f\u2264\u202fN\u202f\u2264\u202f1000)**  \n\nThe greedy fails for those \\(N\\ge25\\) whose remainder modulo \\(25\\) lies in  \n\n\\[\nR=\\{5,6,7,8,9,15,16,17,18,19\\}.\n\\]\n\nFor a fixed residue \\(r\\in R\\),\n\n\\[\nN=r+25k\\qquad (k\\ge1,\\; N\\le1000).\n\\]\n\nThe largest possible \\(k\\) is \\(\\bigl\\lfloor\\frac{1000-r}{25}\\bigr\\rfloor =39\\)\n(because \\(1000-r\\) ranges from \\(981\\) to \\(995\\)).  \nThus each residue contributes \\(39\\) failing numbers.\n\n\\[\n\\#\\text{failures}=|R|\\times 39 = 10\\times39 = 390 .\n\\]\n\nAll other numbers (including the ten numbers \\(5,6,7,8,9,15,16,17,18,19\\) themselves, which are \\(<25\\) and therefore not failures) are successes.\n\n\\[\n\\#\\text{successes}=1000-390 = 610 .\n\\]\n\n---\n\n\\[\n\\boxed{610}\n\\]",
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+        "role": "user",
+        "content": "\nSixteen chairs are arranged in a row. Eight people each select a chair in which to sit so that no person sits next to two other people. Let $ N $ be the number of subsets of 16 chairs that could be selected. Find the remainder when $ N $ is divided by 1000.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n\\[\na_1a_2\\dots a_{16},\\qquad a_i\\in\\{0,1\\}\n\\]\n\nbe a binary string where \\(a_i=1\\) means the \\(i^{\\text{th}}\\) chair is occupied.\nThe condition *no person sits next to two other people* means that a\n\\(1\\) may not have a \\(1\\) on both sides; equivalently the string contains\nno three consecutive \\(1\\)\u2019s.  \nHence we must count the binary strings of length \\(16\\) that\n\n* have exactly eight \\(1\\)\u2019s,\n* contain no substring \\(111\\).\n\n---\n\n### 1.  Decompose the occupied chairs into blocks\n\nSince a block of consecutive \\(1\\)\u2019s can have length at most \\(2\\), the eight\n\\(1\\)\u2019s are split into blocks of length \\(1\\) or \\(2\\).\n\nLet  \n\n* \\(x\\) = number of blocks of length \\(1\\),\n* \\(y\\) = number of blocks of length \\(2\\),\n* \\(m=x+y\\) = total number of blocks.\n\nThen  \n\n\\[\nx+2y=8,\\qquad x+y=m\\Longrightarrow y=8-m,\\;x=2m-8 .\n\\]\n\nThus \\(m\\) can be any integer with \\(\\lceil 8/2\\rceil\\le m\\le 8\\); i.e.  \n\n\\[\nm=4,5,6,7,8 .\n\\]\n\nFor a given \\(m\\) the positions of the \\(y=8-m\\) blocks of length \\(2\\)\namong the \\(m\\) blocks can be chosen in  \n\n\\[\n\\binom{m}{\\,8-m\\,}\n\\]\n\nways.\n\n---\n\n### 2.  Insert the separating zeros\n\nBetween two consecutive blocks there must be at least one \\(0\\).\nWith \\(m\\) blocks there are \\(m-1\\) mandatory zeros.\nThere are \\(16-8=8\\) zeros altogether, so after placing the mandatory ones we\nstill have  \n\n\\[\n8-(m-1)=9-m\n\\]\n\nzeros left.  \n\nThese remaining zeros may be distributed freely among the \\(m+1\\) gaps\n(the two ends and the \\(m-1\\) interior gaps).  By stars\u2011and\u2011bars the number\nof ways is\n\n\\[\n\\binom{(9-m)+(m+1)-1}{(m+1)-1}\n   =\\binom{9}{m}.\n\\]\n\n---\n\n### 3.  Count all possibilities\n\nFor each admissible \\(m\\),\n\n\\[\n\\text{choices}(m)=\\binom{m}{8-m}\\binom{9}{m}.\n\\]\n\nHence  \n\n\\[\n\\begin{aligned}\nN&=\\sum_{m=4}^{8}\\binom{m}{8-m}\\binom{9}{m}\\\\[2mm]\n &=\\binom{4}{4}\\binom{9}{4}\n   +\\binom{5}{3}\\binom{9}{5}\n   +\\binom{6}{2}\\binom{9}{6}\n   +\\binom{7}{1}\\binom{9}{7}\n   +\\binom{8}{0}\\binom{9}{8}\\\\[2mm]\n &=1\\cdot126+10\\cdot126+15\\cdot84+7\\cdot36+1\\cdot9\\\\\n &=126+1260+1260+252+9\\\\\n &=2907 .\n\\end{aligned}\n\\]\n\n---\n\n### 4.  Remainder modulo \\(1000\\)\n\n\\[\n2907\\equiv 907\\pmod{1000}.\n\\]\n\n\\[\n\\boxed{907}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nSuppose $ \\triangle ABC $ has angles $ \\angle BAC = 84^\\circ $, $ \\angle ABC = 60^\\circ $, and $ \\angle ACB = 36^\\circ $. Let $ D, E, $ and $ F $ be the midpoints of sides $ \\overline{BC} $, $ \\overline{AC} $, and $ \\overline{AB} $, respectively. The circumcircle of $ \\triangle DEF $ intersects $ \\overline{BD} $, $ \\overline{AE} $, and $ \\overline{AF} $ at points $ G, H, $ and $ J $, respectively. The points $ G, D, E, H, J, $ and $ F $ divide the circumcircle of $ \\triangle DEF $ into six minor arcs, as shown. Find $ \\widehat{DE} + 2 \\cdot \\widehat{HJ} + 3 \\cdot \\widehat{FG} $, where the arcs are measured in degrees.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n\\[\n\\angle A=84^{\\circ},\\qquad \\angle B=60^{\\circ},\\qquad \\angle C=36^{\\circ}.\n\\]\n\n--------------------------------------------------------------------\n### 1.  The nine\u2011point circle in complex form  \n\nPut the circumcircle of \\(\\triangle ABC\\) as the unit circle and let  \n\n\\[\na=1,\\qquad b=e^{i\\beta},\\qquad c=e^{i\\gamma},\n\\]\n\nwhere  \n\n\\[\n\\beta =72^{\\circ},\\qquad \\gamma =240^{\\circ}\n\\]\n\nbecause the central arcs are twice the opposite angles:\n\\(\\widehat{BC}=2A=168^{\\circ},\\;\\widehat{CA}=2B=120^{\\circ},\n\\;\\widehat{AB}=2C=72^{\\circ}\\).\n\nThe nine\u2011point centre is\n\n\\[\nN=\\frac{a+b+c}{2},\n\\]\n\nand its radius is \\(\\frac12\\) (since \\(|a|=|b|=|c|=1\\)).  \nThe three midpoints are  \n\n\\[\nD=\\frac{b+c}{2},\\qquad \nE=\\frac{c+a}{2},\\qquad \nF=\\frac{a+b}{2}.\n\\]\n\nNotice that\n\n\\[\nD-N=-\\frac{a}{2},\\qquad \nE-N=-\\frac{b}{2},\\qquad \nF-N=-\\frac{c}{2} .\n\\tag{1}\n\\]\n\nHence the central angle \\(\\widehat{DE}\\) equals the angle between vectors\n\\(-a\\) and \\(-b\\); it is the same as the angle between \\(a\\) and \\(b\\).\n\n\\[\n\\widehat{DE}= \\angle aOb = 2\\angle ACB = 2\\cdot36^{\\circ}=72^{\\circ}.\n\\tag{2}\n\\]\n\n--------------------------------------------------------------------\n### 2.  The other intersection points  \n\nThe nine\u2011point circle is the image of the circumcircle under the similarity\n\n\\[\nX\\longmapsto N-\\frac{X}{2},\n\\tag{3}\n\\]\n\ni.e. the homothety with centre the centroid (factor \\(-\\tfrac12\\)).\nConsequently, if a point \\(Y\\) of the nine\u2011point circle is the image of\n\\(X\\) on the circumcircle, then  \n\n\\[\nY = N-\\frac{X}{2}\\qquad\\Longleftrightarrow\\qquad X=2(N-Y).\n\\tag{4}\n\\]\n\n--------------------------------------------------------------------\n#### (a) Point \\(G\\)\n\n\\(G\\) lies on line \\(BD\\).  Since \\(D\\) is the image of \\(A\\) and\n\\(B\\) is the image of the point \\(X\\) with \\(X=b\\), the line \\(BD\\) is the\nimage of the line through \\(A\\) parallel to chord \\(BC\\).\nThus \\(G\\) corresponds to the second intersection of the line through\n\\(A\\;(=a)\\) parallel to \\(BC\\) with the circumcircle.\n\nFor a line through a point \\(e^{i\\alpha}\\) parallel to chord\n\\(e^{i\\beta}e^{i\\gamma}\\) the second intersection is\n\\(e^{i(\\beta+\\gamma-\\alpha)}\\).  \nHere \\(\\alpha=0,\\;\\beta=72^{\\circ},\\;\\gamma=240^{\\circ}\\); therefore\n\n\\[\nX_G = e^{i(\\beta+\\gamma)}=e^{i312^{\\circ}} .\n\\]\n\nFrom (3) the point on the nine\u2011point circle is  \n\n\\[\nG = N-\\frac{X_G}{2}.\n\\]\n\nHence the vector \\(NG=-\\frac{X_G}{2}\\) has direction \\(312^{\\circ}+180^{\\circ}=132^{\\circ}\\).\n\n--------------------------------------------------------------------\n#### (b) Point \\(H\\)\n\n\\(H\\) lies on line \\(AE\\).  This line is parallel to chord \\(CA\\); the\nstarting point on the circumcircle is \\(B\\,(=e^{i72^{\\circ}})\\).  Thus\n\n\\[\nX_H = e^{i(0+240^{\\circ}-72^{\\circ})}=e^{i168^{\\circ}} ,\n\\qquad\nH=N-\\frac{X_H}{2},\n\\]\n\nso the direction of \\(NH\\) is \\(168^{\\circ}+180^{\\circ}=348^{\\circ}\\).\n\n--------------------------------------------------------------------\n#### (c) Point \\(J\\)\n\n\\(J\\) lies on line \\(AF\\), which is parallel to chord \\(AB\\); it starts\nfrom \\(C\\,(=e^{i240^{\\circ}})\\).  Therefore\n\n\\[\nX_J = e^{i(0+72^{\\circ}-240^{\\circ})}=e^{i192^{\\circ}},\n\\qquad\nJ=N-\\frac{X_J}{2},\n\\]\n\nand the direction of \\(NJ\\) is \\(192^{\\circ}+180^{\\circ}=12^{\\circ}\\).\n\n--------------------------------------------------------------------\n### 3.  The required arcs on the nine\u2011point circle  \n\nFrom the directions obtained:\n\n\\[\n\\begin{aligned}\n&\\text{Arc }DE = 252^{\\circ}-180^{\\circ}=72^{\\circ},\\\\[2mm]\n&\\text{Arc }FG = 132^{\\circ}-60^{\\circ}=72^{\\circ},\\\\[2mm]\n&\\text{Arc }HJ = (360^{\\circ}-348^{\\circ})+12^{\\circ}=24^{\\circ}.\n\\end{aligned}\n\\]\n\nAll are the minor arcs (each \\(<180^{\\circ}\\)).\n\n--------------------------------------------------------------------\n### 4.  Computing the requested expression  \n\n\\[\n\\widehat{DE}+2\\widehat{HJ}+3\\widehat{FG}\n=72^{\\circ}+2\\!\\cdot\\!24^{\\circ}+3\\!\\cdot\\!72^{\\circ}\n=72+48+216=336^{\\circ}.\n\\]\n\n--------------------------------------------------------------------\n\\[\n\\boxed{336}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nLet $ S $ be the set of vertices of a regular 24-gon. Find the number of ways to draw 12 segments of equal lengths so that each vertex in $ S $ is an endpoint of exactly one of the 12 segments.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "For a regular 24\u2011gon label the vertices \\(0,1,\\ldots ,23\\) in order.\nIf a segment joins vertex \\(i\\) to vertex \\(j\\) then the chord length depends only on  \n\n\\[\nk=\\min \\{\\,|i-j|\\;,\\;24-|i-j|\\,\\},\n\\qquad 1\\le k\\le 12 .\n\\]\n\nThus a configuration in which all 12 segments have the same length corresponds to a\nperfect matching in the graph whose edges are all chords of a fixed step \\(k\\).\n\n---\n\n### 1.  Structure of the step\u2011\\(k\\) graph  \n\nLet \\(d=\\gcd(24,k)\\).  \nThe vertices split into \\(d\\) disjoint cycles, each of length  \n\n\\[\nL=\\frac{24}{d}.\n\\]\n\nEvery vertex is incident with exactly the two edges of its cycle.  \nA perfect matching can exist only if each cycle has even length, i.e. \\(L\\) must be even.\n\\(L\\) is odd only when \\(d=8\\) (then \\(L=3\\)); this occurs for \\(k=8\\).  \nHence the step \\(k=8\\) gives **no** valid configuration.\n\nFor an even cycle of length \\(L\\ge4\\) there are exactly two perfect matchings\n(the two possible \u201calternating\u201d choices).  \nIf \\(L=2\\) (the case \\(k=12\\)), the matching is forced and there is only one.\n\nConsequently, for a permissible \\(k\\)\n\n\\[\n\\#\\text{ matchings for step }k=\n\\begin{cases}\n2^{d}, & L>2,\\\\[2pt]\n1, & L=2 .\n\\end{cases}\n\\]\n\n---\n\n### 2.  Count for each step \\(k\\)\n\n\\[\n\\begin{array}{c|c|c|c}\nk & d=\\gcd(24,k) & L=24/d & \\#\\text{ matchings}\\\\ \\hline\n1,5,7,11 & 1 & 24 & 2\\\\\n2,10 & 2 & 12 & 2^{2}=4\\\\\n3,9 & 3 & 8 & 2^{3}=8\\\\\n4 & 4 & 6 & 2^{4}=16\\\\\n6 & 6 & 4 & 2^{6}=64\\\\\n12 & 12& 2 & 1\\\\\n8 & 8 & 3 & \\text{none}\n\\end{array}\n\\]\n\nNow sum over all admissible \\(k\\) ( \\(k=1,\\dots ,12\\) except \\(k=8\\) ):\n\n\\[\n\\begin{aligned}\n\\text{Total}&=4\\cdot2\\;+\\;2\\cdot4\\;+\\;2\\cdot8\\;+\\;1\\cdot16\\;+\\;1\\cdot64\\;+\\;1\\cdot1\\\\\n&=8+8+16+16+64+1\\\\\n&=113 .\n\\end{aligned}\n\\]\n\n---\n\n\\[\n\\boxed{113}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nFind the sum of all integer bases $b>9$ for which $17_{b}$ is a divisor of $97_{b}$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n\\[\n17_{b}=1\\cdot b+7=b+7,\\qquad \n97_{b}=9\\cdot b+7=9b+7 .\n\\]\n\nWe need  \n\n\\[\nb+7 \\mid 9b+7 .\n\\]\n\nWrite \\(9b+7\\) in terms of \\(b+7\\):\n\n\\[\n9b+7 = 9(b+7) - 56 .\n\\]\n\nHence the remainder upon division by \\(b+7\\) is \\(-56\\).  \nThus \\(b+7\\) must divide \\(56\\):\n\n\\[\nb+7 \\mid 56 .\n\\]\n\nList the positive divisors of \\(56\\):\n\n\\[\n1,\\;2,\\;4,\\;7,\\;8,\\;14,\\;28,\\;56 .\n\\]\n\nSince the base must satisfy \\(b>9\\) (so that the digit 9 is allowed), we need  \n\n\\[\nb+7>9+7=16 .\n\\]\n\nThe only divisors of \\(56\\) larger than \\(16\\) are \\(28\\) and \\(56\\).\n\n\\[\n\\begin{aligned}\nb+7 &= 28 \\;\\Longrightarrow\\; b=21,\\\\[2pt]\nb+7 &= 56 \\;\\Longrightarrow\\; b=49.\n\\end{aligned}\n\\]\n\nBoth bases exceed \\(9\\) and thus are admissible.\n\nThe sum of all such bases is\n\n\\[\n21+49 = 70 .\n\\]\n\n\\[\n\\boxed{70}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nLet $ A_1A_2 \\ldots A_{11} $ be an 11-sided non-convex simple polygon with the following properties:\n* The area of $ A_iA_1A_{i+1} $ is 1 for each $ 2 \\leq i \\leq 10 $,\n* $ \\cos(\\angle A_iA_1A_{i+1}) = \\frac{12}{13} $ for each $ 2 \\leq i \\leq 10 $,\n* The perimeter of $ A_1A_2 \\ldots A_{11} $ is 20.\nIf $ A_1A_2 + A_1A_{11} $ can be expressed as $ \\frac{m\\sqrt{n} - p}{q} $ for positive integers $ m, n, p, q $ with $ n $ squarefree and no prime divides all of $ m, p, q$, find $ m + n + p + q $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n\\[\na_i=A_1A_i\\qquad (i=2,\\dots ,11),\\qquad s_i=A_iA_{i+1}\\qquad (i=2,\\dots ,10).\n\\]\n\nFor each triangle \\(A_iA_1A_{i+1}\\;(2\\le i\\le10)\\)\n\n* \\(\\displaystyle \\text{Area}=1\\),\n* \\(\\displaystyle\\cos\\angle A_iA_1A_{i+1}= \\frac{12}{13}\\).\n\n--------------------------------------------------------------------\n### 1.  Product of the two sides from \\(A_1\\)\n\nWith \\(\\theta=\\angle A_iA_1A_{i+1}\\) we have  \n\n\\[\n\\sin\\theta=\\sqrt{1-\\cos ^2\\theta}= \\frac{5}{13}.\n\\]\n\nThe area of \\(\\triangle A_iA_1A_{i+1}\\) is  \n\n\\[\n\\frac12 a_i a_{i+1}\\sin\\theta =1\n\\Longrightarrow a_i a_{i+1}= \\frac{2}{\\sin\\theta}= \\frac{2}{5/13}= \\frac{26}{5}\\equiv c .\n\\tag{1}\n\\]\n\nHence for all \\(i\\)\n\n\\[\na_i a_{i+1}=c=\\frac{26}{5}.\n\\]\n\n--------------------------------------------------------------------\n### 2.  Length of the side \\(A_iA_{i+1}\\)\n\nApply the law of cosines in \\(\\triangle A_iA_1A_{i+1}\\):\n\n\\[\ns_i^2=a_i^{\\,2}+a_{i+1}^{\\,2}-2a_i a_{i+1}\\cos\\theta\n      =a_i^{\\,2}+a_{i+1}^{\\,2}-2c\\Bigl(\\frac{12}{13}\\Bigr).\n\\]\n\nBecause \\(2c\\frac{12}{13}= \\frac{624}{65}= \\frac{48}{5}\\),\n\n\\[\ns_i^{\\,2}=a_i^{\\,2}+a_{i+1}^{\\,2}-\\frac{48}{5}. \\tag{2}\n\\]\n\n--------------------------------------------------------------------\n### 3.  The alternating pattern of the radii\n\nFrom (1) we have \\(a_{i+1}=c/a_i\\). Consequently  \n\n\\[\na_{i+2}=c/a_{i+1}=c/(c/a_i)=a_i .\n\\]\n\nThus  \n\n\\[\na_{2}=a_{4}=a_{6}=a_{8}=a_{10}\\equiv x, \\qquad \na_{3}=a_{5}=a_{7}=a_{9}=a_{11}\\equiv \\frac{c}{x}.\n\\]\n\nAll sides \\(s_i\\;(i=2,\\dots ,10)\\) are equal, because each uses the\npair \\((x,\\;c/x)\\) in (2).  Set  \n\n\\[\nS^2=x^{2}+\\Bigl(\\frac{c}{x}\\Bigr)^2-\\frac{48}{5}.\n\\tag{3}\n\\]\n\n--------------------------------------------------------------------\n### 4.  Express everything via \\(t=x+\\dfrac{c}{x}\\)\n\nDefine  \n\n\\[\nt=x+\\frac{c}{x}=a_2+a_{11}.\n\\]\n\nThen  \n\n\\[\nx^{2}+\\Bigl(\\frac{c}{x}\\Bigr)^2=t^{2}-2c .\n\\]\n\nInsert this into (3):\n\n\\[\nS^{2}=t^{2}-2c-\\frac{48}{5}=t^{2}-(2c+\\frac{48}{5}).\n\\]\n\nSince \\(c=\\dfrac{26}{5}\\),\n\n\\[\n2c+\\frac{48}{5}= \\frac{52}{5}+\\frac{48}{5}=20.\n\\]\n\nHence  \n\n\\[\nS^{2}=t^{2}-20,\\qquad S=\\sqrt{t^{2}-20}. \\tag{4}\n\\]\n\n--------------------------------------------------------------------\n### 5.  Use the perimeter\n\nThe perimeter of the 11\u2011gon is  \n\n\\[\na_2+a_{11}+ \\sum_{i=2}^{10}s_i = t+9S =20.\n\\]\n\nSubstituting (4):\n\n\\[\nt+9\\sqrt{t^{2}-20}=20.\n\\]\n\nIsolate the radical and square:\n\n\\[\n9\\sqrt{t^{2}-20}=20-t \\quad\\Longrightarrow\\quad \n81(t^{2}-20)=(20-t)^{2}.\n\\]\n\nSimplifying:\n\n\\[\n80t^{2}+40t-2020=0\n\\Longrightarrow 4t^{2}+2t-101=0.\n\\]\n\nSolve for \\(t\\):\n\n\\[\nt=\\frac{-2\\pm\\sqrt{4+1616}}{8}\n   =\\frac{-2\\pm 18\\sqrt5}{8}\n   =\\frac{-1\\pm 9\\sqrt5}{4}.\n\\]\n\nSince \\(t>0\\), we take the plus sign:\n\n\\[\n\\boxed{t=\\frac{9\\sqrt5-1}{4}}.\n\\]\n\nThus  \n\n\\[\nA_1A_2+A_1A_{11}= \\frac{9\\sqrt5-1}{4}\n            =\\frac{m\\sqrt n-p}{q},\n\\]\nwith \\(m=9,\\;n=5,\\;p=1,\\;q=4\\).\n\n--------------------------------------------------------------------\n### 6.  Compute \\(m+n+p+q\\)\n\n\\[\nm+n+p+q = 9+5+1+4 = 19.\n\\]\n\n\\[\n\\boxed{19}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nThe 9 members of a baseball team went to an ice cream parlor after their game. Each player had a singlescoop cone of chocolate, vanilla, or strawberry ice cream. At least one player chose each flavor, and the number of players who chose chocolate was greater than the number of players who chose vanilla, which was greater than the number of players who chose strawberry. Let $N$ be the number of different assignments of flavors to players that meet these conditions. Find the remainder when $N$ is divided by 1000.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "The nine players are distinct.  Let  \n\n\\[\nc=\\#\\text{chocolate},\\qquad v=\\#\\text{vanilla},\\qquad s=\\#\\text{strawberry}\n\\]\n\nwith  \n\n\\[\nc+v+s=9,\\qquad c>v>s\\ge 1 .\n\\]\n\n---\n\n### 1.  Find all possible triples \\((c,v,s)\\)\n\nSince \\(c>v>s\\),\n\n\\[\nc\\ge v+1,\\qquad v\\ge s+1.\n\\]\n\nWrite \\(v=s+d_2\\) and \\(c=v+d_1\\) where \\(d_1,d_2\\ge 1\\).  \nThen  \n\n\\[\nc+v+s=(s+d_2+d_1)+(s+d_2)+s=3s+2d_2+d_1=9 .\n\\]\n\nBecause \\(s\\ge1\\), we have \\(3s\\le 9\\Rightarrow s=1,2,3\\).\n\n* **\\(s=1\\):** \\(2d_2+d_1=6\\).  \n  \\(d_2=1\\Rightarrow d_1=4\\) \u2192 \\((c,v,s)=(6,2,1)\\).  \n  \\(d_2=2\\Rightarrow d_1=2\\) \u2192 \\((c,v,s)=(5,3,1)\\).\n\n* **\\(s=2\\):** \\(2d_2+d_1=3\\).  \n  \\(d_2=1\\Rightarrow d_1=1\\) \u2192 \\((c,v,s)=(4,3,2)\\).\n\n* **\\(s=3\\):** \\(2d_2+d_1=0\\) \u2013 impossible with \\(d_1,d_2\\ge1\\).\n\nThus the only feasible triples are  \n\n\\[\n(6,2,1),\\;(5,3,1),\\;(4,3,2).\n\\]\n\n---\n\n### 2.  Count assignments for each triple\n\nFor a given \\((c,v,s)\\) the number of ways to assign the flavors to the 9 distinct players is the multinomial coefficient  \n\n\\[\n\\frac{9!}{c!\\,v!\\,s!}.\n\\]\n\n\\[\n\\begin{aligned}\n(6,2,1):\\;&\\frac{9!}{6!\\,2!\\,1!}= \\frac{362880}{720\\cdot2}=252,\\\\[2mm]\n(5,3,1):\\;&\\frac{9!}{5!\\,3!\\,1!}= \\frac{362880}{120\\cdot6}=504,\\\\[2mm]\n(4,3,2):\\;&\\frac{9!}{4!\\,3!\\,2!}= \\frac{362880}{24\\cdot6\\cdot2}=1260.\n\\end{aligned}\n\\]\n\n---\n\n### 3.  Total number of assignments\n\n\\[\nN = 252+504+1260 = 2016.\n\\]\n\n---\n\n### 4.  Remainder modulo \\(1000\\)\n\n\\[\n2016 \\equiv 16 \\pmod{1000}.\n\\]\n\n\\[\n\\boxed{16}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nFind the number of ordered pairs $(x,y)$, where both $x$ and $y$ are integers between $-100$ and $100$, inclusive, such that $12x^{2}-xy-6y^{2}=0$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "The equation  \n\n\\[\n12x^{2}-xy-6y^{2}=0\n\\]\n\nis a homogeneous quadratic form.  \nFactor it over the integers:\n\n\\[\n12x^{2}-xy-6y^{2}= (3x+2y)(4x-3y).\n\\]\n\nIndeed  \n\n\\[\n(3x+2y)(4x-3y)=12x^{2}-9xy+8xy-6y^{2}=12x^{2}-xy-6y^{2}.\n\\]\n\nHence a pair \\((x,y)\\) of integers satisfies the equation iff\n\n\\[\n3x+2y=0\\qquad\\text{or}\\qquad 4x-3y=0 .\n\\]\n\n---\n\n### 1. Solutions of \\(3x+2y=0\\)\n\n\\[\n3x+2y=0 \\;\\Longrightarrow\\; y=-\\frac{3}{2}x .\n\\]\n\nFor \\(y\\) to be an integer, \\(x\\) must be even: write \\(x=2k\\). Then  \n\n\\[\n(x,y)=(2k,-3k),\\qquad k\\in\\mathbb Z .\n\\]\n\nBoth coordinates must lie in \\([-100,100]\\):\n\n\\[\n-100\\le 2k\\le 100\\;\\Longrightarrow\\;-50\\le k\\le 50,\\\\\n-100\\le -3k\\le 100\\;\\Longrightarrow\\;-33\\le k\\le 33.\n\\]\n\nThus \\(k=-33,-32,\\dots ,33\\); there are  \n\n\\[\n33-(-33)+1 = 67\n\\]\n\ninteger solutions on this line.\n\n---\n\n### 2. Solutions of \\(4x-3y=0\\)\n\n\\[\n4x-3y=0 \\;\\Longrightarrow\\; y=\\frac{4}{3}x .\n\\]\n\nFor \\(y\\) to be an integer, \\(x\\) must be a multiple of \\(3\\): put \\(x=3t\\). Then  \n\n\\[\n(x,y)=(3t,4t),\\qquad t\\in\\mathbb Z .\n\\]\n\nAgain impose the bounds:\n\n\\[\n-100\\le 3t\\le 100\\;\\Longrightarrow\\;-33\\le t\\le 33,\\\\\n-100\\le 4t\\le 100\\;\\Longrightarrow\\;-25\\le t\\le 25.\n\\]\n\nThus \\(t=-25,-24,\\dots ,25\\); the number of solutions here is  \n\n\\[\n25-(-25)+1 = 51.\n\\]\n\n---\n\n### 3. Intersection of the two lines\n\nBoth equations hold simultaneously only at the origin:\n\n\\[\n3x+2y=0,\\;4x-3y=0 \\Longrightarrow (x,y)=(0,0).\n\\]\n\nThis point has been counted in both previous totals, so we subtract it once.\n\n---\n\n### 4. Total number of ordered pairs\n\n\\[\n\\#\\text{solutions}=67+51-1=117.\n\\]\n\n\\[\n\\boxed{117}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nAn isosceles trapezoid has an inscribed circle tangent to each of its four sides. The radius of the circle is 3, and the area of the trapezoid is 72. Let the parallel sides of the trapezoid have lengths $r$ and $s$, with $r \\neq s$. Find $r^{2}+s^{2}$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let the trapezoid be \\(ABCD\\) with \\(AB\\parallel CD\\) and  \n\n\\[\nAB=s ,\\qquad CD=r ,\\qquad AD=BC=L \\;( \\text{isosceles}).\n\\]\n\nThe incircle has radius \\(R=3\\) and the area is \\(72\\).\n\n---\n\n### 1.  Semiperimeter\n\nFor any tangential quadrilateral (one with an incircle)\n\n\\[\n\\text{Area}=R\\cdot(\\text{semiperimeter}).\n\\]\n\nHence  \n\n\\[\n72=3\\cdot s_{\\!p}\\quad\\Longrightarrow\\quad s_{\\!p}=24 .\n\\]\n\nThus the perimeter is  \n\n\\[\n2s_{\\!p}=48\\quad\\Longrightarrow\\quad r+s+2L=48. \\tag{1}\n\\]\n\n---\n\n### 2.  Tangential condition\n\nIn a tangential quadrilateral the sums of opposite sides are equal:\n\n\\[\nAB+CD = AD+BC\\quad\\Longrightarrow\\quad r+s = 2L. \\tag{2}\n\\]\n\nFrom (1) and (2),\n\n\\[\n2(r+s)=48 \\;\\Longrightarrow\\; r+s=24,\\qquad\n2L=r+s=24\\;\\Longrightarrow\\; L=12.\n\\]\n\n---\n\n### 3.  Height\n\nThe incircle touches both parallel sides, so the distance between the bases equals twice the radius:\n\n\\[\nh=2R=6.\n\\]\n\n(Alternatively, \\(\\displaystyle 72=\\tfrac12(r+s)h\\) with \\(r+s=24\\) also gives \\(h=6\\).)\n\n---\n\n### 4.  Relating the bases\n\nPlace the trapezoid with its symmetry axis on the \\(y\\)-axis; the bases are horizontal.\nThe horizontal half\u2011difference of the bases is \\(\\dfrac{s-r}{2}\\).\nHence the leg length satisfies\n\n\\[\nL^{2}= \\left(\\frac{s-r}{2}\\right)^{2}+h^{2}.\n\\]\n\nUsing \\(L=12,\\;h=6\\),\n\n\\[\n12^{2}= \\frac{(s-r)^{2}}{4}+6^{2}\n\\quad\\Longrightarrow\\quad\n\\frac{(s-r)^{2}}{4}=108\n\\quad\\Longrightarrow\\quad\ns-r=12\\sqrt3. \\tag{3}\n\\]\n\n---\n\n### 5.  Solving for \\(r\\) and \\(s\\)\n\n\\[\n\\begin{cases}\nr+s=24,\\\\[2pt]\ns-r=12\\sqrt3,\n\\end{cases}\n\\qquad\\Longrightarrow\\qquad\n\\begin{aligned}\ns&=\\frac{24+12\\sqrt3}{2}=12+6\\sqrt3,\\\\\nr&=\\frac{24-12\\sqrt3}{2}=12-6\\sqrt3.\n\\end{aligned}\n\\]\n\n---\n\n### 6.  Required sum of squares\n\n\\[\n\\begin{aligned}\nr^{2}+s^{2}\n&=(12-6\\sqrt3)^{2}+(12+6\\sqrt3)^{2}\\\\\n&= \\bigl(144-144\\sqrt3+108\\bigr)+\\bigl(144+144\\sqrt3+108\\bigr)\\\\\n&= 504.\n\\end{aligned}\n\\]\n\n\\[\n\\boxed{504}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nLet $ \\triangle ABC $ be a right triangle with $ \\angle A = 90^\\circ $ and $ BC = 38 $. There exist points $ K $ and $ L $ inside the triangle such that $ AK = AL = BK = CL = KL = 14. $ The area of the quadrilateral $ BKLC $ can be expressed as $ n \\sqrt{3} $ for some positive integer $ n $. Find $ n $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n* \\(A=(0,0)\\),  \n* \\(B=(u,0)\\) on the \\(x\\)-axis,  \n* \\(C=(0,v)\\) on the \\(y\\)-axis.  \n\nSince \\(\\angle A=90^{\\circ}\\), \\(BC=38\\) gives  \n\n\\[\nu^{2}+v^{2}=38^{2}=1444\\tag{1}\n\\]\n\n---\n\n### 1.  The equilateral triangle \\(AKL\\)\n\nThe conditions  \n\n\\[\nAK=AL=KL=14\n\\]\n\nshow that \\(\\triangle AKL\\) is equilateral.  \nLet the direction of \\(\\overrightarrow{AK}\\) form an angle \\(\\theta\\) with the\npositive \\(x\\)-axis. Then\n\n\\[\nK=(14\\cos\\theta,\\;14\\sin\\theta),\\qquad \nL=(14\\cos(\\theta+60^\\circ),\\;14\\sin(\\theta+60^\\circ)).\\tag{2}\n\\]\n\n---\n\n### 2.  Using \\(BK=14\\) and \\(CL=14\\)\n\n\\[\nBK^{2}= (u-14\\cos\\theta)^2+(14\\sin\\theta)^2=14^{2}\n\\]\n\n\\[\n\\Longrightarrow\\; u=28\\cos\\theta.\\tag{3}\n\\]\n\nSimilarly  \n\n\\[\nCL^{2}= (14\\cos(\\theta+60^\\circ))^{2}+(v-14\\sin(\\theta+60^\\circ))^{2}=14^{2}\n\\]\n\n\\[\n\\Longrightarrow\\; v=28\\sin(\\theta+60^\\circ).\\tag{4}\n\\]\n\n---\n\n### 3.  Determining \\(\\theta\\)\n\nInsert (3) and (4) into (1):\n\n\\[\n(28\\cos\\theta)^{2}+(28\\sin(\\theta+60^\\circ))^{2}=1444\n\\]\n\\[\n\\Longrightarrow\\;\\cos^{2}\\theta+\\sin^{2}(\\theta+60^\\circ)=\\frac{361}{196}.\n\\]\n\nUsing \\(\\sin(\\theta+60^\\circ)=\\tfrac12\\sin\\theta+\\tfrac{\\sqrt3}{2}\\cos\\theta\\),\nthe equation reduces to  \n\n\\[\n6\\cos^{2}\\theta+2\\sqrt3\\sin\\theta\\cos\\theta= \\frac{312}{49}.\n\\]\n\nSolving gives \\(\\cos\\theta=\\frac{13}{14}\\) (the other root gives the same\ntriangle with the legs interchanged).  \n\nHence  \n\n\\[\nu=28\\cos\\theta=28\\cdot\\frac{13}{14}=26,\\qquad\nv=28\\sin(\\theta+60^\\circ)=28\\cdot\\frac{4\\sqrt3}{7}=16\\sqrt3 .\n\\]\n\nThus  \n\n\\[\nAB=26,\\qquad AC=16\\sqrt3,\\qquad BC=38.\n\\]\n\nFrom (2) we obtain the coordinates of the interior points\n\n\\[\nK=(13,\\;3\\sqrt3),\\qquad L=(2,\\;8\\sqrt3).\n\\]\n\n---\n\n### 4.  Area of \\(BKLC\\)\n\nUse the shoelace formula for the polygon \\(B(26,0),K(13,3\\sqrt3),L(2,8\\sqrt3),C(0,16\\sqrt3)\\):\n\n\\[\n\\begin{aligned}\nS_1&=26\\cdot3\\sqrt3+13\\cdot8\\sqrt3+2\\cdot16\\sqrt3+0\\cdot0=214\\sqrt3,\\\\\nS_2&=0\\cdot13+3\\sqrt3\\cdot2+8\\sqrt3\\cdot0+16\\sqrt3\\cdot26=422\\sqrt3.\n\\end{aligned}\n\\]\n\n\\[\n\\text{Area}=\\frac12|S_2-S_1|\n          =\\frac12(422-214)\\sqrt3\n          =104\\sqrt3 .\n\\]\n\nTherefore the area can be written as \\(n\\sqrt3\\) with  \n\n\\[\n\\boxed{n=104}.\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nThere are $8!=40320$ eight-digit positive integers that use each of the digits $1,2,3,4,5,6,7,8$ exactly once. Let $N$ be the number of these integers that are divisible by 22. Find the difference between $N$ and 2025.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "For an eight\u2011digit number formed by a permutation of  \n\n\\[\n\\{1,2,3,4,5,6,7,8\\}\n\\]\n\nlet  \n\n\\[\na_1a_2a_3a_4a_5a_6a_7a_8\n\\]\n\nbe its digits (left to right).  \nA number is divisible by \\(22\\iff\\) it is divisible by \\(2\\) and by \\(11\\).\n\n---\n\n### 1.  Divisibility by 2  \n\nThe last digit \\(a_8\\) must be even, so \\(a_8\\in\\{2,4,6,8\\}\\).\n\n---\n\n### 2.  Divisibility by 11  \n\nFor an 8\u2011digit number the rule for 11 is  \n\n\\[\n(a_1+a_3+a_5+a_7)-(a_2+a_4+a_6+a_8)\\equiv 0\\pmod{11}.\n\\]\n\nSince the total sum of the digits is  \n\n\\[\n1+2+\\cdots+8 = 36,\n\\]\n\nlet  \n\n\\[\nS_{\\text{odd}}=a_1+a_3+a_5+a_7,\\qquad \nS_{\\text{even}}=a_2+a_4+a_6+a_8 .\n\\]\n\nThen \\(S_{\\text{odd}}+S_{\\text{even}}=36\\) and the condition gives  \n\n\\[\nS_{\\text{odd}}-S_{\\text{even}}\\equiv0\\pmod{11}.\n\\]\n\nThe only possible values for \\(S_{\\text{odd}}-S_{\\text{even}}\\) are \\(-22,0,22\\);   \n\\(-22\\) would give \\(S_{\\text{odd}}=7\\) and \\(22\\) would give \\(S_{\\text{odd}}=29\\), both impossible because a sum of four distinct digits from \\(\\{1,\\dots ,8\\}\\) cannot be smaller than \\(10\\) nor larger than \\(26\\).  \nHence\n\n\\[\nS_{\\text{odd}} = S_{\\text{even}} = 18 .\n\\]\n\nThus the four digits in the odd positions must sum to \\(18\\); the same holds for the even positions.\n\n---\n\n### 3.  Choosing the four digits for the odd positions  \n\nWe need 4\u2011element subsets of \\(\\{1,\\dots ,8\\}\\) whose sum is \\(18\\).  \nA quick enumeration gives the eight subsets\n\n\\[\n\\begin{aligned}\n&\\{1,2,7,8\\},\\{1,3,6,8\\},\\{1,4,5,8\\},\\{1,4,6,7\\},\\\\\n&\\{2,3,5,8\\},\\{2,3,6,7\\},\\{2,4,5,7\\},\\{3,4,5,6\\}.\n\\end{aligned}\n\\]\n\nEach contains exactly two even digits (the set \\(\\{2,4,6,8\\}\\)) and two odd digits.  \nHence every admissible odd\u2011position set has **2 even digits**.\n\nLet a chosen subset be \\(S\\) (the odd\u2011position digits) and its complement \\(S^c\\) (the even\u2011position digits).\n\n---\n\n### 4.  Arranging the digits  \n\n* The four digits of \\(S\\) can be placed in the odd positions \\((1,3,5,7)\\) in \\(4! = 24\\) ways.  \n* The four digits of \\(S^c\\) must fill the even positions \\((2,4,6,8)\\) with the extra requirement that the last digit \\(a_8\\) be even.  \n  Since \\(S^c\\) contains exactly \\(2\\) even digits, we have  \n\n\\[\n\\text{choices for }a_8 = 2,\\qquad\n\\text{arrangements of the remaining three even\u2011position digits}=3! = 6 .\n\\]\n\nThus for each set \\(S\\)\n\n\\[\n\\#\\text{numbers}=4!\\times(2\\times3!) = 24\\times12 = 288.\n\\]\n\n---\n\n### 5.  Total number \\(N\\)\n\nThere are \\(8\\) possible subsets \\(S\\); consequently\n\n\\[\nN = 8 \\times 288 = 2304 .\n\\]\n\n---\n\n### 6.  Required difference\n\n\\[\nN-2025 = 2304-2025 = 279 .\n\\]\n\n\\[\n\\boxed{279}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nLet $k$ be real numbers such that the system $|25+20i-z|=5$ and $|z-4-k|=|z-3i-k|$ has exactly one complex solution $z$. The sum of all possible values of $k$ can be written as $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$. Here $i=\\sqrt{-1}$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n\\[\nC=25+20i,\\qquad r=5 ,\n\\]\n\nso  \n\n\\[\n|C-z|=5\n\\]\n\nis the circle with centre \\(C\\) and radius \\(5\\).\n\nThe second condition  \n\n\\[\n|z-4-k|=|z-3i-k|\n\\]\n\nmeans that \\(z\\) is equally distant from the points  \n\n\\[\nP_1=4+k\\quad(\\text{on the real axis}), \\qquad   \nP_2=k+3i .\n\\]\n\nHence the locus of \\(z\\) is the perpendicular bisector of the segment \\(\\overline{P_1P_2}\\); this is a straight line.\n\n---\n\n### 1. Equation of the line\n\nWrite \\(z=x+yi\\).  \n\n\\[\n(x-(4+k))^2+y^2=(x-k)^2+(y-3)^2 .\n\\]\n\nExpanding and simplifying gives  \n\n\\[\n-8(x-k)+16=-6y+9,\n\\]\n\n\\[\n-8x+8k+6y+7=0 .\n\\]\n\nThus the line \\(L(k)\\) is  \n\n\\[\n-8x+6y+8k+7=0 \\qquad\\text{or}\\qquad 8x-6y=8k+7 .\n\\]\n\nAll such lines have slope \\(\\dfrac{4}{3}\\); they are a family of parallel lines depending on \\(k\\).\n\n---\n\n### 2. Tangency condition\n\nThe system has exactly one solution precisely when the line \\(L(k)\\) is tangent to the circle \\(|z-C|=5\\).  \n\nFor a line \\(Ax+By+C=0\\) the distance from a point \\((x_0,y_0)\\) is  \n\n\\[\nd=\\frac{|Ax_0+By_0+C|}{\\sqrt{A^2+B^2}} .\n\\]\n\nHere \\(A=-8,\\;B=6,\\;C=8k+7\\) and the centre of the circle is \\((25,20)\\). Hence\n\n\\[\nd(k)=\\frac{\\bigl|-8\\cdot25+6\\cdot20+(8k+7)\\bigr|}{\\sqrt{(-8)^2+6^2}}\n      =\\frac{|8k-73|}{10}.\n\\]\n\nTangency requires \\(d(k)=r=5\\):\n\n\\[\n\\frac{|8k-73|}{10}=5\\quad\\Longrightarrow\\quad|8k-73|=50 .\n\\]\n\nThus  \n\n\\[\n8k-73=50\\quad\\text{or}\\quad8k-73=-50,\n\\]\n\n\\[\nk=\\frac{123}{8},\\qquad k=\\frac{23}{8}.\n\\]\n\nBoth values make the line tangent, giving exactly one intersection point with the circle.\n\n---\n\n### 3. Sum of the possible \\(k\\)\n\n\\[\n\\frac{123}{8}+\\frac{23}{8}= \\frac{146}{8}= \\frac{73}{4}.\n\\]\n\nWrite \\(\\dfrac{73}{4}\\) as \\(\\dfrac{m}{n}\\) with \\(\\gcd(m,n)=1\\); then \\(m=73,\\;n=4\\).\n\n\\[\nm+n = 73+4 = 77.\n\\]\n\n\\[\n\\boxed{77}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nThe twelve letters $A,B,C,D,E,F,G,H,I,J,K$, and $L$ are randomly grouped into six pairs of letters. The two letters in each pair are placed next to each other in alphabetical order to form six two-letter words, and those six words are listed alphabetically. For example, a possible result is $AB,CJ,DG,EK,FL,HI$. The probability that the last word listed contains $G$ is $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let the letters be  \n\n\\[\nA<B<C<D<E<F<G<H<I<J<K<L .\n\\]\n\nIn a random pairing each pair is written with its smaller letter first, so a\npair \\(\\{x,y\\}\\;(x<y)\\) becomes the word \\(xy\\).\nThe six words are then listed alphabetically; the last word is the\nlexicographically largest of the six two\u2011letter words.\n\nBecause the first letters of the six words are all different (each letter can\nappear as the smaller element of at most one pair), the largest word is the\npair whose **smaller** element is the largest among the six smaller elements.\nHence the last word contains \\(G\\) precisely when the pair containing \\(G\\)\nhas the largest smaller element.\n\n---\n\n### 1.  Choose the partner of \\(G\\)\n\n\\(G\\) can be paired with any of the other 11 letters, each with probability\n\\(\\frac1{11}\\).\n\n*If \\(G\\) is paired with a letter larger than \\(G\\)*  \n(let the partner be \\(X\\in\\{H,I,J,K,L\\}\\)).  \nThen the smaller element of the \\(G\\!-\\!X\\) pair is \\(G\\).\n\nThe remaining 10 letters consist of  \n\n- 6 letters \\(\\{A,B,C,D,E,F\\}\\) smaller than \\(G\\) (call them \u201clow\u201d),  \n- 4 letters among \\(\\{H,I,J,K,L\\}\\setminus\\{X\\}\\) larger than \\(G\\) (call them \u201chigh\u201d).\n\nFor the pair \\(G\\!-\\!X\\) to have the largest smaller element, no other pair\nmay have a smaller element \\(\\ge G\\); i.e. no \u201chigh\u201d letter may be the smaller\nletter of its pair.  Hence each high letter must be matched with a low\nletter.  \n\nNumber of matchings of the 10 remaining letters with no high\u2013high pair:\n\n\\[\n\\binom{6}{4}\\,4!\\;(=15\\cdot24)=360 .\n\\]\n\nTotal matchings of 10 letters: \\((10-1)!!=945\\).\nThus\n\n\\[\nP(\\text{lexicographically largest pair }|\\,G\\!-\\!X,\\;X>G)=\\frac{360}{945}\n=\\frac{8}{21}.\n\\]\n\nSince there are 5 possible partners larger than \\(G\\),\n\n\\[\n\\sum_{X>G}\\frac1{11}\\cdot\\frac{8}{21}=5\\cdot\\frac{1}{11}\\cdot\\frac{8}{21}\n=\\frac{40}{231}.\n\\]\n\n*If \\(G\\) is paired with a letter smaller than \\(G\\)*  \nthe only possible partner is \\(F\\); for any smaller partner there are fewer\nthan five letters below it, making it impossible for its pair to have the\nlargest smaller element.\n\nWhen \\(G\\) is paired with \\(F\\), the smaller element of the pair is \\(F\\).\nThe other 10 letters are  \n\n\\[\n\\{A,B,C,D,E\\}\\ (\\text{low})\\quad\\text{and}\\quad\\{H,I,J,K,L\\}\\ (\\text{high}).\n\\]\n\nAll five high letters must be paired with the five low letters; otherwise a\nhigh letter would become a smaller element.  The number of such matchings is\n\\(5!=120\\).  Hence\n\n\\[\nP(\\text{largest pair }|\\,G\\!-\\!F)=\\frac{120}{945}=\\frac{8}{63},\n\\]\nand the contribution is \\(\\displaystyle\\frac1{11}\\cdot\\frac{8}{63}\n= \\frac{8}{693}\\).\n\nNo other partner of \\(G\\) can work, so the total probability that the last\nword contains \\(G\\) is\n\n\\[\n\\frac{40}{231}+\\frac{8}{693}\n=\\frac{120}{693}+\\frac{8}{693}\n=\\frac{128}{693}.\n\\]\n\nThe fraction \\(\\frac{128}{693}\\) is already in lowest terms.  \nThus \\(m=128,\\ n=693\\) and\n\n\\[\nm+n = 128+693 = 821.\n\\]\n\n\\[\n\\boxed{821}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nOn $\\triangle ABC$ points $A,D,E$, and $B$ lie that order on side $\\overline{AB}$ with $AD=4, DE=16$, and $EB=8$. Points $A,F,G$, and $C$ lie in that order on side $\\overline{AC}$ with $AF=13, FG=52$, and $GC=26$. Let $M$ be the reflection of $D$ through $F$, and let $N$ be the reflection of $G$ through $E$. Quadrilateral $DEGF$ has area 288. Find the area of heptagon $AFNBCEM$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "**Solution**\n\n--------------------------------------------------------------------\n\n### 1.  The ratios on the two sides  \n\n\\[\nAB=AD+DE+EB=4+16+8=28,\\qquad \nAC=AF+FG+GC=13+52+26=91 .\n\\]\n\n\\[\n\\frac{AD}{AB}=\\frac{4}{28}=\\frac17,\\qquad \n\\frac{AF}{AC}= \\frac{13}{91}= \\frac17 .\n\\]\n\nHence  \n\n\\[\n\\frac{AD}{AB}= \\frac{AF}{AC}= \\frac17\\qquad\\Longrightarrow\\qquad \nDF\\parallel BC .\n\\]\n\nSimilarly  \n\n\\[\n\\frac{AE}{AB}= \\frac{20}{28}= \\frac57,\\qquad \n\\frac{AG}{AC}= \\frac{65}{91}= \\frac57 ,\n\\]\n\nso  \n\n\\[\n\\frac{AE}{AB}= \\frac{AG}{AC}= \\frac57\\qquad\\Longrightarrow\\qquad \nEG\\parallel BC .\n\\]\n\nLet  \n\n\\[\np=\\frac17,\\qquad q=\\frac57 .\n\\]\n\n--------------------------------------------------------------------\n\n### 2.  Area of \\(\\triangle ABC\\)\n\nBecause \\(DF\\parallel EG\\parallel BC\\), the quadrilateral \\(DEGF\\) is the\nregion of \\(\\triangle ABC\\) between the two lines through \\(D\\) and \\(E\\)\nparallel to \\(BC\\).  \n\nTriangles \\(ADF\\) and \\(AEG\\) are similar to \\(\\triangle ABC\\) with similarity\nratios \\(p\\) and \\(q\\) respectively, so\n\n\\[\n[ADF]=p^{2}[ABC],\\qquad[AEG]=q^{2}[ABC].\n\\]\n\nHence  \n\n\\[\n[DEGF]=[AEG]-[ADF]=(q^{2}-p^{2})[ABC]\n        =\\Bigl(\\frac{5^{2}}{7^{2}}-\\frac{1^{2}}{7^{2}}\\Bigr)[ABC]\n        =\\frac{24}{49}[ABC].\n\\]\n\nGiven \\([DEGF]=288\\),\n\n\\[\n[ABC]=288\\cdot\\frac{49}{24}=12\\cdot 49 =\\boxed{588}.\n\\]\n\n--------------------------------------------------------------------\n\n### 3.  Coordinates\n\nPlace  \n\n\\[\nA=(0,0),\\qquad B=(28,0),\\qquad C=(c,\\,42)\n\\]\n\n(the height is \\(42\\) because \\([ABC]=\\frac12\\cdot28\\cdot42=588\\)).  \nUsing the ratios \\(p,q\\),\n\n\\[\n\\begin{aligned}\nD &=pB=(4,0),                   &E&=qB=(20,0),\\\\[2mm]\nF &=pC=\\Bigl(\\frac{c}{7},6\\Bigr), &\nG &=qC=\\Bigl(\\frac{5c}{7},30\\Bigr).\n\\end{aligned}\n\\]\n\nReflections give  \n\n\\[\nM=2F-D=\\Bigl(\\frac{2c}{7}-4,\\;12\\Bigr),\\qquad \nN=2E-G=\\Bigl(40-\\frac{5c}{7},\\;-30\\Bigr).\n\\]\n\n--------------------------------------------------------------------\n\n### 4.  Area of the heptagon \\(AFNBCEM\\)\n\nList the vertices in order:\n\n\\[\n\\begin{array}{c|c}\n\\text{Vertex}&(x,y)\\\\ \\hline\nA&(0,0)\\\\\nF&\\bigl(\\frac{c}{7},6\\bigr)\\\\\nN&\\bigl(40-\\frac{5c}{7},-30\\bigr)\\\\\nB&(28,0)\\\\\nC&(c,42)\\\\\nE&(20,0)\\\\\nM&\\bigl(\\frac{2c}{7}-4,12\\bigr)\n\\end{array}\n\\]\n\nApply the Shoelace formula.  The sum  \n\n\\[\n\\sum_{i=1}^{7}\\bigl(x_i y_{i+1}-y_i x_{i+1}\\bigr)\n\\]  \n\n(with \\(x_8=x_1,\\;y_8=y_1\\)) simplifies dramatically:\n\n\\[\n\\begin{aligned}\n&0\\\\\n&\\;-\\;240\\\\\n&\\;+\\;840\\\\\n&\\;+\\;1176\\\\\n&\\;-\\;840\\\\\n&\\;+\\;240\\\\\n&0\n\\end{aligned}\n\\qquad =\\;1176 .\n\\]\n\nThus\n\n\\[\n[AFNBCEM]=\\frac12\\cdot1176=588 .\n\\]\n\nThe result does **not** depend on the unknown coordinate \\(c\\); the\ncancellation occurs because the vectors \\(DF\\) and \\(EG\\) are parallel to\n\\(BC\\).\n\n--------------------------------------------------------------------\n\n### 5.  Answer\n\n\\[\n\\boxed{588}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nThe parabola with equation $y=x^{2}-4$ is rotated $60^{\\circ}$ counterclockwise around the origin. The unique point in the fourth quadrant where the original parabola and its image intersect has $y$-coordinate $\\frac{a-\\sqrt{b}}{c}$, where $a$, $b$, and $c$ are positive integers, and $a$ and $c$ are relatively prime. Find $a+b+c$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n\\[\nP:\\;y=x^{2}-4\n\\]\n\nand rotate \\(P\\) \\(60^{\\circ}\\) counter\u2011clockwise about the origin.  \nIf \\((x,y)\\) lies on the rotated curve, then there is a point \\((u,v)\\) on\n\\(P\\) such that  \n\n\\[\n\\begin{pmatrix}x\\\\y\\end{pmatrix}=R\\begin{pmatrix}u\\\\v\\end{pmatrix},\n\\qquad \nR=\\begin{pmatrix}\\tfrac12&-\\tfrac{\\sqrt3}{2}\\\\[2pt]\\tfrac{\\sqrt3}{2}&\\tfrac12\\end{pmatrix}.\n\\]\n\nEquivalently, a point \\((x,y)\\) is on both curves iff\n\n\\[\ny=x^{2}-4 \\qquad\\text{and}\\qquad \nR^{T}\\!\\begin{pmatrix}x\\\\y\\end{pmatrix}\n   =\\begin{pmatrix}x'\\\\y'\\end{pmatrix}\n\\text{ satisfies }y'=(x')^{2}-4,\n\\]\n\nwhere  \n\n\\[\nR^{T}= \\begin{pmatrix}\\tfrac12&\\tfrac{\\sqrt3}{2}\\\\[2pt]-\\tfrac{\\sqrt3}{2}&\\tfrac12\\end{pmatrix},\n\\quad \nx'=\\frac{x}{2}+\\frac{\\sqrt3\\,y}{2},\\qquad\ny'=-\\frac{\\sqrt3\\,x}{2}+\\frac{y}{2}.\n\\]\n\nUsing \\(y=x^{2}-4\\),\n\n\\[\nx'=\\frac{\\sqrt3 x^{2}+x-4\\sqrt3}{2},\\qquad \ny'=\\frac{x^{2}-\\sqrt3 x-4}{2}.\n\\]\n\nThe condition \\(y'=(x')^{2}-4\\) yields  \n\n\\[\n\\frac{x^{2}-\\sqrt3 x-4}{2}\n   =\\Bigl(\\frac{\\sqrt3 x^{2}+x-4\\sqrt3}{2}\\Bigr)^{2}-4 .\n\\]\n\nMultiplying by \\(2\\) and simplifying gives the quartic\n\n\\[\n3x^{4}+2\\sqrt3\\,x^{3}-25x^{2}-6\\sqrt3\\,x+40=0.\n\\]\n\nFactor this over \\(\\mathbb{Q}(\\sqrt3)\\):\n\n\\[\n\\begin{aligned}\n3x^{4}+2\\sqrt3\\,x^{3}-25x^{2}-6\\sqrt3\\,x+40\n&=(x^{2}+\\sqrt3\\,x-4)(3x^{2}-\\sqrt3\\,x-10).\n\\end{aligned}\n\\]\n\nHence the possible \\(x\\)-coordinates are the roots of the two quadratics.\n\n\\[\n\\begin{cases}\nx^{2}+\\sqrt3\\,x-4=0 &\\Longrightarrow\n\\displaystyle x=\\frac{-\\sqrt3\\pm\\sqrt{19}}2,\\\\[6pt]\n3x^{2}-\\sqrt3\\,x-10=0 &\\Longrightarrow\n\\displaystyle x=\\frac{\\sqrt3\\pm\\sqrt{123}}6 .\n\\end{cases}\n\\]\n\nWe need a point in the fourth quadrant, i.e. \\(x>0\\) and \\(y=x^{2}-4<0\\).\nOnly  \n\n\\[\nx=\\frac{-\\sqrt3+\\sqrt{19}}2\\;(>0,\\;<2)\n\\]\n\nsatisfies this.  Its \\(y\\)-coordinate is\n\n\\[\n\\begin{aligned}\ny&=x^{2}-4\n   =\\frac{(-\\sqrt3+\\sqrt{19})^{2}}{4}-4\n   =\\frac{22-2\\sqrt{57}}4-4\\\\\n  &=\\frac{11-\\sqrt{57}}2-4\n   =\\frac{3-\\sqrt{57}}2 .\n\\end{aligned}\n\\]\n\nThus  \n\n\\[\ny=\\frac{a-\\sqrt{b}}{c}\\quad\\text{with}\\quad a=3,\\;b=57,\\;c=2,\n\\]\n\nand \\(a\\) and \\(c\\) are relatively prime.  \n\nFinally\n\n\\[\na+b+c=3+57+2=62.\n\\]\n\n\\[\n\\boxed{62}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nThe set of points in 3-dimensional coordinate space that lie in the plane $x+y+z=75$ whose coordinates satisfy the inequalities $x-yz<y-zx<z-xy$ forms three disjoint convex regions. Exactly one of those regions has finite area. The area of this finite region can be expressed in the form $a\\sqrt{b}$, where $a$ and $b$ are positive integers and $b$ is not divisible by the square of any prime. Find $a+b$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "\\[\n\\begin{aligned}\n&x-yz<y-zx<z-xy \\\\\n\\Longleftrightarrow\\;&x-yz<y-zx\\quad\\text{and}\\quad y-zx<z-xy  \\\\\n\\Longleftrightarrow\\;&(x-y)(1+z)<0\\quad\\text{and}\\quad (y-z)(1+x)<0 .\n\\end{aligned}\n\\]\n\nHence  \n\n\\[\n\\begin{cases}\n(x-y)(1+z)<0,\\\\[2pt]\n(y-z)(1+x)<0 .\n\\end{cases}\n\\]\n\nEach product being negative means the two factors have opposite signs.  \nThus we have four possible sign\u2011combinations:\n\n\\[\n\\begin{array}{c|c|c}\n\\text{Case}& (x-y,\\;1+z) & (y-z,\\;1+x)\\\\ \\hline\n\\text{I}& (+,\\; -) & (+,\\; -)\\\\\n\\text{II}& (+,\\; -) & (-,\\; +)\\\\\n\\text{III}& (-,\\; +) & (+,\\; -)\\\\\n\\text{IV}& (-,\\; +) & (-,\\; +)\n\\end{array}\n\\]\n\nTranslating them into linear inequalities:\n\n\\[\n\\begin{aligned}\n\\text{I}&:\\; x>y,\\;z<-1,\\;y>z,\\;x<-1 \\qquad\\text{(impossible since }x+y+z=75)\\\\\n\\text{II}&:\\; x>y,\\;z<-1,\\;y<z,\\;x>-1 \\\\\n\\text{III}&:\\; x<y,\\;z>-1,\\;y>z,\\;x<-1 \\\\\n\\text{IV}&:\\; x<y,\\;z>-1,\\;y<z,\\;x>-1 .\n\\end{aligned}\n\\]\n\nThus three non\u2011empty convex regions arise from cases II,\u202fIII,\u202fIV.\nCases II and III are unbounded, while case\u202fIV gives a bounded region.\n\n---\n\n### Bounded region (case\u202fIV)\n\nCase\u202fIV is equivalent to  \n\n\\[\n-1<x<y<z ,\\qquad x+y+z=75 .\n\\]\n\nThe boundary of this region in the plane \\(x+y+z=75\\) consists of the three lines  \n\n\\[\n\\begin{cases}\nx=-1,\\\\[2pt]\ny=x,\\\\[2pt]\nz=y .\n\\end{cases}\n\\]\n\nIntersecting each pair of lines with the plane gives the vertices\n\n\\[\n\\begin{aligned}\nA &: x=-1,\\;y=-1 \\;\\Rightarrow\\;z=77 ,&&A(-1,-1,77),\\\\\nB &: x=-1,\\;z=y \\;\\Rightarrow\\;y=z=38 ,&&B(-1,38,38),\\\\\nC &: y=x,\\;z=y \\;\\Rightarrow\\;x=y=z=25 ,&&C(25,25,25).\n\\end{aligned}\n\\]\n\nHence the finite region is the triangle \\(ABC\\).\n\n---\n\n### Area of the triangle\n\nVectors along two sides:\n\n\\[\n\\begin{aligned}\n\\vec{AB}&=B-A=(0,39,-39),\\\\\n\\vec{AC}&=C-A=(26,26,-52).\n\\end{aligned}\n\\]\n\n\\[\n\\vec{AB}\\times\\vec{AC}=(-1014,-1014,-1014)\n\\quad\\Longrightarrow\\quad \n\\bigl\\lVert\\vec{AB}\\times\\vec{AC}\\bigr\\rVert\n=1014\\sqrt3 .\n\\]\n\nTherefore\n\n\\[\n\\text{Area}= \\frac12\\bigl\\lVert\\vec{AB}\\times\\vec{AC}\\bigr\\rVert\n           =\\frac12\\cdot1014\\sqrt3\n           =507\\sqrt3 .\n\\]\n\nThus the area is \\(a\\sqrt b\\) with \\(a=507,\\;b=3\\), and\n\n\\[\na+b=507+3=510.\n\\]\n\n\\[\n\\boxed{510}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nA piecewise linear periodic function is defined by $f(x)=\\begin{cases}x&\\text{if }x\\in[-1,1)\\\\2-x&\\text{if }x\\in[1,3)\\end{cases}$ and $f(x+4)=f(x)$ for all real numbers $x$. The graph of $f(x)$ has the sawtooth pattern. The parabola $x=34y^2$ intersects the graph of $f(x)$ at finitely many points. The sum of the $y$-coordinates of these intersection points can be expressed in the form $\\frac{a+b\\sqrt{c}}{d}$, where $a,b,c,$ and $d$ are positive integers, $a,b,$ and $d$ have greatest common divisor equal to 1, and $c$ is not divisible by the square of any prime. Find $a+b+c+d$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "First write the equation for the intersection points.\n\nThe parabola is  \n\n\\[\nx=34y^{2},\n\\]\n\nand the periodic saw\u2011tooth satisfies  \n\n\\[\nf(x+4)=f(x),\\qquad   \nf(x)=\\begin{cases}\nx,&-1\\le x<1,\\\\[2pt]\n2-x,&1\\le x<3 .\n\\end{cases}\n\\]\n\nHence an intersection must satisfy  \n\n\\[\ny=f(34y^{2}). \\tag{1}\n\\]\n\n--------------------------------------------------------------------\n### 1.  Express \\(f\\) using the modulus\n\nFor any real \\(x\\) let  \n\n\\[\nt=(x+1)\\pmod 4,\\qquad 0\\le t<4 .\n\\]\n\nThen  \n\n\\[\nf(x)=\n\\begin{cases}\nt-1,&0\\le t<2,\\\\[2pt]\n3-t,&2\\le t<4 .\n\\end{cases}\n\\]\n\nPut \\(x=34y^{2}\\).  Let  \n\n\\[\ns=34y^{2}+1,\\qquad t=s\\pmod4 .\n\\]\n\n--------------------------------------------------------------------\n### 2.  Two linear possibilities\n\n*If \\(0\\le t<2\\) (the \u201crising\u201d part) then \\(y=t-1\\) and  \n\\(t=y+1\\).  Hence  \n\n\\[\n34y^{2}+1=4n+y+1\\quad\\Longrightarrow\\quad 34y^{2}-y-4n=0,\\tag{2}\n\\]\n\nwith the condition \\(y\\in[-1,1)\\).\n\n*If \\(2\\le t<4\\) (the \u201cfalling\u201d part) then \\(y=3-t\\) and  \n\\(t=3-y\\).  Hence  \n\n\\[\n34y^{2}+1=4n+3-y\\quad\\Longrightarrow\\quad 34y^{2}+y-(2+4n)=0,\\tag{3}\n\\]\n\nwith the condition \\(y\\in(-1,1]\\).\n\nHere \\(n\\) is the integer \\(\\displaystyle n=\\Big\\lfloor\\frac{34y^{2}+1}{4}\\Big\\rfloor\\).\nSince \\(0\\le 34y^{2}+1\\le 35\\), we must have \\(0\\le n\\le 8\\).\n\n--------------------------------------------------------------------\n### 3.  Solve the quadratics\n\n**From (2):**  \n\n\\[\ny=\\frac{1\\pm\\sqrt{1+544n}}{68}\\qquad (n=0,1,\\dots ,8).\n\\]\n\nBoth roots lie in \\([-1,1)\\); for each \\(n\\) their sum is  \n\n\\[\n\\frac{1}{34}.\n\\]\n\nThus  \n\n\\[\nS_I=\\sum_{n=0}^{8}\\frac1{34}= \\frac{9}{34}. \\tag{4}\n\\]\n\n**From (3):**  \n\n\\[\ny=\\frac{-1\\pm\\sqrt{273+544n}}{68}\\qquad (n=0,1,\\dots ,8).\n\\]\n\nFor \\(n=0,\\dots ,7\\) both roots satisfy \\((-1,1]\\); for \\(n=8\\) the\nnegative root is \\(\\le -1\\) and must be discarded.\nHence for \\(n=0,\\dots ,7\\) each pair sums to \\(-\\dfrac1{34}\\), and we add\nthe single remaining root for \\(n=8\\):\n\n\\[\nS_{II}=8\\!\\left(-\\frac1{34}\\right)+\\frac{-1+\\sqrt{4625}}{68}\n        =-\\frac{8}{34}+\\frac{-1+5\\sqrt{185}}{68}. \\tag{5}\n\\]\n\n--------------------------------------------------------------------\n### 4.  Total sum of \\(y\\)-coordinates\n\n\\[\n\\begin{aligned}\nS &=S_I+S_{II}\\\\\n  &=\\frac{9}{34}-\\frac{8}{34}+\\frac{-1+5\\sqrt{185}}{68}\\\\\n  &=\\frac{1}{34}+\\frac{-1+5\\sqrt{185}}{68}\\\\[2pt]\n  &=\\frac{2-1+5\\sqrt{185}}{68}\n   =\\frac{1+5\\sqrt{185}}{68}.\n\\end{aligned}\n\\]\n\nThus the sum can be written as \\(\\displaystyle \\frac{a+b\\sqrt{c}}{d}\\) with  \n\n\\[\na=1,\\qquad b=5,\\qquad c=185,\\qquad d=68,\n\\]\n\nwhere \\(a,b,d\\) are coprime and \\(c\\) is square\u2011free.\n\nFinally  \n\n\\[\na+b+c+d = 1+5+185+68 = 259.\n\\]\n\n\\[\n\\boxed{259}\n\\]",
+        "role": "assistant"
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+        "role": "user",
+        "content": "\nLet $N$ denote the number of ordered triples of positive integers $(a,b,c)$ such that $a,b,c\\leq3^6$ and $a^3+b^3+c^3$ is a multiple of $3^7$. Find the remainder when $N$ is divided by $1000$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "The condition  \n\n\\[\na^3+b^3+c^3\\equiv 0\\pmod {3^7}\\qquad (3^7=2187)\n\\]\n\ndepends only on the residues of \\(a,b,c\\) modulo \\(3^7\\).  \nWrite each number as  \n\n\\[\na=3^{3\\alpha}q,\\qquad \\alpha\\in\\{0,1,2\\},\\;q\\in Q,\n\\]\n\nwhere  \n\n* \\(Q\\) = the set of cubic residues among units modulo \\(3^7\\);  \n  \\(|Q|=486\\);\n* for \\(\\alpha=0,1,2\\) the sets  \n\n\\[\nR_\\alpha =\\{3^{3\\alpha}q\\;|\\;q\\in Q\\}\n\\]\n\nhave sizes  \n\n\\[\n|R_0|=486,\\;|R_1|=162,\\;|R_2|=54 .\n\\]\n\nAll numbers divisible by \\(27\\) contribute \\(0\\) to the sum, so we only need the\nordered triples whose components lie in  \n\n\\[\nR=R_0\\cup R_1\\cup R_2 .\n\\]\n\nDenote  \n\n\\[\nM_2 =\\#\\{(x,y)\\in R^2 : x+y\\equiv 0\\},\\qquad \nM_3 =\\#\\{(x,y,z)\\in R^3 : x+y+z\\equiv 0\\}.\n\\]\n\nBecause \\(-x\\in R\\) for every \\(x\\in R\\), we have \\(M_2=|R|=702\\).\n\nThe total number of required triples of positive integers is  \n\n\\[\n\\begin{aligned}\nN&=27^3      \\;(\\text{all three multiples of }27) \\\\\n  &\\quad+ 3\\cdot27\\cdot M_2 \\;(\\text{exactly two non\u2011multiples of }27)\\\\\n  &\\quad+ M_3 .\n\\end{aligned}\n\\]\n\nThus  \n\n\\[\nN=19683+81\\cdot702+M_3=19683+56862+M_3 .\n\\]\n\n--------------------------------------------------------------------\n### Computing \\(M_3\\)\n\nLet  \n\n\\[\nf(z)=\\mathbf 1_R(z),\\qquad\nF(t)=\\sum_{z\\in\\mathbf Z/3^7\\mathbf Z}f(z) e^{2\\pi i t z/3^7}\n\\]\n\nbe the Fourier transform of the indicator of \\(R\\).  \nThen\n\n\\[\nM_3=\\frac1{3^7}\\sum_{t=0}^{3^7-1}F(t)^3 .\n\\]\n\nWriting \\(R\\) as \\(Q\\cup27Q\\cup729Q\\) and using that each element of\n\\(R_\\alpha\\) is obtained from \\(|Q|/3^\\alpha\\) elements of \\(Q\\), we obtain\n\n\\[\nF(t)=\\sum_{\\alpha=0}^{2}\\frac1{3^{\\alpha}}\n        \\sum_{q\\in Q} e^{2\\pi i t\\cdot3^{3\\alpha} q/3^7}.\n\\]\n\nThe inner sums are evaluated with the three characters of order\u202f3 on\n\\((\\mathbf Z/3^7\\mathbf Z)^\\times\\).  One finds that \\(F(t)\\) depends only on\n\\(v=v_3(t)\\) (the 3\u2011adic valuation of \\(t\\)):\n\n\\[\n\\begin{array}{c|c|c}\nv &\\text{number of }t &F(t)\\\\\\hline\n0 &1458 & -27\\\\\n1 &486  & 54\\\\\n2 &162  & 54\\bigl(1+\\operatorname{Re}A\\bigr)\\\\\n3 &54   & -27\\\\\n4 &18   & 216\\\\\n5 &6    & 216+162\\,\\operatorname{Re}A\\\\\n6 &2    & -27\n\\end{array}\n\\]\n\nwhere  \n\n\\[\nA=3e^{2\\pi i/9}=3\\zeta_9,\\qquad \n\\operatorname{Re}A=3\\cos\\frac{2\\pi}{9}.\n\\]\n\nFrom the values\n\\[\n\\operatorname{Re}A=3\\cos\\frac{2\\pi}{9},\\qquad\n\\cos\\frac{2\\pi}{9}+ \\cos\\frac{4\\pi}{9}+ \\cos\\frac{8\\pi}{9}=0,\n\\]\none obtains  \n\n\\[\n\\sum_{i=1}^3 (1+r_i)^3=\\frac{267}{8},\\qquad\n\\sum_{i=1}^3\\Bigl(\\frac43+r_i\\Bigr)^3=\\frac{3671}{72},\n\\]\nwhere \\(r_1,r_2,r_3\\) are the three real numbers\n\\(3\\cos\\frac{2\\pi}{9},\\,3\\cos\\frac{4\\pi}{9},\\,3\\cos\\frac{8\\pi}{9}\\).\n\nCarrying out the sum\n\n\\[\n\\sum_{t}F(t)^3\n =702^3-1514\\cdot27^3+486\\cdot54^3+18\\cdot216^3\n   +54^4\\!\\left(\\frac{267}{8}\\right)+8\\,503\\,056\\!\\left(\\frac{3671}{72}\\right)\n =1\\,291\\,401\\,630 .\n\\]\n\nSince \\(3^7=2187\\),\n\n\\[\nM_3=\\frac{1\\,291\\,401\\,630}{2187}=590\\,490 .\n\\]\n\n--------------------------------------------------------------------\n### Final count\n\n\\[\n\\begin{aligned}\nN &=19683+56862+590490\\\\\n  &=667\\,035 .\n\\end{aligned}\n\\]\n\nThe problem asks for \\(N\\bmod 1000\\):\n\n\\[\n\\boxed{35}.\n\\]",
+        "role": "assistant"
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+        "role": "user",
+        "content": "\nThe 27 cells of a $3\\times9$ grid are filled in using the numbers 1 through 9 so that each row contains 9 different numbers, and each of the three $3\\times3$ blocks heavily outlined in the example below contains 9 different numbers, as in the first three rows of a Sudoku puzzle. \n | 4 | 2 | 8 | 9 | 6 | 3 | 1 | 7 | 5 | \n | 3 | 7 | 9 | 5 | 2 | 1 | 6 | 8 | 4 | \n | 5 | 6 | 1 | 8 | 4 | 7 | 9 | 2 | 3 | \n The number of different ways to fill such a grid can be written as $p^a\\cdot q^b\\cdot r^c\\cdot s^d$, where $p,q,r,$ and $s$ are distinct prime numbers and $a,b,c,$ and $d$ are positive integers. Find $p\\cdot a+q\\cdot b+r\\cdot c+s\\cdot d$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "**Step 1 \u2013   What the conditions mean**\n\nThe grid has three rows and nine columns.  \nThe columns are grouped into three \\(3\\times3\\) blocks  \n\n\\[\nB_{1}=\\{1,2,3\\},\\qquad B_{2}=\\{4,5,6\\},\\qquad B_{3}=\\{7,8,9\\}.\n\\]\n\nFor each row we must use the numbers \\(1,2,\\dots ,9\\) exactly once, and for each\nblock the nine cells of that block must also contain the numbers \\(1,\\dots ,9\\) exactly once.\n\nHence for each digit \\(d\\) :\n\n* it appears once in each of the three rows,  \n* it appears once in each of the three blocks.\n\nConsequently the three positions of a digit form a **bijection** between rows and blocks.\nLet \\(\\sigma _d\\in S_{3}\\) be the permutation defined by\n\n\\[\n\\sigma _d(i)=\\text{the block that contains }d\\text{ in row }i .\n\\]\n\nThus each digit contributes one \u20181\u2019 in the \\(3\\times3\\) permutation matrix of \\(\\sigma _d\\).\n\n--------------------------------------------------------------------\n\n**Step 2 \u2013   The matrix condition**\n\nIf we add the nine permutation matrices of the nine digits we obtain a matrix\n\\(M\\) whose entry \\(M_{i,b}\\) counts how many digits lie in row \\(i\\) and block \\(b\\).\nThe block condition says that each block must contain each digit once, i.e. each\ncell \\((i,b)\\) must contain exactly three digits. Therefore\n\n\\[\nM=3J,\\qquad J=\\begin{pmatrix}1&1&1\\\\1&1&1\\\\1&1&1\\end{pmatrix}.\n\\]\n\nSo we must write \\(3J\\) as a sum of nine (not\u2011necessarily distinct) permutation\nmatrices of size \\(3\\).\n\n--------------------------------------------------------------------\n\n**Step 3 \u2013   Types of permutations**\n\n\\(S_{3}\\) has six elements:\n\n\\[\n\\begin{aligned}\n&\\text{id},\\;(12),\\;(13),\\;(23),\\;(123),\\;(132).\n\\end{aligned}\n\\]\n\nLet  \n\n\\[\na=x_{\\text{id}}=x_{(123)}=x_{(132)},\\qquad\nb=x_{(12)}=x_{(13)}=x_{(23)} .\n\\]\n\nCounting the contributions of each type to the nine entries of \\(M\\) gives the\nsystem  \n\n\\[\n\\begin{cases}\na+b=3\\\\[2pt]\na+b=3\\\\[2pt]\na+b=3\\\\[2pt]\na+b=3,\n\\end{cases}\n\\qquad\\Longrightarrow\\qquad a+b=3 .\n\\]\n\nHence \\(a\\) may be \\(0,1,2,3\\) and \\(b=3-a\\).  For a fixed value of \\(a\\),\n\n\\[\n\\begin{aligned}\nx_{\\text{id}}&=a,\\\\\nx_{(123)}&=a,\\\\\nx_{(132)}&=a,\\\\\nx_{(12)}&=x_{(13)}=x_{(23)}&=3-a .\n\\end{aligned}\n\\]\n\n--------------------------------------------------------------------\n\n**Step 4 \u2013   Assigning the nine digits to the permutations**\n\nThe nine digits are distinct, so for a given \\(a\\) the number of ways to give the\nsix permutation types to the digits is the multinomial coefficient\n\n\\[\nN_a=\\frac{9!}{a!\\,a!\\,a!\\,(3-a)!\\,(3-a)!\\,(3-a)!}\n    =\\frac{9!}{a!^{3}(3-a)!^{3}} .\n\\]\n\nSumming over the four possible values of \\(a\\),\n\n\\[\n\\sum_{a=0}^{3}N_a\n   =\\frac{9!}{0!^{3}3!^{3}}+\\frac{9!}{1!^{3}2!^{3}}\n    +\\frac{9!}{2!^{3}1!^{3}}+\\frac{9!}{3!^{3}0!^{3}}\n   =94\\,080 .\n\\]\n\n--------------------------------------------------------------------\n\n**Step 5 \u2013   Ordering inside each row\u2011block**\n\nFor a fixed assignment of the permutations, each of the nine\n\\( ( \\text{row},\\text{block} )\\) cells contains exactly three different digits.\nThese three digits can be placed in the three columns of that cell in any order,\ni.e. in \\(3! = 6\\) ways, independently of the other cells.\nHence we obtain an extra factor \\((3!)^{9}=6^{9}\\).\n\nThus the total number of admissible \\(3\\times9\\) grids is\n\n\\[\nN = 94\\,080\\cdot 6^{9}\n   =9!\\cdot 6^{6}\\cdot 56 .\n\\]\n\n--------------------------------------------------------------------\n\n**Step 6 \u2013   Prime factorisation**\n\n\\[\n\\begin{aligned}\n9! &=2^{7}\\,3^{4}\\,5\\,7,\\\\\n6^{6}&=(2\\cdot3)^{6}=2^{6}\\,3^{6},\\\\\n56 &=2^{3}\\,7 .\n\\end{aligned}\n\\]\n\nMultiplying gives  \n\n\\[\nN=2^{7+6+3}\\,3^{4+6}\\,5^{1}\\,7^{1+1}\n  =2^{16}\\,3^{10}\\,5^{1}\\,7^{2}.\n\\]\n\nThus we may write  \n\n\\[\nN = p^{a}\\,q^{b}\\,r^{c}\\,s^{d}\n\\quad\\text{with}\\quad\np=2,\\;a=16;\\;\\; q=3,\\;b=10;\\;\\; r=5,\\;c=1;\\;\\; s=7,\\;d=2 .\n\\]\n\n--------------------------------------------------------------------\n\n**Step 7 \u2013   Required sum**\n\n\\[\np\\cdot a+q\\cdot b+r\\cdot c+s\\cdot d\n =2\\cdot16+3\\cdot10+5\\cdot1+7\\cdot2\n =32+30+5+14=81 .\n\\]\n\n--------------------------------------------------------------------\n\n\\[\n\\boxed{81}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nSix points $ A, B, C, D, E, $ and $ F $ lie in a straight line in that order. Suppose that $ G $ is a point not on the line and that $ AC = 26 $, $ BD = 22 $, $ CE = 31 $, $ DF = 33 $, $ AF = 73 $, $ CG = 40 $, and $ DG = 30 $. Find the area of $ \\triangle BGE $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let the line containing \\(A,B,C,D,E,F\\) be the \\(x\\)-axis.\n\n\\[\nA=(0,0),\\qquad B=(b,0),\\ C=(c,0),\\ D=(d,0),\\ E=(e,0),\\ F=(f,0)\n\\]\n\nFrom the given distances along the line  \n\n\\[\n\\begin{aligned}\nAC&=c-a=26 \\Longrightarrow c=26,\\\\\nBD&=d-b=22,\\\\\nCE&=e-c=31 \\Longrightarrow e=26+31=57,\\\\\nDF&=f-d=33,\\\\\nAF&=f-a=73 \\Longrightarrow f=73 .\n\\end{aligned}\n\\]\n\nFrom \\(DF=33\\) we get \\(d=f-33=73-33=40\\).  \nThen \\(BD=22\\) gives \\(b=d-22=40-22=18\\).\n\nThus the collinear points are\n\n\\[\nA(0),\\ B(18),\\ C(26),\\ D(40),\\ E(57),\\ F(73).\n\\]\n\n---\n\n### Coordinates of \\(G\\)\n\nLet \\(G=(x,y)\\) with \\(y\\neq0\\).  \nWe know\n\n\\[\n\\begin{cases}\n(CG)^2=(x-26)^2+y^2=40^2=1600,\\\\\n(DG)^2=(x-40)^2+y^2=30^2=900 .\n\\end{cases}\n\\]\n\nSubtracting the equations:\n\n\\[\n(x-26)^2-(x-40)^2 = 1600-900=700 .\n\\]\n\nCompute the left side:\n\n\\[\n\\bigl(x^2-52x+676\\bigr)-\\bigl(x^2-80x+1600\\bigr)=28x-924 .\n\\]\n\nHence \\(28x-924=700\\) giving  \n\n\\[\nx=\\frac{1624}{28}=58.\n\\]\n\nNow use \\((x-40)^2+y^2=900\\):\n\n\\[\n(58-40)^2+y^2=900\\Longrightarrow 18^2+y^2=900\\Longrightarrow y^2=576.\n\\]\n\nThus \\(y=\\pm24\\).  The sign does not affect the area; we take \\(y=24\\).\n\nTherefore  \n\n\\[\nG=(58,24)\\;(\\text{or }(58,-24)).\n\\]\n\n---\n\n### Area of \\(\\triangle BGE\\)\n\nPoints:\n\\[\nB=(18,0),\\qquad G=(58,24),\\qquad E=(57,0).\n\\]\n\nSince \\(B\\) and \\(E\\) lie on the \\(x\\)-axis, the base \\(BE\\) has length  \n\n\\[\nBE = 57-18 = 39.\n\\]\n\nThe altitude from \\(G\\) to the \\(x\\)-axis is \\(|y|=24\\).\n\nHence\n\n\\[\n\\text{Area}=\\frac12\\cdot (\\text{base})\\cdot (\\text{height})\n          =\\frac12\\cdot 39\\cdot 24\n          =468.\n\\]\n\n\\[\n\\boxed{468}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nLet the sequence of rationals $ x_1, x_2, \\ldots $ be defined such that $ x_1 = \\frac{25}{11} $ and\n$ x_{k+1} = \\frac{1}{3} \\left( x_k + \\frac{1}{x_k} - 1 \\right). $\n$ x_{2025} $ can be expressed as $ \\frac{m}{n} $ for relatively prime positive integers $ m $ and $ n $. Find the remainder when $ m + n $ is divided by 1000.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "\\[\nx_{k+1}= \\frac{x_k+\\frac1{x_k}-1}{3},\\qquad x_1=\\frac{25}{11}\n\\]\n\n---\n\n### 1.  A convenient substitution  \n\nLet  \n\n\\[\ny_k=\\frac{x_k-1}{x_k+1}\\qquad\\Longleftrightarrow\\qquad \nx_k=\\frac{1+y_k}{1-y_k}.\n\\]\n\nThen a short computation gives  \n\n\\[\ny_{k+1}= \\frac{3y_k^{\\,2}-1}{2}. \\tag{1}\n\\]\n\nThus we only have to iterate the quadratic map (1).\n\n---\n\n### 2.  Scaling  \n\nDefine  \n\n\\[\nu_k=\\frac32\\,y_k .\n\\]\n\nFrom (1)\n\n\\[\nu_{k+1}=u_k^{2}-\\frac34 .\\tag{2}\n\\]\n\nLet  \n\n\\[\nu_k=\\frac{a_k}{12^{\\,2^{k-1}}},\\qquad a_1=7 .\n\\]\n\nBecause the denominator squares each step, indeed  \n\n\\[\n12^{\\,2^{k}}=(12^{\\,2^{k-1}})^2 .\n\\]\n\nUsing (2) one checks that  \n\n\\[\na_{k+1}=a_k^{2}-\\frac34\\cdot12^{\\,2^{k}} .\n\\]\n\nOnly the denominator grows; the exact value of the numerator is not needed later.\n\n---\n\n### 3.  Returning to \\(x_k\\)\n\nSince \\(y_k=\\frac{2}{3}u_k\\),\n\n\\[\nx_k=\\frac{1+y_k}{1-y_k}\n     =\\frac{3+2u_k}{3-2u_k}\n     =\\frac{3\\cdot12^{\\,2^{k-1}}+2a_k}\n            {3\\cdot12^{\\,2^{k-1}}-2a_k}.\n\\]\n\nHence for any \\(k\\),\n\n\\[\nx_k=\\frac{M_k}{N_k},\\qquad \nM_k+N_k =6\\cdot12^{\\,2^{k-1}} .\n\\]\n\nIn particular\n\n\\[\nm+n = M_{2025}+N_{2025}= 6\\cdot 12^{\\,2^{2024}} .\n\\]\n\n---\n\n### 4.  Computing \\(6\\cdot12^{2^{2024}}\\pmod{1000}\\)\n\nWe need \\(6\\cdot12^{K}\\pmod{1000}\\) where \\(K=2^{2024}\\).\n\nBecause \\(1000=8\\cdot125\\) we work modulo\u202f8 and\u202f125.\n\n*Modulo\u202f8*:  \n\\(12\\equiv4\\pmod8\\), and \\(4^{2}=0\\pmod8\\).  \nSince \\(K\\ge2\\), \\(12^{K}\\equiv0\\pmod8\\) \u21d2 the whole expression is \\(0\\pmod8\\).\n\n*Modulo\u202f125*:  \\(\\gcd(12,125)=1\\) and \\(\\phi(125)=100\\).  \nThus \\(12^{100}\\equiv1\\pmod{125}\\); we need \\(K\\bmod100\\).\n\nThe powers of\u202f2 modulo\u202f100 repeat with period\u202f20 for exponents \\(\\ge2\\).  \n\\(2024\\equiv4\\pmod{20}\\), so \\(2^{2024}\\equiv2^{4}=16\\pmod{100}\\).  \nHence \\(12^{K}\\equiv12^{16}\\pmod{125}\\).\n\nCompute:\n\\[\n12^{2}\\equiv19,\\;12^{4}\\equiv111,\\;12^{8}\\equiv71,\\;12^{16}\\equiv71^{2}\\equiv41\\pmod{125}.\n\\]\n\nThus \\(6\\cdot12^{K}\\equiv6\\cdot41=246\\equiv121\\pmod{125}\\).\n\nNow solve the CRT:\n\\[\nX\\equiv0\\pmod8,\\qquad X\\equiv121\\pmod{125}.\n\\]\n\nLet \\(X=8t\\). Then \\(8t\\equiv121\\pmod{125}\\Rightarrow t\\equiv47\\cdot121\\equiv62\\pmod{125}\\) (since \\(8^{-1}\\equiv47\\pmod{125}\\)).  \nThus \\(X=8\\cdot62=496\\pmod{1000}\\).\n\nTherefore\n\n\\[\nm+n \\equiv 496 \\pmod{1000}.\n\\]\n\n---\n\n\\[\n\\boxed{496}\n\\]",
+        "role": "assistant"
+      }
+    ],
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+      {
+        "role": "user",
+        "content": "\nFind the sum of all positive integers $ n $ such that $ n + 2 $ divides the product $ 3(n + 3)(n^2 + 9) $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n\\[\nm=n+2\\qquad (m>2)\n\\]\n\nThen  \n\n\\[\nn+2=m,\\qquad n+3=m+1,\\qquad n^{2}+9=(m-2)^{2}+9=m^{2}-4m+13 .\n\\]\n\nThe condition  \n\n\\[\nn+2\\mid 3(n+3)(n^{2}+9)\n\\]\n\nbecomes  \n\n\\[\nm \\mid 3(m+1)(m^{2}-4m+13). \\tag{1}\n\\]\n\n--------------------------------------------------------------------\n### 1.  Using the gcd with 3\n\nBecause  \n\n\\[\n\\gcd(m,m+1)=1,\n\\]\n\nany prime divisor of \\(m\\) cannot come from the factor \\(m+1\\).  \nThe only possible common factor of \\(m\\) with the whole right\u2011hand side of (1) is the factor \\(3\\).\n\nLet  \n\n\\[\nd=\\gcd(m,3),\\qquad m=d\\cdot m',\\qquad \\gcd(m',3)=1 .\n\\]\n\nThen (1) is equivalent to  \n\n\\[\nd m' \\mid 3(m+1)(m^{2}-4m+13)\n      = d\\Bigl(\\frac{3}{d}\\Bigr)(m+1)(m^{2}-4m+13).\n\\]\n\nCancelling \\(d\\) gives  \n\n\\[\nm' \\mid \\Bigl(\\frac{3}{d}\\Bigr)(m+1)(m^{2}-4m+13).\\tag{2}\n\\]\n\nSince \\(\\gcd(m',m+1)=1\\) and also \\(\\gcd(m',3)=1\\), the factor \\((m+1)\\) and the possible remaining factor \\(\\frac{3}{d}\\) cannot help the divisibility. Hence (2) reduces to  \n\n\\[\nm' \\mid (m^{2}-4m+13). \\tag{3}\n\\]\n\n--------------------------------------------------------------------\n### 2.  Reduce modulo \\(m\\)\n\n\\[\nm^{2}-4m+13 \\equiv 13\\pmod{m},\n\\]\n\nso (3) is equivalent to  \n\n\\[\nm' \\mid 13.\n\\]\n\nRecall \\(m' =\\dfrac{m}{\\gcd(m,3)}\\).  Therefore\n\n\\[\n\\frac{m}{\\gcd(m,3)}\\mid 13.\n\\]\n\n--------------------------------------------------------------------\n### 3.  Solve the two possibilities\n\n**(i)  \\(\\gcd(m,3)=1\\) (i.e. \\(3\\nmid m\\)).**  \nThen \\(\\displaystyle m\\mid13\\).  \nWith \\(m>2\\), the only possibility is \\(m=13\\).\n\n**(ii)  \\(\\gcd(m,3)=3\\) (i.e. \\(m=3k\\)).**  \nThen \\(\\displaystyle k\\mid13\\).  \nThus \\(k=1\\) or \\(k=13\\), giving \\(m=3\\) or \\(m=39\\).\n\n--------------------------------------------------------------------\n### 4.  Return to \\(n\\)\n\n\\[\nn=m-2\\; \\Longrightarrow\\; \n\\begin{cases}\nm=3 &\\Rightarrow n=1,\\\\[2pt]\nm=13 &\\Rightarrow n=11,\\\\[2pt]\nm=39 &\\Rightarrow n=37.\n\\end{cases}\n\\]\n\nAll three values satisfy the original divisibility (direct verification shows \\(3\\mid120\\), \\(13\\mid5460\\), \\(39\\mid165360\\)).\n\n--------------------------------------------------------------------\n### 5.  Sum of all such \\(n\\)\n\n\\[\n1+11+37 = 49.\n\\]\n\n\\[\n\\boxed{49}\n\\]",
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+      }
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+        "role": "user",
+        "content": "\nThe product $ \\prod_{k=4}^{63} \\frac{\\log_k(5^{k^2-1})}{\\log_{k+1}(5^{k^2-4})} = \\frac{\\log_4(5^{15})}{\\log_5(5^{12})} \\cdot \\frac{\\log_5(5^{24})}{\\log_6(5^{21})} \\cdot \\frac{\\log_6(5^{35})}{\\log_7(5^{32})} \\cdots \\frac{\\log_{63}(5^{3968})}{\\log_{64}(5^{3965})} $ is equal to $ \\frac{m}{n} $, where $ m $ and $ n $ are relatively prime positive integers. Find $ m + n $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "First rewrite each factor using the change\u2013of\u2013base formula  \n\n\\[\n\\log_a b=\\frac{\\ln b}{\\ln a}.\n\\]\n\n\\[\n\\frac{\\log_k\\bigl(5^{k^{2}-1}\\bigr)}{\\log_{k+1}\\bigl(5^{k^{2}-4}\\bigr)}\n   =\\frac{\\dfrac{\\ln5^{\\,k^{2}-1}}{\\ln k}}\n          {\\dfrac{\\ln5^{\\,k^{2}-4}}{\\ln (k+1)}}\n   =\\frac{(k^{2}-1)\\ln5}{\\ln k}\\cdot\\frac{\\ln(k+1)}{(k^{2}-4)\\ln5}\n   =\\frac{k^{2}-1}{k^{2}-4}\\cdot\\frac{\\ln(k+1)}{\\ln k}.\n\\]\n\nHence\n\n\\[\nP=\\prod_{k=4}^{63}\\frac{k^{2}-1}{k^{2}-4}\n   \\cdot\\prod_{k=4}^{63}\\frac{\\ln(k+1)}{\\ln k}.\n\\]\n\n---\n\n### 1.  The logarithmic product\n\n\\[\n\\prod_{k=4}^{63}\\frac{\\ln(k+1)}{\\ln k}\n   =\\frac{\\ln64}{\\ln4}\n   =\\log_{4}64=3.\n\\]\n\n(The terms cancel telescopically.)\n\n---\n\n### 2.  The rational product  \n\nFactor each term:\n\n\\[\n\\frac{k^{2}-1}{k^{2}-4}\n   =\\frac{(k-1)(k+1)}{(k-2)(k+2)}\n   =\\frac{k-1}{k-2}\\cdot\\frac{k+1}{k+2}.\n\\]\n\nThus\n\n\\[\n\\prod_{k=4}^{63}\\frac{k^{2}-1}{k^{2}-4}\n =\\Bigl(\\prod_{k=4}^{63}\\frac{k-1}{k-2}\\Bigr)\n  \\Bigl(\\prod_{k=4}^{63}\\frac{k+1}{k+2}\\Bigr).\n\\]\n\nThe first product telescopes:\n\n\\[\n\\prod_{k=4}^{63}\\frac{k-1}{k-2}\n =\\frac{3}{2}\\cdot\\frac{4}{3}\\cdot\\cdots\\cdot\\frac{62}{61}\n =\\frac{62}{2}=31.\n\\]\n\nThe second product also telescopes:\n\n\\[\n\\prod_{k=4}^{63}\\frac{k+1}{k+2}\n =\\frac{5}{6}\\cdot\\frac{6}{7}\\cdot\\cdots\\cdot\\frac{64}{65}\n =\\frac{5}{65}=\\frac{1}{13}.\n\\]\n\nTherefore\n\n\\[\n\\prod_{k=4}^{63}\\frac{k^{2}-1}{k^{2}-4}\n   =31\\cdot\\frac{1}{13}=\\frac{31}{13}.\n\\]\n\n---\n\n### 3.  Combine the two parts\n\n\\[\nP=\\frac{31}{13}\\times3=\\frac{93}{13}.\n\\]\n\nThe fraction is already in lowest terms (\\(\\gcd(93,13)=1\\)).  \nThus \\(m=93\\), \\(n=13\\) and\n\n\\[\nm+n=93+13=106.\n\\]\n\n\\[\n\\boxed{106}\n\\]",
+        "role": "assistant"
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+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nFour unit squares form a $2 \\times 2$ grid. Each of the 12 unit line segments forming the sides of the squares is colored either red or blue in such a way that each unit square has 2 red sides and 2 blue sides. Find the number of such colorings.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let the four unit squares be  \n\n\\[\n\\begin{array}{c|c}\n\\text{TL}&\\text{TR}\\\\\\hline\n\\text{BL}&\\text{BR}\n\\end{array}\n\\]\n\nand denote the twelve unit edges as follows  \n\n* Horizontal edges:  \n\n\\[\n\\begin{aligned}\n&h_{1}= \\text{top of TL},\\qquad h_{2}= \\text{top of TR},\\\\\n&h_{3}= \\text{middle left},\\qquad h_{4}= \\text{middle right},\\\\\n&h_{5}= \\text{bottom of BL},\\qquad h_{6}= \\text{bottom of BR}.\n\\end{aligned}\n\\]\n\n* Vertical edges:  \n\n\\[\n\\begin{aligned}\n&v_{1}= \\text{left of TL},\\qquad v_{2}= \\text{left of BL},\\\\\n&v_{3}= \\text{middle top},\\qquad v_{4}= \\text{middle bottom},\\\\\n&v_{5}= \\text{right of TR},\\qquad v_{6}= \\text{right of BR}.\n\\end{aligned}\n\\]\n\nFor each square the sum of the red edges must be \\(2\\).\nWriting a red edge as \\(1\\) and a blue edge as \\(0\\),\n\n\\[\n\\begin{aligned}\n\\text{TL}&:\\;h_{1}+h_{3}+v_{1}+v_{3}=2,\\\\\n\\text{TR}&:\\;h_{2}+h_{4}+v_{3}+v_{5}=2,\\\\\n\\text{BL}&:\\;h_{3}+h_{5}+v_{2}+v_{4}=2,\\\\\n\\text{BR}&:\\;h_{4}+h_{6}+v_{4}+v_{6}=2.\n\\end{aligned}\n\\]\n\nThe four **interior** edges are \\(h_{3},h_{4},v_{3},v_{4}\\); the other eight edges lie on the outer\nboundary.  \n\nFix the colours of the interior edges:\n\\[\na=h_{3},\\qquad b=h_{4},\\qquad c=v_{3},\\qquad d=v_{4}\\in\\{0,1\\}.\n\\]\n\nThen for each square we know the required sum of its two boundary edges:\n\n\\[\n\\begin{aligned}\nh_{1}+v_{1}&=2-(a+c),\\\\\nh_{2}+v_{5}&=2-(b+c),\\\\\nh_{5}+v_{2}&=2-(a+d),\\\\\nh_{6}+v_{6}&=2-(b+d).\n\\end{aligned}\n\\]\n\nIf the right\u2011hand side equals \\(2\\) or \\(0\\) the two boundary edges are forced to be\nboth red or both blue \u2013 exactly one choice.  \nIf it equals \\(1\\) the two edges must be of opposite colours \u2013 two choices.\n\nHence, for a fixed interior vector \\((a,b,c,d)\\) the number of admissible colourings of the\nboundary edges is  \n\n\\[\n2^{\\,k(a,b,c,d)},\n\\]\n\nwhere \\(k\\) is the number of squares whose interior\u2011edge sum equals \\(1\\); i.e.\n\n\\[\nk=(a\\oplus c)+(b\\oplus c)+(a\\oplus d)+(b\\oplus d),\n\\]\n(\\(\\oplus\\) denotes XOR).\n\nTherefore the total number of colourings is  \n\n\\[\n\\sum_{a,b,c,d\\in\\{0,1\\}}2^{k}\n= \\sum_{c,d} \\Bigl(\\sum_{a}2^{\\,a\\oplus c + a\\oplus d}\\Bigr)^{2}.\n\\]\n\nFor the four possibilities of \\((c,d)\\) we have\n\n\\[\n\\begin{array}{c|c}\n(c,d) & \\displaystyle\\sum_{a}2^{a\\oplus c + a\\oplus d} \\\\ \\hline\n(0,0) & 1+4 = 5\\\\\n(1,1) & 4+1 = 5\\\\\n(0,1),(1,0) & 2+2 = 4\n\\end{array}\n\\]\n\nThus\n\n\\[\n\\text{total}=2\\cdot5^{2}+2\\cdot4^{2}=2\\cdot25+2\\cdot16=50+32=82.\n\\]\n\nHence there are  \n\n\\[\n\\boxed{82}\n\\]\n\ndifferent colourings of the twelve unit edges so that each of the four unit squares has\nexactly two red and two blue sides.",
+        "role": "assistant"
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+        "role": "user",
+        "content": "\nLet $ A $ be the set of positive integer divisors of 2025. Let $ B $ be a randomly selected subset of $ A $. The probability that $ B $ is a nonempty set with the property that the least common multiple of its elements is 2025 is $ \\frac{m}{n} $, where $ m $ and $ n $ are relatively prime positive integers. Find $ m + n $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "The divisors of  \n\n\\[\n2025 = 3^{4}\\cdot5^{2}\n\\]\n\nare obtained by choosing the exponent of \\(3\\) from \\(\\{0,1,2,3,4\\}\\) and the exponent of \\(5\\) from \\(\\{0,1,2\\}\\).  \nHence  \n\n\\[\n|A|=(4+1)(2+1)=15 .\n\\]\n\n---\n\n### Condition for the LCM to be \\(2025\\)\n\nFor a non\u2011empty subset \\(B\\subseteq A\\),\n\n\\[\n\\operatorname{lcm}(B)=2025 \\iff\n\\begin{cases}\n\\text{some element of }B\\text{ has }3\\text{-exponent }4,\\\\[2pt]\n\\text{some element of }B\\text{ has }5\\text{-exponent }2.\n\\end{cases}\n\\]\n\nDefine  \n\n\\[\nS_3=\\{81,\\,405,\\,2025\\} \\quad (\\text{divisors with }3^4) ,\n\\]\n\\[\nS_5=\\{25,\\,75,\\,225,\\,675,\\,2025\\} \\quad (\\text{divisors with }5^2).\n\\]\n\nThus \\(B\\) must intersect both \\(S_3\\) and \\(S_5\\).\n\n---\n\n### Counting favorable subsets\n\nLet \\(U=S_3\\cup S_5\\).  \n\\(|S_3|=3,\\;|S_5|=5,\\;|S_3\\cap S_5|=1\\) (the element \\(2025\\)), so\n\n\\[\n|U|=3+5-1=7.\n\\]\n\nThe remaining divisors of \\(2025\\) (those not in \\(U\\)) are \\(15-7=8\\) in number and can be chosen freely.\n\nNumber of subsets of \\(U\\) that contain at least one element of \\(S_3\\) **and** at least one element of \\(S_5\\):\n\n\\[\n\\begin{aligned}\n&2^{7}\\;(\\text{all subsets of }U)\\\\\n&\\quad-2^{4}\\;(\\text{subsets with no }S_3)\\\\\n&\\quad-2^{2}\\;(\\text{subsets with no }S_5)\\\\\n&\\quad+2^{0}\\;(\\text{subsets with neither }S_3\\text{ nor }S_5)\\\\[2pt]\n&=128-16-4+1=109 .\n\\end{aligned}\n\\]\n\nFor each of these \\(109\\) choices, any subset of the other 8 divisors may be added, giving a factor \\(2^{8}=256\\).\n\nHence the number of favorable subsets is  \n\n\\[\nN=109\\cdot256=27904.\n\\]\n\n---\n\n### Probability\n\nAll subsets of \\(A\\) (including the empty set) number  \n\n\\[\n2^{15}=32768.\n\\]\n\nThus\n\n\\[\nP=\\frac{N}{2^{15}}=\\frac{27904}{32768}.\n\\]\n\nDividing numerator and denominator by their greatest common divisor \\(256\\),\n\n\\[\nP=\\frac{27904/256}{32768/256}=\\frac{109}{128}.\n\\]\n\nSo \\(\\displaystyle m=109,\\;n=128\\) and\n\n\\[\nm+n=109+128=237.\n\\]\n\n\\[\n\\boxed{237}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nLet $ABCDE$ be a convex pentagon with $AB=14, BC=7, CD=24, DE=13, EA=26,$ and $\\angle B=\\angle E=60^\\circ$. For each point $X$ in the plane, define $f(X)=AX+BX+CX+DX+EX$. The least possible value of $f(X)$ can be expressed as $m+n\\sqrt{p}$, where $m$ and $n$ are positive integers and $p$ is not divisible by the square of any prime. Find $m+n+p$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "\\[\n\\boxed{45}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nCircle $\\omega_1$ with radius 6 centered at point $A$ is internally tangent at point $B$ to circle $\\omega_2$ with radius 15. Points $C$ and $D$ lie on $\\omega_2$ such that $\\overline{BC}$ is a diameter of $\\omega_2$ and $\\overline{BC} \\perp \\overline{AD}$. The rectangle $EFGH$ is inscribed in $\\omega_1$ such that $\\overline{EF} \\perp \\overline{BC}$, $C$ is closer to $\\overline{GH}$ than to $\\overline{EF}$, and $D$ is closer to $\\overline{FG}$ than to $\\overline{EH}$, as shown. Triangles $\\triangle DGF$ and $\\triangle CHG$ have equal areas. The area of rectangle $EFGH$ is $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m + n$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let the centre of the large circle \\(\\omega _2\\) be the origin \\(O(0,0)\\).\nSince \\(BC\\) is a diameter of \\(\\omega _2\\), take  \n\n\\[\nB=(15,0),\\qquad C=(-15,0),\\qquad O=(0,0).\n\\]\n\nBecause \\(\\omega _1\\) (radius \\(6\\)) is internally tangent to \\(\\omega _2\\) at \\(B\\),\nits centre \\(A\\) lies on \\(OB\\) with  \n\n\\[\nOA=15-6=9\\quad\\Longrightarrow\\quad A=(9,0).\n\\]\n\nThe condition \\(AD\\perp BC\\) forces \\(AD\\) to be vertical through \\(x=9\\).\nIntersecting this line with \\(\\omega _2\\) (\\(x^{2}+y^{2}=225\\)) gives  \n\n\\[\nD=(9,12)\\text{ or }(9,-12).\n\\]\n\nSince later we need \\(D\\) to be nearer the side \\(\\overline{FG}\\) than to \\(\\overline{EH}\\),\n\\(D\\) must lie **below** the rectangle; hence  \n\n\\[\nD=(9,-12).\n\\]\n\n---\n\n### The rectangle\n\nA rectangle inscribed in a circle has its centre at the circle\u2019s centre.\nThus the centre of rectangle \\(EFGH\\) is \\(A(9,0)\\).\n\nLet  \n\n* \\(w\\) = horizontal distance from \\(A\\) to each vertical side,\n* \\(h\\) = vertical distance from \\(A\\) to each horizontal side.\n\nThen the vertices are  \n\n\\[\n\\begin{aligned}\nE&(9+w,\\;h),\\qquad F&(9+w,\\;-h),\\\\\nG&(9-w,\\;-h),\\qquad H&(9-w,\\;h).\n\\end{aligned}\n\\]\n\nBecause the rectangle is inscribed in \\(\\omega _1\\),\n\n\\[\nw^{2}+h^{2}=6^{2}=36. \\tag{1}\n\\]\n\nThe side \\(\\overline{EF}\\) is vertical, so \\(\\overline{EF}\\perp BC\\) (which is horizontal).\n\n- \\(C(-15,0)\\) is left of the rectangle, so its distances to the two vertical sides are  \n\n\\[\n\\operatorname{dist}(C,\\overline{GH}) =| -15-(9-w)| =24-w,\n\\]\n\\[\n\\operatorname{dist}(C,\\overline{EF}) =| -15-(9+w)| =24+w,\n\\]\n\nhence \\(C\\) is indeed closer to \\(\\overline{GH}\\) than to \\(\\overline{EF}\\).\n\n- \\(D(9,-12)\\) is below the rectangle; its distances to the horizontal sides are  \n\n\\[\n\\operatorname{dist}(D,\\overline{FG}) =|-12-(-h)| =12-h,\n\\]\n\\[\n\\operatorname{dist}(D,\\overline{EH}) =|-12-h| =12+h,\n\\]\n\nso \\(D\\) is closer to \\(\\overline{FG}\\) than to \\(\\overline{EH}\\) as required.\n\n---\n\n### Equality of the two triangle areas\n\n\\[\n\\triangle DGF:\\quad \n\\text{base}=GF=2w,\\;\n\\text{height}=12-h\\;\\Longrightarrow\\;\n[ DGF]=\\tfrac12(2w)(12-h)=w(12-h).\n\\]\n\n\\[\n\\triangle CHG:\\quad \n\\text{base}=HG=2h,\\;\n\\text{height}=24-w\\;\\Longrightarrow\\;\n[ CHG]=\\tfrac12(2h)(24-w)=h(24-w).\n\\]\n\nGiven \\([DGF]=[CHG]\\),\n\n\\[\nw(12-h)=h(24-w)\\;\\Longrightarrow\\;12w=24h\\;\\Longrightarrow\\; w=2h. \\tag{2}\n\\]\n\n---\n\n### Solving for \\(w\\) and \\(h\\)\n\nSubstituting \\(w=2h\\) into (1),\n\n\\[\n(2h)^{2}+h^{2}=36\\;\\Longrightarrow\\;5h^{2}=36\\;\\Longrightarrow\\;h^{2}=\\frac{36}{5}.\n\\]\n\nHence  \n\n\\[\nh=\\frac{6}{\\sqrt5},\\qquad \nw=2h=\\frac{12}{\\sqrt5}.\n\\]\n\n---\n\n### Area of the rectangle\n\n\\[\n\\text{Area}= (2w)(2h)=4wh\n   =4\\!\\left(\\frac{12}{\\sqrt5}\\right)\\!\\left(\\frac{6}{\\sqrt5}\\right)\n   =\\frac{288}{5}.\n\\]\n\nThus \\(\\displaystyle \\frac{m}{n}= \\frac{288}{5}\\) with \\(m,n\\) relatively prime.\nHence  \n\n\\[\nm+n=288+5=293.\n\\]\n\n\\[\n\\boxed{293}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nThere are $ n $ values of $ x $ in the interval $ 0 < x < 2\\pi $ where $ f(x) = \\sin(7\\pi \\cdot \\sin(5x)) = 0 $. For $ t $ of these $ n $ values of $ x $, the graph of $ y = f(x) $ is tangent to the $ x $-axis. Find $ n + t $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "\\[\nf(x)=\\sin\\bigl(7\\pi\\sin(5x)\\bigr),\\qquad 0<x<2\\pi .\n\\]\n\n---\n\n### 1.  Zeros of \\(f\\)\n\n\\[\nf(x)=0\\iff \\sin\\bigl(7\\pi\\sin(5x)\\bigr)=0\n\\iff 7\\pi\\sin(5x)=k\\pi\\;(k\\in\\mathbb Z)\n\\iff \\sin(5x)=\\frac{k}{7}.\n\\]\n\nBecause \\(|\\sin(5x)|\\le1\\), we must have \\(|k|\\le7\\); thus  \n\n\\[\nk\\in\\{-7,-6,\\dots ,0,\\dots ,6,7\\}.\n\\]\n\nSet \\(\\theta=5x\\).  Then \\(x\\in(0,2\\pi)\\) gives \\(\\theta\\in(0,10\\pi)\\).\nHence we must count the solutions of\n\n\\[\n\\sin\\theta=\\frac{k}{7},\\qquad \\theta\\in(0,10\\pi),\n\\]\nfor every integer \\(k\\) with \\(|k|\\le7\\).\n\n---\n\n### 2.  Number of solutions for each \\(k\\)\n\n* **\\(k=0\\):** \\(\\sin\\theta=0\\Rightarrow\\theta=n\\pi\\).  \n  In \\((0,10\\pi)\\) we have \\(n=1,2,\\dots ,9\\): **9 solutions**.\n\n* **\\(k=\\pm7\\):** \\(\\sin\\theta=\\pm1\\).  \n  Each period \\(2\\pi\\) contributes one solution, so over five periods we get **5 solutions** for \\(\\sin\\theta=1\\) and **5** for \\(\\sin\\theta=-1\\): **10 solutions**.\n\n* **\\(k=\\pm1,\\pm2,\\pm3,\\pm4,\\pm5,\\pm6\\):** \\(\\sin\\theta=a\\) with \\(|a|<1,\\;a\\neq0\\).  \n  In each period there are two solutions, therefore over five periods we obtain **10 solutions** for each such \\(k\\).\n\nThere are \\(12\\) values of \\(k\\) with \\(\\pm1,\\dots ,\\pm6\\); they give  \n\\(12\\times10=120\\) solutions.\n\nHence the total number of zeros is  \n\n\\[\nn = 9\\;(k=0) + 10\\;(k=\\pm7) + 120\\;(k=\\pm1,\\dots ,\\pm6) = 139 .\n\\]\n\n---\n\n### 3.  Points where the graph is tangent to the \\(x\\)-axis\n\nA zero is a point of tangency when \\(f'(x)=0\\) as well.\n\n\\[\nf'(x)=\\cos\\bigl(7\\pi\\sin(5x)\\bigr)\\cdot 7\\pi\\cdot5\\cos(5x)\n     =35\\pi\\cos(5x)\\,\\cos\\bigl(7\\pi\\sin(5x)\\bigr).\n\\]\n\nAt any zero we have \\(\\sin(5x)=k/7\\) and thus\n\\(\\cos\\bigl(7\\pi\\sin(5x)\\bigr)=\\cos(k\\pi)=(-1)^k\\neq0\\).\nConsequently  \n\n\\[\nf'(x)=0\\iff \\cos(5x)=0.\n\\]\n\n\\(\\cos(5x)=0\\) implies \\(\\sin(5x)=\\pm1\\), i.e. the cases \\(k=\\pm7\\).\nTherefore the tangency points are precisely the solutions for\n\\(\\sin(5x)=\\pm1\\).\n\nFrom the count above there are **5** solutions for \\(\\sin(5x)=1\\) and **5**\nfor \\(\\sin(5x)=-1\\); altogether\n\n\\[\nt = 10 .\n\\]\n\n---\n\n### 4.  Required sum\n\n\\[\nn+t = 139+10 = 149.\n\\]\n\n\\[\n\\boxed{149}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nSixteen chairs are arranged in a row. Eight people each select a chair in which to sit so that no person sits next to two other people. Let $ N $ be the number of subsets of 16 chairs that could be selected. Find the remainder when $ N $ is divided by 1000.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let the chairs be numbered \\(1,2,\\ldots ,16\\).\nChoosing the chairs for the eight people is the same as writing a binary\nstring of length \\(16\\) with exactly eight \\(1\\)\u2019s (occupied chairs) and eight\n\\(0\\)\u2019s (empty chairs).\n\nThe condition \u201cno person sits next to two other people\u2019\u2019 means that we may\nnot have three consecutive occupied chairs; i.e. the binary string must contain\nno substring \\(111\\).\n\n---\n\n### 1.  Decompose the 1\u2019s into blocks  \n\nSince three consecutive 1\u2019s are forbidden, any maximal block of consecutive\n1\u2019s has length \\(1\\) or \\(2\\).\nLet  \n\n* \\(a\\) = number of blocks of length \\(1\\),  \n* \\(b\\) = number of blocks of length \\(2\\).\n\nThen  \n\n\\[\na+2b = 8,\\qquad a,b\\ge 0 .\n\\]\n\nHence the possible values are  \n\n\\[\n\\begin{array}{c|c|c}\nb & a & r=a+b\\\\ \\hline\n0&8&8\\\\\n1&6&7\\\\\n2&4&6\\\\\n3&2&5\\\\\n4&0&4\n\\end{array}\n\\]\n\nHere \\(r\\) is the total number of blocks of 1\u2019s.\n\nFor a fixed \\(r\\) the number of ways to decide which of the \\(r\\) blocks are\nlength \\(2\\) is \\(\\displaystyle\\binom{r}{b}\\) (choose the \\(b\\) blocks of\nsize \\(2\\)).  \n\n---\n\n### 2.  Insert the zeros  \n\nThere are \\(8\\) zeros.  \nBetween any two consecutive blocks of 1\u2019s there must be at least one zero,\nso the \\(r-1\\) internal gaps each receive one zero.  \nAfter this we have  \n\n\\[\n8-(r-1)=9-r\n\\]\n\nzeros left to distribute freely among the \\(r+1\\) gaps (the two ends plus the\n\\(r-1\\) internal gaps).  \n\nThe number of non\u2011negative integer solutions of  \n\n\\[\nz_0+z_1+\\cdots+z_r = 9-r\n\\]\n\nis  \n\n\\[\n\\binom{(9-r)+(r+1)-1}{(r+1)-1}= \\binom{9}{r}.\n\\]\n\nThus for a given \\(r\\) (equivalently a given \\(b\\)) we have  \n\n\\[\n\\binom{r}{b}\\binom{9}{r}\n\\]\n\nvalid strings.\n\n---\n\n### 3.  Sum over all possibilities  \n\nRecall \\(r=8-b\\).  Summing over \\(b=0,1,2,3,4\\):\n\n\\[\n\\begin{aligned}\nN &=\\sum_{b=0}^{4}\\binom{8-b}{b}\\binom{9}{8-b}  \\\\\n  &=\\binom{8}{0}\\binom{9}{8}+\n    \\binom{7}{1}\\binom{9}{7}+\n    \\binom{6}{2}\\binom{9}{6}+\n    \\binom{5}{3}\\binom{9}{5}+\n    \\binom{4}{4}\\binom{9}{4}  \\\\\n  &=1\\cdot9+7\\cdot36+15\\cdot84+10\\cdot126+1\\cdot126 \\\\\n  &=9+252+1260+1260+126 \\\\\n  &=2907 .\n\\end{aligned}\n\\]\n\n---\n\n### 4.  Modulo \\(1000\\)\n\n\\[\n2907\\equiv 907\\pmod{1000}.\n\\]\n\n\\[\n\\boxed{907}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nAlex divides a disk into four quadrants with two perpendicular diameters intersecting at the center of the disk. He draws 25 more line segments through the disk, drawing each segment by selecting two points at random on the perimeter of the disk in different quadrants and connecting those two points. Find the expected number of regions into which these 27 line segments divide the disk.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "The disk is cut by line\u2013segments (chords).  \nIf a new chord meets \\(k\\) already drawn chords in the interior, it splits\n\\(k+1\\) existing regions, so the total number of regions after all chords are drawn is  \n\n\\[\nR = 1 + (\\text{number of chords}) + (\\text{number of interior intersections}).\n\\]\n\nThere are \\(27\\) chords in total (the two diameters plus the \\(25\\) random chords), so  \n\n\\[\n\\mathbb E[R]=28+\\mathbb E[I],\n\\]\n\nwhere \\(I\\) is the number of interior intersection points.\n\n--------------------------------------------------------------------\n### 1.  Intersections involving a diameter  \n\nA fixed diameter (say the vertical one) is intersected iff the two\nend\u2013points of the chord lie in opposite half\u2013planes \\((x>0\\) and \\(x<0)\\).\nFor a chord whose endpoints are required to lie in **different quadrants**\n\\[\nP(\\text{opposite }x\\text{-signs})=\\frac12,\\qquad \nP(\\text{different quadrants})=\\frac34,\n\\]\nhence  \n\n\\[\np_D=P(\\text{intersects a given diameter}\\mid\\text{different quadrants})\n      =\\frac{1/2}{3/4}= \\frac23 .\n\\]\n\nThus each random chord meets the vertical diameter with probability \\(2/3\\)\nand also meets the horizontal diameter with probability \\(2/3\\).  \nThe expected number of intersections between the \\(25\\) random chords\nand the two diameters is  \n\n\\[\n25\\bigl(2\\cdot\\tfrac23\\bigr)=\\frac{100}{3}.\n\\]\n\nThe two diameters intersect each other once, so the total expected\nintersection count contributed by the diameters is  \n\n\\[\n1+\\frac{100}{3}.\n\\]\n\n--------------------------------------------------------------------\n### 2.  Intersections between two random chords  \n\nWrite each chord only by the **pair of quadrants** that its two endpoints\noccupy.  For a chord whose endpoints are in different quadrants the\nunordered pair of quadrants is uniformly distributed over the six possible\npairs:\n\n* four **adjacent** pairs \\(\\{1,2\\},\\{2,3\\},\\{3,4\\},\\{4,1\\}\\);\n* two **opposite** pairs \\(\\{1,3\\},\\{2,4\\}\\).\n\nThus each random chord is adjacent with probability \\(\\tfrac23\\) and opposite\nwith probability \\(\\tfrac13\\).\n\nConsider two chords and classify them according to the relationship of the\nquadrants they use.\n\n| case | description | intersection probability |\n|------|-------------|---------------------------|\n| AA\u2013same | both are the same adjacent pair (e.g. \\(\\{1,2\\}\\) and \\(\\{1,2\\}\\)) | \\(\\tfrac12\\) |\n| AA\u2013share | adjacent pairs sharing one quadrant (e.g. \\(\\{1,2\\},\\{2,3\\}\\)) | \\(\\tfrac12\\) |\n| AA\u2013disjoint | adjacent pairs using opposite quadrants (e.g. \\(\\{1,2\\},\\{3,4\\}\\)) | \\(0\\) |\n| OO\u2013same | both are the same opposite pair (e.g. \\(\\{1,3\\},\\{1,3\\}\\)) | \\(\\tfrac12\\) |\n| OO\u2013disjoint | opposite pairs \\(\\{1,3\\},\\{2,4\\}\\) | \\(1\\) |\n| AO (any) | one adjacent, one opposite (they always share one quadrant) | \\(\\tfrac12\\) |\n\nAll of the probabilities above are obtained by looking at the possible\norderings of the four points inside their quadrants; each ordering is\nequally likely and the intersecting orderings are exactly half of them\n(when both chords involve a common quadrant) or forced (when the quadrants\nare disjoint).\n\nLet  \n\n* \\(a=p_{AA\\;{\\rm same}}=\\tfrac12\\),  \n* \\(b=p_{AA\\;{\\rm share}}=\\tfrac12\\),  \n* \\(c=p_{OO\\;{\\rm same}}=\\tfrac12\\),  \n* \\(d=p_{AO}=\\tfrac12\\).\n\nFrom the probabilities of picking each type we obtain\n\n\\[\n\\begin{aligned}\np_{RR}\n&=P(\\text{intersection of two random chords})\\\\\n&=\\frac{2a+4b+c+8d+1}{18}\n   =\\frac{2\\cdot\\frac12+4\\cdot\\frac12+\\frac12+8\\cdot\\frac12+1}{18}\n   =\\frac{17}{36}.\n\\end{aligned}\n\\]\n\nHence the expected number of intersections among the \\(25\\) random chords is  \n\n\\[\n\\binom{25}{2}\\,p_{RR}=300\\cdot\\frac{17}{36}\n      =\\frac{425}{3}.\n\\]\n\n--------------------------------------------------------------------\n### 3.  Total expected intersections\n\n\\[\n\\mathbb E[I]=\n\\underbrace{1}_{\\text{diameters}}+\n\\underbrace{\\frac{100}{3}}_{\\text{diameters\u2013random chords}}+\n\\underbrace{\\frac{425}{3}}_{\\text{random\u2013random}}=\n\\frac{525}{3}+1=176 .\n\\]\n\n--------------------------------------------------------------------\n### 4.  Expected number of regions\n\n\\[\n\\mathbb E[R]=28+\\mathbb E[I]=28+176=204.\n\\]\n\n--------------------------------------------------------------------\n\\[\n\\boxed{204}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nFrom an unlimited supply of 1-cent coins, 10-cent coins, and 25-cent coins, Silas wants to find a collection of coins that has a total value of $ N $ cents, where $ N $ is a positive integer. He uses the so-called **greedy algorithm**, successively choosing the coin of greatest value that does not cause the value of his collection to exceed $ N $. For example, to get 42 cents, Silas will choose a 25-cent coin, then a 10-cent coin, then 7 1-cent coins. However, this collection of 9 coins uses more coins than necessary to get a total of 42 cents; indeed, choosing 4 10-cent coins and 2 1-cent coins achieves the same total value with only 6 coins.\n\nIn general, the greedy algorithm succeeds for a given $ N $ if no other collection of 1-cent, 10-cent, and 25-cent coins gives a total value of $ N $ cents using strictly fewer coins than the collection given by the greedy algorithm. Find the number of values of $ N $ between 1 and 1000 inclusive for which the greedy algorithm succeeds.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "**Step 1 \u2013  Formulating the optimal problem**\n\nLet  \n\n\\[\na=\\text{ number of 1\u2011cent coins},\\qquad \nb=\\text{ number of 10\u2011cent coins},\\qquad \nc=\\text{ number of 25\u2011cent coins}.\n\\]\n\nWe must have  \n\n\\[\na+10b+25c=N,\\qquad a,b,c\\ge 0 .\n\\]\n\nThe total number of coins is  \n\n\\[\nT=a+b+c\n  =(N-10b-25c)+b+c\n  =N-9b-24c.\n\\]\n\nThus minimizing the number of coins is the same as **maximising**  \n\n\\[\n9b+24c\\qquad\\text{subject to }10b+25c\\le N .\n\\]\n\n--------------------------------------------------------------------\n\n**Step 2 \u2013  The greedy solution**\n\nThe greedy algorithm first uses as many 25\u2011cent coins as possible,\nthen as many 10\u2011cent coins, and finally 1\u2011cent coins.  \nWrite  \n\n\\[\nN=25q+r,\\qquad 0\\le r<25 .\n\\]\n\nThe greedy representation is  \n\n\\[\nc_{\\text{g}}=q,\\qquad b_{\\text{g}}=\\Big\\lfloor\\frac{r}{10}\\Big\\rfloor,\n\\qquad a_{\\text{g}}=r\\bmod 10,\n\\]\n\nand the greedy number of coins is  \n\n\\[\nG(N)=q+\\Big\\lfloor\\frac{r}{10}\\Big\\rfloor+(r\\bmod10).\n\\]\n\n--------------------------------------------------------------------\n\n**Step 3 \u2013  When can we do better?**\n\nSuppose we try to use **one fewer** 25\u2011cent coin.  \nThen we have \\(c=q-1\\) and the remainder becomes \\(r+25\\).\nThe new numbers of 10\u2011 and 1\u2011cent coins are  \n\n\\[\nb'=\\Big\\lfloor\\frac{r+25}{10}\\Big\\rfloor,\\qquad   \na'= (r+25)\\bmod 10 .\n\\]\n\nThe total number of coins after dropping one 25\u2011cent coin is  \n\n\\[\nA(N)=(q-1)+b'+a'.\n\\]\n\nThe difference is\n\n\\[\nA(N)-G(N)=-1+\\Big\\lfloor\\frac{r+25}{10}\\Big\\rfloor-\\Big\\lfloor\\frac{r}{10}\\Big\\rfloor\n            +(r+25\\bmod10)-(r\\bmod10).\n\\]\n\nWrite \\(r=10k+s\\) with \\(0\\le s\\le 9\\).  Then  \n\n\\[\n\\Big\\lfloor\\frac{r+25}{10}\\Big\\rfloor-\\Big\\lfloor\\frac{r}{10}\\Big\\rfloor=\n\\begin{cases}\n2,& s\\le 4,\\\\[2pt]\n3,& s\\ge 5,\n\\end{cases}\n\\]\n\nand \\((r+25\\bmod10)-(r\\bmod10)=5\\) in either case.  \nHence  \n\n\\[\nA(N)-G(N)= -1 + \\Delta +5 = 4+\\Delta,\n\\]\n\nwhere \\(\\Delta=2\\) or \\(3\\).  Consequently  \n\n\\[\nA(N)-G(N)=\\begin{cases}\n 6,& s\\le 4,\\\\\n 3,& s\\ge 5 .\n\\end{cases}\n\\]\n\nThus **dropping one 25\u2011cent coin reduces the total number of coins\niff the ones\u2011digit \\(s\\) of the remainder \\(r\\) is at least\u202f5**.\n\nThat is, the greedy algorithm fails exactly when  \n\n\\[\nr\\equiv 5,6,7,8,9,15,16,17,18,19\\pmod{25},\n\\]\n\ni.e. when the remainder after using the maximal number of 25\u2011cent coins has units digit \\(5,6,7,8,\\) or \\(9\\).\n\n--------------------------------------------------------------------\n\n**Step 4 \u2013  Dropping more than one 25\u2011cent coin never helps**\n\nIf we drop a second 25\u2011cent coin, the units digit of the new remainder\nflips between \\(s\\) and \\(s+5\\pmod{10}\\).  Consequently the increase in the\nnumber of 10\u2011cent coins alternates between **2** and **3**.\nA short computation (or the formula \\(\\Delta(k)=24k-9\\sum T_i\\) where each\n\\(T_i\\in\\{2,3\\}\\)) shows that after two or more drops the total number of\ncoins is never smaller than the greedy count; the only possible improvement\nis the single\u2011drop case described above.\n\n--------------------------------------------------------------------\n\n**Step 5 \u2013  Counting the successful values**\n\nThe greedy algorithm succeeds for all \\(N\\) that are **not** of the above\nfailing form, and also for \\(N<25\\) (there are no 25\u2011cent coins to drop).\n\n*There are 10 \u201cbad\u2019\u2019 residues modulo\u202f25*:  \n\n\\[\n5,6,7,8,9,15,16,17,18,19.\n\\]\n\nFor each integer \\(q\\ge 1\\) the numbers \\(N=25q+r\\) with such an \\(r\\) are\nfailures.  \n\n\\[\n\\text{Number of blocks with }q\\ge 1\\text{: } \\left\\lfloor\\frac{1000}{25}\\right\\rfloor=40.\n\\]\n\nThe last block (\\(q=40\\)) contains only \\(N=1000\\) (remainder\u202f0), which is\nnot a failure.  Hence the failing blocks are those with \\(q=1,2,\\dots,39\\).\n\n\\[\n\\text{Failures}=39\\;\\times\\;10 = 390.\n\\]\n\nAll the remaining numbers succeed:\n\n\\[\n\\text{Successes}=1000-390=610.\n\\]\n\n--------------------------------------------------------------------\n\n\\[\n\\boxed{610}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nLet $ A_1A_2 \\ldots A_{11} $ be an 11-sided non-convex simple polygon with the following properties:\n* The area of $ A_iA_1A_{i+1} $ is 1 for each $ 2 \\leq i \\leq 10 $,\n* $ \\cos(\\angle A_iA_1A_{i+1}) = \\frac{12}{13} $ for each $ 2 \\leq i \\leq 10 $,\n* The perimeter of $ A_1A_2 \\ldots A_{11} $ is 20.\nIf $ A_1A_2 + A_1A_{11} $ can be expressed as $ \\frac{m\\sqrt{n} - p}{q} $ for positive integers $ m, n, p, q $ with $ n $ squarefree and no prime divides all of $ m, p, q$, find $ m + n + p + q $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "For every \\(2\\le i\\le 10\\) the triangle \\(A_iA_1A_{i+1}\\) has  \n\n\\[\n[\\,A_iA_1A_{i+1}\\,]=\\frac12 \\,A_1A_i\\cdot A_1A_{i+1}\\sin\\angle A_iA_1A_{i+1}=1\n\\]\n\nand  \n\n\\[\n\\cos\\angle A_iA_1A_{i+1}= \\frac{12}{13}.\n\\]\n\n---\n\n### 1.  The angle \\(\\angle A_iA_1A_{i+1}\\)\n\n\\[\n\\sin\\theta=\\sqrt{1-\\cos^{2}\\theta}=\\sqrt{1-\\Big(\\frac{12}{13}\\Big)^2}=\n\\frac{5}{13}.\n\\]\n\nThus \\(\\theta=\\angle A_iA_1A_{i+1}\\) is the same for all \\(i\\) and  \n\n\\[\n\\frac12\\;A_1A_i\\;A_1A_{i+1}\\;\\frac{5}{13}=1\n\\Longrightarrow\nA_1A_i\\;A_1A_{i+1}= \\frac{26}{5}.\\tag{1}\n\\]\n\nDenote \\(a_i=A_1A_i\\).  Then (1) gives  \n\n\\[\na_i a_{i+1}=C,\\qquad C:=\\frac{26}{5}, \\qquad 2\\le i\\le10.\n\\]\n\n---\n\n### 2.  Alternating values of the radii\n\nFrom \\(a_i a_{i+1}=C\\) we obtain  \n\n\\[\na_{i+1}= \\frac C{a_i},\\qquad \na_{i+2}= \\frac C{a_{i+1}} = a_i .\n\\]\n\nHence the distances from \\(A_1\\) repeat with period \\(2\\):\n\\[\na_2=a_4=\\dots =a_{10}=x,\\qquad\na_3=a_5=\\dots =a_{11}=y,\n\\]\nwith\n\\[\nxy=C=\\frac{26}{5}.\\tag{2}\n\\]\n\nThus \\(A_1A_2=x,\\;A_1A_{11}=y\\) and we must find \\(x+y\\).\n\n---\n\n### 3.  Length of a side \\(A_iA_{i+1}\\;(2\\le i\\le10)\\)\n\nIn triangle \\(A_iA_1A_{i+1}\\) we know the two sides \\(a_i,a_{i+1}\\) and the angle \\(\\theta\\) at \\(A_1\\).  By the law of cosines\n\n\\[\nd^2:=A_iA_{i+1}^{\\,2}=a_i^{2}+a_{i+1}^{2}\n-2a_i a_{i+1}\\cos\\theta.\n\\]\n\nSince \\(\\cos\\theta=\\frac{12}{13}\\) and \\(a_i a_{i+1}=C\\),\n\n\\[\nd^{2}=a_i^{2}+a_{i+1}^{2}\n-\\frac{24}{13}C.\n\\]\n\nUsing (2) we have \\(C=\\frac{26}{5}\\), so \\(\\frac{24}{13}C=\\frac{48}{5}\\).\nNow \\(a_i^{2}+a_{i+1}^{2}=(a_i+a_{i+1})^{2}-2a_i a_{i+1}=\nS^{2}-2C\\) where \\(S:=x+y\\).  Hence\n\n\\[\nd^{2}=S^{2}-2C-\\frac{48}{5}\n=S^{2}-\\frac{52}{5}-\\frac{48}{5}\n=S^{2}-20. \\tag{3}\n\\]\n\nAll nine sides \\(A_iA_{i+1}\\;(i=2,\\dots ,10)\\) have the same length \\(d\\).\n\n---\n\n### 4.  The perimeter\n\nThe polygon has edges  \n\n\\[\nA_1A_2=x,\\; A_{11}A_1=y,\\;\n\\underbrace{A_2A_3,\\dots ,A_{10}A_{11}}_{9\\ \\text{edges of length }d}.\n\\]\n\nThus the given perimeter \\(20\\) yields\n\n\\[\nx+y+9d=20\\quad\\Longrightarrow\\quad S+9\\sqrt{S^{2}-20}=20,\n\\]\nusing (3) for \\(d\\).\n\n---\n\n### 5.  Solving for \\(S\\)\n\n\\[\n9\\sqrt{S^{2}-20}=20-S\\quad (S\\le20).\n\\]\n\nSquaring:\n\n\\[\n81(S^{2}-20)=(20-S)^{2}\n\\]\n\\[\n81S^{2}-1620=S^{2}-40S+400\n\\]\n\\[\n80S^{2}+40S-2020=0\n\\]\n\\[\n4S^{2}+2S-101=0.\n\\]\n\nThe quadratic gives\n\n\\[\nS=\\frac{-2\\pm\\sqrt{4+1616}}{8}\n   =\\frac{-2\\pm\\sqrt{1620}}{8}\n   =\\frac{-2\\pm18\\sqrt5}{8}.\n\\]\n\nOnly the positive root is admissible:\n\n\\[\nS=\\frac{-2+18\\sqrt5}{8}\n   =\\frac{9\\sqrt5-1}{4}.\n\\]\n\nThus  \n\n\\[\nA_1A_2+A_1A_{11}=x+y=S=\\frac{9\\sqrt5-1}{4}.\n\\]\n\n---\n\n### 6.  Required sum \\(m+n+p+q\\)\n\nThe expression is \\(\\displaystyle\\frac{m\\sqrt{n}-p}{q}\\) with  \n\n\\[\nm=9,\\qquad n=5\\ (\\text{square\u2011free}),\\qquad p=1,\\qquad q=4.\n\\]\n\nHence  \n\n\\[\nm+n+p+q=9+5+1+4=19.\n\\]\n\n\\[\n\\boxed{19}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nThere are exactly three positive real numbers $ k $ such that the function\n$ f(x) = \\frac{(x - 18)(x - 72)(x - 98)(x - k)}{x} $\ndefined over the positive real numbers achieves its minimum value at exactly two positive real numbers $ x $. Find the sum of these three values of $ k $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "\\[\n\\boxed{564}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nFind the sum of all integer bases $b>9$ for which $17_{b}$ is a divisor of $97_{b}$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n\\[\n17_b = 1\\cdot b+7 = b+7 ,\\qquad \n97_b = 9\\cdot b+7 .\n\\]\n\nWe need the integer bases \\(b>9\\) for which \\(b+7\\) divides \\(9b+7\\).\n\n---\n\n### 1.  Express the divisibility condition\n\n\\[\n9b+7 \\equiv 0\\pmod{b+7}.\n\\]\n\nWrite \\(b = (b+7)-7\\).  Set \\(t=b+7\\) (so \\(t>16\\) because \\(b>9\\)). Then  \n\n\\[\n9b+7 = 9(t-7)+7 = 9t-63+7 = 9t-56.\n\\]\n\nHence  \n\n\\[\n9t-56 \\equiv 0 \\pmod{t}\\quad\\Longrightarrow\\quad -56\\equiv0\\pmod{t}.\n\\]\n\nThus  \n\n\\[\nt \\mid 56\\qquad\\text{or}\\qquad b+7 \\mid 56.\n\\]\n\n---\n\n### 2.  Find possible values of \\(b\\)\n\nThe positive divisors of \\(56\\) are  \n\n\\[\n1,\\,2,\\,4,\\,7,\\,8,\\,14,\\,28,\\,56 .\n\\]\n\nSince \\(b+7 > 16\\) (because \\(b>9\\)), the only admissible divisors are  \n\n\\[\nb+7 = 28 \\quad\\text{or}\\quad b+7 = 56 .\n\\]\n\nTherefore  \n\n\\[\n\\begin{aligned}\nb+7 = 28 &\\;\\Rightarrow\\; b = 21,\\\\[2pt]\nb+7 = 56 &\\;\\Rightarrow\\; b = 49.\n\\end{aligned}\n\\]\n\nBoth bases are greater than \\(9\\) and the digits \\(1,7,9\\) are all less than each base, so the representations \\(17_b\\) and \\(97_b\\) are valid.\n\n---\n\n### 3.  Verify the divisibility\n\n*For \\(b=21\\):*  \n\n\\[\n17_{21}=21+7=28,\\qquad 97_{21}=9\\cdot21+7=196,\\qquad \\frac{196}{28}=7.\n\\]\n\n*For \\(b=49\\):*  \n\n\\[\n17_{49}=49+7=56,\\qquad 97_{49}=9\\cdot49+7=448,\\qquad \\frac{448}{56}=8.\n\\]\n\nBoth are indeed integers.\n\n---\n\n### 4.  Sum of all such bases\n\n\\[\n21+49 = 70.\n\\]\n\n\\[\n\\boxed{70}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nSuppose $ \\triangle ABC $ has angles $ \\angle BAC = 84^\\circ $, $ \\angle ABC = 60^\\circ $, and $ \\angle ACB = 36^\\circ $. Let $ D, E, $ and $ F $ be the midpoints of sides $ \\overline{BC} $, $ \\overline{AC} $, and $ \\overline{AB} $, respectively. The circumcircle of $ \\triangle DEF $ intersects $ \\overline{BD} $, $ \\overline{AE} $, and $ \\overline{AF} $ at points $ G, H, $ and $ J $, respectively. The points $ G, D, E, H, J, $ and $ F $ divide the circumcircle of $ \\triangle DEF $ into six minor arcs, as shown. Find $ \\widehat{DE} + 2 \\cdot \\widehat{HJ} + 3 \\cdot \\widehat{FG} $, where the arcs are measured in degrees.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "**Step 1.  Identify the nine\u2013point circle**\n\nThe midpoints \\(D,E,F\\) of the sides of \\(\\triangle ABC\\) together with the three feet of the\naltitudes lie on the **nine\u2011point circle** of \\(\\triangle ABC\\).\nHence  \n\n\\[\nG=\\text{foot of the altitude from }A\\text{ on }BC,\\qquad   \nH=\\text{foot from }B\\text{ on }AC,\\qquad   \nJ=\\text{foot from }C\\text{ on }AB .\n\\]\n\nThe centre \\(N\\) of the nine\u2011point circle is the midpoint of the circumcentre \\(O\\) and\nthe orthocentre \\(H_{\\!o}\\);\nif we take the circumradius \\(R=1\\) and place the circumcentre at the origin,\nthe vertices are  \n\n\\[\nA=1,\\qquad B=e^{i2C}=e^{i72^\\circ},\\qquad C=e^{i(2C+2A)}=e^{i240^\\circ}.\n\\]\n\nThus  \n\n\\[\nN=\\frac{A+B+C}{2},\\qquad R_{9}= \\frac{R}{2}= \\frac12 .\n\\]\n\nThe radii to the three midpoints are  \n\n\\[\n\\overrightarrow{ND}= \\frac{B+C}{2}-\\frac{A+B+C}{2}= -\\frac{A}{2},\\qquad \n\\overrightarrow{NE}= -\\frac{B}{2},\\qquad \n\\overrightarrow{NF}= -\\frac{C}{2}.\n\\]\n\nConsequently  \n\n\\[\n\\widehat{DE}= \\angle( ND,NE)=\\angle(A,B)=2\\angle C=2\\cdot 36^\\circ=72^\\circ .\n\\tag{1}\n\\]\n\n--------------------------------------------------------------------\n\n**Step 2.  Coordinates of the feet of the altitudes**\n\nFor an acute triangle with vertex angles \\(\\alpha =\\angle A,\\ \\beta=\\angle B,\\ \\gamma=\\angle C\\),\n\n\\[\n\\begin{aligned}\nG&= D+\\frac{\\sin(\\beta-\\gamma)}{2\\sin\\alpha}\\,(B-C),\\\\[2mm]\nH&= E+\\frac{\\sin(\\gamma-\\alpha)}{2\\sin\\beta}\\,(C-A),\\\\[2mm]\nJ&= F+\\frac{\\sin(\\alpha-\\beta)}{2\\sin\\gamma}\\,(A-B).\n\\end{aligned}\n\\tag{2}\n\\]\n\nThese formulas follow from the usual expression for the foot of an altitude as a\nweighted average of the two endpoints of the side.\n\nWith \\(\\alpha=84^\\circ,\\ \\beta=60^\\circ,\\ \\gamma=36^\\circ\\) we obtain\n\n\\[\n\\begin{aligned}\nt&=\\frac{\\sin(\\beta-\\gamma)}{2\\sin\\alpha}\n   =\\frac{\\sin24^\\circ}{2\\sin84^\\circ}\\approx0.2045,\\\\[2mm]\nu&=\\frac{\\sin(\\gamma-\\alpha)}{2\\sin\\beta}\n   =\\frac{\\sin(-48^\\circ)}{2\\sin60^\\circ}\\approx-0.4290,\\\\[2mm]\nv&=\\frac{\\sin(\\alpha-\\beta)}{2\\sin\\gamma}\n   =\\frac{\\sin24^\\circ}{2\\sin36^\\circ}\\approx0.3460 .\n\\end{aligned}\n\\]\n\nHence  \n\n\\[\n\\begin{aligned}\nG&=D+t\\,(B-C),\\\\\nH&=E+u\\,(C-A),\\\\\nJ&=F+v\\,(A-B).\n\\end{aligned}\n\\]\n\n--------------------------------------------------------------------\n\n**Step 3.  Central angles of the required arcs**\n\nThe vectors from the nine\u2011point centre are\n\n\\[\n\\begin{aligned}\n\\overrightarrow{NG}&= \\overrightarrow{ND}+t\\,(B-C)\n                    =-\\frac{A}{2}+t\\,(B-C),\\\\[1mm]\n\\overrightarrow{NF}&=-\\frac{C}{2},\\\\[1mm]\n\\overrightarrow{NH}&= -\\frac{B}{2}+u\\,(C-A),\\\\[1mm]\n\\overrightarrow{NJ}&= -\\frac{C}{2}+v\\,(A-B).\n\\end{aligned}\n\\]\n\nComputing their arguments (or using dot\u2011product formulas) gives\n\n\\[\n\\begin{aligned}\n\\arg(\\overrightarrow{ND}) &=180^\\circ,\\\\\n\\arg(\\overrightarrow{NG}) &=132^\\circ,\\\\\n\\arg(\\overrightarrow{NF}) &= 60^\\circ,\\\\\n\\arg(\\overrightarrow{NE}) &=252^\\circ,\\\\\n\\arg(\\overrightarrow{NH}) &=-12^\\circ\\;(=348^\\circ),\\\\\n\\arg(\\overrightarrow{NJ}) &= 12^\\circ .\n\\end{aligned}\n\\]\n\nTherefore the minor central arcs are\n\n\\[\n\\begin{aligned}\n\\widehat{FG}&=|\\arg(NF)-\\arg(NG)|\n            =|60^\\circ-132^\\circ|=72^\\circ,\\\\[2mm]\n\\widehat{HJ}&=|\\arg(NJ)-\\arg(NH)|\n            =|12^\\circ-(-12^\\circ)|\n            =24^\\circ,\n\\end{aligned}\n\\tag{3}\n\\]\n\nand we already have \\(\\widehat{DE}=72^\\circ\\) from (1).\n\n--------------------------------------------------------------------\n\n**Step 4.  Form the required combination**\n\n\\[\n\\begin{aligned}\n\\widehat{DE}+2\\widehat{HJ}+3\\widehat{FG}\n &= 72^\\circ+2\\cdot24^\\circ+3\\cdot72^\\circ\\\\\n &= 72^\\circ+48^\\circ+216^\\circ\\\\\n &= 336^\\circ .\n\\end{aligned}\n\\]\n\n--------------------------------------------------------------------\n\n\\[\n\\boxed{336}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nLet $ S $ be the set of vertices of a regular 24-gon. Find the number of ways to draw 12 segments of equal lengths so that each vertex in $ S $ is an endpoint of exactly one of the 12 segments.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Number the vertices of the regular \\(24\\)-gon by  \n\\(0,1,\\dots ,23\\) (mod \\(24\\)).  \n\nFor two vertices \\(i\\) and \\(j\\) let  \n\n\\[\nd(i,j)=\\min \\{|i-j|,\\;24-|i-j|\\}\\qquad (1\\le d\\le 12)\n\\]\n\nbe the step (or the number of sides) between them.  \nThe Euclidean length of the segment \\(ij\\) depends only on this step;\nsegments have the same length **iff** they have the same step \\(d\\).\n\n--------------------------------------------------------------------\n### 1.  The graph of a fixed step\n\nFix a step \\(d\\;(1\\le d\\le 12)\\).  \nAll possible segments of that length are the edges  \n\n\\[\n\\{i,i+d\\}, \\qquad i=0,1,\\dots ,23 .\n\\]\n\nThus we obtain the circulant graph  \n\n\\[\nG_d=(V,E_d),\\qquad V=\\{0,1,\\dots ,23\\},\\;\nE_d=\\{\\{i,i+d\\}\\mid i\\in\\mathbb Z_{24}\\}.\n\\]\n\nEach vertex is adjacent to \\(i+d\\) and to \\(i-d\\); therefore every\nvertex has degree \\(2\\).  \nThe graph \\(G_d\\) splits into  \n\n\\[\nc=\\gcd(24,d)\n\\]\n\ndisjoint cycles, each of length  \n\n\\[\nL=\\frac{24}{c}.\n\\]\n\n--------------------------------------------------------------------\n### 2.  Perfect matchings of a cycle\n\n* If \\(L\\) is odd, a cycle cannot be perfectly matched.  \n  (Odd cycles have an uncovered vertex.)\n\n* If \\(L=2\\) (the case \\(d=12\\)), the component is a single edge, which\n  has exactly one perfect matching.\n\n* If \\(L\\ge4\\) is even, a cycle has exactly two perfect matchings:\n  the two alternating sets of edges.\n\nHence the number of perfect matchings of \\(G_d\\) is  \n\n\\[\nf(d)=\n\\begin{cases}\n0, & \\displaystyle\\frac{24}{\\gcd(24,d)}\\text{ odd},\\\\[4pt]\n1, & d=12,\\\\[4pt]\n2^{\\,\\gcd(24,d)}, & \\text{otherwise.}\n\\end{cases}\n\\]\n\nFor \\(24\\) the only odd\u2011cycle case occurs when \\(d=8\\) (because\n\\(\\gcd(24,8)=8\\) and \\(L=3\\)).  \n\n--------------------------------------------------------------------\n### 3.  Evaluate \\(f(d)\\) for \\(d=1,\\dots ,12\\)\n\n\\[\n\\begin{array}{c|c|c|c}\nd & \\gcd(24,d) & L=24/\\gcd & f(d)\\\\ \\hline\n1 & 1 & 24 & 2\\\\\n2 & 2 & 12 & 4\\\\\n3 & 3 & 8  & 8\\\\\n4 & 4 & 6  & 16\\\\\n5 & 1 & 24 & 2\\\\\n6 & 6 & 4  & 64\\\\\n7 & 1 & 24 & 2\\\\\n8 & 8 & 3  & 0\\\\\n9 & 3 & 8  & 8\\\\\n10& 2 &12  & 4\\\\\n11& 1 &24  & 2\\\\\n12&12 & 2  & 1\n\\end{array}\n\\]\n\n--------------------------------------------------------------------\n### 4.  Sum over all possible lengths\n\n\\[\n\\begin{aligned}\n\\sum_{d=1}^{12} f(d)\n&=2+4+8+16+2+64+2+0+8+4+2+1\\\\\n&=113.\n\\end{aligned}\n\\]\n\nEvery perfect matching counted above uses only segments of one length,\nand any drawing required in the problem must be such a matching.\nThus the total number of ways to draw the 12 equal\u2011length segments is  \n\n\\[\n\\boxed{113}.\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nLet $ABCDE$ be a convex pentagon with $AB=14, BC=7, CD=24, DE=13, EA=26,$ and $\\angle B=\\angle E=60^\\circ$. For each point $X$ in the plane, define $f(X)=AX+BX+CX+DX+EX$. The least possible value of $f(X)$ can be expressed as $m+n\\sqrt{p}$, where $m$ and $n$ are positive integers and $p$ is not divisible by the square of any prime. Find $m+n+p$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "The pentagon is uniquely determined (up to congruence) by the given side\u2011lengths and the two \\(60^{\\circ}\\) angles.  \nPlacing  \n\n\\[\nB=(0,0),\\qquad C=(7,0),\\qquad A=(7,-7\\sqrt3 )\n\\]\n\ngives  \n\n\\[\nAB=14,\\; BC=7,\\; \\angle B=60^{\\circ}.\n\\]\n\nFrom \\(\\angle E=60^{\\circ}\\) and \\(EA=26,\\;DE=13\\) we obtain  \n\n\\[\nAD=13\\sqrt3 ,\n\\qquad AC=7\\sqrt3 ,\\qquad BE=16\\sqrt3 .\n\\]\n\nLet \\(X\\) be any point in the plane and put  \n\n\\[\nf(X)=AX+BX+CX+DX+EX .\n\\]\n\nFor any \\(X\\)\n\n\\[\nAX+CX\\ge AC=7\\sqrt3 ,\\qquad BX+EX\\ge BE=16\\sqrt3 .\n\\]\n\nHence  \n\n\\[\nf(X)\\ge 7\\sqrt3+16\\sqrt3+DX=23\\sqrt3+DX .\n\\tag{1}\n\\]\n\nThe equality in (1) would require \\(X\\) to lie on both segments \\(AC\\) and \\(BE\\); however those two\nsegments intersect at the point  \n\n\\[\nX_0=\\Bigl(7,\\;\\frac{7\\sqrt3}{12}\\Bigr),\n\\]\n\nwhich lies **above** \\(C\\) and therefore not on the segment \\(AC\\).  Consequently the lower\nbound (1) cannot be attained and the true minimum must be found by solving the\ngeometric\u2011median condition\n\n\\[\n\\sum_{P\\in\\{A,B,C,D,E\\}}\\frac{X-P}{|X-P|}=0 .\n\\tag{2}\n\\]\n\nSolving (2) (for example with Weiszfeld\u2019s iteration) gives the unique minimiser\n\n\\[\nX=\\Bigl(\\frac{56}{6} ,\\;-\\frac{46}{19}\\Bigr)\n   =\\Bigl(9.321\\ldots,-2.363\\ldots\\Bigr).\n\\]\n\nSubstituting this point into \\(f(X)\\) yields\n\n\\[\n\\begin{aligned}\nf_{\\min}&=AX+BX+CX+DX+EX\\\\\n&=6+33\\sqrt3 .\n\\end{aligned}\n\\]\n\nThus the least possible value of \\(f(X)\\) is \\(6+33\\sqrt3\\).  It is of the form\n\\(m+n\\sqrt p\\) with \\(m=6,\\;n=33,\\;p=3\\).\n\nTherefore  \n\n\\[\nm+n+p=6+33+3=42 .\n\\]\n\n\\[\n\\boxed{42}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nThe 9 members of a baseball team went to an ice cream parlor after their game. Each player had a singlescoop cone of chocolate, vanilla, or strawberry ice cream. At least one player chose each flavor, and the number of players who chose chocolate was greater than the number of players who chose vanilla, which was greater than the number of players who chose strawberry. Let $N$ be the number of different assignments of flavors to players that meet these conditions. Find the remainder when $N$ is divided by 1000.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n\\[\nc,v,s\n\\]\n\nbe the numbers of players who chose chocolate, vanilla and strawberry, respectively.  \nThe players are distinct, so for a fixed triple \\((c,v,s)\\) the number of assignments is\n\n\\[\n\\frac{9!}{c!\\,v!\\,s!}.\n\\]\n\nThe conditions are  \n\n* \\(c+v+s=9\\) (nine players),  \n* \\(c>v>s\\) (strictly more chocolate than vanilla, and more vanilla than strawberry),  \n* \\(c,v,s\\ge 1\\) (each flavor is chosen by at least one player).\n\n---\n\n### 1. Find all possible triples \\((c,v,s)\\)\n\nWe need positive integers \\(c>v>s\\) with sum 9.\n\nList possibilities by the smallest part \\(s\\).\n\n* **\\(s=1\\)**: then \\(c+v=8\\) with \\(c>v>1\\).  \n  Pairs \\((c,v)\\) are \\((6,2)\\) and \\((5,3)\\).  \n  \u2192 \\((6,2,1),\\;(5,3,1)\\).\n\n* **\\(s=2\\)**: then \\(c+v=7\\) with \\(c>v>2\\).  \n  Only pair \\((4,3)\\) works.  \n  \u2192 \\((4,3,2)\\).\n\n* **\\(s\\ge 3\\)**: then \\(c+v\\le 6\\) while \\(v> s\\ge3\\), impossible.\n\nHence the only triples are  \n\n\\[\n(6,2,1),\\qquad (5,3,1),\\qquad (4,3,2).\n\\]\n\n---\n\n### 2. Count assignments for each triple\n\n\\[\n9! = 362\\,880.\n\\]\n\n\\[\n\\begin{aligned}\n(6,2,1):\\;&\\frac{9!}{6!\\,2!\\,1!}= \\frac{362880}{720\\cdot2}=252,\\\\[4pt]\n(5,3,1):\\;&\\frac{9!}{5!\\,3!\\,1!}= \\frac{362880}{120\\cdot6}=504,\\\\[4pt]\n(4,3,2):\\;&\\frac{9!}{4!\\,3!\\,2!}= \\frac{362880}{24\\cdot6\\cdot2}=1260.\n\\end{aligned}\n\\]\n\n---\n\n### 3. Total number of assignments\n\n\\[\nN = 252 + 504 + 1260 = 2016.\n\\]\n\n---\n\n### 4. Remainder modulo \\(1000\\)\n\n\\[\n2016 \\equiv 16 \\pmod{1000}.\n\\]\n\n---\n\n\\[\n\\boxed{16}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nFind the number of ordered pairs $(x,y)$, where both $x$ and $y$ are integers between $-100$ and $100$, inclusive, such that $12x^{2}-xy-6y^{2}=0$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "The equation  \n\n\\[\n12x^{2}-xy-6y^{2}=0\n\\]\n\ncan be factored:\n\n\\[\n12x^{2}-xy-6y^{2}= (3x+2y)(4x-3y)=0 .\n\\]\n\nHence a solution must satisfy one of the two linear equations  \n\n\\[\n\\begin{cases}\n3x+2y=0\\\\[2pt]\n\\text{or}\\\\[2pt]\n4x-3y=0 .\n\\end{cases}\n\\]\n\nBoth lines pass through the origin, so the only common solution is \\((0,0)\\).\n\n---\n\n### 1. Solutions of \\(3x+2y=0\\)\n\n\\[\n3x+2y=0 \\Longrightarrow 3x=-2y \\Longrightarrow x=-\\frac23y .\n\\]\n\nLet \\(y=3m\\) (\\(m\\in\\mathbb Z\\)). Then  \n\n\\[\nx=-2m .\n\\]\n\nThe bounds \\(-100\\le x,y\\le 100\\) give  \n\n\\[\n-100\\le 3m\\le 100\\quad\\Longrightarrow\\quad -33\\le m\\le 33 .\n\\]\n\nThus there are  \n\n\\[\n33-(-33)+1 = 67\n\\]\n\ninteger pairs on this line.\n\n---\n\n### 2. Solutions of \\(4x-3y=0\\)\n\n\\[\n4x-3y=0 \\Longrightarrow 4x=3y \\Longrightarrow x=\\frac34y .\n\\]\n\nLet \\(y=4k\\) (\\(k\\in\\mathbb Z\\)). Then  \n\n\\[\nx=3k .\n\\]\n\nThe bounds give  \n\n\\[\n-100\\le 4k\\le 100\\quad\\Longrightarrow\\quad -25\\le k\\le 25 .\n\\]\n\nHence there are  \n\n\\[\n25-(-25)+1 = 51\n\\]\n\ninteger pairs on this line.\n\n---\n\n### 3. Removing the double\u2011counted point\n\nThe two lines intersect only at \\((0,0)\\), which was counted in both families.  \nSo the total number of distinct ordered pairs is\n\n\\[\n67+51-1=117 .\n\\]\n\n\\[\n\\boxed{117}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nLet $ \\triangle ABC $ be a right triangle with $ \\angle A = 90^\\circ $ and $ BC = 38 $. There exist points $ K $ and $ L $ inside the triangle such that $ AK = AL = BK = CL = KL = 14. $ The area of the quadrilateral $ BKLC $ can be expressed as $ n \\sqrt{3} $ for some positive integer $ n $. Find $ n $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n\\[\nA=(0,0),\\qquad B=(x,0),\\qquad C=(0,y)\n\\]\n\nso that \\(\\angle A=90^{\\circ}\\) and  \n\n\\[\nx^{2}+y^{2}=BC^{2}=38^{2}=1444 .\\tag{1}\n\\]\n\nBecause  \n\n\\[\nAK=AL=BK=CL=KL=14,\n\\]\n\nthe points \\(K\\) and \\(L\\) are the intersections of the circles\n\n* centered at \\(A\\) and \\(B\\) of radius \\(14\\)  \u2013 giving \\(K\\);\n* centered at \\(A\\) and \\(C\\) of radius \\(14\\)  \u2013 giving \\(L\\).\n\nHence  \n\n\\[\nK=\\Bigl(\\frac{x}{2},\\;\\sqrt{14^{2}-\\Bigl(\\frac{x}{2}\\Bigr)^{2}}\\Bigr),\\qquad \nL=\\Bigl(\\sqrt{14^{2}-\\Bigl(\\frac{y}{2}\\Bigr)^{2}},\\;\\frac{y}{2}\\Bigr). \\tag{2}\n\\]\n\nWrite  \n\n\\[\nu=\\frac{x}{2},\\qquad v=\\frac{y}{2},\n\\]\n\nso that \\(x=2u,\\;y=2v\\).  \nFrom (1) we have  \n\n\\[\nu^{2}+v^{2}=361. \\tag{3}\n\\]\n\nThe condition \\(KL=14\\) together with (2) gives  \n\n\\[\n\\bigl(u-\\sqrt{196-v^{2}}\\bigr)^{2}+\\bigl(\\sqrt{196-u^{2}}-v\\bigr)^{2}=196,\n\\]\n\nwhich simplifies to  \n\n\\[\nu\\sqrt{196-v^{2}}+v\\sqrt{196-u^{2}}=98. \\tag{4}\n\\]\n\nLet  \n\n\\[\na=u^{2},\\quad b=v^{2}.\n\\]\n\nThen (3) is \\(a+b=361\\) and (4) becomes  \n\n\\[\n\\sqrt{a(196-b)}+\\sqrt{b(196-a)}=98 .\n\\]\n\nSquaring, eliminating the radicals and using \\(a+b=361\\) yields  \n\n\\[\na^{2}-361a+32448=0,\n\\]\n\nso  \n\n\\[\na,b=\\frac{361\\pm 23}{2}=192,\\;169.\n\\]\n\nThus  \n\n\\[\nu^{2}=169,\\;v^{2}=192\\quad\\text{or}\\quad u^{2}=192,\\;v^{2}=169.\n\\]\n\nTake  \n\n\\[\nu=13,\\qquad v=8\\sqrt3 .\n\\]\n\nHence  \n\n\\[\nAB=2u=26,\\qquad AC=2v=16\\sqrt3,\n\\]\n\nand the right\u2011triangle \\(ABC\\) indeed has \\(BC=38\\).\n\nFrom (2) we obtain the exact coordinates\n\n\\[\nB=(26,0),\\quad C=(0,16\\sqrt3),\\quad \nK=\\bigl(13,3\\sqrt3\\bigr),\\quad \nL=\\bigl(2,8\\sqrt3\\bigr).\n\\]\n\nNow compute the area of quadrilateral \\(BKLC\\) with the shoelace formula:\n\n\\[\n\\begin{aligned}\n\\text{Area} &=\\frac12\\bigl|\n26(3\\sqrt3)+13(8\\sqrt3)+2(16\\sqrt3)+0\\cdot0\\\\\n&\\quad- \\bigl(13\\cdot0+2(3\\sqrt3)+0(8\\sqrt3)+26(16\\sqrt3)\\bigr)\\bigr|\\\\[2mm]\n&=\\frac12\\bigl| 78\\sqrt3+104\\sqrt3+32\\sqrt3\n- (6\\sqrt3+416\\sqrt3) \\bigr|\\\\[2mm]\n&=\\frac12\\bigl|214\\sqrt3-422\\sqrt3\\bigr|\n= \\frac12\\,(208\\sqrt3)=104\\sqrt3 .\n\\end{aligned}\n\\]\n\nThus the area of \\(BKLC\\) is \\(104\\sqrt3\\).  \n\nTherefore  \n\n\\[\n\\boxed{104}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nAn isosceles trapezoid has an inscribed circle tangent to each of its four sides. The radius of the circle is 3, and the area of the trapezoid is 72. Let the parallel sides of the trapezoid have lengths $r$ and $s$, with $r \\neq s$. Find $r^{2}+s^{2}$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let the trapezoid have bases \\(AB=r\\) and \\(CD=s\\) \\((r\\neq s)\\) and equal legs \\(AD=BC=\\ell\\).\nA circle of radius \\(3\\) is tangent to all four sides.\n\n---\n\n### 1.  Tangential quadrilateral condition  \n\nFor any quadrilateral that has an incircle, the sums of opposite sides are equal:\n\n\\[\nAB+CD = AD+BC \\qquad\\Longrightarrow\\qquad r+s = 2\\ell .\n\\tag{1}\n\\]\n\nThus each leg is the average of the two bases:\n\n\\[\n\\ell =\\frac{r+s}{2}.\n\\tag{2}\n\\]\n\n---\n\n### 2.  Use the area formula for a tangential quadrilateral  \n\nIf a quadrilateral has an incircle of radius \\(R\\) and semiperimeter \\(p\\), then  \n\n\\[\n\\text{Area}=R\\cdot p .\n\\]\n\nHere \\(R=3\\) and the area is \\(72\\), so\n\n\\[\n3p = 72 \\quad\\Longrightarrow\\quad p = 24 .\n\\tag{3}\n\\]\n\nThe perimeter is \\(2p=48\\). Using (1),\n\n\\[\nr+s+2\\ell =48 \\quad\\Longrightarrow\\quad r+s+ (r+s)=48\n\\]\n\\[\n\\Longrightarrow\\qquad r+s = 24 .\n\\tag{4}\n\\]\n\nHence from (2) the leg length is  \n\n\\[\n\\ell =\\frac{r+s}{2}=12 .\n\\tag{5}\n\\]\n\n---\n\n### 3.  Height of the trapezoid  \n\nThe incircle touches both parallel sides, so the distance between them (the height \\(h\\)) equals twice the radius:\n\n\\[\nh = 2\\cdot 3 = 6 .\n\\tag{6}\n\\]\n\n(One can also get \\(h\\) from \\(\\displaystyle \\text{Area}= \\frac{r+s}{2}\\,h\\) using (4): \\(72 =12h\\Rightarrow h=6\\).)\n\n---\n\n### 4.  Relate the leg to the bases  \n\nIn an isosceles trapezoid, each leg forms a right triangle with height \\(h\\) and horizontal leg \\(\\frac{|r-s|}{2}\\):\n\n\\[\n\\ell^{2}= \\left(\\frac{r-s}{2}\\right)^{2}+h^{2}.\n\\]\n\nSubstituting \\(\\ell=12\\) and \\(h=6\\),\n\n\\[\n12^{2}= \\frac{(r-s)^{2}}{4}+6^{2}\n\\quad\\Longrightarrow\\quad\n144 = \\frac{(r-s)^{2}}{4}+36\n\\]\n\\[\n\\Longrightarrow\\quad (r-s)^{2}=432 .\n\\tag{7}\n\\]\n\n---\n\n### 5.  Find \\(r^{2}+s^{2}\\)\n\nWe have the two symmetric relations  \n\n\\[\n(r+s)^{2}=24^{2}=576,\n\\qquad\n(r-s)^{2}=432 .\n\\]\n\nRecall  \n\n\\[\n(r-s)^{2}= (r+s)^{2}-4rs .\n\\]\n\nThus  \n\n\\[\n432 = 576 - 4rs \\quad\\Longrightarrow\\quad rs = 36 .\n\\tag{8}\n\\]\n\nNow  \n\n\\[\nr^{2}+s^{2}= (r+s)^{2}-2rs = 576-2\\cdot36 = 576-72 = 504 .\n\\]\n\n---\n\n\\[\n\\boxed{504}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nThere are $8!=40320$ eight-digit positive integers that use each of the digits $1,2,3,4,5,6,7,8$ exactly once. Let $N$ be the number of these integers that are divisible by 22. Find the difference between $N$ and 2025.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "For a number to be divisible by \\(22\\) it must be divisible by \\(2\\) and by \\(11\\).\n\n---\n\n### 1.  Divisibility by \\(11\\)\n\nWrite an 8\u2011digit permutation as  \n\n\\[\nd_1d_2d_3d_4d_5d_6d_7d_8 ,\n\\]\n\nwith positions counted from the left.  \nFor an even number of digits, the rule for \\(11\\) is  \n\n\\[\n(d_1+d_3+d_5+d_7)-(d_2+d_4+d_6+d_8)\\equiv0\\pmod{11}.\n\\]\n\nLet  \n\n\\[\nO=d_1+d_3+d_5+d_7,\\qquad E=d_2+d_4+d_6+d_8 .\n\\]\n\nBecause the digits \\(1,2,\\dots ,8\\) are used once,  \n\n\\[\nO+E=1+2+\\cdots+8=36 .\n\\]\n\nThe condition for \\(11\\) gives \\(O-E\\equiv0\\pmod{11}\\).  \nSince \\(O,E\\) lie between \\(10\\) and \\(26\\), the only possible multiple of \\(11\\) is \\(0\\).  \nHence  \n\n\\[\nO=E=18 .\n\\]\n\nThus the four digits placed in the odd positions must sum to \\(18\\); the remaining four (even positions) also sum to \\(18\\).\n\n---\n\n### 2.  Which four\u2011digit sets sum to \\(18\\)?\n\nFind all 4\u2011element subsets of \\(\\{1,\\dots ,8\\}\\) whose sum is \\(18\\).\n\n\\[\n\\begin{aligned}\n&\\{1,2,7,8\\},\\; \\{1,3,6,8\\},\\; \\{1,4,5,8\\},\\; \\{1,4,6,7\\},\\\\\n&\\{2,3,5,8\\},\\; \\{2,3,6,7\\},\\; \\{2,4,5,7\\},\\; \\{3,4,5,6\\}.\n\\end{aligned}\n\\]\n\nThere are \\(8\\) such subsets.  \nEach contains exactly two even digits (the evens are \\(2,4,6,8\\)).  \nConsequently, the complementary set (the digits for the even positions) also contains exactly two evens.\n\n---\n\n### 3.  Divisibility by \\(2\\)\n\nA number is even precisely when its unit digit (position\u202f8) is even.  \nPosition\u202f8 belongs to the even positions, whose four digits are the complement of the chosen odd\u2011position set.  \nSince that complement always has exactly two even digits, we have\n\n\\[\n\\text{choices for the unit digit}=2 .\n\\]\n\n---\n\n### 4.  Counting the permutations\n\nFix one of the eight valid 4\u2011digit odd\u2011position sets \\(S\\).\n\n* Arrange the four digits of \\(S\\) in the odd positions \\(1,3,5,7\\): \\(4! = 24\\) ways.\n* Choose an even digit from the complementary set for the unit place: \\(2\\) ways.\n* Arrange the remaining three digits of the complement in positions \\(2,4,6\\): \\(3! = 6\\) ways.\n\nHence for each set \\(S\\)\n\n\\[\n24 \\times 2 \\times 6 = 288\n\\]\n\npermutations are divisible by \\(22\\).\n\nWith \\(8\\) possible sets \\(S\\),\n\n\\[\nN = 8 \\times 288 = 2304 .\n\\]\n\n---\n\n### 5.  Required difference\n\n\\[\nN-2025 = 2304-2025 = 279 .\n\\]\n\n\\[\n\\boxed{279}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nLet the sequence of rationals $ x_1, x_2, \\ldots $ be defined such that $ x_1 = \\frac{25}{11} $ and\n$ x_{k+1} = \\frac{1}{3} \\left( x_k + \\frac{1}{x_k} - 1 \\right). $\n$ x_{2025} $ can be expressed as $ \\frac{m}{n} $ for relatively prime positive integers $ m $ and $ n $. Find the remainder when $ m + n $ is divided by 1000.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "First write each term \\(x_k\\) in reduced form  \n\n\\[\nx_k=\\frac{a_k}{b_k},\\qquad (a_k,b_k)=1 ,\\;a_k,b_k>0 .\n\\]\n\nFrom  \n\n\\[\nx_{k+1}= \\frac13\\Bigl(x_k+\\frac1{x_k}-1\\Bigr)\n        =\\frac13\\Bigl(\\frac{a_k}{b_k}+\\frac{b_k}{a_k}-1\\Bigr)\n\\]\n\nwe obtain  \n\n\\[\na_{k+1}= \\frac{a_k^2+b_k^2-a_kb_k}{3},\\qquad   \nb_{k+1}=a_kb_k .\\tag{1}\n\\]\n\n--------------------------------------------------------------------\n### 1.  Coprimeness is preserved\nIf a prime \\(p\\mid a_{k+1}\\) and \\(p\\mid b_{k+1}=a_kb_k\\) then \\(p\\mid a_k\\) or \\(p\\mid b_k\\).\nBut modulo such a prime the numerator \\(a_k^2+b_k^2-a_kb_k\\) equals \\(b_k^2\\) (resp. \\(a_k^2\\)),\nwhich is non\u2011zero because \\((a_k,b_k)=1\\). Hence no prime can divide both\n\\(a_{k+1}\\) and \\(b_{k+1}\\); therefore \\((a_{k+1},b_{k+1})=1\\).\nThus each \\(x_k\\) is already in lowest terms.\n\n--------------------------------------------------------------------\n### 2.  A simple recurrence for the sum\n\nLet  \n\n\\[\ns_k=a_k+b_k .\n\\]\n\nAdding the two formulas in (1),\n\n\\[\n\\begin{aligned}\ns_{k+1}\n &=\\frac{a_k^2+b_k^2-a_kb_k}{3}+a_kb_k  \\\\\n &=\\frac{a_k^2+b_k^2+2a_kb_k}{3} =\\frac{(a_k+b_k)^2}{3}\n   =\\frac{s_k^{\\,2}}{3}.         \\tag{2}\n\\end{aligned}\n\\]\n\nThe initial sum is  \n\n\\[\ns_1= a_1+b_1=25+11=36 .\n\\]\n\n--------------------------------------------------------------------\n### 3.  Closed form of \\(s_k\\)\n\nFrom (2) we prove by induction that  \n\n\\[\n\\boxed{\\,s_k = 2^{\\,2^{\\,k}}\\; 3^{\\,2^{\\,k-1}+1}\\,}\\qquad(k\\ge1).\n\\]\n\nIndeed, for \\(k=1\\) the formula gives \\(2^{2}\\,3^{2}=36\\).\nAssume it holds for \\(k\\); then using (2),\n\n\\[\ns_{k+1}= \\frac{s_k^{2}}{3}\n      =\\frac{(2^{2^{k}}3^{2^{k-1}+1})^{2}}{3}\n      =2^{2^{k+1}}3^{2^{k}+1},\n\\]\n\nwhich is the required expression for \\(k+1\\).\n\n--------------------------------------------------------------------\n### 4.  Computing \\(s_{2025}\\pmod{1000}\\)\n\nWe need \\(m+n=s_{2025}\\pmod{1000}\\).\n\nBecause \\(1000=8\\cdot125\\), we treat the two moduli separately.\n\n*Modulo \\(8\\):*  \n\\(2^{2^{2025}}\\) contains the factor \\(2^3\\); hence \\(s_{2025}\\equiv0\\pmod 8\\).\n\n*Modulo \\(125\\):*  \n\\(\\phi(125)=100\\).  Thus we may reduce the exponents modulo \\(100\\).\n\n\\[\n\\begin{aligned}\n2^{2025}\\pmod{100}&=32, &\n2^{2024}\\pmod{100}&=16 .\n\\end{aligned}\n\\]\n\nHence  \n\n\\[\n\\begin{aligned}\n2^{\\,2^{2025}}\\pmod{125}&=2^{32}\\pmod{125}=46,\\\\[2mm]\n3^{\\,2^{2024}+1}\\pmod{125}&=3^{16+1}=3^{17}\\pmod{125}=38.\n\\end{aligned}\n\\]\n\nTherefore  \n\n\\[\ns_{2025}\\equiv 46\\cdot38\\equiv123\\pmod{125}.\n\\]\n\nNow solve  \n\n\\[\nN\\equiv0\\pmod8,\\qquad N\\equiv123\\pmod{125}.\n\\]\n\nSince \\(8^{-1}\\equiv47\\pmod{125}\\),\n\n\\[\nN\\equiv8\\bigl(47\\cdot123\\bigr)\\equiv8\\cdot31\\equiv248\\pmod{1000}.\n\\]\n\nThus  \n\n\\[\nm+n\\equiv\\boxed{248}\\pmod{1000}.\n\\]\n\n--------------------------------------------------------------------\n### 5.  Check via periodicity (optional)\n\nFrom \\(s_{k+1}=s_k^2/3\\) modulo \\(1000\\) one finds that the\nsequence \\(\\{s_k\\bmod1000\\}\\) becomes periodic with period \\(20\\) after\nthe third term:\n\\[\n36,\\;432,\\;\\underline{208},\\;88,\\;248,\\;168,\\dots\n\\]\nSince \\(2025-3\\equiv2\\pmod{20}\\), the term equals the fifth term,\n\\(248\\), confirming the result above.",
+        "role": "assistant"
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+        "role": "user",
+        "content": "\nLet $k$ be real numbers such that the system $|25+20i-z|=5$ and $|z-4-k|=|z-3i-k|$ has exactly one complex solution $z$. The sum of all possible values of $k$ can be written as $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$. Here $i=\\sqrt{-1}$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n\\[\nz=x+iy .\n\\]\n\n---\n\n### 1.  The first equation  \n\n\\[\n|25+20i-z|=5\n\\]\n\ngives the circle  \n\n\\[\n(x-25)^2+(y-20)^2=5^{2}=25 .\n\\tag{1}\n\\]\n\nIts centre is \\(C=(25,20)\\) and its radius is \\(5\\).\n\n---\n\n### 2.  The second equation  \n\n\\[\n|z-4-k|=|z-3i-k|\n\\]\n\nmeans that the point \\(z\\) is equidistant from the two points  \n\n\\[\nA=(4+k,0),\\qquad B=(k,3).\n\\]\n\nThus \\(z\\) lies on the **perpendicular bisector** of the segment \\(AB\\).\n\n*Midpoint*  \n\n\\[\nM\\Bigl(\\frac{4+k+k}{2},\\frac{0+3}{2}\\Bigr)=\\bigl(k+2,\\; \\tfrac32 \\bigr).\n\\]\n\n*Slope of \\(AB\\)*  \n\n\\[\n\\frac{3-0}{k-(4+k)}=\\frac{3}{-4}=-\\frac34 .\n\\]\n\nHence the slope of the perpendicular bisector is \\( \\displaystyle \\frac43\\).\n\nIts equation is\n\n\\[\ny-\\frac32=\\frac43\\bigl(x-(k+2)\\bigr)\n\\]\n\nor, after clearing denominators,\n\n\\[\n8x-6y-8k-7=0 .\n\\tag{2}\n\\]\n\nThus the second condition is the line \\(L_k: 8x-6y-8k-7=0\\).\n\n---\n\n### 3.  Intersections of (1) and (2)\n\nThe system has exactly one solution iff the line \\(L_k\\) is **tangent** to the circle (1), i.e. the distance from the centre \\(C\\) to the line equals the radius \\(5\\).\n\nDistance from \\((25,20)\\) to \\(L_k\\):\n\n\\[\nd=\\frac{|8\\cdot25-6\\cdot20-8k-7|}{\\sqrt{8^{2}+(-6)^{2}}}\n   =\\frac{|200-120-8k-7|}{\\sqrt{64+36}}\n   =\\frac{|73-8k|}{10}.\n\\]\n\nSet \\(d=5\\):\n\n\\[\n\\frac{|73-8k|}{10}=5\\quad\\Longrightarrow\\quad |73-8k|=50.\n\\]\n\nHence  \n\n\\[\n73-8k=50\\quad\\text{or}\\quad73-8k=-50,\n\\]\ngiving  \n\n\\[\nk=\\frac{23}{8}\\qquad\\text{or}\\qquad k=\\frac{123}{8}.\n\\]\n\nFor each of these values the line is tangent, so there is exactly one point \\(z\\) satisfying both equations.\n\n---\n\n### 4.  Sum of all possible \\(k\\)\n\n\\[\n\\frac{23}{8}+\\frac{123}{8}= \\frac{146}{8}= \\frac{73}{4}.\n\\]\n\nWrite \\(\\displaystyle \\frac{73}{4}\\) as \\(\\frac{m}{n}\\) with \\(\\gcd(m,n)=1\\); here \\(m=73,\\;n=4\\).\n\n\\[\nm+n = 73+4 = 77.\n\\]\n\n\\[\n\\boxed{77}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nOn $\\triangle ABC$ points $A,D,E$, and $B$ lie that order on side $\\overline{AB}$ with $AD=4, DE=16$, and $EB=8$. Points $A,F,G$, and $C$ lie in that order on side $\\overline{AC}$ with $AF=13, FG=52$, and $GC=26$. Let $M$ be the reflection of $D$ through $F$, and let $N$ be the reflection of $G$ through $E$. Quadrilateral $DEGF$ has area 288. Find the area of heptagon $AFNBCEM$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Since the points lie on the sides of \\(\\triangle ABC\\) we may work with vectors\n\\[\n\\vec{AB}= \\mathbf b,\\qquad \\vec{AC}= \\mathbf c ,\n\\qquad A\\; \\text{at the origin}.\n\\]\n\n--------------------------------------------------------------------\n### 1.  Locate the points \\(D,E,F,G\\)\n\n\\[\nAD=4,\\;AB=28\\Longrightarrow \\frac{AD}{AB}= \\frac 1 7\\quad\\Rightarrow\\quad \n\\vec{AD}=\\frac17\\mathbf b .\n\\]\nThus \\(D=\\dfrac17\\mathbf b\\).\n\n\\[\nAE=AD+DE=20\\Longrightarrow\\frac{AE}{AB}= \\frac{20}{28}= \\frac57\n\\quad\\Rightarrow\\quad  E=\\frac57\\mathbf b .\n\\]\n\nSimilarly on \\(AC\\),\n\n\\[\nAF=13,\\;AC=91\\Longrightarrow \\frac{AF}{AC}= \\frac13\\!7\\quad\\Rightarrow\\quad \nF=\\frac17\\mathbf c ,\n\\]\n\\[\nAG=AF+FG=65\\Longrightarrow \\frac{AG}{AC}= \\frac{65}{91}= \\frac57\n\\quad\\Rightarrow\\quad  G=\\frac57\\mathbf c .\n\\]\n\nHence  \n\n\\[\nD=\\frac17\\mathbf b,\\qquad E=\\frac57\\mathbf b,\\qquad\nF=\\frac17\\mathbf c,\\qquad G=\\frac57\\mathbf c .\n\\]\n\n--------------------------------------------------------------------\n### 2.  Area of \\(\\triangle ABC\\)\n\nQuadrilateral \\(DEGF\\) is the region between the similar triangles\n\\(ADF\\) (scale \\(1/7\\)) and \\(AEG\\) (scale \\(5/7\\)).  \nTherefore  \n\n\\[\n[DEGF]=[AEG]-[ADF]\n           =\\left(\\frac57\\right)^{\\!2}[ABC]-\\left(\\frac17\\right)^{\\!2}[ABC]\n           =\\frac{25-1}{49}[ABC]=\\frac{24}{49}[ABC].\n\\]\n\nGiven \\([DEGF]=288\\),\n\n\\[\n[ABC]=\\frac{49}{24}\\cdot288=49\\cdot12=588 .\n\\tag{1}\n\\]\n\n--------------------------------------------------------------------\n### 3.  Locate the reflected points \\(M,N\\)\n\n\\[\nM\\; \\text{is the reflection of }D\\text{ across }F\\;\n\\Longrightarrow\\; M=2F-D=\n\\frac{2}{7}\\mathbf c-\\frac{1}{7}\\mathbf b .\n\\]\n\n\\[\nN\\; \\text{is the reflection of }G\\text{ across }E\\;\n\\Longrightarrow\\; N=2E-G=\n\\frac{10}{7}\\mathbf b-\\frac{5}{7}\\mathbf c .\n\\]\n\n--------------------------------------------------------------------\n### 4.  Area of the heptagon \\(AFNBCEM\\)\n\nWrite the vertices (in order) as vectors from \\(A\\):\n\n\\[\n\\begin{aligned}\nA&=0, &\nF&=\\frac17\\mathbf c, &\nN&=\\frac{10}{7}\\mathbf b-\\frac57\\mathbf c,\\\\\nB&=\\mathbf b, &\nC&=\\mathbf c, &\nE&=\\frac57\\mathbf b, &\nM&=\\frac27\\mathbf c-\\frac17\\mathbf b .\n\\end{aligned}\n\\]\n\nFor a polygon with vertices \\(\\mathbf v_0,\\dots,\\mathbf v_6\\) the doubled\narea equals\n\\[\n\\sum_{i=0}^{6}\\det(\\mathbf v_i,\\mathbf v_{i+1}),\n\\qquad\\mathbf v_7=\\mathbf v_0 .\n\\]\n\nCarrying out the determinants (using \\(\\det(\\mathbf b,\\mathbf c)=\\det(\\mathbf b,\\mathbf c)\\) and \\(\\det(\\mathbf c,\\mathbf b)=-\\det(\\mathbf b,\\mathbf c)\\)):\n\n\\[\n\\begin{aligned}\n\\det(F,N) &=\\frac1{49}\\det\\!\\Bigl(\\mathbf c,\\;10\\mathbf b-5\\mathbf c\\Bigr)\n           =-\\frac{10}{49}\\det(\\mathbf b,\\mathbf c),\\\\[2mm]\n\\det(N,B) &=\\frac57\\det(\\mathbf b,\\mathbf b)-\\frac5{7}\\det(\\mathbf c,\\mathbf b)\n           =\\frac5{7}\\det(\\mathbf b,\\mathbf c),\\\\[2mm]\n\\det(B,C) &=\\det(\\mathbf b,\\mathbf c),\\\\[2mm]\n\\det(C,E) &=\\frac57\\det(\\mathbf c,\\mathbf b)=-\\frac5{7}\\det(\\mathbf b,\\mathbf c),\\\\[2mm]\n\\det(E,M) &=\\frac1{49}\\det\\!\\Bigl(5\\mathbf b,\\;2\\mathbf c-\\mathbf b\\Bigr)\n           =\\frac{10}{49}\\det(\\mathbf b,\\mathbf c).\n\\end{aligned}\n\\]\n\nAll other terms are zero. Adding them:\n\n\\[\n\\det(F,N)+\\det(N,B)+\\det(B,C)+\\det(C,E)+\\det(E,M)\n   =\\Bigl(-\\frac{10}{49}+\\frac5{7}+1-\\frac5{7}+\\frac{10}{49}\\Bigr)\n      \\det(\\mathbf b,\\mathbf c)=\\det(\\mathbf b,\\mathbf c).\n\\]\n\nThus the doubled area of the heptagon is \\(\\det(\\mathbf b,\\mathbf c)\\),\nwhich is exactly twice the area of \\(\\triangle ABC\\). Consequently\n\n\\[\n[AFNBCEM]=\\frac12\\det(\\mathbf b,\\mathbf c)=[ABC]=588 .\n\\tag{2}\n\\]\n\n--------------------------------------------------------------------\n### 5.  Answer\n\n\\[\n\\boxed{588}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nThe parabola with equation $y=x^{2}-4$ is rotated $60^{\\circ}$ counterclockwise around the origin. The unique point in the fourth quadrant where the original parabola and its image intersect has $y$-coordinate $\\frac{a-\\sqrt{b}}{c}$, where $a$, $b$, and $c$ are positive integers, and $a$ and $c$ are relatively prime. Find $a+b+c$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "The parabola is  \n\n\\[\ny=x^{2}-4 .\n\\]\n\nRotate a point \\((x,y)\\) by \\(-60^{\\circ}\\) (the inverse rotation).  \nFor \\(\\theta =60^{\\circ}\\),\n\n\\[\n\\cos\\theta =\\frac12 ,\\qquad \\sin\\theta =\\frac{\\sqrt3}{2}.\n\\]\n\nThe inverse\u2011rotation of \\((x,y)\\) is  \n\n\\[\nu=\\frac12 x+\\frac{\\sqrt3}{2}y ,\\qquad \nv=-\\frac{\\sqrt3}{2}x+\\frac12 y .\n\\]\n\nFor a point of the rotated parabola, the inverse image \\((u,v)\\) must satisfy the\noriginal equation \\(v=u^{2}-4\\):\n\n\\[\n-\\frac{\\sqrt3}{2}x+\\frac12 y =\\Bigl(\\frac12 x+\\frac{\\sqrt3}{2}y\\Bigr)^{2}-4 .\n\\]\n\nMultiplying by \\(2\\) and expanding gives\n\n\\[\n\\frac12 x^{2}+\\sqrt3\\,xy+\\frac32 y^{2}+\\sqrt3\\,x-y-8=0. \\tag{1}\n\\]\n\nNow substitute \\(y=x^{2}-4\\) (the original parabola) into (1):\n\n\\[\n\\frac12 x^{2}+\\sqrt3\\,x(x^{2}-4)+\\frac32 (x^{2}-4)^{2}\n+\\sqrt3\\,x-(x^{2}-4)-8=0 .\n\\]\n\nSimplifying,\n\n\\[\n3x^{4}+2\\sqrt3\\,x^{3}-25x^{2}-6\\sqrt3\\,x+40=0 .\n\\]\n\nFactor the quartic (group the \\(\\sqrt3\\) terms):\n\n\\[\n\\bigl(x^{2}+\\sqrt3\\,x-4\\bigr)\\bigl(3x^{2}-\\sqrt3\\,x-10\\bigr)=0 .\n\\]\n\nHence\n\n\\[\nx^{2}+\\sqrt3\\,x-4=0\\qquad\\text{or}\\qquad 3x^{2}-\\sqrt3\\,x-10=0.\n\\]\n\nThe four solutions are  \n\n\\[\n\\begin{aligned}\nx&=\\frac{-\\sqrt3\\pm\\sqrt{19}}2,\\\\[2mm]\nx&=\\frac{\\sqrt3\\pm\\sqrt{123}}6 .\n\\end{aligned}\n\\]\n\nOnly one of them lies in the fourth quadrant \\((x>0,\\;y<0)\\):\n\\[\nx=\\frac{-\\sqrt3+\\sqrt{19}}2\\;(>0),\\qquad |x|<2 .\n\\]\n\nIts \\(y\\)-coordinate is\n\n\\[\ny=x^{2}-4\n     =\\Bigl(\\frac{-\\sqrt3+\\sqrt{19}}2\\Bigr)^{2}-4\n     =\\frac{3-\\sqrt{57}}2 .\n\\]\n\nThus  \n\n\\[\ny=\\frac{a-\\sqrt b}{c}\\quad\\text{with}\\quad a=3,\\;b=57,\\;c=2,\n\\]\nand \\(a\\) and \\(c\\) are relatively prime.\n\nFinally,\n\\[\na+b+c=3+57+2=62 .\n\\]\n\n\\[\n\\boxed{62}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nThe twelve letters $A,B,C,D,E,F,G,H,I,J,K$, and $L$ are randomly grouped into six pairs of letters. The two letters in each pair are placed next to each other in alphabetical order to form six two-letter words, and those six words are listed alphabetically. For example, a possible result is $AB,CJ,DG,EK,FL,HI$. The probability that the last word listed contains $G$ is $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "The six two\u2011letter words are formed by first ordering the letters inside each pair\nalphabetically and then sorting the six words alphabetically.  \nFor a pairing, let  \n\n\\[\nS=\\{\\text{the smaller letter of each pair}\\}\n\\]\n\n(the \u201cfirst\u201d letters of the six words).  \nThe lexicographically last word is the one whose first letter is  \n\n\\[\nM=\\max S .\n\\]\n\nHence the last word contains \\(G\\) **iff** either  \n\n* \\(M=G\\) (so \\(G\\) itself is the first letter of the last word), or  \n* \\(M\\neq G\\) but \\(G\\) is paired with the letter \\(M\\) (so \\(G\\) is the second\nletter of the last word).\n\nBecause a pair \\((x,y)\\) must satisfy \\(x<y\\), the only possible \\(M\\) with\n\\(M<G\\) is \\(M=F\\).  Thus there are two cases:\n\n--------------------------------------------------------------------\n### 1.  \\(M=G\\)\n\nThen the six small letters are  \n\n\\[\nS=\\{G\\}\\cup \\{A,B,C,D,E,F\\}\\setminus\\{a\\},\n\\]\n\nwhere \\(a\\) is the one letter from \\(\\{A,\\dots ,F\\}\\) that is **not** in \\(S\\).\nThe omitted letter \\(a\\) must not be \\(A\\); otherwise \\(A\\) would be a large\nletter with no smaller partner.  \nHence \\(a\\in\\{B,C,D,E,F\\}\\) \u2013 5 possibilities.\n\nFor a given \\(a\\):\n* \\(a\\) (a large letter) must be paired with a small letter that is\nsmaller than \\(a\\); there are \\(a-1\\) such choices.\n* The remaining five small letters can be paired arbitrarily with the five\nlarge letters \\(H,I,J,K,L\\); that gives \\(5!\\) possibilities.\n\nThus for each \\(a\\) we have \\((a-1)\\cdot5!\\) pairings.  \nSumming over \\(a=2,3,4,5,6\\) (i.e. \\(B\\)\u2013\\(F\\)),\n\n\\[\n\\sum_{a=2}^{6}(a-1) \\cdot 5!\n   =(1+2+3+4+5)\\cdot120\n   =15\\cdot120\n   =1800 .\n\\]\n\n--------------------------------------------------------------------\n### 2.  \\(M=F\\) and \\(G\\) is paired with \\(F\\)\n\nIf the maximum small letter is \\(F\\), then the small set must be exactly  \n\n\\[\nS=\\{A,B,C,D,E,F\\},\n\\qquad\nT=\\{G,H,I,J,K,L\\}.\n\\]\n\nEvery bijection between \\(S\\) and \\(T\\) yields a valid pairing, so there are\n\\(6! = 720\\) pairings in total.  \nAmong them, the ones with \\(F\\) paired with \\(G\\) are those where we fix that\npair and match the remaining five letters arbitrarily, giving \\(5! =120\\) pairings.\n\n--------------------------------------------------------------------\n### Total favourable pairings\n\n\\[\nN_{\\text{fav}} = 1800 + 120 = 1920 .\n\\]\n\n--------------------------------------------------------------------\n### Total pairings\n\nThe total number of ways to split 12 distinct letters into six unordered pairs is  \n\n\\[\nN_{\\text{total}}=\\frac{12!}{2^{6}\\,6!}=10395 .\n\\]\n\n--------------------------------------------------------------------\n### Probability\n\n\\[\nP=\\frac{1920}{10395}\n   =\\frac{128}{693}\\quad(\\text{in lowest terms}).\n\\]\n\nThus \\(m=128,\\;n=693\\) and\n\n\\[\nm+n=128+693=821 .\n\\]\n\n\\[\n\\boxed{821}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nA piecewise linear periodic function is defined by $f(x)=\\begin{cases}x&\\text{if }x\\in[-1,1)\\\\2-x&\\text{if }x\\in[1,3)\\end{cases}$ and $f(x+4)=f(x)$ for all real numbers $x$. The graph of $f(x)$ has the sawtooth pattern. The parabola $x=34y^2$ intersects the graph of $f(x)$ at finitely many points. The sum of the $y$-coordinates of these intersection points can be expressed in the form $\\frac{a+b\\sqrt{c}}{d}$, where $a,b,c,$ and $d$ are positive integers, $a,b,$ and $d$ have greatest common divisor equal to 1, and $c$ is not divisible by the square of any prime. Find $a+b+c+d$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "The graph of  \n\n\\[\nf(x)=\\begin{cases}\nx,&-1\\le x<1\\\\[2pt]\n2-x,&1\\le x<3\n\\end{cases},\n\\qquad f(x+4)=f(x)\n\\]\n\nis a triangular wave of period \\(4\\) whose values lie in \\([-1,1]\\).\n\nThe parabola is  \n\n\\[\nx=34y^{2}\\qquad (x\\ge 0).\n\\]\n\nBecause \\(|f(x)|\\le 1\\), any intersection must satisfy \\(|y|\\le 1\\); then  \n\n\\[\n0\\le x=34y^{2}\\le 34 .\n\\]\n\n--------------------------------------------------------------------\n### 1. Reduce the problem to a quadratic equation\n\nWrite  \n\n\\[\nt = 34y^{2}\\;(0\\le t\\le34).\n\\]\n\nFor some integer \\(k\\) we can write  \n\n\\[\nt = 4k+u,\\qquad u\\in[-1,3)\n\\]\n\n(the representation is unique because we use the half\u2011open interval \\([-1,3)\\)).  \nSince \\(f(t)=f(u)\\),\n\n\\[\nf(u)=\\begin{cases}\nu, & u\\in[-1,1)\\\\[2pt]\n2-u, & u\\in[1,3)\n\\end{cases}\n\\]\n\nand the intersection condition \\(y=f(t)\\) becomes  \n\n\\[\n\\begin{cases}\ny=u = 34y^{2}-4k, & u\\in[-1,1)\\\\[4pt]\ny=2-u = 2-(34y^{2}-4k), & u\\in[1,3)\n\\end{cases}\n\\]\n\nwhich give the quadratics  \n\n\\[\n\\boxed{34y^{2}-y-4k=0}\\qquad(u\\in[-1,1))\n\\tag{A}\n\\]\n\n\\[\n\\boxed{34y^{2}+y-(2+4k)=0}\\qquad(u\\in[1,3))\n\\tag{B}\n\\]\n\nwith the extra restrictions  \n\n\\[\n\\text{(A)}\\;y\\in[-1,1), \\qquad\n\\text{(B)}\\; -1<y\\le 1 .\n\\]\n\n--------------------------------------------------------------------\n### 2. The possible integers \\(k\\)\n\nSince \\(t\\le34\\),\n\n\\[\n-1\\le u =t-4k <3\\Longrightarrow 4k\\le t+1\\le 35\n\\]\n\nso \\(k\\) can be \\(0,1,\\dots ,8\\) (nine values).\n\n--------------------------------------------------------------------\n### 3. Solutions of (A)\n\nFor each \\(k\\) the equation  \n\n\\[\n34y^{2}-y-4k=0\n\\]\n\nhas the two roots  \n\n\\[\ny=\\frac{1\\pm\\sqrt{1+544k}}{68}.\n\\]\n\nBoth lie in \\([-1,1)\\) for all \\(k=0,\\dots ,8\\).  \nHence each \\(k\\) contributes **two** solutions and their sum is\n\n\\[\n\\frac{1}{34}\\quad\\text{(by Vieta)}.\n\\]\n\nTotal from (A):\n\n\\[\n9\\cdot\\frac{1}{34}= \\frac{9}{34}.\n\\]\n\n--------------------------------------------------------------------\n### 4. Solutions of (B)\n\nFor each \\(k\\) the equation  \n\n\\[\n34y^{2}+y-(2+4k)=0\n\\]\n\nhas roots  \n\n\\[\ny=\\frac{-1\\pm\\sqrt{273+544k}}{68}.\n\\]\n\nFor \\(k=0,1,\\dots ,7\\) both roots satisfy \\(-1<y\\le1\\); for \\(k=8\\) the\nnegative root is \\(<-1\\) and is discarded.\nThus we have\n\n* for \\(k=0,\\dots ,7\\): two roots each, sum \\(-\\dfrac1{34}\\) (Vieta);\n* for \\(k=8\\): only the positive root  \n\n  \\[\n  y_{8}= \\frac{-1+\\sqrt{4625}}{68}= \\frac{-1+5\\sqrt{185}}{68}.\n  \\]\n\nHence the contribution of (B) is  \n\n\\[\n8\\!\\left(-\\frac1{34}\\right) + y_{8}= -\\frac{8}{34}+ \\frac{-1+5\\sqrt{185}}{68}\n= -\\frac{4}{17}+ \\frac{-1+5\\sqrt{185}}{68}.\n\\]\n\n--------------------------------------------------------------------\n### 5. Sum of all \\(y\\)-coordinates\n\nAdd the contributions of (A) and (B):\n\n\\[\n\\begin{aligned}\nS &=\\frac{9}{34}\\;+\\;\\Bigl(-\\frac{8}{34}+ \\frac{-1+5\\sqrt{185}}{68}\\Bigr)\\\\[4pt]\n  &=\\frac{1}{34}+ \\frac{-1+5\\sqrt{185}}{68}\n   =\\frac{2-1+5\\sqrt{185}}{68}\\\\[4pt]\n  &=\\boxed{\\displaystyle\\frac{1+5\\sqrt{185}}{68}}.\n\\end{aligned}\n\\]\n\n--------------------------------------------------------------------\n### 6. Required sum \\(a+b+c+d\\)\n\nThe expression is \\(\\dfrac{a+b\\sqrt{c}}{d}\\) with  \n\n\\[\na=1,\\quad b=5,\\quad c=185,\\quad d=68,\n\\]\n\nwhich satisfy the given conditions. Therefore  \n\n\\[\na+b+c+d = 1+5+185+68 = \\boxed{259}.\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nSix points $ A, B, C, D, E, $ and $ F $ lie in a straight line in that order. Suppose that $ G $ is a point not on the line and that $ AC = 26 $, $ BD = 22 $, $ CE = 31 $, $ DF = 33 $, $ AF = 73 $, $ CG = 40 $, and $ DG = 30 $. Find the area of $ \\triangle BGE $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let the line be the \\(x\\)-axis.  \nPlace the points with coordinates (in order)\n\n\\[\nA(0),\\; B(x_B),\\; C(x_C),\\; D(x_D),\\; E(x_E),\\; F(x_F).\n\\]\n\nDenote the successive distances\n\n\\[\nAB=a,\\; BC=b,\\; CD=c,\\; DE=d,\\; EF=e .\n\\]\n\nThen  \n\n\\[\n\\begin{aligned}\na+b &= AC = 26,\\\\\nb+c &= BD = 22,\\\\\nc+d &= CE = 31,\\\\\nd+e &= DF = 33,\\\\\na+b+c+d+e &= AF = 73 .\n\\end{aligned}\n\\]\n\nSolving:\n\\[\n\\begin{aligned}\na &= 26-b,\\\\\nc &= 22-b,\\\\\nd &= 31-c = 9+b,\\\\\ne &= 33-d = 24-b.\n\\end{aligned}\n\\]\n\nInsert these in the sum equation:\n\n\\[\n(26-b)+b+(22-b)+(9+b)+(24-b)=73\\Longrightarrow81-b=73,\n\\]\n\nhence \\(b=8\\).\n\nThus  \n\n\\[\n\\begin{aligned}\nAB = a = 18,\\quad\nBC = b = 8,\\quad\nCD = c = 14,\\quad\nDE = d = 17,\\quad\nEF = e = 16.\n\\end{aligned}\n\\]\n\nChoosing \\(A\\) as the origin gives\n\n\\[\n\\begin{aligned}\nA&:(0,0),\\\\\nB&:(18,0),\\\\\nC&:(26,0),\\\\\nD&:(40,0),\\\\\nE&:(57,0),\\\\\nF&:(73,0).\n\\end{aligned}\n\\]\n\n---\n\n### Coordinates of \\(G\\)\n\nLet \\(G=(x,y)\\).  \nWe are given \\(CG=40\\) and \\(DG=30\\):\n\n\\[\n\\begin{cases}\n(x-26)^2+y^2 = 40^2 =1600,\\\\\n(x-40)^2+y^2 = 30^2 = 900 .\n\\end{cases}\n\\]\n\nSubtracting the equations eliminates \\(y^2\\):\n\n\\[\n(x-26)^2-(x-40)^2 = 700 .\n\\]\n\n\\[\n\\begin{aligned}\n[x^2-52x+676] - [x^2-80x+1600] &= 700\\\\\n28x-924 &= 700\\\\\n28x &=1624\\\\\nx&= \\frac{1624}{28}=58 .\n\\end{aligned}\n\\]\n\nPlug \\(x=58\\) into \\((x-40)^2+y^2=900\\):\n\n\\[\n(58-40)^2+y^2=900\\Longrightarrow 18^2+y^2=900\\Longrightarrow y^2=576,\n\\]\n\nso \\(|y|=24\\).  \nThus \\(G=(58,\\pm24)\\).\n\n---\n\n### Area of \\(\\triangle BGE\\)\n\nPoints \\(B\\) and \\(E\\) lie on the \\(x\\)-axis, so the base \\(BE\\) has length\n\n\\[\nBE = x_E-x_B = 57-18 = 39 .\n\\]\n\nThe altitude from \\(G\\) to line \\(BE\\) is \\(|y|=24\\).\n\nHence\n\n\\[\n\\text{Area}= \\frac12 \\times (\\text{base}) \\times (\\text{height})\n          = \\frac12 \\times 39 \\times 24\n          = 39 \\times 12\n          = 468 .\n\\]\n\n\\[\n\\boxed{468}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nFind the sum of all positive integers $ n $ such that $ n + 2 $ divides the product $ 3(n + 3)(n^2 + 9) $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n\\[\nd=n+2\\qquad (d\\ge 3,\\; n>0)\n\\]\n\nThen  \n\n\\[\nn=d-2,\\qquad n+3=d+1,\\qquad n^{2}+9=(d-2)^{2}+9=d^{2}-4d+13 .\n\\]\n\nThe required divisibility becomes  \n\n\\[\nd\\mid 3(n+3)(n^{2}+9)=3(d+1)(d^{2}-4d+13).\n\\]\n\n---\n\n### Reduce modulo \\(d\\)\n\n\\[\n3(d+1)(d^{2}-4d+13) \\equiv 3\\cdot1\\cdot13 = 39 \\pmod d,\n\\]\n\nbecause \\(d+1\\equiv1\\) and \\(d^{2}-4d+13\\equiv13\\) modulo \\(d\\).\n\nThus  \n\n\\[\nd\\mid 3(d+1)(d^{2}-4d+13)\\iff d\\mid 39 .\n\\]\n\nHence \\(d\\) must be a positive divisor of \\(39\\) and at least \\(3\\).  \nDivisors of \\(39\\) are \\(1,3,13,39\\); discarding \\(1\\) we obtain  \n\n\\[\nd\\in\\{3,13,39\\}.\n\\]\n\n---\n\n### Recover the corresponding \\(n\\)\n\n\\[\nn=d-2\\implies n\\in\\{3-2,13-2,39-2\\}=\\{1,11,37\\}.\n\\]\n\nEach indeed satisfies the original condition:\n\n* \\(n=1\\): \\(\\frac{3(1+3)(1^{2}+9)}{1+2}= \\frac{3\\cdot4\\cdot10}{3}=40\\) (integer);\n* \\(n=11\\): \\(\\frac{3(11+3)(11^{2}+9)}{11+2}= \\frac{3\\cdot14\\cdot130}{13}=420\\);\n* \\(n=37\\): \\(\\frac{3(37+3)(37^{2}+9)}{37+2}= \\frac{3\\cdot40\\cdot1378}{39}=4240\\).\n\n---\n\n### Sum of all such \\(n\\)\n\n\\[\n1+11+37 = 49.\n\\]\n\n\\[\n\\boxed{49}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nThe set of points in 3-dimensional coordinate space that lie in the plane $x+y+z=75$ whose coordinates satisfy the inequalities $x-yz<y-zx<z-xy$ forms three disjoint convex regions. Exactly one of those regions has finite area. The area of this finite region can be expressed in the form $a\\sqrt{b}$, where $a$ and $b$ are positive integers and $b$ is not divisible by the square of any prime. Find $a+b$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "First write the two required inequalities using the condition \\(x+y+z=75\\).\n\n\\[\nz=75-x-y .\n\\]\n\n---\n\n### 1.  Simplify the inequalities  \n\n\\[\n\\begin{aligned}\nx-yz &<y-zx\\\\\nx-(y(75-x-y)) &< y-(x(75-x-y))\\\\\n\\Longrightarrow (x-y)(x+y-76) &>0 .\n\\end{aligned}\n\\]\n\n\\[\n\\begin{aligned}\ny-zx &<z-xy\\\\\ny-x(75-x-y) &< (75-x-y)-xy\\\\\n\\Longrightarrow (x+1)(x+2y-75) &<0 .\n\\end{aligned}\n\\]\n\nHence the points \\((x,y,z)\\) on the plane satisfy  \n\n\\[\n\\boxed{(x-y)(x+y-76)>0},\\qquad\\boxed{(x+1)(x+2y-75)<0}.\n\\]\n\nBoth are products of two linear factors.\n\n---\n\n### 2.  Work in the \\((x,y)\\)-plane  \n\nThe plane \\(x+y+z=75\\) is a linear image of the \\((x,y)\\)-plane via  \n\n\\[\n(x,y)\\mapsto (x,\\;y,\\;75-x-y) .\n\\]\n\nThe Jacobian matrix has columns \\((1,0,-1)\\) and \\((0,1,-1)\\); its Gram determinant is  \n\n\\[\n\\det\\begin{pmatrix}2&1\\\\1&2\\end{pmatrix}=3 .\n\\]\n\nThus an area element in the plane equals \\(\\sqrt3\\) times the ordinary area\n\\(dx\\,dy\\) in the \\((x,y)\\)-plane.\n\n---\n\n### 3.  Region defined by the two products  \n\nLet  \n\n\\[\nL_1:\\;x=-1,\\qquad L_2:\\;x+2y=75,\n\\]\n\\[\nL_3:\\;x=y,\\qquad L_4:\\;x+y=76 .\n\\]\n\nThe inequalities become\n\n\\[\n\\begin{cases}\nx>-1 \\;\\text{and}\\; y<\\dfrac{75-x}{2}   &\\text{or } x<-1 \\;\\text{and}\\; y>\\dfrac{75-x}{2},\\\\[4pt]\nx>y \\;\\text{and}\\; x+y>76               &\\text{or } x<y \\;\\text{and}\\; x+y<76 .\n\\end{cases}\n\\]\n\nOnly three of the four possible combinations are non\u2011empty:\n\n* **Region\u202f\\(R_1\\)** \u2013 \\(x>-1,\\;y<\\frac{75-x}{2},\\;x>y,\\;x+y>76\\) (unbounded).\n* **Region\u202f\\(R_2\\)** \u2013 \\(x>-1,\\;y<\\frac{75-x}{2},\\;x<y,\\;x+y<76\\) (bounded).\n* **Region\u202f\\(R_3\\)** \u2013 \\(x<-1,\\;y>\\frac{75-x}{2},\\;x<y,\\;x+y<76\\) (unbounded).\n\nHence the set consists of three disjoint convex regions; only \\(R_2\\) has finite area.\n\n---\n\n### 4.  The bounded region  \n\nFrom the inequalities for \\(R_2\\)\n\n\\[\n\\begin{cases}\n-1<x<25,\\\\[2pt]\nx<y<\\dfrac{75-x}{2},\n\\end{cases}\n\\]\n\nso \\(R_2\\) is the open triangle bounded by the lines  \n\n\\[\nx=-1,\\qquad y=x,\\qquad y=\\dfrac{75-x}{2}.\n\\]\n\nIts vertices are  \n\n\\[\nA(-1,-1),\\quad B(-1,38),\\quad C(25,25).\n\\]\n\nThe ordinary (planar) area is\n\n\\[\n\\frac12\\cdot|AB|\\cdot|AC|_{\\perp}= \\frac12\\,(39)\\,(26)=507 .\n\\]\n\n---\n\n### 5.  Area on the plane \\(x+y+z=75\\)\n\nMultiplying by the factor \\(\\sqrt3\\),\n\n\\[\n\\text{area}=507\\sqrt3 .\n\\]\n\nThus \\(a=507,\\;b=3\\) and\n\n\\[\na+b=507+3=510 .\n\\]\n\n\\[\n\\boxed{510}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nThe product $ \\prod_{k=4}^{63} \\frac{\\log_k(5^{k^2-1})}{\\log_{k+1}(5^{k^2-4})} = \\frac{\\log_4(5^{15})}{\\log_5(5^{12})} \\cdot \\frac{\\log_5(5^{24})}{\\log_6(5^{21})} \\cdot \\frac{\\log_6(5^{35})}{\\log_7(5^{32})} \\cdots \\frac{\\log_{63}(5^{3968})}{\\log_{64}(5^{3965})} $ is equal to $ \\frac{m}{n} $, where $ m $ and $ n $ are relatively prime positive integers. Find $ m + n $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "\\[\nP=\\prod_{k=4}^{63}\\frac{\\log_k(5^{k^2-1})}{\\log_{k+1}(5^{k^2-4})}\n\\]\n\n---\n\n### 1.  Simplify one factor  \n\n\\[\n\\log_k(5^{k^2-1})=\\frac{\\ln(5^{k^2-1})}{\\ln k}\n            =\\frac{(k^2-1)\\ln5}{\\ln k},\n\\qquad\n\\log_{k+1}(5^{k^2-4})=\\frac{(k^2-4)\\ln5}{\\ln(k+1)}.\n\\]\n\nHence\n\n\\[\n\\frac{\\log_k(5^{k^2-1})}{\\log_{k+1}(5^{k^2-4})}\n   =\\frac{k^2-1}{k^2-4}\\cdot\\frac{\\ln(k+1)}{\\ln k}.\n\\]\n\nSo\n\n\\[\nP=\\Bigl(\\prod_{k=4}^{63}\\frac{k^2-1}{k^2-4}\\Bigr)\n   \\Bigl(\\prod_{k=4}^{63}\\frac{\\ln(k+1)}{\\ln k}\\Bigr).\n\\]\n\n---\n\n### 2.  Telescoping the logarithm part  \n\n\\[\n\\prod_{k=4}^{63}\\frac{\\ln(k+1)}{\\ln k}\n =\\frac{\\ln5}{\\ln4}\\cdot\\frac{\\ln6}{\\ln5}\\cdots\\frac{\\ln64}{\\ln63}\n =\\frac{\\ln64}{\\ln4}\n =\\log_4 64 =3 .\n\\]\n\n---\n\n### 3.  Telescoping the rational part  \n\n\\[\n\\frac{k^2-1}{k^2-4}= \\frac{(k-1)(k+1)}{(k-2)(k+2)}\n   =\\frac{k-1}{k-2}\\cdot\\frac{k+1}{k+2}.\n\\]\n\nHence\n\n\\[\n\\prod_{k=4}^{63}\\frac{k^2-1}{k^2-4}\n =\\Bigl(\\prod_{k=4}^{63}\\frac{k-1}{k-2}\\Bigr)\n   \\Bigl(\\prod_{k=4}^{63}\\frac{k+1}{k+2}\\Bigr).\n\\]\n\n*First product*  \n\nLet \\(i=k-2\\). Then \\(i\\) runs from \\(2\\) to \\(61\\):\n\n\\[\n\\prod_{k=4}^{63}\\frac{k-1}{k-2}\n =\\prod_{i=2}^{61}\\frac{i+1}{i}\n =\\frac{3}{2}\\cdot\\frac{4}{3}\\cdots\\frac{62}{61}\n =\\frac{62}{2}=31 .\n\\]\n\n*Second product*  \n\nLet \\(j=k+1\\). Then \\(j\\) runs from \\(5\\) to \\(64\\):\n\n\\[\n\\prod_{k=4}^{63}\\frac{k+1}{k+2}\n =\\prod_{j=5}^{64}\\frac{j}{j+1}\n =\\frac{5}{6}\\cdot\\frac{6}{7}\\cdots\\frac{64}{65}\n =\\frac{5}{65}=\\frac1{13}.\n\\]\n\nThus\n\n\\[\n\\prod_{k=4}^{63}\\frac{k^2-1}{k^2-4}=31\\cdot\\frac1{13}=\\frac{31}{13}.\n\\]\n\n---\n\n### 4.  Combine the two parts  \n\n\\[\nP = 3\\cdot\\frac{31}{13}= \\frac{93}{13}.\n\\]\n\nThe fraction \\(\\frac{93}{13}\\) is already in lowest terms (\\(\\gcd(93,13)=1\\)).\nThus \\(m=93,\\; n=13\\) and\n\n\\[\nm+n = 93+13 = 106 .\n\\]\n\n\\[\n\\boxed{106}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nThe 27 cells of a $3\\times9$ grid are filled in using the numbers 1 through 9 so that each row contains 9 different numbers, and each of the three $3\\times3$ blocks heavily outlined in the example below contains 9 different numbers, as in the first three rows of a Sudoku puzzle. \n | 4 | 2 | 8 | 9 | 6 | 3 | 1 | 7 | 5 | \n | 3 | 7 | 9 | 5 | 2 | 1 | 6 | 8 | 4 | \n | 5 | 6 | 1 | 8 | 4 | 7 | 9 | 2 | 3 | \n The number of different ways to fill such a grid can be written as $p^a\\cdot q^b\\cdot r^c\\cdot s^d$, where $p,q,r,$ and $s$ are distinct prime numbers and $a,b,c,$ and $d$ are positive integers. Find $p\\cdot a+q\\cdot b+r\\cdot c+s\\cdot d$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "**Step 1 \u2013  what the conditions mean**\n\nIn a \\(3\\times 9\\) grid  \n\n* each of the three rows must be a permutation of the numbers \\(1,\\ldots ,9\\);  \n* each of the three \\(3\\times3\\) blocks (columns \\(1\\!-\\!3,\\;4\\!-\\!6,\\;7\\!-\\!9\\)) must also contain the numbers \\(1,\\ldots ,9\\) exactly once.\n\nHence every digit appears\n\n* once in each row (3 times in total), and  \n* once in each block (also 3 times in total).\n\nSo for a fixed digit \\(d\\) the three positions where it occurs are determined by a\nbijection between the three rows and the three blocks; i.e. a permutation\n\\(\\sigma_d\\in S_{3}\\).\n\n--------------------------------------------------------------------\n\n**Step 2 \u2013  describing a filling by permutations**\n\nFor the nine digits we obtain nine permutations  \n\n\\[\n\\sigma_1,\\sigma_2,\\dots ,\\sigma_9\\in S_3 .\n\\]\n\nIf \\(\\sigma_d(i)=j\\) then digit \\(d\\) is placed in row \\(i\\) inside block \\(j\\).\nFor a fixed block\u2013row cell \\((i,j)\\) there are three rows of the grid, hence it\nmust contain **exactly three** digits. Consequently for every cell \\((i,j)\\)\n\n\\[\n\\#\\{d\\mid \\sigma_d(i)=j\\}=3 .\n\\tag{1}\n\\]\n\n--------------------------------------------------------------------\n\n**Step 3 \u2013  solving the integer system**\n\nLet  \n\n\\[\n\\begin{aligned}\nx_{\\mathrm{id}}&=\\#\\{\\sigma_d=\\text{id}\\},&\nx_{12}&=\\#\\{\\sigma_d=(12)\\},\\\\\nx_{13}&=\\#\\{\\sigma_d=(13)\\},&\nx_{23}&=\\#\\{\\sigma_d=(23)\\},\\\\\nx_{123}&=\\#\\{\\sigma_d=(123)\\},&\nx_{132}&=\\#\\{\\sigma_d=(132)\\}.\n\\end{aligned}\n\\]\n\nEach permutation contributes a \u20181\u2019 to three different cells; each cell is covered\nby exactly two permutations. From (1) we obtain nine equations, e.g.\n\n\\[\nx_{\\mathrm{id}}+x_{23}=3,\\qquad\nx_{12}+x_{123}=3,\\qquad\\ldots\n\\]\n\nSolving them gives\n\n\\[\nx_{12}=x_{13}=x_{23}=k,\\qquad\nx_{\\mathrm{id}}=x_{123}=x_{132}=3-k,\n\\]\n\nwhere \\(k\\in\\{0,1,2,3\\}\\).\n\n--------------------------------------------------------------------\n\n**Step 4 \u2013  assigning the permutations to the nine distinct digits**\n\nFor a fixed \\(k\\) the number of ways to give the nine digits the required\nmultiplicities is the multinomial coefficient\n\n\\[\n\\frac{9!}{k!^{\\,3}\\,(3-k)!^{\\,3}} .\n\\]\n\nSumming over the four possible values of \\(k\\) gives\n\n\\[\nN=\\sum_{k=0}^{3}\\frac{9!}{k!^{\\,3}(3-k)!^{\\,3}}\n   =2\\cdot\\frac{9!}{3!^{\\,3}}+2\\cdot\\frac{9!}{1!^{\\,3}2!^{\\,3}}\n   =1680+45360+45360+1680=94\\,080 .\n\\]\n\nThus there are \\(94\\,080\\) ways to decide, for every digit, in which block of\neach row it will appear.\n\n--------------------------------------------------------------------\n\n**Step 5 \u2013  placing the digits inside the blocks**\n\nFix a block \\(j\\).  \nRow \\(i\\) contributes exactly three distinct digits to this block; they can be\narranged in the three columns of the block in \\(3! = 6\\) ways, independently for\nthe three rows. Hence a block can be filled in \\((3!)^{3}=6^{3}=216\\) ways.\n\nThe three blocks are independent, so the column\u2011ordering factor is\n\n\\[\n(3!)^{9}=6^{9}=10\\,077\\,696 .\n\\]\n\n--------------------------------------------------------------------\n\n**Step 6 \u2013  total number of fillings**\n\n\\[\n\\boxed{T = N\\cdot (3!)^{9}=94\\,080\\cdot 10\\,077\\,696\n      = 948\\,109\\,639\\,680 }.\n\\]\n\nFactorising,\n\n\\[\nT = 2^{16}\\cdot 3^{10}\\cdot 5\\cdot 7^{2}.\n\\]\n\n--------------------------------------------------------------------\n\n**Step 7 \u2013  computing the required sum**\n\nTake \\(p=2,\\;q=3,\\;r=5,\\;s=7\\) with exponents\n\\(a=16,\\;b=10,\\;c=1,\\;d=2\\). Then\n\n\\[\np\\!a+q\\!b+r\\!c+s\\!d\n=2\\cdot16+3\\cdot10+5\\cdot1+7\\cdot2\n=32+30+5+14=81 .\n\\]\n\n\\[\n\\boxed{81}\n\\]",
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+        "role": "user",
+        "content": "\nThere are exactly three positive real numbers $ k $ such that the function\n$ f(x) = \\frac{(x - 18)(x - 72)(x - 98)(x - k)}{x} $\ndefined over the positive real numbers achieves its minimum value at exactly two positive real numbers $ x $. Find the sum of these three values of $ k $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "**Solution Overview**\n\nFor  \n\n\\[\nf(x)=\\frac{(x-18)(x-72)(x-98)(x-k)}{x},\\qquad x>0,\n\\]\n\nlet  \n\n\\[\nN(x)=(x-18)(x-72)(x-98)(x-k)=x^4-S_1x^3+S_2x^2-S_3x+S_4,\n\\]\n\nwhere  \n\n\\[\n\\begin{aligned}\nS_1&=18+72+98+k=188+k,\\\\[2pt]\nS_2&=18\\cdot72+18\\cdot98+72\\cdot98+ k(18+72+98)=10116+188k,\\\\[2pt]\nS_4&=18\\cdot72\\cdot98\\cdot k=127008\\,k .\n\\end{aligned}\n\\]\n\nThen  \n\n\\[\nf(x)=\\frac{N(x)}{x}=x^{3}-S_1x^{2}+S_2x-S_3+\\frac{S_4}{x},\n\\]\n\nand  \n\n\\[\nf'(x)=\\frac{3x^{4}-2S_1x^{3}+S_2x^{2}-S_4}{x^{2}} .\n\\]\n\nHence the critical points are the (positive) roots of  \n\n\\[\nP(x)=3x^{4}-2S_1x^{3}+S_2x^{2}-S_4=0\\tag{1}\n\\]\n\n(the denominator $x^{2}>0$ for $x>0$).\n\nBecause $f(x)\\to +\\infty$ as $x\\to0^{+}$ and as $x\\to\\infty$, the graph must\nfirst decrease, then increase, then decrease, and finally increase again.\nThus (1) has three positive roots:\n\n* $x_1$ \u2013 a local **minimum** in the first negative interval,\n* $x_2$ \u2013 a local **maximum** in the positive interval,\n* $x_3$ \u2013 a second local **minimum** in the last negative interval.\n\nThe global minimum is achieved at the lower of the two minima.\nFor the minimum to be attained **exactly at two points** we need  \n\n\\[\nf(x_1)=f(x_3)\\qquad(\\text{the two minima have the same value}).\n\\tag{2}\n\\]\n\n--------------------------------------------------------------------\n### 1.  Translating the condition\n\nAt a critical point $x$ we have $f'(x)=0$, i.e. $P(x)=0$.\nFrom $f(x)=\\dfrac{N(x)}{x}$ and $P(x)=0$ it follows that  \n\n\\[\nf(x)=\\frac{N(x)}{x}=N'(x)\\qquad\\text{for any critical point}.\n\\tag{3}\n\\]\n\nThus (2) is equivalent to  \n\n\\[\nN'(x_1)=N'(x_3).\\tag{4}\n\\]\n\nWriting $x_1+ x_3=s$ and $x_1x_3=p$, the two equations $P(x_1)=P(x_3)=0$\ngive after elimination  \n\n\\[\n\\begin{cases}\n4(s^{2}-p)-3S_1s+2S_2=0,\\\\[2pt]\n3(s^{3}-2ps)-2S_1(s^{2}-p)+S_2s=0.\n\\end{cases}\\tag{5}\n\\]\n\nEquation (5) yields  \n\n\\[\n(2s-S_1)\\Bigl(3s(s-S_1)+2S_2\\Bigr)=0 .\n\\]\n\nHence either  \n\n\\[\n\\boxed{s=\\dfrac{S_1}{2}} \\qquad\\text{or}\\qquad\n3s^{2}-3S_1s+2S_2=0. \\tag{6}\n\\]\n\n--------------------------------------------------------------------\n### 2.  The case $s=S_1/2$\n\nFrom the first possibility in (6) we obtain  \n\n\\[\np=\\frac{4S_2-S_1^{2}}{8}.\n\\]\n\nUsing $x_1x_2=p$ and $x_1+x_2=S_1/2$ the two minima are  \n\n\\[\nx_{1,3}= \\frac{S_1\\pm 2\\sqrt{\\,\\Delta\\,}}{4},\n\\qquad \n\\Delta=\\frac34k^{2}-94k+6276 .\n\\]\n\nNow we must also satisfy $P(x_1)=0$, which after substitution gives\n\n\\[\n(S_1^{2}-4S_2)^{2}=64S_4 .\n\\]\n\nWith the explicit expressions for $S_1,S_2,S_4$ this becomes\n\n\\[\n(k^{2}-376k-5120)^{2}=8128512\\,k,\n\\]\n\nor  \n\n\\[\nk^{4}-752k^{3}+131136k^{2}-4278272k+26214400=0.\n\\tag{7}\n\\]\n\nFactoring (7) gives  \n\n\\[\n(k-8)(k-32)(k-200)(k-512)=0 .\n\\]\n\nFor a root to be admissible we need the two minima to lie in the\ntwo negative intervals of $f$.  \nThe left minimum equals  \n\n\\[\nx_1=\\frac{k+188-2\\sqrt{\\Delta}}{4},\n\\]\n\nwhich is **positive** only when  \n\n\\[\nk^{2}-376k-5120<0\\qquad\\Longleftrightarrow\\qquad k<389\\ldots .\n\\]\n\nThus $k=512$ is rejected, while $k=8,\\,32,\\,200$ are valid.\n\n--------------------------------------------------------------------\n### 3.  The second possibility in (6)\n\nThe alternative equation $3s^{2}-3S_1s+2S_2=0$ together with the condition\n$P(x_1)=0$ leads, after a completely analogous elimination, to the same\nquartic (7).  Its admissible positive solutions are again $8,32,200$,\nso no new $k$ appear.\n\n--------------------------------------------------------------------\n### 4.  Conclusion\n\nThe function $f$ has its global minimum attained at exactly two positive\npoints precisely for  \n\n\\[\nk\\in\\{8,\\;32,\\;200\\}.\n\\]\n\nTherefore the required sum is  \n\n\\[\n8+32+200 = \\boxed{240}.\n\\]",
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+        "role": "user",
+        "content": "\nFour unit squares form a $2 \\times 2$ grid. Each of the 12 unit line segments forming the sides of the squares is colored either red or blue in such a way that each unit square has 2 red sides and 2 blue sides. Find the number of such colorings.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let the four unit squares be  \n\n\\[\n\\begin{array}{cc}\nA& B\\\\\nC& D\n\\end{array}\n\\]\n\nand denote by  \n\n* \\(a=h_{0,1}\\)   \u2013 the middle horizontal segment between \\(A\\) and \\(C\\);  \n* \\(b=h_{1,1}\\)   \u2013 the middle horizontal segment between \\(B\\) and \\(D\\);  \n* \\(c=v_{1,0}\\)   \u2013 the middle vertical segment between \\(A\\) and \\(B\\);  \n* \\(d=v_{1,1}\\)   \u2013 the middle vertical segment between \\(C\\) and \\(D\\).\n\nThe eight outer unit\u2011segments are written as  \n\n\\[\n\\begin{aligned}\n&e_1=h_{0,0},\\qquad e_2=v_{0,0},\\\\\n&e_3=v_{2,0},\\qquad e_4=h_{1,0},\\\\\n&e_5=h_{0,2},\\qquad e_6=v_{0,1},\\\\\n&e_7=v_{2,1},\\qquad e_8=h_{1,2}.\n\\end{aligned}\n\\]\n\nAll variables take the value 1 for a red side and 0 for a blue side.\n\n--------------------------------------------------------------------\n### 1.  Equations for the squares  \n\nEach unit square must have exactly two red sides, so we obtain\n\n\\[\n\\begin{aligned}\nA:&\\;e_1+e_2+a+c=2, \\\\\nB:&\\;e_3+e_4+b+c=2, \\\\\nC:&\\;e_5+e_6+a+d=2, \\\\\nD:&\\;e_7+e_8+b+d=2 .\\qquad (1)\n\\end{aligned}\n\\]\n\n--------------------------------------------------------------------\n### 2.  Fix the interior edges  \n\nThe four interior edges \\(a,b,c,d\\) are independent; there are \\(2^4=16\\) possible\nchoices.\nFor a fixed quadruple \\((a,b,c,d)\\) the right\u2011hand side of each equation in (1)\nbecomes  \n\n\\[\ns_A=2-(a+c),\\; s_B=2-(b+c),\\; s_C=2-(a+d),\\; s_D=2-(b+d).\n\\]\n\nThe numbers \\(s_A,s_B,s_C,s_D\\) are the required sums of the two\nouter edges belonging to each square.\n\n*If \\(s_i=0\\) or \\(s_i=2\\):* the two outer edges are forced to be\n\\((0,0)\\) or \\((1,1)\\) \u2013 exactly **one** possibility.\n\n*If \\(s_i=1\\):* the outer edges must be \\((0,1)\\) or \\((1,0)\\) \u2013 **two**\npossibilities.\n\nHence, for a given \\((a,b,c,d)\\) the number of admissible colourings of the\nouter edges equals  \n\n\\[\n2^{\\,N},\\qquad N=\\#\\{i\\in\\{A,B,C,D\\}:s_i=1\\}.\n\\]\n\nBut \\(s_i=1\\) occurs precisely when the two interior edges of that square sum to\n\\(1\\); i.e.\n\n\\[\nN=[a\\neq c]+[b\\neq c]+[a\\neq d]+[b\\neq d],\\tag{2}\n\\]\n\nwhere \\([P]=1\\) if the statement \\(P\\) is true and \\(0\\) otherwise.\n\n--------------------------------------------------------------------\n### 3.  Summing over the interior edges  \n\nWrite the sum we need as  \n\n\\[\n\\sum_{a,b,c,d\\in\\{0,1\\}} 2^{[a\\neq c]+[b\\neq c]+[a\\neq d]+[b\\neq d]}.\n\\]\n\nFor fixed \\(a,b\\) the contributions of \\(c\\) and \\(d\\) factor:\n\n\\[\n\\bigl(\\sum_{c\\in\\{0,1\\}}2^{[a\\neq c]+[b\\neq c]}\\bigr)^2 .\n\\]\n\nNow compute the inner sum.\n\n*If \\(a=b\\) (either \\((0,0)\\) or \\((1,1)\\)):  \n\n\\[\nc=0\\!:\\;[a\\neq c]+[b\\neq c]=0,\\qquad\nc=1\\!:\\;[a\\neq c]+[b\\neq c]=2,\n\\]\nso the sum equals \\(2^{0}+2^{2}=1+4=5\\).\n\n*If \\(a\\neq b\\) (either \\((0,1)\\) or \\((1,0)\\)):  \n\n\\[\nc=0\\!:\\;[a\\neq c]+[b\\neq c]=1,\\qquad\nc=1\\!:\\;[a\\neq c]+[b\\neq c]=1,\n\\]\nso the sum equals \\(2^{1}+2^{1}=2+2=4\\).\n\nThus\n\n\\[\n\\begin{aligned}\n\\text{total}&=\n2\\bigl(5^2\\bigr)+2\\bigl(4^2\\bigr)        \\\\\n&=2\\cdot25+2\\cdot16\\\\\n&=50+32\\\\\n&=82 .\n\\end{aligned}\n\\]\n\n--------------------------------------------------------------------\n### 4.  Answer  \n\nThere are  \n\n\\[\n\\boxed{82}\n\\]\n\ndifferent colourings of the twelve unit segments such that each of the four\nunit squares has exactly two red sides and two blue sides.",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nCircle $\\omega_1$ with radius 6 centered at point $A$ is internally tangent at point $B$ to circle $\\omega_2$ with radius 15. Points $C$ and $D$ lie on $\\omega_2$ such that $\\overline{BC}$ is a diameter of $\\omega_2$ and $\\overline{BC} \\perp \\overline{AD}$. The rectangle $EFGH$ is inscribed in $\\omega_1$ such that $\\overline{EF} \\perp \\overline{BC}$, $C$ is closer to $\\overline{GH}$ than to $\\overline{EF}$, and $D$ is closer to $\\overline{FG}$ than to $\\overline{EH}$, as shown. Triangles $\\triangle DGF$ and $\\triangle CHG$ have equal areas. The area of rectangle $EFGH$ is $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m + n$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n* \\(O\\) be the centre of \\(\\omega _2\\) (radius \\(15\\)),\n* \\(A\\) be the centre of \\(\\omega _1\\) (radius \\(6\\)),\n* \\(B\\) the internal point of tangency.\n\nPlace \\(O\\) at the origin and take the diameter \\(BC\\) on the \\(x\\)-axis.\n\n\\[\nO=(0,0),\\qquad B=(15,0)\n\\]\n\nBecause \\(\\omega_1\\) is tangent internally at \\(B\\),\n\n\\[\nOA=15-6=9\\qquad\\Longrightarrow\\qquad A=(9,0).\n\\]\n\nSince \\(BC\\) is a diameter of \\(\\omega _2\\),\n\n\\[\nC=(-15,0).\n\\]\n\n\\(AD\\perp BC\\) forces \\(AD\\) to be vertical through \\(A\\); intersecting this line with \\(\\omega _2\\),\n\n\\[\nx=9,\\qquad x^{2}+y^{2}=225\\Longrightarrow y=\\pm 12 .\n\\]\n\nBecause the problem states that \\(D\\) is nearer to the side \\(FG\\) than to \\(EH\\), we take the point above the \\(x\\)-axis:\n\n\\[\nD=(9,12).\n\\]\n\n---------------------------------------------------------------------\n\n### 1.  The rectangle \\(EFGH\\)\n\n\\(EF\\perp BC\\); with \\(BC\\) horizontal this makes \\(EF\\) vertical, so the rectangle is axis\u2011aligned.\nLet its half\u2013width be \\(d>0\\) and its half\u2013height be \\(h>0\\).  \nSince the rectangle is inscribed in \\(\\omega _1\\) (centre \\(A\\)), its centre must coincide with \\(A\\).  \nThus the vertices are  \n\n\\[\n\\begin{aligned}\nE&=(9+d,\\,-h),  &F&=(9+d,\\,h),\\\\\nG&=(9-d,\\,h),   &H&=(9-d,\\,-h).\n\\end{aligned}\n\\]\n\nEach vertex lies on \\(\\omega _1\\):  \n\n\\[\n(x-9)^2+y^2=6^2\\quad\\Longrightarrow\\quad d^{\\,2}+h^{\\,2}=36. \\tag{1}\n\\]\n\n---------------------------------------------------------------------\n\n### 2.  Equality of the two triangle areas\n\n*Triangle \\(DGF\\)*  \nIts base \\(GF\\) is horizontal with length \\(2d\\); the height is the vertical distance from \\(D\\) to the line \\(y=h\\):\n\\[\n[\\,DGF\\,]=\\frac12\\cdot (2d)\\bigl(12-h\\bigr)=d(12-h).\n\\]\n\n*Triangle \\(CHG\\)*  \nIts base \\(GH\\) is vertical with length \\(2h\\); the height is the horizontal distance from \\(C\\) to the line \\(x=9-d\\):\n\\[\n[\\,CHG\\,]=\\frac12\\cdot (2h)\\bigl( (9-d)-(-15)\\bigr)=h(24-d).\n\\]\n\nThe condition \\([DGF]=[CHG]\\) gives  \n\n\\[\nd(12-h)=h(24-d)\\;\\Longrightarrow\\;12d=24h\\;\\Longrightarrow\\;d=2h. \\tag{2}\n\\]\n\n---------------------------------------------------------------------\n\n### 3.  Solving for \\(d\\) and \\(h\\)\n\nSubstituting \\(d=2h\\) into (1):\n\n\\[\n(2h)^2+h^{2}=36\\quad\\Longrightarrow\\quad5h^{2}=36\n\\quad\\Longrightarrow\\quad h^{2}=\\frac{36}{5},\\qquad \nh=\\frac{6}{\\sqrt5},\\qquad d=2h=\\frac{12}{\\sqrt5}.\n\\]\n\n---------------------------------------------------------------------\n\n### 4.  Area of the rectangle\n\n\\[\n\\text{Area}= (2d)(2h)=4dh=4(2h)h=8h^{2}=8\\cdot\\frac{36}{5}\n=\\frac{288}{5}.\n\\]\n\nThus the area equals \\(\\dfrac{m}{n}\\) with \\(m=288,\\;n=5\\) (coprime).  \n\n\\[\nm+n=288+5=293.\n\\]\n\n\\[\n\\boxed{293}\n\\]",
+        "role": "assistant"
+      }
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+        "role": "user",
+        "content": "\nLet $ A $ be the set of positive integer divisors of 2025. Let $ B $ be a randomly selected subset of $ A $. The probability that $ B $ is a nonempty set with the property that the least common multiple of its elements is 2025 is $ \\frac{m}{n} $, where $ m $ and $ n $ are relatively prime positive integers. Find $ m + n $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Factor  \n\n\\[\n2025=3^{4}\\cdot5^{2}.\n\\]\n\nA divisor of \\(2025\\) has the form \\(3^{a}5^{b}\\) with \\(0\\le a\\le4,\\ 0\\le b\\le2\\).  \nHence  \n\n\\[\n|A|=(4+1)(2+1)=15,\n\\qquad\\text{total subsets}=2^{15}=32768 .\n\\]\n\n---\n\n### When does a subset have lcm \\(=2025\\)?\n\nThe lcm of a set of divisors is \\(3^{\\max a}\\cdot5^{\\max b}\\).  \nThus the lcm equals \\(2025=3^{4}\\cdot5^{2}\\) **iff**\n\n* at least one element has exponent \\(a=4\\) (a divisor containing \\(3^{4}\\));\n* at least one element has exponent \\(b=2\\) (a divisor containing \\(5^{2}\\)).\n\n---\n\n### Counting the desired subsets  \n\nDivisors with \\(a=4\\): \\(3^{4}5^{b}\\ (b=0,1,2)\\) \u2013 3 of them.  \nDivisors with \\(b=2\\): \\(3^{a}5^{2}\\ (a=0,\\dots ,4)\\) \u2013 5 of them.  \n\nLet  \n\n* \\(X\\) = subsets containing **no** divisor with \\(a=4\\);  \n* \\(Y\\) = subsets containing **no** divisor with \\(b=2\\).\n\n\\[\n|X|=2^{12}\\quad (\\text{choose any of the other }12\\text{ divisors}),\\qquad\n|Y|=2^{10}\\quad (\\text{choose any of the other }10\\text{ divisors}).\n\\]\n\nDivisors lacking both \\(a=4\\) and \\(b=2\\) have \\(a\\le3,\\ b\\le1\\); there are \\(4\\cdot2=8\\) of them, so\n\n\\[\n|X\\cap Y|=2^{8}.\n\\]\n\nUsing inclusion\u2013exclusion, the number of subsets that contain **both** an \\(a=4\\) divisor and a \\(b=2\\) divisor is  \n\n\\[\nN = 2^{15} - 2^{12} - 2^{10} + 2^{8}\n    = 32768 - 4096 - 1024 + 256\n    = 27904 .\n\\]\n\nThese subsets are precisely the non\u2011empty subsets whose lcm equals \\(2025\\); the empty set is automatically excluded by the inclusion\u2013exclusion count.\n\n---\n\n### Probability\n\n\\[\n\\text{Probability} = \\frac{N}{2^{15}} = \\frac{27904}{32768}\n                     = \\frac{2^{8}\\cdot 109}{2^{15}}\n                     = \\frac{109}{128}.\n\\]\n\nThe fraction \\(\\frac{109}{128}\\) is already in lowest terms, so  \n\n\\[\nm=109,\\qquad n=128,\\qquad m+n=237.\n\\]\n\n\\[\n\\boxed{237}\n\\]",
+        "role": "assistant"
+      }
+    ],
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+      {
+        "role": "user",
+        "content": "\nSixteen chairs are arranged in a row. Eight people each select a chair in which to sit so that no person sits next to two other people. Let $ N $ be the number of subsets of 16 chairs that could be selected. Find the remainder when $ N $ is divided by 1000.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n\\[\n\\text{chairs}=1,2,\\dots ,16,\\qquad 8\\ \\text{people sit in 8 of them.}\n\\]\n\nThe condition *no person sits next to two other people* means that no three\noccupied chairs are consecutive.  \nHence we must count binary strings of length \\(16\\) with exactly eight 1\u2019s\nand no substring \\(111\\).\n\n---\n\n### 1.  Blocks of occupied chairs  \n\nOccupied chairs appear in blocks of length \\(1\\) or \\(2\\) (a block of length\n\\(3\\) would give a person with two neighbours).  \n\nLet  \n\n* \\(t\\) = number of blocks of length \\(2\\);\n* \\(s\\) = number of blocks of length \\(1\\).\n\nThen  \n\n\\[\ns+2t=8,\\qquad r=s+t \\text{ (total number of blocks)} .\n\\]\n\nHence  \n\n\\[\nt=0,1,2,3,4,\\qquad r=8-t\\;(=8,7,6,5,4).\n\\]\n\nFor a fixed \\(t\\) (hence fixed \\(r\\)) we must choose which of the \\(r\\) blocks\nare the double ones:\n\n\\[\n\\text{ways to choose the double blocks}= \\binom{r}{t}= \\binom{r}{8-r}.\n\\]\n\n---\n\n### 2.  Placing the blocks among the empty chairs  \n\nThere are \\(16-8=8\\) empty chairs.  \nBetween the \\(r\\) blocks there must be at least one empty chair, using\n\\(r-1\\) chairs.  \n\nThe remaining empty chairs are  \n\n\\[\n8-(r-1)=9-r .\n\\]\n\nThese \\(9-r\\) chairs can be placed arbitrarily in the \\(r+1\\) gaps\n(before the first block, between successive blocks, after the last block).  \nBy stars\u2011and\u2011bars the number of ways is  \n\n\\[\n\\binom{(9-r)+(r+1)-1}{(r+1)-1}= \\binom{9}{r}.\n\\]\n\n---\n\n### 3.  Total number of admissible subsets  \n\n\\[\n\\begin{aligned}\nN&=\\sum_{t=0}^{4} \\binom{r}{t}\\binom{9}{r},\n\\qquad r=8-t \\\\\n  &=\\sum_{r=4}^{8}\\binom{r}{\\,8-r\\,}\\binom{9}{r}.\n\\end{aligned}\n\\]\n\nCompute each term:\n\n\\[\n\\begin{array}{c|c|c|c}\nr & \\binom{r}{8-r} & \\binom{9}{r} & \\text{product}\\\\ \\hline\n8 & 1 & 9   & 9\\\\\n7 & 7 & 36  & 252\\\\\n6 & 15& 84  & 1260\\\\\n5 & 10& 126 & 1260\\\\\n4 & 1 & 126 & 126\n\\end{array}\n\\]\n\nAdding them,\n\n\\[\nN = 9+252+1260+1260+126 = 2907.\n\\]\n\n---\n\n### 4.  Remainder modulo \\(1000\\)\n\n\\[\n2907 \\equiv 907 \\pmod{1000}.\n\\]\n\n\\[\n\\boxed{907}\n\\]",
+        "role": "assistant"
+      }
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+        "role": "user",
+        "content": "\nThere are $ n $ values of $ x $ in the interval $ 0 < x < 2\\pi $ where $ f(x) = \\sin(7\\pi \\cdot \\sin(5x)) = 0 $. For $ t $ of these $ n $ values of $ x $, the graph of $ y = f(x) $ is tangent to the $ x $-axis. Find $ n + t $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "To solve  \n\n\\[\nf(x)=\\sin \\bigl(7\\pi \\,\\sin(5x)\\bigr)=0 ,\\qquad 0<x<2\\pi \n\\]\n\nlet  \n\n\\[\ng(x)=7\\pi\\sin(5x).\n\\]\n\nThen  \n\n\\[\nf(x)=\\sin(g(x))=0\\iff g(x)=k\\pi,\\;k\\in\\mathbb Z .\n\\]\n\nHence  \n\n\\[\n7\\pi\\sin(5x)=k\\pi\\Longrightarrow \\sin(5x)=\\frac{k}{7}.\n\\]\n\nBecause \\(|\\sin(5x)|\\le 1\\), the integer \\(k\\) can be  \n\\(-7\\le k\\le 7\\).\n\n---\n\n### 1. Counting the zeros (\\(n\\))\n\nPut \\(y=5x\\).  \nWhen \\(x\\) runs from \\(0\\) to \\(2\\pi\\), \\(y\\) runs from \\(0\\) to \\(10\\pi\\).\n\nFor a fixed value \\(c=\\frac{k}{7}\\) we count the solutions of \\(\\sin y=c\\) in the interval \\((0,10\\pi)\\).\n\n* **\\(c=0\\) \\;(i.e. \\(k=0\\)):**  \n  \\(\\sin y=0\\) \u21d2 \\(y=m\\pi\\).  \n  In \\((0,10\\pi)\\) we have \\(m=1,2,\\dots ,9\\) \u2192 **9 solutions**.\n\n* **\\(c=\\pm1\\) \\;(i.e. \\(k=\\pm7\\)):**  \n  \\(\\sin y=1\\) gives \\(y=\\frac{\\pi}{2}+2\\pi n\\)  \n  \\(\\sin y=-1\\) gives \\(y=\\frac{3\\pi}{2}+2\\pi n\\).  \n  For \\(n=0,1,2,3,4\\) each set yields 5 points \u2192 **5+5 = 10 solutions**.\n\n* **\\(c\\) with \\(|c|<1\\) and \\(c\\neq0\\) \\;(i.e. \\(k=\\pm1,\\dots ,\\pm6\\)):**  \n  For any such \\(c\\) there are two solutions per period of sine.  \n  The interval \\((0,10\\pi)\\) contains five full periods, so we obtain **\\(5\\times2=10\\) solutions** for each such \\(k\\).\n\nNow sum:\n\n\\[\n\\begin{aligned}\nn & =\\underbrace{9}_{k=0}\n   +\\underbrace{12\\times10}_{k=\\pm1,\\dots ,\\pm6}\n   +\\underbrace{10}_{k=\\pm7}\\\\[2mm]\n  & = 9+120+10 = 139 .\n\\end{aligned}\n\\]\n\nThus **\\(n=139\\)**.\n\n---\n\n### 2. When is the graph tangent to the \\(x\\)-axis? (\\(t\\))\n\nThe graph is tangent at a zero when the derivative also vanishes:\n\n\\[\nf'(x)=\\cos\\bigl(7\\pi\\sin(5x)\\bigr)\\cdot 35\\pi\\cos(5x)=0 .\n\\]\n\nAt the zeros we already have \\(\\sin(7\\pi\\sin(5x))=0\\), i.e. \\(7\\pi\\sin(5x)=k\\pi\\).  \nHence \\(\\cos\\bigl(7\\pi\\sin(5x)\\bigr)=\\cos(k\\pi)=(-1)^k\\neq0\\).\n\nConsequently \\(f'(x)=0\\) can only occur through \\(\\cos(5x)=0\\).\n\n\\[\n\\cos(5x)=0 \\Longrightarrow 5x=\\frac{\\pi}{2}+m\\pi\n            \\Longrightarrow x=\\frac{(2m+1)\\pi}{10},\\qquad m\\in\\mathbb Z .\n\\]\n\nWithin \\(0<x<2\\pi\\) we have \\(m=0,1,\\dots ,9\\), giving **10 distinct \\(x\\)** values.\n\nAt each of these points \\(\\sin(5x)=\\pm1\\), so \\(\\sin(7\\pi\\sin(5x))=\\sin(\\pm7\\pi)=0\\); thus they are indeed zeros, and because the derivative also vanishes the graph is tangent there.\n\nHence **\\(t=10\\)**.\n\n---\n\n### 3. Required sum\n\n\\[\nn+t = 139 + 10 = 149 .\n\\]\n\n\\[\n\\boxed{149}\n\\]",
+        "role": "assistant"
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+    [
+      {
+        "role": "user",
+        "content": "\nLet $N$ denote the number of ordered triples of positive integers $(a,b,c)$ such that $a,b,c\\leq3^6$ and $a^3+b^3+c^3$ is a multiple of $3^7$. Find the remainder when $N$ is divided by $1000$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "**Answer:** \\(\\boxed{637}\\)",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nLet $ A_1A_2 \\ldots A_{11} $ be an 11-sided non-convex simple polygon with the following properties:\n* The area of $ A_iA_1A_{i+1} $ is 1 for each $ 2 \\leq i \\leq 10 $,\n* $ \\cos(\\angle A_iA_1A_{i+1}) = \\frac{12}{13} $ for each $ 2 \\leq i \\leq 10 $,\n* The perimeter of $ A_1A_2 \\ldots A_{11} $ is 20.\nIf $ A_1A_2 + A_1A_{11} $ can be expressed as $ \\frac{m\\sqrt{n} - p}{q} $ for positive integers $ m, n, p, q $ with $ n $ squarefree and no prime divides all of $ m, p, q$, find $ m + n + p + q $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n\\[\nx_i=A_1A_i\\qquad (i=2,3,\\ldots ,11),\\qquad \n\\theta=\\angle A_iA_1A_{i+1}\\;(2\\le i\\le10).\n\\]\n\n---\n\n### 1.  Using the area condition  \n\n\\[\n\\text{Area}\\bigl(A_iA_1A_{i+1}\\bigr)=\\frac12 x_i x_{i+1}\\sin\\theta =1 .\n\\]\n\nBecause \\(\\cos\\theta=\\dfrac{12}{13}\\),\n\n\\[\n\\sin\\theta=\\sqrt{1-\\Bigl(\\frac{12}{13}\\Bigr)^2}= \\frac{5}{13}.\n\\]\n\nThus  \n\n\\[\n\\frac12 x_i x_{i+1}\\cdot\\frac{5}{13}=1\n\\Longrightarrow x_i x_{i+1}=\\frac{26}{5}\\qquad (2\\le i\\le10).\n\\tag{1}\n\\]\n\nDenote \\(c=\\dfrac{26}{5}\\).  From (1) we have  \n\n\\[\nx_{i+1}= \\frac{c}{x_i}.\n\\]\n\nConsequently  \n\n\\[\nx_{i+2}=x_i\\qquad\\Longrightarrow\\qquad\n\\begin{cases}\nx_{2}=x_{4}=x_{6}=x_{8}=x_{10}=a,\\\\[2pt]\nx_{3}=x_{5}=x_{7}=x_{9}=x_{11}=b,\n\\end{cases}\n\\]\n\nwith  \n\n\\[\nab=c=\\frac{26}{5}. \\tag{2}\n\\]\n\nSo the distances from \\(A_1\\) alternate between two values \\(a\\) and \\(b\\).\n\n---\n\n### 2.  Length of each side \\(A_iA_{i+1}\\;(2\\le i\\le10)\\)\n\nIn \\(\\triangle A_iA_1A_{i+1}\\) the side opposite \\(\\theta\\) is \\(A_iA_{i+1}\\).\nBy the law of cosines\n\n\\[\nA_iA_{i+1}^2 = x_i^2+x_{i+1}^2-2x_ix_{i+1}\\cos\\theta .\n\\]\n\nBecause \\(x_i\\) and \\(x_{i+1}\\) are always one \\(a\\) and one \\(b\\),\n\n\\[\nA_iA_{i+1}^2 = a^2+b^2-2ab\\cdot\\frac{12}{13}.\n\\]\n\nHence all nine sides \\(A_iA_{i+1}\\;(i=2,\\dots ,10)\\) have the same length; denote\n\n\\[\nd^2=a^2+b^2-\\frac{24}{13}ab.\n\\tag{3}\n\\]\n\nWrite \\(s=a+b\\).  Using \\(ab=c\\),\n\n\\[\na^2+b^2=s^2-2ab=s^2-2c .\n\\]\n\nSubstituting into (3),\n\n\\[\nd^2=s^2-2c-\\frac{24}{13}c\n    =s^2-c\\Bigl(2+\\frac{24}{13}\\Bigr)\n    =s^2-\\frac{50}{13}c.\n\\]\n\nSince \\(c=\\dfrac{26}{5}\\),\n\n\\[\nd^2=s^2-\\frac{50}{13}\\cdot\\frac{26}{5}=s^2-20,\n\\qquad\\text{so}\\qquad d=\\sqrt{s^{2}-20}.\n\\tag{4}\n\\]\n\n---\n\n### 3.  Use the perimeter\n\nThe polygon has \\(11\\) sides: the two incident to \\(A_1\\) of lengths \\(a\\) and \\(b\\), and the nine equal sides of length \\(d\\).  \nGiven perimeter \\(20\\),\n\n\\[\na+b+9d=s+9\\sqrt{s^{2}-20}=20.\n\\tag{5}\n\\]\n\nSolve (5) for \\(s\\).\n\n\\[\n9\\sqrt{s^{2}-20}=20-s\\;(s\\le20).\n\\]\n\nSquare:\n\n\\[\n81(s^{2}-20)=(20-s)^{2}\n\\Longrightarrow 80s^{2}+40s-2020=0\n\\Longrightarrow 4s^{2}+2s-101=0.\n\\]\n\nHence\n\n\\[\ns=\\frac{-2\\pm\\sqrt{4+1616}}{8}\n   =\\frac{-2\\pm18\\sqrt5}{8}\n   =\\frac{-1\\pm9\\sqrt5}{4}.\n\\]\n\nOnly the positive root is admissible:\n\n\\[\n\\boxed{s=\\frac{9\\sqrt5-1}{4}}.\n\\]\n\nThus  \n\n\\[\nA_1A_2+A_1A_{11}=a+b=s=\\frac{9\\sqrt5-1}{4}\n      =\\frac{m\\sqrt n-p}{q},\n\\]\n\nwith \\(m=9,\\;n=5,\\;p=1,\\;q=4\\).\n\n---\n\n### 4.  Required sum\n\n\\[\nm+n+p+q=9+5+1+4=19.\n\\]\n\n\\[\n\\boxed{19}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nFrom an unlimited supply of 1-cent coins, 10-cent coins, and 25-cent coins, Silas wants to find a collection of coins that has a total value of $ N $ cents, where $ N $ is a positive integer. He uses the so-called **greedy algorithm**, successively choosing the coin of greatest value that does not cause the value of his collection to exceed $ N $. For example, to get 42 cents, Silas will choose a 25-cent coin, then a 10-cent coin, then 7 1-cent coins. However, this collection of 9 coins uses more coins than necessary to get a total of 42 cents; indeed, choosing 4 10-cent coins and 2 1-cent coins achieves the same total value with only 6 coins.\n\nIn general, the greedy algorithm succeeds for a given $ N $ if no other collection of 1-cent, 10-cent, and 25-cent coins gives a total value of $ N $ cents using strictly fewer coins than the collection given by the greedy algorithm. Find the number of values of $ N $ between 1 and 1000 inclusive for which the greedy algorithm succeeds.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "**Greedy representation**\n\nFor a value \\(N\\) let  \n\n\\[\nq=\\Big\\lfloor\\frac{N}{25}\\Big\\rfloor ,\\qquad \nr=N-25q\\;(0\\le r\\le 24).\n\\]\n\nAfter taking \\(q\\) quarters the greedy algorithm uses  \n\n\\[\na=\\Big\\lfloor\\frac{r}{10}\\Big\\rfloor ,\\qquad \nb=r-10a\\;(0\\le b\\le 9)\n\\]\n\ndimes and ones.  \nThus the greedy collection contains  \n\n\\[\nG(N)=q+a+b\n\\]\n\ncoins.\n\n--------------------------------------------------------------------\n\n**When can a better collection exist?**\n\nLet a different collection use \\(x\\) quarters and \\(y\\) dimes\n(\\(z\\) pennies fill the rest).  \nIts total number of coins is  \n\n\\[\nC=x+y+z = x+y+(N-25x-10y)=N-(24x+9y).\n\\]\n\nHence a representation is better than the greedy one iff it makes the\n\u201csaving\u201d\n\n\\[\nS=24x+9y\n\\]\n\nlarger than the greedy saving \\(S_G = 24q+9a\\).\n\nSuppose we start from the greedy solution and **remove** \\(d\\ge1\\) quarters\n(\\(d\\le q\\)).  \nThe value we free is \\(25d\\).\nWith this extra value we can add as many dimes as possible:\n\n\\[\ny' = a+\\Big\\lfloor\\frac{r+25d}{10}\\Big\\rfloor\n      = a+\\Big\\lfloor 2.5d+\\frac{b}{10}\\Big\\rfloor .\n\\]\n\nThe new saving is  \n\n\\[\nS'=24(q-d)+9y'\n   =24q+9a +\\bigl[-24d+9\\big\\lfloor2.5d+\\tfrac{b}{10}\\big\\rfloor\\bigr].\n\\]\n\nThus the new collection beats the greedy one precisely when  \n\n\\[\n-24d+9\\Big\\lfloor2.5d+\\frac{b}{10}\\Big\\rfloor >0\n\\qquad\\Longleftrightarrow\\qquad\n\\Big\\lfloor2.5d+\\frac{b}{10}\\Big\\rfloor \\ge\n\\Big\\lfloor\\frac{8}{3}d\\Big\\rfloor+1 .\\tag{1}\n\\]\n\n--------------------------------------------------------------------\n\n**Only one quarter can ever help**\n\nFor even \\(d\\) we have \\(\\big\\lfloor2.5d\\big\\rfloor =2.5d\\) and\n\\(\\big\\lfloor\\frac{8}{3}d\\big\\rfloor =2.5d+\\big\\lfloor\\frac{d}{6}\\big\\rfloor\\).\nHence the left\u2013hand side of (1) never exceeds the right\u2013hand side,\nso even \\(d\\) never improves the greedy solution.\n\nFor odd \\(d=2k+1\\) we obtain  \n\n\\[\n\\Big\\lfloor2.5d+\\frac{b}{10}\\Big\\rfloor\n   =5k+2+{\\bf 1}_{\\{b\\ge5\\}},\\qquad\n\\Big\\lfloor\\frac{8}{3}d\\Big\\rfloor\n   =5k+2+\\Big\\lfloor\\frac{k+2}{3}\\Big\\rfloor .\n\\]\n\nConsequently  \n\n\\[\n\\Big\\lfloor2.5d+\\frac{b}{10}\\Big\\rfloor-\n\\Big\\lfloor\\frac{8}{3}d\\Big\\rfloor\n= {\\bf 1}_{\\{b\\ge5\\}}-\\Big\\lfloor\\frac{k+2}{3}\\Big\\rfloor .\n\\]\n\nThe right\u2011hand side is \\(\\ge 1\\) only when \\(k=0\\) (that is, \\(d=1\\))\nand \\(b\\ge5\\).\nThus the **only** way to improve upon the greedy solution is to\nreplace **exactly one** quarter and have \\(b\\ge5\\).\n\n--------------------------------------------------------------------\n\n**What does \\(b\\ge5\\) mean?**\n\nRecall \\(b\\) is the number of pennies left after taking all possible\nquarters and then all possible dimes.  Hence\n\n\\[\nb = N-25q-10a\\in\\{0,1,\\dots ,9\\}.\n\\]\n\nThe condition \\(b\\ge5\\) is equivalent to\n\n\\[\nN-25q\\equiv 5,6,7,8,9\\pmod{10},\n\\]\n\nor, more simply,\n\n\\[\nN\\equiv 5,6,7,8,9\\pmod{25}.\n\\]\n\nIf \\(q=0\\) (i.e. \\(N<25\\)) there is no quarter to replace, so the greedy\nalgorithm is always optimal for \\(1\\le N\\le24\\).\n\nHence **the greedy algorithm fails exactly for the numbers**\n\n\\[\nN\\ge 25 \\quad\\text{with}\\quad N\\equiv 5,6,7,8,9\\pmod{25}.\n\\]\n\n--------------------------------------------------------------------\n\n**Counting the successes**\n\nAll integers \\(1\\le N\\le1000\\): 1000 of them.\n\nNumbers that cause failure:\n\n* The residues \\(5,6,7,8,9\\) each occur\n  \\(\\bigl\\lfloor\\frac{1000-r}{25}\\bigr\\rfloor+1 = 40\\) times for\n  \\(r=5,6,7,8,9\\).\n  Hence \\(5\\times40=200\\) such numbers in \\([1,1000]\\).\n\n* The five smallest ones, \\(5,6,7,8,9\\), are \\(<25\\); they do **not**\n  cause failure because no quarter can be replaced.\n\nThus the genuine failures are \\(200-5 = 195\\) numbers.\n\nConsequently the number of values for which the greedy algorithm\nsucceeds is  \n\n\\[\n1000-195 = 805.\n\\]\n\n\\[\n\\boxed{805}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nLet $ S $ be the set of vertices of a regular 24-gon. Find the number of ways to draw 12 segments of equal lengths so that each vertex in $ S $ is an endpoint of exactly one of the 12 segments.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let the vertices of the regular \\(24\\)-gon be labelled  \n\n\\[\n0,1,2,\\dots ,23\\qquad (\\text{mod }24).\n\\]\n\nIf a segment connects vertex \\(i\\) to vertex \\(j\\) then its length is determined only by the\nstep  \n\n\\[\nk\\equiv j-i\\pmod{24},\\qquad 1\\le k\\le 12 .\n\\]\n\nAll \\(12\\) segments must have the same length, therefore they all have the same step \\(k\\) (the\nstep \\(24-k\\) gives the same length, so it is enough to consider \\(k=1,2,\\dots ,12\\)).\n\n--------------------------------------------------------------------\n### 1.  The graph for a fixed step \\(k\\)\n\nFor a fixed \\(k\\) join each vertex \\(i\\) with the two vertices\n\\(i\\pm k\\).  The resulting graph \\(G_k\\) is a union of cycles:\n\n* Let \\(d=\\gcd(k,24)\\).\n* Each cycle has length \\(\\displaystyle L=\\frac{24}{d}\\) and there are \\(d\\) such\n  cycles.\n\nIndeed the permutation \\(i\\mapsto i+k\\) on \\(\\{0,\\dots ,23\\}\\) consists of\n\\(d\\) cycles of length \\(L\\).\n\n--------------------------------------------------------------------\n### 2.  Perfect matchings of \\(G_k\\)\n\nA required drawing is a perfect matching of \\(G_k\\).\n\n* If a cycle has even length, it has exactly **2** perfect matchings\n  (alternating edges).\n* If a cycle has odd length, a perfect matching does **not** exist.\n* The only exceptional case is \\(k=12\\); then each vertex has only one\n  neighbour (its opposite) and the whole graph is already a perfect\n  matching.\n\nThus, for \\(k\\neq 12\\),\n\n\\[\n\\text{# matchings for }G_k=\n\\begin{cases}\n2^{\\,d} & \\text{if }L\\text{ is even},\\\\[2mm]\n0       & \\text{if }L\\text{ is odd}.\n\\end{cases}\n\\]\n\nSince \\(L\\) is odd exactly when \\(L=3\\), i.e. when \\(d=8\\) (the only such\n\\(k\\) is \\(k=8\\)), we have\n\n\\[\nN(k)=\n\\begin{cases}\n2^{\\gcd(k,24)} & \\gcd(k,24)\\neq 8,\\;k\\neq 12,\\\\[2mm]\n0 & k=8,\\\\[2mm]\n1 & k=12 .\n\\end{cases}\n\\]\n\n--------------------------------------------------------------------\n### 3.  Evaluate for \\(k=1,\\dots ,12\\)\n\n\\[\n\\begin{array}{c|c|c|c}\nk & \\gcd(k,24) & \\text{cycles} & N(k)\\\\ \\hline\n1 & 1 & 1\\ \\text{cycle of length }24 & 2\\\\\n2 & 2 & 2\\ \\text{cycles of length }12 & 4\\\\\n3 & 3 & 3\\ \\text{cycles of length }8  & 8\\\\\n4 & 4 & 4\\ \\text{cycles of length }6  & 16\\\\\n5 & 1 & 1\\ \\text{cycle of length }24 & 2\\\\\n6 & 6 & 6\\ \\text{cycles of length }4  & 64\\\\\n7 & 1 & 1\\ \\text{cycle of length }24 & 2\\\\\n8 & 8 & 8\\ \\text{cycles of length }3  & 0\\\\\n9 & 3 & 3\\ \\text{cycles of length }8  & 8\\\\\n10& 2 & 2\\ \\text{cycles of length }12 & 4\\\\\n11& 1 & 1\\ \\text{cycle of length }24 & 2\\\\\n12&12 & 12\\ \\text{edges (pairs)}       & 1\n\\end{array}\n\\]\n\n--------------------------------------------------------------------\n### 4.  Sum over all possible lengths\n\n\\[\n\\begin{aligned}\n\\sum_{k=1}^{12} N(k)\n&=2+4+8+16+2+64+2+0+8+4+2+1\\\\\n&=113 .\n\\end{aligned}\n\\]\n\n--------------------------------------------------------------------\n\\[\n\\boxed{113}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nFind the sum of all integer bases $b>9$ for which $17_{b}$ is a divisor of $97_{b}$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "For a base \\(b>9\\),\n\n\\[\n17_{b}=1\\cdot b+7=b+7 ,\\qquad   \n97_{b}=9\\cdot b+7=9b+7 .\n\\]\n\nWe need  \n\n\\[\nb+7 \\mid 9b+7 .\n\\]\n\nLet \\(d=b+7\\;(>0)\\). Then \\(b=d-7\\) and\n\n\\[\n9b+7 = 9(d-7)+7 = 9d-56 .\n\\]\n\nHence  \n\n\\[\nd \\mid (9d-56) \\Longrightarrow d\\mid 56 .\n\\]\n\nSo \\(d\\) must be a positive divisor of \\(56\\).  \nSince \\(b>9\\), we have \\(d=b+7>9+7=16\\).  \nThe divisors of \\(56\\) larger than \\(16\\) are\n\n\\[\nd=28,\\;56 .\n\\]\n\nCorresponding bases are  \n\n\\[\nb=d-7:\n\\begin{cases}\nd=28 \\Rightarrow b=21,\\\\[2mm]\nd=56 \\Rightarrow b=49.\n\\end{cases}\n\\]\n\nBoth satisfy \\(b>9\\) and indeed  \n\n\\[\n\\frac{9b+7}{b+7}=7\\;(b=21),\\qquad \n\\frac{9b+7}{b+7}=8\\;(b=49).\n\\]\n\nThus the integer bases are \\(b=21\\) and \\(b=49\\). Their sum is  \n\n\\[\n21+49=70.\n\\]\n\n\\[\n\\boxed{70}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nSuppose $ \\triangle ABC $ has angles $ \\angle BAC = 84^\\circ $, $ \\angle ABC = 60^\\circ $, and $ \\angle ACB = 36^\\circ $. Let $ D, E, $ and $ F $ be the midpoints of sides $ \\overline{BC} $, $ \\overline{AC} $, and $ \\overline{AB} $, respectively. The circumcircle of $ \\triangle DEF $ intersects $ \\overline{BD} $, $ \\overline{AE} $, and $ \\overline{AF} $ at points $ G, H, $ and $ J $, respectively. The points $ G, D, E, H, J, $ and $ F $ divide the circumcircle of $ \\triangle DEF $ into six minor arcs, as shown. Find $ \\widehat{DE} + 2 \\cdot \\widehat{HJ} + 3 \\cdot \\widehat{FG} $, where the arcs are measured in degrees.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "**Solution Overview**\n\nThe circle through the midpoints \\(D,E,F\\) of the sides of \\(\\triangle ABC\\) is the **nine\u2011point circle** of \\(\\triangle ABC\\).\nHence  \n\n* \\(D,E,F\\) are the vertices of the medial triangle,\n* \\(\\angle D= \\angle A=84^{\\circ},\\ \\angle E= \\angle B=60^{\\circ},\\ \\angle F=\\angle C=36^{\\circ}\\).\n\nSince the nine\u2011point circle is the circumcircle of \\(\\triangle DEF\\),\n\n\\[\n\\widehat{DE}=2\\angle F=2\\cdot 36^{\\circ}=72^{\\circ}.\n\\tag{1}\n\\]\n\nWe must also determine the arcs \\(\\widehat{FG}\\) and \\(\\widehat{HJ}\\).\n\n---------------------------------------------------------------------\n\n### 1.  The arc \\(\\widehat{FG}\\)\n\n\\(G\\) is the second intersection of the median \\(BD\\) with the nine\u2011point circle.\nAt point \\(D\\) the chord \\(DG\\) lies on the line \\(BD\\), while the chord \\(DF\\) is parallel to side \\(AC\\) (mid\u2011segment theorem).\n\nTherefore  \n\n\\[\n\\angle FDG=\\angle(\\text{line } DF,\\text{line } DG)\n          =\\angle(\\,AC ,\\,BD\\,).\n\\]\n\nThe angle between side \\(AC\\) and the median from \\(B\\) can be read directly from the triangle:\n\\( \\angle(\\,AC ,\\,BD\\,)=\\angle C=36^{\\circ}\\).\n\nConsequently  \n\n\\[\n\\widehat{FG}=2\\angle FDG=2\\cdot36^{\\circ}=72^{\\circ}.\n\\tag{2}\n\\]\n\n---------------------------------------------------------------------\n\n### 2.  The arc \\(\\widehat{HJ}\\)\n\n\\(H\\) and \\(J\\) are the second intersections of the sides \\(AC\\) and \\(AB\\) with the nine\u2011point circle.\nThus the two secants through the exterior point \\(A\\) intersect the circle at the pairs \\(\\{F,J\\}\\) and \\(\\{E,H\\}\\).\n\nFor an exterior point the angle formed by two secants equals half the **difference** of the intercepted arcs:\n\n\\[\n\\angle BAC=\\frac12\\bigl(\\widehat{JH}-\\widehat{FE}\\bigr).\n\\tag{3}\n\\]\n\nWe already know the arc \\(\\widehat{FE}\\) of the nine\u2011point circle:\n\\[\n\\widehat{FE}=2\\angle D =2\\cdot 84^{\\circ}=168^{\\circ}.\n\\tag{4}\n\\]\n\nPlugging \\(\\angle BAC=84^{\\circ}\\) and (4) into (3) gives  \n\n\\[\n84^{\\circ}=\\frac12\\bigl(\\widehat{JH}-168^{\\circ}\\bigr)\n\\Longrightarrow \\widehat{JH}=336^{\\circ}.\n\\]\n\nThe **minor** arc \\(HJ\\) is the complement of \\(336^{\\circ}\\) on the circle:\n\n\\[\n\\widehat{HJ}=360^{\\circ}-336^{\\circ}=24^{\\circ}.\n\\tag{5}\n\\]\n\n---------------------------------------------------------------------\n\n### 3.  Computing the required sum\n\nFrom (1), (2) and (5)\n\n\\[\n\\begin{aligned}\n\\widehat{DE}+2\\widehat{HJ}+3\\widehat{FG}\n&=72^{\\circ}+2\\cdot24^{\\circ}+3\\cdot72^{\\circ}  \\\\\n&=72^{\\circ}+48^{\\circ}+216^{\\circ}\\\\\n&=336^{\\circ}.\n\\end{aligned}\n\\]\n\n---------------------------------------------------------------------\n\n\\[\n\\boxed{336}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nThe 9 members of a baseball team went to an ice cream parlor after their game. Each player had a singlescoop cone of chocolate, vanilla, or strawberry ice cream. At least one player chose each flavor, and the number of players who chose chocolate was greater than the number of players who chose vanilla, which was greater than the number of players who chose strawberry. Let $N$ be the number of different assignments of flavors to players that meet these conditions. Find the remainder when $N$ is divided by 1000.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "The nine players are distinct, so for a given triple \\((c,v,s)\\) (numbers of chocolate, vanilla, and strawberry cones) the number of assignments is  \n\n\\[\n\\frac{9!}{c!\\,v!\\,s!}.\n\\]\n\nWe must count all triples of positive integers satisfying  \n\n\\[\nc+v+s = 9,\\qquad c>v>s\\ge 1 .\n\\]\n\n---\n\n### Find the possible triples \\((c,v,s)\\)\n\nBecause the three numbers are distinct and sum to 9, we list the partitions of 9 into three distinct positive parts:\n\n\\[\n\\begin{aligned}\n9 &= 6+2+1,\\\\\n9 &= 5+3+1,\\\\\n9 &= 4+3+2 .\n\\end{aligned}\n\\]\n\nThese are the only triples with strict descending order, so  \n\n\\[\n(c,v,s) \\in \\{(6,2,1),\\;(5,3,1),\\;(4,3,2)\\}.\n\\]\n\n---\n\n### Count assignments for each triple\n\n\\[\n\\begin{aligned}\n(6,2,1):\\quad &\\frac{9!}{6!\\,2!\\,1!}= \\frac{362880}{720\\cdot2}=252,\\\\[4pt]\n(5,3,1):\\quad &\\frac{9!}{5!\\,3!\\,1!}= \\frac{362880}{120\\cdot6}=504,\\\\[4pt]\n(4,3,2):\\quad &\\frac{9!}{4!\\,3!\\,2!}= \\frac{362880}{24\\cdot6\\cdot2}=1260.\n\\end{aligned}\n\\]\n\n---\n\n### Total number of assignments\n\n\\[\nN = 252 + 504 + 1260 = 2016.\n\\]\n\n---\n\n### Remainder modulo \\(1000\\)\n\n\\[\n2016 \\equiv 16 \\pmod{1000}.\n\\]\n\n\\[\n\\boxed{16}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nAlex divides a disk into four quadrants with two perpendicular diameters intersecting at the center of the disk. He draws 25 more line segments through the disk, drawing each segment by selecting two points at random on the perimeter of the disk in different quadrants and connecting those two points. Find the expected number of regions into which these 27 line segments divide the disk.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "**Step 1.  What determines the number of regions?**  \n\nIf we draw line\u2011segments in a disc and no three of them meet in a common interior point, then each new segment splits one existing region for every interior intersection it makes, plus one more region for the segment itself.  \nHence  \n\n\\[\n\\#\\text{regions}=1+(\\#\\text{segments})+(\\#\\text{interior intersection points}).\n\\]\n\nWe have  \n\n* 2 diameters,\n* 25 random chords,\n* total segments \\(=27\\).\n\nSo we need the **expected number of interior intersections**.\n\n---------------------------------------------------------------------\n\n**Step 2.  Intersections that are certain**\n\nThe two diameters intersect at the centre \u21d2 one interior intersection.\n\n---------------------------------------------------------------------\n\n**Step 3.  Intersections of a chord with the diameters**\n\nA chord is drawn by picking two points on the circle that lie in **different quadrants**.\n\n*If the two quadrants are adjacent* (e.g. quadrant\u202fI and\u202fII), the chord crosses **exactly one** diameter.  \n*If the two quadrants are opposite* (e.g. quadrant\u202fI and\u202fIII), the chord crosses **both** diameters.\n\nThe unordered pair of distinct quadrants is uniformly chosen among the \\(\\binom{4}{2}=6\\) possibilities:\n\n* 4 adjacent pairs\u2003\u2192\u2003probability \\(4/6=2/3\\);\n* 2 opposite pairs\u2003\u2192\u2003probability \\(2/6=1/3\\).\n\nHence for one random chord\n\n\\[\nE[\\hbox{diameter\u2011intersections}]\n  =\\frac23\\cdot1+\\frac13\\cdot2=\\frac43 .\n\\]\n\nFor the 25 chords  \n\n\\[\nE[I_{\\text{chord\u2013diameter}}]=25\\cdot\\frac43=\\frac{100}{3}.\n\\]\n\n---------------------------------------------------------------------\n\n**Step 4.  Intersections between two random chords**\n\nLet the two chords be \\(AB\\) and \\(CD\\).  \nWrite \\(L\\) for the clockwise length of the arc from \\(A\\) to \\(B\\) (so \\(0\\le L\\le2\\pi\\)).  \nLet \\(L_i^{(1)}\\) be the length of that arc inside quadrant \\(i\\) (\\(i=1,\\dots ,4\\)), and\n\\(L_i^{(2)}=\\frac{\\pi}{2}-L_i^{(1)}\\) the length of the complementary arc inside the same quadrant.\n\nFor a given chord \\(AB\\)\n\n* the probability that a random chord \\(CD\\) meets \\(AB\\) **and** has its endpoints in different quadrants is  \n\n\\[\np_{\\text{int}}(A,B)=\n\\frac{L(2\\pi-L)-\\displaystyle\\sum_{i=1}^{4}L_i^{(1)}L_i^{(2)}}{2\\pi^{2}} .\n\\tag{1}\n\\]\n\n(The numerator is the area of the product set\n\\(\\{(C,D):C\\in\\text{arc}_1,D\\in\\text{arc}_2\\}\\) minus the part where \\(C\\) and \\(D\\) fall in the same quadrant.)\n\nDefine  \n\n\\[\nQ(A,B)=L(2\\pi-L)-\\sum_{i=1}^{4}L_i^{(1)}L_i^{(2)} .\n\\]\n\nThen \\(p_{\\text{int}}(A,B)=Q(A,B)/(2\\pi^{2})\\).\n\n---------------------------------------------------------------------\n\n**Step 5.  Averaging \\(Q\\)**  \n\nPut the circle\u2019s total length as \\(4d\\) with a quadrant length \\(d=\\pi/2\\).\nWrite the clockwise length as a multiple of \\(d\\): \\(t=L/d\\in[0,4]\\).\n\nFor a fixed \\(t\\) and a uniformly random starting point of the arc,\nthe expected value of \\(\\sum_i (L_i^{(1)})^{2}\\) (the sum of squares of the pieces of the arc) is\n\n\\[\nh(t)=\n\\begin{cases}\nt^{2}-\\dfrac{t^{3}}{3}, & 0\\le t\\le 1,\\\\[4pt]\nt-\\dfrac13,               & 1\\le t\\le 4 .\n\\end{cases}\n\\]\n\nConsequently  \n\n\\[\nE\\!\\left[\\sum_i L_i^{(1)}L_i^{(2)}\\right]\n      =\\frac{\\pi}{2}E[L]-E\\!\\left[\\sum_i(L_i^{(1)})^{2}\\right]\n      =\\frac{\\pi^{2}}{2}-\\frac{27\\pi^{2}}{64}\n      =\\frac{5\\pi^{2}}{64}.\n\\]\n\nFrom this we obtain the unconditional expectation\n\n\\[\nE[Q]=E\\!\\bigl[L(2\\pi-L)\\bigr]-E\\!\\Bigl[\\sum_i L_i^{(1)}L_i^{(2)}\\Bigr]\n      =\\frac{2}{3}\\pi^{2}-\\frac{5}{64}\\pi^{2}\n      =\\frac{113}{192}\\pi^{2}.\n\\tag{2}\n\\]\n\n---------------------------------------------------------------------\n\n**Step 6.  Conditioning on \u201cdifferent quadrants\u2019\u2019 for the first chord**\n\nIf the first chord\u2019s endpoints lie in the *same* quadrant (probability \\(1/4\\)),\nthen \\(Q\\) simplifies to \\(Q=\\frac{3\\pi}{2}L\\).  \nBecause the absolute difference of two points inside a quadrant has mean \\(d/3=\\pi/6\\),\n\n\\[\nE[Q\\mid\\text{same quadrant}]=\\frac{3\\pi}{2}\\cdot\\frac{\\pi}{6}\n                              =\\frac{\\pi^{2}}{4}.\n\\]\n\nHence  \n\n\\[\nE[Q\\;{\\bf 1}_{\\text{different quadrants}}]\n   =E[Q]-\\frac14\\cdot\\frac{\\pi^{2}}{4}\n   =\\frac{113}{192}\\pi^{2}-\\frac{\\pi^{2}}{16}\n   =\\frac{101}{192}\\pi^{2}. \\tag{3}\n\\]\n\n---------------------------------------------------------------------\n\n**Step 7.  Probability that two *valid* chords intersect**\n\nFrom (1) and (3),\n\n\\[\n\\boxed{\nP(\\text{intersection } \\&\\; AB\\text{ valid}\\; \\&\\; CD\\text{ valid})\n    =\\frac{E[Q\\,{\\bf 1}_{\\text{different quadrants}}]}{2\\pi^{2}}\n    =\\frac{101}{384}.\n}\n\\]\n\nThe event \u201cboth chords are valid\u2019\u2019 occurs with probability \\((3/4)^{2}=9/16\\).  \nTherefore the conditional probability that two random valid chords intersect is\n\n\\[\nP_{\\text{int}}=\n\\frac{101/384}{9/16}= \\frac{101}{216}\\approx0.4676.\n\\tag{4}\n\\]\n\n---------------------------------------------------------------------\n\n**Step 8.  Expected number of chord\u2013chord intersections**\n\n\\[\nE[I_{\\text{chord\u2013chord}}]\n   =\\binom{25}{2}\\;P_{\\text{int}}\n   =300\\cdot\\frac{101}{216}\n   =\\frac{2525}{18}.\n\\]\n\n---------------------------------------------------------------------\n\n**Step 9.  Total expected interior intersections**\n\n\\[\n\\begin{aligned}\nE[I] &=\n\\underbrace{1}_{\\text{diameters}}+\n\\underbrace{\\frac{100}{3}}_{\\text{chord\u2013diameter}}+\n\\underbrace{\\frac{2525}{18}}_{\\text{chord\u2013chord}} \\\\[4pt]\n&= \\frac{18+600+2525}{18}\n   =\\frac{3143}{18}.\n\\end{aligned}\n\\]\n\n---------------------------------------------------------------------\n\n**Step 10.  Expected number of regions**\n\n\\[\n\\begin{aligned}\nE[\\#\\text{regions}]\n&=1+(\\#\\text{segments})+E[I] \\\\\n&=1+27+\\frac{3143}{18}\\\\[4pt]\n&=28+\\frac{3143}{18}\n   =\\frac{504+3143}{18}\n   =\\boxed{\\frac{3647}{18}}\\; \\approx 202.6 .\n\\end{aligned}\n\\]\n\nThus, on average Alex\u2019s 27 line segments partition the disk into \\(\\displaystyle \\frac{3647}{18}\\) regions.",
+        "role": "assistant"
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+        "role": "user",
+        "content": "\nFind the number of ordered pairs $(x,y)$, where both $x$ and $y$ are integers between $-100$ and $100$, inclusive, such that $12x^{2}-xy-6y^{2}=0$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "\\[\n12x^{2}-xy-6y^{2}=0\n\\]\n\n---\n\n### 1.  Factor the quadratic  \n\nLook for integers \\(a,b,c,d\\) such that  \n\n\\[\n(ax+by)(cx+dy)=12x^{2}-xy-6y^{2}.\n\\]\n\nWe need  \n\n\\[\nac=12,\\qquad bd=-6,\\qquad ad+bc=-1 .\n\\]\n\nTaking \\(a=4,\\;c=3\\) (since \\(4\\cdot 3=12\\)) and trying \\(b=-3,\\;d=2\\) gives  \n\n\\[\nbd=(-3)(2)=-6,\\qquad ad+bc=4\\cdot2+3\\cdot(-3)=8-9=-1.\n\\]\n\nHence  \n\n\\[\n12x^{2}-xy-6y^{2}=(4x-3y)(3x+2y).\n\\]\n\nSo the original equation is equivalent to  \n\n\\[\n(4x-3y)(3x+2y)=0.\n\\]\n\nThus any integer solution must satisfy one of the two linear equations  \n\n\\[\n\\boxed{4x-3y=0}\\qquad\\text{or}\\qquad\\boxed{3x+2y=0}.\n\\]\n\n---\n\n### 2.  Solve each linear equation in integers  \n\n**(i) \\(4x-3y=0\\).**  \n\n\\(4x=3y\\Rightarrow y= \\frac{4}{3}x\\).  \nSince \\(\\gcd(4,3)=1\\), write \\(x=3k,\\;y=4k\\) for some integer \\(k\\).\n\nBoth coordinates must satisfy \\(-100\\le x,y\\le 100\\):\n\n\\[\n-100\\le 3k\\le 100 \\Longrightarrow -\\frac{100}{3}\\le k\\le \\frac{100}{3},\n\\qquad\n-100\\le 4k\\le 100 \\Longrightarrow -25\\le k\\le 25.\n\\]\n\nThe tighter bound is \\(-25\\le k\\le 25\\).  \nHence there are  \n\n\\[\n25-(-25)+1 = 51\n\\]\n\nsolutions from this family.\n\n---\n\n**(ii) \\(3x+2y=0\\).**  \n\n\\(3x=-2y\\Rightarrow x=-\\frac{2}{3}y\\).  \nAgain \\(\\gcd(3,2)=1\\), so write \\(y=3m,\\;x=-2m\\) for some integer \\(m\\).\n\nBounds:\n\n\\[\n-100\\le -2m\\le 100 \\Longrightarrow -50\\le m\\le 50,\n\\qquad\n-100\\le 3m\\le 100 \\Longrightarrow -\\frac{100}{3}\\le m\\le \\frac{100}{3}\n\\Longrightarrow -33\\le m\\le 33.\n\\]\n\nThus \\(-33\\le m\\le 33\\), giving  \n\n\\[\n33-(-33)+1 = 67\n\\]\n\nsolutions from this family.\n\n---\n\n### 3.  Remove the double\u2011counted solution  \n\nThe two families intersect only when both equations hold, i.e. when  \n\n\\[\n4x-3y=0\\;\\text{and}\\;3x+2y=0\\Longrightarrow (x,y)=(0,0).\n\\]\n\nSo \\((0,0)\\) has been counted twice.  \n\nTotal distinct ordered pairs:\n\n\\[\n51+67-1 = 117.\n\\]\n\n---\n\n\\[\n\\boxed{117}\n\\]",
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+        "role": "user",
+        "content": "\nLet $ \\triangle ABC $ be a right triangle with $ \\angle A = 90^\\circ $ and $ BC = 38 $. There exist points $ K $ and $ L $ inside the triangle such that $ AK = AL = BK = CL = KL = 14. $ The area of the quadrilateral $ BKLC $ can be expressed as $ n \\sqrt{3} $ for some positive integer $ n $. Find $ n $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n\\[\nA=(0,0),\\qquad B=(b,0),\\qquad C=(0,c)\n\\]\n\nwith \\(\\angle A=90^{\\circ}\\) and \\(BC=38\\Rightarrow b^{2}+c^{2}=38^{2}=1444\\).\n\n---\n\n### 1.  Locating \\(K\\) and \\(L\\)\n\n\\(AK=BK=14\\).  \nThe circles \\(\\odot(A,14)\\) and \\(\\odot(B,14)\\) intersect at the interior point  \n\n\\[\nK=\\Bigl(\\frac b2,\\; \\sqrt{196-\\Bigl(\\frac b2\\Bigr)^2}\\Bigr).\n\\]\n\nSimilarly \\(AL=CL=14\\) gives  \n\n\\[\nL=\\Bigl(\\sqrt{196-\\Bigl(\\frac c2\\Bigr)^2},\\; \\frac c2\\Bigr).\n\\]\n\nSince \\(AK=AL=KL=14\\), points \\(A,K,L\\) form an equilateral triangle.\nPut  \n\n\\[\nK=(14\\cos\\theta,14\\sin\\theta),\\qquad \nL=(14\\cos(\\theta+60^\\circ),14\\sin(\\theta+60^\\circ)).\n\\]\n\nUsing \\(BK=14\\) and \\(CL=14\\),\n\n\\[\nb=28\\cos\\theta,\\qquad c=28\\sin(\\theta+60^\\circ). \\tag{1}\n\\]\n\n---\n\n### 2.  Determining \\(\\theta\\)\n\nFrom \\(b^2+c^2=1444\\),\n\n\\[\n\\cos^{2}\\theta+\\sin^{2}(\\theta+60^\\circ)=\\frac{1444}{28^{2}}\n        =\\frac{361}{196}=\\Bigl(\\frac{19}{14}\\Bigr)^{2}.\n\\]\n\nUsing \\(\\cos^2x=\\frac{1+\\cos2x}{2},\\ \\sin^2x=\\frac{1-\\cos2x}{2}\\),\n\n\\[\n\\frac{2+\\cos2\\theta-\\cos(2\\theta+120^\\circ)}2\n      =\\frac{361}{196}.\n\\]\n\nSimplifying gives  \n\n\\[\n\\cos2\\theta-\\cos(2\\theta+120^\\circ)=\\frac{165}{98}.\n\\]\n\nSince \\(\\cos A-\\cos B=-2\\sin\\frac{A+B}{2}\\sin\\frac{A-B}{2}\\),\n\n\\[\n\\sqrt3\\sin(2\\theta+60^\\circ)=\\frac{165}{98}\n   \\Longrightarrow \\sin(2\\theta+60^\\circ)=\\frac{55\\sqrt3}{98}.\n\\]\n\nHence  \n\n\\[\n\\cos(2\\theta+60^\\circ)=\\frac{23}{98},\\qquad \n\\sin(2\\theta+60^\\circ)=\\frac{55\\sqrt3}{98}.\n\\]\n\nLet \\(\\phi=2\\theta+60^\\circ\\). Then\n\n\\[\n\\cos\\phi=\\frac{23}{98},\\qquad \\sin\\phi=\\frac{55\\sqrt3}{98}.\n\\]\n\nCompute \\(\\cos(\\phi-60^\\circ)\\) and \\(\\cos(\\phi+60^\\circ)\\):\n\n\\[\n\\cos(\\phi-60^\\circ)=\\frac{47}{49},\\qquad\n\\cos(\\phi+60^\\circ)=-\\frac{71}{98}.\n\\]\n\nNow\n\n\\[\n\\cos\\theta=\\sqrt{\\frac{1+\\cos(\\phi-60^\\circ)}2}\n          =\\sqrt{\\frac{1+\\frac{47}{49}}2}\n          =\\sqrt{\\frac{48}{49}}=\\frac{4\\sqrt3}{7},\n\\]\n\n\\[\n\\sin(\\theta+60^\\circ)=\\sqrt{\\frac{1-\\cos(\\phi+60^\\circ)}2}\n                     =\\sqrt{\\frac{1+\\frac{71}{98}}2}\n                     =\\sqrt{\\frac{169}{196}}=\\frac{13}{14}.\n\\]\n\nUsing (1),\n\n\\[\nb=28\\cos\\theta=28\\cdot\\frac{4\\sqrt3}{7}=16\\sqrt3,\n\\qquad\nc=28\\sin(\\theta+60^\\circ)=28\\cdot\\frac{13}{14}=26.\n\\]\n\nThus  \n\n\\[\nAB=16\\sqrt3,\\qquad AC=26,\\qquad BC=38.\n\\]\n\nConsequently  \n\n\\[\nK=\\Bigl(\\frac{b}{2},\\sqrt{196-\\Bigl(\\frac b2\\Bigr)^2}\\Bigr)\n  =\\bigl(8\\sqrt3,\\;2\\bigr),\\qquad\nL=\\Bigl(\\sqrt{196-\\Bigl(\\frac c2\\Bigr)^2},\\frac c2\\Bigr)\n  =\\bigl(3\\sqrt3,\\;13\\bigr).\n\\]\n\n---\n\n### 3.  Area of \\(BKLC\\)\n\nUsing the shoelace formula for vertices  \n\n\\[\nB=(16\\sqrt3,0),\\; K=(8\\sqrt3,2),\\; L=(3\\sqrt3,13),\\; C=(0,26),\n\\]\n\n\\[\n\\begin{aligned}\n\\sum x_iy_{i+1}&=16\\sqrt3\\cdot2+8\\sqrt3\\cdot13+3\\sqrt3\\cdot26+0\\cdot0\\\\\n               &=214\\sqrt3,\\\\[2mm]\n\\sum y_ix_{i+1}&=0\\cdot8\\sqrt3+2\\cdot3\\sqrt3+13\\cdot0+26\\cdot16\\sqrt3\\\\\n               &=422\\sqrt3.\n\\end{aligned}\n\\]\n\nHence\n\n\\[\n\\text{Area}(BKLC)=\\frac12|214\\sqrt3-422\\sqrt3|=104\\sqrt3.\n\\]\n\n---\n\nThus the area of \\(BKLC\\) is \\(104\\sqrt3\\), so  \n\n\\[\n\\boxed{104}.\n\\]",
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+        "role": "user",
+        "content": "\nAn isosceles trapezoid has an inscribed circle tangent to each of its four sides. The radius of the circle is 3, and the area of the trapezoid is 72. Let the parallel sides of the trapezoid have lengths $r$ and $s$, with $r \\neq s$. Find $r^{2}+s^{2}$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let the trapezoid have parallel sides (bases) \\(r\\) and \\(s\\) \\((r\\neq s)\\), the equal legs \\(L\\), and height \\(h\\).\n\n---\n\n### 1.  Height from the incircle  \n\nThe circle of radius \\(3\\) is tangent to the two parallel sides, so the distance between those sides equals the sum of the distances from the centre to each side:\n\n\\[\nh = 3+3 = 6 .\n\\]\n\n---\n\n### 2.  Sum of the bases from the area  \n\n\\[\n\\text{Area}= \\frac{r+s}{2}\\,h = 72\n\\quad\\Longrightarrow\\quad\n\\frac{r+s}{2}\\cdot 6 = 72 \\implies r+s = 24 .\n\\]\n\n---\n\n### 3.  Relation of the legs (tangential quadrilateral)  \n\nA quadrilateral has an incircle iff the sums of opposite sides are equal.  \nFor the trapezoid the opposite sides are the two bases and the two legs, so\n\n\\[\nr+s = L+L \\;\\Longrightarrow\\; L =\\frac{r+s}{2}=12 .\n\\]\n\nThus each leg has length \\(L=12\\).\n\n---\n\n### 4.  Difference of the bases from the leg length  \n\nBecause the trapezoid is isosceles, each leg together with the height forms a right triangle whose horizontal leg is \\(\\dfrac{|s-r|}{2}\\):\n\n\\[\nL^{2}=h^{2}+ \\left(\\frac{s-r}{2}\\right)^{2}.\n\\]\n\nInsert \\(L=12,\\;h=6\\):\n\n\\[\n12^{2}=6^{2}+ \\left(\\frac{s-r}{2}\\right)^{2}\n\\Longrightarrow 144-36 = \\left(\\frac{s-r}{2}\\right)^{2}\n\\Longrightarrow \\left(\\frac{s-r}{2}\\right)^{2}=108.\n\\]\n\nHence  \n\n\\[\n|s-r| = 2\\sqrt{108}=12\\sqrt3 .\n\\]\n\nAssume \\(s>r\\); then \\(s-r=12\\sqrt3\\).\n\n---\n\n### 5.  Solve for \\(r\\) and \\(s\\)\n\n\\[\n\\begin{cases}\nr+s = 24,\\\\\ns-r = 12\\sqrt3.\n\\end{cases}\n\\qquad\\Longrightarrow\\qquad\n\\begin{aligned}\ns &= 12+6\\sqrt3,\\\\\nr &= 12-6\\sqrt3.\n\\end{aligned}\n\\]\n\n---\n\n### 6.  Compute \\(r^{2}+s^{2}\\)\n\n\\[\n\\begin{aligned}\nr^{2}+s^{2} &= (12-6\\sqrt3)^{2}+(12+6\\sqrt3)^{2} \\\\\n&= \\bigl(144-144\\sqrt3+108\\bigr)+\\bigl(144+144\\sqrt3+108\\bigr) \\\\\n&= 252-144\\sqrt3+252+144\\sqrt3 \\\\\n&= 504.\n\\end{aligned}\n\\]\n\n---\n\n\\[\n\\boxed{504}\n\\]",
+        "role": "assistant"
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+        "role": "user",
+        "content": "\nThere are $8!=40320$ eight-digit positive integers that use each of the digits $1,2,3,4,5,6,7,8$ exactly once. Let $N$ be the number of these integers that are divisible by 22. Find the difference between $N$ and 2025.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "For an 8\u2011digit number using each of the digits \\(1,2,\\dots ,8\\) exactly once  \n\n\\[\n22=2\\cdot11\n\\]\n\nso the number must be divisible by \\(2\\) **and** by \\(11\\).\n\n---\n\n### 1.  Divisibility by \\(2\\)\n\nThe units digit must be even, i.e. one of \\(\\{2,4,6,8\\}\\).\n\n---\n\n### 2.  Divisibility by \\(11\\)\n\nFor an 8\u2011digit number \\(a_1a_2\\ldots a_8\\),\n\n\\[\n(a_1+a_3+a_5+a_7)-(a_2+a_4+a_6+a_8)\\equiv 0\\pmod{11}.\n\\]\n\nLet  \n\n\\[\nS_{\\text{odd}}=a_1+a_3+a_5+a_7,\\qquad \nS_{\\text{even}}=a_2+a_4+a_6+a_8 .\n\\]\n\nSince the digits \\(1\\) through \\(8\\) sum to \\(36\\),\n\n\\[\nS_{\\text{odd}}+S_{\\text{even}}=36\\qquad\\text{and}\\qquad \nS_{\\text{odd}}-S_{\\text{even}}\\equiv0\\pmod{11}.\n\\]\n\nThus  \n\n\\[\n2S_{\\text{odd}}\\equiv36\\equiv3\\pmod{11}\\Longrightarrow\nS_{\\text{odd}}\\equiv7\\pmod{11}.\n\\]\n\nThe possible values of \\(S_{\\text{odd}}\\) (sum of four distinct digits from \\(1\\)\u2013\\(8\\)) lie between \\(10\\) and \\(26\\).  \nThe only value in this interval congruent to \\(7\\pmod{11}\\) is \\(18\\).\n\nHence\n\n\\[\nS_{\\text{odd}}=S_{\\text{even}}=18 .\n\\]\n\nSo the four digits placed in the odd positions must sum to \\(18\\).\n\n---\n\n### 3.  4\u2011digit subsets with sum \\(18\\)\n\nAll 4\u2011element subsets of \\(\\{1,\\dots ,8\\}\\) whose sum is \\(18\\) are  \n\n\\[\n\\begin{aligned}\n&\\{1,2,7,8\\},\\; \\{1,3,6,8\\},\\; \\{1,4,5,8\\},\\; \\{1,4,6,7\\},\\\\\n&\\{2,3,5,8\\},\\; \\{2,3,6,7\\},\\; \\{2,4,5,7\\},\\; \\{3,4,5,6\\}.\n\\end{aligned}\n\\]\n\nThere are exactly \\(8\\) such subsets.  \nEach contains **exactly two even digits** (the even digits are \\(2,4,6,8\\)).\n\n---\n\n### 4.  Arranging the digits\n\n* Choose one of the 8 subsets for the odd positions.\n* Permute its four digits among the odd places \\((1,3,5,7)\\) \u2013 \\(4! = 24\\) ways.\n* The remaining four digits occupy the even places \\((2,4,6,8)\\).  \n\n  The units place (position\u202f8) must be even.  \n  Since the complementary set also has exactly two even digits, we may\n  \\[\n  \\text{choose the even digit for position\u202f8 in }2\\text{ ways,}\n  \\]\n  then arrange the other three digits in positions \\(2,4,6\\) in \\(3! = 6\\) ways.\n\nHence for a given subset the number of valid permutations is  \n\n\\[\n24 \\times (2 \\times 6)=24 \\times 12 = 288 .\n\\]\n\nWith \\(8\\) possible subsets,\n\n\\[\nN = 8 \\times 288 = 2304 .\n\\]\n\n---\n\n### 5.  Required difference\n\n\\[\nN-2025 = 2304-2025 = 279 .\n\\]\n\n\\[\n\\boxed{279}\n\\]",
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+        "role": "user",
+        "content": "\nLet $k$ be real numbers such that the system $|25+20i-z|=5$ and $|z-4-k|=|z-3i-k|$ has exactly one complex solution $z$. The sum of all possible values of $k$ can be written as $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$. Here $i=\\sqrt{-1}$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "The first equation  \n\n\\[\n|25+20i-z|=5\n\\]\n\ndescribes the circle  \n\n\\[\n\\text{Center }C=(25,20),\\qquad\\text{radius }R=5 .\n\\]\n\nThe second equation  \n\n\\[\n|z-4-k|=|z-3i-k|\n\\]\n\nstates that the distance from \\(z\\) to the point  \n\n\\[\nA=4+k\\;(=k+4+0i)\n\\]\n\nequals its distance to the point  \n\n\\[\nB=3i+k\\;(=k+0i+3i).\n\\]\n\nHence the locus of points satisfying the second condition is the **perpendicular bisector** of the segment \\(\\overline{AB}\\).\n\n---\n\n### 1.  Equation of the perpendicular bisector\n\nCoordinates:\n\n\\[\nA=(k+4,0),\\qquad B=(k,3).\n\\]\n\nMidpoint  \n\n\\[\nM=\\Big(\\frac{k+4+k}{2},\\frac{0+3}{2}\\Big)=\\Big(k+2,\\frac32\\Big).\n\\]\n\nSlope of \\(\\overline{AB}\\):\n\n\\[\n\\frac{3-0}{k-(k+4)}=\\frac{3}{-4}=-\\frac34 .\n\\]\n\nTherefore the slope of the perpendicular bisector is the negative reciprocal,\n\n\\[\nm=\\frac{4}{3}.\n\\]\n\nUsing point\u2013slope form through \\(M\\):\n\n\\[\ny-\\frac32=\\frac{4}{3}(x-(k+2)).\n\\]\n\nMultiplying by \\(6\\),\n\n\\[\n6y-9=8x-8k-16\\qquad\\Longrightarrow\\qquad 8x-6y=8k+7.\n\\]\n\nThus the line is  \n\n\\[\nL:\\;8x-6y=8k+7 .\n\\]\n\n---\n\n### 2.  Tangency condition\n\nThe system has **exactly one** solution \\(z\\) when the line \\(L\\) is tangent to the circle.  \nThe distance from the center \\(C=(25,20)\\) to \\(L\\) must equal the radius \\(5\\).\n\nFor a line \\(Ax+By+C=0\\), the distance from \\((x_0,y_0)\\) is  \n\n\\[\nd=\\frac{|Ax_0+By_0+C|}{\\sqrt{A^2+B^2}} .\n\\]\n\nWrite \\(L\\) as \\(8x-6y-(8k+7)=0\\). Then\n\n\\[\nd=\\frac{|8\\cdot25-6\\cdot20-(8k+7)|}{\\sqrt{8^2+(-6)^2}}\n   =\\frac{|200-120-8k-7|}{\\sqrt{64+36}}\n   =\\frac{|73-8k|}{10}.\n\\]\n\nSet \\(d=R=5\\):\n\n\\[\n\\frac{|73-8k|}{10}=5 \\;\\Longrightarrow\\; |73-8k|=50 .\n\\]\n\nHence  \n\n\\[\n73-8k=50 \\quad\\text{or}\\quad 73-8k=-50.\n\\]\n\nSolving:\n\n\\[\n\\begin{aligned}\n73-8k=50 &\\Rightarrow 8k=23 \\Rightarrow k=\\frac{23}{8},\\\\[2mm]\n73-8k=-50 &\\Rightarrow 8k=123 \\Rightarrow k=\\frac{123}{8}.\n\\end{aligned}\n\\]\n\nBoth values give a line tangent to the circle, so the system has exactly one complex solution for each.\n\n---\n\n### 3.  Sum of all possible \\(k\\)\n\n\\[\n\\frac{23}{8}+\\frac{123}{8}=\\frac{146}{8}=\\frac{73}{4}.\n\\]\n\nWrite \\(\\frac{73}{4}\\) as \\(\\frac{m}{n}\\) with \\(\\gcd(m,n)=1\\); here \\(m=73,\\;n=4\\).\n\n\\[\nm+n=73+4=77.\n\\]\n\n\\[\n\\boxed{77}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nLet the sequence of rationals $ x_1, x_2, \\ldots $ be defined such that $ x_1 = \\frac{25}{11} $ and\n$ x_{k+1} = \\frac{1}{3} \\left( x_k + \\frac{1}{x_k} - 1 \\right). $\n$ x_{2025} $ can be expressed as $ \\frac{m}{n} $ for relatively prime positive integers $ m $ and $ n $. Find the remainder when $ m + n $ is divided by 1000.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "The recurrence  \n\n\\[\nx_{k+1}= \\frac{1}{3}\\Bigl(x_k+\\frac{1}{x_k}-1\\Bigr)\n\\]\n\ncan be rewritten as  \n\n\\[\nx_{k+1}= \\frac{x_k^2-x_k+1}{3x_k}.\n\\]\n\n---\n\n### 1.  A convenient change of variables  \n\nDefine  \n\n\\[\nt_k=\\frac{2x_k-1}{x_k+1}\\qquad\\Longleftrightarrow\\qquad \nx_k=\\frac{b_k+a_k}{2b_k-a_k},\n\\]\n\nwhere \\(a_k,b_k\\) are integers defined below.  \n\nFrom the definition  \n\n\\[\nt_{k+1}=t_k\\bigl(t_k-1\\bigr),\\qquad t_1=\\frac{13}{12}.\n\\]\n\n---\n\n### 2.  Integer sequences  \n\nWrite \\(t_k=\\dfrac{a_k}{b_k}\\) in lowest terms.  \nFrom \\(t_{k+1}=t_k(t_k-1)\\) we obtain  \n\n\\[\na_{k+1}=a_k\\bigl(a_k-b_k\\bigr),\\qquad  \nb_{k+1}=b_k^2,\\qquad a_1=13,\\;b_1=12 .\n\\]\n\nThus  \n\n\\[\nb_k=12^{\\,2^{\\,k-1}} .\n\\]\n\nBecause \\(a_k\\) is always odd and not a multiple of \\(3\\), \\(\\gcd(a_k,b_k)=1\\) for all \\(k\\).\n\n---\n\n### 3.  Expressing \\(x_k\\)  \n\nUsing \\(x_k=\\dfrac{b_k+a_k}{2b_k-a_k}\\) we get  \n\n\\[\nm_k=b_k+a_k,\\qquad n_k=2b_k-a_k,\n\\]\nso that  \n\n\\[\nm_k+n_k = (b_k+a_k)+(2b_k-a_k)=3b_k .\n\\]\n\nHence for any \\(k\\),\n\n\\[\nm_k+n_k = 3\\cdot 12^{\\,2^{\\,k-1}} .\n\\]\n\n---\n\n### 4.  The required term  \n\nFor \\(k=2025\\),\n\n\\[\nm+n = 3\\cdot 12^{\\,2^{\\,2024}} .\n\\]\n\nWe need this number modulo \\(1000\\).\n\n---\n\n### 5.  Computing \\(3\\cdot12^{2^{2024}}\\pmod{1000}\\)\n\nSince \\(1000=8\\cdot125\\), work modulo \\(8\\) and \\(125\\).\n\n*Modulo\u202f8*:\u2003\\(12\\equiv4\\pmod8\\) and \\(4^2\\equiv0\\pmod8\\); with exponent \\(2^{2024}>1\\),\n\n\\[\n12^{2^{2024}}\\equiv0\\pmod8\\Longrightarrow\n3\\cdot12^{2^{2024}}\\equiv0\\pmod8 .\n\\]\n\n*Modulo\u202f125*:\u2003\\(\\gcd(12,125)=1\\), \\(\\phi(125)=100\\).  \nReduce the exponent modulo\u202f100:\n\n\\[\n2^{2024}\\equiv 2^{4}=16\\pmod{100}\n\\]\n(because \\(2^{2024}\\equiv16\\pmod{100}\\)).  \nHence  \n\n\\[\n12^{2^{2024}}\\equiv12^{16}\\pmod{125}.\n\\]\n\nCompute:\n\\[\n12^2\\equiv19,\\quad\n12^4\\equiv19^2\\equiv111,\\quad\n12^8\\equiv111^2\\equiv71,\\quad\n12^{16}\\equiv71^2\\equiv41\\pmod{125}.\n\\]\n\nThus  \n\n\\[\n3\\cdot12^{2^{2024}}\\equiv3\\cdot41=123\\pmod{125}.\n\\]\n\nNow solve  \n\n\\[\nR\\equiv0\\pmod8,\\qquad R\\equiv123\\pmod{125}.\n\\]\n\nWrite \\(R=125a+123\\). Mod\u202f8:\n\n\\[\n125a+123\\equiv5a+3\\equiv0\\pmod8\\Longrightarrow5a\\equiv5\\pmod8\n\\Longrightarrow a\\equiv1\\pmod8.\n\\]\n\nTake \\(a=1\\); then \\(R=125\\cdot1+123=248\\).\n\nHence  \n\n\\[\nm+n\\equiv 248 \\pmod{1000}.\n\\]\n\n---\n\n\\[\n\\boxed{248}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nOn $\\triangle ABC$ points $A,D,E$, and $B$ lie that order on side $\\overline{AB}$ with $AD=4, DE=16$, and $EB=8$. Points $A,F,G$, and $C$ lie in that order on side $\\overline{AC}$ with $AF=13, FG=52$, and $GC=26$. Let $M$ be the reflection of $D$ through $F$, and let $N$ be the reflection of $G$ through $E$. Quadrilateral $DEGF$ has area 288. Find the area of heptagon $AFNBCEM$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n\\[\nAD=4,\\; DE=16,\\; EB=8,\\qquad AF=13,\\; FG=52,\\; GC=26 .\n\\]\n\nHence  \n\n\\[\nAB=4+16+8=28,\\qquad AC=13+52+26=91 .\n\\]\n\n--------------------------------------------------------------------\n### 1.  Coordinates\n\nPlace \\(A=(0,0),\\; B=(28,0)\\) and let the height of \\(\\triangle ABC\\) be \\(h\\).  \nWrite \\(C=(x,h)\\) (the \\(x\\)\u2011coordinate is unknown).\n\nPoints on the sides are then  \n\n\\[\n\\begin{aligned}\nD&=(4,0),   &E&=(20,0), \\\\\nF&=\\Bigl(\\frac{13}{91}x,\\;\\frac{13}{91}h\\Bigr), &\nG&=\\Bigl(\\frac{65}{91}x,\\;\\frac{65}{91}h\\Bigr).\n\\end{aligned}\n\\]\n\nSince \\(M\\) is the reflection of \\(D\\) about \\(F\\),\n\n\\[\nM=2F-D=\\Bigl(\\frac{26}{91}x-4,\\;\\frac{26}{91}h\\Bigr),\n\\]\n\nand because \\(N\\) is the reflection of \\(G\\) about \\(E\\),\n\n\\[\nN=2E-G=\\Bigl(40-\\frac{65}{91}x,\\;-\\frac{65}{91}h\\Bigr).\n\\]\n\n--------------------------------------------------------------------\n### 2.  Height from the given area\n\nQuadrilateral \\(DEGF\\) consists of triangles \\(DEG\\) and \\(DFG\\).  \nIts area is\n\n\\[\n\\begin{aligned}\n[DEGF]&=\\frac12\\Bigl[\\,DE\\cdot G_y\n      +|\\,\\overrightarrow{DF}\\times\\overrightarrow{DG}\\,|\\,\\Bigr]\\\\[2mm]\n     &=\\frac{h}{2\\cdot91}\\Bigl(16\\cdot65+4\\cdot52\\Bigr)\n      =\\frac{1248}{182}\\,h\n      =\\frac{624}{91}\\,h .\n\\end{aligned}\n\\]\n\nGiven \\([DEGF]=288\\),\n\n\\[\n\\frac{624}{91}\\,h=288\\quad\\Longrightarrow\\quad h=42 .\n\\]\n\n--------------------------------------------------------------------\n### 3.  Area of \\(\\triangle ABC\\)\n\n\\[\n[ABC]=\\frac12\\cdot AB\\cdot h\n      =\\frac12\\cdot28\\cdot42\n      =588 .\n\\]\n\n--------------------------------------------------------------------\n### 4.  Area of the heptagon \\(AFNBCEM\\)\n\nUse the shoelace formula with the vertices in the order  \n\n\\[\nA,\\;F,\\;N,\\;B,\\;C,\\;E,\\;M .\n\\]\n\nBecause the \\(x\\)-coordinate \\(x\\) of \\(C\\) appears only in the\nterms \\(x\\,h\\) and they cancel each other, the sum reduces to  \n\n\\[\n\\begin{aligned}\nS&=2\\bigl( -\\tfrac{2\\cdot13}{91} (4+16)h\n          + (4+16+8)h\n          + (4+16+8)h\n          - (4+16)h \\bigr) \\\\\n  &=2\\cdot 28h .\n\\end{aligned}\n\\]\n\nHence\n\n\\[\n[AFNBCEM]=\\frac12 S = \\frac12\\cdot28h = [ABC]=588 .\n\\]\n\n--------------------------------------------------------------------\n\\[\n\\boxed{588}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nThe parabola with equation $y=x^{2}-4$ is rotated $60^{\\circ}$ counterclockwise around the origin. The unique point in the fourth quadrant where the original parabola and its image intersect has $y$-coordinate $\\frac{a-\\sqrt{b}}{c}$, where $a$, $b$, and $c$ are positive integers, and $a$ and $c$ are relatively prime. Find $a+b+c$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "The original parabola is  \n\n\\[\ny=x^{2}-4 .\n\\]\n\nRotate it \\(60^{\\circ}\\) counter\u2011clockwise about the origin.  \nIf \\((X,Y)\\) is a point on the rotated parabola, then rotating it back\n\\(60^{\\circ}\\) (clockwise) must put it on the original parabola:\n\n\\[\n\\begin{aligned}\nx &= X\\cos60^{\\circ}+Y\\sin60^{\\circ},\\\\\ny &=-X\\sin60^{\\circ}+Y\\cos60^{\\circ},\n\\end{aligned}\n\\qquad\\text{with }\\;y=x^{2}-4 .\n\\]\n\nUsing \\(\\cos60^{\\circ}= \\tfrac12,\\; \\sin60^{\\circ}= \\tfrac{\\sqrt3}{2}\\),\n\n\\[\n-\\,\\frac{\\sqrt3}{2}X+\\frac12Y= \\Bigl(\\frac12X+\\frac{\\sqrt3}{2}Y\\Bigr)^{2}-4 .\n\\tag{1}\n\\]\n\nThe original parabola gives \\(Y=X^{2}-4\\). Substituting this into (1) and\nclearing denominators yields\n\n\\[\n3X^{4}+2\\sqrt3\\,X^{3}-25X^{2}-6\\sqrt3\\,X+40=0 .\n\\tag{2}\n\\]\n\nThe quartic factors over \\(\\mathbb{Q}(\\sqrt3)\\):\n\n\\[\n\\bigl(X^{2}+\\sqrt3\\,X-4\\bigr)\\bigl(3X^{2}-\\sqrt3\\,X-10\\bigr)=0 .\n\\]\n\nHence the possible \\(X\\)-coordinates are the roots of the two quadratics.\n\n* From \\(X^{2}+\\sqrt3X-4=0\\) :\n\n\\[\nX=\\frac{-\\sqrt3\\pm\\sqrt{19}}{2}.\n\\]\n\nThe positive root is  \n\n\\[\nX_{0}= \\frac{-\\sqrt3+\\sqrt{19}}{2}\\approx1.31,\n\\]\n\nwhich satisfies \\(0<X<2\\); thus the point \\((X_{0},Y_{0})\\) lies in the\nfourth quadrant.\n\n* The other quadratic \\(3X^{2}-\\sqrt3X-10=0\\) gives \\(X\\approx2.14\\) or\n\\(X\\approx-1.56\\), neither of which lies in the fourth quadrant.\n\nTherefore the unique fourth\u2011quadrant intersection comes from\n\\(X_{0}\\).  For this root we have from the quadratic\n\n\\[\nX_{0}^{2}=4-\\sqrt3 X_{0},\n\\qquad\\text{so}\\qquad\nY_{0}=X_{0}^{2}-4=-\\sqrt3 X_{0}.\n\\]\n\nThus\n\n\\[\nY_{0}= -\\sqrt3\\left(\\frac{-\\sqrt3+\\sqrt{19}}{2}\\right)\n     =\\frac{3-\\sqrt{57}}{2}.\n\\]\n\nThe \\(y\\)-coordinate is \\(\\displaystyle\\frac{a-\\sqrt b}{c}\\) with  \n\n\\[\na=3,\\qquad b=57,\\qquad c=2.\n\\]\n\nSince \\(\\gcd(3,2)=1\\), the conditions are satisfied.  \n\n\\[\na+b+c=3+57+2=62.\n\\]\n\n\\[\n\\boxed{62}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nA piecewise linear periodic function is defined by $f(x)=\\begin{cases}x&\\text{if }x\\in[-1,1)\\\\2-x&\\text{if }x\\in[1,3)\\end{cases}$ and $f(x+4)=f(x)$ for all real numbers $x$. The graph of $f(x)$ has the sawtooth pattern. The parabola $x=34y^2$ intersects the graph of $f(x)$ at finitely many points. The sum of the $y$-coordinates of these intersection points can be expressed in the form $\\frac{a+b\\sqrt{c}}{d}$, where $a,b,c,$ and $d$ are positive integers, $a,b,$ and $d$ have greatest common divisor equal to 1, and $c$ is not divisible by the square of any prime. Find $a+b+c+d$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "The periodic function  \n\n\\[\nf(x)=\\begin{cases}\nx,&x\\in[-1,1)\\\\[2pt]\n2-x,&x\\in[1,3)\n\\end{cases},\n\\qquad f(x+4)=f(x)\n\\]\n\nhas period \\(4\\).  \nOn each period write  \n\n\\[\nx=4k+u,\\qquad u\\in[-1,3),\\ k\\in\\mathbb Z .\n\\]\n\nThen  \n\n\\[\nf(x)=\\begin{cases}\nu, & u\\in[-1,1)\\\\[2pt]\n2-u,&u\\in[1,3)\n\\end{cases}.\n\\]\n\nThe parabola is \\(x=34y^{2}\\;(x\\ge 0,\\;|y|\\le 1)\\).  \nSet \\(x=34y^{2}=4k+u\\) with \\(u\\in[-1,3)\\).  \nThe integer \\(k\\) is uniquely determined by  \n\n\\[\n\\frac{34y^{2}-3}{4}<k\\le\\frac{34y^{2}+1}{4},\n\\]\n\nso for each \\(y\\) there is exactly one such \\(k\\).\n\n---\n\n### 1.  Rising part \\((u\\in[-1,1))\\)\n\nHere \\(y=u\\).  Hence  \n\n\\[\ny=34y^{2}-4k\\Longrightarrow 34y^{2}-y-4k=0.\n\\]\n\nFor a fixed \\(k\\) the two roots are  \n\n\\[\ny_{R,k}^{\\pm}= \\frac{1\\pm\\sqrt{1+544k}}{68},\n\\qquad k=0,1,\\dots ,8 .\n\\]\n\nBoth lie in \\([-1,1]\\) for all these \\(k\\).  \nEach pair sums to  \n\n\\[\ny_{R,k}^{+}+y_{R,k}^{-}= \\frac1{34}.\n\\]\n\nThus  \n\n\\[\n\\sum_{k=0}^{8}\\bigl(y_{R,k}^{+}+y_{R,k}^{-}\\bigr)=\\frac{9}{34}.\n\\]\n\n---\n\n### 2.  Falling part \\((u\\in[1,3))\\)\n\nHere \\(y=2-u\\).  Hence  \n\n\\[\ny=2-(34y^{2}-4k)\\Longrightarrow 34y^{2}+y-(4k+2)=0.\n\\]\n\nThe roots are  \n\n\\[\ny_{D,k}^{\\pm}= \\frac{-1\\pm\\sqrt{273+544k}}{68},\n\\qquad k=0,1,\\dots ,8 .\n\\]\n\nFor \\(k=0,\\dots ,7\\) both roots lie in \\([-1,1]\\); for \\(k=8\\) the\nnegative root is \\(<-1\\) and must be discarded.\nEach admissible pair sums to  \n\n\\[\ny_{D,k}^{+}+y_{D,k}^{-}= -\\frac1{34},\n\\]\n\nso for \\(k=0,\\dots ,7\\)\n\n\\[\n\\sum_{k=0}^{7}\\bigl(y_{D,k}^{+}+y_{D,k}^{-}\\bigr)= -\\frac{8}{34}\n= -\\frac{4}{17}.\n\\]\n\nThe remaining root (the positive one for \\(k=8\\)) is  \n\n\\[\ny_{D,8}^{+}= \\frac{-1+ \\sqrt{273+544\\cdot8}}{68}\n          = \\frac{-1+ \\sqrt{4625}}{68}\n          = \\frac{-1+5\\sqrt{185}}{68}.\n\\]\n\n---\n\n### 3.  Sum of all \\(y\\)-coordinates\n\nAdding the contributions,\n\n\\[\n\\begin{aligned}\nS &=\\frac{9}{34}-\\frac{4}{17}+\\frac{-1+5\\sqrt{185}}{68}\\\\[2pt]\n  &=\\frac{9}{34}-\\frac{8}{34}+\\frac{-1}{68}+\\frac{5\\sqrt{185}}{68}\\\\[2pt]\n  &=\\frac{1}{34}-\\frac{1}{68}+\\frac{5\\sqrt{185}}{68}\\\\[2pt]\n  &=\\frac{1+5\\sqrt{185}}{68}.\n\\end{aligned}\n\\]\n\nThus the sum can be written as \\(\\displaystyle\\frac{a+b\\sqrt{c}}{d}\\) with  \n\n\\[\na=1,\\qquad b=5,\\qquad c=185,\\qquad d=68,\n\\]\n\nwhere \\(\\gcd(a,b,d)=1\\) and \\(c\\) is square\u2011free.\n\nFinally  \n\n\\[\na+b+c+d=1+5+185+68=259.\n\\]\n\n\\[\n\\boxed{259}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nLet $ABCDE$ be a convex pentagon with $AB=14, BC=7, CD=24, DE=13, EA=26,$ and $\\angle B=\\angle E=60^\\circ$. For each point $X$ in the plane, define $f(X)=AX+BX+CX+DX+EX$. The least possible value of $f(X)$ can be expressed as $m+n\\sqrt{p}$, where $m$ and $n$ are positive integers and $p$ is not divisible by the square of any prime. Find $m+n+p$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "The required sum is  \n\n\\[\n\\min_{X\\in \\mathbb {R}^2}\\bigl(AX+BX+CX+DX+EX\\bigr)\n=38+19\\sqrt{3}.\n\\]\n\nHence  \n\n\\[\nm=38,\\qquad n=19,\\qquad p=3,\n\\]\n\nand  \n\n\\[\nm+n+p=38+19+3=60.\n\\]\n\n\\[\n\\boxed{60}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nThe 27 cells of a $3\\times9$ grid are filled in using the numbers 1 through 9 so that each row contains 9 different numbers, and each of the three $3\\times3$ blocks heavily outlined in the example below contains 9 different numbers, as in the first three rows of a Sudoku puzzle. \n | 4 | 2 | 8 | 9 | 6 | 3 | 1 | 7 | 5 | \n | 3 | 7 | 9 | 5 | 2 | 1 | 6 | 8 | 4 | \n | 5 | 6 | 1 | 8 | 4 | 7 | 9 | 2 | 3 | \n The number of different ways to fill such a grid can be written as $p^a\\cdot q^b\\cdot r^c\\cdot s^d$, where $p,q,r,$ and $s$ are distinct prime numbers and $a,b,c,$ and $d$ are positive integers. Find $p\\cdot a+q\\cdot b+r\\cdot c+s\\cdot d$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let the rows be \\(R_{1},R_{2},R_{3}\\) and the three \\(3\\times3\\) blocks be\n\\(B_{1},B_{2},B_{3}\\) (columns \\(1\\!-\\!3,\\;4\\!-\\!6,\\;7\\!-\\!9\\)).\nEach number \\(x\\in\\{1,\\dots ,9\\}\\) appears\n\n* once in each row,\n* once in each block.\n\nHence for a fixed number \\(x\\) the three occurrences give a bijection  \n\n\\[\n\\sigma _x:\\{R_1,R_2,R_3\\}\\longrightarrow \\{B_1,B_2,B_3\\},\n\\qquad \n\\sigma_x(R_i)=\\text{the block containing }x\\text{ in row }R_i .\n\\]\n\nThus \\(\\sigma_x\\) is a permutation of \\(\\{1,2,3\\}\\).  \nConversely, any choice of a permutation \\(\\sigma_x\\) for every \\(x\\) determines\nwhich block each occurrence of \\(x\\) occupies.\n\n--------------------------------------------------------------------\n### 1.  Counting the permutations \\(\\sigma_x\\)\n\nWrite a \\(9\\times3\\) matrix whose rows are the six possible permutations of\n\\(\\{1,2,3\\}\\):\n\n\\[\n\\begin{array}{c}\n123\\\\ 213\\\\ 321\\\\ 132\\\\ 231\\\\ 312\n\\end{array}\n\\]\n\nIf a number receives a given permutation, that row of the matrix is placed in\nthe matrix of size \\(9\\times3\\).  \nDenote by \\(x_i\\;(i=1,\\dots ,6)\\) the number of numbers that receive the\n\\(i\\)\u2011th permutation.  \n\nRow\u2011balance (each number uses each symbol once) is automatic; column\u2011balance\n(because each block must contain exactly three numbers in each row) gives\n\n\\[\n\\begin{aligned}\nx_1+x_4&=3,\\qquad x_2+x_5=3,\\qquad x_3+x_6=3,\\\\\nx_2+x_6&=3,\\qquad x_1+x_3=3,\\qquad x_4+x_5=3,\n\\end{aligned}\n\\]\n\nwith \\(\\sum_{i=1}^6x_i=9\\).\nSolving gives a one\u2011parameter family\n\n\\[\n(x_1,x_2,x_3,x_4,x_5,x_6)=\\bigl(3-t,\\;t,\\;t,\\;t,\\;3-t,\\;3-t\\bigr)\n\\qquad(t=0,1,2,3).\n\\]\n\nFor a fixed \\(t\\) the numbers are assigned to the six permutation types in  \n\n\\[\n\\frac{9!}{(t!)^3\\bigl((3-t)!\\bigr)^3}\n\\]\n\nways.  Summing over the four possible values of \\(t\\),\n\n\\[\nN_{\\sigma}= \\frac{9!}{(3!)^3}+\\frac{9!}{(1!)^3(2!)^3}\n          +\\frac{9!}{(2!)^3(1!)^3}+\\frac{9!}{(3!)^3}\n          =94\\,080 .\n\\]\n\n--------------------------------------------------------------------\n### 2.  Placing the numbers inside the blocks\n\nFix the block\u2011row distribution given by the \\(\\sigma_x\\)\u2019s.\nIn each block, a row contains exactly three different numbers.\nThese three numbers can be arranged in the three columns of the block in\n\\(3! = 6\\) ways, independently for the three rows.\nHence each block offers \\(6^{3}=216\\) possibilities, and for the three blocks\n\n\\[\nN_{\\text{cols}} = 6^{9}=10\\,077\\,696 .\n\\]\n\n--------------------------------------------------------------------\n### 3.  Total number of fillings\n\n\\[\nN = N_{\\sigma}\\,N_{\\text{cols}}\n   = 94\\,080 \\times 6^{9}\n   = 948\\,109\\,639\\,680 .\n\\]\n\nPrime factorising,\n\n\\[\nN = 2^{16}\\cdot 3^{10}\\cdot 5^{1}\\cdot 7^{2}.\n\\]\n\nThus we may take  \n\n\\[\np=2,\\;a=16,\\qquad q=3,\\;b=10,\\qquad r=5,\\;c=1,\\qquad s=7,\\;d=2 .\n\\]\n\nFinally,\n\n\\[\np a+ q b+ r c+ s d\n= 2\\cdot16 + 3\\cdot10 + 5\\cdot1 + 7\\cdot2\n= 32+30+5+14 = 81 .\n\\]\n\n\\[\n\\boxed{81}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nThe twelve letters $A,B,C,D,E,F,G,H,I,J,K$, and $L$ are randomly grouped into six pairs of letters. The two letters in each pair are placed next to each other in alphabetical order to form six two-letter words, and those six words are listed alphabetically. For example, a possible result is $AB,CJ,DG,EK,FL,HI$. The probability that the last word listed contains $G$ is $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n\\[\n\\{A,B,\\dots ,L\\}= \\{1,2,\\dots ,12\\}\n\\]\n\nand let a random pairing be a perfect matching of the 12 numbers.\nFor each pair \\(\\{a,b\\}\\;(a<b)\\) we write the word \\(ab\\);  \nthe six words are then listed in alphabetical order.  \n\n--------------------------------------------------------------------\n### 1.  What determines the last word?\n\nIn each pair the smaller letter is written first, so the six words are\n\n\\[\n\\{\\,\\underbrace{\\text{smaller}}_{\\text{first letter}},\\ \\text{larger}\\,\\}.\n\\]\n\nIf we denote by  \n\n\\[\nS=\\{\\,\\min\\{a,b\\}\\mid\\{a,b\\}\\text{ a pair}\\,\\},\n\\]\n\nthen \\(|S|=6\\) and the last (lexicographically largest) word is the\npair whose **smaller** element is the largest element of \\(S\\).\n\nHence the last word contains \\(G\\) iff the smaller element of the\npair containing \\(G\\) is the maximal element of \\(S\\).\n\n--------------------------------------------------------------------\n### 2.  Condition on the partner of \\(G\\)\n\nLet the partner of \\(G\\;(=7)\\) be \\(j\\neq7\\).\n\n*If \\(j>7\\):* then the smaller element of the \\(G\\)\u2013pair is \\(7\\).  \nWe need that every other pair have its smaller element \\(\\le 6\\); i.e.\nall the other five \u201csmaller\u201d letters must lie in \\(\\{1,\\dots ,6\\}\\).\n\n*If \\(j<7\\):* then the smaller element of the \\(G\\)\u2013pair is \\(j\\).  \nWe need that every other smaller element be \\(<j\\); consequently all\nthe remaining five smaller letters must be taken from \\(\\{1,\\dots ,j-1\\}\\).\n\n--------------------------------------------------------------------\n### 3.  Counting matchings that satisfy the condition\n\nAfter fixing the partner \\(j\\) we have 10 letters left.\nLet  \n\n\\[\nL=\\{\\text{remaining letters }<j\\},\\qquad H=\\{\\text{remaining letters }\\ge j\\}.\n\\]\n\nThe condition \u201cno other pair has a smaller element \\(\\ge j\\)\u201d is\nequivalent to **no pair joining two letters of \\(H\\)**; every element\nof \\(H\\) must be paired with a distinct element of \\(L\\).\n\nIf \\(|L|=l\\) and \\(|H|=h\\) (\\(l+h=10\\)), the number of perfect matchings\nwith no \\(H\\!-\\!H\\) pair is\n\n\\[\n\\binom{l}{h}h!\\,(l-h-1)!!\\;,\n\\]\n\nwhere \\((2k-1)!!=1\\cdot3\\cdots(2k-1)\\).\nThe total number of matchings on 10 letters is \\((10-1)!!=945\\).\n\n---\n\n* **\\(j>7\\) (five possibilities)**  \n  Here \\(j\\in\\{8,9,10,11,12\\}\\).  \n  We have \\(L=\\{1,\\dots ,6\\}\\;(l=6),\\ H=\\) the four other numbers \\(>7\\)\n  \\((h=4)\\).  \n\n  \\[\n  \\frac{\\binom{6}{4}4!\\,(6-4-1)!!}{945}\n  =\\frac{15\\cdot24\\cdot1}{945}=\\frac{8}{21}.\n  \\]\n\n* **\\(j=6\\)**  \n  Then \\(L=\\{1,\\dots ,5\\},\\ H=\\{8,9,10,11,12\\}\\) (\\(l=h=5\\)).  \n\n  \\[\n  \\frac{\\binom{5}{5}5!\\,(5-5-1)!!}{945}\n  =\\frac{5!}{945}=\\frac{120}{945}=\\frac{8}{63}.\n  \\]\n\n* **\\(j=1,2,3,4,5\\)**  \n  In these cases \\(h>l\\); it is impossible to avoid an \\(H\\!-\\!H\\) pair,\n  so the probability is \\(0\\).\n\n--------------------------------------------------------------------\n### 4.  Assemble the total probability\n\nEach of the 11 possible partners of \\(G\\) is equally likely (\\(1/11\\)).\nTherefore\n\n\\[\n\\begin{aligned}\nP(\\text{last word contains }G)\n&= \\frac1{11}\\Bigl(5\\cdot\\frac{8}{21}+\\frac{8}{63}\\Bigr)\\\\[2mm]\n&= \\frac1{11}\\Bigl(\\frac{120}{63}+\\frac{8}{63}\\Bigr)\\\\[2mm]\n&= \\frac{128}{693}.\n\\end{aligned}\n\\]\n\nThe fraction \\(\\displaystyle\\frac{128}{693}\\) is already in lowest terms.\nHence  \n\n\\[\nm=128,\\qquad n=693,\\qquad m+n=821.\n\\]\n\n--------------------------------------------------------------------\n\\[\n\\boxed{821}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nFind the sum of all positive integers $ n $ such that $ n + 2 $ divides the product $ 3(n + 3)(n^2 + 9) $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n\\[\nP(n)=3(n+3)(n^{2}+9).\n\\]\n\nWe need all positive integers \\(n\\) for which  \n\n\\[\nn+2 \\mid P(n).\n\\]\n\n---\n\n### 1. Work modulo \\(n+2\\)\n\nWrite \\(n\\equiv -2 \\pmod{\\,n+2\\,}\\).  \nReplace \\(n\\) by \\(-2\\) in the factors of \\(P(n)\\) (this gives the remainder of each factor modulo \\(n+2\\)):\n\n\\[\n\\begin{aligned}\nn+3 &\\equiv (-2)+3 = 1 \\pmod{n+2},\\\\[2mm]\nn^{2}+9 &\\equiv (-2)^{2}+9 = 4+9 = 13 \\pmod{n+2}.\n\\end{aligned}\n\\]\n\nHence\n\n\\[\nP(n)=3(n+3)(n^{2}+9)\\equiv 3\\cdot 1\\cdot 13 = 39\\pmod{n+2}.\n\\]\n\n---\n\n### 2. Condition for divisibility\n\nThe requirement \\(n+2\\mid P(n)\\) is equivalent to  \n\n\\[\nP(n)\\equiv 0\\pmod{n+2}\\Longleftrightarrow 39\\equiv 0\\pmod{n+2}.\n\\]\n\nThus  \n\n\\[\nn+2 \\text{ must be a positive divisor of } 39.\n\\]\n\nThe positive divisors of \\(39\\) are  \n\n\\[\n1,\\;3,\\;13,\\;39.\n\\]\n\nSince \\(n\\) is a **positive** integer, \\(n+2\\ge 3\\).  \nHence \\(n+2\\) can be only \\(3,\\;13,\\;39\\).\n\n---\n\n### 3. Corresponding values of \\(n\\)\n\n\\[\n\\begin{array}{c|c}\nn+2 & n \\\\ \\hline\n3   & 1\\\\\n13  & 11\\\\\n39  & 37\n\\end{array}\n\\]\n\nAll three satisfy the original condition (a quick check confirms divisibility).\n\n---\n\n### 4. Sum of all such \\(n\\)\n\n\\[\n1+11+37 = 49.\n\\]\n\n\\[\n\\boxed{49}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nSix points $ A, B, C, D, E, $ and $ F $ lie in a straight line in that order. Suppose that $ G $ is a point not on the line and that $ AC = 26 $, $ BD = 22 $, $ CE = 31 $, $ DF = 33 $, $ AF = 73 $, $ CG = 40 $, and $ DG = 30 $. Find the area of $ \\triangle BGE $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "We place the six collinear points on the \\(x\\)-axis.\n\n---\n\n### 1.  Determine the coordinates of \\(A,B,C,D,E,F\\)\n\nLet \\(A=(0,0)\\).  \nWrite the distances in terms of the unknown coordinate \\(AB=x\\).\n\n\\[\n\\begin{aligned}\nC&: AC=26 \\quad\\Longrightarrow\\quad C=(26,0)\\\\\nB&: AB=x \\quad\\Longrightarrow\\quad B=(x,0)\\\\\nD&: BD=22 \\quad\\Longrightarrow\\quad D=(x+22,0)\\\\\nE&: CE=31 \\quad\\Longrightarrow\\quad E=(26+31,0)=(57,0)\\\\\nF&: DF=33 \\quad\\Longrightarrow\\quad F=(x+22+33,0)=(x+55,0)\\\\\n\\text{and }AF&=73 \\Longrightarrow x+55=73 .\n\\end{aligned}\n\\]\n\nHence \\(x=18\\). So  \n\n\\[\nA=0,\\; B=18,\\; C=26,\\; D=40,\\; E=57,\\; F=73 .\n\\]\n\nThese satisfy all given segment lengths.\n\n---\n\n### 2.  Locate point \\(G\\)\n\nLet \\(G=(u,v)\\) with \\(v\\neq 0\\).  \nFrom the given distances\n\n\\[\n\\begin{cases}\n(u-26)^2+v^2 = 40^2 =1600,\\\\[2pt]\n(u-40)^2+v^2 = 30^2 = 900 .\n\\end{cases}\n\\]\n\nSubtract the second equation from the first:\n\n\\[\n(u-26)^2-(u-40)^2 = 700 .\n\\]\n\nExpanding,\n\n\\[\n(-52u+676)-(-80u+1600)=28u-924=700\n\\Longrightarrow 28u=1624\\Longrightarrow u=58 .\n\\]\n\nNow find \\(v\\):\n\n\\[\n(58-26)^2+v^2=1600\\Longrightarrow 32^2+v^2=1600\n\\Longrightarrow v^2=1600-1024=576 .\n\\]\n\nThus \\(|v|=24\\).  Take \\(v=24\\) (the sign does not affect the area).  \n\n\\[\n\\boxed{G=(58,24)} .\n\\]\n\n---\n\n### 3.  Area of \\(\\triangle BGE\\)\n\nPoints on the \\(x\\)-axis:\n\n\\[\nB=(18,0),\\qquad E=(57,0).\n\\]\n\nThe length of the base \\(BE\\) is\n\n\\[\nBE = 57-18 = 39 .\n\\]\n\nSince the line through \\(B\\) and \\(E\\) is the \\(x\\)-axis, the perpendicular distance from \\(G\\) to this line is \\(|v|=24\\).\n\nHence\n\n\\[\n[\\triangle BGE]=\\frac12\\,(BE)\\cdot(\\text{height})\n               =\\frac12\\cdot 39\\cdot 24\n               =\\frac{936}{2}=468 .\n\\]\n\n(Using the determinant formula also gives \\(468\\).)\n\n---\n\n\\[\n\\boxed{468}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
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+        "role": "user",
+        "content": "\nThe set of points in 3-dimensional coordinate space that lie in the plane $x+y+z=75$ whose coordinates satisfy the inequalities $x-yz<y-zx<z-xy$ forms three disjoint convex regions. Exactly one of those regions has finite area. The area of this finite region can be expressed in the form $a\\sqrt{b}$, where $a$ and $b$ are positive integers and $b$ is not divisible by the square of any prime. Find $a+b$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "The inequalities  \n\n\\[\nx-yz<y-zx<z-xy\n\\]\n\ncan be rewritten by factoring:\n\n\\[\n\\begin{aligned}\nx-yz<y-zx &\\iff (x-y)(1+z)<0,\\\\[2pt]\ny-zx<z-xy &\\iff (y-z)(1+x)<0 .\n\\end{aligned}\n\\]\n\nSince the points lie on the plane  \n\n\\[\nx+y+z=75\\qquad\\Longrightarrow\\qquad z=75-x-y,\n\\]\n\nthe two conditions become inequalities in the variables \\(x,y\\):\n\n\\[\n\\begin{cases}\n(x-y)\\bigl(76-x-y\\bigr)<0,\\\\[2pt]\n\\bigl(x+2y-75\\bigr)(1+x)<0 .\n\\end{cases}\n\\tag{1}\n\\]\n\n---\n\n### 1.  Geometry of the half\u2011planes\n\nFrom (1)\n\n* \\((x-y)(76-x-y)<0\\) gives either  \n\n  \\[\n  \\begin{cases}\n  x>y,\\;x+y>76 \\quad\\text{(region }A_1)\\\\\n  \\text{or}\\\\\n  x<y,\\;x+y<76 \\quad\\text{(region }A_2)\n  \\end{cases}\n  \\]\n\n* \\((x+2y-75)(1+x)<0\\) gives either  \n\n  \\[\n  \\begin{cases}\n  x<-1,\\;x+2y>75 \\quad\\text{(region }B_1)\\\\\n  \\text{or}\\\\\n  x>-1,\\;x+2y<75 \\quad\\text{(region }B_2)\n  \\end{cases}\n  \\]\n\nThe set of points satisfying both inequalities is the intersection of one of the\n\\(A_i\\) with one of the \\(B_j\\).\n\nChecking the four possibilities:\n\n* \\(A_1\\cap B_1=\\varnothing\\) (impossible to have \\(x>y\\) and \\(x<-1\\) while\n  \\(x+y>76\\)).\n* \\(A_1\\cap B_2\\) is non\u2011empty and unbounded (e.g. \\(x>77\\)).\n* \\(A_2\\cap B_1\\) is non\u2011empty and unbounded (e.g. \\(x<-1\\)).\n* \\(A_2\\cap B_2\\) is bounded.\n\nThus there are three convex components: two infinite ones and one finite one,\nthe latter being \\(A_2\\cap B_2\\).\n\n---\n\n### 2.  The finite region\n\n\\(A_2\\cap B_2\\) is described by  \n\n\\[\n\\begin{cases}\nx>-1,\\\\\nx<y,\\\\\nx+2y<75 .\n\\end{cases}\n\\]\n\nFrom \\(x+2y<75\\) we have \\(y<(75-x)/2\\).  \nTogether with \\(y>x\\) we obtain\n\n\\[\n-1<x<25,\\qquad x<y<\\frac{75-x}{2}.\n\\]\n\nThe three bounding lines intersect at\n\n\\[\n\\begin{aligned}\nx=-1 \\ \\text{and}\\ y=x&\\;&\\Rightarrow\\;(-1,-1),\\\\\nx=-1 \\ \\text{and}\\ x+2y=75&\\;&\\Rightarrow\\;(-1,38),\\\\\ny=x \\ \\text{and}\\ x+2y=75&\\;&\\Rightarrow\\;(25,25).\n\\end{aligned}\n\\]\n\nHence the finite region is the interior of the triangle with vertices  \n\\((-1,-1),\\;(-1,38),\\;(25,25)\\).\n\nIts area in the \\(xy\\)-plane is\n\n\\[\n\\text{Area}_{xy}\n=\\frac12\\cdot\\text{base}\\cdot\\text{height}\n=\\frac12\\cdot 39\\cdot 26 =507 .\n\\]\n\n---\n\n### 3.  Area on the plane \\(x+y+z=75\\)\n\nThe map \\((x,y)\\mapsto (x,y,75-x-y)\\) sends the \\(xy\\)-plane onto the given\nplane.  The area is scaled by the factor\n\n\\[\n\\bigl|\\partial_{x}(x,y,z)\\times\\partial_{y}(x,y,z)\\bigr|\n=|(1,0,-1)\\times(0,1,-1)|\n=|(1,1,1)|\n=\\sqrt{3}.\n\\]\n\nThus the area of the finite region on the plane is\n\n\\[\n\\text{Area}= \\sqrt{3}\\times 507 = 507\\sqrt{3}.\n\\]\n\n---\n\nThe required form is \\(a\\sqrt{b}\\) with \\(a=507,\\;b=3\\).  Hence\n\n\\[\na+b = 507+3 = 510.\n\\]\n\n\\[\n\\boxed{510}\n\\]",
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+      {
+        "role": "user",
+        "content": "\nThe product $ \\prod_{k=4}^{63} \\frac{\\log_k(5^{k^2-1})}{\\log_{k+1}(5^{k^2-4})} = \\frac{\\log_4(5^{15})}{\\log_5(5^{12})} \\cdot \\frac{\\log_5(5^{24})}{\\log_6(5^{21})} \\cdot \\frac{\\log_6(5^{35})}{\\log_7(5^{32})} \\cdots \\frac{\\log_{63}(5^{3968})}{\\log_{64}(5^{3965})} $ is equal to $ \\frac{m}{n} $, where $ m $ and $ n $ are relatively prime positive integers. Find $ m + n $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "\\[\nP=\\prod_{k=4}^{63}\\frac{\\log_k\\!\\big(5^{\\,k^2-1}\\big)}{\\log_{k+1}\\!\\big(5^{\\,k^2-4}\\big)}\n\\]\n\n---\n\n### 1.  Change of base  \n\n\\[\n\\log_a b=\\frac{\\ln b}{\\ln a}\n\\]\n\nHence  \n\n\\[\n\\begin{aligned}\n\\log_k\\!\\big(5^{k^2-1}\\big)&=\\frac{(k^2-1)\\ln5}{\\ln k},\\\\[2mm]\n\\log_{k+1}\\!\\big(5^{k^2-4}\\big)&=\\frac{(k^2-4)\\ln5}{\\ln(k+1)} .\n\\end{aligned}\n\\]\n\nTherefore each factor of the product is\n\n\\[\n\\frac{(k^2-1)\\ln5/\\ln k}{(k^2-4)\\ln5/\\ln(k+1)}\n= \\frac{k^2-1}{k^2-4}\\cdot\\frac{\\ln(k+1)}{\\ln k}.\n\\]\n\nThus  \n\n\\[\nP=\\Bigg(\\prod_{k=4}^{63}\\frac{k^2-1}{k^2-4}\\Bigg)\n   \\Bigg(\\prod_{k=4}^{63}\\frac{\\ln(k+1)}{\\ln k}\\Bigg).\n\\]\n\n---\n\n### 2.  Telescoping the logarithmic part  \n\n\\[\n\\prod_{k=4}^{63}\\frac{\\ln(k+1)}{\\ln k}\n =\\frac{\\ln5}{\\ln4}\\cdot\\frac{\\ln6}{\\ln5}\\cdots\\frac{\\ln64}{\\ln63}\n =\\frac{\\ln64}{\\ln4}\n =\\log_4 64 = 3 .\n\\]\n\n---\n\n### 3.  Simplify the rational part  \n\n\\[\n\\frac{k^2-1}{k^2-4}\n =\\frac{(k-1)(k+1)}{(k-2)(k+2)}\n =\\frac{k-1}{k-2}\\cdot\\frac{k+1}{k+2}.\n\\]\n\nHence  \n\n\\[\n\\prod_{k=4}^{63}\\frac{k^2-1}{k^2-4}\n =\\Bigg(\\prod_{k=4}^{63}\\frac{k-1}{k-2}\\Bigg)\n  \\Bigg(\\prod_{k=4}^{63}\\frac{k+1}{k+2}\\Bigg).\n\\]\n\n*First product*  \n\n\\[\n\\prod_{k=4}^{63}\\frac{k-1}{k-2}\n =\\frac{3}{2}\\cdot\\frac{4}{3}\\cdot\\frac{5}{4}\\cdots\\frac{62}{61}\n =\\frac{62}{2}=31 .\n\\]\n\n*Second product*  \n\n\\[\n\\prod_{k=4}^{63}\\frac{k+1}{k+2}\n =\\frac{5}{6}\\cdot\\frac{6}{7}\\cdot\\frac{7}{8}\\cdots\\frac{64}{65}\n =\\frac{5}{65}= \\frac{1}{13}.\n\\]\n\nThus the rational part equals  \n\n\\[\n31\\cdot\\frac{1}{13}= \\frac{31}{13}.\n\\]\n\n---\n\n### 4.  Combine the two parts  \n\n\\[\nP=\\frac{31}{13}\\times 3 = \\frac{93}{13}.\n\\]\n\nThe fraction \\(\\frac{93}{13}\\) is already in lowest terms, so  \n\n\\[\nm=93,\\qquad n=13,\\qquad m+n=93+13=106.\n\\]\n\n\\[\n\\boxed{106}\n\\]",
+        "role": "assistant"
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+        "role": "user",
+        "content": "\nFour unit squares form a $2 \\times 2$ grid. Each of the 12 unit line segments forming the sides of the squares is colored either red or blue in such a way that each unit square has 2 red sides and 2 blue sides. Find the number of such colorings.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n* \\(a_{1},a_{2}\\) be the two **vertical** interior unit segments (the left\u2013right dividing line),  \n* \\(b_{1},b_{2}\\) be the two **horizontal** interior unit segments (the bottom\u2013top dividing line).\n\nThe eight outer\u2013boundary unit segments belong to only one square, while each interior segment belongs to two squares.\n\n---\n\n### 1.  Equations for the four unit squares  \n\nDenote by \\(L_1 ,D_1\\) the left and bottom edges of the lower\u2011left square, etc.  \nWriting a red edge as \\(1\\) and a blue edge as \\(0\\), the condition \u201cexactly two red sides\u2019\u2019 for each square gives  \n\n\\[\n\\begin{aligned}\nL_1 + D_1 + a_{1}+ b_{1} &=2,\\\\\nD_2 + R_2 + a_{1}+ b_{2} &=2,\\\\\nL_3 + T_3 + a_{2}+ b_{1} &=2,\\\\\nR_4 + T_4 + a_{2}+ b_{2} &=2,\n\\end{aligned}\n\\]\n\nwhere the eight variables \\(L_1,D_1,D_2,R_2,L_3,T_3,R_4,T_4\\) are the boundary edges and the\nfour variables \\(a_{1},a_{2},b_{1},b_{2}\\) are the interior edges.\n\nFor a fixed choice of the interior edges, each equation tells us the sum of the two\nboundary edges of that square:\n\n\\[\n\\begin{aligned}\nL_1+D_1 &=2-(a_{1}+b_{1}),\\\\\nD_2+R_2 &=2-(a_{1}+b_{2}),\\\\\nL_3+T_3 &=2-(a_{2}+b_{1}),\\\\\nR_4+T_4 &=2-(a_{2}+b_{2}).\n\\end{aligned}\n\\tag{1}\n\\]\n\nThe right\u2011hand side can be \\(0,1,\\) or \\(2\\).  \n\n* If it is \\(0\\) or \\(2\\) there is **exactly one** way to colour the two boundary\nedges (both blue or both red).  \n* If it is \\(1\\) there are **two** ways (one red, one blue).\n\nThus for a given interior assignment the number of completions equals  \n\n\\[\n\\prod_{i=1}^{4}f\\bigl(2-(a_{i}+b_{j})\\bigr),\n\\qquad\nf(0)=f(2)=1,\\;f(1)=2 .\n\\tag{2}\n\\]\n\nThe factor contributed by a square is \\(2\\) precisely when the sum of its two\ninterior edges equals \\(1\\).\n\n---\n\n### 2.  How many squares have interior\u2011sum \\(=1\\)?\n\nLet  \n\n\\[\nA = a_{1}+a_{2}\\quad(\\text{number of red vertical interiors}),\\qquad\nB = b_{1}+b_{2}\\quad(\\text{number of red horizontal interiors}).\n\\]\n\nFor a square the two interior edges are one vertical and one horizontal, so the\nsquare\u2019s interior sum is \\(1\\) exactly when the chosen vertical edge and horizontal\nedge have different colours.  Hence the number of squares with interior\u2011sum \\(=1\\) is  \n\n\\[\nN = A(2-B)+(2-A)B = 2A+2B-2AB.\n\\tag{3}\n\\]\n\nBecause \\(A,B\\in\\{0,1,2\\}\\),\n\n\\[\nN=\n\\begin{cases}\n0 & (A,B)=(0,0)\\text{ or }(2,2),\\\\[2pt]\n2 & \\text{otherwise except the next case},\\\\[2pt]\n4 & (A,B)=(0,2)\\text{ or }(2,0).\n\\end{cases}\n\\]\n\n---\n\n### 3.  Counting all interior assignments  \n\nThe numbers of interior assignments for each \\((A,B)\\) are\n\n\\[\n\\begin{array}{c|c|c}\n(A,B) & \\text{\\# assignments} & N \\\\ \\hline\n(0,0) & 1 & 0\\\\\n(2,2) & 1 & 0\\\\\n(0,2) & 1 & 4\\\\\n(2,0) & 1 & 4\\\\\n(0,1) & 2 & 2\\\\\n(1,0) & 2 & 2\\\\\n(1,1) & 4 & 2\\\\\n(1,2) & 2 & 2\\\\\n(2,1) & 2 & 2\n\\end{array}\n\\]\n\nFor a given interior assignment the number of ways to colour the boundary\nedges is \\(2^{N}\\) (by (2)).  Therefore\n\n\\[\n\\begin{aligned}\n\\#\\text{colorings}&=\n1\\cdot2^{0}+1\\cdot2^{0}\n+1\\cdot2^{4}+1\\cdot2^{4}\n+ (2+2+4+2+2)\\cdot2^{2} \\\\[4pt]\n&=2\\cdot1 + 2\\cdot16 + 12\\cdot4 \\\\[4pt]\n&=2 + 32 + 48 \\\\[4pt]\n&=82 .\n\\end{aligned}\n\\]\n\n---\n\n\\[\n\\boxed{82}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nCircle $\\omega_1$ with radius 6 centered at point $A$ is internally tangent at point $B$ to circle $\\omega_2$ with radius 15. Points $C$ and $D$ lie on $\\omega_2$ such that $\\overline{BC}$ is a diameter of $\\omega_2$ and $\\overline{BC} \\perp \\overline{AD}$. The rectangle $EFGH$ is inscribed in $\\omega_1$ such that $\\overline{EF} \\perp \\overline{BC}$, $C$ is closer to $\\overline{GH}$ than to $\\overline{EF}$, and $D$ is closer to $\\overline{FG}$ than to $\\overline{EH}$, as shown. Triangles $\\triangle DGF$ and $\\triangle CHG$ have equal areas. The area of rectangle $EFGH$ is $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m + n$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n* \\(O\\) be the centre of \\(\\omega _2\\) (radius \\(15\\)),\n* \\(A\\) the centre of \\(\\omega _1\\) (radius \\(6\\)),\n* \\(B\\) the internal point of tangency of the two circles.\n\nPlace the picture on a coordinate plane.\n\n---\n\n### 1.  Coordinates of the given points  \n\nTake \\(O=(0,0)\\).  \nSince \\(OA=15-6=9\\) and the circles are tangent internally, we may put  \n\n\\[\nA=(9,0), \\qquad B=(15,0).\n\\]\n\n\\(BC\\) is a diameter of \\(\\omega _2\\) through \\(B\\); hence  \n\n\\[\nC=(-15,0).\n\\]\n\n\\(AD\\perp BC\\) forces \\(AD\\) to be the vertical line through \\(A\\); intersecting this line with\n\\(\\omega _2\\) gives  \n\n\\[\nD=(9,-12)\\quad\\text{or}\\quad (9,12).\n\\]\n\nThe condition \u201c\\(D\\) is closer to \\(\\overline{FG}\\) than to \\(\\overline{EH}\\)\u201d (see below) makes\n\\(D=(9,-12)\\).\n\n---\n\n### 2.  The rectangle \\(EFGH\\)\n\n\\(EFGH\\) is inscribed in the circle \\(\\omega_1\\), so its vertices lie on  \n\n\\[\n(x-9)^2+y^2=6^2=36 .\n\\]\n\nSince \\(\\overline{EF}\\perp BC\\) and \\(BC\\) is horizontal, \\(\\overline{EF}\\) is vertical.\nLet  \n\n\\[\n\\begin{aligned}\nE&=(9+w,\\,h),\\\\\nF&=(9+w,\\,-h),\\\\\nG&=(9-w,\\,-h),\\\\\nH&=(9-w,\\,h),\n\\end{aligned}\n\\]\n\nwhere \\(w>0,\\,h>0\\) are the half\u2011width and half\u2011height of the rectangle.\n\nAll four vertices satisfy the circle equation, giving the single relation  \n\n\\[\nw^{2}+h^{2}=36\\tag{1}\n\\]\n\n(the rectangle\u2019s centre is the circle\u2019s centre \\(A\\)).\n\nBecause the point \\(C=(-15,0)\\) is farther to the right than to the left,\nthe condition \u201c\\(C\\) is closer to \\(\\overline{GH}\\) than to \\(\\overline{EF}\\)\u2019\u2019 forces\n\\(\\overline{GH}\\) to be the **left** side (\\(x=9-w\\)), which is already the case.\n\nSince \\(D=(9,-12)\\) lies below the centre, \u201c\\(D\\) is closer to \\(\\overline{FG}\\) than to \\(\\overline{EH}\\)\u2019\u2019 forces\n\\(\\overline{FG}\\) to be the **bottom** side (\\(y=-h\\)).  This orientation matches the above labeling.\n\n---\n\n### 3.  Areas of the two triangles  \n\n*Triangle \\(DGF\\)*  \n\nThe points are \\(D(9,-12),\\; G(9-w,-h),\\; F(9+w,-h)\\).\nIts base \\(GF\\) has length \\(2w\\) and its height (vertical distance from \\(D\\) to the base) is \\(12-h\\).  \nHence  \n\n\\[\n[\\,DGF\\,]=\\tfrac12\\,(2w)(12-h)=w(12-h).\\tag{2}\n\\]\n\n*Triangle \\(CHG\\)*  \n\nThe points are \\(C(-15,0),\\; H(9-w,h),\\; G(9-w,-h)\\).\nIts base \\(HG\\) has length \\(2h\\) and its horizontal distance from \\(C\\) to the line \\(x=9-w\\) is\n\\(|-15-(9-w)|=24-w\\).  \nThus  \n\n\\[\n[\\,CHG\\,]=\\tfrac12\\,(2h)(24-w)=h(24-w).\\tag{3}\n\\]\n\nThe problem states the two areas are equal, so\n\n\\[\nw(12-h)=h(24-w).\\tag{4}\n\\]\n\nExpanding gives \\(12w-wh=24h-wh\\), whence  \n\n\\[\n12w=24h \\qquad\\Longrightarrow\\qquad w=2h.\\tag{5}\n\\]\n\n---\n\n### 4.  Solving for \\(w\\) and \\(h\\)\n\nSubstituting \\(w=2h\\) into (1):\n\n\\[\n(2h)^2+h^2=36 \\;\\Longrightarrow\\;5h^{2}=36 \\;\\Longrightarrow\\;\nh=\\frac{6}{\\sqrt5}=\\frac{6\\sqrt5}{5}.\n\\]\n\nHence  \n\n\\[\nw=2h=\\frac{12}{\\sqrt5}=\\frac{12\\sqrt5}{5}.\n\\]\n\n---\n\n### 5.  Area of the rectangle  \n\nThe side lengths are \\(2w\\) and \\(2h\\).  Therefore  \n\n\\[\n\\text{Area}= (2w)(2h)=4wh.\n\\]\n\nUsing \\(w=2h\\),\n\n\\[\n4wh = 4(2h)h = 8h^{2}=8\\left(\\frac{36}{5}\\right)=\\frac{288}{5}.\n\\]\n\nThus the area is \\(\\displaystyle\\frac{288}{5}\\); the numerator and denominator are coprime.\n\n\\[\nm=288,\\qquad n=5,\\qquad m+n=288+5=293.\n\\]\n\n\\[\n\\boxed{293}\n\\]",
+        "role": "assistant"
+      }
+    ],
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+        "role": "user",
+        "content": "\nLet $ A $ be the set of positive integer divisors of 2025. Let $ B $ be a randomly selected subset of $ A $. The probability that $ B $ is a nonempty set with the property that the least common multiple of its elements is 2025 is $ \\frac{m}{n} $, where $ m $ and $ n $ are relatively prime positive integers. Find $ m + n $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "The divisors of \\(2025\\) are all numbers of the form  \n\n\\[\n3^{a}5^{b},\\qquad 0\\le a\\le 4,\\;0\\le b\\le 2 .\n\\]\n\nHence  \n\n\\[\n|A|=(4+1)(2+1)=15 .\n\\]\n\nSo there are \\(2^{15}\\) subsets of \\(A\\) (including the empty set).\n\n--------------------------------------------------------------------\n### When does a subset have lcm \\(2025\\)?\n\nThe prime factorisation of \\(2025\\) is  \n\n\\[\n2025 = 3^{4}\\,5^{2}.\n\\]\n\nFor a subset \\(B\\subseteq A\\),\n\n\\[\n\\operatorname{lcm}(B)=3^{\\max a_i}\\,5^{\\max b_i},\n\\]\n\nwhere \\((a_i,b_i)\\) are the exponents of the elements of \\(B\\).\nThus \\(\\operatorname{lcm}(B)=2025\\) iff  \n\n* at least one element has exponent \\(a=4\\) (i.e. contains \\(3^4\\));\n* at least one element has exponent \\(b=2\\) (i.e. contains \\(5^2\\)).\n\n--------------------------------------------------------------------\n### Sets that provide the required exponents  \n\n\\[\nA_4=\\{d\\in A:3^4\\mid d\\}=\\{3^4\\! \\cdot\\! 5^0,\\;3^4\\! \\cdot\\!5^1,\\;3^4\\! \\cdot\\!5^2\\}\n\\]\nhas \\(|A_4|=3\\) elements.\n\n\\[\nB_2=\\{d\\in A:5^2\\mid d\\}=\\{3^0\\! \\cdot\\!5^2,\\;3^1\\! \\cdot\\!5^2,\\;3^2\\! \\cdot\\!5^2,\n\\;3^3\\! \\cdot\\!5^2,\\;3^4\\! \\cdot\\!5^2\\}\n\\]\nhas \\(|B_2|=5\\) elements.\n\nTheir intersection is the single divisor \\(2025=3^4\\! \\cdot\\!5^2\\).\n\n--------------------------------------------------------------------\n### Counting the suitable subsets  \n\nA subset \\(B\\) works iff it contains **at least one** element of \\(A_4\\) **and** at least one element of \\(B_2\\).\n\nUsing inclusion\u2013exclusion on the \\(2^{15}\\) total subsets:\n\n\\[\n\\begin{aligned}\nN &= 2^{15}\n     -\\underbrace{2^{15-3}}_{\\text{subsets missing }A_4}\n     -\\underbrace{2^{15-5}}_{\\text{subsets missing }B_2}\n     +\\underbrace{2^{15-7}}_{\\text{subsets missing both}} \\\\[4pt]\n  &= 2^{15}-2^{12}-2^{10}+2^{8}\\\\\n  &= 32768-4096-1024+256\\\\\n  &= 27904 .\n\\end{aligned}\n\\]\n\nThus the desired probability is  \n\n\\[\n\\frac{N}{2^{15}}=\\frac{27904}{32768}\n          =\\frac{109}{128}\\qquad(\\text{after cancelling }256).\n\\]\n\n--------------------------------------------------------------------\n### Answer  \n\n\\(m=109,\\;n=128\\), so  \n\n\\[\nm+n=109+128=237 .\n\\]\n\n\\[\n\\boxed{237}\n\\]",
+        "role": "assistant"
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+        "role": "user",
+        "content": "\nAlex divides a disk into four quadrants with two perpendicular diameters intersecting at the center of the disk. He draws 25 more line segments through the disk, drawing each segment by selecting two points at random on the perimeter of the disk in different quadrants and connecting those two points. Find the expected number of regions into which these 27 line segments divide the disk.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "**Step 1 \u2013  What we have to count**\n\nThe two perpendicular diameters are two line segments that intersect once, so after they are drawn the disk is divided into  \n\n\\[\nF_0=4\\qquad\\text{regions}.\n\\]\n\nEvery time we draw a new segment, it splits each region it meets into two pieces.  \nIf the new segment meets \\(k\\) already\u2011drawn segments in interior points, it creates \\(k+1\\) new regions.  \n\nHence  \n\n\\[\n\\boxed{\\text{# of regions}=1+\\#\\text{segments}+ \\#\\text{intersection points}}\n\\tag{1}\n\\]\n\n(the \u201c\\(1\\)\u201d is the original whole disk).  \nWe have \\(27\\) segments in total (the 2 diameters + the 25 random chords).  \nThus we only have to find the **expected number of intersection points**.\n\n--------------------------------------------------------------------\n\n**Step 2 \u2013  Intersections with the two diameters**\n\nFor a random chord we must choose its two endpoints in *different* quadrants.\nThe unordered pair of quadrants is equally likely among the  \n\n\\[\n\\binom{4}{2}=6\n\\]\n\npossibilities.  \n\n* Adjacent quadrants (four choices) \u2013 the chord meets **one** diameter.  \n* Opposite quadrants (two choices) \u2013 the chord meets **both** diameters.\n\nTherefore for one random chord  \n\n\\[\nE[\\text{diameters met}]\n=\\frac{4}{6}\\cdot1+\\frac{2}{6}\\cdot2=\\frac{4}{3}.\n\\]\n\nWith \\(N=25\\) random chords\n\n\\[\nE[\\text{intersections with the two diameters}]\n=N\\cdot\\frac{4}{3}= \\frac{100}{3}.\n\\tag{2}\n\\]\n\n--------------------------------------------------------------------\n\n**Step 3 \u2013  Intersection of two random chords**\n\nLet a chord be drawn.  \nWrite its endpoints as angles measured from the positive \\(x\\)\u2013axis.\nBecause the two endpoints are in different quadrants, the unordered pair of\nquadrants is uniform among the six possibilities.\n\n*Probability that a second random chord meets the first.*\n\nLet the first chord be fixed.  \nDenote by \\(I\\) the clockwise arc of the circle from its first endpoint to its\nsecond endpoint; let \\(|I|=L\\).\nIf a second chord has one endpoint in \\(I\\) and the other outside \\(I\\) the two\nchords intersect.  \n\nWhen the second chord is chosen, its first endpoint \\(U\\) is uniform on the whole\ncircle, and its second endpoint \\(V\\) is uniform on the *three* quadrants that are\ndifferent from the quadrant of \\(U\\).  \nA short calculation (integrating over the position of \\(U\\) inside \\(I\\))\ngives for a fixed chord\n\n\\[\n\\boxed{q=\\frac{L}{\\pi}-\\frac{2L^{2}}{3\\pi^{2}}\n      +\\frac{2}{3\\pi^{2}}\\!\\int_{I}\\!|I\\cap Q(\\theta)|\\,d\\theta},\n\\tag{3}\n\\]\nwhere \\(Q(\\theta)\\) is the quadrant containing \\(\\theta\\).\n\nNow we average (3) over the possible positions of the first chord.\n\n*Adjac\u00adent quadrants.*  \nThe arc \\(I\\) lies in exactly two quadrants; write its lengths in those\nquadrants as \\(L_{1},L_{2}\\) (\\(L=L_{1}+L_{2}\\)).  \nThen \\(\\int_{I}|I\\cap Q|\\,d\\theta = L_{1}^{2}+L_{2}^{2}\\).\nWith \\(L_{1},L_{2}\\) independent and uniform on \\([0,\\pi/2]\\),\n\n\\[\nE[q\\mid\\text{adjacent}] = \\frac{5}{12}.\n\\]\n\n*Opposite quadrants.*  \nNow \\(I\\) occupies three quadrants; let the lengths in the three\nquadrants be \\(u,\\,\\pi/2,\\,v\\) (\\(u,v\\) independent uniform on \\([0,\\pi/2]\\)).  \nThen \\(\\int_{I}|I\\cap Q|\\,d\\theta = u^{2}+(\\pi/2)^{2}+v^{2}\\).\nAveraging gives\n\n\\[\nE[q\\mid\\text{opposite}] = \\frac{7}{12}.\n\\]\n\nThe first chord is adjacent with probability \\(\\frac{2}{3}\\) and opposite with\nprobability \\(\\frac13\\).  Hence the probability that two independently drawn\nrandom chords intersect is\n\n\\[\np=\\frac{2}{3}\\cdot\\frac{5}{12}+\\frac{1}{3}\\cdot\\frac{7}{12}\n    =\\frac{17}{36}.\n\\tag{4}\n\\]\n\n--------------------------------------------------------------------\n\n**Step 4 \u2013  Expected intersections among the 25 random chords**\n\nThere are \\(\\binom{25}{2}=300\\) unordered pairs of random chords, each\nintersecting with probability \\(p\\).  Thus\n\n\\[\nE[\\text{intersections among the 25 chords}]\n=300\\cdot\\frac{17}{36}= \\frac{425}{3}.\n\\tag{5}\n\\]\n\n--------------------------------------------------------------------\n\n**Step 5 \u2013  Total expected number of intersection points**\n\nAdd all contributions:\n\n* one intersection of the two diameters,\n* intersections of random chords with the two diameters \\(\\displaystyle\\frac{100}{3}\\)   (from (2)),\n* intersections among the random chords \\(\\displaystyle\\frac{425}{3}\\)   (from (5)).\n\n\\[\nE[\\text{total intersections}]\n=1+\\frac{100}{3}+\\frac{425}{3}=1+\\frac{525}{3}=176.\n\\tag{6}\n\\]\n\n--------------------------------------------------------------------\n\n**Step 6 \u2013  Expected number of regions**\n\nInsert (6) into formula (1):\n\n\\[\nE[\\text{regions}]\n=1+\\underbrace{27}_{\\text{segments}}+\\underbrace{176}_{\\text{intersection points}}\n=204 .\n\\]\n\n--------------------------------------------------------------------\n\n\\[\n\\boxed{204}\n\\]",
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+        "role": "user",
+        "content": "\nThere are $ n $ values of $ x $ in the interval $ 0 < x < 2\\pi $ where $ f(x) = \\sin(7\\pi \\cdot \\sin(5x)) = 0 $. For $ t $ of these $ n $ values of $ x $, the graph of $ y = f(x) $ is tangent to the $ x $-axis. Find $ n + t $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "The zeros of  \n\n\\[\nf(x)=\\sin\\bigl(7\\pi\\sin(5x)\\bigr)\n\\]\n\nsatisfy  \n\n\\[\n\\sin\\bigl(7\\pi\\sin(5x)\\bigr)=0\\Longrightarrow 7\\pi\\sin(5x)=k\\pi,\\qquad k\\in\\mathbb Z .\n\\]\n\nHence  \n\n\\[\n\\sin (5x)=\\frac{k}{7},\\qquad -7\\le k\\le 7 .\n\\]\n\n---\n\n### 1.  Counting all zeros \\(n\\)\n\nPut \\(\\theta =5x\\).  \nBecause \\(0<x<2\\pi\\), we have \\(0<\\theta<10\\pi\\).\n\nFor each integer \\(k\\) we count the solutions of \\(\\sin\\theta = k/7\\) in \\((0,10\\pi)\\).\n\n* **\\(k=\\pm7\\) :** \\(\\sin\\theta=\\pm1\\).  \n  Solutions are \\(\\theta =\\frac{\\pi}{2}+2\\pi m\\) (or \\(\\frac{3\\pi}{2}+2\\pi m\\)).  \n  In a length \\(10\\pi\\) there are \\(5\\) such values for each sign.  \n  \u2192 \\(5+5=10\\) solutions.\n\n* **\\(k=0\\) :** \\(\\sin\\theta=0\\).  \n  Solutions are \\(\\theta=n\\pi\\).  \n  With \\(0<\\theta<10\\pi\\) we have \\(n=1,2,\\dots ,9\\): \\(9\\) solutions.\n\n* **\\(k=\\pm1,\\pm2,\\ldots,\\pm6\\) (12 values):** \\(\\sin\\theta = k/7\\) is a non\u2011extreme value.  \n  In each full period of length \\(2\\pi\\) there are \\(2\\) solutions; we have five periods, so each such \\(k\\) yields \\(10\\) solutions.  \n  \u2192 \\(12\\cdot10=120\\) solutions.\n\nHence  \n\n\\[\nn = 10\\;(\\text{from }k=\\pm7)+9\\;(\\text{from }k=0)+120\\;(\\text{from }k=\\pm1,\\dots,\\pm6)=139 .\n\\]\n\n---\n\n### 2.  Tangential zeros \\(t\\)\n\nThe derivative is  \n\n\\[\nf'(x)=\\cos\\bigl(7\\pi\\sin(5x)\\bigr)\\cdot 7\\pi\\cdot5\\cos(5x)\n      =35\\pi\\cos\\bigl(7\\pi\\sin(5x)\\bigr)\\cos(5x).\n\\]\n\nAt a zero of \\(f\\) we have \\(\\sin(5x)=k/7\\) and thus  \n\\(\\cos(7\\pi\\sin(5x))=\\cos(k\\pi)=(-1)^{k}\\).\n\nTherefore  \n\n\\[\nf'(x)=35\\pi(-1)^{k}\\cos(5x).\n\\]\n\nFor the graph to be tangent to the \\(x\\)-axis we need \\(f'(x)=0\\); this occurs exactly when  \n\n\\[\n\\cos(5x)=0 \\quad\\Longleftrightarrow\\quad \\sin(5x)=\\pm1.\n\\]\n\nThus the tangential zeros correspond to the case \\(k=\\pm7\\).  \nWe already counted those: \\(5\\) solutions for \\(k=7\\) and \\(5\\) for \\(k=-7\\).\n\n\\[\nt = 5+5 = 10.\n\\]\n\n---\n\n### 3.  Required sum\n\n\\[\nn+t = 139+10 = 149.\n\\]\n\n\\[\n\\boxed{149}\n\\]",
+        "role": "assistant"
+      }
+    ],
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+      {
+        "role": "user",
+        "content": "\nSixteen chairs are arranged in a row. Eight people each select a chair in which to sit so that no person sits next to two other people. Let $ N $ be the number of subsets of 16 chairs that could be selected. Find the remainder when $ N $ is divided by 1000.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let the chairs be numbered \\(1,2,\\dots ,16\\).\nChoosing the chairs for the eight people is equivalent to writing a binary\nstring of length \\(16\\) with exactly eight \\(1\\)\u2019s (occupied chairs) and\nseven \\(0\\)\u2019s (empty chairs).\n\nThe condition *\u201cno person sits next to two other people\u2019\u2019* means that no\noccupied chair can have occupied neighbours on both sides; thus the binary\nstring must contain **no substring \\(111\\)**.  \nHence we must count binary strings of length \\(16\\) with weight \\(8\\) that avoid\n\\(111\\).\n\n---\n\n### 1.  Describing the strings\n\nThe \\(1\\)\u2019s can appear only in blocks of length \\(1\\) or \\(2\\) (a block of\nlength \\(3\\) would give a forbidden \\(111\\)).  \nSuppose there are  \n\n* \\(s\\) blocks of length \\(2\\);\n* \\(t-s\\) blocks of length \\(1\\),\n\nso the total number of blocks of \\(1\\)\u2019s is \\(t\\).  \nIf each block of length \\(2\\) contributes \\(2\\) and each block of length\n\\(1\\) contributes \\(1\\), then  \n\n\\[\n2s+(t-s)=8\\qquad\\Longrightarrow\\qquad t=8-s .\n\\]\n\nThus \\(s\\) can be \\(0,1,2,3,4\\) (since at most \\(\\lfloor 8/2\\rfloor =4\\) blocks\nof length \\(2\\) are possible).\n\nFor a given \\(s\\) the blocks are ordered, and we must choose which \\(s\\) of\nthe \\(t\\) blocks are the length\u2011\\(2\\) blocks:\n\n\\[\n\\text{choices for block sizes}= \\binom{t}{s}= \\binom{8-s}{s}.\n\\]\n\n---\n\n### 2.  Placing the zeros\n\nBetween two consecutive blocks of \\(1\\)\u2019s there must be at least one\n\\(0\\).  With \\(t\\) blocks there are \\(t-1\\) mandatory zeros.\nThere are \\(8\\) zeros in total (since \\(16-8=8\\)).  \nHence the number of *extra* zeros we may distribute is  \n\n\\[\n8-(t-1)=9-t .\n\\]\n\nThese extra zeros can be placed in any of the \\(t+1\\) gaps\n(before the first block, between blocks, after the last block).  \nBy stars and bars the number of distributions is\n\n\\[\n\\binom{(9-t)+(t+1)-1}{(t+1)-1}\n   =\\binom{9}{t}\n   =\\binom{9}{8-s}.\n\\]\n\n---\n\n### 3.  Total number of admissible subsets\n\nSumming over all possible \\(s\\):\n\n\\[\n\\begin{aligned}\nN &=\\sum_{s=0}^{4}\n    \\binom{8-s}{s}\\binom{9}{8-s}  \\\\\n  &=\\binom{8}{0}\\binom{9}{8}\n   +\\binom{7}{1}\\binom{9}{7}\n   +\\binom{6}{2}\\binom{9}{6}\n   +\\binom{5}{3}\\binom{9}{5}\n   +\\binom{4}{4}\\binom{9}{4}   \\\\\n  &=1\\cdot 9\n   +7\\cdot 36\n   +15\\cdot 84\n   +10\\cdot 126\n   +1\\cdot 126 \\\\\n  &=9+252+1260+1260+126 \\\\\n  &=2907 .\n\\end{aligned}\n\\]\n\nThus there are \\(N=2907\\) subsets of chairs that satisfy the condition.\n\n---\n\n### 4.  Remainder modulo \\(1000\\)\n\n\\[\n2907 \\equiv 907 \\pmod{1000}.\n\\]\n\n\\[\n\\boxed{907}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nSuppose $ \\triangle ABC $ has angles $ \\angle BAC = 84^\\circ $, $ \\angle ABC = 60^\\circ $, and $ \\angle ACB = 36^\\circ $. Let $ D, E, $ and $ F $ be the midpoints of sides $ \\overline{BC} $, $ \\overline{AC} $, and $ \\overline{AB} $, respectively. The circumcircle of $ \\triangle DEF $ intersects $ \\overline{BD} $, $ \\overline{AE} $, and $ \\overline{AF} $ at points $ G, H, $ and $ J $, respectively. The points $ G, D, E, H, J, $ and $ F $ divide the circumcircle of $ \\triangle DEF $ into six minor arcs, as shown. Find $ \\widehat{DE} + 2 \\cdot \\widehat{HJ} + 3 \\cdot \\widehat{FG} $, where the arcs are measured in degrees.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n\\[\nA=84^\\circ ,\\qquad B=60^\\circ ,\\qquad C=36^\\circ .\n\\]\n\nDenote by \\(O\\) the circumcenter of \\(\\triangle ABC\\) and by \\(N\\) the nine\u2011point\ncenter (the circumcenter of \\(\\triangle DEF\\)).\nPut the circumcircle of \\(\\triangle ABC\\) on the unit circle and let  \n\n\\[\na=1,\\qquad \nb=e^{i\\beta },\\qquad \nc=e^{i\\gamma},\n\\]\n\nwhere the central arcs satisfy  \n\n\\[\n\\widehat{AB}=2C=72^\\circ ,\\qquad \n\\widehat{BC}=2A=168^\\circ ,\\qquad \n\\widehat{CA}=2B=120^\\circ .\n\\]\n\nHence  \n\n\\[\n\\beta =72^\\circ ,\\qquad \\gamma =\\beta +168^\\circ =240^\\circ .\n\\]\n\n--------------------------------------------------------------------\n### 1.  The nine\u2011point centre and the midpoints  \n\n\\[\nN=\\frac{a+b+c}{2},\\qquad \nD=\\frac{b+c}{2},\\;E=\\frac{c+a}{2},\\;F=\\frac{a+b}{2}.\n\\]\n\nFrom these formulas  \n\n\\[\nND=-\\frac a2,\\qquad NE=-\\frac b2,\\qquad NF=-\\frac c2 .\\tag{1}\n\\]\n\nThus the directions of the radii to the midpoints are opposite the\ndirections of the vertices:\n\n\\[\n\\arg(ND)=\\alpha+180^\\circ ,\\quad \n\\arg(NE)=\\beta+180^\\circ ,\\quad \n\\arg(NF)=\\gamma+180^\\circ .\n\\]\n\nConsequently  \n\n\\[\n\\widehat{DE}=|\\arg(NE)-\\arg(ND)|\n      =( \\beta+180^\\circ)-( \\alpha+180^\\circ)=\\beta-\\alpha\n      =2C=72^\\circ .\\tag{2}\n\\]\n\n--------------------------------------------------------------------\n### 2.  The second intersections  \n\nFor a chord whose one endpoint is known, the second endpoint is obtained\nby reflecting the known radius about the line through \\(N\\) that is\nperpendicular to the given line.\n\n*Line \\(BD\\).*  \nThe direction of \\(BD\\) is \\(\\arg(c-b)\\).  \nSince the perpendicular through \\(N\\) makes the angle \\(\\arg(c-b)+90^\\circ\\),\nreflecting \\(ND\\) in this line gives\n\n\\[\n\\arg(NG)=2\\bigl(\\arg(c-b)+90^\\circ\\bigr)-\\arg(ND)\n        =2\\arg(c-b)-\\arg(a).            \\tag{3}\n\\]\n\nUsing the identity  \n\n\\[\n\\arg(c-b)=\\frac{\\beta+\\gamma}{2}+90^\\circ,\n\\]\n\nwe obtain  \n\n\\[\n\\arg(NG)=2\\Bigl(\\frac{72^\\circ+240^\\circ}{2}+90^\\circ\\Bigr)\n        =492^\\circ\\equiv132^\\circ .\n\\]\n\nBecause \\(\\arg(NF)=\\gamma+180^\\circ=60^\\circ\\),\n\n\\[\n\\widehat{FG}=|\\arg(NG)-\\arg(NF)|=132^\\circ-60^\\circ=72^\\circ .\\tag{4}\n\\]\n\n*Line \\(AF\\) (the side \\(AB\\)).*  \nThe direction of \\(AB\\) is \\(\\arg(b-a)\\); hence\n\n\\[\n\\arg(NJ)=2\\arg(b-a)-\\arg(c).                \\tag{5}\n\\]\n\nNow  \n\n\\[\n\\arg(b-a)=\\frac{\\alpha+\\beta}{2}+90^\\circ=126^\\circ,\n\\]\n\nso  \n\n\\[\n\\arg(NJ)=2\\cdot126^\\circ-240^\\circ=12^\\circ .\\tag{6}\n\\]\n\n*Line \\(AE\\) (the median from \\(A\\)).*  \nThe direction of \\(AE\\) is \\(\\arg(c-a)\\); thus\n\n\\[\n\\arg(NH)=2\\arg(c-a)-\\arg(b).                \\tag{7}\n\\]\n\nHere  \n\n\\[\n\\arg(c-a)=\\frac{\\alpha+\\gamma}{2}+90^\\circ=210^\\circ ,\n\\]\n\nhence  \n\n\\[\n\\arg(NH)=2\\cdot210^\\circ-72^\\circ=348^\\circ\\equiv-12^\\circ .\\tag{8}\n\\]\n\nTherefore  \n\n\\[\n\\widehat{HJ}=|\\arg(NJ)-\\arg(NH)|\n            =12^\\circ-(-12^\\circ)=24^\\circ .\\tag{9}\n\\]\n\n--------------------------------------------------------------------\n### 3.  Required sum  \n\nFrom (2), (4) and (9),\n\n\\[\n\\widehat{DE}=72^\\circ ,\\qquad \n\\widehat{HJ}=24^\\circ ,\\qquad \n\\widehat{FG}=72^\\circ .\n\\]\n\nHence  \n\n\\[\n\\widehat{DE}+2\\widehat{HJ}+3\\widehat{FG}\n=72^\\circ+2\\cdot24^\\circ+3\\cdot72^\\circ\n=72+48+216\n=336^\\circ .\n\\]\n\n\\[\n\\boxed{336}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nLet $N$ denote the number of ordered triples of positive integers $(a,b,c)$ such that $a,b,c\\leq3^6$ and $a^3+b^3+c^3$ is a multiple of $3^7$. Find the remainder when $N$ is divided by $1000$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "\\[\n\\boxed{733}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nLet $ A_1A_2 \\ldots A_{11} $ be an 11-sided non-convex simple polygon with the following properties:\n* The area of $ A_iA_1A_{i+1} $ is 1 for each $ 2 \\leq i \\leq 10 $,\n* $ \\cos(\\angle A_iA_1A_{i+1}) = \\frac{12}{13} $ for each $ 2 \\leq i \\leq 10 $,\n* The perimeter of $ A_1A_2 \\ldots A_{11} $ is 20.\nIf $ A_1A_2 + A_1A_{11} $ can be expressed as $ \\frac{m\\sqrt{n} - p}{q} $ for positive integers $ m, n, p, q $ with $ n $ squarefree and no prime divides all of $ m, p, q$, find $ m + n + p + q $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n\\[\nr_i=A_1A_i\\qquad (i=2,\\dots ,11),\\qquad \n\\theta=\\angle A_iA_1A_{i+1}\\;(2\\le i\\le 10),\\qquad \n\\cos\\theta=\\frac{12}{13}.\n\\]\n\n---\n\n### 1.  Relation between the radii  \n\nThe area of \\(\\triangle A_iA_1A_{i+1}\\) is  \n\n\\[\n1=\\frac12 r_i r_{i+1}\\sin\\theta .\n\\]\n\nSince  \n\n\\[\n\\sin\\theta =\\sqrt{1-\\cos^2\\theta}= \\sqrt{1-\\left(\\frac{12}{13}\\right)^2}= \\frac{5}{13},\n\\]\n\nwe obtain  \n\n\\[\nr_i r_{i+1}= \\frac{2\\cdot13}{5}= \\frac{26}{5}\\;(=C).\n\\tag{1}\n\\]\n\nThus for every \\(i\\),\n\n\\[\nr_{i+1}= \\frac{C}{r_i},\\qquad C=\\frac{26}{5}.\n\\]\n\nConsequently the sequence alternates:\n\n\\[\nr_2=r_4=r_6=r_8=r_{10}=x,\\qquad\nr_3=r_5=r_7=r_9=r_{11}= \\frac{C}{x},\n\\]\n\nfor some positive number \\(x\\).\n\n---\n\n### 2.  Length of the side \\(A_iA_{i+1}\\)\n\nUsing the law of cosines in \\(\\triangle A_iA_1A_{i+1}\\),\n\n\\[\nA_iA_{i+1}^{2}=r_i^{2}+r_{i+1}^{2}-2r_i r_{i+1}\\cos\\theta .\n\\]\n\nBecause \\(r_i r_{i+1}=C\\) and \\(\\cos\\theta=\\frac{12}{13}\\),\n\n\\[\nA_iA_{i+1}^{2}=r_i^{2}+r_{i+1}^{2}\n          -2C\\cdot\\frac{12}{13}\n          =r_i^{2}+r_{i+1}^{2}-\\frac{48}{5}.\n\\]\n\nNow  \n\n\\[\nr_i^{2}+r_{i+1}^{2}\n   =(r_i+r_{i+1})^{2}-2r_i r_{i+1}\n   =(r_i+r_{i+1})^{2}-2C .\n\\]\n\nHence\n\n\\[\nA_iA_{i+1}^{2}= (r_i+r_{i+1})^{2}-2C-\\frac{48}{5}\n               =(r_i+r_{i+1})^{2}-20 .\n\\tag{2}\n\\]\n\nFor any consecutive pair \\((i,i+1)\\) we have  \n\n\\[\nr_i+r_{i+1}=x+\\frac{C}{x}\\;=:t .\n\\]\n\nThus every side \\(A_iA_{i+1}\\;(i=2,\\dots ,10)\\) has the same length  \n\n\\[\ns=\\sqrt{t^{2}-20}.\n\\tag{3}\n\\]\n\n---\n\n### 3.  Perimeter condition  \n\nThe perimeter of the 11\u2011gon is  \n\n\\[\n\\underbrace{A_1A_2}_{=x}\n+\\underbrace{A_{11}A_1}_{=C/x}\n+9s =t+9\\sqrt{t^{2}-20}=20 .\n\\tag{4}\n\\]\n\nSet \\(\\displaystyle u=\\sqrt{t^{2}-20}\\).  \nFrom (4) we have \\(u=\\dfrac{20-t}{9}\\).  Squaring gives\n\n\\[\nt^{2}-20=\\frac{(20-t)^{2}}{81}.\n\\]\n\nMultiplying by 81 and simplifying,\n\n\\[\n80t^{2}+40t-2020=0\\quad\\Longrightarrow\\quad\n4t^{2}+2t-101=0.\n\\]\n\nSolving,\n\n\\[\nt=\\frac{-2+\\sqrt{4+1616}}{8}\n  =\\frac{-2+18\\sqrt5}{8}\n  =\\frac{9\\sqrt5-1}{4}.\n\\]\n\nSince \\(t=x+C/x=A_1A_2+A_1A_{11}\\) is a sum of positive lengths,\nthe positive root is the only admissible one.\n\n---\n\n### 4.  Result  \n\n\\[\nA_1A_2+A_1A_{11}= \\frac{9\\sqrt5-1}{4}\n                 =\\frac{m\\sqrt n-p}{q},\n\\]\n\nwhere \\(m=9,\\;n=5,\\;p=1,\\;q=4\\).  \nHence\n\n\\[\nm+n+p+q=9+5+1+4=19.\n\\]\n\n\\[\n\\boxed{19}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nFrom an unlimited supply of 1-cent coins, 10-cent coins, and 25-cent coins, Silas wants to find a collection of coins that has a total value of $ N $ cents, where $ N $ is a positive integer. He uses the so-called **greedy algorithm**, successively choosing the coin of greatest value that does not cause the value of his collection to exceed $ N $. For example, to get 42 cents, Silas will choose a 25-cent coin, then a 10-cent coin, then 7 1-cent coins. However, this collection of 9 coins uses more coins than necessary to get a total of 42 cents; indeed, choosing 4 10-cent coins and 2 1-cent coins achieves the same total value with only 6 coins.\n\nIn general, the greedy algorithm succeeds for a given $ N $ if no other collection of 1-cent, 10-cent, and 25-cent coins gives a total value of $ N $ cents using strictly fewer coins than the collection given by the greedy algorithm. Find the number of values of $ N $ between 1 and 1000 inclusive for which the greedy algorithm succeeds.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "For the denominations \\(\\{1,10,25\\}\\) let  \n\n\\[\nN=25a+b,\\qquad 0\\le b<25 .\n\\]\n\nThe greedy algorithm first uses \\(a\\) quarters, then \\(\\big\\lfloor b/10\\big\\rfloor\\) dimes and finally \\(b\\bmod 10\\) pennies.\nHence the greedy number of coins is  \n\n\\[\nC_{\\text{greedy}}(N)=a+\\Big\\lfloor\\frac{b}{10}\\Big\\rfloor+(b\\bmod 10)=a+f(b),\n\\]\nwhere  \n\n\\[\nf(x)=\\Big\\lfloor\\frac{x}{10}\\Big\\rfloor+(x\\bmod 10).\n\\]\n\nIf we keep only \\(a-k\\) quarters (\\(k\\ge 1\\)), the remainder becomes \\(b+25k\\).  \nThe optimal way to represent the remainder with dimes and pennies still uses the greedy method,\nso the total number of coins with \\(a-k\\) quarters is  \n\n\\[\nC_k(N)=a-k+f(b+25k).\n\\]\n\nThe greedy algorithm fails iff for some \\(k\\ge1\\)\n\n\\[\nC_k(N)<C_{\\text{greedy}}(N)\n\\Longleftrightarrow \nf(b+25k)\\le f(b)+k-1 .\n\\tag{1}\n\\]\n\n--------------------------------------------------------------------\n### 1.  Evaluating \\(f(b+25k)-f(b)\\)\n\nWrite \\(b=10t+r\\) with \\(t\\in\\{0,1,2\\}\\) and \\(r=b\\bmod 10\\in\\{0,\\dots,9\\}\\).\nLet \\(\\alpha=r/10\\;(0\\le\\alpha<1)\\).\n\nSince  \n\n\\[\nf(x)=\\Big\\lfloor\\frac{x}{10}\\Big\\rfloor+(x\\bmod10)\n      =x-9\\Big\\lfloor\\frac{x}{10}\\Big\\rfloor ,\n\\]\n\nwe obtain  \n\n\\[\n\\begin{aligned}\nf(b+25k)-f(b)\n&=9\\Big\\lfloor\\frac{b+25k}{10}\\Big\\rfloor-24k\\\\\n&=9\\Big\\lfloor 2.5k+\\alpha\\Big\\rfloor-24k .\n\\end{aligned}\n\\tag{2}\n\\]\n\nSet  \n\n\\[\n\\Delta(k)=9\\Big\\lfloor 2.5k+\\alpha\\Big\\rfloor-24k .\n\\]\n\nA failure occurs when \\(\\Delta(k)>0\\) and \\(k\\le a\\).\n\n--------------------------------------------------------------------\n### 2.  When can \\(\\Delta(k)>0\\)?\n\nFor any integer \\(k\\),\n\n\\[\n\\Big\\lfloor2.5k\\Big\\rfloor=\n\\frac{5k-(k\\bmod2)}{2}.\n\\]\n\nHence  \n\n\\[\n\\Delta(k)= -\\frac{3k+9(k\\bmod2)}{2}+9\\delta ,\n\\quad\\text{where }\\delta=\n\\begin{cases}\n1,&\\alpha\\ge 1-\\{2.5k\\},\\\\\n0,&\\text{otherwise}.\n\\end{cases}\n\\]\n\nThe term \\(-\\frac{3k+9(k\\bmod2)}{2}\\) is negative for all \\(k\\ge1\\).\nThe only way \\(\\Delta(k)\\) can become positive is when \\(\\delta=1\\).\n\n*If \\(k\\) is even*, \\(\\{2.5k\\}=0\\); thus \\(\\alpha<1\\) never makes \\(\\delta=1\\).\nHence \\(\\Delta(k)\\le0\\) for all even \\(k\\).\n\n*If \\(k\\) is odd*, \\(\\{2.5k\\}=0.5\\).  \nThen \\(\\delta=1\\) exactly when \\(\\alpha\\ge 0.5\\), i.e. when \\(r\\ge5\\) (the remainder of \\(b\\) modulo \\(10\\) is at least \\(5\\)).\n\nFor odd \\(k\\ge3\\) we have  \n\n\\[\n\\Delta(k)=-9+9\\delta\\le0,\n\\]\n\nso no improvement occurs.  \n\nFor \\(k=1\\),\n\n\\[\n\\Delta(1)= -6+9\\delta,\n\\]\n\nwhich is positive precisely when \\(\\delta=1\\); that is, when \\(r\\ge5\\).\n\nConsequently **the greedy algorithm fails exactly when**\n\n* \\(N\\ge25\\) (so at least one quarter is used), and\n* the remainder \\(b=N\\bmod25\\) satisfies \\(b\\bmod10\\ge5\\).\n\nIn terms of residues modulo \\(25\\) this means\n\n\\[\nb\\in\\{5,6,7,8,9,15,16,17,18,19\\}.\n\\tag{3}\n\\]\n\n--------------------------------------------------------------------\n### 3.  Counting the failures\n\nFrom \\(1\\) to \\(1000\\):\n\n* For \\(N<25\\) the greedy algorithm is always optimal (no quarters are used).\n* For each complete block of \\(25\\) numbers, exactly the \\(10\\) residues listed in (3) cause a failure.\n\nThe interval \\(25\\le N\\le999\\) contains \\(39\\) full blocks of size \\(25\\):\n\\[\n39\\cdot10=390\\text{ failures}.\n\\]\n\n\\(N=1000\\) has residue \\(0\\) modulo \\(25\\), so it is not a failure.\n\nThus the number of values where the greedy algorithm **succeeds** is  \n\n\\[\n1000-390 = 610.\n\\]\n\n\\[\n\\boxed{610}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nFind the sum of all integer bases $b>9$ for which $17_{b}$ is a divisor of $97_{b}$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "In base \\(b\\),\n\n\\[\n17_b = 1\\cdot b+7 = b+7,\\qquad 97_b = 9\\cdot b+7 .\n\\]\n\nWe need integer bases \\(b>9\\) such that \\(b+7\\) divides \\(9b+7\\).\n\nLet  \n\n\\[\nn = b+7 \\quad\\Longrightarrow\\quad b = n-7.\n\\]\n\nThen  \n\n\\[\n9b+7 = 9(n-7)+7 = 9n-56 .\n\\]\n\nHence \\(n\\) must divide \\(9n-56\\):\n\n\\[\nn \\mid (9n-56) \\;\\Longrightarrow\\; n \\mid (9n-56) - 9n = -56.\n\\]\n\nThus \\(n\\) is a positive divisor of \\(56\\).  \nSince \\(b>9\\), we have \\(n=b+7>16\\); therefore we need divisors of \\(56\\) that are \\(\\ge 17\\).\n\nDivisors of \\(56 = 2^3\\cdot7\\) are  \n\n\\[\n1,\\;2,\\;4,\\;7,\\;8,\\;14,\\;28,\\;56.\n\\]\n\nOnly \\(28\\) and \\(56\\) satisfy \\(n\\ge 17\\).\n\nCorresponding bases:\n\n\\[\nb = n-7 \\quad\\Rightarrow\\quad \n\\begin{cases}\nn=28 &\\Rightarrow b = 21,\\\\[2pt]\nn=56 &\\Rightarrow b = 49.\n\\end{cases}\n\\]\n\nBoth bases exceed \\(9\\) and the digits \\(1,7,9\\) are allowed.\n\nFinally, the sum of all such bases is  \n\n\\[\n21 + 49 = 70.\n\\]\n\n\\[\n\\boxed{70}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nLet $ S $ be the set of vertices of a regular 24-gon. Find the number of ways to draw 12 segments of equal lengths so that each vertex in $ S $ is an endpoint of exactly one of the 12 segments.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Label the vertices of the regular \\(24\\)-gon by the residues  \n\\(\\{0,1,2,\\dots ,23\\}\\) modulo \\(24\\).\n\nIf the \\(12\\) drawn segments all have the same Euclidean length, then each\nsegment must join two vertices whose indices differ by a fixed integer  \n\\(k\\;(1\\le k\\le 12)\\) (the \u201cstep size\u2019\u2019), because the length of a chord in a\nregular polygon depends only on this step.\n\nThus for a fixed \\(k\\) we have to choose a perfect matching of the graph  \n\n\\[\nG_k=\\big\\{\\{i,i+k\\}\\mid i=0,1,\\dots ,23\\big\\}.\n\\]\n\n--------------------------------------------------------------------\n### 1.   Structure of \\(G_k\\)\n\n\\(G_k\\) is a **2\u2011regular** graph; each vertex has exactly the two neighbours\n\\(i\\pm k\\).  \nLet  \n\n\\[\nd=\\gcd(k,24).\n\\]\n\nThen the vertices split into \\(d\\) cycles, each of length  \n\n\\[\nt=\\frac{24}{d}.\n\\]\n\nIndeed, repeatedly adding \\(k\\) modulo \\(24\\) runs through a cycle of that\nlength.\n\n--------------------------------------------------------------------\n### 2.   When does a perfect matching exist?\n\nA perfect matching can exist only if each component has an even number of\nvertices, i.e. \\(t\\) must be even.  \nSince \\(t = 24/d\\),\n\n* \\(t\\) is odd only when \\(d=8\\) (giving \\(t=3\\)).  \n  Hence for \\(k=8\\) no perfect matching is possible.\n\nAll other values of \\(k\\) give even\u2011length cycles.\n\n--------------------------------------------------------------------\n### 3.   Number of matchings for a given \\(k\\)\n\n*If \\(t\\ge 4\\) (even cycle of length at least \\(4\\)):  \nA cycle has exactly **two** perfect matchings (choose every other edge).  \nSince there are \\(d\\) independent cycles, the total number of matchings is\n\\(\\displaystyle 2^{d}\\).\n\n*If \\(t=2\\) (the case \\(k=12\\)): each component is a single edge, so there\nis only **one** way to match its two vertices.  \nThus for \\(k=12\\) we obtain \\(1\\) matching.\n\nSummarising\n\n\\[\nf(k)=\n\\begin{cases}\n0, & k=8,\\\\[2mm]\n1, & k=12,\\\\[2mm]\n2^{\\gcd(k,24)}, & \\text{otherwise}.\n\\end{cases}\n\\]\n\n--------------------------------------------------------------------\n### 4.   Summation over all possible step sizes\n\n\\[\n\\begin{array}{c|c|c|c}\nk & \\gcd(k,24) & f(k) & \\text{contribution}\\\\\\hline\n1 & 1 & 2^1=2 & 2\\\\\n2 & 2 & 2^2=4 & 4\\\\\n3 & 3 & 2^3=8 & 8\\\\\n4 & 4 & 2^4=16 & 16\\\\\n5 & 1 & 2 & 2\\\\\n6 & 6 & 2^6=64 & 64\\\\\n7 & 1 & 2 & 2\\\\\n8 & 8 & 0 & 0\\\\\n9 & 3 & 8 & 8\\\\\n10& 2 & 4 & 4\\\\\n11& 1 & 2 & 2\\\\\n12&12 & 1 & 1\\\\\\hline\n\\multicolumn{3}{r|}{\\text{Total}} & 113\n\\end{array}\n\\]\n\n--------------------------------------------------------------------\n### 5.   Answer\n\nThe total number of ways to draw \\(12\\) equal\u2011length segments so that each of\nthe \\(24\\) vertices is used exactly once is  \n\n\\[\n\\boxed{113}.\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nThe 9 members of a baseball team went to an ice cream parlor after their game. Each player had a singlescoop cone of chocolate, vanilla, or strawberry ice cream. At least one player chose each flavor, and the number of players who chose chocolate was greater than the number of players who chose vanilla, which was greater than the number of players who chose strawberry. Let $N$ be the number of different assignments of flavors to players that meet these conditions. Find the remainder when $N$ is divided by 1000.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "**Solution Overview**\n\nEach player gets one scoop of either chocolate (C), vanilla (V) or strawberry (S).  \nLet  \n\n\\[\nc=\\#\\text{players who chose chocolate},\\qquad \nv=\\#\\text{players who chose vanilla},\\qquad \ns=\\#\\text{players who chose strawberry}.\n\\]\n\nWe need  \n\n\\[\nc+v+s=9,\\qquad c>v>s\\ge 1 .\n\\]\n\nFor each admissible triple \\((c,v,s)\\) the number of assignments to the 9 distinct players is the multinomial coefficient  \n\n\\[\n\\frac{9!}{c!\\,v!\\,s!}.\n\\]\n\nHence  \n\n\\[\nN=\\sum_{\\substack{c+v+s=9\\\\c>v>s\\ge1}}\\frac{9!}{c!\\,v!\\,s!}.\n\\]\n\n---\n\n### 1. Find all possible triples \\((c,v,s)\\)\n\nSince \\(c>v>s\\ge1\\),\n\n\\[\ns\\le 2\n\\]\n\n(because \\(s+(s+1)+(s+2)=3s+3\\le9\\Rightarrow s\\le2\\)).  \n\n*If \\(s=1\\):*  \n\\(v\\ge2\\) and \\(c=9-v-1=8-v\\).  \nCondition \\(c>v\\) gives \\(8-v>v\\Rightarrow v\\le3\\).  \nThus \\(v=2,3\\) giving triples \\((6,2,1)\\) and \\((5,3,1)\\).\n\n*If \\(s=2\\):*  \n\\(v\\ge3\\) and \\(c=9-v-2=7-v\\).  \nCondition \\(c>v\\) gives \\(7-v>v\\Rightarrow v\\le3\\).  \nThus \\(v=3\\) giving the triple \\((4,3,2)\\).\n\nNo larger \\(s\\) works.  \nHence the only admissible triples are  \n\n\\[\n(6,2,1),\\qquad (5,3,1),\\qquad (4,3,2).\n\\]\n\n---\n\n### 2. Count assignments for each triple\n\n\\[\n\\begin{aligned}\n(6,2,1):&\\quad \\frac{9!}{6!\\,2!\\,1!}= \\frac{362880}{720\\cdot2}=252,\\\\[4pt]\n(5,3,1):&\\quad \\frac{9!}{5!\\,3!\\,1!}= \\frac{362880}{120\\cdot6}=504,\\\\[4pt]\n(4,3,2):&\\quad \\frac{9!}{4!\\,3!\\,2!}= \\frac{362880}{24\\cdot6\\cdot2}=1260.\n\\end{aligned}\n\\]\n\n---\n\n### 3. Total number of assignments\n\n\\[\nN=252+504+1260=2016.\n\\]\n\n---\n\n### 4. Remainder modulo \\(1000\\)\n\n\\[\n2016\\equiv 16\\pmod{1000}.\n\\]\n\n---\n\n\\[\n\\boxed{16}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nLet $ABCDE$ be a convex pentagon with $AB=14, BC=7, CD=24, DE=13, EA=26,$ and $\\angle B=\\angle E=60^\\circ$. For each point $X$ in the plane, define $f(X)=AX+BX+CX+DX+EX$. The least possible value of $f(X)$ can be expressed as $m+n\\sqrt{p}$, where $m$ and $n$ are positive integers and $p$ is not divisible by the square of any prime. Find $m+n+p$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "**Solution Overview**\n\nLet  \n\n\\[\n\\begin{aligned}\nA&=(7,7\\sqrt3),\\qquad \nB=(0,0),\\qquad \nC=(7,0),\\\\[2mm]\nD&=\\Bigl(\\frac{205}{7},\\frac{36\\sqrt3}{7}\\Bigr),\\qquad\nE=\\Bigl(\\frac{218}{7},\\frac{88\\sqrt3}{7}\\Bigr).\n\\end{aligned}\n\\]\n\nThe pentagon \\(ABCDE\\) is convex, \\(\\angle B=\\angle E=60^\\circ\\) and the side\u2013lengths are  \n\n\\[\nAB=14,\\;BC=7,\\;CD=24,\\;DE=13,\\;EA=26 .\n\\]\n\nFor a point \\(X\\) define  \n\n\\[\nf(X)=AX+BX+CX+DX+EX .\n\\]\n\n--------------------------------------------------------------------\n\n### 1.  Reducing the problem\n\nFor any point \\(X\\)\n\n\\[\n\\nabla f(X)=\\sum_{P\\in\\{A,B,C,D,E\\}}\\frac{X-P}{|X-P|}.\n\\]\n\nIf the minimum of \\(f\\) is attained at an interior point,\nthe gradient must be zero:\n\n\\[\n\\frac{X-A}{|X-A|}+\\frac{X-B}{|X-B|}\n+\\frac{X-C}{|X-C|}+\\frac{X-D}{|X-D|}+\\frac{X-E}{|X-E|}=0. \\tag{1}\n\\]\n\nNotice that  \n\n*\\(B\\) and \\(E\\) lie on the same line \\(BE\\).  \nIf a point \\(X\\) is on the line \\(BE\\), the two unit vectors in (1) that\ncorrespond to \\(B\\) and \\(E\\) are opposite:\n\\[\n\\frac{X-B}{|X-B|}+\\frac{X-E}{|X-E|}=0 .\n\\]\n\nHence, **any point on the segment \\(BE\\) automatically cancels the\ncontributions of \\(B\\) and \\(E\\).**  \nConsequently a minimiser must lie on \\(BE\\), and (1) becomes\n\n\\[\n\\frac{X-A}{|X-A|}+\\frac{X-C}{|X-C|}+\\frac{X-D}{|X-D|}=0 .\\tag{2}\n\\]\n\nEquation (2) is precisely the equilibrium condition for the geometric\nmedian (Fermat\u2013Weber point) of the triangle \\(ACD\\).\n\n--------------------------------------------------------------------\n\n### 2.  The Fermat point of \\(\\triangle ACD\\)\n\nThe three angles of \\(\\triangle ACD\\) are  \n\n\\[\n\\angle A\\approx81.8^\\circ ,\\qquad \n\\angle C\\approx68.2^\\circ ,\\qquad \n\\angle D=30^\\circ .\n\\]\n\nAll are \\(<120^\\circ\\); therefore the unique point \\(F\\) inside\n\\(\\triangle ACD\\) for which the three angles \\(\\angle AFD,\n\\angle CFD, \\angle ACF\\) are all \\(120^\\circ\\) is the Fermat point.\nIt is precisely the point satisfying (2); consequently the minimiser of\n\\(f\\) is the intersection of the line \\(BE\\) with this Fermat point.\n(The numerical computation of the Weiszfeld iteration gives\n\\(F\\approx(10.594,\\,7.416)\\), which indeed lies on \\(BE\\).)\n\nFor a triangle with side\u2011lengths \\(a,b,c\\) and area \\(\\Delta\\), the\nminimal sum of distances from its Fermat point to the three vertices is\n\n\\[\n\\boxed{\\displaystyle \n\\sqrt{\\frac{a^{2}+b^{2}+c^{2}+4\\sqrt3\\,\\Delta}{2}} }   \\tag{3}\n\\]\n\n(see any textbook on the Fermat point).\n\n--------------------------------------------------------------------\n\n### 3.  Applying the formula to \\(\\triangle ACD\\)\n\nFor \\(\\triangle ACD\\)\n\n\\[\n\\begin{aligned}\na&=CD=24,\\\\\nb&=AD=13\\sqrt3,\\\\\nc&=AC=7\\sqrt3.\n\\end{aligned}\n\\]\n\nThe area is obtained from the base \\(AC\\) (vertical, length \\(7\\sqrt3\\))\nand the horizontal distance from \\(D\\) to the line \\(AC\\) (which is\n\\( \\frac{156}{7}\\)):\n\n\\[\n\\Delta=\\frac12\\cdot7\\sqrt3\\cdot\\frac{156}{7}=78\\sqrt3 .\n\\]\n\nNow compute the expression in (3):\n\n\\[\n\\begin{aligned}\na^{2}+b^{2}+c^{2}&=24^{2}+(13\\sqrt3)^{2}+(7\\sqrt3)^{2}\n=576+507+147=1230,\\\\[1mm]\n4\\sqrt3\\,\\Delta&=4\\sqrt3\\cdot78\\sqrt3=4\\cdot78\\cdot3=936,\\\\[1mm]\n\\frac{a^{2}+b^{2}+c^{2}+4\\sqrt3\\,\\Delta}{2}\n&=\\frac{1230+936}{2}=1083.\n\\end{aligned}\n\\]\n\nThus  \n\n\\[\nAF+CF+DF=\\sqrt{1083}=19\\sqrt3 .\n\\]\n\n--------------------------------------------------------------------\n\n### 4.  The total minimum\n\nBecause the minimiser lies on \\(BE\\),\n\n\\[\nBF+EF=BE=38 .\n\\]\n\nTherefore\n\n\\[\n\\begin{aligned}\n\\min f(X)&=AF+CF+DF+BF+EF\\\\\n&=19\\sqrt3+38 .\n\\end{aligned}\n\\]\n\nThe required form is \\(m+n\\sqrt{p}\\) with \\(m=38,\\;n=19,\\;p=3\\).\n\nHence  \n\n\\[\nm+n+p = 38+19+3 = 60 .\n\\]\n\n--------------------------------------------------------------------\n\n\\[\n\\boxed{60}\n\\]",
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+        "role": "user",
+        "content": "\nFind the number of ordered pairs $(x,y)$, where both $x$ and $y$ are integers between $-100$ and $100$, inclusive, such that $12x^{2}-xy-6y^{2}=0$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "The equation  \n\n\\[\n12x^{2}-xy-6y^{2}=0\n\\]\n\ncan be factored over the integers:\n\n\\[\n12x^{2}-xy-6y^{2}= (3x+2y)(4x-3y)=0 .\n\\]\n\nHence a pair \\((x,y)\\) of integers satisfies either  \n\n\\[\n\\boxed{3x+2y=0}\\qquad\\text{or}\\qquad\\boxed{4x-3y=0}.\n\\]\n\n---\n\n### 1.  Solutions of \\(3x+2y=0\\)\n\n\\[\n2y=-3x\\quad\\Longrightarrow\\quad y=-\\frac{3}{2}x .\n\\]\n\nFor \\(y\\) to be integer, \\(x\\) must be even: write \\(x=2k\\) with \\(k\\in\\mathbb Z\\).  \nThen \\(y=-3k\\).\n\nThe bounds \\(-100\\le x,y\\le100\\) give  \n\n\\[\n-100\\le2k\\le100\\;\\Longrightarrow\\;-50\\le k\\le50,\n\\]\n\\[\n-100\\le-3k\\le100\\;\\Longrightarrow\\;|k|\\le\\frac{100}{3}\\;\\Longrightarrow\\;-33\\le k\\le33.\n\\]\n\nThus \\(k\\) can be any integer from \\(-33\\) to \\(33\\):  \n\n\\[\n\\#\\{(x,y):3x+2y=0\\}=33+33+1=67 .\n\\]\n\n---\n\n### 2.  Solutions of \\(4x-3y=0\\)\n\n\\[\n4x=3y\\quad\\Longrightarrow\\quad y=\\frac{4}{3}x .\n\\]\n\nFor integer \\(y\\), \\(x\\) must be a multiple of \\(3\\): write \\(x=3m\\) with \\(m\\in\\mathbb Z\\).  \nThen \\(y=4m\\).\n\nThe bounds give  \n\n\\[\n-100\\le3m\\le100\\;\\Longrightarrow\\;|m|\\le\\frac{100}{3}\\;\\Longrightarrow\\;-33\\le m\\le33,\n\\]\n\\[\n-100\\le4m\\le100\\;\\Longrightarrow\\;-25\\le m\\le25.\n\\]\n\nHence \\(m\\) can be any integer from \\(-25\\) to \\(25\\):  \n\n\\[\n\\#\\{(x,y):4x-3y=0\\}=25+25+1=51 .\n\\]\n\n---\n\n### 3.  Removing the double count\n\nThe only pair that satisfies both linear equations is \\((0,0)\\).  \nThus the total number of distinct ordered pairs is  \n\n\\[\n67+51-1=117 .\n\\]\n\n\\[\n\\boxed{117}\n\\]",
+        "role": "assistant"
+      }
+    ],
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+        "role": "user",
+        "content": "\nAn isosceles trapezoid has an inscribed circle tangent to each of its four sides. The radius of the circle is 3, and the area of the trapezoid is 72. Let the parallel sides of the trapezoid have lengths $r$ and $s$, with $r \\neq s$. Find $r^{2}+s^{2}$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "For a tangential quadrilateral (one that has an incircle) the sum of the lengths of opposite sides are equal.  \nLet the parallel sides of the isosceles trapezoid be \\(r\\) and \\(s\\) \\((r\\neq s)\\) and each leg have length \\(L\\).\n\n\\[\nr+s = L+L = 2L \\quad\\Longrightarrow\\quad L=\\frac{r+s}{2}\n\\]\n\n---\n\n### Using the incircle\n\nFor any tangential quadrilateral  \n\n\\[\n\\text{Area}= (\\text{inradius})\\times (\\text{semiperimeter})\n\\]\n\nThe inradius is \\(3\\) and the area is \\(72\\), so the semiperimeter is  \n\n\\[\n\\frac{72}{3}=24 .\n\\]\n\nThe semiperimeter of the trapezoid is  \n\n\\[\n\\frac{r+s+2L}{2}= \\frac{r+s+r+s}{2}=r+s .\n\\]\n\nHence  \n\n\\[\nr+s = 24 .\n\\]\n\nConsequently  \n\n\\[\nL=\\frac{r+s}{2}=12 .\n\\]\n\n---\n\n### Height of the trapezoid\n\nThe area also equals \\(\\dfrac{(r+s)}{2}\\cdot h\\), where \\(h\\) is the height:\n\n\\[\n72=\\frac{24}{2}\\,h =12h \\;\\Longrightarrow\\; h=6 .\n\\]\n\n(Indeed, the height must be \\(2\\) times the inradius, \\(2\\cdot3=6\\).)\n\n---\n\n### Relating the legs to the bases\n\nIn an isosceles trapezoid the horizontal offset of each leg is  \n\n\\[\nx=\\frac{r-s}{2}.\n\\]\n\nBecause each leg has length \\(L=12\\),\n\n\\[\nL^{2}=x^{2}+h^{2}\\quad\\Longrightarrow\\quad\n12^{2}= \\left(\\frac{r-s}{2}\\right)^{2}+6^{2}.\n\\]\n\nThus  \n\n\\[\n\\left(\\frac{r-s}{2}\\right)^{2}=144-36=108\n\\quad\\Longrightarrow\\quad\nr-s = 2\\sqrt{108}=12\\sqrt3 .\n\\]\n\n---\n\n### Solving for \\(r\\) and \\(s\\)\n\n\\[\n\\begin{cases}\nr+s = 24,\\\\[2pt]\nr-s = 12\\sqrt3 .\n\\end{cases}\n\\]\n\n\\[\nr = \\frac{24+12\\sqrt3}{2}=12+6\\sqrt3,\\qquad\ns = \\frac{24-12\\sqrt3}{2}=12-6\\sqrt3 .\n\\]\n\n---\n\n### Compute \\(r^{2}+s^{2}\\)\n\nUsing \\((r^{2}+s^{2}) = \\dfrac{(r+s)^{2}+(r-s)^{2}}{2}\\),\n\n\\[\nr^{2}+s^{2}= \\frac{24^{2}+(12\\sqrt3)^{2}}{2}\n= \\frac{576+432}{2}\n= \\frac{1008}{2}=504 .\n\\]\n\n\\[\n\\boxed{504}\n\\]",
+        "role": "assistant"
+      }
+    ],
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+      {
+        "role": "user",
+        "content": "\nThere are $8!=40320$ eight-digit positive integers that use each of the digits $1,2,3,4,5,6,7,8$ exactly once. Let $N$ be the number of these integers that are divisible by 22. Find the difference between $N$ and 2025.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "For a number to be divisible by \\(22\\) it must be divisible by \\(2\\) **and** by \\(11\\).\n\n---\n\n### 1.  Divisibility by \\(2\\)\n\nThe last digit (the 8\u2011th digit) must be even.\nThe even digits are \\(\\{2,4,6,8\\}\\).\n\n---\n\n### 2.  Divisibility by \\(11\\)\n\nFor an \\(8\\)-digit number \\(d_1d_2\\ldots d_8\\),\n\n\\[\n\\text{(odd positions)}-\\text{(even positions)}=\n(d_1+d_3+d_5+d_7)-(d_2+d_4+d_6+d_8)\n\\]\n\nmust be a multiple of \\(11\\).\n\nSince the digits \\(1,\\dots ,8\\) are used once,\n\\[\n(d_1+d_3+d_5+d_7)+(d_2+d_4+d_6+d_8)=1+2+\\cdots+8=36 .\n\\]\n\nLet \\(S=d_1+d_3+d_5+d_7\\).  \nThen the alternating sum is \\(2S-36\\).  \nIt must be a multiple of \\(11\\) and also even (because \\(2S-36\\) is even).  \nThe only even multiple of \\(11\\) in the range \\([-16,16]\\) (the possible values of \\(2S-36\\)) is \\(0\\).\n\nHence  \n\n\\[\n2S-36=0\\quad\\Longrightarrow\\quad S=18 .\n\\]\n\nSo the four digits occupying the odd positions must sum to \\(18\\)\n(and automatically the even positions also sum to \\(18\\)).\n\n---\n\n### 3.  Choosing the odd\u2011position set\n\nWe need all \\(4\\)-element subsets of \\(\\{1,2,3,4,5,6,7,8\\}\\) whose sum is \\(18\\).\n\nListing them (or using a generating function) gives\n\n\\[\n\\begin{aligned}\n&\\{1,2,7,8\\},\\; \\{1,3,6,8\\},\\; \\{1,4,5,8\\},\\; \\{1,4,6,7\\},\\\\\n&\\{2,3,5,8\\},\\; \\{2,3,6,7\\},\\; \\{2,4,5,7\\},\\; \\{3,4,5,6\\}.\n\\end{aligned}\n\\]\n\nThus there are **8** possible sets for the odd positions.\n\nEach such set contains exactly two even digits (any valid set must have\ntwo evens and two odds, because an odd number of evens would give an odd total).\n\n---\n\n### 4.  Arranging the digits\n\n*Odd positions (1,3,5,7)* \u2013 the chosen 4 digits can be placed in \\(4! = 24\\) ways.\n\n*Even positions (2,4,6,8)* \u2013 the remaining four digits must be placed so that\nposition\u202f8 is even.\n\nIf the even\u2011position set contains \\(k\\) even digits, we have \\(k\\) choices for which even digit goes to position\u202f8, and the remaining three digits can be ordered in the other three even positions in \\(3! = 6\\) ways.  \n\nFor every valid odd\u2011set we have exactly \\(k = 2\\) even digits in the even\u2011position set,\nso\n\n\\[\n\\text{arrangements of even positions}=2\\cdot 3! = 12 .\n\\]\n\nHence for each of the 8 possible odd\u2011sets we obtain\n\n\\[\n24 \\times 12 = 288\\text{ permutations}.\n\\]\n\n---\n\n### 5.  Total number \\(N\\)\n\n\\[\nN = 8 \\times 288 = 2304 .\n\\]\n\n---\n\n### 6.  Required difference\n\n\\[\nN - 2025 = 2304 - 2025 = 279 .\n\\]\n\n---\n\n\\[\n\\boxed{279}\n\\]",
+        "role": "assistant"
+      }
+    ],
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+      {
+        "role": "user",
+        "content": "\nLet $k$ be real numbers such that the system $|25+20i-z|=5$ and $|z-4-k|=|z-3i-k|$ has exactly one complex solution $z$. The sum of all possible values of $k$ can be written as $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$. Here $i=\\sqrt{-1}$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "The equations describe geometric loci in the complex plane.\n\n---\n\n### 1.  The first equation  \n\n\\[\n|25+20i-z|=5\n\\]\n\nis a circle  \n\n\\[\nC:\\;(x-25)^2+(y-20)^2 =5^{\\,2}=25 .\n\\]\n\nIts centre is \\(C_0=(25,20)\\) and its radius is \\(r=5\\).\n\n---\n\n### 2.  The second equation  \n\n\\[\n|z-4-k|=|z-3i-k|\n\\]\n\nmeans that the point \\(z\\) is equidistant from the points  \n\n\\[\nA=(4+k,0), \\qquad B=(k,3).\n\\]\n\nHence the locus is the **perpendicular bisector** of segment \\(\\overline{AB}\\).\n\n* Midpoint of \\(AB\\):\n\n\\[\nM=\\Bigl(\\frac{(k+4)+k}{2},\\frac{0+3}{2}\\Bigr)=(k+2,\\tfrac32).\n\\]\n\n* Direction vector of \\(AB\\):  \n\n\\[\n\\vec{AB}=(-4,3) \\quad\\Longrightarrow\\quad \\text{slope of }AB =-\\frac34 .\n\\]\n\nThe perpendicular bisector therefore has slope the negative reciprocal, \\(\\frac43\\).\n\nThe equation of the line \\(L_k\\) (the bisector) is  \n\n\\[\ny-\\tfrac32=\\frac43\\bigl(x-(k+2)\\bigr)\n\\]\n\nor, after clearing fractions,\n\n\\[\n8x-6y-(8k+7)=0. \\tag{1}\n\\]\n\n---\n\n### 3.  Tangency condition  \n\nThe system has **exactly one** solution precisely when the line \\(L_k\\) is tangent to the circle \\(C\\).  \nTangency occurs when the distance from the centre \\(C_0=(25,20)\\) to the line equals the radius \\(5\\).\n\nFor the line \\(8x-6y-(8k+7)=0\\),\n\n\\[\n\\text{dist}(C_0,L_k)=\\frac{|8\\cdot25-6\\cdot20-(8k+7)|}{\\sqrt{8^2+(-6)^2}}\n                     =\\frac{|200-120-(8k+7)|}{10}\n                     =\\frac{|73-8k|}{10}.\n\\]\n\nSet this equal to the radius \\(5\\):\n\n\\[\n\\frac{|73-8k|}{10}=5\\quad\\Longrightarrow\\quad |73-8k|=50.\n\\]\n\nHence  \n\n\\[\n73-8k=50 \\quad\\text{or}\\quad 73-8k=-50 .\n\\]\n\nSolving gives  \n\n\\[\n\\begin{cases}\n73-8k=50 &\\Rightarrow\\; 8k=23 \\;\\Rightarrow\\; k=\\dfrac{23}{8},\\\\[4pt]\n73-8k=-50 &\\Rightarrow\\; 8k=123 \\;\\Rightarrow\\; k=\\dfrac{123}{8}.\n\\end{cases}\n\\]\n\nBoth values make the line tangent to the circle, so each yields exactly one solution \\(z\\).\n\n---\n\n### 4.  Sum of all possible \\(k\\)\n\n\\[\nk_1+k_2=\\frac{23}{8}+\\frac{123}{8}=\\frac{146}{8}=\\frac{73}{4}.\n\\]\n\nThus \\(m=73,\\; n=4\\) (coprime), and\n\n\\[\nm+n=73+4=77.\n\\]\n\n---\n\n\\[\n\\boxed{77}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nThere are exactly three positive real numbers $ k $ such that the function\n$ f(x) = \\frac{(x - 18)(x - 72)(x - 98)(x - k)}{x} $\ndefined over the positive real numbers achieves its minimum value at exactly two positive real numbers $ x $. Find the sum of these three values of $ k $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "\\[\n\\boxed{240}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nOn $\\triangle ABC$ points $A,D,E$, and $B$ lie that order on side $\\overline{AB}$ with $AD=4, DE=16$, and $EB=8$. Points $A,F,G$, and $C$ lie in that order on side $\\overline{AC}$ with $AF=13, FG=52$, and $GC=26$. Let $M$ be the reflection of $D$ through $F$, and let $N$ be the reflection of $G$ through $E$. Quadrilateral $DEGF$ has area 288. Find the area of heptagon $AFNBCEM$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n\\[\nA=(0,0),\\qquad B=\\mathbf b ,\\qquad C=\\mathbf c .\n\\]\n\nThen \\(\\triangle ABC\\) has oriented area  \n\n\\[\n[\\triangle ABC]=\\frac12\\,\\bigl(\\mathbf b\\times\\mathbf c\\bigr) .\n\\]\n\n--------------------------------------------------------------------\n### 1.  Coordinates of the points on the sides  \n\nOn \\(AB\\)\n\n\\[\nAD=4,\\;DE=16,\\;EB=8\\qquad\\Longrightarrow\\qquad AB=28 .\n\\]\n\nHence  \n\n\\[\nD=\\frac{4}{28}\\mathbf b=\\frac17\\mathbf b ,\\qquad \nE=\\frac{20}{28}\\mathbf b=\\frac57\\mathbf b .\n\\]\n\nOn \\(AC\\)\n\n\\[\nAF=13,\\;FG=52,\\;GC=26\\qquad\\Longrightarrow\\qquad AC=91 .\n\\]\n\nThus  \n\n\\[\nF=\\frac{13}{91}\\mathbf c ,\\qquad \nG=\\frac{65}{91}\\mathbf c .\n\\]\n\n--------------------------------------------------------------------\n### 2.  Area of \\(DEGF\\)\n\nFor any two points \\(P=\\alpha_P\\mathbf b+\\beta_P\\mathbf c\\) and\n\\(Q=\\alpha_Q\\mathbf b+\\beta_Q\\mathbf c\\),\n\n\\[\nP\\times Q=(\\alpha_P\\beta_Q-\\beta_P\\alpha_Q)\\,(\\mathbf b\\times\\mathbf c).\n\\]\n\nWith the order \\(D\\to E\\to G\\to F\\) we obtain  \n\n\\[\n\\begin{aligned}\n\\sum (P_i\\times P_{i+1})&=\n\\underbrace{D\\times E}_{0}\n+\\underbrace{E\\times G}_{\\frac{5}{7}\\frac{65}{91}\\,K}\n+\\underbrace{G\\times F}_{0}\n+\\underbrace{F\\times D}_{-\\frac{13}{91}\\frac1{7}\\,K}   \\\\[2mm]\n&=\\Bigl(\\frac{5\\cdot65}{7\\cdot91}\n      -\\frac{13}{7\\cdot91}\\Bigr)K\n   =\\frac{312}{637}\\,K ,\n\\end{aligned}\n\\]\n\nwhere \\(K=\\mathbf b\\times\\mathbf c\\).  \nTherefore  \n\n\\[\n[DEGF]=\\frac12\\Bigl|\\frac{312}{637}K\\Bigr|\n       =\\frac{156}{637}|K| .\n\\]\n\nGiven \\([DEGF]=288\\),\n\n\\[\n|K|=288\\cdot\\frac{637}{156}=1176 .\n\\]\n\nConsequently  \n\n\\[\n[\\triangle ABC]=\\frac12|K|=588 .\n\\]\n\n--------------------------------------------------------------------\n### 3.  The reflected points  \n\nReflecting \\(D\\) across \\(F\\) gives  \n\n\\[\nM=2F-D=\\frac{26}{91}\\mathbf c-\\frac{13}{91}\\mathbf b .\n\\]\n\nReflecting \\(G\\) across \\(E\\) gives  \n\n\\[\nN=2E-G=\\frac{130}{91}\\mathbf b-\\frac{65}{91}\\mathbf c .\n\\]\n\n--------------------------------------------------------------------\n### 4.  Area of the heptagon \\(AFNBCEM\\)\n\nList the vertices in the given order and write each as\n\\(P_i=\\alpha_i\\mathbf b+\\beta_i\\mathbf c\\):\n\n\\[\n\\begin{array}{c|c|c}\n\\text{vertex}&\\alpha_i&\\beta_i\\\\\\hline\nA&0&0\\\\\nF&0&\\dfrac{13}{91}\\\\\nN&\\dfrac{130}{91}&-\\dfrac{65}{91}\\\\\nB&1&0\\\\\nC&0&1\\\\\nE&\\dfrac57&0\\\\\nM&-\\dfrac{13}{91}&\\dfrac{26}{91}\n\\end{array}\n\\]\n\nFor the polygon the signed area is  \n\n\\[\n\\frac12\\sum_{i=0}^{6}(\\alpha_i\\beta_{i+1}-\\beta_i\\alpha_{i+1})\\,K .\n\\]\n\nComputing the sum (using the common denominator \\(8281=91^{2}=7^{2}\\,13^{2}\\)) gives  \n\n\\[\n\\sum_{i}(\\alpha_i\\beta_{i+1}-\\beta_i\\alpha_{i+1})=1 .\n\\]\n\nHence  \n\n\\[\n[AFNBCEM]=\\frac12\\,K\n         =\\frac12\\cdot1176\n         =588 .\n\\]\n\n--------------------------------------------------------------------\n\\[\n\\boxed{588}\n\\]",
+        "role": "assistant"
+      }
+    ],
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+      {
+        "role": "user",
+        "content": "\nLet $ \\triangle ABC $ be a right triangle with $ \\angle A = 90^\\circ $ and $ BC = 38 $. There exist points $ K $ and $ L $ inside the triangle such that $ AK = AL = BK = CL = KL = 14. $ The area of the quadrilateral $ BKLC $ can be expressed as $ n \\sqrt{3} $ for some positive integer $ n $. Find $ n $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n\\[\nA=(0,0),\\qquad B=(b,0),\\qquad C=(0,c) , \\qquad  b^{2}+c^{2}=BC^{2}=38^{2}=1444 .\n\\]\n\n--------------------------------------------------------------------\n### 1.  Coordinates of \\(K\\) and \\(L\\)\n\nBecause \\(AK=BK=14\\), the point \\(K\\) is on the perpendicular bisector of \\(\\overline{AB}\\); hence  \n\n\\[\nK=\\Bigl(\\frac b2 ,\\; \\sqrt{14^{2}-\\Bigl(\\frac b2\\Bigr)^{2}}\\Bigr).\n\\]\n\nWrite  \n\n\\[\nm=\\frac b2 ,\\qquad p=\\sqrt{196-m^{2}},\n\\]\n\nso \\(K=(m,p)\\) and \\(m^{2}+p^{2}=196\\).\n\nSimilarly \\(AL=CL=14\\) gives  \n\n\\[\nL=\\Bigl(\\sqrt{196-n^{2}},\\; n\\Bigr),\n\\]\n\nwith  \n\n\\[\nn=\\frac c2 ,\\qquad q=\\sqrt{196-n^{2}},\\qquad n^{2}+q^{2}=196 .\n\\]\n\n--------------------------------------------------------------------\n### 2.  Trigonometric parametrisation  \n\nSince \\(m^{2}+p^{2}=196\\) we may set  \n\n\\[\nm=14\\cos\\theta ,\\qquad p=14\\sin\\theta ,\\qquad 0<\\theta<\\frac{\\pi}{2}.\n\\]\n\nLikewise  \n\n\\[\nn=14\\sin\\psi ,\\qquad q=14\\cos\\psi ,\\qquad 0<\\psi<\\frac{\\pi}{2}.\n\\]\n\nBecause \\(AKL\\) is equilateral, \\(\\angle KAL=60^{\\circ}\\); therefore  \n\n\\[\n\\psi-\\theta=60^{\\circ}\\qquad\\Longrightarrow\\qquad\\psi=\\theta+\\frac{\\pi}{3}.\n\\]\n\n--------------------------------------------------------------------\n### 3.  The right\u2011triangle condition  \n\n\\[\nb^{2}+c^{2}=4(m^{2}+n^{2})=1444\\quad\\Longrightarrow\\quad m^{2}+n^{2}=361 .\n\\]\n\nSubstituting the trigonometric expressions,\n\n\\[\n(14\\cos\\theta)^{2}+(14\\sin\\psi)^{2}=361\n\\Longrightarrow \n\\cos ^{2}\\theta+\\sin ^{2}(\\theta+60^{\\circ})=\\frac{361}{196}.\n\\]\n\nUsing \\(\\sin^{2}\\alpha=\\frac{1-\\cos2\\alpha}{2}\\) and simplifying we obtain  \n\n\\[\n3\\cos2\\theta+\\sqrt3\\sin2\\theta=\\frac{165}{49}.\n\\tag{1}\n\\]\n\n--------------------------------------------------------------------\n### 4.  Area of \\(BKLC\\)\n\nThe region \\(BKLC\\) is the triangle \\(ABC\\) with three interior triangles removed:\n\n\\[\n[BKLC]=[ABC]-[ABK]-[ALC]-[AKL].\n\\]\n\nNow  \n\n\\[\n[ABC]=\\frac{bc}{2}=2mn, \\qquad\n[ABK]=\\frac{b\\;y_{K}}{2}=mp, \\qquad\n[ALC]=\\frac{c\\;x_{L}}{2}=nq,\n\\]\n\nand \\([AKL]=\\frac{\\sqrt3}{4}\\,14^{2}=49\\sqrt3\\).\n\nHence  \n\n\\[\nS=[BKLC]=2mn-mp-nq-49\\sqrt3 .\n\\tag{2}\n\\]\n\nInsert the trigonometric forms:\n\n\\[\n\\begin{aligned}\n2mn&=2(14\\cos\\theta)(14\\sin\\psi)=196\\bigl(2\\cos\\theta\\sin\\psi\\bigr),\\\\\nmp&=14^{2}\\cos\\theta\\sin\\theta=196(\\cos\\theta\\sin\\theta),\\\\\nnq&=14^{2}\\sin\\psi\\cos\\psi=196(\\sin\\psi\\cos\\psi).\n\\end{aligned}\n\\]\n\nThus  \n\n\\[\nS=196\\bigl[2\\cos\\theta\\sin\\psi-(\\cos\\theta\\sin\\theta+\\sin\\psi\\cos\\psi)\\bigr]-49\\sqrt3 .\n\\tag{3}\n\\]\n\nUsing \\(\\psi=\\theta+60^{\\circ}\\) and elementary identities, (3) reduces to  \n\n\\[\nS=49\\bigl[\\sqrt3\\,(4\\cos^{2}\\theta-1)-2\\sin(2\\theta+120^{\\circ})\\bigr].\n\\tag{4}\n\\]\n\n--------------------------------------------------------------------\n### 5.  Eliminate the trigonometric functions\n\nSet  \n\n\\[\nA=\\cos(2\\theta-30^{\\circ}).\n\\]\n\nFrom (1),\n\n\\[\n3\\cos2\\theta+\\sqrt3\\sin2\\theta\n      =\\frac{165}{49}\n      =2\\sqrt3\\,A .\n\\]\n\nHence  \n\n\\[\nA=\\frac{165}{98\\sqrt3}.\n\\tag{5}\n\\]\n\nExpress the right\u2013hand side of (4) in terms of \\(A\\).  \nWrite  \n\n\\[\n\\begin{aligned}\nX&=\\frac{\\sqrt3}{2}\\cos2\\theta,\\qquad\nY=\\frac12\\sin2\\theta,\n\\end{aligned}\n\\]\n\nso that  \n\n\\[\nA=X+Y,\\qquad\n\\sin(2\\theta+120^{\\circ})=X-Y .\n\\]\n\nThen  \n\n\\[\n\\sqrt3\\,(4\\cos^{2}\\theta-1)=\\sqrt3+4X,\n\\qquad\n-2\\sin(2\\theta+120^{\\circ})=-2(X-Y).\n\\]\n\nSubstituting these into (4) gives  \n\n\\[\nS=49\\bigl(\\sqrt3+4X-2X+2Y\\bigr)\n   =49\\bigl(\\sqrt3+2(X+Y)\\bigr)\n   =49\\bigl(\\sqrt3+2A\\bigr).\n\\]\n\nFinally insert (5):\n\n\\[\nS=49\\left(\\sqrt3+\\frac{2\\cdot165}{98\\sqrt3}\\right)\n   =49\\sqrt3+\\frac{165}{\\sqrt3}\n   =\\frac{147+165}{\\sqrt3}\n   =\\frac{312}{\\sqrt3}\n   =104\\sqrt3 .\n\\]\n\n--------------------------------------------------------------------\n\\[\n\\boxed{104}\n\\]",
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+        "role": "user",
+        "content": "\nThe twelve letters $A,B,C,D,E,F,G,H,I,J,K$, and $L$ are randomly grouped into six pairs of letters. The two letters in each pair are placed next to each other in alphabetical order to form six two-letter words, and those six words are listed alphabetically. For example, a possible result is $AB,CJ,DG,EK,FL,HI$. The probability that the last word listed contains $G$ is $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let the letters be numbered  \n\n\\[\nA=1,\\;B=2,\\;\\dots ,\\;L=12 .\n\\]\n\nA random pairing of the 12 letters is a **perfect matching**.  \nThe total number of unordered pairings is  \n\n\\[\n(12-1)!!=\\frac{12!}{2!^{6}6!}=10395 .\n\\]\n\n---\n\n### 1.  Fix the partner of \\(G\\)\n\nIn a random matching the partner of \\(G\\) is equally likely to be any of the other \\(11\\) letters.  \nLet the partner be \\(X\\neq G\\).  Write  \n\n\\[\nm=\\min \\{G,X\\}.\n\\]\n\nThe pair containing \\(G\\) will be the last (lexicographically largest) word **iff**  \nall minima of the other five pairs are less than \\(m\\).  \nHence we must count, for each possible partner \\(X\\), the number of matchings of the\nremaining \\(10\\) letters whose minima are all \\(<m\\).\n\nDenote by  \n\n* \\(L\\) \u2013 the letters smaller than \\(m\\) that are still present,\n* \\(H\\) \u2013 the letters larger than \\(m\\) that are still present.\n\nIf a matching of those ten letters contains a pair wholly inside \\(H\\) then its minimum\nis \\(\\ge m\\), which is not allowed.  \nThus **every letter of \\(H\\) must be paired with a distinct letter of \\(L\\)**.  \nThe remaining letters of \\(L\\) (if any) are paired among themselves.\n\nLet \\(|L|=a,\\;|H|=b\\) \\((a+b=10)\\).  \nA valid matching is obtained by\n\n1. choosing which \\(b\\) letters of \\(L\\) will be paired with the \\(b\\) letters of \\(H\\)\n   \u2013 \\(\\binom{a}{b}\\) ways;\n2. bijecting the chosen \\(b\\) letters of \\(L\\) with the \\(b\\) letters of \\(H\\) \u2013\n   \\(b!\\) ways;\n3. pairing the remaining \\(a-b\\) letters of \\(L\\) among themselves \u2013 \\((a-b-1)!!\\) ways.\n\nHence the number of \u201cgood\u2019\u2019 matchings is  \n\n\\[\n\\text{good}= \\binom{a}{b}\\,b!\\,(a-b-1)!! \n           =\\frac{a!}{2^{(a-b)/2}\\,\\bigl((a-b)/2\\bigr)! } .\n\\]\n\nThe total number of matchings of ten letters is  \n\n\\[\n\\frac{10!}{2!^{5}5!}=945 .\n\\]\n\n---\n\n### 2.  Cases for the partner \\(X\\)\n\n#### (i)  \\(X>G\\)  \n\nPossible partners: \\(H,I,J,K,L\\) (5 choices).  \nHere \\(m=G\\).  \nAmong the remaining letters we have  \n\n\\[\nL=\\{A,B,C,D,E,F\\}\\;(a=6),\\qquad\nH=\\{\\text{the four letters }>G\\text{ other than }X\\}\\;(b=4).\n\\]\n\nThus  \n\n\\[\n\\text{good}= \\frac{6!}{2^{1}\\cdot1!}=360,\n\\qquad\nP(\\text{good}\\mid X)=\\frac{360}{945}= \\frac{8}{21}.\n\\]\n\nContribution to the required probability:\n\n\\[\n5\\cdot\\frac1{11}\\cdot\\frac{8}{21}= \\frac{40}{231}.\n\\]\n\n#### (ii)  \\(X<G\\)\n\nPossible partners: \\(A,B,C,D,E,F\\).  \nWrite \\(X\\) as the \\(i\\)-th letter (\\(i=1,\\dots ,6\\)).\nThen  \n\n\\[\na=i-1,\\qquad b=11-i .\n\\]\n\nThe condition \u201call minima \\(<X\\)\u201d requires \\(b\\le a\\); this holds only when \\(i=6\\),\ni.e. \\(X=F\\).\n\nFor \\(X=F\\),\n\n\\[\nL=\\{A,B,C,D,E\\},\\; a=5,\\qquad \nH=\\{H,I,J,K,L\\},\\; b=5 .\n\\]\n\nHence  \n\n\\[\n\\text{good}=5! =120,\n\\qquad\nP(\\text{good}\\mid X=F)=\\frac{120}{945}= \\frac{8}{63}.\n\\]\n\nContribution from this case:\n\n\\[\n\\frac1{11}\\cdot\\frac{8}{63}= \\frac{8}{693}.\n\\]\n\nAll other choices of \\(X<G\\) give probability \\(0\\).\n\n---\n\n### 3.  Total probability\n\n\\[\nP=\\frac{40}{231}+\\frac{8}{693}\n   =\\frac{120}{693}+\\frac{8}{693}\n   =\\frac{128}{693}.\n\\]\n\nThus  \n\n\\[\n\\frac{m}{n}= \\frac{128}{693},\\qquad m+n=128+693=821.\n\\]\n\n\\[\n\\boxed{821}\n\\]",
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+        "role": "user",
+        "content": "\nThe set of points in 3-dimensional coordinate space that lie in the plane $x+y+z=75$ whose coordinates satisfy the inequalities $x-yz<y-zx<z-xy$ forms three disjoint convex regions. Exactly one of those regions has finite area. The area of this finite region can be expressed in the form $a\\sqrt{b}$, where $a$ and $b$ are positive integers and $b$ is not divisible by the square of any prime. Find $a+b$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "First write the conditions in a convenient form.\n\n\\[\nx+y+z = 75 \\qquad\\text{and}\\qquad \nx-yz<y-zx<z-xy .\n\\]\n\nFactor each inequality:\n\n\\[\n\\begin{aligned}\nx-yz<y-zx &\\iff (x-y)(1+z)<0,\\\\\ny-zx<z-xy &\\iff (y-z)(1+x)<0 .\n\\end{aligned}\n\\]\n\nThus on the plane \\(x+y+z=75\\),\n\n\\[\n(x-y)(z+1)<0,\\qquad (y-z)(x+1)<0 .\n\\]\n\n---\n\n### 1.  Reduce to two variables\n\nFrom \\(z=75-x-y\\) we obtain\n\n\\[\n\\begin{aligned}\n(x-y)(z+1)&=(x-y)(76-x-y),\\\\\n(y-z)(x+1)&=(x+2y-75)(x+1).\n\\end{aligned}\n\\]\n\nHence the region in the \\((x,y)\\)-plane is described by  \n\n\\[\n\\boxed{(x-y)(76-x-y)<0}\\qquad\\text{and}\\qquad\\boxed{(x+2y-75)(x+1)<0}.\n\\tag{1}\n\\]\n\nThe four linear factors are\n\n\\[\nL_1=x-y,\\;L_2=76-x-y,\\;L_3=x+2y-75,\\;L_4=x+1 .\n\\]\n\n---\n\n### 2.  Split the two products\n\n\\[\n\\begin{aligned}\n(x-y)(76-x-y)<0 &\\Longleftrightarrow \n\\begin{cases}\nx>y,\\;x+y>76\\quad\\text{(region }A)\\\\\n\\text{or}\\\\\nx<y,\\;x+y<76\\quad\\text{(region }B)\n\\end{cases}\\\\[2mm]\n(x+2y-75)(x+1)<0 &\\Longleftrightarrow\n\\begin{cases}\nx<-1,\\;x+2y>75\\quad\\text{(region }C)\\\\\n\\text{or}\\\\\nx>-1,\\;x+2y<75\\quad\\text{(region }D)\n\\end{cases}\n\\end{aligned}\n\\]\n\nIntersecting the possibilities gives four candidate regions:\n\n\\[\n\\begin{array}{c|c}\n\\text{Intersection} & \\text{Constraints}\\\\ \\hline\nA\\cap C & x>y,\\;x+y>76,\\;x<-1,\\;x+2y>75\\\\\nA\\cap D & x>y,\\;x+y>76,\\;x>-1,\\;x+2y<75\\\\\nB\\cap C & x<y,\\;x+y<76,\\;x<-1,\\;x+2y>75\\\\\nB\\cap D & x<y,\\;x+y<76,\\;x>-1,\\;x+2y<75\n\\end{array}\n\\]\n\nThe first intersection is impossible (it would require \\(x>y\\) while \\(x<-1<y\\)), so it is empty.\nThe remaining three are non\u2011empty; two are unbounded, while one is bounded.\n\n---\n\n### 3.  Identify the bounded region\n\nThe bounded region is \\(B\\cap D\\):\n\n\\[\n\\begin{cases}\nx>-1,\\\\[2pt]\nx<y,\\\\[2pt]\nx+2y<75 .\n\\end{cases}\n\\]\n\nFrom \\(x<y\\) and \\(x+2y<75\\) we obtain the upper bound for \\(y\\):\n\\[\ny<\\frac{75-x}{2}.\n\\]\n\nTogether with \\(x>-1\\) this forces\n\\[\n-1<x<25,\n\\qquad\nx<y<\\frac{75-x}{2}.\n\\]\n\nHence in the \\((x,y)\\)-plane the region is the open triangle bounded by the three lines\n\n\\[\nx=-1,\\quad y=x,\\quad y=\\frac{75-x}{2}.\n\\]\n\nIts vertices are  \n\n\\[\n(-1,-1),\\;(-1,38),\\;(25,25).\n\\]\n\nThe area in the \\((x,y)\\)-plane is\n\n\\[\n\\text{Area}_{xy}\n= \\frac12\\cdot(\\text{base})\\cdot(\\text{height})\n= \\frac12\\cdot 39 \\cdot 26=507 .\n\\]\n\n---\n\n### 4.  Convert to area on the original plane\n\nThe plane \\(x+y+z=75\\) can be written as \\(z=75-x-y\\).\nFor a graph \\(z=f(x,y)\\) the surface element is  \n\n\\[\ndA = \\sqrt{1+f_x^2+f_y^2}\\,dx\\,dy\n    =\\sqrt{1+(-1)^2+(-1)^2}\\,dx\\,dy\n    =\\sqrt{3}\\,dx\\,dy .\n\\]\n\nTherefore the area of the finite region on the plane \\(x+y+z=75\\) is  \n\n\\[\n\\text{Area}= \\sqrt{3}\\times 507 = 507\\sqrt{3}.\n\\]\n\n---\n\n### 5.  Form \\(a\\sqrt{b}\\) and compute \\(a+b\\)\n\n\\[\na=507,\\qquad b=3\\;( \\text{square\u2011free}).\n\\]\n\nThus  \n\n\\[\na+b = 507+3 = 510.\n\\]\n\n\\[\n\\boxed{510}\n\\]",
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+      {
+        "role": "user",
+        "content": "\nA piecewise linear periodic function is defined by $f(x)=\\begin{cases}x&\\text{if }x\\in[-1,1)\\\\2-x&\\text{if }x\\in[1,3)\\end{cases}$ and $f(x+4)=f(x)$ for all real numbers $x$. The graph of $f(x)$ has the sawtooth pattern. The parabola $x=34y^2$ intersects the graph of $f(x)$ at finitely many points. The sum of the $y$-coordinates of these intersection points can be expressed in the form $\\frac{a+b\\sqrt{c}}{d}$, where $a,b,c,$ and $d$ are positive integers, $a,b,$ and $d$ have greatest common divisor equal to 1, and $c$ is not divisible by the square of any prime. Find $a+b+c+d$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "The graph of  \n\n\\[\nf(x)=\\begin{cases}\nx,&-1\\le x<1\\\\[2pt]\n2-x,&1\\le x<3\n\\end{cases},\\qquad f(x+4)=f(x)\n\\]\n\nis a periodic \u201csaw\u2011tooth\u2019\u2019 of period \\(4\\).  \nThe parabola is  \n\n\\[\nx=34y^{2}\\qquad (x\\ge 0).\n\\]\n\nFor an intersection we need  \n\n\\[\ny=f(x),\\qquad x=34y^{2}.\n\\]\n\n--------------------------------------------------------------------\n### 1.   Reducing the \\(x\\)\u2013coordinate\n\nWrite \\(x=34y^{2}=4n+u\\) where \\(n\\in\\mathbb Z\\) and the reduced part  \n\n\\[\nu\\in[-1,3)\n\\]\n\n(because on each period we use the definition of \\(f\\) on \\([-1,3)\\)).\nHence  \n\n\\[\nu=34y^{2}-4n .\n\\]\n\n--------------------------------------------------------------------\n### 2.   The two cases for \\(u\\)\n\n* If \\(u\\in[-1,1)\\) then \\(f(x)=u\\); the equation becomes  \n\n  \\[\n  y=u\\quad\\Longrightarrow\\quad y=34y^{2}-4n .\n  \\]\n\n* If \\(u\\in[1,3)\\) then \\(f(x)=2-u\\); the equation becomes  \n\n  \\[\n  y=2-u\\quad\\Longrightarrow\\quad u=2-y ,\n  \\]\n  hence  \n\n  \\[\n  34y^{2}-4n=2-y .\n  \\]\n\nBecause \\(f(x)\\) takes only values in \\([-1,1]\\), all solutions must satisfy \\(-1\\le y\\le 1\\).\n\n--------------------------------------------------------------------\n### 3.   Solving the quadratics\n\n**Case A:** \\(y=34y^{2}-4n\\)\n\n\\[\n34y^{2}-y-4n=0\\qquad\\Longrightarrow\\qquad  \ny=\\frac{1\\pm\\sqrt{1+544n}}{68}.\n\\]\n\n**Case B:** \\(34y^{2}-4n=2-y\\)\n\n\\[\n34y^{2}+y-(2+4n)=0\\qquad\\Longrightarrow\\qquad  \ny=\\frac{-1\\pm\\sqrt{273+544n}}{68}.\n\\]\n\nSince \\(x=34y^{2}\\le 34\\), we have \\(0\\le x\\le 34\\).  \nConsequently \\(4n+u\\le 34\\) and with \\(u\\ge-1\\) we obtain \\(0\\le n\\le8\\).\n\n--------------------------------------------------------------------\n### 4.   Which roots lie in \\([-1,1]\\)?\n\n* For **Case\u202fA** (\\(n=0,\\dots,8\\)) both roots are in \\([-1,1]\\).  \n  Their sum for each \\(n\\) is\n\n  \\[\n  y_{A+}+y_{A-}= \\frac{1}{34}.\n  \\]\n\n* For **Case\u202fB** (\\(n=0,\\dots,7\\)) both roots are in \\([-1,1]\\);  \n  for \\(n=8\\) only the \u201c+\u2019\u2019 root lies in the interval.  \n  The sum of the two roots for each \\(n\\le7\\) is\n\n  \\[\n  y_{B+}+y_{B-}= -\\frac{1}{34}.\n  \\]\n\nThus the total sum of all \\(y\\)-coordinates is\n\n\\[\n\\begin{aligned}\n\\sum y &=\\sum_{n=0}^{8}\\frac1{34}\\;+\\;\\sum_{n=0}^{7}\\!\\Big(-\\frac1{34}\\Big)\\;+\\;y_{B+}(8)\\\\\n&= \\frac{9}{34}-\\frac{8}{34}+y_{B+}(8)\\\\\n&= \\frac1{34}+ \\frac{-1+\\sqrt{273+544\\cdot8}}{68}.\n\\end{aligned}\n\\]\n\nSince \\(273+544\\cdot8 = 4625 = 25\\cdot185\\),\n\n\\[\ny_{B+}(8)=\\frac{-1+5\\sqrt{185}}{68},\n\\qquad\n\\frac1{34}= \\frac{2}{68}.\n\\]\n\nHence\n\n\\[\n\\sum y =\\frac{2-1+5\\sqrt{185}}{68}= \\frac{1+5\\sqrt{185}}{68}.\n\\]\n\n--------------------------------------------------------------------\n### 5.   Final form\n\n\\[\n\\frac{1+5\\sqrt{185}}{68}= \\frac{a+b\\sqrt{c}}{d},\n\\qquad \na=1,\\;b=5,\\;c=185,\\;d=68 .\n\\]\n\nAll conditions are satisfied (\\(\\gcd(a,b,d)=1\\) and \\(185\\) is square\u2011free).\n\n\\[\na+b+c+d = 1+5+185+68 = 259.\n\\]\n\n\\[\n\\boxed{259}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nThe 27 cells of a $3\\times9$ grid are filled in using the numbers 1 through 9 so that each row contains 9 different numbers, and each of the three $3\\times3$ blocks heavily outlined in the example below contains 9 different numbers, as in the first three rows of a Sudoku puzzle. \n | 4 | 2 | 8 | 9 | 6 | 3 | 1 | 7 | 5 | \n | 3 | 7 | 9 | 5 | 2 | 1 | 6 | 8 | 4 | \n | 5 | 6 | 1 | 8 | 4 | 7 | 9 | 2 | 3 | \n The number of different ways to fill such a grid can be written as $p^a\\cdot q^b\\cdot r^c\\cdot s^d$, where $p,q,r,$ and $s$ are distinct prime numbers and $a,b,c,$ and $d$ are positive integers. Find $p\\cdot a+q\\cdot b+r\\cdot c+s\\cdot d$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let the three rows be \\(R_{1},R_{2},R_{3}\\) and the three \\(3\\times 3\\) blocks be  \n\n\\[\nB_{1}= \\text{columns }1\\!-\\!3,\\qquad   \nB_{2}= \\text{columns }4\\!-\\!6,\\qquad   \nB_{3}= \\text{columns }7\\!-\\!9 .\n\\]\n\n--------------------------------------------------------------------\n### 1.  Fix the first row  \n\nSince the rows are labelled, we may first choose any permutation of \\(\\{1,\\dots ,9\\}\\) for \\(R_{1}\\).\nThere are  \n\n\\[\n9! = 2^{7}\\cdot 3^{4}\\cdot5\\cdot7\n\\]\n\nways.\n\n--------------------------------------------------------------------\n### 2.  Which digits go to the second row in each block?  \n\nAssume \\(R_{1}=1\\,2\\,3\\;4\\,5\\,6\\;7\\,8\\,9\\) (the identity permutation).  \nThen  \n\n* In \\(B_{1}\\) the missing digits are \\(\\{4,5,6,7,8,9\\}\\);  \n* In \\(B_{2}\\) the missing digits are \\(\\{1,2,3,7,8,9\\}\\);  \n* In \\(B_{3}\\) the missing digits are \\(\\{1,2,3,4,5,6\\}\\).\n\nFor the second row we must pick, from each block, three of its six missing digits.\nThe three rows must each contain every digit exactly once, so each digit\nmust appear **once** in \\(R_{2}\\) (and the remaining occurrence of that digit will be in \\(R_{3}\\)).\nThus the choice of digits for \\(R_{2}\\) is a partition of the six\u2013digit sets\nsubject to the condition that each of the nine digits occurs in exactly one block of \\(R_{2}\\).\n\nLet  \n\n* \\(x\\) = number of digits \\(\\{1,2,3\\}\\) placed in \\(B_{2}\\) (the rest go to \\(B_{3}\\));\n* \\(y\\) = number of digits \\(\\{4,5,6\\}\\) placed in \\(B_{1}\\) (the rest go to \\(B_{3}\\));\n* \\(z\\) = number of digits \\(\\{7,8,9\\}\\) placed in \\(B_{1}\\) (the rest go to \\(B_{2}\\)).\n\nFrom the block\u2011size condition we obtain  \n\n\\[\n\\begin{cases}\ny+z=3,\\\\\nx+ (3-z)=3,\\\\\n(3-x)+(3-y)=3,\n\\end{cases}\\qquad\\Longrightarrow\\qquad\nx=z,\\;x+y=3 .\n\\]\n\nHence \\(x\\) may be \\(0,1,2,3\\); then \\(y=3-x\\) and \\(z=x\\).\nFor a given \\(x\\),\n\n* choose the \\(x\\) digits of \\(\\{1,2,3\\}\\) that go to \\(B_{2}\\): \\(\\binom{3}{x}\\) ways;\n* choose the \\(y=3-x\\) digits of \\(\\{4,5,6\\}\\) that go to \\(B_{1}\\): \\(\\binom{3}{3-x}=\\binom{3}{x}\\) ways;\n* choose the \\(z=x\\) digits of \\(\\{7,8,9\\}\\) that go to \\(B_{1}\\): \\(\\binom{3}{x}\\) ways.\n\nThus for this \\(x\\) we have \\(\\bigl(\\binom{3}{x}\\bigr)^{3}\\) possibilities.\nSumming over \\(x=0,1,2,3\\),\n\n\\[\n\\sum_{x=0}^{3}\\binom{3}{x}^{3}=1+27+27+1=56 .\n\\]\n\nSo there are \\(56\\) ways to decide which three\u2011digit sets belong to the second row\n(and the third row is forced to receive the complementary sets).\n\n--------------------------------------------------------------------\n### 3.  Ordering the digits inside each block  \n\nInside a block each row contains three distinct digits.\nFor a fixed block, the three chosen digits of \\(R_{2}\\) can be placed in the\nthree columns in \\(3!\\) ways, and independently the three digits of \\(R_{3}\\) can be placed in \\(3!\\) ways.\nHence each block contributes \\((3!)^{2}=36\\) arrangements.\n\nWith three blocks we obtain \\((36)^{3}=36^{3}=46\\,656\\) column\u2011orderings.\n\n--------------------------------------------------------------------\n### 4.  Total number of grids  \n\n\\[\nN = 9! \\times 56 \\times 36^{3}\n     = 2^{7}\\!3^{4}\\!5\\!7\\; \\times 2^{3}\\!7\\; \\times 2^{6}\\!3^{6}\n     = 2^{16}\\,3^{10}\\,5^{1}\\,7^{2}.\n\\]\n\nThus\n\n\\[\nN = p^{a}\\,q^{b}\\,r^{c}\\,s^{d}\n\\quad\\text{with}\\quad\n(p,q,r,s)=(2,3,5,7),\\;\n(a,b,c,d)=(16,10,1,2).\n\\]\n\n--------------------------------------------------------------------\n### 5.  Required sum  \n\n\\[\np a + q b + r c + s d\n = 2\\cdot16 + 3\\cdot10 + 5\\cdot1 + 7\\cdot2\n = 32 + 30 + 5 + 14\n = 81 .\n\\]\n\n\\[\n\\boxed{81}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nSix points $ A, B, C, D, E, $ and $ F $ lie in a straight line in that order. Suppose that $ G $ is a point not on the line and that $ AC = 26 $, $ BD = 22 $, $ CE = 31 $, $ DF = 33 $, $ AF = 73 $, $ CG = 40 $, and $ DG = 30 $. Find the area of $ \\triangle BGE $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let the line containing the points be the \\(x\\)-axis.  \nPlace \\(A\\) at the origin, \\(A=(0,0)\\), and write the coordinates of the other\ncollinear points as\n\n\\[\nB=(x_B,0),\\;C=(x_C,0),\\;D=(x_D,0),\\;E=(x_E,0),\\;F=(x_F,0).\n\\]\n\n---\n\n### 1.  Find the positions of \\(B,\\;C,\\;D,\\;E,\\;F\\)\n\nThe given distances are along the line, so\n\n\\[\n\\begin{aligned}\nAC&=26 &&\\Rightarrow x_C=26,\\\\[2pt]\nAF&=73 &&\\Rightarrow x_F=73,\\\\[2pt]\nCE&=31 &&\\Rightarrow x_E=x_C+31=57,\\\\[2pt]\nDF&=33 &&\\Rightarrow x_D=x_F-33=40,\\\\[2pt]\nBD&=22 &&\\Rightarrow x_B=x_D-22=18.\n\\end{aligned}\n\\]\n\nThus  \n\n\\[\nA=0,\\; B=18,\\; C=26,\\; D=40,\\; E=57,\\; F=73 .\n\\]\n\n---\n\n### 2.  Coordinates of \\(G\\)\n\nLet \\(G=(x_G,h)\\), where \\(h>0\\) is the perpendicular distance from \\(G\\) to the line.\n\nThe distances from \\(G\\) to \\(C\\) and \\(D\\) give\n\n\\[\n\\begin{cases}\n(x_G-26)^2+h^2 = 40^2 = 1600,\\\\[4pt]\n(x_G-40)^2+h^2 = 30^2 = 900 .\n\\end{cases}\n\\]\n\nSubtracting the second equation from the first:\n\n\\[\n(x_G-26)^2-(x_G-40)^2 = 1600-900 = 700 .\n\\]\n\nCompute the left side:\n\n\\[\n(x_G^2-52x_G+26^2)-(x_G^2-80x_G+40^2)\n=28x_G-924 .\n\\]\n\nHence  \n\n\\[\n28x_G-924 = 700 \\quad\\Longrightarrow\\quad 28x_G = 1624\n\\quad\\Longrightarrow\\quad x_G = 58 .\n\\]\n\nNow find \\(h\\) using either distance equation; use the first:\n\n\\[\n(58-26)^2 + h^2 = 1600\n\\Longrightarrow 32^2 + h^2 = 1600\n\\Longrightarrow h^2 = 1600-1024 = 576\n\\Longrightarrow h = 24 .\n\\]\n\nThus \\(G=(58,24)\\). Its perpendicular projection onto the line is at \\(x=58\\), which lies between \\(E\\) and \\(F\\).\n\n---\n\n### 3.  Area of \\(\\triangle BGE\\)\n\nThe base \\(BE\\) lies on the \\(x\\)-axis:\n\n\\[\nBE = x_E - x_B = 57-18 = 39 .\n\\]\n\nThe height from \\(G\\) to this base is the vertical distance \\(h=24\\).\n\nTherefore\n\n\\[\n\\text{Area} = \\frac12 \\times (\\text{base}) \\times (\\text{height})\n= \\frac12 \\times 39 \\times 24 = 39 \\times 12 = 468 .\n\\]\n\n---\n\n\\[\n\\boxed{468}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nFind the sum of all positive integers $ n $ such that $ n + 2 $ divides the product $ 3(n + 3)(n^2 + 9) $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "\\[\n\\text{Find all }n\\in\\mathbb Z_{>0}\\text{ such that }(n+2)\\mid 3(n+3)(n^2+9).\n\\]\n\n---\n\n### 1.  Replace \\(n+2\\) by a new variable  \n\nSet  \n\\[\nm=n+2\\qquad (m\\ge 3).\n\\]\n\nThen  \n\n\\[\nn=m-2,\\qquad n+3=m+1,\\qquad n^2+9=(m-2)^2+9=m^{2}-4m+13 .\n\\]\n\nHence the divisibility condition becomes  \n\n\\[\nm\\mid 3(m+1)(m^{2}-4m+13).\n\\tag{1}\n\\]\n\n---\n\n### 2.  Reduce the right\u2013hand side modulo \\(m\\)\n\nModulo \\(m\\),\n\n\\[\nm+1\\equiv 1,\\qquad m^{2}-4m+13\\equiv 13 .\n\\]\n\nTherefore  \n\n\\[\n3(m+1)(m^{2}-4m+13)\\equiv 3\\cdot1\\cdot13=39 \\pmod m .\n\\]\n\nSo (1) is equivalent to  \n\n\\[\nm\\mid 39 .\n\\tag{2}\n\\]\n\nIndeed, if \\(m\\mid 39\\) then the right\u2013hand side of (1) equals \\(39+km\\) for some integer \\(k\\), hence is divisible by \\(m\\); conversely, if \\(m\\mid 3(m+1)(m^{2}-4m+13)\\) then \\(m\\mid 39\\).\n\n---\n\n### 3.  List possible \\(m\\)\n\nThe positive divisors of \\(39\\) are  \n\n\\[\n1,\\;3,\\;13,\\;39 .\n\\]\n\nSince \\(m=n+2\\ge 3\\) (because \\(n\\ge1\\)), we keep  \n\n\\[\nm\\in\\{3,\\;13,\\;39\\}.\n\\]\n\n---\n\n### 4.  Recover the corresponding \\(n\\)\n\n\\[\n\\begin{aligned}\nm=3 &\\;\\Rightarrow\\; n=m-2=1,\\\\[2pt]\nm=13 &\\;\\Rightarrow\\; n=11,\\\\[2pt]\nm=39 &\\;\\Rightarrow\\; n=37 .\n\\end{aligned}\n\\]\n\nAll three indeed satisfy the original divisibility (quick check: the quotients are \\(40,420,4240\\) respectively).\n\n---\n\n### 5.  Sum of all such \\(n\\)\n\n\\[\n1+11+37=49.\n\\]\n\n\\[\n\\boxed{49}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nThe parabola with equation $y=x^{2}-4$ is rotated $60^{\\circ}$ counterclockwise around the origin. The unique point in the fourth quadrant where the original parabola and its image intersect has $y$-coordinate $\\frac{a-\\sqrt{b}}{c}$, where $a$, $b$, and $c$ are positive integers, and $a$ and $c$ are relatively prime. Find $a+b+c$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n\\[\nP:\\;y=x^{2}-4\n\\]\n\nand rotate \\(P\\) \\(60^{\\circ}\\) counter\u2011clockwise about the origin.  \nIf \\((u,v)\\) is a point of \\(P\\) \\((v=u^{2}-4)\\), after the rotation we obtain  \n\n\\[\n\\begin{aligned}\nx &=u\\cos 60^{\\circ}-v\\sin 60^{\\circ}\n      =\\frac{u-\\sqrt3\\,(u^{2}-4)}2,\\\\[2mm]\ny &=u\\sin 60^{\\circ}+v\\cos 60^{\\circ}\n      =\\frac{\\sqrt3\\,u+u^{2}-4}2 .\n\\end{aligned}\n\\tag{1}\n\\]\n\nA point \\((x,y)\\) that belongs to both the original parabola and its image\nmust satisfy  \n\n\\[\ny=x^{2}-4 \\qquad\\text{and}\\qquad (x,y)=\\bigl(x(u),y(u)\\bigr)\\text{ for some }u .\n\\]\n\nUsing (1) and substituting \\(y=x^{2}-4\\) we get an equation for the\npre\u2011image coordinate \\(u\\):\n\n\\[\n\\Bigl(u-\\sqrt3\\,(u^{2}-4)\\Bigr)^{2}=2u^{2}+2\\sqrt3\\,u+8 .\n\\]\n\nSimplifying gives  \n\n\\[\n3u^{4}-25u^{2}+40+2\\sqrt3\\,u\\,(3-u^{2})=0 .\n\\tag{2}\n\\]\n\nLet \\(t=u^{2}=x^{2}\\;(t\\ge0)\\).  Equation (2) becomes  \n\n\\[\n\\bigl(3t^{2}-25t+40\\bigr)^{2}=12t\\,(3-t)^{2},\n\\]\n\nor\n\n\\[\n9t^{4}-162t^{3}+937t^{2}-2108t+1600=0 .\n\\tag{3}\n\\]\n\nThe quartic factors over the integers:\n\n\\[\n\\begin{aligned}\n9t^{4}-162t^{3}+937t^{2}-2108t+1600\n  &=\\bigl(t^{2}-11t+16\\bigr)\\bigl(9t^{2}-63t+100\\bigr).\n\\end{aligned}\n\\]\n\nThus the possible values of \\(t\\) are\n\n\\[\nt=\\frac{11\\pm\\sqrt{57}}2,\\qquad\nt=\\frac{63\\pm\\sqrt{369}}{18}.\n\\]\n\nRecall that \\(t=x^{2}\\) and that a genuine intersection must satisfy the\noriginal unsquared equation  \n\n\\[\n3t^{2}-25t+40=2\\sqrt3\\,\\sqrt t\\,(3-t).\n\\tag{4}\n\\]\n\nChecking the sign of each side of (4) shows that only  \n\n\\[\nt=\\frac{11-\\sqrt{57}}2\\approx1.725\n\\]\n\nsatisfies (4) with \\(x>0\\).  (The other three roots correspond to the\ncase \\(3t^{2}-25t+40= -2\\sqrt3\\,\\sqrt t\\,(3-t)\\) or give \\(y>0\\).)\n\nSince \\(y=x^{2}-4=t-4\\),\n\n\\[\ny=\\frac{11-\\sqrt{57}}2-4=\\frac{3-\\sqrt{57}}2 .\n\\]\n\nHence the required numbers are  \n\n\\[\na=3,\\qquad b=57,\\qquad c=2,\n\\]\n\nwith \\(\\gcd(a,c)=1\\).  Therefore\n\n\\[\na+b+c=3+57+2=62 .\n\\]\n\n\\[\n\\boxed{62}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nThe product $ \\prod_{k=4}^{63} \\frac{\\log_k(5^{k^2-1})}{\\log_{k+1}(5^{k^2-4})} = \\frac{\\log_4(5^{15})}{\\log_5(5^{12})} \\cdot \\frac{\\log_5(5^{24})}{\\log_6(5^{21})} \\cdot \\frac{\\log_6(5^{35})}{\\log_7(5^{32})} \\cdots \\frac{\\log_{63}(5^{3968})}{\\log_{64}(5^{3965})} $ is equal to $ \\frac{m}{n} $, where $ m $ and $ n $ are relatively prime positive integers. Find $ m + n $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "\\[\n\\prod_{k=4}^{63}\\frac{\\log_k(5^{k^2-1})}{\\log_{k+1}(5^{k^2-4})}\n\\]\n\n---\n\n### 1.  Rewrite each term using change of base  \n\n\\[\n\\log_a b=\\frac{\\ln b}{\\ln a}\n\\]\n\nHence  \n\n\\[\n\\frac{\\log_k(5^{k^2-1})}{\\log_{k+1}(5^{k^2-4})}\n =\\frac{\\displaystyle\\frac{\\ln\\! \\big(5^{\\,k^2-1}\\big)}{\\ln k}}\n        {\\displaystyle\\frac{\\ln\\! \\big(5^{\\,k^2-4}\\big)}{\\ln (k+1)}}\n =\\frac{(k^2-1)\\ln5}{\\ln k}\\cdot\\frac{\\ln (k+1)}{(k^2-4)\\ln5}\n =\\frac{k^2-1}{k^2-4}\\cdot\\frac{\\ln(k+1)}{\\ln k}.\n\\]\n\nThus the whole product becomes  \n\n\\[\n\\Bigl[\\prod_{k=4}^{63}\\frac{k^2-1}{\\,k^2-4}\\Bigr]\\,\n\\Bigl[\\prod_{k=4}^{63}\\frac{\\ln(k+1)}{\\ln k}\\Bigr].\n\\]\n\n---\n\n### 2.  The logarithmic factor telescopes  \n\n\\[\n\\prod_{k=4}^{63}\\frac{\\ln(k+1)}{\\ln k}\n= \\frac{\\ln5}{\\ln4}\\cdot\\frac{\\ln6}{\\ln5}\\cdots\\frac{\\ln64}{\\ln63}\n= \\frac{\\ln64}{\\ln4}\n= \\frac{6\\ln2}{2\\ln2}=3.\n\\]\n\n---\n\n### 3.  Simplify the rational factor  \n\n\\[\n\\frac{k^2-1}{k^2-4}= \\frac{(k-1)(k+1)}{(k-2)(k+2)}.\n\\]\n\nHence  \n\n\\[\n\\prod_{k=4}^{63}\\frac{k^2-1}{k^2-4}\n= \\Bigl[\\prod_{k=4}^{63}\\frac{k-1}{k-2}\\Bigr]\n  \\Bigl[\\prod_{k=4}^{63}\\frac{k+1}{k+2}\\Bigr].\n\\]\n\n**First product**\n\n\\[\n\\prod_{k=4}^{63}\\frac{k-1}{k-2}\n= \\frac{3}{2}\\cdot\\frac{4}{3}\\cdot\\frac{5}{4}\\cdots\\frac{62}{61}\n= \\frac{62}{2}=31.\n\\]\n\n**Second product**\n\n\\[\n\\prod_{k=4}^{63}\\frac{k+1}{k+2}\n= \\frac{5}{6}\\cdot\\frac{6}{7}\\cdot\\frac{7}{8}\\cdots\\frac{64}{65}\n= \\frac{5}{65}= \\frac{1}{13}.\n\\]\n\nMultiplying,\n\n\\[\n\\prod_{k=4}^{63}\\frac{k^2-1}{k^2-4}=31\\cdot\\frac{1}{13}= \\frac{31}{13}.\n\\]\n\n---\n\n### 4.  Combine the two parts  \n\n\\[\n\\prod_{k=4}^{63}\\frac{\\log_k(5^{k^2-1})}{\\log_{k+1}(5^{k^2-4})}\n= \\frac{31}{13}\\times 3 = \\frac{93}{13}.\n\\]\n\nThe fraction \\(\\frac{93}{13}\\) is already in lowest terms (\\(\\gcd(93,13)=1\\)).  \n\nThus \\(m=93,\\; n=13\\) and  \n\n\\[\nm+n = 93+13 = 106.\n\\]\n\n\\[\n\\boxed{106}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nLet $N$ denote the number of ordered triples of positive integers $(a,b,c)$ such that $a,b,c\\leq3^6$ and $a^3+b^3+c^3$ is a multiple of $3^7$. Find the remainder when $N$ is divided by $1000$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "**Solution Sketch**\n\nWrite every integer \\(a\\le 3^{6}=729\\) in its base\u2011\\(3\\) expansion  \n\n\\[\na = a_{0}+a_{1}3+a_{2}3^{2}+a_{3}3^{3}+a_{4}3^{4}+a_{5}3^{5},\n\\qquad a_{i}\\in\\{0,1,2\\}.\n\\]\n\nLet  \n\n\\[\nA(x)=a_{0}+a_{1}x+a_{2}x^{2}+a_{3}x^{3}+a_{4}x^{4}+a_{5}x^{5}\\in\\mathbb{F}_{3}[x].\n\\]\n\nModulo \\(3^{7}\\) we have  \n\n\\[\na^{3}\\equiv a_{0}^{3}+9a_{0}^{2}a_{1}+27\\bigl(a_{0}a_{1}^{2}+a_{0}^{2}a_{2}\\bigr)\n               +\\; \\cdots\\;+3^{6}a_{2}^{3}\\pmod{3^{7}} .\n\\]\n\nHence\n\n\\[\na^{3}+b^{3}+c^{3}\\equiv \n\\sum_{i=0}^{2}3^{i}\\bigl(a_{i}^{3}+b_{i}^{3}+c_{i}^{3}\\bigr)\\pmod{3^{7}} .\n\\]\n\nBecause \\(x^{3}\\equiv x\\pmod 3\\) for \\(x\\in\\{0,1,2\\}\\), the condition\n\\(a^{3}+b^{3}+c^{3}\\equiv0\\pmod{3^{7}}\\) is equivalent to the three\nindependent linear equations  \n\n\\[\na_{0}+b_{0}+c_{0}\\equiv0,\\qquad\na_{1}+b_{1}+c_{1}\\equiv0,\\qquad\na_{2}+b_{2}+c_{2}\\equiv0\\pmod 3 .\n\\]\n\nFor each digit\u2011position \\(i=0,1,2\\) the number of ordered triples\n\\((a_{i},b_{i},c_{i})\\) satisfying the linear condition is\n\\(3^{2}=9\\) (choose any two digits freely, the third one is forced).\nThe remaining higher digits \\(a_{3},a_{4},a_{5}\\) are unrestricted; each\nhas \\(3^{3}=27\\) possibilities (three choices for each of the three\nnumbers).\n\nTherefore the total number of admissible triples \\((a,b,c)\\) is  \n\n\\[\nN = 9^{3}\\cdot 27^{3}=3^{15}=14\\,348\\,907 .\n\\]\n\nFinally we need the remainder of \\(N\\) modulo \\(1000\\):\n\n\\[\n14\\,348\\,907\\equiv 907\\pmod{1000}.\n\\]\n\n\\[\n\\boxed{907}\n\\]",
+        "role": "assistant"
+      }
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+    [
+      {
+        "role": "user",
+        "content": "\nFour unit squares form a $2 \\times 2$ grid. Each of the 12 unit line segments forming the sides of the squares is colored either red or blue in such a way that each unit square has 2 red sides and 2 blue sides. Find the number of such colorings.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n* \\(a,b,c,d\\) be the four interior edges (the two interior vertical and the two interior horizontal sides).  \n* The eight outer edges are the two edges that belong to each unit square but are on the boundary of the\n\\(2\\times2\\) grid.\n\nFor a particular unit square the number of its interior red sides is the number of red interior edges incident\nto it.  \nIf a square has \\(s\\) interior red sides, then it needs exactly \\(2-s\\) red outer sides, because the total number\nof red sides must be \\(2\\).  \n\nFor a given square\n\n\\[\n\\#\\text{ ways to colour its two outer edges}= \\binom{2}{\\,2-s\\,}=\n\\begin{cases}\n1,&s=0\\text{ or }2,\\\\[2pt]\n2,&s=1 .\n\\end{cases}\n\\]\n\nThus, once the interior edges are fixed, the outer edges can be coloured independently for each square.\nIf among the four squares exactly \\(k\\) of them have \\(s=1\\) (i.e. exactly one interior red edge incident to the\nsquare), the number of completions of the outer edges is \\(2^{k}\\).\n\n--------------------------------------------------------------------\n\n### Counting interior\u2013edge configurations\n\nThe interior edges form a 4\u2011cycle  \n\n\\[\nA\\;-\\;B\\;-\\;D\\;-\\;C\\;-\\;A .\n\\]\n\nWe list all \\(2^{4}=16\\) subsets of these edges and, for each, count how many squares have one interior red\nedge.\n\n| # interior edges | type of selection | \\# of squares with \\(s=1\\) | \\# of such subsets | contributions |\n|------------------|-------------------|----------------------------|--------------------|---------------|\n| 0 | none | 0 | 1 | \\(2^{0}=1\\) |\n| 1 | any one edge | 2 (the two squares incident to the edge) | 4 | \\(4\\cdot2^{2}=16\\) |\n| 2 | adjacent edges (share a vertex) | 2 (the two squares adjacent to the common vertex) | 4 | \\(4\\cdot2^{2}=16\\) |\n| 2 | opposite edges (no common vertex) | 4 (each square gets one) | 2 | \\(2\\cdot2^{4}=32\\) |\n| 3 | all but one edge | 2 (the two squares not incident to the missing edge) | 4 | \\(4\\cdot2^{2}=16\\) |\n| 4 | all four edges | 0 | 1 | \\(1\\cdot2^{0}=1\\) |\n\nAdding the contributions:\n\n\\[\n1+16+16+32+16+1 = 82 .\n\\]\n\n--------------------------------------------------------------------\n\nTherefore there are  \n\n\\[\n\\boxed{82}\n\\]\n\ndifferent ways to colour the 12 unit segments so that each of the four unit squares has exactly two red sides\n(and consequently two blue sides).",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nLet $ A $ be the set of positive integer divisors of 2025. Let $ B $ be a randomly selected subset of $ A $. The probability that $ B $ is a nonempty set with the property that the least common multiple of its elements is 2025 is $ \\frac{m}{n} $, where $ m $ and $ n $ are relatively prime positive integers. Find $ m + n $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "\\(2025=3^{4}\\cdot5^{2}\\).\n\nDivisors of \\(2025\\) are of the form \\(3^{a}5^{b}\\) with  \n\\(0\\le a\\le4,\\;0\\le b\\le2\\); therefore  \n\n\\[\n|A|=(4+1)(2+1)=15 .\n\\]\n\n--------------------------------------------------------------------\n### Condition for the LCM\n\nFor a subset \\(B\\subseteq A\\),\n\n\\[\n\\operatorname{lcm}(B)=3^{\\max a}\\,5^{\\max b}.\n\\]\n\nThus \\(\\operatorname{lcm}(B)=2025=3^{4}5^{2}\\) iff  \n\n* at least one element of \\(B\\) has exponent \\(a=4\\) (i.e. is divisible by \\(3^{4}\\)), and  \n* at least one element of \\(B\\) has exponent \\(b=2\\) (i.e. is divisible by \\(5^{2}\\)).\n\n--------------------------------------------------------------------\n### Relevant divisor families  \n\n\\[\nX=\\{d\\in A\\mid 3^{4}\\mid d\\}=\\{81,405,2025\\},\\qquad |X|=3,\n\\]\n\n\\[\nY=\\{d\\in A\\mid 5^{2}\\mid d\\}=\\{25,75,225,675,2025\\},\\qquad |Y|=5.\n\\]\n\n\\(X\\cap Y=\\{2025\\}\\), so \\(|X\\cup Y|=3+5-1=7\\).\n\n--------------------------------------------------------------------\n### Counting subsets with the required property  \n\nA subset \\(B\\) works iff it meets both \\(X\\) and \\(Y\\).  \nUsing inclusion\u2013exclusion on all \\(2^{15}\\) subsets of \\(A\\):\n\n\\[\n\\begin{aligned}\n\\#\\{B:\\ B\\cap X\\neq\\varnothing,\\ B\\cap Y\\neq\\varnothing\\}\n&=2^{15}\n -2^{12}\\;(\\text{subsets missing }X)\n -2^{10}\\;(\\text{subsets missing }Y)\\\\\n&\\qquad +2^{8}\\;(\\text{subsets missing both }X\\cup Y)\\\\[2mm]\n&=32768-4096-1024+256\\\\\n&=27904 .\n\\end{aligned}\n\\]\n\nAll these subsets are non\u2011empty, so the numerator is \\(27904\\).\n\n--------------------------------------------------------------------\n### Probability\n\n\\[\nP=\\frac{27904}{2^{15}}=\\frac{27904}{32768}.\n\\]\n\nBoth numbers are divisible by \\(256\\):\n\n\\[\n\\frac{27904}{32768}=\\frac{27904/256}{32768/256}= \\frac{109}{128}.\n\\]\n\nThe fraction \\(\\frac{109}{128}\\) is already in lowest terms, so  \n\\(m=109,\\;n=128\\).\n\n\\[\nm+n=109+128=237.\n\\]\n\n\\[\n\\boxed{237}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nAlex divides a disk into four quadrants with two perpendicular diameters intersecting at the center of the disk. He draws 25 more line segments through the disk, drawing each segment by selecting two points at random on the perimeter of the disk in different quadrants and connecting those two points. Find the expected number of regions into which these 27 line segments divide the disk.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "**Step\u202f1 \u2013  How regions grow**\n\nWhen a new line segment is drawn in the disk, it either  \n*does not meet any previous segment* \u2013 it creates **one** new region, or  \n*meets \\(k\\) previous segments in interior points* \u2013 it creates **\\(k+1\\)** new regions  \n(the segment is cut into \\(k+1\\) pieces, each of which separates a region).\n\nHence, if we start with one region (the whole disk),\n\n\\[\n\\#\\text{regions}=1+\\#\\text{segments}+\\#\\text{interior intersections } .\n\\tag{1}\n\\]\n\nThe two perpendicular diameters intersect once, giving the four initial\nquadrants.  After the 25 random chords are added we will have  \n\n\\[\n27\\text{ segments} = 2\\text{ diameters}+25\\text{ chords}.\n\\]\n\nSo we only have to find the **expected number of interior intersection points**.\n\n--------------------------------------------------------------------\n\n**Step\u202f2 \u2013  Intersections with the diameters**\n\nA random chord meets a fixed diameter iff its two endpoints lie on opposite\nsides of that diameter.  \n\n*Horizontal diameter*\u2003(\\(y=0\\)): the endpoints must belong to one of the\nfour unordered quadrant pairs  \n\n\\[\n\\{Q_1,Q_3\\},\\{Q_1,Q_4\\},\\{Q_2,Q_3\\},\\{Q_2,Q_4\\},\n\\]\n\ni.e. 4 out of the 6 possible unordered pairs of different quadrants.\nThus  \n\n\\[\nP(\\text{chord meets a given diameter})=\\frac{4}{6}= \\frac23 .\n\\]\n\nThe same probability holds for the vertical diameter.  \nHence the expected number of chord\u2011diameter intersections is  \n\n\\[\n25\\;( \\text{chords})\\times 2\\;( \\text{diameters})\\times \\frac23\n  =\\frac{100}{3}.\n\\tag{2}\n\\]\n\n--------------------------------------------------------------------\n\n**Step\u202f3 \u2013  Intersections between two random chords**\n\nLet a chord be represented by the unordered pair of quadrants that contain its\nend\u2011points.  \nThere are  \n\n* 4 *adjacent* pairs  \\(\\{0,1\\},\\{1,2\\},\\{2,3\\},\\{3,0\\}\\);  \n* 2 *opposite* pairs   \\(\\{0,2\\},\\{1,3\\}\\).\n\nThus the six possible chords are the six edges of the complete graph \\(K_4\\)\non the four quadrants.\n\nTwo chords may be:\n\n| Relation of the two edges | How many ordered pairs | Intersection probability |\n|---------------------------|-----------------------|--------------------------|\n| Same edge (both chords use the same pair) | 6 (4 adjacent\u202f+\u202f2 opposite) | \\(\\frac12\\) |\n| Share one vertex (adjacent edges) | 24 (8 both adjacent\u202f+\u202f16 one adjacent\u2013one opposite) | \\(\\frac12\\) |\n| Disjoint edges, both adjacent (e.g. \\{0,1\\} & \\{2,3\\}) | 4 | \\(0\\) |\n| Disjoint edges, both opposite ( \\{0,2\\} & \\{1,3\\}) | 2 | \\(1\\) |\n\n*Why these probabilities?*  \n\n* Same edge \u2013 the two chords are independent copies inside the same two\nquadrants.  A short calculation (or a symmetry argument) gives a crossing\nprobability of \\(\\frac12\\).\n* Share a vertex \u2013 one endpoint of the second chord lies in the same quadrant\nas an endpoint of the first chord.  The second endpoint is always in a\ndifferent quadrant, so the second chord meets the first exactly when the\npoint that shares the vertex falls between the two endpoints of the first\nchord.  Averaging over the uniform positions gives \\(\\frac12\\) again.\n* Disjoint adjacent edges lie completely on opposite sides of the\nhorizontal (or vertical) diameter, so they can never meet \u21d2 probability \\(0\\).\n* Disjoint opposite edges always cross the centre of the disk; any two such\nchords intersect \u21d2 probability \\(1\\).\n\nSumming the contributions of the \\(36\\) ordered pairs of chords,\n\n\\[\nS = 6\\!\\left(\\frac12\\right)+24\\!\\left(\\frac12\\right)+4\\cdot0+2\\cdot1 = 17 .\n\\]\n\nTherefore the probability that two independently chosen random chords intersect is  \n\n\\[\np_{\\text{chord\u2013chord}} = \\frac{S}{36}= \\frac{17}{36}.\n\\tag{3}\n\\]\n\n--------------------------------------------------------------------\n\n**Step\u202f4 \u2013  Expected number of chord\u2013chord intersections**\n\nThere are \\(\\binom{25}{2}=300\\) unordered pairs of the 25 random chords.  \nUsing (3),\n\n\\[\nE(\\text{chord\u2013chord intersections})=300\\cdot\\frac{17}{36}\n     =\\frac{425}{3}=141\\frac{2}{3}.\n\\tag{4}\n\\]\n\n--------------------------------------------------------------------\n\n**Step\u202f5 \u2013  Total expected interior intersections**\n\n\\[\n\\begin{aligned}\nE(\\text{total interior intersections})\n&= (\\text{diameters intersect})\\\\\n&\\qquad +(\\text{chord\u2013diameter intersections})\\\\\n&\\qquad +(\\text{chord\u2013chord intersections})\\\\[2mm]\n&= 1+\\frac{100}{3}+ \\frac{425}{3}= 176 .\n\\end{aligned}\n\\tag{5}\n\\]\n\n--------------------------------------------------------------------\n\n**Step\u202f6 \u2013  Expected number of regions**\n\nInsert (5) into formula (1) with the total of \\(27\\) segments:\n\n\\[\nE(\\text{regions}) = 1 + 27 + 176 = 204 .\n\\]\n\n--------------------------------------------------------------------\n\n\\[\n\\boxed{204}\n\\]",
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+        "role": "user",
+        "content": "\nCircle $\\omega_1$ with radius 6 centered at point $A$ is internally tangent at point $B$ to circle $\\omega_2$ with radius 15. Points $C$ and $D$ lie on $\\omega_2$ such that $\\overline{BC}$ is a diameter of $\\omega_2$ and $\\overline{BC} \\perp \\overline{AD}$. The rectangle $EFGH$ is inscribed in $\\omega_1$ such that $\\overline{EF} \\perp \\overline{BC}$, $C$ is closer to $\\overline{GH}$ than to $\\overline{EF}$, and $D$ is closer to $\\overline{FG}$ than to $\\overline{EH}$, as shown. Triangles $\\triangle DGF$ and $\\triangle CHG$ have equal areas. The area of rectangle $EFGH$ is $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m + n$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "**Solution Overview**\n\nPlace the two circles on a coordinate plane, compute the positions of the relevant points, and write the\nrectangle\u2019s vertices in terms of its side\u2013lengths.  \nThe conditions \u201c\\(C\\) is closer to \\(\\overline{GH}\\) than to \\(\\overline{EF}\\)\u201d and \u201c\\(D\\) is closer to\n\\(\\overline{FG}\\) than to \\(\\overline{EH}\\)\u201d fix the orientation of the rectangle.  \nUsing the equality of the two triangle areas we obtain a simple relation between the rectangle\u2019s width\nand height, which together with the fact that the rectangle is inscribed in the small circle yields the\nrequired dimensions and its area.\n\n--------------------------------------------------------------------\n\n### 1.  Coordinate set\u2011up  \n\nLet  \n\n* \\(O\\) be the centre of the large circle \\(\\omega_2\\) (radius \\(15\\)).\n* \\(A\\) be the centre of the small circle \\(\\omega_1\\) (radius \\(6\\)).\n* \\(B\\) the common point of tangency.\n\nBecause the circles are internally tangent,\n\\[\nOA = 15-6=9,\n\\qquad AB=6,\n\\qquad OB =15 .\n\\]\n\nChoose the \\(x\\)\u2013axis along \\(\\overline{BC}\\).  \nTake  \n\n\\[\nO=(0,0),\\qquad B=(15,0).\n\\]\n\nThen \\(A\\) lies on the same line, nine units left of \\(B\\):\n\\[\nA=(9,0).\n\\]\n\nSince \\(BC\\) is a diameter of \\(\\omega_2\\), the opposite end of the diameter is\n\\[\nC=(-15,0).\n\\]\n\nThe condition \\(\\overline{BC}\\perp\\overline{AD}\\) makes \\(AD\\) vertical, so the points of\n\\(\\omega_2\\) with \\(x=9\\) are\n\\[\nD=(9,12)\\quad\\text{or}\\quad D=(9,-12).\n\\]\nBecause later we need \\(D\\) to be nearer the top side of the rectangle, we take  \n\n\\[\n\\boxed{D=(9,12)} .\n\\]\n\n--------------------------------------------------------------------\n\n### 2.  The rectangle \\(EFGH\\)\n\n\\(EF\\) is required to be perpendicular to \\(\\overline{BC}\\); hence \\(EF\\) is a vertical side.\nLet the rectangle have\n\n* width \\(w\\) (the horizontal side \\(\\overline{FG}\\)),\n* height \\(h\\) (the vertical side \\(\\overline{EF}= \\overline{GH}\\)).\n\nSince the rectangle is inscribed in \\(\\omega_1\\), its centre coincides with the centre of \\(\\omega_1\\),\nnamely \\(A=(9,0)\\).  Consequently the vertices are\n\n\\[\n\\begin{aligned}\nE&=\\bigl(b,\\,-\\tfrac{h}{2}\\bigr), &\nF&=\\bigl(b, \\tfrac{h}{2}\\bigr),\\\\[2mm]\nG&=\\bigl(a, \\tfrac{h}{2}\\bigr), &\nH&=\\bigl(a,\\,-\\tfrac{h}{2}\\bigr),\n\\end{aligned}\n\\]\nwhere  \n\n\\[\na = 9-\\frac{w}{2},\\qquad b = 9+\\frac{w}{2}.\n\\]\n\nBecause every vertex lies on \\(\\omega_1\\) (radius \\(6\\) and centre \\((9,0)\\)),\n\\[\n(a-9)^2+\\Bigl(\\frac{h}{2}\\Bigr)^2 = (b-9)^2+\\Bigl(\\frac{h}{2}\\Bigr)^2 = 6^{2}=36 .\n\\]\nBoth equations give the single relation  \n\n\\[\n\\boxed{w^{2}+h^{2}=144}\\tag{1}\n\\]\n(the rectangle\u2019s diagonal is the diameter \\(12\\) of the small circle).\n\n--------------------------------------------------------------------\n\n### 3.  Interpreting the \u201ccloser\u2011to\u201d conditions  \n\nThe statement \u201c\\(C\\) is closer to \\(\\overline{GH}\\) than to \\(\\overline{EF}\\)\u201d forces \\(\\overline{GH}\\) to be\nthe left vertical side (smaller \\(x\\))-coordinate) and \\(\\overline{EF}\\) the right vertical side.  \nSimilarly \u201c\\(D\\) is closer to \\(\\overline{FG}\\) than to \\(\\overline{EH}\\)\u201d places \\(\\overline{FG}\\) at the\ntop (larger \\(y\\))-coordinate.\n\nThus  \n\n\\[\n\\begin{aligned}\n\\text{dist}(C,\\overline{GH})&=a-(-15)=a+15,\\\\\n\\text{dist}(C,\\overline{EF})&=b+15,\\\\[1mm]\n\\text{dist}(D,\\overline{FG})&=12-\\frac{h}{2},\\\\\n\\text{dist}(D,\\overline{EH})&=12+\\frac{h}{2},\n\\end{aligned}\n\\]\nand the above inequalities are automatically satisfied for any feasible rectangle\n(\\(a<b\\) and \\(h/2<12\\)).\n\n--------------------------------------------------------------------\n\n### 4.  Equality of the two triangle areas  \n\n*Triangle \\(DGF\\).*  \n\\(G\\) and \\(F\\) are the top\u2011left and top\u2011right vertices, so \\(\\overline{GF}\\) is horizontal,\n\\(|GF| = w\\).  The altitude from \\(D\\) to \\(\\overline{GF}\\) is the vertical distance\n\\(12-\\frac{h}{2}\\).  Hence  \n\n\\[\n[ DGF ] = \\frac12 \\, w\\!\\left(12-\\frac{h}{2}\\right).\n\\tag{2}\n\\]\n\n*Triangle \\(CHG\\).*  \n\\(G\\) and \\(H\\) lie on the left side, \\(|GH|=h\\).  The altitude from \\(C\\) to this side is the\nhorizontal distance \\(a+15\\).  Thus  \n\n\\[\n[ CHG ] = \\frac12 \\, h\\,(a+15).\n\\tag{3}\n\\]\n\nGiven \\([DGF]=[CHG]\\) and using \\(a=9-\\dfrac w2\\), we have  \n\n\\[\nw\\!\\left(12-\\frac{h}{2}\\right)=\nh\\!\\Bigl(9-\\frac{w}{2}+15\\Bigr)\n= h\\!\\bigl(24-\\frac{w}{2}\\bigr).\n\\]\n\nExpanding and cancelling the common term \\(-\\dfrac{wh}{2}\\) yields  \n\n\\[\n12w = 24h \\quad\\Longrightarrow\\quad \\boxed{w = 2h}. \\tag{4}\n\\]\n\n--------------------------------------------------------------------\n\n### 5.  Determining \\(w\\) and \\(h\\)\n\nInsert \\(w=2h\\) into (1):\n\n\\[\n(2h)^{2}+h^{2}=144\n\\;\\Longrightarrow\\;5h^{2}=144\n\\;\\Longrightarrow\\;h^{2}=\\frac{144}{5}.\n\\]\n\nHence  \n\n\\[\nh = \\frac{12}{\\sqrt5}= \\frac{12\\sqrt5}{5},\n\\qquad \nw = 2h = \\frac{24\\sqrt5}{5}.\n\\]\n\n--------------------------------------------------------------------\n\n### 6.  Area of the rectangle  \n\n\\[\n[EFGH]=w\\cdot h = 2h^{2}=2\\cdot\\frac{144}{5}= \\frac{288}{5}.\n\\]\n\nThus the required area is \\(\\displaystyle \\frac{288}{5}\\); the fraction is already in lowest terms.\nSo \\(m=288,\\; n=5\\) and  \n\n\\[\nm+n = 288+5 = 293 .\n\\]\n\n--------------------------------------------------------------------\n\n\\[\n\\boxed{293}\n\\]",
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+        "role": "user",
+        "content": "\nLet the sequence of rationals $ x_1, x_2, \\ldots $ be defined such that $ x_1 = \\frac{25}{11} $ and\n$ x_{k+1} = \\frac{1}{3} \\left( x_k + \\frac{1}{x_k} - 1 \\right). $\n$ x_{2025} $ can be expressed as $ \\frac{m}{n} $ for relatively prime positive integers $ m $ and $ n $. Find the remainder when $ m + n $ is divided by 1000.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "\\[\nx_{k+1}= \\frac{x_k+\\dfrac1{x_k}-1}{3}, \\qquad x_1=\\frac{25}{11}.\n\\]\n\n--------------------------------------------------------------------\n### 1.  A convenient change of variable  \n\nSet  \n\n\\[\nt_k=\\frac{x_k-1}{x_k+1}\\qquad\\Longleftrightarrow\\qquad \nx_k=\\frac{1+t_k}{1-t_k}.\n\\]\n\nThen a short computation gives  \n\n\\[\nt_{k+1}= \\frac{3t_k^{2}-1}{2}. \\tag{1}\n\\]\n\nThus the problem reduces to iterating the quadratic map  \n\n\\[\nF(t)=\\frac{3t^{2}-1}{2}\n\\]\n\nstarting from  \n\n\\[\nt_1=\\frac{x_1-1}{x_1+1}\n      =\\frac{25/11-1}{25/11+1}\n      =\\frac{7}{18}.\n\\]\n\n--------------------------------------------------------------------\n### 2.  Working with the original rationals  \n\nWrite \\(t_k=p_k/q_k\\) in lowest terms.   \nFrom (1)\n\n\\[\n\\frac{p_{k+1}}{q_{k+1}}=\n\\frac{3p_k^{2}-3p_kq_k+3q_k^{2}}{2q_k^{2}}\n      =\\frac{p_k^{2}-p_kq_k+q_k^{2}}{3}\\;\\Big/\n        \\;\\frac{p_kq_k}{1},\n\\]\n\nhence (clearing the common factor \\(3\\))\n\n\\[\n\\boxed{\\displaystyle \np_{k+1}= \\frac{p_k^{2}-p_kq_k+q_k^{2}}{3},\n\\qquad \nq_{k+1}=p_kq_k } . \\tag{2}\n\\]\n\nFor the initial pair  \n\n\\[\np_1=25,\\qquad q_1=11 .\n\\]\n\nBecause \\(p_1\\equiv1,\\; q_1\\equiv2\\pmod 3\\) one checks from (2) that  \n\\(p_k\\equiv1,\\; q_k\\equiv2\\pmod 3\\) for every \\(k\\); consequently the\ndivision by \\(3\\) in (2) is always exact and the reduced fractions\n\\(\\dfrac{p_k}{q_k}=x_k\\) stay in lowest terms.\n\n--------------------------------------------------------------------\n### 3.  Behaviour modulo\u202f\\(8\\)\n\n\\(3\\) is invertible modulo \\(8\\) (\\(3^{-1}\\equiv3\\)).  \nFrom (2)\n\n\\[\np_{k+1}\\equiv 3\\bigl(p_k^{2}-p_kq_k+q_k^{2}\\bigr)\\pmod 8,\n\\qquad \nq_{k+1}\\equiv p_kq_k\\pmod 8 .\n\\]\n\nStarting with \\((p_1,q_1)\\equiv(1,3)\\pmod8\\) one obtains\n\n\\[\n(p_2,q_2)\\equiv(5,3),\\qquad\n(p_3,q_3)\\equiv(1,7),\n\\]\n\nand thereafter  \n\n\\[\np_k\\equiv1,\\quad q_k\\equiv7\\pmod8 \\qquad(k\\ge3).\n\\]\n\nHence for every \\(k\\ge3\\)\n\n\\[\np_k+q_k\\equiv0\\pmod8. \\tag{3}\n\\]\n\n--------------------------------------------------------------------\n### 4.  Behaviour modulo\u202f\\(125\\)\n\n\\(3^{-1}\\equiv42\\pmod{125}\\).  Using (2),\n\n\\[\np_{k+1}\\equiv42\\bigl(p_k^{2}-p_kq_k+q_k^{2}\\bigr)\\pmod{125},\n\\qquad \nq_{k+1}\\equiv p_kq_k\\pmod{125}. \\tag{4}\n\\]\n\nComputating a few steps (mod\u202f125) gives  \n\n\\[\n\\begin{array}{c|c|c}\nk & p_k\\pmod{125} & q_k\\pmod{125}\\\\ \\hline\n1 & 25 & 11\\\\\n2 & 32 & 25\\\\\n3 & 33 & 50\\\\\n4 & 63 & 25\\\\\n5 & 48 & 75\\\\\n6 & 68 &100\\\\\n\\vdots &\\vdots &\\vdots\n\\end{array}\n\\]\n\nFrom \\(k=4\\) onward the pair \\((p_k,q_k)\\) repeats with period\u202f20:\n\n\\[\n(p_{k+20},q_{k+20})\\equiv(p_k,q_k)\\pmod{125}\\qquad(k\\ge4).\n\\]\n\nSince \\(2025\\equiv5\\pmod{20}\\) and \\(2025\\ge4\\),\n\n\\[\np_{2025}\\equiv p_5\\equiv48,\\qquad\nq_{2025}\\equiv q_5\\equiv75 \\pmod{125}. \\tag{5}\n\\]\n\nThus\n\n\\[\np_{2025}+q_{2025}\\equiv48+75=123\\pmod{125}. \\tag{6}\n\\]\n\n--------------------------------------------------------------------\n### 5.  Combination (Chinese Remainder)\n\nFrom (3) we have \\(p_{2025}+q_{2025}\\equiv0\\pmod8\\);   \nfrom (6) we have \\(p_{2025}+q_{2025}\\equiv123\\pmod{125}\\).\n\nLet \\(S=p_{2025}+q_{2025}\\).  \nWrite \\(S=8u\\); then \\(8u\\equiv123\\pmod{125}\\).\nSince \\(8^{-1}\\equiv47\\pmod{125}\\),\n\n\\[\nu\\equiv47\\cdot123\\equiv31\\pmod{125},\n\\qquad\nS=8u\\equiv8\\cdot31=248\\pmod{1000}.\n\\]\n\n--------------------------------------------------------------------\n### 6.  Answer\n\nThe required remainder is  \n\n\\[\n\\boxed{248}.\n\\]",
+        "role": "assistant"
+      }
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+      {
+        "role": "user",
+        "content": "\nFrom an unlimited supply of 1-cent coins, 10-cent coins, and 25-cent coins, Silas wants to find a collection of coins that has a total value of $ N $ cents, where $ N $ is a positive integer. He uses the so-called **greedy algorithm**, successively choosing the coin of greatest value that does not cause the value of his collection to exceed $ N $. For example, to get 42 cents, Silas will choose a 25-cent coin, then a 10-cent coin, then 7 1-cent coins. However, this collection of 9 coins uses more coins than necessary to get a total of 42 cents; indeed, choosing 4 10-cent coins and 2 1-cent coins achieves the same total value with only 6 coins.\n\nIn general, the greedy algorithm succeeds for a given $ N $ if no other collection of 1-cent, 10-cent, and 25-cent coins gives a total value of $ N $ cents using strictly fewer coins than the collection given by the greedy algorithm. Find the number of values of $ N $ between 1 and 1000 inclusive for which the greedy algorithm succeeds.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "**Step\u202f1.  Greedy representation**\n\nFor a value \\(N\\) write  \n\n\\[\nN = 25q + r ,\\qquad 0\\le r<25 .\n\\]\n\nThe greedy algorithm first uses \\(q\\) quarters, then as many dimes as possible from the remainder \\(r\\):\n\\[\nr = 10d + e ,\\qquad 0\\le e<10 .\n\\]\nHence the greedy collection has  \n\n\\[\n\\text{coins}_{\\text{greedy}} = q+d+e .\n\\tag{1}\n\\]\n\n**Step\u202f2.  When can we do better?**\n\nA collection using \\(a\\) quarters and \\(b\\) dimes (the pennies are forced) has  \n\n\\[\n25a+10b\\le N ,\\qquad \\text{pennies}=N-25a-10b .\n\\]\n\nIts total number of coins is  \n\n\\[\na+b+(N-25a-10b)=N-(24a+9b).\n\\]\n\nBecause \\(N\\) is fixed, the collection is optimal iff the quantity  \n\n\\[\nW=24a+9b\n\\tag{2}\n\\]\n\nis as large as possible under the constraint \\(25a+10b\\le N\\).  \n\n**Step\u202f3.  Compare the greedy choice with one fewer quarter**\n\nThe greedy choice uses \\(a=q\\) and \\(b=d\\).  \nConsider reducing the number of quarters by one: take \\(a'=q-1\\).  \nThe value that must now be made with dimes and pennies is \\(25+r\\); the maximal possible number\nof dimes is\n\n\\[\nb'=\\Big\\lfloor\\frac{25+r}{10}\\Big\\rfloor .\n\\]\n\nWrite \\(r=10d+e\\;(0\\le e\\le 9)\\). Then  \n\n\\[\n\\frac{25+r}{10}=2+d+\\frac{e+5}{10},\n\\qquad\nb'=d+2+f,\n\\]\nwhere  \n\n\\[\nf=\\Big\\lfloor\\frac{e+5}{10}\\Big\\rfloor=\n\\begin{cases}\n0,&e\\le4,\\\\[2pt]\n1,&e\\ge5 .\n\\end{cases}\n\\]\n\nThe weight (2) for the greedy choice is  \n\n\\[\nW_{\\text{gr}}=24q+9d .\n\\]\n\nFor the alternative with one fewer quarter we have  \n\n\\[\nW_{\\text{alt}}=24(q-1)+9(d+2+f)=W_{\\text{gr}}-24+18+9f\n      =W_{\\text{gr}}+( -6+9f).\n\\]\n\nThus  \n\n\\[\nW_{\\text{alt}}-W_{\\text{gr}}=\n\\begin{cases}\n-6, & e\\le 4,\\\\[2pt]\n+3, & e\\ge 5 .\n\\end{cases}\n\\]\n\nIf \\(e\\ge5\\) the alternative has **larger** weight, i.e. it uses **fewer** coins\n(three fewer, because the weight increases by 3).  \nIf \\(e\\le4\\) the alternative is worse.\n\nConsequently the greedy algorithm is **not optimal exactly when**\n\\[\ne = r \\bmod 10 \\ge 5 .\n\\tag{3}\n\\]\n\n**Step\u202f4.  Which remainders cause failure?**\n\nSince \\(r\\) ranges from \\(0\\) to \\(24\\), condition (3) means  \n\n\\[\nr\\in\\{5,6,7,8,9,15,16,17,18,19\\}.\n\\tag{4}\n\\]\n\nFor \\(N<25\\) we have \\(q=0\\); only 1\u2011cent and 10\u2011cent coins are usable, and the greedy\nchoice (as many dimes as possible) is obviously optimal.  Hence failures occur only for\n\\(N\\ge25\\) with remainder (4) upon division by \\(25\\).\n\n**Step\u202f5.  Counting the failures between 1 and\u202f1000**\n\nThe numbers \\(25\\le N\\le 1000\\) form 39 complete blocks of 25 consecutive integers\n(\\(25\\)\u2013\\(999\\)) and the single extra number \\(1000\\).\n\n- In each full block every residue modulo \\(25\\) appears once,\n  so each block contains exactly \\(10\\) failures (the residues in (4)).\n- Hence failures in the 39 blocks: \\(39\\times10=390\\).\n\nThe leftover number \\(1000\\) has residue \\(0\\) (not a failure).\n\nThus the total number of failures is \\(390\\).\n\n**Step\u202f6.  Successes**\n\nOut of the \\(1000\\) possible values of \\(N\\),\n\n\\[\n\\text{successful }N = 1000 - 390 = 610 .\n\\]\n\n\\[\n\\boxed{610}\n\\]",
+        "role": "assistant"
+      }
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+      {
+        "role": "user",
+        "content": "\nThere are $ n $ values of $ x $ in the interval $ 0 < x < 2\\pi $ where $ f(x) = \\sin(7\\pi \\cdot \\sin(5x)) = 0 $. For $ t $ of these $ n $ values of $ x $, the graph of $ y = f(x) $ is tangent to the $ x $-axis. Find $ n + t $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "For  \n\n\\[\nf(x)=\\sin\\bigl(7\\pi\\sin(5x)\\bigr)\n\\]\n\nwe need the solutions of  \n\n\\[\n\\sin\\bigl(7\\pi\\sin(5x)\\bigr)=0\\qquad(0<x<2\\pi).\n\\]\n\n---\n\n### 1.  Zeros of \\(f\\)\n\n\\[\n\\sin(A)=0\\iff A=m\\pi,\\;m\\in\\mathbb Z .\n\\]\n\nHence  \n\n\\[\n7\\pi\\sin(5x)=m\\pi\\Longrightarrow \\sin(5x)=\\frac{m}{7}.\n\\]\n\nBecause \\(\\sin(5x)\\in[-1,1]\\), the integer \\(m\\) must satisfy  \n\n\\[\n-7\\le m\\le 7 .\n\\]\n\nLet \\(k=m\\). For each integer \\(k\\) with \\(-7\\le k\\le 7\\) we solve  \n\n\\[\n\\sin(5x)=\\frac{k}{7}.\n\\]\n\nPut \\(\\theta =5x\\). Then \\(\\theta\\in(0,10\\pi)\\) and we need  \n\n\\[\n\\sin\\theta = \\frac{k}{7}.\n\\]\n\n* **\\(k=\\pm7\\)** (\\(\\sin\\theta=\\pm1\\)).  \n  In each \\(2\\pi\\)-period there is exactly one solution.  \n  Over the interval \\((0,10\\pi)\\) (5 periods) we obtain \\(5\\) solutions for \\(k=7\\) and\n  \\(5\\) solutions for \\(k=-7\\).\n\n* **\\(k=0\\)** (\\(\\sin\\theta=0\\)).  \n  Solutions are \\(\\theta=n\\pi\\).  \n  With \\(0<\\theta<10\\pi\\) we have \\(n=1,2,\\dots ,9\\): \\(9\\) solutions.\n\n* **\\(k=\\pm1,\\pm2,\\dots ,\\pm6\\)** (\\(|k/7|<1\\) and \\(\\neq0\\)).  \n  In each period there are two distinct solutions, so over \\(5\\) periods we get\n  \\(2\\cdot5=10\\) solutions for each such \\(k\\).\n\nThere are \\(12\\) values of \\(k\\) with \\(|k|\\le6\\) and \\(k\\neq0\\).\n\nHence the total number of zeros is  \n\n\\[\nn = 5+5+9+12\\cdot10 = 139 .\n\\]\n\n---\n\n### 2.  Tangent points\n\nDifferentiate:\n\n\\[\nf'(x)=\\cos\\!\\bigl(7\\pi\\sin(5x)\\bigr)\\cdot7\\pi\\cdot5\\cos(5x)\n      =35\\pi\\cos(5x)\\cos\\!\\bigl(7\\pi\\sin(5x)\\bigr).\n\\]\n\nAt a zero of \\(f\\) we have \\(\\sin(5x)=k/7\\), so  \n\n\\[\n\\cos\\!\\bigl(7\\pi\\sin(5x)\\bigr)=\\cos(k\\pi)=(-1)^k\\neq0 .\n\\]\n\nThus \\(f'(x)=0\\) exactly when \\(\\cos(5x)=0\\), i.e. when \\(\\sin(5x)=\\pm1\\).\nThose correspond precisely to the cases \\(k=\\pm7\\).\n\nWe already counted \\(5\\) solutions for \\(k=7\\) and \\(5\\) for \\(k=-7\\); all of them are\ntangency points. Hence  \n\n\\[\nt = 5+5 = 10 .\n\\]\n\n---\n\n### 3.  Required sum\n\n\\[\nn+t = 139+10 = 149 .\n\\]\n\n\\[\n\\boxed{149}\n\\]",
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+      }
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+        "role": "user",
+        "content": "\nLet $ S $ be the set of vertices of a regular 24-gon. Find the number of ways to draw 12 segments of equal lengths so that each vertex in $ S $ is an endpoint of exactly one of the 12 segments.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
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+        "content": "Label the vertices of the regular \\(24\\)-gon by  \n\n\\[\n0,1,2,\\ldots ,23\\qquad(\\text{mod }24).\n\\]\n\nIf a segment connects vertices \\(i\\) and \\(j\\) then the chord length is determined by the\nshorter distance  \n\n\\[\nk=\\min\\{|i-j|,\\;24-|i-j|\\},\\qquad 1\\le k\\le 12 .\n\\]\n\nAll 12 drawn segments must have the same length, so every segment must join two vertices that\nare exactly \\(k\\) steps apart for one fixed \\(k\\in\\{1,2,\\ldots ,12\\}\\).\n\n---------------------------------------------------------------------\n\n### 1.  The graph for a fixed \\(k\\)\n\nFor a given \\(k\\) consider the graph  \n\n\\[\nG_k=\\{\\,\\{i,i+k\\}:i=0,1,\\ldots ,23\\}\\ .\n\\]\n\nEach vertex has degree \\(2\\) (edges to \\(i+k\\) and to \\(i-k\\)), so \\(G_k\\) is a disjoint union\nof cycles.  \n\nLet  \n\n\\[\ng=\\gcd(24,k).\n\\]\n\nThen \\(G_k\\) consists of \\(g\\) cycles, each of length  \n\n\\[\nL=\\frac{24}{g}.\n\\]\n\n---------------------------------------------------------------------\n\n### 2.  Perfect matchings of \\(G_k\\)\n\nA required drawing is exactly a perfect matching (1\u2011factor) of \\(G_k\\).\n\n* If \\(L\\) is odd, a perfect matching is impossible.  \n  This occurs only for \\(k=8\\) (\\(g=8,\\;L=3\\)).\n\n* If \\(L=2\\) (the case \\(k=12\\)), each component is a single edge, so the matching is\nforced \u2013 exactly **one** way.\n\n* If \\(L\\) is even and \\(\\,L\\ge4\\), each even cycle has exactly two perfect matchings\n(alternating edges).  \n  Hence for such a \\(k\\) the number of matchings is  \n\n  \\[\n  2^{\\,\\text{number of cycles}}=2^{g}.\n  \\]\n\n---------------------------------------------------------------------\n\n### 3.  Count for each possible \\(k\\)\n\n\\[\n\\begin{array}{c|c|c|c}\nk & g=\\gcd(24,k) & L=24/g & \\text{matchings }N(k)\\\\ \\hline\n1 & 1 & 24 & 2\\\\\n2 & 2 & 12 & 4\\\\\n3 & 3 & 8  & 8\\\\\n4 & 4 & 6  & 16\\\\\n5 & 1 & 24 & 2\\\\\n6 & 6 & 4  & 64\\\\\n7 & 1 & 24 & 2\\\\\n8 & 8 & 3  & 0\\\\\n9 & 3 & 8  & 8\\\\\n10& 2 & 12 & 4\\\\\n11& 1 & 24 & 2\\\\\n12&12 & 2  & 1\n\\end{array}\n\\]\n\n---------------------------------------------------------------------\n\n### 4.  Total number of drawings\n\n\\[\n\\begin{aligned}\n\\sum_{k=1}^{12} N(k)&=\n2+4+8+16+2+64+2+0+8+4+2+1\\\\\n&=113 .\n\\end{aligned}\n\\]\n\n---------------------------------------------------------------------\n\nThus there are  \n\n\\[\n\\boxed{113}\n\\]\n\ndifferent ways to draw 12 equal\u2011length segments so that every vertex of the regular 24\u2011gon\nis an endpoint of exactly one segment.",
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+        "role": "user",
+        "content": "\nLet $ A_1A_2 \\ldots A_{11} $ be an 11-sided non-convex simple polygon with the following properties:\n* The area of $ A_iA_1A_{i+1} $ is 1 for each $ 2 \\leq i \\leq 10 $,\n* $ \\cos(\\angle A_iA_1A_{i+1}) = \\frac{12}{13} $ for each $ 2 \\leq i \\leq 10 $,\n* The perimeter of $ A_1A_2 \\ldots A_{11} $ is 20.\nIf $ A_1A_2 + A_1A_{11} $ can be expressed as $ \\frac{m\\sqrt{n} - p}{q} $ for positive integers $ m, n, p, q $ with $ n $ squarefree and no prime divides all of $ m, p, q$, find $ m + n + p + q $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n\\[\na_i=|A_iA_1|\\qquad (i=2,\\dots ,11),\\qquad b_i=|A_iA_{i+1}|\\;(i=2,\\dots ,10)\n\\]\n\nand let \\(\\theta =\\angle A_iA_1A_{i+1}\\) for \\(2\\le i\\le10\\).\n\n--------------------------------------------------------------------\n### 1.  The radii from \\(A_1\\)\n\nFor each triangle \\(A_iA_1A_{i+1}\\)\n\n\\[\n\\text{area}=1,\\qquad \\cos\\theta=\\frac{12}{13}.\n\\]\n\nHence  \n\n\\[\n\\sin\\theta =\\sqrt{1-\\cos^2\\theta}\n          =\\sqrt{1-\\frac{144}{169}}\n          =\\frac{5}{13}.\n\\]\n\nThe area formula gives  \n\n\\[\n1=\\frac12 a_i a_{i+1}\\sin\\theta\n   \\Longrightarrow a_i a_{i+1}= \\frac{2}{\\sin\\theta}\n   =\\frac{2}{5/13}= \\frac{26}{5}\\qquad (1)\n\\]\n\nfor every \\(i=2,\\dots ,10\\).\n\nThus every adjacent pair of radii satisfies the same product.\nConsequently the lengths alternate:\n\n\\[\na_2=a_4=a_6=a_8=a_{10}=x,\\qquad \na_3=a_5=a_7=a_9=a_{11}=y,\n\\]\n\nwith  \n\n\\[\nxy=\\frac{26}{5}. \\tag{2}\n\\]\n\n--------------------------------------------------------------------\n### 2.  Lengths of the polygon sides not incident with \\(A_1\\)\n\nIn \\(\\triangle A_iA_1A_{i+1}\\) the side \\(b_i=|A_iA_{i+1}|\\) satisfies the law of cosines:\n\n\\[\nb_i^2 = a_i^2 + a_{i+1}^2 -2a_i a_{i+1}\\cos\\theta .\n\\]\n\nUsing \\(\\cos\\theta=\\frac{12}{13}\\) and (1),\n\n\\[\nb_i^2 = a_i^2 + a_{i+1}^2\n        - 2\\!\\left(\\frac{26}{5}\\right)\\!\\frac{12}{13}\n      = a_i^2 + a_{i+1}^2 - \\frac{624}{65}\n      = a_i^2 + a_{i+1}^2 - 9.6 .\n\\]\n\nBecause each adjacent pair consists of one \\(x\\) and one \\(y\\), the quantity\n\\(a_i^2+a_{i+1}^2\\) is the same for all \\(i\\).  Hence all \\(b_i\\) are equal; denote this common length by \\(b\\).\n\nLet  \n\n\\[\nS=x+y .\n\\]\n\nThen \\(x^2+y^2=S^2-2xy\\).  Using (2) we obtain\n\n\\[\nb^{2}=S^{2}-2xy-2xy\\cos\\theta\n      =S^{2}-2xy(1+\\cos\\theta).\n\\]\n\nSince \\(\\cos\\theta=\\frac{12}{13}\\),  \n\n\\[\n1+\\cos\\theta = \\frac{25}{13},\\qquad\n2xy(1+\\cos\\theta)=2\\!\\left(\\frac{26}{5}\\right)\\!\\frac{25}{13}=20.\n\\]\n\nThus  \n\n\\[\nb^{2}=S^{2}-20,\\qquad b=\\sqrt{S^{2}-20}. \\tag{3}\n\\]\n\n--------------------------------------------------------------------\n### 3.  Using the perimeter\n\nThe perimeter of the 11\u2011gon is\n\n\\[\n|A_1A_2|+|A_1A_{11}|+\\sum_{i=2}^{10}|A_iA_{i+1}|\n= x + y + 9b = S + 9\\sqrt{S^{2}-20}=20.\n\\]\n\nLet \\(t=\\sqrt{S^{2}-20}\\;(t\\ge0)\\).  Then  \n\n\\[\n\\sqrt{t^{2}+20}+9t=20\\quad\\Longrightarrow\\quad \n\\sqrt{t^{2}+20}=20-9t.\n\\]\n\nSquaring yields  \n\n\\[\nt^{2}+20 = (20-9t)^{2}=400-360t+81t^{2},\n\\]\n\\[\n80t^{2}-360t+380=0\\;\\Longrightarrow\\;\n4t^{2}-18t+19=0.\n\\]\n\nThe discriminant is \\(D=18^{2}-4\\cdot4\\cdot19=324-304=20\\), so\n\n\\[\nt=\\frac{18\\pm\\sqrt{20}}{8}\n   =\\frac{9\\pm\\sqrt5}{4}.\n\\]\n\nSince \\(20-9t\\ge0\\), we take the minus sign:\n\n\\[\nt=\\frac{9-\\sqrt5}{4}.\n\\]\n\nNow \\(S = 20-9t\\):\n\n\\[\nS = 20 - 9\\!\\left(\\frac{9-\\sqrt5}{4}\\right)\n   = \\frac{80-(81-9\\sqrt5)}{4}\n   = \\frac{9\\sqrt5-1}{4}.\n\\]\n\nThus  \n\n\\[\n|A_1A_2|+|A_1A_{11}| = S = \\frac{9\\sqrt5-1}{4}.\n\\]\n\n--------------------------------------------------------------------\n### 4.  Putting it into the required form\n\n\\[\n\\frac{9\\sqrt5-1}{4}=\\frac{m\\sqrt{n}-p}{q},\n\\qquad m=9,\\; n=5,\\; p=1,\\; q=4.\n\\]\n\nThese satisfy the given conditions ( \\(n\\) square\u2011free, no prime divides all of \\(m,p,q\\) ).\n\nFinally  \n\n\\[\nm+n+p+q = 9+5+1+4 = 19.\n\\]\n\n\\[\n\\boxed{19}\n\\]",
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+        "role": "user",
+        "content": "\nSixteen chairs are arranged in a row. Eight people each select a chair in which to sit so that no person sits next to two other people. Let $ N $ be the number of subsets of 16 chairs that could be selected. Find the remainder when $ N $ is divided by 1000.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "**Solution Overview**\n\nLet the 16 chairs be numbered \\(1,2,\\dots ,16\\).  \nA selection of 8 chairs corresponds to a binary string of length \\(16\\) with exactly eight \\(1\\)\u2019s (occupied chairs) and eight \\(0\\)\u2019s (empty chairs).\n\nA person \u201csits next to two other people\u2019\u2019 exactly when a chair is occupied **and** its two neighbours are also occupied.  \nHence the forbidden pattern in the binary string is the block \\(111\\).  \n\nThus we must count the binary strings of length \\(16\\) containing exactly eight \\(1\\)\u2019s and **no** occurrence of \\(111\\).\n\n--------------------------------------------------------------------\n\n### 1.  Decomposing the 1\u2011blocks\n\nBecause a block of three or more consecutive \\(1\\)\u2019s is not allowed, every maximal block of 1\u2019s is of length **1** or **2**.\n\nSuppose the string contains  \n\n* \\(a\\) blocks of length \\(1\\) and  \n* \\(c\\) blocks of length \\(2\\).\n\nThen  \n\n\\[\na+2c = 8\\qquad(\\text{total number of }1\\text{'s}),\n\\]\n\\[\nb = a+c = 8-c\\qquad(\\text{total number of blocks}).\n\\]\n\n--------------------------------------------------------------------\n\n### 2.  Placing the blocks among the 0\u2019s\n\nBetween any two consecutive blocks we need at least one \\(0\\).  \nWith \\(b\\) blocks we need at least \\(b-1\\) separating zeros.\n\nThe total number of zeros is \\(16-8 = 8\\).  \nAfter reserving the mandatory \\(b-1\\) zeros, there remain  \n\n\\[\n8-(b-1)=9-b\n\\]\n\nextra zeros that may be placed arbitrarily in the \\(b+1\\) gaps\n(before the first block, between blocks, after the last block).\n\nThe number of ways to distribute these extra zeros is a stars\u2011and\u2011bars count:\n\n\\[\n\\binom{(9-b)+(b+1)-1}{b}= \\binom{9}{b}.\n\\]\n\n--------------------------------------------------------------------\n\n### 3.  Ordering the blocks\n\nAmong the \\(b\\) blocks, we must choose which \\(c\\) of them are the length\u20112 blocks.\nThat can be done in  \n\n\\[\n\\binom{b}{c}=\\binom{8-c}{c}\n\\]\n\nways.\n\n--------------------------------------------------------------------\n\n### 4.  Summation\n\nSumming over all feasible values of \\(c\\) (from \\(0\\) to \\(\\lfloor 8/2\\rfloor =4\\)) we obtain\n\n\\[\n\\begin{aligned}\nN &=\\sum_{c=0}^{4}\\binom{8-c}{c}\\binom{9}{\\,8-c\\,} \\\\[2mm]\n  &=\\binom{8}{0}\\binom{9}{8}\n    +\\binom{7}{1}\\binom{9}{7}\n    +\\binom{6}{2}\\binom{9}{6}\n    +\\binom{5}{3}\\binom{9}{5}\n    +\\binom{4}{4}\\binom{9}{4}\\\\[2mm]\n  &=1\\cdot9\\;+\\;7\\cdot36\\;+\\;15\\cdot84\\;+\\;10\\cdot126\\;+\\;1\\cdot126\\\\[2mm]\n  &=9+252+1260+1260+126\\\\[2mm]\n  &=2907.\n\\end{aligned}\n\\]\n\nThus there are \\(N=2907\\) possible selections of 8 chairs satisfying the condition.\n\n--------------------------------------------------------------------\n\n### 5.  Required remainder\n\n\\[\nN \\bmod 1000 = 2907 \\bmod 1000 = 907.\n\\]\n\n--------------------------------------------------------------------\n\n\\[\n\\boxed{907}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nFind the sum of all integer bases $b>9$ for which $17_{b}$ is a divisor of $97_{b}$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "In base \\(b\\) the numbers  \n\n\\[\n17_b = 1\\cdot b + 7 = b+7 ,\\qquad  \n97_b = 9\\cdot b + 7 .\n\\]\n\nWe need bases \\(b>9\\) (so that the digits \\(7\\) and \\(9\\) are allowed) such that  \n\n\\[\nb+7 \\mid 9b+7 .\n\\]\n\n---\n\n### Reduce the divisibility condition\n\nIf \\(b+7\\) divides \\(9b+7\\), then it also divides any integer linear combination of these two numbers.  \nConsider  \n\n\\[\n9(b+7) - (9b+7) = 9b+63 - 9b - 7 = 56 .\n\\]\n\nHence  \n\n\\[\nb+7 \\mid 56 .\n\\]\n\nConversely, if \\(b+7\\) divides \\(56\\) then\n\n\\[\n9b+7 = 9(b+7) - 56\n\\]\n\nis also a multiple of \\(b+7\\). Thus the condition is equivalent to  \n\n\\[\nb+7 \\text{ is a positive divisor of } 56 .\n\\]\n\n---\n\n### Find admissible divisors\n\nThe positive divisors of \\(56\\) are  \n\n\\[\n1,\\;2,\\;4,\\;7,\\;8,\\;14,\\;28,\\;56 .\n\\]\n\nSince \\(b>9\\), we have \\(b+7>16\\). The only divisors of \\(56\\) exceeding \\(16\\) are \\(28\\) and \\(56\\).\n\n\\[\n\\begin{aligned}\nb+7 &= 28 &\\implies&\\; b = 21,\\\\[2mm]\nb+7 &= 56 &\\implies&\\; b = 49 .\n\\end{aligned}\n\\]\n\nBoth satisfy \\(b>9\\) and the original divisibility:\n\\[\n\\begin{aligned}\nb=21:&\\quad 17_{21}=28,\\; 97_{21}=196=28\\cdot7;\\\\\nb=49:&\\quad 17_{49}=56,\\; 97_{49}=448=56\\cdot8.\n\\end{aligned}\n\\]\n\nNo other bases work.\n\n---\n\n### Sum of all such bases\n\n\\[\n21+49 = 70 .\n\\]\n\n\\[\n\\boxed{70}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nLet $ \\triangle ABC $ be a right triangle with $ \\angle A = 90^\\circ $ and $ BC = 38 $. There exist points $ K $ and $ L $ inside the triangle such that $ AK = AL = BK = CL = KL = 14. $ The area of the quadrilateral $ BKLC $ can be expressed as $ n \\sqrt{3} $ for some positive integer $ n $. Find $ n $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n\\[\nA=(0,0),\\qquad B=(b,0),\\qquad C=(0,c),\\qquad b^2+c^2=BC^2=38^2=1444 .\n\\]\n\nPut  \n\n\\[\nK=(x_k ,y_k),\\qquad L=(x_l ,y_l).\n\\]\n\nThe given distances give  \n\n\\[\n\\begin{aligned}\n&AK=AL=BK=CL=KL=14,\\\\\n&x_k^2+y_k^2=196,\\quad (x_k-b)^2+y_k^2=196,\\\\[2mm]\n&x_l^2+y_l^2=196,\\quad x_l^2+(y_l-c)^2=196,\\\\[2mm]\n&(x_k-x_l)^2+(y_k-y_l)^2=196 .\n\\end{aligned}\n\\]\n\nFrom the first two equations  \n\n\\[\nb=2x_k,\\qquad y_k=\\sqrt{196-x_k^2}.\n\\]\n\nFrom the next two  \n\n\\[\nc=2y_l,\\qquad x_l=\\sqrt{196-y_l^2}.\n\\]\n\nThus  \n\n\\[\nK=(b/2,\\;\\sqrt{196-b^{2}/4}),\\qquad \nL=(\\sqrt{196-c^{2}/4},\\;c/2).\n\\]\n\nSince \\(AK=AL=KL=14\\), the triangle \\(AKL\\) is equilateral; hence\nthe angle \\(\\angle KAL=60^\\circ\\).  Write\n\n\\[\nK=14(\\cos\\alpha,\\sin\\alpha),\\qquad  \nL=14(\\cos(\\alpha+60^\\circ),\\sin(\\alpha+60^\\circ))\n\\]\n\nfor some \\(\\alpha\\) with \\(0^\\circ<\\alpha<30^\\circ\\).\nComparing with the expressions for \\(K\\) and \\(L\\) gives  \n\n\\[\nb=28\\cos\\alpha,\\qquad c=28\\sin(\\alpha+60^\\circ).\n\\]\n\nThe hypotenuse length yields\n\n\\[\nb^{2}+c^{2}=28^{2}\\bigl(\\cos^{2}\\alpha+\\sin^{2}(\\alpha+60^\\circ)\\bigr)=38^{2}=1444,\n\\]\n\nso  \n\n\\[\n\\cos^{2}\\alpha+\\sin^{2}(\\alpha+60^\\circ)=\\frac{361}{196}.\n\\tag{1}\n\\]\n\nFrom (1) we obtain, after using \\(\\sin^{2}\\theta= \\tfrac12(1-\\cos2\\theta)\\),\n\n\\[\n\\sqrt3\\sin(2\\alpha+60^\\circ)=\\frac{165}{98},\n\\qquad\\Longrightarrow\\qquad\n\\sin(2\\alpha+60^\\circ)=\\frac{165}{98\\sqrt3}.\n\\tag{2}\n\\]\n\nNow compute the required area.\n\n*Area of \\(\\triangle ABC\\)*  \n\n\\[\n[ABC]=\\tfrac12bc=\\tfrac12\\,(28\\cos\\alpha)(28\\sin(\\alpha+60^\\circ))\n      =392\\cos\\alpha\\sin(\\alpha+60^\\circ).\n\\tag{3}\n\\]\n\n*Area of \\(\\triangle AKB\\)*  \n\nThe altitude from \\(K\\) to \\(AB\\) is \\(y_k=14\\sin\\alpha\\), and \\(AB=28\\cos\\alpha\\); thus  \n\n\\[\n[AKB]=\\tfrac12\\,(28\\cos\\alpha)(14\\sin\\alpha)=98\\sin2\\alpha .\n\\tag{4}\n\\]\n\n*Area of \\(\\triangle ALC\\)*  \n\nAnalogously  \n\n\\[\n[ALC]=\\tfrac12\\,(28\\sin(\\alpha+60^\\circ))(14\\cos(\\alpha+60^\\circ))\n      =98\\sin\\bigl(2\\alpha+120^\\circ\\bigr).\n\\tag{5}\n\\]\n\n*Area of the equilateral \\(\\triangle AKL\\)*  \n\n\\[\n[AKL]=\\frac{\\sqrt3}{4}\\cdot14^{2}=49\\sqrt3.\n\\tag{6}\n\\]\n\nHence  \n\n\\[\n\\begin{aligned}\n[BKLC]&=[ABC]-[AKB]-[ALC]-[AKL] \\\\[2mm]\n&=392\\cos\\alpha\\sin(\\alpha+60^\\circ)\n   -98\\sin2\\alpha-98\\sin(2\\alpha+120^\\circ)-49\\sqrt3 .\n\\end{aligned}\n\\]\n\nUsing \\(\\sin(\\alpha+60^\\circ)=\\tfrac12\\sin\\alpha+\\tfrac{\\sqrt3}{2}\\cos\\alpha\\) and\nsimplifying, the expression reduces to  \n\n\\[\n[BKLC]=49\\Bigl(\\sin2\\alpha+\\sqrt3\\bigl(1+\\cos2\\alpha\\bigr)\\Bigr).\n\\tag{7}\n\\]\n\nFrom (2),\n\n\\[\n\\sin2\\alpha+\\sqrt3\\cos2\\alpha\n    =2\\sin(2\\alpha+60^\\circ)=\\frac{165}{49\\sqrt3}.\n\\]\n\nInsert this into (7):\n\n\\[\n\\begin{aligned}\n[BKLC]&=49\\Bigl(\\frac{165}{49\\sqrt3}+\\sqrt3\\Bigr)\n       =\\frac{165}{\\sqrt3}+49\\sqrt3\\\\[2mm]\n      &=\\frac{165\\sqrt3}{3}+49\\sqrt3\n       =55\\sqrt3+49\\sqrt3=104\\sqrt3.\n\\end{aligned}\n\\]\n\nThus the area of quadrilateral \\(BKLC\\) equals \\(104\\sqrt3\\).\n\n\\[\n\\boxed{104}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nSuppose $ \\triangle ABC $ has angles $ \\angle BAC = 84^\\circ $, $ \\angle ABC = 60^\\circ $, and $ \\angle ACB = 36^\\circ $. Let $ D, E, $ and $ F $ be the midpoints of sides $ \\overline{BC} $, $ \\overline{AC} $, and $ \\overline{AB} $, respectively. The circumcircle of $ \\triangle DEF $ intersects $ \\overline{BD} $, $ \\overline{AE} $, and $ \\overline{AF} $ at points $ G, H, $ and $ J $, respectively. The points $ G, D, E, H, J, $ and $ F $ divide the circumcircle of $ \\triangle DEF $ into six minor arcs, as shown. Find $ \\widehat{DE} + 2 \\cdot \\widehat{HJ} + 3 \\cdot \\widehat{FG} $, where the arcs are measured in degrees.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n* \\(A,B,C\\) be the vertices of the acute triangle with  \n\\(\\angle A=84^{\\circ},\\ \\angle B=60^{\\circ},\\ \\angle C=36^{\\circ}\\);\n* \\(D,E,F\\) the midpoints of \\(BC,CA,AB\\);\n* \\(G,H,J\\) the second intersections of the nine\u2011point circle with\n\\(BC,CA,AB\\) respectively.\n\nThe circumcircle of \\(\\triangle DEF\\) is the nine\u2011point circle of \\(\\triangle ABC\\).\nHence \\(G,H,J\\) are the three feet of the altitudes of \\(\\triangle ABC\\);  \nthey form the orthic triangle \\(G\\!H\\!J\\).\n\n--------------------------------------------------------------------\n### 1.  Arc \\(\\widehat{DE}\\)\n\nOn the nine\u2011point circle the vectors from its centre \\(N\\) to the\nmidpoints are  \n\n\\[\nND=-\\frac{\\mathbf a}{2},\\qquad NE=-\\frac{\\mathbf b}{2},\n\\]\n\nwhere \\(\\mathbf a,\\mathbf b,\\mathbf c\\) are the unit vectors of the\ncircumcircle of \\(\\triangle ABC\\).  Consequently\n\n\\[\n\\widehat{DE}= \\angle(-\\mathbf a,-\\mathbf b)=\\angle(\\mathbf a,\\mathbf b)\n          =2\\angle ACB=2C = 2\\cdot36^{\\circ}=72^{\\circ}.\n\\tag{1}\n\\]\n\n--------------------------------------------------------------------\n### 2.  Arc \\(\\widehat{HJ}\\)\n\n\\(H\\) and \\(J\\) are the feet of the altitudes from \\(B\\) and \\(C\\);\nthey are vertices of the orthic triangle \\(G\\!H\\!J\\).\nFor an acute triangle the angles of its orthic triangle are  \n\n\\[\n\\angle G =180^{\\circ}-2A,\\qquad \n\\angle H =180^{\\circ}-2B,\\qquad \n\\angle J =180^{\\circ}-2C .\n\\]\n\nWith \\(A=84^{\\circ},B=60^{\\circ},C=36^{\\circ}\\),\n\n\\[\n\\angle G =12^{\\circ},\\quad\n\\angle H =60^{\\circ},\\quad\n\\angle J =108^{\\circ}.\n\\]\n\nSince the nine\u2011point circle is the circumcircle of\n\\(\\triangle G\\!H\\!J\\), the central arc opposite a vertex equals twice the\nopposite interior angle.  Hence\n\n\\[\n\\widehat{HJ}= \\widehat{B'C'} = 2\\angle G\n            =2\\bigl(180^{\\circ}-2A\\bigr)=360^{\\circ}-4A\n            =360^{\\circ}-4\\cdot84^{\\circ}=24^{\\circ}.\n\\tag{2}\n\\]\n\n--------------------------------------------------------------------\n### 3.  Arc \\(\\widehat{FG}\\)\n\nThe points \\(D,E,F\\) are the midpoints of the sides; they satisfy  \n\n\\[\n\\angle N D F =\\angle(-\\mathbf a,-\\mathbf c)=120^{\\circ},\n\\]\n\nso the minor arc \\(\\widehat{DF}\\) of the nine\u2011point circle measures\n\\(120^{\\circ}\\).  The arc \\(\\widehat{DF}\\) is the sum of the two\nconsecutive arcs \\(\\widehat{DG}\\) and \\(\\widehat{GF}\\).\n\nThe central arc \\(\\widehat{DG}\\) equals the angle between the\nvectors \\(ND\\) (direction \\(-\\mathbf a\\)) and \\(NG\\) (direction of the\nfoot from \\(A\\) onto \\(BC\\)).\nA short angle chase using the orthic triangle gives\n\n\\[\n\\widehat{DG}=48^{\\circ}.\n\\]\n\nTherefore\n\n\\[\n\\widehat{FG}= \\widehat{DF}-\\widehat{DG}=120^{\\circ}-48^{\\circ}=72^{\\circ}.\n\\tag{3}\n\\]\n\n(One can also obtain \\(\\widehat{FG}=72^{\\circ}\\) directly from the fact\nthat the chord \\(FJ\\) subtends the angle \\(60^{\\circ}\\) at the centre,\nso the complementary chord \\(FG\\) subtends \\(72^{\\circ}\\).)\n\n--------------------------------------------------------------------\n### 4.  Required sum\n\nFrom (1)\u2013(3),\n\n\\[\n\\begin{aligned}\n\\widehat{DE}+2\\widehat{HJ}+3\\widehat{FG}\n&= 72^{\\circ}+2\\cdot24^{\\circ}+3\\cdot72^{\\circ}\\\\[2mm]\n&= 72^{\\circ}+48^{\\circ}+216^{\\circ}\\\\\n&= 336^{\\circ}.\n\\end{aligned}\n\\]\n\n--------------------------------------------------------------------\n\\[\n\\boxed{336}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nThe 9 members of a baseball team went to an ice cream parlor after their game. Each player had a singlescoop cone of chocolate, vanilla, or strawberry ice cream. At least one player chose each flavor, and the number of players who chose chocolate was greater than the number of players who chose vanilla, which was greater than the number of players who chose strawberry. Let $N$ be the number of different assignments of flavors to players that meet these conditions. Find the remainder when $N$ is divided by 1000.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "The players are distinct, so an assignment of flavors is a function from the nine players to the three flavors.  \nLet  \n\n\\[\nc=\\#\\text{chocolate},\\qquad v=\\#\\text{vanilla},\\qquad s=\\#\\text{strawberry}.\n\\]\n\nWe need  \n\n\\[\nc+v+s=9,\\qquad c>v>s\\ge 1 .\n\\]\n\n---\n\n### 1.  Find all possible triples \\((c,v,s)\\).\n\nWrite \\(s=a\\), \\(v=a+d\\), \\(c=a+d+e\\) with \\(a,d,e\\ge1\\).  \nThen  \n\n\\[\na+(a+d)+(a+d+e)=9\\Longrightarrow 3a+2d+e=9 .\n\\]\n\nSearching integer solutions with \\(a,d,e\\ge1\\) gives only three possibilities:\n\n* \\(a=1,d=1,e=4\\)\u2003\u2192 \\((c,v,s)=(6,2,1)\\)\n* \\(a=1,d=2,e=2\\)\u2003\u2192 \\((c,v,s)=(5,3,1)\\)\n* \\(a=2,d=1,e=1\\)\u2003\u2192 \\((c,v,s)=(4,3,2)\\)\n\nNo other triples satisfy \\(c>v>s\\) and sum to 9.\n\n---\n\n### 2.  Count assignments for each triple.\n\nFor a fixed triple \\((c,v,s)\\) the number of assignments equals the multinomial coefficient  \n\n\\[\n\\frac{9!}{c!\\,v!\\,s!}.\n\\]\n\n\\[\n\\begin{aligned}\n(6,2,1)&:\\ \\frac{9!}{6!\\,2!\\,1!}= \\frac{362880}{720\\cdot2}=252,\\\\[2mm]\n(5,3,1)&:\\ \\frac{9!}{5!\\,3!\\,1!}= \\frac{362880}{120\\cdot6}=504,\\\\[2mm]\n(4,3,2)&:\\ \\frac{9!}{4!\\,3!\\,2!}= \\frac{362880}{24\\cdot6\\cdot2}=1260.\n\\end{aligned}\n\\]\n\n---\n\n### 3.  Total number of assignments.\n\n\\[\nN=252+504+1260=2016.\n\\]\n\n---\n\n### 4.  Remainder modulo \\(1000\\).\n\n\\[\n2016\\equiv 16 \\pmod{1000}.\n\\]\n\n---\n\n\\[\n\\boxed{16}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nFind the number of ordered pairs $(x,y)$, where both $x$ and $y$ are integers between $-100$ and $100$, inclusive, such that $12x^{2}-xy-6y^{2}=0$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "First factor the quadratic form.\n\n\\[\n12x^{2}-xy-6y^{2}= (4x-3y)(3x+2y)\n\\]\n\nHence  \n\n\\[\n(4x-3y)(3x+2y)=0\\Longrightarrow \n\\begin{cases}\n4x-3y=0\\\\[2mm]\n\\text{or}\\\\[2mm]\n3x+2y=0\n\\end{cases}\n\\]\n\n---\n\n### 1.  Solutions of \\(4x-3y=0\\)\n\n\\(4x=3y\\Rightarrow y=\\dfrac{4}{3}x\\).  \nSince \\(x,y\\) are integers, \\(x\\) must be a multiple of \\(3\\): set \\(x=3k\\), then  \n\n\\[\ny=4k,\\qquad k\\in\\mathbb Z .\n\\]\n\nBoth coordinates must satisfy \\(-100\\le x,y\\le100\\):\n\n\\[\n|3k|\\le100,\\qquad|4k|\\le100\\Longrightarrow |k|\\le \\Big\\lfloor\\frac{100}{4}\\Big\\rfloor =25 .\n\\]\n\nThus \\(k=-25,-24,\\dots ,25\\):  \\(51\\) integer pairs.\n\n---\n\n### 2.  Solutions of \\(3x+2y=0\\)\n\n\\(3x=-2y\\Rightarrow y=-\\dfrac{3}{2}x\\).  \nFor integers we need \\(x\\) even: write \\(x=2m\\), then  \n\n\\[\ny=-3m,\\qquad m\\in\\mathbb Z .\n\\]\n\nAgain \\(-100\\le x,y\\le100\\) gives  \n\n\\[\n|2m|\\le100,\\qquad|3m|\\le100\\Longrightarrow |m|\\le\\Big\\lfloor\\frac{100}{3}\\Big\\rfloor =33 .\n\\]\n\nThus \\(m=-33,-32,\\dots ,33\\):  \\(67\\) integer pairs.\n\n---\n\n### 3.  Remove double counting\n\nThe two families intersect only at \\((0,0)\\) (when \\(k=m=0\\)).  \nHence the total number of distinct ordered pairs is  \n\n\\[\n51+67-1=117 .\n\\]\n\n\\[\n\\boxed{117}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nThere are exactly three positive real numbers $ k $ such that the function\n$ f(x) = \\frac{(x - 18)(x - 72)(x - 98)(x - k)}{x} $\ndefined over the positive real numbers achieves its minimum value at exactly two positive real numbers $ x $. Find the sum of these three values of $ k $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "The function  \n\n\\[\nf(x)=\\frac{(x-18)(x-72)(x-98)(x-k)}{x}\\qquad (x>0)\n\\]\n\nhas zeros at \\(x=18,\\;72,\\;98,\\;k\\) and  \n\\(\\displaystyle \\lim_{x\\to0^+}f(x)=\\lim_{x\\to\\infty}f(x)=+\\infty\\).\nHence \\(f\\) is positive near the ends and negative on each of the two\nintervals bounded by the smallest two zeros and by the largest two zeros.\nConsequently \\(f\\) has exactly two local minima (one in each negative\ninterval).\n\nLet the common minimal value be \\(m<0\\).  At a minimum the graph of\n\\(y=f(x)\\) is tangent to the horizontal line \\(y=m\\); therefore the\nequation  \n\n\\[\nf(x)=m\\quad\\Longleftrightarrow\\quad (x-18)(x-72)(x-98)(x-k)-mx=0\n\\]\n\nmust have a **double root** at each minimum.  Thus the quartic polynomial\nmust be a perfect square of a quadratic:\n\n\\[\n(x-18)(x-72)(x-98)(x-k)-mx=(x^{2}-Sx+P)^{2},\n\\]\nwhere \\(S,P,m\\) are constants.\n\nExpanding and equating coefficients with  \n\n\\[\nN(x)-mx=x^{4}-(188+k)x^{3}+(10116+188k)x^{2}-(127008+10116k+m)x+127008k\n\\]\n\ngives  \n\n\\[\n\\begin{cases}\nS=\\dfrac{188+k}{2},\\\\[4pt]\nS^{2}+2P=10116+188k,\\\\[4pt]\nm=2SP-(127008+10116k),\\\\[4pt]\nP^{2}=127008\\,k .\n\\end{cases}\n\\]\n\nFrom \\(P^{2}=127008k\\) set \\(t=\\sqrt{2k}>0\\); then  \n\n\\[\nP=252t,\\qquad k=\\dfrac{t^{2}}{2},\n\\quad S=\\frac{188+k}{2}=94+\\frac{t^{2}}{4}.\n\\]\n\nSubstituting these into \\(S^{2}+2P=10116+188k\\) yields an equation in\n\\(t\\):\n\n\\[\n\\frac{(188+k)^{2}}{4}+504\\sqrt{2k}=10116+188k\n\\Longrightarrow\nt^{4}-752t^{2}+8064t-20480=0 .\n\\]\n\nFactoring,\n\n\\[\nt^{4}-752t^{2}+8064t-20480=(t-4)(t-8)(t-20)(t+32)=0 .\n\\]\n\nSince \\(t>0\\), we obtain  \n\n\\[\nt=4,\\;8,\\;20\\quad\\Longrightarrow\\quad \nk=\\frac{t^{2}}{2}=8,\\;32,\\;200 .\n\\]\n\nFor each of these \\(k\\) one computes \\(\\Delta=S^{2}-4P>0\\), so the\nquadratic \\(x^{2}-Sx+P\\) has two distinct real roots.  They lie exactly in\nthe two negative intervals, giving two distinct points where \\(f\\) attains\nthe value \\(m\\).  Moreover \\(m<0\\), while all zeros of \\(f\\) are at\n\\(0\\), so these are the global minima.  \nNo other positive \\(k\\) satisfies the required condition.\n\nHence the three admissible values of \\(k\\) are \\(8,\\;32,\\;200\\), and their\nsum is\n\n\\[\n8+32+200 = 240.\n\\]\n\n\\[\n\\boxed{240}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nAn isosceles trapezoid has an inscribed circle tangent to each of its four sides. The radius of the circle is 3, and the area of the trapezoid is 72. Let the parallel sides of the trapezoid have lengths $r$ and $s$, with $r \\neq s$. Find $r^{2}+s^{2}$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "For a quadrilateral that has an incircle (a **tangential quadrilateral**)  \n\n\\[\n\\text{area}=r_{\\text{in}}\\cdot\\frac{\\text{perimeter}}2 .\n\\tag{1}\n\\]\n\n---\n\n### 1.  Using the given area\n\nLet the parallel sides be \\(r\\) and \\(s\\) \\((r\\neq s)\\) and the equal legs be \\(\\ell\\).\nThe incircle radius is \\(r_{\\text{in}}=3\\) and the area is \\(72\\).\n\nFrom (1),\n\n\\[\n72=3\\cdot\\frac{r+s+2\\ell}{2}\\Longrightarrow\nr+s+2\\ell=48.\n\\tag{2}\n\\]\n\n---\n\n### 2.  Pitot\u2019s theorem\n\nA tangential quadrilateral satisfies Pitot\u2019s theorem: the sum of opposite sides are equal.  \nThus for our isosceles trapezoid  \n\n\\[\nr+s= \\ell+\\ell =2\\ell \\Longrightarrow \\ell=\\frac{r+s}{2}.\n\\tag{3}\n\\]\n\nSubstituting (3) into (2),\n\n\\[\nr+s+2\\Bigl(\\frac{r+s}{2}\\Bigr)=48\\Longrightarrow 2(r+s)=48\n\\Longrightarrow r+s=24.\n\\tag{4}\n\\]\n\nHence each leg is  \n\n\\[\n\\ell=\\frac{r+s}{2}=12.\n\\]\n\n---\n\n### 3.  Height of the trapezoid\n\nA circle tangent to two parallel lines must have its centre midway between them, so the distance (the height \\(h\\)) between the bases equals twice the radius:\n\n\\[\nh=2\\cdot3=6.\n\\]\n\nThe area of a trapezoid is also  \n\n\\[\n\\text{Area}= \\frac{r+s}{2}\\,h = \\frac{24}{2}\\cdot6 = 72,\n\\]\n\nwhich checks with the given data.\n\n---\n\n### 4.  Relating the legs, height, and bases  \n\nIn an isosceles trapezoid the leg \\(\\ell\\) together with the height \\(h\\) and half the difference of the bases forms a right triangle:\n\n\\[\n\\ell^{2}=h^{2}+\\Bigl(\\frac{s-r}{2}\\Bigr)^{2}.\n\\]\n\nPlugging \\(\\ell=12\\) and \\(h=6\\),\n\n\\[\n12^{2}=6^{2}+\\Bigl(\\frac{s-r}{2}\\Bigr)^{2}\n\\Longrightarrow 144=36+\\frac{(s-r)^{2}}{4}\n\\Longrightarrow (s-r)^{2}=432.\n\\]\n\nThus  \n\n\\[\ns-r= \\sqrt{432}=12\\sqrt3 .\n\\tag{5}\n\\]\n\n---\n\n### 5.  Solving for \\(r\\) and \\(s\\)\n\nFrom (4) and (5):\n\n\\[\n\\begin{cases}\ns+r = 24,\\\\[2pt]\ns-r = 12\\sqrt3,\n\\end{cases}\n\\qquad\\Longrightarrow\\qquad\ns = 12+6\\sqrt3,\\;\\; r = 12-6\\sqrt3.\n\\]\n\n---\n\n### 6.  Computing \\(r^{2}+s^{2}\\)\n\n\\[\nr^{2}+s^{2}= (12-6\\sqrt3)^{2}+(12+6\\sqrt3)^{2}\n= (252-144\\sqrt3)+(252+144\\sqrt3)=504.\n\\]\n\n(Alternatively, using \\((r+s)^{2}=r^{2}+s^{2}+2rs\\) and \\(rs=36\\) from \\((s+r)^{2}-(s-r)^{2}=4rs\\) also gives \\(r^{2}+s^{2}=504\\).)\n\n\\[\n\\boxed{504}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nThere are exactly three positive real numbers $ k $ such that the function\n$ f(x) = \\frac{(x - 18)(x - 72)(x - 98)(x - k)}{x} $\ndefined over the positive real numbers achieves its minimum value at exactly two positive real numbers $ x $. Find the sum of these three values of $ k $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "\\[\n\\boxed{240}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nThere are $8!=40320$ eight-digit positive integers that use each of the digits $1,2,3,4,5,6,7,8$ exactly once. Let $N$ be the number of these integers that are divisible by 22. Find the difference between $N$ and 2025.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "The number must be divisible by \\(22=2\\cdot 11\\).\n\n---\n\n### 1.  Divisibility by \\(2\\)\n\nThe last digit (the 8\u2011th digit) must be even, i.e. one of \\(2,4,6,8\\).\n\n---\n\n### 2.  Divisibility by \\(11\\)\n\nFor an 8\u2011digit number \\(d_1d_2\\ldots d_8\\)\n\n\\[\nd_1-d_2+d_3-d_4+d_5-d_6+d_7-d_8\\equiv0\\pmod{11}.\n\\]\n\nLet  \n\n\\[\nS_{\\text{odd}}=d_1+d_3+d_5+d_7,\\qquad  \nS_{\\text{even}}=d_2+d_4+d_6+d_8 .\n\\]\n\nThen the condition becomes  \n\n\\[\nS_{\\text{odd}}-S_{\\text{even}}\\equiv0\\pmod{11}.\n\\]\n\nSince the digits \\(1,2,\\dots ,8\\) are used exactly once,  \n\n\\[\nS_{\\text{odd}}+S_{\\text{even}}=1+2+\\cdots +8=36 .\n\\]\n\nHence  \n\n\\[\n2S_{\\text{even}}\\equiv36\\pmod{11}\\Longrightarrow2S_{\\text{even}}\\equiv3\\pmod{11}\n\\]\n\\[\n\\Longrightarrow S_{\\text{even}}\\equiv3\\cdot 6\\equiv18\\equiv7\\pmod{11}.\n\\]\n\nThe possible values for a sum of four distinct digits from \\(\\{1,\\ldots ,8\\}\\) lie between \\(10\\) and \\(26\\); the only value congruent to \\(7\\pmod{11}\\) in this interval is \\(18\\).  \nThus we must have  \n\n\\[\nS_{\\text{even}}=18\\qquad\\text{and}\\qquad S_{\\text{odd}}=18 .\n\\]\n\n---\n\n### 3.  Choosing the four digits that go to even positions\n\nWe need all 4\u2011element subsets of \\(\\{1,2,3,4,5,6,7,8\\}\\) whose sum is \\(18\\).\n\nListing them:\n\n\\[\n\\begin{aligned}\n&\\{1,2,7,8\\},\\; \\{1,3,6,8\\},\\; \\{1,4,5,8\\},\\; \\{1,4,6,7\\},\\\\\n&\\{2,3,5,8\\},\\; \\{2,3,6,7\\},\\; \\{2,4,5,7\\},\\; \\{3,4,5,6\\}.\n\\end{aligned}\n\\]\n\nThere are **8** such subsets.  \nEach of them contains exactly two even digits (the evens are \\(2,4,6,8\\)).\n\n---\n\n### 4.  Arranging the digits\n\nFor a fixed subset \\(S\\) (the digits that occupy the even positions 2,4,6,8):\n\n* The last position (position 8) must be even.  \n  Since \\(S\\) has exactly two evens, we have \\(2\\) choices for the digit that goes to position\u202f8.\n* The remaining three digits of \\(S\\) can be placed in positions 2,4,6 in any order: \\(3! = 6\\) ways.\n\nHence the even positions can be filled in \\(2\\cdot6 = 12\\) ways.\n\nThe four digits not in \\(S\\) occupy the odd positions \\(1,3,5,7\\) and may be arranged arbitrarily:\n\\(4! = 24\\) ways.\n\nThus each subset contributes  \n\n\\[\n12 \\times 24 = 288\n\\]\n\ndifferent 8\u2011digit numbers.\n\nWith 8 admissible subsets, the total number of 8\u2011digit numbers divisible by 22 is  \n\n\\[\nN = 8 \\times 288 = 2304.\n\\]\n\n---\n\n### 5.  Required difference\n\n\\[\nN-2025 = 2304-2025 = 279.\n\\]\n\n\\[\n\\boxed{279}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nLet the sequence of rationals $ x_1, x_2, \\ldots $ be defined such that $ x_1 = \\frac{25}{11} $ and\n$ x_{k+1} = \\frac{1}{3} \\left( x_k + \\frac{1}{x_k} - 1 \\right). $\n$ x_{2025} $ can be expressed as $ \\frac{m}{n} $ for relatively prime positive integers $ m $ and $ n $. Find the remainder when $ m + n $ is divided by 1000.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "\\[\nx_{k+1}=\\frac{x_k+\\dfrac1{x_k}-1}{3}\n      =\\frac{x_k^2-x_k+1}{3x_k}\\qquad (k\\ge 1),\\qquad \nx_1=\\frac{25}{11}.\n\\]\n\n--------------------------------------------------------------------\n### 1.  A convenient change of variable  \n\nPut  \n\n\\[\ny_k=\\frac{x_k-1}{x_k+1}\\qquad\\Longleftrightarrow\\qquad \nx_k=\\frac{1+y_k}{1-y_k}.\n\\]\n\nThen  \n\n\\[\ny_{k+1}= \\frac{x_{k+1}-1}{x_{k+1}+1}\n        =\\frac{3y_k^{2}-1}{2}.\n\\tag{1}\n\\]\n\nIndeed,\n\\[\n\\frac{x_k+1/x_k-1}{3}= \\frac{1+y_k}{1-y_k}\n        \\Longrightarrow\ny_{k+1}= \\frac{3y_k^{2}-1}{2}.\n\\]\n\nFrom \\(x_1=25/11\\) we obtain\n\n\\[\ny_1=\\frac{25/11-1}{25/11+1}= \\frac{14/11}{36/11}= \\frac{7}{18}.\n\\]\n\n--------------------------------------------------------------------\n### 2.  Removing the common factor  \n\nWrite \\(y_k =\\dfrac{a_k}{b_k}\\) with \\(\\gcd(a_k,b_k)=1\\).\nFrom (1)\n\n\\[\n\\frac{a_{k+1}}{b_{k+1}}=\\frac{3a_k^{2}-b_k^{2}}{2b_k^{2}} .\n\\]\n\nBecause \\(b_k\\) is always a multiple of \\(3\\), the fraction can be reduced by the\nfactor \\(3\\) and we obtain the **integer** recurrences\n\n\\[\n\\boxed{\\;\n\\begin{aligned}\na_{k+1}&=\\frac{3a_k^{2}-b_k^{2}}{3},\\\\[2mm]\nb_{k+1}&=\\frac{2b_k^{2}}{3},\n\\end{aligned}\\qquad a_1=7,\\;b_1=18.}\n\\tag{2}\n\\]\n\n--------------------------------------------------------------------\n### 3.  Closed form for \\(b_k\\)\n\nFrom the second line of (2)\n\n\\[\nb_{k+1}=\\frac{2}{3}b_k^{2}, \\qquad b_1=18.\n\\]\n\nInduction gives  \n\n\\[\n\\boxed{\\,b_k=2^{\\,2^{\\,k}-1}\\;3^{\\,2^{\\,k-1}+1}\\,}\\qquad(k\\ge1).   \\tag{3}\n\\]\n\nCheck: \\(b_1=2^{2-1}3^{1+1}=2\\cdot 9=18\\).\n\n--------------------------------------------------------------------\n### 4.  The reduced form of \\(x_k\\)\n\nSince \\(x_k=\\dfrac{1+y_k}{1-y_k}\\) and \\(y_k=a_k/b_k\\),\n\n\\[\nx_k=\\frac{a_k+b_k}{\\,b_k-a_k\\,}.\n\\]\n\nThus the reduced numerator and denominator are  \n\n\\[\nm_k=a_k+b_k,\\qquad n_k=b_k-a_k,\n\\]\n\nand\n\n\\[\nm_k+n_k=2b_k. \\tag{4}\n\\]\n\nConsequently we only need \\(2b_{2025}\\pmod{1000}\\).\n\n--------------------------------------------------------------------\n### 5.  Computing \\(2b_{2025}\\pmod{1000}\\)\n\nFrom (3)\n\n\\[\n2b_{2025}=2\\cdot\n2^{\\,2^{2025}-1}\\;3^{\\,2^{2024}+1}\n=2^{\\,2^{2025}}\\;3^{\\,2^{2024}+1}.\n\\]\n\nWork modulo \\(1000=8\\cdot125\\).\n\n*Modulo \\(8\\):*  \n\\(2^{\\,2^{2025}}\\) is a multiple of \\(8\\) (the exponent is \\(\\ge3\\)), so the product is\n\\(0\\pmod 8\\).\n\n*Modulo \\(125\\):*  \nBoth bases are invertible, so we may reduce the exponents modulo \\(\\varphi(125)=100\\).\n\n\\[\n\\begin{aligned}\n2^{2025}\\pmod{100}&\\equiv 32,\\\\\n2^{2024}\\pmod{100}&\\equiv 16,\n\\end{aligned}\n\\qquad\\Longrightarrow\\qquad\n\\begin{aligned}\n2^{\\,2^{2025}} &\\equiv 2^{32}\\pmod{125},\\\\\n3^{\\,2^{2024}+1}&\\equiv 3^{17}\\pmod{125}.\n\\end{aligned}\n\\]\n\n\\[\n2^{32}\\equiv46\\pmod{125},\\qquad \n3^{17}\\equiv38\\pmod{125}.\n\\]\n\nHence  \n\n\\[\n2^{\\,2^{2025}}3^{\\,2^{2024}+1}\\equiv46\\cdot38\\equiv123\\pmod{125}.\n\\]\n\n*Chinese remainder:*  Find \\(N\\) with  \n\n\\[\nN\\equiv0\\pmod8,\\qquad N\\equiv123\\pmod{125}.\n\\]\n\nWriting \\(N=125a+123\\) and testing \\(a=0,\\dots,7\\) gives \\(a=1\\) as the solution,\nso \\(N=125\\cdot1+123=248\\).\n\nThus  \n\n\\[\n2b_{2025}\\equiv 248\\pmod{1000}.\n\\]\n\nBy (4) this is exactly \\((m+n)\\pmod{1000}\\).\n\n--------------------------------------------------------------------\n\\[\n\\boxed{248}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nLet $k$ be real numbers such that the system $|25+20i-z|=5$ and $|z-4-k|=|z-3i-k|$ has exactly one complex solution $z$. The sum of all possible values of $k$ can be written as $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$. Here $i=\\sqrt{-1}$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n\\[\nz=x+yi .\n\\]\n\nThe first equation  \n\n\\[\n|25+20i-z|=5\n\\]\n\nrepresents the circle  \n\n\\[\n(x-25)^2+(y-20)^2=5^2        \\tag{1}\n\\]\n\ncentered at \\(C=(25,20)\\) with radius \\(r=5\\).\n\n---\n\n### Locus of the second equation  \n\n\\[\n|z-4-k|=|z-3i-k|\n\\]\n\nmeans that the distance from \\(z\\) to the point  \n\n\\[\nA=(4+k,0)\n\\]\n\nequals its distance to the point  \n\n\\[\nB=(k,3).\n\\]\n\nHence the set of all such \\(z\\) is the **perpendicular bisector** of the segment \\(AB\\).\n\n- Midpoint of \\(AB\\):\n  \\[\n  M=\\Bigl(\\frac{4+k+k}{2},\\frac{0+3}{2}\\Bigr)=(2+k,\\tfrac32).\n  \\]\n\n- Slope of \\(AB\\):\n  \\[\n  m_{AB}= \\frac{3-0}{k-(4+k)}=\\frac{3}{-4}=-\\frac34 .\n  \\]\n\n- Slope of the perpendicular bisector:\n  \\[\n  m_{L}= \\frac{4}{3}.\n  \\]\n\nThus the line \\(L_k\\) (the perpendicular bisector) has equation  \n\n\\[\ny-\\frac32=\\frac43\\Bigl(x-(2+k)\\Bigr).\n\\]\n\nWriting it in the form \\(Ax+By+C=0\\),\n\n\\[\n8x-6y-(8k+7)=0\\qquad\\Longleftrightarrow\\qquad 8x-6y=8k+7. \\tag{2}\n\\]\n\n---\n\n### Tangency condition  \n\nThe system has exactly one solution \\(z\\) iff the line \\(L_k\\) is **tangent** to the circle \\((1)\\); i.e. the distance from the centre \\(C\\) to the line equals the radius \\(5\\).\n\nDistance from \\(C=(25,20)\\) to line \\((2)\\):\n\n\\[\nd=\\frac{|\\,8\\cdot25-6\\cdot20-(8k+7)\\,|}{\\sqrt{8^{2}+(-6)^{2}}}\n   =\\frac{|200-120-8k-7|}{10}\n   =\\frac{|73-8k|}{10}.\n\\]\n\nSet \\(d=5\\):\n\n\\[\n\\frac{|73-8k|}{10}=5 \\Longrightarrow |73-8k|=50.\n\\]\n\nHence  \n\n\\[\n73-8k=50 \\quad\\text{or}\\quad 73-8k=-50,\n\\]\n\nwhich give  \n\n\\[\nk=\\frac{23}{8},\\qquad k=\\frac{123}{8}.\n\\]\n\nBoth values indeed make the line tangent (the discriminant of the combined equations becomes zero), so each yields exactly one complex solution \\(z\\).\n\n---\n\n### Sum of all possible \\(k\\)\n\n\\[\n\\frac{23}{8}+\\frac{123}{8}= \\frac{146}{8}= \\frac{73}{4}.\n\\]\n\nWrite \\(\\frac{73}{4}\\) as \\(\\frac{m}{n}\\) with \\(\\gcd(m,n)=1\\): \\(m=73,\\; n=4\\).\n\n\\[\nm+n=73+4=77.\n\\]\n\n\\[\n\\boxed{77}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nThe 27 cells of a $3\\times9$ grid are filled in using the numbers 1 through 9 so that each row contains 9 different numbers, and each of the three $3\\times3$ blocks heavily outlined in the example below contains 9 different numbers, as in the first three rows of a Sudoku puzzle. \n | 4 | 2 | 8 | 9 | 6 | 3 | 1 | 7 | 5 | \n | 3 | 7 | 9 | 5 | 2 | 1 | 6 | 8 | 4 | \n | 5 | 6 | 1 | 8 | 4 | 7 | 9 | 2 | 3 | \n The number of different ways to fill such a grid can be written as $p^a\\cdot q^b\\cdot r^c\\cdot s^d$, where $p,q,r,$ and $s$ are distinct prime numbers and $a,b,c,$ and $d$ are positive integers. Find $p\\cdot a+q\\cdot b+r\\cdot c+s\\cdot d$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "The grid has three rows and three \\(3\\times3\\) blocks.  \nEach row must contain the numbers \\(1,\\dots ,9\\) once, and each block must also contain every number once.\n\n---\n\n### 1.  Fix the first row  \n\nBecause the numbers are distinct, we may fix the first row to be  \n\n\\[\n(1,2,3,4,5,6,7,8,9)\n\\]\n\nand later multiply the count by the \\(9!\\) possible permutations of this row.\n\n---\n\n### 2.  What must the other two rows contain?\n\n* Block\u202f1 (columns\u202f1\u20133): row\u202f1 already has \\(\\{1,2,3\\}\\); thus rows\u202f2\u20133 must contain the six numbers \\(\\{4,5,6,7,8,9\\}\\).\n\n* Block\u202f2 (columns\u202f4\u20136): rows\u202f2\u20133 must contain \\(\\{1,2,3,7,8,9\\}\\).\n\n* Block\u202f3 (columns\u202f7\u20139): rows\u202f2\u20133 must contain \\(\\{1,2,3,4,5,6\\}\\).\n\nEach of rows\u202f2 and\u202f3 must be a permutation of \\(\\{1,\\dots ,9\\}\\).\n\nHence for each number \\(m\\) (which appears in two of the three blocks) we must decide in which of those two blocks it will be placed in row\u202f2 (the other occurrence will go to row\u202f3).  \n\nThe numbers are grouped as\n\n\\[\n\\begin{aligned}\n&\\{1,2,3\\}\\ \\text{appear in blocks }2\\text{ and }3,\\\\\n&\\{4,5,6\\}\\ \\text{appear in blocks }1\\text{ and }3,\\\\\n&\\{7,8,9\\}\\ \\text{appear in blocks }1\\text{ and }2.\n\\end{aligned}\n\\]\n\nLet  \n\n* \\(x\\) = how many of \\(\\{1,2,3\\}\\) go to block\u202f2 (the rest go to block\u202f3);\n* \\(y\\) = how many of \\(\\{4,5,6\\}\\) go to block\u202f1 (the rest go to block\u202f3);\n* \\(z\\) = how many of \\(\\{7,8,9\\}\\) go to block\u202f1 (the rest go to block\u202f2).\n\nBecause each block must receive exactly three numbers for row\u202f2 we obtain  \n\n\\[\n\\begin{cases}\ny+z=3 &(\\text{block }1)\\\\\nx+(3-z)=3 &(\\text{block }2)\\\\\n(3-x)+(3-y)=3 &(\\text{block }3)\n\\end{cases}\n\\Longrightarrow x=z,\\quad y=3-x .\n\\]\n\nThus \\(x\\) can be \\(0,1,2,3\\).  \nFor a given \\(x\\),\n\n* choose \\(x\\) of the three numbers \\(\\{1,2,3\\}\\) to go to block\u202f2: \\(\\binom{3}{x}\\) ways;\n* choose \\(y=3-x\\) of \\(\\{4,5,6\\}\\) to go to block\u202f1: \\(\\binom{3}{3-x}=\\binom{3}{x}\\) ways;\n* choose \\(z=x\\) of \\(\\{7,8,9\\}\\) to go to block\u202f1: \\(\\binom{3}{x}\\) ways.\n\nHence the number of ways to decide **which numbers** belong to row\u202f2 in each block is  \n\n\\[\n\\sum_{x=0}^{3}\\binom{3}{x}^3=1^3+3^3+3^3+1^3=56 .\n\\]\n\n---\n\n### 3.  Placing the chosen numbers in the cells  \n\nWithin each block, row\u202f2 has three cells and row\u202f3 three cells.  \nThe three numbers assigned to row\u202f2 can be arranged in those three cells in \\(3!\\) ways, and similarly for row\u202f3.  \n\nThus for each block there are \\(3!\\times3! = 36\\) placements, and for the three blocks\n\n\\[\n36^3 = 46656\n\\]\n\nplacements.\n\nConsequently, with the first row fixed,\n\n\\[\n\\text{# grids} = 56 \\times 36^3 = 56 \\times 46656 = 2\\,612\\,736 .\n\\]\n\n---\n\n### 4.  Restore the first row  \n\nThe first row could be any permutation of the numbers \\(1\\)\u2013\\(9\\); there are \\(9! = 362880\\) possibilities.\n\n\\[\nN = 2\\,612\\,736 \\times 362\\,880 = 948\\,109\\,639\\,680 .\n\\]\n\n---\n\n### 5.  Prime factorisation  \n\n\\[\n\\begin{aligned}\n56 &= 2^3 \\cdot 7,\\\\[2pt]\n36^3 &= (2^2 3^2)^3 = 2^6 \\cdot 3^6,\\\\[2pt]\n9! &= 2^7 \\cdot 3^4 \\cdot 5 \\cdot 7 .\n\\end{aligned}\n\\]\n\nMultiplying:\n\n\\[\nN = 2^{3+6+7}\\, 3^{6+4}\\, 5^{1}\\, 7^{1+1}\n   = 2^{16} \\cdot 3^{10} \\cdot 5^{1} \\cdot 7^{2}.\n\\]\n\nThus we have the representation  \n\n\\[\nN = p^{a}\\, q^{b}\\, r^{c}\\, s^{d}\n\\]\n\nwith distinct primes  \n\n\\[\np=2,\\ a=16;\\qquad q=3,\\ b=10;\\qquad r=5,\\ c=1;\\qquad s=7,\\ d=2 .\n\\]\n\n---\n\n### 6.  Compute \\(p a + q b + r c + s d\\)\n\n\\[\n\\begin{aligned}\np a + q b + r c + s d &= 2\\cdot16 + 3\\cdot10 + 5\\cdot1 + 7\\cdot2\\\\\n&= 32 + 30 + 5 + 14\\\\\n&= 81.\n\\end{aligned}\n\\]\n\n\\[\n\\boxed{81}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nThe parabola with equation $y=x^{2}-4$ is rotated $60^{\\circ}$ counterclockwise around the origin. The unique point in the fourth quadrant where the original parabola and its image intersect has $y$-coordinate $\\frac{a-\\sqrt{b}}{c}$, where $a$, $b$, and $c$ are positive integers, and $a$ and $c$ are relatively prime. Find $a+b+c$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n\\[\ny=x^{2}-4\\qquad (1)\n\\]\n\nand rotate the whole plane \\(60^{\\circ}\\) counter\u2011clockwise about the origin.\nFor a point \\((u,v)\\) on the original parabola, the image after the rotation is  \n\n\\[\n(x,y)=\\bigl(u\\cos60^\\circ -v\\sin60^\\circ,\\;u\\sin60^\\circ+v\\cos60^\\circ\\bigr)\n     =\\Bigl(\\frac12u-\\frac{\\sqrt3}{2}v,\\;\\frac{\\sqrt3}{2}u+\\frac12v\\Bigr). \\tag{2}\n\\]\n\nBecause \\((u,v)\\) lies on the original curve, \\(v=u^{2}-4\\).\nSubstituting this into (2) gives a parametric description of the rotated curve:\n\n\\[\n\\begin{cases}\nx= -\\frac{\\sqrt3}{2}u^{2}+\\frac12u+2\\sqrt3,\\\\[2mm]\ny= \\frac{\\sqrt3}{2}u+\\frac12u^{2}-2 .\n\\end{cases} \\tag{3}\n\\]\n\nThe intersection points of the original parabola and its image satisfy both\n\\(y=x^{2}-4\\) and (3).  Using (3) we replace \\(x\\) and \\(y\\) in \\(y=x^{2}-4\\):\n\n\\[\n\\frac{\\sqrt3}{2}u+\\frac12u^{2}-2=\n\\Bigl(-\\frac{\\sqrt3}{2}u^{2}+\\frac12u+2\\sqrt3\\Bigr)^{2}-4 .\n\\]\n\nAfter expanding and simplifying we obtain the quartic equation for \\(u\\)\n\n\\[\n3u^{4}-2\\sqrt3\\,u^{3}-25u^{2}+6\\sqrt3\\,u+40=0. \\tag{4}\n\\]\n\nBecause the coefficients involve \\(\\sqrt3\\) it is natural to try a factorisation\ninto quadratics with linear terms that are multiples of \\(\\sqrt3\\).  Indeed,\n\n\\[\n3u^{4}-2\\sqrt3\\,u^{3}-25u^{2}+6\\sqrt3\\,u+40\n  =(3u^{2}+\\sqrt3\\,u-10)(u^{2}-\\sqrt3\\,u-4). \\tag{5}\n\\]\n\nThus the possible values of \\(u\\) are the roots of  \n\n\\[\n\\begin{cases}\n3u^{2}+\\sqrt3\\,u-10=0,\\\\[1mm]\nu^{2}-\\sqrt3\\,u-4=0.\n\\end{cases}\n\\]\n\nSolving,\n\n\\[\n\\begin{aligned}\nu&=\\frac{-\\sqrt3\\pm\\sqrt{123}}{6},\\\\[1mm]\nu&=\\frac{\\sqrt3\\pm\\sqrt{19}}{2}.\n\\end{aligned}\n\\]\n\nPlug each value into (3) to obtain the corresponding point \\((x,y)\\).\n\n\\[\n\\begin{array}{c|c|c}\nu & x & y\\\\ \\hline\n\\displaystyle\\frac{-\\sqrt3+\\sqrt{123}}6 & 2.136\\ldots & 0.566\\ldots\\\\[2mm]\n\\displaystyle\\frac{-\\sqrt3-\\sqrt{123}}6 & -1.561\\ldots & -1.568\\ldots\\\\[2mm]\n\\displaystyle\\frac{\\sqrt3+\\sqrt{19}}2 & -3.046\\ldots & 5.276\\ldots\\\\[2mm]\n\\displaystyle\\frac{\\sqrt3-\\sqrt{19}}2 & 1.313\\ldots & -2.275\\ldots\n\\end{array}\n\\]\n\nOnly the last point lies in the fourth quadrant \\((x>0,\\;y<0)\\).  \nHence the required intersection point is obtained from  \n\n\\[\nu=\\frac{\\sqrt3-\\sqrt{19}}2 .\n\\]\n\nIts \\(y\\)-coordinate is, using (3),\n\n\\[\n\\begin{aligned}\ny&=\\frac{\\sqrt3}{2}u+\\frac12u^{2}-2\\\\\n  &=\\frac{\\sqrt3}{2}\\cdot\\frac{\\sqrt3-\\sqrt{19}}2\n    +\\frac12\\Bigl(\\frac{\\sqrt3-\\sqrt{19}}2\\Bigr)^{2}-2\\\\[1mm]\n  &=\\frac{3-\\sqrt{57}}4+\\frac{11-\\sqrt{57}}4-2\\\\[1mm]\n  &=\\frac{3-\\sqrt{57}}2 .\n\\end{aligned}\n\\]\n\nThus  \n\n\\[\ny=\\frac{a-\\sqrt b}{c}\\qquad\\text{with}\\quad a=3,\\;b=57,\\;c=2.\n\\]\n\nSince \\(\\gcd(3,2)=1\\) the representation is in lowest terms.  Therefore\n\n\\[\na+b+c = 3+57+2 = 62.\n\\]\n\n\\[\n\\boxed{62}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nOn $\\triangle ABC$ points $A,D,E$, and $B$ lie that order on side $\\overline{AB}$ with $AD=4, DE=16$, and $EB=8$. Points $A,F,G$, and $C$ lie in that order on side $\\overline{AC}$ with $AF=13, FG=52$, and $GC=26$. Let $M$ be the reflection of $D$ through $F$, and let $N$ be the reflection of $G$ through $E$. Quadrilateral $DEGF$ has area 288. Find the area of heptagon $AFNBCEM$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "**Solution.**  \n\nPut \\(A=(0,0)\\) and let \\(AB\\) be the \\(x\\)-axis.  \nSince  \n\n\\[\nAD=4,\\qquad DE=16,\\qquad EB=8,\n\\]\n\nwe have  \n\n\\[\nA=(0,0),\\;D=(4,0),\\;E=(20,0),\\;B=(28,0),\\qquad AB=28 .\n\\]\n\nLet \\(C=(x,y)\\) with \\(y>0\\).  \nBecause \\(AF=13,\\;FG=52,\\;GC=26\\),\n\n\\[\nAC=13+52+26=91,\\qquad \n\\frac{AF}{AC}=\\frac{13}{91}=\\frac17 ,\\qquad \n\\frac{AG}{AC}=\\frac{13+52}{91}= \\frac{65}{91}= \\frac57 .\n\\]\n\nHence  \n\n\\[\nF=\\Bigl(\\frac{x}{7},\\frac{y}{7}\\Bigr),\\qquad \nG=\\Bigl(\\frac{5x}{7},\\frac{5y}{7}\\Bigr).\n\\]\n\n--------------------------------------------------------------------\n### 1.  Height of \\(\\triangle ABC\\)\n\nThe quadrilateral \\(DEGF\\) has vertices  \n\n\\[\nD(4,0),\\;E(20,0),\\;G\\Bigl(\\frac{5x}{7},\\frac{5y}{7}\\Bigr),\\;F\\Bigl(\\frac{x}{7},\\frac{y}{7}\\Bigr).\n\\]\n\nIts area by the shoelace formula is  \n\n\\[\n\\begin{aligned}\n[DEGF]\n&=\\frac12\\Bigl|\n\\bigl(4\\cdot0+20\\cdot\\frac{5y}{7}\n+\\frac{5x}{7}\\cdot\\frac{y}{7}+ \\frac{x}{7}\\cdot0\\bigr) \\\\\n&\\qquad\\ -\\bigl(0\\cdot20+0\\cdot\\frac{5x}{7}\n+\\frac{5y}{7}\\cdot\\frac{x}{7}+ \\frac{y}{7}\\cdot4\\bigr)\\Bigr| \\\\\n&=\\frac{624}{91}\\,y .\n\\end{aligned}\n\\]\n\nWe are given \\([DEGF]=288\\), so  \n\n\\[\n\\frac{624}{91}\\,y=288\\Longrightarrow y=42 .\n\\]\n\nTherefore the height of \\(\\triangle ABC\\) above \\(AB\\) is \\(y=42\\) and  \n\n\\[\n[ABC]=\\frac12\\cdot AB\\cdot y=\\frac12\\cdot28\\cdot42=588 .\n\\]\n\n--------------------------------------------------------------------\n### 2.  Points \\(M\\) and \\(N\\)\n\n\\(M\\) is the reflection of \\(D\\) across \\(F\\); thus \\(F\\) is the midpoint of\n\\(DM\\):\n\n\\[\nM=2F-D=\\Bigl(\\frac{2x}{7}-4,\\; \\frac{2y}{7}\\Bigr)=\\Bigl(\\frac{2x}{7}-4,12\\Bigr).\n\\]\n\n\\(N\\) is the reflection of \\(G\\) across \\(E\\); hence\n\n\\[\nN=2E-G=\\Bigl(40-\\frac{5x}{7},\\; -\\frac{5y}{7}\\Bigr)=\\Bigl(40-\\frac{5x}{7},-30\\Bigr).\n\\]\n\n--------------------------------------------------------------------\n### 3.  Area of the heptagon \\(AFNBCEM\\)\n\nList the vertices in the given order:\n\n\\[\n\\begin{array}{c|c}\n\\text{vertex}&(x,y)\\\\ \\hline\nA&(0,0)\\\\\nF&\\bigl(\\frac{x}{7},\\frac{y}{7}\\bigr)\\\\\nN&\\bigl(40-\\frac{5x}{7},-30\\bigr)\\\\\nB&(28,0)\\\\\nC&(x,y)\\\\\nE&(20,0)\\\\\nM&\\bigl(\\frac{2x}{7}-4,12\\bigr)\n\\end{array}\n\\]\n\nApply the shoelace formula:\n\n\\[\n\\begin{aligned}\n[AFNBCEM]&=\\frac12\\Bigl|\n\\underbrace{0\\cdot\\frac{y}{7}}_{\\!0}\n+\\frac{x}{7}\\cdot(-30)\n+(40-\\tfrac{5x}{7})\\cdot0\n+28\\cdot y\n+x\\cdot0\n+20\\cdot12\n+\\bigl(\\tfrac{2x}{7}-4\\bigr)\\cdot0 \\\\\n&\\qquad\n-\\bigl(0\\cdot\\frac{x}{7}\n+ \\frac{y}{7}\\bigl(40-\\tfrac{5x}{7}\\bigr)\n+(-30)\\cdot28\n+0\\cdot x\n+y\\cdot20\n+0\\bigl(\\tfrac{2x}{7}-4\\bigr)\n+12\\cdot0\\bigr)\\Bigr|\\\\\n&=\\frac12\\Bigl|\n\\Bigl(-\\frac{30x}{7}+1176+240\\Bigr)\n-\\Bigl(\\frac{40y}{7}-\\frac{5xy}{49}-840+20y\\Bigr)\\Bigr| .\n\\end{aligned}\n\\]\n\nAll terms containing \\(x\\) cancel, leaving\n\n\\[\n[AFNBCEM]=\\frac12\\bigl(1416-240\\bigr)=\\frac12\\cdot1176=588 .\n\\]\n\nThus the heptagon has the same area as \\(\\triangle ABC\\).\n\n--------------------------------------------------------------------\n### 4.  Answer\n\n\\[\n\\boxed{588}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nLet $ABCDE$ be a convex pentagon with $AB=14, BC=7, CD=24, DE=13, EA=26,$ and $\\angle B=\\angle E=60^\\circ$. For each point $X$ in the plane, define $f(X)=AX+BX+CX+DX+EX$. The least possible value of $f(X)$ can be expressed as $m+n\\sqrt{p}$, where $m$ and $n$ are positive integers and $p$ is not divisible by the square of any prime. Find $m+n+p$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "The least possible value of  \n\n\\[\nf(X)=AX+BX+CX+DX+EX\n\\]\n\nis  \n\n\\[\n6+18\\sqrt{13}.\n\\]\n\nHence \\(m=6\\), \\(n=18\\), \\(p=13\\) and  \n\n\\[\nm+n+p=6+18+13=37.\n\\]\n\n\\[\n\\boxed{37}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nThe twelve letters $A,B,C,D,E,F,G,H,I,J,K$, and $L$ are randomly grouped into six pairs of letters. The two letters in each pair are placed next to each other in alphabetical order to form six two-letter words, and those six words are listed alphabetically. For example, a possible result is $AB,CJ,DG,EK,FL,HI$. The probability that the last word listed contains $G$ is $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n\\[\nA=1,\\;B=2,\\dots ,L=12\n\\]\n\nand consider a random perfect matching of the 12 letters.  \nFor each pair we write the two letters in alphabetical order; thus each\npair is an unordered 2\u2011subset \\(\\{x,y\\}\\) with the smaller element first.\nWhen the six resulting two\u2011letter \u201cwords\u2019\u2019 are listed alphabetically, the\nlast (lexicographically largest) word is the pair whose **first letter**\n(the smaller element of the pair) is the largest among the six first\nletters.\n\nHence the problem asks for the probability that the pair containing the\nletter \\(G\\;(=7)\\) has the largest first\u2011letter among the six pairs.\n\n--------------------------------------------------------------------\n### 1.  How a matching looks\n\nIn any matching exactly six letters are the *smaller* element of their\npair; call this set \\(S\\) ( \\(|S|=6\\) ).  \nThe remaining six letters are the larger elements of their pairs.\n\nThe last word is the pair whose smaller element is  \n\n\\[\nM=\\max S .\n\\]\n\nWe need the probability that the pair containing \\(G\\) also contains\n\\(M\\).  This can happen in two mutually exclusive ways:\n\n* **Case\u202f1.** \\(G\\) is the smaller element of its pair, so \\(M=G\\).\n* **Case\u202f2.** \\(G\\) is the larger element of its pair; then the smaller\n  element of that pair must be \\(M\\).\n\n--------------------------------------------------------------------\n### 2.  Case\u202f2 \u2013 \\(G\\) is the larger element\n\nIf \\(G\\) is larger, its partner must be a smaller letter.\nLet that partner be \\(x\\ (<G)\\).  \nFor \\(x\\) to be the maximum of \\(S\\), all letters larger than \\(x\\)\nmust be the larger elements of their pairs.  Since \\(|S|=6\\), this forces\n\n\\[\nx=F\\;(=6),\\qquad S=\\{1,2,3,4,5,6\\}.\n\\]\n\nThus the only possible pairing is \\(\\{F,G\\}\\); the remaining letters are\n\\(\\{A,B,C,D,E\\}\\) (small) and \\(\\{H,I,J,K,L\\}\\) (large), which can be\nmatched arbitrarily.  There are  \n\n\\[\n5! =120\n\\]\n\nmatchings of this type.\n\n--------------------------------------------------------------------\n### 3.  Case\u202f1 \u2013 \\(G\\) is the smaller element\n\nNow \\(G\\) must be paired with a larger letter \\(j\\in\\{8,9,10,11,12\\}\\)\n(\\(5\\) choices).  \nFor \\(G\\) to be the maximal element of \\(S\\), none of the other letters\n\\(8,9,10,11,12\\) may belong to \\(S\\).  Hence  \n\n\\[\nS=\\{7\\}\\cup T,\\qquad T\\subset\\{1,2,3,4,5,6\\},\\ |T|=5.\n\\]\n\nChoose the omitted small letter \\(r\\in\\{1,\\dots ,6\\}\\); then\n\\(T=\\{1,\\dots ,6\\}\\setminus\\{r\\}\\) ( \\(6\\) choices).\n\nFor a fixed \\(j\\) and \\(r\\) we must match the five small letters\n\\(T\\) with the five large letters \\(\\{r\\}\\cup\\{8,9,10,11,12\\}\\setminus\\{j\\}\\)\nso that each small letter is paired with a larger one.  \nThe four large letters \\(\\{8,9,10,11,12\\}\\setminus\\{j\\}\\) can be paired\nwith any four of the small letters \u2013 that gives \\(4!=24\\) possibilities.\nThe remaining large letter \\(r\\) can only be paired with a small letter\nthat is smaller than \\(r\\); there are \\(r-1\\) such choices.\n\nHence for this \\(j,r\\) we have \\((r-1)\\cdot4!\\) matchings.\nSumming over \\(r\\) gives  \n\n\\[\n\\sum_{r=1}^{6}(r-1)\\cdot24=15\\cdot24=360\n\\]\n\nmatchings for each of the five possible \\(j\\).  Thus\n\n\\[\n\\text{Case\u202f1 count}=5\\cdot360=1800 .\n\\]\n\n--------------------------------------------------------------------\n### 4.  Total favourable matchings\n\n\\[\nN_{\\text{fav}}=1800+120=1920 .\n\\]\n\nThe total number of perfect matchings of 12 letters is  \n\n\\[\nN_{\\text{tot}}=\\frac{12!}{2^{6}\\,6!}=10395 .\n\\]\n\nTherefore\n\n\\[\nP=\\frac{1920}{10395}= \\frac{128}{693}\\qquad(\\gcd(128,693)=1).\n\\]\n\n--------------------------------------------------------------------\n### 5.  Answer\n\n\\[\n\\boxed{m+n=128+693=821}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nThe set of points in 3-dimensional coordinate space that lie in the plane $x+y+z=75$ whose coordinates satisfy the inequalities $x-yz<y-zx<z-xy$ forms three disjoint convex regions. Exactly one of those regions has finite area. The area of this finite region can be expressed in the form $a\\sqrt{b}$, where $a$ and $b$ are positive integers and $b$ is not divisible by the square of any prime. Find $a+b$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "The inequalities  \n\n\\[\nx-yz<y-zx<z-xy\n\\]\n\nare equivalent to  \n\n\\[\n(x-y)(1+z)<0,\\qquad (y-z)(1+x)<0 .\n\\]\n\n---\n\n### 1.  Introduce convenient variables\n\nLet  \n\n\\[\nu=x-y,\\qquad v=y-z .\n\\]\n\nOn the plane \\(x+y+z=75\\) we can solve for \\((x,y,z)\\) in terms of \\((u,v)\\):\n\n\\[\n\\begin{aligned}\nx&=\\frac{75+2u+v}{3},\\\\[2pt]\ny&=\\frac{75-u+v}{3},\\\\[2pt]\nz&=\\frac{75-u-2v}{3}.\n\\end{aligned}\n\\]\n\nThus  \n\n\\[\n1+z=\\frac{78-u-2v}{3},\\qquad \n1+x=\\frac{78+2u+v}{3}.\n\\]\n\nThe two inequalities become  \n\n\\[\nu\\,(78-u-2v)<0,\\qquad v\\,(78+2u+v)<0 .\n\\tag{1}\n\\]\n\n---\n\n### 2.  Determine the regions in the \\((u,v)\\)-plane  \n\nFrom (1)\n\n\\[\n\\begin{cases}\nu(78-u-2v)<0,\\\\[2pt]\nv(78+2u+v)<0,\n\\end{cases}\n\\]\n\nwhich splits the \\((u,v)\\)-plane into four sign cases.\n\n| case | signs of \\(u,v\\) | resulting linear conditions |\n|------|------------------|----------------------------|\n| \\(u>0,\\ v>0\\) | empty (contradiction) |\n| \\(u>0,\\ v<0\\) | \\(u+2v>78\\) (unbounded) |\n| \\(u<0,\\ v>0\\) | \\(u+2v<78,\\;2u+v<-78\\) (unbounded) |\n| \\(u<0,\\ v<0\\) | \\(2u+v>-78\\) (bounded) |\n\nOnly the last case gives a bounded region.  \nWith \\(u<0,\\ v<0\\) the condition \\(u+2v<78\\) is automatic, so the region is\n\n\\[\n\\boxed{\\;u<0,\\;v<0,\\;2u+v>-78\\;}\n\\]\n\nwhich is the interior of the right\u2011triangle with vertices  \n\n\\[\n(0,0),\\;(-39,0),\\;(0,-78).\n\\]\n\nIts area in the \\((u,v)\\)-coordinates is\n\n\\[\nA_{uv}= \\frac12\\cdot39\\cdot78 =1521 .\n\\]\n\n---\n\n### 3.  Convert to area on the plane \\(x+y+z=75\\)\n\nThe linear map \\((u,v)\\mapsto (x,y,z)\\) has Jacobian matrix  \n\n\\[\n\\frac{\\partial(x,y,z)}{\\partial(u,v)}=\n\\begin{pmatrix}\n\\frac{2}{3}&\\frac13\\\\[2pt]\n-\\frac13&\\frac13\\\\[2pt]\n-\\frac13&-\\frac23\n\\end{pmatrix}.\n\\]\n\nThe area\u2011scale factor is the magnitude of the cross product of its column vectors:\n\n\\[\n\\bigl\\lVert( \\tfrac23,-\\tfrac13,-\\tfrac13)\\times\n(\\tfrac13,\\tfrac13,-\\tfrac23)\\bigr\\rVert\n= \\frac1{\\sqrt3}.\n\\]\n\nHence the area of the finite region on the given plane is  \n\n\\[\nA =\\frac1{\\sqrt3}\\,A_{uv}= \\frac{1521}{\\sqrt3}\n      =\\frac{1521\\sqrt3}{3}= 507\\sqrt3 .\n\\]\n\n---\n\n### 4.  Answer\n\nThe area is \\(507\\sqrt3\\), i.e. \\(a=507\\) and \\(b=3\\).  \nThus  \n\n\\[\na+b = 507+3 = \\boxed{510}.\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nSix points $ A, B, C, D, E, $ and $ F $ lie in a straight line in that order. Suppose that $ G $ is a point not on the line and that $ AC = 26 $, $ BD = 22 $, $ CE = 31 $, $ DF = 33 $, $ AF = 73 $, $ CG = 40 $, and $ DG = 30 $. Find the area of $ \\triangle BGE $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let the points be placed on the \\(x\\)-axis.\n\n\\[\nA(0,0),\\;B(b,0),\\;C(c,0),\\;D(d,0),\\;E(e,0),\\;F(f,0)\n\\]\n\nSet the successive segment lengths  \n\n\\[\nAB=x_1,\\;BC=x_2,\\;CD=x_3,\\;DE=x_4,\\;EF=x_5 .\n\\]\n\nFrom the given distances\n\n\\[\n\\begin{aligned}\nx_1+x_2 &= AC = 26,\\\\\nx_2+x_3 &= BD = 22,\\\\\nx_3+x_4 &= CE = 31,\\\\\nx_4+x_5 &= DF = 33,\\\\\nx_1+x_2+x_3+x_4+x_5 &= AF = 73 .\n\\end{aligned}\n\\]\n\nSolving,\n\\[\nx_2=8,\\qquad x_1=18,\\qquad x_3=14,\\qquad x_4=17,\\qquad x_5=16 .\n\\]\n\nHence  \n\n\\[\n\\begin{aligned}\nA&=(0,0),\\\\\nB&=(18,0),\\\\\nC&=(26,0),\\\\\nD&=(40,0),\\\\\nE&=(57,0),\\\\\nF&=(73,0).\n\\end{aligned}\n\\]\n\nLet \\(G=(x,y)\\).  From the distances \\(CG=40\\) and \\(DG=30\\),\n\n\\[\n\\begin{cases}\n(x-26)^2+y^2=40^2=1600,\\\\[2pt]\n(x-40)^2+y^2=30^2=900 .\n\\end{cases}\n\\]\n\nSubtracting the equations,\n\n\\[\n(x-26)^2-(x-40)^2=700\\Longrightarrow 28x-924=700\\Longrightarrow x=58.\n\\]\n\nThen  \n\n\\[\n(58-26)^2+y^2=1600\\Longrightarrow 1024+y^2=1600\\Longrightarrow y^2=576\\Longrightarrow y=\\pm24.\n\\]\n\nThus \\(G=(58,24)\\) (the sign of \\(y\\) does not affect the area).\n\nThe base \\(BE\\) lies on the \\(x\\)-axis:\n\n\\[\nBE = e-b = 57-18 = 39 .\n\\]\n\nThe height from \\(G\\) to the line \\(AB\\!E\\) is \\(|y|=24\\).\n\nHence the area of \\(\\triangle BGE\\) is\n\n\\[\n\\frac12\\cdot BE\\cdot|y|\n   =\\frac12\\cdot 39 \\cdot 24\n   =\\frac12\\cdot 936\n   =468 .\n\\]\n\n\\[\n\\boxed{468}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nA piecewise linear periodic function is defined by $f(x)=\\begin{cases}x&\\text{if }x\\in[-1,1)\\\\2-x&\\text{if }x\\in[1,3)\\end{cases}$ and $f(x+4)=f(x)$ for all real numbers $x$. The graph of $f(x)$ has the sawtooth pattern. The parabola $x=34y^2$ intersects the graph of $f(x)$ at finitely many points. The sum of the $y$-coordinates of these intersection points can be expressed in the form $\\frac{a+b\\sqrt{c}}{d}$, where $a,b,c,$ and $d$ are positive integers, $a,b,$ and $d$ have greatest common divisor equal to 1, and $c$ is not divisible by the square of any prime. Find $a+b+c+d$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "The intersection points satisfy  \n\n\\[\ny=f(x),\\qquad x=34y^{2}\\Longrightarrow y=f(34y^{2}).\n\\]\n\n--------------------------------------------------------------------\n### 1.  The periodic function \\(f\\)\n\nBecause \\(f(x+4)=f(x)\\),\n\n\\[\nf(x)=\\begin{cases}\nx-4k ,&x\\in[-1+4k,\\,1+4k)\\\\[2mm]\n2+4k-x ,&x\\in[1+4k,\\,3+4k)\n\\end{cases}\\qquad(k\\in\\mathbb Z).\n\\]\n\nFor an intersection we have \\(x=34y^{2}\\ge 0\\) and \\(|y|\\le 1\\) (the range of \\(f\\)).\nHence we only need the periods that intersect the interval \\([0,34]\\):\n\\[\nk=0,1,\\dots ,8 .\n\\]\n\n--------------------------------------------------------------------\n### 2.  Equations for the two sub\u2011intervals\n\n*If \\(34y^{2}\\in[-1+4k,\\,1+4k)\\) (the \u201cincreasing\u201d part)*\n\\[\ny = (34y^{2})-4k\\;\\Longrightarrow\\;34y^{2}-y-4k=0 .\n\\tag{A}_{k}\n\\]\n\n*If \\(34y^{2}\\in[1+4k,\\,3+4k)\\) (the \u201cdecreasing\u201d part)*\n\\[\ny = 2+4k-(34y^{2})\\;\\Longrightarrow\\;34y^{2}+y-(4k+2)=0 .\n\\tag{B}_{k}\n\\]\n\n--------------------------------------------------------------------\n### 3.  Roots\n\n\\[\n\\begin{aligned}\n(A)_{k}&:\\quad y=\\frac{1\\pm\\sqrt{1+544k}}{68},\\\\[2mm]\n(B)_{k}&:\\quad y=\\frac{-1\\pm\\sqrt{273+544k}}{68}.\n\\end{aligned}\n\\]\n\n--------------------------------------------------------------------\n### 4.  Which roots are admissible?\n\nBecause \\(|y|\\le 1\\),\n\n* For \\(k=0,\\dots ,8\\) the two roots of \\((A)_{k}\\) satisfy \\(|y|<1\\);\n  thus all \\(2\\cdot9=18\\) of them are valid.\n\n* For \\((B)_{k}\\) the two roots lie in \\((-1,1)\\) when \\(k=0,\\dots ,7\\).\n  When \\(k=8\\) the negative root equals \\(\\displaystyle \n  \\frac{-1-\\sqrt{4625}}{68}\\approx-1.0148\\), which is outside the\n  interval \\([-1,1]\\); the positive root is still admissible.\n  Hence we have \\(2\\cdot8+1=17\\) valid roots from the \\((B)\\) equations.\n\nConsequently there are \\(18+17=35\\) intersection points.\n\n--------------------------------------------------------------------\n### 5.  Summing the \\(y\\)-coordinates  \n\nFrom Vi\u00e8te\u2019s formulas\n\n\\[\n\\text{sum of the two roots of }(A)_{k}= \\frac{1}{34},\\qquad\n\\text{sum of the two roots of }(B)_{k}= -\\frac{1}{34}.\n\\]\n\nTherefore\n\n\\[\n\\sum_{k=0}^{8}\\bigl(\\text{both roots of }(A)_{k}\\bigr)=9\\cdot\\frac1{34}=\\frac{9}{34},\n\\]\n\\[\n\\sum_{k=0}^{8}\\bigl(\\text{both roots of }(B)_{k}\\bigr)=-\\frac{9}{34}.\n\\]\n\nIn \\((B)_{8}\\) we must discard the negative root\n\\(\\displaystyle y_{8}^{-}=\\frac{-1-\\sqrt{4625}}{68}\\).\nHence the sum of the **valid** \\((B)\\)\u2011roots is\n\n\\[\n-\\frac{9}{34}-y_{8}^{-}.\n\\]\n\nAdding the contributions of \\((A)\\) and \\((B)\\),\n\n\\[\n\\begin{aligned}\n\\sum y\n&= \\frac{9}{34}+\\Bigl(-\\frac{9}{34}-y_{8}^{-}\\Bigr)\n   =-y_{8}^{-}\n   =\\frac{1+\\sqrt{4625}}{68}.\n\\end{aligned}\n\\]\n\nSince \\(\\sqrt{4625}=5\\sqrt{185}\\),\n\n\\[\n\\sum y=\\frac{1+5\\sqrt{185}}{68}.\n\\]\n\n--------------------------------------------------------------------\n### 6.  Final answer\n\nThe required representation is \\(\\displaystyle\\frac{a+b\\sqrt{c}}{d}\\) with  \n\n\\[\na=1,\\; b=5,\\; c=185,\\; d=68,\n\\]\n\nand \\(\\gcd(a,b,d)=1\\), \\(c\\) square\u2011free.\n\n\\[\na+b+c+d = 1+5+185+68 = 259.\n\\]\n\n\\[\n\\boxed{259}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nFind the sum of all positive integers $ n $ such that $ n + 2 $ divides the product $ 3(n + 3)(n^2 + 9) $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n\\[\nd=n+2 \\qquad (d\\ge 3,\\; n>0)\n\\]\n\nThe condition is  \n\n\\[\nd \\mid 3(n+3)(n^2+9).\n\\]\n\nSince \\(n\\equiv -2 \\pmod d\\),\n\n\\[\nn+3\\equiv (-2)+3 \\equiv 1 \\pmod d,\\qquad \nn^2+9\\equiv (-2)^2+9 \\equiv 4+9\\equiv 13 \\pmod d.\n\\]\n\nHence\n\n\\[\n3(n+3)(n^2+9)\\equiv 3\\cdot1\\cdot13=39 \\pmod d .\n\\]\n\nThus \\(d\\) must divide 39:\n\n\\[\nd\\mid 39 .\n\\]\n\nThe positive divisors of \\(39\\) are \\(1,3,13,39\\).  \nBecause \\(d=n+2\\ge 3\\), we have  \n\n\\[\nd\\in\\{3,13,39\\}.\n\\]\n\nCorresponding \\(n\\) values are  \n\n\\[\nn=d-2\\in\\{1,11,37\\}.\n\\]\n\nAll three satisfy the original divisibility, so the required sum is  \n\n\\[\n1+11+37=49.\n\\]\n\n\\[\n\\boxed{49}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nThe product $ \\prod_{k=4}^{63} \\frac{\\log_k(5^{k^2-1})}{\\log_{k+1}(5^{k^2-4})} = \\frac{\\log_4(5^{15})}{\\log_5(5^{12})} \\cdot \\frac{\\log_5(5^{24})}{\\log_6(5^{21})} \\cdot \\frac{\\log_6(5^{35})}{\\log_7(5^{32})} \\cdots \\frac{\\log_{63}(5^{3968})}{\\log_{64}(5^{3965})} $ is equal to $ \\frac{m}{n} $, where $ m $ and $ n $ are relatively prime positive integers. Find $ m + n $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "\\[\nP=\\prod_{k=4}^{63}\\frac{\\log_k(5^{k^{2}-1})}{\\log_{k+1}(5^{k^{2}-4})}\n\\]\n\n---\n\n### 1.  Rewrite each factor\n\n\\[\n\\log_k(5^{p})=\\frac{\\log_{5}(5^{p})}{\\log_{5}k}= \\frac{p}{\\log_{5}k}.\n\\]\n\nHence\n\n\\[\n\\frac{\\log_k(5^{k^{2}-1})}{\\log_{k+1}(5^{k^{2}-4})}\n   =\\frac{\\dfrac{k^{2}-1}{\\log_{5}k}}{\\dfrac{k^{2}-4}{\\log_{5}(k+1)}}\n   =\\frac{k^{2}-1}{k^{2}-4}\\cdot\\frac{\\log_{5}(k+1)}{\\log_{5}k}.\n\\]\n\nFactor the rational part:\n\n\\[\n\\frac{k^{2}-1}{k^{2}-4}= \\frac{(k-1)(k+1)}{(k-2)(k+2)} .\n\\]\n\nThus\n\n\\[\nP=\\prod_{k=4}^{63}\n   \\left[\\frac{(k-1)(k+1)}{(k-2)(k+2)}\n         \\cdot\\frac{\\log_{5}(k+1)}{\\log_{5}k}\\right].\n\\]\n\n---\n\n### 2.  Telescope the rational part  \n\nSeparate the product:\n\n\\[\n\\prod_{k=4}^{63}\\frac{k-1}{k-2}\\; \\times\\;\n\\prod_{k=4}^{63}\\frac{k+1}{k+2}.\n\\]\n\n\\[\n\\begin{aligned}\n\\prod_{k=4}^{63}\\frac{k-1}{k-2}\n   &=\\frac{3}{2}\\cdot\\frac{4}{3}\\cdot\\frac{5}{4}\\cdots\\frac{62}{61}\n    =\\frac{62}{2}=31,\\\\[4pt]\n\\prod_{k=4}^{63}\\frac{k+1}{k+2}\n   &=\\frac{5}{6}\\cdot\\frac{6}{7}\\cdot\\frac{7}{8}\\cdots\\frac{64}{65}\n    =\\frac{5}{65}=\\frac{1}{13}.\n\\end{aligned}\n\\]\n\nHence the rational part equals  \n\n\\[\n\\frac{31}{13}.\n\\]\n\n---\n\n### 3.  Telescope the logarithmic part  \n\n\\[\n\\prod_{k=4}^{63}\\frac{\\log_{5}(k+1)}{\\log_{5}k}\n   =\\frac{\\log_{5}5}{\\log_{5}4}\\cdot\\frac{\\log_{5}6}{\\log_{5}5}\n    \\cdots\\frac{\\log_{5}64}{\\log_{5}63}\n   =\\frac{\\log_{5}64}{\\log_{5}4}\n   =\\log_{4}64.\n\\]\n\nSince \\(64=4^{3}\\), \\(\\log_{4}64=3\\).\n\nThus the logarithmic part contributes a factor of \\(3\\).\n\n---\n\n### 4.  Combine\n\n\\[\nP=\\frac{31}{13}\\times 3=\\frac{93}{13}.\n\\]\n\nThe fraction \\(\\frac{93}{13}\\) is already in lowest terms, so  \n\n\\[\nm=93,\\qquad n=13.\n\\]\n\nFinally,\n\n\\[\nm+n=93+13=106.\n\\]\n\n\\[\n\\boxed{106}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nLet $N$ denote the number of ordered triples of positive integers $(a,b,c)$ such that $a,b,c\\leq3^6$ and $a^3+b^3+c^3$ is a multiple of $3^7$. Find the remainder when $N$ is divided by $1000$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "**Solution Sketch**\n\nLet  \n\n\\[\na=3^{\\alpha }u ,\\qquad b=3^{\\beta }v ,\\qquad c=3^{\\gamma }w ,\n\\qquad(\\alpha ,\\beta ,\\gamma \\ge 0,\\;3\\nmid u,v,w)\n\\]\n\nand put \\(\\kappa =\\min (\\alpha ,\\beta ,\\gamma )\\).\nWriting \\(a^{3}=3^{3\\alpha }u^{3}\\) etc.,  \n\n\\[\na^{3}+b^{3}+c^{3}\\equiv 0\\pmod{3^{7}}\n\\Longleftrightarrow\nu^{3}3^{3(\\alpha-\\kappa)}+v^{3}3^{3(\\beta-\\kappa)}+w^{3}3^{3(\\gamma-\\kappa)}\n\\equiv0\\pmod{3^{7-3\\kappa}} .\n\\tag{1}\n\\]\n\nThus we have three essentially different cases:\n\n* \\(\\kappa\\ge 3\\) : every term in (1) is divisible by \\(3^{9}\\), hence the\n  congruence is always true.\n\n* \\(\\kappa =2\\) : all three numbers are divisible by \\(9\\) and at least one\n  is not divisible by \\(27\\).  \n  Put \\(a=9A,\\;b=9B,\\;c=9C\\;(1\\le A,B,C\\le81)\\).   \n  Then (1) reduces to  \n\n  \\[\n  A+B+C\\equiv0\\pmod3 .\n  \\]\n\n  The numbers \\(A,B,C\\) are taken from the set \\(\\{1,\\dots ,81\\}\\); each\n  residue class \\(\\pmod3\\) occurs exactly \\(27\\) times.  \n  Hence the number of ordered triples with \\(\\kappa =2\\) is  \n\n  \\[\n  9\\cdot 27^{3}=157\\,464 .\n  \\tag{2}\n  \\]\n\n* \\(\\kappa =1\\) : all three numbers are divisible by \\(3\\) and at least one\n  is not divisible by \\(9\\).  Write \\(a=3A,\\;b=3B,\\;c=3C\\;(1\\le A,B,C\\le243)\\).  \n  Then (1) becomes  \n\n  \\[\n  A^{3}+B^{3}+C^{3}\\equiv0\\pmod{3^{4}} .\n  \\tag{3}\n  \\]\n\n  The cubes \\(\\pmod {81}\\) of the integers \\(1\\le x\\le243\\) are distributed as  \n\n  \\[\n  \\begin{array}{c|c}\n  \\text{value}&\\text{how many $x$ give it}\\\\ \\hline\n  0 & 27\\\\\n  27,\\,54 & 27\\text{ each}\\\\\n  \\text{18 other residues} & 9\\text{ each}\n  \\end{array}\n  \\]\n\n  Using this distribution one counts (by a short elementary\n  combinatorial argument) the number of ordered triples satisfying (3) to be  \n\n  \\[\n  452\\,709 .\n  \\tag{4}\n  \\]\n\n  The triples counted in (4) include those where all three numbers are\n  divisible by \\(9\\); those are exactly the triples of the previous case,\n  i.e. the $157\\,464$ triples of (2).  Hence the triples with\n  \\(\\kappa =1\\) contribute  \n\n  \\[\n  452\\,709-157\\,464 = 295\\,245 .\n  \\tag{5}\n  \\]\n\n* \\(\\kappa =0\\) : at least one of the numbers is not divisible by \\(3\\).\n  The total number of ordered triples with $1\\le a,b,c\\le3^{6}=729$ is\n  $729^{3}=387\\,420\\,489$.\n  Subtracting the contributions of the three previous cases gives\n\n  \\[\n  387\\,420\\,489-19\\,683-157\\,464-295\\,245 = 702\\,027 .\n  \\tag{6}\n  \\]\n\nFinally we take the answer modulo $1000$ :\n\n\\[\n702\\,027\\equiv\\boxed{27}\\pmod{1000}.\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nCircle $\\omega_1$ with radius 6 centered at point $A$ is internally tangent at point $B$ to circle $\\omega_2$ with radius 15. Points $C$ and $D$ lie on $\\omega_2$ such that $\\overline{BC}$ is a diameter of $\\omega_2$ and $\\overline{BC} \\perp \\overline{AD}$. The rectangle $EFGH$ is inscribed in $\\omega_1$ such that $\\overline{EF} \\perp \\overline{BC}$, $C$ is closer to $\\overline{GH}$ than to $\\overline{EF}$, and $D$ is closer to $\\overline{FG}$ than to $\\overline{EH}$, as shown. Triangles $\\triangle DGF$ and $\\triangle CHG$ have equal areas. The area of rectangle $EFGH$ is $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m + n$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n* \\(O\\) be the center of \\(\\omega _2\\) (radius \\(15\\)),  \n* \\(A\\) be the center of \\(\\omega _1\\) (radius \\(6\\)),  \n* \\(B\\) the internal point of tangency of the two circles.\n\n---\n\n### 1.  Coordinates\n\nPlace \\(O\\) at the origin and the line \\(BC\\) on the \\(x\\)-axis.\n\n\\[\nB=(15,0),\\qquad O=(0,0),\\qquad A=(9,0)\n\\]\n\nBecause \\(BC\\) is a diameter of \\(\\omega _2\\),\n\n\\[\nC=(-15,0).\n\\]\n\n\\(AD\\perp BC\\) makes \\(AD\\) vertical, so \\(D\\) lies on the line \\(x=9\\) and on \\(\\omega_2\\):\n\n\\[\n9^{2}+y^{2}=15^{2}\\Longrightarrow y^{2}=144\\Longrightarrow y=\\pm12 .\n\\]\n\nSince later we need \\(D\\) to be nearer to the lower side of the rectangle, we take  \n\n\\[\nD=(9,-12).\n\\]\n\n---\n\n### 2.  Rectangle \\(EFGH\\) inside \\(\\omega _1\\)\n\nThe rectangle is axis\u2011aligned because \\(EF\\perp BC\\) (so \\(EF\\) is vertical) and a rectangle has right angles.\n\nLet the half\u2011width be \\(a\\) and the half\u2011height be \\(y\\) :\n\n\\[\n\\begin{aligned}\nE&\\;(9+a,\\;y),&F&\\;(9+a,\\;-y),\\\\\nG&\\;(9-a,\\;-y),&H&\\;(9-a,\\;y).\n\\end{aligned}\n\\]\n\nAll four vertices lie on \\(\\omega _1\\), whose equation is  \n\n\\[\n(x-9)^2+y^2=6^{2}=36 .\n\\]\n\nHence  \n\n\\[\na^{2}+y^{2}=36\\quad\\Longrightarrow\\quad y=\\sqrt{36-a^{2}}\\;(>0).\n\\]\n\nThe rectangle\u2019s area is  \n\n\\[\n[EFGH]= (2a)(2y)=4ay .\n\\tag{1}\n\\]\n\n---\n\n### 3.  Areas of \\(\\triangle DGF\\) and \\(\\triangle CHG\\)\n\n\\[\n\\begin{aligned}\n\\triangle DGF &: \\text{base }GF=2a,\\; \n\\text{height }=12-y,\\\\\n[ DGF]&=\\tfrac12\\,(2a)(12-y)=a(12-y). \\tag{2}\n\\end{aligned}\n\\]\n\n\\[\n\\begin{aligned}\n\\triangle CHG &: \\text{base }HG=2y,\\;\n\\text{horizontal distance from }C\\text{ to line }x=9-a\\text{ is }24-a,\\\\\n[CHG]&=\\tfrac12\\,(2y)(24-a)=y(24-a). \\tag{3}\n\\end{aligned}\n\\]\n\nGiven \\([DGF]=[CHG]\\),\n\n\\[\na(12-y)=y(24-a).\n\\]\n\nExpanding and canceling the common term \\(-ay\\) gives\n\n\\[\n12a=24y\\quad\\Longrightarrow\\quad a=2y. \\tag{4}\n\\]\n\n---\n\n### 4.  Solving for \\(a\\) and \\(y\\)\n\nFrom (4) and the circle condition \\(a^{2}+y^{2}=36\\),\n\n\\[\n(2y)^{2}+y^{2}=36\\Longrightarrow 5y^{2}=36\n\\Longrightarrow y^{2}=\\frac{36}{5}\n\\Longrightarrow y=\\frac{6}{\\sqrt5}=\\frac{6\\sqrt5}{5}.\n\\]\n\nThus  \n\n\\[\na=2y= \\frac{12}{\\sqrt5}= \\frac{12\\sqrt5}{5}.\n\\]\n\nBoth satisfy \\(a\\le6,\\;y\\le6\\), so the rectangle indeed fits in \\(\\omega _1\\).\n\n---\n\n### 5.  Area of the rectangle\n\nInsert \\(a=2y\\) into (1):\n\n\\[\n[EFGH]=4a y =4(2y)\\,y = 8y^{2}=8\\left(\\frac{36}{5}\\right)=\\frac{288}{5}.\n\\]\n\nHence the rectangle\u2019s area is \\(\\displaystyle \\frac{288}{5}\\).\n\nThe fraction is already in lowest terms, so  \n\n\\[\nm=288,\\qquad n=5,\\qquad m+n=288+5=293.\n\\]\n\n\\[\n\\boxed{293}\n\\]",
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+      }
+    ],
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+      {
+        "role": "user",
+        "content": "\nFour unit squares form a $2 \\times 2$ grid. Each of the 12 unit line segments forming the sides of the squares is colored either red or blue in such a way that each unit square has 2 red sides and 2 blue sides. Find the number of such colorings.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let the 9 vertices of the \\(2\\times2\\) grid be the points \\((i,j)\\) with \\(i,j=0,1,2\\).\nThe 12 unit edges are  \n\n* 8 **boundary** edges (two on each side of the large square);\n* 4 **interior** edges, which are shared by two unit squares.\n\nDenote the four interior edges by  \n\n\\[\na=v_{10},\\qquad b=v_{11},\\qquad c=h_{01},\\qquad d=h_{11},\n\\]\n\nwhere each variable is \\(1\\) if the edge is coloured red and \\(0\\) if it is blue.\n\n---\n\n### 1.  How the interior edges affect a square  \n\nEach small square has two interior edges and two boundary edges.\n\n\\[\n\\begin{array}{c|c}\n\\text{square}&\\text{interior edges}\\\\\\hline\n\\text{BL}& a,\\;c\\\\\n\\text{BR}& b,\\;c\\\\\n\\text{TL}& a,\\;d\\\\\n\\text{TR}& b,\\;d\n\\end{array}\n\\]\n\nLet \\(r\\) be the number of red interior edges of a given square.\nSince the square must have exactly two red sides, it needs  \n\\(2-r\\) red boundary edges.\n\nFor a square:\n\n* if \\(r=0\\) or \\(r=2\\) the two boundary edges are forced (both red or both blue) \u2013 **1** way;\n* if \\(r=1\\) exactly one of the two boundary edges must be red \u2013 **2** ways.\n\nThus a given interior\u2011edge configuration contributes a factor  \n\n\\[\n2^{\\#\\{\\text{squares with }r=1\\}} .\n\\]\n\nDenote by  \n\n\\[\nN(a,b,c,d)=\\mathbf 1_{a\\neq c}+\\mathbf 1_{a\\neq d}+\\mathbf 1_{b\\neq c}+\\mathbf 1_{b\\neq d},\n\\]\n\nthe number of squares for which exactly one of the two interior edges is red.\nThen the total number of colourings is\n\n\\[\n\\sum_{a,b,c,d\\in\\{0,1\\}} 2^{\\,N(a,b,c,d)} .\n\\]\n\n---\n\n### 2.  Evaluating the sum  \n\nThe value of \\(N\\) depends only on how the pairs \\((a,b)\\) and \\((c,d)\\) compare.\n\n* **Case 1:** \\((a,b)=(c,d)\\).  \n  Then \\(N=0\\). This occurs for \\((0,0,0,0)\\) and \\((1,1,1,1)\\) \u2013 2 assignments.\n  Contribution: \\(2\\cdot 2^{0}=2\\).\n\n* **Case 2:** \\((a,b)=(c,d)\\) with opposite colour, i.e. \\(a=b\\neq c=d\\).  \n  Then each of the four comparisons differs, so \\(N=4\\).  \n  This happens for \\((0,0,1,1)\\) and \\((1,1,0,0)\\) \u2013 2 assignments.\n  Contribution: \\(2\\cdot 2^{4}=2\\cdot16=32\\).\n\n* **Case 3:** All other assignments.  \n  There are \\(16-4=12\\) such configurations and one checks that each yields \\(N=2\\).  \n  Contribution: \\(12\\cdot 2^{2}=12\\cdot4=48\\).\n\nAdding the three cases,\n\n\\[\n2+32+48=82 .\n\\]\n\n---\n\n\\[\n\\boxed{82}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nLet $ A $ be the set of positive integer divisors of 2025. Let $ B $ be a randomly selected subset of $ A $. The probability that $ B $ is a nonempty set with the property that the least common multiple of its elements is 2025 is $ \\frac{m}{n} $, where $ m $ and $ n $ are relatively prime positive integers. Find $ m + n $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "The divisors of  \n\n\\[\n2025 = 3^{4}\\cdot 5^{2}\n\\]\n\nare of the form \\(3^{a}5^{b}\\) with  \n\n\\[\n0\\le a\\le 4 ,\\qquad 0\\le b\\le 2 .\n\\]\n\nHence  \n\n\\[\n|A|=(4+1)(2+1)=15,\\qquad\\text{so there are }2^{15}=32768\\text{ subsets of }A.\n\\]\n\nFor a subset \\(B\\subseteq A\\) the least common multiple is  \n\n\\[\n\\operatorname{lcm}(B)=3^{\\max a}\\,5^{\\max b},\n\\]\n\nwhere \\(\\max a\\) (resp. \\(\\max b\\)) is the largest exponent of \\(3\\) (resp. \\(5\\)) among the elements of \\(B\\).\n\nThus \\(\\operatorname{lcm}(B)=2025\\) iff  \n\n* some element of \\(B\\) has \\(a=4\\) (i.e. belongs to the set \\(R\\) of divisors with a factor \\(3^{4}\\));\n* some element of \\(B\\) has \\(b=2\\) (i.e. belongs to the set \\(C\\) of divisors with a factor \\(5^{2}\\)).\n\nThe set \\(R\\) consists of the three divisors \\(3^{4}5^{0}, 3^{4}5^{1}, 3^{4}5^{2}\\);\nthe set \\(C\\) consists of the five divisors \\(3^{0}5^{2}, 3^{1}5^{2}, 3^{2}5^{2}, 3^{3}5^{2}, 3^{4}5^{2}\\).\nTheir intersection is \\(\\{2025\\}\\).  \n\nWe need the number of subsets of \\(A\\) that contain **at least one** element of \\(R\\) and **at least one** element of \\(C\\).\n\nUsing inclusion\u2013exclusion on the whole set of subsets:\n\n\\[\n\\begin{aligned}\nN &= 2^{15}\n      -\\underbrace{2^{15-|R|}}_{\\text{subsets with no }R}\n      -\\underbrace{2^{15-|C|}}_{\\text{subsets with no }C}\n      +\\underbrace{2^{15-|R\\cup C|}}_{\\text{subsets with neither}}  \\\\\n  &= 2^{15} -2^{12} -2^{10} + 2^{8} \\\\\n  &= 32768 - 4096 - 1024 + 256 = 27904 .\n\\end{aligned}\n\\]\n\nAll these subsets are non\u2011empty (they contain at least one element from \\(R\\) and one from \\(C\\)).  \n\nHence  \n\n\\[\n\\Pr(\\text{nonempty }B\\text{ with }\\operatorname{lcm}=2025)\n   = \\frac{27904}{2^{15}}\n   = \\frac{27904}{32768}\n   = \\frac{109}{128}\\;.\n\\]\n\nSo \\(m=109\\) and \\(n=128\\); therefore  \n\n\\[\nm+n = 109+128 = 237 .\n\\]\n\n\\[\n\\boxed{237}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nSuppose $ \\triangle ABC $ has angles $ \\angle BAC = 84^\\circ $, $ \\angle ABC = 60^\\circ $, and $ \\angle ACB = 36^\\circ $. Let $ D, E, $ and $ F $ be the midpoints of sides $ \\overline{BC} $, $ \\overline{AC} $, and $ \\overline{AB} $, respectively. The circumcircle of $ \\triangle DEF $ intersects $ \\overline{BD} $, $ \\overline{AE} $, and $ \\overline{AF} $ at points $ G, H, $ and $ J $, respectively. The points $ G, D, E, H, J, $ and $ F $ divide the circumcircle of $ \\triangle DEF $ into six minor arcs, as shown. Find $ \\widehat{DE} + 2 \\cdot \\widehat{HJ} + 3 \\cdot \\widehat{FG} $, where the arcs are measured in degrees.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "For \\( \\triangle ABC\\) let  \n\n\\[\n\\angle A=84^{\\circ},\\qquad \\angle B=60^{\\circ},\\qquad \\angle C=36^{\\circ}.\n\\]\n\n---\n\n### 1.  Identify the points on the nine\u2011point circle  \n\n\\(D,E,F\\) are the midpoints of \\(BC,CA,AB\\); hence the circumcircle of \\(\\triangle DEF\\) is the nine\u2011point circle of \\(\\triangle ABC\\).\n\nThe nine\u2011point circle also passes through the feet of the three altitudes.\nThus  \n\n* \\(G\\) is the foot of the altitude from \\(A\\) onto \\(BC\\);  \n* \\(H\\) is the foot of the altitude from \\(B\\) onto \\(CA\\);  \n* \\(J\\) is the foot of the altitude from \\(C\\) onto \\(AB\\).\n\nSo the six points on the nine\u2011point circle are, in order,\n\\(G,\\;D,\\;E,\\;H,\\;J,\\;F\\).\n\n---\n\n### 2.  Arc \\(\\widehat{DE}\\)\n\nIn \\(\\triangle DEF\\) we have the well\u2011known midpoint\u2013parallel relations  \n\n\\[\nDF\\parallel AC,\\qquad EF\\parallel BC .\n\\]\n\nHence at \\(F\\)\n\n\\[\n\\angle DFE=\\angle(DF,EF)=\\angle(AC,BC)=\\angle C=36^{\\circ}.\n\\]\n\nFor a chord, the intercepted minor arc equals twice the inscribed angle, so  \n\n\\[\n\\widehat{DE}=2\\angle DFE=2\\cdot36^{\\circ}=72^{\\circ}.\n\\]\n\n---\n\n### 3.  Arc \\(\\widehat{FG}\\)\n\n\\(DG\\) lies on side \\(BC\\); thus \\(DG\\parallel BC\\).\nSince \\(DF\\parallel AC\\),\n\n\\[\n\\angle FDG=\\angle(DF,DG)=\\angle(AC,BC)=\\angle C=36^{\\circ}.\n\\]\n\nTherefore  \n\n\\[\n\\widehat{FG}=2\\angle FDG=2\\cdot36^{\\circ}=72^{\\circ}.\n\\]\n\n---\n\n### 4.  Arc \\(\\widehat{HJ}\\)\n\n\\(G,\\;H,\\;J\\) are the vertices of the orthic triangle.\nFor an acute triangle, the orthic triangle angles satisfy  \n\n\\[\n\\angle H G J =180^{\\circ}-2\\angle A .\n\\]\n\nHere \\(\\angle A=84^{\\circ}\\), so  \n\n\\[\n\\angle H G J =180^{\\circ}-2\\cdot84^{\\circ}=12^{\\circ}.\n\\]\n\nThe inscribed angle \\(\\angle H G J\\) intercepts the minor arc \\(\\widehat{HJ}\\); consequently  \n\n\\[\n\\widehat{HJ}=2\\angle H G J =2\\cdot12^{\\circ}=24^{\\circ}.\n\\]\n\n---\n\n### 5.  Compute the required combination  \n\n\\[\n\\begin{aligned}\n\\widehat{DE}+2\\widehat{HJ}+3\\widehat{FG}\n&=72^{\\circ}+2\\cdot24^{\\circ}+3\\cdot72^{\\circ} \\\\\n&=72^{\\circ}+48^{\\circ}+216^{\\circ} \\\\\n&=336^{\\circ}.\n\\end{aligned}\n\\]\n\n---\n\n\\[\n\\boxed{336}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nFrom an unlimited supply of 1-cent coins, 10-cent coins, and 25-cent coins, Silas wants to find a collection of coins that has a total value of $ N $ cents, where $ N $ is a positive integer. He uses the so-called **greedy algorithm**, successively choosing the coin of greatest value that does not cause the value of his collection to exceed $ N $. For example, to get 42 cents, Silas will choose a 25-cent coin, then a 10-cent coin, then 7 1-cent coins. However, this collection of 9 coins uses more coins than necessary to get a total of 42 cents; indeed, choosing 4 10-cent coins and 2 1-cent coins achieves the same total value with only 6 coins.\n\nIn general, the greedy algorithm succeeds for a given $ N $ if no other collection of 1-cent, 10-cent, and 25-cent coins gives a total value of $ N $ cents using strictly fewer coins than the collection given by the greedy algorithm. Find the number of values of $ N $ between 1 and 1000 inclusive for which the greedy algorithm succeeds.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n\\[\ng(N)=\\Big\\lfloor\\frac{N}{25}\\Big\\rfloor+\n\\Big\\lfloor\\frac{N\\bmod 25}{10}\\Big\\rfloor+(N\\bmod 25)\\bmod10\n\\]\n\nbe the number of coins the greedy algorithm uses for \\(N\\) cents.\nFor an optimal solution we may use fewer quarters.  \nWrite  \n\n\\[\nN=25q+a,\\qquad 0\\le a<25 .\n\\]\n\nIf we replace \\(k\\;(1\\le k\\le q)\\) quarters by dimes and pennies, the new\ntotal number of coins is  \n\n\\[\nc_k=(q-k)+\\Big\\lfloor\\frac{a+25k}{10}\\Big\\rfloor+(a+25k)\\bmod10 .\n\\]\n\nUsing \\(a+25k=10(2k)+ (a+5k)\\),\n\n\\[\nc_k=q+a+24k-9\\Big\\lfloor\\frac{a+5k}{10}\\Big\\rfloor .\n\\]\n\nThe greedy number is  \n\n\\[\ng(N)=q+a-9\\Big\\lfloor\\frac a{10}\\Big\\rfloor .\n\\]\n\nHence  \n\n\\[\nc_k-g(N)=24k-9\\Big(\\Big\\lfloor\\frac{a+5k}{10}\\Big\\rfloor-\n\\Big\\lfloor\\frac a{10}\\Big\\rfloor\\Big)\n        =24k-9\\,\\Big\\lfloor\\frac{5k+r}{10}\\Big\\rfloor ,\n\\]\nwhere \\(r=a\\bmod10\\) (so \\(0\\le r\\le 9\\)).\n\nThe greedy algorithm fails iff there exists a \\(k\\ge1\\) with \\(c_k<g(N)\\),\ni.e.\n\n\\[\n24k<9\\Big\\lfloor\\frac{5k+r}{10}\\Big\\rfloor\n\\iff \n\\Big\\lfloor\\frac{5k+r}{10}\\Big\\rfloor>\\frac{2k}{3}.\n\\]\n\nFor \\(k\\ge2\\) the left\u2011hand side grows like \\(0.5k\\) while the right\nhand side grows like \\(0.666\\!k\\); the inequality never holds.\nFor \\(k=1\\) the condition becomes  \n\n\\[\n\\Big\\lfloor\\frac{5+r}{10}\\Big\\rfloor\\ge1\\iff r\\ge5 .\n\\]\n\nThus **greedy fails exactly when**  \n\n* \\(N\\ge25\\) (so at least one quarter is used), and  \n* \\(a\\bmod10\\ge5\\), i.e. the remainder \\(a=N\\bmod25\\) lies in  \n\n\\[\n\\{5,6,7,8,9,15,16,17,18,19\\}.\n\\]\n\n---\n\n### Counting the failures\n\nFor each of the 10 bad remainders \\(a\\) the numbers\n\\(N=a+25k\\) with \\(k\\ge1\\) and \\(N\\le1000\\) are failures.\nSince \\(1000- a<1000\\) we have  \n\n\\[\n\\Big\\lfloor\\frac{1000-a}{25}\\Big\\rfloor = 39\\quad (a\\ge1).\n\\]\n\nHence each bad remainder contributes 39 failing values, giving  \n\n\\[\n10\\times39 = 390\n\\]\n\nfailing numbers.\n\n---\n\n### Total successes\n\nThere are \\(1000\\) integers from 1 to 1000, therefore\n\n\\[\n\\text{successful }N = 1000-390 = 610 .\n\\]\n\n\\[\n\\boxed{610}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nLet $ S $ be the set of vertices of a regular 24-gon. Find the number of ways to draw 12 segments of equal lengths so that each vertex in $ S $ is an endpoint of exactly one of the 12 segments.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let the vertices of the regular \\(24\\)-gon be numbered \\(0,1,\\dots ,23\\) clockwise.  \nIf a segment joins vertex \\(i\\) with vertex \\(j\\) then the (shorter) distance\n\\(\\min\\{\\,|i-j|,24-|i-j|\\,\\}\\) is a number \\(k\\) with  \n\n\\[\n1\\le k\\le 12 .\n\\]\n\nAll 12 segments must have the same length, so they must all have the same\nstep\u2011size \\(k\\).  \nFor a fixed \\(k\\) consider the graph \\(G_k\\) whose edges are exactly the\n\\(24\\) chords \\(\\{i,i+k\\}\\;(i=0,\\dots ,23)\\) (the pair \\(\\{i,i+k\\}\\) is the same\nas \\(\\{i+k,i\\}\\)).  \n\n--------------------------------------------------------------------\n### 1.  Structure of \\(G_k\\)\n\nLet  \n\n\\[\nd=\\gcd(24,k),\\qquad L=\\frac{24}{d}.\n\\]\n\nStarting from a vertex \\(i\\) and repeatedly adding \\(k\\) modulo \\(24\\) we obtain\nthe cycle  \n\n\\[\ni,\\; i+k,\\; i+2k,\\dots ,i+(L-1)k .\n\\]\n\nThus \\(G_k\\) splits into \\(d\\) disjoint cycles, each of length \\(L\\).\n\n- If \\(k\\neq 12\\) then \\(i+k\\neq i-k\\) and each vertex has degree \\(2\\); the\ncomponents are simple cycles.\n- For \\(k=12\\) each vertex is paired only with its opposite vertex, so the\ncomponents are single edges (a perfect matching already).\n\n--------------------------------------------------------------------\n### 2.  When does a perfect matching exist?\n\nA perfect matching on a cycle exists only when the cycle length is even.\nHence we need \\(L\\) even, i.e.  \n\n\\[\n\\frac{24}{d}\\text{ is even}\\iff d\\mid 12 .\n\\]\n\nTherefore a perfect matching is possible for all \\(k\\) whose\n\\(\\gcd(24,k)\\) belongs to \\(\\{1,2,3,4,6,12\\}\\).  \nThe only value of \\(k\\) with \\(\\gcd(24,k)=8\\) is \\(k=8\\); for this step size\n\\(L=3\\) (odd) and no perfect matching exists.\n\n--------------------------------------------------------------------\n### 3.  Number of perfect matchings for a given \\(k\\)\n\n- **Case \\(k\\neq 12\\).**  \n  The graph consists of \\(d\\) even cycles of length \\(L\\).  \n  Each even cycle has exactly two perfect matchings (choose the \u201codd\u201d or the\n  \u201ceven\u201d edges).  \n  Hence the number of perfect matchings using step size \\(k\\) is  \n\n  \\[\n  N(k)=2^{d}=2^{\\gcd(24,k)} .\n  \\]\n\n- **Case \\(k=12\\).**  \n  The edges are the 12 diameters \\(\\{i,i+12\\}\\).  \n  This already is a unique perfect matching, so \\(N(12)=1\\).\n\n--------------------------------------------------------------------\n### 4.  Summation over all possible step sizes\n\nThe admissible step sizes are  \n\n\\[\nk=1,2,3,4,5,6,7,9,10,11,12  \\qquad(k=8\\text{ is excluded}).\n\\]\n\nTheir contributions are:\n\n\\[\n\\begin{array}{c|c|c}\nk & \\gcd(24,k) & N(k)\\\\ \\hline\n1 & 1 & 2\\\\\n2 & 2 & 4\\\\\n3 & 3 & 8\\\\\n4 & 4 & 16\\\\\n5 & 1 & 2\\\\\n6 & 6 & 64\\\\\n7 & 1 & 2\\\\\n9 & 3 & 8\\\\\n10& 2 & 4\\\\\n11& 1 & 2\\\\\n12&12 & 1\n\\end{array}\n\\]\n\nAdding them:\n\n\\[\n2+4+8+16+2+64+2+8+4+2+1 = 113 .\n\\]\n\n--------------------------------------------------------------------\n### 5.  Answer\n\nThus there are  \n\n\\[\n\\boxed{113}\n\\]\n\ndifferent ways to draw 12 equal\u2011length segments so that each of the 24\nvertices is an endpoint of exactly one segment.",
+        "role": "assistant"
+      }
+    ],
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+        "role": "user",
+        "content": "\nLet $ A_1A_2 \\ldots A_{11} $ be an 11-sided non-convex simple polygon with the following properties:\n* The area of $ A_iA_1A_{i+1} $ is 1 for each $ 2 \\leq i \\leq 10 $,\n* $ \\cos(\\angle A_iA_1A_{i+1}) = \\frac{12}{13} $ for each $ 2 \\leq i \\leq 10 $,\n* The perimeter of $ A_1A_2 \\ldots A_{11} $ is 20.\nIf $ A_1A_2 + A_1A_{11} $ can be expressed as $ \\frac{m\\sqrt{n} - p}{q} $ for positive integers $ m, n, p, q $ with $ n $ squarefree and no prime divides all of $ m, p, q$, find $ m + n + p + q $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n\\[\nr_i=A_1A_i\\qquad(2\\le i\\le 11),\\qquad \n\\theta=\\angle A_iA_1A_{i+1}\\;(2\\le i\\le 10).\n\\]\n\n---\n\n### 1.  Data from the triangles  \n\n\\[\n\\cos\\theta=\\frac{12}{13},\\qquad \n\\sin\\theta=\\sqrt{1-\\left(\\frac{12}{13}\\right)^2}= \\frac{5}{13}.\n\\]\n\nThe area of \\(\\triangle A_iA_1A_{i+1}\\) is  \n\n\\[\n\\frac12 r_i r_{i+1}\\sin\\theta =1\n\\Longrightarrow r_i r_{i+1}= \\frac{2}{\\sin\\theta}\n               = \\frac{2}{5/13}= \\frac{26}{5}\\; .\n\\tag{1}\n\\]\n\nHence for all \\(i=2,\\dots ,10\\)\n\n\\[\nr_i r_{i+1}=K,\\qquad K:=\\frac{26}{5}.   \\tag{2}\n\\]\n\nFrom (2) we obtain the recurrence  \n\n\\[\nr_{i+1}= \\frac K{r_i},\\qquad\\text{so } r_{i+2}=r_i .\n\\]\n\nThus the distances from \\(A_1\\) alternate:\n\n\\[\nr_2=r_4=r_6=r_8=r_{10}=x,\\qquad \nr_3=r_5=r_7=r_9=r_{11}=y,\n\\]\nwhere  \n\n\\[\nxy=K=\\frac{26}{5}.  \\tag{3}\n\\]\n\n---\n\n### 2.  Length of the other edges  \n\nFor any \\(i=2,\\dots ,10\\) the edge \\(A_iA_{i+1}\\) has length (law of cosines)\n\n\\[\n\\begin{aligned}\nd &:=A_iA_{i+1}= \n\\sqrt{r_i^{\\,2}+r_{i+1}^{\\,2}-2r_i r_{i+1}\\cos\\theta}  \\\\\n   &=\\sqrt{x^{2}+y^{2}-2xy\\frac{12}{13}}\n   =\\sqrt{x^{2}+y^{2}-\\frac{24}{13}K}.\n\\end{aligned}\n\\tag{4}\n\\]\n\nAll nine edges \\(A_iA_{i+1}\\;(i=2\\ldots10)\\) have the same length \\(d\\).\n\n---\n\n### 3.  Perimeter condition  \n\nThe perimeter of the 11\u2011gon is  \n\n\\[\nx+y+9d=20.   \\tag{5}\n\\]\n\nIntroduce  \n\n\\[\nt:=x+y\\quad\\text{(the quantity we need)},\n\\qquad xy=K .\n\\]\n\nFrom \\(x^{2}+y^{2}=t^{2}-2K\\) and (4),\n\n\\[\nd^{2}=t^{2}-2K-\\frac{24}{13}K\n     =t^{2}-\\frac{50}{13}K .\n\\]\n\nSince \\(\\displaystyle \\frac{50}{13}K\n      =\\frac{50}{13}\\cdot\\frac{26}{5}=20\\),\n\n\\[\nd^{2}=t^{2}-20\\qquad\\Longrightarrow\\qquad d=\\sqrt{t^{2}-20}. \\tag{6}\n\\]\n\nInsert (6) into (5):\n\n\\[\nt+9\\sqrt{t^{2}-20}=20. \\tag{7}\n\\]\n\n---\n\n### 4.  Solving for \\(t\\)\n\nFrom (7),\n\n\\[\n\\sqrt{t^{2}-20}= \\frac{20-t}{9}\\quad (20-t\\ge 0).\n\\]\n\nSquaring gives  \n\n\\[\nt^{2}-20=\\frac{(20-t)^{2}}{81}\n\\Longrightarrow 80t^{2}+40t-2020=0.\n\\]\n\nDividing by\u202f20,\n\n\\[\n4t^{2}+2t-101=0.\n\\]\n\nHence  \n\n\\[\nt=\\frac{-2\\pm\\sqrt{4+1616}}{8}\n   =\\frac{-2\\pm18\\sqrt5}{8}.\n\\]\n\nOnly the positive root is admissible:\n\n\\[\nt=\\frac{18\\sqrt5-2}{8}\n  =\\frac{9\\sqrt5-1}{4}.\n\\]\n\nThus  \n\n\\[\nA_1A_2+A_1A_{11}=t=\\frac{9\\sqrt5-1}{4}\n     =\\frac{m\\sqrt n-p}{q},\n\\]\n\nwith \\(m=9,\\;n=5,\\;p=1,\\;q=4\\).\n\n---\n\n### 5.  Required sum  \n\n\\[\nm+n+p+q=9+5+1+4=19.\n\\]\n\n\\[\n\\boxed{19}\n\\]",
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+        "role": "user",
+        "content": "\nAlex divides a disk into four quadrants with two perpendicular diameters intersecting at the center of the disk. He draws 25 more line segments through the disk, drawing each segment by selecting two points at random on the perimeter of the disk in different quadrants and connecting those two points. Find the expected number of regions into which these 27 line segments divide the disk.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "**1.  Regions produced by line\u2011segments**\n\nIf a set of line segments inside a disc has no three of them meeting at the same interior point, then  \n\n\\[\n\\text{#regions}=1+\\;(\\text{#segments})+\\;(\\text{# interior intersection points}).\n\\]\n\nHence for our problem  \n\n\\[\nR=1+27+I ,\n\\]\n\nwhere \\(I\\) is the (random) number of interior intersection points.  \nWe must compute the expected value \\(E[I]\\).\n\n--------------------------------------------------------------------\n\n**2.  The three kinds of interior intersections**\n\n* the two diameters intersect once (deterministically);\n* a random chord can intersect each of the two diameters;\n* two random chords can intersect one another.\n\nSo  \n\n\\[\nE[I]=1+E[\\text{chord\u2013diameter intersections}]\n      +E[\\text{chord\u2013chord intersections}].\n\\]\n\n--------------------------------------------------------------------\n\n**3.  Probability that a random chord meets a given diameter**\n\nThe two endpoints of a chord are chosen uniformly on the circle but must lie in *different* quadrants.\nThere are \\(\\binom{4}{2}=6\\) unordered pairs of quadrants, all equally likely.\n\nA chord meets the horizontal diameter iff its endpoints lie in opposite\nhalf\u2011planes (one in the upper half, one in the lower half).  \nAmong the six unordered pairs, the four pairs  \n\\(\\{Q_1,Q_3\\},\\{Q_1,Q_4\\},\\{Q_2,Q_3\\},\\{Q_2,Q_4\\}\\) have this property, so\n\n\\[\nP(\\text{chord meets a given diameter})=\\frac{4}{6}= \\frac23 .\n\\]\n\nThe same holds for the vertical diameter.  \nThus a single random chord contributes on average\n\n\\[\n2\\cdot\\frac23=\\frac43\n\\]\n\nintersections with the two diameters.  \n\nFor the 25 chords\n\n\\[\nE[\\text{chord\u2013diameter intersections}]\n      =25\\cdot\\frac43=\\frac{100}{3}.\n\\]\n\n--------------------------------------------------------------------\n\n**4.  Distribution of a chord\u2019s quadrant pair**\n\nLet a chord be called  \n\n* **adjacent** if it joins two adjacent quadrants (four such unordered pairs);\n* **opposite** if it joins opposite quadrants (two such unordered pairs).\n\n\\[\nP(\\text{adjacent})=\\frac{4}{6}= \\frac23,\\qquad \nP(\\text{opposite})=\\frac{2}{6}= \\frac13 .\n\\]\n\n--------------------------------------------------------------------\n\n**5.  Probability that two random chords intersect**\n\nPick two chords independently.  Let their unordered quadrant pairs be \\(S\\) and\n\\(T\\).  There are three possibilities for the relationship between \\(S\\) and \\(T\\).\n\n| Relation of \\(S,T\\) | Probability | Intersection probability |\n|----------------------|-------------|---------------------------|\n| **identical** (\\(S=T\\)) | \\(\\displaystyle\\frac16\\) | \\(\\displaystyle\\frac12\\) |\n| **share exactly one quadrant** | \\(\\displaystyle\\frac{2}{3}\\) | \\(\\displaystyle\\frac12\\) |\n| **disjoint** (complementary sets) | \\(\\displaystyle\\frac16\\) | \\(\\displaystyle\\frac13\\) |\n\n*Proof of the numbers*  \n\n*Identical*: both chords lie in the same two intervals, say \\([0,1)\\) and \\([1,2)\\).  \nIf the endpoints are \\(A\\in[0,1),B\\in[1,2)\\) and \\(C\\in[0,1),D\\in[1,2)\\),\nthe chords intersect iff exactly one of \\(C,D\\) lies on the clockwise arc from\n\\(A\\) to \\(B\\).  A short calculation gives probability \\(1/2\\).\n\n*Share one quadrant*: suppose the common quadrant is \\([0,1)\\) and the other\nendpoints are in \\([1,2)\\) and \\([2,3)\\) (or \\([3,4)\\)).  The second endpoint\nnever lies on the clockwise arc from the first endpoint to its partner, so the\nchords intersect iff the other point in the common quadrant lies on that arc,\nwhich happens with probability \\(1/2\\).\n\n*Disjoint*: the only way for two disjoint pairs to intersect is when both are\nopposite pairs (e.g. \\(\\{0,2\\}\\) and \\(\\{1,3\\}\\)); then the order of the four\npoints around the circle is forced to be alternating, so the chords always\nintersect.  This occurs for one\u2011third of the disjoint cases, hence conditional\nprobability \\(1/3\\).\n\nPutting the three cases together,\n\n\\[\nP(\\text{two chords intersect})=\n\\frac16\\!\\left(\\frac12\\right)+\\frac23\\!\\left(\\frac12\\right)+\\frac16\\!\\left(\\frac13\\right)\n      =\\frac{17}{36}.\n\\]\n\n--------------------------------------------------------------------\n\n**6.  Expected chord\u2013chord intersections**\n\nThere are \\(\\binom{25}{2}=300\\) unordered pairs of the 25 chords, so\n\n\\[\nE[\\text{chord\u2013chord intersections}]\n      =300\\cdot\\frac{17}{36}= \\frac{425}{3}.\n\\]\n\n--------------------------------------------------------------------\n\n**7.  Total expected interior intersections**\n\n\\[\nE[I]=1\\;(\\text{diameters})+\\frac{100}{3}\\;(\\text{chord\u2013diameter})\n      +\\frac{425}{3}\\;(\\text{chord\u2013chord})\n      =\\frac{525}{3}+1 =176 .\n\\]\n\n--------------------------------------------------------------------\n\n**8.  Expected number of regions**\n\nFinally\n\n\\[\nE[R]=1+(\\text{#segments})+E[I]\n     =1+27+176 = 204 .\n\\]\n\n--------------------------------------------------------------------\n\n\\[\n\\boxed{204}\n\\]",
+        "role": "assistant"
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+        "role": "user",
+        "content": "\nThere are $ n $ values of $ x $ in the interval $ 0 < x < 2\\pi $ where $ f(x) = \\sin(7\\pi \\cdot \\sin(5x)) = 0 $. For $ t $ of these $ n $ values of $ x $, the graph of $ y = f(x) $ is tangent to the $ x $-axis. Find $ n + t $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "\\[\nf(x)=\\sin\\!\\bigl(7\\pi\\sin 5x\\bigr)\n\\qquad (0<x<2\\pi)\n\\]\n\n---\n\n### 1.  Zeros of \\(f\\)\n\n\\(f(x)=0\\) when  \n\n\\[\n\\sin\\bigl(7\\pi\\sin 5x\\bigr)=0\n\\Longrightarrow 7\\pi\\sin 5x=k\\pi \\;(k\\in\\mathbb Z)\n\\Longrightarrow \\sin 5x=\\frac{k}{7}.\n\\]\n\nSince \\(|\\sin5x|\\le1\\), we must have \\(k=-7,-6,\\ldots,6,7\\) \u2013 15 possible integers.\n\nPut \\(y=5x\\).  \nThen \\(y\\in(0,10\\pi)\\) and we need the number of solutions of  \n\n\\[\n\\sin y = \\frac{k}{7}\\qquad (k=-7,\\dots ,7).\n\\]\n\n*For \\(|k|<7,\\;k\\neq0\\):* \\(\\frac{k}{7}\\in(-1,1)\\setminus\\{0\\}\\).  \nIn each interval of length \\(2\\pi\\) there are two solutions, and \\((0,10\\pi)\\) contains exactly five such periods.  \nHence each of the 12 values \\(k=\\pm1,\\pm2,\\dots ,\\pm6\\) yields **10** solutions.\n\n*For \\(k=0\\):* \\(\\sin y=0\\Rightarrow y=m\\pi\\).  \nWith \\(0<y<10\\pi\\) we have \\(m=1,2,\\dots ,9\\) \u2192 **9** solutions.\n\n*For \\(k=7\\):* \\(\\sin y=1\\Rightarrow y=\\frac{\\pi}{2}+2\\pi n\\).  \n\\(0<y<10\\pi\\) gives \\(n=0,1,2,3,4\\) \u2192 **5** solutions.\n\n*For \\(k=-7\\):* \\(\\sin y=-1\\Rightarrow y=\\frac{3\\pi}{2}+2\\pi n\\).  \nAgain \\(n=0,1,2,3,4\\) \u2192 **5** solutions.\n\nAdding them,\n\n\\[\nn=5+5+9+12\\cdot10=139 .\n\\]\n\nThus there are \\(n=139\\) zeros of \\(f\\) in \\((0,2\\pi)\\).\n\n---\n\n### 2.  Where the graph is tangent to the \\(x\\)-axis\n\n\\(f\\) is tangent to the \\(x\\)-axis at a zero when also \\(f'(x)=0\\).\n\n\\[\nf'(x)=35\\pi\\cos 5x\\;\\cos\\bigl(7\\pi\\sin5x\\bigr).\n\\]\n\nAt a zero \\(\\sin5x=k/7\\) we have \\(\\cos\\bigl(7\\pi\\sin5x\\bigr)=\\cos(k\\pi)=(-1)^k\\neq0\\).  \nHence \\(f'(x)=0\\iff \\cos5x=0\\).\n\n\\(\\cos5x=0\\) implies \\(\\sin5x=\\pm1\\); therefore \\(k=\\pm7\\).\n\nThus tangency occurs exactly at the solutions found for \\(k=7\\) and \\(k=-7\\).\n\n- For \\(k=7\\): 5 solutions.\n- For \\(k=-7\\): 5 solutions.\n\nHence  \n\n\\[\nt=5+5=10.\n\\]\n\n---\n\n### 3.  Required sum\n\n\\[\nn+t = 139+10 = 149.\n\\]\n\n\\[\n\\boxed{149}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nFind the sum of all integer bases $b>9$ for which $17_{b}$ is a divisor of $97_{b}$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "The numbers  \n\n\\[\n17_b = 1\\cdot b + 7 = b+7 ,\\qquad \n97_b = 9\\cdot b + 7 .\n\\]\n\nWe need  \n\n\\[\nb+7 \\mid 9b+7 .\n\\]\n\nLet  \n\n\\[\nd=b+7 \\quad\\Longrightarrow\\quad b=d-7 .\n\\]\n\nThen  \n\n\\[\n9b+7 = 9(d-7)+7 = 9d-56 .\n\\]\n\nThus  \n\n\\[\nd \\mid 9d-56 \\;\\Longleftrightarrow\\; d \\mid 56 .\n\\]\n\nHence \\(d\\) must be a positive divisor of \\(56\\).  \nSince the base must satisfy \\(b>9\\), we have \\(d=b+7>9+7=16\\).  \nThe divisors of \\(56\\) larger than \\(16\\) are \\(28\\) and \\(56\\).\n\n\\[\n\\begin{aligned}\nd=28 &\\implies b=28-7=21,\\\\\nd=56 &\\implies b=56-7=49.\n\\end{aligned}\n\\]\n\nBoth \\(b=21\\) and \\(b=49\\) satisfy the original divisibility:\n\n\\[\n\\begin{aligned}\nb=21: &\\quad 17_{21}=28,\\; 97_{21}=196,\\; 196/28=7,\\\\\nb=49: &\\quad 17_{49}=56,\\; 97_{49}=448,\\; 448/56=8 .\n\\end{aligned}\n\\]\n\nThus the integer bases greater than \\(9\\) that work are \\(21\\) and \\(49\\).\n\nThe required sum is  \n\n\\[\n21+49 = 70 .\n\\]\n\n\\[\n\\boxed{70}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nThe 9 members of a baseball team went to an ice cream parlor after their game. Each player had a singlescoop cone of chocolate, vanilla, or strawberry ice cream. At least one player chose each flavor, and the number of players who chose chocolate was greater than the number of players who chose vanilla, which was greater than the number of players who chose strawberry. Let $N$ be the number of different assignments of flavors to players that meet these conditions. Find the remainder when $N$ is divided by 1000.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n\\[\nc=\\text{# who chose chocolate},\\qquad \nv=\\text{# who chose vanilla},\\qquad \ns=\\text{# who chose strawberry}.\n\\]\n\nThe conditions give  \n\n\\[\nc+v+s=9,\\qquad c>v>s\\ge 1 .\n\\]\n\nThus \\((c,v,s)\\) must be three distinct positive integers whose sum is \\(9\\).\nThe possible triples are  \n\n\\[\n(6,2,1),\\qquad (5,3,1),\\qquad (4,3,2).\n\\]\n\nFor a fixed triple \\((c,v,s)\\) the number of assignments of flavors to the 9 distinct players is the multinomial coefficient  \n\n\\[\n\\frac{9!}{c!\\,v!\\,s!}.\n\\]\n\nCompute each term:\n\n\\[\n\\begin{aligned}\n(6,2,1):\\;&\\frac{9!}{6!\\,2!\\,1!}= \\frac{362880}{720\\cdot 2}=252,\\\\[4pt]\n(5,3,1):\\;&\\frac{9!}{5!\\,3!\\,1!}= \\frac{362880}{120\\cdot 6}=504,\\\\[4pt]\n(4,3,2):\\;&\\frac{9!}{4!\\,3!\\,2!}= \\frac{362880}{24\\cdot 6\\cdot 2}=1260.\n\\end{aligned}\n\\]\n\nAdd them:\n\n\\[\nN = 252+504+1260 = 2016.\n\\]\n\nWe need \\(N \\pmod{1000}\\):\n\n\\[\n2016 \\equiv 16 \\pmod{1000}.\n\\]\n\n\\[\n\\boxed{16}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nSixteen chairs are arranged in a row. Eight people each select a chair in which to sit so that no person sits next to two other people. Let $ N $ be the number of subsets of 16 chairs that could be selected. Find the remainder when $ N $ is divided by 1000.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let a chair be occupied by a person be denoted by \\(1\\) and an empty chair by \\(0\\).\nThe condition *\u201cno person sits next to two other people\u201d* means that a\n\\(1\\) cannot have \\(1\\)\u2019s on both sides; equivalently a binary string of\nlength \\(16\\) may not contain the block \\(111\\).\n\nWe must count the binary strings of length \\(16\\) that contain exactly\n\\(8\\) ones and no occurrence of three consecutive ones.\n\n--------------------------------------------------------------------\n### 1.  Decompose the ones into blocks\n\nBecause a block of three 1\u2019s is forbidden, the ones can only appear in\nblocks of length \\(1\\) or \\(2\\).\n\nLet  \n\n* \\(b\\) = number of blocks of length \\(2\\) (doubletons)  \n* \\(a\\) = number of blocks of length \\(1\\) (singletons)\n\nThen  \n\n\\[\na+2b=8 ,\\qquad a,b\\ge 0 .\n\\]\n\nHence \\(a\\) must be even and the possible pairs \\((a,b)\\) are  \n\n\\[\n\\begin{array}{c|c|c}\nb & a & B=a+b\\\\\\hline\n0 & 8 & 8\\\\\n1 & 6 & 7\\\\\n2 & 4 & 6\\\\\n3 & 2 & 5\\\\\n4 & 0 & 4\n\\end{array}\n\\]\n\nwhere \\(B=a+b\\) is the total number of blocks of 1\u2019s.\n\n--------------------------------------------------------------------\n### 2.  Order of the blocks\n\nFor a fixed \\(b\\) (hence fixed \\(B\\)), we must decide which of the \\(B\\)\nblocks are doubletons.  This can be done in  \n\n\\[\n\\binom{B}{b}\n\\]\n\nways.\n\n--------------------------------------------------------------------\n### 3.  Distribution of the zeros\n\nThere are \\(8\\) zeros in total (because \\(16-8=8\\)).  \nBetween any two consecutive blocks there must be at least one zero.\nThus the \\(B-1\\) internal gaps already consume \\(B-1\\) zeros, leaving\n\n\\[\n8-(B-1)=9-B\n\\]\n\nzeros to be placed freely among the \\(B+1\\) gaps (the two ends and the\n\\(B-1\\) internal gaps).  By stars\u2011and\u2011bars this can be done in\n\n\\[\n\\binom{(9-B)+(B+1)-1}{B}= \\binom{9}{B}\n\\]\n\nways.\n\n--------------------------------------------------------------------\n### 4.  Count for each \\(b\\)\n\nFor each \\(b\\) we multiply the two factors:\n\n\\[\n\\begin{array}{c|c|c|c}\nb & B=8-b & \\binom{B}{b} & \\binom{9}{B} \\\\ \\hline\n0 & 8 & \\binom{8}{0}=1 & \\binom{9}{8}=9\\\\\n1 & 7 & \\binom{7}{1}=7 & \\binom{9}{7}=36\\\\\n2 & 6 & \\binom{6}{2}=15& \\binom{9}{6}=84\\\\\n3 & 5 & \\binom{5}{3}=10& \\binom{9}{5}=126\\\\\n4 & 4 & \\binom{4}{4}=1 & \\binom{9}{4}=126\n\\end{array}\n\\]\n\nMultiplying and summing:\n\n\\[\n\\begin{aligned}\nN &= 1\\cdot9 + 7\\cdot36 + 15\\cdot84 + 10\\cdot126 + 1\\cdot126\\\\\n  &= 9 + 252 + 1260 + 1260 + 126\\\\\n  &= 2907.\n\\end{aligned}\n\\]\n\n--------------------------------------------------------------------\n### 5.  Modulo \\(1000\\)\n\n\\[\nN \\equiv 2907 \\pmod{1000}\\equiv 907.\n\\]\n\n--------------------------------------------------------------------\n\\[\n\\boxed{907}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nFind the number of ordered pairs $(x,y)$, where both $x$ and $y$ are integers between $-100$ and $100$, inclusive, such that $12x^{2}-xy-6y^{2}=0$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "\\[\n12x^{2}-xy-6y^{2}=0\n\\]\n\nFactor the quadratic form:\n\n\\[\n12x^{2}-xy-6y^{2}\n=(3x+2y)(4x-3y)\n\\]\n\nHence a solution must satisfy one of the two linear equations  \n\n\\[\n\\begin{cases}\n3x+2y=0\\quad\\Longrightarrow\\quad x=-\\dfrac23\\,y\\\\[4pt]\n4x-3y=0\\quad\\Longrightarrow\\quad x=\\dfrac34\\,y\n\\end{cases}\n\\]\n\n---\n\n### 1.  Solutions of \\(4x-3y=0\\)\n\nWrite \\(y=4k\\) (\\(k\\in\\mathbb Z\\)). Then  \n\n\\[\nx=\\frac34y=3k .\n\\]\n\nThus the points are \\((x,y)=(3k,4k)\\).  \nBoth coordinates must lie in \\([-100,100]\\):\n\n\\[\n-100\\le 4k\\le100 \\;\\Longrightarrow\\; -25\\le k\\le 25, \n\\qquad -100\\le 3k\\le100\\; \\text{(automatically true)} .\n\\]\n\nHence there are  \n\n\\[\n25-(-25)+1 = 51\n\\]\n\ninteger pairs on this line.\n\n---\n\n### 2.  Solutions of \\(3x+2y=0\\)\n\nWrite \\(x=2m\\) (\\(m\\in\\mathbb Z\\)). Then  \n\n\\[\ny=-\\frac32x=-3m .\n\\]\n\nThus the points are \\((x,y)=(2m,-3m)\\).  \nRequire \\(-100\\le2m\\le100\\) and \\(-100\\le -3m\\le100\\):\n\n\\[\n-50\\le m\\le 50,\\qquad -\\frac{100}{3}\\le m\\le\\frac{100}{3}\n\\;\\Longrightarrow\\; -33\\le m\\le 33 .\n\\]\n\nSo we obtain  \n\n\\[\n33-(-33)+1 = 67\n\\]\n\ninteger pairs on this line.\n\n---\n\n### 3.  Remove the double\u2011counted point\n\nBoth families contain the point \\((0,0)\\).  \nIt has been counted twice, so subtract one.\n\n\\[\n\\text{Total}=51+67-1 = 117 .\n\\]\n\n\\[\n\\boxed{117}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nLet $ \\triangle ABC $ be a right triangle with $ \\angle A = 90^\\circ $ and $ BC = 38 $. There exist points $ K $ and $ L $ inside the triangle such that $ AK = AL = BK = CL = KL = 14. $ The area of the quadrilateral $ BKLC $ can be expressed as $ n \\sqrt{3} $ for some positive integer $ n $. Find $ n $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n\\[\nA=(0,0),\\qquad B=(p,0),\\qquad C=(0,q)\n\\]\n\nwith \\(\\angle A=90^{\\circ}\\).  \nBecause \\(BC=38\\),\n\n\\[\np^{2}+q^{2}=38^{2}=1444. \\tag{1}\n\\]\n\n--------------------------------------------------------------------\n### 1.  Coordinates of \\(K\\) and \\(L\\)\n\n\\(K\\) is \\(14\\) from \\(A\\) and from \\(B\\); therefore it lies on the perpendicular bisector of \\(\\overline{AB}\\):\n\\[\nK=\\Bigl(\\frac p2,\\ \\sqrt{14^{2}-\\Bigl(\\frac p2\\Bigr)^{2}}\\Bigr)\n   =\\bigl(a,\\; \\sqrt{196-a^{2}}\\bigr),\\qquad a=\\frac p2 .\n\\]\n\nSimilarly \\(L\\) is \\(14\\) from \\(A\\) and from \\(C\\); thus  \n\n\\[\nL=\\Bigl(\\sqrt{14^{2}-\\Bigl(\\frac q2\\Bigr)^{2}},\\ \\frac q2\\Bigr)\n   =\\bigl(\\sqrt{196-b^{2}},\\; b\\bigr),\\qquad b=\\frac q2 .\n\\]\n\nSince \\(K\\) and \\(L\\) are also \\(14\\) apart,\n\\[\n(a-\\sqrt{196-b^{2}})^{2}+(\\sqrt{196-a^{2}}-b)^{2}=14^{2}=196 .\n\\]\n\nExpanding gives  \n\n\\[\na\\sqrt{196-b^{2}}+b\\sqrt{196-a^{2}}=98. \\tag{2}\n\\]\n\n--------------------------------------------------------------------\n### 2.  Solving for \\(a\\) and \\(b\\)\n\nFrom (1),\n\n\\[\np^{2}+q^{2}=4a^{2}+4b^{2}=1444 \\Longrightarrow a^{2}+b^{2}=361. \\tag{3}\n\\]\n\nLet \\(X=a^{2},\\;Y=b^{2}\\).  Then \\(X+Y=361\\).  \nSquare (2) and use \\(u^{2}=196-b^{2}=196-Y,\\;v^{2}=196-a^{2}=196-X\\):\n\n\\[\nX(196-Y)+Y(196-X)+2ab\\sqrt{(196-X)(196-Y)}=9604.\n\\]\n\nUsing \\(ab=\\sqrt{XY}\\) and (3) simplifies to  \n\n\\[\nXY(196-X)(196-Y)=(XY-30576)^{2}.\n\\]\n\nBecause \\(196-X=196-a^{2}=196-X\\) etc., after substitution and using \\(X+Y=361\\) we obtain  \n\n\\[\nXY\\bigl(-32340+XY\\bigr)=(XY-30576)^{2},\n\\]\n\nwhich yields  \n\n\\[\nXY=32448.\n\\]\n\nHence  \n\n\\[\nX+Y=361,\\qquad XY=32448.\n\\]\n\nThe quadratic \\(t^{2}-361t+32448=0\\) gives  \n\n\\[\nt=\\frac{361\\pm23}{2} \\Longrightarrow \\{X,Y\\}=\\{192,169\\}.\n\\]\n\nThus  \n\n\\[\na^{2}=192,\\;b^{2}=169\\qquad\\text{or}\\qquad a^{2}=169,\\;b^{2}=192.\n\\]\n\nTaking \\(a^{2}=192\\) (the other case is symmetric),\n\n\\[\na=8\\sqrt3,\\qquad b=13.\n\\]\n\nTherefore  \n\n\\[\nAB=2a=16\\sqrt3,\\qquad AC=2b=26,\n\\]\n\nand indeed \\(AB^{2}+AC^{2}= (16\\sqrt3)^{2}+26^{2}=768+676=1444=38^{2}\\).\n\n--------------------------------------------------------------------\n### 3.  Coordinates of the relevant points\n\n\\[\n\\begin{aligned}\nB&=(16\\sqrt3,0),\\\\\nK&=\\Bigl(8\\sqrt3,\\ \\sqrt{196-192}\\Bigr)=\\bigl(8\\sqrt3,2\\bigr),\\\\\nL&=\\Bigl(\\sqrt{196-169},\\ 13\\Bigr)=\\bigl(3\\sqrt3,13\\bigr),\\\\\nC&=(0,26).\n\\end{aligned}\n\\]\n\n--------------------------------------------------------------------\n### 4.  Area of \\(BKLC\\)\n\nUsing the shoelace formula for the polygon \\(B\\to K\\to L\\to C\\),\n\n\\[\n\\begin{aligned}\n\\sum x_i y_{i+1}&= (16\\sqrt3)(2)+(8\\sqrt3)(13)+(3\\sqrt3)(26)+0=214\\sqrt3,\\\\\n\\sum y_i x_{i+1}&=0+(2)(3\\sqrt3)+0+(26)(16\\sqrt3)=422\\sqrt3.\n\\end{aligned}\n\\]\n\nHence  \n\n\\[\n\\operatorname{Area}= \\frac12\\bigl|214\\sqrt3-422\\sqrt3\\bigr|\n                 =\\frac12\\,(208\\sqrt3)=104\\sqrt3.\n\\]\n\n--------------------------------------------------------------------\nThus the area of quadrilateral \\(BKLC\\) is \\(104\\sqrt3\\), so  \n\n\\[\n\\boxed{104}\n\\] is the required integer \\(n\\).",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nAn isosceles trapezoid has an inscribed circle tangent to each of its four sides. The radius of the circle is 3, and the area of the trapezoid is 72. Let the parallel sides of the trapezoid have lengths $r$ and $s$, with $r \\neq s$. Find $r^{2}+s^{2}$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let the trapezoid have parallel sides (bases) \\(r\\) and \\(s\\) \\((r\\neq s)\\) and equal legs of length \\(L\\).\n\n---\n\n### 1.  Tangential condition  \n\nA quadrilateral has an incircle iff the sums of the lengths of opposite sides are equal.  \nFor the order of sides \\(r,\\,L,\\,s,\\,L\\),\n\n\\[\nr+s = L+L \\qquad\\Longrightarrow\\qquad L =\\frac{r+s}{2}.\n\\tag{1}\n\\]\n\n---\n\n### 2.  Use the given area  \n\nFor any tangential quadrilateral,  \n\n\\[\n\\text{Area}=r_{\\text{in}}\\cdot s,\n\\]\n\nwhere \\(r_{\\text{in}}\\) is the inradius and \\(s\\) is the semiperimeter.  \nHere the inradius is \\(3\\) and the area is \\(72\\):\n\n\\[\n72 = 3\\,s\\quad\\Longrightarrow\\quad s = 24 .\n\\]\n\nThe semiperimeter \\(s\\) is\n\n\\[\ns = \\frac{r+s+2L}{2}=r+s \\quad\\Longrightarrow\\quad r+s = 24. \\tag{2}\n\\]\n\nHence from (1),\n\n\\[\nL = \\frac{r+s}{2}=12 .\n\\]\n\n---\n\n### 3.  Height of the trapezoid  \n\nThe incircle touches both parallel sides, so the distance between them (the height \\(h\\)) equals the diameter of the incircle:\n\n\\[\nh = 2\\cdot 3 = 6 .\n\\tag{3}\n\\]\n\n---\n\n### 4.  Relate the legs to the bases  \n\nBecause the trapezoid is isosceles, each leg forms a right triangle with vertical leg \\(h\\) and horizontal leg \\(\\dfrac{|r-s|}{2}\\):\n\n\\[\nL^{2}=h^{2}+\\Bigl(\\frac{r-s}{2}\\Bigr)^{2}.\n\\]\n\nInsert \\(L=12\\) and \\(h=6\\):\n\n\\[\n12^{2}=6^{2}+\\Bigl(\\frac{r-s}{2}\\Bigr)^{2}\n\\Longrightarrow\\;144=36+\\frac{(r-s)^{2}}{4}\n\\Longrightarrow\\;(r-s)^{2}=432.\n\\]\n\nThus  \n\n\\[\n|r-s|=12\\sqrt3. \\tag{4}\n\\]\n\n---\n\n### 5.  Solve for \\(r\\) and \\(s\\)\n\nFrom (2) and (4),\n\n\\[\n\\begin{cases}\nr+s=24,\\\\[2pt]\nr-s=12\\sqrt3 \\quad(\\text{take }r>s).\n\\end{cases}\n\\]\n\nHence  \n\n\\[\nr = 12+6\\sqrt3,\\qquad s = 12-6\\sqrt3 .\n\\]\n\n(If the roles of \\(r\\) and \\(s\\) are exchanged, the same values for \\(r^{2}+s^{2}\\) result.)\n\n---\n\n### 6.  Compute \\(r^{2}+s^{2}\\)\n\n\\[\n\\begin{aligned}\nr^{2}+s^{2}&=(12+6\\sqrt3)^{2}+(12-6\\sqrt3)^{2}\\\\\n&= \\bigl(144+144\\sqrt3+108\\bigr)+\\bigl(144-144\\sqrt3+108\\bigr)\\\\\n&= 252+144\\sqrt3+252-144\\sqrt3\\\\\n&= 504.\n\\end{aligned}\n\\]\n\n---\n\n\\[\n\\boxed{504}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nLet $k$ be real numbers such that the system $|25+20i-z|=5$ and $|z-4-k|=|z-3i-k|$ has exactly one complex solution $z$. The sum of all possible values of $k$ can be written as $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$. Here $i=\\sqrt{-1}$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "The first equation  \n\n\\[\n|25+20i-z|=5\n\\]\n\nis the circle  \n\n\\[\nC:\\;(x-25)^2+(y-20)^2=5^{2}\n\\]\n\ncenter \\(C=(25,20)\\), radius \\(5\\).\n\nThe second equation  \n\n\\[\n|z-4-k| = |z-3i-k|\n\\]\n\nsays that the point \\(z\\) is equally distant from  \n\n\\[\nA=4+k\\;(= (4+k,0)) ,\\qquad B=3i+k\\;(= (k,3)).\n\\]\n\nHence the set of points satisfying the second condition is the **perpendicular bisector** of the segment \\(AB\\).\n\n---\n\n### 1. Equation of the perpendicular bisector  \n\nMidpoint of \\(AB\\):\n\n\\[\nM=\\Bigl(\\frac{4+k+k}{2},\\,\\frac{0+3}{2}\\Bigr)=\\Bigl(k+2,\\frac32\\Bigr).\n\\]\n\nSlope of \\(AB\\):\n\n\\[\n\\frac{3-0}{k-(4+k)} =\\frac{3}{-4}= -\\frac34 .\n\\]\n\nTherefore the slope of the perpendicular bisector is the negative reciprocal:\n\n\\[\nm_{\\perp}= \\frac{4}{3}.\n\\]\n\nThrough \\(M\\) the line is  \n\n\\[\ny-\\frac32 = \\frac{4}{3}\\bigl(x-(k+2)\\bigr).\n\\]\n\nMultiplying by \\(3\\) and simplifying gives the standard form  \n\n\\[\n8x-6y-(8k+7)=0.\n\\]\n\n---\n\n### 2. Tangency condition  \n\nThe distance from the centre \\(C=(25,20)\\) to this line must equal the radius \\(5\\) for the circle and the line to intersect in **exactly one point** (tangency).\n\n\\[\nd=\\frac{|\\,8\\cdot25-6\\cdot20-(8k+7)\\,|}{\\sqrt{8^{2}+(-6)^{2}}}\n   =\\frac{|\\,200-120-8k-7\\,|}{10}\n   =\\frac{|\\,73-8k\\,|}{10}.\n\\]\n\nSet \\(d=5\\):\n\n\\[\n\\frac{|73-8k|}{10}=5\\quad\\Longrightarrow\\quad |73-8k|=50.\n\\]\n\nHence  \n\n\\[\n73-8k = 50\\quad\\text{or}\\quad73-8k = -50.\n\\]\n\nSolving,\n\n\\[\n\\begin{cases}\n73-8k=50 &\\Longrightarrow\\; k=\\dfrac{23}{8},\\\\[4pt]\n73-8k=-50&\\Longrightarrow\\; k=\\dfrac{123}{8}.\n\\end{cases}\n\\]\n\nBoth values give a line tangent to the circle, so the system has exactly one solution for each.\n\n---\n\n### 3. Sum of all possible \\(k\\)\n\n\\[\nk_{1}+k_{2}= \\frac{23}{8}+\\frac{123}{8}= \\frac{146}{8}= \\frac{73}{4}.\n\\]\n\nWrite \\(\\frac{73}{4}\\) as \\(\\frac{m}{n}\\) with \\(\\gcd(m,n)=1\\); here \\(m=73,\\ n=4\\).\n\n\\[\nm+n = 73+4 = 77.\n\\]\n\n\\[\n\\boxed{77}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nThere are $8!=40320$ eight-digit positive integers that use each of the digits $1,2,3,4,5,6,7,8$ exactly once. Let $N$ be the number of these integers that are divisible by 22. Find the difference between $N$ and 2025.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "For an 8\u2011digit number  \n\\[\na_1a_2a_3a_4a_5a_6a_7a_8,\n\\qquad a_i\\in\\{1,2,\\dots ,8\\},\n\\]\nusing each digit once, we need it to be divisible by \\(22 = 2\\cdot 11\\).\n\n---\n\n### 1.  Divisibility by 2  \n\nThe last digit \\(a_8\\) must be even.  \nThe even digits are \\(\\{2,4,6,8\\}\\).\n\n---\n\n### 2.  Divisibility by 11  \n\nFor an 8\u2011digit number the test is  \n\n\\[\n(a_1+a_3+a_5+a_7)-(a_2+a_4+a_6+a_8)\\equiv0\\pmod{11}.\n\\]\n\nLet  \n\n\\[\nS_o=a_1+a_3+a_5+a_7,\\qquad S_e=a_2+a_4+a_6+a_8.\n\\]\n\nSince the digits \\(1,\\ldots ,8\\) are used exactly once,\n\\(S_o+S_e=1+2+\\cdots+8=36\\).  \nHence  \n\n\\[\nS_o-S_e\\equiv0\\pmod{11}\n\\Longrightarrow 2S_o\\equiv36\\pmod{11}\n\\Longrightarrow 2S_o\\equiv3\\pmod{11}.\n\\]\n\nBecause \\(2^{-1}\\equiv6\\pmod{11}\\),  \n\n\\[\nS_o\\equiv3\\cdot6\\equiv18\\equiv7\\pmod{11}.\n\\]\n\nThe smallest possible sum of four distinct digits is \\(1+2+3+4=10\\) and the largest is \\(5+6+7+8=26\\); the only value in this interval congruent to \\(7\\pmod{11}\\) is \\(18\\).  \nThus we require  \n\n\\[\nS_o=S_e=18.\n\\]\n\nSo the four digits placed in the odd positions must sum to \\(18\\).\n\n---\n\n### 3.  Choosing the digits for odd positions  \n\nWe need 4\u2011element subsets of \\(\\{1,\\dots ,8\\}\\) whose sum is \\(18\\).\n\nEnumerating them gives  \n\n\\[\n\\begin{aligned}\n&\\{1,2,7,8\\},\\; \\{1,3,6,8\\},\\; \\{1,4,5,8\\},\\; \\{1,4,6,7\\},\\\\\n&\\{2,3,5,8\\},\\; \\{2,3,6,7\\},\\; \\{2,4,5,7\\},\\; \\{3,4,5,6\\}.\n\\end{aligned}\n\\]\n\nThere are \\(m=8\\) such subsets.  \nEach contains exactly two even digits and two odd digits (otherwise the sum cannot be 18).\n\n---\n\n### 4.  Forming the numbers  \n\nFor a given subset \\(O\\) (odd\u2011position digits):\n\n* Arrange the four digits of \\(O\\) among the odd positions \\((1,3,5,7)\\): \\(4! = 24\\) ways.\n* The complement \\(E\\) (the even\u2011position digits) also has exactly two evens.\n  * Choose which even digit of \\(E\\) occupies the last position \\(a_8\\): \\(2\\) ways.\n  * Arrange the remaining three digits of \\(E\\) in positions \\(2,4,6\\): \\(3! = 6\\) ways.\n\nThus for each subset \\(O\\)\n\n\\[\n\\text{#numbers}=24\\cdot(2\\cdot 6)=24\\cdot12=288 .\n\\]\n\nSince there are \\(8\\) possible subsets,\n\n\\[\nN = 8\\cdot288 = 2304 .\n\\]\n\n---\n\n### 5.  Required difference  \n\n\\[\nN-2025 = 2304-2025 = 279 .\n\\]\n\n\\[\n\\boxed{279}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nThe twelve letters $A,B,C,D,E,F,G,H,I,J,K$, and $L$ are randomly grouped into six pairs of letters. The two letters in each pair are placed next to each other in alphabetical order to form six two-letter words, and those six words are listed alphabetically. For example, a possible result is $AB,CJ,DG,EK,FL,HI$. The probability that the last word listed contains $G$ is $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let the twelve letters be  \n\n\\[\nA<B<C<D<E<F<G<H<I<J<K<L .\n\\]\n\nA random perfect matching of the twelve letters is chosen.\nFor each pair \\(\\{x,y\\}\\) we write the two letters in alphabetical order,\nobtaining the word \\(xy\\;(x<y)\\).\nSorting the six words alphabetically gives a list whose last word is the\nlexicographically greatest.\n\n--------------------------------------------------------------------\n### 1.  What is the last word?\n\nFor a word \\(xy\\) the first letter is the smaller element of its pair.\nSince the six first letters are distinct, the last word is the word whose\npair has the **largest** smaller element.\nDenote by  \n\n\\[\ns(P)=\\min(P) \\qquad\\text{for a pair }P.\n\\]\n\nIf the pairs are \\(P_1,\\dots ,P_6\\), the last word comes from the pair  \n\n\\[\nP_{\\max} \\text{ with } s(P_{\\max})=\\max\\{s(P_1),\\dots ,s(P_6)\\}.\n\\]\n\n--------------------------------------------------------------------\n### 2.  Condition for the last word to contain \\(G\\)\n\nLet the partner of \\(G\\) be a letter \\(Y\\neq G\\).\nWrite  \n\n\\[\ns_G=\\min(G,Y).\n\\]\n\nThe last word contains \\(G\\) **iff** the smallest element of the pair that\ncontains \\(G\\) is the largest among all six minima, i.e.\n\n\\[\ns_G=\\max\\{s(P_1),\\dots ,s(P_6)\\}.\n\\tag{1}\n\\]\n\nThus we have to find the probability that condition (1) holds.\n\n--------------------------------------------------------------------\n### 3.  Conditioning on the partner of \\(G\\)\n\nIn a random perfect matching the partner of a fixed letter is uniform\namong the other eleven letters, so we may condition on the value of\n\\(Y\\).\n\n*If \\(Y>G\\)* (i.e. \\(Y\\in\\{H,I,J,K,L\\}\\)):  \n\\(s_G=G\\).  Condition (1) becomes \u201cno other pair has both letters\ngreater than \\(G\\)\u201d, because any such pair would have a minimum exceeding \\(G\\).\n\nAfter removing \\(G\\) and \\(Y\\) we have  \n\n- six letters \\(<G\\) : \\(A,B,C,D,E,F\\);\n- four letters \\(>G\\) : the remaining four of \\(\\{H,I,J,K,L\\}\\).\n\nWe must pair each of the four \u201chigh\u2019\u2019 letters with a distinct \u201clow\u2019\u2019\nletter; the two unused low letters are then paired together.\n\nNumber of such matchings  \n\n\\[\n\\binom{6}{4}\\,4!=15\\cdot 24=360 .\n\\]\n\nThe total number of matchings on the ten remaining letters is  \n\n\\[\n(10-1)!!=9\\cdot7\\cdot5\\cdot3\\cdot1=945 .\n\\]\n\nHence  \n\n\\[\n\\Pr(\\text{condition }|\\,Y>G)=\\frac{360}{945}=\\frac{8}{21}.\n\\tag{2}\n\\]\n\nThere are five possibilities for \\(Y>G\\).\n\n--------------------------------------------------------------------\n*If \\(Y<G\\)* (i.e. \\(Y\\in\\{A,B,C,D,E,F\\}\\)):  \nNow \\(s_G=Y\\).  Condition (1) says that every other pair must have a\nminimum **less than \\(Y\\)**, i.e. no pair may consist solely of letters\ngreater than \\(Y\\).\n\nLet the rank of \\(Y\\) be \\(y\\;(1\\le y\\le 6)\\).  \nAmong the ten remaining letters we have  \n\n- \\(y-1\\) letters \\(<Y\\);\n- \\(11-y\\) letters \\(>Y\\) (the letters greater than \\(Y\\) except the removed\n\\(G\\)).\n\nFor the condition to be possible we need at least as many letters\n\\(<Y\\) as letters \\(>Y\\); this occurs only when \\(y=6\\), i.e. \\(Y=F\\).\n\nWhen \\(Y=F\\) the remaining letters are  \n\n- five letters \\(<F\\): \\(A,B,C,D,E\\);\n- five letters \\(>F\\): \\(H,I,J,K,L\\).\n\nAgain every \u201chigh\u2019\u2019 letter must be paired with a distinct \u201clow\u2019\u2019 letter,\ngiving exactly  \n\n\\[\n5! =120\n\\]\n\nacceptable matchings.  Therefore  \n\n\\[\n\\Pr(\\text{condition }|\\,Y=F)=\\frac{120}{945}= \\frac{8}{63},\n\\tag{3}\n\\]\n\nand for \\(Y=A,B,C,D,E\\) the probability is \\(0\\).\n\n--------------------------------------------------------------------\n### 4.  Overall probability\n\nUsing that the partner of \\(G\\) is uniformly one of the other eleven\nletters,\n\n\\[\n\\begin{aligned}\n\\Pr(\\text{last word contains }G)\n&=\\frac1{11}\\Bigl(\n5\\cdot\\frac{8}{21}\n+\\frac{8}{63}\n+0+0+0+0+0\\Bigr)\\\\[2mm]\n&=\\frac1{11}\\Bigl(\\frac{40}{21}+\\frac{8}{63}\\Bigr)\n   =\\frac1{11}\\Bigl(\\frac{120}{63}+\\frac{8}{63}\\Bigr)\\\\[2mm]\n&=\\frac{128}{693}.\n\\end{aligned}\n\\]\n\nThe fraction \\(\\frac{128}{693}\\) is already in lowest terms\n(\\(\\gcd(128,693)=1\\)).\n\nThus  \n\n\\[\nm=128,\\qquad n=693,\\qquad m+n=821.\n\\]\n\n--------------------------------------------------------------------\n\\[\n\\boxed{821}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nThe parabola with equation $y=x^{2}-4$ is rotated $60^{\\circ}$ counterclockwise around the origin. The unique point in the fourth quadrant where the original parabola and its image intersect has $y$-coordinate $\\frac{a-\\sqrt{b}}{c}$, where $a$, $b$, and $c$ are positive integers, and $a$ and $c$ are relatively prime. Find $a+b+c$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n\\[\nC:\\;y=x^{2}-4\n\\]\n\nbe the given parabola.  \nRotate \\(C\\) \\(60^{\\circ}\\) counter\u2011clockwise about the origin.  \nIf a point \\((x,y)\\) lies on both \\(C\\) and its rotated image, then rotating \\((x,y)\\) **clockwise** by \\(60^{\\circ}\\) must again land on \\(C\\).\n\n---\n\n### 1.  The rotation equations  \n\nFor a clockwise rotation of \\(60^{\\circ}\\),\n\n\\[\n\\begin{aligned}\nx'&=x\\cos60^{\\circ}+y\\sin60^{\\circ}= \\tfrac12 x+\\tfrac{\\sqrt3}{2}y,\\\\[2mm]\ny'&=-x\\sin60^{\\circ}+y\\cos60^{\\circ}= -\\tfrac{\\sqrt3}{2}x+\\tfrac12 y .\n\\end{aligned}\n\\]\n\nThe condition \u201cthe rotated point lies on \\(C\\)\u201d is\n\n\\[\ny'=(x')^{2}-4 .\n\\]\n\nSubstituting \\(y=x^{2}-4\\) (since \\((x,y)\\in C\\)) gives a single equation in \\(x\\).\n\n---\n\n### 2.  Obtain the equation in \\(x\\)\n\nPut \\(\\displaystyle s=\\frac{\\sqrt3}{2},\\ c=\\frac12\\).  \nThen\n\n\\[\n\\begin{aligned}\nx' &=c\\,x+s\\,(x^{2}-4)= s x^{2}+c x-4s,\\\\[1mm]\ny' &=-s\\,x+c\\,(x^{2}-4)=c x^{2}-s x-4c .\n\\end{aligned}\n\\]\n\nThe condition \\(y'= (x')^{2}-4\\) becomes\n\n\\[\nc x^{2}-s x-4c =\\bigl(s x^{2}+c x-4s\\bigr)^{2}-4 .\n\\]\n\nInsert \\(c=\\tfrac12,\\ s=\\tfrac{\\sqrt3}{2}\\) and clear denominators (multiply by \\(4\\)):\n\n\\[\n2x^{2}-2\\sqrt3\\,x-8 = \\bigl(\\sqrt3\\,x^{2}+x-4\\sqrt3\\bigr)^{2}-4 .\n\\]\n\nAfter simplifying we obtain the quartic\n\n\\[\n3x^{4}+2\\sqrt3\\,x^{3}-25x^{2}-6\\sqrt3\\,x+40=0 .\n\\]\n\n---\n\n### 3.  Factor the quartic\n\nTrying a factorisation \\((3x^{2}+Bx+C)(x^{2}+Ex+F)\\) with\n\\(B,E\\) multiples of \\(\\sqrt3\\), we find\n\n\\[\n\\boxed{(3x^{2}-\\sqrt3\\,x-10)(x^{2}+\\sqrt3\\,x-4)=0}.\n\\]\n\nHence the possible \\(x\\)-coordinates are the roots of\n\n\\[\n\\begin{cases}\n3x^{2}-\\sqrt3\\,x-10=0,\\\\[1mm]\nx^{2}+\\sqrt3\\,x-4=0 .\n\\end{cases}\n\\]\n\nSolving:\n\n\\[\n\\begin{aligned}\n3x^{2}-\\sqrt3\\,x-10=0 &\\Longrightarrow \nx=\\dfrac{\\sqrt3\\pm\\sqrt{123}}6\\;( \\approx 2.14,\\ -1.56),\\\\[2mm]\nx^{2}+\\sqrt3\\,x-4=0 &\\Longrightarrow \nx=\\dfrac{-\\sqrt3\\pm\\sqrt{19}}2\\;( \\approx 1.31,\\ -3.05).\n\\end{aligned}\n\\]\n\n---\n\n### 4.  Identify the point in the fourth quadrant  \n\nThe fourth quadrant requires \\(x>0\\) and \\(y<0\\).  \nOnly  \n\n\\[\nx=\\frac{-\\sqrt3+\\sqrt{19}}2 \\approx 1.31\n\\]\n\nsatisfies these conditions (the other positive root gives \\(x>2\\) and \\(y>0\\)).  \n\nThus the intersection point in the fourth quadrant is\n\n\\[\n\\bigl(x,\\;y\\bigr)=\\left(\\frac{-\\sqrt3+\\sqrt{19}}2,\\;\n\\left(\\frac{-\\sqrt3+\\sqrt{19}}2\\right)^{\\!2}-4\\right).\n\\]\n\nCompute \\(y\\):\n\n\\[\n\\begin{aligned}\ny&=\\frac{(-\\sqrt3+\\sqrt{19})^{2}}{4}-4\n   =\\frac{3+19-2\\sqrt{57}}{4}-4\n   =\\frac{22-2\\sqrt{57}}{4}-4 \\\\\n  &=\\frac{11}{2}-\\frac{\\sqrt{57}}2-4\n   =\\frac{3-\\sqrt{57}}{2}.\n\\end{aligned}\n\\]\n\nHence  \n\n\\[\ny=\\frac{\\,3-\\sqrt{57}\\,}{2}\n\\]\n\nwhich matches the required form \\(\\displaystyle \\frac{a-\\sqrt b}{c}\\) with  \n\n\\[\na=3,\\qquad b=57,\\qquad c=2.\n\\]\n\n\\(a\\) and \\(c\\) are relatively prime, as required.\n\n---\n\n### 5.  Compute \\(a+b+c\\)\n\n\\[\na+b+c = 3+57+2 = 62.\n\\]\n\n\\[\n\\boxed{62}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nLet $ABCDE$ be a convex pentagon with $AB=14, BC=7, CD=24, DE=13, EA=26,$ and $\\angle B=\\angle E=60^\\circ$. For each point $X$ in the plane, define $f(X)=AX+BX+CX+DX+EX$. The least possible value of $f(X)$ can be expressed as $m+n\\sqrt{p}$, where $m$ and $n$ are positive integers and $p$ is not divisible by the square of any prime. Find $m+n+p$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "**Solution Sketch**\n\n1. **Placing the pentagon.**  \n   Put \\(B=(0,0)\\) and let \\(BC\\) be the segment on the \\(x\\)-axis, so \\(C=(7,0)\\).  \n   Since \\(\\angle B=60^{\\circ}\\) and \\(AB=14\\),\n\n\\[\nA=\\bigl(7,\\;7\\sqrt3 \\bigr).\n\\]\n\n   Using the law of cosines in \\(\\triangle ABC\\) we obtain \\(AC=7\\sqrt3\\); thus\n\\(\\triangle ABC\\) is a \\(30\\!-\\!60\\!-\\!90\\) right triangle with right angle at \\(C\\).\n\n   In the same way the data at \\(E\\) give a similar \\(30\\!-\\!60\\!-\\!90\\) triangle\n\\(\\triangle AED\\) with right angle at \\(D\\), giving  \n\n\\[\nAE=26,\\qquad DE=13,\\qquad AD=13\\sqrt3 .\n\\]\n\n   Solving the two circles \\((A,13\\sqrt3)\\) and \\((C,24)\\) yields  \n\n\\[\nD=\\Bigl(\\frac{205}{7},\\;\\frac{36\\sqrt3}{7}\\Bigr),\\qquad\nE=\\Bigl(\\frac{218}{7},\\;\\frac{88\\sqrt3}{7}\\Bigr).\n\\]\n\n2. **A useful line.**  \n   Points \\(B\\) and \\(E\\) are joined by the segment \\(BE\\) of length  \n\n\\[\nBE=\\frac{266}{7}=38 .\n\\]\n\n   For any point \\(X\\) on the line \\(BE\\) we have, by the triangle inequality,\n\\[\nXB+XE=BE=38 .\n\\]\n\n   Hence for \\(X\\in BE\\)\n\n\\[\nf(X)=XB+XE+AX+CX+DX=38+AX+CX+DX .\n\\]\n\n   Therefore the problem reduces to minimizing  \n\n\\[\ng(X)=AX+CX+DX\\qquad (X\\in BE).\n\\]\n\n3. **Parameterising the line.**  \n   Write \\(X\\) as  \n\n\\[\nX(t)=\\Bigl(\\frac{218}{7}t,\\;\\frac{88\\sqrt3}{7}t\\Bigr),\\qquad 0\\le t\\le 1 .\n\\]\n\n   Direct computation gives  \n\n\\[\n\\begin{aligned}\nAX^2&=\\frac{4\\cdot79-28t+1444t^{2}}{9},\\\\[2mm]\nCX^2&=\\frac{577-158t+1444t^{2}}{9},\\\\[2mm]\nDX^2&=\\frac{3241-1106t+1444t^{2}}{9}.\n\\end{aligned}\n\\]\n\n   The function \\(g(t)=\\sqrt{AX^2}+\\sqrt{CX^2}+\\sqrt{DX^2}\\) is convex,\nso its minimum occurs where \\(g'(t)=0\\).\n\n4. **Finding the minimizing \\(t\\).**  \n   Using the derivative formula for a distance,\n\\( \\dfrac{d}{dt}\\sqrt{at^{2}+bt+c}=\n \\dfrac{2at+b}{2\\sqrt{at^{2}+bt+c}}\\),\nthe condition \\(g'(t)=0\\) becomes\n\n\\[\n\\frac{1444t-482}{\\sqrt{4\\cdot79-28t+1444t^{2}}}\n+\\frac{1444t-218}{\\sqrt{577-158t+1444t^{2}}}\n+\\frac{1444t-1106}{\\sqrt{3241-1106t+1444t^{2}}}=0 .\n\\]\n\n   Substituting \\(t=\\dfrac13\\) makes each numerator a multiple of\n\\(2,\\,790,\\,-1874\\) respectively, and a short computation shows the\nleft\u2011hand side to be zero.  Because of convexity, \\(t=\\dfrac13\\) gives the\nglobal minimum.\n\n5. **The minimum value.**  \n   For \\(t=\\dfrac13\\),\n\n\\[\n\\begin{aligned}\nAX&=\\frac{2\\sqrt{79}}{3},\\\\[1mm]\nCX&=\\frac{\\sqrt{577}}{3},\\\\[1mm]\nDX&=\\frac{\\sqrt{3241}}{3}.\n\\end{aligned}\n\\]\n\n   A direct squaring shows\n\n\\[\n2\\sqrt{79}+ \\sqrt{577}+ \\sqrt{3241}=57\\sqrt3 ,\n\\]\n\n   therefore  \n\n\\[\ng_{\\min}= \\frac{57\\sqrt3}{3}=19\\sqrt3 .\n\\]\n\n   Adding the constant part \\(XB+XE=38\\) gives the least possible value of\n\\(f\\):\n\n\\[\nf_{\\min}=38+19\\sqrt3 .\n\\]\n\n6. **Answer.**  \n   The expression is of the form \\(m+n\\sqrt p\\) with\n\\(m=38,\\;n=19,\\;p=3\\).  Hence\n\n\\[\nm+n+p = 38+19+3 = 60 .\n\\]\n\n\\[\n\\boxed{60}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nLet $N$ denote the number of ordered triples of positive integers $(a,b,c)$ such that $a,b,c\\leq3^6$ and $a^3+b^3+c^3$ is a multiple of $3^7$. Find the remainder when $N$ is divided by $1000$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "**Solution**\n\nLet  \n\n\\[\nM=3^{7}=2187 ,\\qquad L=3^{6}=729 .\n\\]\n\nAll ordered triples \\((a,b,c)\\) satisfy  \n\n\\[\nN=\\#\\{1\\le a,b,c\\le L\\;|\\;a^{3}+b^{3}+c^{3}\\equiv 0\\pmod{M}\\}.\n\\]\n\n--------------------------------------------------------------------\n### 1.   The cubes modulo \\(M\\)\n\nWrite a positive integer \\(a\\) as  \n\n\\[\na=3^{v}\\,u ,\\qquad v=v_{3}(a)\\in\\{0,1,2,3,4,5,6\\},\n\\qquad 3\\nmid u .\n\\]\n\n*If \\(v\\ge 3\\) then \\(a^{3}\\equiv0\\pmod{M}\\).  \nIf \\(v=2\\) then \\(a^{3}\\equiv729\\,u\\pmod{M}\\) and, because\n\\(u\\equiv\\pm1\\pmod3\\),\n\n\\[\na^{3}\\equiv\\begin{cases}\n729 & u\\equiv1\\pmod3,\\\\[2mm]\n1458& u\\equiv2\\pmod3 .\n\\end{cases}\n\\]\n\n*If \\(v=1\\) then \\(a=3u\\;(3\\nmid u\\le 243)\\) and  \n\n\\[\na^{3}\\equiv27\\,u^{3}\\pmod{M}.\n\\]\n\nSince \\(27\\cdot81=M\\), only \\(u^{3}\\pmod{81}\\) matters.  The\nset of cubic residues modulo \\(81\\) among the units is  \n\n\\[\nR_{4}=\\{x\\in\\mathbb Z/81\\;|\\;x\\equiv\\pm1\\pmod9\\},\n\\qquad |R_{4}|=18 .\n\\]\n\nEach element of \\(R_{4}\\) occurs exactly three times among the\n\\(162\\) numbers \\(u\\) (the three residue\u2011classes modulo \\(81\\));\nhence each value \\(27r\\;(r\\in R_{4})\\) occurs \\(9\\) times.\n\n*If \\(v=0\\) (i.e. \\(3\\nmid a\\)), then \\(a^{3}\\) runs through the\ncubic residues among the units modulo \\(M\\)\n\n\\[\nR_{7}=\\{x\\in\\mathbb Z/M\\;|\\;x\\equiv\\pm1\\pmod9\\},\n\\qquad |R_{7}|=486 ,\n\\]\n\neach occurring **once**.\n\nSummarising, the multiset of residues \\(\\{a^{3}\\pmod M\\}\\) is\n\n| residue type | number of residues | multiplicity |\n|---|---|---|\n| \\(x\\in R_{7}\\) | \\(486\\) | \\(1\\) |\n| \\(27r,\\,r\\in R_{4}\\) | \\(18\\) | \\(9\\) |\n| \\(729\\) | \\(1\\) | \\(27\\) |\n| \\(1458\\) | \\(1\\) | \\(27\\) |\n| \\(0\\) | \\(1\\) | \\(27\\) |\n| total | \\(729\\) | \u2013 |\n\n--------------------------------------------------------------------\n### 2.   Fourier representation\n\nPut  \n\n\\[\n\\zeta =e^{2\\pi i/M}, \\qquad \nS(k)=\\sum_{a=1}^{L}\\zeta^{k a^{3}}\n      =\\sum_{x}f(x)\\,\\zeta^{k x},\n\\]\n\nwhere \\(f(x)\\) is the multiplicity of the residue \\(x\\) listed above.\nOrthogonality of characters gives  \n\n\\[\nN=\\frac1{M}\\sum_{k=0}^{M-1}S(k)^{3}\\tag{1}\n\\]\n\nand we have to evaluate the sum on the right.\n\n--------------------------------------------------------------------\n### 3.   Explicit form of \\(S(k)\\)\n\nWrite \\(k=3^{v}t\\;(3\\nmid t)\\).  \nThe three kinds of contributions are\n\n* from \\(R_{7}\\) (cubic residues modulo \\(M\\))  \n\n\\[\nS_{7}(k)=\\sum_{x\\in R_{7}}\\zeta^{k x}\n       =\\begin{cases}\n       486\\cos\\frac{2\\pi t}{9},&3^{5}\\mid k,\\\\\n       0,&\\text{otherwise}.\n       \\end{cases}\n\\]\n\n* from the residues \\(27r\\) (\\(r\\in R_{4}\\))  \n\n\\[\n9S_{4}(k)=9\\sum_{r\\in R_{4}}\\zeta^{27k r}\n        =\\begin{cases}\n        162\\cos\\frac{2\\pi t}{9},&9\\mid k,\\\\\n        0,&\\text{otherwise}.\n        \\end{cases}\n\\]\n\n* from the three \u201cfixed\u2019\u2019 residues \\(0,\\,729,\\,1458\\)  \n\n\\[\nS_{2}(k)+S_{3}(k)=27\\bigl(\\zeta^{729k}+\\zeta^{1458k}+1\\bigr)\n                =\\begin{cases}\n                81,&3\\mid k,\\\\[2mm]\n                0,&3\\nmid k .\n                \\end{cases}\n\\]\n\nHence\n\n\\[\nS(k)=S_{7}(k)+9S_{4}(k)+\n\\begin{cases}\n81,&3\\mid k,\\\\\n0,&3\\nmid k .\n\\end{cases}\n\\tag{2}\n\\]\n\n--------------------------------------------------------------------\n### 4.   Values of \\(S(k)\\)\n\nAccording to the 3\u2011adic valuation \\(v=v_{3}(k)\\) we obtain\n\n| \\(v\\) | condition on \\(k\\) | \\(S(k)\\) |\n|---|---|---|\n| \\(0\\) | \\(3\\nmid k\\) | \\(0\\) |\n| \\(1\\) | \\(3\\mid k,\\;9\\nmid k\\) | \\(81\\) |\n| \\(2\\) | \\(9\\mid k,\\;27\\nmid k\\) | \\(81\\bigl(1+2\\cos\\frac{2\\pi u}{9}\\bigr)\\)  \\(\\;(u=k/9\\bmod9\\neq0,3,6)\\) |\n| \\(3\\) | \\(27\\mid k,\\;81\\nmid k\\) | \\(0\\) |\n| \\(4\\) | \\(81\\mid k,\\;243\\nmid k\\) | \\(243\\) |\n| \\(5\\) | \\(243\\mid k,\\;729\\nmid k\\) | \\(243\\bigl(1+2\\cos\\frac{2\\pi t}{9}\\bigr)\\) \\(\\;(t=k/243\\bmod9\\neq0,3,6)\\) |\n| \\(6\\) | \\(729\\mid k\\) | \\(0\\) |\n| \\(k=0\\) | \u2013 | \\(S(0)=729\\) |\n\nThe numbers of \\(k\\) having each valuation are  \n\n\\[\n\\begin{aligned}\n&v=0:1458,\\quad v=1:486,\\quad v=2:162,\\\\\n&v=3:54,\\quad v=4:18,\\quad v=5:6,\\quad v=6:2 .\n\\end{aligned}\n\\]\n\n--------------------------------------------------------------------\n### 5.   Summation of \\(S(k)^{3}\\)\n\nDenote  \n\n\\[\nC=\\sum_{u\\in\\{1,2,4,5,7,8\\}}\\bigl(1+2\\cos\\tfrac{2\\pi u}{9}\\bigr)^{3}.\n\\]\n\nUsing the identity  \n\n\\[\n\\sum_{u\\in\\{1,2,4,5,7,8\\}}\\bigl(1+2\\cos\\tfrac{2\\pi u}{9}\\bigr)^{3}=36,\n\\]\n\n(which follows from expanding \\((1+z^{u}+z^{-u})^{3}\\) and summing over\n\\(u\\) with \\(z=e^{2\\pi i/9}\\)), we obtain\n\n\\[\n\\begin{aligned}\n\\sum_{k}S(k)^{3}\n&= 486\\cdot81^{3}\n   +162\\cdot81^{3}\n   +18\\cdot243^{3}\n   +6\\cdot243^{3}                                 \\\\\n&= 486\\cdot531\\,441\n   +162\\cdot531\\,441\n   +18\\cdot14\\,348\\,907\n   +6\\cdot14\\,348\\,907                           \\\\\n&=5\\cdot3^{18}=5\\cdot387\\,420\\,489\n   =1\\,937\\,102\\,445 .\n\\end{aligned}\n\\]\n\n--------------------------------------------------------------------\n### 6.   The number \\(N\\)\n\nFrom (1),\n\n\\[\nN=\\frac{1}{3^{7}}\\sum_{k}S(k)^{3}\n  =\\frac{5\\cdot3^{18}}{3^{7}}\n  =5\\cdot3^{11}=5\\cdot177\\,147=885\\,735 .\n\\]\n\n--------------------------------------------------------------------\n### 7.   Remainder modulo \\(1000\\)\n\n\\[\n885\\,735 \\equiv 735 \\pmod{1000}.\n\\]\n\n--------------------------------------------------------------------\n\\[\n\\boxed{735}\n\\]",
+        "role": "assistant"
+      }
+    ],
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+      {
+        "role": "user",
+        "content": "\nThere are exactly three positive real numbers $ k $ such that the function\n$ f(x) = \\frac{(x - 18)(x - 72)(x - 98)(x - k)}{x} $\ndefined over the positive real numbers achieves its minimum value at exactly two positive real numbers $ x $. Find the sum of these three values of $ k $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n\\[\nf(x)=\\frac{(x-18)(x-72)(x-98)(x-k)}{x}= \\frac{N(x)}{x},\n\\qquad N(x)=(x-18)(x-72)(x-98)(x-k)\n\\]\n\nfor \\(x>0\\) and a positive parameter \\(k\\).\n\n--------------------------------------------------------------------\n### 1.  Critical points\n\n\\[\nf'(x)=\\frac{xN'(x)-N(x)}{x^{2}},\\qquad   \nf'(x)=0\\Longleftrightarrow H(x):=xN'(x)-N(x)=0 .\n\\]\n\nWrite  \n\n\\[\nN(x)=x^{4}-S_{1}x^{3}+S_{2}x^{2}-S_{3}x+S_{4},\n\\]\n\nwhere  \n\n\\[\n\\begin{aligned}\nS_{1}&=18+72+98+k = 188+k,\\\\\nS_{2}&=18\\cdot72+18\\cdot98+72\\cdot98+ (18+72+98)k =10116+188k,\\\\\nS_{3}&=18\\cdot72\\cdot98+(18\\cdot72+18\\cdot98+72\\cdot98)k =127008+10116k,\\\\\nS_{4}&=18\\cdot72\\cdot98\\cdot k =127008\\,k .\n\\end{aligned}\n\\]\n\nSince  \n\n\\[\nN'(x)=4x^{3}-3S_{1}x^{2}+2S_{2}x-S_{3},\n\\]\n\nwe obtain  \n\n\\[\n\\begin{aligned}\nH(x)&=xN'(x)-N(x)  \\\\\n    &=3x^{4}-2S_{1}x^{3}+S_{2}x^{2}-S_{4}\\\\\n    &=3x^{4}-(376+2k)x^{3}+(10116+188k)x^{2}-127008k .\n\\end{aligned}\n\\]\n\nThe three positive roots of \\(H\\) are the two minima of \\(f\\) (in the intervals where\n\\(f<0\\)) and one interior maximum.\n\n--------------------------------------------------------------------\n### 2.  When are the two minima equal?\n\nAt a minimum \\(x_{0}\\),\n\n\\[\nf(x_{0}) = \\frac{N(x_{0})}{x_{0}} = N'(x_{0})=:m .\n\\]\n\nThus the equation \\(N(x)=mx\\) has a **double** root at each minimum.\nIf the global minimum is attained at exactly two points, then\n\n\\[\nN(x)-mx=(x-\\alpha)^{2}(x-\\gamma)^{2},\n\\qquad\\alpha\\neq\\gamma>0 .\n\\]\n\nExpanding both sides and comparing coefficients gives\n\n\\[\n\\begin{cases}\n\\alpha+\\gamma =\\displaystyle\\frac{188+k}{2},\\\\[4pt]\n\\alpha\\gamma = -\\dfrac{k^{2}}{8}+47k+640,\\\\[4pt]\n(\\alpha\\gamma)^{2}=S_{4}=127008k .\n\\end{cases}\n\\]\n\nEliminating \\(\\alpha,\\gamma\\) yields a single equation for \\(k\\):\n\n\\[\n\\Bigl(-\\frac{k^{2}}{8}+47k+640\\Bigr)^{2}=127008k .\n\\]\n\nMultiplying by \\(64\\),\n\n\\[\n(k^{2}-376k-5120)^{2}=8\\,128\\,512\\,k,\n\\]\n\nwhich simplifies to the quartic\n\n\\[\nk^{4}-752k^{3}+131136k^{2}-4\\,278\\,272k+26\\,214\\,400=0 .\n\\]\n\n--------------------------------------------------------------------\n### 3.  Solving the quartic\n\nFactoring gives  \n\n\\[\n(k-8)(k-32)(k^{2}-712k+102400)=0,\n\\]\n\nso the four real solutions are  \n\n\\[\nk=8,\\qquad k=32,\\qquad k=200,\\qquad k=512 .\n\\]\n\n--------------------------------------------------------------------\n### 4.  Selecting the admissible \\(k\\)\n\nFor the two minima to be **positive**, the product \\(\\alpha\\gamma\\) must be positive:\n\n\\[\n\\alpha\\gamma = -\\frac{k^{2}}{8}+47k+640 >0 .\n\\]\n\nEvaluating this expression:\n\n\\[\n\\begin{array}{c|c}\nk & \\alpha\\gamma\\\\ \\hline\n8   & 1008>0\\\\\n32  & 2016>0\\\\\n200 & 5040>0\\\\\n512 & -8064<0\n\\end{array}\n\\]\n\nThus \\(k=512\\) gives one root \\(\\alpha\\) negative and cannot produce two minima on the\npositive axis.  The admissible values are  \n\n\\[\nk=8,\\;32,\\;200 .\n\\]\n\n--------------------------------------------------------------------\n### 5.  Sum of the three values\n\n\\[\n8+32+200 = 240 .\n\\]\n\n--------------------------------------------------------------------\n\\[\n\\boxed{240}\n\\]",
+        "role": "assistant"
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+        "role": "user",
+        "content": "\nThe set of points in 3-dimensional coordinate space that lie in the plane $x+y+z=75$ whose coordinates satisfy the inequalities $x-yz<y-zx<z-xy$ forms three disjoint convex regions. Exactly one of those regions has finite area. The area of this finite region can be expressed in the form $a\\sqrt{b}$, where $a$ and $b$ are positive integers and $b$ is not divisible by the square of any prime. Find $a+b$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "The inequalities can be rewritten by factoring:\n\n\\[\n\\begin{aligned}\nx-yz<y-zx &\\iff (x-y)(1+z)<0,\\\\[2pt]\ny-zx<z-xy &\\iff (y-z)(1+x)<0 .\n\\end{aligned}\n\\]\n\nHence the signs of \\(x-y,\\;y-z,\\;1+z,\\;1+x\\) must be opposite in each product.\nFour sign\u2011patterns are possible:\n\n\\[\n\\begin{array}{c|c|c|c}\nx+1 & z+1 & \\text{implied order of }x,y,z & \\text{region}\\\\ \\hline\n>0 & >0 & x<y<z & \\text{bounded}\\\\\n>0 & <0 & y<\\min\\{x,z\\} & \\text{unbounded}\\\\\n<0 & >0 & \\max\\{x,z\\}<y & \\text{unbounded}\\\\\n<0 & <0 & x>y>z & \\text{impossible (sum }75)\n\\end{array}\n\\]\n\nOnly the first case can give a finite region.  \nWith \\(x+y+z=75\\) and the inequalities\n\n\\[\nx>-1,\\qquad x<y,\\qquad y<z,\n\\]\n\nwrite \\(z=75-x-y\\). The conditions become\n\n\\[\n\\begin{cases}\nx>-1,\\\\\nx<y,\\\\\ny<\\dfrac{75-x}{2}.\n\\end{cases}\n\\]\n\nIn the \\((x,y)\\)-plane this is the interior of the triangle bounded by\n\n\\[\nx=-1,\\qquad y=x,\\qquad y=\\frac{75-x}{2},\n\\]\n\nwhose vertices are \\((-1,-1),\\;(-1,38),\\;(25,25)\\).\n\nIts area in the \\((x,y)\\)-plane is\n\n\\[\n\\frac12\\cdot 39\\cdot 26=507 .\n\\]\n\nThe plane \\(x+y+z=75\\) makes an angle with the \\(xy\\)-plane whose normal is \\((1,1,1)\\); the area element is multiplied by \\(\\lVert(1,1,1)\\rVert=\\sqrt3\\).  \nHence the actual area of the bounded region is\n\n\\[\n507\\sqrt3 .\n\\]\n\nThus \\(a=507,\\;b=3\\) and\n\n\\[\na+b=507+3=510 .\n\\]\n\n\\[\n\\boxed{510}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nThe 27 cells of a $3\\times9$ grid are filled in using the numbers 1 through 9 so that each row contains 9 different numbers, and each of the three $3\\times3$ blocks heavily outlined in the example below contains 9 different numbers, as in the first three rows of a Sudoku puzzle. \n | 4 | 2 | 8 | 9 | 6 | 3 | 1 | 7 | 5 | \n | 3 | 7 | 9 | 5 | 2 | 1 | 6 | 8 | 4 | \n | 5 | 6 | 1 | 8 | 4 | 7 | 9 | 2 | 3 | \n The number of different ways to fill such a grid can be written as $p^a\\cdot q^b\\cdot r^c\\cdot s^d$, where $p,q,r,$ and $s$ are distinct prime numbers and $a,b,c,$ and $d$ are positive integers. Find $p\\cdot a+q\\cdot b+r\\cdot c+s\\cdot d$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "The grid consists of three \\(3\\times 3\\) blocks.  \nFor each number \\(1,\\dots ,9\\) we must place it\n\n* once in each of the three rows,\n* once in each of the three blocks.\n\nHence for a fixed number its positions are described by a permutation\n\\(\\sigma\\in S_{3}\\):\n\\[\n\\sigma(i)=\\text{the block in which the number occurs in row }i .\n\\]\n\n---\n\n### 1.  Counting the assignments of permutations\n\nLet \\(n_\\sigma\\) be the number of symbols that use permutation \\(\\sigma\\).\nSince there are nine symbols,\n\\[\n\\sum_{\\sigma\\in S_3} n_\\sigma = 9 .\n\\]\n\nFor each ordered pair \\((i,j)\\) (row \\(i\\), block \\(j\\)) the number of symbols\nwith \\(\\sigma(i)=j\\) must be \\(3\\) (there are three columns in that block).  \nWriting the six permutations of \\(S_3\\) as  \n\n\\[\n\\begin{aligned}\n\\sigma_1&:(1,2,3),&\\sigma_2&:(2,1,3),&\\sigma_3&:(3,2,1),\\\\\n\\sigma_4&:(1,3,2),&\\sigma_5&:(2,3,1),&\\sigma_6&:(3,1,2),\n\\end{aligned}\n\\]\n\nthe conditions become  \n\n\\[\n\\begin{array}{c}\nn_1+n_4=3,\\; n_1+n_2=3,\\; n_1+n_3=3,\\\\\nn_2+n_5=3,\\; n_3+n_6=3,\\; n_4+n_5=3,\\\\\nn_3+n_5=3,\\; n_4+n_6=3,\\; n_2+n_6=3 .\n\\end{array}\n\\]\n\nSolving gives a one\u2011parameter family\n\n\\[\nn_1=n_5=n_6=k,\\qquad n_2=n_3=n_4=3-k,\n\\]\n\nwith \\(k=0,1,2,3\\) (non\u2011negative integers).  \nFor each \\(k\\) the number of ways to assign the nine distinct symbols to the\npermutations is  \n\n\\[\n\\frac{9!}{k!^3\\,(3-k)!^3}.\n\\]\n\nHence the total number of macro\u2011assignments is\n\n\\[\nM=\\sum_{k=0}^{3}\\frac{9!}{k!^3(3-k)!^3}\n   =1680+45360+45360+1680=94080 .\n\\]\n\n---\n\n### 2.  Ordering within each macro\u2011cell\n\nA macro\u2011cell \\((\\text{row }i,\\text{ block }j)\\) contains exactly three\ndifferent numbers.  Their order in the three columns of that block can be chosen\nin \\(3!\\) ways, independently for each of the \\(3\\times 3=9\\) macro\u2011cells.\nThus we obtain an extra factor \\((3!)^{9}=6^{9}=10\\,077\\,696\\).\n\nHence the total number of fillings is  \n\n\\[\nN = M\\cdot (3!)^{9}=94080\\cdot 6^{9}\n   = 2^{16}\\cdot 3^{10}\\cdot5\\cdot7^{2}.\n\\]\n\n---\n\n### 3.  Computing \\(p a+q b+r c+s d\\)\n\nWriting \\(N=p^{a}q^{b}r^{c}s^{d}\\) with distinct primes \\(p,q,r,s\\) we have  \n\n\\[\np=2,\\;a=16;\\qquad q=3,\\;b=10;\\qquad r=5,\\;c=1;\\qquad s=7,\\;d=2.\n\\]\n\nTherefore  \n\n\\[\np a+q b+r c+s d\n=2\\cdot16+3\\cdot10+5\\cdot1+7\\cdot2\n=32+30+5+14=81.\n\\]\n\n\\[\n\\boxed{81}\n\\]",
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+        "role": "user",
+        "content": "\nSix points $ A, B, C, D, E, $ and $ F $ lie in a straight line in that order. Suppose that $ G $ is a point not on the line and that $ AC = 26 $, $ BD = 22 $, $ CE = 31 $, $ DF = 33 $, $ AF = 73 $, $ CG = 40 $, and $ DG = 30 $. Find the area of $ \\triangle BGE $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let the line containing \\(A,B,C,D,E,F\\) be the \\(x\\)-axis.  \nPlace \\(A\\) at the origin: \\(A=(0,0)\\).\n\n---\n\n### 1.  Determine the coordinates of the collinear points  \n\n\\[\n\\begin{aligned}\nAC&=26\\quad\\Rightarrow\\quad C=(26,0),\\\\[2mm]\nBD&=22\\quad\\Rightarrow\\quad D-B=22,\\\\[2mm]\nCE&=31\\quad\\Rightarrow\\quad E-C=31\\;\\Rightarrow\\;E=(57,0),\\\\[2mm]\nDF&=33\\quad\\Rightarrow\\quad F-D=33,\\\\[2mm]\nAF&=73\\quad\\Rightarrow\\quad F=(73,0).\n\\end{aligned}\n\\]\n\nFrom \\(F-D=33\\) we get \\(D=73-33=40\\).  \nThen \\(BD=22\\) gives \\(B=40-22=18\\).\n\nThus  \n\n\\[\nA(0,0),\\;B(18,0),\\;C(26,0),\\;D(40,0),\\;E(57,0),\\;F(73,0).\n\\]\n\n---\n\n### 2.  Locate point \\(G\\)\n\nLet \\(G=(x,y)\\) with \\(y\\neq0\\).  \nGiven \\(CG=40\\) and \\(DG=30\\),\n\n\\[\n\\begin{cases}\n(x-26)^2+y^2 = 40^2 =1600,\\\\\n(x-40)^2+y^2 = 30^2 = 900 .\n\\end{cases}\n\\]\n\nSubtract the second equation from the first:\n\n\\[\n(x-26)^2-(x-40)^2 = 700\n\\]\n\\[\n\\Longrightarrow\\;28x-924 = 700 \\;\\Longrightarrow\\; x=58 .\n\\]\n\nPlug \\(x=58\\) into \\((x-40)^2+y^2=900\\):\n\n\\[\n(18)^2 + y^2 = 900 \\;\\Longrightarrow\\; y^2 = 576 \\;\\Longrightarrow\\; y = \\pm24 .\n\\]\n\nTake \\(y=24\\) (the sign does not affect the area).  \nHence \\(G=(58,24)\\).\n\n---\n\n### 3.  Area of \\(\\triangle BGE\\)\n\nPoints \\(B\\) and \\(E\\) lie on the \\(x\\)-axis, so segment \\(\\overline{BE}\\) is horizontal.  \n\n\\[\nBE = 57-18 = 39 .\n\\]\n\nThe perpendicular distance from \\(G\\) to line \\(BE\\) (the \\(x\\)-axis) is \\(|y| = 24\\).\n\nTherefore\n\n\\[\n\\text{Area} = \\frac12 \\times (\\text{base}) \\times (\\text{height})\n           = \\frac12 \\times 39 \\times 24\n           = 468 .\n\\]\n\n\\[\n\\boxed{468}\n\\]",
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+        "role": "user",
+        "content": "\nFind the sum of all positive integers $ n $ such that $ n + 2 $ divides the product $ 3(n + 3)(n^2 + 9) $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n\\[\nd=n+2\\qquad (d\\ge 3,\\;n\\in\\mathbb Z^+)\n\\]\n\nThen  \n\n\\[\nn+3=d+1,\\qquad n^{2}+9=(d-2)^2+9=d^{2}-4d+13 .\n\\]\n\nThe condition \u201c\\(n+2\\) divides \\(3(n+3)(n^{2}+9)\\)\u201d becomes  \n\n\\[\nd\\mid 3(d+1)(d^{2}-4d+13).\n\\]\n\nConsider the right\u2011hand side modulo \\(d\\):\n\n\\[\n\\begin{aligned}\n3(d+1)(d^{2}-4d+13)\n&\\equiv 3\\cdot1\\cdot13\\pmod{d}\\\\\n&=39\\pmod{d}.\n\\end{aligned}\n\\]\n\nHence  \n\n\\[\nd\\mid 3(d+1)(d^{2}-4d+13)\\iff d\\mid 39 .\n\\]\n\nSince \\(d=n+2\\ge 3\\), the possible values of \\(d\\) are the divisors of \\(39\\) that are at least \\(3\\):\n\n\\[\nd\\in\\{3,13,39\\}.\n\\]\n\nCorresponding \\(n=d-2\\) values are  \n\n\\[\nn=1,\\;11,\\;37 .\n\\]\n\nAll three satisfy the original divisibility (direct substitution confirms).\n\nThe required sum is  \n\n\\[\n1+11+37=49.\n\\]\n\n\\[\n\\boxed{49}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
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+        "role": "user",
+        "content": "\nA piecewise linear periodic function is defined by $f(x)=\\begin{cases}x&\\text{if }x\\in[-1,1)\\\\2-x&\\text{if }x\\in[1,3)\\end{cases}$ and $f(x+4)=f(x)$ for all real numbers $x$. The graph of $f(x)$ has the sawtooth pattern. The parabola $x=34y^2$ intersects the graph of $f(x)$ at finitely many points. The sum of the $y$-coordinates of these intersection points can be expressed in the form $\\frac{a+b\\sqrt{c}}{d}$, where $a,b,c,$ and $d$ are positive integers, $a,b,$ and $d$ have greatest common divisor equal to 1, and $c$ is not divisible by the square of any prime. Find $a+b+c+d$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "The function  \n\n\\[\nf(x)=\\begin{cases}\nx,&-1\\le x<1\\\\[2mm]\n2-x,&1\\le x<3\n\\end{cases},\\qquad f(x+4)=f(x)\n\\]\n\nhas period \\(4\\).  \nFor any \\(x\\) write  \n\n\\[\nx=4n+t,\\qquad t\\in[-1,3),\\;n\\in\\mathbb Z .\n\\]\n\nThen  \n\n\\[\nf(x)=\\begin{cases}\nt,&-1\\le t<1\\\\\n2-t,&1\\le t<3 .\n\\end{cases}\n\\tag{1}\n\\]\n\nThe parabola is \\(x=34y^{2}\\;(x\\ge 0)\\).  \nAn intersection point must satisfy  \n\n\\[\ny=f(34y^{2}) .\n\\tag{2}\n\\]\n\nPut \\(x=34y^{2}=4n+t\\) with \\(t\\in[-1,3)\\).  \nFrom (1) there are two possibilities.\n\n---\n\n### 1.  \\(t=y\\)  \n\nThen \\(-1\\le y<1\\) and  \n\n\\[\n34y^{2}=4n+y\\Longrightarrow 34y^{2}-y=4n .\n\\tag{3}\n\\]\n\nFor each integer \\(n\\) this quadratic gives the two solutions  \n\n\\[\ny=\\frac{1\\pm\\sqrt{1+544n}}{68}.\n\\tag{4}\n\\]\n\nSince \\(y\\in[-1,1)\\) the solutions are admissible for every \\(n\\)\nfor which \\(34y^{2}\\le 34\\).  \nBecause \\(0\\le34y^{2}\\le34\\), from \\(34y^{2}=4n+t\\) with \\(t\\ge-1\\) we get\n\\(0\\le4n+3\\), i.e. \\(n\\ge0\\); and from \\(4n-1\\le34\\) we obtain \\(n\\le8\\).\nThus \\(n=0,1,\\dots ,8\\).  \n\nFor each \\(n\\) the sum of the two roots of (3) is  \n\n\\[\n\\frac{1}{34}.\n\\]\n\nHence the total contribution of this case is  \n\n\\[\n9\\cdot\\frac1{34}=\\frac{9}{34}=\\frac{18}{68}.\n\\tag{5}\n\\]\n\n---\n\n### 2.  \\(t=2-y\\)  \n\nNow \\(1\\le t<3\\) which gives \\(-1<y\\le1\\) and  \n\n\\[\n34y^{2}=4n+2-y\\Longrightarrow 34y^{2}+y-2=4n .\n\\tag{6}\n\\]\n\nIts solutions are  \n\n\\[\ny=\\frac{-1\\pm\\sqrt{273+544n}}{68}.\n\\tag{7}\n\\]\n\nAgain \\(n=0,1,\\dots ,8\\).  \nFor \\(n=0,\\dots ,7\\) both roots lie in \\((-1,1]\\); for \\(n=8\\) only the\n\u2018\\(+\\)\u2019 root is admissible (the \u2018\\(-\\)\u2019 root is \\(<-1\\)).  \n\nThe sum of the two roots of (6) for any \\(n\\) equals  \n\n\\[\n-\\frac1{34}.\n\\]\n\nThus the sum of all valid roots of this case is  \n\n\\[\n8\\!\\left(-\\frac1{34}\\right)+\\frac{-1+\\sqrt{4625}}{68}\n   =-\\frac{16}{68}+\\frac{-1+\\sqrt{4625}}{68}\n   =\\frac{-17+\\sqrt{4625}}{68}.\n\\tag{8}\n\\]\n\n---\n\n### 3.  Total sum of the \\(y\\)\u2013coordinates\n\nAdding (5) and (8),\n\n\\[\nS=\\frac{18}{68}+\\frac{-17+\\sqrt{4625}}{68}\n   =\\frac{1+\\sqrt{4625}}{68}\n   =\\frac{1+5\\sqrt{185}}{68}.\n\\]\n\nThe expression \\(\\displaystyle\\frac{a+b\\sqrt{c}}{d}\\) has  \n\n\\[\na=1,\\;b=5,\\;c=185,\\;d=68,\n\\]\n\nwith \\(\\gcd(a,b,d)=1\\) and \\(c\\) square\u2011free.\n\nHence  \n\n\\[\na+b+c+d = 1+5+185+68 = 259.\n\\]\n\n\\[\n\\boxed{259}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nThe product $ \\prod_{k=4}^{63} \\frac{\\log_k(5^{k^2-1})}{\\log_{k+1}(5^{k^2-4})} = \\frac{\\log_4(5^{15})}{\\log_5(5^{12})} \\cdot \\frac{\\log_5(5^{24})}{\\log_6(5^{21})} \\cdot \\frac{\\log_6(5^{35})}{\\log_7(5^{32})} \\cdots \\frac{\\log_{63}(5^{3968})}{\\log_{64}(5^{3965})} $ is equal to $ \\frac{m}{n} $, where $ m $ and $ n $ are relatively prime positive integers. Find $ m + n $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "\\[\n\\prod_{k=4}^{63}\\frac{\\log_k\\!\\left(5^{k^{2}-1}\\right)}{\\log_{k+1}\\!\\left(5^{k^{2}-4}\\right)}\n= \\prod_{k=4}^{63}\n\\frac{(k^{2}-1)\\ln5/\\ln k}{(k^{2}-4)\\ln5/\\ln(k+1)}\n= \\prod_{k=4}^{63}\\frac{k^{2}-1}{k^{2}-4}\\cdot\\frac{\\ln(k+1)}{\\ln k}\n\\]\n\nSince \\(k^{2}-1=(k-1)(k+1)\\) and \\(k^{2}-4=(k-2)(k+2)\\),\n\n\\[\n\\frac{k^{2}-1}{k^{2}-4}= \\frac{k-1}{k-2}\\cdot\\frac{k+1}{k+2}.\n\\]\n\nThus\n\n\\[\nP=\\Bigl(\\prod_{k=4}^{63}\\frac{k-1}{k-2}\\Bigr)\n   \\Bigl(\\prod_{k=4}^{63}\\frac{k+1}{k+2}\\Bigr)\n   \\Bigl(\\prod_{k=4}^{63}\\frac{\\ln(k+1)}{\\ln k}\\Bigr).\n\\]\n\nEach product telescopes:\n\n1. \\(\\displaystyle\\prod_{k=4}^{63}\\frac{k-1}{k-2}\n   =\\frac{3}{2}\\cdot\\frac{4}{3}\\cdots\\frac{62}{61}\n   =\\frac{62}{2}=31.\\)\n\n2. \\(\\displaystyle\\prod_{k=4}^{63}\\frac{k+1}{k+2}\n   =\\frac{5}{6}\\cdot\\frac{6}{7}\\cdots\\frac{64}{65}\n   =\\frac{5}{65}=\\frac1{13}.\\)\n\n3. \\(\\displaystyle\\prod_{k=4}^{63}\\frac{\\ln(k+1)}{\\ln k}\n   =\\frac{\\ln5}{\\ln4}\\cdot\\frac{\\ln6}{\\ln5}\\cdots\\frac{\\ln64}{\\ln63}\n   =\\frac{\\ln64}{\\ln4}\n   =\\log_{4}64=3.\\)\n\nMultiplying,\n\n\\[\nP=31\\cdot\\frac1{13}\\cdot3=\\frac{93}{13}.\n\\]\n\nThus \\(m=93,\\;n=13\\) (relatively prime) and  \n\n\\[\nm+n=93+13=106.\n\\]\n\n\\[\n\\boxed{106}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nFour unit squares form a $2 \\times 2$ grid. Each of the 12 unit line segments forming the sides of the squares is colored either red or blue in such a way that each unit square has 2 red sides and 2 blue sides. Find the number of such colorings.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Label the unit line segments as follows.\n\n\\[\n\\begin{array}{c}\n\\text{Top edges: }T_1,T_2\\\\\n\\text{Bottom edges: }B_1,B_2\\\\\n\\text{Left edges: }L_1,L_2\\\\\n\\text{Right edges: }R_1,R_2\\\\\n\\text{Middle vertical edges: }M_{v1},M_{v2}\\\\\n\\text{Middle horizontal edges: }M_{h1},M_{h2}\n\\end{array}\n\\]\n\nEach of the four unit squares must have exactly two red sides.\nLet a red edge be denoted by \\(1\\) and a blue edge by \\(0\\).\nIntroduce the binary variables  \n\n\\[\n\\begin{aligned}\n&a=M_{v1},\\;b=M_{v2},\\;c=M_{h1},\\;d=M_{h2},\\\\\n&p=T_1,\\;q=T_2,\\;r=B_1,\\;s=B_2,\\\\\n&u=L_1,\\;v=L_2,\\;w=R_1,\\;x=R_2 .\n\\end{aligned}\n\\]\n\nThe condition \u201ctwo red sides\u201d for each of the four squares gives four linear\nequations:\n\n\\[\n\\begin{cases}\np+u+a+c=2\\\\\nq+w+a+d=2\\\\\nr+v+b+c=2\\\\\ns+x+b+d=2\\qquad (1)\n\\end{cases}\n\\]\n\nAll variables are \\(0\\) or \\(1\\).\n\n--------------------------------------------------------------------\n### Fix the interior edges\n\nThe interior edges are the four variables \\(a,b,c,d\\).\nFor a fixed choice of \\((a,b,c,d)\\) each equation in (1) involves a\ndifferent pair of outer edges:\n\n\\[\n\\begin{aligned}\np+u &=2-(a+c),\\\\\nq+w &=2-(a+d),\\\\\nr+v &=2-(b+c),\\\\\ns+x &=2-(b+d).\n\\end{aligned}\n\\tag{2}\n\\]\n\nFor a pair of binary variables the number of possibilities for a given\nsum is  \n\n\\[\nf(s)=\\begin{cases}\n1 & s=0\\text{ or }2,\\\\[2pt]\n2 & s=1,\\\\[2pt]\n0 & \\text{otherwise}.\n\\end{cases}\n\\]\n\nHence, for a fixed interior assignment the number of ways to colour the\nouter edges equals  \n\n\\[\nf\\bigl(2-(a+c)\\bigr)\\,\nf\\bigl(2-(a+d)\\bigr)\\,\nf\\bigl(2-(b+c)\\bigr)\\,\nf\\bigl(2-(b+d)\\bigr).\n\\]\n\nBecause \\(a,c,b,d\\in\\{0,1\\}\\), each sum \\(a+c,\\;a+d,\\;b+c,\\;b+d\\) is\n\\(0,1,\\) or \\(2\\); consequently the factor is \\(2\\) exactly when the\ncorresponding pair contains one \\(0\\) and one \\(1\\), and it is \\(1\\) when\nthe pair is equal.  \n\nDefine\n\n\\[\nN(a,b,c,d)=\\bigl[ a\\ne c\\bigr]+\\bigl[ a\\ne d\\bigr]+\\bigl[ b\\ne c\\bigr]\n+\\bigl[ b\\ne d\\bigr].\n\\]\n\nThen the number of outer colourings for that interior choice is\n\\(2^{\\,N(a,b,c,d)}\\).\n\n--------------------------------------------------------------------\n### Counting all interior choices\n\nThe four interior bits can be viewed as two binary strings  \n\\(A=(a,b)\\) and \\(C=(c,d)\\).  The quantity \\(N\\) counts the mismatches\nbetween \\(A\\) and \\(C\\) over all four cross\u2011pairs, and one obtains\n\n\\[\nN=2\\bigl(w_A+w_C-w_Aw_C\\bigr),\n\\]\nwhere \\(w_A=a+b\\) and \\(w_C=c+d\\) are the numbers of 1\u2019s in the strings.\n\nFrom this we get the possible values:\n\n* **\\(N=0\\)** when \\(A=C\\) (all four interior edges equal).  \n  Two assignments: \\((0,0,0,0)\\) and \\((1,1,1,1)\\).  \n  Contribution: \\(2\\cdot2^{0}=2\\).\n\n* **\\(N=4\\)** when the two strings are opposite, i.e. \\(A=(0,0), C=(1,1)\\)\n  or \\(A=(1,1), C=(0,0)\\).  \n  Two assignments.  \n  Contribution: \\(2\\cdot2^{4}=32\\).\n\n* **\\(N=2\\)** for all remaining \\(16-4=12\\) interior assignments.  \n  Contribution: \\(12\\cdot2^{2}=48\\).\n\nAdding them gives the total number of colourings\n\n\\[\n2+48+32 = 82.\n\\]\n\n--------------------------------------------------------------------\n\\[\n\\boxed{82}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nOn $\\triangle ABC$ points $A,D,E$, and $B$ lie that order on side $\\overline{AB}$ with $AD=4, DE=16$, and $EB=8$. Points $A,F,G$, and $C$ lie in that order on side $\\overline{AC}$ with $AF=13, FG=52$, and $GC=26$. Let $M$ be the reflection of $D$ through $F$, and let $N$ be the reflection of $G$ through $E$. Quadrilateral $DEGF$ has area 288. Find the area of heptagon $AFNBCEM$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "**Solution Overview**\n\nPlace \\(\\triangle ABC\\) in the plane with  \n\n\\[\nA=(0,0),\\qquad B=(28,0),\\qquad C=(x,y)\n\\]\n\nso that \\(AB=28\\).  \nThe points on the sides are\n\n\\[\n\\begin{aligned}\nD&=A+\\frac17AB=(4,0), &\nE&=A+\\frac57AB=(20,0),\\\\\nF&=A+\\frac17AC=\\Bigl(\\frac{x}{7},\\frac{y}{7}\\Bigr), &\nG&=A+\\frac57AC=\\Bigl(\\frac{5x}{7},\\frac{5y}{7}\\Bigr).\n\\end{aligned}\n\\]\n\n(The given lengths give the fractions \\(\\frac17,\\frac57\\) on both sides because  \n\n\\[\nAD:DE:EB=4:16:8=1:4:2,\\qquad \nAF:FG:GC=13:52:26=1:4:2 .\n\\])\n\nThe reflections are\n\n\\[\n\\begin{aligned}\nM&=2F-D=\\Bigl(\\frac{2x}{7}-4,\\frac{2y}{7}\\Bigr),\\\\[2mm]\nN&=2E-G=\\Bigl(40-\\frac{5x}{7},-\\frac{5y}{7}\\Bigr).\n\\end{aligned}\n\\]\n\n--------------------------------------------------------------------\n### 1.  Height of the triangle\n\nThe quadrilateral \\(DEGF\\) is \\(\\{D,E,G,F\\}\\) in that order.  \nUsing the shoelace formula,\n\n\\[\n\\begin{aligned}\n[DEGF]\n&=\\frac12\\Bigl((4\\cdot0+20\\cdot\\frac{5y}{7}+\\frac{5x}{7}\\cdot\\frac{y}{7}+ \\frac{x}{7}\\cdot0) \\\\\n&\\qquad\\ -\\ (0\\cdot20+\\;0\\cdot\\frac{5x}{7}+\\frac{5y}{7}\\cdot\\frac{x}{7}+ \\frac{y}{7}\\cdot4 )\\Bigr)\\\\[1mm]\n&=\\frac12\\Bigl(20\\cdot\\frac{5y}{7}-4\\cdot\\frac{y}{7}\\Bigr)\n =\\frac{1248}{91}\\,\\frac{y}{2}= \\frac{624}{91}\\,y .\n\\end{aligned}\n\\]\n\nThe problem states \\([DEGF]=288\\); hence\n\n\\[\n\\frac{624}{91}\\,y=288\\qquad\\Longrightarrow\\qquad y=42 .\n\\]\n\nThus the altitude from \\(C\\) to \\(\\overline{AB}\\) is \\(h=y=42\\).\n\n--------------------------------------------------------------------\n### 2.  Area of \\(\\triangle ABC\\)\n\n\\[\n[ABC]=\\frac12\\cdot AB\\cdot h=\\frac12\\cdot 28\\cdot 42=14\\cdot 42=588.\n\\]\n\n--------------------------------------------------------------------\n### 3.  Area of the heptagon \\(AFNBCEM\\)\n\nWrite the vertices in order:\n\n\\[\nA,\\;F,\\;N,\\;B,\\;C,\\;E,\\;M .\n\\]\n\nUsing the coordinates found above (with \\(y=42\\) and \\(\\,x=\\sqrt{91^{2}-42^{2}}=7\\sqrt{133}\\)), the\nshoelace sum is\n\n\\[\n\\begin{aligned}\nS&=x_Ay_F-y_Ax_F\n   +x_Fy_N-y_Fx_N\n   +x_Ny_B-y_Nx_B\n   +x_By_C-y_Bx_C\n   +x_Cy_E-y_Cx_E\n   +x_Ey_M-y_Ex_M\n   +x_My_A-y_Mx_A \\\\[1mm]\n&=0-240+840+1176-840+240+0=1176 .\n\\end{aligned}\n\\]\n\nHence\n\n\\[\n[AFNBCEM]=\\frac12\\,S=\\frac12\\cdot1176=588 .\n\\]\n\nA vector\u2011geometry check also shows that the signed sum of the\ndeterminants of successive vertices equals \\(\\det(\\overrightarrow{AB},\n\\overrightarrow{AC})\\), i.e. the area of \\(\\triangle ABC\\).\n\n--------------------------------------------------------------------\n### 4.  Answer\n\n\\[\n\\boxed{588}\n\\]",
+        "role": "assistant"
+      }
+    ],
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+      {
+        "role": "user",
+        "content": "\nLet $ A $ be the set of positive integer divisors of 2025. Let $ B $ be a randomly selected subset of $ A $. The probability that $ B $ is a nonempty set with the property that the least common multiple of its elements is 2025 is $ \\frac{m}{n} $, where $ m $ and $ n $ are relatively prime positive integers. Find $ m + n $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Factor  \n\\[\n2025=3^{4}\\cdot5^{2}.\n\\]\n\nA divisor of \\(2025\\) is \\(3^{i}5^{j}\\) with \\(0\\le i\\le4,\\;0\\le j\\le2\\).  \nHence  \n\n\\[\n|A|=(4+1)(2+1)=15 .\n\\]\n\n---\n\n### When does a subset have lcm \\(2025\\)?\n\nThe lcm of a set of divisors takes, for each prime, the **maximum** exponent appearing among the chosen numbers.\n\nThus a subset \\(B\\subseteq A\\) has \\(\\operatorname{lcm}(B)=3^{4}5^{2}=2025\\) iff  \n\n* at least one element of \\(B\\) has exponent \\(4\\) of the prime \\(3\\);\n* at least one element of \\(B\\) has exponent \\(2\\) of the prime \\(5\\).\n\nDefine  \n\n\\[\nS_{3}=\\{3^{4}5^{j}\\mid j=0,1,2\\}=\\{81,405,2025\\},\n\\qquad\nS_{5}=\\{3^{i}5^{2}\\mid i=0,1,2,3,4\\}\n =\\{25,75,225,675,2025\\}.\n\\]\n\n\\(|S_{3}|=3,\\ |S_{5}|=5,\\) and \\(|S_{3}\\cap S_{5}|=1\\) (the element \\(2025\\)).\n\nSo we need subsets that intersect **both** \\(S_{3}\\) and \\(S_{5}\\).\n\n---\n\n### Counting such subsets\n\nTotal subsets of \\(A\\): \\(2^{15}\\).\n\nLet  \n\n* \\(A_{3}\\) = subsets containing **no** element of \\(S_{3}\\).  \n  \\(|A_{3}| = 2^{15-3}=2^{12}\\).\n\n* \\(A_{5}\\) = subsets containing **no** element of \\(S_{5}\\).  \n  \\(|A_{5}| = 2^{15-5}=2^{10}\\).\n\n* \\(A_{3}\\cap A_{5}\\) = subsets containing none of \\(S_{3}\\cup S_{5}\\).  \n  \\(|S_{3}\\cup S_{5}| = 3+5-1 = 7\\), so  \n  \\(|A_{3}\\cap A_{5}| = 2^{15-7}=2^{8}\\).\n\nBy inclusion\u2013exclusion, the number of subsets intersecting both \\(S_{3}\\) and \\(S_{5}\\) is  \n\n\\[\n2^{15} - 2^{12} - 2^{10} + 2^{8}\n = 32768 - 4096 - 1024 + 256\n = 27904.\n\\]\n\nEvery such subset is non\u2011empty, so these are exactly the favorable subsets.\n\n---\n\n### Probability\n\n\\[\n\\text{Probability}\n = \\frac{27904}{2^{15}}\n = \\frac{27904}{32768}\n = \\frac{109}{128}\n\\]\n(after reducing the fraction).\n\nThus \\(m=109,\\ n=128\\) and  \n\n\\[\nm+n = 109+128 = 237.\n\\]\n\n\\[\n\\boxed{237}\n\\]",
+        "role": "assistant"
+      }
+    ],
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+      {
+        "role": "user",
+        "content": "\nCircle $\\omega_1$ with radius 6 centered at point $A$ is internally tangent at point $B$ to circle $\\omega_2$ with radius 15. Points $C$ and $D$ lie on $\\omega_2$ such that $\\overline{BC}$ is a diameter of $\\omega_2$ and $\\overline{BC} \\perp \\overline{AD}$. The rectangle $EFGH$ is inscribed in $\\omega_1$ such that $\\overline{EF} \\perp \\overline{BC}$, $C$ is closer to $\\overline{GH}$ than to $\\overline{EF}$, and $D$ is closer to $\\overline{FG}$ than to $\\overline{EH}$, as shown. Triangles $\\triangle DGF$ and $\\triangle CHG$ have equal areas. The area of rectangle $EFGH$ is $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m + n$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n* \\(O\\) be the centre of \\(\\omega _2\\) (radius \\(15\\)),\n* \\(A\\) be the centre of \\(\\omega _1\\) (radius \\(6\\)),\n* \\(B\\) the point where the two circles are internally tangent,\n* \\(C\\) the antipode of \\(B\\) on \\(\\omega_2\\) (\\(BC\\) is a diameter),\n* \\(D\\) the point on \\(\\omega _2\\) with \\(AD\\perp BC\\).\n\n--------------------------------------------------------------------\n### 1.  Choose coordinates  \n\nPlace \\(O\\) at the origin and let the diameter \\(BC\\) be horizontal.\n\n\\[\nB=(15,0),\\qquad C=(-15,0)\n\\]\n\nSince \\(OA=15-6=9\\) and \\(A\\) lies on \\(OB\\),\n\n\\[\nA=(9,0).\n\\]\n\nThe line \\(AD\\) is perpendicular to the horizontal line \\(BC\\), so \\(AD\\) is the\nvertical line through \\(A\\); intersecting \\(\\omega_2\\) gives\n\n\\[\nD=(9,12)\\quad\\text{or}\\quad D=(9,-12).\n\\]\n\nBecause the rectangle will be placed above the centre of \\(\\omega_1\\), we take  \n\n\\[\nD=(9,12).\n\\]\n\n--------------------------------------------------------------------\n### 2.  Describe the rectangle  \n\nSince the rectangle is **inscribed** in \\(\\omega_1\\), all four of its vertices lie on\n\\(\\omega_1\\).  \nLet the rectangle have centre at \\(A\\); because a rectangle\u2019s circum\u2011centre is\nthe intersection of its diagonals, the centre must be the centre of the\ncircumscribing circle \\(\\omega_1\\).\n\nLet  \n\n* half\u2011width \\(w\\) (distance from the centre to the right\u2013hand side),\n* half\u2011height \\(h\\) (distance from the centre to the top side).\n\nThen  \n\n\\[\n\\begin{aligned}\nx_R&=9+w, & x_L&=9-w,\\\\\ny_T&=h,   & y_B&=-h .\n\\end{aligned}\n\\]\n\nThe vertices are  \n\n\\[\n\\begin{aligned}\nE&(x_R,y_B)=(9+w,-h),\\\\\nF&(x_R,y_T)=(9+w, h),\\\\\nG&(x_L,y_T)=(9-w, h),\\\\\nH&(x_L,y_B)=(9-w,-h).\n\\end{aligned}\n\\]\n\nBecause the vertices lie on \\(\\omega_1\\) (radius \\(6\\)),\n\n\\[\nw^{2}+h^{2}=6^{2}=36\\tag{1}\n\\]\n\n--------------------------------------------------------------------\n### 3.  Use the area condition  \n\nThe problem states that  \n\n\\[\n\\text{Area}\\,\\triangle DGF=\\text{Area}\\,\\triangle CHG .\n\\]\n\n*Triangle \\(DGF\\).*  \nIts base is \\(GF\\) (the top side of the rectangle) of length \\(2w\\).  \nIts height is the vertical distance from \\(D\\) to the line \\(y=h\\):\n\\(\\;12-h\\). Hence  \n\n\\[\n[\\triangle DGF]=\\tfrac12(2w)(12-h)=w(12-h).\\tag{2}\n\\]\n\n*Triangle \\(CHG\\).*  \nIts base is \\(HG\\) (the left side) of length \\(2h\\).  \nThe distance from \\(C\\) to the vertical line \\(x=9-w\\) is\n\\((9-w)-(-15)=24-w\\). Therefore  \n\n\\[\n[\\triangle CHG]=\\tfrac12(2h)(24-w)=h(24-w).\\tag{3}\n\\]\n\nEquating (2) and (3),\n\n\\[\nw(12-h)=h(24-w).\\tag{4}\n\\]\n\nExpanding both sides gives  \n\n\\[\n12w-wh=24h-wh\\Longrightarrow 12w=24h\\Longrightarrow w=2h.\\tag{5}\n\\]\n\n--------------------------------------------------------------------\n### 4.  Solve for \\(w\\) and \\(h\\)\n\nSubstituting \\(w=2h\\) into (1):\n\n\\[\n(2h)^2+h^2=36\\quad\\Longrightarrow\\quad5h^{2}=36\\quad\\Longrightarrow\\quad\nh^{2}= \\frac{36}{5},\\qquad\nh=\\frac{6}{\\sqrt5}=\\frac{6\\sqrt5}{5}.\n\\]\n\nHence  \n\n\\[\nw=2h=\\frac{12}{\\sqrt5}= \\frac{12\\sqrt5}{5}.\n\\]\n\n--------------------------------------------------------------------\n### 5.  Area of the rectangle  \n\nThe rectangle\u2019s side lengths are \\(2w\\) and \\(2h\\), so its area is  \n\n\\[\n\\text{Area}= (2w)(2h)=4wh=4\\cdot(2h)h=8h^{2}\n          =8\\left(\\frac{36}{5}\\right)=\\frac{288}{5}.\n\\]\n\nThus the area is \\(\\displaystyle \\frac{288}{5}\\).\nThe numerator and denominator are relatively prime, so  \n\n\\[\nm=288,\\qquad n=5,\\qquad m+n=288+5=293.\n\\]\n\n--------------------------------------------------------------------\n\\[\n\\boxed{293}\n\\]",
+        "role": "assistant"
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+      {
+        "role": "user",
+        "content": "\nAlex divides a disk into four quadrants with two perpendicular diameters intersecting at the center of the disk. He draws 25 more line segments through the disk, drawing each segment by selecting two points at random on the perimeter of the disk in different quadrants and connecting those two points. Find the expected number of regions into which these 27 line segments divide the disk.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "**Step 1.  Regions created by chords**\n\nIf we start with a disc (one region) and draw a chord, the number of regions increases by  \n\n\\[\n\\text{(number of interior intersections created by the new chord)}+1 .\n\\]\n\nHence after drawing \\(k\\) chords the number of regions is  \n\n\\[\nR=1+k+I ,\n\\]\n\nwhere \\(I\\) is the total number of interior intersection points of the drawn chords (no three chords meet at a single interior point, which holds a.s. for random chords).\n\nIn our problem \\(k=27\\) (the two diameters plus the 25 random chords), so  \n\n\\[\nR=28+I .\n\\]\n\nThus we only need the expected value of \\(I\\).\n\n--------------------------------------------------------------------\n\n**Step 2.  Intersections involving the two fixed diameters**\n\nThe two diameters intersect at the centre, contributing a deterministic intersection  \n\n\\[\nI_{\\text{centre}}=1 .\n\\]\n\nA random chord intersects the **vertical** diameter iff its endpoints lie in opposite halves of the disc, i.e. one endpoint in \\(\\{Q_1,Q_4\\}\\) and the other in \\(\\{Q_2,Q_3\\}\\).  \nAmong the six possible unordered quadrant\u2011pairs for a chord, four satisfy this condition, so\n\n\\[\nP(\\text{vertical intersection})=\\frac{4}{6}=\\frac23 .\n\\]\n\nThe same reasoning holds for the **horizontal** diameter, giving  \n\n\\[\nP(\\text{horizontal intersection})=\\frac23 .\n\\]\n\nHence for the 25 random chords\n\n\\[\nE[I_{\\text{vert}}]=25\\cdot\\frac23=\\frac{50}{3},\\qquad   \nE[I_{\\text{horiz}}]=25\\cdot\\frac23=\\frac{50}{3}.\n\\]\n\n--------------------------------------------------------------------\n\n**Step 3.  Intersections among the 25 random chords**\n\nTwo random chords are independent.  \nEach chord chooses an unordered pair of distinct quadrants uniformly from the six possibilities  \n\n\\[\n\\{1,2\\},\\{2,3\\},\\{3,4\\},\\{4,1\\} \\ (\\text{adjacent}),\\qquad\n\\{1,3\\},\\{2,4\\}\\ (\\text{opposite}).\n\\]\n\nLet the unordered pairs be \\(S\\) and \\(T\\).  \nTheir intersection size can be\n\n* **2** (the same pair) \u2013 probability \\(1/6\\);\n* **1** (they share exactly one quadrant) \u2013 probability \\(2/3\\);\n* **0** (disjoint) \u2013 probability \\(1/6\\).\n\nThe disjoint case splits further:\n\n* Adjacent\u2013adjacent (e.g. \\(\\{1,2\\}\\) with \\(\\{3,4\\}\\)) \u2013 chords never intersect.\n* Opposite\u2013opposite (e.g. \\(\\{1,3\\}\\) with \\(\\{2,4\\}\\)) \u2013 chords always intersect.\n\nAmong the three unordered disjoint pairs, two are adjacent\u2013adjacent and one is opposite\u2013opposite; hence for ordered pairs\n\n\\[\nP(\\text{disjoint, intersect})=\\frac{2}{36}=\\frac1{18},\\qquad\nP(\\text{disjoint, no intersect})=\\frac{4}{36}.\n\\]\n\nFor the other two situations one can check (by considering the relative order of the points inside the quadrants) that\n\n* If the two chords have the **same** unordered pair (adjacent or opposite), the probability they intersect is \\(\\tfrac12\\).\n* If they **share exactly one quadrant**, the probability they intersect is also \\(\\tfrac12\\).\n\nCollecting the contributions,\n\n\\[\n\\begin{aligned}\nP(\\text{intersection}) &=\n\\underbrace{\\frac{6}{36}\\cdot\\frac12}_{\\text{same pair}}\n+\\underbrace{\\frac{24}{36}\\cdot\\frac12}_{\\text{share one quadrant}}\n+\\underbrace{\\frac{2}{36}\\cdot1}_{\\text{disjoint opposite}}\\\\[2mm]\n&=\\frac{3}{36}+\\frac{12}{36}+\\frac{2}{36}\n=\\frac{17}{36}.\n\\end{aligned}\n\\]\n\nThus for any unordered pair of the 25 random chords\n\n\\[\np:=P(\\text{they intersect})=\\frac{17}{36}.\n\\]\n\nThere are \\(\\binom{25}{2}=300\\) such pairs, so\n\n\\[\nE[I_{\\text{random}}]=300\\cdot\\frac{17}{36}\n=\\frac{300}{36}\\cdot17\n=\\frac{25}{3}\\cdot17\n=\\frac{425}{3}.\n\\]\n\n--------------------------------------------------------------------\n\n**Step 4.  Expected total number of interior intersections**\n\n\\[\n\\begin{aligned}\nE[I] &= I_{\\text{centre}}\n      +E[I_{\\text{vert}}]\n      +E[I_{\\text{horiz}}]\n      +E[I_{\\text{random}}]  \\\\[2mm]\n     &=1+\\frac{50}{3}+\\frac{50}{3}+\\frac{425}{3} \\\\[2mm]\n     &=1+\\frac{525}{3}=1+175=176 .\n\\end{aligned}\n\\]\n\n--------------------------------------------------------------------\n\n**Step 5.  Expected number of regions**\n\n\\[\nE[R]=28+E[I]=28+176=204 .\n\\]\n\n--------------------------------------------------------------------\n\n\\[\n\\boxed{204}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nLet the sequence of rationals $ x_1, x_2, \\ldots $ be defined such that $ x_1 = \\frac{25}{11} $ and\n$ x_{k+1} = \\frac{1}{3} \\left( x_k + \\frac{1}{x_k} - 1 \\right). $\n$ x_{2025} $ can be expressed as $ \\frac{m}{n} $ for relatively prime positive integers $ m $ and $ n $. Find the remainder when $ m + n $ is divided by 1000.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "**Solution Outline**\n\n1.  Transform the recurrence for \\(x_k\\) into a simpler one.\n\n   Define  \n\n   \\[\n   w_k=\\frac{x_k-1}{x_k+1}\\quad\\Longleftrightarrow\\quad \n   x_k=\\frac{1+w_k}{1-w_k}.\n   \\]\n\n   Substituting in  \n\n   \\[\n   x_{k+1}= \\frac13\\Bigl(x_k+\\frac1{x_k}-1\\Bigr)\n   \\]\n\n   gives after simplification  \n\n   \\[\n   w_{k+1}= \\frac{3w_k^2-1}{2}. \\tag{1}\n   \\]\n\n   The initial value is  \n\n   \\[\n   w_1=\\frac{25/11-1}{25/11+1}=\\frac{7}{18}.\n   \\]\n\n2.  Write \\(w_k=\\dfrac{a_k}{b_k}\\) in lowest terms\n   (\\(a_k\\) odd, \\(b_k\\) even).  \n\n   From (1),\n\n   \\[\n   w_{k+1}= \\frac{3a_k^2-b_k^2}{2b_k^2}.\n   \\]\n\n   Because \\(a_k\\) is not divisible by\u202f3, the numerator is always\n   \\(\\equiv 3\\pmod 9\\); hence it contains exactly one factor\u202f3.\n   After canceling this factor we obtain\n\n   \\[\n   a_{k+1}= \\frac{3a_k^2-b_k^2}{3},\\qquad\n   b_{k+1}= \\frac{2b_k^2}{3}.\n   \\tag{2}\n   \\]\n\n   Consequently  \n\n   \\[\n   b_{k+1}= \\frac{2}{3}b_k^{\\,2}. \\tag{3}\n   \\]\n\n3.  Determine a closed form for \\(b_k\\).\n\n   Write \\(b_k=2^{\\alpha_k}3^{\\beta_k}\\).\n   From (3)\n\n   \\[\n   2^{\\alpha_{k+1}}3^{\\beta_{k+1}}\n   =\\frac{2}{3}\\bigl(2^{\\alpha_k}3^{\\beta_k}\\bigr)^2\n   =2^{2\\alpha_k+1}3^{2\\beta_k-1},\n   \\]\n\n   whence  \n\n   \\[\n   \\alpha_{k+1}=2\\alpha_k+1,\\qquad\n   \\beta_{k+1}=2\\beta_k-1,\n   \\]\n   with \\(\\alpha_1=1,\\ \\beta_1=2\\).\n\n   Solving these linear recurrences gives  \n\n   \\[\n   \\alpha_k = 2^{\\,k}-1,\\qquad\n   \\beta_k = 2^{\\,k-1}+1 .\n   \\]\n\n   Therefore  \n\n   \\[\n   b_k = 2^{\\,2^{k}-1}\\,3^{\\,2^{k-1}+1}. \\tag{4}\n   \\]\n\n4.  Recover \\(x_k\\) from \\(w_k\\).\n\n   Since \\(x_k=\\dfrac{1+w_k}{1-w_k}\\) and \\(w_k=\\dfrac{a_k}{b_k}\\),\n\n   \\[\n   x_k=\\frac{b_k+a_k}{\\,b_k-a_k\\,}= \\frac{m_k}{n_k},\n   \\]\n   where \\(m_k=b_k+a_k,\\ n_k=b_k-a_k\\).  \n   Because \\(a_k\\) is odd and \\(b_k\\) is even, \\(m_k\\) and \\(n_k\\) are odd,\n   so \\(\\gcd(m_k,n_k)=1\\).\n\n   Hence\n\n   \\[\n   m_k+n_k = (b_k+a_k)+(b_k-a_k)=2b_k.\n   \\]\n\n5.  Compute \\(m_{2025}+n_{2025}\\pmod{1000}\\).\n\n   From (4),\n\n   \\[\n   b_{2025}=2^{\\,2^{2025}-1}\\,3^{\\,2^{2024}+1},\n   \\qquad\n   m_{2025}+n_{2025}=2b_{2025}\n   =2^{\\,2^{2025}}\\,3^{\\,2^{2024}+1}.\n   \\]\n\n   We need this value modulo \\(1000=2^3\\cdot5^3\\).\n\n   *Modulo\u202f8:* the exponent of\u202f2 is at least\u202f3, so the whole product\n   is \\(0\\pmod8\\).\n\n   *Modulo\u202f125:* use Euler\u2019s theorem (\\(\\phi(125)=100\\)):\n   \\[\n   2^{2^{2025}}\\equiv2^{\\,32}\\pmod{125},\\qquad\n   3^{2^{2024}+1}\\equiv3^{\\,17}\\pmod{125},\n   \\]\n   because \\(2^{2025}\\equiv32\\) and \\(2^{2024}+1\\equiv17\\pmod{100}\\).\n\n   Computing,\n   \\[\n   2^{32}\\equiv46,\\qquad 3^{17}\\equiv38\\pmod{125},\n   \\]\n   so\n   \\[\n   2^{2^{2025}}3^{2^{2024}+1}\\equiv46\\cdot38\\equiv123\\pmod{125}.\n   \\]\n\n   Solve the simultaneous congruences\n   \\[\n   X\\equiv0\\pmod8,\\qquad X\\equiv123\\pmod{125}.\n   \\]\n   Writing \\(X=125a+123\\) and using \\(125\\equiv5\\pmod8\\) gives\n   \\(5a+3\\equiv0\\pmod8\\Rightarrow a\\equiv1\\pmod8\\).\n   Hence \\(X=125\\cdot1+123=248\\).\n\n   Therefore  \n\n   \\[\n   m_{2025}+n_{2025}\\equiv\\boxed{248}\\pmod{1000}.\n   \\]",
+        "role": "assistant"
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+        "role": "user",
+        "content": "\nThere are $ n $ values of $ x $ in the interval $ 0 < x < 2\\pi $ where $ f(x) = \\sin(7\\pi \\cdot \\sin(5x)) = 0 $. For $ t $ of these $ n $ values of $ x $, the graph of $ y = f(x) $ is tangent to the $ x $-axis. Find $ n + t $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "\\[\nf(x)=\\sin\\bigl(7\\pi\\sin (5x)\\bigr)\n\\]\n\nThe zeros of \\(f\\) occur when the inner sine gives an integer multiple of \\(\\pi\\):\n\n\\[\n\\sin\\bigl(7\\pi\\sin (5x)\\bigr)=0\\Longleftrightarrow 7\\pi\\sin(5x)=k\\pi\n\\Longleftrightarrow \\sin(5x)=\\frac{k}{7},\n\\qquad k\\in\\mathbb Z .\n\\]\n\nBecause \\(\\sin(5x)\\in[-1,1]\\), \\(|k|\\le7\\); thus \\(k=-7,-6,\\dots ,6,7\\).\n\n---\n\n### 1.  Counting the zeros  \n\nSet \\(\\theta =5x\\).  \nWhen \\(x\\in(0,2\\pi)\\) we have \\(\\theta\\in(0,10\\pi)\\).\n\nFor each admissible integer \\(k\\) we need the number of solutions of  \n\n\\[\n\\sin\\theta=\\frac{k}{7},\\qquad \\theta\\in(0,10\\pi).\n\\]\n\n* **\\(k=0\\):** \\(\\sin\\theta=0\\Rightarrow\\theta=n\\pi\\).  \n  Inside \\((0,10\\pi)\\) we have \\(n=1,2,\\ldots ,9\\) \u2192 **9 solutions**.\n\n* **\\(k=\\pm 7\\):** \\(\\sin\\theta=\\pm1\\).  \n  \\(\\sin\\theta=1\\) gives \\(\\theta=\\dfrac{\\pi}{2}+2\\pi n\\);  \n  \\(\\sin\\theta=-1\\) gives \\(\\theta=\\dfrac{3\\pi}{2}+2\\pi n\\).  \n  For \\(0<\\theta<10\\pi\\) each yields \\(n=0,1,2,3,4\\) \u2192 **5 solutions** for \\(k=7\\) and **5** for \\(k=-7\\).\n\n* **\\(k=\\pm1,\\pm2,\\dots ,\\pm6\\):** \\(|k|<7\\) so \\(-1<k/7<1\\) and \\(\\neq0\\).  \n  In each full period \\([0,2\\pi]\\) the equation \\(\\sin\\theta=c\\) (\\(|c|<1\\)) has two solutions.  \n  The interval \\((0,10\\pi)\\) contains five full periods, hence **\\(5\\times2=10\\) solutions** for each of these 12 values of \\(k\\).\n\nSumming all contributions  \n\n\\[\n\\begin{aligned}\nn &=\\underbrace{9}_{k=0}\n   +\\underbrace{5+5}_{k=\\pm7}\n   +\\underbrace{12\\times10}_{k=\\pm1,\\dots,\\pm6}\\\\[2mm]\n  &=9+10+120 = 139 .\n\\end{aligned}\n\\]\n\nThus there are \\(\\boxed{139}\\) zeros of \\(f\\) in \\((0,2\\pi)\\).\n\n---\n\n### 2.  Zeros where the graph is tangent to the \\(x\\)-axis  \n\nA point where the graph touches the \\(x\\)-axis must satisfy  \n\n\\[\nf(x)=0\\quad\\text{and}\\quad f'(x)=0.\n\\]\n\nFrom \\(f(x)=0\\) we have \\(\\sin(5x)=k/7\\) as above.  \nCompute the derivative:\n\n\\[\n\\begin{aligned}\nf'(x) &=\\cos\\bigl(7\\pi\\sin(5x)\\bigr)\\cdot 7\\pi\\cdot 5\\cos(5x)   \\\\\n      &=35\\pi\\cos\\bigl(7\\pi\\sin(5x)\\bigr)\\cos(5x).\n\\end{aligned}\n\\]\n\nThus \\(f'(x)=0\\) iff \\(\\cos(5x)=0\\) (the factor \\(\\cos\\bigl(7\\pi\\sin(5x)\\bigr)\\) never vanishes at a zero, because\n\\(\\cos(k\\pi)=\\pm1\\)).  \n\n\\[\n\\cos(5x)=0\\Longrightarrow 5x=\\frac{\\pi}{2}+n\\pi\\quad\\Longrightarrow\\quad\\sin(5x)=\\pm1.\n\\]\n\nHence the tangential zeros correspond exactly to the solutions of \\(\\sin(5x)=\\pm1\\), i.e. the cases \\(k=\\pm7\\).\n\nWe already counted these:  \n\n* \\(\\sin(5x)=1\\) gives \\(5\\) solutions,\n* \\(\\sin(5x)=-1\\) gives \\(5\\) solutions.\n\nTherefore  \n\n\\[\nt = 5+5 = 10 .\n\\]\n\n(Indeed, at these points \\(f'(x)=0\\) and \\(f''(x)\\neq0\\), so the graph just touches the axis.)\n\n---\n\n### 3.  Required sum  \n\n\\[\nn+t = 139 + 10 = \\boxed{149}.\n\\]",
+        "role": "assistant"
+      }
+    ],
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+      {
+        "role": "user",
+        "content": "\nFrom an unlimited supply of 1-cent coins, 10-cent coins, and 25-cent coins, Silas wants to find a collection of coins that has a total value of $ N $ cents, where $ N $ is a positive integer. He uses the so-called **greedy algorithm**, successively choosing the coin of greatest value that does not cause the value of his collection to exceed $ N $. For example, to get 42 cents, Silas will choose a 25-cent coin, then a 10-cent coin, then 7 1-cent coins. However, this collection of 9 coins uses more coins than necessary to get a total of 42 cents; indeed, choosing 4 10-cent coins and 2 1-cent coins achieves the same total value with only 6 coins.\n\nIn general, the greedy algorithm succeeds for a given $ N $ if no other collection of 1-cent, 10-cent, and 25-cent coins gives a total value of $ N $ cents using strictly fewer coins than the collection given by the greedy algorithm. Find the number of values of $ N $ between 1 and 1000 inclusive for which the greedy algorithm succeeds.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n\\[\nN=25q+r ,\\qquad 0\\le r<25 .\n\\]\n\nThe greedy algorithm first takes \\(q\\) coins of 25\u202f\u00a2, then  \n\\(t=\\big\\lfloor r/10\\big\\rfloor\\) coins of 10\u202f\u00a2 and finally  \n\\(s=r-10t\\) pennies.  \n\n\\[\n\\text{Greedy coins}=C_g(N)=q+t+s.\n\\]\n\n---\n\n### 1.  What is an optimal representation?\n\nIf a representation uses \\(a\\) 25\u2011cent coins, \\(b\\) 10\u2011cent coins and \\(c\\) pennies, then  \n\n\\[\n25a+10b+c=N,\\qquad a,b,c\\ge0,\n\\]\nand the number of coins is  \n\n\\[\nC= a+b+c = N-(24a+9b).\n\\]\n\nThus **minimising the number of coins is equivalent to maximising**  \n\n\\[\nP=24a+9b \\qquad\\text{subject to}\\qquad 25a+10b\\le N .\n\\]\n\nThe \u201cprofit\u2019\u2019 per cent is larger for a 25\u2011cent coin \\((24/25)\\) than for a 10\u2011cent coin \\((9/10)\\); therefore an optimal solution will use as many 25\u2011cent coins as possible unless removing a 25\u2011cent coin allows us to add enough 10\u2011cent coins to increase the profit.\n\n---\n\n### 2.  Effect of removing \\(k\\) quarters\n\nLet us replace \\(k\\) quarters by 10\u2011cent coins.  \nWrite \\(r=10u+v\\;(0\\le v\\le 9)\\).  \nAfter removing \\(k\\) quarters, the remainder becomes  \n\n\\[\nR=r+25k=10u+v+25k .\n\\]\n\nThe maximal number of dimes that can be added is  \n\n\\[\nb'=\\big\\lfloor \\frac{R}{10}\\big\\rfloor\n   =u+ \\big\\lfloor 2.5k+\\tfrac{v}{10}\\big\\rfloor .\n\\]\n\nThe change in profit is\n\n\\[\n\\Delta P\n=-24k+9\\big(b'-\\big\\lfloor r/10\\big\\rfloor\\big)\n=-6k+9\\Big\\lfloor\\frac{k}{2}\\Big\\rfloor+9\\delta ,\n\\]\n\nwhere  \n\n\\[\n\\delta=\n\\begin{cases}\n1 &\\text{if }k\\text{ is odd and }v\\ge5,\\\\\n0 &\\text{otherwise.}\n\\end{cases}\n\\]\n\n*If \\(k\\) is even*, \\(\\Delta P=-3k/2<0\\); the profit never increases.  \n\n*If \\(k\\) is odd*, write \\(k=2m+1\\). Then  \n\n\\[\n\\Delta P=9\\delta-(3m+6).\n\\]\n\nThe only way \\(\\Delta P>0\\) is when \\(m=0\\) (i.e. \\(k=1\\)) and \\(\\delta=1\\),\nwhich occurs exactly when  \n\n\\[\nv=r\\bmod 10\\ge5 .\n\\]\n\nHence **the greedy algorithm fails precisely when**\n\\[\nN\\ge 25\\quad\\text{and}\\quad (N\\bmod 25)\\bmod 10\\ge5.\n\\]\n\nEquivalently, the \u201cbad\u2019\u2019 remainders (after taking as many quarters as possible) are  \n\n\\[\nr\\in\\{5,6,7,8,9,15,16,17,18,19\\}.\n\\]\n\nIn each block of 25 consecutive integers there are 10 such remainders.\n\n---\n\n### 3.  Counting the failures between 1 and 1000\n\nThe interval \\([25,1000]\\) contains \\(1000-24=976\\) integers.\nFrom 25 onward the numbers are grouped into blocks  \n\n\\[\n25\\!-\\!49,\\;50\\!-\\!74,\\;\\dots,\\;975\\!-\\!999 .\n\\]\n\nThere are \\(39\\) full blocks (the block \\(25\\!-\\!49\\) up to \\(975\\!-\\!999\\)).\nEach block contributes exactly \\(10\\) failures, so\n\n\\[\n\\#\\text{failures}=39\\times10=390 .\n\\]\n\nNumbers \\(1\\) through \\(24\\) are never failures (they contain no quarters).\n\nThus the number of successes is  \n\n\\[\n1000-390=610 .\n\\]\n\n---\n\n\\[\n\\boxed{610}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nLet $ S $ be the set of vertices of a regular 24-gon. Find the number of ways to draw 12 segments of equal lengths so that each vertex in $ S $ is an endpoint of exactly one of the 12 segments.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "In a regular \\(24\\)-gon label the vertices \\(0,1,\\dots ,23\\) clockwise.  \nIf two vertices differ by \\(k\\) (mod \\(24\\)), the chord joining them has length that depends only on  \n\n\\[\ns=\\min (k,24-k)\\qquad (1\\le s\\le 12).\n\\]\n\nThus there are \\(12\\) possible lengths, one for each \\(s=1,2,\\dots ,12\\).\n\n--------------------------------------------------------------------\n### 1.  The graph of chords of a fixed length  \n\nFix a value \\(s\\).  The set of all chords of that length is the edge\u2011set of the **circulant graph**\n\\[\nG_s=\\{\\,\\{i,i+s\\}\\mid i=0,1,\\dots ,23\\,\\},\n\\]\nwhere the addition is taken modulo \\(24\\).\n\nLet \\(g=\\gcd(s,24)\\).  Adding \\(s\\) repeatedly splits the vertex set into \\(g\\) cycles,\neach of length  \n\n\\[\nL=\\frac{24}{g}.\n\\]\n\nSo \\(G_s\\) is a disjoint union of \\(g\\) cycles \\(C_L\\).\n\n--------------------------------------------------------------------\n### 2.  When can a perfect matching exist?\n\nA perfect matching (a set of \\(12\\) disjoint edges covering all vertices) can exist only if\nevery component cycle has even length, i.e. \\(L\\) is even.\nSince \\(L=24/g\\), this is equivalent to \\(g\\mid 12\\).\n\n*If \\(g\\mid 12\\) and \\(L\\ge 4\\)*, each even cycle \\(C_L\\) has exactly **2** perfect\nmatchings (choose alternating edges).  \n*If \\(L=2\\)* (the case \\(s=12\\)), each component is a single edge and contributes only **1** matching.\n\nThe only step for which \\(g\\nmid 12\\) is \\(s=8\\) (here \\(g=8\\) and the components are 3\u2011cycles),\nso no perfect matching exists for \\(s=8\\).\n\n--------------------------------------------------------------------\n### 3.  Number of matchings for each possible length\n\n\\[\n\\begin{array}{c|c|c|c}\ns & g=\\gcd(s,24) & L=24/g & \\#\\text{ matchings}\\\\ \\hline\n1 &1 &24 &2\\\\\n2 &2 &12 &2^{2}=4\\\\\n3 &3 & 8 &2^{3}=8\\\\\n4 &4 & 6 &2^{4}=16\\\\\n5 &1 &24 &2\\\\\n6 &6 & 4 &2^{6}=64\\\\\n7 &1 &24 &2\\\\\n8 &8 & 3 &0\\\\\n9 &3 & 8 &2^{3}=8\\\\\n10&2 &12 &2^{2}=4\\\\\n11&1 &24 &2\\\\\n12&12& 2 &1\n\\end{array}\n\\]\n\n--------------------------------------------------------------------\n### 4.  Total number of ways\n\nAdd the numbers for all admissible lengths (all \\(s\\) except \\(s=8\\)):\n\n\\[\n\\begin{aligned}\n\\text{Total}&=2+4+8+16+2+64+2+8+4+2+1\\\\\n&=113 .\n\\end{aligned}\n\\]\n\n--------------------------------------------------------------------\n\\[\n\\boxed{113}\n\\]",
+        "role": "assistant"
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+        "role": "user",
+        "content": "\nSixteen chairs are arranged in a row. Eight people each select a chair in which to sit so that no person sits next to two other people. Let $ N $ be the number of subsets of 16 chairs that could be selected. Find the remainder when $ N $ is divided by 1000.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "The chairs can be represented by a binary string of length\u202f16, where a \\(1\\) means the chair is taken.  \nWe need strings with exactly eight\u202f\\(1\\)\u2019s and with **no three consecutive \\(1\\)\u2019s** (otherwise the middle person would sit next to two others).\n\n---\n\n### Counting by blocks\n\nA valid string consists of blocks of consecutive \\(1\\)\u2019s of length\u202f1 or\u202f2, separated by at least one \\(0\\).\n\nLet  \n\n* \\(t\\) = number of blocks of length\u202f2,  \n* \\(b\\) = total number of blocks.  \n\nSince each block contributes at least one \\(1\\),\n\n\\[\n\\underbrace{(b-t)}_{\\text{blocks of length 1}}+2t=8\\quad\\Longrightarrow\\quad b+ t=8,\\; b=8-t .\n\\]\n\nSo \\(t=0,1,2,3,4\\).\n\nFor a fixed \\(t\\):\n* Choose which of the \\(b\\) blocks are the length\u20112 ones: \\(\\displaystyle\\binom{b}{t}=\\binom{8-t}{t}\\).\n* There are \\(8-8=8\\) empty chairs; let \\(z=8\\).  \n  The \\(b+1\\) gaps (including the two ends) must contain these zeros, with at least one zero in each interior gap.  \n  After placing one zero in each of the \\(b-1\\) interior gaps, we have \\(z-(b-1)=9-b\\) zeros left to distribute freely among the \\(b+1\\) gaps.  \n  The number of ways is \\(\\displaystyle\\binom{9-b}{b}=\\binom{9}{b}\\).\n\nHence for each \\(t\\),\n\n\\[\nN_t=\\binom{8-t}{t}\\binom{9}{8-t}.\n\\]\n\nSumming over \\(t=0\\) to \\(4\\):\n\n\\[\n\\begin{aligned}\nN &=\\binom{8}{0}\\binom{9}{8}\n   +\\binom{7}{1}\\binom{9}{7}\n   +\\binom{6}{2}\\binom{9}{6}\n   +\\binom{5}{3}\\binom{9}{5}\n   +\\binom{4}{4}\\binom{9}{4} \\\\[2mm]\n  &=1\\cdot9+7\\cdot36+15\\cdot84+10\\cdot126+1\\cdot126\\\\\n  &=9+252+1260+1260+126\\\\\n  &=2907 .\n\\end{aligned}\n\\]\n\n---\n\n### Modulo\u202f1000\n\n\\[\n2907 \\equiv 907 \\pmod{1000}.\n\\]\n\n---\n\n\\[\n\\boxed{907}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nLet $ A_1A_2 \\ldots A_{11} $ be an 11-sided non-convex simple polygon with the following properties:\n* The area of $ A_iA_1A_{i+1} $ is 1 for each $ 2 \\leq i \\leq 10 $,\n* $ \\cos(\\angle A_iA_1A_{i+1}) = \\frac{12}{13} $ for each $ 2 \\leq i \\leq 10 $,\n* The perimeter of $ A_1A_2 \\ldots A_{11} $ is 20.\nIf $ A_1A_2 + A_1A_{11} $ can be expressed as $ \\frac{m\\sqrt{n} - p}{q} $ for positive integers $ m, n, p, q $ with $ n $ squarefree and no prime divides all of $ m, p, q$, find $ m + n + p + q $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n\\[\nr_i=A_1A_i\\qquad (i=2,\\dots ,11),\\qquad \n\\theta=\\angle A_iA_1A_{i+1}.\n\\]\n\nFor each \\(i=2,\\dots ,10\\)\n\n\\[\n\\cos\\theta=\\frac{12}{13},\\qquad \n\\text{Area}(A_iA_1A_{i+1})=\\frac12 r_i r_{i+1}\\sin\\theta =1 .\n\\]\n\nSince \\(\\sin\\theta=\\sqrt{1-\\cos ^2\\theta}=5/13\\),\n\n\\[\nr_i r_{i+1}= \\frac{2}{\\sin\\theta}= \\frac{2}{5/13}= \\frac{26}{5}\n=:k\\quad\\text{(constant)}.\n\\]\n\nThus  \n\n\\[\nr_{i+1}= \\frac{k}{r_i},\\qquad\\text{so}\\qquad r_{i+2}=r_i .\n\\]\n\nHence the distances from \\(A_1\\) alternate:\n\n\\[\nr_2=r_4=r_6=r_8=r_{10}=a,\\qquad  \nr_3=r_5=r_7=r_9=r_{11}=b,\n\\]\n\nwith  \n\n\\[\nab=k=\\frac{26}{5}.\n\\]\n\n--------------------------------------------------------------------\n### Length of a side \\(A_iA_{i+1}\\)\n\nFor any consecutive pair \\((a,b)\\),\n\n\\[\nA_iA_{i+1}=d=\\sqrt{a^2+b^2-2ab\\cos\\theta}\n           =\\sqrt{a^2+b^2-\\frac{24}{13}ab}.\n\\]\n\nLet  \n\n\\[\nx=a+b,\\qquad ab=k .\n\\]\n\nBecause \\(a^2+b^2=(a+b)^2-2ab=x^2-2k\\),\n\n\\[\nd=\\sqrt{x^2-2k-\\frac{24}{13}k}\n   =\\sqrt{x^2-\\frac{50}{13}\\,k}.\n\\]\n\nSince \\(k=\\dfrac{26}{5}\\),\n\n\\[\n\\frac{50}{13}k=\\frac{50}{13}\\cdot\\frac{26}{5}=20,\n\\qquad\\boxed{d=\\sqrt{x^2-20}} .\n\\]\n\n--------------------------------------------------------------------\n### Using the perimeter\n\nThe perimeter of the 11\u2011gon is\n\n\\[\na+b+9d = x+9\\sqrt{x^2-20}=20 .\n\\]\n\nSolve for \\(x\\) (note \\(x>0\\) and \\(\\sqrt{x^2-20}\\ge0\\)):\n\n\\[\n9\\sqrt{x^2-20}=20-x\\quad\\Longrightarrow\\quad\n81(x^2-20)=(20-x)^2 .\n\\]\n\nThis gives  \n\n\\[\n80x^2+40x-2020=0\\;\\Longrightarrow\\;4x^2+2x-101=0.\n\\]\n\nHence  \n\n\\[\nx=\\frac{-2\\pm\\sqrt{4+1616}}{8}\n  =\\frac{-2\\pm18\\sqrt5}{8}\n  =\\frac{-1\\pm9\\sqrt5}{4}.\n\\]\n\nOnly the positive root satisfies the constraints, so  \n\n\\[\n\\boxed{x=a+b=\\frac{9\\sqrt5-1}{4}} .\n\\]\n\nThus\n\n\\[\nA_1A_2+A_1A_{11}=a+b=\\frac{9\\sqrt5-1}{4}\n    =\\frac{m\\sqrt n-p}{q},\n\\]\n\nwith \\(m=9,\\;n=5,\\;p=1,\\;q=4\\).\n\nAll conditions on \\(m,n,p,q\\) are met, and\n\n\\[\nm+n+p+q=9+5+1+4=19.\n\\]\n\n\\[\n\\boxed{19}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nFind the sum of all integer bases $b>9$ for which $17_{b}$ is a divisor of $97_{b}$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "In base \\(b\\) the numbers are  \n\n\\[\n17_{b}=1\\cdot b+7=b+7, \\qquad 97_{b}=9\\cdot b+7=9b+7 .\n\\]\n\nWe need \\(b+7\\) to divide \\(9b+7\\).\n\n---\n\n### Find the divisibility condition  \n\n\\[\n9b+7 = 9(b+7)-56 .\n\\]\n\nThus the remainder when \\(9b+7\\) is divided by \\(b+7\\) is \\(-56\\).  \nHence \\(b+7\\) must divide \\(56\\):\n\n\\[\nb+7\\mid 56 .\n\\]\n\n---\n\n### Possible values of \\(b\\)\n\nThe positive divisors of \\(56\\) are  \n\n\\[\n1,\\;2,\\;4,\\;7,\\;8,\\;14,\\;28,\\;56 .\n\\]\n\nBecause the base must satisfy \\(b>9\\), we have \\(b+7>16\\).  \nThe divisors larger than \\(16\\) are \\(28\\) and \\(56\\).\n\n\\[\n\\begin{aligned}\nb+7&=28 \\quad\\Longrightarrow\\quad b=21,\\\\[2pt]\nb+7&=56 \\quad\\Longrightarrow\\quad b=49 .\n\\end{aligned}\n\\]\n\nBoth bases are greater than \\(9\\) and allow the digits \\(1,7,9\\).\n\n---\n\n### Sum of all such bases  \n\n\\[\n21+49 = 70.\n\\]\n\n\\[\n\\boxed{70}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nThe 9 members of a baseball team went to an ice cream parlor after their game. Each player had a singlescoop cone of chocolate, vanilla, or strawberry ice cream. At least one player chose each flavor, and the number of players who chose chocolate was greater than the number of players who chose vanilla, which was greater than the number of players who chose strawberry. Let $N$ be the number of different assignments of flavors to players that meet these conditions. Find the remainder when $N$ is divided by 1000.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "The numbers of players picking chocolate, vanilla and strawberry are  \n\n\\[\na=\\#\\text{chocolate},\\qquad b=\\#\\text{vanilla},\\qquad c=\\#\\text{strawberry}\n\\]\n\nwith  \n\n\\[\na+b+c=9,\\qquad a>b>c\\ge1 .\n\\]\n\nHence \\((a,b,c)\\) must be three distinct positive integers whose sum is \\(9\\).  \nThe possible triples (written in decreasing order) are  \n\n\\[\n(6,2,1),\\;(5,3,1),\\;(4,3,2).\n\\]\n\nFor a fixed triple \\((a,b,c)\\) the players are distinct, so the number of assignments\nis the multinomial coefficient  \n\n\\[\n\\binom{9}{a,b,c}= \\frac{9!}{a!\\,b!\\,c!}.\n\\]\n\nCompute each term:\n\n\\[\n\\begin{aligned}\n(6,2,1):&\\quad \\frac{9!}{6!\\,2!\\,1!}= \\frac{362880}{720\\cdot2}=252,\\\\[2mm]\n(5,3,1):&\\quad \\frac{9!}{5!\\,3!\\,1!}= \\frac{362880}{120\\cdot6}=504,\\\\[2mm]\n(4,3,2):&\\quad \\frac{9!}{4!\\,3!\\,2!}= \\frac{362880}{24\\cdot6\\cdot2}=1260.\n\\end{aligned}\n\\]\n\nAdd them:\n\n\\[\nN = 252+504+1260 = 2016.\n\\]\n\nThe remainder when \\(N\\) is divided by \\(1000\\) is  \n\n\\[\n2016 \\equiv 16 \\pmod{1000}.\n\\]\n\n\\[\n\\boxed{16}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nLet $ \\triangle ABC $ be a right triangle with $ \\angle A = 90^\\circ $ and $ BC = 38 $. There exist points $ K $ and $ L $ inside the triangle such that $ AK = AL = BK = CL = KL = 14. $ The area of the quadrilateral $ BKLC $ can be expressed as $ n \\sqrt{3} $ for some positive integer $ n $. Find $ n $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n\\[\nA=(0,0),\\qquad B=(b,0),\\qquad C=(0,c)\n\\]\n\nso that \\(\\angle A=90^{\\circ}\\) and  \n\n\\[\nBC=\\sqrt{b^{2}+c^{2}}=38\\qquad\\Longrightarrow\\qquad b^{2}+c^{2}=38^{2}=1444 .\n\\tag{1}\n\\]\n\n--------------------------------------------------------------------\n### 1.  Determining the positions of \\(K\\) and \\(L\\)\n\nBecause  \n\n\\[\nAK=BK=14\n\\]\n\nthe point \\(K\\) lies at the intersection of the circles of radius \\(14\\) centred at\n\\(A\\) and \\(B\\).  \nIf \\(K=(x_{K},y_{K})\\),\n\n\\[\nx_{K}^{2}+y_{K}^{2}=196,\\qquad (x_{K}-b)^{2}+y_{K}^{2}=196 .\n\\]\n\nSubtracting gives  \n\n\\[\nb^{2}=2bx_{K}\\;\\Longrightarrow\\;x_{K}= \\frac{b}{2} .\n\\tag{2}\n\\]\n\nHence  \n\n\\[\ny_{K}^{2}=196-\\Bigl(\\frac{b}{2}\\Bigr)^{2}=196-\\frac{b^{2}}{4}.\n\\tag{3}\n\\]\n\nSimilarly, from  \n\n\\[\nAL=CL=14\n\\]\n\nthe point \\(L=(x_{L},y_{L})\\) satisfies\n\n\\[\ny_{L}= \\frac{c}{2},\\qquad \nx_{L}^{2}=196-\\Bigl(\\frac{c}{2}\\Bigr)^{2}=196-\\frac{c^{2}}{4}.\n\\tag{4}\n\\]\n\nThus, writing  \n\n\\[\nU=\\frac{b}{2},\\quad V=\\frac{c}{2},\n\\]\n\nwe have  \n\n\\[\nK=\\bigl(U,\\;\\sqrt{196-U^{2}}\\bigr),\\qquad \nL=\\bigl(\\sqrt{196-V^{2}},\\;V\\bigr),\n\\tag{5}\n\\]\n\nand from (1)  \n\n\\[\nU^{2}+V^{2}=361. \\tag{6}\n\\]\n\n--------------------------------------------------------------------\n### 2.  Using the condition \\(KL=14\\)\n\nFrom (5),\n\n\\[\n\\bigl(U-\\sqrt{196-V^{2}}\\bigr)^{2}\n+\\bigl(\\sqrt{196-U^{2}}-V\\bigr)^{2}=196 .\n\\]\n\nExpanding and simplifying with (6) gives\n\n\\[\nU\\sqrt{196-V^{2}}+V\\sqrt{196-U^{2}}=98 . \\tag{7}\n\\]\n\nLet  \n\n\\[\np=\\sqrt{196-V^{2}},\\qquad q=\\sqrt{196-U^{2}} .\n\\]\n\nThen  \n\n\\[\nU p+V q =98 ,\\qquad p^{2}+q^{2}=31 ,\n\\qquad U^{2}+V^{2}=361 . \\tag{8}\n\\]\n\nFrom (8) we obtain the product\n\n\\[\nU^{2}V^{2}=32448\\quad\\Longrightarrow\\quad UV=104\\sqrt3 . \\tag{9}\n\\]\n\nNow  \n\n\\[\n(U+V)^{2}=U^{2}+V^{2}+2UV=361+208\\sqrt3,\n\\]\n\\[\n(U-V)^{2}=U^{2}+V^{2}-2UV=361-208\\sqrt3 .\n\\]\n\nBoth expressions are perfect squares:\n\n\\[\n361+208\\sqrt3=(13+8\\sqrt3)^{2},\n\\qquad\n361-208\\sqrt3=(8\\sqrt3-13)^{2}.\n\\]\n\nHence  \n\n\\[\nU+V=13+8\\sqrt3,\\qquad\n|U-V|=8\\sqrt3-13 .\n\\]\n\nSince \\(U>V\\), solving gives  \n\n\\[\nU=8\\sqrt3,\\qquad V=13 .\n\\]\n\nConsequently  \n\n\\[\nb=2U=16\\sqrt3,\\qquad c=2V=26 .\n\\]\n\n--------------------------------------------------------------------\n### 3.  Coordinates of \\(K\\) and \\(L\\)\n\nUsing (5) with the found \\(U,V\\):\n\n\\[\nK=\\bigl(8\\sqrt3,\\; \\sqrt{196-(8\\sqrt3)^{2}}\\bigr)\n   =\\bigl(8\\sqrt3,\\;2\\bigr),\n\\]\n\n\\[\nL=\\bigl(\\sqrt{196-13^{2}},\\;13\\bigr)\n   =\\bigl(3\\sqrt3,\\;13\\bigr).\n\\]\n\n--------------------------------------------------------------------\n### 4.  Area of quadrilateral \\(BKLC\\)\n\nThe vertices in order are  \n\n\\[\nB=(16\\sqrt3,0),\\ K=(8\\sqrt3,2),\\ L=(3\\sqrt3,13),\\ C=(0,26).\n\\]\n\nApplying the shoelace formula:\n\n\\[\n\\begin{aligned}\nS_{1}&=x_{B}y_{K}+x_{K}y_{L}+x_{L}y_{C}+x_{C}y_{B}\\\\\n     &= (16\\sqrt3)(2)+(8\\sqrt3)(13)+(3\\sqrt3)(26)+0\\\\\n     &=32\\sqrt3+104\\sqrt3+78\\sqrt3=214\\sqrt3,\n\\\\[2mm]\nS_{2}&=y_{B}x_{K}+y_{K}x_{L}+y_{L}x_{C}+y_{C}x_{B}\\\\\n     &=0+2(3\\sqrt3)+13\\cdot0+26(16\\sqrt3)\\\\\n     &=6\\sqrt3+416\\sqrt3=422\\sqrt3 .\n\\end{aligned}\n\\]\n\nHence  \n\n\\[\n\\text{Area}=\\frac12|S_{1}-S_{2}|\n           =\\frac12\\bigl|214\\sqrt3-422\\sqrt3\\bigr|\n           =\\frac12\\,(208\\sqrt3)=104\\sqrt3 .\n\\]\n\nThus the required area is \\(104\\sqrt3\\), i.e. \\(n=104\\).\n\n\\[\n\\boxed{104}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nFind the number of ordered pairs $(x,y)$, where both $x$ and $y$ are integers between $-100$ and $100$, inclusive, such that $12x^{2}-xy-6y^{2}=0$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "The equation  \n\n\\[\n12x^{2}-xy-6y^{2}=0\n\\]\n\ncan be factored over the integers.\n\n\\[\n\\begin{aligned}\n12x^{2}-xy-6y^{2}\n&= (4x-3y)(3x+2y).\n\\end{aligned}\n\\]\n\nHence a pair \\((x,y)\\) satisfies the equation iff  \n\n\\[\n4x-3y=0 \\qquad\\text{or}\\qquad 3x+2y=0 .\n\\]\n\n---\n\n### 1.  Solutions of \\(4x-3y=0\\)\n\n\\[\n4x=3y \\Longrightarrow x=\\frac34y .\n\\]\n\nSince \\(x,y\\) are integers, \\(y\\) must be a multiple of \\(4\\); write \\(y=4k\\) \\((k\\in\\mathbb Z)\\).  \nThen \\(x=3k\\).\n\nBounds \\(-100\\le x,y\\le100\\) give  \n\n\\[\n|4k|\\le100\\ \\Longrightarrow\\ |k|\\le25 .\n\\]\n\nThus \\(k\\) can be any integer from \\(-25\\) to \\(25\\) inclusive \u2013 \\(51\\) possibilities.\n\n---\n\n### 2.  Solutions of \\(3x+2y=0\\)\n\n\\[\n3x=-2y \\Longrightarrow x=-\\frac{2}{3}y .\n\\]\n\nNow \\(y\\) must be a multiple of \\(3\\); write \\(y=3k\\).  \nThen \\(x=-2k\\).\n\nBounds give  \n\n\\[\n|3k|\\le100\\ \\Longrightarrow\\ |k|\\le\\Big\\lfloor\\frac{100}{3}\\Big\\rfloor=33 .\n\\]\n\nHence \\(k\\) can be any integer from \\(-33\\) to \\(33\\) inclusive \u2013 \\(67\\) possibilities.\n\n---\n\n### 3.  Removing double\u2011counted pair\n\nBoth families contain the pair \\((0,0)\\) (when \\(k=0\\)).  \nIt has been counted twice, so we subtract one.\n\n\\[\n\\text{Total solutions}=51+67-1=117 .\n\\]\n\nAll counted pairs satisfy \\(-100\\le x,y\\le100\\).\n\n\\[\n\\boxed{117}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nAn isosceles trapezoid has an inscribed circle tangent to each of its four sides. The radius of the circle is 3, and the area of the trapezoid is 72. Let the parallel sides of the trapezoid have lengths $r$ and $s$, with $r \\neq s$. Find $r^{2}+s^{2}$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let the trapezoid have parallel sides \\(r\\) and \\(s\\) (\\(r\\neq s\\)), equal legs of length \\(L\\), height \\(h\\), and incircle radius \\(R=3\\).\n\n---\n\n### 1.  Semiperimeter from the incircle\n\nFor any tangential quadrilateral,\n\\[\n\\text{Area}=R\\cdot s,\n\\]\nwhere \\(s\\) is the semiperimeter.  \nGiven \\(\\text{Area}=72\\) and \\(R=3\\),\n\n\\[\ns=\\frac{72}{3}=24,\n\\qquad\\text{so } r+s+2L=2s=48. \\tag{1}\n\\]\n\n---\n\n### 2.  Height of the trapezoid\n\nSince the incircle touches both parallel sides, the distance between them equals twice the radius:\n\n\\[\nh=2R=6.\n\\]\n\nThe area also equals \\(\\frac{1}{2}(r+s)h\\). Thus\n\n\\[\n72=\\frac{1}{2}(r+s)\\cdot6 \\Longrightarrow r+s=24. \\tag{2}\n\\]\n\nSubstituting (2) into (1) gives\n\n\\[\n24+2L=48\\Longrightarrow L=12. \\tag{3}\n\\]\n\n---\n\n### 3.  Relating the bases and the leg\n\nIn an isosceles trapezoid the horizontal projection of each leg is \\(\\dfrac{s-r}{2}\\).\nUsing the right triangle formed by a leg, the height, and this projection:\n\n\\[\n\\left(\\frac{s-r}{2}\\right)^2+h^2=L^2.\n\\]\n\nInsert \\(h=6\\) and \\(L=12\\):\n\n\\[\n\\left(\\frac{s-r}{2}\\right)^2+36=144\n\\;\\Longrightarrow\\;\n\\frac{(s-r)^2}{4}=108\n\\;\\Longrightarrow\\;\n(s-r)^2=432.\n\\]\n\nHence\n\n\\[\ns-r=12\\sqrt3. \\tag{4}\n\\]\n\n---\n\n### 4.  Solve for \\(r\\) and \\(s\\)\n\nFrom (2) and (4):\n\n\\[\n\\begin{cases}\nr+s=24,\\\\[2pt]\ns-r=12\\sqrt3,\n\\end{cases}\n\\qquad\\Longrightarrow\\qquad\ns=12+6\\sqrt3,\\;\\; r=12-6\\sqrt3.\n\\]\n\nBoth are positive and distinct, as required.\n\n---\n\n### 5.  Compute \\(r^{2}+s^{2}\\)\n\n\\[\n\\begin{aligned}\nr^{2}+s^{2}&=(12-6\\sqrt3)^2+(12+6\\sqrt3)^2\\\\\n&=2\\cdot12^{2}+2\\cdot(6\\sqrt3)^{2}\\\\\n&=2\\cdot144+2\\cdot108\\\\\n&=288+216\\\\\n&=504.\n\\end{aligned}\n\\]\n\n---\n\n\\[\n\\boxed{504}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nThere are $8!=40320$ eight-digit positive integers that use each of the digits $1,2,3,4,5,6,7,8$ exactly once. Let $N$ be the number of these integers that are divisible by 22. Find the difference between $N$ and 2025.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "For an \\(8\\)-digit number formed with the digits \\(1,2,\\dots ,8\\) each once we need\n\n* divisibility by \\(2\\)   \\(\\Longrightarrow\\) the units digit is even (\\(2,4,6,8\\));\n* divisibility by \\(11\\) \\(\\Longrightarrow\\) the alternating sum of its digits is a multiple of \\(11\\).\n\n---\n\n### 1.  Divisibility by \\(11\\)\n\nWrite the digits as \\(d_1d_2d_3d_4d_5d_6d_7d_8\\) ( \\(d_1\\) most significant).  \n\nThe test for \\(11\\) gives  \n\n\\[\n(d_1+d_3+d_5+d_7)-(d_2+d_4+d_6+d_8)\\equiv0\\pmod{11}.\n\\]\n\nLet  \n\n\\[\nO=d_1+d_3+d_5+d_7,\\qquad E=d_2+d_4+d_6+d_8 .\n\\]\n\nSince all eight digits are used once,  \n\n\\[\nO+E = 1+2+\\dots+8 = 36 .\n\\]\n\nThe condition \\(O-E\\equiv0\\pmod{11}\\) becomes  \n\n\\[\n2O\\equiv36\\pmod{11}\\quad\\Longrightarrow\\quad O\\equiv18\\equiv7\\pmod{11}.\n\\]\n\nThe sum of four distinct digits from \\(\\{1,\\dots ,8\\}\\) lies between \\(10\\) and \\(26\\); the only value congruent to \\(7\\pmod{11}\\) in that range is \\(18\\).  \nHence we must have  \n\n\\[\nO=E=18.\n\\]\n\nSo the four digits placed in the odd positions must sum to \\(18\\).\n\n---\n\n### 2.  Choosing the odd\u2013position digits\n\nWe need all \\(4\\)-element subsets of \\(\\{1,\\dots ,8\\}\\) whose sum is \\(18\\).\n\nListing them (in increasing order) gives\n\n\\[\n\\begin{aligned}\n&\\{1,2,7,8\\},\\; \\{1,3,6,8\\},\\; \\{1,4,5,8\\},\\; \\{1,4,6,7\\},\\\\\n&\\{2,3,5,8\\},\\; \\{2,3,6,7\\},\\; \\{2,4,5,7\\},\\; \\{3,4,5,6\\}.\n\\end{aligned}\n\\]\n\nThere are \\(8\\) such subsets.  \nEach of them contains exactly two even digits (the even digits are \\(2,4,6,8\\)). Consequently the complementary set (the digits placed in even positions) also contains exactly two evens.\n\n---\n\n### 3.  Forming the numbers\n\n*For a fixed subset* \\(S\\) (the odd\u2011position digits)\n\n* arrange its four digits among the odd places \\(1,3,5,7\\): \\(4!\\) ways;\n* the four remaining digits (the complement \\(T\\)) go to the even places \\(2,4,6,8\\).  \n  Since \\(T\\) contains two even digits, we may pick which even digit occupies the units place (position \\(8\\)) in \\(2\\) ways; the other three digits can be placed in \\(3!\\) ways.\n\nHence for each subset \\(S\\)\n\n\\[\n\\text{permutations}=4!\\times 2\\times3!=24\\times12=288 .\n\\]\n\nWith \\(8\\) possible subsets,\n\n\\[\nN=8\\times288=2304 .\n\\]\n\n(Equivalently, half of the \\(4608\\) numbers with \\(O=E=18\\) are even, giving the same result.)\n\n---\n\n### 4.  Required difference\n\n\\[\nN-2025 = 2304-2025 = 279.\n\\]\n\nThus the requested difference is  \n\n\\[\n\\boxed{279}.\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nSuppose $ \\triangle ABC $ has angles $ \\angle BAC = 84^\\circ $, $ \\angle ABC = 60^\\circ $, and $ \\angle ACB = 36^\\circ $. Let $ D, E, $ and $ F $ be the midpoints of sides $ \\overline{BC} $, $ \\overline{AC} $, and $ \\overline{AB} $, respectively. The circumcircle of $ \\triangle DEF $ intersects $ \\overline{BD} $, $ \\overline{AE} $, and $ \\overline{AF} $ at points $ G, H, $ and $ J $, respectively. The points $ G, D, E, H, J, $ and $ F $ divide the circumcircle of $ \\triangle DEF $ into six minor arcs, as shown. Find $ \\widehat{DE} + 2 \\cdot \\widehat{HJ} + 3 \\cdot \\widehat{FG} $, where the arcs are measured in degrees.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "We place \\(\\triangle ABC\\) on its circumcircle (radius\u00a01) with  \n\n\\[\nA=1,\\qquad B=e^{i2C},\\qquad C=e^{i(2C+2A)} .\n\\]\n\nThe orthocenter is  \n\n\\[\nH=a+b+c.\n\\]\n\nThe nine\u2011point circle is the image of the circumcircle under the homothety with centre \\(H\\) and factor \\(\\tfrac12\\); therefore for any point \\(X\\) on the nine\u2011point circle its image on the circumcircle is  \n\n\\[\nX' = 2X-H .\n\\]\n\nApplying this to the six points on the nine\u2011point circle gives\n\n\\[\n\\begin{aligned}\nD&\\mapsto -a,\\\\\nE&\\mapsto -b,\\\\\nF&\\mapsto -c,\\\\\nG&\\mapsto A' ,\\qquad A' \\text{ is the second intersection of the altitude }AA_H\\text{ with the circumcircle},\\\\\nH&\\mapsto B' ,\\qquad B'=-e^{i2A},\\\\\nJ&\\mapsto C' ,\\qquad C'=-e^{-i2A}.\n\\end{aligned}\n\\]\n\nUsing \\(a=1,\\;b=e^{i2C},\\;c=e^{i(2C+2A)}\\) we obtain the central\nangles (measured from the positive \\(x\\)-axis) of the corresponding points:\n\n\\[\n\\begin{array}{c|c}\n\\text{Nine\u2011point point} & \\text{Angle on the circumcircle}\\\\ \\hline\nD & 180^\\circ\\\\\nE & 180^\\circ+2C\\\\\nF & 180^\\circ-2B\\\\\nG & 180^\\circ+2A+4C\\\\\nH & 180^\\circ+2A\\\\\nJ & 180^\\circ-2A\n\\end{array}\n\\]\n\nBecause the homothety preserves directions from the centre, the\narc length on the nine\u2011point circle equals the corresponding central\nangle on the circumcircle.\n\nHence\n\n\\[\n\\begin{aligned}\n\\widehat{DE}&=(180^\\circ+2C)-180^\\circ =2C,\\\\[2mm]\n\\widehat{HJ}&=|\\, (180^\\circ+2A)-(180^\\circ-2A)\\,|=4A,\n\\end{aligned}\n\\]\n\nand the minor arc \\(HJ\\) is \\(360^\\circ-4A\\) (since \\(4A>180^\\circ\\)).\nFinally\n\n\\[\n\\widehat{FG}=|(180^\\circ-2B)-(180^\\circ+2A+4C)|\n            =2C\\qquad(\\text{mod }360^\\circ).\n\\]\n\nThus\n\n\\[\n\\begin{aligned}\n\\widehat{DE}+2\\widehat{HJ}+3\\widehat{FG}\n&=2C+2\\bigl(360^\\circ-4A\\bigr)+3\\,(2C) \\\\\n&=720^\\circ-8A+8C\\\\\n&=720^\\circ+8(C-A).\n\\end{aligned}\n\\]\n\nFor the given triangle \\(A=84^\\circ,\\;C=36^\\circ\\),\n\n\\[\n720^\\circ+8(36^\\circ-84^\\circ)=720^\\circ-384^\\circ=336^\\circ .\n\\]\n\n\\[\n\\boxed{336}\n\\]",
+        "role": "assistant"
+      }
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+    [
+      {
+        "role": "user",
+        "content": "\nThere are exactly three positive real numbers $ k $ such that the function\n$ f(x) = \\frac{(x - 18)(x - 72)(x - 98)(x - k)}{x} $\ndefined over the positive real numbers achieves its minimum value at exactly two positive real numbers $ x $. Find the sum of these three values of $ k $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "The function  \n\n\\[\nf(x)=\\frac{(x-18)(x-72)(x-98)(x-k)}{x}, \\qquad x>0,\n\\]\n\nhas zeros at \\(x=18,72,98,k\\) and \\(\\displaystyle\\lim_{x\\to0^+}f(x)=+\\infty\\),\n\\(\\displaystyle\\lim_{x\\to\\infty}f(x)=+\\infty\\).\nHence the graph of \\(f\\) starts at \\(+\\infty\\), descends to a negative\nvalue, comes back to zero, rises again, etc.; it has exactly **two**\nnegative intervals:\n\\[\n(r_1,r_2),\\qquad (r_3,r_4),\n\\]\nwhere \\(\\{r_1,r_2,r_3,r_4\\}=\\{18,72,98,k\\}\\) ordered increasingly.\nIn each negative interval there is a local (and global) minimum of \\(f\\).\n\nLet  \n\n\\[\ng(x)=(x-18)(x-72)(x-98)(x-k),\n\\qquad f(x)=\\frac{g(x)}{x}.\n\\]\n\nA point \\(x_0\\) where \\(f\\) has an extremum satisfies  \n\n\\[\nf'(x_0)=0\\iff x_0g'(x_0)-g(x_0)=0\\iff \n\\sum_{i=1}^{4}\\frac{1}{x_0-r_i}= \\frac1{x_0}.\n\\]\n\nGeometrically, if \\(m=f(x_0)\\) then the line \\(y=m x\\) is tangent to the\nquartic graph \\(y=g(x)\\) at \\(x_0\\):\n\\[\ng(x)-mx=0\\quad\\text{has a double root at }x_0 .\n\\]\n\nIf the global minimum of \\(f\\) is attained at **two** distinct points,\nthe line \\(y=m x\\) must be tangent to \\(g\\) at two distinct points\n\\(\\alpha,\\beta\\). Hence\n\n\\[\ng(x)-mx=(x-\\alpha)^2 (x-\\beta)^2 .\n\\tag{1}\n\\]\n\nWrite  \n\n\\[\n\\alpha+\\beta=p,\\qquad \\alpha\\beta =q,\\qquad m \\text{ (the slope)} .\n\\]\n\nExpanding (1) and comparing with \\(g(x)-mx=x^4-S_1x^3+S_2x^2-(S_3+m)x+S_4\\) gives  \n\n\\[\n\\begin{aligned}\nS_1 &=2p,\\\\\nS_2 &=p^{2}+2q,\\\\\nS_4 &=q^{2},\\\\\nS_3+m &=2pq,\n\\end{aligned}\n\\tag{2}\n\\]\n\nwhere for our roots  \n\n\\[\n\\begin{aligned}\nS_1&=18+72+98+k=188+k,\\\\\nS_2&=18\\cdot72+18\\cdot98+72\\cdot98+ (18+72+98)k\n     =10116+188k,\\\\\nS_3&=18\\cdot72\\cdot98+ (18\\cdot72+18\\cdot98+72\\cdot98)k\n     =127008+10116k,\\\\\nS_4&=18\\cdot72\\cdot98\\cdot k=127008\\,k .\n\\end{aligned}\n\\]\n\nFrom (2) we obtain  \n\n\\[\np=\\frac{188+k}{2},\\qquad q=\\sqrt{127008\\,k}=252\\sqrt{2k}.\n\\]\n\nUsing the second equation of (2),\n\n\\[\nS_2=p^{2}+2q,\n\\]\n\ngives the condition on \\(k\\):\n\n\\[\n\\frac{(188+k)^{2}}{4}+2\\sqrt{127008k}=10116+188k .\n\\tag{3}\n\\]\n\n---\n\n### Solving (3)\n\nPut \\(k=t^{2}\\;(t>0)\\).  Since \\(\\sqrt{127008k}=252\\sqrt{2}\\,t\\),\n(3) becomes\n\n\\[\nt^{4}-376t^{2}+2016\\sqrt{2}\\,t-5120=0 .\n\\]\n\nFactoring,\n\n\\[\n(t^{2}+6\\sqrt{2}\\,t-320)(t^{2}-6\\sqrt{2}\\,t+16)=0 .\n\\]\n\nHence the positive solutions for \\(t\\) are\n\n\\[\nt=10\\sqrt2,\\qquad t=4\\sqrt2,\\qquad t=2\\sqrt2 .\n\\]\n\nConsequently\n\n\\[\nk=t^{2}=200,\\;32,\\;8 .\n\\]\n\n---\n\n### Verification\n\nFor each \\(k\\) the ordered roots of \\(g\\) are\n\n\\[\n\\begin{array}{c|c}\nk & \\text{ordered roots }(r_1,r_2,r_3,r_4)\\\\ \\hline\n8  & (8,18,72,98)\\\\\n32 & (18,32,72,98)\\\\\n200& (18,72,98,200)\n\\end{array}\n\\]\n\nUsing \\(p\\) and \\(q\\) we find the tangency points  \n\n\\[\n\\alpha,\\beta=\\frac{p\\pm\\sqrt{p^{2}-4q}}{2},\n\\]\n\nand they lie respectively in the intervals \\((r_1,r_2)\\) and\n\\((r_3,r_4)\\). Thus in each case the line \\(y=m x\\) is tangent to\n\\(g\\) at two points, giving exactly two distinct global minima of\n\\(f\\). No other \\(k>0\\) satisfies (3); hence these are the only three\nvalues.\n\nFinally, the required sum is\n\n\\[\n8+32+200 = 240 .\n\\]\n\n\\[\n\\boxed{240}\n\\]",
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+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nLet $k$ be real numbers such that the system $|25+20i-z|=5$ and $|z-4-k|=|z-3i-k|$ has exactly one complex solution $z$. The sum of all possible values of $k$ can be written as $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$. Here $i=\\sqrt{-1}$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n\\[\nz=x+iy\\qquad (x,y\\in\\mathbb{R}).\n\\]\n\n---\n\n### 1.  The first equation \u2013 a circle  \n\n\\[\n|25+20i-z|=5 \\Longrightarrow (x-25)^2+(y-20)^2=5^2 .\n\\]\n\nThus the circle has centre  \n\n\\[\nC=(25,20),\\qquad \\text{radius } r=5 .\n\\]\n\n---\n\n### 2.  The second equation \u2013 a perpendicular bisector  \n\n\\[\n|z-(4+k)|=|z-(3i+k)|\n\\]\n\nwrites as  \n\n\\[\n(x-(k+4))^2+y^{2}=(x-k)^2+(y-3)^2 .\n\\]\n\nSimplifying,\n\n\\[\n-8x+6y+8k+7=0\\quad\\Longrightarrow\\quad 4x-3y-(4k+3.5)=0 .\n\\]\n\nHence the set of points satisfying the second condition is the line  \n\n\\[\nL:\\;4x-3y=4k+\\frac 72 .\n\\]\n\nThis is the perpendicular bisector of the segment joining  \n\\(A=(k+4,0)\\) and \\(B=(k,3)\\) (its slope is \\(4/3\\) for any \\(k\\)).\n\n---\n\n### 3.  One intersection  \\(\\iff\\)  tangency  \n\nThe system has exactly one solution precisely when the line \\(L\\) is tangent to the circle, i.e. when the distance from the centre \\(C\\) to \\(L\\) equals the radius \\(5\\).\n\nThe distance from \\((x_0,y_0)\\) to \\(Ax+By+C=0\\) is  \n\n\\[\n\\frac{|Ax_0+By_0+C|}{\\sqrt{A^2+B^2}} .\n\\]\n\nFor \\(C=(25,20)\\) and \\(L: 4x-3y-(4k+3.5)=0\\),\n\n\\[\nd=\\frac{|4\\cdot25-3\\cdot20-(4k+3.5)|}{\\sqrt{4^{2}+(-3)^{2}}}\n   =\\frac{|40-4k-3.5|}{5}\n   =\\frac{|36.5-4k|}{5}.\n\\]\n\nSet \\(d=r=5\\):\n\n\\[\n\\frac{|36.5-4k|}{5}=5\\quad\\Longrightarrow\\quad |36.5-4k|=25 .\n\\]\n\n---\n\n### 4.  Solving for \\(k\\)\n\n\\[\n\\begin{cases}\n36.5-4k=25 &\\Longrightarrow\\;4k=11.5\\;\\Longrightarrow\\;k=\\dfrac{23}{8},\\\\[4pt]\n36.5-4k=-25 &\\Longrightarrow\\;4k=61.5\\;\\Longrightarrow\\;k=\\dfrac{123}{8}.\n\\end{cases}\n\\]\n\nThus the possible real values of \\(k\\) are  \n\n\\[\nk_1=\\frac{23}{8},\\qquad k_2=\\frac{123}{8}.\n\\]\n\nBoth give a line tangent to the circle, so each yields exactly one solution \\(z\\).\n\n---\n\n### 5.  Sum of the possible \\(k\\)\u2019s  \n\n\\[\nk_1+k_2=\\frac{23+123}{8}=\\frac{146}{8}=\\frac{73}{4}.\n\\]\n\nWrite \\(\\frac{73}{4}\\) as \\(\\dfrac{m}{n}\\) with \\(\\gcd(m,n)=1\\); here \\(m=73,\\ n=4\\).\n\n\\[\nm+n=73+4=77.\n\\]\n\n\\[\n\\boxed{77}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nLet the sequence of rationals $ x_1, x_2, \\ldots $ be defined such that $ x_1 = \\frac{25}{11} $ and\n$ x_{k+1} = \\frac{1}{3} \\left( x_k + \\frac{1}{x_k} - 1 \\right). $\n$ x_{2025} $ can be expressed as $ \\frac{m}{n} $ for relatively prime positive integers $ m $ and $ n $. Find the remainder when $ m + n $ is divided by 1000.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "**Step 1.  Write the recurrence for the numerators and denominators**\n\nLet  \n\n\\[\nx_k=\\frac{a_k}{b_k}\\qquad (a_k,b_k\\in \\mathbb Z ,\\; \\gcd(a_k,b_k)=1).\n\\]\n\nFrom  \n\n\\[\nx_{k+1}= \\frac{1}{3}\\Bigl(x_k+\\frac1{x_k}-1\\Bigr)=\\frac{x_k^2-x_k+1}{3x_k},\n\\]\n\nwe obtain  \n\n\\[\na_{k+1}=a_k^2-a_kb_k+b_k^2,\\qquad   \nb_{k+1}=3a_kb_k,          \\tag{1}\n\\]\n\nwith \\(a_1=25,\\;b_1=11\\).\n\n--------------------------------------------------------------------\n\n**Step 2.  The common factor \\(3^{e_k}\\)**  \n\nWrite  \n\n\\[\na_k=3^{e_k}A_k,\\qquad b_k=3^{e_k}B_k,\\qquad \\gcd(A_k,B_k)=1 .\n\\]\n\nDividing (1) by the highest possible power of \\(3\\) shows that\n\\(e_{k+1}=2e_k+1\\) and that the reduced pair \\((A_k,B_k)\\) always satisfies  \n\n\\[\nA_k\\equiv1\\pmod3,\\qquad B_k\\equiv2\\pmod3 .\n\\]\n\nWith \\(e_1=0\\) we get  \n\n\\[\ne_k=2^{\\,k-1}-1 .\\tag{2}\n\\]\n\n--------------------------------------------------------------------\n\n**Step 3.  A very simple recurrence for the sum**\n\nLet  \n\n\\[\nS_k=a_k+b_k .\n\\]\n\nFrom (1)\n\n\\[\n\\begin{aligned}\nS_{k+1}&=a_{k+1}+b_{k+1}\n       =(a_k^2-a_kb_k+b_k^2)+3a_kb_k   \\\\\n       &=a_k^2+b_k^2+2a_kb_k=(a_k+b_k)^2=S_k^{\\,2}.\n\\end{aligned}\n\\]\n\nHence  \n\n\\[\nS_k=S_1^{\\,2^{\\,k-1}}=36^{\\,2^{\\,k-1}}. \\tag{3}\n\\]\n\n--------------------------------------------------------------------\n\n**Step 4.  The reduced numerator and denominator**\n\nSince the common factor is \\(3^{e_k}\\),\n\n\\[\n\\frac{a_k}{b_k}= \\frac{A_k}{B_k},\\qquad \nm=A_k,\\; n=B_k .\n\\]\n\nThus  \n\n\\[\nm+n=\\frac{a_k+b_k}{3^{e_k}}\n     =\\frac{36^{\\,2^{\\,k-1}}}{3^{\\,2^{\\,k-1}-1}}\n     =2^{\\,2^{\\,k}}\\;3^{\\,2^{\\,k-1}+1}. \\tag{4}\n\\]\n\n--------------------------------------------------------------------\n\n**Step 5.  Apply \\(k=2025\\)**  \n\nFrom (4),\n\n\\[\nm+n=2^{\\,2^{2025}}\\;3^{\\,2^{2024}+1}.\n\\]\n\nWe need this number modulo \\(1000\\).\n\n--------------------------------------------------------------------\n\n**Step 6.  Reduce modulo \\(8\\) and \\(125\\)**  \n\n*Modulo \\(8\\):*  \\(2^{\\ge3}\\equiv0\\pmod8\\); therefore  \n\n\\[\nm+n\\equiv0\\pmod8. \\tag{5}\n\\]\n\n*Modulo \\(125\\):*  Because \\(\\phi(125)=100\\),\n\n\\[\n2^{2^{2025}}\\equiv 2^{\\,2^{2025}\\bmod100},\n\\qquad\n3^{2^{2024}+1}\\equiv 3^{\\,(2^{2024}+1)\\bmod100}\\pmod{125}.\n\\]\n\nCompute the exponents.\n\n- \\(2^{2025}\\bmod100\\):  \n  \\(2^{2025}\\equiv32\\pmod{100}\\) (by CRT: \\(2^{2025}\\equiv0\\pmod4\\), \\(2^{2025}\\equiv7\\pmod{25}\\)).\n- \\(2^{2024}\\bmod100\\):  \n  \\(2^{2024}\\equiv16\\pmod{100}\\).\n\nHence  \n\n\\[\n2^{2^{2025}}\\equiv2^{32}\\equiv46\\pmod{125},\n\\qquad\n3^{2^{2024}+1}\\equiv3^{17}\\equiv38\\pmod{125}.\n\\]\n\nTherefore  \n\n\\[\nm+n\\equiv46\\cdot38\\equiv123\\pmod{125}. \\tag{6}\n\\]\n\n--------------------------------------------------------------------\n\n**Step 7.  Chinese Remainder Theorem**\n\nFind \\(N\\) such that  \n\n\\[\nN\\equiv0\\pmod8,\\qquad N\\equiv123\\pmod{125}.\n\\]\n\nWrite \\(N=8k\\).  Then \\(8k\\equiv123\\pmod{125}\\), i.e.  \n\n\\[\nk\\equiv123\\cdot8^{-1}\\pmod{125}.\n\\]\n\nSince \\(8^{-1}\\equiv47\\pmod{125}\\),  \n\n\\[\nk\\equiv123\\cdot47\\equiv31\\pmod{125}.\n\\]\n\nThus \\(k=31+125t\\) and  \n\n\\[\nN=8k=8\\cdot31=248\\pmod{1000}.\n\\]\n\n--------------------------------------------------------------------\n\n**Answer**\n\n\\[\n\\boxed{248}\n\\]",
+        "role": "assistant"
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+        "role": "user",
+        "content": "\nThe twelve letters $A,B,C,D,E,F,G,H,I,J,K$, and $L$ are randomly grouped into six pairs of letters. The two letters in each pair are placed next to each other in alphabetical order to form six two-letter words, and those six words are listed alphabetically. For example, a possible result is $AB,CJ,DG,EK,FL,HI$. The probability that the last word listed contains $G$ is $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n\\[\nA<B<C<D<E<F<G<H<I<J<K<L\n\\]\n\nand suppose the letters are randomly paired.  \nFor a pair \\(\\{x,y\\}\\) we write the word \\(xy\\) with the letters in\nalphabetical order (\\(x<y\\)).  \nThe six words are then ordered alphabetically; the last word is the\nlexicographically largest word.\n\n--------------------------------------------------------------------\n### 1.  Conditioning on the partner of \\(G\\)\n\nIn a random perfect matching each of the other \\(11\\) letters is equally\nlikely to be paired with \\(G\\).  \nLet the partner be \\(X\\).  The probability we need is  \n\n\\[\nP=\\frac1{11}\\sum_{X\\neq G}\n\\Pr\\bigl(\\text{the pair } \\{G,X\\}\\text{ is the maximal word}\\mid\nG\\text{ is paired with }X\\bigr).\n\\]\n\nThus we must evaluate the conditional probability for each possible\n\\(X\\).\n\n--------------------------------------------------------------------\n### 2.  When \\(X<G\\)\n\nIf \\(X<G\\) the word is \\(XG\\) and its first letter is \\(X\\).  \nFor it to be the maximal word, the first letters (the smaller letters)\nof all other five pairs must be **smaller than \\(X\\)**.\nHence among the remaining ten letters we need five distinct letters\nall less than \\(X\\).\n\nThe only letter with five smaller letters is \\(F\\) (the letters\n\\(A,B,C,D,E\\) are smaller).  \nThus:\n\n* \\(X=F\\) is possible;\n* \\(X=A,B,C,D,E\\) are impossible (there are not enough smaller\nletters).\n\nWhen \\(X=F\\) the remaining letters are  \n\\(\\{A,B,C,D,E\\}\\) and \\(\\{H,I,J,K,L\\}\\).  \nTo keep every other pair\u2019s first letter \\(<F\\), each of the five large\nletters must be paired with a distinct small one.  \nThe number of such matchings is \\(5!=120\\).\n\nThe total number of matchings of those ten letters is  \n\n\\[\n\\frac{10!}{2^5\\,5!}=945 .\n\\]\n\nHence  \n\n\\[\n\\Pr(\\text{maximal}\\mid G\\text{\u2013}F)=\\frac{120}{945}=\\frac{8}{63}.\n\\]\n\n--------------------------------------------------------------------\n### 3.  When \\(X>G\\)\n\nNow the word is \\(GX\\) and its first letter is \\(G\\).\nFor it to be maximal, **no other pair may have a first letter larger\nthan \\(G\\)**; i.e. no remaining pair may consist of two letters both\ngreater than \\(G\\).\n\nAfter fixing the pair \\(\\{G,X\\}\\) (with \\(X\\in\\{H,I,J,K,L\\}\\)), the\nremaining letters are\n\n* the six letters \\(\\{A,B,C,D,E,F\\}\\) (all \\(<G\\));\n* the four letters among \\(\\{H,I,J,K,L\\}\\) that are not \\(X\\) (all\n\\(>G\\)).\n\nThus each of those four \u201clarge\u2019\u2019 letters must be paired with a distinct\nsmall letter, leaving two small letters to pair together.\n\nNumber of valid matchings:\n\n\\[\n\\binom{6}{4}\\cdot4!\\cdot1=15\\cdot24=360 .\n\\]\n\nAgain the total number of matchings of the ten remaining letters is\n\\(945\\). Therefore\n\n\\[\n\\Pr(\\text{maximal}\\mid G\\text{\u2013}X)=\\frac{360}{945}=\\frac{8}{21}\n\\qquad (X=H,I,J,K,L).\n\\]\n\n--------------------------------------------------------------------\n### 4.  Assemble the probability\n\n\\[\n\\begin{aligned}\nP&=\\frac1{11}\\Bigl(\\frac{8}{63}\n+5\\cdot\\frac{8}{21}\\Bigr)    \\\\\n &=\\frac1{11}\\Bigl(\\frac{8}{63}+\\frac{40}{21}\\Bigr)\n   =\\frac1{11}\\Bigl(\\frac{8+120}{63}\\Bigr)\n   =\\frac{128}{693}.\n\\end{aligned}\n\\]\n\nThe fraction \\(\\displaystyle\\frac{128}{693}\\) is already in lowest\nterms.  Hence \\(m=128,\\;n=693\\) and\n\n\\[\nm+n = 128+693 = 821 .\n\\]\n\n--------------------------------------------------------------------\n\\[\n\\boxed{821}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nLet $N$ denote the number of ordered triples of positive integers $(a,b,c)$ such that $a,b,c\\leq3^6$ and $a^3+b^3+c^3$ is a multiple of $3^7$. Find the remainder when $N$ is divided by $1000$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n\\[\nS(t)=\\sum_{a=1}^{3^{6}}\\exp\\!\\Big(2\\pi i\\,\\frac{t a^{3}}{3^{7}}\\Big) \\qquad(0\\le t<3^{7})\n\\]\n\nand denote  \n\n\\[\nN=\\#\\{(a,b,c)\\mid 1\\le a,b,c\\le 3^{6},\n\\ a^{3}+b^{3}+c^{3}\\equiv 0\\pmod{3^{7}}\\}.\n\\]\n\nFor any modulus \\(m\\),\n\n\\[\n\\#\\{(x,y,z):x+y+z\\equiv0\\pmod m\\}=\n\\frac1m\\sum_{t=0}^{m-1}\\Bigl(\\sum_{x}e^{2\\pi i t x/m}\\Bigr)^3 .\n\\]\n\nHence  \n\n\\[\nN=\\frac1{3^{7}}\\sum_{t=0}^{3^{7}-1} S(t)^{3}. \\tag{1}\n\\]\n\n--------------------------------------------------------------------\n### 1.  Splitting the summation\n\nWrite each \\(a\\) as \\(a=3^{v}u\\) where \\(v=v_{3}(a)\\) and \\(u\\) is not\ndivisible by \\(3\\).  \nFor \\(0\\le v\\le 2\\) define  \n\n\\[\nU_{v}=\\{\\,u:1\\le u\\le 3^{6-v},\\;3\\nmid u\\,\\},\n\\qquad |U_{0}|=486,\\ |U_{1}|=162,\\ |U_{2}|=54 .\n\\]\n\nIf \\(v\\ge3\\) then \\(a^{3}\\equiv0\\pmod{3^{7}}\\); there are  \n\\(n_{3}=27\\) such numbers.\nThus\n\n\\[\nS(t)=f_{0}(t)+f_{1}(t)+f_{2}(t)+n_{3},\n\\]\nwhere  \n\n\\[\n\\begin{aligned}\nf_{0}(t)&=\\sum_{x\\in U_{0}}\\zeta^{t x^{3}},\\\\[2mm]\nf_{1}(t)&=\\sum_{x\\in U_{1}}\\zeta^{t\\,27x^{3}},\\\\[2mm]\nf_{2}(t)&=\\sum_{x\\in U_{2}}\\zeta^{t\\,729x^{3}},\n\\end{aligned}\n\\qquad \n\\zeta=e^{2\\pi i/3^{7}} .\n\\]\n\n--------------------------------------------------------------------\n### 2.  Evaluating \\(f_{0},f_{1},f_{2}\\)\n\n*For \\(f_{0}\\).*  \nLet \\(G_{7}=(\\mathbb Z/3^{7}\\mathbb Z)^{\\times}\\) (\\(|G_{7}|=1458\\)).\nThe map \\(x\\mapsto x^{3}\\) from \\(G_{7}\\) onto the set of cubes\n\\(C_{6}\\) has kernel of size \\(3\\); consequently\n\n\\[\n\\sum_{x\\in G_{7}}\\zeta^{t x}=3\\sum_{r\\in C_{6}}\\zeta^{t r}=3f_{0}(t).\n\\]\n\nFor \\(t\\neq0\\) one has  \n\n\\[\n\\sum_{x\\in G_{7}}\\zeta^{t x}= -\\!\\!\\sum_{\\substack{x\\;(\\bmod 3^{7})\\\\3\\mid x}}\\!\\!\\zeta^{t x}\n=\\begin{cases}\n-729,&v_{3}(t)=6,\\\\\n0,&0\\le v_{3}(t)\\le5 .\n\\end{cases}\n\\]\n\nHence  \n\n\\[\nf_{0}(t)=\n\\begin{cases}\n486,&t=0,\\\\[2mm]\n-243,&v_{3}(t)=6,\\\\[2mm]\n0,&\\text{otherwise.}\n\\end{cases}\n\\tag{2}\n\\]\n\n*For \\(f_{1}\\).*  \nWriting each \\(x\\in U_{1}\\) as \\(x=v+81k\\;(k=0,1,2)\\) one finds\n\\(x^{3}\\equiv v^{3}\\pmod{81}\\). Consequently  \n\n\\[\nf_{1}(t)=3\\!\\!\\sum_{\\substack{v\\in(\\mathbb Z/81)^{\\times}}}\\!\n\\exp\\!\\Big(2\\pi i\\,\\frac{t v^{3}}{81}\\Big).\n\\]\n\nUsing again that the cube map on \\((\\mathbb Z/81)^{\\times}\\) has kernel\nsize \\(3\\),\n\n\\[\nf_{1}(t)=3\\!\\cdot\\!3\\!\\!\\sum_{r\\in C_{1}}\\!\n\\exp\\!\\Big(2\\pi i\\,\\frac{t r}{81}\\Big) ,\n\\]\n\nwhere \\(C_{1}\\) is the set of cube\u2011residues modulo \\(81\\) (\\(|C_{1}|=18\\)).\nNow\n\n\\[\n\\sum_{x\\in(\\mathbb Z/81)^{\\times}}\\exp\\!\\Big(2\\pi i\\,\n\\frac{t x}{81}\\Big)=\n\\begin{cases}\n54,&v_{3}(t)\\ge4,\\\\[1mm]\n-27,&v_{3}(t)=3,\\\\[1mm]\n0,&v_{3}(t)\\le2 .\n\\end{cases}\n\\]\n\nThus\n\n\\[\nf_{1}(t)=\n\\begin{cases}\n162,&v_{3}(t)\\ge4,\\\\[2mm]\n-81,&v_{3}(t)=3,\\\\[2mm]\n0,&v_{3}(t)\\le2 .\n\\end{cases}\n\\tag{3}\n\\]\n\n*For \\(f_{2}\\).*  \nHere \\(x^{3}\\equiv x\\pmod 3\\), and among the \\(54\\) numbers in \\(U_{2}\\)\nexactly half are \\(\\equiv1\\pmod3\\) and half \\(\\equiv2\\pmod3\\). Hence  \n\n\\[\nf_{2}(t)=27\\bigl(\\zeta^{t}+ \\zeta^{2t}\\bigr)=\n\\begin{cases}\n-27,&v_{3}(t)=0,\\\\[2mm]\n54,&v_{3}(t)\\ge1 .\n\\end{cases}\n\\tag{4}\n\\]\n\n--------------------------------------------------------------------\n### 3.  The values of \\(S(t)\\)\n\nFrom (2)\u2013(4) (and remembering the constant term \\(n_{3}=27\\))\n\n\\[\nS(t)=f_{0}(t)+f_{1}(t)+f_{2}(t)+27=\n\\begin{array}{c|c}\nv_{3}(t) & S(t)\\\\ \\hline\n\\infty\\;(t=0) & 729\\\\\n0 & 0\\\\\n1 & 81\\\\\n2 & 81\\\\\n3 & 0\\\\\n4 & 243\\\\\n5 & 243\\\\\n6 & 0\n\\end{array}\n\\]\n\n--------------------------------------------------------------------\n### 4.  Computing \\(N\\)\n\nOnly the classes with non\u2011zero \\(S(t)\\) contribute to (1).  \nThe numbers of \\(t\\) in each class are\n\n\\[\n\\begin{array}{c|c}\nv_{3}(t) & \\#t\\\\ \\hline\n\\infty & 1\\\\\n0 & 1458\\\\\n1 & 486\\\\\n2 & 162\\\\\n3 & 54\\\\\n4 & 18\\\\\n5 & 6\\\\\n6 & 2\n\\end{array}\n\\]\n\nHence\n\n\\[\n\\begin{aligned}\nN&=\\frac1{3^{7}}\\Bigl( 729^{3}\n+ (486+162) \\,81^{3}\n+ (18+6)\\,243^{3}\\Bigr)\\\\[2mm]\n&=\\frac1{3^{7}}\\Bigl(3^{18}+648\\cdot3^{12}+24\\cdot3^{15}\\Bigr)\\\\\n&=3^{5}\\cdot2025 = 243\\cdot2025 = 492\\,075 .\n\\end{aligned}\n\\]\n\n--------------------------------------------------------------------\n### 5.  Remainder modulo \\(1000\\)\n\n\\[\n492\\,075 \\equiv 75 \\pmod{1000}.\n\\]\n\n--------------------------------------------------------------------\n\\[\n\\boxed{75}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nOn $\\triangle ABC$ points $A,D,E$, and $B$ lie that order on side $\\overline{AB}$ with $AD=4, DE=16$, and $EB=8$. Points $A,F,G$, and $C$ lie in that order on side $\\overline{AC}$ with $AF=13, FG=52$, and $GC=26$. Let $M$ be the reflection of $D$ through $F$, and let $N$ be the reflection of $G$ through $E$. Quadrilateral $DEGF$ has area 288. Find the area of heptagon $AFNBCEM$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "**Solution Overview**\n\nThe given lengths on the sides of \\(\\triangle ABC\\) give  \n\n\\[\nAD=4,\\;DE=16,\\;EB=8 \\qquad\\Longrightarrow\\qquad AB=28,\n\\]\n\\[\nAF=13,\\;FG=52,\\;GC=26 \\qquad\\Longrightarrow\\qquad AC=91 .\n\\]\n\n--------------------------------------------------------------------\n\n### 1.  Two lines parallel to \\(BC\\)\n\n\\[\n\\frac{AD}{AB}= \\frac{4}{28}= \\frac{1}{7},\\qquad \n\\frac{AF}{AC}= \\frac{13}{91}= \\frac{1}{7}.\n\\]\n\nHence the points \\(D\\in AB\\) and \\(F\\in AC\\) divide the two sides in the same\nratio; therefore \\(DF\\parallel BC\\).\n\nSimilarly  \n\n\\[\n\\frac{AE}{AB}= \\frac{AD+DE}{AB}= \\frac{20}{28}= \\frac57,\n\\qquad \n\\frac{AG}{AC}= \\frac{AF+FG}{AC}= \\frac{65}{91}= \\frac57,\n\\]\n\nso \\(E\\in AB,\\;G\\in AC\\) also give a line parallel to \\(BC\\); i.e. \\(EG\\parallel BC\\).\n\nThus the quadrilateral \\(DEGF\\) is bounded by two parallel sides \\(DF,EG\\) and\nthe two segments of the sides of the triangle, and it is the region between the\ntwo similar triangles \\(ADF\\) and \\(AEG\\).\n\n--------------------------------------------------------------------\n\n### 2.  Area of \\(\\triangle ABC\\)\n\nIf \\([XYZ]\\) denotes area, similarity gives  \n\n\\[\n[ADF]=\\Bigl(\\frac{AD}{AB}\\Bigr)^2[ABC]=\\Bigl(\\frac17\\Bigr)^2[ABC]=\\frac{[ABC]}{49},\n\\]\n\n\\[\n[AEG]=\\Bigl(\\frac{AE}{AB}\\Bigr)\\Bigl(\\frac{AG}{AC}\\Bigr)[ABC]\n      =\\frac57\\cdot\\frac57[ABC]=\\frac{25}{49}[ABC].\n\\]\n\nHence  \n\n\\[\n[DEGF]=[AEG]-[ADF]=\\Bigl(\\frac{25}{49}-\\frac1{49}\\Bigr)[ABC]\n       =\\frac{24}{49}[ABC].\n\\]\n\nGiven \\([DEGF]=288\\),\n\n\\[\n\\frac{24}{49}[ABC]=288\\quad\\Longrightarrow\\quad[ABC]=288\\cdot\\frac{49}{24}\n                  =12\\cdot49=588.\n\\]\n\n--------------------------------------------------------------------\n\n### 3.  Area of the heptagon \\(AFNBCEM\\)\n\nPlace the triangle with \\(A=(0,0),\\;B=(28,0)\\) and\n\\(C=(91\\cos\\theta,\\,91\\sin\\theta)\\).\nBecause \\([ABC]=\\tfrac12\\cdot28\\cdot91\\sin\\theta\\),\n\n\\[\n\\sin\\theta=\\frac{[ABC]}{1274}= \\frac{588}{1274}= \\frac{6}{13}.\n\\]\n\nThus  \n\n\\[\n\\cos\\theta=\\frac{\\sqrt{1-\\sin^2\\theta}}{\\,}= \\frac{\\sqrt{133}}{13}.\n\\]\n\nThe coordinates of the relevant points are\n\n\\[\n\\begin{aligned}\n&F=(13\\cos\\theta,13\\sin\\theta)=(\\sqrt{133},6), \\\\\n&G=(65\\cos\\theta,65\\sin\\theta)=(5\\sqrt{133},30),\\\\\n&D=(4,0),\\qquad\nE=(20,0),\\\\\n&M=2F-D=(2\\sqrt{133}-4,12),\\\\\n&N=2E-G=(40-5\\sqrt{133},-30).\n\\end{aligned}\n\\]\n\nUsing the shoelace formula for the polygon\n\\(A\\,(0,0),\\;F,\\;N,\\;B,\\;C,\\;E,\\;M\\) we obtain\n\n\\[\n\\begin{aligned}\n\\sum (x_i y_{i+1}-y_i x_{i+1})\n&= -240+840+1176-840+240 = 1176,\\\\[2mm]\n\\text{Area}&=\\frac12\\cdot1176=588.\n\\end{aligned}\n\\]\n\nThus the heptagon \\(AFNBCEM\\) has the same area as \\(\\triangle ABC\\).\n\n--------------------------------------------------------------------\n\n\\[\n\\boxed{588}\n\\]",
+        "role": "assistant"
+      }
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+    [
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+        "role": "user",
+        "content": "\nThe parabola with equation $y=x^{2}-4$ is rotated $60^{\\circ}$ counterclockwise around the origin. The unique point in the fourth quadrant where the original parabola and its image intersect has $y$-coordinate $\\frac{a-\\sqrt{b}}{c}$, where $a$, $b$, and $c$ are positive integers, and $a$ and $c$ are relatively prime. Find $a+b+c$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n\\[\nP:\\; y=x^{2}-4\n\\]\n\nand rotate \\(P\\) about the origin \\(60^{\\circ}\\) counter\u2011clockwise.  \nIf \\((x,y)\\) is a point of \\(P\\) then its image \\((X,Y)\\) satisfies  \n\n\\[\n\\begin{pmatrix}X\\\\Y\\end{pmatrix}= \n\\begin{pmatrix}\\cos 60^\\circ & -\\sin 60^\\circ\\\\[2pt] \n\\sin 60^\\circ & \\ \\cos 60^\\circ\\end{pmatrix}\n\\begin{pmatrix}x\\\\y\\end{pmatrix},\n\\qquad \n\\cos60^\\circ=\\frac12,\\;\\sin60^\\circ=\\frac{\\sqrt3}{2}.\n\\]\n\nHence  \n\n\\[\nX=\\frac{x}{2}-\\frac{\\sqrt3}{2}y,\\qquad\nY=\\frac{\\sqrt3}{2}x+\\frac{y}{2}.\n\\]\n\nTo obtain the equation of the rotated curve in the original \\((x,y)\\)\u2013coordinates,\nsolve for \\((x,y)\\) in terms of \\((X,Y)\\) (rotate back by \\(-60^\\circ\\)):\n\n\\[\nx = \\frac{X}{2}+\\frac{\\sqrt3}{2}Y,\\qquad\ny = -\\frac{\\sqrt3}{2}X+\\frac{Y}{2}.\n\\]\n\nSince the original points satisfy \\(y=x^{2}-4\\), substituting the expressions above gives the equation of the image:\n\n\\[\nx^{2}+2\\sqrt3\\,xy+3y^{2}+2\\sqrt3\\,x-2y-16=0. \\tag{1}\n\\]\n\n--------------------------------------------------------------------\n### Intersection with the original parabola\n\nThe intersection points satisfy simultaneously  \n\n\\[\ny=x^{2}-4\\qquad\\text{and}\\qquad (1).\n\\]\n\nSubstituting \\(y=x^{2}-4\\) into (1) yields\n\n\\[\n3x^{4}-25x^{2}+40+2\\sqrt3\\,x^{3}-6\\sqrt3\\,x=0.\n\\]\n\nFactor this quartic in the field \\(\\mathbb{Q}(\\sqrt3)\\):\n\n\\[\n\\begin{aligned}\n3x^{4}-25x^{2}+40+2\\sqrt3\\,x^{3}-6\\sqrt3\\,x\n&=(x^{2}+\\sqrt3\\,x-4)\\bigl(3x^{2}-\\sqrt3\\,x-10\\bigr).\n\\end{aligned}\n\\]\n\nThus the intersection points satisfy one of  \n\n\\[\n\\begin{cases}\nx^{2}+\\sqrt3\\,x-4=0,\\\\[2pt]\n\\text{or}\\\\[2pt]\n3x^{2}-\\sqrt3\\,x-10=0 .\n\\end{cases}\n\\]\n\n--------------------------------------------------------------------\n### Selecting the point in the fourth quadrant\n\n*From* \\(x^{2}+\\sqrt3\\,x-4=0\\)\n\n\\[\nx=\\frac{-\\sqrt3\\pm\\sqrt{19}}{2}.\n\\]\n\nThe root \\(\\displaystyle x=\\frac{-\\sqrt3+\\sqrt{19}}{2}>0\\) gives  \n\n\\[\ny=x^{2}-4=\\frac{11-\\sqrt{57}}{2}-4=\\frac{3-\\sqrt{57}}{2}<0,\n\\]\n\nso \\((x,y)\\) lies in the fourth quadrant.\n\n*From* \\(3x^{2}-\\sqrt3\\,x-10=0\\)\n\n\\[\nx=\\frac{\\sqrt3\\pm\\sqrt{123}}{6},\n\\]\n\nwhich yields either \\(y>0\\) (first root) or \\(x<0\\) (second root); neither point is in the fourth quadrant.\n\nHence the unique fourth\u2011quadrant intersection point is  \n\n\\[\n\\Bigl(\\frac{-\\sqrt3+\\sqrt{19}}{2}\\,,\\; \\frac{3-\\sqrt{57}}{2}\\Bigr).\n\\]\n\n--------------------------------------------------------------------\n### Required \\(y\\)-coordinate\n\nThe \\(y\\)-coordinate is \\(\\displaystyle \\frac{3-\\sqrt{57}}{2}\\).\n\nWrite it as \\(\\frac{a-\\sqrt{b}}{c}\\) with \\(a,b,c\\) positive integers and \\(\\gcd(a,c)=1\\):\n\\[\na=3,\\qquad b=57,\\qquad c=2.\n\\]\n\nTherefore  \n\n\\[\na+b+c = 3+57+2 = 62.\n\\]\n\n\\[\n\\boxed{62}\n\\]",
+        "role": "assistant"
+      }
+    ],
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+      {
+        "role": "user",
+        "content": "\nSix points $ A, B, C, D, E, $ and $ F $ lie in a straight line in that order. Suppose that $ G $ is a point not on the line and that $ AC = 26 $, $ BD = 22 $, $ CE = 31 $, $ DF = 33 $, $ AF = 73 $, $ CG = 40 $, and $ DG = 30 $. Find the area of $ \\triangle BGE $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let the line containing \\(A,B,C,D,E,F\\) be the \\(x\\)-axis.\n\n\\[\nA=(0,0),\\qquad B=(b,0),\\qquad C=(c,0),\\qquad D=(d,0),\\qquad \nE=(e,0),\\qquad F=(f,0)\n\\]\n\nBecause the points are in the order \\(A,B,C,D,E,F\\),\n\n\\[\nc-b=AC-AB,\\; d-b=BD,\\; e-c=CE,\\; f-d=DF,\\; f-0=AF.\n\\]\n\nTake \\(A\\) at the origin.  From the data\n\n\\[\nAC=26\\implies c=26,\n\\]\n\\[\nBD=22\\implies d=b+22,\n\\]\n\\[\nCE=31\\implies e=c+31=57,\n\\]\n\\[\nDF=33\\implies f=d+33=b+55,\n\\]\n\\[\nAF=73\\implies f=73.\n\\]\n\nHence \\(b+55=73\\Rightarrow b=18\\).  \nThus the coordinates are  \n\n\\[\nB=(18,0),\\; C=(26,0),\\; D=(40,0),\\; E=(57,0),\\; F=(73,0).\n\\]\n\n---\n\n### Locate \\(G\\)\n\n\\(G\\) is off the line and satisfies  \n\n\\[\nCG=40,\\qquad DG=30.\n\\]\n\nLet \\(G=(x,y)\\) with \\(y\\neq0\\). Then  \n\n\\[\n(x-26)^2+y^{2}=40^{2}=1600,\\tag{1}\n\\]\n\\[\n(x-40)^2+y^{2}=30^{2}=900.\\tag{2}\n\\]\n\nSubtract (2) from (1):\n\n\\[\n(x-26)^2-(x-40)^2=700.\n\\]\n\nExpanding,\n\n\\[\n[x^{2}-52x+676]-[x^{2}-80x+1600]=28x-924=700,\n\\]\n\\[\n28x=1624\\quad\\Longrightarrow\\quad x=58.\n\\]\n\nPlugging \\(x=58\\) into (2):\n\n\\[\n(58-40)^{2}+y^{2}=900\\;\\Longrightarrow\\;18^{2}+y^{2}=900\n\\]\n\\[\ny^{2}=576\\;\\Longrightarrow\\;|y|=24.\n\\]\n\nSo \\(G=(58,\\,24)\\) (the point \\((58,-24)\\) gives the same area).\n\n---\n\n### Area of \\(\\triangle BGE\\)\n\nPoints \\(B\\) and \\(E\\) lie on the \\(x\\)-axis, so the base \\(BE\\) has length\n\n\\[\nBE = e-b = 57-18 = 39.\n\\]\n\nThe altitude from \\(G\\) to the line \\(BE\\) (the \\(x\\)-axis) is \\(|y| = 24\\).\n\nHence  \n\n\\[\n\\text{Area} = \\frac12 \\times BE \\times \\text{height}\n= \\frac12 \\times 39 \\times 24 = 468.\n\\]\n\n\\[\n\\boxed{468}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nFind the sum of all positive integers $ n $ such that $ n + 2 $ divides the product $ 3(n + 3)(n^2 + 9) $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "We need the positive integers \\(n\\) such that  \n\n\\[\nn+2\\mid 3(n+3)(n^{2}+9).\n\\]\n\n---\n\n### 1.  Replace \\(n+2\\) by a new variable  \n\nLet  \n\n\\[\nk=n+2\\qquad (k\\ge 3), \\qquad n=k-2 .\n\\]\n\nThen  \n\n\\[\n\\begin{aligned}\nn+3 &= (k-2)+3 = k+1,\\\\[2pt]\nn^{2}+9 &= (k-2)^{2}+9 = k^{2}-4k+13 .\n\\end{aligned}\n\\]\n\nHence  \n\n\\[\n3(n+3)(n^{2}+9)=3(k+1)(k^{2}-4k+13).\n\\]\n\nThe condition becomes  \n\n\\[\nk \\mid 3(k+1)(k^{2}-4k+13).\n\\]\n\n---\n\n### 2.  Reduce modulo \\(k\\)\n\nModulo \\(k\\),\n\n\\[\nk+1\\equiv 1,\\qquad k^{2}-4k+13\\equiv 13,\n\\]\n\nbecause \\(k\\equiv 0\\) gives \\(k^{2}\\equiv 0\\) and \\(-4k\\equiv 0\\).\n\nThus  \n\n\\[\n3(k+1)(k^{2}-4k+13)\\equiv 3\\cdot 1\\cdot 13=39 \\pmod{k}.\n\\]\n\nHence the divisibility condition is equivalent to  \n\n\\[\nk\\mid 39.\n\\]\n\n---\n\n### 3.  Find admissible \\(k\\) and corresponding \\(n\\)\n\nThe positive divisors of \\(39\\) are \\(1,3,13,39\\).\nSince \\(k=n+2\\ge 3\\), we keep  \n\n\\[\nk\\in \\{3,13,39\\}.\n\\]\n\nTherefore  \n\n\\[\nn=k-2\\in\\{1,11,37\\}.\n\\]\n\nAll three values satisfy the original condition (a quick check confirms the division).\n\n---\n\n### 4.  Sum of all such \\(n\\)\n\n\\[\n1+11+37 = 49.\n\\]\n\n\\[\n\\boxed{49}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nThe set of points in 3-dimensional coordinate space that lie in the plane $x+y+z=75$ whose coordinates satisfy the inequalities $x-yz<y-zx<z-xy$ forms three disjoint convex regions. Exactly one of those regions has finite area. The area of this finite region can be expressed in the form $a\\sqrt{b}$, where $a$ and $b$ are positive integers and $b$ is not divisible by the square of any prime. Find $a+b$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "The inequalities\n\n\\[\nx-yz<y-zx<z-xy\n\\]\n\nwith the plane \\(x+y+z=75\\) can be simplified.  \nWrite \\(z=75-x-y\\). Then\n\n\\[\n\\begin{aligned}\ny-zx-(x-yz) &= (y-x)(1+z)= (y-x)(76-x-y),\\\\\nz-xy-(y-zx) &= (z-y)(1+x)= (75-x-2y)(1+x).\n\\end{aligned}\n\\]\n\nThus the points on the plane satisfy  \n\n\\[\n(y-x)(76-x-y)>0,\\qquad (75-x-2y)(1+x)>0 .\n\\tag{1}\n\\]\n\nDefine in the \\(xy\\)-plane the lines  \n\n\\[\n\\begin{aligned}\nL_1 &: y=x,\\\\\nL_2 &: x+y=76,\\\\\nL_3 &: x=-1,\\\\\nL_4 &: x+2y=75\\;(y=(75-x)/2).\n\\end{aligned}\n\\]\n\nFrom (1) we obtain two possibilities for each product, giving four possible\nintersections of half\u2011planes.  One of these intersections is empty; the other three\nare convex.  The region for which both products in (1) are **positive** is\n\n\\[\n\\begin{cases}\ny>x,\\\\\nx+y<76,\\\\\ny<(75-x)/2,\\\\\nx>-1,\n\\end{cases}\n\\]\n\nwhich in the \\(xy\\)-plane is the interior of the triangle with vertices\n\n\\[\nA(-1,-1),\\qquad B(-1,38),\\qquad C(25,25).\n\\]\n\nThe other two regions are unbounded.  Hence the finite region is this triangle.\n\n---\n\n### Area in the \\(xy\\)-plane\n\n\\[\n\\text{Area}_{xy}= \\frac12\\bigl|AB\\times AC\\bigr|\n               =\\frac12\\bigl| (0,39)\\times (26,26)\\bigr|\n               =\\frac12\\cdot1014 = 507 .\n\\]\n\n---\n\n### Area on the plane \\(x+y+z=75\\)\n\nThe plane is given by \\(z=75-x-y\\).  Its area element satisfies  \n\n\\[\ndS = \\sqrt{1+(\\partial_xz)^2+(\\partial_yz)^2}\\;dx\\,dy\n    =\\sqrt{1+1+1}\\;dx\\,dy =\\sqrt3\\,dx\\,dy .\n\\]\n\nHence  \n\n\\[\n\\text{Area}_{\\text{plane}} = \\sqrt3\\;\\text{Area}_{xy}\n                            = 507\\sqrt3 .\n\\]\n\nSo the area can be written as \\(a\\sqrt b\\) with \\(a=507,\\ b=3\\).\nTherefore  \n\n\\[\na+b = 507+3 = 510 .\n\\]\n\n\\[\n\\boxed{510}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nA piecewise linear periodic function is defined by $f(x)=\\begin{cases}x&\\text{if }x\\in[-1,1)\\\\2-x&\\text{if }x\\in[1,3)\\end{cases}$ and $f(x+4)=f(x)$ for all real numbers $x$. The graph of $f(x)$ has the sawtooth pattern. The parabola $x=34y^2$ intersects the graph of $f(x)$ at finitely many points. The sum of the $y$-coordinates of these intersection points can be expressed in the form $\\frac{a+b\\sqrt{c}}{d}$, where $a,b,c,$ and $d$ are positive integers, $a,b,$ and $d$ have greatest common divisor equal to 1, and $c$ is not divisible by the square of any prime. Find $a+b+c+d$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "The intersection points satisfy  \n\n\\[\ny=f(x),\\qquad x=34y^{2}\\;( \\ge 0).\n\\]\n\nBecause \\(f\\) has period \\(4\\),\n\n\\[\nf(x)=\\begin{cases}\nx-4k ,&x\\in[-1+4k,\\,1+4k),\\\\[2mm]\n2+4k-x ,&x\\in[1+4k,\\,3+4k),\n\\end{cases}\\qquad k\\in\\mathbb Z .\n\\]\n\n--------------------------------------------------------------------\n### 1.  Equations for the two linear pieces  \n\n*Ascending piece*  \\((x-4k)\\):  \n\n\\[\ny=x-4k,\\qquad x=34y^{2}\n\\Longrightarrow 34y^{2}-y-4k=0. \\tag{1}\n\\]\n\n*Descending piece*  \\((2+4k-x)\\):  \n\n\\[\ny=2+4k-x,\\qquad x=34y^{2}\n\\Longrightarrow 34y^{2}+y-(2+4k)=0. \\tag{2}\n\\]\n\nBoth are quadratics in \\(y\\); each can give at most two real roots.\n\n--------------------------------------------------------------------\n### 2.  Which integers \\(k\\) give admissible roots?\n\nBecause \\(|y|\\le 1\\) (the range of \\(f\\)), the roots must lie in \\([-1,1]\\).\n\n*For (1):*  \nThe sum of the two roots equals \\(\\frac{1}{34}\\); the product is \\(-\\frac{4k}{34}\\).  \nThe discriminant must be non\u2011negative:\n\n\\[\n\\Delta_1=1+544k\\ge 0\\Longrightarrow k\\ge0 .\n\\]\n\nFor a root to be in \\([-1,1)\\) we also need  \n\n\\[\n-1\\le\\frac{1\\pm\\sqrt{1+544k}}{68}<1 .\n\\]\n\nThe last inequality forces \\(k\\le8\\).  Hence (1) yields real admissible roots for  \n\n\\[\nk=0,1,\\dots ,8 .\n\\]\n\nBoth roots are in \\([-1,1)\\) for each of these values.\n\n*For (2):*  \n\\[\n\\Delta_2=273+544k\\ge0\\Longrightarrow k\\ge0 .\n\\]\n\nThe condition \\(-1<y\\le 1\\) gives \\(k\\le8\\).  \nFor \\(k=0,\\dots ,7\\) both roots lie in \\((-1,1]\\); for \\(k=8\\) only the \u201c\\(+\\)\u201d root\n\\[\ny=\\frac{-1+\\sqrt{273+544\\cdot8}}{68}\n      =\\frac{-1+5\\sqrt{185}}{68}\n\\]\nremains in the interval (the \u201c\\(-\\)\u201d root is \\(<-1\\)).\n\nThus  \n\n* (1) contributes \\(2\\) solutions for each \\(k=0,\\dots ,8\\)  \\(\\Rightarrow 18\\) points;  \n* (2) contributes \\(2\\) solutions for each \\(k=0,\\dots ,7\\) and \\(1\\) solution for \\(k=8\\)  \\(\\Rightarrow 17\\) points.\n\nHence there are \\(35\\) intersection points altogether.\n\n--------------------------------------------------------------------\n### 3.  Sum of the \\(y\\)-coordinates  \n\nFor each fixed \\(k\\) the sum of the two roots of (1) is, by Vieta,\n\n\\[\n\\Sigma_{A}(k)=\\frac{1}{34}.\n\\]\n\nSo the total contribution of (1) is  \n\n\\[\n\\sum_{k=0}^{8}\\Sigma_{A}(k)=9\\cdot\\frac{1}{34}= \\frac{9}{34}.\n\\]\n\nFor (2), when both roots exist their sum is  \n\n\\[\n\\Sigma_{B}(k)=-\\frac{1}{34}.\n\\]\n\nThus for \\(k=0,\\dots ,7\\) the total is  \n\n\\[\n8\\cdot\\Bigl(-\\frac{1}{34}\\Bigr)=-\\frac{8}{34}.\n\\]\n\nFor \\(k=8\\) only the positive root remains:\n\n\\[\ny_{8}= \\frac{-1+5\\sqrt{185}}{68}.\n\\]\n\nAdding everything,\n\n\\[\n\\begin{aligned}\n\\text{Sum of all }y\n&=\\frac{9}{34}-\\frac{8}{34}+y_{8}\n   =\\frac{1}{34}+ \\frac{-1+5\\sqrt{185}}{68}\\\\[2mm]\n&= \\frac{2}{68}+ \\frac{-1+5\\sqrt{185}}{68}\n   =\\frac{1+5\\sqrt{185}}{68}.\n\\end{aligned}\n\\]\n\n--------------------------------------------------------------------\n### 4.  Final answer  \n\nThe sum is \\(\\displaystyle\\frac{1+5\\sqrt{185}}{68}\\).  \nThus  \n\n\\[\na=1,\\; b=5,\\; c=185,\\; d=68,\\qquad\na+b+c+d=1+5+185+68=259.\n\\]\n\n\\[\n\\boxed{259}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nThe 27 cells of a $3\\times9$ grid are filled in using the numbers 1 through 9 so that each row contains 9 different numbers, and each of the three $3\\times3$ blocks heavily outlined in the example below contains 9 different numbers, as in the first three rows of a Sudoku puzzle. \n | 4 | 2 | 8 | 9 | 6 | 3 | 1 | 7 | 5 | \n | 3 | 7 | 9 | 5 | 2 | 1 | 6 | 8 | 4 | \n | 5 | 6 | 1 | 8 | 4 | 7 | 9 | 2 | 3 | \n The number of different ways to fill such a grid can be written as $p^a\\cdot q^b\\cdot r^c\\cdot s^d$, where $p,q,r,$ and $s$ are distinct prime numbers and $a,b,c,$ and $d$ are positive integers. Find $p\\cdot a+q\\cdot b+r\\cdot c+s\\cdot d$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let the three rows be \\(R_1,R_2,R_3\\) and the three \\(3\\times3\\) blocks be \\(B_1,B_2,B_3\\) (columns \\(1\\!-\\!3,\\;4\\!-\\!6,\\;7\\!-\\!9\\)).\nEach row must be a permutation of \\(\\{1,\\dots ,9\\}\\) and each block must also contain every digit once.\n\n--------------------------------------------------------------------\n### 1.  Where does a digit appear in the three rows?\n\nFor a fixed digit \\(d\\) its three copies (one in each row) must lie in three *different* blocks; otherwise a block would miss that digit.  \nThus for each digit we obtain a bijection  \n\n\\[\n\\phi_d:\\{1,2,3\\}\\longrightarrow\\{1,2,3\\},\\qquad \n\\phi_d(i)=\\text{block containing }d\\text{ in row }i .\n\\]\n\nSo each digit corresponds to a permutation of the three blocks.  \nThere are six permutations, listed with the cells \\((i,\\phi(i))\\) they occupy:\n\n\\[\n\\begin{array}{c|c}\n\\text{perm.} & \\text{cells}\\\\ \\hline\n(1)(2)(3) & (1,1),(2,2),(3,3)\\\\\n(12) & (1,2),(2,1),(3,3)\\\\\n(13) & (1,3),(2,2),(3,1)\\\\\n(23) & (1,1),(2,3),(3,2)\\\\\n(123) & (1,2),(2,3),(3,1)\\\\\n(132) & (1,3),(2,1),(3,2)\n\\end{array}\n\\]\n\nLet \\(x_1,\\dots ,x_6\\) be the numbers of digits that use the six permutations (in the order shown).  \nBecause each block must contain three digits from each row, each of the nine cells \\((i,k)\\) must be hit by exactly three digits, giving\n\n\\[\n\\begin{aligned}\nx_1+x_4 &=3, & x_2+x_5 &=3, & x_3+x_6 &=3,\\\\\nx_2+x_6 &=3, & x_1+x_3 &=3, & x_4+x_5 &=3,\\\\\nx_3+x_5 &=3, & x_4+x_6 &=3, & x_1+x_2 &=3 .\n\\end{aligned}\n\\]\n\nSolving, all solutions have the form  \n\n\\[\n(x_1,x_2,x_3,x_4,x_5,x_6)=(a,\\,3-a,\\,3-a,\\,3-a,\\,a,\\,a),\\qquad a\\in\\{0,1,2,3\\}.\n\\]\n\n--------------------------------------------------------------------\n### 2.  Assign the digits to the permutations\n\nFor a fixed \\(a\\) the number of ways to choose which digits get which permutation is\n\n\\[\n\\frac{9!}{x_1!\\,x_2!\\,x_3!\\,x_4!\\,x_5!\\,x_6!}\n   =\\frac{9!}{a!^{\\,3}\\,(3-a)!^{\\,3}} .\n\\]\n\nSumming over the four possible values of \\(a\\),\n\n\\[\n\\sum_{a=0}^3\\frac{9!}{a!^{\\,3}(3-a)!^{\\,3}}\n   =9!\\Bigl(\\frac1{3!^{\\,3}}{0\\choose0}^3\n            +\\frac1{3!^{\\,3}}{3\\choose1}^3\n            +\\frac1{3!^{\\,3}}{3\\choose2}^3\n            +\\frac1{3!^{\\,3}}{3\\choose3}^3\\Bigr)\n   =9!\\,\\frac{56}{216}\n   =9!\\,\\frac{7}{27}.\n\\]\n\n--------------------------------------------------------------------\n### 3.  Order the digits inside each block\n\nWithin a fixed block and a fixed row there are three column positions.\nThe three digits that belong to that macro\u2011cell can be placed in these\npositions in \\(3! = 6\\) ways.\nThere are \\(3\\) rows \\(\\times\\) \\(3\\) blocks \\(=9\\) such macro\u2011cells, giving a factor \\(6^9\\).\n\n--------------------------------------------------------------------\n### 4.  Total number of fillings\n\n\\[\nN = \\Bigl(9!\\,\\frac{7}{27}\\Bigr)\\,6^{9}\n   = 2^{16}\\,3^{10}\\,5\\,7^{2}.\n\\]\n\nThus the factorisation uses the four distinct primes  \n\n\\[\np=2,\\;q=3,\\;r=5,\\;s=7,\\qquad \na=16,\\;b=10,\\;c=1,\\;d=2 .\n\\]\n\nFinally,\n\n\\[\np\\,a+q\\,b+r\\,c+s\\,d\n   =2\\cdot16+3\\cdot10+5\\cdot1+7\\cdot2\n   =32+30+5+14=81.\n\\]\n\n\\[\n\\boxed{81}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nLet $ABCDE$ be a convex pentagon with $AB=14, BC=7, CD=24, DE=13, EA=26,$ and $\\angle B=\\angle E=60^\\circ$. For each point $X$ in the plane, define $f(X)=AX+BX+CX+DX+EX$. The least possible value of $f(X)$ can be expressed as $m+n\\sqrt{p}$, where $m$ and $n$ are positive integers and $p$ is not divisible by the square of any prime. Find $m+n+p$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "We place the pentagon in the plane.  \nSet  \n\n\\[\n\\begin{aligned}\nA&=(7,7\\sqrt3),\\qquad B=(0,0),\\qquad C=(7,0),\\\\[2mm]\nD&=\\Bigl(\\frac{205}{7},\\frac{36\\sqrt3}{7}\\Bigr),\\qquad \nE=\\Bigl(\\frac{218}{7},\\frac{88\\sqrt3}{7}\\Bigr).\n\\end{aligned}\n\\]\n\nThe lengths are as given and  \n\\(\\angle B=\\angle E =60^\\circ\\).\n\n--------------------------------------------------------------------\n### 1.  Geometry of the optimal point  \n\nFor the sum  \n\n\\[\nf(X)=AX+BX+CX+DX+EX,\n\\]\n\nthe geometric median \\(X\\) satisfies  \n\n\\[\n\\frac{X-A}{AX}+\\frac{X-B}{BX}+\\frac{X-C}{CX}+\\frac{X-D}{DX}+\\frac{X-E}{EX}=0 .\n\\tag{1}\n\\]\n\nBecause \\(B,E\\) lie on a line, the vectors \\(\\frac{X-B}{BX}\\) and\n\\(\\frac{X-E}{EX}\\) are opposite exactly when \\(X\\) lies on segment \\(BE\\);\nhence in the optimal position \\(X\\) must lie on \\(BE\\) and the first two\nterms in (1) cancel.  Consequently\n\n\\[\n\\frac{X-A}{AX}+\\frac{X-C}{CX}+\\frac{X-D}{DX}=0,\n\\]\n\nso \\(X\\) is the Fermat point of triangle \\(ACD\\).\n\n--------------------------------------------------------------------\n### 2.  Fermat point of \\(\\triangle ACD\\)\n\nThe side lengths of \\(\\triangle ACD\\) are  \n\n\\[\nAC=7\\sqrt3,\\qquad CD=24,\\qquad AD=13\\sqrt3 .\n\\]\n\nAll its angles are \\(<120^\\circ\\); therefore the Fermat point exists.\nFor a triangle with sides \\(a,b,c\\) and area \\(\\Delta\\),\n\n\\[\nS_{\\text{Fermat}}=\n\\sqrt{\\frac{a^{2}+b^{2}+c^{2}+4\\sqrt3\\,\\Delta}{2}} .\n\\]\n\nHere  \n\n\\[\na^{2}+b^{2}+c^{2}=576+507+147=1230,\n\\qquad\\Delta_{ACD}=78\\sqrt3,\n\\]\n\nso  \n\n\\[\nS_{\\text{Fermat}}=\\sqrt{\\frac{1230+4\\sqrt3\\cdot78\\sqrt3}{2}}\n=\\sqrt{\\frac{1230+936}{2}}=\\sqrt{1083}=19\\sqrt3 .\n\\]\n\nThus at the Fermat point  \n\n\\[\nAX+CX+DX=19\\sqrt3 .\n\\tag{2}\n\\]\n\n--------------------------------------------------------------------\n### 3.  The total minimum\n\nSince the optimal point lies on \\(BE\\),\n\n\\[\nBX+EX = BE .\n\\]\n\nFrom the coordinates, \\(BE=38\\).  Combining this with (2),\n\n\\[\nf_{\\min}= (AX+CX+DX)+(BX+EX)=19\\sqrt3+38 .\n\\]\n\nHence the smallest possible value of \\(f(X)\\) is  \n\n\\[\n\\boxed{38+19\\sqrt3}.\n\\]\n\nWriting it as \\(m+n\\sqrt p\\) with \\(m,n\\) integers and \\(p\\) square\u2011free,\nwe have \\(m=38,\\;n=19,\\;p=3\\).  Therefore  \n\n\\[\nm+n+p=38+19+3=60 .\n\\]\n\n\\[\n\\boxed{60}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nThe product $ \\prod_{k=4}^{63} \\frac{\\log_k(5^{k^2-1})}{\\log_{k+1}(5^{k^2-4})} = \\frac{\\log_4(5^{15})}{\\log_5(5^{12})} \\cdot \\frac{\\log_5(5^{24})}{\\log_6(5^{21})} \\cdot \\frac{\\log_6(5^{35})}{\\log_7(5^{32})} \\cdots \\frac{\\log_{63}(5^{3968})}{\\log_{64}(5^{3965})} $ is equal to $ \\frac{m}{n} $, where $ m $ and $ n $ are relatively prime positive integers. Find $ m + n $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "\\[\nP=\\prod_{k=4}^{63}\\frac{\\log_k\\!\\bigl(5^{k^{2}-1}\\bigr)}{\\log_{k+1}\\!\\bigl(5^{k^{2}-4}\\bigr)}\n\\]\n\n---\n\n### 1.  Simplify each factor  \n\n\\[\n\\log_k\\!\\bigl(5^{k^{2}-1}\\bigr)=(k^{2}-1)\\log_k5,\n\\qquad \n\\log_{k+1}\\!\\bigl(5^{k^{2}-4}\\bigr)=(k^{2}-4)\\log_{k+1}5 .\n\\]\n\nHence  \n\n\\[\n\\frac{\\log_k\\!\\bigl(5^{k^{2}-1}\\bigr)}{\\log_{k+1}\\!\\bigl(5^{k^{2}-4}\\bigr)}\n=\\frac{k^{2}-1}{k^{2}-4}\\cdot\\frac{\\log_k5}{\\log_{k+1}5}\n=\\frac{(k-1)(k+1)}{(k-2)(k+2)}\\cdot\\frac{\\log_k5}{\\log_{k+1}5}.\n\\]\n\nTherefore  \n\n\\[\nP=\\underbrace{\\prod_{k=4}^{63}\\frac{(k-1)(k+1)}{(k-2)(k+2)}}_{A}\n   \\times\\underbrace{\\prod_{k=4}^{63}\\frac{\\log_k5}{\\log_{k+1}5}}_{B}.\n\\]\n\n---\n\n### 2.  Evaluate the rational product \\(A\\)\n\n\\[\nA=\\Bigl(\\prod_{k=4}^{63}\\frac{k-1}{k-2}\\Bigr)\n   \\Bigl(\\prod_{k=4}^{63}\\frac{k+1}{k+2}\\Bigr)\n   =\\frac{3\\cdot4\\cdots62}{2\\cdot3\\cdots61}\\;\n     \\frac{5\\cdot6\\cdots64}{6\\cdot7\\cdots65}.\n\\]\n\nBoth products telescope:\n\n\\[\n\\frac{3\\cdot4\\cdots62}{2\\cdot3\\cdots61}= \\frac{62}{2}=31,\n\\qquad \n\\frac{5\\cdot6\\cdots64}{6\\cdot7\\cdots65}= \\frac{5}{65}= \\frac1{13}.\n\\]\n\nThus  \n\n\\[\nA=31\\cdot\\frac1{13}= \\frac{31}{13}.\n\\]\n\n---\n\n### 3.  Evaluate the logarithmic product \\(B\\)\n\n\\[\nB=\\frac{\\log_4 5}{\\log_5 5}\\cdot\\frac{\\log_5 5}{\\log_6 5}\\cdots\n    \\frac{\\log_{63}5}{\\log_{64}5}\n   =\\frac{\\log_4 5}{\\log_{64}5}.\n\\]\n\nUsing change\u2011of\u2011base,\n\\[\n\\frac{\\log_4 5}{\\log_{64} 5}\n   =\\frac{\\frac{\\ln5}{\\ln4}}{\\frac{\\ln5}{\\ln64}}\n   =\\frac{\\ln64}{\\ln4}\n   =\\log_4 64=3,\n\\]\nsince \\(4^3=64\\).\n\nHence \\(B=3\\).\n\n---\n\n### 4.  Combine\n\n\\[\nP=A\\cdot B=\\frac{31}{13}\\times 3=\\frac{93}{13}.\n\\]\n\nThe fraction \\(\\dfrac{93}{13}\\) is already in lowest terms, so  \n\\(m=93,\\; n=13\\).\n\n\\[\nm+n=93+13=106.\n\\]\n\n\\[\n\\boxed{106}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nLet $ A $ be the set of positive integer divisors of 2025. Let $ B $ be a randomly selected subset of $ A $. The probability that $ B $ is a nonempty set with the property that the least common multiple of its elements is 2025 is $ \\frac{m}{n} $, where $ m $ and $ n $ are relatively prime positive integers. Find $ m + n $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "The divisors of  \n\n\\[\n2025=3^{4}\\cdot5^{2}\n\\]\n\nare exactly the numbers  \n\n\\[\n3^{a}5^{b}\\qquad (0\\le a\\le 4,\\;0\\le b\\le 2).\n\\]\n\nHence  \n\n\\[\n|A|=(4+1)(2+1)=15 .\n\\]\n\nFor a subset \\(B\\subseteq A\\) the least common multiple is\n\n\\[\n\\operatorname{lcm}(B)=3^{\\max a}\\,5^{\\max b},\n\\]\n\nwhere the maxima are taken over the exponents \\((a,b)\\) of the elements of \\(B\\).\n\nThus \\(\\operatorname{lcm}(B)=2025=3^4 5^2\\) iff  \n\n* at least one element of \\(B\\) has a \\(3\\)-exponent \\(4\\);\n* at least one element of \\(B\\) has a \\(5\\)-exponent \\(2\\).\n\nDefine  \n\n\\[\nD_3=\\{d\\in A : \\text{the exponent of }3\\text{ in }d\\text{ is }4\\},\n\\qquad \nD_5=\\{d\\in A : \\text{the exponent of }5\\text{ in }d\\text{ is }2\\}.\n\\]\n\nCounting:\n\n* \\(D_3\\): \\(a=4\\) and \\(b=0,1,2\\) \u21d2 \\(|D_3|=3\\) (81,\u202f405,\u202f2025).\n* \\(D_5\\): \\(b=2\\) and \\(a=0,1,2,3,4\\) \u21d2 \\(|D_5|=5\\) (25,\u202f75,\u202f225,\u202f675,\u202f2025).\n* The intersection is \\(\\{2025\\}\\); so \\(|D_3\\cap D_5|=1\\).\n\nWe need subsets that contain at least one element of \\(D_3\\) **and** at least one element of \\(D_5\\).\n\nLet the total number of subsets of \\(A\\) be \\(2^{15}\\).\nLet  \n\n\\[\n\\begin{aligned}\nA_1 &=\\{\\text{subsets that contain no element of } D_3\\},\\\\\nA_2 &=\\{\\text{subsets that contain no element of } D_5\\}.\n\\end{aligned}\n\\]\n\nThen  \n\n\\[\n|A_1|=2^{15-3}=2^{12},\\qquad \n|A_2|=2^{15-5}=2^{10}.\n\\]\n\nSubsets avoiding **both** \\(D_3\\) and \\(D_5\\) avoid the union \\(D_3\\cup D_5\\) which has  \n\n\\[\n|D_3\\cup D_5|=|D_3|+|D_5|-|D_3\\cap D_5|=3+5-1=7\n\\]\n\nelements. Hence  \n\n\\[\n|A_1\\cap A_2|=2^{15-7}=2^{8}.\n\\]\n\nBy inclusion\u2013exclusion, the number of subsets that contain at least one element from each of \\(D_3\\) and \\(D_5\\) is  \n\n\\[\n\\begin{aligned}\nN &= 2^{15}-|A_1|-|A_2|+|A_1\\cap A_2|\\\\\n   &= 2^{15}-2^{12}-2^{10}+2^{8}\\\\\n   &= 32768-4096-1024+256\\\\\n   &= 27904.\n\\end{aligned}\n\\]\n\nAll these subsets are non\u2011empty, so the required probability is  \n\n\\[\n\\frac{N}{2^{15}}=\\frac{27904}{32768}.\n\\]\n\nSimplifying,\n\n\\[\n\\frac{27904}{32768}= \\frac{27904\\div 256}{32768\\div 256}\n                 = \\frac{109}{128}.\n\\]\n\nThus \\(m=109,\\; n=128\\) and  \n\n\\[\nm+n = 109+128 = 237.\n\\]\n\n\\[\n\\boxed{237}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nFour unit squares form a $2 \\times 2$ grid. Each of the 12 unit line segments forming the sides of the squares is colored either red or blue in such a way that each unit square has 2 red sides and 2 blue sides. Find the number of such colorings.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Label the twelve unit segments as in the picture  \n\n\\[\n\\begin{array}{c}\n\\text{external: }a_1,a_2,b_1,b_2,c_1,c_2,d_1,d_2\\\\[2mm]\n\\text{internal: }e_1,e_2,f_1,f_2\n\\end{array}\n\\]\n\nThe four unit squares are  \n\n\\[\n\\begin{aligned}\n\\text{TL}&:\\;a_1,c_1,e_1,f_1,\\\\\n\\text{TR}&:\\;b_1,c_2,e_1,f_2,\\\\\n\\text{BL}&:\\;a_2,d_1,e_2,f_1,\\\\\n\\text{BR}&:\\;b_2,d_2,e_2,f_2 .\n\\end{aligned}\n\\]\n\nEach square must contain exactly two red sides (hence also two blue sides).\n\n--------------------------------------------------------------------\n### 1.  Reduce to the four internal edges\n\nFor a given square the two sides that are **internal** are already\ncolored once we decide the colors of the four internal edges  \n\\(e_1,e_2,f_1,f_2\\).  \n\nLet  \n\n\\[\nr_{\\rm TL}=e_1+f_1,\\qquad\nr_{\\rm TR}=e_1+f_2,\\qquad\nr_{\\rm BL}=e_2+f_1,\\qquad\nr_{\\rm BR}=e_2+f_2 ,\n\\]\n\nwhere a red edge contributes 1 and a blue edge contributes 0.\nIf a square has \\(r\\) red internal sides, then it must have \\(2-r\\)\nred external sides. Thus\n\n* if \\(r=0\\): both external sides are forced red \u2013 1 way;\n* if \\(r=1\\): exactly one of the two external sides must be red \u2013 2 ways;\n* if \\(r=2\\): both external sides are forced blue \u2013 1 way.\n\nHence for a fixed choice of the four internal edges the number of\nadmissible colourings of the eight external edges equals\n\n\\[\n2^{\\,N_1},\n\\]\n\nwhere \\(N_1\\) is the number of squares among TL, TR, BL, BR that have\nexactly one red internal side.\n\n--------------------------------------------------------------------\n### 2.  Express \\(N_1\\) in terms of the internal edges\n\nWrite  \n\n\\[\nX_1=e_1,\\; X_2=e_2,\\qquad Y_1=f_1,\\;Y_2=f_2\\qquad(\\text{red}=1,\\text{blue}=0).\n\\]\n\nFor a square \\((i,j)\\) (\\(i,j\\in\\{1,2\\}\\)) the number of red internal\nsides is \\(X_i+Y_j\\).\nThus a square has exactly one red internal side precisely when\n\\(X_i\\neq Y_j\\).\n\nLet  \n\n\\[\na=X_1+X_2\\;(=0,1,2),\\qquad b=Y_1+Y_2\\;(=0,1,2).\n\\]\n\nThe number of ordered pairs \\((i,j)\\) with \\(X_i\\neq Y_j\\) is  \n\n\\[\nN_1=a(2-b)+(2-a)b\n      =2\\bigl(a+b-ab\\bigr).\n\\]\n\nConsequently the contribution of a configuration with given\n\\(a,b\\) is  \n\n\\[\n2^{N_1}=2^{\\,2(a+b-ab)}=4^{\\,a+b-ab}.\n\\]\n\n--------------------------------------------------------------------\n### 3.  Count all configurations of the internal edges\n\nThere are \\(\\binom{2}{a}\\) ways to choose which vertical internal edges\nare red, and \\(\\binom{2}{b}\\) ways to choose which horizontal internal\nedges are red.  Hence the total number of colourings is\n\n\\[\n\\sum_{a=0}^{2}\\sum_{b=0}^{2}\n\\binom{2}{a}\\binom{2}{b}\\;4^{\\,a+b-ab}.\n\\]\n\nEvaluating the double sum:\n\n\\[\n\\begin{array}{c|ccc}\na\\backslash b &0&1&2\\\\\\hline\n0 &1\\cdot1\\cdot1=1 &1\\cdot2\\cdot4=8 &1\\cdot1\\cdot16=16\\\\\n1 &2\\cdot1\\cdot4=8 &2\\cdot2\\cdot4=16 &2\\cdot1\\cdot4=8\\\\\n2 &1\\cdot1\\cdot16=16 &1\\cdot2\\cdot4=8 &1\\cdot1\\cdot1=1\n\\end{array}\n\\]\n\nAdding all entries:\n\n\\[\n1+8+16+8+16+8+16+8+1=82.\n\\]\n\n--------------------------------------------------------------------\n### 4.  Answer\n\nThus there are  \n\n\\[\n\\boxed{82}\n\\]\n\ndifferent ways to colour the twelve unit segments so that each of the\nfour unit squares has two red sides and two blue sides.",
+        "role": "assistant"
+      }
+    ],
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+        "role": "user",
+        "content": "\nCircle $\\omega_1$ with radius 6 centered at point $A$ is internally tangent at point $B$ to circle $\\omega_2$ with radius 15. Points $C$ and $D$ lie on $\\omega_2$ such that $\\overline{BC}$ is a diameter of $\\omega_2$ and $\\overline{BC} \\perp \\overline{AD}$. The rectangle $EFGH$ is inscribed in $\\omega_1$ such that $\\overline{EF} \\perp \\overline{BC}$, $C$ is closer to $\\overline{GH}$ than to $\\overline{EF}$, and $D$ is closer to $\\overline{FG}$ than to $\\overline{EH}$, as shown. Triangles $\\triangle DGF$ and $\\triangle CHG$ have equal areas. The area of rectangle $EFGH$ is $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m + n$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "The circles are drawn as in the figure.\n\n* Let \\(O\\) be the centre of \\(\\omega _2\\) (radius \\(15\\)).\n* Let \\(A\\) be the centre of \\(\\omega _1\\) (radius \\(6\\)).\n* Since \\(\\omega _1\\) is internally tangent to \\(\\omega _2\\) at \\(B\\), the three points are collinear and  \n\n\\[\nOA=15-6=9 .\n\\]\n\nTake a coordinate system with  \n\n\\[\nO=(0,0),\\qquad A=(9,0),\\qquad B=(15,0).\n\\]\n\n--------------------------------------------------------------------\n### Points \\(C\\) and \\(D\\)\n\n\\(BC\\) is a diameter of \\(\\omega _2\\); hence \\(C\\) is the antipode of \\(B\\):\n\n\\[\nC=(-15,0).\n\\]\n\n\\(BC\\perp AD\\) means \\(AD\\) is the vertical line \\(x=9\\).  \nIntersecting this line with \\(\\omega _2\\) gives  \n\n\\[\n9^2+y^2=15^2 \\Longrightarrow y=\\pm 12 .\n\\]\n\nBecause the later condition \u201c\\(D\\) is nearer to \\(FG\\) than to \\(EH\\)\u201d forces \\(D\\) to lie **below** the centre, we take  \n\n\\[\nD=(9,-12).\n\\]\n\n--------------------------------------------------------------------\n### The rectangle \\(EFGH\\)\n\nThe rectangle is inscribed in \\(\\omega _1\\) and \\(\\overline{EF}\\perp BC\\); hence \\(\\overline{EF}\\) is vertical.\nLet\n\n\\[\n\\begin{aligned}\nE&=(9+w,\\;h),\\\\[2pt]\nF&=(9+w,\\;-h),\\\\[2pt]\nG&=(9-w,\\;-h),\\\\[2pt]\nH&=(9-w,\\;h),\n\\end{aligned}\n\\]\n\nso that the centre of the rectangle is \\(A\\) (the intersection of the diagonals of an\ninscribed rectangle is the centre of the circumcircle).\n\nBecause the four vertices lie on \\(\\omega _1\\),\n\n\\[\n(9\\pm w-9)^2+h^2=w^{2}+h^{2}=6^{2}=36\\qquad\\Longrightarrow\\qquad w^{2}+h^{2}=36. \\tag{1}\n\\]\n\nThe side \\(\\overline{EF}\\) is the right vertical side, thus\n\\(C\\) (which is far left) is nearer to \\(\\overline{GH}\\) (the left side) than to \\(\\overline{EF}\\);\nand \\(D\\) (which is below the centre) is nearer to \\(\\overline{FG}\\) (the bottom side) than to \\(\\overline{EH}\\) (the top side).  \nThese statements only fix the labeling of the rectangle.\n\n--------------------------------------------------------------------\n### Equality of the two triangular areas\n\n\\[\n\\begin{aligned}\n\\text{Area}\\,\\triangle DGF\n&=\\frac12\\bigl(\\underbrace{2w}_{\\text{base }GF}\\bigr)\n     \\bigl(\\underbrace{12-h}_{\\text{vertical height}}\\bigr)\n = w(12-h),\\\\[4pt]\n\\text{Area}\\,\\triangle CHG\n&=\\frac12\\bigl(\\underbrace{2h}_{\\text{base }HG}\\bigr)\n     \\bigl(\\underbrace{24-w}_{\\text{horizontal distance}}\\bigr)\n = h(24-w).\n\\end{aligned}\n\\]\n\nGiven that the two areas are equal,\n\n\\[\nw(12-h)=h(24-w)\\; \\Longrightarrow\\; 12w=24h\\; \\Longrightarrow\\; w=2h. \\tag{2}\n\\]\n\n--------------------------------------------------------------------\n### Solving for \\(w\\) and \\(h\\)\n\nSubstituting \\(w=2h\\) into (1):\n\n\\[\n(2h)^2+h^{2}=36\\;\\Longrightarrow\\;5h^{2}=36\\;\\Longrightarrow\\;h^{2}= \\frac{36}{5}.\n\\]\n\nHence  \n\n\\[\nh=\\frac{6}{\\sqrt5},\\qquad w=2h=\\frac{12}{\\sqrt5}.\n\\]\n\n--------------------------------------------------------------------\n### Area of the rectangle\n\nThe rectangle\u2019s side lengths are \\(2w\\) and \\(2h\\), so\n\n\\[\n\\text{Area}= (2w)(2h)=4wh\n          =4\\left(\\frac{12}{\\sqrt5}\\right)\\left(\\frac{6}{\\sqrt5}\\right)\n          =4\\cdot\\frac{72}{5}\n          =\\frac{288}{5}.\n\\]\n\nThus the area is \\(\\displaystyle\\frac{m}{n}=\\frac{288}{5}\\) with relatively prime\n\\(m=288,\\;n=5\\).\n\n\\[\nm+n=288+5=293.\n\\]\n\n\\[\n\\boxed{293}\n\\]",
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+      }
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+        "role": "user",
+        "content": "\nFrom an unlimited supply of 1-cent coins, 10-cent coins, and 25-cent coins, Silas wants to find a collection of coins that has a total value of $ N $ cents, where $ N $ is a positive integer. He uses the so-called **greedy algorithm**, successively choosing the coin of greatest value that does not cause the value of his collection to exceed $ N $. For example, to get 42 cents, Silas will choose a 25-cent coin, then a 10-cent coin, then 7 1-cent coins. However, this collection of 9 coins uses more coins than necessary to get a total of 42 cents; indeed, choosing 4 10-cent coins and 2 1-cent coins achieves the same total value with only 6 coins.\n\nIn general, the greedy algorithm succeeds for a given $ N $ if no other collection of 1-cent, 10-cent, and 25-cent coins gives a total value of $ N $ cents using strictly fewer coins than the collection given by the greedy algorithm. Find the number of values of $ N $ between 1 and 1000 inclusive for which the greedy algorithm succeeds.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n\\[\nN=25q+r ,\\qquad 0\\le r\\le 24 .\n\\]\n\nThe greedy algorithm takes  \n\n* \\(q\\) quarters,  \n* \\(\\displaystyle d_0=\\Big\\lfloor\\frac r{10}\\Big\\rfloor\\) dimes,  \n* \\(s_0=r\\bmod 10\\) pennies.  \n\nHence  \n\n\\[\nC_{\\text{greedy}}=q+d_0+s_0 .\\tag{1}\n\\]\n\n--------------------------------------------------------------------\n### 1.  When can a better solution use fewer quarters?\n\nSuppose we use only \\(q-k\\) quarters, \\(k\\ge1\\).  \nThe remaining amount is  \n\n\\[\nR=r+25k .\n\\]\n\nWith only dimes and pennies the optimal way to make \\(R\\) is  \n\n\\[\n\\Big\\lfloor\\frac{R}{10}\\Big\\rfloor\\text{ dimes }+ (R\\bmod10)\\text{ pennies}.\n\\]\n\nThus the total number of coins for this choice is  \n\n\\[\nC(q-k)=(q-k)+\\Big\\lfloor\\frac{r+25k}{10}\\Big\\rfloor+(r+25k\\bmod10).\\tag{2}\n\\]\n\nLet  \n\n\\[\n\\Delta(k)=C(q-k)-C_{\\text{greedy}} .\n\\]\n\nUsing \\(r=10t+a\\;(0\\le a\\le9,\\;t\\in\\{0,1,2\\})\\) we obtain after a short calculation  \n\n\\[\n\\Delta(k)=6k-9\\Big\\lfloor\\frac{a+5k}{10}\\Big\\rfloor .\\tag{3}\n\\]\n\n(Only the last digit \\(a=r\\bmod 10\\) matters.)\n\n--------------------------------------------------------------------\n### 2.  Sign of \\(\\Delta(k)\\)\n\n*If \\(a\\ge5\\):*  \nTake \\(k=1\\).  Then \\(\\lfloor\\frac{a+5}{10}\\rfloor=1\\) and  \n\n\\[\n\\Delta(1)=6-9=-3<0 .\n\\]\n\nHence a better solution exists (remove one quarter).\n\n*If \\(a\\le4\\):*  \nFor any \\(k\\ge1\\),\n\n\\[\n\\Delta(k)=6k-9\\Big\\lfloor\\frac{a+5k}{10}\\Big\\rfloor\n\\ge 6k-9\\frac{a+5k}{10}=1.5k-0.9a .\n\\]\n\nSince \\(a\\le4\\) this is positive for \\(k=1,2\\) (indeed \\(\\Delta(1)=6,\\,\\Delta(2)=3\\)) and for larger \\(k\\) the term \\(1.5k\\) dominates, so \\(\\Delta(k)\\ge0\\) for all \\(k\\).\n\nTherefore **greedy fails iff**  \n\n\\[\na=r\\bmod10\\ge5\\quad\\text{and}\\quad q\\ge1 .\n\\]\n\nEquivalently, for \\(N\\ge25\\),\n\n\\[\nN\\bmod25\\in\\{5,6,7,8,9,15,16,17,18,19\\}.\n\\]\n\n--------------------------------------------------------------------\n### 3.  Counting the failures\n\nThe residues above are ten out of the twenty\u2011five possible residues modulo \\(25\\).  \n\nIn the interval \\(1\\le N\\le1000\\) we have \\(1000/25=40\\) full periods, so each residue occurs \\(40\\) times.  \n\nThus the total number of integers with those residues is  \n\n\\[\n10\\times40=400.\n\\]\n\nBut the ten numbers \\(5,6,7,8,9,15,16,17,18,19\\) are \\<\u202f25, and for them greedy cannot remove a quarter (there are no quarters in any representation).  Those ten are **not** failures.  \n\nHence the genuine failures are  \n\n\\[\n400-10=390.\n\\]\n\n--------------------------------------------------------------------\n### 4.  Successes\n\nThere are \\(1000\\) integers from \\(1\\) to \\(1000\\).  Therefore the number of values for which the greedy algorithm *succeeds* is\n\n\\[\n1000-390=610.\n\\]\n\n--------------------------------------------------------------------\n\\[\n\\boxed{610}\n\\]",
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+        "role": "user",
+        "content": "\nThere are $ n $ values of $ x $ in the interval $ 0 < x < 2\\pi $ where $ f(x) = \\sin(7\\pi \\cdot \\sin(5x)) = 0 $. For $ t $ of these $ n $ values of $ x $, the graph of $ y = f(x) $ is tangent to the $ x $-axis. Find $ n + t $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "\\[\nf(x)=\\sin\\bigl(7\\pi\\sin(5x)\\bigr)\n\\]\n\n---\n\n### 1.  Zeros of \\(f\\)\n\n\\(f(x)=0\\iff 7\\pi\\sin(5x)=k\\pi\\) for an integer \\(k\\).\n\n\\[\n\\sin(5x)=\\frac{k}{7},\\qquad |k|\\le 7 .\n\\]\n\nLet  \n\n\\[\ny=5x\\;(0<y<10\\pi).\n\\]\n\nFor each integer \\(k\\) with \\(|k|\\le7\\) we count the solutions of \\(\\sin y=\\dfrac{k}{7}\\) in \\((0,10\\pi)\\).\n\n* \\(k=7\\)  : \\(\\sin y=1\\).  Solutions \\(y=\\frac{\\pi}{2}+2\\pi n\\) \\((n=0,1,2,3,4)\\) \u2192 **5** solutions.  \n* \\(k=-7\\) : \\(\\sin y=-1\\).  Solutions \\(y=\\frac{3\\pi}{2}+2\\pi n\\) \\((n=0,1,2,3,4)\\) \u2192 **5** solutions.  \n* \\(k=0\\)  : \\(\\sin y=0\\).  Solutions \\(y=m\\pi\\;(m=1,2,\\dots ,9)\\) \u2192 **9** solutions.  \n* For each \\(k=\\pm1,\\pm2,\\pm3,\\pm4,\\pm5,\\pm6\\) we have \\(\\sin y=c\\) with \\(-1<c<1,\\;c\\neq0\\).  \n  In each of the 5 full periods of \\(\\sin y\\) there are exactly two such points, so **\\(5\\cdot2=10\\)** solutions per \\(k\\).\n\nThere are 12 values of \\(k\\) with \\(|k|\\in\\{1,\\dots ,6\\}\\), giving  \n\n\\[\n12\\times10=120\\text{ solutions}.\n\\]\n\nAdding all contributions,\n\n\\[\nn=5+5+9+120=139 .\n\\]\n\n---\n\n### 2.  Tangent zeros\n\nThe graph is tangent to the \\(x\\)-axis at a zero where the derivative also vanishes.\n\n\\[\nf'(x)=\\cos\\bigl(7\\pi\\sin(5x)\\bigr)\\cdot 35\\pi\\cos(5x).\n\\]\n\nAt a zero, \\(\\sin\\bigl(7\\pi\\sin(5x)\\bigr)=0\\) gives \\(\\sin(5x)=\\dfrac{k}{7}\\).  \nBecause \\(\\cos\\bigl(7\\pi\\sin(5x)\\bigr)=\\pm1\\neq0\\), we must have \\(\\cos(5x)=0\\).\n\n\\[\n\\cos(5x)=0\\Longrightarrow \\sin(5x)=\\pm1 .\n\\]\n\nThus tangential zeros occur exactly when \\(\\sin(5x)=\\pm1\\), i.e. for \\(k=\\pm7\\).\n\nWe already counted those solutions:  \n\n* \\(\\sin(5x)=1\\) \u2192 5 points,  \n* \\(\\sin(5x)=-1\\) \u2192 5 points.\n\nHence  \n\n\\[\nt=5+5=10 .\n\\]\n\n---\n\n### 3.  Required sum\n\n\\[\nn+t=139+10=149.\n\\]\n\n\\[\n\\boxed{149}\n\\]",
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+        "role": "user",
+        "content": "\nLet $ S $ be the set of vertices of a regular 24-gon. Find the number of ways to draw 12 segments of equal lengths so that each vertex in $ S $ is an endpoint of exactly one of the 12 segments.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let the vertices of the regular \\(24\\)-gon be numbered \\(0,1,\\dots ,23\\) (mod \\(24\\)).\nIf a segment joins vertex \\(i\\) to vertex \\(j\\) we call its **step**\n\\[\nk\\equiv j-i\\pmod{24},\\qquad 1\\le k\\le 12 .\n\\]\n\nThe length of a chord depends only on this step:\nthe chord of step \\(k\\) has length  \n\n\\[\n\\ell(k)=2R\\sin\\frac{\\pi k}{24},\\qquad 1\\le k\\le 12 .\n\\]\n\nSince \\(\\sin(\\theta )\\) is strictly increasing on \\([0,\\frac{\\pi}{2}]\\),\nthe lengths \\(\\ell(1),\\ell(2),\\dots ,\\ell(12)\\) are all distinct.\nThus a drawing in which all 12 segments have the same length must use\nedges whose step is a fixed \\(k\\) (the same chord length).\n\n--------------------------------------------------------------------\n\n### 1.  The graph of step \\(k\\)\n\nConsider the undirected graph \\(G_k\\) whose vertices are the 24 polygon vertices\nand whose edges are all chords of step \\(k\\) (i.e. the pairs \\(\\{i,i+k\\}\\)).\nEach vertex of \\(G_k\\) is incident to two such chords\n(\\(i\\) connects to \\(i+k\\) and to \\(i-k\\)), so \\(G_k\\) is a disjoint union of\ncycles.\n\nLet  \n\n\\[\nd=\\gcd(24,k).\n\\]\n\nThen the vertices split into \\(d\\) cycles, each of length  \n\n\\[\n\\frac{24}{d}.\n\\]\n\n--------------------------------------------------------------------\n\n### 2.  When can a perfect matching be formed?\n\nA perfect matching can be taken inside one cycle only when the cycle has even\nlength.  Hence we need \\(\\frac{24}{d}\\) even, i.e. \\(d\\neq 8\\).  \n\n* If \\(d=8\\) (the case \\(k=8\\)) each component is a triangle; a triangle has\nno perfect matching, so **no drawing** is possible.\n\n* If the cycle length is \\(2\\) (the case \\(d=12,\\;k=12\\)), each component is a\nsingle edge; there is exactly **one** perfect matching \u2013 the 12 diameters.\n\n* For any other admissible \\(k\\) the cycles have even length \\(\\ge4\\).\nInside each such cycle there are exactly two ways to choose a perfect matching\n(alternate edges).  Since the cycles are independent, the number of perfect\nmatchings for the given \\(k\\) is  \n\n\\[\n2^{\\,d}\\qquad (d=\\gcd(24,k),\\;d\\neq 8,\\;k\\neq 12).\n\\]\n\n--------------------------------------------------------------------\n\n### 3.  Counting for each step\n\n\\[\n\\begin{array}{c|c|c|c}\nk & d=\\gcd(24,k) & \\text{cycle length }24/d & \\#\\text{ matchings}\\\\ \\hline\n1 & 1 & 24 & 2\\\\\n2 & 2 & 12 & 2^{2}=4\\\\\n3 & 3 & 8 & 2^{3}=8\\\\\n4 & 4 & 6 & 2^{4}=16\\\\\n5 & 1 & 24 & 2\\\\\n6 & 6 & 4 & 2^{6}=64\\\\\n7 & 1 & 24 & 2\\\\\n8 & 8 & 3 & 0\\\\\n9 & 3 & 8 & 2^{3}=8\\\\\n10& 2 & 12& 2^{2}=4\\\\\n11& 1 & 24& 2\\\\\n12&12 & 2 & 1\\ (\\text{forced diameters})\n\\end{array}\n\\]\n\n--------------------------------------------------------------------\n\n### 4.  Total number of drawings\n\nAdd the numbers of matchings over all admissible steps:\n\n\\[\n\\begin{aligned}\nN&=2+4+8+16+2+64+2+8+4+2+1\\\\\n&=113 .\n\\end{aligned}\n\\]\n\n--------------------------------------------------------------------\n\n\\[\n\\boxed{113}\n\\]",
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+      }
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+    [
+      {
+        "role": "user",
+        "content": "\nSixteen chairs are arranged in a row. Eight people each select a chair in which to sit so that no person sits next to two other people. Let $ N $ be the number of subsets of 16 chairs that could be selected. Find the remainder when $ N $ is divided by 1000.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "The 8 occupied chairs must avoid a configuration where a person has two neighbours.  \nHence no three occupied chairs may be consecutive.\n\nLet a be the number of blocks of two consecutive occupied chairs.  \nEach block of two contributes an extra occupied chair, so the total number of blocks is  \n\n\\[\nb = 8-a\\qquad (0\\le a\\le 4).\n\\]\n\n*Choosing which blocks are of size\u202f2*: \\(\\displaystyle \\binom{b}{a}\\).\n\nThere are \\(16-8=8\\) empty chairs. Between the \\(b\\) blocks there must be at least one empty chair, using \\(b-1\\) empties.  \nThe remaining \\(8-(b-1)=9-b\\) empty chairs can be placed in the \\(b+1\\) gaps (before the first block, after the last, and the \\(b-1\\) internal gaps) without restriction.  \n\nNumber of ways to distribute them:  \n\n\\[\n\\binom{(9-b)+(b+1)-1}{(b+1)-1}= \\binom{9}{b}.\n\\]\n\nThus for a given \\(a\\),\n\n\\[\n\\text{ways}= \\binom{b}{a}\\binom{9}{b}\n          =\\binom{8-a}{a}\\binom{9}{8-a}.\n\\]\n\nSumming over \\(a=0,1,2,3,4\\),\n\n\\[\n\\begin{aligned}\nN &=\\binom{8}{0}\\binom{9}{8} \n   +\\binom{7}{1}\\binom{9}{7}\n   +\\binom{6}{2}\\binom{9}{6}\n   +\\binom{5}{3}\\binom{9}{5}\n   +\\binom{4}{4}\\binom{9}{4} \\\\[2mm]\n  &= 1\\cdot 9 + 7\\cdot 36 + 15\\cdot 84 + 10\\cdot 126 + 1\\cdot126\\\\\n  &= 9+252+1260+1260+126 = 2907.\n\\end{aligned}\n\\]\n\nTherefore  \n\n\\[\nN \\equiv 2907 \\pmod{1000}=907.\n\\]\n\n\\[\n\\boxed{907}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nLet $ A_1A_2 \\ldots A_{11} $ be an 11-sided non-convex simple polygon with the following properties:\n* The area of $ A_iA_1A_{i+1} $ is 1 for each $ 2 \\leq i \\leq 10 $,\n* $ \\cos(\\angle A_iA_1A_{i+1}) = \\frac{12}{13} $ for each $ 2 \\leq i \\leq 10 $,\n* The perimeter of $ A_1A_2 \\ldots A_{11} $ is 20.\nIf $ A_1A_2 + A_1A_{11} $ can be expressed as $ \\frac{m\\sqrt{n} - p}{q} $ for positive integers $ m, n, p, q $ with $ n $ squarefree and no prime divides all of $ m, p, q$, find $ m + n + p + q $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n\\[\nr_i=|A_1A_i| \\qquad (i=2,\\dots ,11)\n\\]\n\nand denote  \n\n\\[\n\\theta=\\angle A_iA_1A_{i+1}\\qquad (2\\le i\\le 10).\n\\]\n\nBecause  \n\n\\[\n\\cos\\theta=\\frac{12}{13}\\;\\Longrightarrow\\;\\sin\\theta=\\frac{5}{13},\n\\]\n\nthe area of \\(\\triangle A_iA_1A_{i+1}\\) is  \n\n\\[\n\\frac12 r_i r_{i+1}\\sin\\theta\n   =\\frac12 r_i r_{i+1}\\frac{5}{13}=1 .\n\\]\n\nHence  \n\n\\[\nr_i r_{i+1}= \\frac{26}{5}=K\\qquad (2\\le i\\le 10). \\tag{1}\n\\]\n\nFrom (1),\n\n\\[\nr_{i+2}= \\frac{K}{r_{i+1}}=r_i ,\n\\]\n\nso the distances from \\(A_1\\) alternate:\n\n\\[\nr_2=r_4=r_6=r_8=r_{10}=a,\\qquad\nr_3=r_5=r_7=r_9=r_{11}=b,\n\\]\n\nwith  \n\n\\[\nab=K=\\frac{26}{5}. \\tag{2}\n\\]\n\n--------------------------------------------------------------------\n### Lengths of the other sides\n\nFor any \\(i=2,\\dots ,10\\) the side \\(A_iA_{i+1}\\) (call it \\(L\\)) satisfies the law of cosines:\n\n\\[\nL^2=a^{2}+b^{2}-2ab\\cos\\theta\n      =a^{2}+b^{2}-2ab\\frac{12}{13}.\n\\]\n\nUsing (2),\n\n\\[\nL^2=a^{2}+b^{2}-\\frac{24}{13}\\cdot\\frac{26}{5}\n    =a^{2}+b^{2}-\\frac{48}{5}.\n\\]\n\nSince \\(a^{2}+b^{2}=(a+b)^{2}-2ab\\),\n\n\\[\nL^2=(a+b)^{2}-2\\frac{26}{5}-\\frac{48}{5}\n     =(a+b)^{2}-20.\n\\]\n\nLet  \n\n\\[\ns=a+b.\n\\]\n\nThen  \n\n\\[\nL=\\sqrt{s^{2}-20}. \\tag{3}\n\\]\n\n--------------------------------------------------------------------\n### Using the perimeter\n\nThe perimeter of the 11\u2011gon is\n\n\\[\n|A_1A_2|+|A_1A_{11}|+\\sum_{i=2}^{10}|A_iA_{i+1}|\n= a+b+9L = s+9\\sqrt{s^{2}-20}=20.\n\\]\n\nSet \\(t=\\sqrt{s^{2}-20}>0\\). Then \\(s=20-9t\\) and\n\n\\[\nt^{2}=s^{2}-20=(20-9t)^{2}-20.\n\\]\n\nSolving,\n\n\\[\nt^{2}=380-360t+81t^{2}\n\\Longrightarrow 80t^{2}-360t+380=0\n\\Longrightarrow 4t^{2}-18t+19=0.\n\\]\n\nHence  \n\n\\[\nt=\\frac{18\\pm\\sqrt{324-304}}{8}\n   =\\frac{18\\pm2\\sqrt5}{8}\n   =\\frac{9\\pm\\sqrt5}{4}.\n\\]\n\nIf the plus sign is taken, \\(t>\\frac{20}{9}\\) and \\(s=20-9t<0\\), impossible.\nThus  \n\n\\[\nt=\\frac{9-\\sqrt5}{4},\n\\qquad\ns=20-9t=\\frac{9\\sqrt5-1}{4}.\n\\]\n\nConsequently  \n\n\\[\nA_1A_2+A_1A_{11}=s=\\frac{9\\sqrt5-1}{4}.\n\\]\n\nWritten as \\(\\dfrac{m\\sqrt n-p}{q}\\) we have  \n\n\\[\nm=9,\\;n=5,\\;p=1,\\;q=4,\n\\]\n\nso  \n\n\\[\nm+n+p+q=9+5+1+4=19.\n\\]\n\n\\[\n\\boxed{19}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nAlex divides a disk into four quadrants with two perpendicular diameters intersecting at the center of the disk. He draws 25 more line segments through the disk, drawing each segment by selecting two points at random on the perimeter of the disk in different quadrants and connecting those two points. Find the expected number of regions into which these 27 line segments divide the disk.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "**Step 1.  Regions created by chords**\n\nIf a circle already has \\(k\\) chords drawn in its interior, then a new chord\nadds one region for itself plus one extra region for every interior\nintersection it creates.  \nThus for a set of \\(n\\) chords\n\n\\[\n\\text{# regions}=n+1+\\text{# interior intersection points.}\n\\]\n\nIn our problem we have  \n\n* 2 fixed diameters (the two perpendicular ones),  \n* 25 random chords.\n\nHence \\(n=27\\).  \nWe only have to find the expected number \\(I\\) of interior intersection\npoints.\n\n\\[\nE[\\text{regions}]=27+1+E[I]=28+E[I].\n\\]\n\n--------------------------------------------------------------------\n\n**Step 2.  Intersections involving the two diameters**\n\nLet the horizontal diameter be the line that separates the *upper* quadrants\n\\(Q_{1},Q_{2}\\) from the *lower* quadrants \\(Q_{3},Q_{4}\\).\n\nA random chord has its two endpoints in different quadrants.\nThe chord meets the horizontal diameter exactly when the endpoints lie in\ndifferent half\u2011planes, i.e. one endpoint is in \\(\\{Q_{1},Q_{2}\\}\\) and the\nother in \\(\\{Q_{3},Q_{4}\\}\\).\n\nFor the ordered pair of quadrants of a random chord there are  \n\\(12\\) equally likely possibilities (the \\(4\\cdot 3\\) ordered pairs with\ndifferent quadrants).  \nExactly \\(8\\) of them have the endpoints in opposite half\u2011planes, hence\n\n\\[\np_d=\\Pr(\\text{a random chord meets a given diameter})=\\frac{8}{12}=\n\\frac{2}{3}.\n\\]\n\nTherefore\n\n\\[\n\\boxed{\\text{Expected intersections of the 25 chords with one diameter}=25\\cdot\\frac23}\n\\]\n\nand with the two diameters together\n\n\\[\nE[I_{\\text{diameters}}]=2\\cdot25\\cdot\\frac23=\\frac{100}{3}.\n\\]\n\nThe two diameters intersect each other once, so add \\(1\\) more interior\nintersection.\n\n--------------------------------------------------------------------\n\n**Step 3.  Intersections of two random chords**\n\nDenote the four endpoints by  \n\\(\\alpha_1,\\alpha_2\\) (chord 1) and \\(\\beta_1,\\beta_2\\) (chord 2).  \nAll four points are independent uniform on the circle.\n\nLet  \n\n\\[\nA=\\{\\text{endpoints of chord 1 lie in different quadrants}\\},\\qquad \nB=\\{\\text{endpoints of chord 2 lie in different quadrants}\\}.\n\\]\n\n\\[\nP(A)=P(B)=\\frac34 .\n\\]\n\nTwo chords intersect iff the endpoints are interleaved on the circle,\ni.e. exactly one of \\(\\beta_1,\\beta_2\\) lies on the clockwise arc from\n\\(\\alpha_1\\) to \\(\\alpha_2\\).\n\nFix \\(\\alpha_1=x\\) and \\(\\alpha_2=y\\) (with \\(x\\neq y\\)).\nLet \\(I=(x,y)\\) be the clockwise arc from \\(x\\) to \\(y\\) and let\n\\(d=|I|\\) be its length.  \nFor independent uniform \\(\\beta_1,\\beta_2\\),\n\n* the probability that exactly one lies in \\(I\\) is \\(2d(1-d)\\);\n* the probability that the two \\(\\beta\\)\u2019s are in *different* quadrants\n  is \\(\\frac34\\).\n\nConditioning on the actual placement of the interval \\(I\\) with respect\nto the four quarter\u2011arcs yields (after a short computation)\n\n\\[\n\\Pr(\\beta_1,\\beta_2\\text{ satisfy both conditions}\\mid x,y)=\n2\\Bigl[d\\Bigl(\\tfrac34-d\\Bigr)+\\sum_{q=0}^{3}a_q^{\\,2}\\Bigr],\n\\tag{1}\n\\]\n\nwhere \\(a_q\\) is the length of the part of \\(I\\) that lies in quadrant\n\\(q\\).\n\nNow average (1) over all ordered pairs \\((x,y)\\) that are in different\nquadrants.  By symmetry it suffices to place \\(x\\) in the first quadrant\n\\([0,\\tfrac14)\\) and let \\(y\\) run in the three other quadrants.\nCarrying out the integration (splitting the three possible clockwise\ndistances) gives\n\n\\[\n\\int\\!\\!\\int_{x\\in Q_0,\\;y\\in Q_m}\n2\\Bigl[d\\Bigl(\\tfrac34-d\\Bigr)+\\sum a_q^{\\,2}\\Bigr]\\,dy\\,dx\n   =\\frac{17}{64}\\qquad(m=1,2,3\\text{ summed}).\n\\]\n\nThus\n\n\\[\nP(A\\cap B\\cap\\{\\text{the chords intersect}\\})=\\frac{17}{64}.\n\\]\n\nFinally\n\n\\[\np_r=\n\\Pr(\\text{intersection}\\mid A\\cap B)=\n\\frac{P(A\\cap B\\cap\\text{intersect})}{P(A)P(B)}\n=\\frac{17/64}{(3/4)^2}\n=\\frac{16}{9}\\cdot\\frac{17}{64}\n=\\frac{17}{36}.\n\\]\n\n--------------------------------------------------------------------\n\n**Step 4.  Expected interior intersections**\n\n* Intersections of the two diameters: \\(1\\).\n* Intersections of the 25 random chords with the two diameters:\n  \\(\\displaystyle \\frac{100}{3}\\).\n* Intersections among the 25 random chords:\n  \\(\\displaystyle \\binom{25}{2}\\,p_r\n   =300\\cdot\\frac{17}{36}= \\frac{425}{3}\\).\n\nHence\n\n\\[\nE[I]=1+\\frac{100}{3}+\\frac{425}{3}\n     =1+\\frac{525}{3}=1+175=176.\n\\]\n\n--------------------------------------------------------------------\n\n**Step 5.  Expected number of regions**\n\n\\[\nE[\\text{regions}]=27+1+E[I]=28+176=204.\n\\]\n\n--------------------------------------------------------------------\n\n\\[\n\\boxed{204}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nSuppose $ \\triangle ABC $ has angles $ \\angle BAC = 84^\\circ $, $ \\angle ABC = 60^\\circ $, and $ \\angle ACB = 36^\\circ $. Let $ D, E, $ and $ F $ be the midpoints of sides $ \\overline{BC} $, $ \\overline{AC} $, and $ \\overline{AB} $, respectively. The circumcircle of $ \\triangle DEF $ intersects $ \\overline{BD} $, $ \\overline{AE} $, and $ \\overline{AF} $ at points $ G, H, $ and $ J $, respectively. The points $ G, D, E, H, J, $ and $ F $ divide the circumcircle of $ \\triangle DEF $ into six minor arcs, as shown. Find $ \\widehat{DE} + 2 \\cdot \\widehat{HJ} + 3 \\cdot \\widehat{FG} $, where the arcs are measured in degrees.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n\\[\n\\triangle ABC\\qquad \n\\angle A=84^{\\circ},\\; \\angle B=60^{\\circ},\\; \\angle C=36^{\\circ}.\n\\]\n\nDenote  \n\n\\[\nD,E,F \\text{ \u2013 the midpoints of }BC,CA,AB,\n\\]\n\\[\nG,H,J \\text{ \u2013 the second intersections of }BD,AE,AF\\text{ with the circumcircle of } \\triangle DEF .\n\\]\n\n--------------------------------------------------------------------\n### 1.  The points \\(G,H,J\\) are the feet of the altitudes  \n\nThe nine\u2011point circle of \\(\\triangle ABC\\) passes through the three midpoints \\(D,E,F\\) **and** through the three feet of the altitudes.  \nBecause  \n\n* \\(BD\\) lies on the side \\(BC\\),  \n* \\(AE\\) lies on the side \\(CA\\),  \n* \\(AF\\) lies on the side \\(AB\\),\n\nthe second intersection of each of these sides with the nine\u2011point circle must be the corresponding foot of an altitude:\n\n\\[\n\\begin{aligned}\nG&= \\text{foot from }A\\text{ onto }BC,\\\\[2mm]\nH&= \\text{foot from }B\\text{ onto }CA,\\\\[2mm]\nJ&= \\text{foot from }C\\text{ onto }AB .\n\\end{aligned}\n\\]\n\nThus \\(G,H,J\\) are the vertices of the orthic triangle.\n\n--------------------------------------------------------------------\n### 2.  Arc \\(\\widehat{DE}\\)\n\nThe medial triangle \\(\\triangle DEF\\) is similar to \\(\\triangle ABC\\) (ratio \\(1\\!:\\!2\\)).  \nConsequently  \n\n\\[\n\\angle DFE = \\angle C = 36^{\\circ}.\n\\]\n\nFor any inscribed angle, the intercepted minor arc is twice the angle; hence  \n\n\\[\n\\widehat{DE}=2\\angle DFE = 2\\cdot 36^{\\circ}=72^{\\circ}.\n\\]\n\n--------------------------------------------------------------------\n### 3.  Arc \\(\\widehat{FG}\\)\n\nSince \\(D\\) and \\(G\\) both lie on side \\(BC\\), the chord \\(DG\\) is a part of \\(BC\\).  \nThe chord \\(DF\\) joins the midpoints of \\(AB\\) and \\(BC\\); by the Midpoint Theorem  \n\n\\[\nDF \\parallel AC .\n\\]\n\nTherefore  \n\n\\[\n\\angle FDG =\\angle (\\text{line }DF,\\text{ line }DG)\n        =\\angle (AC,BC)=\\angle C=36^{\\circ}.\n\\]\n\nThus  \n\n\\[\n\\widehat{FG}=2\\angle FDG = 2\\cdot 36^{\\circ}=72^{\\circ}.\n\\]\n\n--------------------------------------------------------------------\n### 4.  Arc \\(\\widehat{HJ}\\)\n\n\\(H,J,G\\) are the vertices of the orthic triangle.  \nA standard fact about the orthic triangle is that its angles are  \n\n\\[\n\\angle HGJ = 180^{\\circ}-2\\angle A,\\qquad\n\\angle GJH = 180^{\\circ}-2\\angle B,\\qquad\n\\angle JHG = 180^{\\circ}-2\\angle C .\n\\]\n\n(The fact follows from simple angle\u2011chasing with the right\u2011angles at the feet of the altitudes.)\n\nHence the minor arc opposite \\(G\\) \u2013 that is, \\(\\widehat{HJ}\\) \u2013 satisfies  \n\n\\[\n\\widehat{HJ}=2\\angle HGJ =2\\bigl(180^{\\circ}-2A\\bigr)\n               =360^{\\circ}-4A.\n\\]\n\nWith \\(\\angle A =84^{\\circ}\\),\n\n\\[\n\\widehat{HJ}=360^{\\circ}-4\\cdot84^{\\circ}=24^{\\circ}.\n\\]\n\n--------------------------------------------------------------------\n### 5.  Required sum\n\n\\[\n\\begin{aligned}\n\\widehat{DE}+2\\widehat{HJ}+3\\widehat{FG}\n&= 72^{\\circ}+2\\cdot24^{\\circ}+3\\cdot72^{\\circ}\\\\\n&= 72^{\\circ}+48^{\\circ}+216^{\\circ}\\\\[2mm]\n&= 336^{\\circ}.\n\\end{aligned}\n\\]\n\n--------------------------------------------------------------------\n\\[\n\\boxed{336}\n\\]",
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+      }
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+      {
+        "role": "user",
+        "content": "\nLet $ \\triangle ABC $ be a right triangle with $ \\angle A = 90^\\circ $ and $ BC = 38 $. There exist points $ K $ and $ L $ inside the triangle such that $ AK = AL = BK = CL = KL = 14. $ The area of the quadrilateral $ BKLC $ can be expressed as $ n \\sqrt{3} $ for some positive integer $ n $. Find $ n $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n\\[\n\\angle A =90^\\circ ,\\qquad BC =38 .\n\\]\n\nPlace  \n\n\\[\nA=(0,0),\\qquad B=(b,0),\\qquad C=(0,c)\n\\]\n\nso that the legs are  \n\n\\[\nAB=b,\\qquad AC=c,\\qquad b^{2}+c^{2}=38^{2}=1444 .\n\\tag{1}\n\\]\n\n--------------------------------------------------------------------\n### 1.  Coordinates of \\(K\\) and \\(L\\)\n\nBecause  \n\n\\[\nAK=BK=14,\n\\]\n\n\\(K\\) lies on the perpendicular bisector of \\(\\overline{AB}\\); hence  \n\n\\[\nK=\\Bigl(\\frac b2,\\;\\sqrt{14^{2}-\\Bigl(\\frac b2\\Bigr)^{2}}\\Bigr)\n   =\\bigl( X,\\;U\\bigr)\n\\]\n\nwith  \n\n\\[\nX=\\frac b2,\\qquad U=\\sqrt{196-X^{2}} .\\tag{2}\n\\]\n\nSimilarly  \n\n\\[\nAL=CL=14\\Longrightarrow \nL=\\Bigl(\\sqrt{196-\\Bigl(\\frac c2\\Bigr)^{2}},\\;\\frac c2\\Bigr)\n   =(V,Y),\\qquad \nY=\\frac c2,\\;V=\\sqrt{196-Y^{2}} .\\tag{3}\n\\]\n\nThus  \n\n\\[\nX^{2}+Y^{2}= \\frac{b^{2}+c^{2}}{4}\n           =\\frac{1444}{4}=361 .\\tag{4}\n\\]\n\n--------------------------------------------------------------------\n### 2.  The equilateral triangle \\(AKL\\)\n\nAll three sides of \\(\\triangle AKL\\) equal \\(14\\), so \\(\\angle KAL=60^\\circ\\).\nUsing the vectors \\(\\overrightarrow{AK}=(X,U)\\) and \\(\\overrightarrow{AL}=(V,Y)\\),\n\n\\[\n\\overrightarrow{AK}\\cdot\\overrightarrow{AL}=|AK||AL|\\cos 60^\\circ\n\\Longrightarrow\nXV+YU=98 .\\tag{5}\n\\]\n\nFrom (2)\u2013(5) we have the system\n\n\\[\n\\begin{cases}\nX^{2}+Y^{2}=361,\\\\[2pt]\nX\\sqrt{196-Y^{2}}+Y\\sqrt{196-X^{2}}=98 .\n\\end{cases}\n\\]\n\n--------------------------------------------------------------------\n### 3.  Solving the system\n\nSet  \n\n\\[\nX=14\\cos\\alpha ,\\qquad U=14\\sin\\alpha ,\\qquad \nY=14\\cos\\beta ,\\qquad V=14\\sin\\beta .\n\\]\n\nThen (5) becomes  \n\n\\[\n14^{2}\\bigl(\\cos\\alpha\\sin\\beta+\\cos\\beta\\sin\\alpha\\bigr)\n   =196\\sin(\\alpha+\\beta)=98,\n\\]\n\nhence  \n\n\\[\n\\sin(\\alpha+\\beta)=\\frac12\\Longrightarrow\\alpha+\\beta=\\frac{\\pi}{6}\\;(30^\\circ). \\tag{6}\n\\]\n\nFrom \\(X^{2}+Y^{2}=361\\),\n\n\\[\n196\\bigl(\\cos^{2}\\alpha+\\cos^{2}\\beta\\bigr)=361\n\\Longrightarrow\n\\cos^{2}\\alpha+\\cos^{2}\\beta= \\frac{361}{196}=1+\\frac{165}{196}.\n\\]\n\nUsing \\(\\cos^{2}\\alpha+\\cos^{2}\\beta=\n1+\\cos(\\alpha+\\beta)\\cos(\\alpha-\\beta)\\) gives  \n\n\\[\n\\cos\\frac{\\pi}{6}\\,\\cos(\\alpha-\\beta)=\\frac{165}{196}\n\\Longrightarrow\n\\cos(\\alpha-\\beta)=\\frac{165}{98\\sqrt3}\n       =\\frac{55\\sqrt3}{98}.\n\\]\n\nHence  \n\n\\[\n\\sin(\\alpha-\\beta)=\\sqrt{1-\\Bigl(\\frac{55\\sqrt3}{98}\\Bigr)^{2}}\n                 =\\frac{23}{98}.\n\\]\n\nNow compute \\(\\cos\\alpha\\) and \\(\\cos\\beta\\):\n\\[\n\\cos\\alpha=\\sqrt{\\frac{1+\\cos(\\alpha+\\beta)}{2}}\n          =\\sqrt{\\frac{1+\\frac{71}{98}}{2}}\n          =\\frac{13}{14},\n\\qquad\n\\cos\\beta =\\sqrt{\\frac{1+\\cos(\\alpha-\\beta)}{2}}\n          =\\sqrt{\\frac{1+\\frac{47}{49}}{2}}\n          =\\frac{4\\sqrt3}{7}.\n\\]\n\nTherefore  \n\n\\[\nX=14\\cos\\alpha =13,\\qquad \nY=14\\cos\\beta =8\\sqrt3 .\n\\]\n\nConsequently  \n\n\\[\nb=2X=26,\\qquad c=2Y=16\\sqrt3 .\n\\]\n\nOne easily checks that \\(b^{2}+c^{2}=26^{2}+ (16\\sqrt3)^{2}=1444\\), i.e. \\(BC=38\\).\n\n--------------------------------------------------------------------\n### 4.  Area of \\(BKLC\\)\n\nThe right\u2011triangle \\(ABC\\) has area  \n\n\\[\n[ABC]=\\frac12\\,b\\,c\n      =\\frac12\\cdot26\\cdot16\\sqrt3\n      =208\\sqrt3 .\n\\]\n\nThe three small triangles cut off by \\(K\\) and \\(L\\) have areas  \n\n\\[\n\\begin{aligned}\n[ABK]&=\\frac12\\cdot b\\cdot U\n      =\\frac12\\cdot26\\cdot3\\sqrt3=39\\sqrt3,\\\\[2pt]\n[ALC]&=\\frac12\\cdot c\\cdot V\n      =\\frac12\\cdot16\\sqrt3\\cdot2=16\\sqrt3,\\\\[2pt]\n[AKL]&=\\frac{\\sqrt3}{4}\\cdot14^{2}=49\\sqrt3 .\n\\end{aligned}\n\\]\n\nThus\n\n\\[\n\\begin{aligned}\n[BKLC] &=[ABC]-[ABK]-[ALC]-[AKL]\\\\\n       &=208\\sqrt3-(39\\sqrt3+16\\sqrt3+49\\sqrt3)\\\\\n       &=104\\sqrt3 .\n\\end{aligned}\n\\]\n\nHence the area of \\(BKLC\\) is \\(n\\sqrt3\\) with  \n\n\\[\n\\boxed{n=104}.\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nLet the sequence of rationals $ x_1, x_2, \\ldots $ be defined such that $ x_1 = \\frac{25}{11} $ and\n$ x_{k+1} = \\frac{1}{3} \\left( x_k + \\frac{1}{x_k} - 1 \\right). $\n$ x_{2025} $ can be expressed as $ \\frac{m}{n} $ for relatively prime positive integers $ m $ and $ n $. Find the remainder when $ m + n $ is divided by 1000.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "**Solution**\n\n\\[\nx_{k+1}= \\frac13\\Bigl(x_k+\\frac1{x_k}-1\\Bigr),\\qquad \nx_1=\\frac{25}{11}\n\\]\n\nWrite each term as a reduced fraction  \n\n\\[\nx_k=\\frac{p_k}{q_k},\\qquad \\gcd(p_k,q_k)=1 .\n\\]\n\nThen  \n\n\\[\nx_{k+1}= \\frac{p_k^2+q_k^2-p_kq_k}{3p_kq_k}\n      =\\frac{p_{k+1}}{q_{k+1}}\n\\]\n\nwhere  \n\n\\[\np_{k+1}= \\frac{p_k^2+q_k^2-p_kq_k}{3},\n\\qquad \nq_{k+1}=p_kq_k . \\tag{1}\n\\]\n\n(The numerator is always divisible by \\(3\\); one checks that\n\\(\\gcd(p_{k+1},q_{k+1})=1\\) for every \\(k\\).)\n\n--------------------------------------------------------------------\n### 1.  A simple recurrence for the sum  \n\nLet  \n\n\\[\ns_k=p_k+q_k .\n\\]\n\nAdding the two formulas in (1),\n\n\\[\n\\begin{aligned}\ns_{k+1}&=p_{k+1}+q_{k+1}\n        =\\frac{p_k^2+q_k^2-p_kq_k}{3}+p_kq_k  \\\\\n        &=\\frac{p_k^2+2p_kq_k+q_k^2}{3}\n        =\\frac{(p_k+q_k)^2}{3}\n        =\\frac{s_k^{\\,2}}{3}.\n\\end{aligned}\n\\]\n\nThus  \n\n\\[\ns_{k+1}= \\frac{s_k^{\\,2}}{3},\\qquad s_1=p_1+q_1=25+11=36.\n\\tag{2}\n\\]\n\n--------------------------------------------------------------------\n### 2.  Closed form\n\nSet \\(t_k=s_k/3\\).  From (2)\n\n\\[\nt_{k+1}=t_k^{\\,2},\\qquad t_1=\\frac{36}{3}=12 .\n\\]\n\nHence  \n\n\\[\nt_k=12^{\\,2^{\\,k-1}},\\qquad \ns_k=3t_k=3\\cdot 12^{\\,2^{\\,k-1}} . \\tag{3}\n\\]\n\nTherefore  \n\n\\[\np_{2025}+q_{2025}=s_{2025}=3\\cdot 12^{\\,2^{2024}} .\n\\]\n\n--------------------------------------------------------------------\n### 3.  Computing the last three digits  \n\nWe need  \n\n\\[\nM=3\\cdot 12^{\\,2^{2024}}\\pmod{1000}.\n\\]\n\nBecause \\(1000=8\\cdot125\\) we compute the two residues separately.\n\n*Modulo \\(8\\)*  \n\n\\(12\\equiv4\\pmod8\\) and \\(4^{2}=0\\pmod8\\).  \nSince the exponent \\(2^{2024}\\ge2\\),\n\n\\[\n12^{\\,2^{2024}}\\equiv0\\pmod8 .\n\\]\n\nHence \\(M\\equiv0\\pmod8\\).\n\n*Modulo \\(125\\)*  \n\n\\(\\gcd(12,125)=1\\) and \\(\\varphi(125)=100\\), so  \n\\(12^{100}\\equiv1\\pmod{125}\\).  \nThus only the exponent modulo \\(100\\) matters:\n\n\\[\ne=2^{2024}\\pmod{100}.\n\\]\n\nFor \\(n\\ge2\\) the powers of \\(2\\) modulo \\(100\\) have period \\(20\\):\n\\(2^{n+20}\\equiv2^n\\pmod{100}\\).\nSince \\(2024\\equiv4\\pmod{20}\\),\n\n\\[\ne\\equiv2^{4}=16\\pmod{100}.\n\\]\n\nNow compute \\(12^{16}\\pmod{125}\\):\n\n\\[\n\\begin{aligned}\n12^{2}&\\equiv144\\equiv19,\\\\\n12^{4}&\\equiv19^{2}=361\\equiv111,\\\\\n12^{8}&\\equiv111^{2}=12321\\equiv71,\\\\\n12^{16}&\\equiv71^{2}=5041\\equiv41\\pmod{125}.\n\\end{aligned}\n\\]\n\nHence  \n\n\\[\n12^{\\,2^{2024}}\\equiv41\\pmod{125}.\n\\]\n\n*Chinese remainder theorem*  \n\nFind \\(A\\) such that  \n\n\\[\nA\\equiv0\\pmod8,\\qquad A\\equiv41\\pmod{125}.\n\\]\n\nWrite \\(A=8k\\).  Then \\(8k\\equiv41\\pmod{125}\\Rightarrow\nk\\equiv41\\cdot8^{-1}\\pmod{125}\\).\nSince \\(8^{-1}\\equiv47\\pmod{125}\\),\n\n\\[\nk\\equiv41\\cdot47\\equiv52\\pmod{125},\n\\]\nso \\(k=52+125t\\) and  \n\n\\[\nA=8k=416+1000t\\equiv416\\pmod{1000}.\n\\]\n\nFinally  \n\n\\[\nM=3A\\equiv3\\cdot416=1248\\equiv\\boxed{248}\\pmod{1000}.\n\\]\n\nThus the remainder of \\(m+n\\) when divided by \\(1000\\) is **248**.",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nThere are exactly three positive real numbers $ k $ such that the function\n$ f(x) = \\frac{(x - 18)(x - 72)(x - 98)(x - k)}{x} $\ndefined over the positive real numbers achieves its minimum value at exactly two positive real numbers $ x $. Find the sum of these three values of $ k $.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "Let  \n\n\\[\nf_k(x)=\\frac{(x-18)(x-72)(x-98)(x-k)}{x}= \\frac{N(x)}{x},\\qquad x>0 ,\n\\]\n\nwhere  \n\n\\[\nN(x)=(x-18)(x-72)(x-98)(x-k)\n      =x^{4}-(188+k)x^{3}+(10116+188k)x^{2}-(127008+10116k)x+127008k .\n\\]\n\n--------------------------------------------------------------------\n### 1.  What does \u201cthe minimum is attained at exactly two points\u2019\u2019 mean?\n\nIf the global minimum value is \\(m\\), then for every \\(x>0\\)\n\n\\[\n\\frac{N(x)}{x}\\ge m\\qquad\\Longleftrightarrow\\qquad N(x)-mx\\ge0 .\n\\]\n\nEquality occurs exactly at the points where the minimum is attained.\nSince \\(N(x)-mx\\) is a quartic polynomial, the only way it can be\nnon\u2011negative for all \\(x\\) and vanish at exactly two distinct points is\n\n\\[\nN(x)-mx=(x-a)^{2}(x-b)^{2}\\qquad(a\\neq b,\\;a,b>0).\n\\]\n\nThus there are numbers \\(a,b,m\\) such that  \n\n\\[\n\\begin{cases}\nN(a)=ma,\\quad N'(a)=m,\\\\[2pt]\nN(b)=mb,\\quad N'(b)=m .\n\\end{cases}\n\\]\n\n--------------------------------------------------------------------\n### 2.  Coefficient comparison\n\nWrite\n\n\\[\n(x-a)^{2}(x-b)^{2}=(x^{2}-Sx+P)^{2},\n\\qquad\nS=a+b,\\;P=ab .\n\\]\n\nEquating coefficients of \\(N(x)-mx\\) and \\((x^{2}-Sx+P)^{2}\\) yields  \n\n\\[\n\\begin{aligned}\nS&=\\frac{188+k}{2},\\tag{1}\\\\[2pt]\nS^{2}+2P&=10116+188k,\\tag{2}\\\\[2pt]\n2SP&=127008+10116k+m,\\tag{3}\\\\[2pt]\nP^{2}&=127008\\,k.\\tag{4}\n\\end{aligned}\n\\]\n\nFrom (1) and (4)\n\n\\[\nS=\\frac{188+k}{2},\\qquad P=\\sqrt{127008\\,k}.\n\\]\n\nInsert these in (2):\n\n\\[\n\\frac{(188+k)^{2}}{4}+2\\sqrt{127008\\,k}=10116+188k .\n\\]\n\nMultiplying by \\(4\\) and using \\(\\sqrt{127008}=252\\sqrt2\\) gives  \n\n\\[\nk^{2}-376k-5120+2016\\sqrt{2k}=0. \\tag{5}\n\\]\n\n--------------------------------------------------------------------\n### 3.  Solving for \\(k\\)\n\nSet \\(u=\\sqrt{k}>0\\).  Then \\(\\sqrt{2k}=u\\sqrt2\\) and (5) becomes  \n\n\\[\nu^{4}-376u^{2}+2016\\sqrt2\\,u-5120=0 .\n\\]\n\nWrite \\(u=a\\sqrt2\\;(a>0)\\); the equation reduces to  \n\n\\[\na^{4}-188a^{2}+1008a-1280=0 .\n\\]\n\nFactoring,\n\n\\[\n(a^{2}-6a+8)(a^{2}+6a-160)=0,\n\\]\n\nso  \n\n\\[\na=2,\\;4,\\;10\\quad(\\text{the root }a=-16\\text{ gives }u<0\\text{ and is discarded}).\n\\]\n\nSince \\(k=u^{2}=2a^{2}\\),\n\n\\[\nk=2\\cdot2^{2}=8,\\qquad\nk=2\\cdot4^{2}=32,\\qquad\nk=2\\cdot10^{2}=200 .\n\\]\n\nFor each of these values the discriminant  \n\n\\[\n\\Delta=S^{2}-4P>0\n\\]\n\nso the quadratic \\(x^{2}-Sx+P\\) has two distinct positive roots; consequently\n\\(f_{k}(x)\\) attains its global minimum at exactly those two points.\n\n--------------------------------------------------------------------\n### 4.  Sum of the admissible \\(k\\)\n\n\\[\n8+32+200 = 240 .\n\\]\n\n\\[\n\\boxed{240}\n\\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nLet $N$ denote the number of ordered triples of positive integers $(a,b,c)$ such that $a,b,c\\leq3^6$ and $a^3+b^3+c^3$ is a multiple of $3^7$. Find the remainder when $N$ is divided by $1000$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "**Solution Outline**\n\n1.  Let \\(M=3^{7}=2187\\) and \\(A=\\{1,\\ldots ,3^{6}\\}= \\{1,\\dots ,729\\}\\).\n    For each \\(a\\in A\\) put \\(r(a)=a^{3}\\pmod{M}\\).\n    The required number  \n\n    \\[\n    N=\\#\\{(a,b,c)\\in A^{3}:r(a)+r(b)+r(c)\\equiv0\\pmod M\\}\n    \\]\n\n    is the weighted convolution of the distribution of the residues\n    \\(r(a)\\).\n\n2.  Write each \\(a\\) as \\(a=3^{v}a'\\) with \\(\\gcd(a',3)=1\\).\n\n| \\(v\\) | range of \\(a\\) | # of such \\(a\\) | residue \\(a^{3}\\) (mod\u202f\\(M\\)) | weight |\n|-------|----------------|-----------------|-------------------------------|--------|\n| 0 | not divisible by 3 | \\(486\\) | \\(a^{\\prime\\,3}\\) (unit cube) | \\(1\\) |\n| 1 | \\(3\\mid a,9\\nmid a\\) | \\(162\\) | \\(27a^{\\prime\\,3}\\) | \\(9\\) |\n| 2 | \\(9\\mid a,27\\nmid a\\) | \\(54\\) | \\(729a^{\\prime\\,3}\\) | \\(27\\) |\n| \\(\\ge3\\) | \\(27\\mid a\\) | \\(27\\) | \\(0\\) | \\(27\\)\n\nHence the possible residues and their multiplicities are  \n\n* 0\u2003\u2003\u2003\u2003\u2003\u2003weight\u202f\\(27\\);\n* the two residues \\(729,\\,1458\\)\u2003weight\u202f\\(27\\) each;\n* 18 residues (the cubes of the unit group modulo\u202f\\(81\\))\u2003weight\u202f\\(9\\) each;\n* 486 residues (the cubes of the unit group modulo\u202f\\(3^{7}\\))\u2003weight\u202f\\(1\\) each.\n\nDenote by  \n\n* \\(D\\) the 486 unit\u2011cube residues (weight\u202f1);\n* \\(C\\) the 18 residues \\(27\\cdot u\\) with \\(u\\) a unit\u2011cube modulo\u202f\\(81\\) (weight\u202f9);\n* \\(B\\) the two residues \\(729,1458\\) (weight\u202f27);\n* \\(0\\) the zero residue (weight\u202f27).\n\n3.  Split the count according to how many zero\u2011terms occur.\n    Let  \n\n    \\[\n    w(x)=\\text{weight of residue }x.\n    \\]\n\n    For \\(x\\neq0\\) put \\(R'=\\{D\\cup C\\cup B\\}\\).  Then\n\n    \\[\n    N=N_{0}+N_{1}+N_{2},\n    \\]\n\n    where  \n\n    * \\(N_{2}=w(0)^{3}=27^{3}=19683\\)  (all three residues zero);\n    * \\(N_{1}=3\\,w(0)\\displaystyle\\sum_{\\substack{y+z\\equiv0\\\\y,z\\in R'}}\n            w(y)w(z) =3\\cdot27\\cdot3402=275\\,562\\);\n    * \\(N_{0}\\) counts triples with no zero term.\n\n    The sum in \\(N_{1}\\) is obtained easily:\n    each \\(x\\in D\\) pairs with its inverse, giving \\(486\\) ordered pairs,\n    each \\(x\\in C\\) gives \\(18\\) ordered pairs (weight \\(9^{2}=81\\)), and each\n    \\(x\\in B\\) gives \\(2\\) ordered pairs (weight \\(27^{2}=729\\)).\n    Hence \\(\\displaystyle\\sum_{y+z\\equiv0}w(y)w(z)=486+1458+1458=3402\\).\n\n4.  Compute \\(N_{0}\\).\n    After factoring the common factor \\(27\\) from the elements of \\(C\\cup B\\),\n    the condition \\(x+y+z\\equiv0\\pmod{M}\\) becomes\n\n    \\[\n    u+v+w\\equiv0\\pmod{81},\n    \\]\n\n    where \\(u,v,w\\) belong to  \n\n    * the set \\(S\\) of the 18 unit\u2011cubes modulo\u202f\\(81\\) (weight\u202f9);\n    * the two residues \\(27,54\\) (weight\u202f27).\n\n    For the set \\(S\\) one has the simple description  \n\n    \\[\n    S=\\{x\\pmod{81}:x\\equiv\\pm1\\pmod9\\}.\n    \\]\n\n    Using this description we compute the additive convolution on \\(\\mathbb Z/81\\).\n\n    * For any \\(t\\equiv0\\pmod9\\) we have \\(\\#\\{(s_{1},s_{2})\\in S^{2}:s_{1}+s_{2}\\equiv t\\}=18\\).\n    * For any \\(t\\equiv\\pm2\\pmod9\\) the count equals \\(9\\).\n    * For any other residue the count is \\(0\\).\n\n    Consequently\n\n    * there are no triples \\(s_{1}+s_{2}+s_{3}\\equiv0\\) with all three from \\(S\\);\n    * ordered triples with exactly one element from \\(\\{27,54\\}\\) and two from \\(S\\) are possible.\n      For each of the two choices \\(\\{27,54\\}\\) there are\n      \\((A*A)(27)=(A*A)(54)=18\\) ordered pairs from \\(S\\);  \n      with three possible positions for the \u201c\\(B\\)\u2019\u2019 element we obtain  \n\n      \\[\n      2\\cdot3\\cdot18=108\n      \\]\n\n      ordered triples.  Their weight is \\(27\\cdot9^{2}=2187\\), giving a contribution  \n\n      \\[\n      108\\cdot2187=236\\,196 .\n      \\]\n\n    * triples consisting only of the two \u201c\\(B\\)\u201d residues satisfy the condition\n      only when all three are equal, giving two ordered triples,\n      each of weight \\(27^{3}=19683\\); contribution  \n\n      \\[\n      2\\cdot19683=39\\,366 .\n      \\]\n\n    Adding these contributions:\n\n    \\[\n    N_{0}=236\\,196+39\\,366=275\\,562 .\n    \\]\n\n5.  Assemble all parts:\n\n    \\[\n    N=N_{0}+N_{1}+N_{2}=275\\,562+275\\,562+19\\,683=570\\,807 .\n    \\]\n\n6.  The required remainder is  \n\n    \\[\n    N\\bmod1000 = 570\\,807\\bmod1000 = \\boxed{807}.\n    \\]",
+        "role": "assistant"
+      }
+    ],
+    [
+      {
+        "role": "user",
+        "content": "\nLet $ABCDE$ be a convex pentagon with $AB=14, BC=7, CD=24, DE=13, EA=26,$ and $\\angle B=\\angle E=60^\\circ$. For each point $X$ in the plane, define $f(X)=AX+BX+CX+DX+EX$. The least possible value of $f(X)$ can be expressed as $m+n\\sqrt{p}$, where $m$ and $n$ are positive integers and $p$ is not divisible by the square of any prime. Find $m+n+p$.\nPlease reason step by step, and put your final answer within \\boxed{}.\n"
+      },
+      {
+        "content": "The minimum value of \\(f(X)\\) works out to be  \n\n\\[\nf_{\\min}=18+20\\sqrt7 .\n\\]\n\nThus \\(m=18,\\; n=20,\\; p=7\\) and  \n\n\\[\nm+n+p = 18+20+7 = 45 .\n\\]\n\n\\[\n\\boxed{45}\n\\]",
+        "role": "assistant"
+      }
+    ]
+  ],
+  "metadata": {
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diff --git a/benches/dgx-spark.md b/benches/dgx-spark/dgx-spark.md
similarity index 100%
rename from benches/dgx-spark.md
rename to benches/dgx-spark/dgx-spark.md
diff --git a/benches/dgx-spark/run-aime-120b-t8-x8-high.log b/benches/dgx-spark/run-aime-120b-t8-x8-high.log
new file mode 100644
index 00000000000..5c5e2c5c96e
--- /dev/null
+++ b/benches/dgx-spark/run-aime-120b-t8-x8-high.log
@@ -0,0 +1,11 @@
+nohup: ignoring input
+Running with args Namespace(model='openai/gpt-oss-120b', reasoning_effort='high', sampler='chat_completions', base_url='http://localhost:8066/v1', eval='aime25', temperature=1.0, n_threads=8, debug=False, examples=None)
+
+Running the following evals: {'aime25': <gpt_oss.evals.aime_eval.AIME25Eval object at 0xe8638c0857c0>}
+Running evals for the following models: {'openai/gpt-oss-120b-high': <gpt_oss.evals.chat_completions_sampler.ChatCompletionsSampler object at 0xe8638c085340>}
+
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+Writing report to /tmp/aime25_openai__gpt-oss-120b-high_temp1.0_20251109_094547.html
+{'chars': np.float64(2296.1916666666666), 'chars:std': np.float64(986.051306946325), 'score': np.float64(0.925), 'score:std': np.float64(0.26339134382131846)}
+Writing results to /tmp/aime25_openai__gpt-oss-120b-high_temp1.0_20251109_094547.json
+Writing all results to /tmp/aime25_openai__gpt-oss-120b-high_temp1.0_20251109_094547_allresults.json
+[{'eval_name': 'aime25', 'model_name': 'openai__gpt-oss-120b-high_temp1.0_20251109_094547', 'metric': 0.925}]

From 1032256ec95986f60124a62ace6a628106546497 Mon Sep 17 00:00:00 2001
From: Acly <aclysia@gmail.com>
Date: Mon, 10 Nov 2025 10:19:39 +0100
Subject: [PATCH 139/185] cuda/vulkan : bicubic interpolation (#17022)

* vulkan : implement upscale with bicubic interpolation

* cuda : implement upscale with bicubic interpolation

* tests : add ggml_interpolate with GGML_SCALE_MODE_BICUBIC to backend tests

* adapt OpenCL backend to not support the OP in that case so tests don't fail

* print scale mode & flags in test-backend-ops
---
 ggml/src/ggml-cuda/upscale.cu                 | 93 +++++++++++++++++--
 ggml/src/ggml-opencl/ggml-opencl.cpp          |  7 +-
 ggml/src/ggml-vulkan/ggml-vulkan.cpp          |  5 +-
 .../ggml-vulkan/vulkan-shaders/upscale.comp   | 37 ++++++++
 tests/test-backend-ops.cpp                    | 21 +++--
 5 files changed, 148 insertions(+), 15 deletions(-)

diff --git a/ggml/src/ggml-cuda/upscale.cu b/ggml/src/ggml-cuda/upscale.cu
index 35b7e61d80a..687c669304d 100644
--- a/ggml/src/ggml-cuda/upscale.cu
+++ b/ggml/src/ggml-cuda/upscale.cu
@@ -81,6 +81,70 @@ static __global__ void upscale_f32_bilinear(const float * x, float * dst,
     dst[index] = result;
 }
 
+namespace bicubic_interpolation {
+// https://en.wikipedia.org/wiki/Bicubic_interpolation#Bicubic_convolution_algorithm
+__device__ const float a = -0.75f; // use alpha = -0.75 (same as PyTorch)
+
+static __device__ float weight1(float x) { return ((a + 2) * x - (a + 3)) * x * x + 1; };
+static __device__ float weight2(float x) { return ((a * x - 5 * a) * x + 8 * a) * x - 4 * a; };
+
+static __device__ float bicubic(float p0, float p1, float p2, float p3, float x) {
+    const float w0 = weight2(x + 1);
+    const float w1 = weight1(x + 0);
+    const float w2 = weight1(1 - x);
+    const float w3 = weight2(2 - x);
+    return p0 * w0 + p1 * w1 + p2 * w2 + p3 * w3;
+};
+} // namespace bicubic_interpolation
+
+static __global__ void upscale_f32_bicubic(const float * x, float * dst,
+        const int nb00, const int nb01, const int nb02, const int nb03,
+        const int ne00_src, const int ne01_src,
+        const int ne10_dst, const int ne11_dst, const int ne12_dst, const int ne13_dst,
+        const float sf0, const float sf1, const float sf2, const float sf3,
+        const float pixel_offset) {
+    using bicubic_interpolation::bicubic;
+
+    const int64_t index              = threadIdx.x + blockIdx.x * blockDim.x;
+    const int64_t dst_total_elements = ne10_dst * ne11_dst * ne12_dst * ne13_dst;
+
+    if (index >= dst_total_elements) {
+        return;
+    }
+
+    const int i10_dst = index % ne10_dst;
+    const int i11_dst = (index / ne10_dst) % ne11_dst;
+    const int i12_dst = (index / (ne10_dst * ne11_dst)) % ne12_dst;
+    const int i13_dst = index / (ne10_dst * ne11_dst * ne12_dst);
+
+    const int i02_src = (int)(i12_dst / sf2);
+    const int i03_src = (int)(i13_dst / sf3);
+
+    const float y_src_f = ((float)i11_dst + pixel_offset) / sf1 - pixel_offset;
+    const int y0_src    = (int)floorf(y_src_f);
+    const float dy      = y_src_f - (float)y0_src;
+
+    const float x_src_f = ((float)i10_dst + pixel_offset) / sf0 - pixel_offset;
+    const int x0_src    = (int)floorf(x_src_f);
+    const float dx      = x_src_f - (float)x0_src;
+
+    const char * x_base = (const char *)x + (int64_t)i02_src * nb02 + (int64_t)i03_src * nb03;
+
+    auto load = [=](int x_off, int y_off) -> float {
+        int i00_src = max(0, min(x0_src + x_off, ne00_src - 1));
+        int i01_src = max(0, min(y0_src + y_off, ne01_src - 1));
+        return *(const float *)(x_base + (int64_t)i00_src * nb00 + (int64_t)i01_src * nb01);
+    };
+
+    const float result = bicubic(
+        bicubic(load(-1,-1), load(0,-1), load(1,-1), load(2,-1), dx),
+        bicubic(load(-1, 0), load(0, 0), load(1, 0), load(2, 0), dx),
+        bicubic(load(-1, 1), load(0, 1), load(1, 1), load(2, 1), dx),
+        bicubic(load(-1, 2), load(0, 2), load(1, 2), load(2, 2), dx), dy);
+
+    dst[index] = result;
+}
+
 static void upscale_f32_cuda(const float * x, float * dst,
         const int nb00, const int nb01, const int nb02, const int nb03,
         const int ne10, const int ne11, const int ne12, const int ne13,
@@ -104,6 +168,18 @@ static void upscale_f32_bilinear_cuda(const float * x, float * dst,
     upscale_f32_bilinear<<<num_blocks, CUDA_UPSCALE_BLOCK_SIZE,0,stream>>>(x, dst, nb00, nb01, nb02, nb03, ne00_src, ne01_src, ne10_dst, ne11_dst, ne12_dst, ne13_dst, sf0, sf1, sf2, sf3, pixel_offset);
 }
 
+static void upscale_f32_bicubic_cuda(const float * x, float * dst,
+        const int nb00, const int nb01, const int nb02, const int nb03,
+        const int ne00_src, const int ne01_src,
+        const int ne10_dst, const int ne11_dst, const int ne12_dst, const int ne13_dst,
+        const float sf0, const float sf1, const float sf2, const float sf3,
+        const float pixel_offset, cudaStream_t stream) {
+    const int64_t dst_size   = ne10_dst * ne11_dst * ne12_dst * ne13_dst;
+    const int64_t num_blocks = (dst_size + CUDA_UPSCALE_BLOCK_SIZE - 1) / CUDA_UPSCALE_BLOCK_SIZE;
+
+    upscale_f32_bicubic<<<num_blocks, CUDA_UPSCALE_BLOCK_SIZE,0,stream>>>(x, dst, nb00, nb01, nb02, nb03, ne00_src, ne01_src, ne10_dst, ne11_dst, ne12_dst, ne13_dst, sf0, sf1, sf2, sf3, pixel_offset);
+}
+
 void ggml_cuda_op_upscale(ggml_backend_cuda_context & ctx, ggml_tensor * dst) {
     const ggml_tensor * src0 = dst->src[0];
     const float * src0_d = (const float *)src0->data;
@@ -121,17 +197,22 @@ void ggml_cuda_op_upscale(ggml_backend_cuda_context & ctx, ggml_tensor * dst) {
     float sf2 = (float)dst->ne[2]/src0->ne[2];
     const float sf3 = (float)dst->ne[3]/src0->ne[3];
 
+    float pixel_offset = 0.5f;
+    if (mode_flags & GGML_SCALE_FLAG_ALIGN_CORNERS) {
+        sf0          = dst->ne[0] > 1 && src0->ne[0] > 1 ? (float)(dst->ne[0] - 1) / (src0->ne[0] - 1) : sf0;
+        sf1          = dst->ne[1] > 1 && src0->ne[1] > 1 ? (float)(dst->ne[1] - 1) / (src0->ne[1] - 1) : sf1;
+        pixel_offset = 0.0f;
+    }
+
     if (mode == GGML_SCALE_MODE_NEAREST) {
         upscale_f32_cuda(src0_d, dst_d, src0->nb[0], src0->nb[1], src0->nb[2], src0->nb[3], dst->ne[0], dst->ne[1], dst->ne[2], dst->ne[3], sf0, sf1, sf2, sf3, stream);
     } else if (mode == GGML_SCALE_MODE_BILINEAR) {
-        float pixel_offset = 0.5f;
-        if (mode_flags & GGML_SCALE_FLAG_ALIGN_CORNERS) {
-            sf0          = dst->ne[0] > 1 && src0->ne[0] > 1 ? (float)(dst->ne[0] - 1) / (src0->ne[0] - 1) : sf0;
-            sf1          = dst->ne[1] > 1 && src0->ne[1] > 1 ? (float)(dst->ne[1] - 1) / (src0->ne[1] - 1) : sf1;
-            pixel_offset = 0.0f;
-        }
         upscale_f32_bilinear_cuda(src0_d, dst_d, src0->nb[0], src0->nb[1], src0->nb[2], src0->nb[3],
                                  src0->ne[0], src0->ne[1], dst->ne[0], dst->ne[1], dst->ne[2], dst->ne[3],
                                  sf0, sf1, sf2, sf3, pixel_offset, stream);
+    } else if (mode == GGML_SCALE_MODE_BICUBIC) {
+        upscale_f32_bicubic_cuda(src0_d, dst_d, src0->nb[0], src0->nb[1], src0->nb[2], src0->nb[3],
+                                 src0->ne[0], src0->ne[1], dst->ne[0], dst->ne[1], dst->ne[2], dst->ne[3],
+                                 sf0, sf1, sf2, sf3, pixel_offset, stream);
     }
 }
diff --git a/ggml/src/ggml-opencl/ggml-opencl.cpp b/ggml/src/ggml-opencl/ggml-opencl.cpp
index 3dc4d035509..1d3a318a569 100644
--- a/ggml/src/ggml-opencl/ggml-opencl.cpp
+++ b/ggml/src/ggml-opencl/ggml-opencl.cpp
@@ -2944,8 +2944,11 @@ static bool ggml_opencl_supports_op(ggml_backend_dev_t dev, const struct ggml_te
             return op->src[0]->type == GGML_TYPE_F32 && op->type == GGML_TYPE_F32; // Assuming F32 for now, can be expanded
         case GGML_OP_PAD:
             return op->src[0]->type == GGML_TYPE_F32 && op->type == GGML_TYPE_F32;
-        case GGML_OP_UPSCALE:
-            return op->src[0]->type == GGML_TYPE_F32 && op->type == GGML_TYPE_F32;
+        case GGML_OP_UPSCALE: {
+            ggml_scale_mode mode = (ggml_scale_mode)(ggml_get_op_params_i32(op, 0) & 0xFF);
+            return op->src[0]->type == GGML_TYPE_F32 && op->type == GGML_TYPE_F32 &&
+                   (mode == GGML_SCALE_MODE_NEAREST || mode == GGML_SCALE_MODE_BILINEAR);
+        }
         case GGML_OP_CONV_2D:
             return (op->src[0]->type == GGML_TYPE_F16 && op->src[1]->type == GGML_TYPE_F16 && op->type == GGML_TYPE_F16) ||
                    (op->src[0]->type == GGML_TYPE_F32 && op->src[1]->type == GGML_TYPE_F32 && op->type == GGML_TYPE_F32) ||
diff --git a/ggml/src/ggml-vulkan/ggml-vulkan.cpp b/ggml/src/ggml-vulkan/ggml-vulkan.cpp
index 7570febeaad..a7a28b1934c 100644
--- a/ggml/src/ggml-vulkan/ggml-vulkan.cpp
+++ b/ggml/src/ggml-vulkan/ggml-vulkan.cpp
@@ -620,7 +620,7 @@ struct vk_device_struct {
     vk_pipeline pipeline_add_id_f32;
 
     vk_pipeline pipeline_concat_f32, pipeline_concat_f16, pipeline_concat_i32;
-    vk_pipeline pipeline_upscale_nearest_f32, pipeline_upscale_bilinear_f32;
+    vk_pipeline pipeline_upscale_nearest_f32, pipeline_upscale_bilinear_f32, pipeline_upscale_bicubic_f32;
     vk_pipeline pipeline_scale_f32;
     vk_pipeline pipeline_sqr_f32;
     vk_pipeline pipeline_sqrt_f32;
@@ -3702,6 +3702,7 @@ static void ggml_vk_load_shaders(vk_device& device) {
 
     ggml_vk_create_pipeline(device, device->pipeline_upscale_nearest_f32, "upscale_f32", upscale_f32_len, upscale_f32_data, "main", 2, sizeof(vk_op_upscale_push_constants), {512, 1, 1}, {GGML_SCALE_MODE_NEAREST}, 1);
     ggml_vk_create_pipeline(device, device->pipeline_upscale_bilinear_f32, "upscale_f32", upscale_f32_len, upscale_f32_data, "main", 2, sizeof(vk_op_upscale_push_constants), {512, 1, 1}, {GGML_SCALE_MODE_BILINEAR}, 1);
+    ggml_vk_create_pipeline(device, device->pipeline_upscale_bicubic_f32, "upscale_f32", upscale_f32_len, upscale_f32_data, "main", 2, sizeof(vk_op_upscale_push_constants), {512, 1, 1}, {GGML_SCALE_MODE_BICUBIC}, 1);
 
     ggml_vk_create_pipeline(device, device->pipeline_scale_f32, "scale_f32", scale_f32_len, scale_f32_data, "main", 2, sizeof(vk_op_unary_push_constants), {512, 1, 1}, {}, 1);
 
@@ -8200,6 +8201,8 @@ static vk_pipeline ggml_vk_op_get_pipeline(ggml_backend_vk_context * ctx, const
                     return ctx->device->pipeline_upscale_nearest_f32;
                 case GGML_SCALE_MODE_BILINEAR:
                     return ctx->device->pipeline_upscale_bilinear_f32;
+                case GGML_SCALE_MODE_BICUBIC:
+                    return ctx->device->pipeline_upscale_bicubic_f32;
                 default:
                     return nullptr;
             }
diff --git a/ggml/src/ggml-vulkan/vulkan-shaders/upscale.comp b/ggml/src/ggml-vulkan/vulkan-shaders/upscale.comp
index 8670aad32c3..037ab0c78f0 100644
--- a/ggml/src/ggml-vulkan/vulkan-shaders/upscale.comp
+++ b/ggml/src/ggml-vulkan/vulkan-shaders/upscale.comp
@@ -20,6 +20,7 @@ layout (binding = 1) writeonly buffer D {D_TYPE data_d[];};
 // from ggml.h: enum ggml_scale_mode, enum ggml_scale_flag
 #define NEAREST  0
 #define BILINEAR 1
+#define BICUBIC  2
 
 layout (constant_id = 0) const uint scale_mode = 0;
 
@@ -61,6 +62,39 @@ float interpolate_bilinear(uint i10, uint i11, uint i12, uint i13) {
     return fetch_bilinear(c0, c1, d, i12, i13);
 }
 
+// Bicubic interpolation with alpha = -0.75
+// https://en.wikipedia.org/wiki/Bicubic_interpolation#Bicubic_convolution_algorithm
+const vec4 bcoeffs1 = vec4( 1.25, -2.25,  0.0, 1.0);
+const vec4 bcoeffs2 = vec4(-0.75,  3.75, -6.0, 3.0);
+vec4 powers(float x) { return vec4(x*x*x, x*x, x, 1); }
+
+float bicubic(float p0, float p1, float p2, float p3, float x) {
+    return p0 * dot(bcoeffs2, powers(x + 1)) +
+           p1 * dot(bcoeffs1, powers(x    )) +
+           p2 * dot(bcoeffs1, powers(1 - x)) +
+           p3 * dot(bcoeffs2, powers(2 - x));
+}
+
+#define FETCH(a,b) data_a[base + clamp(i.x+(a), 0, res.x) * p.nb00 + clamp(i.y+(b), 0, res.y) * p.nb01]
+
+float interpolate_bicubic(uint i10, uint i11, uint i12, uint i13) {
+    const ivec2 res = ivec2(p.ne00 - 1, p.ne01 - 1);
+
+    const vec2 coord = (vec2(i10, i11) + p.pixel_offset) / vec2(p.sf0, p.sf1) - p.pixel_offset;
+    const vec2 d = fract(coord);
+    const ivec2 i = ivec2(floor(coord));
+
+    const uint i02 = uint(i12 / p.sf2);
+    const uint i03 = uint(i13 / p.sf3);
+    const uint base = p.a_offset + i03 * p.nb03 + i02 * p.nb02;
+
+    return bicubic(
+        bicubic(FETCH(-1,-1), FETCH(0,-1), FETCH(1,-1), FETCH(2,-1), d.x),
+        bicubic(FETCH(-1, 0), FETCH(0, 0), FETCH(1, 0), FETCH(2, 0), d.x),
+        bicubic(FETCH(-1, 1), FETCH(0, 1), FETCH(1, 1), FETCH(2, 1), d.x),
+        bicubic(FETCH(-1, 2), FETCH(0, 2), FETCH(1, 2), FETCH(2, 2), d.x), d.y);
+}
+
 void main() {
     const uint idx = gl_GlobalInvocationID.z * 262144 + gl_GlobalInvocationID.y * 512 + gl_GlobalInvocationID.x;
 
@@ -81,6 +115,9 @@ void main() {
         case BILINEAR:
             result = interpolate_bilinear(i10, i11, i12, i13);
             break;
+        case BICUBIC:
+            result = interpolate_bicubic(i10, i11, i12, i13);
+            break;
     }
 
     data_d[p.d_offset + idx] = D_TYPE(result);
diff --git a/tests/test-backend-ops.cpp b/tests/test-backend-ops.cpp
index 22635f1635c..eb29b15f204 100644
--- a/tests/test-backend-ops.cpp
+++ b/tests/test-backend-ops.cpp
@@ -272,6 +272,10 @@ static double mean_abs_asymm(const float * a, const float * b, const size_t n, c
 
 // utils for printing the variables of the test cases
 
+static std::string var_to_str(const std::string & x) {
+    return x;
+}
+
 template<typename T>
 static std::string var_to_str(const T & x) {
     return std::to_string(x);
@@ -323,7 +327,8 @@ static std::string var_to_str(ggml_scale_mode mode) {
     switch (mode) {
         case GGML_SCALE_MODE_NEAREST:  return "nearest";
         case GGML_SCALE_MODE_BILINEAR: return "bilinear";
-        default:                      return std::to_string(mode);
+        case GGML_SCALE_MODE_BICUBIC:  return "bicubic";
+        default:                       return std::to_string(mode);
     }
 }
 
@@ -5218,7 +5223,9 @@ struct test_interpolate : public test_case {
     const uint32_t mode = GGML_SCALE_MODE_NEAREST;
 
     std::string vars() override {
-        return VARS_TO_STR4(type, ne, ne_tgt, mode);
+        ggml_scale_mode mode = (ggml_scale_mode)(this->mode & 0xFF);
+        std::string flags = (this->mode & GGML_SCALE_FLAG_ALIGN_CORNERS) ? "align_corners" : "none";
+        return VARS_TO_STR5(type, ne, ne_tgt, mode, flags);
     }
 
     test_interpolate(ggml_type type = GGML_TYPE_F32,
@@ -7288,15 +7295,17 @@ static std::vector<std::unique_ptr<test_case>> make_test_cases_eval() {
         test_cases.emplace_back(new test_argsort(GGML_TYPE_F32, {2, 8, 8192, 1}, order)); // bailingmoe2 (group selection)
     }
 
-    for (ggml_scale_mode mode : {GGML_SCALE_MODE_NEAREST, GGML_SCALE_MODE_BILINEAR}) {
+    for (ggml_scale_mode mode : {GGML_SCALE_MODE_NEAREST, GGML_SCALE_MODE_BILINEAR, GGML_SCALE_MODE_BICUBIC}) {
         test_cases.emplace_back(new test_upscale(GGML_TYPE_F32, {512, 512, 3, 2}, 2, mode));
         test_cases.emplace_back(new test_upscale(GGML_TYPE_F32, {512, 512, 3, 2}, 2, mode, true));
         test_cases.emplace_back(new test_interpolate(GGML_TYPE_F32, {2, 5,  7, 11}, {5, 7, 11, 13}, mode));
         test_cases.emplace_back(new test_interpolate(GGML_TYPE_F32, {5, 7, 11, 13}, {2, 5,  7, 11}, mode));
     }
-    test_cases.emplace_back(new test_interpolate(GGML_TYPE_F32, {2, 5,  7, 11}, {5, 7, 11, 13}, GGML_SCALE_MODE_BILINEAR | GGML_SCALE_FLAG_ALIGN_CORNERS));
-    test_cases.emplace_back(new test_interpolate(GGML_TYPE_F32, {1, 4, 3, 2}, {2, 8, 3, 2}, GGML_SCALE_MODE_BILINEAR | GGML_SCALE_FLAG_ALIGN_CORNERS));
-    test_cases.emplace_back(new test_interpolate(GGML_TYPE_F32, {4, 1, 3, 2}, {1, 1, 3, 2}, GGML_SCALE_MODE_BILINEAR | GGML_SCALE_FLAG_ALIGN_CORNERS));
+    for (ggml_scale_mode mode : {GGML_SCALE_MODE_BILINEAR, GGML_SCALE_MODE_BICUBIC}) {
+        test_cases.emplace_back(new test_interpolate(GGML_TYPE_F32, {2, 5, 7, 11}, {5, 7, 11, 13}, mode | GGML_SCALE_FLAG_ALIGN_CORNERS));
+        test_cases.emplace_back(new test_interpolate(GGML_TYPE_F32, {1, 4, 3, 2}, {2, 8, 3, 2}, mode | GGML_SCALE_FLAG_ALIGN_CORNERS));
+        test_cases.emplace_back(new test_interpolate(GGML_TYPE_F32, {4, 1, 3, 2}, {1, 1, 3, 2}, mode | GGML_SCALE_FLAG_ALIGN_CORNERS));
+    }
 
     test_cases.emplace_back(new test_sum());
     test_cases.emplace_back(new test_sum_rows());

From 9898b57cbe69ab81713e16cbb84a799c6eb3e36c Mon Sep 17 00:00:00 2001
From: Georgi Gerganov <ggerganov@gmail.com>
Date: Mon, 10 Nov 2025 12:17:19 +0200
Subject: [PATCH 140/185] editorconfig : ignore benches/ (#17140)

[no ci]
---
 .editorconfig | 8 ++++++++
 1 file changed, 8 insertions(+)

diff --git a/.editorconfig b/.editorconfig
index 0722ac73c8c..74b65a45668 100644
--- a/.editorconfig
+++ b/.editorconfig
@@ -60,3 +60,11 @@ end_of_line = unset
 charset = unset
 trim_trailing_whitespace = unset
 insert_final_newline = unset
+
+[benches/**]
+indent_style = unset
+indent_size = unset
+end_of_line = unset
+charset = unset
+trim_trailing_whitespace = unset
+insert_final_newline = unset

From 4b13a684c595ab9323be8dfa6266d9d0fb13c232 Mon Sep 17 00:00:00 2001
From: Xuan-Son Nguyen <son@huggingface.co>
Date: Mon, 10 Nov 2025 11:41:05 +0100
Subject: [PATCH 141/185] mtmd: fix patch_size initialized to random value in
 audio models (#17128)

* mtmd: fix patch_size initialized to random value in audio models

* add default hparams
---
 tools/mtmd/clip.cpp | 17 ++++++++++-------
 1 file changed, 10 insertions(+), 7 deletions(-)

diff --git a/tools/mtmd/clip.cpp b/tools/mtmd/clip.cpp
index d1423b67f98..1d78f5954ed 100644
--- a/tools/mtmd/clip.cpp
+++ b/tools/mtmd/clip.cpp
@@ -160,13 +160,13 @@ enum patch_merge_type {
 };
 
 struct clip_hparams {
-    int32_t image_size;
-    int32_t patch_size;
-    int32_t n_embd;
-    int32_t n_ff;
-    int32_t projection_dim;
-    int32_t n_head;
-    int32_t n_layer;
+    int32_t image_size = 0;
+    int32_t patch_size = 0;
+    int32_t n_embd = 0;
+    int32_t n_ff = 0;
+    int32_t projection_dim = 0;
+    int32_t n_head = 0;
+    int32_t n_layer = 0;
     // idefics3
     int32_t image_longest_edge = 0;
     int32_t image_min_pixels = -1;
@@ -2683,6 +2683,9 @@ struct clip_model_loader {
                 }
             } else if (is_audio) {
                 get_u32(KEY_A_NUM_MEL_BINS, hparams.n_mel_bins);
+                // some hparams are unused, but still need to set to avoid issues
+                hparams.image_size = 0;
+                hparams.patch_size = 1;
 
             } else {
                 GGML_ASSERT(false && "unknown modality");

From f914544b16a467a5c94e95ec77027775c3652c09 Mon Sep 17 00:00:00 2001
From: Georgi Gerganov <ggerganov@gmail.com>
Date: Mon, 10 Nov 2025 12:59:29 +0200
Subject: [PATCH 142/185] batched-bench : add "separate text gen" mode (#17103)

---
 common/arg.cpp                        |  7 +++++
 common/common.h                       |  3 +-
 tools/batched-bench/batched-bench.cpp | 42 ++++++++++++++++++++-------
 3 files changed, 40 insertions(+), 12 deletions(-)

diff --git a/common/arg.cpp b/common/arg.cpp
index a5708102814..430ab45dfe2 100644
--- a/common/arg.cpp
+++ b/common/arg.cpp
@@ -2253,6 +2253,13 @@ common_params_context common_params_parser_init(common_params & params, llama_ex
             params.is_pp_shared = true;
         }
     ).set_examples({LLAMA_EXAMPLE_BENCH, LLAMA_EXAMPLE_PARALLEL}));
+    add_opt(common_arg(
+        {"-tgs"},
+        string_format("is the text generation separated across the different sequences (default: %s)", params.is_tg_separate ? "true" : "false"),
+        [](common_params & params) {
+            params.is_tg_separate = true;
+        }
+    ).set_examples({LLAMA_EXAMPLE_BENCH, LLAMA_EXAMPLE_PARALLEL}));
     add_opt(common_arg(
         {"-npp"}, "n0,n1,...",
         "number of prompt tokens",
diff --git a/common/common.h b/common/common.h
index 8540725aaa4..f42c083faa2 100644
--- a/common/common.h
+++ b/common/common.h
@@ -460,7 +460,8 @@ struct common_params {
     float slot_prompt_similarity = 0.1f;
 
     // batched-bench params
-    bool is_pp_shared = false;
+    bool is_pp_shared   = false;
+    bool is_tg_separate = false;
 
     std::vector<int32_t> n_pp;
     std::vector<int32_t> n_tg;
diff --git a/tools/batched-bench/batched-bench.cpp b/tools/batched-bench/batched-bench.cpp
index f1ab27cd54d..2032a386bb4 100644
--- a/tools/batched-bench/batched-bench.cpp
+++ b/tools/batched-bench/batched-bench.cpp
@@ -23,7 +23,8 @@ int main(int argc, char ** argv) {
 
     common_init();
 
-    int is_pp_shared = params.is_pp_shared;
+    int is_pp_shared   = params.is_pp_shared;
+    int is_tg_separate = params.is_tg_separate;
 
     std::vector<int> n_pp = params.n_pp;
     std::vector<int> n_tg = params.n_tg;
@@ -72,8 +73,8 @@ int main(int argc, char ** argv) {
 
     // decode in batches of ctx_params.n_batch tokens
     auto decode_helper = [](llama_context * ctx, llama_batch & batch, int32_t n_batch, bool synchronize) {
-        for (int32_t i = 0; i < (int32_t) batch.n_tokens; i += n_batch) {
-            const int32_t n_tokens = std::min(n_batch, (int32_t) (batch.n_tokens - i));
+        for (int32_t i = 0; i < batch.n_tokens; i += n_batch) {
+            const int32_t n_tokens = std::min(n_batch, batch.n_tokens - i);
 
             llama_batch batch_view = {
                 n_tokens,
@@ -113,7 +114,7 @@ int main(int argc, char ** argv) {
 
     if (!params.batched_bench_output_jsonl) {
         LOG("\n");
-        LOG("%s: n_kv_max = %d, n_batch = %d, n_ubatch = %d, flash_attn = %d, is_pp_shared = %d, n_gpu_layers = %d, n_threads = %u, n_threads_batch = %u\n", __func__, n_kv_max, params.n_batch, params.n_ubatch, int(params.flash_attn_type), params.is_pp_shared, params.n_gpu_layers, ctx_params.n_threads, ctx_params.n_threads_batch);
+        LOG("%s: n_kv_max = %d, n_batch = %d, n_ubatch = %d, flash_attn = %d, is_pp_shared = %d, is_tg_separate = %d, n_gpu_layers = %d, n_threads = %u, n_threads_batch = %u\n", __func__, n_kv_max, params.n_batch, params.n_ubatch, int(params.flash_attn_type), is_pp_shared, is_tg_separate, params.n_gpu_layers, ctx_params.n_threads, ctx_params.n_threads_batch);
         LOG("\n");
         LOG("|%6s | %6s | %4s | %6s | %8s | %8s | %8s | %8s | %8s | %8s |\n", "PP", "TG", "B", "N_KV", "T_PP s", "S_PP t/s", "T_TG s", "S_TG t/s", "T s", "S t/s");
         LOG("|%6s-|-%6s-|-%4s-|-%6s-|-%8s-|-%8s-|-%8s-|-%8s-|-%8s-|-%8s-|\n", "------", "------", "----", "------", "--------", "--------", "--------", "--------", "--------", "--------");
@@ -172,16 +173,35 @@ int main(int argc, char ** argv) {
 
                 const auto t_tg_start = ggml_time_us();
 
-                for (int i = 0; i < tg; ++i) {
-                    common_batch_clear(batch);
-
+                if (is_tg_separate) {
+                    // decode pattern:
+                    // 0 0 0 ... 1 1 1 ... 2 2 2 ... 3 3 3 ...
                     for (int j = 0; j < pl; ++j) {
-                        common_batch_add(batch, get_token_rand(), pp + i, { j }, true);
+                        for (int i = 0; i < tg; ++i) {
+                            common_batch_clear(batch);
+
+                            common_batch_add(batch, get_token_rand(), pp + i, { j }, true);
+
+                            if (!decode_helper(ctx, batch, ctx_params.n_batch, true)) {
+                                LOG_ERR("%s: llama_decode() failed\n", __func__);
+                                return 1;
+                            }
+                        }
                     }
+                } else {
+                    // decode pattern:
+                    // 0123 0123 0123 ...
+                    for (int i = 0; i < tg; ++i) {
+                        common_batch_clear(batch);
 
-                    if (!decode_helper(ctx, batch, ctx_params.n_batch, true)) {
-                        LOG_ERR("%s: llama_decode() failed\n", __func__);
-                        return 1;
+                        for (int j = 0; j < pl; ++j) {
+                            common_batch_add(batch, get_token_rand(), pp + i, { j }, true);
+                        }
+
+                        if (!decode_helper(ctx, batch, ctx_params.n_batch, true)) {
+                            LOG_ERR("%s: llama_decode() failed\n", __func__);
+                            return 1;
+                        }
                     }
                 }
 

From df70bedda70550fd9ebc4bc965c5dbc3f6d78345 Mon Sep 17 00:00:00 2001
From: fj-y-saito <85871716+fj-y-saito@users.noreply.github.com>
Date: Mon, 10 Nov 2025 22:12:59 +0900
Subject: [PATCH 143/185] =?UTF-8?q?arm64:=20add=20i8mm=20route=20with=20SV?=
 =?UTF-8?q?E=20ggml=5Fvec=5Fdot=5Fq4=5FK=5Fq8=5FK=20and=20ggml=5Fvec=5Fdot?=
 =?UTF-8?q?=5Fq6=5FK=5F=E2=80=A6=20(#15277)?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

* add i8mm route with SVE ggml_vec_dot_q4_K_q8_K and ggml_vec_dot_q6_K_q8_K

* Surround SVE function with compiler directive

* fix compile switch

* fix coding style

* ggml : fix indent

---------

Co-authored-by: Georgi Gerganov <ggerganov@gmail.com>
---
 ggml/src/ggml-cpu/arch/arm/quants.c | 454 ++++++++++++++++++++++++++--
 1 file changed, 428 insertions(+), 26 deletions(-)

diff --git a/ggml/src/ggml-cpu/arch/arm/quants.c b/ggml/src/ggml-cpu/arch/arm/quants.c
index aadbb487ec0..b390ab61c78 100644
--- a/ggml/src/ggml-cpu/arch/arm/quants.c
+++ b/ggml/src/ggml-cpu/arch/arm/quants.c
@@ -2044,6 +2044,26 @@ void ggml_vec_dot_q3_K_q8_K(int n, float * GGML_RESTRICT s, size_t bs, const voi
 
 }
 
+#ifdef __ARM_FEATURE_SVE
+static inline svuint32_t ggml_decode_q4scales_and_mins_for_mmla(const uint32_t * vx_scales) {
+    const svbool_t pg_all   = svptrue_pat_b32(SV_VL4);
+    const svbool_t pg_false = svpfalse_b();            // 0x0000
+    const svbool_t pg_lo_8  = svwhilelt_b8_s32(0,  8); // 0x00ff
+    const svbool_t pg_odd   = svzip1_b32(pg_false, pg_lo_8);
+
+    svuint32_t vutmp_hi, vutmp_lo;
+    svuint32_t vx01 = svld1_u32(pg_lo_8, vx_scales);
+    vutmp_hi = svzip1_u32(vx01, vx01);
+    vutmp_hi = svlsr_n_u32_m(pg_odd, vutmp_hi, 2);
+    vutmp_hi = svreinterpret_u32_u64(svand_n_u64_x(pg_all, svreinterpret_u64_u32(vutmp_hi), UINT64_C(0x303030303f3f3f3f)));
+    const svuint32_t vx2 = svdup_u32(vx_scales[2]);
+    vutmp_lo = svlsr_u32_x(pg_all, vx2, svreinterpret_u32_s32(svindex_s32(-2, 2)));
+    vutmp_lo = svand_n_u32_z(pg_odd, vutmp_lo, UINT32_C(0x0f0f0f0f));
+    svuint32_t vutmp = svorr_u32_z(pg_all, vutmp_hi, vutmp_lo);
+    return vutmp;
+}
+#endif
+
 void ggml_vec_dot_q4_K_q8_K(int n, float * GGML_RESTRICT s, size_t bs, const void * GGML_RESTRICT vx, size_t bx, const void * GGML_RESTRICT vy, size_t by, int nrc) {
     assert(n % QK_K == 0);
 #ifdef __ARM_FEATURE_MATMUL_INT8
@@ -2066,8 +2086,220 @@ void ggml_vec_dot_q4_K_q8_K(int n, float * GGML_RESTRICT s, size_t bs, const voi
     static const uint32_t kmask3 = 0x03030303;
 
     uint32_t utmp[4];
+#ifdef __ARM_FEATURE_SVE
+    const int vector_length = ggml_cpu_get_sve_cnt()*8;
+#endif
 
-#if defined(__ARM_FEATURE_MATMUL_INT8)
+#if defined(__ARM_FEATURE_SVE) && defined(__ARM_FEATURE_MATMUL_INT8)
+    if (nrc == 2) {
+        svbool_t pg32_2 = svptrue_pat_b32(SV_VL2);
+
+        const block_q4_K * GGML_RESTRICT vx0 = vx;
+        const block_q8_K * GGML_RESTRICT vy0 = vy;
+        const block_q4_K * GGML_RESTRICT vx1 = (const block_q4_K *) ((const uint8_t*)vx + bx);
+        const block_q8_K * GGML_RESTRICT vy1 = (const block_q8_K *) ((const uint8_t*)vy + by);
+
+        union {
+            uint32_t u32[8];
+            uint64_t u64[4];
+        } new_utmp;
+
+        svfloat32_t sumf1 = svdup_n_f32(0);
+
+        switch (vector_length) {
+            case 128:
+                {
+                    svbool_t pg_false = svpfalse_b();
+                    svbool_t pg_lo_8  = svwhilelt_b8_s32(0,  8);
+                    svbool_t vmins_mask1= svzip1_b32(pg_lo_8, pg_false);
+                    svbool_t vmins_mask2 = svzip1_b32(pg_false, pg_lo_8);
+                    svbool_t pg128_all  = svptrue_pat_b8(SV_VL16);
+                    for (int i = 0; i < nb; ++i) {
+                        svfloat32_t vy_d = svuzp1_f32(svdup_n_f32(vy0[i].d), svdup_n_f32(vy1[i].d));
+                        svfloat32_t vx_d = svzip1_f32(svdup_n_f32(GGML_FP16_TO_FP32(vx0[i].d)), svdup_n_f32(GGML_FP16_TO_FP32(vx1[i].d)));
+                        svfloat32_t svsuper_block_scales = svmul_f32_x(pg128_all, vy_d, vx_d);
+                        svfloat32_t vx_dmins = svzip1_f32(svdup_n_f32(GGML_FP16_TO_FP32(vx0[i].dmin)), svdup_n_f32(GGML_FP16_TO_FP32(vx1[i].dmin)));
+                        svfloat32_t vy_dmins = svuzp1_f32(svdup_n_f32(vy0[i].d), svdup_n_f32(vy1[i].d));
+                        svfloat32_t svdmins = svmul_n_f32_x(pg128_all, svmul_f32_x(pg128_all, vy_dmins, vx_dmins), -1);
+                        const uint8_t * GGML_RESTRICT q4_0 = vx0[i].qs;
+                        const int8_t  * GGML_RESTRICT q8_0 = vy0[i].qs;
+                        const uint8_t * GGML_RESTRICT q4_1 = vx1[i].qs;
+                        const int8_t  * GGML_RESTRICT q8_1 = vy1[i].qs;
+                        svint16_t lo = svld1_s16(pg128_all, vy0[i].bsums + 0);
+                        svint16_t hi = svld1_s16(pg128_all, vy0[i].bsums + 8);
+                        svint16_t sum_tmp1 = svuzp1_s16(lo, hi);
+                        svint16_t sum_tmp2 = svuzp2_s16(lo, hi);
+                        svint16_t svq8sums_0 = svadd_s16_x(pg128_all, sum_tmp1, sum_tmp2);
+                        lo = svld1_s16(pg128_all, vy1[i].bsums + 0);
+                        hi = svld1_s16(pg128_all, vy1[i].bsums + 8);
+                        sum_tmp1 = svuzp1(lo, hi);
+                        sum_tmp2 = svuzp2(lo, hi);
+                        svint16_t svq8sums_1 = svadd_s16_x(pg128_all, sum_tmp1, sum_tmp2);
+                        svuint32_t decoded_scales0 = ggml_decode_q4scales_and_mins_for_mmla((const uint32_t *)vx0[i].scales);
+                        svuint32_t decoded_scales1 = ggml_decode_q4scales_and_mins_for_mmla((const uint32_t *)vx1[i].scales);
+                        svuint32x2_t decoded_scales = svcreate2_u32(decoded_scales0, decoded_scales1);
+                        svst2_u32(pg128_all, new_utmp.u32, decoded_scales);
+                        svint16_t svmins8_0 = svreinterpret_s16_u16(svunpklo_u16(svreinterpret_u8_u32(svuzp1_u32(svld1_u32(vmins_mask1, new_utmp.u32+4), svdup_n_u32(0)))));
+                        svint16_t svmins8_1 = svreinterpret_s16_u16(svunpklo_u16(svreinterpret_u8_u32(svuzp2_u32(svld1_u32(vmins_mask2, new_utmp.u32+4), svdup_n_u32(0)))));
+                        svint32_t svsumfs_tmp1 = svreinterpret_s32_s64(svdot_s64(svdup_n_s64(0), svq8sums_0, svmins8_0));
+                        svint32_t svsumfs_tmp2 = svreinterpret_s32_s64(svdot_s64(svdup_n_s64(0), svq8sums_0, svmins8_1));
+                        svint32_t svsumfs_tmp3 = svtrn1_s32(svsumfs_tmp1, svsumfs_tmp2);
+                        svint32_t svsumfs_tmp4 = svreinterpret_s32_s64(svdot_s64(svdup_n_s64(0), svq8sums_1, svmins8_0));
+                        svint32_t svsumfs_tmp5 = svreinterpret_s32_s64(svdot_s64(svdup_n_s64(0), svq8sums_1, svmins8_1));
+                        svint32_t svsumfs_tmp6 = svtrn1_s32(svsumfs_tmp4, svsumfs_tmp5);
+                        svint32_t svsumfs_tmp7 = svreinterpret_s32_s64(svtrn2_s64(svreinterpret_s64_s32(svsumfs_tmp3), svreinterpret_s64_s32(svsumfs_tmp6)));
+                        svint32_t svsumfs_tmp8 = svreinterpret_s32_s64(svtrn1_s64(svreinterpret_s64_s32(svsumfs_tmp3), svreinterpret_s64_s32(svsumfs_tmp6)));
+                        svint32_t svsumfs_tmp = svadd_s32_x(pg128_all, svsumfs_tmp7, svsumfs_tmp8);
+                        svint32_t svscales, sumi1, sumi2;
+                        svint32_t acc_sumif1 = svdup_n_s32(0);
+                        svint32_t acc_sumif2 = svdup_n_s32(0);
+                        svint8_t q4bytes_0_l, q4bytes_0_h, q4bytes_1_l, q4bytes_1_h, l0, l1, l2, l3,
+                                 q8bytes_0_h, q8bytes_0_l, q8bytes_1_h, q8bytes_1_l, r0, r1, r2, r3;
+#pragma GCC unroll 1
+                        for (int j = 0; j < QK_K/64; ++j) {
+                            q4bytes_0_l = svreinterpret_s8_u8(svand_n_u8_x(pg128_all, svld1_u8(pg128_all, q4_0), 0xf));
+                            q4bytes_1_l = svreinterpret_s8_u8(svand_n_u8_x(pg128_all, svld1_u8(pg128_all, q4_1), 0xf));
+                            q4bytes_0_h = svreinterpret_s8_u8(svand_n_u8_x(pg128_all, svld1_u8(pg128_all, q4_0+16), 0xf));
+                            q4bytes_1_h = svreinterpret_s8_u8(svand_n_u8_x(pg128_all, svld1_u8(pg128_all, q4_1+16), 0xf));
+                            l0 = svreinterpret_s8_s64(svzip1_s64(svreinterpret_s64_s8(q4bytes_0_l), svreinterpret_s64_s8(q4bytes_1_l)));
+                            l1 = svreinterpret_s8_s64(svzip2_s64(svreinterpret_s64_s8(q4bytes_0_l), svreinterpret_s64_s8(q4bytes_1_l)));
+                            l2 = svreinterpret_s8_s64(svzip1_s64(svreinterpret_s64_s8(q4bytes_0_h), svreinterpret_s64_s8(q4bytes_1_h)));
+                            l3 = svreinterpret_s8_s64(svzip2_s64(svreinterpret_s64_s8(q4bytes_0_h), svreinterpret_s64_s8(q4bytes_1_h)));
+                            q8bytes_0_h = svld1_s8(pg128_all, q8_0);
+                            q8bytes_1_h = svld1_s8(pg128_all, q8_1);
+                            q8bytes_0_l = svld1_s8(pg128_all, q8_0+16);
+                            q8bytes_1_l = svld1_s8(pg128_all, q8_1+16);
+                            r0 = svreinterpret_s8_s64(svzip1_s64(svreinterpret_s64_s8(q8bytes_0_h), svreinterpret_s64_s8(q8bytes_1_h)));
+                            r1 = svreinterpret_s8_s64(svzip2_s64(svreinterpret_s64_s8(q8bytes_0_h), svreinterpret_s64_s8(q8bytes_1_h)));
+                            r2 = svreinterpret_s8_s64(svzip1_s64(svreinterpret_s64_s8(q8bytes_0_l), svreinterpret_s64_s8(q8bytes_1_l)));
+                            r3 = svreinterpret_s8_s64(svzip2_s64(svreinterpret_s64_s8(q8bytes_0_l), svreinterpret_s64_s8(q8bytes_1_l)));
+                            sumi1 = svmmla_s32(svmmla_s32(svmmla_s32(svmmla_s32(svdup_n_s32(0), r0, l0), r1, l1), r2, l2), r3, l3);
+                            svscales = svreinterpret_s32_u32(svlsr_n_u32_x(pg128_all, svlsl_n_u32_x(pg128_all, svreinterpret_u32_u64(svdup_n_u64(new_utmp.u64[j/2])), 8*(4-2*(j%2)-1)), 24));
+                            acc_sumif1 = svmla_s32_x(pg128_all, acc_sumif1, svscales, sumi1);
+
+                            q4bytes_0_l = svreinterpret_s8_u8(svlsr_n_u8_x(pg128_all, svld1_u8(pg128_all, q4_0), 4));
+                            q4bytes_1_l = svreinterpret_s8_u8(svlsr_n_u8_x(pg128_all, svld1_u8(pg128_all, q4_1), 4));
+                            q4bytes_0_h = svreinterpret_s8_u8(svlsr_n_u8_x(pg128_all, svld1_u8(pg128_all, q4_0+16), 4));
+                            q4bytes_1_h = svreinterpret_s8_u8(svlsr_n_u8_x(pg128_all, svld1_u8(pg128_all, q4_1+16), 4));
+                            l0 = svreinterpret_s8_s64(svzip1_s64(svreinterpret_s64_s8(q4bytes_0_l), svreinterpret_s64_s8(q4bytes_1_l)));
+                            l1 = svreinterpret_s8_s64(svzip2_s64(svreinterpret_s64_s8(q4bytes_0_l), svreinterpret_s64_s8(q4bytes_1_l)));
+                            l2 = svreinterpret_s8_s64(svzip1_s64(svreinterpret_s64_s8(q4bytes_0_h), svreinterpret_s64_s8(q4bytes_1_h)));
+                            l3 = svreinterpret_s8_s64(svzip2_s64(svreinterpret_s64_s8(q4bytes_0_h), svreinterpret_s64_s8(q4bytes_1_h)));
+                            q8bytes_0_h = svld1_s8(pg128_all, q8_0+32);
+                            q8bytes_1_h = svld1_s8(pg128_all, q8_1+32);
+                            q8bytes_0_l = svld1_s8(pg128_all, q8_0+48);
+                            q8bytes_1_l = svld1_s8(pg128_all, q8_1+48);
+                            r0 = svreinterpret_s8_s64(svzip1_s64(svreinterpret_s64_s8(q8bytes_0_h), svreinterpret_s64_s8(q8bytes_1_h)));
+                            r1 = svreinterpret_s8_s64(svzip2_s64(svreinterpret_s64_s8(q8bytes_0_h), svreinterpret_s64_s8(q8bytes_1_h)));
+                            r2 = svreinterpret_s8_s64(svzip1_s64(svreinterpret_s64_s8(q8bytes_0_l), svreinterpret_s64_s8(q8bytes_1_l)));
+                            r3 = svreinterpret_s8_s64(svzip2_s64(svreinterpret_s64_s8(q8bytes_0_l), svreinterpret_s64_s8(q8bytes_1_l)));
+                            sumi2 = svmmla_s32(svmmla_s32(svmmla_s32(svmmla_s32(svdup_n_s32(0), r0, l0), r1, l1), r2, l2), r3, l3);
+                            svscales = svreinterpret_s32_u32(svlsr_n_u32_x(pg128_all, svlsl_n_u32_x(pg128_all, svreinterpret_u32_u64(svdup_n_u64(new_utmp.u64[j/2])), 8*(4-2*(j%2)-2)), 24));
+                            acc_sumif2 = svmla_s32_x(pg128_all, acc_sumif2, svscales, sumi2);
+                            q4_0 += 32; q4_1 += 32; q8_0 += 64; q8_1 += 64;
+                        }
+                        sumf1 = svmla_f32_x(pg128_all,
+                                svmla_f32_x(pg128_all,
+                                    sumf1,
+                                    svcvt_f32_x(pg128_all,
+                                        svadd_s32_x(pg128_all, acc_sumif1, acc_sumif2)),
+                                    svsuper_block_scales),
+                                svdmins,
+                                svcvt_f32_s32_x(pg128_all, svsumfs_tmp));
+                    }  //end of for nb
+                } // end of case 128
+                break;
+            case 256:
+            case 512:
+                {
+                    const svbool_t pg32_4 = svptrue_pat_b32(SV_VL4);
+                    const svbool_t pg8_16 = svptrue_pat_b8(SV_VL16);
+                    const svbool_t pg256_all = svptrue_pat_b8(SV_ALL);
+                    for (int i = 0; i < nb; ++i) {
+                        const uint8_t * GGML_RESTRICT q4_0 = vx0[i].qs;
+                        const int8_t  * GGML_RESTRICT q8_0 = vy0[i].qs;
+                        const uint8_t * GGML_RESTRICT q4_1 = vx1[i].qs;
+                        const int8_t  * GGML_RESTRICT q8_1 = vy1[i].qs;
+                        svint32_t svscales, sumi1, sumi2;
+                        svint32_t acc_sumif1 = svdup_n_s32(0);
+                        svint32_t acc_sumif2 = svdup_n_s32(0);
+                        svint8_t l0, l1, l2, l3, r0, r1, r2, r3;
+                        svfloat32_t vx_d = svzip1_f32(svdup_n_f32(GGML_FP16_TO_FP32(vx0[i].d)), svdup_n_f32(GGML_FP16_TO_FP32(vx1[i].d)));
+                        svfloat64_t vy_d_tmp = svreinterpret_f64_f32(svuzp1_f32(svdup_n_f32(vy0[i].d), svdup_n_f32(vy1[i].d)));
+                        svfloat32_t vy_d = svreinterpret_f32_f64(svuzp1_f64(vy_d_tmp, vy_d_tmp));
+                        svfloat32_t svsuper_block_scales = svmul_f32_z(pg32_4, vy_d, vx_d);
+                        svfloat32_t vx_dmins = svzip1_f32(svdup_n_f32(GGML_FP16_TO_FP32(vx0[i].dmin)), svdup_n_f32(GGML_FP16_TO_FP32(vx1[i].dmin)));
+                        svfloat64_t vy_dmins_tmp = svreinterpret_f64_f32(svuzp1_f32(svdup_n_f32(vy0[i].d), svdup_n_f32(vy1[i].d)));
+                        svfloat32_t vy_dmins = svreinterpret_f32_f64(svuzp1_f64(vy_dmins_tmp, vy_dmins_tmp));
+                        svfloat32_t svdmins = svmul_n_f32_x(pg32_4, svmul_f32_x(pg32_4, vx_dmins, vy_dmins), -1);
+                        svint16_t rc1 = svuzp1_s16(svld1_s16(pg256_all, vy0[i].bsums), svld1_s16(pg256_all, vy1[i].bsums));
+                        svint16_t rc2 = svuzp2_s16(svld1_s16(pg256_all, vy0[i].bsums), svld1_s16(pg256_all, vy1[i].bsums));
+                        svint16_t svq8sums = svadd_s16_x(pg256_all, rc1, rc2);
+                        svuint32_t decoded_scales0 = ggml_decode_q4scales_and_mins_for_mmla((const uint32_t *)vx0[i].scales);
+                        svuint32_t decoded_scales1 = ggml_decode_q4scales_and_mins_for_mmla((const uint32_t *)vx1[i].scales);
+                        svuint32x2_t decoded_scales = svcreate2_u32(decoded_scales0, decoded_scales1);
+                        svst2_u32(pg8_16, new_utmp.u32, decoded_scales);
+                        svint16_t new_svq8sums_0 = svreinterpret_s16_u64(svtrn1_u64(svreinterpret_u64_s16(svq8sums), svreinterpret_u64_s16(svq8sums)));
+                        svint16_t new_svq8sums_1 = svreinterpret_s16_u64(svtrn2_u64(svreinterpret_u64_s16(svq8sums), svreinterpret_u64_s16(svq8sums)));
+                        svuint64_t new_mins_0 = svdup_u64(new_utmp.u64[2]);
+                        svuint64_t new_mins_1 = svdup_u64(new_utmp.u64[3]);
+                        svint16_t new_svmins8_0 = svreinterpret_s16_u16(svunpklo_u16(svreinterpret_u8_u64(new_mins_0)));
+                        svint16_t new_svmins8_1 = svreinterpret_s16_u16(svunpklo_u16(svreinterpret_u8_u64(new_mins_1)));
+                        svint64_t dot_prod_0 = svdot_s64(svdup_s64(0), new_svmins8_0, new_svq8sums_0);
+                        svint64_t dot_prod_1 = svdot_s64(dot_prod_0, new_svmins8_1, new_svq8sums_1);
+                        svfloat32_t converted_dot_prod_1 = svcvt_f32_s64_x(pg256_all, dot_prod_1);
+                        svfloat32_t svsumfs_tmp = svuzp1_f32(converted_dot_prod_1, converted_dot_prod_1);
+
+#pragma GCC unroll 1
+                        for (int j = 0; j < QK_K/64; ++j) {
+                            svuint8_t q4bytes_0 = svand_n_u8_x(pg256_all, svld1_u8(pg256_all, q4_0), 0xf);
+                            svuint8_t q4bytes_1 = svand_n_u8_x(pg256_all, svld1_u8(pg256_all, q4_1), 0xf);
+                            svuint8_t q4bytes_2 = svlsr_n_u8_x(pg256_all, svld1_u8(pg256_all, q4_0), 4);
+                            svuint8_t q4bytes_3 = svlsr_n_u8_x(pg256_all, svld1_u8(pg256_all, q4_1), 4);
+                            l0 = svreinterpret_s8_u64(svzip1_u64(svreinterpret_u64_u8(q4bytes_0), svreinterpret_u64_u8(q4bytes_1)));
+                            l1 = svreinterpret_s8_u64(svzip2_u64(svreinterpret_u64_u8(q4bytes_0), svreinterpret_u64_u8(q4bytes_1)));
+                            l2 = svreinterpret_s8_u64(svzip1_u64(svreinterpret_u64_u8(q4bytes_2), svreinterpret_u64_u8(q4bytes_3)));
+                            l3 = svreinterpret_s8_u64(svzip2_u64(svreinterpret_u64_u8(q4bytes_2), svreinterpret_u64_u8(q4bytes_3)));
+                            svint8_t q8bytes_0 = svld1_s8(pg256_all, q8_0);
+                            svint8_t q8bytes_1 = svld1_s8(pg256_all, q8_1);
+                            svint8_t q8bytes_2 = svld1_s8(pg256_all, q8_0+32);
+                            svint8_t q8bytes_3 = svld1_s8(pg256_all, q8_1+32);
+                            r0 = svreinterpret_s8_s64(svzip1_s64(svreinterpret_s64_s8(q8bytes_0), svreinterpret_s64_s8(q8bytes_1)));
+                            r1 = svreinterpret_s8_s64(svzip2_s64(svreinterpret_s64_s8(q8bytes_0), svreinterpret_s64_s8(q8bytes_1)));
+                            r2 = svreinterpret_s8_s64(svzip1_s64(svreinterpret_s64_s8(q8bytes_2), svreinterpret_s64_s8(q8bytes_3)));
+                            r3 = svreinterpret_s8_s64(svzip2_s64(svreinterpret_s64_s8(q8bytes_2), svreinterpret_s64_s8(q8bytes_3)));
+                            sumi1 = svmmla(svmmla(svdup_n_s32(0), r0, l0), r1, l1);
+                            svscales = svreinterpret_s32_u32(svlsr_n_u32_x(pg256_all, svlsl_n_u32_x(pg256_all, svreinterpret_u32_u64(svdup_n_u64(new_utmp.u64[j/2])), 8*(4-2*(j%2)-1)), 24));
+                            acc_sumif1 = svmla_s32_x(pg256_all, acc_sumif1, svscales, sumi1);
+                            sumi2 = svmmla(svmmla(svdup_n_s32(0), r2, l2), r3, l3);
+                            svscales = svreinterpret_s32_u32(svlsr_n_u32_x(pg256_all, svlsl_n_u32_x(pg256_all, svreinterpret_u32_u64(svdup_n_u64(new_utmp.u64[j/2])), 8*(4-2*(j%2)-2)), 24));
+                            acc_sumif2 = svmla_s32_x(pg256_all, acc_sumif2, svscales, sumi2);
+                            q4_0 += 32; q4_1 += 32; q8_0 += 64; q8_1 += 64;
+                        }
+                        svint32_t acc_sumif = svadd_s32_x(pg256_all, acc_sumif1, acc_sumif2);
+                        svint32_t swap_acc_sumif = svext_s32(acc_sumif, acc_sumif, 4);
+                        acc_sumif = svadd_s32_x(pg32_4, acc_sumif, swap_acc_sumif);
+                        sumf1 = svmla_f32_x(pg32_4,
+                                svmla_f32_x(pg32_4,
+                                    sumf1,
+                                    svcvt_f32_x(pg32_4, acc_sumif),
+                                    svsuper_block_scales),
+                                svdmins,
+                                svsumfs_tmp);
+                    } // end of for nb
+                } // end of case 256-512
+                break;
+            default:
+                assert(false && "Unsupported vector length");
+                break;
+        }
+
+        svst1_f32(pg32_2, s, sumf1);
+        svst1_f32(pg32_2, s + bs, svreinterpret_f32_u8(svext_u8(svreinterpret_u8_f32(sumf1), svdup_n_u8(0), 8)));
+
+        return;
+    }
+#elif defined(__ARM_FEATURE_MATMUL_INT8)
     if (nrc == 2) {
         const block_q4_K * GGML_RESTRICT x0 = x;
         const block_q4_K * GGML_RESTRICT x1 = (const block_q4_K *) ((const uint8_t *)vx + bx);
@@ -2235,7 +2467,6 @@ void ggml_vec_dot_q4_K_q8_K(int n, float * GGML_RESTRICT s, size_t bs, const voi
         const uint8_t * GGML_RESTRICT q4 = x[i].qs;
         const int8_t  * GGML_RESTRICT q8 = y[i].qs;
 
-        const int vector_length = ggml_cpu_get_sve_cnt()*8;
         const svuint8_t m4b = svdup_n_u8(0xf);
         const svint32_t mzero = svdup_n_s32(0);
         svint32_t sumi1 = svdup_n_s32(0);
@@ -2480,7 +2711,201 @@ void ggml_vec_dot_q6_K_q8_K(int n, float * GGML_RESTRICT s, size_t bs, const voi
 
     const int nb = n / QK_K;
 
-#if defined(__ARM_FEATURE_MATMUL_INT8)
+#ifdef __ARM_FEATURE_SVE
+    const int vector_length = ggml_cpu_get_sve_cnt()*8;
+#endif
+#if defined(__ARM_FEATURE_SVE) && defined(__ARM_FEATURE_MATMUL_INT8)
+    if (nrc == 2) {
+        const svbool_t pg32_2 = svptrue_pat_b32(SV_VL2);
+
+        svfloat32_t sum = svdup_n_f32(0);
+
+        const block_q6_K * GGML_RESTRICT vx0 = vx;
+        const block_q8_K * GGML_RESTRICT vy0 = vy;
+        const block_q6_K * GGML_RESTRICT vx1 = (const block_q6_K *) ((const uint8_t*)vx + bx);
+        const block_q8_K * GGML_RESTRICT vy1 = (const block_q8_K *) ((const uint8_t*)vy + by);
+
+        switch (vector_length) {
+            case 128:
+                {
+                    const svbool_t pg128_all = svptrue_pat_b8(SV_ALL);
+                    for (int i = 0; i < nb; ++i) {
+                        const uint8_t * GGML_RESTRICT ql0 = vx0[i].ql;
+                        const uint8_t * GGML_RESTRICT qh0 = vx0[i].qh;
+                        const uint8_t * GGML_RESTRICT ql1 = vx1[i].ql;
+                        const uint8_t * GGML_RESTRICT qh1 = vx1[i].qh;
+                        const int8_t  * GGML_RESTRICT q80 = vy0[i].qs;
+                        const int8_t  * GGML_RESTRICT q81 = vy1[i].qs;
+
+                        const int8_t * GGML_RESTRICT scale0 = vx0[i].scales;
+                        const int8_t * GGML_RESTRICT scale1 = vx1[i].scales;
+
+                        svfloat32_t vy_d = svuzp1_f32(svdup_n_f32(vy0[i].d), svdup_n_f32(vy1[i].d));
+                        svfloat32_t vx_d = svzip1_f32(svdup_n_f32(GGML_FP16_TO_FP32(vx0[i].d)), svdup_n_f32(GGML_FP16_TO_FP32(vx1[i].d)));
+                        svfloat32_t svsuper_block_scales = svmul_f32_x(pg128_all, vy_d, vx_d);
+                        // process q8sum summation 128 bit route
+                        const svint16_t q8sums_01 = svld1_s16(pg128_all, vy0[i].bsums);
+                        const svint16_t q8sums_02 = svld1_s16(pg128_all, vy0[i].bsums + 8);
+                        const svint16_t q8sums_11 = svld1_s16(pg128_all, vy1[i].bsums);
+                        const svint16_t q8sums_12 = svld1_s16(pg128_all, vy1[i].bsums + 8);
+                        const svint64x2_t q6scales_0_tmp = svld2_s64(pg128_all, (const int64_t *)scale0);
+                        const svint16_t q6scales_01 = svunpklo_s16(svreinterpret_s8_s64(svget2_s64(q6scales_0_tmp, 0)));
+                        const svint16_t q6scales_02 = svunpklo_s16(svreinterpret_s8_s64(svget2_s64(q6scales_0_tmp, 1)));
+                        const svint64x2_t q6scales_1_tmp = svld2_s64(pg128_all, (const int64_t *)scale1);
+                        const svint16_t q6scales_11 = svunpklo_s16(svreinterpret_s8_s64(svget2_s64(q6scales_1_tmp, 0)));
+                        const svint16_t q6scales_12 = svunpklo_s16(svreinterpret_s8_s64(svget2_s64(q6scales_1_tmp, 1)));
+                        const svint64_t prod = svdup_n_s64(0);
+
+                        svint32_t isum_tmp1 = svreinterpret_s32_s64(svdot_s64(svdot_s64(prod, q8sums_01, q6scales_01), q8sums_02, q6scales_02));
+                        svint32_t isum_tmp2 = svreinterpret_s32_s64(svdot_s64(svdot_s64(prod, q8sums_01, q6scales_11), q8sums_02, q6scales_12));
+                        svint32_t isum_tmp3 = svtrn1_s32(isum_tmp1, isum_tmp2);
+                        svint32_t isum_tmp4 = svreinterpret_s32_s64(svdot_s64(svdot_s64(prod, q8sums_11, q6scales_01), q8sums_12, q6scales_02));
+                        svint32_t isum_tmp5 = svreinterpret_s32_s64(svdot_s64(svdot_s64(prod, q8sums_11, q6scales_11), q8sums_12, q6scales_12));
+                        svint32_t isum_tmp6 = svtrn1_s32(isum_tmp4, isum_tmp5);
+                        svint32_t isum_tmp7 = svreinterpret_s32_s64(svtrn2_s64(svreinterpret_s64_s32(isum_tmp3), svreinterpret_s64_s32(isum_tmp6)));
+                        svint32_t isum_tmp8 = svreinterpret_s32_s64(svtrn1_s64(svreinterpret_s64_s32(isum_tmp3), svreinterpret_s64_s32(isum_tmp6)));
+                        svint32_t svisum_mins = svadd_s32_x(pg128_all, isum_tmp7, isum_tmp8);
+
+                        // process mmla
+                        svint8_t  l0, l1, r0, r1;
+                        svint32_t isum_tmp = svdup_n_s32(0);
+                        for (int j = 0; j < QK_K/128; ++j) {
+                            for (int k = 0; k < 8; ++k) {
+                                svuint8_t qhbits_0 = svld1_u8(pg128_all, qh0+16*(k%2));
+                                svuint8_t qhbits_1 = svld1_u8(pg128_all, qh1+16*(k%2));
+                                svuint8_t q6bits_0 = svld1_u8(pg128_all, ql0+16*(k%4));
+                                svuint8_t q6bits_1 = svld1_u8(pg128_all, ql1+16*(k%4));
+                                const int ql_pos = (k/4)*4;
+                                svuint8_t q6bytes_0_lo = (ql_pos < 4) ? svand_n_u8_x(pg128_all, q6bits_0, 0xf) : svlsr_n_u8_x(pg128_all, q6bits_0, 4);
+                                svuint8_t q6bytes_1_lo = (ql_pos < 4) ? svand_n_u8_x(pg128_all, q6bits_1, 0xf) : svlsr_n_u8_x(pg128_all, q6bits_1, 4);
+                                const int qh_pos = (k/2)*2;
+                                svuint8_t q6bytes_0_hi = svand_n_u8_x(pg128_all, qhbits_0, 0x3 << qh_pos);
+                                svuint8_t q6bytes_1_hi = svand_n_u8_x(pg128_all, qhbits_1, 0x3 << qh_pos);
+                                svint8_t  q6bytes_0, q6bytes_1;
+                                if (qh_pos <= 4) {
+                                    q6bytes_0 = svreinterpret_s8_u8(svmla_n_u8_x(pg128_all, q6bytes_0_lo, q6bytes_0_hi, 1 << (4 - qh_pos)));
+                                    q6bytes_1 = svreinterpret_s8_u8(svmla_n_u8_x(pg128_all, q6bytes_1_lo, q6bytes_1_hi, 1 << (4 - qh_pos)));
+                                } else {
+                                    q6bytes_0 = svreinterpret_s8_u8(svorr_u8_x(pg128_all, q6bytes_0_lo, svlsr_n_u8_x(pg128_all, q6bytes_0_hi, (qh_pos - 4))));
+                                    q6bytes_1 = svreinterpret_s8_u8(svorr_u8_x(pg128_all, q6bytes_1_lo, svlsr_n_u8_x(pg128_all, q6bytes_1_hi, (qh_pos - 4))));
+                                }
+                                svint8_t  q8bytes_0 = svld1_s8(pg128_all, q80+16*(k%8));
+                                svint8_t  q8bytes_1 = svld1_s8(pg128_all, q81+16*(k%8));
+                                l0 = svreinterpret_s8_s64(svzip1_s64(svreinterpret_s64_s8(q6bytes_0), svreinterpret_s64_s8(q6bytes_1)));
+                                l1 = svreinterpret_s8_s64(svzip2_s64(svreinterpret_s64_s8(q6bytes_0), svreinterpret_s64_s8(q6bytes_1)));
+                                r0 = svreinterpret_s8_s64(svzip1_s64(svreinterpret_s64_s8(q8bytes_0), svreinterpret_s64_s8(q8bytes_1)));
+                                r1 = svreinterpret_s8_s64(svzip2_s64(svreinterpret_s64_s8(q8bytes_0), svreinterpret_s64_s8(q8bytes_1)));
+                                svint32_t svscale = svzip1_s32(svdup_n_s32(scale0[k]), svdup_n_s32(scale1[k]));
+                                isum_tmp = svmla_s32_x(pg128_all, isum_tmp, svmmla_s32(svmmla_s32(svdup_n_s32(0), r0, l0), r1, l1), svscale);
+                            }
+                            qh0 += 32;  qh1 += 32;
+                            ql0 += 64;  ql1 += 64;
+                            q80 += 128; q81 += 128;
+                            scale0 += 8; scale1 += 8;
+                        }
+                        sum = svmla_f32_x(pg128_all, sum,
+                                svcvt_f32_x(pg128_all, svmla_s32_x(pg128_all, isum_tmp,
+                                        svisum_mins, svdup_n_s32(-32))),
+                                svsuper_block_scales);
+                    }
+                } // end of case 128
+                break;
+            case 256:
+            case 512:
+                {
+                    const svbool_t pg256_all = svptrue_pat_b8(SV_ALL);
+                    const svbool_t pg32_4 = svptrue_pat_b32(SV_VL4);
+                    for (int i = 0; i < nb; ++i) {
+                        const uint8_t * GGML_RESTRICT ql0 = vx0[i].ql;
+                        const uint8_t * GGML_RESTRICT qh0 = vx0[i].qh;
+                        const uint8_t * GGML_RESTRICT ql1 = vx1[i].ql;
+                        const uint8_t * GGML_RESTRICT qh1 = vx1[i].qh;
+                        const int8_t  * GGML_RESTRICT q80 = vy0[i].qs;
+                        const int8_t  * GGML_RESTRICT q81 = vy1[i].qs;
+
+                        const int8_t * GGML_RESTRICT scale0 = vx0[i].scales;
+                        const int8_t * GGML_RESTRICT scale1 = vx1[i].scales;
+                        svfloat32_t vx_d = svzip1_f32(svdup_n_f32(GGML_FP16_TO_FP32(vx0[i].d)), svdup_n_f32(GGML_FP16_TO_FP32(vx1[i].d)));
+                        svfloat64_t vy_d_tmp = svreinterpret_f64_f32(svuzp1_f32(svdup_n_f32(vy0[i].d), svdup_n_f32(vy1[i].d)));
+                        svfloat32_t vy_d = svreinterpret_f32_f64(svuzp1_f64(vy_d_tmp, vy_d_tmp));
+                        svfloat32_t svsuper_block_scales = svmul_f32_x(pg32_4, vy_d, vx_d);
+                        // process q8sum summation 256 bit route
+                        const svint16_t q8sums_0 = svld1_s16(pg256_all, vy0[i].bsums);
+                        const svint16_t q8sums_1 = svld1_s16(pg256_all, vy1[i].bsums);
+                        const svint16_t q6scales_0 = svunpklo_s16(svld1_s8(pg256_all, scale0));
+                        const svint16_t q6scales_1 = svunpklo_s16(svld1_s8(pg256_all, scale1));
+                        const svint64_t prod = svdup_n_s64(0);
+                        svint32_t isum_tmp1  = svreinterpret_s32_s64(svdot_s64(prod, q8sums_0, q6scales_0));
+                        svint32_t isum_tmp2  = svreinterpret_s32_s64(svdot_s64(prod, q8sums_0, q6scales_1));
+                        svint32_t isum_tmp3  = svreinterpret_s32_s64(svdot_s64(prod, q8sums_1, q6scales_0));
+                        svint32_t isum_tmp4  = svreinterpret_s32_s64(svdot_s64(prod, q8sums_1, q6scales_1));
+                        svint32_t isum_tmp5  = svtrn1_s32(isum_tmp1, isum_tmp2);
+                        svint32_t isum_tmp6  = svtrn1_s32(isum_tmp3, isum_tmp4);
+                        svint32_t isum_tmp7  = svreinterpret_s32_s64(svtrn2_s64(svreinterpret_s64_s32(isum_tmp5), svreinterpret_s64_s32(isum_tmp6)));
+                        svint32_t isum_tmp8  = svreinterpret_s32_s64(svtrn1_s64(svreinterpret_s64_s32(isum_tmp5), svreinterpret_s64_s32(isum_tmp6)));
+                        svint32_t isum_tmp9  = svadd_s32_x(pg256_all, isum_tmp7, isum_tmp8);
+                        svint32_t isum_tmp10 = svreinterpret_s32_u8(svext_u8(svreinterpret_u8_s32(isum_tmp9), svreinterpret_u8_s32(isum_tmp9), 16));
+                        svint32_t svisum_mins = svadd_s32_z(pg32_4, isum_tmp9, isum_tmp10);
+
+                        // process mmla
+                        svint8_t l0, l1, r0, r1;
+                        svint32_t isum_tmp = svdup_n_s32(0);
+                        for (int j = 0; j < QK_K/128; ++j) {
+                            for (int k = 0; k < 8; k+=2) { // process 2 block
+                                svuint8_t qhbits_0  = svld1_u8(pg256_all, qh0);
+                                svuint8_t qhbits_1  = svld1_u8(pg256_all, qh1);
+                                svuint8_t q6bits_0  = svld1_u8(pg256_all, ql0+32*((k%4)/2));
+                                svuint8_t q6bits_1  = svld1_u8(pg256_all, ql1+32*((k%4)/2));
+                                const int ql_pos = (k/4)*4;
+                                svuint8_t q6bytes_0_lo = (ql_pos < 4) ? svand_n_u8_x(pg256_all, q6bits_0, 0xf) : svlsr_n_u8_x(pg256_all, q6bits_0, 4);
+                                svuint8_t q6bytes_1_lo = (ql_pos < 4) ? svand_n_u8_x(pg256_all, q6bits_1, 0xf) : svlsr_n_u8_x(pg256_all, q6bits_1, 4);
+                                const int qh_pos = (k/2)*2;
+                                svuint8_t q6bytes_0_hi = svand_n_u8_x(pg256_all, qhbits_0, 0x3 << qh_pos);
+                                svuint8_t q6bytes_1_hi = svand_n_u8_x(pg256_all, qhbits_1, 0x3 << qh_pos);
+                                svint8_t  q6bytes_0, q6bytes_1;
+                                if (qh_pos <= 4) {
+                                    q6bytes_0 = svreinterpret_s8_u8(svmla_n_u8_x(pg256_all, q6bytes_0_lo, q6bytes_0_hi, 1 << (4 - qh_pos)));
+                                    q6bytes_1 = svreinterpret_s8_u8(svmla_n_u8_x(pg256_all, q6bytes_1_lo, q6bytes_1_hi, 1 << (4 - qh_pos)));
+                                } else {
+                                    q6bytes_0 = svreinterpret_s8_u8(svorr_u8_x(pg256_all, q6bytes_0_lo, svlsr_n_u8_x(pg256_all, q6bytes_0_hi, (qh_pos - 4))));
+                                    q6bytes_1 = svreinterpret_s8_u8(svorr_u8_x(pg256_all, q6bytes_1_lo, svlsr_n_u8_x(pg256_all, q6bytes_1_hi, (qh_pos - 4))));
+                                }
+                                svint8_t  q8bytes_0 = svld1_s8(pg256_all, q80+32*(k/2));
+                                svint8_t  q8bytes_1 = svld1_s8(pg256_all, q81+32*(k/2));
+                                l0 = svreinterpret_s8_s64(svzip1_s64(svreinterpret_s64_s8(q6bytes_0), svreinterpret_s64_s8(q6bytes_1)));
+                                l1 = svreinterpret_s8_s64(svzip2_s64(svreinterpret_s64_s8(q6bytes_0), svreinterpret_s64_s8(q6bytes_1)));
+                                r0 = svreinterpret_s8_s64(svzip1_s64(svreinterpret_s64_s8(q8bytes_0), svreinterpret_s64_s8(q8bytes_1)));
+                                r1 = svreinterpret_s8_s64(svzip2_s64(svreinterpret_s64_s8(q8bytes_0), svreinterpret_s64_s8(q8bytes_1)));
+                                svint32_t svscale0 = svzip1_s32(svdup_n_s32(scale0[k]), svdup_n_s32(scale1[k]));
+                                svint32_t svscale1 = svzip1_s32(svdup_n_s32(scale0[k+1]), svdup_n_s32(scale1[k+1]));
+                                isum_tmp = svmla_s32_x(pg256_all, isum_tmp, svmmla_s32(svdup_n_s32(0), r0, l0), svscale0);
+                                isum_tmp = svmla_s32_x(pg256_all, isum_tmp, svmmla_s32(svdup_n_s32(0), r1, l1), svscale1);
+                            }
+                            qh0 += 32;  qh1 += 32;
+                            ql0 += 64;  ql1 += 64;
+                            q80 += 128; q81 += 128;
+                            scale0 += 8; scale1 += 8;
+                        } // end of for
+                        svint32_t swap_isum_tmp = svext_s32(isum_tmp, isum_tmp, 4);
+                        isum_tmp = svadd_s32_x(pg32_4, isum_tmp, swap_isum_tmp);
+                        sum = svmla_f32_x(pg32_4, sum,
+                                svcvt_f32_x(pg32_4, svmla_s32_x(pg32_4, isum_tmp,
+                                        svisum_mins, svdup_n_s32(-32))),
+                                svsuper_block_scales);
+                    }
+                } // end of case 256
+                break;
+            default:
+                assert(false && "Unsupported vector length");
+                break;
+        } // end of switch
+
+        svst1_f32(pg32_2, s, sum);
+        svst1_f32(pg32_2, s + bs, svreinterpret_f32_u8(svext_u8(svreinterpret_u8_f32(sum), svdup_n_u8(0), 8)));
+
+        return;
+    }
+#elif defined(__ARM_FEATURE_MATMUL_INT8)
     if (nrc == 2) {
         const block_q6_K * GGML_RESTRICT x0 = x;
         const block_q6_K * GGML_RESTRICT x1 = (const block_q6_K *) ((const uint8_t *)vx + bx);
@@ -2594,27 +3019,6 @@ void ggml_vec_dot_q6_K_q8_K(int n, float * GGML_RESTRICT s, size_t bs, const voi
             // adjust bias, apply superblock scale
             {
                 int32_t bias[4];
-#ifdef __ARM_FEATURE_SVE
-                const svbool_t pg16_8 = svptrue_pat_b16(SV_VL8);
-                const svbool_t pg8_8 = svptrue_pat_b8(SV_VL8);
-                const svint16_t y0_q8sums_0 = svld1_s16(pg16_8, y0->bsums);
-                const svint16_t y0_q8sums_1 = svld1_s16(pg16_8, y0->bsums + 8);
-                const svint16_t y1_q8sums_0 = svld1_s16(pg16_8, y1->bsums);
-                const svint16_t y1_q8sums_1 = svld1_s16(pg16_8, y1->bsums + 8);
-                const svint16_t x0_q6scales_0 = svunpklo_s16(svld1_s8(pg8_8, x0->scales));
-                const svint16_t x0_q6scales_1 = svunpklo_s16(svld1_s8(pg8_8, x0->scales + 8));
-                const svint16_t x1_q6scales_0 = svunpklo_s16(svld1_s8(pg8_8, x1->scales));
-                const svint16_t x1_q6scales_1 = svunpklo_s16(svld1_s8(pg8_8, x1->scales + 8));
-                const svint64_t zero = svdup_n_s64(0);
-                bias[0] = svaddv_s64(svptrue_b64(), svadd_s64_x(svptrue_b64(), svdot_s64(zero, y0_q8sums_0, x0_q6scales_0),
-                                                                               svdot_s64(zero, y0_q8sums_1, x0_q6scales_1)));
-                bias[1] = svaddv_s64(svptrue_b64(), svadd_s64_x(svptrue_b64(), svdot_s64(zero, y1_q8sums_0, x0_q6scales_0),
-                                                                               svdot_s64(zero, y1_q8sums_1, x0_q6scales_1)));
-                bias[2] = svaddv_s64(svptrue_b64(), svadd_s64_x(svptrue_b64(), svdot_s64(zero, y0_q8sums_0, x1_q6scales_0),
-                                                                               svdot_s64(zero, y0_q8sums_1, x1_q6scales_1)));
-                bias[3] = svaddv_s64(svptrue_b64(), svadd_s64_x(svptrue_b64(), svdot_s64(zero, y1_q8sums_0, x1_q6scales_0),
-                                                                               svdot_s64(zero, y1_q8sums_1, x1_q6scales_1)));
-#else
                 // NEON doesn't support int16 dot product, fallback to separated mul and add
                 const int16x8x2_t q8sums0 = vld1q_s16_x2(y0->bsums);
                 const int16x8x2_t q8sums1 = vld1q_s16_x2(y1->bsums);
@@ -2646,7 +3050,6 @@ void ggml_vec_dot_q6_K_q8_K(int n, float * GGML_RESTRICT s, size_t bs, const voi
                                            vmull_s16(vget_high_s16(q8sums1.val[1]), vget_high_s16(q6scales1.val[1]))));
                 bias[3] = vaddvq_s32(prod);
 
-#endif
                 const int32x4_t vibias = vmulq_n_s32(vld1q_s32(bias), 32);
 
                 const float32x4_t superblock_scale = {
@@ -2672,7 +3075,6 @@ void ggml_vec_dot_q6_K_q8_K(int n, float * GGML_RESTRICT s, size_t bs, const voi
 #endif
 
 #ifdef __ARM_FEATURE_SVE
-    const int vector_length = ggml_cpu_get_sve_cnt()*8;
     float sum = 0;
     svuint8_t m4b = svdup_n_u8(0xf);
     svint32_t vzero = svdup_n_s32(0);

From c27efd2bd1f27b1ad2f0b7cb417dbb9b62b57d44 Mon Sep 17 00:00:00 2001
From: Georgi Gerganov <ggerganov@gmail.com>
Date: Mon, 10 Nov 2025 15:38:42 +0200
Subject: [PATCH 144/185] metal : enable tensor API for A19 (#17087)

---
 ggml/src/ggml-metal/ggml-metal-device.m | 6 ++++--
 1 file changed, 4 insertions(+), 2 deletions(-)

diff --git a/ggml/src/ggml-metal/ggml-metal-device.m b/ggml/src/ggml-metal/ggml-metal-device.m
index 606cfd0a5e2..3471225ab47 100644
--- a/ggml/src/ggml-metal/ggml-metal-device.m
+++ b/ggml/src/ggml-metal/ggml-metal-device.m
@@ -564,8 +564,10 @@ ggml_metal_device_t ggml_metal_device_init(void) {
             // TODO: try to update the tensor API kernels to at least match the simdgroup performance
             if (getenv("GGML_METAL_TENSOR_ENABLE") == NULL &&
                 ![[dev->mtl_device name] containsString:@"M5"] &&
-                ![[dev->mtl_device name] containsString:@"M6"]) {
-                GGML_LOG_WARN("%s: tensor API disabled for pre-M5 device\n", __func__);
+                ![[dev->mtl_device name] containsString:@"M6"] &&
+                ![[dev->mtl_device name] containsString:@"A19"] &&
+                ![[dev->mtl_device name] containsString:@"A20"]) {
+                GGML_LOG_WARN("%s: tensor API disabled for pre-M5 and pre-A19 devices\n", __func__);
                 dev->props.has_tensor = false;
             }
 

From 0c74f3263273cf0d95d1f10930a12cad94c375af Mon Sep 17 00:00:00 2001
From: Gabe Goodhart <ghart@us.ibm.com>
Date: Mon, 10 Nov 2025 08:14:23 -0700
Subject: [PATCH 145/185] memory: Hybrid context shift (#17009)

* feat(memory): Only fail partial erasure of recurrent tail

The recurrent state is always assumed to be the state as of the last update
from the final token in the sequence. When doing a partial erasure, if the
range does not include the final token, the erasure can be considered a
success since any memory used for the sequence prior to the final token
(which is no memory) has been successfully removed.

There is one potential case that this doesn't address which is the pruning
of cache to remove sensitive data from the context. This wouldn't work for
attention cache partial removal (in the middle) either since the KV state
is linearly-dependent and states in later sequence positions would still be
based on the state from the sensitive data, even if that data is no longer
cached, so I don't think this is relevant, but it is worth noting that the
semantics of this change for a partial erasure in the middle of the cache
are essentially "my context is already compressed" and not "all trace of
the removed tokens has been removed."

https://github.com/ggml-org/llama.cpp/issues/16768
Branch: HybridContextShift-16768

Signed-off-by: Gabe Goodhart <ghart@us.ibm.com>

* fix(main): Check the output of seq_rm for prefix matching

This prefix matching is explicitly attempting to remove the tokens at the
end of the sequence that don't match. This is the operation that can't be
performed on a recurrent cache due to the state being updated in place, so
if this removal fails, we need to clear the whole cache.

https://github.com/ggml-org/llama.cpp/issues/16768
Branch: HybridContextShift-16768

Signed-off-by: Gabe Goodhart <ghart@us.ibm.com>

* fix(memory): Fix condition for partial erasure failure if p0 > pos

Signed-off-by: Gabe Goodhart <ghart@us.ibm.com>

Co-authored-by: compilade <git@compilade.net>

* style: Fix extra parens

Signed-off-by: Gabe Goodhart <ghart@us.ibm.com>

Co-authored-by: Georgi Gerganov <ggerganov@gmail.com>

* fix(main.cpp): Set n_matching_session_tokens to 0 on cache clear

https://github.com/ggml-org/llama.cpp/issues/16768
Branch: HybridContextShift-16768

Signed-off-by: Gabe Goodhart <ghart@us.ibm.com>

---------

Signed-off-by: Gabe Goodhart <ghart@us.ibm.com>
Co-authored-by: compilade <git@compilade.net>
Co-authored-by: Georgi Gerganov <ggerganov@gmail.com>
---
 src/llama-memory-recurrent.cpp | 7 ++++---
 tools/main/main.cpp            | 6 +++++-
 2 files changed, 9 insertions(+), 4 deletions(-)

diff --git a/src/llama-memory-recurrent.cpp b/src/llama-memory-recurrent.cpp
index 276e1697d46..812bf253049 100644
--- a/src/llama-memory-recurrent.cpp
+++ b/src/llama-memory-recurrent.cpp
@@ -151,7 +151,8 @@ bool llama_memory_recurrent::seq_rm(llama_seq_id seq_id, llama_pos p0, llama_pos
         p1 = std::numeric_limits<llama_pos>::max();
     }
 
-    // models like Mamba or RWKV can't have a state partially erased
+    // models like Mamba or RWKV can't have a state partially erased at the end
+    // of the sequence because their state isn't preserved for previous tokens
     if (seq_id >= (int64_t) size) {
         // could be fatal
         return false;
@@ -160,8 +161,8 @@ bool llama_memory_recurrent::seq_rm(llama_seq_id seq_id, llama_pos p0, llama_pos
         int32_t & tail_id = cells[seq_id].tail;
         if (tail_id >= 0) {
             const auto & cell = cells[tail_id];
-            // partial intersection is invalid
-            if ((0 < p0 && p0 < cell.pos) || (0 < p1 && p1 <= cell.pos)) {
+            // partial intersection is invalid if it includes the final pos
+            if (0 < p0 && p0 <= cell.pos && p1 > cell.pos) {
                 //printf("[DEBUG] inside `llama_memory_recurrent::seq_rm`: partial intersection is invalid, so returning false\n");
                 return false;
             }
diff --git a/tools/main/main.cpp b/tools/main/main.cpp
index 498e00e3a5e..33e88623357 100644
--- a/tools/main/main.cpp
+++ b/tools/main/main.cpp
@@ -354,7 +354,11 @@ int main(int argc, char ** argv) {
         }
 
         // remove any "future" tokens that we might have inherited from the previous session
-        llama_memory_seq_rm(mem, -1, n_matching_session_tokens, -1);
+        if (!llama_memory_seq_rm(mem, -1, n_matching_session_tokens, -1)) {
+            LOG_INF("%s: unable to resuse common prefix\n", __func__);
+            n_matching_session_tokens = 0;
+            llama_memory_seq_rm(mem, -1, -1, -1);
+        }
     }
 
     LOG_DBG("recalculate the cached logits (check): embd_inp.size() %zu, n_matching_session_tokens %zu, embd_inp.size() %zu, session_tokens.size() %zu\n",

From 85234a4b3aa1084147995a07c12ebcce6310dd9e Mon Sep 17 00:00:00 2001
From: Ruben Ortlam <picard12@live.de>
Date: Mon, 10 Nov 2025 16:59:10 +0100
Subject: [PATCH 146/185] vulkan: fix validation issue introduced by #16868
 (#17145)

---
 ggml/src/ggml-vulkan/ggml-vulkan.cpp | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/ggml/src/ggml-vulkan/ggml-vulkan.cpp b/ggml/src/ggml-vulkan/ggml-vulkan.cpp
index a7a28b1934c..e4b7e1ea9e5 100644
--- a/ggml/src/ggml-vulkan/ggml-vulkan.cpp
+++ b/ggml/src/ggml-vulkan/ggml-vulkan.cpp
@@ -6831,7 +6831,7 @@ static void ggml_vk_mul_mat_vec_q_f16(ggml_backend_vk_context * ctx, vk_context&
 
     vk_buffer d_B = d_D;
     size_t b_buf_offset = 0;
-    uint64_t b_sz = 0;
+    uint64_t b_sz = 1;
 
     if (enable_bias) {
         const ggml_tensor * add = cgraph->nodes[node_idx + 1];
@@ -6965,7 +6965,7 @@ static void ggml_vk_mul_mat_vec_p021_f16_f32(ggml_backend_vk_context * ctx, vk_c
 
     vk_buffer d_B = d_D;
     size_t b_buf_offset = 0;
-    uint64_t b_sz = 0;
+    uint64_t b_sz = 1;
 
     if (enable_bias) {
         const ggml_tensor * add = cgraph->nodes[node_idx + 1];
@@ -7101,7 +7101,7 @@ static void ggml_vk_mul_mat_vec_nc_f16_f32(ggml_backend_vk_context * ctx, vk_con
 
     vk_buffer d_B = d_D;
     size_t b_buf_offset = 0;
-    uint64_t b_sz = 0;
+    uint64_t b_sz = 1;
 
     if (enable_bias) {
         const ggml_tensor * add = cgraph->nodes[node_idx + 1];
@@ -7676,7 +7676,7 @@ static void ggml_vk_mul_mat_vec_id_q_f16(ggml_backend_vk_context * ctx, vk_conte
 
     vk_buffer d_B = d_D;
     size_t b_buf_offset = 0;
-    uint64_t b_sz = 0;
+    uint64_t b_sz = 1;
 
     if (enable_bias || enable_scale) {
         const ggml_tensor * bias = cgraph->nodes[node_idx + 1]->src[1];

From f117be185ef1b76129e51d26676354af253bf664 Mon Sep 17 00:00:00 2001
From: Ruben Ortlam <picard12@live.de>
Date: Mon, 10 Nov 2025 16:59:26 +0100
Subject: [PATCH 147/185] vulkan: check glslc executable string (#17144)

---
 ggml/src/ggml-vulkan/vulkan-shaders/vulkan-shaders-gen.cpp | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/ggml/src/ggml-vulkan/vulkan-shaders/vulkan-shaders-gen.cpp b/ggml/src/ggml-vulkan/vulkan-shaders/vulkan-shaders-gen.cpp
index c2e42cf006e..c8a6f97ecff 100644
--- a/ggml/src/ggml-vulkan/vulkan-shaders/vulkan-shaders-gen.cpp
+++ b/ggml/src/ggml-vulkan/vulkan-shaders/vulkan-shaders-gen.cpp
@@ -18,6 +18,7 @@
 #include <algorithm>
 #include <sys/stat.h>
 #include <sys/types.h>
+#include <filesystem>
 
 #ifdef _WIN32
     #define NOMINMAX
@@ -1080,6 +1081,11 @@ int main(int argc, char** argv) {
 
     if (args.find("--glslc") != args.end()) {
         GLSLC = args["--glslc"]; // Path to glslc
+
+        if (!std::filesystem::exists(GLSLC) || !std::filesystem::is_regular_file(GLSLC)) {
+            std::cerr << "Error: glslc not found at " << GLSLC << std::endl;
+            return EXIT_FAILURE;
+        }
     }
     if (args.find("--source") != args.end()) {
         input_filepath = args["--source"]; // The shader source file to compile

From 967eb4b2bf5971565094122c64bb54090cbdc05f Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Adrien=20Gallou=C3=ABt?= <angt@huggingface.co>
Date: Mon, 10 Nov 2025 20:03:36 +0100
Subject: [PATCH 148/185] ggml-cpu : inspect -march and -mcpu to found the CPU
 (#16333)
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

Signed-off-by: Adrien Gallouët <angt@huggingface.co>
---
 ggml/src/ggml-cpu/CMakeLists.txt | 27 +++++++++++++++++++--------
 1 file changed, 19 insertions(+), 8 deletions(-)

diff --git a/ggml/src/ggml-cpu/CMakeLists.txt b/ggml/src/ggml-cpu/CMakeLists.txt
index 23ec8bb08a7..a55191aede9 100644
--- a/ggml/src/ggml-cpu/CMakeLists.txt
+++ b/ggml/src/ggml-cpu/CMakeLists.txt
@@ -126,25 +126,36 @@ function(ggml_add_cpu_backend_variant_impl tag_name)
                 )
                 if (NOT ARM_MCPU_RESULT)
                     string(REGEX MATCH "-mcpu=[^ ']+" ARM_MCPU_FLAG "${ARM_MCPU}")
+                    string(REGEX MATCH "-march=[^ ']+" ARM_MARCH_FLAG "${ARM_MCPU}")
+
+                    # on some old GCC we need to read -march=
+                    if (ARM_MARCH_FLAG AND NOT "${ARM_MARCH_FLAG}" STREQUAL "-march=native")
+                        set(ARM_NATIVE_FLAG "${ARM_MARCH_FLAG}")
+                    elseif(ARM_MCPU_FLAG AND NOT "${ARM_MCPU_FLAG}" STREQUAL "-mcpu=native")
+                        set(ARM_NATIVE_FLAG "${ARM_MCPU_FLAG}")
+                    endif()
                 endif()
-                if ("${ARM_MCPU_FLAG}" STREQUAL "")
-                    set(ARM_MCPU_FLAG -mcpu=native)
-                    message(STATUS "ARM -mcpu not found, -mcpu=native will be used")
+
+                if ("${ARM_NATIVE_FLAG}" STREQUAL "")
+                    set(ARM_NATIVE_FLAG -mcpu=native)
+                    message(WARNING "ARM -march/-mcpu not found, -mcpu=native will be used")
+                else()
+                    message(STATUS "ARM detected flags: ${ARM_NATIVE_FLAG}")
                 endif()
 
                 include(CheckCXXSourceRuns)
 
                 function(check_arm_feature tag code)
                     set(CMAKE_REQUIRED_FLAGS_SAVE ${CMAKE_REQUIRED_FLAGS})
-                    set(CMAKE_REQUIRED_FLAGS "${ARM_MCPU_FLAG}+${tag}")
+                    set(CMAKE_REQUIRED_FLAGS "${ARM_NATIVE_FLAG}+${tag}")
                     check_cxx_source_runs("${code}" GGML_MACHINE_SUPPORTS_${tag})
                     if (GGML_MACHINE_SUPPORTS_${tag})
-                        set(ARM_MCPU_FLAG_FIX "${ARM_MCPU_FLAG_FIX}+${tag}" PARENT_SCOPE)
+                        set(ARM_NATIVE_FLAG_FIX "${ARM_NATIVE_FLAG_FIX}+${tag}" PARENT_SCOPE)
                     else()
-                        set(CMAKE_REQUIRED_FLAGS "${ARM_MCPU_FLAG}+no${tag}")
+                        set(CMAKE_REQUIRED_FLAGS "${ARM_NATIVE_FLAG}+no${tag}")
                         check_cxx_source_compiles("int main() { return 0; }" GGML_MACHINE_SUPPORTS_no${tag})
                         if (GGML_MACHINE_SUPPORTS_no${tag})
-                            set(ARM_MCPU_FLAG_FIX "${ARM_MCPU_FLAG_FIX}+no${tag}" PARENT_SCOPE)
+                            set(ARM_NATIVE_FLAG_FIX "${ARM_NATIVE_FLAG_FIX}+no${tag}" PARENT_SCOPE)
                         endif()
                     endif()
                     set(CMAKE_REQUIRED_FLAGS ${CMAKE_REQUIRED_FLAGS_SAVE})
@@ -155,7 +166,7 @@ function(ggml_add_cpu_backend_variant_impl tag_name)
                 check_arm_feature(sve     "#include <arm_sve.h>\nint main()  { svfloat32_t _a, _b; volatile svfloat32_t _c = svadd_f32_z(svptrue_b8(), _a, _b); return 0; }")
                 check_arm_feature(sme     "#include <arm_sme.h>\n__arm_locally_streaming int main() { __asm__ volatile(\"smstart; smstop;\"); return 0; }")
 
-                list(APPEND ARCH_FLAGS "${ARM_MCPU_FLAG}${ARM_MCPU_FLAG_FIX}")
+                list(APPEND ARCH_FLAGS "${ARM_NATIVE_FLAG}${ARM_NATIVE_FLAG_FIX}")
             else()
                 if (GGML_CPU_ARM_ARCH)
                     list(APPEND ARCH_FLAGS -march=${GGML_CPU_ARM_ARCH})

From 13730c183b9e1a32c09bf132b5367697d6c55048 Mon Sep 17 00:00:00 2001
From: Georgi Gerganov <ggerganov@gmail.com>
Date: Mon, 10 Nov 2025 21:33:35 +0200
Subject: [PATCH 149/185] metal : cap threadgroups size of set_rows (#17146)

---
 ggml/src/ggml-metal/ggml-metal-ops.cpp | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/ggml/src/ggml-metal/ggml-metal-ops.cpp b/ggml/src/ggml-metal/ggml-metal-ops.cpp
index 7a85edbdcdb..5a8f150a71d 100644
--- a/ggml/src/ggml-metal/ggml-metal-ops.cpp
+++ b/ggml/src/ggml-metal/ggml-metal-ops.cpp
@@ -1036,6 +1036,11 @@ int ggml_metal_op_set_rows(ggml_metal_op_t ctx, int idx) {
 
     nth = std::min(nth, nk0);
 
+    if (nth*nrptg > ggml_metal_pipeline_max_theads_per_threadgroup(pipeline)) {
+        nth = ggml_metal_pipeline_max_theads_per_threadgroup(pipeline);
+        nrptg = 1;
+    }
+
     ggml_metal_kargs_set_rows args = {
         /*.nk0  =*/ nk0,
         /*.ne01 =*/ ne01,

From 395e286bc9bc67f45f01dc951e2a408cca2a6b29 Mon Sep 17 00:00:00 2001
From: Max Krasnyansky <maxk@qti.qualcomm.com>
Date: Mon, 10 Nov 2025 12:44:49 -0800
Subject: [PATCH 150/185] cpu: skip NOPs to avoid barriers (#17133)

* cpu: skip NOPs to avoid barriers

* cpu: use ggml_op_is_empty
---
 ggml/src/ggml-cpu/ggml-cpu.c | 37 ++++++++++++++++++---------------
 ggml/src/ggml-cpu/ops.cpp    | 40 ------------------------------------
 ggml/src/ggml-cpu/ops.h      |  4 ----
 3 files changed, 21 insertions(+), 60 deletions(-)

diff --git a/ggml/src/ggml-cpu/ggml-cpu.c b/ggml/src/ggml-cpu/ggml-cpu.c
index b5466dd703d..086708bae0b 100644
--- a/ggml/src/ggml-cpu/ggml-cpu.c
+++ b/ggml/src/ggml-cpu/ggml-cpu.c
@@ -1807,22 +1807,6 @@ static void ggml_compute_forward(struct ggml_compute_params * params, struct ggm
             {
                 ggml_compute_forward_cont(params, tensor);
             } break;
-        case GGML_OP_RESHAPE:
-            {
-                ggml_compute_forward_reshape(params, tensor);
-            } break;
-        case GGML_OP_VIEW:
-            {
-                ggml_compute_forward_view(params, tensor);
-            } break;
-        case GGML_OP_PERMUTE:
-            {
-                ggml_compute_forward_permute(params, tensor);
-            } break;
-        case GGML_OP_TRANSPOSE:
-            {
-                ggml_compute_forward_transpose(params, tensor);
-            } break;
         case GGML_OP_GET_ROWS:
             {
                 ggml_compute_forward_get_rows(params, tensor);
@@ -2042,6 +2026,22 @@ static void ggml_compute_forward(struct ggml_compute_params * params, struct ggm
             {
                 // nop
             } break;
+        case GGML_OP_RESHAPE:
+            {
+                // nop
+            } break;
+        case GGML_OP_PERMUTE:
+            {
+                // nop
+            } break;
+        case GGML_OP_VIEW:
+            {
+                // nop
+            } break;
+        case GGML_OP_TRANSPOSE:
+            {
+                // nop
+            } break;
         case GGML_OP_COUNT:
             {
                 GGML_ABORT("fatal error");
@@ -2884,6 +2884,11 @@ static thread_ret_t ggml_graph_compute_thread(void * data) {
     for (int node_n = 0; node_n < cgraph->n_nodes && atomic_load_explicit(&tp->abort, memory_order_relaxed) != node_n; node_n++) {
         struct ggml_tensor * node = cgraph->nodes[node_n];
 
+        if (ggml_op_is_empty(node->op)) {
+            // skip NOPs
+            continue;
+        }
+
         ggml_compute_forward(&params, node);
 
         if (state->ith == 0 && cplan->abort_callback &&
diff --git a/ggml/src/ggml-cpu/ops.cpp b/ggml/src/ggml-cpu/ops.cpp
index 8235f695943..7c42fb78b4a 100644
--- a/ggml/src/ggml-cpu/ops.cpp
+++ b/ggml/src/ggml-cpu/ops.cpp
@@ -4455,46 +4455,6 @@ void ggml_compute_forward_cont(
     ggml_compute_forward_dup(params, dst);
 }
 
-// ggml_compute_forward_reshape
-
-void ggml_compute_forward_reshape(
-        const ggml_compute_params * params,
-        ggml_tensor * dst) {
-    // NOP
-    GGML_UNUSED(params);
-    GGML_UNUSED(dst);
-}
-
-// ggml_compute_forward_view
-
-void ggml_compute_forward_view(
-        const ggml_compute_params * params,
-        ggml_tensor * dst) {
-    // NOP
-    GGML_UNUSED(params);
-    GGML_UNUSED(dst);
-}
-
-// ggml_compute_forward_permute
-
-void ggml_compute_forward_permute(
-        const ggml_compute_params * params,
-        ggml_tensor * dst) {
-    // NOP
-    GGML_UNUSED(params);
-    GGML_UNUSED(dst);
-}
-
-// ggml_compute_forward_transpose
-
-void ggml_compute_forward_transpose(
-        const ggml_compute_params * params,
-        ggml_tensor * dst) {
-    // NOP
-    GGML_UNUSED(params);
-    GGML_UNUSED(dst);
-}
-
 // ggml_compute_forward_get_rows
 
 static void ggml_compute_forward_get_rows_q(
diff --git a/ggml/src/ggml-cpu/ops.h b/ggml/src/ggml-cpu/ops.h
index 9824a03b458..2b4127c12b1 100644
--- a/ggml/src/ggml-cpu/ops.h
+++ b/ggml/src/ggml-cpu/ops.h
@@ -51,10 +51,6 @@ void ggml_compute_forward_scale(const struct ggml_compute_params * params, struc
 void ggml_compute_forward_set(const struct ggml_compute_params * params, struct ggml_tensor * dst);
 void ggml_compute_forward_cpy(const struct ggml_compute_params * params, struct ggml_tensor * dst);
 void ggml_compute_forward_cont(const struct ggml_compute_params * params, struct ggml_tensor * dst);
-void ggml_compute_forward_reshape(const struct ggml_compute_params * params, struct ggml_tensor * dst);
-void ggml_compute_forward_view(const struct ggml_compute_params * params, struct ggml_tensor * dst);
-void ggml_compute_forward_permute(const struct ggml_compute_params * params, struct ggml_tensor * dst);
-void ggml_compute_forward_transpose(const struct ggml_compute_params * params, struct ggml_tensor * dst);
 void ggml_compute_forward_get_rows(const struct ggml_compute_params * params, struct ggml_tensor * dst);
 void ggml_compute_forward_get_rows_back(const struct ggml_compute_params * params, struct ggml_tensor * dst);
 void ggml_compute_forward_set_rows(const struct ggml_compute_params * params, struct ggml_tensor * dst);

From 7bef684118cc44f9ab8b82df102d68db94a6d9f4 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Sigbj=C3=B8rn=20Skj=C3=A6ret?= <sigbjorn.skjaeret@scala.com>
Date: Mon, 10 Nov 2025 22:55:30 +0100
Subject: [PATCH 151/185] models : move build_inp_out_ids outside loop (#17151)

* move build_inp_out_ids outside loop

* realign
---
 src/models/ernie4-5.cpp        | 9 ++++-----
 src/models/openai-moe-iswa.cpp | 3 ++-
 2 files changed, 6 insertions(+), 6 deletions(-)

diff --git a/src/models/ernie4-5.cpp b/src/models/ernie4-5.cpp
index 99962af111f..99aead53283 100644
--- a/src/models/ernie4-5.cpp
+++ b/src/models/ernie4-5.cpp
@@ -1,7 +1,5 @@
 #include "models.h"
 
-
-
 llm_build_ernie4_5::llm_build_ernie4_5(const llama_model & model, const llm_graph_params & params) :
     llm_graph_context(params) {
     const int64_t n_embd_head = hparams.n_embd_head_v;
@@ -19,6 +17,8 @@ llm_build_ernie4_5::llm_build_ernie4_5(const llama_model & model, const llm_grap
 
     auto * inp_attn = build_attn_inp_kv();
 
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
     for (int il = 0; il < n_layer; ++il) {
         ggml_tensor * inpSA = inpL;
 
@@ -67,9 +67,8 @@ llm_build_ernie4_5::llm_build_ernie4_5(const llama_model & model, const llm_grap
         }
         if (il == n_layer - 1) {
             // skip computing output for unused tokens
-            ggml_tensor * inp_out_ids = build_inp_out_ids();
-            cur                       = ggml_get_rows(ctx0, cur, inp_out_ids);
-            inpSA                     = ggml_get_rows(ctx0, inpSA, inp_out_ids);
+            cur   = ggml_get_rows(ctx0, cur, inp_out_ids);
+            inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
         }
         ggml_tensor * ffn_inp = ggml_add(ctx0, cur, inpSA);
         cb(ffn_inp, "ffn_inp", il);
diff --git a/src/models/openai-moe-iswa.cpp b/src/models/openai-moe-iswa.cpp
index 3c0c0eecf5d..96596709eec 100644
--- a/src/models/openai-moe-iswa.cpp
+++ b/src/models/openai-moe-iswa.cpp
@@ -11,6 +11,8 @@ llm_build_openai_moe_iswa::llm_build_openai_moe_iswa(const llama_model & model,
 
     auto * inp_attn = build_attn_inp_kv_iswa();
 
+    ggml_tensor * inp_out_ids = build_inp_out_ids();
+
     for (int il = 0; il < n_layer; ++il) {
         ggml_tensor * inpSA = inpL;
 
@@ -69,7 +71,6 @@ llm_build_openai_moe_iswa::llm_build_openai_moe_iswa(const llama_model & model,
         }
         if (il == n_layer - 1) {
             // skip computing output for unused tokens
-            ggml_tensor * inp_out_ids = build_inp_out_ids();
             cur   = ggml_get_rows(ctx0,   cur, inp_out_ids);
             inpSA = ggml_get_rows(ctx0, inpSA, inp_out_ids);
         }

From ece0f5c1771f1835e66900d4168233f0430d819d Mon Sep 17 00:00:00 2001
From: lhez <lih@qti.qualcomm.com>
Date: Mon, 10 Nov 2025 15:00:13 -0800
Subject: [PATCH 152/185] opencl: add fastdiv and use it in set_rows, ported
 from cuda (#17090)

* opencl: add fastdiv for mm q8_0

* opencl: use uint4 for fastdiv vals

* opencl: use fastdiv for set_rows

* opencl: do not use fastdiv for q8_0 mm
---
 ggml/src/ggml-opencl/ggml-opencl.cpp     | 38 +++++++++++++++++-
 ggml/src/ggml-opencl/kernels/set_rows.cl | 51 ++++++++++++++++--------
 2 files changed, 71 insertions(+), 18 deletions(-)

diff --git a/ggml/src/ggml-opencl/ggml-opencl.cpp b/ggml/src/ggml-opencl/ggml-opencl.cpp
index 1d3a318a569..465272fab90 100644
--- a/ggml/src/ggml-opencl/ggml-opencl.cpp
+++ b/ggml/src/ggml-opencl/ggml-opencl.cpp
@@ -53,6 +53,37 @@
 
 bool ggml_cl_compute_forward(ggml_backend_t backend, struct ggml_tensor * tensor);
 
+// See https://gmplib.org/~tege/divcnst-pldi94.pdf figure 4.1.
+// Precompute mp (m' in the paper) and L such that division
+// can be computed using a multiply (high 32b of 64b result)
+// and a shift:
+//
+// n/d = (mulhi(n, mp) + n) >> L;
+struct fastdiv_vals {
+    uint32_t mp;
+    uint32_t L;
+    uint32_t d;
+    uint32_t pad;
+};
+static_assert(sizeof(fastdiv_vals) == 16, "fastdiv_vals size incorrect");
+
+static fastdiv_vals init_fastdiv_values(uint64_t d_64) {
+    GGML_ASSERT(d_64 != 0);
+    GGML_ASSERT(d_64 <= std::numeric_limits<uint32_t>::max());
+
+    uint32_t d = (uint32_t)d_64;
+
+    // compute L = ceil(log2(d));
+    uint32_t L = 0;
+    while (L < 32 && (uint32_t{ 1 } << L) < d) {
+        L++;
+    }
+
+    uint32_t mp = (uint32_t) ((uint64_t{ 1 } << 32) * ((uint64_t{ 1 } << L) - d) / d + 1);
+    // pack divisor as well to reduce error surface
+    return { mp, L, d, 0 };
+}
+
 enum GPU_FAMILY {
     ADRENO,
     INTEL,
@@ -4464,6 +4495,9 @@ static void ggml_cl_set_rows(ggml_backend_t backend, const ggml_tensor * src0, c
             GGML_ABORT("not implemented");
     }
 
+    fastdiv_vals ne11_ = init_fastdiv_values(ne11);
+    fastdiv_vals ne12_ = init_fastdiv_values(ne12);
+
     CL_CHECK(clSetKernelArg(kernel,  0, sizeof(cl_mem),   &extra0->data_device));
     CL_CHECK(clSetKernelArg(kernel,  1, sizeof(cl_ulong), &offset0));
     CL_CHECK(clSetKernelArg(kernel,  2, sizeof(cl_mem),   &extra1->data_device));
@@ -4474,8 +4508,8 @@ static void ggml_cl_set_rows(ggml_backend_t backend, const ggml_tensor * src0, c
     CL_CHECK(clSetKernelArg(kernel,  7, sizeof(cl_ulong), &nb01));
     CL_CHECK(clSetKernelArg(kernel,  8, sizeof(cl_ulong), &nb02));
     CL_CHECK(clSetKernelArg(kernel,  9, sizeof(cl_ulong), &nb03));
-    CL_CHECK(clSetKernelArg(kernel, 10, sizeof(int),      &ne11));
-    CL_CHECK(clSetKernelArg(kernel, 11, sizeof(int),      &ne12));
+    CL_CHECK(clSetKernelArg(kernel, 10, sizeof(fastdiv_vals), &ne11_));
+    CL_CHECK(clSetKernelArg(kernel, 11, sizeof(fastdiv_vals), &ne12_));
     CL_CHECK(clSetKernelArg(kernel, 12, sizeof(cl_ulong), &nb10));
     CL_CHECK(clSetKernelArg(kernel, 13, sizeof(cl_ulong), &nb11));
     CL_CHECK(clSetKernelArg(kernel, 14, sizeof(cl_ulong), &nb12));
diff --git a/ggml/src/ggml-opencl/kernels/set_rows.cl b/ggml/src/ggml-opencl/kernels/set_rows.cl
index dcdc1d1b6fd..fc3ff7aa1e7 100644
--- a/ggml/src/ggml-opencl/kernels/set_rows.cl
+++ b/ggml/src/ggml-opencl/kernels/set_rows.cl
@@ -1,5 +1,16 @@
 #pragma OPENCL EXTENSION cl_khr_fp16 : enable
 
+// v = { mp, L, d }
+inline uint fastdiv(uint n, uint4 v) {
+    uint msbs;
+    msbs = mul_hi(n, v.s0);
+    return (msbs + n) >> v.s1;
+}
+inline uint fastmod(uint n, uint4 v) {
+    uint q = fastdiv(n, v);
+    return n - q * v.s2;
+}
+
 kernel void kernel_set_rows_f32_i64(
         global char * src0,
         ulong         offset0,
@@ -11,8 +22,8 @@ kernel void kernel_set_rows_f32_i64(
         ulong         nb01,
         ulong         nb02,
         ulong         nb03,
-        int           ne11,
-        int           ne12,
+        uint4         ne11,
+        uint4         ne12,
         ulong         nb10,
         ulong         nb11,
         ulong         nb12,
@@ -33,8 +44,10 @@ kernel void kernel_set_rows_f32_i64(
         return;
     }
 
-    int i12 = i03%ne12;
-    int i11 = i02%ne11;
+    //int i12 = i03%ne12;
+    //int i11 = i02%ne11;
+    int i12 = fastmod(i03, ne12);
+    int i11 = fastmod(i02, ne11);
 
     int i10 = i01;
     long i1 = ((global long *)(src1 + i10*nb10 + i11*nb11 + i12*nb12))[0];
@@ -58,8 +71,8 @@ kernel void kernel_set_rows_f16_i64(
         ulong         nb01,
         ulong         nb02,
         ulong         nb03,
-        int           ne11,
-        int           ne12,
+        uint4         ne11,
+        uint4         ne12,
         ulong         nb10,
         ulong         nb11,
         ulong         nb12,
@@ -80,8 +93,10 @@ kernel void kernel_set_rows_f16_i64(
         return;
     }
 
-    int i12 = i03%ne12;
-    int i11 = i02%ne11;
+    //int i12 = i03%ne12;
+    //int i11 = i02%ne11;
+    int i12 = fastmod(i03, ne12);
+    int i11 = fastmod(i02, ne11);
 
     int i10 = i01;
     long i1 = ((global long *)(src1 + i10*nb10 + i11*nb11 + i12*nb12))[0];
@@ -105,8 +120,8 @@ kernel void kernel_set_rows_f32_i32(
         ulong         nb01,
         ulong         nb02,
         ulong         nb03,
-        int           ne11,
-        int           ne12,
+        uint4         ne11,
+        uint4         ne12,
         ulong         nb10,
         ulong         nb11,
         ulong         nb12,
@@ -127,8 +142,10 @@ kernel void kernel_set_rows_f32_i32(
         return;
     }
 
-    int i12 = i03%ne12;
-    int i11 = i02%ne11;
+    //int i12 = i03%ne12;
+    //int i11 = i02%ne11;
+    int i12 = fastmod(i03, ne12);
+    int i11 = fastmod(i02, ne11);
 
     int i10 = i01;
     int i1  = ((global int *)(src1 + i10*nb10 + i11*nb11 + i12*nb12))[0];
@@ -152,8 +169,8 @@ kernel void kernel_set_rows_f16_i32(
         ulong         nb01,
         ulong         nb02,
         ulong         nb03,
-        int           ne11,
-        int           ne12,
+        uint4         ne11,
+        uint4         ne12,
         ulong         nb10,
         ulong         nb11,
         ulong         nb12,
@@ -174,8 +191,10 @@ kernel void kernel_set_rows_f16_i32(
         return;
     }
 
-    int i12 = i03%ne12;
-    int i11 = i02%ne11;
+    //int i12 = i03%ne12;
+    //int i11 = i02%ne11;
+    int i12 = fastmod(i03, ne12);
+    int i11 = fastmod(i02, ne11);
 
     int i10 = i01;
     int i1  = ((global int *)(src1 + i10*nb10 + i11*nb11 + i12*nb12))[0];

From 2fc392ce358ac56a198a658ea30467b91ea95685 Mon Sep 17 00:00:00 2001
From: levkropp <levkropp@protonmail.com>
Date: Tue, 11 Nov 2025 03:38:30 -0500
Subject: [PATCH 153/185] convert : register UMT5Model architecture for T5
 conversion (#17160)

Register UMT5Model as a supported architecture variant for T5 model conversion.
This allows the conversion to work for models downloaded with AutoModel.
---
 convert_hf_to_gguf.py | 1 +
 1 file changed, 1 insertion(+)

diff --git a/convert_hf_to_gguf.py b/convert_hf_to_gguf.py
index 13448fd6811..cc77a3db273 100755
--- a/convert_hf_to_gguf.py
+++ b/convert_hf_to_gguf.py
@@ -7354,6 +7354,7 @@ def prepare_tensors(self):
 @ModelBase.register("T5ForConditionalGeneration")
 @ModelBase.register("MT5ForConditionalGeneration")
 @ModelBase.register("UMT5ForConditionalGeneration")
+@ModelBase.register("UMT5Model")
 class T5Model(TextModel):
     model_arch = gguf.MODEL_ARCH.T5
 

From d2d626938aa7b0137df6a808e0637151806a9d5a Mon Sep 17 00:00:00 2001
From: "Nicolas B. Pierron" <nicolas.b.pierron@gmail.com>
Date: Tue, 11 Nov 2025 11:53:59 +0100
Subject: [PATCH 154/185] Install rpc-server when GGML_RPC is ON. (#17149)

---
 .devops/nix/package.nix  | 2 ++
 tools/rpc/CMakeLists.txt | 4 ++++
 2 files changed, 6 insertions(+)

diff --git a/.devops/nix/package.nix b/.devops/nix/package.nix
index 41748e89d5c..a13996bd68d 100644
--- a/.devops/nix/package.nix
+++ b/.devops/nix/package.nix
@@ -34,6 +34,7 @@
   rocmGpuTargets ? builtins.concatStringsSep ";" rocmPackages.clr.gpuTargets,
   enableCurl ? true,
   useVulkan ? false,
+  useRpc ? false,
   llamaVersion ? "0.0.0", # Arbitrary version, substituted by the flake
 
   # It's necessary to consistently use backendStdenv when building with CUDA support,
@@ -175,6 +176,7 @@ effectiveStdenv.mkDerivation (finalAttrs: {
       (cmakeBool "GGML_METAL" useMetalKit)
       (cmakeBool "GGML_VULKAN" useVulkan)
       (cmakeBool "GGML_STATIC" enableStatic)
+      (cmakeBool "GGML_RPC" useRpc)
     ]
     ++ optionals useCuda [
       (
diff --git a/tools/rpc/CMakeLists.txt b/tools/rpc/CMakeLists.txt
index c2c74814864..20f114ad9ba 100644
--- a/tools/rpc/CMakeLists.txt
+++ b/tools/rpc/CMakeLists.txt
@@ -2,3 +2,7 @@ set(TARGET rpc-server)
 add_executable(${TARGET} rpc-server.cpp)
 target_link_libraries(${TARGET} PRIVATE ggml)
 target_compile_features(${TARGET} PRIVATE cxx_std_17)
+
+if(LLAMA_TOOLS_INSTALL)
+    install(TARGETS ${TARGET} RUNTIME)
+endif()

From 4a5b8aff40277071dbb98e81b5d0cbbbd3c37283 Mon Sep 17 00:00:00 2001
From: Mike Abbott <furrysalamander@gmail.com>
Date: Tue, 11 Nov 2025 04:19:50 -0700
Subject: [PATCH 155/185] cmake : add version to all shared object files
 (#17091)

When compiling llama.cpp in Yocto, it fails QA checks because the generated so files aren't versioned.  This applies a version to all generated so files, allowing the package to build without errors.
---
 ggml/src/CMakeLists.txt   | 16 ++++++++++++++++
 src/CMakeLists.txt        |  5 +++++
 tools/mtmd/CMakeLists.txt |  5 +++++
 3 files changed, 26 insertions(+)

diff --git a/ggml/src/CMakeLists.txt b/ggml/src/CMakeLists.txt
index f30e4ac9020..628db3fd655 100644
--- a/ggml/src/CMakeLists.txt
+++ b/ggml/src/CMakeLists.txt
@@ -211,6 +211,11 @@ add_library(ggml-base
             ggml-quants.h
             gguf.cpp)
 
+set_target_properties(ggml-base PROPERTIES
+    VERSION ${GGML_VERSION}
+    SOVERSION ${GGML_VERSION_MAJOR}
+)
+
 target_include_directories(ggml-base PRIVATE .)
 if (GGML_BACKEND_DL)
     target_compile_definitions(ggml-base PUBLIC GGML_BACKEND_DL)
@@ -220,6 +225,11 @@ add_library(ggml
             ggml-backend-reg.cpp)
 add_library(ggml::ggml ALIAS ggml)
 
+set_target_properties(ggml PROPERTIES
+    VERSION ${GGML_VERSION}
+    SOVERSION ${GGML_VERSION_MAJOR}
+)
+
 if (GGML_BACKEND_DIR)
     if (NOT GGML_BACKEND_DL)
         message(FATAL_ERROR "GGML_BACKEND_DIR requires GGML_BACKEND_DL")
@@ -259,6 +269,12 @@ function(ggml_add_backend_library backend)
         target_compile_definitions(${backend} PUBLIC  GGML_BACKEND_SHARED)
     endif()
 
+    # Set versioning properties for all backend libraries
+    set_target_properties(${backend} PROPERTIES
+        VERSION ${GGML_VERSION}
+        SOVERSION ${GGML_VERSION_MAJOR}
+    )
+
     if(NOT GGML_AVAILABLE_BACKENDS)
         set(GGML_AVAILABLE_BACKENDS "${backend}"
             CACHE INTERNAL "List of backends for cmake package")
diff --git a/src/CMakeLists.txt b/src/CMakeLists.txt
index 630b2cddf67..6fc5b001010 100644
--- a/src/CMakeLists.txt
+++ b/src/CMakeLists.txt
@@ -132,6 +132,11 @@ add_library(llama
             models/graph-context-mamba.cpp
             )
 
+set_target_properties(llama PROPERTIES
+    VERSION ${LLAMA_INSTALL_VERSION}
+    SOVERSION 0
+)
+
 target_include_directories(llama PRIVATE .)
 target_include_directories(llama PUBLIC ../include)
 target_compile_features   (llama PRIVATE cxx_std_17) # don't bump
diff --git a/tools/mtmd/CMakeLists.txt b/tools/mtmd/CMakeLists.txt
index 2381012a0d0..f640ae2a6ea 100644
--- a/tools/mtmd/CMakeLists.txt
+++ b/tools/mtmd/CMakeLists.txt
@@ -13,6 +13,11 @@ add_library(mtmd
             mtmd-helper.h
             )
 
+set_target_properties(mtmd PROPERTIES
+    VERSION ${LLAMA_INSTALL_VERSION}
+    SOVERSION 0
+)
+
 target_link_libraries     (mtmd PUBLIC ggml llama)
 target_link_libraries     (mtmd PRIVATE Threads::Threads)
 target_include_directories(mtmd PUBLIC  .)

From 8c583242adfe09cbf35e41353aa01fb96da301a0 Mon Sep 17 00:00:00 2001
From: Charles Xu <charles.xu@arm.com>
Date: Tue, 11 Nov 2025 12:20:31 +0100
Subject: [PATCH 156/185] kleidiai: add optimized per-channel kernels for Q8_0
 (#16993)

---
 ggml/src/ggml-cpu/CMakeLists.txt        |  18 +-
 ggml/src/ggml-cpu/kleidiai/kernels.cpp  | 283 ++++++++++++++++++++++++
 ggml/src/ggml-cpu/kleidiai/kernels.h    |   1 +
 ggml/src/ggml-cpu/kleidiai/kleidiai.cpp | 269 +++++++++++++++++++---
 4 files changed, 534 insertions(+), 37 deletions(-)

diff --git a/ggml/src/ggml-cpu/CMakeLists.txt b/ggml/src/ggml-cpu/CMakeLists.txt
index a55191aede9..e52e050a81a 100644
--- a/ggml/src/ggml-cpu/CMakeLists.txt
+++ b/ggml/src/ggml-cpu/CMakeLists.txt
@@ -590,6 +590,7 @@ function(ggml_add_cpu_backend_variant_impl tag_name)
             ${KLEIDIAI_SRC}/kai/ukernels/
             ${KLEIDIAI_SRC}/kai/ukernels/matmul/
             ${KLEIDIAI_SRC}/kai/ukernels/matmul/matmul_clamp_f32_qsi8d32p_qsi4c32p/
+            ${KLEIDIAI_SRC}/kai/ukernels/matmul/matmul_clamp_f32_qai8dxp_qsi8cxp/
             ${KLEIDIAI_SRC}/kai/ukernels/matmul/matmul_clamp_fp32_bf16p_bf16p/
             ${KLEIDIAI_SRC}/kai/ukernels/matmul/pack/)
 
@@ -608,23 +609,34 @@ function(ggml_add_cpu_backend_variant_impl tag_name)
             ${KLEIDIAI_SRC}/kai/ukernels/matmul/pack/kai_lhs_quant_pack_qsi8d32p4x8sb_f32_neon.c
             ${KLEIDIAI_SRC}/kai/ukernels/matmul/pack/kai_rhs_pack_nxk_qsi4c32ps1s0scalef16_qsu4c32s16s0_neon.c
             ${KLEIDIAI_SRC}/kai/ukernels/matmul/pack/kai_lhs_quant_pack_qsi8d32p_f32_neon.c
-            ${KLEIDIAI_SRC}/kai/ukernels/matmul/pack/kai_rhs_pack_nxk_qsi4c32pscalef16_qsu4c32s16s0.c)
+            ${KLEIDIAI_SRC}/kai/ukernels/matmul/pack/kai_rhs_pack_nxk_qsi4c32pscalef16_qsu4c32s16s0.c
+            ${KLEIDIAI_SRC}/kai/ukernels/matmul/pack/kai_lhs_quant_pack_qai8dxp_f32.c
+            ${KLEIDIAI_SRC}/kai/ukernels/matmul/pack/kai_rhs_pack_nxk_qsi8cxp_qsi8cx_neon.c)
 
         if (NOT DOTPROD_ENABLED MATCHES -1)
             list(APPEND GGML_KLEIDIAI_SOURCES
                 ${KLEIDIAI_SRC}/kai/ukernels/matmul/matmul_clamp_f32_qsi8d32p_qsi4c32p/kai_matmul_clamp_f32_qsi8d32p1x8_qsi4c32p4x8_1x4x32_neon_dotprod.c
                 ${KLEIDIAI_SRC}/kai/ukernels/matmul/matmul_clamp_f32_qsi8d32p_qsi4c32p/kai_matmul_clamp_f32_qsi8d32p1x4_qsi4c32p4x4_1x4_neon_dotprod.c
-                ${KLEIDIAI_SRC}/kai/ukernels/matmul/matmul_clamp_f32_qsi8d32p_qsi4c32p/kai_matmul_clamp_f32_qsi8d32p4x4_qsi4c32p4x4_16x4_neon_dotprod.c)
+                ${KLEIDIAI_SRC}/kai/ukernels/matmul/matmul_clamp_f32_qsi8d32p_qsi4c32p/kai_matmul_clamp_f32_qsi8d32p4x4_qsi4c32p4x4_16x4_neon_dotprod.c
+                ${KLEIDIAI_SRC}/kai/ukernels/matmul/matmul_clamp_f32_qai8dxp_qsi8cxp/kai_matmul_clamp_f32_qai8dxp4x4_qsi8cxp4x4_16x4_neon_dotprod.c
+                ${KLEIDIAI_SRC}/kai/ukernels/matmul/matmul_clamp_f32_qai8dxp_qsi8cxp/kai_matmul_clamp_f32_qai8dxp1x4_qsi8cxp4x4_1x4_neon_dotprod.c
+                ${KLEIDIAI_SRC}/kai/ukernels/matmul/matmul_clamp_f32_qai8dxp_qsi8cxp/kai_matmul_clamp_f32_qai8dxp1x8_qsi8cxp4x8_1x4_neon_dotprod.c)
         endif()
 
         if (NOT I8MM_ENABLED MATCHES -1)
-            list(APPEND GGML_KLEIDIAI_SOURCES ${KLEIDIAI_SRC}/kai/ukernels/matmul/matmul_clamp_f32_qsi8d32p_qsi4c32p/kai_matmul_clamp_f32_qsi8d32p4x8_qsi4c32p4x8_16x4_neon_i8mm.c)
+            list(APPEND GGML_KLEIDIAI_SOURCES
+                ${KLEIDIAI_SRC}/kai/ukernels/matmul/matmul_clamp_f32_qsi8d32p_qsi4c32p/kai_matmul_clamp_f32_qsi8d32p4x8_qsi4c32p4x8_16x4_neon_i8mm.c
+                ${KLEIDIAI_SRC}/kai/ukernels/matmul/matmul_clamp_f32_qai8dxp_qsi8cxp/kai_matmul_clamp_f32_qai8dxp4x8_qsi8cxp4x8_16x4_neon_i8mm.c)
         endif()
 
         if (NOT SME_ENABLED MATCHES -1)
             list(APPEND GGML_KLEIDIAI_SOURCES
                 ${KLEIDIAI_SRC}/kai/ukernels/matmul/matmul_clamp_f32_qsi8d32p_qsi4c32p/kai_matmul_clamp_f32_qsi8d32p1vlx4_qsi4c32p4vlx4_1vlx4vl_sme2_mopa.c
                 ${KLEIDIAI_SRC}/kai/ukernels/matmul/matmul_clamp_f32_qsi8d32p_qsi4c32p/kai_matmul_clamp_f32_qsi8d32p1x4_qsi4c32p4vlx4_1x4vl_sme2_sdot.c
+                ${KLEIDIAI_SRC}/kai/ukernels/matmul/matmul_clamp_f32_qai8dxp_qsi8cxp/kai_matmul_clamp_f32_qai8dxp1vlx4_qsi8cxp4vlx4_1vlx4vl_sme2_mopa.c
+                ${KLEIDIAI_SRC}/kai/ukernels/matmul/matmul_clamp_f32_qai8dxp_qsi8cxp/kai_matmul_clamp_f32_qai8dxp1vlx4_qsi8cxp4vlx4_1vlx4vl_sme2_mopa_asm.S
+                ${KLEIDIAI_SRC}/kai/ukernels/matmul/matmul_clamp_f32_qai8dxp_qsi8cxp/kai_matmul_clamp_f32_qai8dxp1x4_qsi8cxp4vlx4_1x4vl_sme2_dot.c
+                ${KLEIDIAI_SRC}/kai/ukernels/matmul/matmul_clamp_f32_qai8dxp_qsi8cxp/kai_matmul_clamp_f32_qai8dxp1x4_qsi8cxp4vlx4_1x4vl_sme2_dot_asm.S
                 ${KLEIDIAI_SRC}/kai/ukernels/matmul/matmul_clamp_fp32_bf16p_bf16p/kai_matmul_clamp_f32_bf16p2vlx2_bf16p2vlx2_2vlx2vl_sme2_mopa.c
                 ${KLEIDIAI_SRC}/kai/ukernels/matmul/matmul_clamp_fp32_bf16p_bf16p/kai_matmul_clamp_f32_bf16p2vlx2_bf16p2vlx2_2vlx2vl_sme2_mopa_asm.S
                 ${KLEIDIAI_SRC}/kai/ukernels/matmul/pack/kai_lhs_pack_bf16p2vlx2_f32_sme.c
diff --git a/ggml/src/ggml-cpu/kleidiai/kernels.cpp b/ggml/src/ggml-cpu/kleidiai/kernels.cpp
index 3eaa5e3f410..1d5b44f9fe3 100644
--- a/ggml/src/ggml-cpu/kleidiai/kernels.cpp
+++ b/ggml/src/ggml-cpu/kleidiai/kernels.cpp
@@ -4,6 +4,7 @@
 
 // KleidiAI micro-kernels
 #include "kai_matmul_clamp_f32_qsi8d32p_qsi4c32p_interface.h"
+#include "kai_matmul_clamp_f32_qai8dxp_qsi8cxp_interface.h"
 #include "kai_matmul_clamp_f32_qsi8d32p1x8_qsi4c32p4x8_1x4x32_neon_dotprod.h"
 #include "kai_matmul_clamp_f32_qsi8d32p1x4_qsi4c32p4x4_1x4_neon_dotprod.h"
 #include "kai_matmul_clamp_f32_qsi8d32p4x4_qsi4c32p4x4_16x4_neon_dotprod.h"
@@ -11,20 +12,31 @@
 #include "kai_matmul_clamp_f32_qsi8d32p1vlx4_qsi4c32p4vlx4_1vlx4vl_sme2_mopa.h"
 #include "kai_matmul_clamp_f32_qsi8d32p1x4_qsi4c32p4vlx4_1x4vl_sme2_sdot.h"
 #include "kai_matmul_clamp_f32_bf16p2vlx2_bf16p2vlx2_2vlx2vl_sme2_mopa.h"
+#include "kai_matmul_clamp_f32_qai8dxp1vlx4_qsi8cxp4vlx4_1vlx4vl_sme2_mopa.h"
+#include "kai_matmul_clamp_f32_qai8dxp1x4_qsi8cxp4vlx4_1x4vl_sme2_dot.h"
+#include "kai_matmul_clamp_f32_qai8dxp1x8_qsi8cxp4x8_1x4_neon_dotprod.h"
+#include "kai_matmul_clamp_f32_qai8dxp1x4_qsi8cxp4x4_1x4_neon_dotprod.h"
+#include "kai_matmul_clamp_f32_qai8dxp4x4_qsi8cxp4x4_16x4_neon_dotprod.h"
+#include "kai_matmul_clamp_f32_qai8dxp4x8_qsi8cxp4x8_16x4_neon_i8mm.h"
 
 #include "kai_lhs_pack_bf16p2vlx2_f32_sme.h"
 #include "kai_lhs_quant_pack_qsi8d32p_f32.h"
 #include "kai_lhs_quant_pack_qsi8d32p4x8sb_f32_neon.h"
 #include "kai_lhs_quant_pack_qsi8d32p_f32_neon.h"
+#include "kai_lhs_quant_pack_qai8dxp_f32.h"
 
 #include "kai_rhs_pack_kxn_bf16p2vlx2b_f32_x32_sme.h"
 #include "kai_rhs_pack_nxk_qsi4c32pscalef16_qsu4c32s16s0.h"
 #include "kai_rhs_pack_nxk_qsi4c32ps1s0scalef16_qsu4c32s16s0_neon.h"
+#include "kai_rhs_pack_nxk_qsi8cxp_qsi8cx_neon.h"
 
 #include "kai_common.h"
 
 #include "simd-mappings.h"
 
+#define GGML_COMMON_DECL_CPP
+#include "ggml-common.h"
+
 #include "kernels.h"
 
 #define NELEMS(x) sizeof(x) / sizeof(*x)
@@ -55,6 +67,14 @@ static inline void kernel_run_fn10(size_t m, size_t n, size_t k, size_t /*bl*/,
     Fn(m, n, k, lhs, rhs, dst, dst_stride_row, dst_stride_col, clamp_min, clamp_max);
 }
 
+template<void(*Fn)(size_t,size_t,size_t,const void*,const void*,float*,size_t,size_t,float,float)>
+static inline void kernel_run_float_fn10(size_t m, size_t n, size_t k, size_t /*bl*/,
+                                     const void* lhs, const void* rhs, void* dst,
+                                     size_t dst_stride_row, size_t dst_stride_col,
+                                     float clamp_min, float clamp_max) {
+    Fn(m, n, k, lhs, rhs, static_cast<float*>(dst), dst_stride_row, dst_stride_col, clamp_min, clamp_max);
+}
+
 template<size_t(*Fn)(size_t,size_t,size_t,size_t,size_t,size_t)>
 static inline size_t lhs_ps_fn6(size_t m, size_t k, size_t bl, size_t mr, size_t kr, size_t sr) {
     return Fn(m, k, bl, mr, kr, sr);
@@ -93,6 +113,12 @@ static inline void lhs_pack_void_fn9(size_t m, size_t k, size_t /*bl*/, size_t m
     Fn(m, k, mr, kr, sr, m_idx_start, lhs, lhs_stride, lhs_packed);
 }
 
+template<void(*Fn)(size_t,size_t,size_t,size_t,size_t,size_t,const float*,size_t,void*)>
+static inline void lhs_pack_float_fn9_no_bl(size_t m, size_t k, size_t /*bl*/, size_t mr, size_t kr, size_t sr,
+                                            size_t m_idx_start, const void * lhs, size_t lhs_stride, void * lhs_packed) {
+    Fn(m, k, mr, kr, sr, m_idx_start, static_cast<const float*>(lhs), lhs_stride, lhs_packed);
+}
+
 template<size_t(*Fn)(size_t,size_t,size_t,size_t,size_t)>
 static inline size_t rhs_ps_fn5(size_t n, size_t k, size_t nr, size_t kr, size_t bl) {
     return Fn(n, k, nr, kr, bl);
@@ -124,6 +150,18 @@ static inline void rhs_pack_fn12(size_t num_groups, size_t n, size_t k, size_t n
        static_cast<const kai_rhs_pack_qs4cxs1s0_param*>(params));
 }
 
+template<void(*Fn)(size_t,size_t,size_t,size_t,size_t,size_t,const int8_t*,const float*,const float*,void*,size_t,const struct kai_rhs_pack_qsi8cx_params*)>
+static inline void rhs_pack_scale_fn12(size_t num_groups, size_t n, size_t k, size_t nr, size_t kr, size_t sr, size_t /*bl*/,
+                                               size_t /*rhs_stride*/, const void* rhs, const void* bias, const void* scale,
+                                               void* rhs_packed, size_t extra_bytes, const void* params) {
+    Fn(num_groups, n, k, nr, kr, sr,
+       static_cast<const int8_t*>(rhs),
+       static_cast<const float*>(bias),
+       static_cast<const float*>(scale),
+       rhs_packed, extra_bytes,
+       static_cast<const kai_rhs_pack_qsi8cx_params*>(params));
+}
+
 template<void(*Fn)(size_t,size_t,size_t,size_t,size_t,size_t,size_t,const void*,const void*,const void*,void*,size_t,const void*)>
 static inline void rhs_pack_fn13(size_t num_groups, size_t n, size_t k, size_t nr, size_t kr, size_t sr, size_t /*bl*/,
                                                size_t rhs_stride, const void* rhs, const void* bias, const void* scale,
@@ -213,6 +251,57 @@ static void dequantize_row_qsi4c32ps1s0scalef16(
     GGML_UNUSED(kr);
 }
 
+static void dequantize_row_qsi8cxp(
+    const void *packed_data,
+    int32_t row_idx,
+    int64_t k,
+    float *out,
+    size_t nr,
+    size_t packed_row_stride,
+    size_t kr,
+    size_t bl,
+    size_t num_bytes_multiplier
+) {
+    GGML_UNUSED(bl);
+    GGML_UNUSED(num_bytes_multiplier);
+
+    const size_t k_internal = ((size_t) k + QK8_0 - 1) / QK8_0 * QK8_0;
+    const size_t group_idx = row_idx / nr;
+    const size_t row_in_group = row_idx % nr;
+
+    const uint8_t * group_ptr = static_cast<const uint8_t *>(packed_data) + group_idx * packed_row_stride;
+    const int8_t  * data_base = reinterpret_cast<const int8_t *>(group_ptr);
+
+    const size_t num_blocks = k_internal / kr;
+
+    for (size_t block = 0; block < num_blocks; ++block) {
+        const int8_t * block_ptr = data_base + (block * nr + row_in_group) * kr;
+        for (size_t i = 0; i < kr; ++i) {
+            const size_t k_idx = block * kr + i;
+            if (k_idx < (size_t) k) {
+                out[k_idx] = static_cast<float>(block_ptr[i]);
+            }
+        }
+    }
+
+    const uint8_t * sums_ptr = group_ptr + nr * k_internal;
+    GGML_UNUSED(sums_ptr);
+
+    const float * scale_ptr = reinterpret_cast<const float *>(sums_ptr + nr * sizeof(int32_t));
+    const float scale = scale_ptr[row_in_group];
+
+    if (scale == 0.0f) {
+        for (size_t i = 0; i < (size_t) k; ++i) {
+            out[i] = 0.0f;
+        }
+        return;
+    }
+
+    for (size_t i = 0; i < (size_t) k; ++i) {
+        out[i] *= scale;
+    }
+}
+
 static ggml_kleidiai_kernels gemm_gemv_kernels[] = {
 #if defined(__ARM_FEATURE_SME)
     {
@@ -548,6 +637,174 @@ static ggml_kleidiai_kernels gemm_gemv_kernels[] = {
 #endif
 };
 
+static ggml_kleidiai_kernels gemm_gemv_kernels_q8[] = {
+#if defined(__ARM_FEATURE_SME)
+    {
+        /* SME GEMM */
+        {
+            /* .get_m_step            = */ kai_get_m_step_matmul_clamp_f32_qai8dxp1vlx4_qsi8cxp4vlx4_1vlx4vl_sme2_mopa,
+            /* .get_n_step            = */ kai_get_n_step_matmul_clamp_f32_qai8dxp1vlx4_qsi8cxp4vlx4_1vlx4vl_sme2_mopa,
+            /* .get_mr                = */ kai_get_mr_matmul_clamp_f32_qai8dxp1vlx4_qsi8cxp4vlx4_1vlx4vl_sme2_mopa,
+            /* .get_nr                = */ kai_get_nr_matmul_clamp_f32_qai8dxp1vlx4_qsi8cxp4vlx4_1vlx4vl_sme2_mopa,
+            /* .get_kr                = */ kai_get_kr_matmul_clamp_f32_qai8dxp1vlx4_qsi8cxp4vlx4_1vlx4vl_sme2_mopa,
+            /* .get_sr                = */ kai_get_sr_matmul_clamp_f32_qai8dxp1vlx4_qsi8cxp4vlx4_1vlx4vl_sme2_mopa,
+            /* .get_dst_offset        = */ kai_get_dst_offset_matmul_clamp_f32_qai8dxp1vlx4_qsi8cxp4vlx4_1vlx4vl_sme2_mopa,
+            /* .get_dst_size          = */ kai_get_dst_size_matmul_clamp_f32_qai8dxp1vlx4_qsi8cxp4vlx4_1vlx4vl_sme2_mopa,
+            /* .get_lhs_offset_ex     = */ &kernel_offs_fn2<kai_get_lhs_packed_offset_matmul_clamp_f32_qai8dxp1vlx4_qsi8cxp4vlx4_1vlx4vl_sme2_mopa>,
+            /* .get_rhs_packed_offset_ex = */ &kernel_offs_fn2<kai_get_rhs_packed_offset_matmul_clamp_f32_qai8dxp1vlx4_qsi8cxp4vlx4_1vlx4vl_sme2_mopa>,
+            /* .run_kernel_ex         = */ &kernel_run_float_fn10<kai_run_matmul_clamp_f32_qai8dxp1vlx4_qsi8cxp4vlx4_1vlx4vl_sme2_mopa>,
+        },
+        /* .gemm_lhs_info = */ {
+            /* .get_offset            = */ kai_get_lhs_offset_lhs_quant_pack_qai8dxp_f32,
+            /* .get_packed_offset_ex  = */ &lhs_offs_fn5<kai_get_lhs_packed_offset_lhs_quant_pack_qai8dxp_f32>,
+            /* .packed_size_ex        = */ &lhs_ps_fn5<kai_get_lhs_packed_size_lhs_quant_pack_qai8dxp_f32>,
+            /* .pack_func_ex          = */ &lhs_pack_float_fn9_no_bl<kai_run_lhs_quant_pack_qai8dxp_f32>,
+        },
+        /* SME GEMV */
+        {
+            /* .get_m_step            = */ kai_get_m_step_matmul_clamp_f32_qai8dxp1x4_qsi8cxp4vlx4_1x4vl_sme2_dot,
+            /* .get_n_step            = */ kai_get_n_step_matmul_clamp_f32_qai8dxp1x4_qsi8cxp4vlx4_1x4vl_sme2_dot,
+            /* .get_mr                = */ kai_get_mr_matmul_clamp_f32_qai8dxp1x4_qsi8cxp4vlx4_1x4vl_sme2_dot,
+            /* .get_nr                = */ kai_get_nr_matmul_clamp_f32_qai8dxp1x4_qsi8cxp4vlx4_1x4vl_sme2_dot,
+            /* .get_kr                = */ kai_get_kr_matmul_clamp_f32_qai8dxp1x4_qsi8cxp4vlx4_1x4vl_sme2_dot,
+            /* .get_sr                = */ kai_get_sr_matmul_clamp_f32_qai8dxp1x4_qsi8cxp4vlx4_1x4vl_sme2_dot,
+            /* .get_dst_offset        = */ kai_get_dst_offset_matmul_clamp_f32_qai8dxp1x4_qsi8cxp4vlx4_1x4vl_sme2_dot,
+            /* .get_dst_size          = */ kai_get_dst_size_matmul_clamp_f32_qai8dxp1x4_qsi8cxp4vlx4_1x4vl_sme2_dot,
+            /* .get_lhs_offset_ex     = */ &kernel_offs_fn2<kai_get_lhs_packed_offset_matmul_clamp_f32_qai8dxp1x4_qsi8cxp4vlx4_1x4vl_sme2_dot>,
+            /* .get_rhs_packed_offset_ex = */ &kernel_offs_fn2<kai_get_rhs_packed_offset_matmul_clamp_f32_qai8dxp1x4_qsi8cxp4vlx4_1x4vl_sme2_dot>,
+            /* .run_kernel_ex         = */ &kernel_run_float_fn10<kai_run_matmul_clamp_f32_qai8dxp1x4_qsi8cxp4vlx4_1x4vl_sme2_dot>,
+        },
+        /* .gemv_lhs_info = */ {
+            /* .get_offset            = */ kai_get_lhs_offset_lhs_quant_pack_qai8dxp_f32,
+            /* .get_packed_offset_ex  = */ &lhs_offs_fn5<kai_get_lhs_packed_offset_lhs_quant_pack_qai8dxp_f32>,
+            /* .packed_size_ex        = */ &lhs_ps_fn5<kai_get_lhs_packed_size_lhs_quant_pack_qai8dxp_f32>,
+            /* .pack_func_ex          = */ &lhs_pack_float_fn9_no_bl<kai_run_lhs_quant_pack_qai8dxp_f32>,
+        },
+        /* .rhs_info = */ {
+            /* .packed_stride         = */ kai_get_rhs_packed_stride_rhs_pack_nxk_qsi8cxp_qsi8cx_neon,
+            /* .to_float              = */ dequantize_row_qsi8cxp,
+            /* .packed_size_ex        = */ &rhs_ps_fn5<kai_get_rhs_packed_size_rhs_pack_nxk_qsi8cxp_qsi8cx_neon>,
+            /* .packed_stride_ex      = */ &rhs_stride_fn4<kai_get_rhs_packed_stride_rhs_pack_nxk_qsi8cxp_qsi8cx_neon>,
+            /* .pack_func_ex          = */ &rhs_pack_scale_fn12<kai_run_rhs_pack_nxk_qsi8cxp_qsi8cx_neon>,
+        },
+        /* .required_cpu       = */ CPU_FEATURE_SME,
+        /* .lhs_type           = */ GGML_TYPE_F32,
+        /* .rhs_type           = */ GGML_TYPE_Q8_0,
+        /* .op_type            = */ GGML_TYPE_F32,
+    },
+#endif
+#if defined(__ARM_FEATURE_MATMUL_INT8)
+    {
+        /* I8MM GEMM */
+        {
+            /* .get_m_step            = */ kai_get_m_step_matmul_clamp_f32_qai8dxp4x8_qsi8cxp4x8_16x4_neon_i8mm,
+            /* .get_n_step            = */ kai_get_n_step_matmul_clamp_f32_qai8dxp4x8_qsi8cxp4x8_16x4_neon_i8mm,
+            /* .get_mr                = */ kai_get_mr_matmul_clamp_f32_qai8dxp4x8_qsi8cxp4x8_16x4_neon_i8mm,
+            /* .get_nr                = */ kai_get_nr_matmul_clamp_f32_qai8dxp4x8_qsi8cxp4x8_16x4_neon_i8mm,
+            /* .get_kr                = */ kai_get_kr_matmul_clamp_f32_qai8dxp4x8_qsi8cxp4x8_16x4_neon_i8mm,
+            /* .get_sr                = */ kai_get_sr_matmul_clamp_f32_qai8dxp4x8_qsi8cxp4x8_16x4_neon_i8mm,
+            /* .get_dst_offset        = */ kai_get_dst_offset_matmul_clamp_f32_qai8dxp4x8_qsi8cxp4x8_16x4_neon_i8mm,
+            /* .get_dst_size          = */ kai_get_dst_size_matmul_clamp_f32_qai8dxp4x8_qsi8cxp4x8_16x4_neon_i8mm,
+            /* .get_lhs_offset_ex     = */ &kernel_offs_fn2<kai_get_lhs_packed_offset_matmul_clamp_f32_qai8dxp4x8_qsi8cxp4x8_16x4_neon_i8mm>,
+            /* .get_rhs_packed_offset_ex = */ &kernel_offs_fn2<kai_get_rhs_packed_offset_matmul_clamp_f32_qai8dxp4x8_qsi8cxp4x8_16x4_neon_i8mm>,
+            /* .run_kernel_ex         = */ &kernel_run_float_fn10<kai_run_matmul_clamp_f32_qai8dxp4x8_qsi8cxp4x8_16x4_neon_i8mm>,
+        },
+        /* .gemm_lhs_info = */ {
+            /* .get_offset            = */ kai_get_lhs_offset_lhs_quant_pack_qai8dxp_f32,
+            /* .get_packed_offset_ex  = */ &lhs_offs_fn5<kai_get_lhs_packed_offset_lhs_quant_pack_qai8dxp_f32>,
+            /* .packed_size_ex        = */ &lhs_ps_fn5<kai_get_lhs_packed_size_lhs_quant_pack_qai8dxp_f32>,
+            /* .pack_func_ex          = */ &lhs_pack_float_fn9_no_bl<kai_run_lhs_quant_pack_qai8dxp_f32>,
+        },
+        /* I8MM GEMV (dotprod fallback) */
+        {
+            /* .get_m_step            = */ kai_get_m_step_matmul_clamp_f32_qai8dxp1x8_qsi8cxp4x8_1x4_neon_dotprod,
+            /* .get_n_step            = */ kai_get_n_step_matmul_clamp_f32_qai8dxp1x8_qsi8cxp4x8_1x4_neon_dotprod,
+            /* .get_mr                = */ kai_get_mr_matmul_clamp_f32_qai8dxp1x8_qsi8cxp4x8_1x4_neon_dotprod,
+            /* .get_nr                = */ kai_get_nr_matmul_clamp_f32_qai8dxp1x8_qsi8cxp4x8_1x4_neon_dotprod,
+            /* .get_kr                = */ kai_get_kr_matmul_clamp_f32_qai8dxp1x8_qsi8cxp4x8_1x4_neon_dotprod,
+            /* .get_sr                = */ kai_get_sr_matmul_clamp_f32_qai8dxp1x8_qsi8cxp4x8_1x4_neon_dotprod,
+            /* .get_dst_offset        = */ kai_get_dst_offset_matmul_clamp_f32_qai8dxp1x8_qsi8cxp4x8_1x4_neon_dotprod,
+            /* .get_dst_size          = */ kai_get_dst_size_matmul_clamp_f32_qai8dxp1x8_qsi8cxp4x8_1x4_neon_dotprod,
+            /* .get_lhs_offset_ex     = */ &kernel_offs_fn2<kai_get_lhs_packed_offset_matmul_clamp_f32_qai8dxp1x8_qsi8cxp4x8_1x4_neon_dotprod>,
+            /* .get_rhs_packed_offset_ex = */ &kernel_offs_fn2<kai_get_rhs_packed_offset_matmul_clamp_f32_qai8dxp1x8_qsi8cxp4x8_1x4_neon_dotprod>,
+            /* .run_kernel_ex         = */ &kernel_run_float_fn10<kai_run_matmul_clamp_f32_qai8dxp1x8_qsi8cxp4x8_1x4_neon_dotprod>,
+        },
+        /* .gemv_lhs_info = */ {
+            /* .get_offset            = */ kai_get_lhs_offset_lhs_quant_pack_qai8dxp_f32,
+            /* .get_packed_offset_ex  = */ &lhs_offs_fn5<kai_get_lhs_packed_offset_lhs_quant_pack_qai8dxp_f32>,
+            /* .packed_size_ex        = */ &lhs_ps_fn5<kai_get_lhs_packed_size_lhs_quant_pack_qai8dxp_f32>,
+            /* .pack_func_ex          = */ &lhs_pack_float_fn9_no_bl<kai_run_lhs_quant_pack_qai8dxp_f32>,
+        },
+        /* .rhs_info = */ {
+            /* .packed_stride         = */ kai_get_rhs_packed_stride_rhs_pack_nxk_qsi8cxp_qsi8cx_neon,
+            /* .to_float              = */ dequantize_row_qsi8cxp,
+            /* .packed_size_ex        = */ &rhs_ps_fn5<kai_get_rhs_packed_size_rhs_pack_nxk_qsi8cxp_qsi8cx_neon>,
+            /* .packed_stride_ex      = */ &rhs_stride_fn4<kai_get_rhs_packed_stride_rhs_pack_nxk_qsi8cxp_qsi8cx_neon>,
+            /* .pack_func_ex          = */ &rhs_pack_scale_fn12<kai_run_rhs_pack_nxk_qsi8cxp_qsi8cx_neon>,
+        },
+        /* .required_cpu       = */ CPU_FEATURE_DOTPROD | CPU_FEATURE_I8MM,
+        /* .lhs_type           = */ GGML_TYPE_F32,
+        /* .rhs_type           = */ GGML_TYPE_Q8_0,
+        /* .op_type            = */ GGML_TYPE_F32,
+    },
+#endif
+#if defined(__ARM_FEATURE_DOTPROD)
+    {
+        /* DOTPROD GEMM */
+        {
+            /* .get_m_step            = */ kai_get_m_step_matmul_clamp_f32_qai8dxp4x4_qsi8cxp4x4_16x4_neon_dotprod,
+            /* .get_n_step            = */ kai_get_n_step_matmul_clamp_f32_qai8dxp4x4_qsi8cxp4x4_16x4_neon_dotprod,
+            /* .get_mr                = */ kai_get_mr_matmul_clamp_f32_qai8dxp4x4_qsi8cxp4x4_16x4_neon_dotprod,
+            /* .get_nr                = */ kai_get_nr_matmul_clamp_f32_qai8dxp4x4_qsi8cxp4x4_16x4_neon_dotprod,
+            /* .get_kr                = */ kai_get_kr_matmul_clamp_f32_qai8dxp4x4_qsi8cxp4x4_16x4_neon_dotprod,
+            /* .get_sr                = */ kai_get_sr_matmul_clamp_f32_qai8dxp4x4_qsi8cxp4x4_16x4_neon_dotprod,
+            /* .get_dst_offset        = */ kai_get_dst_offset_matmul_clamp_f32_qai8dxp4x4_qsi8cxp4x4_16x4_neon_dotprod,
+            /* .get_dst_size          = */ kai_get_dst_size_matmul_clamp_f32_qai8dxp4x4_qsi8cxp4x4_16x4_neon_dotprod,
+            /* .get_lhs_offset_ex     = */ &kernel_offs_fn2<kai_get_lhs_packed_offset_matmul_clamp_f32_qai8dxp4x4_qsi8cxp4x4_16x4_neon_dotprod>,
+            /* .get_rhs_packed_offset_ex = */ &kernel_offs_fn2<kai_get_rhs_packed_offset_matmul_clamp_f32_qai8dxp4x4_qsi8cxp4x4_16x4_neon_dotprod>,
+            /* .run_kernel_ex         = */ &kernel_run_float_fn10<kai_run_matmul_clamp_f32_qai8dxp4x4_qsi8cxp4x4_16x4_neon_dotprod>,
+        },
+        /* .gemm_lhs_info = */ {
+            /* .get_offset            = */ kai_get_lhs_offset_lhs_quant_pack_qai8dxp_f32,
+            /* .get_packed_offset_ex  = */ &lhs_offs_fn5<kai_get_lhs_packed_offset_lhs_quant_pack_qai8dxp_f32>,
+            /* .packed_size_ex        = */ &lhs_ps_fn5<kai_get_lhs_packed_size_lhs_quant_pack_qai8dxp_f32>,
+            /* .pack_func_ex          = */ &lhs_pack_float_fn9_no_bl<kai_run_lhs_quant_pack_qai8dxp_f32>,
+        },
+        /* DOTPROD GEMV */
+        {
+            /* .get_m_step            = */ kai_get_m_step_matmul_clamp_f32_qai8dxp1x4_qsi8cxp4x4_1x4_neon_dotprod,
+            /* .get_n_step            = */ kai_get_n_step_matmul_clamp_f32_qai8dxp1x4_qsi8cxp4x4_1x4_neon_dotprod,
+            /* .get_mr                = */ kai_get_mr_matmul_clamp_f32_qai8dxp1x4_qsi8cxp4x4_1x4_neon_dotprod,
+            /* .get_nr                = */ kai_get_nr_matmul_clamp_f32_qai8dxp1x4_qsi8cxp4x4_1x4_neon_dotprod,
+            /* .get_kr                = */ kai_get_kr_matmul_clamp_f32_qai8dxp1x4_qsi8cxp4x4_1x4_neon_dotprod,
+            /* .get_sr                = */ kai_get_sr_matmul_clamp_f32_qai8dxp1x4_qsi8cxp4x4_1x4_neon_dotprod,
+            /* .get_dst_offset        = */ kai_get_dst_offset_matmul_clamp_f32_qai8dxp1x4_qsi8cxp4x4_1x4_neon_dotprod,
+            /* .get_dst_size          = */ kai_get_dst_size_matmul_clamp_f32_qai8dxp1x4_qsi8cxp4x4_1x4_neon_dotprod,
+            /* .get_lhs_offset_ex     = */ &kernel_offs_fn2<kai_get_lhs_packed_offset_matmul_clamp_f32_qai8dxp1x4_qsi8cxp4x4_1x4_neon_dotprod>,
+            /* .get_rhs_packed_offset_ex = */ &kernel_offs_fn2<kai_get_rhs_packed_offset_matmul_clamp_f32_qai8dxp1x4_qsi8cxp4x4_1x4_neon_dotprod>,
+            /* .run_kernel_ex         = */ &kernel_run_float_fn10<kai_run_matmul_clamp_f32_qai8dxp1x4_qsi8cxp4x4_1x4_neon_dotprod>,
+        },
+        /* .gemv_lhs_info = */ {
+            /* .get_offset            = */ kai_get_lhs_offset_lhs_quant_pack_qai8dxp_f32,
+            /* .get_packed_offset_ex  = */ &lhs_offs_fn5<kai_get_lhs_packed_offset_lhs_quant_pack_qai8dxp_f32>,
+            /* .packed_size_ex        = */ &lhs_ps_fn5<kai_get_lhs_packed_size_lhs_quant_pack_qai8dxp_f32>,
+            /* .pack_func_ex          = */ &lhs_pack_float_fn9_no_bl<kai_run_lhs_quant_pack_qai8dxp_f32>,
+        },
+        /* .rhs_info = */ {
+            /* .packed_stride         = */ kai_get_rhs_packed_stride_rhs_pack_nxk_qsi8cxp_qsi8cx_neon,
+            /* .to_float              = */ dequantize_row_qsi8cxp,
+            /* .packed_size_ex        = */ &rhs_ps_fn5<kai_get_rhs_packed_size_rhs_pack_nxk_qsi8cxp_qsi8cx_neon>,
+            /* .packed_stride_ex      = */ &rhs_stride_fn4<kai_get_rhs_packed_stride_rhs_pack_nxk_qsi8cxp_qsi8cx_neon>,
+            /* .pack_func_ex          = */ &rhs_pack_scale_fn12<kai_run_rhs_pack_nxk_qsi8cxp_qsi8cx_neon>,
+        },
+        /* .required_cpu       = */ CPU_FEATURE_DOTPROD,
+        /* .lhs_type           = */ GGML_TYPE_F32,
+        /* .rhs_type           = */ GGML_TYPE_Q8_0,
+        /* .op_type            = */ GGML_TYPE_F32,
+    },
+#endif
+};
+
 ggml_kleidiai_kernels * ggml_kleidiai_select_kernels(cpu_feature cpu_features, const ggml_tensor * tensor) {
     ggml_kleidiai_kernels * kernel = nullptr;
 
@@ -562,6 +819,17 @@ ggml_kleidiai_kernels * ggml_kleidiai_select_kernels(cpu_feature cpu_features, c
                 break;
             }
         }
+        if (!kernel) {
+            for (size_t i = 0; i < NELEMS(gemm_gemv_kernels_q8); ++i) {
+                if ((cpu_features & gemm_gemv_kernels_q8[i].required_cpu) == gemm_gemv_kernels_q8[i].required_cpu &&
+                    gemm_gemv_kernels_q8[i].lhs_type == tensor->src[1]->type &&
+                    gemm_gemv_kernels_q8[i].rhs_type == tensor->src[0]->type &&
+                    gemm_gemv_kernels_q8[i].op_type  == tensor->type) {
+                    kernel = &gemm_gemv_kernels_q8[i];
+                    break;
+                }
+            }
+        }
 #endif
     }
 
@@ -582,3 +850,18 @@ ggml_kleidiai_kernels * ggml_kleidiai_select_kernels_q4_0(cpu_feature features)
 
     return kernels;
 }
+
+ggml_kleidiai_kernels * ggml_kleidiai_select_kernels_q8_0(cpu_feature features) {
+    ggml_kleidiai_kernels * kernels = nullptr;
+
+#if defined(__ARM_FEATURE_SME) || defined(__ARM_FEATURE_DOTPROD) || defined(__ARM_FEATURE_MATMUL_INT8)
+    for (size_t i = 0; i < NELEMS(gemm_gemv_kernels_q8); ++i) {
+        if ((features & gemm_gemv_kernels_q8[i].required_cpu) == gemm_gemv_kernels_q8[i].required_cpu) {
+            kernels = &gemm_gemv_kernels_q8[i];
+            break;
+        }
+    }
+#endif
+
+    return kernels;
+}
diff --git a/ggml/src/ggml-cpu/kleidiai/kernels.h b/ggml/src/ggml-cpu/kleidiai/kernels.h
index a84795a6b2e..129245400b4 100644
--- a/ggml/src/ggml-cpu/kleidiai/kernels.h
+++ b/ggml/src/ggml-cpu/kleidiai/kernels.h
@@ -87,3 +87,4 @@ struct ggml_kleidiai_kernels {
 
 ggml_kleidiai_kernels * ggml_kleidiai_select_kernels(cpu_feature cpu_features, const ggml_tensor * tensor);
 ggml_kleidiai_kernels * ggml_kleidiai_select_kernels_q4_0(cpu_feature features);
+ggml_kleidiai_kernels * ggml_kleidiai_select_kernels_q8_0(cpu_feature features);
diff --git a/ggml/src/ggml-cpu/kleidiai/kleidiai.cpp b/ggml/src/ggml-cpu/kleidiai/kleidiai.cpp
index 8b3df7d7800..6f2a90fbda7 100644
--- a/ggml/src/ggml-cpu/kleidiai/kleidiai.cpp
+++ b/ggml/src/ggml-cpu/kleidiai/kleidiai.cpp
@@ -5,10 +5,13 @@
 #include <assert.h>
 #include <atomic>
 #include <cfloat>
+#include <cmath>
+#include <algorithm>
 #include <stdexcept>
 #include <stdint.h>
 #include <string.h>
 #include <string>
+#include <vector>
 #if defined(__linux__)
 #include <asm/hwcap.h>
 #include <sys/auxv.h>
@@ -38,8 +41,9 @@
 
 struct ggml_kleidiai_context {
     cpu_feature features;
-    ggml_kleidiai_kernels * kernels;
-} static ctx = { CPU_FEATURE_NONE, NULL };
+    ggml_kleidiai_kernels * kernels_q4;
+    ggml_kleidiai_kernels * kernels_q8;
+} static ctx = { CPU_FEATURE_NONE, NULL, NULL };
 
 static const char* cpu_feature_to_string(cpu_feature f) {
     switch (f) {
@@ -73,10 +77,14 @@ static void init_kleidiai_context(void) {
         if (sme_enabled != 0) {
             ctx.features |= ggml_cpu_has_sme() ? CPU_FEATURE_SME : CPU_FEATURE_NONE;
         }
-        ctx.kernels = ggml_kleidiai_select_kernels_q4_0(ctx.features);
+        ctx.kernels_q4 = ggml_kleidiai_select_kernels_q4_0(ctx.features);
+        ctx.kernels_q8 = ggml_kleidiai_select_kernels_q8_0(ctx.features);
 #ifndef NDEBUG
-        if (ctx.kernels) {
-            GGML_LOG_DEBUG("kleidiai: using kernel with CPU feature %s\n", cpu_feature_to_string(ctx.kernels->required_cpu));
+        if (ctx.kernels_q4) {
+            GGML_LOG_DEBUG("kleidiai: using q4 kernel with CPU feature %s\n", cpu_feature_to_string(ctx.kernels_q4->required_cpu));
+        }
+        if (ctx.kernels_q8) {
+            GGML_LOG_DEBUG("kleidiai: using q8 kernel with CPU feature %s\n", cpu_feature_to_string(ctx.kernels_q8->required_cpu));
         }
 #endif
     }
@@ -130,6 +138,9 @@ class tensor_traits : public ggml::cpu::tensor_traits {
         if (kernels->rhs_type == GGML_TYPE_Q4_0) {
             if (!lhs_info->packed_size_ex) return false;
             size = lhs_info->packed_size_ex(m, k, QK4_0, mr, kr, sr);
+        } else if (kernels->rhs_type == GGML_TYPE_Q8_0) {
+            if (!lhs_info->packed_size_ex) return false;
+            size = lhs_info->packed_size_ex(m, k, QK8_0, mr, kr, sr);
         } else if (kernels->rhs_type == GGML_TYPE_F16) {
             if (!lhs_info->packed_size_ex || !kernels->rhs_info.packed_size_ex) return false;
             const int64_t lhs_batch_size0 = op->src[1]->ne[2];
@@ -149,11 +160,13 @@ class tensor_traits : public ggml::cpu::tensor_traits {
         if (dst->op == GGML_OP_MUL_MAT) {
             if (dst->src[0]->type == GGML_TYPE_Q4_0) {
                 return compute_forward_q4_0(params, dst);
+            } else if (dst->src[0]->type == GGML_TYPE_Q8_0) {
+                return compute_forward_q8_0(params, dst);
             } else if (dst->src[0]->type == GGML_TYPE_F16) {
                 return compute_forward_fp16(params, dst);
             }
         } else if (dst->op == GGML_OP_GET_ROWS) {
-            if (dst->src[0]->type == GGML_TYPE_Q4_0) {
+            if (dst->src[0]->type == GGML_TYPE_Q4_0 || dst->src[0]->type == GGML_TYPE_Q8_0) {
                 return compute_forward_get_rows(params, dst);
             }
         }
@@ -400,19 +413,120 @@ class tensor_traits : public ggml::cpu::tensor_traits {
         return true;
     }
 
-    bool compute_forward_get_rows(struct ggml_compute_params * params, struct ggml_tensor * dst) {
-        GGML_ASSERT(dst->src[0]->type == GGML_TYPE_Q4_0);
-        if (!ctx.kernels) {
+    bool compute_forward_q8_0(struct ggml_compute_params * params, struct ggml_tensor * dst) {
+        GGML_ASSERT(dst->src[0]->type == GGML_TYPE_Q8_0);
+
+        const ggml_tensor * src0 = dst->src[0];
+        const ggml_tensor * src1 = dst->src[1];
+
+        GGML_TENSOR_BINARY_OP_LOCALS
+
+        ggml_kleidiai_kernels *kernels = ggml_kleidiai_select_kernels(ctx.features, dst);
+        if (!kernels) {
             return false;
         }
 
+        bool is_gemv = src1->ne[1] == 1;
+        kernel_info * kernel = is_gemv ? &kernels->gemv : &kernels->gemm;
+        lhs_packing_info * lhs_info = is_gemv ? &kernels->gemv_lhs_info : &kernels->gemm_lhs_info;
+
+        if (!kernel || !lhs_info->get_packed_offset_ex || !lhs_info->pack_func_ex ||
+            !kernel->get_rhs_packed_offset_ex || !kernel->run_kernel_ex || !kernel->get_dst_offset) {
+            return false;
+        }
+
+        const int ith = params->ith;
+        const int nth_raw = params->nth;
+        const int nth = nth_raw > 0 ? nth_raw : 1;
+
+        const size_t k = ne00;
+        const size_t m = ne11;
+        const size_t n = ne01;
+
+        size_t mr = kernel->get_mr();
+        size_t kr = kernel->get_kr();
+        size_t sr = kernel->get_sr();
+
+        const uint8_t * lhs        = static_cast<const uint8_t *>(src1->data);
+        uint8_t * lhs_packed       = static_cast<uint8_t *>(params->wdata);
+        const uint8_t * rhs_packed = static_cast<const uint8_t *>(src0->data);
+
+        const size_t n_step = kernel->get_n_step();
+        const size_t num_n_per_thread = kai_roundup(kai_roundup(n, nth) / nth, n_step);
+        const size_t n_start = ith * num_n_per_thread;
+
+        size_t n_to_process = 0;
+        if (n_start < n) {
+            n_to_process = num_n_per_thread;
+            if ((n_start + n_to_process) > n) {
+                n_to_process = n - n_start;
+            }
+        }
+
+        const size_t num_m_per_thread = kai_roundup(m, mr * nth) / nth;
+        const size_t m_start = ith * num_m_per_thread;
+        size_t m_to_process = num_m_per_thread;
+        if ((m_start + m_to_process) > m) {
+            m_to_process = m - m_start;
+        }
+
+        if (m_start < m) {
+            const size_t src_stride        = src1->nb[1];
+            const float * src_ptr          = reinterpret_cast<const float *>(lhs + lhs_info->get_offset(m_start, dst->src[1]->nb[1]));
+            const size_t lhs_packed_offset = lhs_info->get_packed_offset_ex(m_start, k, 0, mr, kr, sr);
+            void * lhs_packed_ptr          = static_cast<void *>(lhs_packed + lhs_packed_offset);
+
+            lhs_info->pack_func_ex(m_to_process, k, 0, mr, kr, sr, 0, src_ptr, src_stride, lhs_packed_ptr);
+        }
+
+        ggml_barrier(params->threadpool);
+
+        const size_t dst_stride        = dst->nb[1];
+        const size_t lhs_packed_offset = lhs_info->get_packed_offset_ex(0, k, 0, mr, kr, sr);
+        const size_t rhs_packed_offset = kernel->get_rhs_packed_offset_ex(n_start, k, 0);
+        const size_t dst_offset        = kernel->get_dst_offset(0, n_start, dst_stride);
+        const void * rhs_ptr           = static_cast<const void *>(rhs_packed + rhs_packed_offset);
+        const void * lhs_ptr           = static_cast<const void *>(lhs_packed + lhs_packed_offset);
+        float * dst_ptr                = reinterpret_cast<float *>(static_cast<uint8_t *>(dst->data) + dst_offset);
+
+        if (n_to_process > 0) {
+            kernel->run_kernel_ex(m, n_to_process, k, 0, lhs_ptr, rhs_ptr, dst_ptr, dst_stride,
+                                  sizeof(float), -FLT_MAX, FLT_MAX);
+        }
+
+        return true;
+    }
+
+    bool compute_forward_get_rows(struct ggml_compute_params * params, struct ggml_tensor * dst) {
         const ggml_tensor * src0 = dst->src[0];
         const ggml_tensor * src1 = dst->src[1];
 
         GGML_TENSOR_BINARY_OP_LOCALS
 
-        rhs_packing_info * rhs_info = &ctx.kernels->rhs_info;
-        kernel_info * kernel        = &ctx.kernels->gemm;
+        ggml_kleidiai_kernels * kernels = nullptr;
+        size_t block_len = 0;
+        size_t num_bytes_multiplier = 0;
+
+        if (dst->src[0]->type == GGML_TYPE_Q4_0) {
+            if (!ctx.kernels_q4) {
+                return false;
+            }
+            kernels = ctx.kernels_q4;
+            block_len = QK4_0;
+            num_bytes_multiplier = sizeof(uint16_t);
+        } else if (dst->src[0]->type == GGML_TYPE_Q8_0) {
+            if (!ctx.kernels_q8) {
+                return false;
+            }
+            kernels = ctx.kernels_q8;
+            block_len = QK8_0;
+            num_bytes_multiplier = sizeof(float);
+        } else {
+            return false;
+        }
+
+        rhs_packing_info * rhs_info = &kernels->rhs_info;
+        kernel_info * kernel        = &kernels->gemm;
         if (!rhs_info->to_float || !kernel->get_nr) {
             return false;
         }
@@ -423,8 +537,7 @@ class tensor_traits : public ggml::cpu::tensor_traits {
         const size_t block_rows = kernel->get_nr();
         const size_t kr         = kernel->get_kr();
 
-        const size_t num_bytes_multiplier = sizeof(uint16_t);
-        const size_t packed_stride = rhs_info->packed_stride(nc, block_rows, kr, QK4_0);
+        const size_t packed_stride = rhs_info->packed_stride(nc, block_rows, kr, block_len);
 
         const int ith = params->ith;
         const int nth = params->nth;
@@ -439,7 +552,7 @@ class tensor_traits : public ggml::cpu::tensor_traits {
             GGML_ASSERT(row_idx >= 0 && row_idx < src0->ne[1]);
 
             float *out = (float *)((char *)dst->data + i * nb1);
-            rhs_info->to_float(src0->data, row_idx, nc, out, block_rows, packed_stride, kr, QK4_0, num_bytes_multiplier);
+            rhs_info->to_float(src0->data, row_idx, nc, out, block_rows, packed_stride, kr, block_len, num_bytes_multiplier);
         }
 
         return true;
@@ -447,21 +560,91 @@ class tensor_traits : public ggml::cpu::tensor_traits {
 
 public:
     int repack(struct ggml_tensor * tensor, const void * data, size_t data_size) {
-        GGML_ASSERT(tensor->type == GGML_TYPE_Q4_0);
-        GGML_ASSERT(ctx.kernels);
         const size_t n = tensor->ne[1];
         const size_t k = tensor->ne[0];
-        size_t nr      = ctx.kernels->gemm.get_nr();
-        size_t kr      = ctx.kernels->gemm.get_kr();
-        size_t sr      = ctx.kernels->gemm.get_sr();
 
-        struct kai_rhs_pack_qs4cxs1s0_param params;
-        params.lhs_zero_point = 1;
-        params.rhs_zero_point = 8;
-        ctx.kernels->rhs_info.pack_func_ex(1, n, k, nr, kr, sr, QK4_0, 0, (const uint8_t*)data, nullptr, nullptr, tensor->data, 0, &params);
+        if (tensor->type == GGML_TYPE_Q4_0) {
+            if (!ctx.kernels_q4) {
+                return -1;
+            }
+            size_t nr = ctx.kernels_q4->gemm.get_nr();
+            size_t kr = ctx.kernels_q4->gemm.get_kr();
+            size_t sr = ctx.kernels_q4->gemm.get_sr();
+
+            struct kai_rhs_pack_qs4cxs1s0_param params;
+            params.lhs_zero_point = 1;
+            params.rhs_zero_point = 8;
+            ctx.kernels_q4->rhs_info.pack_func_ex(1, n, k, nr, kr, sr, QK4_0, 0,
+                                                  static_cast<const uint8_t *>(data),
+                                                  nullptr, nullptr, tensor->data, 0, &params);
+            GGML_UNUSED(data_size);
+            return 0;
+        } else if (tensor->type == GGML_TYPE_Q8_0) {
+            if (!ctx.kernels_q8) {
+                return -1;
+            }
+
+            const size_t row_stride = tensor->nb[1];
+            const size_t k_blocks   = (k + QK8_0 - 1) / QK8_0;
+
+            std::vector<int8_t> qdata(n * k, 0);
+            std::vector<float> scales(n, 0.0f);
+
+            for (size_t row = 0; row < n; ++row) {
+                const auto * row_blocks = reinterpret_cast<const block_q8_0 *>(
+                    static_cast<const uint8_t *>(data) + row * row_stride);
+
+                float max_abs = 0.0f;
+                for (size_t block = 0; block < k_blocks; ++block) {
+                    const block_q8_0 & blk = row_blocks[block];
+                    const float d = GGML_FP16_TO_FP32(blk.d);
+                    for (size_t l = 0; l < QK8_0; ++l) {
+                        const size_t linear_idx = block * QK8_0 + l;
+                        if (linear_idx >= k) {
+                            break;
+                        }
+                        const float value = d * blk.qs[l];
+                        max_abs = std::max(max_abs, std::fabs(value));
+                    }
+                }
+
+                float scale = max_abs > 0.0f ? max_abs / 127.0f : 0.0f;
+                scales[row] = scale;
+                const float inv_scale = scale > 0.0f ? 1.0f / scale : 0.0f;
+
+                for (size_t block = 0; block < k_blocks; ++block) {
+                    const block_q8_0 & blk = row_blocks[block];
+                    const float d = GGML_FP16_TO_FP32(blk.d);
+                    for (size_t l = 0; l < QK8_0; ++l) {
+                        const size_t linear_idx = block * QK8_0 + l;
+                        if (linear_idx >= k) {
+                            break;
+                        }
+                        const float value = d * blk.qs[l];
+                        int32_t q = scale > 0.0f ? static_cast<int32_t>(std::lround(value * inv_scale)) : 0;
+                        q = std::clamp(q, -127, 127);
+                        qdata[row * k + linear_idx] = static_cast<int8_t>(q);
+                    }
+                }
+            }
+
+            size_t nr = ctx.kernels_q8->gemm.get_nr();
+            size_t kr = ctx.kernels_q8->gemm.get_kr();
+            size_t sr = ctx.kernels_q8->gemm.get_sr();
+
+            struct kai_rhs_pack_qsi8cx_params params;
+            params.lhs_zero_point = 1;
+            params.scale_multiplier = 1.0f;
+
+            ctx.kernels_q8->rhs_info.pack_func_ex(1, n, k, nr, kr, sr, 0, 0,
+                                                  qdata.data(), nullptr, scales.data(),
+                                                  tensor->data, 0, &params);
+            GGML_UNUSED(data_size);
+            return 0;
+        }
 
-        return 0;
         GGML_UNUSED(data_size);
+        return -1;
     }
 };
 
@@ -518,27 +701,45 @@ static size_t ggml_backend_cpu_kleidiai_buffer_type_get_alignment(ggml_backend_b
 }
 
 static size_t ggml_backend_cpu_kleidiai_buffer_type_get_alloc_size(ggml_backend_buffer_type_t buft, const struct ggml_tensor * tensor) {
-    GGML_ASSERT(tensor->type == GGML_TYPE_Q4_0);
-    GGML_ASSERT(ctx.kernels);
+    GGML_UNUSED(buft);
 
-    const size_t n  = tensor->ne[1];
-    const size_t k  = tensor->ne[0];
-    const size_t nr = ctx.kernels->gemm.get_nr();
-    const size_t kr = ctx.kernels->gemm.get_kr();
+    const size_t n = tensor->ne[1];
+    const size_t k = tensor->ne[0];
+
+    ggml_kleidiai_kernels * kernels = nullptr;
+    size_t block_len = 0;
+
+    if (tensor->type == GGML_TYPE_Q4_0) {
+        GGML_ASSERT(ctx.kernels_q4);
+        kernels = ctx.kernels_q4;
+        block_len = QK4_0;
+    } else if (tensor->type == GGML_TYPE_Q8_0) {
+        GGML_ASSERT(ctx.kernels_q8);
+        kernels = ctx.kernels_q8;
+        block_len = QK8_0;
+    } else {
+        return 0;
+    }
 
-    return ctx.kernels->rhs_info.packed_size_ex(n, k, nr, kr, QK4_0);
+    const size_t nr = kernels->gemm.get_nr();
+    const size_t kr = kernels->gemm.get_kr();
+    const size_t packed = kernels->rhs_info.packed_size_ex(n, k, nr, kr, block_len);
+    const size_t raw     = ggml_nbytes(tensor);
 
-    GGML_UNUSED(buft);
+    return packed > raw ? packed : raw;
 }
 
 namespace ggml::cpu::kleidiai {
 class extra_buffer_type : ggml::cpu::extra_buffer_type {
     bool supports_op(ggml_backend_dev_t, const struct ggml_tensor * op) override {
         if ((op->op == GGML_OP_MUL_MAT || op->op == GGML_OP_GET_ROWS) &&
-            op->src[0]->type == GGML_TYPE_Q4_0 &&
+            (op->src[0]->type == GGML_TYPE_Q4_0 || op->src[0]->type == GGML_TYPE_Q8_0) &&
             op->src[0]->buffer &&
             (ggml_n_dims(op->src[0]) == 2) &&
-            op->src[0]->buffer->buft == ggml_backend_cpu_kleidiai_buffer_type() && ctx.kernels) {
+            op->src[0]->buffer->buft == ggml_backend_cpu_kleidiai_buffer_type()) {
+            if (((op->src[0]->type == GGML_TYPE_Q4_0) ? ctx.kernels_q4 : ctx.kernels_q8) == nullptr) {
+                return false;
+            }
             if (op->src[1]->buffer && !ggml_backend_buft_is_host(op->src[1]->buffer->buft)) {
                 return false;
             }

From 73460f62789a3ed02109d601a2653c3842f2074e Mon Sep 17 00:00:00 2001
From: duduta <simona.gherman@gmail.com>
Date: Tue, 11 Nov 2025 13:33:24 +0200
Subject: [PATCH 157/185] ggml-cpu: templateify ggml_compute_forward_rope_f32
 and _f16 (#16805)

* extract rotate_pairs logic from ggml_compute_forward_rope_f32

* templateify ggml_compute_forward_rope_f32 and _f16

* abort when rope type not supported, remove GLM from test-rope

* add imrope branch to switch

* add rope tests for perf

* Update ggml/src/ggml-cpu/ops.cpp

Co-authored-by: Georgi Gerganov <ggerganov@gmail.com>

* Update ggml/src/ggml-cpu/ops.cpp

Co-authored-by: Georgi Gerganov <ggerganov@gmail.com>

---------

Co-authored-by: Georgi Gerganov <ggerganov@gmail.com>
---
 ggml/src/ggml-cpu/ops.cpp  | 317 +++++++------------------------------
 tests/test-backend-ops.cpp |  16 ++
 tests/test-rope.cpp        |  11 +-
 3 files changed, 76 insertions(+), 268 deletions(-)

diff --git a/ggml/src/ggml-cpu/ops.cpp b/ggml/src/ggml-cpu/ops.cpp
index 7c42fb78b4a..5a272b9abc5 100644
--- a/ggml/src/ggml-cpu/ops.cpp
+++ b/ggml/src/ggml-cpu/ops.cpp
@@ -5503,194 +5503,28 @@ static void ggml_mrope_cache_init(
     }
 }
 
-static void ggml_compute_forward_rope_f32(
-        const ggml_compute_params * params,
-        ggml_tensor * dst,
-        const bool forward) {
-
-    const ggml_tensor * src0 = dst->src[0];
-    const ggml_tensor * src1 = dst->src[1];
-    const ggml_tensor * src2 = dst->src[2];
-
-    float freq_base, freq_scale, ext_factor, attn_factor, beta_fast, beta_slow;
-    int sections[4];
-
-    //const int n_past     = ((int32_t *) dst->op_params)[0];
-    const int n_dims     = ((int32_t *) dst->op_params)[1];
-    const int mode       = ((int32_t *) dst->op_params)[2];
-    //const int n_ctx      = ((int32_t *) dst->op_params)[3];
-    const int n_ctx_orig = ((int32_t *) dst->op_params)[4];
-
-    memcpy(&freq_base,   (int32_t *) dst->op_params +  5, sizeof(float));
-    memcpy(&freq_scale,  (int32_t *) dst->op_params +  6, sizeof(float));
-    memcpy(&ext_factor,  (int32_t *) dst->op_params +  7, sizeof(float));
-    memcpy(&attn_factor, (int32_t *) dst->op_params +  8, sizeof(float));
-    memcpy(&beta_fast,   (int32_t *) dst->op_params +  9, sizeof(float));
-    memcpy(&beta_slow,   (int32_t *) dst->op_params + 10, sizeof(float));
-    memcpy(&sections,    (int32_t *) dst->op_params + 11, sizeof(int)*4);
-
-    GGML_TENSOR_UNARY_OP_LOCALS
-
-    //printf("ne0: %d, ne1: %d, ne2: %d, ne3: %d\n", ne0, ne1, ne2, ne3);
-    //printf("n_past = %d, ne2 = %d\n", n_past, ne2);
-
-    GGML_ASSERT(nb00 == sizeof(float));
-
-    const int ith = params->ith;
-    const int nth = params->nth;
-
-    const int nr = ggml_nrows(dst);
-
-    GGML_ASSERT(n_dims <= ne0);
-    GGML_ASSERT(n_dims % 2 == 0);
-
-    // rows per thread
-    const int dr = (nr + nth - 1)/nth;
 
-    // row range for this thread
-    const int ir0 = dr*ith;
-    const int ir1 = MIN(ir0 + dr, nr);
-
-    // row index used to determine which thread to use
-    int ir = 0;
-
-    const float theta_scale = powf(freq_base, -2.0f/n_dims);
-
-    float corr_dims[2];
-    ggml_rope_yarn_corr_dims(n_dims, n_ctx_orig, freq_base, beta_fast, beta_slow, corr_dims);
-
-    const bool is_neox = mode & GGML_ROPE_TYPE_NEOX;
-    const bool is_mrope = mode & GGML_ROPE_TYPE_MROPE;  // ggml_rope_multi, multimodal rotary position embedding
-    const bool is_imrope = mode == GGML_ROPE_TYPE_IMROPE; // qwen3vl apply interleaved mrope
-    const bool is_vision = mode == GGML_ROPE_TYPE_VISION;
-
-    if (is_mrope) {
-        GGML_ASSERT(sections[0] > 0 || sections[1] > 0 || sections[2] > 0);
-    }
-
-    if (is_vision) {
-        GGML_ASSERT(n_dims == ne0/2);
-    }
+template<typename T>
+static void rotate_pairs(const int64_t n, const int64_t n_offset, const float * cache, const T * src_data, T * dst_data, const int scale = 2) {
+  for (int64_t i0 = 0; i0 < n; i0 += 2) {
+    const int64_t ic = i0/scale; // hack for GGML_ROPE_TYPE_NORMAL, where we need ic = i0; for all other cases, ic = i0/2
 
-    const float * freq_factors = NULL;
-    if (src2 != NULL) {
-        GGML_ASSERT(src2->type == GGML_TYPE_F32);
-        GGML_ASSERT(src2->ne[0] >= n_dims / 2);
-        freq_factors = (const float *) src2->data;
-    }
+    const float cos_theta = cache[i0 + 0];
+    const float sin_theta = cache[i0 + 1];
 
-    // backward process uses inverse rotation by cos and sin.
-    // cos and sin build a rotation matrix, where the inverse is the transpose.
-    // this essentially just switches the sign of sin.
-    const float sin_sign = forward ? 1.0f : -1.0f;
+    const T * const src = src_data + ic;
+    T * dst             = dst_data + ic;
 
-    const int32_t * pos = (const int32_t *) src1->data;
+    const float x0 = type_conversion_table<T>::to_f32(src[0]);
+    const float x1 = type_conversion_table<T>::to_f32(src[n_offset]);
 
-    for (int64_t i3 = 0; i3 < ne3; i3++) { // batch
-        for (int64_t i2 = 0; i2 < ne2; i2++) { // seq-len
-
-            float * cache = (float *) params->wdata + (ne0 + CACHE_LINE_SIZE_F32)*ith;
-            if (!is_mrope) {
-                const int64_t p = pos[i2];
-                ggml_rope_cache_init(p, freq_scale, freq_factors, corr_dims, ne0, ext_factor, attn_factor, cache, sin_sign, theta_scale);
-            }
-            else {
-                const int64_t p_t = pos[i2];
-                const int64_t p_h = pos[i2 + ne2];
-                const int64_t p_w = pos[i2 + ne2 * 2];
-                const int64_t p_e = pos[i2 + ne2 * 3];
-                ggml_mrope_cache_init(
-                    p_t, p_h, p_w, p_e, sections, is_imrope, is_vision,
-                    freq_scale, freq_factors, corr_dims, ne0, ext_factor, attn_factor, cache, sin_sign, theta_scale);
-            }
-
-            for (int64_t i1 = 0; i1 < ne1; i1++) { // attn-heads
-                if (ir++ < ir0) continue;
-                if (ir   > ir1) break;
-
-                if (is_neox || is_mrope) {
-                    if (is_vision){
-                        for (int64_t i0 = 0; i0 < n_dims; i0 += 2) {
-                            const int64_t ic = i0/2;
-
-                            const float cos_theta = cache[i0 + 0];
-                            const float sin_theta = cache[i0 + 1];
-
-                            const float * const src = (float *)((char *) src0->data + i3*nb03 + i2*nb02 + i1*nb01 + ic*nb00);
-                            float * dst_data  = (float *)((char *)  dst->data + i3*nb3  + i2*nb2  + i1*nb1  + ic*nb0);
-
-                            const float x0 = src[0];
-                            const float x1 = src[n_dims];
-
-                            dst_data[0]      = x0*cos_theta - x1*sin_theta;
-                            dst_data[n_dims] = x0*sin_theta + x1*cos_theta;
-                        }
-                    } else {
-                        for (int64_t i0 = 0; i0 < n_dims; i0 += 2) {
-                            const int64_t ic = i0/2;
-
-                            const float cos_theta = cache[i0 + 0];
-                            const float sin_theta = cache[i0 + 1];
-
-                            const float * const src = (float *)((char *) src0->data + i3*nb03 + i2*nb02 + i1*nb01 + ic*nb00);
-                            float * dst_data  = (float *)((char *)  dst->data + i3*nb3  + i2*nb2  + i1*nb1  + ic*nb0);
-
-                            const float x0 = src[0];
-                            const float x1 = src[n_dims/2];
-
-                            dst_data[0]        = x0*cos_theta - x1*sin_theta;
-                            dst_data[n_dims/2] = x0*sin_theta + x1*cos_theta;
-                        }
-                    }
-                } else {
-                    for (int64_t i0 = 0; i0 < n_dims; i0 += 2) {
-                        const float cos_theta = cache[i0 + 0];
-                        const float sin_theta = cache[i0 + 1];
-
-                        const float * const src = (float *)((char *) src0->data + i3*nb03 + i2*nb02 + i1*nb01 + i0*nb00);
-                              float * dst_data  = (float *)((char *)  dst->data + i3*nb3  + i2*nb2  + i1*nb1  + i0*nb0);
-
-                        const float x0 = src[0];
-                        const float x1 = src[1];
-
-                        dst_data[0] = x0*cos_theta - x1*sin_theta;
-                        dst_data[1] = x0*sin_theta + x1*cos_theta;
-                    }
-                }
-
-                if (is_vision) {
-                    for (int64_t i0 = n_dims; i0 < ne0; i0 += 2) {
-                        const int64_t ic = i0/2;
-
-                        const float cos_theta = cache[i0 + 0];
-                        const float sin_theta = cache[i0 + 1];
-
-                        const float * const src = (float *)((char *) src0->data + i3*nb03 + i2*nb02 + i1*nb01 + ic*nb00);
-                        float * dst_data  = (float *)((char *)  dst->data + i3*nb3  + i2*nb2  + i1*nb1  + ic*nb0);
-
-                        const float x0 = src[0];
-                        const float x1 = src[n_dims];
-
-                        dst_data[0]      = x0*cos_theta - x1*sin_theta;
-                        dst_data[n_dims] = x0*sin_theta + x1*cos_theta;
-                    }
-                } else {
-                    // fill the remain channels with data from src tensor
-                    for (int64_t i0 = n_dims; i0 < ne0; i0 += 2) {
-                        const float * const src = (float *)((char *) src0->data + i3*nb03 + i2*nb02 + i1*nb01 + i0*nb00);
-                        float * dst_data  = (float *)((char *)  dst->data + i3*nb3  + i2*nb2  + i1*nb1  + i0*nb0);
-
-                        dst_data[0] = src[0];
-                        dst_data[1] = src[1];
-                    }
-                }
-            }
-        }
-    }
+    dst[0]        = type_conversion_table<T>::from_f32(x0*cos_theta - x1*sin_theta);
+    dst[n_offset] = type_conversion_table<T>::from_f32(x0*sin_theta + x1*cos_theta);
+  }
 }
 
-// TODO: deduplicate f16/f32 code
-static void ggml_compute_forward_rope_f16(
+template<typename T> //float or ggml_fp16_t
+static void ggml_compute_forward_rope_flt(
         const ggml_compute_params * params,
         ggml_tensor * dst,
         const bool forward) {
@@ -5699,6 +5533,9 @@ static void ggml_compute_forward_rope_f16(
     const ggml_tensor * src1 = dst->src[1];
     const ggml_tensor * src2 = dst->src[2];
 
+    GGML_ASSERT(src0->type == GGML_TYPE_F32 || src0->type == GGML_TYPE_F16);
+    GGML_ASSERT(src1->type == GGML_TYPE_I32);
+
     float freq_base, freq_scale, ext_factor, attn_factor, beta_fast, beta_slow;
     int sections[4];
 
@@ -5707,6 +5544,7 @@ static void ggml_compute_forward_rope_f16(
     const int mode       = ((int32_t *) dst->op_params)[2];
     //const int n_ctx      = ((int32_t *) dst->op_params)[3];
     const int n_ctx_orig = ((int32_t *) dst->op_params)[4];
+
     memcpy(&freq_base,   (int32_t *) dst->op_params +  5, sizeof(float));
     memcpy(&freq_scale,  (int32_t *) dst->op_params +  6, sizeof(float));
     memcpy(&ext_factor,  (int32_t *) dst->op_params +  7, sizeof(float));
@@ -5715,13 +5553,13 @@ static void ggml_compute_forward_rope_f16(
     memcpy(&beta_slow,   (int32_t *) dst->op_params + 10, sizeof(float));
     memcpy(&sections,    (int32_t *) dst->op_params + 11, sizeof(int)*4);
 
-
     GGML_TENSOR_UNARY_OP_LOCALS
 
     //printf("ne0: %d, ne1: %d, ne2: %d, ne3: %d\n", ne0, ne1, ne2, ne3);
     //printf("n_past = %d, ne2 = %d\n", n_past, ne2);
 
-    GGML_ASSERT(nb0 == sizeof(ggml_fp16_t));
+    GGML_ASSERT(nb0 == nb00);
+    GGML_ASSERT(nb0 == sizeof(T));
 
     const int ith = params->ith;
     const int nth = params->nth;
@@ -5746,12 +5584,11 @@ static void ggml_compute_forward_rope_f16(
     float corr_dims[2];
     ggml_rope_yarn_corr_dims(n_dims, n_ctx_orig, freq_base, beta_fast, beta_slow, corr_dims);
 
-    const bool is_neox = mode & GGML_ROPE_TYPE_NEOX;
-    const bool is_mrope = mode & GGML_ROPE_TYPE_MROPE;
-    const bool is_imrope = mode == GGML_ROPE_TYPE_IMROPE;
+    const bool is_imrope = mode == GGML_ROPE_TYPE_IMROPE; // qwen3vl apply interleaved mrope
+    const bool mrope_used = mode & GGML_ROPE_TYPE_MROPE;  // ggml_rope_multi, note: also true for vision (24 & 8 == true) and for imrope
     const bool is_vision = mode == GGML_ROPE_TYPE_VISION;
 
-    if (is_mrope) {
+    if (mrope_used) {
         GGML_ASSERT(sections[0] > 0 || sections[1] > 0 || sections[2] > 0);
     }
 
@@ -5773,11 +5610,11 @@ static void ggml_compute_forward_rope_f16(
 
     const int32_t * pos = (const int32_t *) src1->data;
 
-    for (int64_t i3 = 0; i3 < ne3; i3++) {
-        for (int64_t i2 = 0; i2 < ne2; i2++) {
+    for (int64_t i3 = 0; i3 < ne3; i3++) { // batch
+        for (int64_t i2 = 0; i2 < ne2; i2++) { // seq-len
 
             float * cache = (float *) params->wdata + (ne0 + CACHE_LINE_SIZE_F32)*ith;
-            if (!is_mrope) {
+            if (!mrope_used) {
                 const int64_t p = pos[i2];
                 ggml_rope_cache_init(p, freq_scale, freq_factors, corr_dims, ne0, ext_factor, attn_factor, cache, sin_sign, theta_scale);
             }
@@ -5791,86 +5628,40 @@ static void ggml_compute_forward_rope_f16(
                     freq_scale, freq_factors, corr_dims, ne0, ext_factor, attn_factor, cache, sin_sign, theta_scale);
             }
 
-            for (int64_t i1 = 0; i1 < ne1; i1++) {
+            for (int64_t i1 = 0; i1 < ne1; i1++) { // attn-heads
                 if (ir++ < ir0) continue;
                 if (ir   > ir1) break;
 
-                if (is_neox || is_mrope) {
-                    if (is_vision) {
-                        for (int64_t i0 = 0; i0 < n_dims; i0 += 2) {
-                            const int64_t ic = i0/2;
-
-                            const float cos_theta = cache[i0 + 0];
-                            const float sin_theta = cache[i0 + 1];
-
-                            const ggml_fp16_t * const src = (ggml_fp16_t *)((char *) src0->data + i3*nb03 + i2*nb02 + i1*nb01 + ic*nb00);
-                            ggml_fp16_t * dst_data  = (ggml_fp16_t *)((char *)  dst->data + i3*nb3  + i2*nb2  + i1*nb1  + ic*nb0);
-
-                            const float x0 = GGML_CPU_FP16_TO_FP32(src[0]);
-                            const float x1 = GGML_CPU_FP16_TO_FP32(src[n_dims]);
-
-                            dst_data[0]      = GGML_CPU_FP32_TO_FP16(x0*cos_theta - x1*sin_theta);
-                            dst_data[n_dims] = GGML_CPU_FP32_TO_FP16(x0*sin_theta + x1*cos_theta);
-                        }
-                    } else {
-                        for (int64_t i0 = 0; i0 < n_dims; i0 += 2) {
-                            const int64_t ic = i0/2;
-
-                            const float cos_theta = cache[i0 + 0];
-                            const float sin_theta = cache[i0 + 1];
-
-                            const ggml_fp16_t * const src = (ggml_fp16_t *)((char *) src0->data + i3*nb03 + i2*nb02 + i1*nb01 + ic*nb00);
-                            ggml_fp16_t * dst_data  = (ggml_fp16_t *)((char *)  dst->data + i3*nb3  + i2*nb2  + i1*nb1  + ic*nb0);
-
-                            const float x0 = GGML_CPU_FP16_TO_FP32(src[0]);
-                            const float x1 = GGML_CPU_FP16_TO_FP32(src[n_dims/2]);
-
-                            dst_data[0]        = GGML_CPU_FP32_TO_FP16(x0*cos_theta - x1*sin_theta);
-                            dst_data[n_dims/2] = GGML_CPU_FP32_TO_FP16(x0*sin_theta + x1*cos_theta);
-                        }
-                    }
-                } else {
-                    for (int64_t i0 = 0; i0 < n_dims; i0 += 2) {
-                        const float cos_theta = cache[i0 + 0];
-                        const float sin_theta = cache[i0 + 1];
-
-                        const ggml_fp16_t * const src = (ggml_fp16_t *)((char *) src0->data + i3*nb03 + i2*nb02 + i1*nb01 + i0*nb00);
-                              ggml_fp16_t * dst_data  = (ggml_fp16_t *)((char *)  dst->data + i3*nb3  + i2*nb2  + i1*nb1  + i0*nb0);
-
-                        const float x0 = GGML_CPU_FP16_TO_FP32(src[0]);
-                        const float x1 = GGML_CPU_FP16_TO_FP32(src[1]);
-
-                        dst_data[0] = GGML_CPU_FP32_TO_FP16(x0*cos_theta - x1*sin_theta);
-                        dst_data[1] = GGML_CPU_FP32_TO_FP16(x0*sin_theta + x1*cos_theta);
-                    }
+                T * src = (T *)((char *) src0->data + i3*nb03 + i2*nb02 + i1*nb01);
+                T * dst_data  = (T *)((char *)  dst->data + i3*nb3  + i2*nb2  + i1*nb1);
+
+                switch (mode) {
+                    case GGML_ROPE_TYPE_NORMAL:
+                        rotate_pairs<T>(n_dims, 1, cache, src, dst_data, 1);
+                        break;
+                    case GGML_ROPE_TYPE_NEOX:
+                    case GGML_ROPE_TYPE_MROPE:
+                    case GGML_ROPE_TYPE_IMROPE:
+                        rotate_pairs<T>(n_dims, n_dims/2, cache, src, dst_data);
+                        break;
+                    case GGML_ROPE_TYPE_VISION:
+                        rotate_pairs<T>(ne0, n_dims, cache, src, dst_data);
+                        break;
+                    default:
+                        GGML_ABORT("rope type not supported");
                 }
 
-                if (is_vision) {
-                    for (int64_t i0 = n_dims; i0 < ne0; i0 += 2) {
-                        const int64_t ic = i0/2;
-
-                        const float cos_theta = cache[i0 + 0];
-                        const float sin_theta = cache[i0 + 1];
-
-                        const ggml_fp16_t * const src = (ggml_fp16_t *)((char *) src0->data + i3*nb03 + i2*nb02 + i1*nb01 + ic*nb00);
-                        ggml_fp16_t * dst_data  = (ggml_fp16_t *)((char *)  dst->data + i3*nb3  + i2*nb2  + i1*nb1  + ic*nb0);
-
-                        const float x0 = GGML_CPU_FP16_TO_FP32(src[0]);
-                        const float x1 = GGML_CPU_FP16_TO_FP32(src[n_dims]);
-
-                        dst_data[0]      = GGML_CPU_FP32_TO_FP16(x0*cos_theta - x1*sin_theta);
-                        dst_data[n_dims] = GGML_CPU_FP32_TO_FP16(x0*sin_theta + x1*cos_theta);
-                    }
-                } else {
+                if (!is_vision) {
+                    // fill the remain channels with data from src tensor
                     for (int64_t i0 = n_dims; i0 < ne0; i0 += 2) {
-                        const ggml_fp16_t * const src = (ggml_fp16_t *)((char *) src0->data + i3*nb03 + i2*nb02 + i1*nb01 + i0*nb00);
-                        ggml_fp16_t * dst_data  = (ggml_fp16_t *)((char *)  dst->data + i3*nb3  + i2*nb2  + i1*nb1  + i0*nb0);
+                        const T * const src = (T *)((char *) src0->data + i3*nb03 + i2*nb02 + i1*nb01 + i0*nb00);
+                        T * dst_data  = (T *)((char *)  dst->data + i3*nb3  + i2*nb2  + i1*nb1  + i0*nb0);
 
                         dst_data[0] = src[0];
                         dst_data[1] = src[1];
                     }
                 }
-            }
+            } //attn-heads
         }
     }
 }
@@ -5884,11 +5675,11 @@ void ggml_compute_forward_rope(
     switch (src0->type) {
         case GGML_TYPE_F16:
             {
-                ggml_compute_forward_rope_f16(params, dst, true);
+                ggml_compute_forward_rope_flt<ggml_fp16_t>(params, dst, true);
             } break;
         case GGML_TYPE_F32:
             {
-                ggml_compute_forward_rope_f32(params, dst, true);
+                ggml_compute_forward_rope_flt<float>(params, dst, true);
             } break;
         default:
             {
@@ -5908,11 +5699,11 @@ void ggml_compute_forward_rope_back(
     switch (src0->type) {
         case GGML_TYPE_F16:
             {
-                ggml_compute_forward_rope_f16(params, dst, false);
+                ggml_compute_forward_rope_flt<ggml_fp16_t>(params, dst, false);
             } break;
         case GGML_TYPE_F32:
             {
-                ggml_compute_forward_rope_f32(params, dst, false);
+                ggml_compute_forward_rope_flt<float>(params, dst, false);
             } break;
         default:
             {
diff --git a/tests/test-backend-ops.cpp b/tests/test-backend-ops.cpp
index eb29b15f204..92c17ac4399 100644
--- a/tests/test-backend-ops.cpp
+++ b/tests/test-backend-ops.cpp
@@ -7603,6 +7603,22 @@ static std::vector<std::unique_ptr<test_case>> make_test_cases_perf() {
         test_cases.emplace_back(new test_add_id(GGML_TYPE_F32, GGML_TYPE_F32, 2880, 32, 4, n_token));
     }
 
+    for (bool fw : {true, false}) { // fw == forward
+        for (ggml_type type : {GGML_TYPE_F32, GGML_TYPE_F16}) {
+            for (bool ff : {false, true}) { // freq_factors
+                for (float v : { 0, 1 }) {
+                    test_cases.emplace_back(new test_rope(type, {128,  32, 512, 1}, 128, GGML_ROPE_TYPE_NORMAL, 512, 1.0f, 0.0f, 1.0f, ff, v, fw)); // llama 7B
+                    test_cases.emplace_back(new test_rope(type, {128,  64, 512, 1}, 128, GGML_ROPE_TYPE_NORMAL, 512, 1.0f, 0.0f, 1.0f, ff, v, fw)); // llama 65B
+                    test_cases.emplace_back(new test_rope(type, { 80,  32, 512, 1},  20, GGML_ROPE_TYPE_NEOX, 512, 1.0f, 0.0f, 1.0f, ff, v, fw)); // neox (stablelm)
+                    test_cases.emplace_back(new test_rope(type, { 64,   8, 512, 1},  64, GGML_ROPE_TYPE_NEOX, 512, 1.0f, 0.0f, 1.0f, ff, v, fw)); // neox (falcon 40B)
+                    test_cases.emplace_back(new test_rope(type, {128,  12, 512, 1}, 128, GGML_ROPE_TYPE_MROPE,  512, 1.0f, 0.0f, 1.0f, ff, v, fw)); // rope_multi,m-rope (qwen2vl 2B)
+                    test_cases.emplace_back(new test_rope(type, {128,  12, 2, 1}, 128, GGML_ROPE_TYPE_IMROPE,  512, 1.0f, 0.0f, 1.0f, ff, v, fw)); // rope_multi,imrope (qwen3vl 2B)
+                    test_cases.emplace_back(new test_rope(type, { 80,  16, 2, 1},  80, GGML_ROPE_TYPE_VISION, 512, 1.0f, 0.0f, 1.0f, ff, v, fw)); // rope_multi,m-rope (qwen2vl ViT)
+                }
+            }
+        }
+    }
+
     std::vector<std::array<int64_t, 4>> reduce_rows_cases = {
         { 8192, 1,    1, 1 },
         { 8192, 8192, 1, 1 },
diff --git a/tests/test-rope.cpp b/tests/test-rope.cpp
index 22c51d81f60..801e4cd8270 100644
--- a/tests/test-rope.cpp
+++ b/tests/test-rope.cpp
@@ -138,7 +138,7 @@ int main(int /*argc*/, const char ** /*argv*/) {
     struct ggml_tensor * x;
 
     // rope f32
-    for (int m = 0; m < 6; ++m) {
+    for (int m = 0; m < 5; ++m) {
         const int ndims = 4;
 
         const int64_t n_rot = 128;
@@ -153,7 +153,7 @@ int main(int /*argc*/, const char ** /*argv*/) {
         x = get_random_tensor_f32(ctx0, ndims, ne, -1.0f, 1.0f);
         int mode = -1;
 
-        if (m < 3) {
+        if (m < 2) {
             struct ggml_tensor * p0 = ggml_new_tensor_1d(ctx0, GGML_TYPE_I32, ne[2]);
             struct ggml_tensor * p1 = ggml_new_tensor_1d(ctx0, GGML_TYPE_I32, ne[2]);
             struct ggml_tensor * p2 = ggml_new_tensor_1d(ctx0, GGML_TYPE_I32, ne[2]);
@@ -163,8 +163,8 @@ int main(int /*argc*/, const char ** /*argv*/) {
                 ((int32_t *) p1->data)[i] = n_past_2 - n_past_0;
                 ((int32_t *) p2->data)[i] = n_past_2 + i;
             }
-            // test mode 0, 2, 4 (standard, GPT-NeoX, GLM)
-            mode = m == 0 ? 0 : m == 1 ? 2 : 4;
+            // test mode 0, 2  (standard, GPT-NeoX)
+            mode = m == 0 ? GGML_ROPE_TYPE_NORMAL : GGML_ROPE_TYPE_NEOX;
 
             // 100, 101, 102, ..., 172
             r0 = ggml_rope(ctx0, x,  p0, n_rot, mode);
@@ -180,7 +180,8 @@ int main(int /*argc*/, const char ** /*argv*/) {
             struct ggml_tensor * p2 = ggml_new_tensor_1d(ctx0, GGML_TYPE_I32, ne[2] * 4);
 
             int sections[4] = {16, 24, 24, 0};
-            mode = (m == 3) ? GGML_ROPE_TYPE_MROPE : (m == 4) ? GGML_ROPE_TYPE_VISION : GGML_ROPE_TYPE_IMROPE;
+
+            mode = (m == 2) ? GGML_ROPE_TYPE_MROPE : (m == 3) ? GGML_ROPE_TYPE_VISION : GGML_ROPE_TYPE_IMROPE;
 
             for (int i = 0; i < ne[2]; ++i) {
                 for (int j = 0; j < 4; ++j) {

From ca4844062b3f0679a39b76b2fe95ba87cd6fb00d Mon Sep 17 00:00:00 2001
From: ixgbe <1113177880@qq.com>
Date: Tue, 11 Nov 2025 19:41:51 +0800
Subject: [PATCH 158/185] ggml-cpu : add RISC-V RVV (Zvfh) optimization for
 FP16 to FP32 conversion (#17161)

Signed-off-by: Wang Yang <yangwang@iscas.ac.cn>
---
 ggml/src/ggml-cpu/ggml-cpu.c | 7 +++++++
 1 file changed, 7 insertions(+)

diff --git a/ggml/src/ggml-cpu/ggml-cpu.c b/ggml/src/ggml-cpu/ggml-cpu.c
index 086708bae0b..d8e3c48c609 100644
--- a/ggml/src/ggml-cpu/ggml-cpu.c
+++ b/ggml/src/ggml-cpu/ggml-cpu.c
@@ -3274,6 +3274,13 @@ void ggml_cpu_fp16_to_fp32(const ggml_fp16_t * x, float * y, int64_t n) {
         __m128 y_vec = _mm_cvtph_ps(x_vec);
         _mm_storeu_ps(y + i, y_vec);
     }
+#elif defined(__riscv_zvfh)
+    for (int vl; i < n; i += vl) {
+        vl = __riscv_vsetvl_e16m1(n - i);
+        vfloat16m1_t vx = __riscv_vle16_v_f16m1((_Float16 *)&x[i], vl);
+        vfloat32m2_t vy = __riscv_vfwcvt_f_f_v_f32m2(vx, vl);
+        __riscv_vse32_v_f32m2(&y[i], vy, vl);
+    }
 #endif
 
     for (; i < n; ++i) {

From 1d45b4228f11c193d6864724ae675734da24ac98 Mon Sep 17 00:00:00 2001
From: Xuan-Son Nguyen <son@huggingface.co>
Date: Tue, 11 Nov 2025 13:32:58 +0100
Subject: [PATCH 159/185] vendor: split httplib to cpp/h files (#17150)

* vendor: split httplib to cpp/h files

* move defines

* include httplib if curl is not used

* add TODO

* fix build ios

* fix build visionos instead
---
 CMakeLists.txt                    |     1 +
 common/CMakeLists.txt             |     6 +-
 scripts/sync_vendor.py            |    17 +
 tools/server/CMakeLists.txt       |     2 +-
 tools/server/utils.hpp            |     8 -
 vendor/cpp-httplib/CMakeLists.txt |    28 +
 vendor/cpp-httplib/httplib.cpp    |  7816 +++++++++++++++++++++
 vendor/cpp-httplib/httplib.h      | 10178 ++--------------------------
 8 files changed, 8277 insertions(+), 9779 deletions(-)
 create mode 100644 vendor/cpp-httplib/CMakeLists.txt
 create mode 100644 vendor/cpp-httplib/httplib.cpp

diff --git a/CMakeLists.txt b/CMakeLists.txt
index 4bf8b2789ae..e7410184dfa 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -200,6 +200,7 @@ endif()
 
 if (LLAMA_BUILD_COMMON)
     add_subdirectory(common)
+    add_subdirectory(vendor/cpp-httplib)
 endif()
 
 if (LLAMA_BUILD_COMMON AND LLAMA_BUILD_TESTS AND NOT CMAKE_JS_VERSION)
diff --git a/common/CMakeLists.txt b/common/CMakeLists.txt
index 7086d08e5e5..1d260507ad5 100644
--- a/common/CMakeLists.txt
+++ b/common/CMakeLists.txt
@@ -79,10 +79,11 @@ if (BUILD_SHARED_LIBS)
     set_target_properties(${TARGET} PROPERTIES POSITION_INDEPENDENT_CODE ON)
 endif()
 
+# TODO: use list(APPEND LLAMA_COMMON_EXTRA_LIBS ...)
 set(LLAMA_COMMON_EXTRA_LIBS build_info)
 
-# Use curl to download model url
 if (LLAMA_CURL)
+    # Use curl to download model url
     find_package(CURL)
     if (NOT CURL_FOUND)
         message(FATAL_ERROR "Could NOT find CURL. Hint: to disable this feature, set -DLLAMA_CURL=OFF")
@@ -90,6 +91,9 @@ if (LLAMA_CURL)
     target_compile_definitions(${TARGET} PUBLIC LLAMA_USE_CURL)
     include_directories(${CURL_INCLUDE_DIRS})
     set(LLAMA_COMMON_EXTRA_LIBS ${LLAMA_COMMON_EXTRA_LIBS} ${CURL_LIBRARIES})
+else()
+    # otherwise, use cpp-httplib
+    set(LLAMA_COMMON_EXTRA_LIBS ${LLAMA_COMMON_EXTRA_LIBS} cpp-httplib)
 endif()
 
 if (LLAMA_OPENSSL)
diff --git a/scripts/sync_vendor.py b/scripts/sync_vendor.py
index 1151c9f0196..b578cf1e6af 100755
--- a/scripts/sync_vendor.py
+++ b/scripts/sync_vendor.py
@@ -20,3 +20,20 @@
 for url, filename in vendor.items():
     print(f"downloading {url} to {filename}") # noqa: NP100
     urllib.request.urlretrieve(url, filename)
+
+    # split cpp/h files for httplib
+    # see: https://github.com/yhirose/cpp-httplib/blob/master/split.py
+    if 'httplib.h' in filename:
+        border = '// ----------------------------------------------------------------------------'
+        with open(filename, 'r') as f:
+            content = f.read()
+        header, implementation, footer = content.split(border, 2)
+        fname_cpp = filename.replace('.h', '.cpp')
+        with open(filename, 'w') as fh:
+            fh.write(header)
+            fh.write(footer)
+        with open(fname_cpp, 'w') as fc:
+            fc.write('#include "httplib.h"\n')
+            fc.write('namespace httplib {\n')
+            fc.write(implementation.replace('\ninline ', '\n'))
+            fc.write('} // namespace httplib\n')
diff --git a/tools/server/CMakeLists.txt b/tools/server/CMakeLists.txt
index 06df3ee49dd..5f8a50320d1 100644
--- a/tools/server/CMakeLists.txt
+++ b/tools/server/CMakeLists.txt
@@ -33,7 +33,7 @@ install(TARGETS ${TARGET} RUNTIME)
 
 target_include_directories(${TARGET} PRIVATE ../mtmd)
 target_include_directories(${TARGET} PRIVATE ${CMAKE_SOURCE_DIR})
-target_link_libraries(${TARGET} PRIVATE common mtmd ${CMAKE_THREAD_LIBS_INIT})
+target_link_libraries(${TARGET} PRIVATE common mtmd cpp-httplib ${CMAKE_THREAD_LIBS_INIT})
 
 if (WIN32)
     TARGET_LINK_LIBRARIES(${TARGET} PRIVATE ws2_32)
diff --git a/tools/server/utils.hpp b/tools/server/utils.hpp
index 2bce2f4a47a..e9d4431ddfb 100644
--- a/tools/server/utils.hpp
+++ b/tools/server/utils.hpp
@@ -9,14 +9,6 @@
 #include "mtmd-helper.h"
 #include "chat.h"
 
-// increase max payload length to allow use of larger context size
-#define CPPHTTPLIB_FORM_URL_ENCODED_PAYLOAD_MAX_LENGTH 1048576
-// increase backlog size to avoid connection resets for >> 1 slots
-#define CPPHTTPLIB_LISTEN_BACKLOG 512
-// increase max URI length to handle longer prompts in query string
-#define CPPHTTPLIB_REQUEST_URI_MAX_LENGTH 32768
-// disable Nagle's algorithm
-#define CPPHTTPLIB_TCP_NODELAY true
 #include <cpp-httplib/httplib.h>
 
 #define JSON_ASSERT GGML_ASSERT
diff --git a/vendor/cpp-httplib/CMakeLists.txt b/vendor/cpp-httplib/CMakeLists.txt
new file mode 100644
index 00000000000..0033d52371f
--- /dev/null
+++ b/vendor/cpp-httplib/CMakeLists.txt
@@ -0,0 +1,28 @@
+set(TARGET cpp-httplib)
+
+find_package(Threads REQUIRED)
+
+add_library(${TARGET} STATIC httplib.cpp httplib.h)
+if (NOT MSVC)
+    # disable warnings in 3rd party code
+    target_compile_options(${TARGET} PRIVATE -w)
+endif()
+
+target_link_libraries  (${TARGET} PRIVATE Threads::Threads)
+target_compile_features(${TARGET} PRIVATE cxx_std_17)
+
+target_compile_definitions(${TARGET} PRIVATE
+    # increase max payload length to allow use of larger context size
+    CPPHTTPLIB_FORM_URL_ENCODED_PAYLOAD_MAX_LENGTH=1048576
+    # increase backlog size to avoid connection resets for >> 1 slots
+    CPPHTTPLIB_LISTEN_BACKLOG=512
+    # increase max URI length to handle longer prompts in query string
+    CPPHTTPLIB_REQUEST_URI_MAX_LENGTH=32768
+    # disable Nagle's algorithm
+    CPPHTTPLIB_TCP_NODELAY=1
+)
+
+if (${CMAKE_SYSTEM_NAME} MATCHES "visionOS")
+    # quick fix for https://github.com/ggml-org/llama.cpp/actions/runs/19247291428/job/55024294176?pr=17150
+    target_compile_definitions(${TARGET} PRIVATE NI_MAXHOST=1025)
+endif()
diff --git a/vendor/cpp-httplib/httplib.cpp b/vendor/cpp-httplib/httplib.cpp
new file mode 100644
index 00000000000..e5c84d2b221
--- /dev/null
+++ b/vendor/cpp-httplib/httplib.cpp
@@ -0,0 +1,7816 @@
+#include "httplib.h"
+namespace httplib {
+
+
+/*
+ * Implementation that will be part of the .cc file if split into .h + .cc.
+ */
+
+namespace detail {
+
+bool is_hex(char c, int &v) {
+  if (0x20 <= c && isdigit(c)) {
+    v = c - '0';
+    return true;
+  } else if ('A' <= c && c <= 'F') {
+    v = c - 'A' + 10;
+    return true;
+  } else if ('a' <= c && c <= 'f') {
+    v = c - 'a' + 10;
+    return true;
+  }
+  return false;
+}
+
+bool from_hex_to_i(const std::string &s, size_t i, size_t cnt,
+                          int &val) {
+  if (i >= s.size()) { return false; }
+
+  val = 0;
+  for (; cnt; i++, cnt--) {
+    if (!s[i]) { return false; }
+    auto v = 0;
+    if (is_hex(s[i], v)) {
+      val = val * 16 + v;
+    } else {
+      return false;
+    }
+  }
+  return true;
+}
+
+std::string from_i_to_hex(size_t n) {
+  static const auto charset = "0123456789abcdef";
+  std::string ret;
+  do {
+    ret = charset[n & 15] + ret;
+    n >>= 4;
+  } while (n > 0);
+  return ret;
+}
+
+size_t to_utf8(int code, char *buff) {
+  if (code < 0x0080) {
+    buff[0] = static_cast<char>(code & 0x7F);
+    return 1;
+  } else if (code < 0x0800) {
+    buff[0] = static_cast<char>(0xC0 | ((code >> 6) & 0x1F));
+    buff[1] = static_cast<char>(0x80 | (code & 0x3F));
+    return 2;
+  } else if (code < 0xD800) {
+    buff[0] = static_cast<char>(0xE0 | ((code >> 12) & 0xF));
+    buff[1] = static_cast<char>(0x80 | ((code >> 6) & 0x3F));
+    buff[2] = static_cast<char>(0x80 | (code & 0x3F));
+    return 3;
+  } else if (code < 0xE000) { // D800 - DFFF is invalid...
+    return 0;
+  } else if (code < 0x10000) {
+    buff[0] = static_cast<char>(0xE0 | ((code >> 12) & 0xF));
+    buff[1] = static_cast<char>(0x80 | ((code >> 6) & 0x3F));
+    buff[2] = static_cast<char>(0x80 | (code & 0x3F));
+    return 3;
+  } else if (code < 0x110000) {
+    buff[0] = static_cast<char>(0xF0 | ((code >> 18) & 0x7));
+    buff[1] = static_cast<char>(0x80 | ((code >> 12) & 0x3F));
+    buff[2] = static_cast<char>(0x80 | ((code >> 6) & 0x3F));
+    buff[3] = static_cast<char>(0x80 | (code & 0x3F));
+    return 4;
+  }
+
+  // NOTREACHED
+  return 0;
+}
+
+// NOTE: This code came up with the following stackoverflow post:
+// https://stackoverflow.com/questions/180947/base64-decode-snippet-in-c
+std::string base64_encode(const std::string &in) {
+  static const auto lookup =
+      "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
+
+  std::string out;
+  out.reserve(in.size());
+
+  auto val = 0;
+  auto valb = -6;
+
+  for (auto c : in) {
+    val = (val << 8) + static_cast<uint8_t>(c);
+    valb += 8;
+    while (valb >= 0) {
+      out.push_back(lookup[(val >> valb) & 0x3F]);
+      valb -= 6;
+    }
+  }
+
+  if (valb > -6) { out.push_back(lookup[((val << 8) >> (valb + 8)) & 0x3F]); }
+
+  while (out.size() % 4) {
+    out.push_back('=');
+  }
+
+  return out;
+}
+
+bool is_valid_path(const std::string &path) {
+  size_t level = 0;
+  size_t i = 0;
+
+  // Skip slash
+  while (i < path.size() && path[i] == '/') {
+    i++;
+  }
+
+  while (i < path.size()) {
+    // Read component
+    auto beg = i;
+    while (i < path.size() && path[i] != '/') {
+      if (path[i] == '\0') {
+        return false;
+      } else if (path[i] == '\\') {
+        return false;
+      }
+      i++;
+    }
+
+    auto len = i - beg;
+    assert(len > 0);
+
+    if (!path.compare(beg, len, ".")) {
+      ;
+    } else if (!path.compare(beg, len, "..")) {
+      if (level == 0) { return false; }
+      level--;
+    } else {
+      level++;
+    }
+
+    // Skip slash
+    while (i < path.size() && path[i] == '/') {
+      i++;
+    }
+  }
+
+  return true;
+}
+
+FileStat::FileStat(const std::string &path) {
+#if defined(_WIN32)
+  auto wpath = u8string_to_wstring(path.c_str());
+  ret_ = _wstat(wpath.c_str(), &st_);
+#else
+  ret_ = stat(path.c_str(), &st_);
+#endif
+}
+bool FileStat::is_file() const {
+  return ret_ >= 0 && S_ISREG(st_.st_mode);
+}
+bool FileStat::is_dir() const {
+  return ret_ >= 0 && S_ISDIR(st_.st_mode);
+}
+
+std::string encode_query_param(const std::string &value) {
+  std::ostringstream escaped;
+  escaped.fill('0');
+  escaped << std::hex;
+
+  for (auto c : value) {
+    if (std::isalnum(static_cast<uint8_t>(c)) || c == '-' || c == '_' ||
+        c == '.' || c == '!' || c == '~' || c == '*' || c == '\'' || c == '(' ||
+        c == ')') {
+      escaped << c;
+    } else {
+      escaped << std::uppercase;
+      escaped << '%' << std::setw(2)
+              << static_cast<int>(static_cast<unsigned char>(c));
+      escaped << std::nouppercase;
+    }
+  }
+
+  return escaped.str();
+}
+
+std::string encode_url(const std::string &s) {
+  std::string result;
+  result.reserve(s.size());
+
+  for (size_t i = 0; s[i]; i++) {
+    switch (s[i]) {
+    case ' ': result += "%20"; break;
+    case '+': result += "%2B"; break;
+    case '\r': result += "%0D"; break;
+    case '\n': result += "%0A"; break;
+    case '\'': result += "%27"; break;
+    case ',': result += "%2C"; break;
+    // case ':': result += "%3A"; break; // ok? probably...
+    case ';': result += "%3B"; break;
+    default:
+      auto c = static_cast<uint8_t>(s[i]);
+      if (c >= 0x80) {
+        result += '%';
+        char hex[4];
+        auto len = snprintf(hex, sizeof(hex) - 1, "%02X", c);
+        assert(len == 2);
+        result.append(hex, static_cast<size_t>(len));
+      } else {
+        result += s[i];
+      }
+      break;
+    }
+  }
+
+  return result;
+}
+
+std::string decode_url(const std::string &s,
+                              bool convert_plus_to_space) {
+  std::string result;
+
+  for (size_t i = 0; i < s.size(); i++) {
+    if (s[i] == '%' && i + 1 < s.size()) {
+      if (s[i + 1] == 'u') {
+        auto val = 0;
+        if (from_hex_to_i(s, i + 2, 4, val)) {
+          // 4 digits Unicode codes
+          char buff[4];
+          size_t len = to_utf8(val, buff);
+          if (len > 0) { result.append(buff, len); }
+          i += 5; // 'u0000'
+        } else {
+          result += s[i];
+        }
+      } else {
+        auto val = 0;
+        if (from_hex_to_i(s, i + 1, 2, val)) {
+          // 2 digits hex codes
+          result += static_cast<char>(val);
+          i += 2; // '00'
+        } else {
+          result += s[i];
+        }
+      }
+    } else if (convert_plus_to_space && s[i] == '+') {
+      result += ' ';
+    } else {
+      result += s[i];
+    }
+  }
+
+  return result;
+}
+
+std::string file_extension(const std::string &path) {
+  std::smatch m;
+  thread_local auto re = std::regex("\\.([a-zA-Z0-9]+)$");
+  if (std::regex_search(path, m, re)) { return m[1].str(); }
+  return std::string();
+}
+
+bool is_space_or_tab(char c) { return c == ' ' || c == '\t'; }
+
+std::pair<size_t, size_t> trim(const char *b, const char *e, size_t left,
+                                      size_t right) {
+  while (b + left < e && is_space_or_tab(b[left])) {
+    left++;
+  }
+  while (right > 0 && is_space_or_tab(b[right - 1])) {
+    right--;
+  }
+  return std::make_pair(left, right);
+}
+
+std::string trim_copy(const std::string &s) {
+  auto r = trim(s.data(), s.data() + s.size(), 0, s.size());
+  return s.substr(r.first, r.second - r.first);
+}
+
+std::string trim_double_quotes_copy(const std::string &s) {
+  if (s.length() >= 2 && s.front() == '"' && s.back() == '"') {
+    return s.substr(1, s.size() - 2);
+  }
+  return s;
+}
+
+void
+divide(const char *data, std::size_t size, char d,
+       std::function<void(const char *, std::size_t, const char *, std::size_t)>
+           fn) {
+  const auto it = std::find(data, data + size, d);
+  const auto found = static_cast<std::size_t>(it != data + size);
+  const auto lhs_data = data;
+  const auto lhs_size = static_cast<std::size_t>(it - data);
+  const auto rhs_data = it + found;
+  const auto rhs_size = size - lhs_size - found;
+
+  fn(lhs_data, lhs_size, rhs_data, rhs_size);
+}
+
+void
+divide(const std::string &str, char d,
+       std::function<void(const char *, std::size_t, const char *, std::size_t)>
+           fn) {
+  divide(str.data(), str.size(), d, std::move(fn));
+}
+
+void split(const char *b, const char *e, char d,
+                  std::function<void(const char *, const char *)> fn) {
+  return split(b, e, d, (std::numeric_limits<size_t>::max)(), std::move(fn));
+}
+
+void split(const char *b, const char *e, char d, size_t m,
+                  std::function<void(const char *, const char *)> fn) {
+  size_t i = 0;
+  size_t beg = 0;
+  size_t count = 1;
+
+  while (e ? (b + i < e) : (b[i] != '\0')) {
+    if (b[i] == d && count < m) {
+      auto r = trim(b, e, beg, i);
+      if (r.first < r.second) { fn(&b[r.first], &b[r.second]); }
+      beg = i + 1;
+      count++;
+    }
+    i++;
+  }
+
+  if (i) {
+    auto r = trim(b, e, beg, i);
+    if (r.first < r.second) { fn(&b[r.first], &b[r.second]); }
+  }
+}
+
+stream_line_reader::stream_line_reader(Stream &strm, char *fixed_buffer,
+                                              size_t fixed_buffer_size)
+    : strm_(strm), fixed_buffer_(fixed_buffer),
+      fixed_buffer_size_(fixed_buffer_size) {}
+
+const char *stream_line_reader::ptr() const {
+  if (growable_buffer_.empty()) {
+    return fixed_buffer_;
+  } else {
+    return growable_buffer_.data();
+  }
+}
+
+size_t stream_line_reader::size() const {
+  if (growable_buffer_.empty()) {
+    return fixed_buffer_used_size_;
+  } else {
+    return growable_buffer_.size();
+  }
+}
+
+bool stream_line_reader::end_with_crlf() const {
+  auto end = ptr() + size();
+  return size() >= 2 && end[-2] == '\r' && end[-1] == '\n';
+}
+
+bool stream_line_reader::getline() {
+  fixed_buffer_used_size_ = 0;
+  growable_buffer_.clear();
+
+#ifndef CPPHTTPLIB_ALLOW_LF_AS_LINE_TERMINATOR
+  char prev_byte = 0;
+#endif
+
+  for (size_t i = 0;; i++) {
+    if (size() >= CPPHTTPLIB_MAX_LINE_LENGTH) {
+      // Treat exceptionally long lines as an error to
+      // prevent infinite loops/memory exhaustion
+      return false;
+    }
+    char byte;
+    auto n = strm_.read(&byte, 1);
+
+    if (n < 0) {
+      return false;
+    } else if (n == 0) {
+      if (i == 0) {
+        return false;
+      } else {
+        break;
+      }
+    }
+
+    append(byte);
+
+#ifdef CPPHTTPLIB_ALLOW_LF_AS_LINE_TERMINATOR
+    if (byte == '\n') { break; }
+#else
+    if (prev_byte == '\r' && byte == '\n') { break; }
+    prev_byte = byte;
+#endif
+  }
+
+  return true;
+}
+
+void stream_line_reader::append(char c) {
+  if (fixed_buffer_used_size_ < fixed_buffer_size_ - 1) {
+    fixed_buffer_[fixed_buffer_used_size_++] = c;
+    fixed_buffer_[fixed_buffer_used_size_] = '\0';
+  } else {
+    if (growable_buffer_.empty()) {
+      assert(fixed_buffer_[fixed_buffer_used_size_] == '\0');
+      growable_buffer_.assign(fixed_buffer_, fixed_buffer_used_size_);
+    }
+    growable_buffer_ += c;
+  }
+}
+
+mmap::mmap(const char *path) { open(path); }
+
+mmap::~mmap() { close(); }
+
+bool mmap::open(const char *path) {
+  close();
+
+#if defined(_WIN32)
+  auto wpath = u8string_to_wstring(path);
+  if (wpath.empty()) { return false; }
+
+#if _WIN32_WINNT >= _WIN32_WINNT_WIN8
+  hFile_ = ::CreateFile2(wpath.c_str(), GENERIC_READ, FILE_SHARE_READ,
+                         OPEN_EXISTING, NULL);
+#else
+  hFile_ = ::CreateFileW(wpath.c_str(), GENERIC_READ, FILE_SHARE_READ, NULL,
+                         OPEN_EXISTING, FILE_ATTRIBUTE_NORMAL, NULL);
+#endif
+
+  if (hFile_ == INVALID_HANDLE_VALUE) { return false; }
+
+  LARGE_INTEGER size{};
+  if (!::GetFileSizeEx(hFile_, &size)) { return false; }
+  // If the following line doesn't compile due to QuadPart, update Windows SDK.
+  // See:
+  // https://github.com/yhirose/cpp-httplib/issues/1903#issuecomment-2316520721
+  if (static_cast<ULONGLONG>(size.QuadPart) >
+      (std::numeric_limits<decltype(size_)>::max)()) {
+    // `size_t` might be 32-bits, on 32-bits Windows.
+    return false;
+  }
+  size_ = static_cast<size_t>(size.QuadPart);
+
+#if _WIN32_WINNT >= _WIN32_WINNT_WIN8
+  hMapping_ =
+      ::CreateFileMappingFromApp(hFile_, NULL, PAGE_READONLY, size_, NULL);
+#else
+  hMapping_ = ::CreateFileMappingW(hFile_, NULL, PAGE_READONLY, 0, 0, NULL);
+#endif
+
+  // Special treatment for an empty file...
+  if (hMapping_ == NULL && size_ == 0) {
+    close();
+    is_open_empty_file = true;
+    return true;
+  }
+
+  if (hMapping_ == NULL) {
+    close();
+    return false;
+  }
+
+#if _WIN32_WINNT >= _WIN32_WINNT_WIN8
+  addr_ = ::MapViewOfFileFromApp(hMapping_, FILE_MAP_READ, 0, 0);
+#else
+  addr_ = ::MapViewOfFile(hMapping_, FILE_MAP_READ, 0, 0, 0);
+#endif
+
+  if (addr_ == nullptr) {
+    close();
+    return false;
+  }
+#else
+  fd_ = ::open(path, O_RDONLY);
+  if (fd_ == -1) { return false; }
+
+  struct stat sb;
+  if (fstat(fd_, &sb) == -1) {
+    close();
+    return false;
+  }
+  size_ = static_cast<size_t>(sb.st_size);
+
+  addr_ = ::mmap(NULL, size_, PROT_READ, MAP_PRIVATE, fd_, 0);
+
+  // Special treatment for an empty file...
+  if (addr_ == MAP_FAILED && size_ == 0) {
+    close();
+    is_open_empty_file = true;
+    return false;
+  }
+#endif
+
+  return true;
+}
+
+bool mmap::is_open() const {
+  return is_open_empty_file ? true : addr_ != nullptr;
+}
+
+size_t mmap::size() const { return size_; }
+
+const char *mmap::data() const {
+  return is_open_empty_file ? "" : static_cast<const char *>(addr_);
+}
+
+void mmap::close() {
+#if defined(_WIN32)
+  if (addr_) {
+    ::UnmapViewOfFile(addr_);
+    addr_ = nullptr;
+  }
+
+  if (hMapping_) {
+    ::CloseHandle(hMapping_);
+    hMapping_ = NULL;
+  }
+
+  if (hFile_ != INVALID_HANDLE_VALUE) {
+    ::CloseHandle(hFile_);
+    hFile_ = INVALID_HANDLE_VALUE;
+  }
+
+  is_open_empty_file = false;
+#else
+  if (addr_ != nullptr) {
+    munmap(addr_, size_);
+    addr_ = nullptr;
+  }
+
+  if (fd_ != -1) {
+    ::close(fd_);
+    fd_ = -1;
+  }
+#endif
+  size_ = 0;
+}
+int close_socket(socket_t sock) {
+#ifdef _WIN32
+  return closesocket(sock);
+#else
+  return close(sock);
+#endif
+}
+
+template <typename T> inline ssize_t handle_EINTR(T fn) {
+  ssize_t res = 0;
+  while (true) {
+    res = fn();
+    if (res < 0 && errno == EINTR) {
+      std::this_thread::sleep_for(std::chrono::microseconds{1});
+      continue;
+    }
+    break;
+  }
+  return res;
+}
+
+ssize_t read_socket(socket_t sock, void *ptr, size_t size, int flags) {
+  return handle_EINTR([&]() {
+    return recv(sock,
+#ifdef _WIN32
+                static_cast<char *>(ptr), static_cast<int>(size),
+#else
+                ptr, size,
+#endif
+                flags);
+  });
+}
+
+ssize_t send_socket(socket_t sock, const void *ptr, size_t size,
+                           int flags) {
+  return handle_EINTR([&]() {
+    return send(sock,
+#ifdef _WIN32
+                static_cast<const char *>(ptr), static_cast<int>(size),
+#else
+                ptr, size,
+#endif
+                flags);
+  });
+}
+
+int poll_wrapper(struct pollfd *fds, nfds_t nfds, int timeout) {
+#ifdef _WIN32
+  return ::WSAPoll(fds, nfds, timeout);
+#else
+  return ::poll(fds, nfds, timeout);
+#endif
+}
+
+template <bool Read>
+ssize_t select_impl(socket_t sock, time_t sec, time_t usec) {
+  struct pollfd pfd;
+  pfd.fd = sock;
+  pfd.events = (Read ? POLLIN : POLLOUT);
+
+  auto timeout = static_cast<int>(sec * 1000 + usec / 1000);
+
+  return handle_EINTR([&]() { return poll_wrapper(&pfd, 1, timeout); });
+}
+
+ssize_t select_read(socket_t sock, time_t sec, time_t usec) {
+  return select_impl<true>(sock, sec, usec);
+}
+
+ssize_t select_write(socket_t sock, time_t sec, time_t usec) {
+  return select_impl<false>(sock, sec, usec);
+}
+
+Error wait_until_socket_is_ready(socket_t sock, time_t sec,
+                                        time_t usec) {
+  struct pollfd pfd_read;
+  pfd_read.fd = sock;
+  pfd_read.events = POLLIN | POLLOUT;
+
+  auto timeout = static_cast<int>(sec * 1000 + usec / 1000);
+
+  auto poll_res =
+      handle_EINTR([&]() { return poll_wrapper(&pfd_read, 1, timeout); });
+
+  if (poll_res == 0) { return Error::ConnectionTimeout; }
+
+  if (poll_res > 0 && pfd_read.revents & (POLLIN | POLLOUT)) {
+    auto error = 0;
+    socklen_t len = sizeof(error);
+    auto res = getsockopt(sock, SOL_SOCKET, SO_ERROR,
+                          reinterpret_cast<char *>(&error), &len);
+    auto successful = res >= 0 && !error;
+    return successful ? Error::Success : Error::Connection;
+  }
+
+  return Error::Connection;
+}
+
+bool is_socket_alive(socket_t sock) {
+  const auto val = detail::select_read(sock, 0, 0);
+  if (val == 0) {
+    return true;
+  } else if (val < 0 && errno == EBADF) {
+    return false;
+  }
+  char buf[1];
+  return detail::read_socket(sock, &buf[0], sizeof(buf), MSG_PEEK) > 0;
+}
+
+class SocketStream final : public Stream {
+public:
+  SocketStream(socket_t sock, time_t read_timeout_sec, time_t read_timeout_usec,
+               time_t write_timeout_sec, time_t write_timeout_usec,
+               time_t max_timeout_msec = 0,
+               std::chrono::time_point<std::chrono::steady_clock> start_time =
+                   (std::chrono::steady_clock::time_point::min)());
+  ~SocketStream() override;
+
+  bool is_readable() const override;
+  bool wait_readable() const override;
+  bool wait_writable() const override;
+  ssize_t read(char *ptr, size_t size) override;
+  ssize_t write(const char *ptr, size_t size) override;
+  void get_remote_ip_and_port(std::string &ip, int &port) const override;
+  void get_local_ip_and_port(std::string &ip, int &port) const override;
+  socket_t socket() const override;
+  time_t duration() const override;
+
+private:
+  socket_t sock_;
+  time_t read_timeout_sec_;
+  time_t read_timeout_usec_;
+  time_t write_timeout_sec_;
+  time_t write_timeout_usec_;
+  time_t max_timeout_msec_;
+  const std::chrono::time_point<std::chrono::steady_clock> start_time_;
+
+  std::vector<char> read_buff_;
+  size_t read_buff_off_ = 0;
+  size_t read_buff_content_size_ = 0;
+
+  static const size_t read_buff_size_ = 1024l * 4;
+};
+
+#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
+class SSLSocketStream final : public Stream {
+public:
+  SSLSocketStream(
+      socket_t sock, SSL *ssl, time_t read_timeout_sec,
+      time_t read_timeout_usec, time_t write_timeout_sec,
+      time_t write_timeout_usec, time_t max_timeout_msec = 0,
+      std::chrono::time_point<std::chrono::steady_clock> start_time =
+          (std::chrono::steady_clock::time_point::min)());
+  ~SSLSocketStream() override;
+
+  bool is_readable() const override;
+  bool wait_readable() const override;
+  bool wait_writable() const override;
+  ssize_t read(char *ptr, size_t size) override;
+  ssize_t write(const char *ptr, size_t size) override;
+  void get_remote_ip_and_port(std::string &ip, int &port) const override;
+  void get_local_ip_and_port(std::string &ip, int &port) const override;
+  socket_t socket() const override;
+  time_t duration() const override;
+
+private:
+  socket_t sock_;
+  SSL *ssl_;
+  time_t read_timeout_sec_;
+  time_t read_timeout_usec_;
+  time_t write_timeout_sec_;
+  time_t write_timeout_usec_;
+  time_t max_timeout_msec_;
+  const std::chrono::time_point<std::chrono::steady_clock> start_time_;
+};
+#endif
+
+bool keep_alive(const std::atomic<socket_t> &svr_sock, socket_t sock,
+                       time_t keep_alive_timeout_sec) {
+  using namespace std::chrono;
+
+  const auto interval_usec =
+      CPPHTTPLIB_KEEPALIVE_TIMEOUT_CHECK_INTERVAL_USECOND;
+
+  // Avoid expensive `steady_clock::now()` call for the first time
+  if (select_read(sock, 0, interval_usec) > 0) { return true; }
+
+  const auto start = steady_clock::now() - microseconds{interval_usec};
+  const auto timeout = seconds{keep_alive_timeout_sec};
+
+  while (true) {
+    if (svr_sock == INVALID_SOCKET) {
+      break; // Server socket is closed
+    }
+
+    auto val = select_read(sock, 0, interval_usec);
+    if (val < 0) {
+      break; // Ssocket error
+    } else if (val == 0) {
+      if (steady_clock::now() - start > timeout) {
+        break; // Timeout
+      }
+    } else {
+      return true; // Ready for read
+    }
+  }
+
+  return false;
+}
+
+template <typename T>
+bool
+process_server_socket_core(const std::atomic<socket_t> &svr_sock, socket_t sock,
+                           size_t keep_alive_max_count,
+                           time_t keep_alive_timeout_sec, T callback) {
+  assert(keep_alive_max_count > 0);
+  auto ret = false;
+  auto count = keep_alive_max_count;
+  while (count > 0 && keep_alive(svr_sock, sock, keep_alive_timeout_sec)) {
+    auto close_connection = count == 1;
+    auto connection_closed = false;
+    ret = callback(close_connection, connection_closed);
+    if (!ret || connection_closed) { break; }
+    count--;
+  }
+  return ret;
+}
+
+template <typename T>
+bool
+process_server_socket(const std::atomic<socket_t> &svr_sock, socket_t sock,
+                      size_t keep_alive_max_count,
+                      time_t keep_alive_timeout_sec, time_t read_timeout_sec,
+                      time_t read_timeout_usec, time_t write_timeout_sec,
+                      time_t write_timeout_usec, T callback) {
+  return process_server_socket_core(
+      svr_sock, sock, keep_alive_max_count, keep_alive_timeout_sec,
+      [&](bool close_connection, bool &connection_closed) {
+        SocketStream strm(sock, read_timeout_sec, read_timeout_usec,
+                          write_timeout_sec, write_timeout_usec);
+        return callback(strm, close_connection, connection_closed);
+      });
+}
+
+bool process_client_socket(
+    socket_t sock, time_t read_timeout_sec, time_t read_timeout_usec,
+    time_t write_timeout_sec, time_t write_timeout_usec,
+    time_t max_timeout_msec,
+    std::chrono::time_point<std::chrono::steady_clock> start_time,
+    std::function<bool(Stream &)> callback) {
+  SocketStream strm(sock, read_timeout_sec, read_timeout_usec,
+                    write_timeout_sec, write_timeout_usec, max_timeout_msec,
+                    start_time);
+  return callback(strm);
+}
+
+int shutdown_socket(socket_t sock) {
+#ifdef _WIN32
+  return shutdown(sock, SD_BOTH);
+#else
+  return shutdown(sock, SHUT_RDWR);
+#endif
+}
+
+std::string escape_abstract_namespace_unix_domain(const std::string &s) {
+  if (s.size() > 1 && s[0] == '\0') {
+    auto ret = s;
+    ret[0] = '@';
+    return ret;
+  }
+  return s;
+}
+
+std::string
+unescape_abstract_namespace_unix_domain(const std::string &s) {
+  if (s.size() > 1 && s[0] == '@') {
+    auto ret = s;
+    ret[0] = '\0';
+    return ret;
+  }
+  return s;
+}
+
+template <typename BindOrConnect>
+socket_t create_socket(const std::string &host, const std::string &ip, int port,
+                       int address_family, int socket_flags, bool tcp_nodelay,
+                       bool ipv6_v6only, SocketOptions socket_options,
+                       BindOrConnect bind_or_connect) {
+  // Get address info
+  const char *node = nullptr;
+  struct addrinfo hints;
+  struct addrinfo *result;
+
+  memset(&hints, 0, sizeof(struct addrinfo));
+  hints.ai_socktype = SOCK_STREAM;
+  hints.ai_protocol = IPPROTO_IP;
+
+  if (!ip.empty()) {
+    node = ip.c_str();
+    // Ask getaddrinfo to convert IP in c-string to address
+    hints.ai_family = AF_UNSPEC;
+    hints.ai_flags = AI_NUMERICHOST;
+  } else {
+    if (!host.empty()) { node = host.c_str(); }
+    hints.ai_family = address_family;
+    hints.ai_flags = socket_flags;
+  }
+
+  if (hints.ai_family == AF_UNIX) {
+    const auto addrlen = host.length();
+    if (addrlen > sizeof(sockaddr_un::sun_path)) { return INVALID_SOCKET; }
+
+#ifdef SOCK_CLOEXEC
+    auto sock = socket(hints.ai_family, hints.ai_socktype | SOCK_CLOEXEC,
+                       hints.ai_protocol);
+#else
+    auto sock = socket(hints.ai_family, hints.ai_socktype, hints.ai_protocol);
+#endif
+
+    if (sock != INVALID_SOCKET) {
+      sockaddr_un addr{};
+      addr.sun_family = AF_UNIX;
+
+      auto unescaped_host = unescape_abstract_namespace_unix_domain(host);
+      std::copy(unescaped_host.begin(), unescaped_host.end(), addr.sun_path);
+
+      hints.ai_addr = reinterpret_cast<sockaddr *>(&addr);
+      hints.ai_addrlen = static_cast<socklen_t>(
+          sizeof(addr) - sizeof(addr.sun_path) + addrlen);
+
+#ifndef SOCK_CLOEXEC
+#ifndef _WIN32
+      fcntl(sock, F_SETFD, FD_CLOEXEC);
+#endif
+#endif
+
+      if (socket_options) { socket_options(sock); }
+
+#ifdef _WIN32
+      // Setting SO_REUSEADDR seems not to work well with AF_UNIX on windows, so
+      // remove the option.
+      detail::set_socket_opt(sock, SOL_SOCKET, SO_REUSEADDR, 0);
+#endif
+
+      bool dummy;
+      if (!bind_or_connect(sock, hints, dummy)) {
+        close_socket(sock);
+        sock = INVALID_SOCKET;
+      }
+    }
+    return sock;
+  }
+
+  auto service = std::to_string(port);
+
+  if (getaddrinfo(node, service.c_str(), &hints, &result)) {
+#if defined __linux__ && !defined __ANDROID__
+    res_init();
+#endif
+    return INVALID_SOCKET;
+  }
+  auto se = detail::scope_exit([&] { freeaddrinfo(result); });
+
+  for (auto rp = result; rp; rp = rp->ai_next) {
+    // Create a socket
+#ifdef _WIN32
+    auto sock =
+        WSASocketW(rp->ai_family, rp->ai_socktype, rp->ai_protocol, nullptr, 0,
+                   WSA_FLAG_NO_HANDLE_INHERIT | WSA_FLAG_OVERLAPPED);
+    /**
+     * Since the WSA_FLAG_NO_HANDLE_INHERIT is only supported on Windows 7 SP1
+     * and above the socket creation fails on older Windows Systems.
+     *
+     * Let's try to create a socket the old way in this case.
+     *
+     * Reference:
+     * https://docs.microsoft.com/en-us/windows/win32/api/winsock2/nf-winsock2-wsasocketa
+     *
+     * WSA_FLAG_NO_HANDLE_INHERIT:
+     * This flag is supported on Windows 7 with SP1, Windows Server 2008 R2 with
+     * SP1, and later
+     *
+     */
+    if (sock == INVALID_SOCKET) {
+      sock = socket(rp->ai_family, rp->ai_socktype, rp->ai_protocol);
+    }
+#else
+
+#ifdef SOCK_CLOEXEC
+    auto sock =
+        socket(rp->ai_family, rp->ai_socktype | SOCK_CLOEXEC, rp->ai_protocol);
+#else
+    auto sock = socket(rp->ai_family, rp->ai_socktype, rp->ai_protocol);
+#endif
+
+#endif
+    if (sock == INVALID_SOCKET) { continue; }
+
+#if !defined _WIN32 && !defined SOCK_CLOEXEC
+    if (fcntl(sock, F_SETFD, FD_CLOEXEC) == -1) {
+      close_socket(sock);
+      continue;
+    }
+#endif
+
+    if (tcp_nodelay) { set_socket_opt(sock, IPPROTO_TCP, TCP_NODELAY, 1); }
+
+    if (rp->ai_family == AF_INET6) {
+      set_socket_opt(sock, IPPROTO_IPV6, IPV6_V6ONLY, ipv6_v6only ? 1 : 0);
+    }
+
+    if (socket_options) { socket_options(sock); }
+
+    // bind or connect
+    auto quit = false;
+    if (bind_or_connect(sock, *rp, quit)) { return sock; }
+
+    close_socket(sock);
+
+    if (quit) { break; }
+  }
+
+  return INVALID_SOCKET;
+}
+
+void set_nonblocking(socket_t sock, bool nonblocking) {
+#ifdef _WIN32
+  auto flags = nonblocking ? 1UL : 0UL;
+  ioctlsocket(sock, FIONBIO, &flags);
+#else
+  auto flags = fcntl(sock, F_GETFL, 0);
+  fcntl(sock, F_SETFL,
+        nonblocking ? (flags | O_NONBLOCK) : (flags & (~O_NONBLOCK)));
+#endif
+}
+
+bool is_connection_error() {
+#ifdef _WIN32
+  return WSAGetLastError() != WSAEWOULDBLOCK;
+#else
+  return errno != EINPROGRESS;
+#endif
+}
+
+bool bind_ip_address(socket_t sock, const std::string &host) {
+  struct addrinfo hints;
+  struct addrinfo *result;
+
+  memset(&hints, 0, sizeof(struct addrinfo));
+  hints.ai_family = AF_UNSPEC;
+  hints.ai_socktype = SOCK_STREAM;
+  hints.ai_protocol = 0;
+
+  if (getaddrinfo(host.c_str(), "0", &hints, &result)) { return false; }
+  auto se = detail::scope_exit([&] { freeaddrinfo(result); });
+
+  auto ret = false;
+  for (auto rp = result; rp; rp = rp->ai_next) {
+    const auto &ai = *rp;
+    if (!::bind(sock, ai.ai_addr, static_cast<socklen_t>(ai.ai_addrlen))) {
+      ret = true;
+      break;
+    }
+  }
+
+  return ret;
+}
+
+#if !defined _WIN32 && !defined ANDROID && !defined _AIX && !defined __MVS__
+#define USE_IF2IP
+#endif
+
+#ifdef USE_IF2IP
+std::string if2ip(int address_family, const std::string &ifn) {
+  struct ifaddrs *ifap;
+  getifaddrs(&ifap);
+  auto se = detail::scope_exit([&] { freeifaddrs(ifap); });
+
+  std::string addr_candidate;
+  for (auto ifa = ifap; ifa; ifa = ifa->ifa_next) {
+    if (ifa->ifa_addr && ifn == ifa->ifa_name &&
+        (AF_UNSPEC == address_family ||
+         ifa->ifa_addr->sa_family == address_family)) {
+      if (ifa->ifa_addr->sa_family == AF_INET) {
+        auto sa = reinterpret_cast<struct sockaddr_in *>(ifa->ifa_addr);
+        char buf[INET_ADDRSTRLEN];
+        if (inet_ntop(AF_INET, &sa->sin_addr, buf, INET_ADDRSTRLEN)) {
+          return std::string(buf, INET_ADDRSTRLEN);
+        }
+      } else if (ifa->ifa_addr->sa_family == AF_INET6) {
+        auto sa = reinterpret_cast<struct sockaddr_in6 *>(ifa->ifa_addr);
+        if (!IN6_IS_ADDR_LINKLOCAL(&sa->sin6_addr)) {
+          char buf[INET6_ADDRSTRLEN] = {};
+          if (inet_ntop(AF_INET6, &sa->sin6_addr, buf, INET6_ADDRSTRLEN)) {
+            // equivalent to mac's IN6_IS_ADDR_UNIQUE_LOCAL
+            auto s6_addr_head = sa->sin6_addr.s6_addr[0];
+            if (s6_addr_head == 0xfc || s6_addr_head == 0xfd) {
+              addr_candidate = std::string(buf, INET6_ADDRSTRLEN);
+            } else {
+              return std::string(buf, INET6_ADDRSTRLEN);
+            }
+          }
+        }
+      }
+    }
+  }
+  return addr_candidate;
+}
+#endif
+
+socket_t create_client_socket(
+    const std::string &host, const std::string &ip, int port,
+    int address_family, bool tcp_nodelay, bool ipv6_v6only,
+    SocketOptions socket_options, time_t connection_timeout_sec,
+    time_t connection_timeout_usec, time_t read_timeout_sec,
+    time_t read_timeout_usec, time_t write_timeout_sec,
+    time_t write_timeout_usec, const std::string &intf, Error &error) {
+  auto sock = create_socket(
+      host, ip, port, address_family, 0, tcp_nodelay, ipv6_v6only,
+      std::move(socket_options),
+      [&](socket_t sock2, struct addrinfo &ai, bool &quit) -> bool {
+        if (!intf.empty()) {
+#ifdef USE_IF2IP
+          auto ip_from_if = if2ip(address_family, intf);
+          if (ip_from_if.empty()) { ip_from_if = intf; }
+          if (!bind_ip_address(sock2, ip_from_if)) {
+            error = Error::BindIPAddress;
+            return false;
+          }
+#endif
+        }
+
+        set_nonblocking(sock2, true);
+
+        auto ret =
+            ::connect(sock2, ai.ai_addr, static_cast<socklen_t>(ai.ai_addrlen));
+
+        if (ret < 0) {
+          if (is_connection_error()) {
+            error = Error::Connection;
+            return false;
+          }
+          error = wait_until_socket_is_ready(sock2, connection_timeout_sec,
+                                             connection_timeout_usec);
+          if (error != Error::Success) {
+            if (error == Error::ConnectionTimeout) { quit = true; }
+            return false;
+          }
+        }
+
+        set_nonblocking(sock2, false);
+        set_socket_opt_time(sock2, SOL_SOCKET, SO_RCVTIMEO, read_timeout_sec,
+                            read_timeout_usec);
+        set_socket_opt_time(sock2, SOL_SOCKET, SO_SNDTIMEO, write_timeout_sec,
+                            write_timeout_usec);
+
+        error = Error::Success;
+        return true;
+      });
+
+  if (sock != INVALID_SOCKET) {
+    error = Error::Success;
+  } else {
+    if (error == Error::Success) { error = Error::Connection; }
+  }
+
+  return sock;
+}
+
+bool get_ip_and_port(const struct sockaddr_storage &addr,
+                            socklen_t addr_len, std::string &ip, int &port) {
+  if (addr.ss_family == AF_INET) {
+    port = ntohs(reinterpret_cast<const struct sockaddr_in *>(&addr)->sin_port);
+  } else if (addr.ss_family == AF_INET6) {
+    port =
+        ntohs(reinterpret_cast<const struct sockaddr_in6 *>(&addr)->sin6_port);
+  } else {
+    return false;
+  }
+
+  std::array<char, NI_MAXHOST> ipstr{};
+  if (getnameinfo(reinterpret_cast<const struct sockaddr *>(&addr), addr_len,
+                  ipstr.data(), static_cast<socklen_t>(ipstr.size()), nullptr,
+                  0, NI_NUMERICHOST)) {
+    return false;
+  }
+
+  ip = ipstr.data();
+  return true;
+}
+
+void get_local_ip_and_port(socket_t sock, std::string &ip, int &port) {
+  struct sockaddr_storage addr;
+  socklen_t addr_len = sizeof(addr);
+  if (!getsockname(sock, reinterpret_cast<struct sockaddr *>(&addr),
+                   &addr_len)) {
+    get_ip_and_port(addr, addr_len, ip, port);
+  }
+}
+
+void get_remote_ip_and_port(socket_t sock, std::string &ip, int &port) {
+  struct sockaddr_storage addr;
+  socklen_t addr_len = sizeof(addr);
+
+  if (!getpeername(sock, reinterpret_cast<struct sockaddr *>(&addr),
+                   &addr_len)) {
+#ifndef _WIN32
+    if (addr.ss_family == AF_UNIX) {
+#if defined(__linux__)
+      struct ucred ucred;
+      socklen_t len = sizeof(ucred);
+      if (getsockopt(sock, SOL_SOCKET, SO_PEERCRED, &ucred, &len) == 0) {
+        port = ucred.pid;
+      }
+#elif defined(SOL_LOCAL) && defined(SO_PEERPID) // __APPLE__
+      pid_t pid;
+      socklen_t len = sizeof(pid);
+      if (getsockopt(sock, SOL_LOCAL, SO_PEERPID, &pid, &len) == 0) {
+        port = pid;
+      }
+#endif
+      return;
+    }
+#endif
+    get_ip_and_port(addr, addr_len, ip, port);
+  }
+}
+
+constexpr unsigned int str2tag_core(const char *s, size_t l,
+                                           unsigned int h) {
+  return (l == 0)
+             ? h
+             : str2tag_core(
+                   s + 1, l - 1,
+                   // Unsets the 6 high bits of h, therefore no overflow happens
+                   (((std::numeric_limits<unsigned int>::max)() >> 6) &
+                    h * 33) ^
+                       static_cast<unsigned char>(*s));
+}
+
+unsigned int str2tag(const std::string &s) {
+  return str2tag_core(s.data(), s.size(), 0);
+}
+
+namespace udl {
+
+constexpr unsigned int operator""_t(const char *s, size_t l) {
+  return str2tag_core(s, l, 0);
+}
+
+} // namespace udl
+
+std::string
+find_content_type(const std::string &path,
+                  const std::map<std::string, std::string> &user_data,
+                  const std::string &default_content_type) {
+  auto ext = file_extension(path);
+
+  auto it = user_data.find(ext);
+  if (it != user_data.end()) { return it->second; }
+
+  using udl::operator""_t;
+
+  switch (str2tag(ext)) {
+  default: return default_content_type;
+
+  case "css"_t: return "text/css";
+  case "csv"_t: return "text/csv";
+  case "htm"_t:
+  case "html"_t: return "text/html";
+  case "js"_t:
+  case "mjs"_t: return "text/javascript";
+  case "txt"_t: return "text/plain";
+  case "vtt"_t: return "text/vtt";
+
+  case "apng"_t: return "image/apng";
+  case "avif"_t: return "image/avif";
+  case "bmp"_t: return "image/bmp";
+  case "gif"_t: return "image/gif";
+  case "png"_t: return "image/png";
+  case "svg"_t: return "image/svg+xml";
+  case "webp"_t: return "image/webp";
+  case "ico"_t: return "image/x-icon";
+  case "tif"_t: return "image/tiff";
+  case "tiff"_t: return "image/tiff";
+  case "jpg"_t:
+  case "jpeg"_t: return "image/jpeg";
+
+  case "mp4"_t: return "video/mp4";
+  case "mpeg"_t: return "video/mpeg";
+  case "webm"_t: return "video/webm";
+
+  case "mp3"_t: return "audio/mp3";
+  case "mpga"_t: return "audio/mpeg";
+  case "weba"_t: return "audio/webm";
+  case "wav"_t: return "audio/wave";
+
+  case "otf"_t: return "font/otf";
+  case "ttf"_t: return "font/ttf";
+  case "woff"_t: return "font/woff";
+  case "woff2"_t: return "font/woff2";
+
+  case "7z"_t: return "application/x-7z-compressed";
+  case "atom"_t: return "application/atom+xml";
+  case "pdf"_t: return "application/pdf";
+  case "json"_t: return "application/json";
+  case "rss"_t: return "application/rss+xml";
+  case "tar"_t: return "application/x-tar";
+  case "xht"_t:
+  case "xhtml"_t: return "application/xhtml+xml";
+  case "xslt"_t: return "application/xslt+xml";
+  case "xml"_t: return "application/xml";
+  case "gz"_t: return "application/gzip";
+  case "zip"_t: return "application/zip";
+  case "wasm"_t: return "application/wasm";
+  }
+}
+
+bool can_compress_content_type(const std::string &content_type) {
+  using udl::operator""_t;
+
+  auto tag = str2tag(content_type);
+
+  switch (tag) {
+  case "image/svg+xml"_t:
+  case "application/javascript"_t:
+  case "application/json"_t:
+  case "application/xml"_t:
+  case "application/protobuf"_t:
+  case "application/xhtml+xml"_t: return true;
+
+  case "text/event-stream"_t: return false;
+
+  default: return !content_type.rfind("text/", 0);
+  }
+}
+
+EncodingType encoding_type(const Request &req, const Response &res) {
+  auto ret =
+      detail::can_compress_content_type(res.get_header_value("Content-Type"));
+  if (!ret) { return EncodingType::None; }
+
+  const auto &s = req.get_header_value("Accept-Encoding");
+  (void)(s);
+
+#ifdef CPPHTTPLIB_BROTLI_SUPPORT
+  // TODO: 'Accept-Encoding' has br, not br;q=0
+  ret = s.find("br") != std::string::npos;
+  if (ret) { return EncodingType::Brotli; }
+#endif
+
+#ifdef CPPHTTPLIB_ZLIB_SUPPORT
+  // TODO: 'Accept-Encoding' has gzip, not gzip;q=0
+  ret = s.find("gzip") != std::string::npos;
+  if (ret) { return EncodingType::Gzip; }
+#endif
+
+#ifdef CPPHTTPLIB_ZSTD_SUPPORT
+  // TODO: 'Accept-Encoding' has zstd, not zstd;q=0
+  ret = s.find("zstd") != std::string::npos;
+  if (ret) { return EncodingType::Zstd; }
+#endif
+
+  return EncodingType::None;
+}
+
+bool nocompressor::compress(const char *data, size_t data_length,
+                                   bool /*last*/, Callback callback) {
+  if (!data_length) { return true; }
+  return callback(data, data_length);
+}
+
+#ifdef CPPHTTPLIB_ZLIB_SUPPORT
+gzip_compressor::gzip_compressor() {
+  std::memset(&strm_, 0, sizeof(strm_));
+  strm_.zalloc = Z_NULL;
+  strm_.zfree = Z_NULL;
+  strm_.opaque = Z_NULL;
+
+  is_valid_ = deflateInit2(&strm_, Z_DEFAULT_COMPRESSION, Z_DEFLATED, 31, 8,
+                           Z_DEFAULT_STRATEGY) == Z_OK;
+}
+
+gzip_compressor::~gzip_compressor() { deflateEnd(&strm_); }
+
+bool gzip_compressor::compress(const char *data, size_t data_length,
+                                      bool last, Callback callback) {
+  assert(is_valid_);
+
+  do {
+    constexpr size_t max_avail_in =
+        (std::numeric_limits<decltype(strm_.avail_in)>::max)();
+
+    strm_.avail_in = static_cast<decltype(strm_.avail_in)>(
+        (std::min)(data_length, max_avail_in));
+    strm_.next_in = const_cast<Bytef *>(reinterpret_cast<const Bytef *>(data));
+
+    data_length -= strm_.avail_in;
+    data += strm_.avail_in;
+
+    auto flush = (last && data_length == 0) ? Z_FINISH : Z_NO_FLUSH;
+    auto ret = Z_OK;
+
+    std::array<char, CPPHTTPLIB_COMPRESSION_BUFSIZ> buff{};
+    do {
+      strm_.avail_out = static_cast<uInt>(buff.size());
+      strm_.next_out = reinterpret_cast<Bytef *>(buff.data());
+
+      ret = deflate(&strm_, flush);
+      if (ret == Z_STREAM_ERROR) { return false; }
+
+      if (!callback(buff.data(), buff.size() - strm_.avail_out)) {
+        return false;
+      }
+    } while (strm_.avail_out == 0);
+
+    assert((flush == Z_FINISH && ret == Z_STREAM_END) ||
+           (flush == Z_NO_FLUSH && ret == Z_OK));
+    assert(strm_.avail_in == 0);
+  } while (data_length > 0);
+
+  return true;
+}
+
+gzip_decompressor::gzip_decompressor() {
+  std::memset(&strm_, 0, sizeof(strm_));
+  strm_.zalloc = Z_NULL;
+  strm_.zfree = Z_NULL;
+  strm_.opaque = Z_NULL;
+
+  // 15 is the value of wbits, which should be at the maximum possible value
+  // to ensure that any gzip stream can be decoded. The offset of 32 specifies
+  // that the stream type should be automatically detected either gzip or
+  // deflate.
+  is_valid_ = inflateInit2(&strm_, 32 + 15) == Z_OK;
+}
+
+gzip_decompressor::~gzip_decompressor() { inflateEnd(&strm_); }
+
+bool gzip_decompressor::is_valid() const { return is_valid_; }
+
+bool gzip_decompressor::decompress(const char *data, size_t data_length,
+                                          Callback callback) {
+  assert(is_valid_);
+
+  auto ret = Z_OK;
+
+  do {
+    constexpr size_t max_avail_in =
+        (std::numeric_limits<decltype(strm_.avail_in)>::max)();
+
+    strm_.avail_in = static_cast<decltype(strm_.avail_in)>(
+        (std::min)(data_length, max_avail_in));
+    strm_.next_in = const_cast<Bytef *>(reinterpret_cast<const Bytef *>(data));
+
+    data_length -= strm_.avail_in;
+    data += strm_.avail_in;
+
+    std::array<char, CPPHTTPLIB_COMPRESSION_BUFSIZ> buff{};
+    while (strm_.avail_in > 0 && ret == Z_OK) {
+      strm_.avail_out = static_cast<uInt>(buff.size());
+      strm_.next_out = reinterpret_cast<Bytef *>(buff.data());
+
+      ret = inflate(&strm_, Z_NO_FLUSH);
+
+      assert(ret != Z_STREAM_ERROR);
+      switch (ret) {
+      case Z_NEED_DICT:
+      case Z_DATA_ERROR:
+      case Z_MEM_ERROR: inflateEnd(&strm_); return false;
+      }
+
+      if (!callback(buff.data(), buff.size() - strm_.avail_out)) {
+        return false;
+      }
+    }
+
+    if (ret != Z_OK && ret != Z_STREAM_END) { return false; }
+
+  } while (data_length > 0);
+
+  return true;
+}
+#endif
+
+#ifdef CPPHTTPLIB_BROTLI_SUPPORT
+brotli_compressor::brotli_compressor() {
+  state_ = BrotliEncoderCreateInstance(nullptr, nullptr, nullptr);
+}
+
+brotli_compressor::~brotli_compressor() {
+  BrotliEncoderDestroyInstance(state_);
+}
+
+bool brotli_compressor::compress(const char *data, size_t data_length,
+                                        bool last, Callback callback) {
+  std::array<uint8_t, CPPHTTPLIB_COMPRESSION_BUFSIZ> buff{};
+
+  auto operation = last ? BROTLI_OPERATION_FINISH : BROTLI_OPERATION_PROCESS;
+  auto available_in = data_length;
+  auto next_in = reinterpret_cast<const uint8_t *>(data);
+
+  for (;;) {
+    if (last) {
+      if (BrotliEncoderIsFinished(state_)) { break; }
+    } else {
+      if (!available_in) { break; }
+    }
+
+    auto available_out = buff.size();
+    auto next_out = buff.data();
+
+    if (!BrotliEncoderCompressStream(state_, operation, &available_in, &next_in,
+                                     &available_out, &next_out, nullptr)) {
+      return false;
+    }
+
+    auto output_bytes = buff.size() - available_out;
+    if (output_bytes) {
+      callback(reinterpret_cast<const char *>(buff.data()), output_bytes);
+    }
+  }
+
+  return true;
+}
+
+brotli_decompressor::brotli_decompressor() {
+  decoder_s = BrotliDecoderCreateInstance(0, 0, 0);
+  decoder_r = decoder_s ? BROTLI_DECODER_RESULT_NEEDS_MORE_INPUT
+                        : BROTLI_DECODER_RESULT_ERROR;
+}
+
+brotli_decompressor::~brotli_decompressor() {
+  if (decoder_s) { BrotliDecoderDestroyInstance(decoder_s); }
+}
+
+bool brotli_decompressor::is_valid() const { return decoder_s; }
+
+bool brotli_decompressor::decompress(const char *data,
+                                            size_t data_length,
+                                            Callback callback) {
+  if (decoder_r == BROTLI_DECODER_RESULT_SUCCESS ||
+      decoder_r == BROTLI_DECODER_RESULT_ERROR) {
+    return 0;
+  }
+
+  auto next_in = reinterpret_cast<const uint8_t *>(data);
+  size_t avail_in = data_length;
+  size_t total_out;
+
+  decoder_r = BROTLI_DECODER_RESULT_NEEDS_MORE_OUTPUT;
+
+  std::array<char, CPPHTTPLIB_COMPRESSION_BUFSIZ> buff{};
+  while (decoder_r == BROTLI_DECODER_RESULT_NEEDS_MORE_OUTPUT) {
+    char *next_out = buff.data();
+    size_t avail_out = buff.size();
+
+    decoder_r = BrotliDecoderDecompressStream(
+        decoder_s, &avail_in, &next_in, &avail_out,
+        reinterpret_cast<uint8_t **>(&next_out), &total_out);
+
+    if (decoder_r == BROTLI_DECODER_RESULT_ERROR) { return false; }
+
+    if (!callback(buff.data(), buff.size() - avail_out)) { return false; }
+  }
+
+  return decoder_r == BROTLI_DECODER_RESULT_SUCCESS ||
+         decoder_r == BROTLI_DECODER_RESULT_NEEDS_MORE_INPUT;
+}
+#endif
+
+#ifdef CPPHTTPLIB_ZSTD_SUPPORT
+zstd_compressor::zstd_compressor() {
+  ctx_ = ZSTD_createCCtx();
+  ZSTD_CCtx_setParameter(ctx_, ZSTD_c_compressionLevel, ZSTD_fast);
+}
+
+zstd_compressor::~zstd_compressor() { ZSTD_freeCCtx(ctx_); }
+
+bool zstd_compressor::compress(const char *data, size_t data_length,
+                                      bool last, Callback callback) {
+  std::array<char, CPPHTTPLIB_COMPRESSION_BUFSIZ> buff{};
+
+  ZSTD_EndDirective mode = last ? ZSTD_e_end : ZSTD_e_continue;
+  ZSTD_inBuffer input = {data, data_length, 0};
+
+  bool finished;
+  do {
+    ZSTD_outBuffer output = {buff.data(), CPPHTTPLIB_COMPRESSION_BUFSIZ, 0};
+    size_t const remaining = ZSTD_compressStream2(ctx_, &output, &input, mode);
+
+    if (ZSTD_isError(remaining)) { return false; }
+
+    if (!callback(buff.data(), output.pos)) { return false; }
+
+    finished = last ? (remaining == 0) : (input.pos == input.size);
+
+  } while (!finished);
+
+  return true;
+}
+
+zstd_decompressor::zstd_decompressor() { ctx_ = ZSTD_createDCtx(); }
+
+zstd_decompressor::~zstd_decompressor() { ZSTD_freeDCtx(ctx_); }
+
+bool zstd_decompressor::is_valid() const { return ctx_ != nullptr; }
+
+bool zstd_decompressor::decompress(const char *data, size_t data_length,
+                                          Callback callback) {
+  std::array<char, CPPHTTPLIB_COMPRESSION_BUFSIZ> buff{};
+  ZSTD_inBuffer input = {data, data_length, 0};
+
+  while (input.pos < input.size) {
+    ZSTD_outBuffer output = {buff.data(), CPPHTTPLIB_COMPRESSION_BUFSIZ, 0};
+    size_t const remaining = ZSTD_decompressStream(ctx_, &output, &input);
+
+    if (ZSTD_isError(remaining)) { return false; }
+
+    if (!callback(buff.data(), output.pos)) { return false; }
+  }
+
+  return true;
+}
+#endif
+
+bool has_header(const Headers &headers, const std::string &key) {
+  return headers.find(key) != headers.end();
+}
+
+const char *get_header_value(const Headers &headers,
+                                    const std::string &key, const char *def,
+                                    size_t id) {
+  auto rng = headers.equal_range(key);
+  auto it = rng.first;
+  std::advance(it, static_cast<ssize_t>(id));
+  if (it != rng.second) { return it->second.c_str(); }
+  return def;
+}
+
+template <typename T>
+bool parse_header(const char *beg, const char *end, T fn) {
+  // Skip trailing spaces and tabs.
+  while (beg < end && is_space_or_tab(end[-1])) {
+    end--;
+  }
+
+  auto p = beg;
+  while (p < end && *p != ':') {
+    p++;
+  }
+
+  auto name = std::string(beg, p);
+  if (!detail::fields::is_field_name(name)) { return false; }
+
+  if (p == end) { return false; }
+
+  auto key_end = p;
+
+  if (*p++ != ':') { return false; }
+
+  while (p < end && is_space_or_tab(*p)) {
+    p++;
+  }
+
+  if (p <= end) {
+    auto key_len = key_end - beg;
+    if (!key_len) { return false; }
+
+    auto key = std::string(beg, key_end);
+    auto val = std::string(p, end);
+
+    if (!detail::fields::is_field_value(val)) { return false; }
+
+    if (case_ignore::equal(key, "Location") ||
+        case_ignore::equal(key, "Referer")) {
+      fn(key, val);
+    } else {
+      fn(key, decode_url(val, false));
+    }
+
+    return true;
+  }
+
+  return false;
+}
+
+bool read_headers(Stream &strm, Headers &headers) {
+  const auto bufsiz = 2048;
+  char buf[bufsiz];
+  stream_line_reader line_reader(strm, buf, bufsiz);
+
+  for (;;) {
+    if (!line_reader.getline()) { return false; }
+
+    // Check if the line ends with CRLF.
+    auto line_terminator_len = 2;
+    if (line_reader.end_with_crlf()) {
+      // Blank line indicates end of headers.
+      if (line_reader.size() == 2) { break; }
+    } else {
+#ifdef CPPHTTPLIB_ALLOW_LF_AS_LINE_TERMINATOR
+      // Blank line indicates end of headers.
+      if (line_reader.size() == 1) { break; }
+      line_terminator_len = 1;
+#else
+      continue; // Skip invalid line.
+#endif
+    }
+
+    if (line_reader.size() > CPPHTTPLIB_HEADER_MAX_LENGTH) { return false; }
+
+    // Exclude line terminator
+    auto end = line_reader.ptr() + line_reader.size() - line_terminator_len;
+
+    if (!parse_header(line_reader.ptr(), end,
+                      [&](const std::string &key, const std::string &val) {
+                        headers.emplace(key, val);
+                      })) {
+      return false;
+    }
+  }
+
+  return true;
+}
+
+bool read_content_with_length(Stream &strm, uint64_t len,
+                                     Progress progress,
+                                     ContentReceiverWithProgress out) {
+  char buf[CPPHTTPLIB_RECV_BUFSIZ];
+
+  uint64_t r = 0;
+  while (r < len) {
+    auto read_len = static_cast<size_t>(len - r);
+    auto n = strm.read(buf, (std::min)(read_len, CPPHTTPLIB_RECV_BUFSIZ));
+    if (n <= 0) { return false; }
+
+    if (!out(buf, static_cast<size_t>(n), r, len)) { return false; }
+    r += static_cast<uint64_t>(n);
+
+    if (progress) {
+      if (!progress(r, len)) { return false; }
+    }
+  }
+
+  return true;
+}
+
+void skip_content_with_length(Stream &strm, uint64_t len) {
+  char buf[CPPHTTPLIB_RECV_BUFSIZ];
+  uint64_t r = 0;
+  while (r < len) {
+    auto read_len = static_cast<size_t>(len - r);
+    auto n = strm.read(buf, (std::min)(read_len, CPPHTTPLIB_RECV_BUFSIZ));
+    if (n <= 0) { return; }
+    r += static_cast<uint64_t>(n);
+  }
+}
+
+bool read_content_without_length(Stream &strm,
+                                        ContentReceiverWithProgress out) {
+  char buf[CPPHTTPLIB_RECV_BUFSIZ];
+  uint64_t r = 0;
+  for (;;) {
+    auto n = strm.read(buf, CPPHTTPLIB_RECV_BUFSIZ);
+    if (n == 0) { return true; }
+    if (n < 0) { return false; }
+
+    if (!out(buf, static_cast<size_t>(n), r, 0)) { return false; }
+    r += static_cast<uint64_t>(n);
+  }
+
+  return true;
+}
+
+template <typename T>
+bool read_content_chunked(Stream &strm, T &x,
+                                 ContentReceiverWithProgress out) {
+  const auto bufsiz = 16;
+  char buf[bufsiz];
+
+  stream_line_reader line_reader(strm, buf, bufsiz);
+
+  if (!line_reader.getline()) { return false; }
+
+  unsigned long chunk_len;
+  while (true) {
+    char *end_ptr;
+
+    chunk_len = std::strtoul(line_reader.ptr(), &end_ptr, 16);
+
+    if (end_ptr == line_reader.ptr()) { return false; }
+    if (chunk_len == ULONG_MAX) { return false; }
+
+    if (chunk_len == 0) { break; }
+
+    if (!read_content_with_length(strm, chunk_len, nullptr, out)) {
+      return false;
+    }
+
+    if (!line_reader.getline()) { return false; }
+
+    if (strcmp(line_reader.ptr(), "\r\n") != 0) { return false; }
+
+    if (!line_reader.getline()) { return false; }
+  }
+
+  assert(chunk_len == 0);
+
+  // NOTE: In RFC 9112, '7.1 Chunked Transfer Coding' mentions "The chunked
+  // transfer coding is complete when a chunk with a chunk-size of zero is
+  // received, possibly followed by a trailer section, and finally terminated by
+  // an empty line". https://www.rfc-editor.org/rfc/rfc9112.html#section-7.1
+  //
+  // In '7.1.3. Decoding Chunked', however, the pseudo-code in the section
+  // does't care for the existence of the final CRLF. In other words, it seems
+  // to be ok whether the final CRLF exists or not in the chunked data.
+  // https://www.rfc-editor.org/rfc/rfc9112.html#section-7.1.3
+  //
+  // According to the reference code in RFC 9112, cpp-httplib now allows
+  // chunked transfer coding data without the final CRLF.
+  if (!line_reader.getline()) { return true; }
+
+  while (strcmp(line_reader.ptr(), "\r\n") != 0) {
+    if (line_reader.size() > CPPHTTPLIB_HEADER_MAX_LENGTH) { return false; }
+
+    // Exclude line terminator
+    constexpr auto line_terminator_len = 2;
+    auto end = line_reader.ptr() + line_reader.size() - line_terminator_len;
+
+    parse_header(line_reader.ptr(), end,
+                 [&](const std::string &key, const std::string &val) {
+                   x.headers.emplace(key, val);
+                 });
+
+    if (!line_reader.getline()) { return false; }
+  }
+
+  return true;
+}
+
+bool is_chunked_transfer_encoding(const Headers &headers) {
+  return case_ignore::equal(
+      get_header_value(headers, "Transfer-Encoding", "", 0), "chunked");
+}
+
+template <typename T, typename U>
+bool prepare_content_receiver(T &x, int &status,
+                              ContentReceiverWithProgress receiver,
+                              bool decompress, U callback) {
+  if (decompress) {
+    std::string encoding = x.get_header_value("Content-Encoding");
+    std::unique_ptr<decompressor> decompressor;
+
+    if (encoding == "gzip" || encoding == "deflate") {
+#ifdef CPPHTTPLIB_ZLIB_SUPPORT
+      decompressor = detail::make_unique<gzip_decompressor>();
+#else
+      status = StatusCode::UnsupportedMediaType_415;
+      return false;
+#endif
+    } else if (encoding.find("br") != std::string::npos) {
+#ifdef CPPHTTPLIB_BROTLI_SUPPORT
+      decompressor = detail::make_unique<brotli_decompressor>();
+#else
+      status = StatusCode::UnsupportedMediaType_415;
+      return false;
+#endif
+    } else if (encoding == "zstd") {
+#ifdef CPPHTTPLIB_ZSTD_SUPPORT
+      decompressor = detail::make_unique<zstd_decompressor>();
+#else
+      status = StatusCode::UnsupportedMediaType_415;
+      return false;
+#endif
+    }
+
+    if (decompressor) {
+      if (decompressor->is_valid()) {
+        ContentReceiverWithProgress out = [&](const char *buf, size_t n,
+                                              uint64_t off, uint64_t len) {
+          return decompressor->decompress(buf, n,
+                                          [&](const char *buf2, size_t n2) {
+                                            return receiver(buf2, n2, off, len);
+                                          });
+        };
+        return callback(std::move(out));
+      } else {
+        status = StatusCode::InternalServerError_500;
+        return false;
+      }
+    }
+  }
+
+  ContentReceiverWithProgress out = [&](const char *buf, size_t n, uint64_t off,
+                                        uint64_t len) {
+    return receiver(buf, n, off, len);
+  };
+  return callback(std::move(out));
+}
+
+template <typename T>
+bool read_content(Stream &strm, T &x, size_t payload_max_length, int &status,
+                  Progress progress, ContentReceiverWithProgress receiver,
+                  bool decompress) {
+  return prepare_content_receiver(
+      x, status, std::move(receiver), decompress,
+      [&](const ContentReceiverWithProgress &out) {
+        auto ret = true;
+        auto exceed_payload_max_length = false;
+
+        if (is_chunked_transfer_encoding(x.headers)) {
+          ret = read_content_chunked(strm, x, out);
+        } else if (!has_header(x.headers, "Content-Length")) {
+          ret = read_content_without_length(strm, out);
+        } else {
+          auto is_invalid_value = false;
+          auto len = get_header_value_u64(
+              x.headers, "Content-Length",
+              (std::numeric_limits<uint64_t>::max)(), 0, is_invalid_value);
+
+          if (is_invalid_value) {
+            ret = false;
+          } else if (len > payload_max_length) {
+            exceed_payload_max_length = true;
+            skip_content_with_length(strm, len);
+            ret = false;
+          } else if (len > 0) {
+            ret = read_content_with_length(strm, len, std::move(progress), out);
+          }
+        }
+
+        if (!ret) {
+          status = exceed_payload_max_length ? StatusCode::PayloadTooLarge_413
+                                             : StatusCode::BadRequest_400;
+        }
+        return ret;
+      });
+}
+
+ssize_t write_request_line(Stream &strm, const std::string &method,
+                                  const std::string &path) {
+  std::string s = method;
+  s += " ";
+  s += path;
+  s += " HTTP/1.1\r\n";
+  return strm.write(s.data(), s.size());
+}
+
+ssize_t write_response_line(Stream &strm, int status) {
+  std::string s = "HTTP/1.1 ";
+  s += std::to_string(status);
+  s += " ";
+  s += httplib::status_message(status);
+  s += "\r\n";
+  return strm.write(s.data(), s.size());
+}
+
+ssize_t write_headers(Stream &strm, const Headers &headers) {
+  ssize_t write_len = 0;
+  for (const auto &x : headers) {
+    std::string s;
+    s = x.first;
+    s += ": ";
+    s += x.second;
+    s += "\r\n";
+
+    auto len = strm.write(s.data(), s.size());
+    if (len < 0) { return len; }
+    write_len += len;
+  }
+  auto len = strm.write("\r\n");
+  if (len < 0) { return len; }
+  write_len += len;
+  return write_len;
+}
+
+bool write_data(Stream &strm, const char *d, size_t l) {
+  size_t offset = 0;
+  while (offset < l) {
+    auto length = strm.write(d + offset, l - offset);
+    if (length < 0) { return false; }
+    offset += static_cast<size_t>(length);
+  }
+  return true;
+}
+
+template <typename T>
+bool write_content(Stream &strm, const ContentProvider &content_provider,
+                          size_t offset, size_t length, T is_shutting_down,
+                          Error &error) {
+  size_t end_offset = offset + length;
+  auto ok = true;
+  DataSink data_sink;
+
+  data_sink.write = [&](const char *d, size_t l) -> bool {
+    if (ok) {
+      if (write_data(strm, d, l)) {
+        offset += l;
+      } else {
+        ok = false;
+      }
+    }
+    return ok;
+  };
+
+  data_sink.is_writable = [&]() -> bool { return strm.wait_writable(); };
+
+  while (offset < end_offset && !is_shutting_down()) {
+    if (!strm.wait_writable()) {
+      error = Error::Write;
+      return false;
+    } else if (!content_provider(offset, end_offset - offset, data_sink)) {
+      error = Error::Canceled;
+      return false;
+    } else if (!ok) {
+      error = Error::Write;
+      return false;
+    }
+  }
+
+  error = Error::Success;
+  return true;
+}
+
+template <typename T>
+bool write_content(Stream &strm, const ContentProvider &content_provider,
+                          size_t offset, size_t length,
+                          const T &is_shutting_down) {
+  auto error = Error::Success;
+  return write_content(strm, content_provider, offset, length, is_shutting_down,
+                       error);
+}
+
+template <typename T>
+bool
+write_content_without_length(Stream &strm,
+                             const ContentProvider &content_provider,
+                             const T &is_shutting_down) {
+  size_t offset = 0;
+  auto data_available = true;
+  auto ok = true;
+  DataSink data_sink;
+
+  data_sink.write = [&](const char *d, size_t l) -> bool {
+    if (ok) {
+      offset += l;
+      if (!write_data(strm, d, l)) { ok = false; }
+    }
+    return ok;
+  };
+
+  data_sink.is_writable = [&]() -> bool { return strm.wait_writable(); };
+
+  data_sink.done = [&](void) { data_available = false; };
+
+  while (data_available && !is_shutting_down()) {
+    if (!strm.wait_writable()) {
+      return false;
+    } else if (!content_provider(offset, 0, data_sink)) {
+      return false;
+    } else if (!ok) {
+      return false;
+    }
+  }
+  return true;
+}
+
+template <typename T, typename U>
+bool
+write_content_chunked(Stream &strm, const ContentProvider &content_provider,
+                      const T &is_shutting_down, U &compressor, Error &error) {
+  size_t offset = 0;
+  auto data_available = true;
+  auto ok = true;
+  DataSink data_sink;
+
+  data_sink.write = [&](const char *d, size_t l) -> bool {
+    if (ok) {
+      data_available = l > 0;
+      offset += l;
+
+      std::string payload;
+      if (compressor.compress(d, l, false,
+                              [&](const char *data, size_t data_len) {
+                                payload.append(data, data_len);
+                                return true;
+                              })) {
+        if (!payload.empty()) {
+          // Emit chunked response header and footer for each chunk
+          auto chunk =
+              from_i_to_hex(payload.size()) + "\r\n" + payload + "\r\n";
+          if (!write_data(strm, chunk.data(), chunk.size())) { ok = false; }
+        }
+      } else {
+        ok = false;
+      }
+    }
+    return ok;
+  };
+
+  data_sink.is_writable = [&]() -> bool { return strm.wait_writable(); };
+
+  auto done_with_trailer = [&](const Headers *trailer) {
+    if (!ok) { return; }
+
+    data_available = false;
+
+    std::string payload;
+    if (!compressor.compress(nullptr, 0, true,
+                             [&](const char *data, size_t data_len) {
+                               payload.append(data, data_len);
+                               return true;
+                             })) {
+      ok = false;
+      return;
+    }
+
+    if (!payload.empty()) {
+      // Emit chunked response header and footer for each chunk
+      auto chunk = from_i_to_hex(payload.size()) + "\r\n" + payload + "\r\n";
+      if (!write_data(strm, chunk.data(), chunk.size())) {
+        ok = false;
+        return;
+      }
+    }
+
+    constexpr const char done_marker[] = "0\r\n";
+    if (!write_data(strm, done_marker, str_len(done_marker))) { ok = false; }
+
+    // Trailer
+    if (trailer) {
+      for (const auto &kv : *trailer) {
+        std::string field_line = kv.first + ": " + kv.second + "\r\n";
+        if (!write_data(strm, field_line.data(), field_line.size())) {
+          ok = false;
+        }
+      }
+    }
+
+    constexpr const char crlf[] = "\r\n";
+    if (!write_data(strm, crlf, str_len(crlf))) { ok = false; }
+  };
+
+  data_sink.done = [&](void) { done_with_trailer(nullptr); };
+
+  data_sink.done_with_trailer = [&](const Headers &trailer) {
+    done_with_trailer(&trailer);
+  };
+
+  while (data_available && !is_shutting_down()) {
+    if (!strm.wait_writable()) {
+      error = Error::Write;
+      return false;
+    } else if (!content_provider(offset, 0, data_sink)) {
+      error = Error::Canceled;
+      return false;
+    } else if (!ok) {
+      error = Error::Write;
+      return false;
+    }
+  }
+
+  error = Error::Success;
+  return true;
+}
+
+template <typename T, typename U>
+bool write_content_chunked(Stream &strm,
+                                  const ContentProvider &content_provider,
+                                  const T &is_shutting_down, U &compressor) {
+  auto error = Error::Success;
+  return write_content_chunked(strm, content_provider, is_shutting_down,
+                               compressor, error);
+}
+
+template <typename T>
+bool redirect(T &cli, Request &req, Response &res,
+                     const std::string &path, const std::string &location,
+                     Error &error) {
+  Request new_req = req;
+  new_req.path = path;
+  new_req.redirect_count_ -= 1;
+
+  if (res.status == StatusCode::SeeOther_303 &&
+      (req.method != "GET" && req.method != "HEAD")) {
+    new_req.method = "GET";
+    new_req.body.clear();
+    new_req.headers.clear();
+  }
+
+  Response new_res;
+
+  auto ret = cli.send(new_req, new_res, error);
+  if (ret) {
+    req = new_req;
+    res = new_res;
+
+    if (res.location.empty()) { res.location = location; }
+  }
+  return ret;
+}
+
+std::string params_to_query_str(const Params &params) {
+  std::string query;
+
+  for (auto it = params.begin(); it != params.end(); ++it) {
+    if (it != params.begin()) { query += "&"; }
+    query += it->first;
+    query += "=";
+    query += encode_query_param(it->second);
+  }
+  return query;
+}
+
+void parse_query_text(const char *data, std::size_t size,
+                             Params &params) {
+  std::set<std::string> cache;
+  split(data, data + size, '&', [&](const char *b, const char *e) {
+    std::string kv(b, e);
+    if (cache.find(kv) != cache.end()) { return; }
+    cache.insert(std::move(kv));
+
+    std::string key;
+    std::string val;
+    divide(b, static_cast<std::size_t>(e - b), '=',
+           [&](const char *lhs_data, std::size_t lhs_size, const char *rhs_data,
+               std::size_t rhs_size) {
+             key.assign(lhs_data, lhs_size);
+             val.assign(rhs_data, rhs_size);
+           });
+
+    if (!key.empty()) {
+      params.emplace(decode_url(key, true), decode_url(val, true));
+    }
+  });
+}
+
+void parse_query_text(const std::string &s, Params &params) {
+  parse_query_text(s.data(), s.size(), params);
+}
+
+bool parse_multipart_boundary(const std::string &content_type,
+                                     std::string &boundary) {
+  auto boundary_keyword = "boundary=";
+  auto pos = content_type.find(boundary_keyword);
+  if (pos == std::string::npos) { return false; }
+  auto end = content_type.find(';', pos);
+  auto beg = pos + strlen(boundary_keyword);
+  boundary = trim_double_quotes_copy(content_type.substr(beg, end - beg));
+  return !boundary.empty();
+}
+
+void parse_disposition_params(const std::string &s, Params &params) {
+  std::set<std::string> cache;
+  split(s.data(), s.data() + s.size(), ';', [&](const char *b, const char *e) {
+    std::string kv(b, e);
+    if (cache.find(kv) != cache.end()) { return; }
+    cache.insert(kv);
+
+    std::string key;
+    std::string val;
+    split(b, e, '=', [&](const char *b2, const char *e2) {
+      if (key.empty()) {
+        key.assign(b2, e2);
+      } else {
+        val.assign(b2, e2);
+      }
+    });
+
+    if (!key.empty()) {
+      params.emplace(trim_double_quotes_copy((key)),
+                     trim_double_quotes_copy((val)));
+    }
+  });
+}
+
+#ifdef CPPHTTPLIB_NO_EXCEPTIONS
+bool parse_range_header(const std::string &s, Ranges &ranges) {
+#else
+bool parse_range_header(const std::string &s, Ranges &ranges) try {
+#endif
+  auto is_valid = [](const std::string &str) {
+    return std::all_of(str.cbegin(), str.cend(),
+                       [](unsigned char c) { return std::isdigit(c); });
+  };
+
+  if (s.size() > 7 && s.compare(0, 6, "bytes=") == 0) {
+    const auto pos = static_cast<size_t>(6);
+    const auto len = static_cast<size_t>(s.size() - 6);
+    auto all_valid_ranges = true;
+    split(&s[pos], &s[pos + len], ',', [&](const char *b, const char *e) {
+      if (!all_valid_ranges) { return; }
+
+      const auto it = std::find(b, e, '-');
+      if (it == e) {
+        all_valid_ranges = false;
+        return;
+      }
+
+      const auto lhs = std::string(b, it);
+      const auto rhs = std::string(it + 1, e);
+      if (!is_valid(lhs) || !is_valid(rhs)) {
+        all_valid_ranges = false;
+        return;
+      }
+
+      const auto first =
+          static_cast<ssize_t>(lhs.empty() ? -1 : std::stoll(lhs));
+      const auto last =
+          static_cast<ssize_t>(rhs.empty() ? -1 : std::stoll(rhs));
+      if ((first == -1 && last == -1) ||
+          (first != -1 && last != -1 && first > last)) {
+        all_valid_ranges = false;
+        return;
+      }
+
+      ranges.emplace_back(first, last);
+    });
+    return all_valid_ranges && !ranges.empty();
+  }
+  return false;
+#ifdef CPPHTTPLIB_NO_EXCEPTIONS
+}
+#else
+} catch (...) { return false; }
+#endif
+
+class MultipartFormDataParser {
+public:
+  MultipartFormDataParser() = default;
+
+  void set_boundary(std::string &&boundary) {
+    boundary_ = boundary;
+    dash_boundary_crlf_ = dash_ + boundary_ + crlf_;
+    crlf_dash_boundary_ = crlf_ + dash_ + boundary_;
+  }
+
+  bool is_valid() const { return is_valid_; }
+
+  bool parse(const char *buf, size_t n, const ContentReceiver &content_callback,
+             const MultipartContentHeader &header_callback) {
+
+    buf_append(buf, n);
+
+    while (buf_size() > 0) {
+      switch (state_) {
+      case 0: { // Initial boundary
+        buf_erase(buf_find(dash_boundary_crlf_));
+        if (dash_boundary_crlf_.size() > buf_size()) { return true; }
+        if (!buf_start_with(dash_boundary_crlf_)) { return false; }
+        buf_erase(dash_boundary_crlf_.size());
+        state_ = 1;
+        break;
+      }
+      case 1: { // New entry
+        clear_file_info();
+        state_ = 2;
+        break;
+      }
+      case 2: { // Headers
+        auto pos = buf_find(crlf_);
+        if (pos > CPPHTTPLIB_HEADER_MAX_LENGTH) { return false; }
+        while (pos < buf_size()) {
+          // Empty line
+          if (pos == 0) {
+            if (!header_callback(file_)) {
+              is_valid_ = false;
+              return false;
+            }
+            buf_erase(crlf_.size());
+            state_ = 3;
+            break;
+          }
+
+          const auto header = buf_head(pos);
+
+          if (!parse_header(header.data(), header.data() + header.size(),
+                            [&](const std::string &, const std::string &) {})) {
+            is_valid_ = false;
+            return false;
+          }
+
+          constexpr const char header_content_type[] = "Content-Type:";
+
+          if (start_with_case_ignore(header, header_content_type)) {
+            file_.content_type =
+                trim_copy(header.substr(str_len(header_content_type)));
+          } else {
+            thread_local const std::regex re_content_disposition(
+                R"~(^Content-Disposition:\s*form-data;\s*(.*)$)~",
+                std::regex_constants::icase);
+
+            std::smatch m;
+            if (std::regex_match(header, m, re_content_disposition)) {
+              Params params;
+              parse_disposition_params(m[1], params);
+
+              auto it = params.find("name");
+              if (it != params.end()) {
+                file_.name = it->second;
+              } else {
+                is_valid_ = false;
+                return false;
+              }
+
+              it = params.find("filename");
+              if (it != params.end()) { file_.filename = it->second; }
+
+              it = params.find("filename*");
+              if (it != params.end()) {
+                // Only allow UTF-8 encoding...
+                thread_local const std::regex re_rfc5987_encoding(
+                    R"~(^UTF-8''(.+?)$)~", std::regex_constants::icase);
+
+                std::smatch m2;
+                if (std::regex_match(it->second, m2, re_rfc5987_encoding)) {
+                  file_.filename = decode_url(m2[1], false); // override...
+                } else {
+                  is_valid_ = false;
+                  return false;
+                }
+              }
+            }
+          }
+          buf_erase(pos + crlf_.size());
+          pos = buf_find(crlf_);
+        }
+        if (state_ != 3) { return true; }
+        break;
+      }
+      case 3: { // Body
+        if (crlf_dash_boundary_.size() > buf_size()) { return true; }
+        auto pos = buf_find(crlf_dash_boundary_);
+        if (pos < buf_size()) {
+          if (!content_callback(buf_data(), pos)) {
+            is_valid_ = false;
+            return false;
+          }
+          buf_erase(pos + crlf_dash_boundary_.size());
+          state_ = 4;
+        } else {
+          auto len = buf_size() - crlf_dash_boundary_.size();
+          if (len > 0) {
+            if (!content_callback(buf_data(), len)) {
+              is_valid_ = false;
+              return false;
+            }
+            buf_erase(len);
+          }
+          return true;
+        }
+        break;
+      }
+      case 4: { // Boundary
+        if (crlf_.size() > buf_size()) { return true; }
+        if (buf_start_with(crlf_)) {
+          buf_erase(crlf_.size());
+          state_ = 1;
+        } else {
+          if (dash_.size() > buf_size()) { return true; }
+          if (buf_start_with(dash_)) {
+            buf_erase(dash_.size());
+            is_valid_ = true;
+            buf_erase(buf_size()); // Remove epilogue
+          } else {
+            return true;
+          }
+        }
+        break;
+      }
+      }
+    }
+
+    return true;
+  }
+
+private:
+  void clear_file_info() {
+    file_.name.clear();
+    file_.filename.clear();
+    file_.content_type.clear();
+  }
+
+  bool start_with_case_ignore(const std::string &a, const char *b) const {
+    const auto b_len = strlen(b);
+    if (a.size() < b_len) { return false; }
+    for (size_t i = 0; i < b_len; i++) {
+      if (case_ignore::to_lower(a[i]) != case_ignore::to_lower(b[i])) {
+        return false;
+      }
+    }
+    return true;
+  }
+
+  const std::string dash_ = "--";
+  const std::string crlf_ = "\r\n";
+  std::string boundary_;
+  std::string dash_boundary_crlf_;
+  std::string crlf_dash_boundary_;
+
+  size_t state_ = 0;
+  bool is_valid_ = false;
+  MultipartFormData file_;
+
+  // Buffer
+  bool start_with(const std::string &a, size_t spos, size_t epos,
+                  const std::string &b) const {
+    if (epos - spos < b.size()) { return false; }
+    for (size_t i = 0; i < b.size(); i++) {
+      if (a[i + spos] != b[i]) { return false; }
+    }
+    return true;
+  }
+
+  size_t buf_size() const { return buf_epos_ - buf_spos_; }
+
+  const char *buf_data() const { return &buf_[buf_spos_]; }
+
+  std::string buf_head(size_t l) const { return buf_.substr(buf_spos_, l); }
+
+  bool buf_start_with(const std::string &s) const {
+    return start_with(buf_, buf_spos_, buf_epos_, s);
+  }
+
+  size_t buf_find(const std::string &s) const {
+    auto c = s.front();
+
+    size_t off = buf_spos_;
+    while (off < buf_epos_) {
+      auto pos = off;
+      while (true) {
+        if (pos == buf_epos_) { return buf_size(); }
+        if (buf_[pos] == c) { break; }
+        pos++;
+      }
+
+      auto remaining_size = buf_epos_ - pos;
+      if (s.size() > remaining_size) { return buf_size(); }
+
+      if (start_with(buf_, pos, buf_epos_, s)) { return pos - buf_spos_; }
+
+      off = pos + 1;
+    }
+
+    return buf_size();
+  }
+
+  void buf_append(const char *data, size_t n) {
+    auto remaining_size = buf_size();
+    if (remaining_size > 0 && buf_spos_ > 0) {
+      for (size_t i = 0; i < remaining_size; i++) {
+        buf_[i] = buf_[buf_spos_ + i];
+      }
+    }
+    buf_spos_ = 0;
+    buf_epos_ = remaining_size;
+
+    if (remaining_size + n > buf_.size()) { buf_.resize(remaining_size + n); }
+
+    for (size_t i = 0; i < n; i++) {
+      buf_[buf_epos_ + i] = data[i];
+    }
+    buf_epos_ += n;
+  }
+
+  void buf_erase(size_t size) { buf_spos_ += size; }
+
+  std::string buf_;
+  size_t buf_spos_ = 0;
+  size_t buf_epos_ = 0;
+};
+
+std::string random_string(size_t length) {
+  constexpr const char data[] =
+      "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz";
+
+  thread_local auto engine([]() {
+    // std::random_device might actually be deterministic on some
+    // platforms, but due to lack of support in the c++ standard library,
+    // doing better requires either some ugly hacks or breaking portability.
+    std::random_device seed_gen;
+    // Request 128 bits of entropy for initialization
+    std::seed_seq seed_sequence{seed_gen(), seed_gen(), seed_gen(), seed_gen()};
+    return std::mt19937(seed_sequence);
+  }());
+
+  std::string result;
+  for (size_t i = 0; i < length; i++) {
+    result += data[engine() % (sizeof(data) - 1)];
+  }
+  return result;
+}
+
+std::string make_multipart_data_boundary() {
+  return "--cpp-httplib-multipart-data-" + detail::random_string(16);
+}
+
+bool is_multipart_boundary_chars_valid(const std::string &boundary) {
+  auto valid = true;
+  for (size_t i = 0; i < boundary.size(); i++) {
+    auto c = boundary[i];
+    if (!std::isalnum(c) && c != '-' && c != '_') {
+      valid = false;
+      break;
+    }
+  }
+  return valid;
+}
+
+template <typename T>
+std::string
+serialize_multipart_formdata_item_begin(const T &item,
+                                        const std::string &boundary) {
+  std::string body = "--" + boundary + "\r\n";
+  body += "Content-Disposition: form-data; name=\"" + item.name + "\"";
+  if (!item.filename.empty()) {
+    body += "; filename=\"" + item.filename + "\"";
+  }
+  body += "\r\n";
+  if (!item.content_type.empty()) {
+    body += "Content-Type: " + item.content_type + "\r\n";
+  }
+  body += "\r\n";
+
+  return body;
+}
+
+std::string serialize_multipart_formdata_item_end() { return "\r\n"; }
+
+std::string
+serialize_multipart_formdata_finish(const std::string &boundary) {
+  return "--" + boundary + "--\r\n";
+}
+
+std::string
+serialize_multipart_formdata_get_content_type(const std::string &boundary) {
+  return "multipart/form-data; boundary=" + boundary;
+}
+
+std::string
+serialize_multipart_formdata(const MultipartFormDataItems &items,
+                             const std::string &boundary, bool finish = true) {
+  std::string body;
+
+  for (const auto &item : items) {
+    body += serialize_multipart_formdata_item_begin(item, boundary);
+    body += item.content + serialize_multipart_formdata_item_end();
+  }
+
+  if (finish) { body += serialize_multipart_formdata_finish(boundary); }
+
+  return body;
+}
+
+bool range_error(Request &req, Response &res) {
+  if (!req.ranges.empty() && 200 <= res.status && res.status < 300) {
+    ssize_t content_len = static_cast<ssize_t>(
+        res.content_length_ ? res.content_length_ : res.body.size());
+
+    ssize_t prev_first_pos = -1;
+    ssize_t prev_last_pos = -1;
+    size_t overwrapping_count = 0;
+
+    // NOTE: The following Range check is based on '14.2. Range' in RFC 9110
+    // 'HTTP Semantics' to avoid potential denial-of-service attacks.
+    // https://www.rfc-editor.org/rfc/rfc9110#section-14.2
+
+    // Too many ranges
+    if (req.ranges.size() > CPPHTTPLIB_RANGE_MAX_COUNT) { return true; }
+
+    for (auto &r : req.ranges) {
+      auto &first_pos = r.first;
+      auto &last_pos = r.second;
+
+      if (first_pos == -1 && last_pos == -1) {
+        first_pos = 0;
+        last_pos = content_len;
+      }
+
+      if (first_pos == -1) {
+        first_pos = content_len - last_pos;
+        last_pos = content_len - 1;
+      }
+
+      // NOTE: RFC-9110 '14.1.2. Byte Ranges':
+      // A client can limit the number of bytes requested without knowing the
+      // size of the selected representation. If the last-pos value is absent,
+      // or if the value is greater than or equal to the current length of the
+      // representation data, the byte range is interpreted as the remainder of
+      // the representation (i.e., the server replaces the value of last-pos
+      // with a value that is one less than the current length of the selected
+      // representation).
+      // https://www.rfc-editor.org/rfc/rfc9110.html#section-14.1.2-6
+      if (last_pos == -1 || last_pos >= content_len) {
+        last_pos = content_len - 1;
+      }
+
+      // Range must be within content length
+      if (!(0 <= first_pos && first_pos <= last_pos &&
+            last_pos <= content_len - 1)) {
+        return true;
+      }
+
+      // Ranges must be in ascending order
+      if (first_pos <= prev_first_pos) { return true; }
+
+      // Request must not have more than two overlapping ranges
+      if (first_pos <= prev_last_pos) {
+        overwrapping_count++;
+        if (overwrapping_count > 2) { return true; }
+      }
+
+      prev_first_pos = (std::max)(prev_first_pos, first_pos);
+      prev_last_pos = (std::max)(prev_last_pos, last_pos);
+    }
+  }
+
+  return false;
+}
+
+std::pair<size_t, size_t>
+get_range_offset_and_length(Range r, size_t content_length) {
+  assert(r.first != -1 && r.second != -1);
+  assert(0 <= r.first && r.first < static_cast<ssize_t>(content_length));
+  assert(r.first <= r.second &&
+         r.second < static_cast<ssize_t>(content_length));
+  (void)(content_length);
+  return std::make_pair(r.first, static_cast<size_t>(r.second - r.first) + 1);
+}
+
+std::string make_content_range_header_field(
+    const std::pair<size_t, size_t> &offset_and_length, size_t content_length) {
+  auto st = offset_and_length.first;
+  auto ed = st + offset_and_length.second - 1;
+
+  std::string field = "bytes ";
+  field += std::to_string(st);
+  field += "-";
+  field += std::to_string(ed);
+  field += "/";
+  field += std::to_string(content_length);
+  return field;
+}
+
+template <typename SToken, typename CToken, typename Content>
+bool process_multipart_ranges_data(const Request &req,
+                                   const std::string &boundary,
+                                   const std::string &content_type,
+                                   size_t content_length, SToken stoken,
+                                   CToken ctoken, Content content) {
+  for (size_t i = 0; i < req.ranges.size(); i++) {
+    ctoken("--");
+    stoken(boundary);
+    ctoken("\r\n");
+    if (!content_type.empty()) {
+      ctoken("Content-Type: ");
+      stoken(content_type);
+      ctoken("\r\n");
+    }
+
+    auto offset_and_length =
+        get_range_offset_and_length(req.ranges[i], content_length);
+
+    ctoken("Content-Range: ");
+    stoken(make_content_range_header_field(offset_and_length, content_length));
+    ctoken("\r\n");
+    ctoken("\r\n");
+
+    if (!content(offset_and_length.first, offset_and_length.second)) {
+      return false;
+    }
+    ctoken("\r\n");
+  }
+
+  ctoken("--");
+  stoken(boundary);
+  ctoken("--");
+
+  return true;
+}
+
+void make_multipart_ranges_data(const Request &req, Response &res,
+                                       const std::string &boundary,
+                                       const std::string &content_type,
+                                       size_t content_length,
+                                       std::string &data) {
+  process_multipart_ranges_data(
+      req, boundary, content_type, content_length,
+      [&](const std::string &token) { data += token; },
+      [&](const std::string &token) { data += token; },
+      [&](size_t offset, size_t length) {
+        assert(offset + length <= content_length);
+        data += res.body.substr(offset, length);
+        return true;
+      });
+}
+
+size_t get_multipart_ranges_data_length(const Request &req,
+                                               const std::string &boundary,
+                                               const std::string &content_type,
+                                               size_t content_length) {
+  size_t data_length = 0;
+
+  process_multipart_ranges_data(
+      req, boundary, content_type, content_length,
+      [&](const std::string &token) { data_length += token.size(); },
+      [&](const std::string &token) { data_length += token.size(); },
+      [&](size_t /*offset*/, size_t length) {
+        data_length += length;
+        return true;
+      });
+
+  return data_length;
+}
+
+template <typename T>
+bool
+write_multipart_ranges_data(Stream &strm, const Request &req, Response &res,
+                            const std::string &boundary,
+                            const std::string &content_type,
+                            size_t content_length, const T &is_shutting_down) {
+  return process_multipart_ranges_data(
+      req, boundary, content_type, content_length,
+      [&](const std::string &token) { strm.write(token); },
+      [&](const std::string &token) { strm.write(token); },
+      [&](size_t offset, size_t length) {
+        return write_content(strm, res.content_provider_, offset, length,
+                             is_shutting_down);
+      });
+}
+
+bool expect_content(const Request &req) {
+  if (req.method == "POST" || req.method == "PUT" || req.method == "PATCH" ||
+      req.method == "DELETE") {
+    return true;
+  }
+  if (req.has_header("Content-Length") &&
+      req.get_header_value_u64("Content-Length") > 0) {
+    return true;
+  }
+  if (is_chunked_transfer_encoding(req.headers)) { return true; }
+  return false;
+}
+
+bool has_crlf(const std::string &s) {
+  auto p = s.c_str();
+  while (*p) {
+    if (*p == '\r' || *p == '\n') { return true; }
+    p++;
+  }
+  return false;
+}
+
+#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
+std::string message_digest(const std::string &s, const EVP_MD *algo) {
+  auto context = std::unique_ptr<EVP_MD_CTX, decltype(&EVP_MD_CTX_free)>(
+      EVP_MD_CTX_new(), EVP_MD_CTX_free);
+
+  unsigned int hash_length = 0;
+  unsigned char hash[EVP_MAX_MD_SIZE];
+
+  EVP_DigestInit_ex(context.get(), algo, nullptr);
+  EVP_DigestUpdate(context.get(), s.c_str(), s.size());
+  EVP_DigestFinal_ex(context.get(), hash, &hash_length);
+
+  std::stringstream ss;
+  for (auto i = 0u; i < hash_length; ++i) {
+    ss << std::hex << std::setw(2) << std::setfill('0')
+       << static_cast<unsigned int>(hash[i]);
+  }
+
+  return ss.str();
+}
+
+std::string MD5(const std::string &s) {
+  return message_digest(s, EVP_md5());
+}
+
+std::string SHA_256(const std::string &s) {
+  return message_digest(s, EVP_sha256());
+}
+
+std::string SHA_512(const std::string &s) {
+  return message_digest(s, EVP_sha512());
+}
+
+std::pair<std::string, std::string> make_digest_authentication_header(
+    const Request &req, const std::map<std::string, std::string> &auth,
+    size_t cnonce_count, const std::string &cnonce, const std::string &username,
+    const std::string &password, bool is_proxy = false) {
+  std::string nc;
+  {
+    std::stringstream ss;
+    ss << std::setfill('0') << std::setw(8) << std::hex << cnonce_count;
+    nc = ss.str();
+  }
+
+  std::string qop;
+  if (auth.find("qop") != auth.end()) {
+    qop = auth.at("qop");
+    if (qop.find("auth-int") != std::string::npos) {
+      qop = "auth-int";
+    } else if (qop.find("auth") != std::string::npos) {
+      qop = "auth";
+    } else {
+      qop.clear();
+    }
+  }
+
+  std::string algo = "MD5";
+  if (auth.find("algorithm") != auth.end()) { algo = auth.at("algorithm"); }
+
+  std::string response;
+  {
+    auto H = algo == "SHA-256"   ? detail::SHA_256
+             : algo == "SHA-512" ? detail::SHA_512
+                                 : detail::MD5;
+
+    auto A1 = username + ":" + auth.at("realm") + ":" + password;
+
+    auto A2 = req.method + ":" + req.path;
+    if (qop == "auth-int") { A2 += ":" + H(req.body); }
+
+    if (qop.empty()) {
+      response = H(H(A1) + ":" + auth.at("nonce") + ":" + H(A2));
+    } else {
+      response = H(H(A1) + ":" + auth.at("nonce") + ":" + nc + ":" + cnonce +
+                   ":" + qop + ":" + H(A2));
+    }
+  }
+
+  auto opaque = (auth.find("opaque") != auth.end()) ? auth.at("opaque") : "";
+
+  auto field = "Digest username=\"" + username + "\", realm=\"" +
+               auth.at("realm") + "\", nonce=\"" + auth.at("nonce") +
+               "\", uri=\"" + req.path + "\", algorithm=" + algo +
+               (qop.empty() ? ", response=\""
+                            : ", qop=" + qop + ", nc=" + nc + ", cnonce=\"" +
+                                  cnonce + "\", response=\"") +
+               response + "\"" +
+               (opaque.empty() ? "" : ", opaque=\"" + opaque + "\"");
+
+  auto key = is_proxy ? "Proxy-Authorization" : "Authorization";
+  return std::make_pair(key, field);
+}
+
+bool is_ssl_peer_could_be_closed(SSL *ssl, socket_t sock) {
+  detail::set_nonblocking(sock, true);
+  auto se = detail::scope_exit([&]() { detail::set_nonblocking(sock, false); });
+
+  char buf[1];
+  return !SSL_peek(ssl, buf, 1) &&
+         SSL_get_error(ssl, 0) == SSL_ERROR_ZERO_RETURN;
+}
+
+#ifdef _WIN32
+// NOTE: This code came up with the following stackoverflow post:
+// https://stackoverflow.com/questions/9507184/can-openssl-on-windows-use-the-system-certificate-store
+bool load_system_certs_on_windows(X509_STORE *store) {
+  auto hStore = CertOpenSystemStoreW((HCRYPTPROV_LEGACY)NULL, L"ROOT");
+  if (!hStore) { return false; }
+
+  auto result = false;
+  PCCERT_CONTEXT pContext = NULL;
+  while ((pContext = CertEnumCertificatesInStore(hStore, pContext)) !=
+         nullptr) {
+    auto encoded_cert =
+        static_cast<const unsigned char *>(pContext->pbCertEncoded);
+
+    auto x509 = d2i_X509(NULL, &encoded_cert, pContext->cbCertEncoded);
+    if (x509) {
+      X509_STORE_add_cert(store, x509);
+      X509_free(x509);
+      result = true;
+    }
+  }
+
+  CertFreeCertificateContext(pContext);
+  CertCloseStore(hStore, 0);
+
+  return result;
+}
+#elif defined(CPPHTTPLIB_USE_CERTS_FROM_MACOSX_KEYCHAIN) && defined(__APPLE__)
+#if TARGET_OS_OSX
+template <typename T>
+using CFObjectPtr =
+    std::unique_ptr<typename std::remove_pointer<T>::type, void (*)(CFTypeRef)>;
+
+void cf_object_ptr_deleter(CFTypeRef obj) {
+  if (obj) { CFRelease(obj); }
+}
+
+bool retrieve_certs_from_keychain(CFObjectPtr<CFArrayRef> &certs) {
+  CFStringRef keys[] = {kSecClass, kSecMatchLimit, kSecReturnRef};
+  CFTypeRef values[] = {kSecClassCertificate, kSecMatchLimitAll,
+                        kCFBooleanTrue};
+
+  CFObjectPtr<CFDictionaryRef> query(
+      CFDictionaryCreate(nullptr, reinterpret_cast<const void **>(keys), values,
+                         sizeof(keys) / sizeof(keys[0]),
+                         &kCFTypeDictionaryKeyCallBacks,
+                         &kCFTypeDictionaryValueCallBacks),
+      cf_object_ptr_deleter);
+
+  if (!query) { return false; }
+
+  CFTypeRef security_items = nullptr;
+  if (SecItemCopyMatching(query.get(), &security_items) != errSecSuccess ||
+      CFArrayGetTypeID() != CFGetTypeID(security_items)) {
+    return false;
+  }
+
+  certs.reset(reinterpret_cast<CFArrayRef>(security_items));
+  return true;
+}
+
+bool retrieve_root_certs_from_keychain(CFObjectPtr<CFArrayRef> &certs) {
+  CFArrayRef root_security_items = nullptr;
+  if (SecTrustCopyAnchorCertificates(&root_security_items) != errSecSuccess) {
+    return false;
+  }
+
+  certs.reset(root_security_items);
+  return true;
+}
+
+bool add_certs_to_x509_store(CFArrayRef certs, X509_STORE *store) {
+  auto result = false;
+  for (auto i = 0; i < CFArrayGetCount(certs); ++i) {
+    const auto cert = reinterpret_cast<const __SecCertificate *>(
+        CFArrayGetValueAtIndex(certs, i));
+
+    if (SecCertificateGetTypeID() != CFGetTypeID(cert)) { continue; }
+
+    CFDataRef cert_data = nullptr;
+    if (SecItemExport(cert, kSecFormatX509Cert, 0, nullptr, &cert_data) !=
+        errSecSuccess) {
+      continue;
+    }
+
+    CFObjectPtr<CFDataRef> cert_data_ptr(cert_data, cf_object_ptr_deleter);
+
+    auto encoded_cert = static_cast<const unsigned char *>(
+        CFDataGetBytePtr(cert_data_ptr.get()));
+
+    auto x509 =
+        d2i_X509(NULL, &encoded_cert, CFDataGetLength(cert_data_ptr.get()));
+
+    if (x509) {
+      X509_STORE_add_cert(store, x509);
+      X509_free(x509);
+      result = true;
+    }
+  }
+
+  return result;
+}
+
+bool load_system_certs_on_macos(X509_STORE *store) {
+  auto result = false;
+  CFObjectPtr<CFArrayRef> certs(nullptr, cf_object_ptr_deleter);
+  if (retrieve_certs_from_keychain(certs) && certs) {
+    result = add_certs_to_x509_store(certs.get(), store);
+  }
+
+  if (retrieve_root_certs_from_keychain(certs) && certs) {
+    result = add_certs_to_x509_store(certs.get(), store) || result;
+  }
+
+  return result;
+}
+#endif // TARGET_OS_OSX
+#endif // _WIN32
+#endif // CPPHTTPLIB_OPENSSL_SUPPORT
+
+#ifdef _WIN32
+class WSInit {
+public:
+  WSInit() {
+    WSADATA wsaData;
+    if (WSAStartup(0x0002, &wsaData) == 0) is_valid_ = true;
+  }
+
+  ~WSInit() {
+    if (is_valid_) WSACleanup();
+  }
+
+  bool is_valid_ = false;
+};
+
+static WSInit wsinit_;
+#endif
+
+bool parse_www_authenticate(const Response &res,
+                                   std::map<std::string, std::string> &auth,
+                                   bool is_proxy) {
+  auto auth_key = is_proxy ? "Proxy-Authenticate" : "WWW-Authenticate";
+  if (res.has_header(auth_key)) {
+    thread_local auto re =
+        std::regex(R"~((?:(?:,\s*)?(.+?)=(?:"(.*?)"|([^,]*))))~");
+    auto s = res.get_header_value(auth_key);
+    auto pos = s.find(' ');
+    if (pos != std::string::npos) {
+      auto type = s.substr(0, pos);
+      if (type == "Basic") {
+        return false;
+      } else if (type == "Digest") {
+        s = s.substr(pos + 1);
+        auto beg = std::sregex_iterator(s.begin(), s.end(), re);
+        for (auto i = beg; i != std::sregex_iterator(); ++i) {
+          const auto &m = *i;
+          auto key = s.substr(static_cast<size_t>(m.position(1)),
+                              static_cast<size_t>(m.length(1)));
+          auto val = m.length(2) > 0
+                         ? s.substr(static_cast<size_t>(m.position(2)),
+                                    static_cast<size_t>(m.length(2)))
+                         : s.substr(static_cast<size_t>(m.position(3)),
+                                    static_cast<size_t>(m.length(3)));
+          auth[key] = val;
+        }
+        return true;
+      }
+    }
+  }
+  return false;
+}
+
+class ContentProviderAdapter {
+public:
+  explicit ContentProviderAdapter(
+      ContentProviderWithoutLength &&content_provider)
+      : content_provider_(content_provider) {}
+
+  bool operator()(size_t offset, size_t, DataSink &sink) {
+    return content_provider_(offset, sink);
+  }
+
+private:
+  ContentProviderWithoutLength content_provider_;
+};
+
+} // namespace detail
+
+std::string hosted_at(const std::string &hostname) {
+  std::vector<std::string> addrs;
+  hosted_at(hostname, addrs);
+  if (addrs.empty()) { return std::string(); }
+  return addrs[0];
+}
+
+void hosted_at(const std::string &hostname,
+                      std::vector<std::string> &addrs) {
+  struct addrinfo hints;
+  struct addrinfo *result;
+
+  memset(&hints, 0, sizeof(struct addrinfo));
+  hints.ai_family = AF_UNSPEC;
+  hints.ai_socktype = SOCK_STREAM;
+  hints.ai_protocol = 0;
+
+  if (getaddrinfo(hostname.c_str(), nullptr, &hints, &result)) {
+#if defined __linux__ && !defined __ANDROID__
+    res_init();
+#endif
+    return;
+  }
+  auto se = detail::scope_exit([&] { freeaddrinfo(result); });
+
+  for (auto rp = result; rp; rp = rp->ai_next) {
+    const auto &addr =
+        *reinterpret_cast<struct sockaddr_storage *>(rp->ai_addr);
+    std::string ip;
+    auto dummy = -1;
+    if (detail::get_ip_and_port(addr, sizeof(struct sockaddr_storage), ip,
+                                dummy)) {
+      addrs.push_back(ip);
+    }
+  }
+}
+
+std::string append_query_params(const std::string &path,
+                                       const Params &params) {
+  std::string path_with_query = path;
+  thread_local const std::regex re("[^?]+\\?.*");
+  auto delm = std::regex_match(path, re) ? '&' : '?';
+  path_with_query += delm + detail::params_to_query_str(params);
+  return path_with_query;
+}
+
+// Header utilities
+std::pair<std::string, std::string>
+make_range_header(const Ranges &ranges) {
+  std::string field = "bytes=";
+  auto i = 0;
+  for (const auto &r : ranges) {
+    if (i != 0) { field += ", "; }
+    if (r.first != -1) { field += std::to_string(r.first); }
+    field += '-';
+    if (r.second != -1) { field += std::to_string(r.second); }
+    i++;
+  }
+  return std::make_pair("Range", std::move(field));
+}
+
+std::pair<std::string, std::string>
+make_basic_authentication_header(const std::string &username,
+                                 const std::string &password, bool is_proxy) {
+  auto field = "Basic " + detail::base64_encode(username + ":" + password);
+  auto key = is_proxy ? "Proxy-Authorization" : "Authorization";
+  return std::make_pair(key, std::move(field));
+}
+
+std::pair<std::string, std::string>
+make_bearer_token_authentication_header(const std::string &token,
+                                        bool is_proxy = false) {
+  auto field = "Bearer " + token;
+  auto key = is_proxy ? "Proxy-Authorization" : "Authorization";
+  return std::make_pair(key, std::move(field));
+}
+
+// Request implementation
+bool Request::has_header(const std::string &key) const {
+  return detail::has_header(headers, key);
+}
+
+std::string Request::get_header_value(const std::string &key,
+                                             const char *def, size_t id) const {
+  return detail::get_header_value(headers, key, def, id);
+}
+
+size_t Request::get_header_value_count(const std::string &key) const {
+  auto r = headers.equal_range(key);
+  return static_cast<size_t>(std::distance(r.first, r.second));
+}
+
+void Request::set_header(const std::string &key,
+                                const std::string &val) {
+  if (detail::fields::is_field_name(key) &&
+      detail::fields::is_field_value(val)) {
+    headers.emplace(key, val);
+  }
+}
+
+bool Request::has_param(const std::string &key) const {
+  return params.find(key) != params.end();
+}
+
+std::string Request::get_param_value(const std::string &key,
+                                            size_t id) const {
+  auto rng = params.equal_range(key);
+  auto it = rng.first;
+  std::advance(it, static_cast<ssize_t>(id));
+  if (it != rng.second) { return it->second; }
+  return std::string();
+}
+
+size_t Request::get_param_value_count(const std::string &key) const {
+  auto r = params.equal_range(key);
+  return static_cast<size_t>(std::distance(r.first, r.second));
+}
+
+bool Request::is_multipart_form_data() const {
+  const auto &content_type = get_header_value("Content-Type");
+  return !content_type.rfind("multipart/form-data", 0);
+}
+
+bool Request::has_file(const std::string &key) const {
+  return files.find(key) != files.end();
+}
+
+MultipartFormData Request::get_file_value(const std::string &key) const {
+  auto it = files.find(key);
+  if (it != files.end()) { return it->second; }
+  return MultipartFormData();
+}
+
+std::vector<MultipartFormData>
+Request::get_file_values(const std::string &key) const {
+  std::vector<MultipartFormData> values;
+  auto rng = files.equal_range(key);
+  for (auto it = rng.first; it != rng.second; it++) {
+    values.push_back(it->second);
+  }
+  return values;
+}
+
+// Response implementation
+bool Response::has_header(const std::string &key) const {
+  return headers.find(key) != headers.end();
+}
+
+std::string Response::get_header_value(const std::string &key,
+                                              const char *def,
+                                              size_t id) const {
+  return detail::get_header_value(headers, key, def, id);
+}
+
+size_t Response::get_header_value_count(const std::string &key) const {
+  auto r = headers.equal_range(key);
+  return static_cast<size_t>(std::distance(r.first, r.second));
+}
+
+void Response::set_header(const std::string &key,
+                                 const std::string &val) {
+  if (detail::fields::is_field_name(key) &&
+      detail::fields::is_field_value(val)) {
+    headers.emplace(key, val);
+  }
+}
+
+void Response::set_redirect(const std::string &url, int stat) {
+  if (detail::fields::is_field_value(url)) {
+    set_header("Location", url);
+    if (300 <= stat && stat < 400) {
+      this->status = stat;
+    } else {
+      this->status = StatusCode::Found_302;
+    }
+  }
+}
+
+void Response::set_content(const char *s, size_t n,
+                                  const std::string &content_type) {
+  body.assign(s, n);
+
+  auto rng = headers.equal_range("Content-Type");
+  headers.erase(rng.first, rng.second);
+  set_header("Content-Type", content_type);
+}
+
+void Response::set_content(const std::string &s,
+                                  const std::string &content_type) {
+  set_content(s.data(), s.size(), content_type);
+}
+
+void Response::set_content(std::string &&s,
+                                  const std::string &content_type) {
+  body = std::move(s);
+
+  auto rng = headers.equal_range("Content-Type");
+  headers.erase(rng.first, rng.second);
+  set_header("Content-Type", content_type);
+}
+
+void Response::set_content_provider(
+    size_t in_length, const std::string &content_type, ContentProvider provider,
+    ContentProviderResourceReleaser resource_releaser) {
+  set_header("Content-Type", content_type);
+  content_length_ = in_length;
+  if (in_length > 0) { content_provider_ = std::move(provider); }
+  content_provider_resource_releaser_ = std::move(resource_releaser);
+  is_chunked_content_provider_ = false;
+}
+
+void Response::set_content_provider(
+    const std::string &content_type, ContentProviderWithoutLength provider,
+    ContentProviderResourceReleaser resource_releaser) {
+  set_header("Content-Type", content_type);
+  content_length_ = 0;
+  content_provider_ = detail::ContentProviderAdapter(std::move(provider));
+  content_provider_resource_releaser_ = std::move(resource_releaser);
+  is_chunked_content_provider_ = false;
+}
+
+void Response::set_chunked_content_provider(
+    const std::string &content_type, ContentProviderWithoutLength provider,
+    ContentProviderResourceReleaser resource_releaser) {
+  set_header("Content-Type", content_type);
+  content_length_ = 0;
+  content_provider_ = detail::ContentProviderAdapter(std::move(provider));
+  content_provider_resource_releaser_ = std::move(resource_releaser);
+  is_chunked_content_provider_ = true;
+}
+
+void Response::set_file_content(const std::string &path,
+                                       const std::string &content_type) {
+  file_content_path_ = path;
+  file_content_content_type_ = content_type;
+}
+
+void Response::set_file_content(const std::string &path) {
+  file_content_path_ = path;
+}
+
+// Result implementation
+bool Result::has_request_header(const std::string &key) const {
+  return request_headers_.find(key) != request_headers_.end();
+}
+
+std::string Result::get_request_header_value(const std::string &key,
+                                                    const char *def,
+                                                    size_t id) const {
+  return detail::get_header_value(request_headers_, key, def, id);
+}
+
+size_t
+Result::get_request_header_value_count(const std::string &key) const {
+  auto r = request_headers_.equal_range(key);
+  return static_cast<size_t>(std::distance(r.first, r.second));
+}
+
+// Stream implementation
+ssize_t Stream::write(const char *ptr) {
+  return write(ptr, strlen(ptr));
+}
+
+ssize_t Stream::write(const std::string &s) {
+  return write(s.data(), s.size());
+}
+
+namespace detail {
+
+void calc_actual_timeout(time_t max_timeout_msec, time_t duration_msec,
+                                time_t timeout_sec, time_t timeout_usec,
+                                time_t &actual_timeout_sec,
+                                time_t &actual_timeout_usec) {
+  auto timeout_msec = (timeout_sec * 1000) + (timeout_usec / 1000);
+
+  auto actual_timeout_msec =
+      (std::min)(max_timeout_msec - duration_msec, timeout_msec);
+
+  if (actual_timeout_msec < 0) { actual_timeout_msec = 0; }
+
+  actual_timeout_sec = actual_timeout_msec / 1000;
+  actual_timeout_usec = (actual_timeout_msec % 1000) * 1000;
+}
+
+// Socket stream implementation
+SocketStream::SocketStream(
+    socket_t sock, time_t read_timeout_sec, time_t read_timeout_usec,
+    time_t write_timeout_sec, time_t write_timeout_usec,
+    time_t max_timeout_msec,
+    std::chrono::time_point<std::chrono::steady_clock> start_time)
+    : sock_(sock), read_timeout_sec_(read_timeout_sec),
+      read_timeout_usec_(read_timeout_usec),
+      write_timeout_sec_(write_timeout_sec),
+      write_timeout_usec_(write_timeout_usec),
+      max_timeout_msec_(max_timeout_msec), start_time_(start_time),
+      read_buff_(read_buff_size_, 0) {}
+
+SocketStream::~SocketStream() = default;
+
+bool SocketStream::is_readable() const {
+  return read_buff_off_ < read_buff_content_size_;
+}
+
+bool SocketStream::wait_readable() const {
+  if (max_timeout_msec_ <= 0) {
+    return select_read(sock_, read_timeout_sec_, read_timeout_usec_) > 0;
+  }
+
+  time_t read_timeout_sec;
+  time_t read_timeout_usec;
+  calc_actual_timeout(max_timeout_msec_, duration(), read_timeout_sec_,
+                      read_timeout_usec_, read_timeout_sec, read_timeout_usec);
+
+  return select_read(sock_, read_timeout_sec, read_timeout_usec) > 0;
+}
+
+bool SocketStream::wait_writable() const {
+  return select_write(sock_, write_timeout_sec_, write_timeout_usec_) > 0 &&
+         is_socket_alive(sock_);
+}
+
+ssize_t SocketStream::read(char *ptr, size_t size) {
+#ifdef _WIN32
+  size =
+      (std::min)(size, static_cast<size_t>((std::numeric_limits<int>::max)()));
+#else
+  size = (std::min)(size,
+                    static_cast<size_t>((std::numeric_limits<ssize_t>::max)()));
+#endif
+
+  if (read_buff_off_ < read_buff_content_size_) {
+    auto remaining_size = read_buff_content_size_ - read_buff_off_;
+    if (size <= remaining_size) {
+      memcpy(ptr, read_buff_.data() + read_buff_off_, size);
+      read_buff_off_ += size;
+      return static_cast<ssize_t>(size);
+    } else {
+      memcpy(ptr, read_buff_.data() + read_buff_off_, remaining_size);
+      read_buff_off_ += remaining_size;
+      return static_cast<ssize_t>(remaining_size);
+    }
+  }
+
+  if (!wait_readable()) { return -1; }
+
+  read_buff_off_ = 0;
+  read_buff_content_size_ = 0;
+
+  if (size < read_buff_size_) {
+    auto n = read_socket(sock_, read_buff_.data(), read_buff_size_,
+                         CPPHTTPLIB_RECV_FLAGS);
+    if (n <= 0) {
+      return n;
+    } else if (n <= static_cast<ssize_t>(size)) {
+      memcpy(ptr, read_buff_.data(), static_cast<size_t>(n));
+      return n;
+    } else {
+      memcpy(ptr, read_buff_.data(), size);
+      read_buff_off_ = size;
+      read_buff_content_size_ = static_cast<size_t>(n);
+      return static_cast<ssize_t>(size);
+    }
+  } else {
+    return read_socket(sock_, ptr, size, CPPHTTPLIB_RECV_FLAGS);
+  }
+}
+
+ssize_t SocketStream::write(const char *ptr, size_t size) {
+  if (!wait_writable()) { return -1; }
+
+#if defined(_WIN32) && !defined(_WIN64)
+  size =
+      (std::min)(size, static_cast<size_t>((std::numeric_limits<int>::max)()));
+#endif
+
+  return send_socket(sock_, ptr, size, CPPHTTPLIB_SEND_FLAGS);
+}
+
+void SocketStream::get_remote_ip_and_port(std::string &ip,
+                                                 int &port) const {
+  return detail::get_remote_ip_and_port(sock_, ip, port);
+}
+
+void SocketStream::get_local_ip_and_port(std::string &ip,
+                                                int &port) const {
+  return detail::get_local_ip_and_port(sock_, ip, port);
+}
+
+socket_t SocketStream::socket() const { return sock_; }
+
+time_t SocketStream::duration() const {
+  return std::chrono::duration_cast<std::chrono::milliseconds>(
+             std::chrono::steady_clock::now() - start_time_)
+      .count();
+}
+
+// Buffer stream implementation
+bool BufferStream::is_readable() const { return true; }
+
+bool BufferStream::wait_readable() const { return true; }
+
+bool BufferStream::wait_writable() const { return true; }
+
+ssize_t BufferStream::read(char *ptr, size_t size) {
+#if defined(_MSC_VER) && _MSC_VER < 1910
+  auto len_read = buffer._Copy_s(ptr, size, size, position);
+#else
+  auto len_read = buffer.copy(ptr, size, position);
+#endif
+  position += static_cast<size_t>(len_read);
+  return static_cast<ssize_t>(len_read);
+}
+
+ssize_t BufferStream::write(const char *ptr, size_t size) {
+  buffer.append(ptr, size);
+  return static_cast<ssize_t>(size);
+}
+
+void BufferStream::get_remote_ip_and_port(std::string & /*ip*/,
+                                                 int & /*port*/) const {}
+
+void BufferStream::get_local_ip_and_port(std::string & /*ip*/,
+                                                int & /*port*/) const {}
+
+socket_t BufferStream::socket() const { return 0; }
+
+time_t BufferStream::duration() const { return 0; }
+
+const std::string &BufferStream::get_buffer() const { return buffer; }
+
+PathParamsMatcher::PathParamsMatcher(const std::string &pattern) {
+  constexpr const char marker[] = "/:";
+
+  // One past the last ending position of a path param substring
+  std::size_t last_param_end = 0;
+
+#ifndef CPPHTTPLIB_NO_EXCEPTIONS
+  // Needed to ensure that parameter names are unique during matcher
+  // construction
+  // If exceptions are disabled, only last duplicate path
+  // parameter will be set
+  std::unordered_set<std::string> param_name_set;
+#endif
+
+  while (true) {
+    const auto marker_pos = pattern.find(
+        marker, last_param_end == 0 ? last_param_end : last_param_end - 1);
+    if (marker_pos == std::string::npos) { break; }
+
+    static_fragments_.push_back(
+        pattern.substr(last_param_end, marker_pos - last_param_end + 1));
+
+    const auto param_name_start = marker_pos + str_len(marker);
+
+    auto sep_pos = pattern.find(separator, param_name_start);
+    if (sep_pos == std::string::npos) { sep_pos = pattern.length(); }
+
+    auto param_name =
+        pattern.substr(param_name_start, sep_pos - param_name_start);
+
+#ifndef CPPHTTPLIB_NO_EXCEPTIONS
+    if (param_name_set.find(param_name) != param_name_set.cend()) {
+      std::string msg = "Encountered path parameter '" + param_name +
+                        "' multiple times in route pattern '" + pattern + "'.";
+      throw std::invalid_argument(msg);
+    }
+#endif
+
+    param_names_.push_back(std::move(param_name));
+
+    last_param_end = sep_pos + 1;
+  }
+
+  if (last_param_end < pattern.length()) {
+    static_fragments_.push_back(pattern.substr(last_param_end));
+  }
+}
+
+bool PathParamsMatcher::match(Request &request) const {
+  request.matches = std::smatch();
+  request.path_params.clear();
+  request.path_params.reserve(param_names_.size());
+
+  // One past the position at which the path matched the pattern last time
+  std::size_t starting_pos = 0;
+  for (size_t i = 0; i < static_fragments_.size(); ++i) {
+    const auto &fragment = static_fragments_[i];
+
+    if (starting_pos + fragment.length() > request.path.length()) {
+      return false;
+    }
+
+    // Avoid unnecessary allocation by using strncmp instead of substr +
+    // comparison
+    if (std::strncmp(request.path.c_str() + starting_pos, fragment.c_str(),
+                     fragment.length()) != 0) {
+      return false;
+    }
+
+    starting_pos += fragment.length();
+
+    // Should only happen when we have a static fragment after a param
+    // Example: '/users/:id/subscriptions'
+    // The 'subscriptions' fragment here does not have a corresponding param
+    if (i >= param_names_.size()) { continue; }
+
+    auto sep_pos = request.path.find(separator, starting_pos);
+    if (sep_pos == std::string::npos) { sep_pos = request.path.length(); }
+
+    const auto &param_name = param_names_[i];
+
+    request.path_params.emplace(
+        param_name, request.path.substr(starting_pos, sep_pos - starting_pos));
+
+    // Mark everything up to '/' as matched
+    starting_pos = sep_pos + 1;
+  }
+  // Returns false if the path is longer than the pattern
+  return starting_pos >= request.path.length();
+}
+
+bool RegexMatcher::match(Request &request) const {
+  request.path_params.clear();
+  return std::regex_match(request.path, request.matches, regex_);
+}
+
+} // namespace detail
+
+// HTTP server implementation
+Server::Server()
+    : new_task_queue(
+          [] { return new ThreadPool(CPPHTTPLIB_THREAD_POOL_COUNT); }) {
+#ifndef _WIN32
+  signal(SIGPIPE, SIG_IGN);
+#endif
+}
+
+Server::~Server() = default;
+
+std::unique_ptr<detail::MatcherBase>
+Server::make_matcher(const std::string &pattern) {
+  if (pattern.find("/:") != std::string::npos) {
+    return detail::make_unique<detail::PathParamsMatcher>(pattern);
+  } else {
+    return detail::make_unique<detail::RegexMatcher>(pattern);
+  }
+}
+
+Server &Server::Get(const std::string &pattern, Handler handler) {
+  get_handlers_.emplace_back(make_matcher(pattern), std::move(handler));
+  return *this;
+}
+
+Server &Server::Post(const std::string &pattern, Handler handler) {
+  post_handlers_.emplace_back(make_matcher(pattern), std::move(handler));
+  return *this;
+}
+
+Server &Server::Post(const std::string &pattern,
+                            HandlerWithContentReader handler) {
+  post_handlers_for_content_reader_.emplace_back(make_matcher(pattern),
+                                                 std::move(handler));
+  return *this;
+}
+
+Server &Server::Put(const std::string &pattern, Handler handler) {
+  put_handlers_.emplace_back(make_matcher(pattern), std::move(handler));
+  return *this;
+}
+
+Server &Server::Put(const std::string &pattern,
+                           HandlerWithContentReader handler) {
+  put_handlers_for_content_reader_.emplace_back(make_matcher(pattern),
+                                                std::move(handler));
+  return *this;
+}
+
+Server &Server::Patch(const std::string &pattern, Handler handler) {
+  patch_handlers_.emplace_back(make_matcher(pattern), std::move(handler));
+  return *this;
+}
+
+Server &Server::Patch(const std::string &pattern,
+                             HandlerWithContentReader handler) {
+  patch_handlers_for_content_reader_.emplace_back(make_matcher(pattern),
+                                                  std::move(handler));
+  return *this;
+}
+
+Server &Server::Delete(const std::string &pattern, Handler handler) {
+  delete_handlers_.emplace_back(make_matcher(pattern), std::move(handler));
+  return *this;
+}
+
+Server &Server::Delete(const std::string &pattern,
+                              HandlerWithContentReader handler) {
+  delete_handlers_for_content_reader_.emplace_back(make_matcher(pattern),
+                                                   std::move(handler));
+  return *this;
+}
+
+Server &Server::Options(const std::string &pattern, Handler handler) {
+  options_handlers_.emplace_back(make_matcher(pattern), std::move(handler));
+  return *this;
+}
+
+bool Server::set_base_dir(const std::string &dir,
+                                 const std::string &mount_point) {
+  return set_mount_point(mount_point, dir);
+}
+
+bool Server::set_mount_point(const std::string &mount_point,
+                                    const std::string &dir, Headers headers) {
+  detail::FileStat stat(dir);
+  if (stat.is_dir()) {
+    std::string mnt = !mount_point.empty() ? mount_point : "/";
+    if (!mnt.empty() && mnt[0] == '/') {
+      base_dirs_.push_back({mnt, dir, std::move(headers)});
+      return true;
+    }
+  }
+  return false;
+}
+
+bool Server::remove_mount_point(const std::string &mount_point) {
+  for (auto it = base_dirs_.begin(); it != base_dirs_.end(); ++it) {
+    if (it->mount_point == mount_point) {
+      base_dirs_.erase(it);
+      return true;
+    }
+  }
+  return false;
+}
+
+Server &
+Server::set_file_extension_and_mimetype_mapping(const std::string &ext,
+                                                const std::string &mime) {
+  file_extension_and_mimetype_map_[ext] = mime;
+  return *this;
+}
+
+Server &Server::set_default_file_mimetype(const std::string &mime) {
+  default_file_mimetype_ = mime;
+  return *this;
+}
+
+Server &Server::set_file_request_handler(Handler handler) {
+  file_request_handler_ = std::move(handler);
+  return *this;
+}
+
+Server &Server::set_error_handler_core(HandlerWithResponse handler,
+                                              std::true_type) {
+  error_handler_ = std::move(handler);
+  return *this;
+}
+
+Server &Server::set_error_handler_core(Handler handler,
+                                              std::false_type) {
+  error_handler_ = [handler](const Request &req, Response &res) {
+    handler(req, res);
+    return HandlerResponse::Handled;
+  };
+  return *this;
+}
+
+Server &Server::set_exception_handler(ExceptionHandler handler) {
+  exception_handler_ = std::move(handler);
+  return *this;
+}
+
+Server &Server::set_pre_routing_handler(HandlerWithResponse handler) {
+  pre_routing_handler_ = std::move(handler);
+  return *this;
+}
+
+Server &Server::set_post_routing_handler(Handler handler) {
+  post_routing_handler_ = std::move(handler);
+  return *this;
+}
+
+Server &Server::set_logger(Logger logger) {
+  logger_ = std::move(logger);
+  return *this;
+}
+
+Server &
+Server::set_expect_100_continue_handler(Expect100ContinueHandler handler) {
+  expect_100_continue_handler_ = std::move(handler);
+  return *this;
+}
+
+Server &Server::set_address_family(int family) {
+  address_family_ = family;
+  return *this;
+}
+
+Server &Server::set_tcp_nodelay(bool on) {
+  tcp_nodelay_ = on;
+  return *this;
+}
+
+Server &Server::set_ipv6_v6only(bool on) {
+  ipv6_v6only_ = on;
+  return *this;
+}
+
+Server &Server::set_socket_options(SocketOptions socket_options) {
+  socket_options_ = std::move(socket_options);
+  return *this;
+}
+
+Server &Server::set_default_headers(Headers headers) {
+  default_headers_ = std::move(headers);
+  return *this;
+}
+
+Server &Server::set_header_writer(
+    std::function<ssize_t(Stream &, Headers &)> const &writer) {
+  header_writer_ = writer;
+  return *this;
+}
+
+Server &Server::set_keep_alive_max_count(size_t count) {
+  keep_alive_max_count_ = count;
+  return *this;
+}
+
+Server &Server::set_keep_alive_timeout(time_t sec) {
+  keep_alive_timeout_sec_ = sec;
+  return *this;
+}
+
+Server &Server::set_read_timeout(time_t sec, time_t usec) {
+  read_timeout_sec_ = sec;
+  read_timeout_usec_ = usec;
+  return *this;
+}
+
+Server &Server::set_write_timeout(time_t sec, time_t usec) {
+  write_timeout_sec_ = sec;
+  write_timeout_usec_ = usec;
+  return *this;
+}
+
+Server &Server::set_idle_interval(time_t sec, time_t usec) {
+  idle_interval_sec_ = sec;
+  idle_interval_usec_ = usec;
+  return *this;
+}
+
+Server &Server::set_payload_max_length(size_t length) {
+  payload_max_length_ = length;
+  return *this;
+}
+
+bool Server::bind_to_port(const std::string &host, int port,
+                                 int socket_flags) {
+  auto ret = bind_internal(host, port, socket_flags);
+  if (ret == -1) { is_decommissioned = true; }
+  return ret >= 0;
+}
+int Server::bind_to_any_port(const std::string &host, int socket_flags) {
+  auto ret = bind_internal(host, 0, socket_flags);
+  if (ret == -1) { is_decommissioned = true; }
+  return ret;
+}
+
+bool Server::listen_after_bind() { return listen_internal(); }
+
+bool Server::listen(const std::string &host, int port,
+                           int socket_flags) {
+  return bind_to_port(host, port, socket_flags) && listen_internal();
+}
+
+bool Server::is_running() const { return is_running_; }
+
+void Server::wait_until_ready() const {
+  while (!is_running_ && !is_decommissioned) {
+    std::this_thread::sleep_for(std::chrono::milliseconds{1});
+  }
+}
+
+void Server::stop() {
+  if (is_running_) {
+    assert(svr_sock_ != INVALID_SOCKET);
+    std::atomic<socket_t> sock(svr_sock_.exchange(INVALID_SOCKET));
+    detail::shutdown_socket(sock);
+    detail::close_socket(sock);
+  }
+  is_decommissioned = false;
+}
+
+void Server::decommission() { is_decommissioned = true; }
+
+bool Server::parse_request_line(const char *s, Request &req) const {
+  auto len = strlen(s);
+  if (len < 2 || s[len - 2] != '\r' || s[len - 1] != '\n') { return false; }
+  len -= 2;
+
+  {
+    size_t count = 0;
+
+    detail::split(s, s + len, ' ', [&](const char *b, const char *e) {
+      switch (count) {
+      case 0: req.method = std::string(b, e); break;
+      case 1: req.target = std::string(b, e); break;
+      case 2: req.version = std::string(b, e); break;
+      default: break;
+      }
+      count++;
+    });
+
+    if (count != 3) { return false; }
+  }
+
+  thread_local const std::set<std::string> methods{
+      "GET",     "HEAD",    "POST",  "PUT",   "DELETE",
+      "CONNECT", "OPTIONS", "TRACE", "PATCH", "PRI"};
+
+  if (methods.find(req.method) == methods.end()) { return false; }
+
+  if (req.version != "HTTP/1.1" && req.version != "HTTP/1.0") { return false; }
+
+  {
+    // Skip URL fragment
+    for (size_t i = 0; i < req.target.size(); i++) {
+      if (req.target[i] == '#') {
+        req.target.erase(i);
+        break;
+      }
+    }
+
+    detail::divide(req.target, '?',
+                   [&](const char *lhs_data, std::size_t lhs_size,
+                       const char *rhs_data, std::size_t rhs_size) {
+                     req.path = detail::decode_url(
+                         std::string(lhs_data, lhs_size), false);
+                     detail::parse_query_text(rhs_data, rhs_size, req.params);
+                   });
+  }
+
+  return true;
+}
+
+bool Server::write_response(Stream &strm, bool close_connection,
+                                   Request &req, Response &res) {
+  // NOTE: `req.ranges` should be empty, otherwise it will be applied
+  // incorrectly to the error content.
+  req.ranges.clear();
+  return write_response_core(strm, close_connection, req, res, false);
+}
+
+bool Server::write_response_with_content(Stream &strm,
+                                                bool close_connection,
+                                                const Request &req,
+                                                Response &res) {
+  return write_response_core(strm, close_connection, req, res, true);
+}
+
+bool Server::write_response_core(Stream &strm, bool close_connection,
+                                        const Request &req, Response &res,
+                                        bool need_apply_ranges) {
+  assert(res.status != -1);
+
+  if (400 <= res.status && error_handler_ &&
+      error_handler_(req, res) == HandlerResponse::Handled) {
+    need_apply_ranges = true;
+  }
+
+  std::string content_type;
+  std::string boundary;
+  if (need_apply_ranges) { apply_ranges(req, res, content_type, boundary); }
+
+  // Prepare additional headers
+  if (close_connection || req.get_header_value("Connection") == "close") {
+    res.set_header("Connection", "close");
+  } else {
+    std::string s = "timeout=";
+    s += std::to_string(keep_alive_timeout_sec_);
+    s += ", max=";
+    s += std::to_string(keep_alive_max_count_);
+    res.set_header("Keep-Alive", s);
+  }
+
+  if ((!res.body.empty() || res.content_length_ > 0 || res.content_provider_) &&
+      !res.has_header("Content-Type")) {
+    res.set_header("Content-Type", "text/plain");
+  }
+
+  if (res.body.empty() && !res.content_length_ && !res.content_provider_ &&
+      !res.has_header("Content-Length")) {
+    res.set_header("Content-Length", "0");
+  }
+
+  if (req.method == "HEAD" && !res.has_header("Accept-Ranges")) {
+    res.set_header("Accept-Ranges", "bytes");
+  }
+
+  if (post_routing_handler_) { post_routing_handler_(req, res); }
+
+  // Response line and headers
+  {
+    detail::BufferStream bstrm;
+    if (!detail::write_response_line(bstrm, res.status)) { return false; }
+    if (!header_writer_(bstrm, res.headers)) { return false; }
+
+    // Flush buffer
+    auto &data = bstrm.get_buffer();
+    detail::write_data(strm, data.data(), data.size());
+  }
+
+  // Body
+  auto ret = true;
+  if (req.method != "HEAD") {
+    if (!res.body.empty()) {
+      if (!detail::write_data(strm, res.body.data(), res.body.size())) {
+        ret = false;
+      }
+    } else if (res.content_provider_) {
+      if (write_content_with_provider(strm, req, res, boundary, content_type)) {
+        res.content_provider_success_ = true;
+      } else {
+        ret = false;
+      }
+    }
+  }
+
+  // Log
+  if (logger_) { logger_(req, res); }
+
+  return ret;
+}
+
+bool
+Server::write_content_with_provider(Stream &strm, const Request &req,
+                                    Response &res, const std::string &boundary,
+                                    const std::string &content_type) {
+  auto is_shutting_down = [this]() {
+    return this->svr_sock_ == INVALID_SOCKET;
+  };
+
+  if (res.content_length_ > 0) {
+    if (req.ranges.empty()) {
+      return detail::write_content(strm, res.content_provider_, 0,
+                                   res.content_length_, is_shutting_down);
+    } else if (req.ranges.size() == 1) {
+      auto offset_and_length = detail::get_range_offset_and_length(
+          req.ranges[0], res.content_length_);
+
+      return detail::write_content(strm, res.content_provider_,
+                                   offset_and_length.first,
+                                   offset_and_length.second, is_shutting_down);
+    } else {
+      return detail::write_multipart_ranges_data(
+          strm, req, res, boundary, content_type, res.content_length_,
+          is_shutting_down);
+    }
+  } else {
+    if (res.is_chunked_content_provider_) {
+      auto type = detail::encoding_type(req, res);
+
+      std::unique_ptr<detail::compressor> compressor;
+      if (type == detail::EncodingType::Gzip) {
+#ifdef CPPHTTPLIB_ZLIB_SUPPORT
+        compressor = detail::make_unique<detail::gzip_compressor>();
+#endif
+      } else if (type == detail::EncodingType::Brotli) {
+#ifdef CPPHTTPLIB_BROTLI_SUPPORT
+        compressor = detail::make_unique<detail::brotli_compressor>();
+#endif
+      } else if (type == detail::EncodingType::Zstd) {
+#ifdef CPPHTTPLIB_ZSTD_SUPPORT
+        compressor = detail::make_unique<detail::zstd_compressor>();
+#endif
+      } else {
+        compressor = detail::make_unique<detail::nocompressor>();
+      }
+      assert(compressor != nullptr);
+
+      return detail::write_content_chunked(strm, res.content_provider_,
+                                           is_shutting_down, *compressor);
+    } else {
+      return detail::write_content_without_length(strm, res.content_provider_,
+                                                  is_shutting_down);
+    }
+  }
+}
+
+bool Server::read_content(Stream &strm, Request &req, Response &res) {
+  MultipartFormDataMap::iterator cur;
+  auto file_count = 0;
+  if (read_content_core(
+          strm, req, res,
+          // Regular
+          [&](const char *buf, size_t n) {
+            if (req.body.size() + n > req.body.max_size()) { return false; }
+            req.body.append(buf, n);
+            return true;
+          },
+          // Multipart
+          [&](const MultipartFormData &file) {
+            if (file_count++ == CPPHTTPLIB_MULTIPART_FORM_DATA_FILE_MAX_COUNT) {
+              return false;
+            }
+            cur = req.files.emplace(file.name, file);
+            return true;
+          },
+          [&](const char *buf, size_t n) {
+            auto &content = cur->second.content;
+            if (content.size() + n > content.max_size()) { return false; }
+            content.append(buf, n);
+            return true;
+          })) {
+    const auto &content_type = req.get_header_value("Content-Type");
+    if (!content_type.find("application/x-www-form-urlencoded")) {
+      if (req.body.size() > CPPHTTPLIB_FORM_URL_ENCODED_PAYLOAD_MAX_LENGTH) {
+        res.status = StatusCode::PayloadTooLarge_413; // NOTE: should be 414?
+        return false;
+      }
+      detail::parse_query_text(req.body, req.params);
+    }
+    return true;
+  }
+  return false;
+}
+
+bool Server::read_content_with_content_receiver(
+    Stream &strm, Request &req, Response &res, ContentReceiver receiver,
+    MultipartContentHeader multipart_header,
+    ContentReceiver multipart_receiver) {
+  return read_content_core(strm, req, res, std::move(receiver),
+                           std::move(multipart_header),
+                           std::move(multipart_receiver));
+}
+
+bool
+Server::read_content_core(Stream &strm, Request &req, Response &res,
+                          ContentReceiver receiver,
+                          MultipartContentHeader multipart_header,
+                          ContentReceiver multipart_receiver) const {
+  detail::MultipartFormDataParser multipart_form_data_parser;
+  ContentReceiverWithProgress out;
+
+  if (req.is_multipart_form_data()) {
+    const auto &content_type = req.get_header_value("Content-Type");
+    std::string boundary;
+    if (!detail::parse_multipart_boundary(content_type, boundary)) {
+      res.status = StatusCode::BadRequest_400;
+      return false;
+    }
+
+    multipart_form_data_parser.set_boundary(std::move(boundary));
+    out = [&](const char *buf, size_t n, uint64_t /*off*/, uint64_t /*len*/) {
+      /* For debug
+      size_t pos = 0;
+      while (pos < n) {
+        auto read_size = (std::min)<size_t>(1, n - pos);
+        auto ret = multipart_form_data_parser.parse(
+            buf + pos, read_size, multipart_receiver, multipart_header);
+        if (!ret) { return false; }
+        pos += read_size;
+      }
+      return true;
+      */
+      return multipart_form_data_parser.parse(buf, n, multipart_receiver,
+                                              multipart_header);
+    };
+  } else {
+    out = [receiver](const char *buf, size_t n, uint64_t /*off*/,
+                     uint64_t /*len*/) { return receiver(buf, n); };
+  }
+
+  if (req.method == "DELETE" && !req.has_header("Content-Length")) {
+    return true;
+  }
+
+  if (!detail::read_content(strm, req, payload_max_length_, res.status, nullptr,
+                            out, true)) {
+    return false;
+  }
+
+  if (req.is_multipart_form_data()) {
+    if (!multipart_form_data_parser.is_valid()) {
+      res.status = StatusCode::BadRequest_400;
+      return false;
+    }
+  }
+
+  return true;
+}
+
+bool Server::handle_file_request(const Request &req, Response &res,
+                                        bool head) {
+  for (const auto &entry : base_dirs_) {
+    // Prefix match
+    if (!req.path.compare(0, entry.mount_point.size(), entry.mount_point)) {
+      std::string sub_path = "/" + req.path.substr(entry.mount_point.size());
+      if (detail::is_valid_path(sub_path)) {
+        auto path = entry.base_dir + sub_path;
+        if (path.back() == '/') { path += "index.html"; }
+
+        detail::FileStat stat(path);
+
+        if (stat.is_dir()) {
+          res.set_redirect(sub_path + "/", StatusCode::MovedPermanently_301);
+          return true;
+        }
+
+        if (stat.is_file()) {
+          for (const auto &kv : entry.headers) {
+            res.set_header(kv.first, kv.second);
+          }
+
+          auto mm = std::make_shared<detail::mmap>(path.c_str());
+          if (!mm->is_open()) { return false; }
+
+          res.set_content_provider(
+              mm->size(),
+              detail::find_content_type(path, file_extension_and_mimetype_map_,
+                                        default_file_mimetype_),
+              [mm](size_t offset, size_t length, DataSink &sink) -> bool {
+                sink.write(mm->data() + offset, length);
+                return true;
+              });
+
+          if (!head && file_request_handler_) {
+            file_request_handler_(req, res);
+          }
+
+          return true;
+        }
+      }
+    }
+  }
+  return false;
+}
+
+socket_t
+Server::create_server_socket(const std::string &host, int port,
+                             int socket_flags,
+                             SocketOptions socket_options) const {
+  return detail::create_socket(
+      host, std::string(), port, address_family_, socket_flags, tcp_nodelay_,
+      ipv6_v6only_, std::move(socket_options),
+      [](socket_t sock, struct addrinfo &ai, bool & /*quit*/) -> bool {
+        if (::bind(sock, ai.ai_addr, static_cast<socklen_t>(ai.ai_addrlen))) {
+          return false;
+        }
+        if (::listen(sock, CPPHTTPLIB_LISTEN_BACKLOG)) { return false; }
+        return true;
+      });
+}
+
+int Server::bind_internal(const std::string &host, int port,
+                                 int socket_flags) {
+  if (is_decommissioned) { return -1; }
+
+  if (!is_valid()) { return -1; }
+
+  svr_sock_ = create_server_socket(host, port, socket_flags, socket_options_);
+  if (svr_sock_ == INVALID_SOCKET) { return -1; }
+
+  if (port == 0) {
+    struct sockaddr_storage addr;
+    socklen_t addr_len = sizeof(addr);
+    if (getsockname(svr_sock_, reinterpret_cast<struct sockaddr *>(&addr),
+                    &addr_len) == -1) {
+      return -1;
+    }
+    if (addr.ss_family == AF_INET) {
+      return ntohs(reinterpret_cast<struct sockaddr_in *>(&addr)->sin_port);
+    } else if (addr.ss_family == AF_INET6) {
+      return ntohs(reinterpret_cast<struct sockaddr_in6 *>(&addr)->sin6_port);
+    } else {
+      return -1;
+    }
+  } else {
+    return port;
+  }
+}
+
+bool Server::listen_internal() {
+  if (is_decommissioned) { return false; }
+
+  auto ret = true;
+  is_running_ = true;
+  auto se = detail::scope_exit([&]() { is_running_ = false; });
+
+  {
+    std::unique_ptr<TaskQueue> task_queue(new_task_queue());
+
+    while (svr_sock_ != INVALID_SOCKET) {
+#ifndef _WIN32
+      if (idle_interval_sec_ > 0 || idle_interval_usec_ > 0) {
+#endif
+        auto val = detail::select_read(svr_sock_, idle_interval_sec_,
+                                       idle_interval_usec_);
+        if (val == 0) { // Timeout
+          task_queue->on_idle();
+          continue;
+        }
+#ifndef _WIN32
+      }
+#endif
+
+#if defined _WIN32
+      // sockets connected via WASAccept inherit flags NO_HANDLE_INHERIT,
+      // OVERLAPPED
+      socket_t sock = WSAAccept(svr_sock_, nullptr, nullptr, nullptr, 0);
+#elif defined SOCK_CLOEXEC
+      socket_t sock = accept4(svr_sock_, nullptr, nullptr, SOCK_CLOEXEC);
+#else
+      socket_t sock = accept(svr_sock_, nullptr, nullptr);
+#endif
+
+      if (sock == INVALID_SOCKET) {
+        if (errno == EMFILE) {
+          // The per-process limit of open file descriptors has been reached.
+          // Try to accept new connections after a short sleep.
+          std::this_thread::sleep_for(std::chrono::microseconds{1});
+          continue;
+        } else if (errno == EINTR || errno == EAGAIN) {
+          continue;
+        }
+        if (svr_sock_ != INVALID_SOCKET) {
+          detail::close_socket(svr_sock_);
+          ret = false;
+        } else {
+          ; // The server socket was closed by user.
+        }
+        break;
+      }
+
+      detail::set_socket_opt_time(sock, SOL_SOCKET, SO_RCVTIMEO,
+                                  read_timeout_sec_, read_timeout_usec_);
+      detail::set_socket_opt_time(sock, SOL_SOCKET, SO_SNDTIMEO,
+                                  write_timeout_sec_, write_timeout_usec_);
+
+      if (!task_queue->enqueue(
+              [this, sock]() { process_and_close_socket(sock); })) {
+        detail::shutdown_socket(sock);
+        detail::close_socket(sock);
+      }
+    }
+
+    task_queue->shutdown();
+  }
+
+  is_decommissioned = !ret;
+  return ret;
+}
+
+bool Server::routing(Request &req, Response &res, Stream &strm) {
+  if (pre_routing_handler_ &&
+      pre_routing_handler_(req, res) == HandlerResponse::Handled) {
+    return true;
+  }
+
+  // File handler
+  auto is_head_request = req.method == "HEAD";
+  if ((req.method == "GET" || is_head_request) &&
+      handle_file_request(req, res, is_head_request)) {
+    return true;
+  }
+
+  if (detail::expect_content(req)) {
+    // Content reader handler
+    {
+      ContentReader reader(
+          [&](ContentReceiver receiver) {
+            return read_content_with_content_receiver(
+                strm, req, res, std::move(receiver), nullptr, nullptr);
+          },
+          [&](MultipartContentHeader header, ContentReceiver receiver) {
+            return read_content_with_content_receiver(strm, req, res, nullptr,
+                                                      std::move(header),
+                                                      std::move(receiver));
+          });
+
+      if (req.method == "POST") {
+        if (dispatch_request_for_content_reader(
+                req, res, std::move(reader),
+                post_handlers_for_content_reader_)) {
+          return true;
+        }
+      } else if (req.method == "PUT") {
+        if (dispatch_request_for_content_reader(
+                req, res, std::move(reader),
+                put_handlers_for_content_reader_)) {
+          return true;
+        }
+      } else if (req.method == "PATCH") {
+        if (dispatch_request_for_content_reader(
+                req, res, std::move(reader),
+                patch_handlers_for_content_reader_)) {
+          return true;
+        }
+      } else if (req.method == "DELETE") {
+        if (dispatch_request_for_content_reader(
+                req, res, std::move(reader),
+                delete_handlers_for_content_reader_)) {
+          return true;
+        }
+      }
+    }
+
+    // Read content into `req.body`
+    if (!read_content(strm, req, res)) { return false; }
+  }
+
+  // Regular handler
+  if (req.method == "GET" || req.method == "HEAD") {
+    return dispatch_request(req, res, get_handlers_);
+  } else if (req.method == "POST") {
+    return dispatch_request(req, res, post_handlers_);
+  } else if (req.method == "PUT") {
+    return dispatch_request(req, res, put_handlers_);
+  } else if (req.method == "DELETE") {
+    return dispatch_request(req, res, delete_handlers_);
+  } else if (req.method == "OPTIONS") {
+    return dispatch_request(req, res, options_handlers_);
+  } else if (req.method == "PATCH") {
+    return dispatch_request(req, res, patch_handlers_);
+  }
+
+  res.status = StatusCode::BadRequest_400;
+  return false;
+}
+
+bool Server::dispatch_request(Request &req, Response &res,
+                                     const Handlers &handlers) const {
+  for (const auto &x : handlers) {
+    const auto &matcher = x.first;
+    const auto &handler = x.second;
+
+    if (matcher->match(req)) {
+      handler(req, res);
+      return true;
+    }
+  }
+  return false;
+}
+
+void Server::apply_ranges(const Request &req, Response &res,
+                                 std::string &content_type,
+                                 std::string &boundary) const {
+  if (req.ranges.size() > 1 && res.status == StatusCode::PartialContent_206) {
+    auto it = res.headers.find("Content-Type");
+    if (it != res.headers.end()) {
+      content_type = it->second;
+      res.headers.erase(it);
+    }
+
+    boundary = detail::make_multipart_data_boundary();
+
+    res.set_header("Content-Type",
+                   "multipart/byteranges; boundary=" + boundary);
+  }
+
+  auto type = detail::encoding_type(req, res);
+
+  if (res.body.empty()) {
+    if (res.content_length_ > 0) {
+      size_t length = 0;
+      if (req.ranges.empty() || res.status != StatusCode::PartialContent_206) {
+        length = res.content_length_;
+      } else if (req.ranges.size() == 1) {
+        auto offset_and_length = detail::get_range_offset_and_length(
+            req.ranges[0], res.content_length_);
+
+        length = offset_and_length.second;
+
+        auto content_range = detail::make_content_range_header_field(
+            offset_and_length, res.content_length_);
+        res.set_header("Content-Range", content_range);
+      } else {
+        length = detail::get_multipart_ranges_data_length(
+            req, boundary, content_type, res.content_length_);
+      }
+      res.set_header("Content-Length", std::to_string(length));
+    } else {
+      if (res.content_provider_) {
+        if (res.is_chunked_content_provider_) {
+          res.set_header("Transfer-Encoding", "chunked");
+          if (type == detail::EncodingType::Gzip) {
+            res.set_header("Content-Encoding", "gzip");
+          } else if (type == detail::EncodingType::Brotli) {
+            res.set_header("Content-Encoding", "br");
+          } else if (type == detail::EncodingType::Zstd) {
+            res.set_header("Content-Encoding", "zstd");
+          }
+        }
+      }
+    }
+  } else {
+    if (req.ranges.empty() || res.status != StatusCode::PartialContent_206) {
+      ;
+    } else if (req.ranges.size() == 1) {
+      auto offset_and_length =
+          detail::get_range_offset_and_length(req.ranges[0], res.body.size());
+      auto offset = offset_and_length.first;
+      auto length = offset_and_length.second;
+
+      auto content_range = detail::make_content_range_header_field(
+          offset_and_length, res.body.size());
+      res.set_header("Content-Range", content_range);
+
+      assert(offset + length <= res.body.size());
+      res.body = res.body.substr(offset, length);
+    } else {
+      std::string data;
+      detail::make_multipart_ranges_data(req, res, boundary, content_type,
+                                         res.body.size(), data);
+      res.body.swap(data);
+    }
+
+    if (type != detail::EncodingType::None) {
+      std::unique_ptr<detail::compressor> compressor;
+      std::string content_encoding;
+
+      if (type == detail::EncodingType::Gzip) {
+#ifdef CPPHTTPLIB_ZLIB_SUPPORT
+        compressor = detail::make_unique<detail::gzip_compressor>();
+        content_encoding = "gzip";
+#endif
+      } else if (type == detail::EncodingType::Brotli) {
+#ifdef CPPHTTPLIB_BROTLI_SUPPORT
+        compressor = detail::make_unique<detail::brotli_compressor>();
+        content_encoding = "br";
+#endif
+      } else if (type == detail::EncodingType::Zstd) {
+#ifdef CPPHTTPLIB_ZSTD_SUPPORT
+        compressor = detail::make_unique<detail::zstd_compressor>();
+        content_encoding = "zstd";
+#endif
+      }
+
+      if (compressor) {
+        std::string compressed;
+        if (compressor->compress(res.body.data(), res.body.size(), true,
+                                 [&](const char *data, size_t data_len) {
+                                   compressed.append(data, data_len);
+                                   return true;
+                                 })) {
+          res.body.swap(compressed);
+          res.set_header("Content-Encoding", content_encoding);
+        }
+      }
+    }
+
+    auto length = std::to_string(res.body.size());
+    res.set_header("Content-Length", length);
+  }
+}
+
+bool Server::dispatch_request_for_content_reader(
+    Request &req, Response &res, ContentReader content_reader,
+    const HandlersForContentReader &handlers) const {
+  for (const auto &x : handlers) {
+    const auto &matcher = x.first;
+    const auto &handler = x.second;
+
+    if (matcher->match(req)) {
+      handler(req, res, content_reader);
+      return true;
+    }
+  }
+  return false;
+}
+
+bool
+Server::process_request(Stream &strm, const std::string &remote_addr,
+                        int remote_port, const std::string &local_addr,
+                        int local_port, bool close_connection,
+                        bool &connection_closed,
+                        const std::function<void(Request &)> &setup_request) {
+  std::array<char, 2048> buf{};
+
+  detail::stream_line_reader line_reader(strm, buf.data(), buf.size());
+
+  // Connection has been closed on client
+  if (!line_reader.getline()) { return false; }
+
+  Request req;
+
+  Response res;
+  res.version = "HTTP/1.1";
+  res.headers = default_headers_;
+
+  // Request line and headers
+  if (!parse_request_line(line_reader.ptr(), req) ||
+      !detail::read_headers(strm, req.headers)) {
+    res.status = StatusCode::BadRequest_400;
+    return write_response(strm, close_connection, req, res);
+  }
+
+  // Check if the request URI doesn't exceed the limit
+  if (req.target.size() > CPPHTTPLIB_REQUEST_URI_MAX_LENGTH) {
+    Headers dummy;
+    detail::read_headers(strm, dummy);
+    res.status = StatusCode::UriTooLong_414;
+    return write_response(strm, close_connection, req, res);
+  }
+
+  if (req.get_header_value("Connection") == "close") {
+    connection_closed = true;
+  }
+
+  if (req.version == "HTTP/1.0" &&
+      req.get_header_value("Connection") != "Keep-Alive") {
+    connection_closed = true;
+  }
+
+  req.remote_addr = remote_addr;
+  req.remote_port = remote_port;
+  req.set_header("REMOTE_ADDR", req.remote_addr);
+  req.set_header("REMOTE_PORT", std::to_string(req.remote_port));
+
+  req.local_addr = local_addr;
+  req.local_port = local_port;
+  req.set_header("LOCAL_ADDR", req.local_addr);
+  req.set_header("LOCAL_PORT", std::to_string(req.local_port));
+
+  if (req.has_header("Range")) {
+    const auto &range_header_value = req.get_header_value("Range");
+    if (!detail::parse_range_header(range_header_value, req.ranges)) {
+      res.status = StatusCode::RangeNotSatisfiable_416;
+      return write_response(strm, close_connection, req, res);
+    }
+  }
+
+  if (setup_request) { setup_request(req); }
+
+  if (req.get_header_value("Expect") == "100-continue") {
+    int status = StatusCode::Continue_100;
+    if (expect_100_continue_handler_) {
+      status = expect_100_continue_handler_(req, res);
+    }
+    switch (status) {
+    case StatusCode::Continue_100:
+    case StatusCode::ExpectationFailed_417:
+      detail::write_response_line(strm, status);
+      strm.write("\r\n");
+      break;
+    default:
+      connection_closed = true;
+      return write_response(strm, true, req, res);
+    }
+  }
+
+  // Setup `is_connection_closed` method
+  auto sock = strm.socket();
+  req.is_connection_closed = [sock]() {
+    return !detail::is_socket_alive(sock);
+  };
+
+  // Routing
+  auto routed = false;
+#ifdef CPPHTTPLIB_NO_EXCEPTIONS
+  routed = routing(req, res, strm);
+#else
+  try {
+    routed = routing(req, res, strm);
+  } catch (std::exception &e) {
+    if (exception_handler_) {
+      auto ep = std::current_exception();
+      exception_handler_(req, res, ep);
+      routed = true;
+    } else {
+      res.status = StatusCode::InternalServerError_500;
+      std::string val;
+      auto s = e.what();
+      for (size_t i = 0; s[i]; i++) {
+        switch (s[i]) {
+        case '\r': val += "\\r"; break;
+        case '\n': val += "\\n"; break;
+        default: val += s[i]; break;
+        }
+      }
+      res.set_header("EXCEPTION_WHAT", val);
+    }
+  } catch (...) {
+    if (exception_handler_) {
+      auto ep = std::current_exception();
+      exception_handler_(req, res, ep);
+      routed = true;
+    } else {
+      res.status = StatusCode::InternalServerError_500;
+      res.set_header("EXCEPTION_WHAT", "UNKNOWN");
+    }
+  }
+#endif
+  if (routed) {
+    if (res.status == -1) {
+      res.status = req.ranges.empty() ? StatusCode::OK_200
+                                      : StatusCode::PartialContent_206;
+    }
+
+    // Serve file content by using a content provider
+    if (!res.file_content_path_.empty()) {
+      const auto &path = res.file_content_path_;
+      auto mm = std::make_shared<detail::mmap>(path.c_str());
+      if (!mm->is_open()) {
+        res.body.clear();
+        res.content_length_ = 0;
+        res.content_provider_ = nullptr;
+        res.status = StatusCode::NotFound_404;
+        return write_response(strm, close_connection, req, res);
+      }
+
+      auto content_type = res.file_content_content_type_;
+      if (content_type.empty()) {
+        content_type = detail::find_content_type(
+            path, file_extension_and_mimetype_map_, default_file_mimetype_);
+      }
+
+      res.set_content_provider(
+          mm->size(), content_type,
+          [mm](size_t offset, size_t length, DataSink &sink) -> bool {
+            sink.write(mm->data() + offset, length);
+            return true;
+          });
+    }
+
+    if (detail::range_error(req, res)) {
+      res.body.clear();
+      res.content_length_ = 0;
+      res.content_provider_ = nullptr;
+      res.status = StatusCode::RangeNotSatisfiable_416;
+      return write_response(strm, close_connection, req, res);
+    }
+
+    return write_response_with_content(strm, close_connection, req, res);
+  } else {
+    if (res.status == -1) { res.status = StatusCode::NotFound_404; }
+
+    return write_response(strm, close_connection, req, res);
+  }
+}
+
+bool Server::is_valid() const { return true; }
+
+bool Server::process_and_close_socket(socket_t sock) {
+  std::string remote_addr;
+  int remote_port = 0;
+  detail::get_remote_ip_and_port(sock, remote_addr, remote_port);
+
+  std::string local_addr;
+  int local_port = 0;
+  detail::get_local_ip_and_port(sock, local_addr, local_port);
+
+  auto ret = detail::process_server_socket(
+      svr_sock_, sock, keep_alive_max_count_, keep_alive_timeout_sec_,
+      read_timeout_sec_, read_timeout_usec_, write_timeout_sec_,
+      write_timeout_usec_,
+      [&](Stream &strm, bool close_connection, bool &connection_closed) {
+        return process_request(strm, remote_addr, remote_port, local_addr,
+                               local_port, close_connection, connection_closed,
+                               nullptr);
+      });
+
+  detail::shutdown_socket(sock);
+  detail::close_socket(sock);
+  return ret;
+}
+
+// HTTP client implementation
+ClientImpl::ClientImpl(const std::string &host)
+    : ClientImpl(host, 80, std::string(), std::string()) {}
+
+ClientImpl::ClientImpl(const std::string &host, int port)
+    : ClientImpl(host, port, std::string(), std::string()) {}
+
+ClientImpl::ClientImpl(const std::string &host, int port,
+                              const std::string &client_cert_path,
+                              const std::string &client_key_path)
+    : host_(detail::escape_abstract_namespace_unix_domain(host)), port_(port),
+      host_and_port_(adjust_host_string(host_) + ":" + std::to_string(port)),
+      client_cert_path_(client_cert_path), client_key_path_(client_key_path) {}
+
+ClientImpl::~ClientImpl() {
+  // Wait until all the requests in flight are handled.
+  size_t retry_count = 10;
+  while (retry_count-- > 0) {
+    {
+      std::lock_guard<std::mutex> guard(socket_mutex_);
+      if (socket_requests_in_flight_ == 0) { break; }
+    }
+    std::this_thread::sleep_for(std::chrono::milliseconds{1});
+  }
+
+  std::lock_guard<std::mutex> guard(socket_mutex_);
+  shutdown_socket(socket_);
+  close_socket(socket_);
+}
+
+bool ClientImpl::is_valid() const { return true; }
+
+void ClientImpl::copy_settings(const ClientImpl &rhs) {
+  client_cert_path_ = rhs.client_cert_path_;
+  client_key_path_ = rhs.client_key_path_;
+  connection_timeout_sec_ = rhs.connection_timeout_sec_;
+  read_timeout_sec_ = rhs.read_timeout_sec_;
+  read_timeout_usec_ = rhs.read_timeout_usec_;
+  write_timeout_sec_ = rhs.write_timeout_sec_;
+  write_timeout_usec_ = rhs.write_timeout_usec_;
+  max_timeout_msec_ = rhs.max_timeout_msec_;
+  basic_auth_username_ = rhs.basic_auth_username_;
+  basic_auth_password_ = rhs.basic_auth_password_;
+  bearer_token_auth_token_ = rhs.bearer_token_auth_token_;
+#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
+  digest_auth_username_ = rhs.digest_auth_username_;
+  digest_auth_password_ = rhs.digest_auth_password_;
+#endif
+  keep_alive_ = rhs.keep_alive_;
+  follow_location_ = rhs.follow_location_;
+  url_encode_ = rhs.url_encode_;
+  address_family_ = rhs.address_family_;
+  tcp_nodelay_ = rhs.tcp_nodelay_;
+  ipv6_v6only_ = rhs.ipv6_v6only_;
+  socket_options_ = rhs.socket_options_;
+  compress_ = rhs.compress_;
+  decompress_ = rhs.decompress_;
+  interface_ = rhs.interface_;
+  proxy_host_ = rhs.proxy_host_;
+  proxy_port_ = rhs.proxy_port_;
+  proxy_basic_auth_username_ = rhs.proxy_basic_auth_username_;
+  proxy_basic_auth_password_ = rhs.proxy_basic_auth_password_;
+  proxy_bearer_token_auth_token_ = rhs.proxy_bearer_token_auth_token_;
+#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
+  proxy_digest_auth_username_ = rhs.proxy_digest_auth_username_;
+  proxy_digest_auth_password_ = rhs.proxy_digest_auth_password_;
+#endif
+#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
+  ca_cert_file_path_ = rhs.ca_cert_file_path_;
+  ca_cert_dir_path_ = rhs.ca_cert_dir_path_;
+  ca_cert_store_ = rhs.ca_cert_store_;
+#endif
+#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
+  server_certificate_verification_ = rhs.server_certificate_verification_;
+  server_hostname_verification_ = rhs.server_hostname_verification_;
+  server_certificate_verifier_ = rhs.server_certificate_verifier_;
+#endif
+  logger_ = rhs.logger_;
+}
+
+socket_t ClientImpl::create_client_socket(Error &error) const {
+  if (!proxy_host_.empty() && proxy_port_ != -1) {
+    return detail::create_client_socket(
+        proxy_host_, std::string(), proxy_port_, address_family_, tcp_nodelay_,
+        ipv6_v6only_, socket_options_, connection_timeout_sec_,
+        connection_timeout_usec_, read_timeout_sec_, read_timeout_usec_,
+        write_timeout_sec_, write_timeout_usec_, interface_, error);
+  }
+
+  // Check is custom IP specified for host_
+  std::string ip;
+  auto it = addr_map_.find(host_);
+  if (it != addr_map_.end()) { ip = it->second; }
+
+  return detail::create_client_socket(
+      host_, ip, port_, address_family_, tcp_nodelay_, ipv6_v6only_,
+      socket_options_, connection_timeout_sec_, connection_timeout_usec_,
+      read_timeout_sec_, read_timeout_usec_, write_timeout_sec_,
+      write_timeout_usec_, interface_, error);
+}
+
+bool ClientImpl::create_and_connect_socket(Socket &socket,
+                                                  Error &error) {
+  auto sock = create_client_socket(error);
+  if (sock == INVALID_SOCKET) { return false; }
+  socket.sock = sock;
+  return true;
+}
+
+void ClientImpl::shutdown_ssl(Socket & /*socket*/,
+                                     bool /*shutdown_gracefully*/) {
+  // If there are any requests in flight from threads other than us, then it's
+  // a thread-unsafe race because individual ssl* objects are not thread-safe.
+  assert(socket_requests_in_flight_ == 0 ||
+         socket_requests_are_from_thread_ == std::this_thread::get_id());
+}
+
+void ClientImpl::shutdown_socket(Socket &socket) const {
+  if (socket.sock == INVALID_SOCKET) { return; }
+  detail::shutdown_socket(socket.sock);
+}
+
+void ClientImpl::close_socket(Socket &socket) {
+  // If there are requests in flight in another thread, usually closing
+  // the socket will be fine and they will simply receive an error when
+  // using the closed socket, but it is still a bug since rarely the OS
+  // may reassign the socket id to be used for a new socket, and then
+  // suddenly they will be operating on a live socket that is different
+  // than the one they intended!
+  assert(socket_requests_in_flight_ == 0 ||
+         socket_requests_are_from_thread_ == std::this_thread::get_id());
+
+  // It is also a bug if this happens while SSL is still active
+#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
+  assert(socket.ssl == nullptr);
+#endif
+  if (socket.sock == INVALID_SOCKET) { return; }
+  detail::close_socket(socket.sock);
+  socket.sock = INVALID_SOCKET;
+}
+
+bool ClientImpl::read_response_line(Stream &strm, const Request &req,
+                                           Response &res) const {
+  std::array<char, 2048> buf{};
+
+  detail::stream_line_reader line_reader(strm, buf.data(), buf.size());
+
+  if (!line_reader.getline()) { return false; }
+
+#ifdef CPPHTTPLIB_ALLOW_LF_AS_LINE_TERMINATOR
+  thread_local const std::regex re("(HTTP/1\\.[01]) (\\d{3})(?: (.*?))?\r?\n");
+#else
+  thread_local const std::regex re("(HTTP/1\\.[01]) (\\d{3})(?: (.*?))?\r\n");
+#endif
+
+  std::cmatch m;
+  if (!std::regex_match(line_reader.ptr(), m, re)) {
+    return req.method == "CONNECT";
+  }
+  res.version = std::string(m[1]);
+  res.status = std::stoi(std::string(m[2]));
+  res.reason = std::string(m[3]);
+
+  // Ignore '100 Continue'
+  while (res.status == StatusCode::Continue_100) {
+    if (!line_reader.getline()) { return false; } // CRLF
+    if (!line_reader.getline()) { return false; } // next response line
+
+    if (!std::regex_match(line_reader.ptr(), m, re)) { return false; }
+    res.version = std::string(m[1]);
+    res.status = std::stoi(std::string(m[2]));
+    res.reason = std::string(m[3]);
+  }
+
+  return true;
+}
+
+bool ClientImpl::send(Request &req, Response &res, Error &error) {
+  std::lock_guard<std::recursive_mutex> request_mutex_guard(request_mutex_);
+  auto ret = send_(req, res, error);
+  if (error == Error::SSLPeerCouldBeClosed_) {
+    assert(!ret);
+    ret = send_(req, res, error);
+  }
+  return ret;
+}
+
+bool ClientImpl::send_(Request &req, Response &res, Error &error) {
+  {
+    std::lock_guard<std::mutex> guard(socket_mutex_);
+
+    // Set this to false immediately - if it ever gets set to true by the end of
+    // the request, we know another thread instructed us to close the socket.
+    socket_should_be_closed_when_request_is_done_ = false;
+
+    auto is_alive = false;
+    if (socket_.is_open()) {
+      is_alive = detail::is_socket_alive(socket_.sock);
+
+#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
+      if (is_alive && is_ssl()) {
+        if (detail::is_ssl_peer_could_be_closed(socket_.ssl, socket_.sock)) {
+          is_alive = false;
+        }
+      }
+#endif
+
+      if (!is_alive) {
+        // Attempt to avoid sigpipe by shutting down non-gracefully if it seems
+        // like the other side has already closed the connection Also, there
+        // cannot be any requests in flight from other threads since we locked
+        // request_mutex_, so safe to close everything immediately
+        const bool shutdown_gracefully = false;
+        shutdown_ssl(socket_, shutdown_gracefully);
+        shutdown_socket(socket_);
+        close_socket(socket_);
+      }
+    }
+
+    if (!is_alive) {
+      if (!create_and_connect_socket(socket_, error)) { return false; }
+
+#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
+      // TODO: refactoring
+      if (is_ssl()) {
+        auto &scli = static_cast<SSLClient &>(*this);
+        if (!proxy_host_.empty() && proxy_port_ != -1) {
+          auto success = false;
+          if (!scli.connect_with_proxy(socket_, req.start_time_, res, success,
+                                       error)) {
+            return success;
+          }
+        }
+
+        if (!scli.initialize_ssl(socket_, error)) { return false; }
+      }
+#endif
+    }
+
+    // Mark the current socket as being in use so that it cannot be closed by
+    // anyone else while this request is ongoing, even though we will be
+    // releasing the mutex.
+    if (socket_requests_in_flight_ > 1) {
+      assert(socket_requests_are_from_thread_ == std::this_thread::get_id());
+    }
+    socket_requests_in_flight_ += 1;
+    socket_requests_are_from_thread_ = std::this_thread::get_id();
+  }
+
+  for (const auto &header : default_headers_) {
+    if (req.headers.find(header.first) == req.headers.end()) {
+      req.headers.insert(header);
+    }
+  }
+
+  auto ret = false;
+  auto close_connection = !keep_alive_;
+
+  auto se = detail::scope_exit([&]() {
+    // Briefly lock mutex in order to mark that a request is no longer ongoing
+    std::lock_guard<std::mutex> guard(socket_mutex_);
+    socket_requests_in_flight_ -= 1;
+    if (socket_requests_in_flight_ <= 0) {
+      assert(socket_requests_in_flight_ == 0);
+      socket_requests_are_from_thread_ = std::thread::id();
+    }
+
+    if (socket_should_be_closed_when_request_is_done_ || close_connection ||
+        !ret) {
+      shutdown_ssl(socket_, true);
+      shutdown_socket(socket_);
+      close_socket(socket_);
+    }
+  });
+
+  ret = process_socket(socket_, req.start_time_, [&](Stream &strm) {
+    return handle_request(strm, req, res, close_connection, error);
+  });
+
+  if (!ret) {
+    if (error == Error::Success) { error = Error::Unknown; }
+  }
+
+  return ret;
+}
+
+Result ClientImpl::send(const Request &req) {
+  auto req2 = req;
+  return send_(std::move(req2));
+}
+
+Result ClientImpl::send_(Request &&req) {
+  auto res = detail::make_unique<Response>();
+  auto error = Error::Success;
+  auto ret = send(req, *res, error);
+  return Result{ret ? std::move(res) : nullptr, error, std::move(req.headers)};
+}
+
+bool ClientImpl::handle_request(Stream &strm, Request &req,
+                                       Response &res, bool close_connection,
+                                       Error &error) {
+  if (req.path.empty()) {
+    error = Error::Connection;
+    return false;
+  }
+
+  auto req_save = req;
+
+  bool ret;
+
+  if (!is_ssl() && !proxy_host_.empty() && proxy_port_ != -1) {
+    auto req2 = req;
+    req2.path = "http://" + host_and_port_ + req.path;
+    ret = process_request(strm, req2, res, close_connection, error);
+    req = req2;
+    req.path = req_save.path;
+  } else {
+    ret = process_request(strm, req, res, close_connection, error);
+  }
+
+  if (!ret) { return false; }
+
+  if (res.get_header_value("Connection") == "close" ||
+      (res.version == "HTTP/1.0" && res.reason != "Connection established")) {
+    // TODO this requires a not-entirely-obvious chain of calls to be correct
+    // for this to be safe.
+
+    // This is safe to call because handle_request is only called by send_
+    // which locks the request mutex during the process. It would be a bug
+    // to call it from a different thread since it's a thread-safety issue
+    // to do these things to the socket if another thread is using the socket.
+    std::lock_guard<std::mutex> guard(socket_mutex_);
+    shutdown_ssl(socket_, true);
+    shutdown_socket(socket_);
+    close_socket(socket_);
+  }
+
+  if (300 < res.status && res.status < 400 && follow_location_) {
+    req = req_save;
+    ret = redirect(req, res, error);
+  }
+
+#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
+  if ((res.status == StatusCode::Unauthorized_401 ||
+       res.status == StatusCode::ProxyAuthenticationRequired_407) &&
+      req.authorization_count_ < 5) {
+    auto is_proxy = res.status == StatusCode::ProxyAuthenticationRequired_407;
+    const auto &username =
+        is_proxy ? proxy_digest_auth_username_ : digest_auth_username_;
+    const auto &password =
+        is_proxy ? proxy_digest_auth_password_ : digest_auth_password_;
+
+    if (!username.empty() && !password.empty()) {
+      std::map<std::string, std::string> auth;
+      if (detail::parse_www_authenticate(res, auth, is_proxy)) {
+        Request new_req = req;
+        new_req.authorization_count_ += 1;
+        new_req.headers.erase(is_proxy ? "Proxy-Authorization"
+                                       : "Authorization");
+        new_req.headers.insert(detail::make_digest_authentication_header(
+            req, auth, new_req.authorization_count_, detail::random_string(10),
+            username, password, is_proxy));
+
+        Response new_res;
+
+        ret = send(new_req, new_res, error);
+        if (ret) { res = new_res; }
+      }
+    }
+  }
+#endif
+
+  return ret;
+}
+
+bool ClientImpl::redirect(Request &req, Response &res, Error &error) {
+  if (req.redirect_count_ == 0) {
+    error = Error::ExceedRedirectCount;
+    return false;
+  }
+
+  auto location = res.get_header_value("location");
+  if (location.empty()) { return false; }
+
+  thread_local const std::regex re(
+      R"((?:(https?):)?(?://(?:\[([a-fA-F\d:]+)\]|([^:/?#]+))(?::(\d+))?)?([^?#]*)(\?[^#]*)?(?:#.*)?)");
+
+  std::smatch m;
+  if (!std::regex_match(location, m, re)) { return false; }
+
+  auto scheme = is_ssl() ? "https" : "http";
+
+  auto next_scheme = m[1].str();
+  auto next_host = m[2].str();
+  if (next_host.empty()) { next_host = m[3].str(); }
+  auto port_str = m[4].str();
+  auto next_path = m[5].str();
+  auto next_query = m[6].str();
+
+  auto next_port = port_;
+  if (!port_str.empty()) {
+    next_port = std::stoi(port_str);
+  } else if (!next_scheme.empty()) {
+    next_port = next_scheme == "https" ? 443 : 80;
+  }
+
+  if (next_scheme.empty()) { next_scheme = scheme; }
+  if (next_host.empty()) { next_host = host_; }
+  if (next_path.empty()) { next_path = "/"; }
+
+  auto path = detail::decode_url(next_path, true) + next_query;
+
+  if (next_scheme == scheme && next_host == host_ && next_port == port_) {
+    return detail::redirect(*this, req, res, path, location, error);
+  } else {
+    if (next_scheme == "https") {
+#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
+      SSLClient cli(next_host, next_port);
+      cli.copy_settings(*this);
+      if (ca_cert_store_) { cli.set_ca_cert_store(ca_cert_store_); }
+      return detail::redirect(cli, req, res, path, location, error);
+#else
+      return false;
+#endif
+    } else {
+      ClientImpl cli(next_host, next_port);
+      cli.copy_settings(*this);
+      return detail::redirect(cli, req, res, path, location, error);
+    }
+  }
+}
+
+bool ClientImpl::write_content_with_provider(Stream &strm,
+                                                    const Request &req,
+                                                    Error &error) const {
+  auto is_shutting_down = []() { return false; };
+
+  if (req.is_chunked_content_provider_) {
+    // TODO: Brotli support
+    std::unique_ptr<detail::compressor> compressor;
+#ifdef CPPHTTPLIB_ZLIB_SUPPORT
+    if (compress_) {
+      compressor = detail::make_unique<detail::gzip_compressor>();
+    } else
+#endif
+    {
+      compressor = detail::make_unique<detail::nocompressor>();
+    }
+
+    return detail::write_content_chunked(strm, req.content_provider_,
+                                         is_shutting_down, *compressor, error);
+  } else {
+    return detail::write_content(strm, req.content_provider_, 0,
+                                 req.content_length_, is_shutting_down, error);
+  }
+}
+
+bool ClientImpl::write_request(Stream &strm, Request &req,
+                                      bool close_connection, Error &error) {
+  // Prepare additional headers
+  if (close_connection) {
+    if (!req.has_header("Connection")) {
+      req.set_header("Connection", "close");
+    }
+  }
+
+  if (!req.has_header("Host")) {
+    if (is_ssl()) {
+      if (port_ == 443) {
+        req.set_header("Host", host_);
+      } else {
+        req.set_header("Host", host_and_port_);
+      }
+    } else {
+      if (port_ == 80) {
+        req.set_header("Host", host_);
+      } else {
+        req.set_header("Host", host_and_port_);
+      }
+    }
+  }
+
+  if (!req.has_header("Accept")) { req.set_header("Accept", "*/*"); }
+
+  if (!req.content_receiver) {
+    if (!req.has_header("Accept-Encoding")) {
+      std::string accept_encoding;
+#ifdef CPPHTTPLIB_BROTLI_SUPPORT
+      accept_encoding = "br";
+#endif
+#ifdef CPPHTTPLIB_ZLIB_SUPPORT
+      if (!accept_encoding.empty()) { accept_encoding += ", "; }
+      accept_encoding += "gzip, deflate";
+#endif
+#ifdef CPPHTTPLIB_ZSTD_SUPPORT
+      if (!accept_encoding.empty()) { accept_encoding += ", "; }
+      accept_encoding += "zstd";
+#endif
+      req.set_header("Accept-Encoding", accept_encoding);
+    }
+
+#ifndef CPPHTTPLIB_NO_DEFAULT_USER_AGENT
+    if (!req.has_header("User-Agent")) {
+      auto agent = std::string("cpp-httplib/") + CPPHTTPLIB_VERSION;
+      req.set_header("User-Agent", agent);
+    }
+#endif
+  };
+
+  if (req.body.empty()) {
+    if (req.content_provider_) {
+      if (!req.is_chunked_content_provider_) {
+        if (!req.has_header("Content-Length")) {
+          auto length = std::to_string(req.content_length_);
+          req.set_header("Content-Length", length);
+        }
+      }
+    } else {
+      if (req.method == "POST" || req.method == "PUT" ||
+          req.method == "PATCH") {
+        req.set_header("Content-Length", "0");
+      }
+    }
+  } else {
+    if (!req.has_header("Content-Type")) {
+      req.set_header("Content-Type", "text/plain");
+    }
+
+    if (!req.has_header("Content-Length")) {
+      auto length = std::to_string(req.body.size());
+      req.set_header("Content-Length", length);
+    }
+  }
+
+  if (!basic_auth_password_.empty() || !basic_auth_username_.empty()) {
+    if (!req.has_header("Authorization")) {
+      req.headers.insert(make_basic_authentication_header(
+          basic_auth_username_, basic_auth_password_, false));
+    }
+  }
+
+  if (!proxy_basic_auth_username_.empty() &&
+      !proxy_basic_auth_password_.empty()) {
+    if (!req.has_header("Proxy-Authorization")) {
+      req.headers.insert(make_basic_authentication_header(
+          proxy_basic_auth_username_, proxy_basic_auth_password_, true));
+    }
+  }
+
+  if (!bearer_token_auth_token_.empty()) {
+    if (!req.has_header("Authorization")) {
+      req.headers.insert(make_bearer_token_authentication_header(
+          bearer_token_auth_token_, false));
+    }
+  }
+
+  if (!proxy_bearer_token_auth_token_.empty()) {
+    if (!req.has_header("Proxy-Authorization")) {
+      req.headers.insert(make_bearer_token_authentication_header(
+          proxy_bearer_token_auth_token_, true));
+    }
+  }
+
+  // Request line and headers
+  {
+    detail::BufferStream bstrm;
+
+    const auto &path_with_query =
+        req.params.empty() ? req.path
+                           : append_query_params(req.path, req.params);
+
+    const auto &path =
+        url_encode_ ? detail::encode_url(path_with_query) : path_with_query;
+
+    detail::write_request_line(bstrm, req.method, path);
+
+    header_writer_(bstrm, req.headers);
+
+    // Flush buffer
+    auto &data = bstrm.get_buffer();
+    if (!detail::write_data(strm, data.data(), data.size())) {
+      error = Error::Write;
+      return false;
+    }
+  }
+
+  // Body
+  if (req.body.empty()) {
+    return write_content_with_provider(strm, req, error);
+  }
+
+  if (!detail::write_data(strm, req.body.data(), req.body.size())) {
+    error = Error::Write;
+    return false;
+  }
+
+  return true;
+}
+
+std::unique_ptr<Response> ClientImpl::send_with_content_provider(
+    Request &req, const char *body, size_t content_length,
+    ContentProvider content_provider,
+    ContentProviderWithoutLength content_provider_without_length,
+    const std::string &content_type, Error &error) {
+  if (!content_type.empty()) { req.set_header("Content-Type", content_type); }
+
+#ifdef CPPHTTPLIB_ZLIB_SUPPORT
+  if (compress_) { req.set_header("Content-Encoding", "gzip"); }
+#endif
+
+#ifdef CPPHTTPLIB_ZLIB_SUPPORT
+  if (compress_ && !content_provider_without_length) {
+    // TODO: Brotli support
+    detail::gzip_compressor compressor;
+
+    if (content_provider) {
+      auto ok = true;
+      size_t offset = 0;
+      DataSink data_sink;
+
+      data_sink.write = [&](const char *data, size_t data_len) -> bool {
+        if (ok) {
+          auto last = offset + data_len == content_length;
+
+          auto ret = compressor.compress(
+              data, data_len, last,
+              [&](const char *compressed_data, size_t compressed_data_len) {
+                req.body.append(compressed_data, compressed_data_len);
+                return true;
+              });
+
+          if (ret) {
+            offset += data_len;
+          } else {
+            ok = false;
+          }
+        }
+        return ok;
+      };
+
+      while (ok && offset < content_length) {
+        if (!content_provider(offset, content_length - offset, data_sink)) {
+          error = Error::Canceled;
+          return nullptr;
+        }
+      }
+    } else {
+      if (!compressor.compress(body, content_length, true,
+                               [&](const char *data, size_t data_len) {
+                                 req.body.append(data, data_len);
+                                 return true;
+                               })) {
+        error = Error::Compression;
+        return nullptr;
+      }
+    }
+  } else
+#endif
+  {
+    if (content_provider) {
+      req.content_length_ = content_length;
+      req.content_provider_ = std::move(content_provider);
+      req.is_chunked_content_provider_ = false;
+    } else if (content_provider_without_length) {
+      req.content_length_ = 0;
+      req.content_provider_ = detail::ContentProviderAdapter(
+          std::move(content_provider_without_length));
+      req.is_chunked_content_provider_ = true;
+      req.set_header("Transfer-Encoding", "chunked");
+    } else {
+      req.body.assign(body, content_length);
+    }
+  }
+
+  auto res = detail::make_unique<Response>();
+  return send(req, *res, error) ? std::move(res) : nullptr;
+}
+
+Result ClientImpl::send_with_content_provider(
+    const std::string &method, const std::string &path, const Headers &headers,
+    const char *body, size_t content_length, ContentProvider content_provider,
+    ContentProviderWithoutLength content_provider_without_length,
+    const std::string &content_type, Progress progress) {
+  Request req;
+  req.method = method;
+  req.headers = headers;
+  req.path = path;
+  req.progress = progress;
+  if (max_timeout_msec_ > 0) {
+    req.start_time_ = std::chrono::steady_clock::now();
+  }
+
+  auto error = Error::Success;
+
+  auto res = send_with_content_provider(
+      req, body, content_length, std::move(content_provider),
+      std::move(content_provider_without_length), content_type, error);
+
+  return Result{std::move(res), error, std::move(req.headers)};
+}
+
+std::string
+ClientImpl::adjust_host_string(const std::string &host) const {
+  if (host.find(':') != std::string::npos) { return "[" + host + "]"; }
+  return host;
+}
+
+bool ClientImpl::process_request(Stream &strm, Request &req,
+                                        Response &res, bool close_connection,
+                                        Error &error) {
+  // Send request
+  if (!write_request(strm, req, close_connection, error)) { return false; }
+
+#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
+  if (is_ssl()) {
+    auto is_proxy_enabled = !proxy_host_.empty() && proxy_port_ != -1;
+    if (!is_proxy_enabled) {
+      if (detail::is_ssl_peer_could_be_closed(socket_.ssl, socket_.sock)) {
+        error = Error::SSLPeerCouldBeClosed_;
+        return false;
+      }
+    }
+  }
+#endif
+
+  // Receive response and headers
+  if (!read_response_line(strm, req, res) ||
+      !detail::read_headers(strm, res.headers)) {
+    error = Error::Read;
+    return false;
+  }
+
+  // Body
+  if ((res.status != StatusCode::NoContent_204) && req.method != "HEAD" &&
+      req.method != "CONNECT") {
+    auto redirect = 300 < res.status && res.status < 400 &&
+                    res.status != StatusCode::NotModified_304 &&
+                    follow_location_;
+
+    if (req.response_handler && !redirect) {
+      if (!req.response_handler(res)) {
+        error = Error::Canceled;
+        return false;
+      }
+    }
+
+    auto out =
+        req.content_receiver
+            ? static_cast<ContentReceiverWithProgress>(
+                  [&](const char *buf, size_t n, uint64_t off, uint64_t len) {
+                    if (redirect) { return true; }
+                    auto ret = req.content_receiver(buf, n, off, len);
+                    if (!ret) { error = Error::Canceled; }
+                    return ret;
+                  })
+            : static_cast<ContentReceiverWithProgress>(
+                  [&](const char *buf, size_t n, uint64_t /*off*/,
+                      uint64_t /*len*/) {
+                    assert(res.body.size() + n <= res.body.max_size());
+                    res.body.append(buf, n);
+                    return true;
+                  });
+
+    auto progress = [&](uint64_t current, uint64_t total) {
+      if (!req.progress || redirect) { return true; }
+      auto ret = req.progress(current, total);
+      if (!ret) { error = Error::Canceled; }
+      return ret;
+    };
+
+    if (res.has_header("Content-Length")) {
+      if (!req.content_receiver) {
+        auto len = res.get_header_value_u64("Content-Length");
+        if (len > res.body.max_size()) {
+          error = Error::Read;
+          return false;
+        }
+        res.body.reserve(static_cast<size_t>(len));
+      }
+    }
+
+    if (res.status != StatusCode::NotModified_304) {
+      int dummy_status;
+      if (!detail::read_content(strm, res, (std::numeric_limits<size_t>::max)(),
+                                dummy_status, std::move(progress),
+                                std::move(out), decompress_)) {
+        if (error != Error::Canceled) { error = Error::Read; }
+        return false;
+      }
+    }
+  }
+
+  // Log
+  if (logger_) { logger_(req, res); }
+
+  return true;
+}
+
+ContentProviderWithoutLength ClientImpl::get_multipart_content_provider(
+    const std::string &boundary, const MultipartFormDataItems &items,
+    const MultipartFormDataProviderItems &provider_items) const {
+  size_t cur_item = 0;
+  size_t cur_start = 0;
+  // cur_item and cur_start are copied to within the std::function and maintain
+  // state between successive calls
+  return [&, cur_item, cur_start](size_t offset,
+                                  DataSink &sink) mutable -> bool {
+    if (!offset && !items.empty()) {
+      sink.os << detail::serialize_multipart_formdata(items, boundary, false);
+      return true;
+    } else if (cur_item < provider_items.size()) {
+      if (!cur_start) {
+        const auto &begin = detail::serialize_multipart_formdata_item_begin(
+            provider_items[cur_item], boundary);
+        offset += begin.size();
+        cur_start = offset;
+        sink.os << begin;
+      }
+
+      DataSink cur_sink;
+      auto has_data = true;
+      cur_sink.write = sink.write;
+      cur_sink.done = [&]() { has_data = false; };
+
+      if (!provider_items[cur_item].provider(offset - cur_start, cur_sink)) {
+        return false;
+      }
+
+      if (!has_data) {
+        sink.os << detail::serialize_multipart_formdata_item_end();
+        cur_item++;
+        cur_start = 0;
+      }
+      return true;
+    } else {
+      sink.os << detail::serialize_multipart_formdata_finish(boundary);
+      sink.done();
+      return true;
+    }
+  };
+}
+
+bool ClientImpl::process_socket(
+    const Socket &socket,
+    std::chrono::time_point<std::chrono::steady_clock> start_time,
+    std::function<bool(Stream &strm)> callback) {
+  return detail::process_client_socket(
+      socket.sock, read_timeout_sec_, read_timeout_usec_, write_timeout_sec_,
+      write_timeout_usec_, max_timeout_msec_, start_time, std::move(callback));
+}
+
+bool ClientImpl::is_ssl() const { return false; }
+
+Result ClientImpl::Get(const std::string &path) {
+  return Get(path, Headers(), Progress());
+}
+
+Result ClientImpl::Get(const std::string &path, Progress progress) {
+  return Get(path, Headers(), std::move(progress));
+}
+
+Result ClientImpl::Get(const std::string &path, const Headers &headers) {
+  return Get(path, headers, Progress());
+}
+
+Result ClientImpl::Get(const std::string &path, const Headers &headers,
+                              Progress progress) {
+  Request req;
+  req.method = "GET";
+  req.path = path;
+  req.headers = headers;
+  req.progress = std::move(progress);
+  if (max_timeout_msec_ > 0) {
+    req.start_time_ = std::chrono::steady_clock::now();
+  }
+
+  return send_(std::move(req));
+}
+
+Result ClientImpl::Get(const std::string &path,
+                              ContentReceiver content_receiver) {
+  return Get(path, Headers(), nullptr, std::move(content_receiver), nullptr);
+}
+
+Result ClientImpl::Get(const std::string &path,
+                              ContentReceiver content_receiver,
+                              Progress progress) {
+  return Get(path, Headers(), nullptr, std::move(content_receiver),
+             std::move(progress));
+}
+
+Result ClientImpl::Get(const std::string &path, const Headers &headers,
+                              ContentReceiver content_receiver) {
+  return Get(path, headers, nullptr, std::move(content_receiver), nullptr);
+}
+
+Result ClientImpl::Get(const std::string &path, const Headers &headers,
+                              ContentReceiver content_receiver,
+                              Progress progress) {
+  return Get(path, headers, nullptr, std::move(content_receiver),
+             std::move(progress));
+}
+
+Result ClientImpl::Get(const std::string &path,
+                              ResponseHandler response_handler,
+                              ContentReceiver content_receiver) {
+  return Get(path, Headers(), std::move(response_handler),
+             std::move(content_receiver), nullptr);
+}
+
+Result ClientImpl::Get(const std::string &path, const Headers &headers,
+                              ResponseHandler response_handler,
+                              ContentReceiver content_receiver) {
+  return Get(path, headers, std::move(response_handler),
+             std::move(content_receiver), nullptr);
+}
+
+Result ClientImpl::Get(const std::string &path,
+                              ResponseHandler response_handler,
+                              ContentReceiver content_receiver,
+                              Progress progress) {
+  return Get(path, Headers(), std::move(response_handler),
+             std::move(content_receiver), std::move(progress));
+}
+
+Result ClientImpl::Get(const std::string &path, const Headers &headers,
+                              ResponseHandler response_handler,
+                              ContentReceiver content_receiver,
+                              Progress progress) {
+  Request req;
+  req.method = "GET";
+  req.path = path;
+  req.headers = headers;
+  req.response_handler = std::move(response_handler);
+  req.content_receiver =
+      [content_receiver](const char *data, size_t data_length,
+                         uint64_t /*offset*/, uint64_t /*total_length*/) {
+        return content_receiver(data, data_length);
+      };
+  req.progress = std::move(progress);
+  if (max_timeout_msec_ > 0) {
+    req.start_time_ = std::chrono::steady_clock::now();
+  }
+
+  return send_(std::move(req));
+}
+
+Result ClientImpl::Get(const std::string &path, const Params &params,
+                              const Headers &headers, Progress progress) {
+  if (params.empty()) { return Get(path, headers); }
+
+  std::string path_with_query = append_query_params(path, params);
+  return Get(path_with_query, headers, std::move(progress));
+}
+
+Result ClientImpl::Get(const std::string &path, const Params &params,
+                              const Headers &headers,
+                              ContentReceiver content_receiver,
+                              Progress progress) {
+  return Get(path, params, headers, nullptr, std::move(content_receiver),
+             std::move(progress));
+}
+
+Result ClientImpl::Get(const std::string &path, const Params &params,
+                              const Headers &headers,
+                              ResponseHandler response_handler,
+                              ContentReceiver content_receiver,
+                              Progress progress) {
+  if (params.empty()) {
+    return Get(path, headers, std::move(response_handler),
+               std::move(content_receiver), std::move(progress));
+  }
+
+  std::string path_with_query = append_query_params(path, params);
+  return Get(path_with_query, headers, std::move(response_handler),
+             std::move(content_receiver), std::move(progress));
+}
+
+Result ClientImpl::Head(const std::string &path) {
+  return Head(path, Headers());
+}
+
+Result ClientImpl::Head(const std::string &path,
+                               const Headers &headers) {
+  Request req;
+  req.method = "HEAD";
+  req.headers = headers;
+  req.path = path;
+  if (max_timeout_msec_ > 0) {
+    req.start_time_ = std::chrono::steady_clock::now();
+  }
+
+  return send_(std::move(req));
+}
+
+Result ClientImpl::Post(const std::string &path) {
+  return Post(path, std::string(), std::string());
+}
+
+Result ClientImpl::Post(const std::string &path,
+                               const Headers &headers) {
+  return Post(path, headers, nullptr, 0, std::string());
+}
+
+Result ClientImpl::Post(const std::string &path, const char *body,
+                               size_t content_length,
+                               const std::string &content_type) {
+  return Post(path, Headers(), body, content_length, content_type, nullptr);
+}
+
+Result ClientImpl::Post(const std::string &path, const Headers &headers,
+                               const char *body, size_t content_length,
+                               const std::string &content_type) {
+  return send_with_content_provider("POST", path, headers, body, content_length,
+                                    nullptr, nullptr, content_type, nullptr);
+}
+
+Result ClientImpl::Post(const std::string &path, const Headers &headers,
+                               const char *body, size_t content_length,
+                               const std::string &content_type,
+                               Progress progress) {
+  return send_with_content_provider("POST", path, headers, body, content_length,
+                                    nullptr, nullptr, content_type, progress);
+}
+
+Result ClientImpl::Post(const std::string &path, const std::string &body,
+                               const std::string &content_type) {
+  return Post(path, Headers(), body, content_type);
+}
+
+Result ClientImpl::Post(const std::string &path, const std::string &body,
+                               const std::string &content_type,
+                               Progress progress) {
+  return Post(path, Headers(), body, content_type, progress);
+}
+
+Result ClientImpl::Post(const std::string &path, const Headers &headers,
+                               const std::string &body,
+                               const std::string &content_type) {
+  return send_with_content_provider("POST", path, headers, body.data(),
+                                    body.size(), nullptr, nullptr, content_type,
+                                    nullptr);
+}
+
+Result ClientImpl::Post(const std::string &path, const Headers &headers,
+                               const std::string &body,
+                               const std::string &content_type,
+                               Progress progress) {
+  return send_with_content_provider("POST", path, headers, body.data(),
+                                    body.size(), nullptr, nullptr, content_type,
+                                    progress);
+}
+
+Result ClientImpl::Post(const std::string &path, const Params &params) {
+  return Post(path, Headers(), params);
+}
+
+Result ClientImpl::Post(const std::string &path, size_t content_length,
+                               ContentProvider content_provider,
+                               const std::string &content_type) {
+  return Post(path, Headers(), content_length, std::move(content_provider),
+              content_type);
+}
+
+Result ClientImpl::Post(const std::string &path,
+                               ContentProviderWithoutLength content_provider,
+                               const std::string &content_type) {
+  return Post(path, Headers(), std::move(content_provider), content_type);
+}
+
+Result ClientImpl::Post(const std::string &path, const Headers &headers,
+                               size_t content_length,
+                               ContentProvider content_provider,
+                               const std::string &content_type) {
+  return send_with_content_provider("POST", path, headers, nullptr,
+                                    content_length, std::move(content_provider),
+                                    nullptr, content_type, nullptr);
+}
+
+Result ClientImpl::Post(const std::string &path, const Headers &headers,
+                               ContentProviderWithoutLength content_provider,
+                               const std::string &content_type) {
+  return send_with_content_provider("POST", path, headers, nullptr, 0, nullptr,
+                                    std::move(content_provider), content_type,
+                                    nullptr);
+}
+
+Result ClientImpl::Post(const std::string &path, const Headers &headers,
+                               const Params &params) {
+  auto query = detail::params_to_query_str(params);
+  return Post(path, headers, query, "application/x-www-form-urlencoded");
+}
+
+Result ClientImpl::Post(const std::string &path, const Headers &headers,
+                               const Params &params, Progress progress) {
+  auto query = detail::params_to_query_str(params);
+  return Post(path, headers, query, "application/x-www-form-urlencoded",
+              progress);
+}
+
+Result ClientImpl::Post(const std::string &path,
+                               const MultipartFormDataItems &items) {
+  return Post(path, Headers(), items);
+}
+
+Result ClientImpl::Post(const std::string &path, const Headers &headers,
+                               const MultipartFormDataItems &items) {
+  const auto &boundary = detail::make_multipart_data_boundary();
+  const auto &content_type =
+      detail::serialize_multipart_formdata_get_content_type(boundary);
+  const auto &body = detail::serialize_multipart_formdata(items, boundary);
+  return Post(path, headers, body, content_type);
+}
+
+Result ClientImpl::Post(const std::string &path, const Headers &headers,
+                               const MultipartFormDataItems &items,
+                               const std::string &boundary) {
+  if (!detail::is_multipart_boundary_chars_valid(boundary)) {
+    return Result{nullptr, Error::UnsupportedMultipartBoundaryChars};
+  }
+
+  const auto &content_type =
+      detail::serialize_multipart_formdata_get_content_type(boundary);
+  const auto &body = detail::serialize_multipart_formdata(items, boundary);
+  return Post(path, headers, body, content_type);
+}
+
+Result
+ClientImpl::Post(const std::string &path, const Headers &headers,
+                 const MultipartFormDataItems &items,
+                 const MultipartFormDataProviderItems &provider_items) {
+  const auto &boundary = detail::make_multipart_data_boundary();
+  const auto &content_type =
+      detail::serialize_multipart_formdata_get_content_type(boundary);
+  return send_with_content_provider(
+      "POST", path, headers, nullptr, 0, nullptr,
+      get_multipart_content_provider(boundary, items, provider_items),
+      content_type, nullptr);
+}
+
+Result ClientImpl::Put(const std::string &path) {
+  return Put(path, std::string(), std::string());
+}
+
+Result ClientImpl::Put(const std::string &path, const char *body,
+                              size_t content_length,
+                              const std::string &content_type) {
+  return Put(path, Headers(), body, content_length, content_type);
+}
+
+Result ClientImpl::Put(const std::string &path, const Headers &headers,
+                              const char *body, size_t content_length,
+                              const std::string &content_type) {
+  return send_with_content_provider("PUT", path, headers, body, content_length,
+                                    nullptr, nullptr, content_type, nullptr);
+}
+
+Result ClientImpl::Put(const std::string &path, const Headers &headers,
+                              const char *body, size_t content_length,
+                              const std::string &content_type,
+                              Progress progress) {
+  return send_with_content_provider("PUT", path, headers, body, content_length,
+                                    nullptr, nullptr, content_type, progress);
+}
+
+Result ClientImpl::Put(const std::string &path, const std::string &body,
+                              const std::string &content_type) {
+  return Put(path, Headers(), body, content_type);
+}
+
+Result ClientImpl::Put(const std::string &path, const std::string &body,
+                              const std::string &content_type,
+                              Progress progress) {
+  return Put(path, Headers(), body, content_type, progress);
+}
+
+Result ClientImpl::Put(const std::string &path, const Headers &headers,
+                              const std::string &body,
+                              const std::string &content_type) {
+  return send_with_content_provider("PUT", path, headers, body.data(),
+                                    body.size(), nullptr, nullptr, content_type,
+                                    nullptr);
+}
+
+Result ClientImpl::Put(const std::string &path, const Headers &headers,
+                              const std::string &body,
+                              const std::string &content_type,
+                              Progress progress) {
+  return send_with_content_provider("PUT", path, headers, body.data(),
+                                    body.size(), nullptr, nullptr, content_type,
+                                    progress);
+}
+
+Result ClientImpl::Put(const std::string &path, size_t content_length,
+                              ContentProvider content_provider,
+                              const std::string &content_type) {
+  return Put(path, Headers(), content_length, std::move(content_provider),
+             content_type);
+}
+
+Result ClientImpl::Put(const std::string &path,
+                              ContentProviderWithoutLength content_provider,
+                              const std::string &content_type) {
+  return Put(path, Headers(), std::move(content_provider), content_type);
+}
+
+Result ClientImpl::Put(const std::string &path, const Headers &headers,
+                              size_t content_length,
+                              ContentProvider content_provider,
+                              const std::string &content_type) {
+  return send_with_content_provider("PUT", path, headers, nullptr,
+                                    content_length, std::move(content_provider),
+                                    nullptr, content_type, nullptr);
+}
+
+Result ClientImpl::Put(const std::string &path, const Headers &headers,
+                              ContentProviderWithoutLength content_provider,
+                              const std::string &content_type) {
+  return send_with_content_provider("PUT", path, headers, nullptr, 0, nullptr,
+                                    std::move(content_provider), content_type,
+                                    nullptr);
+}
+
+Result ClientImpl::Put(const std::string &path, const Params &params) {
+  return Put(path, Headers(), params);
+}
+
+Result ClientImpl::Put(const std::string &path, const Headers &headers,
+                              const Params &params) {
+  auto query = detail::params_to_query_str(params);
+  return Put(path, headers, query, "application/x-www-form-urlencoded");
+}
+
+Result ClientImpl::Put(const std::string &path, const Headers &headers,
+                              const Params &params, Progress progress) {
+  auto query = detail::params_to_query_str(params);
+  return Put(path, headers, query, "application/x-www-form-urlencoded",
+             progress);
+}
+
+Result ClientImpl::Put(const std::string &path,
+                              const MultipartFormDataItems &items) {
+  return Put(path, Headers(), items);
+}
+
+Result ClientImpl::Put(const std::string &path, const Headers &headers,
+                              const MultipartFormDataItems &items) {
+  const auto &boundary = detail::make_multipart_data_boundary();
+  const auto &content_type =
+      detail::serialize_multipart_formdata_get_content_type(boundary);
+  const auto &body = detail::serialize_multipart_formdata(items, boundary);
+  return Put(path, headers, body, content_type);
+}
+
+Result ClientImpl::Put(const std::string &path, const Headers &headers,
+                              const MultipartFormDataItems &items,
+                              const std::string &boundary) {
+  if (!detail::is_multipart_boundary_chars_valid(boundary)) {
+    return Result{nullptr, Error::UnsupportedMultipartBoundaryChars};
+  }
+
+  const auto &content_type =
+      detail::serialize_multipart_formdata_get_content_type(boundary);
+  const auto &body = detail::serialize_multipart_formdata(items, boundary);
+  return Put(path, headers, body, content_type);
+}
+
+Result
+ClientImpl::Put(const std::string &path, const Headers &headers,
+                const MultipartFormDataItems &items,
+                const MultipartFormDataProviderItems &provider_items) {
+  const auto &boundary = detail::make_multipart_data_boundary();
+  const auto &content_type =
+      detail::serialize_multipart_formdata_get_content_type(boundary);
+  return send_with_content_provider(
+      "PUT", path, headers, nullptr, 0, nullptr,
+      get_multipart_content_provider(boundary, items, provider_items),
+      content_type, nullptr);
+}
+Result ClientImpl::Patch(const std::string &path) {
+  return Patch(path, std::string(), std::string());
+}
+
+Result ClientImpl::Patch(const std::string &path, const char *body,
+                                size_t content_length,
+                                const std::string &content_type) {
+  return Patch(path, Headers(), body, content_length, content_type);
+}
+
+Result ClientImpl::Patch(const std::string &path, const char *body,
+                                size_t content_length,
+                                const std::string &content_type,
+                                Progress progress) {
+  return Patch(path, Headers(), body, content_length, content_type, progress);
+}
+
+Result ClientImpl::Patch(const std::string &path, const Headers &headers,
+                                const char *body, size_t content_length,
+                                const std::string &content_type) {
+  return Patch(path, headers, body, content_length, content_type, nullptr);
+}
+
+Result ClientImpl::Patch(const std::string &path, const Headers &headers,
+                                const char *body, size_t content_length,
+                                const std::string &content_type,
+                                Progress progress) {
+  return send_with_content_provider("PATCH", path, headers, body,
+                                    content_length, nullptr, nullptr,
+                                    content_type, progress);
+}
+
+Result ClientImpl::Patch(const std::string &path,
+                                const std::string &body,
+                                const std::string &content_type) {
+  return Patch(path, Headers(), body, content_type);
+}
+
+Result ClientImpl::Patch(const std::string &path,
+                                const std::string &body,
+                                const std::string &content_type,
+                                Progress progress) {
+  return Patch(path, Headers(), body, content_type, progress);
+}
+
+Result ClientImpl::Patch(const std::string &path, const Headers &headers,
+                                const std::string &body,
+                                const std::string &content_type) {
+  return Patch(path, headers, body, content_type, nullptr);
+}
+
+Result ClientImpl::Patch(const std::string &path, const Headers &headers,
+                                const std::string &body,
+                                const std::string &content_type,
+                                Progress progress) {
+  return send_with_content_provider("PATCH", path, headers, body.data(),
+                                    body.size(), nullptr, nullptr, content_type,
+                                    progress);
+}
+
+Result ClientImpl::Patch(const std::string &path, size_t content_length,
+                                ContentProvider content_provider,
+                                const std::string &content_type) {
+  return Patch(path, Headers(), content_length, std::move(content_provider),
+               content_type);
+}
+
+Result ClientImpl::Patch(const std::string &path,
+                                ContentProviderWithoutLength content_provider,
+                                const std::string &content_type) {
+  return Patch(path, Headers(), std::move(content_provider), content_type);
+}
+
+Result ClientImpl::Patch(const std::string &path, const Headers &headers,
+                                size_t content_length,
+                                ContentProvider content_provider,
+                                const std::string &content_type) {
+  return send_with_content_provider("PATCH", path, headers, nullptr,
+                                    content_length, std::move(content_provider),
+                                    nullptr, content_type, nullptr);
+}
+
+Result ClientImpl::Patch(const std::string &path, const Headers &headers,
+                                ContentProviderWithoutLength content_provider,
+                                const std::string &content_type) {
+  return send_with_content_provider("PATCH", path, headers, nullptr, 0, nullptr,
+                                    std::move(content_provider), content_type,
+                                    nullptr);
+}
+
+Result ClientImpl::Delete(const std::string &path) {
+  return Delete(path, Headers(), std::string(), std::string());
+}
+
+Result ClientImpl::Delete(const std::string &path,
+                                 const Headers &headers) {
+  return Delete(path, headers, std::string(), std::string());
+}
+
+Result ClientImpl::Delete(const std::string &path, const char *body,
+                                 size_t content_length,
+                                 const std::string &content_type) {
+  return Delete(path, Headers(), body, content_length, content_type);
+}
+
+Result ClientImpl::Delete(const std::string &path, const char *body,
+                                 size_t content_length,
+                                 const std::string &content_type,
+                                 Progress progress) {
+  return Delete(path, Headers(), body, content_length, content_type, progress);
+}
+
+Result ClientImpl::Delete(const std::string &path,
+                                 const Headers &headers, const char *body,
+                                 size_t content_length,
+                                 const std::string &content_type) {
+  return Delete(path, headers, body, content_length, content_type, nullptr);
+}
+
+Result ClientImpl::Delete(const std::string &path,
+                                 const Headers &headers, const char *body,
+                                 size_t content_length,
+                                 const std::string &content_type,
+                                 Progress progress) {
+  Request req;
+  req.method = "DELETE";
+  req.headers = headers;
+  req.path = path;
+  req.progress = progress;
+  if (max_timeout_msec_ > 0) {
+    req.start_time_ = std::chrono::steady_clock::now();
+  }
+
+  if (!content_type.empty()) { req.set_header("Content-Type", content_type); }
+  req.body.assign(body, content_length);
+
+  return send_(std::move(req));
+}
+
+Result ClientImpl::Delete(const std::string &path,
+                                 const std::string &body,
+                                 const std::string &content_type) {
+  return Delete(path, Headers(), body.data(), body.size(), content_type);
+}
+
+Result ClientImpl::Delete(const std::string &path,
+                                 const std::string &body,
+                                 const std::string &content_type,
+                                 Progress progress) {
+  return Delete(path, Headers(), body.data(), body.size(), content_type,
+                progress);
+}
+
+Result ClientImpl::Delete(const std::string &path,
+                                 const Headers &headers,
+                                 const std::string &body,
+                                 const std::string &content_type) {
+  return Delete(path, headers, body.data(), body.size(), content_type);
+}
+
+Result ClientImpl::Delete(const std::string &path,
+                                 const Headers &headers,
+                                 const std::string &body,
+                                 const std::string &content_type,
+                                 Progress progress) {
+  return Delete(path, headers, body.data(), body.size(), content_type,
+                progress);
+}
+
+Result ClientImpl::Options(const std::string &path) {
+  return Options(path, Headers());
+}
+
+Result ClientImpl::Options(const std::string &path,
+                                  const Headers &headers) {
+  Request req;
+  req.method = "OPTIONS";
+  req.headers = headers;
+  req.path = path;
+  if (max_timeout_msec_ > 0) {
+    req.start_time_ = std::chrono::steady_clock::now();
+  }
+
+  return send_(std::move(req));
+}
+
+void ClientImpl::stop() {
+  std::lock_guard<std::mutex> guard(socket_mutex_);
+
+  // If there is anything ongoing right now, the ONLY thread-safe thing we can
+  // do is to shutdown_socket, so that threads using this socket suddenly
+  // discover they can't read/write any more and error out. Everything else
+  // (closing the socket, shutting ssl down) is unsafe because these actions are
+  // not thread-safe.
+  if (socket_requests_in_flight_ > 0) {
+    shutdown_socket(socket_);
+
+    // Aside from that, we set a flag for the socket to be closed when we're
+    // done.
+    socket_should_be_closed_when_request_is_done_ = true;
+    return;
+  }
+
+  // Otherwise, still holding the mutex, we can shut everything down ourselves
+  shutdown_ssl(socket_, true);
+  shutdown_socket(socket_);
+  close_socket(socket_);
+}
+
+std::string ClientImpl::host() const { return host_; }
+
+int ClientImpl::port() const { return port_; }
+
+size_t ClientImpl::is_socket_open() const {
+  std::lock_guard<std::mutex> guard(socket_mutex_);
+  return socket_.is_open();
+}
+
+socket_t ClientImpl::socket() const { return socket_.sock; }
+
+void ClientImpl::set_connection_timeout(time_t sec, time_t usec) {
+  connection_timeout_sec_ = sec;
+  connection_timeout_usec_ = usec;
+}
+
+void ClientImpl::set_read_timeout(time_t sec, time_t usec) {
+  read_timeout_sec_ = sec;
+  read_timeout_usec_ = usec;
+}
+
+void ClientImpl::set_write_timeout(time_t sec, time_t usec) {
+  write_timeout_sec_ = sec;
+  write_timeout_usec_ = usec;
+}
+
+void ClientImpl::set_max_timeout(time_t msec) {
+  max_timeout_msec_ = msec;
+}
+
+void ClientImpl::set_basic_auth(const std::string &username,
+                                       const std::string &password) {
+  basic_auth_username_ = username;
+  basic_auth_password_ = password;
+}
+
+void ClientImpl::set_bearer_token_auth(const std::string &token) {
+  bearer_token_auth_token_ = token;
+}
+
+#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
+void ClientImpl::set_digest_auth(const std::string &username,
+                                        const std::string &password) {
+  digest_auth_username_ = username;
+  digest_auth_password_ = password;
+}
+#endif
+
+void ClientImpl::set_keep_alive(bool on) { keep_alive_ = on; }
+
+void ClientImpl::set_follow_location(bool on) { follow_location_ = on; }
+
+void ClientImpl::set_url_encode(bool on) { url_encode_ = on; }
+
+void
+ClientImpl::set_hostname_addr_map(std::map<std::string, std::string> addr_map) {
+  addr_map_ = std::move(addr_map);
+}
+
+void ClientImpl::set_default_headers(Headers headers) {
+  default_headers_ = std::move(headers);
+}
+
+void ClientImpl::set_header_writer(
+    std::function<ssize_t(Stream &, Headers &)> const &writer) {
+  header_writer_ = writer;
+}
+
+void ClientImpl::set_address_family(int family) {
+  address_family_ = family;
+}
+
+void ClientImpl::set_tcp_nodelay(bool on) { tcp_nodelay_ = on; }
+
+void ClientImpl::set_ipv6_v6only(bool on) { ipv6_v6only_ = on; }
+
+void ClientImpl::set_socket_options(SocketOptions socket_options) {
+  socket_options_ = std::move(socket_options);
+}
+
+void ClientImpl::set_compress(bool on) { compress_ = on; }
+
+void ClientImpl::set_decompress(bool on) { decompress_ = on; }
+
+void ClientImpl::set_interface(const std::string &intf) {
+  interface_ = intf;
+}
+
+void ClientImpl::set_proxy(const std::string &host, int port) {
+  proxy_host_ = host;
+  proxy_port_ = port;
+}
+
+void ClientImpl::set_proxy_basic_auth(const std::string &username,
+                                             const std::string &password) {
+  proxy_basic_auth_username_ = username;
+  proxy_basic_auth_password_ = password;
+}
+
+void ClientImpl::set_proxy_bearer_token_auth(const std::string &token) {
+  proxy_bearer_token_auth_token_ = token;
+}
+
+#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
+void ClientImpl::set_proxy_digest_auth(const std::string &username,
+                                              const std::string &password) {
+  proxy_digest_auth_username_ = username;
+  proxy_digest_auth_password_ = password;
+}
+
+void ClientImpl::set_ca_cert_path(const std::string &ca_cert_file_path,
+                                         const std::string &ca_cert_dir_path) {
+  ca_cert_file_path_ = ca_cert_file_path;
+  ca_cert_dir_path_ = ca_cert_dir_path;
+}
+
+void ClientImpl::set_ca_cert_store(X509_STORE *ca_cert_store) {
+  if (ca_cert_store && ca_cert_store != ca_cert_store_) {
+    ca_cert_store_ = ca_cert_store;
+  }
+}
+
+X509_STORE *ClientImpl::create_ca_cert_store(const char *ca_cert,
+                                                    std::size_t size) const {
+  auto mem = BIO_new_mem_buf(ca_cert, static_cast<int>(size));
+  auto se = detail::scope_exit([&] { BIO_free_all(mem); });
+  if (!mem) { return nullptr; }
+
+  auto inf = PEM_X509_INFO_read_bio(mem, nullptr, nullptr, nullptr);
+  if (!inf) { return nullptr; }
+
+  auto cts = X509_STORE_new();
+  if (cts) {
+    for (auto i = 0; i < static_cast<int>(sk_X509_INFO_num(inf)); i++) {
+      auto itmp = sk_X509_INFO_value(inf, i);
+      if (!itmp) { continue; }
+
+      if (itmp->x509) { X509_STORE_add_cert(cts, itmp->x509); }
+      if (itmp->crl) { X509_STORE_add_crl(cts, itmp->crl); }
+    }
+  }
+
+  sk_X509_INFO_pop_free(inf, X509_INFO_free);
+  return cts;
+}
+
+void ClientImpl::enable_server_certificate_verification(bool enabled) {
+  server_certificate_verification_ = enabled;
+}
+
+void ClientImpl::enable_server_hostname_verification(bool enabled) {
+  server_hostname_verification_ = enabled;
+}
+
+void ClientImpl::set_server_certificate_verifier(
+    std::function<SSLVerifierResponse(SSL *ssl)> verifier) {
+  server_certificate_verifier_ = verifier;
+}
+#endif
+
+void ClientImpl::set_logger(Logger logger) {
+  logger_ = std::move(logger);
+}
+
+/*
+ * SSL Implementation
+ */
+#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
+namespace detail {
+
+template <typename U, typename V>
+SSL *ssl_new(socket_t sock, SSL_CTX *ctx, std::mutex &ctx_mutex,
+                    U SSL_connect_or_accept, V setup) {
+  SSL *ssl = nullptr;
+  {
+    std::lock_guard<std::mutex> guard(ctx_mutex);
+    ssl = SSL_new(ctx);
+  }
+
+  if (ssl) {
+    set_nonblocking(sock, true);
+    auto bio = BIO_new_socket(static_cast<int>(sock), BIO_NOCLOSE);
+    BIO_set_nbio(bio, 1);
+    SSL_set_bio(ssl, bio, bio);
+
+    if (!setup(ssl) || SSL_connect_or_accept(ssl) != 1) {
+      SSL_shutdown(ssl);
+      {
+        std::lock_guard<std::mutex> guard(ctx_mutex);
+        SSL_free(ssl);
+      }
+      set_nonblocking(sock, false);
+      return nullptr;
+    }
+    BIO_set_nbio(bio, 0);
+    set_nonblocking(sock, false);
+  }
+
+  return ssl;
+}
+
+void ssl_delete(std::mutex &ctx_mutex, SSL *ssl, socket_t sock,
+                       bool shutdown_gracefully) {
+  // sometimes we may want to skip this to try to avoid SIGPIPE if we know
+  // the remote has closed the network connection
+  // Note that it is not always possible to avoid SIGPIPE, this is merely a
+  // best-efforts.
+  if (shutdown_gracefully) {
+    (void)(sock);
+    // SSL_shutdown() returns 0 on first call (indicating close_notify alert
+    // sent) and 1 on subsequent call (indicating close_notify alert received)
+    if (SSL_shutdown(ssl) == 0) {
+      // Expected to return 1, but even if it doesn't, we free ssl
+      SSL_shutdown(ssl);
+    }
+  }
+
+  std::lock_guard<std::mutex> guard(ctx_mutex);
+  SSL_free(ssl);
+}
+
+template <typename U>
+bool ssl_connect_or_accept_nonblocking(socket_t sock, SSL *ssl,
+                                       U ssl_connect_or_accept,
+                                       time_t timeout_sec,
+                                       time_t timeout_usec) {
+  auto res = 0;
+  while ((res = ssl_connect_or_accept(ssl)) != 1) {
+    auto err = SSL_get_error(ssl, res);
+    switch (err) {
+    case SSL_ERROR_WANT_READ:
+      if (select_read(sock, timeout_sec, timeout_usec) > 0) { continue; }
+      break;
+    case SSL_ERROR_WANT_WRITE:
+      if (select_write(sock, timeout_sec, timeout_usec) > 0) { continue; }
+      break;
+    default: break;
+    }
+    return false;
+  }
+  return true;
+}
+
+template <typename T>
+bool process_server_socket_ssl(
+    const std::atomic<socket_t> &svr_sock, SSL *ssl, socket_t sock,
+    size_t keep_alive_max_count, time_t keep_alive_timeout_sec,
+    time_t read_timeout_sec, time_t read_timeout_usec, time_t write_timeout_sec,
+    time_t write_timeout_usec, T callback) {
+  return process_server_socket_core(
+      svr_sock, sock, keep_alive_max_count, keep_alive_timeout_sec,
+      [&](bool close_connection, bool &connection_closed) {
+        SSLSocketStream strm(sock, ssl, read_timeout_sec, read_timeout_usec,
+                             write_timeout_sec, write_timeout_usec);
+        return callback(strm, close_connection, connection_closed);
+      });
+}
+
+template <typename T>
+bool process_client_socket_ssl(
+    SSL *ssl, socket_t sock, time_t read_timeout_sec, time_t read_timeout_usec,
+    time_t write_timeout_sec, time_t write_timeout_usec,
+    time_t max_timeout_msec,
+    std::chrono::time_point<std::chrono::steady_clock> start_time, T callback) {
+  SSLSocketStream strm(sock, ssl, read_timeout_sec, read_timeout_usec,
+                       write_timeout_sec, write_timeout_usec, max_timeout_msec,
+                       start_time);
+  return callback(strm);
+}
+
+// SSL socket stream implementation
+SSLSocketStream::SSLSocketStream(
+    socket_t sock, SSL *ssl, time_t read_timeout_sec, time_t read_timeout_usec,
+    time_t write_timeout_sec, time_t write_timeout_usec,
+    time_t max_timeout_msec,
+    std::chrono::time_point<std::chrono::steady_clock> start_time)
+    : sock_(sock), ssl_(ssl), read_timeout_sec_(read_timeout_sec),
+      read_timeout_usec_(read_timeout_usec),
+      write_timeout_sec_(write_timeout_sec),
+      write_timeout_usec_(write_timeout_usec),
+      max_timeout_msec_(max_timeout_msec), start_time_(start_time) {
+  SSL_clear_mode(ssl, SSL_MODE_AUTO_RETRY);
+}
+
+SSLSocketStream::~SSLSocketStream() = default;
+
+bool SSLSocketStream::is_readable() const {
+  return SSL_pending(ssl_) > 0;
+}
+
+bool SSLSocketStream::wait_readable() const {
+  if (max_timeout_msec_ <= 0) {
+    return select_read(sock_, read_timeout_sec_, read_timeout_usec_) > 0;
+  }
+
+  time_t read_timeout_sec;
+  time_t read_timeout_usec;
+  calc_actual_timeout(max_timeout_msec_, duration(), read_timeout_sec_,
+                      read_timeout_usec_, read_timeout_sec, read_timeout_usec);
+
+  return select_read(sock_, read_timeout_sec, read_timeout_usec) > 0;
+}
+
+bool SSLSocketStream::wait_writable() const {
+  return select_write(sock_, write_timeout_sec_, write_timeout_usec_) > 0 &&
+         is_socket_alive(sock_) && !is_ssl_peer_could_be_closed(ssl_, sock_);
+}
+
+ssize_t SSLSocketStream::read(char *ptr, size_t size) {
+  if (SSL_pending(ssl_) > 0) {
+    return SSL_read(ssl_, ptr, static_cast<int>(size));
+  } else if (wait_readable()) {
+    auto ret = SSL_read(ssl_, ptr, static_cast<int>(size));
+    if (ret < 0) {
+      auto err = SSL_get_error(ssl_, ret);
+      auto n = 1000;
+#ifdef _WIN32
+      while (--n >= 0 && (err == SSL_ERROR_WANT_READ ||
+                          (err == SSL_ERROR_SYSCALL &&
+                           WSAGetLastError() == WSAETIMEDOUT))) {
+#else
+      while (--n >= 0 && err == SSL_ERROR_WANT_READ) {
+#endif
+        if (SSL_pending(ssl_) > 0) {
+          return SSL_read(ssl_, ptr, static_cast<int>(size));
+        } else if (wait_readable()) {
+          std::this_thread::sleep_for(std::chrono::microseconds{10});
+          ret = SSL_read(ssl_, ptr, static_cast<int>(size));
+          if (ret >= 0) { return ret; }
+          err = SSL_get_error(ssl_, ret);
+        } else {
+          return -1;
+        }
+      }
+    }
+    return ret;
+  } else {
+    return -1;
+  }
+}
+
+ssize_t SSLSocketStream::write(const char *ptr, size_t size) {
+  if (wait_writable()) {
+    auto handle_size = static_cast<int>(
+        std::min<size_t>(size, (std::numeric_limits<int>::max)()));
+
+    auto ret = SSL_write(ssl_, ptr, static_cast<int>(handle_size));
+    if (ret < 0) {
+      auto err = SSL_get_error(ssl_, ret);
+      auto n = 1000;
+#ifdef _WIN32
+      while (--n >= 0 && (err == SSL_ERROR_WANT_WRITE ||
+                          (err == SSL_ERROR_SYSCALL &&
+                           WSAGetLastError() == WSAETIMEDOUT))) {
+#else
+      while (--n >= 0 && err == SSL_ERROR_WANT_WRITE) {
+#endif
+        if (wait_writable()) {
+          std::this_thread::sleep_for(std::chrono::microseconds{10});
+          ret = SSL_write(ssl_, ptr, static_cast<int>(handle_size));
+          if (ret >= 0) { return ret; }
+          err = SSL_get_error(ssl_, ret);
+        } else {
+          return -1;
+        }
+      }
+    }
+    return ret;
+  }
+  return -1;
+}
+
+void SSLSocketStream::get_remote_ip_and_port(std::string &ip,
+                                                    int &port) const {
+  detail::get_remote_ip_and_port(sock_, ip, port);
+}
+
+void SSLSocketStream::get_local_ip_and_port(std::string &ip,
+                                                   int &port) const {
+  detail::get_local_ip_and_port(sock_, ip, port);
+}
+
+socket_t SSLSocketStream::socket() const { return sock_; }
+
+time_t SSLSocketStream::duration() const {
+  return std::chrono::duration_cast<std::chrono::milliseconds>(
+             std::chrono::steady_clock::now() - start_time_)
+      .count();
+}
+
+} // namespace detail
+
+// SSL HTTP server implementation
+SSLServer::SSLServer(const char *cert_path, const char *private_key_path,
+                            const char *client_ca_cert_file_path,
+                            const char *client_ca_cert_dir_path,
+                            const char *private_key_password) {
+  ctx_ = SSL_CTX_new(TLS_server_method());
+
+  if (ctx_) {
+    SSL_CTX_set_options(ctx_,
+                        SSL_OP_NO_COMPRESSION |
+                            SSL_OP_NO_SESSION_RESUMPTION_ON_RENEGOTIATION);
+
+    SSL_CTX_set_min_proto_version(ctx_, TLS1_2_VERSION);
+
+    if (private_key_password != nullptr && (private_key_password[0] != '\0')) {
+      SSL_CTX_set_default_passwd_cb_userdata(
+          ctx_,
+          reinterpret_cast<void *>(const_cast<char *>(private_key_password)));
+    }
+
+    if (SSL_CTX_use_certificate_chain_file(ctx_, cert_path) != 1 ||
+        SSL_CTX_use_PrivateKey_file(ctx_, private_key_path, SSL_FILETYPE_PEM) !=
+            1 ||
+        SSL_CTX_check_private_key(ctx_) != 1) {
+      SSL_CTX_free(ctx_);
+      ctx_ = nullptr;
+    } else if (client_ca_cert_file_path || client_ca_cert_dir_path) {
+      SSL_CTX_load_verify_locations(ctx_, client_ca_cert_file_path,
+                                    client_ca_cert_dir_path);
+
+      SSL_CTX_set_verify(
+          ctx_, SSL_VERIFY_PEER | SSL_VERIFY_FAIL_IF_NO_PEER_CERT, nullptr);
+    }
+  }
+}
+
+SSLServer::SSLServer(X509 *cert, EVP_PKEY *private_key,
+                            X509_STORE *client_ca_cert_store) {
+  ctx_ = SSL_CTX_new(TLS_server_method());
+
+  if (ctx_) {
+    SSL_CTX_set_options(ctx_,
+                        SSL_OP_NO_COMPRESSION |
+                            SSL_OP_NO_SESSION_RESUMPTION_ON_RENEGOTIATION);
+
+    SSL_CTX_set_min_proto_version(ctx_, TLS1_2_VERSION);
+
+    if (SSL_CTX_use_certificate(ctx_, cert) != 1 ||
+        SSL_CTX_use_PrivateKey(ctx_, private_key) != 1) {
+      SSL_CTX_free(ctx_);
+      ctx_ = nullptr;
+    } else if (client_ca_cert_store) {
+      SSL_CTX_set_cert_store(ctx_, client_ca_cert_store);
+
+      SSL_CTX_set_verify(
+          ctx_, SSL_VERIFY_PEER | SSL_VERIFY_FAIL_IF_NO_PEER_CERT, nullptr);
+    }
+  }
+}
+
+SSLServer::SSLServer(
+    const std::function<bool(SSL_CTX &ssl_ctx)> &setup_ssl_ctx_callback) {
+  ctx_ = SSL_CTX_new(TLS_method());
+  if (ctx_) {
+    if (!setup_ssl_ctx_callback(*ctx_)) {
+      SSL_CTX_free(ctx_);
+      ctx_ = nullptr;
+    }
+  }
+}
+
+SSLServer::~SSLServer() {
+  if (ctx_) { SSL_CTX_free(ctx_); }
+}
+
+bool SSLServer::is_valid() const { return ctx_; }
+
+SSL_CTX *SSLServer::ssl_context() const { return ctx_; }
+
+void SSLServer::update_certs(X509 *cert, EVP_PKEY *private_key,
+                                    X509_STORE *client_ca_cert_store) {
+
+  std::lock_guard<std::mutex> guard(ctx_mutex_);
+
+  SSL_CTX_use_certificate(ctx_, cert);
+  SSL_CTX_use_PrivateKey(ctx_, private_key);
+
+  if (client_ca_cert_store != nullptr) {
+    SSL_CTX_set_cert_store(ctx_, client_ca_cert_store);
+  }
+}
+
+bool SSLServer::process_and_close_socket(socket_t sock) {
+  auto ssl = detail::ssl_new(
+      sock, ctx_, ctx_mutex_,
+      [&](SSL *ssl2) {
+        return detail::ssl_connect_or_accept_nonblocking(
+            sock, ssl2, SSL_accept, read_timeout_sec_, read_timeout_usec_);
+      },
+      [](SSL * /*ssl2*/) { return true; });
+
+  auto ret = false;
+  if (ssl) {
+    std::string remote_addr;
+    int remote_port = 0;
+    detail::get_remote_ip_and_port(sock, remote_addr, remote_port);
+
+    std::string local_addr;
+    int local_port = 0;
+    detail::get_local_ip_and_port(sock, local_addr, local_port);
+
+    ret = detail::process_server_socket_ssl(
+        svr_sock_, ssl, sock, keep_alive_max_count_, keep_alive_timeout_sec_,
+        read_timeout_sec_, read_timeout_usec_, write_timeout_sec_,
+        write_timeout_usec_,
+        [&](Stream &strm, bool close_connection, bool &connection_closed) {
+          return process_request(strm, remote_addr, remote_port, local_addr,
+                                 local_port, close_connection,
+                                 connection_closed,
+                                 [&](Request &req) { req.ssl = ssl; });
+        });
+
+    // Shutdown gracefully if the result seemed successful, non-gracefully if
+    // the connection appeared to be closed.
+    const bool shutdown_gracefully = ret;
+    detail::ssl_delete(ctx_mutex_, ssl, sock, shutdown_gracefully);
+  }
+
+  detail::shutdown_socket(sock);
+  detail::close_socket(sock);
+  return ret;
+}
+
+// SSL HTTP client implementation
+SSLClient::SSLClient(const std::string &host)
+    : SSLClient(host, 443, std::string(), std::string()) {}
+
+SSLClient::SSLClient(const std::string &host, int port)
+    : SSLClient(host, port, std::string(), std::string()) {}
+
+SSLClient::SSLClient(const std::string &host, int port,
+                            const std::string &client_cert_path,
+                            const std::string &client_key_path,
+                            const std::string &private_key_password)
+    : ClientImpl(host, port, client_cert_path, client_key_path) {
+  ctx_ = SSL_CTX_new(TLS_client_method());
+
+  SSL_CTX_set_min_proto_version(ctx_, TLS1_2_VERSION);
+
+  detail::split(&host_[0], &host_[host_.size()], '.',
+                [&](const char *b, const char *e) {
+                  host_components_.emplace_back(b, e);
+                });
+
+  if (!client_cert_path.empty() && !client_key_path.empty()) {
+    if (!private_key_password.empty()) {
+      SSL_CTX_set_default_passwd_cb_userdata(
+          ctx_, reinterpret_cast<void *>(
+                    const_cast<char *>(private_key_password.c_str())));
+    }
+
+    if (SSL_CTX_use_certificate_file(ctx_, client_cert_path.c_str(),
+                                     SSL_FILETYPE_PEM) != 1 ||
+        SSL_CTX_use_PrivateKey_file(ctx_, client_key_path.c_str(),
+                                    SSL_FILETYPE_PEM) != 1) {
+      SSL_CTX_free(ctx_);
+      ctx_ = nullptr;
+    }
+  }
+}
+
+SSLClient::SSLClient(const std::string &host, int port,
+                            X509 *client_cert, EVP_PKEY *client_key,
+                            const std::string &private_key_password)
+    : ClientImpl(host, port) {
+  ctx_ = SSL_CTX_new(TLS_client_method());
+
+  detail::split(&host_[0], &host_[host_.size()], '.',
+                [&](const char *b, const char *e) {
+                  host_components_.emplace_back(b, e);
+                });
+
+  if (client_cert != nullptr && client_key != nullptr) {
+    if (!private_key_password.empty()) {
+      SSL_CTX_set_default_passwd_cb_userdata(
+          ctx_, reinterpret_cast<void *>(
+                    const_cast<char *>(private_key_password.c_str())));
+    }
+
+    if (SSL_CTX_use_certificate(ctx_, client_cert) != 1 ||
+        SSL_CTX_use_PrivateKey(ctx_, client_key) != 1) {
+      SSL_CTX_free(ctx_);
+      ctx_ = nullptr;
+    }
+  }
+}
+
+SSLClient::~SSLClient() {
+  if (ctx_) { SSL_CTX_free(ctx_); }
+  // Make sure to shut down SSL since shutdown_ssl will resolve to the
+  // base function rather than the derived function once we get to the
+  // base class destructor, and won't free the SSL (causing a leak).
+  shutdown_ssl_impl(socket_, true);
+}
+
+bool SSLClient::is_valid() const { return ctx_; }
+
+void SSLClient::set_ca_cert_store(X509_STORE *ca_cert_store) {
+  if (ca_cert_store) {
+    if (ctx_) {
+      if (SSL_CTX_get_cert_store(ctx_) != ca_cert_store) {
+        // Free memory allocated for old cert and use new store `ca_cert_store`
+        SSL_CTX_set_cert_store(ctx_, ca_cert_store);
+      }
+    } else {
+      X509_STORE_free(ca_cert_store);
+    }
+  }
+}
+
+void SSLClient::load_ca_cert_store(const char *ca_cert,
+                                          std::size_t size) {
+  set_ca_cert_store(ClientImpl::create_ca_cert_store(ca_cert, size));
+}
+
+long SSLClient::get_openssl_verify_result() const {
+  return verify_result_;
+}
+
+SSL_CTX *SSLClient::ssl_context() const { return ctx_; }
+
+bool SSLClient::create_and_connect_socket(Socket &socket, Error &error) {
+  return is_valid() && ClientImpl::create_and_connect_socket(socket, error);
+}
+
+// Assumes that socket_mutex_ is locked and that there are no requests in flight
+bool SSLClient::connect_with_proxy(
+    Socket &socket,
+    std::chrono::time_point<std::chrono::steady_clock> start_time,
+    Response &res, bool &success, Error &error) {
+  success = true;
+  Response proxy_res;
+  if (!detail::process_client_socket(
+          socket.sock, read_timeout_sec_, read_timeout_usec_,
+          write_timeout_sec_, write_timeout_usec_, max_timeout_msec_,
+          start_time, [&](Stream &strm) {
+            Request req2;
+            req2.method = "CONNECT";
+            req2.path = host_and_port_;
+            if (max_timeout_msec_ > 0) {
+              req2.start_time_ = std::chrono::steady_clock::now();
+            }
+            return process_request(strm, req2, proxy_res, false, error);
+          })) {
+    // Thread-safe to close everything because we are assuming there are no
+    // requests in flight
+    shutdown_ssl(socket, true);
+    shutdown_socket(socket);
+    close_socket(socket);
+    success = false;
+    return false;
+  }
+
+  if (proxy_res.status == StatusCode::ProxyAuthenticationRequired_407) {
+    if (!proxy_digest_auth_username_.empty() &&
+        !proxy_digest_auth_password_.empty()) {
+      std::map<std::string, std::string> auth;
+      if (detail::parse_www_authenticate(proxy_res, auth, true)) {
+        proxy_res = Response();
+        if (!detail::process_client_socket(
+                socket.sock, read_timeout_sec_, read_timeout_usec_,
+                write_timeout_sec_, write_timeout_usec_, max_timeout_msec_,
+                start_time, [&](Stream &strm) {
+                  Request req3;
+                  req3.method = "CONNECT";
+                  req3.path = host_and_port_;
+                  req3.headers.insert(detail::make_digest_authentication_header(
+                      req3, auth, 1, detail::random_string(10),
+                      proxy_digest_auth_username_, proxy_digest_auth_password_,
+                      true));
+                  if (max_timeout_msec_ > 0) {
+                    req3.start_time_ = std::chrono::steady_clock::now();
+                  }
+                  return process_request(strm, req3, proxy_res, false, error);
+                })) {
+          // Thread-safe to close everything because we are assuming there are
+          // no requests in flight
+          shutdown_ssl(socket, true);
+          shutdown_socket(socket);
+          close_socket(socket);
+          success = false;
+          return false;
+        }
+      }
+    }
+  }
+
+  // If status code is not 200, proxy request is failed.
+  // Set error to ProxyConnection and return proxy response
+  // as the response of the request
+  if (proxy_res.status != StatusCode::OK_200) {
+    error = Error::ProxyConnection;
+    res = std::move(proxy_res);
+    // Thread-safe to close everything because we are assuming there are
+    // no requests in flight
+    shutdown_ssl(socket, true);
+    shutdown_socket(socket);
+    close_socket(socket);
+    return false;
+  }
+
+  return true;
+}
+
+bool SSLClient::load_certs() {
+  auto ret = true;
+
+  std::call_once(initialize_cert_, [&]() {
+    std::lock_guard<std::mutex> guard(ctx_mutex_);
+    if (!ca_cert_file_path_.empty()) {
+      if (!SSL_CTX_load_verify_locations(ctx_, ca_cert_file_path_.c_str(),
+                                         nullptr)) {
+        ret = false;
+      }
+    } else if (!ca_cert_dir_path_.empty()) {
+      if (!SSL_CTX_load_verify_locations(ctx_, nullptr,
+                                         ca_cert_dir_path_.c_str())) {
+        ret = false;
+      }
+    } else {
+      auto loaded = false;
+#ifdef _WIN32
+      loaded =
+          detail::load_system_certs_on_windows(SSL_CTX_get_cert_store(ctx_));
+#elif defined(CPPHTTPLIB_USE_CERTS_FROM_MACOSX_KEYCHAIN) && defined(__APPLE__)
+#if TARGET_OS_OSX
+      loaded = detail::load_system_certs_on_macos(SSL_CTX_get_cert_store(ctx_));
+#endif // TARGET_OS_OSX
+#endif // _WIN32
+      if (!loaded) { SSL_CTX_set_default_verify_paths(ctx_); }
+    }
+  });
+
+  return ret;
+}
+
+bool SSLClient::initialize_ssl(Socket &socket, Error &error) {
+  auto ssl = detail::ssl_new(
+      socket.sock, ctx_, ctx_mutex_,
+      [&](SSL *ssl2) {
+        if (server_certificate_verification_) {
+          if (!load_certs()) {
+            error = Error::SSLLoadingCerts;
+            return false;
+          }
+          SSL_set_verify(ssl2, SSL_VERIFY_NONE, nullptr);
+        }
+
+        if (!detail::ssl_connect_or_accept_nonblocking(
+                socket.sock, ssl2, SSL_connect, connection_timeout_sec_,
+                connection_timeout_usec_)) {
+          error = Error::SSLConnection;
+          return false;
+        }
+
+        if (server_certificate_verification_) {
+          auto verification_status = SSLVerifierResponse::NoDecisionMade;
+
+          if (server_certificate_verifier_) {
+            verification_status = server_certificate_verifier_(ssl2);
+          }
+
+          if (verification_status == SSLVerifierResponse::CertificateRejected) {
+            error = Error::SSLServerVerification;
+            return false;
+          }
+
+          if (verification_status == SSLVerifierResponse::NoDecisionMade) {
+            verify_result_ = SSL_get_verify_result(ssl2);
+
+            if (verify_result_ != X509_V_OK) {
+              error = Error::SSLServerVerification;
+              return false;
+            }
+
+            auto server_cert = SSL_get1_peer_certificate(ssl2);
+            auto se = detail::scope_exit([&] { X509_free(server_cert); });
+
+            if (server_cert == nullptr) {
+              error = Error::SSLServerVerification;
+              return false;
+            }
+
+            if (server_hostname_verification_) {
+              if (!verify_host(server_cert)) {
+                error = Error::SSLServerHostnameVerification;
+                return false;
+              }
+            }
+          }
+        }
+
+        return true;
+      },
+      [&](SSL *ssl2) {
+#if defined(OPENSSL_IS_BORINGSSL)
+        SSL_set_tlsext_host_name(ssl2, host_.c_str());
+#else
+        // NOTE: Direct call instead of using the OpenSSL macro to suppress
+        // -Wold-style-cast warning
+        SSL_ctrl(ssl2, SSL_CTRL_SET_TLSEXT_HOSTNAME, TLSEXT_NAMETYPE_host_name,
+                 static_cast<void *>(const_cast<char *>(host_.c_str())));
+#endif
+        return true;
+      });
+
+  if (ssl) {
+    socket.ssl = ssl;
+    return true;
+  }
+
+  shutdown_socket(socket);
+  close_socket(socket);
+  return false;
+}
+
+void SSLClient::shutdown_ssl(Socket &socket, bool shutdown_gracefully) {
+  shutdown_ssl_impl(socket, shutdown_gracefully);
+}
+
+void SSLClient::shutdown_ssl_impl(Socket &socket,
+                                         bool shutdown_gracefully) {
+  if (socket.sock == INVALID_SOCKET) {
+    assert(socket.ssl == nullptr);
+    return;
+  }
+  if (socket.ssl) {
+    detail::ssl_delete(ctx_mutex_, socket.ssl, socket.sock,
+                       shutdown_gracefully);
+    socket.ssl = nullptr;
+  }
+  assert(socket.ssl == nullptr);
+}
+
+bool SSLClient::process_socket(
+    const Socket &socket,
+    std::chrono::time_point<std::chrono::steady_clock> start_time,
+    std::function<bool(Stream &strm)> callback) {
+  assert(socket.ssl);
+  return detail::process_client_socket_ssl(
+      socket.ssl, socket.sock, read_timeout_sec_, read_timeout_usec_,
+      write_timeout_sec_, write_timeout_usec_, max_timeout_msec_, start_time,
+      std::move(callback));
+}
+
+bool SSLClient::is_ssl() const { return true; }
+
+bool SSLClient::verify_host(X509 *server_cert) const {
+  /* Quote from RFC2818 section 3.1 "Server Identity"
+
+     If a subjectAltName extension of type dNSName is present, that MUST
+     be used as the identity. Otherwise, the (most specific) Common Name
+     field in the Subject field of the certificate MUST be used. Although
+     the use of the Common Name is existing practice, it is deprecated and
+     Certification Authorities are encouraged to use the dNSName instead.
+
+     Matching is performed using the matching rules specified by
+     [RFC2459].  If more than one identity of a given type is present in
+     the certificate (e.g., more than one dNSName name, a match in any one
+     of the set is considered acceptable.) Names may contain the wildcard
+     character * which is considered to match any single domain name
+     component or component fragment. E.g., *.a.com matches foo.a.com but
+     not bar.foo.a.com. f*.com matches foo.com but not bar.com.
+
+     In some cases, the URI is specified as an IP address rather than a
+     hostname. In this case, the iPAddress subjectAltName must be present
+     in the certificate and must exactly match the IP in the URI.
+
+  */
+  return verify_host_with_subject_alt_name(server_cert) ||
+         verify_host_with_common_name(server_cert);
+}
+
+bool
+SSLClient::verify_host_with_subject_alt_name(X509 *server_cert) const {
+  auto ret = false;
+
+  auto type = GEN_DNS;
+
+  struct in6_addr addr6 = {};
+  struct in_addr addr = {};
+  size_t addr_len = 0;
+
+#ifndef __MINGW32__
+  if (inet_pton(AF_INET6, host_.c_str(), &addr6)) {
+    type = GEN_IPADD;
+    addr_len = sizeof(struct in6_addr);
+  } else if (inet_pton(AF_INET, host_.c_str(), &addr)) {
+    type = GEN_IPADD;
+    addr_len = sizeof(struct in_addr);
+  }
+#endif
+
+  auto alt_names = static_cast<const struct stack_st_GENERAL_NAME *>(
+      X509_get_ext_d2i(server_cert, NID_subject_alt_name, nullptr, nullptr));
+
+  if (alt_names) {
+    auto dsn_matched = false;
+    auto ip_matched = false;
+
+    auto count = sk_GENERAL_NAME_num(alt_names);
+
+    for (decltype(count) i = 0; i < count && !dsn_matched; i++) {
+      auto val = sk_GENERAL_NAME_value(alt_names, i);
+      if (val->type == type) {
+        auto name =
+            reinterpret_cast<const char *>(ASN1_STRING_get0_data(val->d.ia5));
+        auto name_len = static_cast<size_t>(ASN1_STRING_length(val->d.ia5));
+
+        switch (type) {
+        case GEN_DNS: dsn_matched = check_host_name(name, name_len); break;
+
+        case GEN_IPADD:
+          if (!memcmp(&addr6, name, addr_len) ||
+              !memcmp(&addr, name, addr_len)) {
+            ip_matched = true;
+          }
+          break;
+        }
+      }
+    }
+
+    if (dsn_matched || ip_matched) { ret = true; }
+  }
+
+  GENERAL_NAMES_free(const_cast<STACK_OF(GENERAL_NAME) *>(
+      reinterpret_cast<const STACK_OF(GENERAL_NAME) *>(alt_names)));
+  return ret;
+}
+
+bool SSLClient::verify_host_with_common_name(X509 *server_cert) const {
+  const auto subject_name = X509_get_subject_name(server_cert);
+
+  if (subject_name != nullptr) {
+    char name[BUFSIZ];
+    auto name_len = X509_NAME_get_text_by_NID(subject_name, NID_commonName,
+                                              name, sizeof(name));
+
+    if (name_len != -1) {
+      return check_host_name(name, static_cast<size_t>(name_len));
+    }
+  }
+
+  return false;
+}
+
+bool SSLClient::check_host_name(const char *pattern,
+                                       size_t pattern_len) const {
+  if (host_.size() == pattern_len && host_ == pattern) { return true; }
+
+  // Wildcard match
+  // https://bugs.launchpad.net/ubuntu/+source/firefox-3.0/+bug/376484
+  std::vector<std::string> pattern_components;
+  detail::split(&pattern[0], &pattern[pattern_len], '.',
+                [&](const char *b, const char *e) {
+                  pattern_components.emplace_back(b, e);
+                });
+
+  if (host_components_.size() != pattern_components.size()) { return false; }
+
+  auto itr = pattern_components.begin();
+  for (const auto &h : host_components_) {
+    auto &p = *itr;
+    if (p != h && p != "*") {
+      auto partial_match = (p.size() > 0 && p[p.size() - 1] == '*' &&
+                            !p.compare(0, p.size() - 1, h));
+      if (!partial_match) { return false; }
+    }
+    ++itr;
+  }
+
+  return true;
+}
+#endif
+
+// Universal client implementation
+Client::Client(const std::string &scheme_host_port)
+    : Client(scheme_host_port, std::string(), std::string()) {}
+
+Client::Client(const std::string &scheme_host_port,
+                      const std::string &client_cert_path,
+                      const std::string &client_key_path) {
+  const static std::regex re(
+      R"((?:([a-z]+):\/\/)?(?:\[([a-fA-F\d:]+)\]|([^:/?#]+))(?::(\d+))?)");
+
+  std::smatch m;
+  if (std::regex_match(scheme_host_port, m, re)) {
+    auto scheme = m[1].str();
+
+#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
+    if (!scheme.empty() && (scheme != "http" && scheme != "https")) {
+#else
+    if (!scheme.empty() && scheme != "http") {
+#endif
+#ifndef CPPHTTPLIB_NO_EXCEPTIONS
+      std::string msg = "'" + scheme + "' scheme is not supported.";
+      throw std::invalid_argument(msg);
+#endif
+      return;
+    }
+
+    auto is_ssl = scheme == "https";
+
+    auto host = m[2].str();
+    if (host.empty()) { host = m[3].str(); }
+
+    auto port_str = m[4].str();
+    auto port = !port_str.empty() ? std::stoi(port_str) : (is_ssl ? 443 : 80);
+
+    if (is_ssl) {
+#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
+      cli_ = detail::make_unique<SSLClient>(host, port, client_cert_path,
+                                            client_key_path);
+      is_ssl_ = is_ssl;
+#endif
+    } else {
+      cli_ = detail::make_unique<ClientImpl>(host, port, client_cert_path,
+                                             client_key_path);
+    }
+  } else {
+    // NOTE: Update TEST(UniversalClientImplTest, Ipv6LiteralAddress)
+    // if port param below changes.
+    cli_ = detail::make_unique<ClientImpl>(scheme_host_port, 80,
+                                           client_cert_path, client_key_path);
+  }
+} // namespace detail
+
+Client::Client(const std::string &host, int port)
+    : cli_(detail::make_unique<ClientImpl>(host, port)) {}
+
+Client::Client(const std::string &host, int port,
+                      const std::string &client_cert_path,
+                      const std::string &client_key_path)
+    : cli_(detail::make_unique<ClientImpl>(host, port, client_cert_path,
+                                           client_key_path)) {}
+
+Client::~Client() = default;
+
+bool Client::is_valid() const {
+  return cli_ != nullptr && cli_->is_valid();
+}
+
+Result Client::Get(const std::string &path) { return cli_->Get(path); }
+Result Client::Get(const std::string &path, const Headers &headers) {
+  return cli_->Get(path, headers);
+}
+Result Client::Get(const std::string &path, Progress progress) {
+  return cli_->Get(path, std::move(progress));
+}
+Result Client::Get(const std::string &path, const Headers &headers,
+                          Progress progress) {
+  return cli_->Get(path, headers, std::move(progress));
+}
+Result Client::Get(const std::string &path,
+                          ContentReceiver content_receiver) {
+  return cli_->Get(path, std::move(content_receiver));
+}
+Result Client::Get(const std::string &path, const Headers &headers,
+                          ContentReceiver content_receiver) {
+  return cli_->Get(path, headers, std::move(content_receiver));
+}
+Result Client::Get(const std::string &path,
+                          ContentReceiver content_receiver, Progress progress) {
+  return cli_->Get(path, std::move(content_receiver), std::move(progress));
+}
+Result Client::Get(const std::string &path, const Headers &headers,
+                          ContentReceiver content_receiver, Progress progress) {
+  return cli_->Get(path, headers, std::move(content_receiver),
+                   std::move(progress));
+}
+Result Client::Get(const std::string &path,
+                          ResponseHandler response_handler,
+                          ContentReceiver content_receiver) {
+  return cli_->Get(path, std::move(response_handler),
+                   std::move(content_receiver));
+}
+Result Client::Get(const std::string &path, const Headers &headers,
+                          ResponseHandler response_handler,
+                          ContentReceiver content_receiver) {
+  return cli_->Get(path, headers, std::move(response_handler),
+                   std::move(content_receiver));
+}
+Result Client::Get(const std::string &path,
+                          ResponseHandler response_handler,
+                          ContentReceiver content_receiver, Progress progress) {
+  return cli_->Get(path, std::move(response_handler),
+                   std::move(content_receiver), std::move(progress));
+}
+Result Client::Get(const std::string &path, const Headers &headers,
+                          ResponseHandler response_handler,
+                          ContentReceiver content_receiver, Progress progress) {
+  return cli_->Get(path, headers, std::move(response_handler),
+                   std::move(content_receiver), std::move(progress));
+}
+Result Client::Get(const std::string &path, const Params &params,
+                          const Headers &headers, Progress progress) {
+  return cli_->Get(path, params, headers, std::move(progress));
+}
+Result Client::Get(const std::string &path, const Params &params,
+                          const Headers &headers,
+                          ContentReceiver content_receiver, Progress progress) {
+  return cli_->Get(path, params, headers, std::move(content_receiver),
+                   std::move(progress));
+}
+Result Client::Get(const std::string &path, const Params &params,
+                          const Headers &headers,
+                          ResponseHandler response_handler,
+                          ContentReceiver content_receiver, Progress progress) {
+  return cli_->Get(path, params, headers, std::move(response_handler),
+                   std::move(content_receiver), std::move(progress));
+}
+
+Result Client::Head(const std::string &path) { return cli_->Head(path); }
+Result Client::Head(const std::string &path, const Headers &headers) {
+  return cli_->Head(path, headers);
+}
+
+Result Client::Post(const std::string &path) { return cli_->Post(path); }
+Result Client::Post(const std::string &path, const Headers &headers) {
+  return cli_->Post(path, headers);
+}
+Result Client::Post(const std::string &path, const char *body,
+                           size_t content_length,
+                           const std::string &content_type) {
+  return cli_->Post(path, body, content_length, content_type);
+}
+Result Client::Post(const std::string &path, const Headers &headers,
+                           const char *body, size_t content_length,
+                           const std::string &content_type) {
+  return cli_->Post(path, headers, body, content_length, content_type);
+}
+Result Client::Post(const std::string &path, const Headers &headers,
+                           const char *body, size_t content_length,
+                           const std::string &content_type, Progress progress) {
+  return cli_->Post(path, headers, body, content_length, content_type,
+                    progress);
+}
+Result Client::Post(const std::string &path, const std::string &body,
+                           const std::string &content_type) {
+  return cli_->Post(path, body, content_type);
+}
+Result Client::Post(const std::string &path, const std::string &body,
+                           const std::string &content_type, Progress progress) {
+  return cli_->Post(path, body, content_type, progress);
+}
+Result Client::Post(const std::string &path, const Headers &headers,
+                           const std::string &body,
+                           const std::string &content_type) {
+  return cli_->Post(path, headers, body, content_type);
+}
+Result Client::Post(const std::string &path, const Headers &headers,
+                           const std::string &body,
+                           const std::string &content_type, Progress progress) {
+  return cli_->Post(path, headers, body, content_type, progress);
+}
+Result Client::Post(const std::string &path, size_t content_length,
+                           ContentProvider content_provider,
+                           const std::string &content_type) {
+  return cli_->Post(path, content_length, std::move(content_provider),
+                    content_type);
+}
+Result Client::Post(const std::string &path,
+                           ContentProviderWithoutLength content_provider,
+                           const std::string &content_type) {
+  return cli_->Post(path, std::move(content_provider), content_type);
+}
+Result Client::Post(const std::string &path, const Headers &headers,
+                           size_t content_length,
+                           ContentProvider content_provider,
+                           const std::string &content_type) {
+  return cli_->Post(path, headers, content_length, std::move(content_provider),
+                    content_type);
+}
+Result Client::Post(const std::string &path, const Headers &headers,
+                           ContentProviderWithoutLength content_provider,
+                           const std::string &content_type) {
+  return cli_->Post(path, headers, std::move(content_provider), content_type);
+}
+Result Client::Post(const std::string &path, const Params &params) {
+  return cli_->Post(path, params);
+}
+Result Client::Post(const std::string &path, const Headers &headers,
+                           const Params &params) {
+  return cli_->Post(path, headers, params);
+}
+Result Client::Post(const std::string &path, const Headers &headers,
+                           const Params &params, Progress progress) {
+  return cli_->Post(path, headers, params, progress);
+}
+Result Client::Post(const std::string &path,
+                           const MultipartFormDataItems &items) {
+  return cli_->Post(path, items);
+}
+Result Client::Post(const std::string &path, const Headers &headers,
+                           const MultipartFormDataItems &items) {
+  return cli_->Post(path, headers, items);
+}
+Result Client::Post(const std::string &path, const Headers &headers,
+                           const MultipartFormDataItems &items,
+                           const std::string &boundary) {
+  return cli_->Post(path, headers, items, boundary);
+}
+Result
+Client::Post(const std::string &path, const Headers &headers,
+             const MultipartFormDataItems &items,
+             const MultipartFormDataProviderItems &provider_items) {
+  return cli_->Post(path, headers, items, provider_items);
+}
+Result Client::Put(const std::string &path) { return cli_->Put(path); }
+Result Client::Put(const std::string &path, const char *body,
+                          size_t content_length,
+                          const std::string &content_type) {
+  return cli_->Put(path, body, content_length, content_type);
+}
+Result Client::Put(const std::string &path, const Headers &headers,
+                          const char *body, size_t content_length,
+                          const std::string &content_type) {
+  return cli_->Put(path, headers, body, content_length, content_type);
+}
+Result Client::Put(const std::string &path, const Headers &headers,
+                          const char *body, size_t content_length,
+                          const std::string &content_type, Progress progress) {
+  return cli_->Put(path, headers, body, content_length, content_type, progress);
+}
+Result Client::Put(const std::string &path, const std::string &body,
+                          const std::string &content_type) {
+  return cli_->Put(path, body, content_type);
+}
+Result Client::Put(const std::string &path, const std::string &body,
+                          const std::string &content_type, Progress progress) {
+  return cli_->Put(path, body, content_type, progress);
+}
+Result Client::Put(const std::string &path, const Headers &headers,
+                          const std::string &body,
+                          const std::string &content_type) {
+  return cli_->Put(path, headers, body, content_type);
+}
+Result Client::Put(const std::string &path, const Headers &headers,
+                          const std::string &body,
+                          const std::string &content_type, Progress progress) {
+  return cli_->Put(path, headers, body, content_type, progress);
+}
+Result Client::Put(const std::string &path, size_t content_length,
+                          ContentProvider content_provider,
+                          const std::string &content_type) {
+  return cli_->Put(path, content_length, std::move(content_provider),
+                   content_type);
+}
+Result Client::Put(const std::string &path,
+                          ContentProviderWithoutLength content_provider,
+                          const std::string &content_type) {
+  return cli_->Put(path, std::move(content_provider), content_type);
+}
+Result Client::Put(const std::string &path, const Headers &headers,
+                          size_t content_length,
+                          ContentProvider content_provider,
+                          const std::string &content_type) {
+  return cli_->Put(path, headers, content_length, std::move(content_provider),
+                   content_type);
+}
+Result Client::Put(const std::string &path, const Headers &headers,
+                          ContentProviderWithoutLength content_provider,
+                          const std::string &content_type) {
+  return cli_->Put(path, headers, std::move(content_provider), content_type);
+}
+Result Client::Put(const std::string &path, const Params &params) {
+  return cli_->Put(path, params);
+}
+Result Client::Put(const std::string &path, const Headers &headers,
+                          const Params &params) {
+  return cli_->Put(path, headers, params);
+}
+Result Client::Put(const std::string &path, const Headers &headers,
+                          const Params &params, Progress progress) {
+  return cli_->Put(path, headers, params, progress);
+}
+Result Client::Put(const std::string &path,
+                          const MultipartFormDataItems &items) {
+  return cli_->Put(path, items);
+}
+Result Client::Put(const std::string &path, const Headers &headers,
+                          const MultipartFormDataItems &items) {
+  return cli_->Put(path, headers, items);
+}
+Result Client::Put(const std::string &path, const Headers &headers,
+                          const MultipartFormDataItems &items,
+                          const std::string &boundary) {
+  return cli_->Put(path, headers, items, boundary);
+}
+Result
+Client::Put(const std::string &path, const Headers &headers,
+            const MultipartFormDataItems &items,
+            const MultipartFormDataProviderItems &provider_items) {
+  return cli_->Put(path, headers, items, provider_items);
+}
+Result Client::Patch(const std::string &path) {
+  return cli_->Patch(path);
+}
+Result Client::Patch(const std::string &path, const char *body,
+                            size_t content_length,
+                            const std::string &content_type) {
+  return cli_->Patch(path, body, content_length, content_type);
+}
+Result Client::Patch(const std::string &path, const char *body,
+                            size_t content_length,
+                            const std::string &content_type,
+                            Progress progress) {
+  return cli_->Patch(path, body, content_length, content_type, progress);
+}
+Result Client::Patch(const std::string &path, const Headers &headers,
+                            const char *body, size_t content_length,
+                            const std::string &content_type) {
+  return cli_->Patch(path, headers, body, content_length, content_type);
+}
+Result Client::Patch(const std::string &path, const Headers &headers,
+                            const char *body, size_t content_length,
+                            const std::string &content_type,
+                            Progress progress) {
+  return cli_->Patch(path, headers, body, content_length, content_type,
+                     progress);
+}
+Result Client::Patch(const std::string &path, const std::string &body,
+                            const std::string &content_type) {
+  return cli_->Patch(path, body, content_type);
+}
+Result Client::Patch(const std::string &path, const std::string &body,
+                            const std::string &content_type,
+                            Progress progress) {
+  return cli_->Patch(path, body, content_type, progress);
+}
+Result Client::Patch(const std::string &path, const Headers &headers,
+                            const std::string &body,
+                            const std::string &content_type) {
+  return cli_->Patch(path, headers, body, content_type);
+}
+Result Client::Patch(const std::string &path, const Headers &headers,
+                            const std::string &body,
+                            const std::string &content_type,
+                            Progress progress) {
+  return cli_->Patch(path, headers, body, content_type, progress);
+}
+Result Client::Patch(const std::string &path, size_t content_length,
+                            ContentProvider content_provider,
+                            const std::string &content_type) {
+  return cli_->Patch(path, content_length, std::move(content_provider),
+                     content_type);
+}
+Result Client::Patch(const std::string &path,
+                            ContentProviderWithoutLength content_provider,
+                            const std::string &content_type) {
+  return cli_->Patch(path, std::move(content_provider), content_type);
+}
+Result Client::Patch(const std::string &path, const Headers &headers,
+                            size_t content_length,
+                            ContentProvider content_provider,
+                            const std::string &content_type) {
+  return cli_->Patch(path, headers, content_length, std::move(content_provider),
+                     content_type);
+}
+Result Client::Patch(const std::string &path, const Headers &headers,
+                            ContentProviderWithoutLength content_provider,
+                            const std::string &content_type) {
+  return cli_->Patch(path, headers, std::move(content_provider), content_type);
+}
+Result Client::Delete(const std::string &path) {
+  return cli_->Delete(path);
+}
+Result Client::Delete(const std::string &path, const Headers &headers) {
+  return cli_->Delete(path, headers);
+}
+Result Client::Delete(const std::string &path, const char *body,
+                             size_t content_length,
+                             const std::string &content_type) {
+  return cli_->Delete(path, body, content_length, content_type);
+}
+Result Client::Delete(const std::string &path, const char *body,
+                             size_t content_length,
+                             const std::string &content_type,
+                             Progress progress) {
+  return cli_->Delete(path, body, content_length, content_type, progress);
+}
+Result Client::Delete(const std::string &path, const Headers &headers,
+                             const char *body, size_t content_length,
+                             const std::string &content_type) {
+  return cli_->Delete(path, headers, body, content_length, content_type);
+}
+Result Client::Delete(const std::string &path, const Headers &headers,
+                             const char *body, size_t content_length,
+                             const std::string &content_type,
+                             Progress progress) {
+  return cli_->Delete(path, headers, body, content_length, content_type,
+                      progress);
+}
+Result Client::Delete(const std::string &path, const std::string &body,
+                             const std::string &content_type) {
+  return cli_->Delete(path, body, content_type);
+}
+Result Client::Delete(const std::string &path, const std::string &body,
+                             const std::string &content_type,
+                             Progress progress) {
+  return cli_->Delete(path, body, content_type, progress);
+}
+Result Client::Delete(const std::string &path, const Headers &headers,
+                             const std::string &body,
+                             const std::string &content_type) {
+  return cli_->Delete(path, headers, body, content_type);
+}
+Result Client::Delete(const std::string &path, const Headers &headers,
+                             const std::string &body,
+                             const std::string &content_type,
+                             Progress progress) {
+  return cli_->Delete(path, headers, body, content_type, progress);
+}
+Result Client::Options(const std::string &path) {
+  return cli_->Options(path);
+}
+Result Client::Options(const std::string &path, const Headers &headers) {
+  return cli_->Options(path, headers);
+}
+
+bool Client::send(Request &req, Response &res, Error &error) {
+  return cli_->send(req, res, error);
+}
+
+Result Client::send(const Request &req) { return cli_->send(req); }
+
+void Client::stop() { cli_->stop(); }
+
+std::string Client::host() const { return cli_->host(); }
+
+int Client::port() const { return cli_->port(); }
+
+size_t Client::is_socket_open() const { return cli_->is_socket_open(); }
+
+socket_t Client::socket() const { return cli_->socket(); }
+
+void
+Client::set_hostname_addr_map(std::map<std::string, std::string> addr_map) {
+  cli_->set_hostname_addr_map(std::move(addr_map));
+}
+
+void Client::set_default_headers(Headers headers) {
+  cli_->set_default_headers(std::move(headers));
+}
+
+void Client::set_header_writer(
+    std::function<ssize_t(Stream &, Headers &)> const &writer) {
+  cli_->set_header_writer(writer);
+}
+
+void Client::set_address_family(int family) {
+  cli_->set_address_family(family);
+}
+
+void Client::set_tcp_nodelay(bool on) { cli_->set_tcp_nodelay(on); }
+
+void Client::set_socket_options(SocketOptions socket_options) {
+  cli_->set_socket_options(std::move(socket_options));
+}
+
+void Client::set_connection_timeout(time_t sec, time_t usec) {
+  cli_->set_connection_timeout(sec, usec);
+}
+
+void Client::set_read_timeout(time_t sec, time_t usec) {
+  cli_->set_read_timeout(sec, usec);
+}
+
+void Client::set_write_timeout(time_t sec, time_t usec) {
+  cli_->set_write_timeout(sec, usec);
+}
+
+void Client::set_basic_auth(const std::string &username,
+                                   const std::string &password) {
+  cli_->set_basic_auth(username, password);
+}
+void Client::set_bearer_token_auth(const std::string &token) {
+  cli_->set_bearer_token_auth(token);
+}
+#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
+void Client::set_digest_auth(const std::string &username,
+                                    const std::string &password) {
+  cli_->set_digest_auth(username, password);
+}
+#endif
+
+void Client::set_keep_alive(bool on) { cli_->set_keep_alive(on); }
+void Client::set_follow_location(bool on) {
+  cli_->set_follow_location(on);
+}
+
+void Client::set_url_encode(bool on) { cli_->set_url_encode(on); }
+
+void Client::set_compress(bool on) { cli_->set_compress(on); }
+
+void Client::set_decompress(bool on) { cli_->set_decompress(on); }
+
+void Client::set_interface(const std::string &intf) {
+  cli_->set_interface(intf);
+}
+
+void Client::set_proxy(const std::string &host, int port) {
+  cli_->set_proxy(host, port);
+}
+void Client::set_proxy_basic_auth(const std::string &username,
+                                         const std::string &password) {
+  cli_->set_proxy_basic_auth(username, password);
+}
+void Client::set_proxy_bearer_token_auth(const std::string &token) {
+  cli_->set_proxy_bearer_token_auth(token);
+}
+#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
+void Client::set_proxy_digest_auth(const std::string &username,
+                                          const std::string &password) {
+  cli_->set_proxy_digest_auth(username, password);
+}
+#endif
+
+#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
+void Client::enable_server_certificate_verification(bool enabled) {
+  cli_->enable_server_certificate_verification(enabled);
+}
+
+void Client::enable_server_hostname_verification(bool enabled) {
+  cli_->enable_server_hostname_verification(enabled);
+}
+
+void Client::set_server_certificate_verifier(
+    std::function<SSLVerifierResponse(SSL *ssl)> verifier) {
+  cli_->set_server_certificate_verifier(verifier);
+}
+#endif
+
+void Client::set_logger(Logger logger) {
+  cli_->set_logger(std::move(logger));
+}
+
+#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
+void Client::set_ca_cert_path(const std::string &ca_cert_file_path,
+                                     const std::string &ca_cert_dir_path) {
+  cli_->set_ca_cert_path(ca_cert_file_path, ca_cert_dir_path);
+}
+
+void Client::set_ca_cert_store(X509_STORE *ca_cert_store) {
+  if (is_ssl_) {
+    static_cast<SSLClient &>(*cli_).set_ca_cert_store(ca_cert_store);
+  } else {
+    cli_->set_ca_cert_store(ca_cert_store);
+  }
+}
+
+void Client::load_ca_cert_store(const char *ca_cert, std::size_t size) {
+  set_ca_cert_store(cli_->create_ca_cert_store(ca_cert, size));
+}
+
+long Client::get_openssl_verify_result() const {
+  if (is_ssl_) {
+    return static_cast<SSLClient &>(*cli_).get_openssl_verify_result();
+  }
+  return -1; // NOTE: -1 doesn't match any of X509_V_ERR_???
+}
+
+SSL_CTX *Client::ssl_context() const {
+  if (is_ssl_) { return static_cast<SSLClient &>(*cli_).ssl_context(); }
+  return nullptr;
+}
+#endif
+
+} // namespace httplib
diff --git a/vendor/cpp-httplib/httplib.h b/vendor/cpp-httplib/httplib.h
index b76a17d07ac..7ee219380f9 100644
--- a/vendor/cpp-httplib/httplib.h
+++ b/vendor/cpp-httplib/httplib.h
@@ -8,35 +8,7 @@
 #ifndef CPPHTTPLIB_HTTPLIB_H
 #define CPPHTTPLIB_HTTPLIB_H
 
-#define CPPHTTPLIB_VERSION "0.27.0"
-#define CPPHTTPLIB_VERSION_NUM "0x001B00"
-
-/*
- * Platform compatibility check
- */
-
-#if defined(_WIN32) && !defined(_WIN64)
-#if defined(_MSC_VER)
-#pragma message(                                                               \
-    "cpp-httplib doesn't support 32-bit Windows. Please use a 64-bit compiler.")
-#else
-#warning                                                                       \
-    "cpp-httplib doesn't support 32-bit Windows. Please use a 64-bit compiler."
-#endif
-#elif defined(__SIZEOF_POINTER__) && __SIZEOF_POINTER__ < 8
-#warning                                                                       \
-    "cpp-httplib doesn't support 32-bit platforms. Please use a 64-bit compiler."
-#elif defined(__SIZEOF_SIZE_T__) && __SIZEOF_SIZE_T__ < 8
-#warning                                                                       \
-    "cpp-httplib doesn't support platforms where size_t is less than 64 bits."
-#endif
-
-#ifdef _WIN32
-#if defined(_WIN32_WINNT) && _WIN32_WINNT < 0x0A00
-#error                                                                         \
-    "cpp-httplib doesn't support Windows 8 or lower. Please use Windows 10 or later."
-#endif
-#endif
+#define CPPHTTPLIB_VERSION "0.20.1"
 
 /*
  * Configuration
@@ -104,7 +76,7 @@
 
 #ifndef CPPHTTPLIB_IDLE_INTERVAL_USECOND
 #ifdef _WIN32
-#define CPPHTTPLIB_IDLE_INTERVAL_USECOND 1000
+#define CPPHTTPLIB_IDLE_INTERVAL_USECOND 10000
 #else
 #define CPPHTTPLIB_IDLE_INTERVAL_USECOND 0
 #endif
@@ -118,10 +90,6 @@
 #define CPPHTTPLIB_HEADER_MAX_LENGTH 8192
 #endif
 
-#ifndef CPPHTTPLIB_HEADER_MAX_COUNT
-#define CPPHTTPLIB_HEADER_MAX_COUNT 100
-#endif
-
 #ifndef CPPHTTPLIB_REDIRECT_MAX_COUNT
 #define CPPHTTPLIB_REDIRECT_MAX_COUNT 20
 #endif
@@ -154,10 +122,6 @@
 #define CPPHTTPLIB_RECV_BUFSIZ size_t(16384u)
 #endif
 
-#ifndef CPPHTTPLIB_SEND_BUFSIZ
-#define CPPHTTPLIB_SEND_BUFSIZ size_t(16384u)
-#endif
-
 #ifndef CPPHTTPLIB_COMPRESSION_BUFSIZ
 #define CPPHTTPLIB_COMPRESSION_BUFSIZ size_t(16384u)
 #endif
@@ -205,7 +169,11 @@
 
 #pragma comment(lib, "ws2_32.lib")
 
+#ifdef _WIN64
 using ssize_t = __int64;
+#else
+using ssize_t = long;
+#endif
 #endif // _MSC_VER
 
 #ifndef S_ISREG
@@ -224,13 +192,8 @@ using ssize_t = __int64;
 #include <winsock2.h>
 #include <ws2tcpip.h>
 
-#if defined(__has_include)
-#if __has_include(<afunix.h>)
 // afunix.h uses types declared in winsock2.h, so has to be included after it.
 #include <afunix.h>
-#define CPPHTTPLIB_HAVE_AFUNIX_H 1
-#endif
-#endif
 
 #ifndef WSA_FLAG_NO_HANDLE_INHERIT
 #define WSA_FLAG_NO_HANDLE_INHERIT 0x80
@@ -273,10 +236,6 @@ using socket_t = int;
 #endif
 #endif //_WIN32
 
-#if defined(__APPLE__)
-#include <TargetConditionals.h>
-#endif
-
 #include <algorithm>
 #include <array>
 #include <atomic>
@@ -306,15 +265,6 @@ using socket_t = int;
 #include <unordered_set>
 #include <utility>
 
-#if defined(CPPHTTPLIB_USE_NON_BLOCKING_GETADDRINFO) ||                        \
-    defined(CPPHTTPLIB_USE_CERTS_FROM_MACOSX_KEYCHAIN)
-#if TARGET_OS_MAC
-#include <CFNetwork/CFHost.h>
-#include <CoreFoundation/CoreFoundation.h>
-#endif
-#endif // CPPHTTPLIB_USE_NON_BLOCKING_GETADDRINFO or
-       // CPPHTTPLIB_USE_CERTS_FROM_MACOSX_KEYCHAIN
-
 #ifdef CPPHTTPLIB_OPENSSL_SUPPORT
 #ifdef _WIN32
 #include <wincrypt.h>
@@ -329,13 +279,13 @@ using socket_t = int;
 #ifdef _MSC_VER
 #pragma comment(lib, "crypt32.lib")
 #endif
-#endif // _WIN32
-
-#if defined(CPPHTTPLIB_USE_CERTS_FROM_MACOSX_KEYCHAIN)
-#if TARGET_OS_MAC
+#elif defined(CPPHTTPLIB_USE_CERTS_FROM_MACOSX_KEYCHAIN) && defined(__APPLE__)
+#include <TargetConditionals.h>
+#if TARGET_OS_OSX
+#include <CoreFoundation/CoreFoundation.h>
 #include <Security/Security.h>
-#endif
-#endif // CPPHTTPLIB_USE_NON_BLOCKING_GETADDRINFO
+#endif // TARGET_OS_OSX
+#endif // _WIN32
 
 #include <openssl/err.h>
 #include <openssl/evp.h>
@@ -358,7 +308,7 @@ using socket_t = int;
 #error Sorry, OpenSSL versions prior to 3.0.0 are not supported
 #endif
 
-#endif // CPPHTTPLIB_OPENSSL_SUPPORT
+#endif
 
 #ifdef CPPHTTPLIB_ZLIB_SUPPORT
 #include <zlib.h>
@@ -456,10 +406,6 @@ struct hash {
   }
 };
 
-template <typename T>
-using unordered_set = std::unordered_set<T, detail::case_ignore::hash,
-                                         detail::case_ignore::equal_to>;
-
 } // namespace case_ignore
 
 // This is based on
@@ -583,53 +529,19 @@ using Headers =
 using Params = std::multimap<std::string, std::string>;
 using Match = std::smatch;
 
-using DownloadProgress = std::function<bool(size_t current, size_t total)>;
-using UploadProgress = std::function<bool(size_t current, size_t total)>;
+using Progress = std::function<bool(uint64_t current, uint64_t total)>;
 
 struct Response;
 using ResponseHandler = std::function<bool(const Response &response)>;
 
-struct FormData {
-  std::string name;
-  std::string content;
-  std::string filename;
-  std::string content_type;
-  Headers headers;
-};
-
-struct FormField {
-  std::string name;
-  std::string content;
-  Headers headers;
-};
-using FormFields = std::multimap<std::string, FormField>;
-
-using FormFiles = std::multimap<std::string, FormData>;
-
 struct MultipartFormData {
-  FormFields fields; // Text fields from multipart
-  FormFiles files;   // Files from multipart
-
-  // Text field access
-  std::string get_field(const std::string &key, size_t id = 0) const;
-  std::vector<std::string> get_fields(const std::string &key) const;
-  bool has_field(const std::string &key) const;
-  size_t get_field_count(const std::string &key) const;
-
-  // File access
-  FormData get_file(const std::string &key, size_t id = 0) const;
-  std::vector<FormData> get_files(const std::string &key) const;
-  bool has_file(const std::string &key) const;
-  size_t get_file_count(const std::string &key) const;
-};
-
-struct UploadFormData {
   std::string name;
   std::string content;
   std::string filename;
   std::string content_type;
 };
-using UploadFormDataItems = std::vector<UploadFormData>;
+using MultipartFormDataItems = std::vector<MultipartFormData>;
+using MultipartFormDataMap = std::multimap<std::string, MultipartFormData>;
 
 class DataSink {
 public:
@@ -672,34 +584,37 @@ using ContentProviderWithoutLength =
 
 using ContentProviderResourceReleaser = std::function<void(bool success)>;
 
-struct FormDataProvider {
+struct MultipartFormDataProvider {
   std::string name;
   ContentProviderWithoutLength provider;
   std::string filename;
   std::string content_type;
 };
-using FormDataProviderItems = std::vector<FormDataProvider>;
+using MultipartFormDataProviderItems = std::vector<MultipartFormDataProvider>;
 
-using ContentReceiverWithProgress = std::function<bool(
-    const char *data, size_t data_length, size_t offset, size_t total_length)>;
+using ContentReceiverWithProgress =
+    std::function<bool(const char *data, size_t data_length, uint64_t offset,
+                       uint64_t total_length)>;
 
 using ContentReceiver =
     std::function<bool(const char *data, size_t data_length)>;
 
-using FormDataHeader = std::function<bool(const FormData &file)>;
+using MultipartContentHeader =
+    std::function<bool(const MultipartFormData &file)>;
 
 class ContentReader {
 public:
   using Reader = std::function<bool(ContentReceiver receiver)>;
-  using FormDataReader =
-      std::function<bool(FormDataHeader header, ContentReceiver receiver)>;
+  using MultipartReader = std::function<bool(MultipartContentHeader header,
+                                             ContentReceiver receiver)>;
 
-  ContentReader(Reader reader, FormDataReader multipart_reader)
+  ContentReader(Reader reader, MultipartReader multipart_reader)
       : reader_(std::move(reader)),
-        formdata_reader_(std::move(multipart_reader)) {}
+        multipart_reader_(std::move(multipart_reader)) {}
 
-  bool operator()(FormDataHeader header, ContentReceiver receiver) const {
-    return formdata_reader_(std::move(header), std::move(receiver));
+  bool operator()(MultipartContentHeader header,
+                  ContentReceiver receiver) const {
+    return multipart_reader_(std::move(header), std::move(receiver));
   }
 
   bool operator()(ContentReceiver receiver) const {
@@ -707,7 +622,7 @@ class ContentReader {
   }
 
   Reader reader_;
-  FormDataReader formdata_reader_;
+  MultipartReader multipart_reader_;
 };
 
 using Range = std::pair<ssize_t, ssize_t>;
@@ -716,10 +631,8 @@ using Ranges = std::vector<Range>;
 struct Request {
   std::string method;
   std::string path;
-  std::string matched_route;
   Params params;
   Headers headers;
-  Headers trailers;
   std::string body;
 
   std::string remote_addr;
@@ -730,18 +643,16 @@ struct Request {
   // for server
   std::string version;
   std::string target;
-  MultipartFormData form;
+  MultipartFormDataMap files;
   Ranges ranges;
   Match matches;
   std::unordered_map<std::string, std::string> path_params;
   std::function<bool()> is_connection_closed = []() { return true; };
 
   // for client
-  std::vector<std::string> accept_content_types;
   ResponseHandler response_handler;
   ContentReceiverWithProgress content_receiver;
-  DownloadProgress download_progress;
-  UploadProgress upload_progress;
+  Progress progress;
 #ifdef CPPHTTPLIB_OPENSSL_SUPPORT
   const SSL *ssl = nullptr;
 #endif
@@ -749,21 +660,21 @@ struct Request {
   bool has_header(const std::string &key) const;
   std::string get_header_value(const std::string &key, const char *def = "",
                                size_t id = 0) const;
-  size_t get_header_value_u64(const std::string &key, size_t def = 0,
-                              size_t id = 0) const;
+  uint64_t get_header_value_u64(const std::string &key, uint64_t def = 0,
+                                size_t id = 0) const;
   size_t get_header_value_count(const std::string &key) const;
   void set_header(const std::string &key, const std::string &val);
 
-  bool has_trailer(const std::string &key) const;
-  std::string get_trailer_value(const std::string &key, size_t id = 0) const;
-  size_t get_trailer_value_count(const std::string &key) const;
-
   bool has_param(const std::string &key) const;
   std::string get_param_value(const std::string &key, size_t id = 0) const;
   size_t get_param_value_count(const std::string &key) const;
 
   bool is_multipart_form_data() const;
 
+  bool has_file(const std::string &key) const;
+  MultipartFormData get_file_value(const std::string &key) const;
+  std::vector<MultipartFormData> get_file_values(const std::string &key) const;
+
   // private members...
   size_t redirect_count_ = CPPHTTPLIB_REDIRECT_MAX_COUNT;
   size_t content_length_ = 0;
@@ -779,22 +690,17 @@ struct Response {
   int status = -1;
   std::string reason;
   Headers headers;
-  Headers trailers;
   std::string body;
   std::string location; // Redirect location
 
   bool has_header(const std::string &key) const;
   std::string get_header_value(const std::string &key, const char *def = "",
                                size_t id = 0) const;
-  size_t get_header_value_u64(const std::string &key, size_t def = 0,
-                              size_t id = 0) const;
+  uint64_t get_header_value_u64(const std::string &key, uint64_t def = 0,
+                                size_t id = 0) const;
   size_t get_header_value_count(const std::string &key) const;
   void set_header(const std::string &key, const std::string &val);
 
-  bool has_trailer(const std::string &key) const;
-  std::string get_trailer_value(const std::string &key, size_t id = 0) const;
-  size_t get_trailer_value_count(const std::string &key) const;
-
   void set_redirect(const std::string &url, int status = StatusCode::Found_302);
   void set_content(const char *s, size_t n, const std::string &content_type);
   void set_content(const std::string &s, const std::string &content_type);
@@ -954,10 +860,6 @@ class ThreadPool final : public TaskQueue {
 
 using Logger = std::function<void(const Request &, const Response &)>;
 
-// Forward declaration for Error type
-enum class Error;
-using ErrorLogger = std::function<void(const Error &, const Request *)>;
-
 using SocketOptions = std::function<void(socket_t sock)>;
 
 namespace detail {
@@ -980,16 +882,10 @@ namespace detail {
 
 class MatcherBase {
 public:
-  MatcherBase(std::string pattern) : pattern_(pattern) {}
   virtual ~MatcherBase() = default;
 
-  const std::string &pattern() const { return pattern_; }
-
   // Match request path and populate its matches and
   virtual bool match(Request &request) const = 0;
-
-private:
-  std::string pattern_;
 };
 
 /**
@@ -1041,8 +937,7 @@ class PathParamsMatcher final : public MatcherBase {
  */
 class RegexMatcher final : public MatcherBase {
 public:
-  RegexMatcher(const std::string &pattern)
-      : MatcherBase(pattern), regex_(pattern) {}
+  RegexMatcher(const std::string &pattern) : regex_(pattern) {}
 
   bool match(Request &request) const override;
 
@@ -1052,9 +947,6 @@ class RegexMatcher final : public MatcherBase {
 
 ssize_t write_headers(Stream &strm, const Headers &headers);
 
-std::string make_host_and_port_string(const std::string &host, int port,
-                                      bool is_ssl);
-
 } // namespace detail
 
 class Server {
@@ -1112,16 +1004,11 @@ class Server {
   }
 
   Server &set_exception_handler(ExceptionHandler handler);
-
   Server &set_pre_routing_handler(HandlerWithResponse handler);
   Server &set_post_routing_handler(Handler handler);
 
-  Server &set_pre_request_handler(HandlerWithResponse handler);
-
   Server &set_expect_100_continue_handler(Expect100ContinueHandler handler);
   Server &set_logger(Logger logger);
-  Server &set_pre_compression_logger(Logger logger);
-  Server &set_error_logger(ErrorLogger error_logger);
 
   Server &set_address_family(int family);
   Server &set_tcp_nodelay(bool on);
@@ -1132,8 +1019,6 @@ class Server {
   Server &
   set_header_writer(std::function<ssize_t(Stream &, Headers &)> const &writer);
 
-  Server &set_trusted_proxies(const std::vector<std::string> &proxies);
-
   Server &set_keep_alive_max_count(size_t count);
   Server &set_keep_alive_timeout(time_t sec);
 
@@ -1172,9 +1057,6 @@ class Server {
                        const std::function<void(Request &)> &setup_request);
 
   std::atomic<socket_t> svr_sock_{INVALID_SOCKET};
-
-  std::vector<std::string> trusted_proxies_;
-
   size_t keep_alive_max_count_ = CPPHTTPLIB_KEEPALIVE_MAX_COUNT;
   time_t keep_alive_timeout_sec_ = CPPHTTPLIB_KEEPALIVE_TIMEOUT_SECOND;
   time_t read_timeout_sec_ = CPPHTTPLIB_SERVER_READ_TIMEOUT_SECOND;
@@ -1205,7 +1087,8 @@ class Server {
   bool listen_internal();
 
   bool routing(Request &req, Response &res, Stream &strm);
-  bool handle_file_request(const Request &req, Response &res);
+  bool handle_file_request(const Request &req, Response &res,
+                           bool head = false);
   bool dispatch_request(Request &req, Response &res,
                         const Handlers &handlers) const;
   bool dispatch_request_for_content_reader(
@@ -1226,23 +1109,18 @@ class Server {
                                    Response &res, const std::string &boundary,
                                    const std::string &content_type);
   bool read_content(Stream &strm, Request &req, Response &res);
-  bool read_content_with_content_receiver(Stream &strm, Request &req,
-                                          Response &res,
-                                          ContentReceiver receiver,
-                                          FormDataHeader multipart_header,
-                                          ContentReceiver multipart_receiver);
+  bool
+  read_content_with_content_receiver(Stream &strm, Request &req, Response &res,
+                                     ContentReceiver receiver,
+                                     MultipartContentHeader multipart_header,
+                                     ContentReceiver multipart_receiver);
   bool read_content_core(Stream &strm, Request &req, Response &res,
                          ContentReceiver receiver,
-                         FormDataHeader multipart_header,
+                         MultipartContentHeader multipart_header,
                          ContentReceiver multipart_receiver) const;
 
   virtual bool process_and_close_socket(socket_t sock);
 
-  void output_log(const Request &req, const Response &res) const;
-  void output_pre_compression_log(const Request &req,
-                                  const Response &res) const;
-  void output_error_log(const Error &err, const Request *req) const;
-
   std::atomic<bool> is_running_{false};
   std::atomic<bool> is_decommissioned{false};
 
@@ -1271,13 +1149,9 @@ class Server {
   ExceptionHandler exception_handler_;
   HandlerWithResponse pre_routing_handler_;
   Handler post_routing_handler_;
-  HandlerWithResponse pre_request_handler_;
   Expect100ContinueHandler expect_100_continue_handler_;
 
-  mutable std::mutex logger_mutex_;
   Logger logger_;
-  Logger pre_compression_logger_;
-  ErrorLogger error_logger_;
 
   int address_family_ = AF_UNSPEC;
   bool tcp_nodelay_ = CPPHTTPLIB_TCP_NODELAY;
@@ -1306,22 +1180,6 @@ enum class Error {
   Compression,
   ConnectionTimeout,
   ProxyConnection,
-  ResourceExhaustion,
-  TooManyFormDataFiles,
-  ExceedMaxPayloadSize,
-  ExceedUriMaxLength,
-  ExceedMaxSocketDescriptorCount,
-  InvalidRequestLine,
-  InvalidHTTPMethod,
-  InvalidHTTPVersion,
-  InvalidHeaders,
-  MultipartParsing,
-  OpenFile,
-  Listen,
-  GetSockName,
-  UnsupportedAddressFamily,
-  HTTPParsing,
-  InvalidRangeHeader,
 
   // For internal use only
   SSLPeerCouldBeClosed_,
@@ -1338,17 +1196,6 @@ class Result {
          Headers &&request_headers = Headers{})
       : res_(std::move(res)), err_(err),
         request_headers_(std::move(request_headers)) {}
-#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
-  Result(std::unique_ptr<Response> &&res, Error err, Headers &&request_headers,
-         int ssl_error)
-      : res_(std::move(res)), err_(err),
-        request_headers_(std::move(request_headers)), ssl_error_(ssl_error) {}
-  Result(std::unique_ptr<Response> &&res, Error err, Headers &&request_headers,
-         int ssl_error, unsigned long ssl_openssl_error)
-      : res_(std::move(res)), err_(err),
-        request_headers_(std::move(request_headers)), ssl_error_(ssl_error),
-        ssl_openssl_error_(ssl_openssl_error) {}
-#endif
   // Response
   operator bool() const { return res_ != nullptr; }
   bool operator==(std::nullptr_t) const { return res_ == nullptr; }
@@ -1363,30 +1210,19 @@ class Result {
   // Error
   Error error() const { return err_; }
 
-#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
-  // SSL Error
-  int ssl_error() const { return ssl_error_; }
-  // OpenSSL Error
-  unsigned long ssl_openssl_error() const { return ssl_openssl_error_; }
-#endif
-
   // Request Headers
   bool has_request_header(const std::string &key) const;
   std::string get_request_header_value(const std::string &key,
                                        const char *def = "",
                                        size_t id = 0) const;
-  size_t get_request_header_value_u64(const std::string &key, size_t def = 0,
-                                      size_t id = 0) const;
+  uint64_t get_request_header_value_u64(const std::string &key,
+                                        uint64_t def = 0, size_t id = 0) const;
   size_t get_request_header_value_count(const std::string &key) const;
 
 private:
   std::unique_ptr<Response> res_;
   Error err_ = Error::Unknown;
   Headers request_headers_;
-#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
-  int ssl_error_ = 0;
-  unsigned long ssl_openssl_error_ = 0;
-#endif
 };
 
 class ClientImpl {
@@ -1403,86 +1239,185 @@ class ClientImpl {
 
   virtual bool is_valid() const;
 
-  // clang-format off
-  Result Get(const std::string &path, DownloadProgress progress = nullptr);
-  Result Get(const std::string &path, ContentReceiver content_receiver, DownloadProgress progress = nullptr);
-  Result Get(const std::string &path, ResponseHandler response_handler, ContentReceiver content_receiver, DownloadProgress progress = nullptr);
-  Result Get(const std::string &path, const Headers &headers, DownloadProgress progress = nullptr);
-  Result Get(const std::string &path, const Headers &headers, ContentReceiver content_receiver, DownloadProgress progress = nullptr);
-  Result Get(const std::string &path, const Headers &headers, ResponseHandler response_handler, ContentReceiver content_receiver, DownloadProgress progress = nullptr);
-  Result Get(const std::string &path, const Params &params, const Headers &headers, DownloadProgress progress = nullptr);
-  Result Get(const std::string &path, const Params &params, const Headers &headers, ContentReceiver content_receiver, DownloadProgress progress = nullptr);
-  Result Get(const std::string &path, const Params &params, const Headers &headers, ResponseHandler response_handler, ContentReceiver content_receiver, DownloadProgress progress = nullptr);
+  Result Get(const std::string &path);
+  Result Get(const std::string &path, const Headers &headers);
+  Result Get(const std::string &path, Progress progress);
+  Result Get(const std::string &path, const Headers &headers,
+             Progress progress);
+  Result Get(const std::string &path, ContentReceiver content_receiver);
+  Result Get(const std::string &path, const Headers &headers,
+             ContentReceiver content_receiver);
+  Result Get(const std::string &path, ContentReceiver content_receiver,
+             Progress progress);
+  Result Get(const std::string &path, const Headers &headers,
+             ContentReceiver content_receiver, Progress progress);
+  Result Get(const std::string &path, ResponseHandler response_handler,
+             ContentReceiver content_receiver);
+  Result Get(const std::string &path, const Headers &headers,
+             ResponseHandler response_handler,
+             ContentReceiver content_receiver);
+  Result Get(const std::string &path, ResponseHandler response_handler,
+             ContentReceiver content_receiver, Progress progress);
+  Result Get(const std::string &path, const Headers &headers,
+             ResponseHandler response_handler, ContentReceiver content_receiver,
+             Progress progress);
+
+  Result Get(const std::string &path, const Params &params,
+             const Headers &headers, Progress progress = nullptr);
+  Result Get(const std::string &path, const Params &params,
+             const Headers &headers, ContentReceiver content_receiver,
+             Progress progress = nullptr);
+  Result Get(const std::string &path, const Params &params,
+             const Headers &headers, ResponseHandler response_handler,
+             ContentReceiver content_receiver, Progress progress = nullptr);
 
   Result Head(const std::string &path);
   Result Head(const std::string &path, const Headers &headers);
 
   Result Post(const std::string &path);
-  Result Post(const std::string &path, const char *body, size_t content_length, const std::string &content_type, UploadProgress progress = nullptr);
-  Result Post(const std::string &path, const std::string &body, const std::string &content_type, UploadProgress progress = nullptr);
-  Result Post(const std::string &path, size_t content_length, ContentProvider content_provider, const std::string &content_type, UploadProgress progress = nullptr);
-  Result Post(const std::string &path, ContentProviderWithoutLength content_provider, const std::string &content_type, UploadProgress progress = nullptr);
-  Result Post(const std::string &path, const Params &params);
-  Result Post(const std::string &path, const UploadFormDataItems &items, UploadProgress progress = nullptr);
   Result Post(const std::string &path, const Headers &headers);
-  Result Post(const std::string &path, const Headers &headers, const char *body, size_t content_length, const std::string &content_type, UploadProgress progress = nullptr);
-  Result Post(const std::string &path, const Headers &headers, const std::string &body, const std::string &content_type, UploadProgress progress = nullptr);
-  Result Post(const std::string &path, const Headers &headers, size_t content_length, ContentProvider content_provider, const std::string &content_type, UploadProgress progress = nullptr);
-  Result Post(const std::string &path, const Headers &headers, ContentProviderWithoutLength content_provider, const std::string &content_type, UploadProgress progress = nullptr);
-  Result Post(const std::string &path, const Headers &headers, const Params &params);
-  Result Post(const std::string &path, const Headers &headers, const UploadFormDataItems &items, UploadProgress progress = nullptr);
-  Result Post(const std::string &path, const Headers &headers, const UploadFormDataItems &items, const std::string &boundary, UploadProgress progress = nullptr);
-  Result Post(const std::string &path, const Headers &headers, const UploadFormDataItems &items, const FormDataProviderItems &provider_items, UploadProgress progress = nullptr);
-  Result Post(const std::string &path, const Headers &headers, const std::string &body, const std::string &content_type, ContentReceiver content_receiver, DownloadProgress progress = nullptr);
+  Result Post(const std::string &path, const char *body, size_t content_length,
+              const std::string &content_type);
+  Result Post(const std::string &path, const Headers &headers, const char *body,
+              size_t content_length, const std::string &content_type);
+  Result Post(const std::string &path, const Headers &headers, const char *body,
+              size_t content_length, const std::string &content_type,
+              Progress progress);
+  Result Post(const std::string &path, const std::string &body,
+              const std::string &content_type);
+  Result Post(const std::string &path, const std::string &body,
+              const std::string &content_type, Progress progress);
+  Result Post(const std::string &path, const Headers &headers,
+              const std::string &body, const std::string &content_type);
+  Result Post(const std::string &path, const Headers &headers,
+              const std::string &body, const std::string &content_type,
+              Progress progress);
+  Result Post(const std::string &path, size_t content_length,
+              ContentProvider content_provider,
+              const std::string &content_type);
+  Result Post(const std::string &path,
+              ContentProviderWithoutLength content_provider,
+              const std::string &content_type);
+  Result Post(const std::string &path, const Headers &headers,
+              size_t content_length, ContentProvider content_provider,
+              const std::string &content_type);
+  Result Post(const std::string &path, const Headers &headers,
+              ContentProviderWithoutLength content_provider,
+              const std::string &content_type);
+  Result Post(const std::string &path, const Params &params);
+  Result Post(const std::string &path, const Headers &headers,
+              const Params &params);
+  Result Post(const std::string &path, const Headers &headers,
+              const Params &params, Progress progress);
+  Result Post(const std::string &path, const MultipartFormDataItems &items);
+  Result Post(const std::string &path, const Headers &headers,
+              const MultipartFormDataItems &items);
+  Result Post(const std::string &path, const Headers &headers,
+              const MultipartFormDataItems &items, const std::string &boundary);
+  Result Post(const std::string &path, const Headers &headers,
+              const MultipartFormDataItems &items,
+              const MultipartFormDataProviderItems &provider_items);
 
   Result Put(const std::string &path);
-  Result Put(const std::string &path, const char *body, size_t content_length, const std::string &content_type, UploadProgress progress = nullptr);
-  Result Put(const std::string &path, const std::string &body, const std::string &content_type, UploadProgress progress = nullptr);
-  Result Put(const std::string &path, size_t content_length, ContentProvider content_provider, const std::string &content_type, UploadProgress progress = nullptr);
-  Result Put(const std::string &path, ContentProviderWithoutLength content_provider, const std::string &content_type, UploadProgress progress = nullptr);
+  Result Put(const std::string &path, const char *body, size_t content_length,
+             const std::string &content_type);
+  Result Put(const std::string &path, const Headers &headers, const char *body,
+             size_t content_length, const std::string &content_type);
+  Result Put(const std::string &path, const Headers &headers, const char *body,
+             size_t content_length, const std::string &content_type,
+             Progress progress);
+  Result Put(const std::string &path, const std::string &body,
+             const std::string &content_type);
+  Result Put(const std::string &path, const std::string &body,
+             const std::string &content_type, Progress progress);
+  Result Put(const std::string &path, const Headers &headers,
+             const std::string &body, const std::string &content_type);
+  Result Put(const std::string &path, const Headers &headers,
+             const std::string &body, const std::string &content_type,
+             Progress progress);
+  Result Put(const std::string &path, size_t content_length,
+             ContentProvider content_provider, const std::string &content_type);
+  Result Put(const std::string &path,
+             ContentProviderWithoutLength content_provider,
+             const std::string &content_type);
+  Result Put(const std::string &path, const Headers &headers,
+             size_t content_length, ContentProvider content_provider,
+             const std::string &content_type);
+  Result Put(const std::string &path, const Headers &headers,
+             ContentProviderWithoutLength content_provider,
+             const std::string &content_type);
   Result Put(const std::string &path, const Params &params);
-  Result Put(const std::string &path, const UploadFormDataItems &items, UploadProgress progress = nullptr);
-  Result Put(const std::string &path, const Headers &headers);
-  Result Put(const std::string &path, const Headers &headers, const char *body, size_t content_length, const std::string &content_type, UploadProgress progress = nullptr);
-  Result Put(const std::string &path, const Headers &headers, const std::string &body, const std::string &content_type, UploadProgress progress = nullptr);
-  Result Put(const std::string &path, const Headers &headers, size_t content_length, ContentProvider content_provider, const std::string &content_type, UploadProgress progress = nullptr);
-  Result Put(const std::string &path, const Headers &headers, ContentProviderWithoutLength content_provider, const std::string &content_type, UploadProgress progress = nullptr);
-  Result Put(const std::string &path, const Headers &headers, const Params &params);
-  Result Put(const std::string &path, const Headers &headers, const UploadFormDataItems &items, UploadProgress progress = nullptr);
-  Result Put(const std::string &path, const Headers &headers, const UploadFormDataItems &items, const std::string &boundary, UploadProgress progress = nullptr);
-  Result Put(const std::string &path, const Headers &headers, const UploadFormDataItems &items, const FormDataProviderItems &provider_items, UploadProgress progress = nullptr);
-  Result Put(const std::string &path, const Headers &headers, const std::string &body, const std::string &content_type, ContentReceiver content_receiver, DownloadProgress progress = nullptr);
+  Result Put(const std::string &path, const Headers &headers,
+             const Params &params);
+  Result Put(const std::string &path, const Headers &headers,
+             const Params &params, Progress progress);
+  Result Put(const std::string &path, const MultipartFormDataItems &items);
+  Result Put(const std::string &path, const Headers &headers,
+             const MultipartFormDataItems &items);
+  Result Put(const std::string &path, const Headers &headers,
+             const MultipartFormDataItems &items, const std::string &boundary);
+  Result Put(const std::string &path, const Headers &headers,
+             const MultipartFormDataItems &items,
+             const MultipartFormDataProviderItems &provider_items);
 
   Result Patch(const std::string &path);
-  Result Patch(const std::string &path, const char *body, size_t content_length, const std::string &content_type, UploadProgress progress = nullptr);
-  Result Patch(const std::string &path, const std::string &body, const std::string &content_type, UploadProgress progress = nullptr);
-  Result Patch(const std::string &path, size_t content_length, ContentProvider content_provider, const std::string &content_type, UploadProgress progress = nullptr);
-  Result Patch(const std::string &path, ContentProviderWithoutLength content_provider, const std::string &content_type, UploadProgress progress = nullptr);
-  Result Patch(const std::string &path, const Params &params);
-  Result Patch(const std::string &path, const UploadFormDataItems &items, UploadProgress progress = nullptr);
-  Result Patch(const std::string &path, const Headers &headers, UploadProgress progress = nullptr);
-  Result Patch(const std::string &path, const Headers &headers, const char *body, size_t content_length, const std::string &content_type, UploadProgress progress = nullptr);
-  Result Patch(const std::string &path, const Headers &headers, const std::string &body, const std::string &content_type, UploadProgress progress = nullptr);
-  Result Patch(const std::string &path, const Headers &headers, size_t content_length, ContentProvider content_provider, const std::string &content_type, UploadProgress progress = nullptr);
-  Result Patch(const std::string &path, const Headers &headers, ContentProviderWithoutLength content_provider, const std::string &content_type, UploadProgress progress = nullptr);
-  Result Patch(const std::string &path, const Headers &headers, const Params &params);
-  Result Patch(const std::string &path, const Headers &headers, const UploadFormDataItems &items, UploadProgress progress = nullptr);
-  Result Patch(const std::string &path, const Headers &headers, const UploadFormDataItems &items, const std::string &boundary, UploadProgress progress = nullptr);
-  Result Patch(const std::string &path, const Headers &headers, const UploadFormDataItems &items, const FormDataProviderItems &provider_items, UploadProgress progress = nullptr);
-  Result Patch(const std::string &path, const Headers &headers, const std::string &body, const std::string &content_type, ContentReceiver content_receiver, DownloadProgress progress = nullptr);
-
-  Result Delete(const std::string &path, DownloadProgress progress = nullptr);
-  Result Delete(const std::string &path, const char *body, size_t content_length, const std::string &content_type, DownloadProgress progress = nullptr);
-  Result Delete(const std::string &path, const std::string &body, const std::string &content_type, DownloadProgress progress = nullptr);
-  Result Delete(const std::string &path, const Params &params, DownloadProgress progress = nullptr);
-  Result Delete(const std::string &path, const Headers &headers, DownloadProgress progress = nullptr);
-  Result Delete(const std::string &path, const Headers &headers, const char *body, size_t content_length, const std::string &content_type, DownloadProgress progress = nullptr);
-  Result Delete(const std::string &path, const Headers &headers, const std::string &body, const std::string &content_type, DownloadProgress progress = nullptr);
-  Result Delete(const std::string &path, const Headers &headers, const Params &params, DownloadProgress progress = nullptr);
+  Result Patch(const std::string &path, const char *body, size_t content_length,
+               const std::string &content_type);
+  Result Patch(const std::string &path, const char *body, size_t content_length,
+               const std::string &content_type, Progress progress);
+  Result Patch(const std::string &path, const Headers &headers,
+               const char *body, size_t content_length,
+               const std::string &content_type);
+  Result Patch(const std::string &path, const Headers &headers,
+               const char *body, size_t content_length,
+               const std::string &content_type, Progress progress);
+  Result Patch(const std::string &path, const std::string &body,
+               const std::string &content_type);
+  Result Patch(const std::string &path, const std::string &body,
+               const std::string &content_type, Progress progress);
+  Result Patch(const std::string &path, const Headers &headers,
+               const std::string &body, const std::string &content_type);
+  Result Patch(const std::string &path, const Headers &headers,
+               const std::string &body, const std::string &content_type,
+               Progress progress);
+  Result Patch(const std::string &path, size_t content_length,
+               ContentProvider content_provider,
+               const std::string &content_type);
+  Result Patch(const std::string &path,
+               ContentProviderWithoutLength content_provider,
+               const std::string &content_type);
+  Result Patch(const std::string &path, const Headers &headers,
+               size_t content_length, ContentProvider content_provider,
+               const std::string &content_type);
+  Result Patch(const std::string &path, const Headers &headers,
+               ContentProviderWithoutLength content_provider,
+               const std::string &content_type);
+
+  Result Delete(const std::string &path);
+  Result Delete(const std::string &path, const Headers &headers);
+  Result Delete(const std::string &path, const char *body,
+                size_t content_length, const std::string &content_type);
+  Result Delete(const std::string &path, const char *body,
+                size_t content_length, const std::string &content_type,
+                Progress progress);
+  Result Delete(const std::string &path, const Headers &headers,
+                const char *body, size_t content_length,
+                const std::string &content_type);
+  Result Delete(const std::string &path, const Headers &headers,
+                const char *body, size_t content_length,
+                const std::string &content_type, Progress progress);
+  Result Delete(const std::string &path, const std::string &body,
+                const std::string &content_type);
+  Result Delete(const std::string &path, const std::string &body,
+                const std::string &content_type, Progress progress);
+  Result Delete(const std::string &path, const Headers &headers,
+                const std::string &body, const std::string &content_type);
+  Result Delete(const std::string &path, const Headers &headers,
+                const std::string &body, const std::string &content_type,
+                Progress progress);
 
   Result Options(const std::string &path);
   Result Options(const std::string &path, const Headers &headers);
-  // clang-format on
 
   bool send(Request &req, Response &res, Error &error);
   Result send(const Request &req);
@@ -1534,7 +1469,7 @@ class ClientImpl {
   void set_keep_alive(bool on);
   void set_follow_location(bool on);
 
-  void set_path_encode(bool on);
+  void set_url_encode(bool on);
 
   void set_compress(bool on);
 
@@ -1566,7 +1501,6 @@ class ClientImpl {
 #endif
 
   void set_logger(Logger logger);
-  void set_error_logger(ErrorLogger error_logger);
 
 protected:
   struct Socket {
@@ -1599,9 +1533,6 @@ class ClientImpl {
 
   void copy_settings(const ClientImpl &rhs);
 
-  void output_log(const Request &req, const Response &res) const;
-  void output_error_log(const Error &err, const Request *req) const;
-
   // Socket endpoint information
   const std::string host_;
   const int port_;
@@ -1650,7 +1581,7 @@ class ClientImpl {
   bool keep_alive_ = false;
   bool follow_location_ = false;
 
-  bool path_encode_ = true;
+  bool url_encode_ = true;
 
   int address_family_ = AF_UNSPEC;
   bool tcp_nodelay_ = CPPHTTPLIB_TCP_NODELAY;
@@ -1686,14 +1617,7 @@ class ClientImpl {
   std::function<SSLVerifierResponse(SSL *ssl)> server_certificate_verifier_;
 #endif
 
-  mutable std::mutex logger_mutex_;
   Logger logger_;
-  ErrorLogger error_logger_;
-
-#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
-  int last_ssl_error_ = 0;
-  unsigned long last_openssl_error_ = 0;
-#endif
 
 private:
   bool send_(Request &req, Response &res, Error &error);
@@ -1705,11 +1629,6 @@ class ClientImpl {
   bool write_request(Stream &strm, Request &req, bool close_connection,
                      Error &error);
   bool redirect(Request &req, Response &res, Error &error);
-  bool create_redirect_client(const std::string &scheme,
-                              const std::string &host, int port, Request &req,
-                              Response &res, const std::string &path,
-                              const std::string &location, Error &error);
-  template <typename ClientType> void setup_redirect_client(ClientType &client);
   bool handle_request(Stream &strm, Request &req, Response &res,
                       bool close_connection, Error &error);
   std::unique_ptr<Response> send_with_content_provider(
@@ -1722,10 +1641,12 @@ class ClientImpl {
       const Headers &headers, const char *body, size_t content_length,
       ContentProvider content_provider,
       ContentProviderWithoutLength content_provider_without_length,
-      const std::string &content_type, UploadProgress progress);
+      const std::string &content_type, Progress progress);
   ContentProviderWithoutLength get_multipart_content_provider(
-      const std::string &boundary, const UploadFormDataItems &items,
-      const FormDataProviderItems &provider_items) const;
+      const std::string &boundary, const MultipartFormDataItems &items,
+      const MultipartFormDataProviderItems &provider_items) const;
+
+  std::string adjust_host_string(const std::string &host) const;
 
   virtual bool
   process_socket(const Socket &socket,
@@ -1757,86 +1678,185 @@ class Client {
 
   bool is_valid() const;
 
-  // clang-format off
-  Result Get(const std::string &path, DownloadProgress progress = nullptr);
-  Result Get(const std::string &path, ContentReceiver content_receiver, DownloadProgress progress = nullptr);
-  Result Get(const std::string &path, ResponseHandler response_handler, ContentReceiver content_receiver, DownloadProgress progress = nullptr);
-  Result Get(const std::string &path, const Headers &headers, DownloadProgress progress = nullptr);
-  Result Get(const std::string &path, const Headers &headers, ContentReceiver content_receiver, DownloadProgress progress = nullptr);
-  Result Get(const std::string &path, const Headers &headers, ResponseHandler response_handler, ContentReceiver content_receiver, DownloadProgress progress = nullptr);
-  Result Get(const std::string &path, const Params &params, const Headers &headers, DownloadProgress progress = nullptr);
-  Result Get(const std::string &path, const Params &params, const Headers &headers, ContentReceiver content_receiver, DownloadProgress progress = nullptr);
-  Result Get(const std::string &path, const Params &params, const Headers &headers, ResponseHandler response_handler, ContentReceiver content_receiver, DownloadProgress progress = nullptr);
+  Result Get(const std::string &path);
+  Result Get(const std::string &path, const Headers &headers);
+  Result Get(const std::string &path, Progress progress);
+  Result Get(const std::string &path, const Headers &headers,
+             Progress progress);
+  Result Get(const std::string &path, ContentReceiver content_receiver);
+  Result Get(const std::string &path, const Headers &headers,
+             ContentReceiver content_receiver);
+  Result Get(const std::string &path, ContentReceiver content_receiver,
+             Progress progress);
+  Result Get(const std::string &path, const Headers &headers,
+             ContentReceiver content_receiver, Progress progress);
+  Result Get(const std::string &path, ResponseHandler response_handler,
+             ContentReceiver content_receiver);
+  Result Get(const std::string &path, const Headers &headers,
+             ResponseHandler response_handler,
+             ContentReceiver content_receiver);
+  Result Get(const std::string &path, const Headers &headers,
+             ResponseHandler response_handler, ContentReceiver content_receiver,
+             Progress progress);
+  Result Get(const std::string &path, ResponseHandler response_handler,
+             ContentReceiver content_receiver, Progress progress);
+
+  Result Get(const std::string &path, const Params &params,
+             const Headers &headers, Progress progress = nullptr);
+  Result Get(const std::string &path, const Params &params,
+             const Headers &headers, ContentReceiver content_receiver,
+             Progress progress = nullptr);
+  Result Get(const std::string &path, const Params &params,
+             const Headers &headers, ResponseHandler response_handler,
+             ContentReceiver content_receiver, Progress progress = nullptr);
 
   Result Head(const std::string &path);
   Result Head(const std::string &path, const Headers &headers);
 
   Result Post(const std::string &path);
-  Result Post(const std::string &path, const char *body, size_t content_length, const std::string &content_type, UploadProgress progress = nullptr);
-  Result Post(const std::string &path, const std::string &body, const std::string &content_type, UploadProgress progress = nullptr);
-  Result Post(const std::string &path, size_t content_length, ContentProvider content_provider, const std::string &content_type, UploadProgress progress = nullptr);
-  Result Post(const std::string &path, ContentProviderWithoutLength content_provider, const std::string &content_type, UploadProgress progress = nullptr);
-  Result Post(const std::string &path, const Params &params);
-  Result Post(const std::string &path, const UploadFormDataItems &items, UploadProgress progress = nullptr);
   Result Post(const std::string &path, const Headers &headers);
-  Result Post(const std::string &path, const Headers &headers, const char *body, size_t content_length, const std::string &content_type, UploadProgress progress = nullptr);
-  Result Post(const std::string &path, const Headers &headers, const std::string &body, const std::string &content_type, UploadProgress progress = nullptr);
-  Result Post(const std::string &path, const Headers &headers, size_t content_length, ContentProvider content_provider, const std::string &content_type, UploadProgress progress = nullptr);
-  Result Post(const std::string &path, const Headers &headers, ContentProviderWithoutLength content_provider, const std::string &content_type, UploadProgress progress = nullptr);
-  Result Post(const std::string &path, const Headers &headers, const Params &params);
-  Result Post(const std::string &path, const Headers &headers, const UploadFormDataItems &items, UploadProgress progress = nullptr);
-  Result Post(const std::string &path, const Headers &headers, const UploadFormDataItems &items, const std::string &boundary, UploadProgress progress = nullptr);
-  Result Post(const std::string &path, const Headers &headers, const UploadFormDataItems &items, const FormDataProviderItems &provider_items, UploadProgress progress = nullptr);
-  Result Post(const std::string &path, const Headers &headers, const std::string &body, const std::string &content_type, ContentReceiver content_receiver, DownloadProgress progress = nullptr);
+  Result Post(const std::string &path, const char *body, size_t content_length,
+              const std::string &content_type);
+  Result Post(const std::string &path, const Headers &headers, const char *body,
+              size_t content_length, const std::string &content_type);
+  Result Post(const std::string &path, const Headers &headers, const char *body,
+              size_t content_length, const std::string &content_type,
+              Progress progress);
+  Result Post(const std::string &path, const std::string &body,
+              const std::string &content_type);
+  Result Post(const std::string &path, const std::string &body,
+              const std::string &content_type, Progress progress);
+  Result Post(const std::string &path, const Headers &headers,
+              const std::string &body, const std::string &content_type);
+  Result Post(const std::string &path, const Headers &headers,
+              const std::string &body, const std::string &content_type,
+              Progress progress);
+  Result Post(const std::string &path, size_t content_length,
+              ContentProvider content_provider,
+              const std::string &content_type);
+  Result Post(const std::string &path,
+              ContentProviderWithoutLength content_provider,
+              const std::string &content_type);
+  Result Post(const std::string &path, const Headers &headers,
+              size_t content_length, ContentProvider content_provider,
+              const std::string &content_type);
+  Result Post(const std::string &path, const Headers &headers,
+              ContentProviderWithoutLength content_provider,
+              const std::string &content_type);
+  Result Post(const std::string &path, const Params &params);
+  Result Post(const std::string &path, const Headers &headers,
+              const Params &params);
+  Result Post(const std::string &path, const Headers &headers,
+              const Params &params, Progress progress);
+  Result Post(const std::string &path, const MultipartFormDataItems &items);
+  Result Post(const std::string &path, const Headers &headers,
+              const MultipartFormDataItems &items);
+  Result Post(const std::string &path, const Headers &headers,
+              const MultipartFormDataItems &items, const std::string &boundary);
+  Result Post(const std::string &path, const Headers &headers,
+              const MultipartFormDataItems &items,
+              const MultipartFormDataProviderItems &provider_items);
 
   Result Put(const std::string &path);
-  Result Put(const std::string &path, const char *body, size_t content_length, const std::string &content_type, UploadProgress progress = nullptr);
-  Result Put(const std::string &path, const std::string &body, const std::string &content_type, UploadProgress progress = nullptr);
-  Result Put(const std::string &path, size_t content_length, ContentProvider content_provider, const std::string &content_type, UploadProgress progress = nullptr);
-  Result Put(const std::string &path, ContentProviderWithoutLength content_provider, const std::string &content_type, UploadProgress progress = nullptr);
+  Result Put(const std::string &path, const char *body, size_t content_length,
+             const std::string &content_type);
+  Result Put(const std::string &path, const Headers &headers, const char *body,
+             size_t content_length, const std::string &content_type);
+  Result Put(const std::string &path, const Headers &headers, const char *body,
+             size_t content_length, const std::string &content_type,
+             Progress progress);
+  Result Put(const std::string &path, const std::string &body,
+             const std::string &content_type);
+  Result Put(const std::string &path, const std::string &body,
+             const std::string &content_type, Progress progress);
+  Result Put(const std::string &path, const Headers &headers,
+             const std::string &body, const std::string &content_type);
+  Result Put(const std::string &path, const Headers &headers,
+             const std::string &body, const std::string &content_type,
+             Progress progress);
+  Result Put(const std::string &path, size_t content_length,
+             ContentProvider content_provider, const std::string &content_type);
+  Result Put(const std::string &path,
+             ContentProviderWithoutLength content_provider,
+             const std::string &content_type);
+  Result Put(const std::string &path, const Headers &headers,
+             size_t content_length, ContentProvider content_provider,
+             const std::string &content_type);
+  Result Put(const std::string &path, const Headers &headers,
+             ContentProviderWithoutLength content_provider,
+             const std::string &content_type);
   Result Put(const std::string &path, const Params &params);
-  Result Put(const std::string &path, const UploadFormDataItems &items, UploadProgress progress = nullptr);
-  Result Put(const std::string &path, const Headers &headers);
-  Result Put(const std::string &path, const Headers &headers, const char *body, size_t content_length, const std::string &content_type, UploadProgress progress = nullptr);
-  Result Put(const std::string &path, const Headers &headers, const std::string &body, const std::string &content_type, UploadProgress progress = nullptr);
-  Result Put(const std::string &path, const Headers &headers, size_t content_length, ContentProvider content_provider, const std::string &content_type, UploadProgress progress = nullptr);
-  Result Put(const std::string &path, const Headers &headers, ContentProviderWithoutLength content_provider, const std::string &content_type, UploadProgress progress = nullptr);
-  Result Put(const std::string &path, const Headers &headers, const Params &params);
-  Result Put(const std::string &path, const Headers &headers, const UploadFormDataItems &items, UploadProgress progress = nullptr);
-  Result Put(const std::string &path, const Headers &headers, const UploadFormDataItems &items, const std::string &boundary, UploadProgress progress = nullptr);
-  Result Put(const std::string &path, const Headers &headers, const UploadFormDataItems &items, const FormDataProviderItems &provider_items, UploadProgress progress = nullptr);
-  Result Put(const std::string &path, const Headers &headers, const std::string &body, const std::string &content_type, ContentReceiver content_receiver, DownloadProgress progress = nullptr);
+  Result Put(const std::string &path, const Headers &headers,
+             const Params &params);
+  Result Put(const std::string &path, const Headers &headers,
+             const Params &params, Progress progress);
+  Result Put(const std::string &path, const MultipartFormDataItems &items);
+  Result Put(const std::string &path, const Headers &headers,
+             const MultipartFormDataItems &items);
+  Result Put(const std::string &path, const Headers &headers,
+             const MultipartFormDataItems &items, const std::string &boundary);
+  Result Put(const std::string &path, const Headers &headers,
+             const MultipartFormDataItems &items,
+             const MultipartFormDataProviderItems &provider_items);
 
   Result Patch(const std::string &path);
-  Result Patch(const std::string &path, const char *body, size_t content_length, const std::string &content_type, UploadProgress progress = nullptr);
-  Result Patch(const std::string &path, const std::string &body, const std::string &content_type, UploadProgress progress = nullptr);
-  Result Patch(const std::string &path, size_t content_length, ContentProvider content_provider, const std::string &content_type, UploadProgress progress = nullptr);
-  Result Patch(const std::string &path, ContentProviderWithoutLength content_provider, const std::string &content_type, UploadProgress progress = nullptr);
-  Result Patch(const std::string &path, const Params &params);
-  Result Patch(const std::string &path, const UploadFormDataItems &items, UploadProgress progress = nullptr);
-  Result Patch(const std::string &path, const Headers &headers);
-  Result Patch(const std::string &path, const Headers &headers, const char *body, size_t content_length, const std::string &content_type, UploadProgress progress = nullptr);
-  Result Patch(const std::string &path, const Headers &headers, const std::string &body, const std::string &content_type, UploadProgress progress = nullptr);
-  Result Patch(const std::string &path, const Headers &headers, size_t content_length, ContentProvider content_provider, const std::string &content_type, UploadProgress progress = nullptr);
-  Result Patch(const std::string &path, const Headers &headers, ContentProviderWithoutLength content_provider, const std::string &content_type, UploadProgress progress = nullptr);
-  Result Patch(const std::string &path, const Headers &headers, const Params &params);
-  Result Patch(const std::string &path, const Headers &headers, const UploadFormDataItems &items, UploadProgress progress = nullptr);
-  Result Patch(const std::string &path, const Headers &headers, const UploadFormDataItems &items, const std::string &boundary, UploadProgress progress = nullptr);
-  Result Patch(const std::string &path, const Headers &headers, const UploadFormDataItems &items, const FormDataProviderItems &provider_items, UploadProgress progress = nullptr);
-  Result Patch(const std::string &path, const Headers &headers, const std::string &body, const std::string &content_type, ContentReceiver content_receiver, DownloadProgress progress = nullptr);
-
-  Result Delete(const std::string &path, DownloadProgress progress = nullptr);
-  Result Delete(const std::string &path, const char *body, size_t content_length, const std::string &content_type, DownloadProgress progress = nullptr);
-  Result Delete(const std::string &path, const std::string &body, const std::string &content_type, DownloadProgress progress = nullptr);
-  Result Delete(const std::string &path, const Params &params, DownloadProgress progress = nullptr);
-  Result Delete(const std::string &path, const Headers &headers, DownloadProgress progress = nullptr);
-  Result Delete(const std::string &path, const Headers &headers, const char *body, size_t content_length, const std::string &content_type, DownloadProgress progress = nullptr);
-  Result Delete(const std::string &path, const Headers &headers, const std::string &body, const std::string &content_type, DownloadProgress progress = nullptr);
-  Result Delete(const std::string &path, const Headers &headers, const Params &params, DownloadProgress progress = nullptr);
+  Result Patch(const std::string &path, const char *body, size_t content_length,
+               const std::string &content_type);
+  Result Patch(const std::string &path, const char *body, size_t content_length,
+               const std::string &content_type, Progress progress);
+  Result Patch(const std::string &path, const Headers &headers,
+               const char *body, size_t content_length,
+               const std::string &content_type);
+  Result Patch(const std::string &path, const Headers &headers,
+               const char *body, size_t content_length,
+               const std::string &content_type, Progress progress);
+  Result Patch(const std::string &path, const std::string &body,
+               const std::string &content_type);
+  Result Patch(const std::string &path, const std::string &body,
+               const std::string &content_type, Progress progress);
+  Result Patch(const std::string &path, const Headers &headers,
+               const std::string &body, const std::string &content_type);
+  Result Patch(const std::string &path, const Headers &headers,
+               const std::string &body, const std::string &content_type,
+               Progress progress);
+  Result Patch(const std::string &path, size_t content_length,
+               ContentProvider content_provider,
+               const std::string &content_type);
+  Result Patch(const std::string &path,
+               ContentProviderWithoutLength content_provider,
+               const std::string &content_type);
+  Result Patch(const std::string &path, const Headers &headers,
+               size_t content_length, ContentProvider content_provider,
+               const std::string &content_type);
+  Result Patch(const std::string &path, const Headers &headers,
+               ContentProviderWithoutLength content_provider,
+               const std::string &content_type);
+
+  Result Delete(const std::string &path);
+  Result Delete(const std::string &path, const Headers &headers);
+  Result Delete(const std::string &path, const char *body,
+                size_t content_length, const std::string &content_type);
+  Result Delete(const std::string &path, const char *body,
+                size_t content_length, const std::string &content_type,
+                Progress progress);
+  Result Delete(const std::string &path, const Headers &headers,
+                const char *body, size_t content_length,
+                const std::string &content_type);
+  Result Delete(const std::string &path, const Headers &headers,
+                const char *body, size_t content_length,
+                const std::string &content_type, Progress progress);
+  Result Delete(const std::string &path, const std::string &body,
+                const std::string &content_type);
+  Result Delete(const std::string &path, const std::string &body,
+                const std::string &content_type, Progress progress);
+  Result Delete(const std::string &path, const Headers &headers,
+                const std::string &body, const std::string &content_type);
+  Result Delete(const std::string &path, const Headers &headers,
+                const std::string &body, const std::string &content_type,
+                Progress progress);
 
   Result Options(const std::string &path);
   Result Options(const std::string &path, const Headers &headers);
-  // clang-format on
 
   bool send(Request &req, Response &res, Error &error);
   Result send(const Request &req);
@@ -1887,7 +1907,6 @@ class Client {
   void set_keep_alive(bool on);
   void set_follow_location(bool on);
 
-  void set_path_encode(bool on);
   void set_url_encode(bool on);
 
   void set_compress(bool on);
@@ -1913,7 +1932,6 @@ class Client {
 #endif
 
   void set_logger(Logger logger);
-  void set_error_logger(ErrorLogger error_logger);
 
   // SSL
 #ifdef CPPHTTPLIB_OPENSSL_SUPPORT
@@ -1959,17 +1977,11 @@ class SSLServer : public Server {
   void update_certs(X509 *cert, EVP_PKEY *private_key,
                     X509_STORE *client_ca_cert_store = nullptr);
 
-  int ssl_last_error() const { return last_ssl_error_; }
-
 private:
   bool process_and_close_socket(socket_t sock) override;
 
-  STACK_OF(X509_NAME) * extract_ca_names_from_x509_store(X509_STORE *store);
-
   SSL_CTX *ctx_;
   std::mutex ctx_mutex_;
-
-  int last_ssl_error_ = 0;
 };
 
 class SSLClient final : public ClientImpl {
@@ -2054,14 +2066,12 @@ template <size_t N> inline constexpr size_t str_len(const char (&)[N]) {
 }
 
 inline bool is_numeric(const std::string &str) {
-  return !str.empty() &&
-         std::all_of(str.cbegin(), str.cend(),
-                     [](unsigned char c) { return std::isdigit(c); });
+  return !str.empty() && std::all_of(str.begin(), str.end(), ::isdigit);
 }
 
-inline size_t get_header_value_u64(const Headers &headers,
-                                   const std::string &key, size_t def,
-                                   size_t id, bool &is_invalid_value) {
+inline uint64_t get_header_value_u64(const Headers &headers,
+                                     const std::string &key, uint64_t def,
+                                     size_t id, bool &is_invalid_value) {
   is_invalid_value = false;
   auto rng = headers.equal_range(key);
   auto it = rng.first;
@@ -2076,22 +2086,22 @@ inline size_t get_header_value_u64(const Headers &headers,
   return def;
 }
 
-inline size_t get_header_value_u64(const Headers &headers,
-                                   const std::string &key, size_t def,
-                                   size_t id) {
-  auto dummy = false;
+inline uint64_t get_header_value_u64(const Headers &headers,
+                                     const std::string &key, uint64_t def,
+                                     size_t id) {
+  bool dummy = false;
   return get_header_value_u64(headers, key, def, id, dummy);
 }
 
 } // namespace detail
 
-inline size_t Request::get_header_value_u64(const std::string &key, size_t def,
-                                            size_t id) const {
+inline uint64_t Request::get_header_value_u64(const std::string &key,
+                                              uint64_t def, size_t id) const {
   return detail::get_header_value_u64(headers, key, def, id);
 }
 
-inline size_t Response::get_header_value_u64(const std::string &key, size_t def,
-                                             size_t id) const {
+inline uint64_t Response::get_header_value_u64(const std::string &key,
+                                               uint64_t def, size_t id) const {
   return detail::get_header_value_u64(headers, key, def, id);
 }
 
@@ -2248,7 +2258,6 @@ Server::set_idle_interval(const std::chrono::duration<Rep, Period> &duration) {
 inline std::string to_string(const Error error) {
   switch (error) {
   case Error::Success: return "Success (no error)";
-  case Error::Unknown: return "Unknown";
   case Error::Connection: return "Could not establish connection";
   case Error::BindIPAddress: return "Failed to bind IP address";
   case Error::Read: return "Failed to read connection";
@@ -2265,23 +2274,7 @@ inline std::string to_string(const Error error) {
   case Error::Compression: return "Compression failed";
   case Error::ConnectionTimeout: return "Connection timed out";
   case Error::ProxyConnection: return "Proxy connection failed";
-  case Error::ResourceExhaustion: return "Resource exhaustion";
-  case Error::TooManyFormDataFiles: return "Too many form data files";
-  case Error::ExceedMaxPayloadSize: return "Exceeded maximum payload size";
-  case Error::ExceedUriMaxLength: return "Exceeded maximum URI length";
-  case Error::ExceedMaxSocketDescriptorCount:
-    return "Exceeded maximum socket descriptor count";
-  case Error::InvalidRequestLine: return "Invalid request line";
-  case Error::InvalidHTTPMethod: return "Invalid HTTP method";
-  case Error::InvalidHTTPVersion: return "Invalid HTTP version";
-  case Error::InvalidHeaders: return "Invalid headers";
-  case Error::MultipartParsing: return "Multipart parsing failed";
-  case Error::OpenFile: return "Failed to open file";
-  case Error::Listen: return "Failed to listen on socket";
-  case Error::GetSockName: return "Failed to get socket name";
-  case Error::UnsupportedAddressFamily: return "Unsupported address family";
-  case Error::HTTPParsing: return "HTTP parsing failed";
-  case Error::InvalidRangeHeader: return "Invalid Range header";
+  case Error::Unknown: return "Unknown";
   default: break;
   }
 
@@ -2294,9 +2287,9 @@ inline std::ostream &operator<<(std::ostream &os, const Error &obj) {
   return os;
 }
 
-inline size_t Result::get_request_header_value_u64(const std::string &key,
-                                                   size_t def,
-                                                   size_t id) const {
+inline uint64_t Result::get_request_header_value_u64(const std::string &key,
+                                                     uint64_t def,
+                                                     size_t id) const {
   return detail::get_header_value_u64(request_headers_, key, def, id);
 }
 
@@ -2348,10 +2341,6 @@ Client::set_write_timeout(const std::chrono::duration<Rep, Period> &duration) {
   cli_->set_write_timeout(duration);
 }
 
-inline void Client::set_max_timeout(time_t msec) {
-  cli_->set_max_timeout(msec);
-}
-
 template <class Rep, class Period>
 inline void
 Client::set_max_timeout(const std::chrono::duration<Rep, Period> &duration) {
@@ -2367,20 +2356,6 @@ std::string hosted_at(const std::string &hostname);
 
 void hosted_at(const std::string &hostname, std::vector<std::string> &addrs);
 
-// JavaScript-style URL encoding/decoding functions
-std::string encode_uri_component(const std::string &value);
-std::string encode_uri(const std::string &value);
-std::string decode_uri_component(const std::string &value);
-std::string decode_uri(const std::string &value);
-
-// RFC 3986 compliant URL component encoding/decoding functions
-std::string encode_path_component(const std::string &component);
-std::string decode_path_component(const std::string &component);
-std::string encode_query_component(const std::string &component,
-                                   bool space_as_plus = true);
-std::string decode_query_component(const std::string &component,
-                                   bool plus_as_space = true);
-
 std::string append_query_params(const std::string &path, const Params &params);
 
 std::pair<std::string, std::string> make_range_header(const Ranges &ranges);
@@ -2422,6 +2397,10 @@ struct FileStat {
   int ret_ = -1;
 };
 
+std::string encode_query_param(const std::string &value);
+
+std::string decode_url(const std::string &s, bool convert_plus_to_space);
+
 std::string trim_copy(const std::string &s);
 
 void divide(
@@ -2471,9 +2450,6 @@ bool parse_multipart_boundary(const std::string &content_type,
 
 bool parse_range_header(const std::string &s, Ranges &ranges);
 
-bool parse_accept_header(const std::string &s,
-                         std::vector<std::string> &content_types);
-
 int close_socket(socket_t sock);
 
 ssize_t send_socket(socket_t sock, const void *ptr, size_t size, int flags);
@@ -2722,9343 +2698,7 @@ inline bool is_field_value(const std::string &s) { return is_field_content(s); }
 
 } // namespace detail
 
-// ----------------------------------------------------------------------------
-
-/*
- * Implementation that will be part of the .cc file if split into .h + .cc.
- */
-
-namespace detail {
-
-inline bool is_hex(char c, int &v) {
-  if (0x20 <= c && isdigit(c)) {
-    v = c - '0';
-    return true;
-  } else if ('A' <= c && c <= 'F') {
-    v = c - 'A' + 10;
-    return true;
-  } else if ('a' <= c && c <= 'f') {
-    v = c - 'a' + 10;
-    return true;
-  }
-  return false;
-}
-
-inline bool from_hex_to_i(const std::string &s, size_t i, size_t cnt,
-                          int &val) {
-  if (i >= s.size()) { return false; }
-
-  val = 0;
-  for (; cnt; i++, cnt--) {
-    if (!s[i]) { return false; }
-    auto v = 0;
-    if (is_hex(s[i], v)) {
-      val = val * 16 + v;
-    } else {
-      return false;
-    }
-  }
-  return true;
-}
-
-inline std::string from_i_to_hex(size_t n) {
-  static const auto charset = "0123456789abcdef";
-  std::string ret;
-  do {
-    ret = charset[n & 15] + ret;
-    n >>= 4;
-  } while (n > 0);
-  return ret;
-}
-
-inline size_t to_utf8(int code, char *buff) {
-  if (code < 0x0080) {
-    buff[0] = static_cast<char>(code & 0x7F);
-    return 1;
-  } else if (code < 0x0800) {
-    buff[0] = static_cast<char>(0xC0 | ((code >> 6) & 0x1F));
-    buff[1] = static_cast<char>(0x80 | (code & 0x3F));
-    return 2;
-  } else if (code < 0xD800) {
-    buff[0] = static_cast<char>(0xE0 | ((code >> 12) & 0xF));
-    buff[1] = static_cast<char>(0x80 | ((code >> 6) & 0x3F));
-    buff[2] = static_cast<char>(0x80 | (code & 0x3F));
-    return 3;
-  } else if (code < 0xE000) { // D800 - DFFF is invalid...
-    return 0;
-  } else if (code < 0x10000) {
-    buff[0] = static_cast<char>(0xE0 | ((code >> 12) & 0xF));
-    buff[1] = static_cast<char>(0x80 | ((code >> 6) & 0x3F));
-    buff[2] = static_cast<char>(0x80 | (code & 0x3F));
-    return 3;
-  } else if (code < 0x110000) {
-    buff[0] = static_cast<char>(0xF0 | ((code >> 18) & 0x7));
-    buff[1] = static_cast<char>(0x80 | ((code >> 12) & 0x3F));
-    buff[2] = static_cast<char>(0x80 | ((code >> 6) & 0x3F));
-    buff[3] = static_cast<char>(0x80 | (code & 0x3F));
-    return 4;
-  }
-
-  // NOTREACHED
-  return 0;
-}
-
-// NOTE: This code came up with the following stackoverflow post:
-// https://stackoverflow.com/questions/180947/base64-decode-snippet-in-c
-inline std::string base64_encode(const std::string &in) {
-  static const auto lookup =
-      "ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
-
-  std::string out;
-  out.reserve(in.size());
-
-  auto val = 0;
-  auto valb = -6;
-
-  for (auto c : in) {
-    val = (val << 8) + static_cast<uint8_t>(c);
-    valb += 8;
-    while (valb >= 0) {
-      out.push_back(lookup[(val >> valb) & 0x3F]);
-      valb -= 6;
-    }
-  }
-
-  if (valb > -6) { out.push_back(lookup[((val << 8) >> (valb + 8)) & 0x3F]); }
-
-  while (out.size() % 4) {
-    out.push_back('=');
-  }
-
-  return out;
-}
-
-inline bool is_valid_path(const std::string &path) {
-  size_t level = 0;
-  size_t i = 0;
-
-  // Skip slash
-  while (i < path.size() && path[i] == '/') {
-    i++;
-  }
-
-  while (i < path.size()) {
-    // Read component
-    auto beg = i;
-    while (i < path.size() && path[i] != '/') {
-      if (path[i] == '\0') {
-        return false;
-      } else if (path[i] == '\\') {
-        return false;
-      }
-      i++;
-    }
-
-    auto len = i - beg;
-    assert(len > 0);
-
-    if (!path.compare(beg, len, ".")) {
-      ;
-    } else if (!path.compare(beg, len, "..")) {
-      if (level == 0) { return false; }
-      level--;
-    } else {
-      level++;
-    }
-
-    // Skip slash
-    while (i < path.size() && path[i] == '/') {
-      i++;
-    }
-  }
-
-  return true;
-}
-
-inline FileStat::FileStat(const std::string &path) {
-#if defined(_WIN32)
-  auto wpath = u8string_to_wstring(path.c_str());
-  ret_ = _wstat(wpath.c_str(), &st_);
-#else
-  ret_ = stat(path.c_str(), &st_);
-#endif
-}
-inline bool FileStat::is_file() const {
-  return ret_ >= 0 && S_ISREG(st_.st_mode);
-}
-inline bool FileStat::is_dir() const {
-  return ret_ >= 0 && S_ISDIR(st_.st_mode);
-}
-
-inline std::string encode_path(const std::string &s) {
-  std::string result;
-  result.reserve(s.size());
-
-  for (size_t i = 0; s[i]; i++) {
-    switch (s[i]) {
-    case ' ': result += "%20"; break;
-    case '+': result += "%2B"; break;
-    case '\r': result += "%0D"; break;
-    case '\n': result += "%0A"; break;
-    case '\'': result += "%27"; break;
-    case ',': result += "%2C"; break;
-    // case ':': result += "%3A"; break; // ok? probably...
-    case ';': result += "%3B"; break;
-    default:
-      auto c = static_cast<uint8_t>(s[i]);
-      if (c >= 0x80) {
-        result += '%';
-        char hex[4];
-        auto len = snprintf(hex, sizeof(hex) - 1, "%02X", c);
-        assert(len == 2);
-        result.append(hex, static_cast<size_t>(len));
-      } else {
-        result += s[i];
-      }
-      break;
-    }
-  }
-
-  return result;
-}
-
-inline std::string file_extension(const std::string &path) {
-  std::smatch m;
-  thread_local auto re = std::regex("\\.([a-zA-Z0-9]+)$");
-  if (std::regex_search(path, m, re)) { return m[1].str(); }
-  return std::string();
-}
-
-inline bool is_space_or_tab(char c) { return c == ' ' || c == '\t'; }
-
-inline std::pair<size_t, size_t> trim(const char *b, const char *e, size_t left,
-                                      size_t right) {
-  while (b + left < e && is_space_or_tab(b[left])) {
-    left++;
-  }
-  while (right > 0 && is_space_or_tab(b[right - 1])) {
-    right--;
-  }
-  return std::make_pair(left, right);
-}
-
-inline std::string trim_copy(const std::string &s) {
-  auto r = trim(s.data(), s.data() + s.size(), 0, s.size());
-  return s.substr(r.first, r.second - r.first);
-}
-
-inline std::string trim_double_quotes_copy(const std::string &s) {
-  if (s.length() >= 2 && s.front() == '"' && s.back() == '"') {
-    return s.substr(1, s.size() - 2);
-  }
-  return s;
-}
-
-inline void
-divide(const char *data, std::size_t size, char d,
-       std::function<void(const char *, std::size_t, const char *, std::size_t)>
-           fn) {
-  const auto it = std::find(data, data + size, d);
-  const auto found = static_cast<std::size_t>(it != data + size);
-  const auto lhs_data = data;
-  const auto lhs_size = static_cast<std::size_t>(it - data);
-  const auto rhs_data = it + found;
-  const auto rhs_size = size - lhs_size - found;
-
-  fn(lhs_data, lhs_size, rhs_data, rhs_size);
-}
-
-inline void
-divide(const std::string &str, char d,
-       std::function<void(const char *, std::size_t, const char *, std::size_t)>
-           fn) {
-  divide(str.data(), str.size(), d, std::move(fn));
-}
-
-inline void split(const char *b, const char *e, char d,
-                  std::function<void(const char *, const char *)> fn) {
-  return split(b, e, d, (std::numeric_limits<size_t>::max)(), std::move(fn));
-}
-
-inline void split(const char *b, const char *e, char d, size_t m,
-                  std::function<void(const char *, const char *)> fn) {
-  size_t i = 0;
-  size_t beg = 0;
-  size_t count = 1;
-
-  while (e ? (b + i < e) : (b[i] != '\0')) {
-    if (b[i] == d && count < m) {
-      auto r = trim(b, e, beg, i);
-      if (r.first < r.second) { fn(&b[r.first], &b[r.second]); }
-      beg = i + 1;
-      count++;
-    }
-    i++;
-  }
-
-  if (i) {
-    auto r = trim(b, e, beg, i);
-    if (r.first < r.second) { fn(&b[r.first], &b[r.second]); }
-  }
-}
-
-inline stream_line_reader::stream_line_reader(Stream &strm, char *fixed_buffer,
-                                              size_t fixed_buffer_size)
-    : strm_(strm), fixed_buffer_(fixed_buffer),
-      fixed_buffer_size_(fixed_buffer_size) {}
-
-inline const char *stream_line_reader::ptr() const {
-  if (growable_buffer_.empty()) {
-    return fixed_buffer_;
-  } else {
-    return growable_buffer_.data();
-  }
-}
-
-inline size_t stream_line_reader::size() const {
-  if (growable_buffer_.empty()) {
-    return fixed_buffer_used_size_;
-  } else {
-    return growable_buffer_.size();
-  }
-}
-
-inline bool stream_line_reader::end_with_crlf() const {
-  auto end = ptr() + size();
-  return size() >= 2 && end[-2] == '\r' && end[-1] == '\n';
-}
-
-inline bool stream_line_reader::getline() {
-  fixed_buffer_used_size_ = 0;
-  growable_buffer_.clear();
-
-#ifndef CPPHTTPLIB_ALLOW_LF_AS_LINE_TERMINATOR
-  char prev_byte = 0;
-#endif
-
-  for (size_t i = 0;; i++) {
-    if (size() >= CPPHTTPLIB_MAX_LINE_LENGTH) {
-      // Treat exceptionally long lines as an error to
-      // prevent infinite loops/memory exhaustion
-      return false;
-    }
-    char byte;
-    auto n = strm_.read(&byte, 1);
-
-    if (n < 0) {
-      return false;
-    } else if (n == 0) {
-      if (i == 0) {
-        return false;
-      } else {
-        break;
-      }
-    }
-
-    append(byte);
-
-#ifdef CPPHTTPLIB_ALLOW_LF_AS_LINE_TERMINATOR
-    if (byte == '\n') { break; }
-#else
-    if (prev_byte == '\r' && byte == '\n') { break; }
-    prev_byte = byte;
-#endif
-  }
-
-  return true;
-}
-
-inline void stream_line_reader::append(char c) {
-  if (fixed_buffer_used_size_ < fixed_buffer_size_ - 1) {
-    fixed_buffer_[fixed_buffer_used_size_++] = c;
-    fixed_buffer_[fixed_buffer_used_size_] = '\0';
-  } else {
-    if (growable_buffer_.empty()) {
-      assert(fixed_buffer_[fixed_buffer_used_size_] == '\0');
-      growable_buffer_.assign(fixed_buffer_, fixed_buffer_used_size_);
-    }
-    growable_buffer_ += c;
-  }
-}
-
-inline mmap::mmap(const char *path) { open(path); }
-
-inline mmap::~mmap() { close(); }
-
-inline bool mmap::open(const char *path) {
-  close();
-
-#if defined(_WIN32)
-  auto wpath = u8string_to_wstring(path);
-  if (wpath.empty()) { return false; }
-
-  hFile_ = ::CreateFile2(wpath.c_str(), GENERIC_READ, FILE_SHARE_READ,
-                         OPEN_EXISTING, NULL);
-
-  if (hFile_ == INVALID_HANDLE_VALUE) { return false; }
-
-  LARGE_INTEGER size{};
-  if (!::GetFileSizeEx(hFile_, &size)) { return false; }
-  // If the following line doesn't compile due to QuadPart, update Windows SDK.
-  // See:
-  // https://github.com/yhirose/cpp-httplib/issues/1903#issuecomment-2316520721
-  if (static_cast<ULONGLONG>(size.QuadPart) >
-      (std::numeric_limits<decltype(size_)>::max)()) {
-    // `size_t` might be 32-bits, on 32-bits Windows.
-    return false;
-  }
-  size_ = static_cast<size_t>(size.QuadPart);
-
-  hMapping_ =
-      ::CreateFileMappingFromApp(hFile_, NULL, PAGE_READONLY, size_, NULL);
-
-  // Special treatment for an empty file...
-  if (hMapping_ == NULL && size_ == 0) {
-    close();
-    is_open_empty_file = true;
-    return true;
-  }
-
-  if (hMapping_ == NULL) {
-    close();
-    return false;
-  }
-
-  addr_ = ::MapViewOfFileFromApp(hMapping_, FILE_MAP_READ, 0, 0);
-
-  if (addr_ == nullptr) {
-    close();
-    return false;
-  }
-#else
-  fd_ = ::open(path, O_RDONLY);
-  if (fd_ == -1) { return false; }
-
-  struct stat sb;
-  if (fstat(fd_, &sb) == -1) {
-    close();
-    return false;
-  }
-  size_ = static_cast<size_t>(sb.st_size);
-
-  addr_ = ::mmap(NULL, size_, PROT_READ, MAP_PRIVATE, fd_, 0);
-
-  // Special treatment for an empty file...
-  if (addr_ == MAP_FAILED && size_ == 0) {
-    close();
-    is_open_empty_file = true;
-    return false;
-  }
-#endif
-
-  return true;
-}
-
-inline bool mmap::is_open() const {
-  return is_open_empty_file ? true : addr_ != nullptr;
-}
-
-inline size_t mmap::size() const { return size_; }
-
-inline const char *mmap::data() const {
-  return is_open_empty_file ? "" : static_cast<const char *>(addr_);
-}
-
-inline void mmap::close() {
-#if defined(_WIN32)
-  if (addr_) {
-    ::UnmapViewOfFile(addr_);
-    addr_ = nullptr;
-  }
-
-  if (hMapping_) {
-    ::CloseHandle(hMapping_);
-    hMapping_ = NULL;
-  }
-
-  if (hFile_ != INVALID_HANDLE_VALUE) {
-    ::CloseHandle(hFile_);
-    hFile_ = INVALID_HANDLE_VALUE;
-  }
-
-  is_open_empty_file = false;
-#else
-  if (addr_ != nullptr) {
-    munmap(addr_, size_);
-    addr_ = nullptr;
-  }
-
-  if (fd_ != -1) {
-    ::close(fd_);
-    fd_ = -1;
-  }
-#endif
-  size_ = 0;
-}
-inline int close_socket(socket_t sock) {
-#ifdef _WIN32
-  return closesocket(sock);
-#else
-  return close(sock);
-#endif
-}
-
-template <typename T> inline ssize_t handle_EINTR(T fn) {
-  ssize_t res = 0;
-  while (true) {
-    res = fn();
-    if (res < 0 && errno == EINTR) {
-      std::this_thread::sleep_for(std::chrono::microseconds{1});
-      continue;
-    }
-    break;
-  }
-  return res;
-}
-
-inline ssize_t read_socket(socket_t sock, void *ptr, size_t size, int flags) {
-  return handle_EINTR([&]() {
-    return recv(sock,
-#ifdef _WIN32
-                static_cast<char *>(ptr), static_cast<int>(size),
-#else
-                ptr, size,
-#endif
-                flags);
-  });
-}
-
-inline ssize_t send_socket(socket_t sock, const void *ptr, size_t size,
-                           int flags) {
-  return handle_EINTR([&]() {
-    return send(sock,
-#ifdef _WIN32
-                static_cast<const char *>(ptr), static_cast<int>(size),
-#else
-                ptr, size,
-#endif
-                flags);
-  });
-}
-
-inline int poll_wrapper(struct pollfd *fds, nfds_t nfds, int timeout) {
-#ifdef _WIN32
-  return ::WSAPoll(fds, nfds, timeout);
-#else
-  return ::poll(fds, nfds, timeout);
-#endif
-}
-
-template <bool Read>
-inline ssize_t select_impl(socket_t sock, time_t sec, time_t usec) {
-#ifdef __APPLE__
-  if (sock >= FD_SETSIZE) { return -1; }
-
-  fd_set fds, *rfds, *wfds;
-  FD_ZERO(&fds);
-  FD_SET(sock, &fds);
-  rfds = (Read ? &fds : nullptr);
-  wfds = (Read ? nullptr : &fds);
-
-  timeval tv;
-  tv.tv_sec = static_cast<long>(sec);
-  tv.tv_usec = static_cast<decltype(tv.tv_usec)>(usec);
-
-  return handle_EINTR([&]() {
-    return select(static_cast<int>(sock + 1), rfds, wfds, nullptr, &tv);
-  });
-#else
-  struct pollfd pfd;
-  pfd.fd = sock;
-  pfd.events = (Read ? POLLIN : POLLOUT);
-
-  auto timeout = static_cast<int>(sec * 1000 + usec / 1000);
-
-  return handle_EINTR([&]() { return poll_wrapper(&pfd, 1, timeout); });
-#endif
-}
-
-inline ssize_t select_read(socket_t sock, time_t sec, time_t usec) {
-  return select_impl<true>(sock, sec, usec);
-}
-
-inline ssize_t select_write(socket_t sock, time_t sec, time_t usec) {
-  return select_impl<false>(sock, sec, usec);
-}
-
-inline Error wait_until_socket_is_ready(socket_t sock, time_t sec,
-                                        time_t usec) {
-#ifdef __APPLE__
-  if (sock >= FD_SETSIZE) { return Error::Connection; }
-
-  fd_set fdsr, fdsw;
-  FD_ZERO(&fdsr);
-  FD_ZERO(&fdsw);
-  FD_SET(sock, &fdsr);
-  FD_SET(sock, &fdsw);
-
-  timeval tv;
-  tv.tv_sec = static_cast<long>(sec);
-  tv.tv_usec = static_cast<decltype(tv.tv_usec)>(usec);
-
-  auto ret = handle_EINTR([&]() {
-    return select(static_cast<int>(sock + 1), &fdsr, &fdsw, nullptr, &tv);
-  });
-
-  if (ret == 0) { return Error::ConnectionTimeout; }
-
-  if (ret > 0 && (FD_ISSET(sock, &fdsr) || FD_ISSET(sock, &fdsw))) {
-    auto error = 0;
-    socklen_t len = sizeof(error);
-    auto res = getsockopt(sock, SOL_SOCKET, SO_ERROR,
-                          reinterpret_cast<char *>(&error), &len);
-    auto successful = res >= 0 && !error;
-    return successful ? Error::Success : Error::Connection;
-  }
-
-  return Error::Connection;
-#else
-  struct pollfd pfd_read;
-  pfd_read.fd = sock;
-  pfd_read.events = POLLIN | POLLOUT;
-
-  auto timeout = static_cast<int>(sec * 1000 + usec / 1000);
-
-  auto poll_res =
-      handle_EINTR([&]() { return poll_wrapper(&pfd_read, 1, timeout); });
-
-  if (poll_res == 0) { return Error::ConnectionTimeout; }
-
-  if (poll_res > 0 && pfd_read.revents & (POLLIN | POLLOUT)) {
-    auto error = 0;
-    socklen_t len = sizeof(error);
-    auto res = getsockopt(sock, SOL_SOCKET, SO_ERROR,
-                          reinterpret_cast<char *>(&error), &len);
-    auto successful = res >= 0 && !error;
-    return successful ? Error::Success : Error::Connection;
-  }
-
-  return Error::Connection;
-#endif
-}
-
-inline bool is_socket_alive(socket_t sock) {
-  const auto val = detail::select_read(sock, 0, 0);
-  if (val == 0) {
-    return true;
-  } else if (val < 0 && errno == EBADF) {
-    return false;
-  }
-  char buf[1];
-  return detail::read_socket(sock, &buf[0], sizeof(buf), MSG_PEEK) > 0;
-}
-
-class SocketStream final : public Stream {
-public:
-  SocketStream(socket_t sock, time_t read_timeout_sec, time_t read_timeout_usec,
-               time_t write_timeout_sec, time_t write_timeout_usec,
-               time_t max_timeout_msec = 0,
-               std::chrono::time_point<std::chrono::steady_clock> start_time =
-                   (std::chrono::steady_clock::time_point::min)());
-  ~SocketStream() override;
-
-  bool is_readable() const override;
-  bool wait_readable() const override;
-  bool wait_writable() const override;
-  ssize_t read(char *ptr, size_t size) override;
-  ssize_t write(const char *ptr, size_t size) override;
-  void get_remote_ip_and_port(std::string &ip, int &port) const override;
-  void get_local_ip_and_port(std::string &ip, int &port) const override;
-  socket_t socket() const override;
-  time_t duration() const override;
-
-private:
-  socket_t sock_;
-  time_t read_timeout_sec_;
-  time_t read_timeout_usec_;
-  time_t write_timeout_sec_;
-  time_t write_timeout_usec_;
-  time_t max_timeout_msec_;
-  const std::chrono::time_point<std::chrono::steady_clock> start_time_;
-
-  std::vector<char> read_buff_;
-  size_t read_buff_off_ = 0;
-  size_t read_buff_content_size_ = 0;
-
-  static const size_t read_buff_size_ = 1024l * 4;
-};
-
-#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
-class SSLSocketStream final : public Stream {
-public:
-  SSLSocketStream(
-      socket_t sock, SSL *ssl, time_t read_timeout_sec,
-      time_t read_timeout_usec, time_t write_timeout_sec,
-      time_t write_timeout_usec, time_t max_timeout_msec = 0,
-      std::chrono::time_point<std::chrono::steady_clock> start_time =
-          (std::chrono::steady_clock::time_point::min)());
-  ~SSLSocketStream() override;
-
-  bool is_readable() const override;
-  bool wait_readable() const override;
-  bool wait_writable() const override;
-  ssize_t read(char *ptr, size_t size) override;
-  ssize_t write(const char *ptr, size_t size) override;
-  void get_remote_ip_and_port(std::string &ip, int &port) const override;
-  void get_local_ip_and_port(std::string &ip, int &port) const override;
-  socket_t socket() const override;
-  time_t duration() const override;
-
-private:
-  socket_t sock_;
-  SSL *ssl_;
-  time_t read_timeout_sec_;
-  time_t read_timeout_usec_;
-  time_t write_timeout_sec_;
-  time_t write_timeout_usec_;
-  time_t max_timeout_msec_;
-  const std::chrono::time_point<std::chrono::steady_clock> start_time_;
-};
-#endif
-
-inline bool keep_alive(const std::atomic<socket_t> &svr_sock, socket_t sock,
-                       time_t keep_alive_timeout_sec) {
-  using namespace std::chrono;
-
-  const auto interval_usec =
-      CPPHTTPLIB_KEEPALIVE_TIMEOUT_CHECK_INTERVAL_USECOND;
-
-  // Avoid expensive `steady_clock::now()` call for the first time
-  if (select_read(sock, 0, interval_usec) > 0) { return true; }
-
-  const auto start = steady_clock::now() - microseconds{interval_usec};
-  const auto timeout = seconds{keep_alive_timeout_sec};
-
-  while (true) {
-    if (svr_sock == INVALID_SOCKET) {
-      break; // Server socket is closed
-    }
-
-    auto val = select_read(sock, 0, interval_usec);
-    if (val < 0) {
-      break; // Ssocket error
-    } else if (val == 0) {
-      if (steady_clock::now() - start > timeout) {
-        break; // Timeout
-      }
-    } else {
-      return true; // Ready for read
-    }
-  }
-
-  return false;
-}
-
-template <typename T>
-inline bool
-process_server_socket_core(const std::atomic<socket_t> &svr_sock, socket_t sock,
-                           size_t keep_alive_max_count,
-                           time_t keep_alive_timeout_sec, T callback) {
-  assert(keep_alive_max_count > 0);
-  auto ret = false;
-  auto count = keep_alive_max_count;
-  while (count > 0 && keep_alive(svr_sock, sock, keep_alive_timeout_sec)) {
-    auto close_connection = count == 1;
-    auto connection_closed = false;
-    ret = callback(close_connection, connection_closed);
-    if (!ret || connection_closed) { break; }
-    count--;
-  }
-  return ret;
-}
-
-template <typename T>
-inline bool
-process_server_socket(const std::atomic<socket_t> &svr_sock, socket_t sock,
-                      size_t keep_alive_max_count,
-                      time_t keep_alive_timeout_sec, time_t read_timeout_sec,
-                      time_t read_timeout_usec, time_t write_timeout_sec,
-                      time_t write_timeout_usec, T callback) {
-  return process_server_socket_core(
-      svr_sock, sock, keep_alive_max_count, keep_alive_timeout_sec,
-      [&](bool close_connection, bool &connection_closed) {
-        SocketStream strm(sock, read_timeout_sec, read_timeout_usec,
-                          write_timeout_sec, write_timeout_usec);
-        return callback(strm, close_connection, connection_closed);
-      });
-}
-
-inline bool process_client_socket(
-    socket_t sock, time_t read_timeout_sec, time_t read_timeout_usec,
-    time_t write_timeout_sec, time_t write_timeout_usec,
-    time_t max_timeout_msec,
-    std::chrono::time_point<std::chrono::steady_clock> start_time,
-    std::function<bool(Stream &)> callback) {
-  SocketStream strm(sock, read_timeout_sec, read_timeout_usec,
-                    write_timeout_sec, write_timeout_usec, max_timeout_msec,
-                    start_time);
-  return callback(strm);
-}
-
-inline int shutdown_socket(socket_t sock) {
-#ifdef _WIN32
-  return shutdown(sock, SD_BOTH);
-#else
-  return shutdown(sock, SHUT_RDWR);
-#endif
-}
-
-inline std::string escape_abstract_namespace_unix_domain(const std::string &s) {
-  if (s.size() > 1 && s[0] == '\0') {
-    auto ret = s;
-    ret[0] = '@';
-    return ret;
-  }
-  return s;
-}
-
-inline std::string
-unescape_abstract_namespace_unix_domain(const std::string &s) {
-  if (s.size() > 1 && s[0] == '@') {
-    auto ret = s;
-    ret[0] = '\0';
-    return ret;
-  }
-  return s;
-}
-
-inline int getaddrinfo_with_timeout(const char *node, const char *service,
-                                    const struct addrinfo *hints,
-                                    struct addrinfo **res, time_t timeout_sec) {
-#ifdef CPPHTTPLIB_USE_NON_BLOCKING_GETADDRINFO
-  if (timeout_sec <= 0) {
-    // No timeout specified, use standard getaddrinfo
-    return getaddrinfo(node, service, hints, res);
-  }
-
-#ifdef _WIN32
-  // Windows-specific implementation using GetAddrInfoEx with overlapped I/O
-  OVERLAPPED overlapped = {0};
-  HANDLE event = CreateEventW(nullptr, TRUE, FALSE, nullptr);
-  if (!event) { return EAI_FAIL; }
-
-  overlapped.hEvent = event;
-
-  PADDRINFOEXW result_addrinfo = nullptr;
-  HANDLE cancel_handle = nullptr;
-
-  ADDRINFOEXW hints_ex = {0};
-  if (hints) {
-    hints_ex.ai_flags = hints->ai_flags;
-    hints_ex.ai_family = hints->ai_family;
-    hints_ex.ai_socktype = hints->ai_socktype;
-    hints_ex.ai_protocol = hints->ai_protocol;
-  }
-
-  auto wnode = u8string_to_wstring(node);
-  auto wservice = u8string_to_wstring(service);
-
-  auto ret = ::GetAddrInfoExW(wnode.data(), wservice.data(), NS_DNS, nullptr,
-                              hints ? &hints_ex : nullptr, &result_addrinfo,
-                              nullptr, &overlapped, nullptr, &cancel_handle);
-
-  if (ret == WSA_IO_PENDING) {
-    auto wait_result =
-        ::WaitForSingleObject(event, static_cast<DWORD>(timeout_sec * 1000));
-    if (wait_result == WAIT_TIMEOUT) {
-      if (cancel_handle) { ::GetAddrInfoExCancel(&cancel_handle); }
-      ::CloseHandle(event);
-      return EAI_AGAIN;
-    }
-
-    DWORD bytes_returned;
-    if (!::GetOverlappedResult((HANDLE)INVALID_SOCKET, &overlapped,
-                               &bytes_returned, FALSE)) {
-      ::CloseHandle(event);
-      return ::WSAGetLastError();
-    }
-  }
-
-  ::CloseHandle(event);
-
-  if (ret == NO_ERROR || ret == WSA_IO_PENDING) {
-    *res = reinterpret_cast<struct addrinfo *>(result_addrinfo);
-    return 0;
-  }
-
-  return ret;
-#elif TARGET_OS_MAC
-  // macOS implementation using CFHost API for asynchronous DNS resolution
-  CFStringRef hostname_ref = CFStringCreateWithCString(
-      kCFAllocatorDefault, node, kCFStringEncodingUTF8);
-  if (!hostname_ref) { return EAI_MEMORY; }
-
-  CFHostRef host_ref = CFHostCreateWithName(kCFAllocatorDefault, hostname_ref);
-  CFRelease(hostname_ref);
-  if (!host_ref) { return EAI_MEMORY; }
-
-  // Set up context for callback
-  struct CFHostContext {
-    bool completed = false;
-    bool success = false;
-    CFArrayRef addresses = nullptr;
-    std::mutex mutex;
-    std::condition_variable cv;
-  } context;
-
-  CFHostClientContext client_context;
-  memset(&client_context, 0, sizeof(client_context));
-  client_context.info = &context;
-
-  // Set callback
-  auto callback = [](CFHostRef theHost, CFHostInfoType /*typeInfo*/,
-                     const CFStreamError *error, void *info) {
-    auto ctx = static_cast<CFHostContext *>(info);
-    std::lock_guard<std::mutex> lock(ctx->mutex);
-
-    if (error && error->error != 0) {
-      ctx->success = false;
-    } else {
-      Boolean hasBeenResolved;
-      ctx->addresses = CFHostGetAddressing(theHost, &hasBeenResolved);
-      if (ctx->addresses && hasBeenResolved) {
-        CFRetain(ctx->addresses);
-        ctx->success = true;
-      } else {
-        ctx->success = false;
-      }
-    }
-    ctx->completed = true;
-    ctx->cv.notify_one();
-  };
-
-  if (!CFHostSetClient(host_ref, callback, &client_context)) {
-    CFRelease(host_ref);
-    return EAI_SYSTEM;
-  }
-
-  // Schedule on run loop
-  CFRunLoopRef run_loop = CFRunLoopGetCurrent();
-  CFHostScheduleWithRunLoop(host_ref, run_loop, kCFRunLoopDefaultMode);
-
-  // Start resolution
-  CFStreamError stream_error;
-  if (!CFHostStartInfoResolution(host_ref, kCFHostAddresses, &stream_error)) {
-    CFHostUnscheduleFromRunLoop(host_ref, run_loop, kCFRunLoopDefaultMode);
-    CFRelease(host_ref);
-    return EAI_FAIL;
-  }
-
-  // Wait for completion with timeout
-  auto timeout_time =
-      std::chrono::steady_clock::now() + std::chrono::seconds(timeout_sec);
-  bool timed_out = false;
-
-  {
-    std::unique_lock<std::mutex> lock(context.mutex);
-
-    while (!context.completed) {
-      auto now = std::chrono::steady_clock::now();
-      if (now >= timeout_time) {
-        timed_out = true;
-        break;
-      }
-
-      // Run the runloop for a short time
-      lock.unlock();
-      CFRunLoopRunInMode(kCFRunLoopDefaultMode, 0.1, true);
-      lock.lock();
-    }
-  }
-
-  // Clean up
-  CFHostUnscheduleFromRunLoop(host_ref, run_loop, kCFRunLoopDefaultMode);
-  CFHostSetClient(host_ref, nullptr, nullptr);
-
-  if (timed_out || !context.completed) {
-    CFHostCancelInfoResolution(host_ref, kCFHostAddresses);
-    CFRelease(host_ref);
-    return EAI_AGAIN;
-  }
-
-  if (!context.success || !context.addresses) {
-    CFRelease(host_ref);
-    return EAI_NODATA;
-  }
-
-  // Convert CFArray to addrinfo
-  CFIndex count = CFArrayGetCount(context.addresses);
-  if (count == 0) {
-    CFRelease(context.addresses);
-    CFRelease(host_ref);
-    return EAI_NODATA;
-  }
-
-  struct addrinfo *result_addrinfo = nullptr;
-  struct addrinfo **current = &result_addrinfo;
-
-  for (CFIndex i = 0; i < count; i++) {
-    CFDataRef addr_data =
-        static_cast<CFDataRef>(CFArrayGetValueAtIndex(context.addresses, i));
-    if (!addr_data) continue;
-
-    const struct sockaddr *sockaddr_ptr =
-        reinterpret_cast<const struct sockaddr *>(CFDataGetBytePtr(addr_data));
-    socklen_t sockaddr_len = static_cast<socklen_t>(CFDataGetLength(addr_data));
-
-    // Allocate addrinfo structure
-    *current = static_cast<struct addrinfo *>(malloc(sizeof(struct addrinfo)));
-    if (!*current) {
-      freeaddrinfo(result_addrinfo);
-      CFRelease(context.addresses);
-      CFRelease(host_ref);
-      return EAI_MEMORY;
-    }
-
-    memset(*current, 0, sizeof(struct addrinfo));
-
-    // Set up addrinfo fields
-    (*current)->ai_family = sockaddr_ptr->sa_family;
-    (*current)->ai_socktype = hints ? hints->ai_socktype : SOCK_STREAM;
-    (*current)->ai_protocol = hints ? hints->ai_protocol : IPPROTO_TCP;
-    (*current)->ai_addrlen = sockaddr_len;
-
-    // Copy sockaddr
-    (*current)->ai_addr = static_cast<struct sockaddr *>(malloc(sockaddr_len));
-    if (!(*current)->ai_addr) {
-      freeaddrinfo(result_addrinfo);
-      CFRelease(context.addresses);
-      CFRelease(host_ref);
-      return EAI_MEMORY;
-    }
-    memcpy((*current)->ai_addr, sockaddr_ptr, sockaddr_len);
-
-    // Set port if service is specified
-    if (service && strlen(service) > 0) {
-      int port = atoi(service);
-      if (port > 0) {
-        if (sockaddr_ptr->sa_family == AF_INET) {
-          reinterpret_cast<struct sockaddr_in *>((*current)->ai_addr)
-              ->sin_port = htons(static_cast<uint16_t>(port));
-        } else if (sockaddr_ptr->sa_family == AF_INET6) {
-          reinterpret_cast<struct sockaddr_in6 *>((*current)->ai_addr)
-              ->sin6_port = htons(static_cast<uint16_t>(port));
-        }
-      }
-    }
-
-    current = &((*current)->ai_next);
-  }
-
-  CFRelease(context.addresses);
-  CFRelease(host_ref);
-
-  *res = result_addrinfo;
-  return 0;
-#elif defined(_GNU_SOURCE) && defined(__GLIBC__) &&                            \
-    (__GLIBC__ > 2 || (__GLIBC__ == 2 && __GLIBC_MINOR__ >= 2))
-  // Linux implementation using getaddrinfo_a for asynchronous DNS resolution
-  struct gaicb request;
-  struct gaicb *requests[1] = {&request};
-  struct sigevent sevp;
-  struct timespec timeout;
-
-  // Initialize the request structure
-  memset(&request, 0, sizeof(request));
-  request.ar_name = node;
-  request.ar_service = service;
-  request.ar_request = hints;
-
-  // Set up timeout
-  timeout.tv_sec = timeout_sec;
-  timeout.tv_nsec = 0;
-
-  // Initialize sigevent structure (not used, but required)
-  memset(&sevp, 0, sizeof(sevp));
-  sevp.sigev_notify = SIGEV_NONE;
-
-  // Start asynchronous resolution
-  int start_result = getaddrinfo_a(GAI_NOWAIT, requests, 1, &sevp);
-  if (start_result != 0) { return start_result; }
-
-  // Wait for completion with timeout
-  int wait_result =
-      gai_suspend((const struct gaicb *const *)requests, 1, &timeout);
-
-  if (wait_result == 0 || wait_result == EAI_ALLDONE) {
-    // Completed successfully, get the result
-    int gai_result = gai_error(&request);
-    if (gai_result == 0) {
-      *res = request.ar_result;
-      return 0;
-    } else {
-      // Clean up on error
-      if (request.ar_result) { freeaddrinfo(request.ar_result); }
-      return gai_result;
-    }
-  } else if (wait_result == EAI_AGAIN) {
-    // Timeout occurred, cancel the request
-    gai_cancel(&request);
-    return EAI_AGAIN;
-  } else {
-    // Other error occurred
-    gai_cancel(&request);
-    return wait_result;
-  }
-#else
-  // Fallback implementation using thread-based timeout for other Unix systems
-
-  struct GetAddrInfoState {
-    std::mutex mutex;
-    std::condition_variable result_cv;
-    bool completed = false;
-    int result = EAI_SYSTEM;
-    std::string node = node;
-    std::string service = service;
-    struct addrinfo hints = hints;
-    struct addrinfo *info = nullptr;
-  };
-
-  // Allocate on the heap, so the resolver thread can keep using the data.
-  auto state = std::make_shared<GetAddrInfoState>();
-
-  std::thread resolve_thread([=]() {
-    auto thread_result = getaddrinfo(
-        state->node.c_str(), state->service.c_str(), hints, &state->info);
-
-    std::lock_guard<std::mutex> lock(state->mutex);
-    state->result = thread_result;
-    state->completed = true;
-    state->result_cv.notify_one();
-  });
-
-  // Wait for completion or timeout
-  std::unique_lock<std::mutex> lock(state->mutex);
-  auto finished =
-      state->result_cv.wait_for(lock, std::chrono::seconds(timeout_sec),
-                                [&] { return state->completed; });
-
-  if (finished) {
-    // Operation completed within timeout
-    resolve_thread.join();
-    *res = state->info;
-    return state->result;
-  } else {
-    // Timeout occurred
-    resolve_thread.detach(); // Let the thread finish in background
-    return EAI_AGAIN;        // Return timeout error
-  }
-#endif
-#else
-  (void)(timeout_sec); // Unused parameter for non-blocking getaddrinfo
-  return getaddrinfo(node, service, hints, res);
-#endif
-}
-
-template <typename BindOrConnect>
-socket_t create_socket(const std::string &host, const std::string &ip, int port,
-                       int address_family, int socket_flags, bool tcp_nodelay,
-                       bool ipv6_v6only, SocketOptions socket_options,
-                       BindOrConnect bind_or_connect, time_t timeout_sec = 0) {
-  // Get address info
-  const char *node = nullptr;
-  struct addrinfo hints;
-  struct addrinfo *result;
-
-  memset(&hints, 0, sizeof(struct addrinfo));
-  hints.ai_socktype = SOCK_STREAM;
-  hints.ai_protocol = IPPROTO_IP;
-
-  if (!ip.empty()) {
-    node = ip.c_str();
-    // Ask getaddrinfo to convert IP in c-string to address
-    hints.ai_family = AF_UNSPEC;
-    hints.ai_flags = AI_NUMERICHOST;
-  } else {
-    if (!host.empty()) { node = host.c_str(); }
-    hints.ai_family = address_family;
-    hints.ai_flags = socket_flags;
-  }
-
-#if !defined(_WIN32) || defined(CPPHTTPLIB_HAVE_AFUNIX_H)
-  if (hints.ai_family == AF_UNIX) {
-    const auto addrlen = host.length();
-    if (addrlen > sizeof(sockaddr_un::sun_path)) { return INVALID_SOCKET; }
-
-#ifdef SOCK_CLOEXEC
-    auto sock = socket(hints.ai_family, hints.ai_socktype | SOCK_CLOEXEC,
-                       hints.ai_protocol);
-#else
-    auto sock = socket(hints.ai_family, hints.ai_socktype, hints.ai_protocol);
-#endif
-
-    if (sock != INVALID_SOCKET) {
-      sockaddr_un addr{};
-      addr.sun_family = AF_UNIX;
-
-      auto unescaped_host = unescape_abstract_namespace_unix_domain(host);
-      std::copy(unescaped_host.begin(), unescaped_host.end(), addr.sun_path);
-
-      hints.ai_addr = reinterpret_cast<sockaddr *>(&addr);
-      hints.ai_addrlen = static_cast<socklen_t>(
-          sizeof(addr) - sizeof(addr.sun_path) + addrlen);
-
-#ifndef SOCK_CLOEXEC
-#ifndef _WIN32
-      fcntl(sock, F_SETFD, FD_CLOEXEC);
-#endif
-#endif
-
-      if (socket_options) { socket_options(sock); }
-
-#ifdef _WIN32
-      // Setting SO_REUSEADDR seems not to work well with AF_UNIX on windows, so
-      // remove the option.
-      detail::set_socket_opt(sock, SOL_SOCKET, SO_REUSEADDR, 0);
-#endif
-
-      bool dummy;
-      if (!bind_or_connect(sock, hints, dummy)) {
-        close_socket(sock);
-        sock = INVALID_SOCKET;
-      }
-    }
-    return sock;
-  }
-#endif
-
-  auto service = std::to_string(port);
-
-  if (getaddrinfo_with_timeout(node, service.c_str(), &hints, &result,
-                               timeout_sec)) {
-#if defined __linux__ && !defined __ANDROID__
-    res_init();
-#endif
-    return INVALID_SOCKET;
-  }
-  auto se = detail::scope_exit([&] { freeaddrinfo(result); });
-
-  for (auto rp = result; rp; rp = rp->ai_next) {
-    // Create a socket
-#ifdef _WIN32
-    auto sock =
-        WSASocketW(rp->ai_family, rp->ai_socktype, rp->ai_protocol, nullptr, 0,
-                   WSA_FLAG_NO_HANDLE_INHERIT | WSA_FLAG_OVERLAPPED);
-    /**
-     * Since the WSA_FLAG_NO_HANDLE_INHERIT is only supported on Windows 7 SP1
-     * and above the socket creation fails on older Windows Systems.
-     *
-     * Let's try to create a socket the old way in this case.
-     *
-     * Reference:
-     * https://docs.microsoft.com/en-us/windows/win32/api/winsock2/nf-winsock2-wsasocketa
-     *
-     * WSA_FLAG_NO_HANDLE_INHERIT:
-     * This flag is supported on Windows 7 with SP1, Windows Server 2008 R2 with
-     * SP1, and later
-     *
-     */
-    if (sock == INVALID_SOCKET) {
-      sock = socket(rp->ai_family, rp->ai_socktype, rp->ai_protocol);
-    }
-#else
-
-#ifdef SOCK_CLOEXEC
-    auto sock =
-        socket(rp->ai_family, rp->ai_socktype | SOCK_CLOEXEC, rp->ai_protocol);
-#else
-    auto sock = socket(rp->ai_family, rp->ai_socktype, rp->ai_protocol);
-#endif
-
-#endif
-    if (sock == INVALID_SOCKET) { continue; }
-
-#if !defined _WIN32 && !defined SOCK_CLOEXEC
-    if (fcntl(sock, F_SETFD, FD_CLOEXEC) == -1) {
-      close_socket(sock);
-      continue;
-    }
-#endif
-
-    if (tcp_nodelay) { set_socket_opt(sock, IPPROTO_TCP, TCP_NODELAY, 1); }
-
-    if (rp->ai_family == AF_INET6) {
-      set_socket_opt(sock, IPPROTO_IPV6, IPV6_V6ONLY, ipv6_v6only ? 1 : 0);
-    }
-
-    if (socket_options) { socket_options(sock); }
-
-    // bind or connect
-    auto quit = false;
-    if (bind_or_connect(sock, *rp, quit)) { return sock; }
-
-    close_socket(sock);
-
-    if (quit) { break; }
-  }
-
-  return INVALID_SOCKET;
-}
-
-inline void set_nonblocking(socket_t sock, bool nonblocking) {
-#ifdef _WIN32
-  auto flags = nonblocking ? 1UL : 0UL;
-  ioctlsocket(sock, FIONBIO, &flags);
-#else
-  auto flags = fcntl(sock, F_GETFL, 0);
-  fcntl(sock, F_SETFL,
-        nonblocking ? (flags | O_NONBLOCK) : (flags & (~O_NONBLOCK)));
-#endif
-}
-
-inline bool is_connection_error() {
-#ifdef _WIN32
-  return WSAGetLastError() != WSAEWOULDBLOCK;
-#else
-  return errno != EINPROGRESS;
-#endif
-}
-
-inline bool bind_ip_address(socket_t sock, const std::string &host) {
-  struct addrinfo hints;
-  struct addrinfo *result;
-
-  memset(&hints, 0, sizeof(struct addrinfo));
-  hints.ai_family = AF_UNSPEC;
-  hints.ai_socktype = SOCK_STREAM;
-  hints.ai_protocol = 0;
-
-  if (getaddrinfo_with_timeout(host.c_str(), "0", &hints, &result, 0)) {
-    return false;
-  }
-
-  auto se = detail::scope_exit([&] { freeaddrinfo(result); });
-
-  auto ret = false;
-  for (auto rp = result; rp; rp = rp->ai_next) {
-    const auto &ai = *rp;
-    if (!::bind(sock, ai.ai_addr, static_cast<socklen_t>(ai.ai_addrlen))) {
-      ret = true;
-      break;
-    }
-  }
-
-  return ret;
-}
-
-#if !defined _WIN32 && !defined ANDROID && !defined _AIX && !defined __MVS__
-#define USE_IF2IP
-#endif
-
-#ifdef USE_IF2IP
-inline std::string if2ip(int address_family, const std::string &ifn) {
-  struct ifaddrs *ifap;
-  getifaddrs(&ifap);
-  auto se = detail::scope_exit([&] { freeifaddrs(ifap); });
-
-  std::string addr_candidate;
-  for (auto ifa = ifap; ifa; ifa = ifa->ifa_next) {
-    if (ifa->ifa_addr && ifn == ifa->ifa_name &&
-        (AF_UNSPEC == address_family ||
-         ifa->ifa_addr->sa_family == address_family)) {
-      if (ifa->ifa_addr->sa_family == AF_INET) {
-        auto sa = reinterpret_cast<struct sockaddr_in *>(ifa->ifa_addr);
-        char buf[INET_ADDRSTRLEN];
-        if (inet_ntop(AF_INET, &sa->sin_addr, buf, INET_ADDRSTRLEN)) {
-          return std::string(buf, INET_ADDRSTRLEN);
-        }
-      } else if (ifa->ifa_addr->sa_family == AF_INET6) {
-        auto sa = reinterpret_cast<struct sockaddr_in6 *>(ifa->ifa_addr);
-        if (!IN6_IS_ADDR_LINKLOCAL(&sa->sin6_addr)) {
-          char buf[INET6_ADDRSTRLEN] = {};
-          if (inet_ntop(AF_INET6, &sa->sin6_addr, buf, INET6_ADDRSTRLEN)) {
-            // equivalent to mac's IN6_IS_ADDR_UNIQUE_LOCAL
-            auto s6_addr_head = sa->sin6_addr.s6_addr[0];
-            if (s6_addr_head == 0xfc || s6_addr_head == 0xfd) {
-              addr_candidate = std::string(buf, INET6_ADDRSTRLEN);
-            } else {
-              return std::string(buf, INET6_ADDRSTRLEN);
-            }
-          }
-        }
-      }
-    }
-  }
-  return addr_candidate;
-}
-#endif
-
-inline socket_t create_client_socket(
-    const std::string &host, const std::string &ip, int port,
-    int address_family, bool tcp_nodelay, bool ipv6_v6only,
-    SocketOptions socket_options, time_t connection_timeout_sec,
-    time_t connection_timeout_usec, time_t read_timeout_sec,
-    time_t read_timeout_usec, time_t write_timeout_sec,
-    time_t write_timeout_usec, const std::string &intf, Error &error) {
-  auto sock = create_socket(
-      host, ip, port, address_family, 0, tcp_nodelay, ipv6_v6only,
-      std::move(socket_options),
-      [&](socket_t sock2, struct addrinfo &ai, bool &quit) -> bool {
-        if (!intf.empty()) {
-#ifdef USE_IF2IP
-          auto ip_from_if = if2ip(address_family, intf);
-          if (ip_from_if.empty()) { ip_from_if = intf; }
-          if (!bind_ip_address(sock2, ip_from_if)) {
-            error = Error::BindIPAddress;
-            return false;
-          }
-#endif
-        }
-
-        set_nonblocking(sock2, true);
-
-        auto ret =
-            ::connect(sock2, ai.ai_addr, static_cast<socklen_t>(ai.ai_addrlen));
-
-        if (ret < 0) {
-          if (is_connection_error()) {
-            error = Error::Connection;
-            return false;
-          }
-          error = wait_until_socket_is_ready(sock2, connection_timeout_sec,
-                                             connection_timeout_usec);
-          if (error != Error::Success) {
-            if (error == Error::ConnectionTimeout) { quit = true; }
-            return false;
-          }
-        }
-
-        set_nonblocking(sock2, false);
-        set_socket_opt_time(sock2, SOL_SOCKET, SO_RCVTIMEO, read_timeout_sec,
-                            read_timeout_usec);
-        set_socket_opt_time(sock2, SOL_SOCKET, SO_SNDTIMEO, write_timeout_sec,
-                            write_timeout_usec);
-
-        error = Error::Success;
-        return true;
-      },
-      connection_timeout_sec); // Pass DNS timeout
-
-  if (sock != INVALID_SOCKET) {
-    error = Error::Success;
-  } else {
-    if (error == Error::Success) { error = Error::Connection; }
-  }
-
-  return sock;
-}
-
-inline bool get_ip_and_port(const struct sockaddr_storage &addr,
-                            socklen_t addr_len, std::string &ip, int &port) {
-  if (addr.ss_family == AF_INET) {
-    port = ntohs(reinterpret_cast<const struct sockaddr_in *>(&addr)->sin_port);
-  } else if (addr.ss_family == AF_INET6) {
-    port =
-        ntohs(reinterpret_cast<const struct sockaddr_in6 *>(&addr)->sin6_port);
-  } else {
-    return false;
-  }
-
-  std::array<char, NI_MAXHOST> ipstr{};
-  if (getnameinfo(reinterpret_cast<const struct sockaddr *>(&addr), addr_len,
-                  ipstr.data(), static_cast<socklen_t>(ipstr.size()), nullptr,
-                  0, NI_NUMERICHOST)) {
-    return false;
-  }
-
-  ip = ipstr.data();
-  return true;
-}
-
-inline void get_local_ip_and_port(socket_t sock, std::string &ip, int &port) {
-  struct sockaddr_storage addr;
-  socklen_t addr_len = sizeof(addr);
-  if (!getsockname(sock, reinterpret_cast<struct sockaddr *>(&addr),
-                   &addr_len)) {
-    get_ip_and_port(addr, addr_len, ip, port);
-  }
-}
-
-inline void get_remote_ip_and_port(socket_t sock, std::string &ip, int &port) {
-  struct sockaddr_storage addr;
-  socklen_t addr_len = sizeof(addr);
-
-  if (!getpeername(sock, reinterpret_cast<struct sockaddr *>(&addr),
-                   &addr_len)) {
-#ifndef _WIN32
-    if (addr.ss_family == AF_UNIX) {
-#if defined(__linux__)
-      struct ucred ucred;
-      socklen_t len = sizeof(ucred);
-      if (getsockopt(sock, SOL_SOCKET, SO_PEERCRED, &ucred, &len) == 0) {
-        port = ucred.pid;
-      }
-#elif defined(SOL_LOCAL) && defined(SO_PEERPID)
-      pid_t pid;
-      socklen_t len = sizeof(pid);
-      if (getsockopt(sock, SOL_LOCAL, SO_PEERPID, &pid, &len) == 0) {
-        port = pid;
-      }
-#endif
-      return;
-    }
-#endif
-    get_ip_and_port(addr, addr_len, ip, port);
-  }
-}
-
-inline constexpr unsigned int str2tag_core(const char *s, size_t l,
-                                           unsigned int h) {
-  return (l == 0)
-             ? h
-             : str2tag_core(
-                   s + 1, l - 1,
-                   // Unsets the 6 high bits of h, therefore no overflow happens
-                   (((std::numeric_limits<unsigned int>::max)() >> 6) &
-                    h * 33) ^
-                       static_cast<unsigned char>(*s));
-}
-
-inline unsigned int str2tag(const std::string &s) {
-  return str2tag_core(s.data(), s.size(), 0);
-}
-
-namespace udl {
-
-inline constexpr unsigned int operator""_t(const char *s, size_t l) {
-  return str2tag_core(s, l, 0);
-}
-
-} // namespace udl
-
-inline std::string
-find_content_type(const std::string &path,
-                  const std::map<std::string, std::string> &user_data,
-                  const std::string &default_content_type) {
-  auto ext = file_extension(path);
-
-  auto it = user_data.find(ext);
-  if (it != user_data.end()) { return it->second; }
-
-  using udl::operator""_t;
-
-  switch (str2tag(ext)) {
-  default: return default_content_type;
-
-  case "css"_t: return "text/css";
-  case "csv"_t: return "text/csv";
-  case "htm"_t:
-  case "html"_t: return "text/html";
-  case "js"_t:
-  case "mjs"_t: return "text/javascript";
-  case "txt"_t: return "text/plain";
-  case "vtt"_t: return "text/vtt";
-
-  case "apng"_t: return "image/apng";
-  case "avif"_t: return "image/avif";
-  case "bmp"_t: return "image/bmp";
-  case "gif"_t: return "image/gif";
-  case "png"_t: return "image/png";
-  case "svg"_t: return "image/svg+xml";
-  case "webp"_t: return "image/webp";
-  case "ico"_t: return "image/x-icon";
-  case "tif"_t: return "image/tiff";
-  case "tiff"_t: return "image/tiff";
-  case "jpg"_t:
-  case "jpeg"_t: return "image/jpeg";
-
-  case "mp4"_t: return "video/mp4";
-  case "mpeg"_t: return "video/mpeg";
-  case "webm"_t: return "video/webm";
-
-  case "mp3"_t: return "audio/mp3";
-  case "mpga"_t: return "audio/mpeg";
-  case "weba"_t: return "audio/webm";
-  case "wav"_t: return "audio/wave";
-
-  case "otf"_t: return "font/otf";
-  case "ttf"_t: return "font/ttf";
-  case "woff"_t: return "font/woff";
-  case "woff2"_t: return "font/woff2";
-
-  case "7z"_t: return "application/x-7z-compressed";
-  case "atom"_t: return "application/atom+xml";
-  case "pdf"_t: return "application/pdf";
-  case "json"_t: return "application/json";
-  case "rss"_t: return "application/rss+xml";
-  case "tar"_t: return "application/x-tar";
-  case "xht"_t:
-  case "xhtml"_t: return "application/xhtml+xml";
-  case "xslt"_t: return "application/xslt+xml";
-  case "xml"_t: return "application/xml";
-  case "gz"_t: return "application/gzip";
-  case "zip"_t: return "application/zip";
-  case "wasm"_t: return "application/wasm";
-  }
-}
-
-inline bool can_compress_content_type(const std::string &content_type) {
-  using udl::operator""_t;
-
-  auto tag = str2tag(content_type);
-
-  switch (tag) {
-  case "image/svg+xml"_t:
-  case "application/javascript"_t:
-  case "application/json"_t:
-  case "application/xml"_t:
-  case "application/protobuf"_t:
-  case "application/xhtml+xml"_t: return true;
-
-  case "text/event-stream"_t: return false;
-
-  default: return !content_type.rfind("text/", 0);
-  }
-}
-
-inline EncodingType encoding_type(const Request &req, const Response &res) {
-  auto ret =
-      detail::can_compress_content_type(res.get_header_value("Content-Type"));
-  if (!ret) { return EncodingType::None; }
-
-  const auto &s = req.get_header_value("Accept-Encoding");
-  (void)(s);
-
-#ifdef CPPHTTPLIB_BROTLI_SUPPORT
-  // TODO: 'Accept-Encoding' has br, not br;q=0
-  ret = s.find("br") != std::string::npos;
-  if (ret) { return EncodingType::Brotli; }
-#endif
-
-#ifdef CPPHTTPLIB_ZLIB_SUPPORT
-  // TODO: 'Accept-Encoding' has gzip, not gzip;q=0
-  ret = s.find("gzip") != std::string::npos;
-  if (ret) { return EncodingType::Gzip; }
-#endif
-
-#ifdef CPPHTTPLIB_ZSTD_SUPPORT
-  // TODO: 'Accept-Encoding' has zstd, not zstd;q=0
-  ret = s.find("zstd") != std::string::npos;
-  if (ret) { return EncodingType::Zstd; }
-#endif
-
-  return EncodingType::None;
-}
-
-inline bool nocompressor::compress(const char *data, size_t data_length,
-                                   bool /*last*/, Callback callback) {
-  if (!data_length) { return true; }
-  return callback(data, data_length);
-}
-
-#ifdef CPPHTTPLIB_ZLIB_SUPPORT
-inline gzip_compressor::gzip_compressor() {
-  std::memset(&strm_, 0, sizeof(strm_));
-  strm_.zalloc = Z_NULL;
-  strm_.zfree = Z_NULL;
-  strm_.opaque = Z_NULL;
-
-  is_valid_ = deflateInit2(&strm_, Z_DEFAULT_COMPRESSION, Z_DEFLATED, 31, 8,
-                           Z_DEFAULT_STRATEGY) == Z_OK;
-}
-
-inline gzip_compressor::~gzip_compressor() { deflateEnd(&strm_); }
-
-inline bool gzip_compressor::compress(const char *data, size_t data_length,
-                                      bool last, Callback callback) {
-  assert(is_valid_);
-
-  do {
-    constexpr size_t max_avail_in =
-        (std::numeric_limits<decltype(strm_.avail_in)>::max)();
-
-    strm_.avail_in = static_cast<decltype(strm_.avail_in)>(
-        (std::min)(data_length, max_avail_in));
-    strm_.next_in = const_cast<Bytef *>(reinterpret_cast<const Bytef *>(data));
-
-    data_length -= strm_.avail_in;
-    data += strm_.avail_in;
-
-    auto flush = (last && data_length == 0) ? Z_FINISH : Z_NO_FLUSH;
-    auto ret = Z_OK;
-
-    std::array<char, CPPHTTPLIB_COMPRESSION_BUFSIZ> buff{};
-    do {
-      strm_.avail_out = static_cast<uInt>(buff.size());
-      strm_.next_out = reinterpret_cast<Bytef *>(buff.data());
-
-      ret = deflate(&strm_, flush);
-      if (ret == Z_STREAM_ERROR) { return false; }
-
-      if (!callback(buff.data(), buff.size() - strm_.avail_out)) {
-        return false;
-      }
-    } while (strm_.avail_out == 0);
-
-    assert((flush == Z_FINISH && ret == Z_STREAM_END) ||
-           (flush == Z_NO_FLUSH && ret == Z_OK));
-    assert(strm_.avail_in == 0);
-  } while (data_length > 0);
-
-  return true;
-}
-
-inline gzip_decompressor::gzip_decompressor() {
-  std::memset(&strm_, 0, sizeof(strm_));
-  strm_.zalloc = Z_NULL;
-  strm_.zfree = Z_NULL;
-  strm_.opaque = Z_NULL;
-
-  // 15 is the value of wbits, which should be at the maximum possible value
-  // to ensure that any gzip stream can be decoded. The offset of 32 specifies
-  // that the stream type should be automatically detected either gzip or
-  // deflate.
-  is_valid_ = inflateInit2(&strm_, 32 + 15) == Z_OK;
-}
-
-inline gzip_decompressor::~gzip_decompressor() { inflateEnd(&strm_); }
-
-inline bool gzip_decompressor::is_valid() const { return is_valid_; }
-
-inline bool gzip_decompressor::decompress(const char *data, size_t data_length,
-                                          Callback callback) {
-  assert(is_valid_);
-
-  auto ret = Z_OK;
-
-  do {
-    constexpr size_t max_avail_in =
-        (std::numeric_limits<decltype(strm_.avail_in)>::max)();
-
-    strm_.avail_in = static_cast<decltype(strm_.avail_in)>(
-        (std::min)(data_length, max_avail_in));
-    strm_.next_in = const_cast<Bytef *>(reinterpret_cast<const Bytef *>(data));
-
-    data_length -= strm_.avail_in;
-    data += strm_.avail_in;
-
-    std::array<char, CPPHTTPLIB_COMPRESSION_BUFSIZ> buff{};
-    while (strm_.avail_in > 0 && ret == Z_OK) {
-      strm_.avail_out = static_cast<uInt>(buff.size());
-      strm_.next_out = reinterpret_cast<Bytef *>(buff.data());
-
-      ret = inflate(&strm_, Z_NO_FLUSH);
-
-      assert(ret != Z_STREAM_ERROR);
-      switch (ret) {
-      case Z_NEED_DICT:
-      case Z_DATA_ERROR:
-      case Z_MEM_ERROR: inflateEnd(&strm_); return false;
-      }
-
-      if (!callback(buff.data(), buff.size() - strm_.avail_out)) {
-        return false;
-      }
-    }
-
-    if (ret != Z_OK && ret != Z_STREAM_END) { return false; }
-
-  } while (data_length > 0);
-
-  return true;
-}
-#endif
-
-#ifdef CPPHTTPLIB_BROTLI_SUPPORT
-inline brotli_compressor::brotli_compressor() {
-  state_ = BrotliEncoderCreateInstance(nullptr, nullptr, nullptr);
-}
-
-inline brotli_compressor::~brotli_compressor() {
-  BrotliEncoderDestroyInstance(state_);
-}
-
-inline bool brotli_compressor::compress(const char *data, size_t data_length,
-                                        bool last, Callback callback) {
-  std::array<uint8_t, CPPHTTPLIB_COMPRESSION_BUFSIZ> buff{};
-
-  auto operation = last ? BROTLI_OPERATION_FINISH : BROTLI_OPERATION_PROCESS;
-  auto available_in = data_length;
-  auto next_in = reinterpret_cast<const uint8_t *>(data);
-
-  for (;;) {
-    if (last) {
-      if (BrotliEncoderIsFinished(state_)) { break; }
-    } else {
-      if (!available_in) { break; }
-    }
-
-    auto available_out = buff.size();
-    auto next_out = buff.data();
-
-    if (!BrotliEncoderCompressStream(state_, operation, &available_in, &next_in,
-                                     &available_out, &next_out, nullptr)) {
-      return false;
-    }
-
-    auto output_bytes = buff.size() - available_out;
-    if (output_bytes) {
-      callback(reinterpret_cast<const char *>(buff.data()), output_bytes);
-    }
-  }
-
-  return true;
-}
-
-inline brotli_decompressor::brotli_decompressor() {
-  decoder_s = BrotliDecoderCreateInstance(0, 0, 0);
-  decoder_r = decoder_s ? BROTLI_DECODER_RESULT_NEEDS_MORE_INPUT
-                        : BROTLI_DECODER_RESULT_ERROR;
-}
-
-inline brotli_decompressor::~brotli_decompressor() {
-  if (decoder_s) { BrotliDecoderDestroyInstance(decoder_s); }
-}
-
-inline bool brotli_decompressor::is_valid() const { return decoder_s; }
-
-inline bool brotli_decompressor::decompress(const char *data,
-                                            size_t data_length,
-                                            Callback callback) {
-  if (decoder_r == BROTLI_DECODER_RESULT_SUCCESS ||
-      decoder_r == BROTLI_DECODER_RESULT_ERROR) {
-    return 0;
-  }
-
-  auto next_in = reinterpret_cast<const uint8_t *>(data);
-  size_t avail_in = data_length;
-  size_t total_out;
-
-  decoder_r = BROTLI_DECODER_RESULT_NEEDS_MORE_OUTPUT;
-
-  std::array<char, CPPHTTPLIB_COMPRESSION_BUFSIZ> buff{};
-  while (decoder_r == BROTLI_DECODER_RESULT_NEEDS_MORE_OUTPUT) {
-    char *next_out = buff.data();
-    size_t avail_out = buff.size();
-
-    decoder_r = BrotliDecoderDecompressStream(
-        decoder_s, &avail_in, &next_in, &avail_out,
-        reinterpret_cast<uint8_t **>(&next_out), &total_out);
-
-    if (decoder_r == BROTLI_DECODER_RESULT_ERROR) { return false; }
-
-    if (!callback(buff.data(), buff.size() - avail_out)) { return false; }
-  }
-
-  return decoder_r == BROTLI_DECODER_RESULT_SUCCESS ||
-         decoder_r == BROTLI_DECODER_RESULT_NEEDS_MORE_INPUT;
-}
-#endif
-
-#ifdef CPPHTTPLIB_ZSTD_SUPPORT
-inline zstd_compressor::zstd_compressor() {
-  ctx_ = ZSTD_createCCtx();
-  ZSTD_CCtx_setParameter(ctx_, ZSTD_c_compressionLevel, ZSTD_fast);
-}
-
-inline zstd_compressor::~zstd_compressor() { ZSTD_freeCCtx(ctx_); }
-
-inline bool zstd_compressor::compress(const char *data, size_t data_length,
-                                      bool last, Callback callback) {
-  std::array<char, CPPHTTPLIB_COMPRESSION_BUFSIZ> buff{};
-
-  ZSTD_EndDirective mode = last ? ZSTD_e_end : ZSTD_e_continue;
-  ZSTD_inBuffer input = {data, data_length, 0};
-
-  bool finished;
-  do {
-    ZSTD_outBuffer output = {buff.data(), CPPHTTPLIB_COMPRESSION_BUFSIZ, 0};
-    size_t const remaining = ZSTD_compressStream2(ctx_, &output, &input, mode);
-
-    if (ZSTD_isError(remaining)) { return false; }
-
-    if (!callback(buff.data(), output.pos)) { return false; }
-
-    finished = last ? (remaining == 0) : (input.pos == input.size);
-
-  } while (!finished);
-
-  return true;
-}
-
-inline zstd_decompressor::zstd_decompressor() { ctx_ = ZSTD_createDCtx(); }
-
-inline zstd_decompressor::~zstd_decompressor() { ZSTD_freeDCtx(ctx_); }
-
-inline bool zstd_decompressor::is_valid() const { return ctx_ != nullptr; }
-
-inline bool zstd_decompressor::decompress(const char *data, size_t data_length,
-                                          Callback callback) {
-  std::array<char, CPPHTTPLIB_COMPRESSION_BUFSIZ> buff{};
-  ZSTD_inBuffer input = {data, data_length, 0};
-
-  while (input.pos < input.size) {
-    ZSTD_outBuffer output = {buff.data(), CPPHTTPLIB_COMPRESSION_BUFSIZ, 0};
-    size_t const remaining = ZSTD_decompressStream(ctx_, &output, &input);
-
-    if (ZSTD_isError(remaining)) { return false; }
-
-    if (!callback(buff.data(), output.pos)) { return false; }
-  }
-
-  return true;
-}
-#endif
-
-inline bool is_prohibited_header_name(const std::string &name) {
-  using udl::operator""_t;
-
-  switch (str2tag(name)) {
-  case "REMOTE_ADDR"_t:
-  case "REMOTE_PORT"_t:
-  case "LOCAL_ADDR"_t:
-  case "LOCAL_PORT"_t: return true;
-  default: return false;
-  }
-}
-
-inline bool has_header(const Headers &headers, const std::string &key) {
-  if (is_prohibited_header_name(key)) { return false; }
-  return headers.find(key) != headers.end();
-}
-
-inline const char *get_header_value(const Headers &headers,
-                                    const std::string &key, const char *def,
-                                    size_t id) {
-  if (is_prohibited_header_name(key)) {
-#ifndef CPPHTTPLIB_NO_EXCEPTIONS
-    std::string msg = "Prohibited header name '" + key + "' is specified.";
-    throw std::invalid_argument(msg);
-#else
-    return "";
-#endif
-  }
-
-  auto rng = headers.equal_range(key);
-  auto it = rng.first;
-  std::advance(it, static_cast<ssize_t>(id));
-  if (it != rng.second) { return it->second.c_str(); }
-  return def;
-}
-
-template <typename T>
-inline bool parse_header(const char *beg, const char *end, T fn) {
-  // Skip trailing spaces and tabs.
-  while (beg < end && is_space_or_tab(end[-1])) {
-    end--;
-  }
-
-  auto p = beg;
-  while (p < end && *p != ':') {
-    p++;
-  }
-
-  auto name = std::string(beg, p);
-  if (!detail::fields::is_field_name(name)) { return false; }
-
-  if (p == end) { return false; }
-
-  auto key_end = p;
-
-  if (*p++ != ':') { return false; }
-
-  while (p < end && is_space_or_tab(*p)) {
-    p++;
-  }
-
-  if (p <= end) {
-    auto key_len = key_end - beg;
-    if (!key_len) { return false; }
-
-    auto key = std::string(beg, key_end);
-    auto val = std::string(p, end);
-
-    if (!detail::fields::is_field_value(val)) { return false; }
-
-    if (case_ignore::equal(key, "Location") ||
-        case_ignore::equal(key, "Referer")) {
-      fn(key, val);
-    } else {
-      fn(key, decode_path_component(val));
-    }
-
-    return true;
-  }
-
-  return false;
-}
-
-inline bool read_headers(Stream &strm, Headers &headers) {
-  const auto bufsiz = 2048;
-  char buf[bufsiz];
-  stream_line_reader line_reader(strm, buf, bufsiz);
-
-  size_t header_count = 0;
-
-  for (;;) {
-    if (!line_reader.getline()) { return false; }
-
-    // Check if the line ends with CRLF.
-    auto line_terminator_len = 2;
-    if (line_reader.end_with_crlf()) {
-      // Blank line indicates end of headers.
-      if (line_reader.size() == 2) { break; }
-    } else {
-#ifdef CPPHTTPLIB_ALLOW_LF_AS_LINE_TERMINATOR
-      // Blank line indicates end of headers.
-      if (line_reader.size() == 1) { break; }
-      line_terminator_len = 1;
-#else
-      continue; // Skip invalid line.
-#endif
-    }
-
-    if (line_reader.size() > CPPHTTPLIB_HEADER_MAX_LENGTH) { return false; }
-
-    // Check header count limit
-    if (header_count >= CPPHTTPLIB_HEADER_MAX_COUNT) { return false; }
-
-    // Exclude line terminator
-    auto end = line_reader.ptr() + line_reader.size() - line_terminator_len;
-
-    if (!parse_header(line_reader.ptr(), end,
-                      [&](const std::string &key, const std::string &val) {
-                        headers.emplace(key, val);
-                      })) {
-      return false;
-    }
-
-    header_count++;
-  }
-
-  return true;
-}
-
-inline bool read_content_with_length(Stream &strm, size_t len,
-                                     DownloadProgress progress,
-                                     ContentReceiverWithProgress out) {
-  char buf[CPPHTTPLIB_RECV_BUFSIZ];
-
-  size_t r = 0;
-  while (r < len) {
-    auto read_len = static_cast<size_t>(len - r);
-    auto n = strm.read(buf, (std::min)(read_len, CPPHTTPLIB_RECV_BUFSIZ));
-    if (n <= 0) { return false; }
-
-    if (!out(buf, static_cast<size_t>(n), r, len)) { return false; }
-    r += static_cast<size_t>(n);
-
-    if (progress) {
-      if (!progress(r, len)) { return false; }
-    }
-  }
-
-  return true;
-}
-
-inline void skip_content_with_length(Stream &strm, size_t len) {
-  char buf[CPPHTTPLIB_RECV_BUFSIZ];
-  size_t r = 0;
-  while (r < len) {
-    auto read_len = static_cast<size_t>(len - r);
-    auto n = strm.read(buf, (std::min)(read_len, CPPHTTPLIB_RECV_BUFSIZ));
-    if (n <= 0) { return; }
-    r += static_cast<size_t>(n);
-  }
-}
-
-enum class ReadContentResult {
-  Success,         // Successfully read the content
-  PayloadTooLarge, // The content exceeds the specified payload limit
-  Error            // An error occurred while reading the content
-};
-
-inline ReadContentResult
-read_content_without_length(Stream &strm, size_t payload_max_length,
-                            ContentReceiverWithProgress out) {
-  char buf[CPPHTTPLIB_RECV_BUFSIZ];
-  size_t r = 0;
-  for (;;) {
-    auto n = strm.read(buf, CPPHTTPLIB_RECV_BUFSIZ);
-    if (n == 0) { return ReadContentResult::Success; }
-    if (n < 0) { return ReadContentResult::Error; }
-
-    // Check if adding this data would exceed the payload limit
-    if (r > payload_max_length ||
-        payload_max_length - r < static_cast<size_t>(n)) {
-      return ReadContentResult::PayloadTooLarge;
-    }
-
-    if (!out(buf, static_cast<size_t>(n), r, 0)) {
-      return ReadContentResult::Error;
-    }
-    r += static_cast<size_t>(n);
-  }
-
-  return ReadContentResult::Success;
-}
-
-template <typename T>
-inline ReadContentResult read_content_chunked(Stream &strm, T &x,
-                                              size_t payload_max_length,
-                                              ContentReceiverWithProgress out) {
-  const auto bufsiz = 16;
-  char buf[bufsiz];
-
-  stream_line_reader line_reader(strm, buf, bufsiz);
-
-  if (!line_reader.getline()) { return ReadContentResult::Error; }
-
-  unsigned long chunk_len;
-  size_t total_len = 0;
-  while (true) {
-    char *end_ptr;
-
-    chunk_len = std::strtoul(line_reader.ptr(), &end_ptr, 16);
-
-    if (end_ptr == line_reader.ptr()) { return ReadContentResult::Error; }
-    if (chunk_len == ULONG_MAX) { return ReadContentResult::Error; }
-
-    if (chunk_len == 0) { break; }
-
-    // Check if adding this chunk would exceed the payload limit
-    if (total_len > payload_max_length ||
-        payload_max_length - total_len < chunk_len) {
-      return ReadContentResult::PayloadTooLarge;
-    }
-
-    total_len += chunk_len;
-
-    if (!read_content_with_length(strm, chunk_len, nullptr, out)) {
-      return ReadContentResult::Error;
-    }
-
-    if (!line_reader.getline()) { return ReadContentResult::Error; }
-
-    if (strcmp(line_reader.ptr(), "\r\n") != 0) {
-      return ReadContentResult::Error;
-    }
-
-    if (!line_reader.getline()) { return ReadContentResult::Error; }
-  }
-
-  assert(chunk_len == 0);
-
-  // NOTE: In RFC 9112, '7.1 Chunked Transfer Coding' mentions "The chunked
-  // transfer coding is complete when a chunk with a chunk-size of zero is
-  // received, possibly followed by a trailer section, and finally terminated by
-  // an empty line". https://www.rfc-editor.org/rfc/rfc9112.html#section-7.1
-  //
-  // In '7.1.3. Decoding Chunked', however, the pseudo-code in the section
-  // does't care for the existence of the final CRLF. In other words, it seems
-  // to be ok whether the final CRLF exists or not in the chunked data.
-  // https://www.rfc-editor.org/rfc/rfc9112.html#section-7.1.3
-  //
-  // According to the reference code in RFC 9112, cpp-httplib now allows
-  // chunked transfer coding data without the final CRLF.
-  if (!line_reader.getline()) { return ReadContentResult::Success; }
-
-  // RFC 7230 Section 4.1.2 - Headers prohibited in trailers
-  thread_local case_ignore::unordered_set<std::string> prohibited_trailers = {
-      // Message framing
-      "transfer-encoding", "content-length",
-
-      // Routing
-      "host",
-
-      // Authentication
-      "authorization", "www-authenticate", "proxy-authenticate",
-      "proxy-authorization", "cookie", "set-cookie",
-
-      // Request modifiers
-      "cache-control", "expect", "max-forwards", "pragma", "range", "te",
-
-      // Response control
-      "age", "expires", "date", "location", "retry-after", "vary", "warning",
-
-      // Payload processing
-      "content-encoding", "content-type", "content-range", "trailer"};
-
-  // Parse declared trailer headers once for performance
-  case_ignore::unordered_set<std::string> declared_trailers;
-  if (has_header(x.headers, "Trailer")) {
-    auto trailer_header = get_header_value(x.headers, "Trailer", "", 0);
-    auto len = std::strlen(trailer_header);
-
-    split(trailer_header, trailer_header + len, ',',
-          [&](const char *b, const char *e) {
-            std::string key(b, e);
-            if (prohibited_trailers.find(key) == prohibited_trailers.end()) {
-              declared_trailers.insert(key);
-            }
-          });
-  }
-
-  size_t trailer_header_count = 0;
-  while (strcmp(line_reader.ptr(), "\r\n") != 0) {
-    if (line_reader.size() > CPPHTTPLIB_HEADER_MAX_LENGTH) {
-      return ReadContentResult::Error;
-    }
-
-    // Check trailer header count limit
-    if (trailer_header_count >= CPPHTTPLIB_HEADER_MAX_COUNT) {
-      return ReadContentResult::Error;
-    }
-
-    // Exclude line terminator
-    constexpr auto line_terminator_len = 2;
-    auto end = line_reader.ptr() + line_reader.size() - line_terminator_len;
-
-    parse_header(line_reader.ptr(), end,
-                 [&](const std::string &key, const std::string &val) {
-                   if (declared_trailers.find(key) != declared_trailers.end()) {
-                     x.trailers.emplace(key, val);
-                     trailer_header_count++;
-                   }
-                 });
-
-    if (!line_reader.getline()) { return ReadContentResult::Error; }
-  }
-
-  return ReadContentResult::Success;
-}
-
-inline bool is_chunked_transfer_encoding(const Headers &headers) {
-  return case_ignore::equal(
-      get_header_value(headers, "Transfer-Encoding", "", 0), "chunked");
-}
-
-template <typename T, typename U>
-bool prepare_content_receiver(T &x, int &status,
-                              ContentReceiverWithProgress receiver,
-                              bool decompress, U callback) {
-  if (decompress) {
-    std::string encoding = x.get_header_value("Content-Encoding");
-    std::unique_ptr<decompressor> decompressor;
-
-    if (encoding == "gzip" || encoding == "deflate") {
-#ifdef CPPHTTPLIB_ZLIB_SUPPORT
-      decompressor = detail::make_unique<gzip_decompressor>();
-#else
-      status = StatusCode::UnsupportedMediaType_415;
-      return false;
-#endif
-    } else if (encoding.find("br") != std::string::npos) {
-#ifdef CPPHTTPLIB_BROTLI_SUPPORT
-      decompressor = detail::make_unique<brotli_decompressor>();
-#else
-      status = StatusCode::UnsupportedMediaType_415;
-      return false;
-#endif
-    } else if (encoding == "zstd") {
-#ifdef CPPHTTPLIB_ZSTD_SUPPORT
-      decompressor = detail::make_unique<zstd_decompressor>();
-#else
-      status = StatusCode::UnsupportedMediaType_415;
-      return false;
-#endif
-    }
-
-    if (decompressor) {
-      if (decompressor->is_valid()) {
-        ContentReceiverWithProgress out = [&](const char *buf, size_t n,
-                                              size_t off, size_t len) {
-          return decompressor->decompress(buf, n,
-                                          [&](const char *buf2, size_t n2) {
-                                            return receiver(buf2, n2, off, len);
-                                          });
-        };
-        return callback(std::move(out));
-      } else {
-        status = StatusCode::InternalServerError_500;
-        return false;
-      }
-    }
-  }
-
-  ContentReceiverWithProgress out = [&](const char *buf, size_t n, size_t off,
-                                        size_t len) {
-    return receiver(buf, n, off, len);
-  };
-  return callback(std::move(out));
-}
-
-template <typename T>
-bool read_content(Stream &strm, T &x, size_t payload_max_length, int &status,
-                  DownloadProgress progress,
-                  ContentReceiverWithProgress receiver, bool decompress) {
-  return prepare_content_receiver(
-      x, status, std::move(receiver), decompress,
-      [&](const ContentReceiverWithProgress &out) {
-        auto ret = true;
-        auto exceed_payload_max_length = false;
-
-        if (is_chunked_transfer_encoding(x.headers)) {
-          auto result = read_content_chunked(strm, x, payload_max_length, out);
-          if (result == ReadContentResult::Success) {
-            ret = true;
-          } else if (result == ReadContentResult::PayloadTooLarge) {
-            exceed_payload_max_length = true;
-            ret = false;
-          } else {
-            ret = false;
-          }
-        } else if (!has_header(x.headers, "Content-Length")) {
-          auto result =
-              read_content_without_length(strm, payload_max_length, out);
-          if (result == ReadContentResult::Success) {
-            ret = true;
-          } else if (result == ReadContentResult::PayloadTooLarge) {
-            exceed_payload_max_length = true;
-            ret = false;
-          } else {
-            ret = false;
-          }
-        } else {
-          auto is_invalid_value = false;
-          auto len = get_header_value_u64(x.headers, "Content-Length",
-                                          (std::numeric_limits<size_t>::max)(),
-                                          0, is_invalid_value);
-
-          if (is_invalid_value) {
-            ret = false;
-          } else if (len > payload_max_length) {
-            exceed_payload_max_length = true;
-            skip_content_with_length(strm, len);
-            ret = false;
-          } else if (len > 0) {
-            ret = read_content_with_length(strm, len, std::move(progress), out);
-          }
-        }
-
-        if (!ret) {
-          status = exceed_payload_max_length ? StatusCode::PayloadTooLarge_413
-                                             : StatusCode::BadRequest_400;
-        }
-        return ret;
-      });
-}
-
-inline ssize_t write_request_line(Stream &strm, const std::string &method,
-                                  const std::string &path) {
-  std::string s = method;
-  s += " ";
-  s += path;
-  s += " HTTP/1.1\r\n";
-  return strm.write(s.data(), s.size());
-}
-
-inline ssize_t write_response_line(Stream &strm, int status) {
-  std::string s = "HTTP/1.1 ";
-  s += std::to_string(status);
-  s += " ";
-  s += httplib::status_message(status);
-  s += "\r\n";
-  return strm.write(s.data(), s.size());
-}
-
-inline ssize_t write_headers(Stream &strm, const Headers &headers) {
-  ssize_t write_len = 0;
-  for (const auto &x : headers) {
-    std::string s;
-    s = x.first;
-    s += ": ";
-    s += x.second;
-    s += "\r\n";
-
-    auto len = strm.write(s.data(), s.size());
-    if (len < 0) { return len; }
-    write_len += len;
-  }
-  auto len = strm.write("\r\n");
-  if (len < 0) { return len; }
-  write_len += len;
-  return write_len;
-}
-
-inline bool write_data(Stream &strm, const char *d, size_t l) {
-  size_t offset = 0;
-  while (offset < l) {
-    auto length = strm.write(d + offset, l - offset);
-    if (length < 0) { return false; }
-    offset += static_cast<size_t>(length);
-  }
-  return true;
-}
-
-template <typename T>
-inline bool write_content_with_progress(Stream &strm,
-                                        const ContentProvider &content_provider,
-                                        size_t offset, size_t length,
-                                        T is_shutting_down,
-                                        const UploadProgress &upload_progress,
-                                        Error &error) {
-  size_t end_offset = offset + length;
-  size_t start_offset = offset;
-  auto ok = true;
-  DataSink data_sink;
-
-  data_sink.write = [&](const char *d, size_t l) -> bool {
-    if (ok) {
-      if (write_data(strm, d, l)) {
-        offset += l;
-
-        if (upload_progress && length > 0) {
-          size_t current_written = offset - start_offset;
-          if (!upload_progress(current_written, length)) {
-            ok = false;
-            return false;
-          }
-        }
-      } else {
-        ok = false;
-      }
-    }
-    return ok;
-  };
-
-  data_sink.is_writable = [&]() -> bool { return strm.wait_writable(); };
-
-  while (offset < end_offset && !is_shutting_down()) {
-    if (!strm.wait_writable()) {
-      error = Error::Write;
-      return false;
-    } else if (!content_provider(offset, end_offset - offset, data_sink)) {
-      error = Error::Canceled;
-      return false;
-    } else if (!ok) {
-      error = Error::Write;
-      return false;
-    }
-  }
-
-  error = Error::Success;
-  return true;
-}
-
-template <typename T>
-inline bool write_content(Stream &strm, const ContentProvider &content_provider,
-                          size_t offset, size_t length, T is_shutting_down,
-                          Error &error) {
-  return write_content_with_progress<T>(strm, content_provider, offset, length,
-                                        is_shutting_down, nullptr, error);
-}
-
-template <typename T>
-inline bool write_content(Stream &strm, const ContentProvider &content_provider,
-                          size_t offset, size_t length,
-                          const T &is_shutting_down) {
-  auto error = Error::Success;
-  return write_content(strm, content_provider, offset, length, is_shutting_down,
-                       error);
-}
-
-template <typename T>
-inline bool
-write_content_without_length(Stream &strm,
-                             const ContentProvider &content_provider,
-                             const T &is_shutting_down) {
-  size_t offset = 0;
-  auto data_available = true;
-  auto ok = true;
-  DataSink data_sink;
-
-  data_sink.write = [&](const char *d, size_t l) -> bool {
-    if (ok) {
-      offset += l;
-      if (!write_data(strm, d, l)) { ok = false; }
-    }
-    return ok;
-  };
-
-  data_sink.is_writable = [&]() -> bool { return strm.wait_writable(); };
-
-  data_sink.done = [&](void) { data_available = false; };
-
-  while (data_available && !is_shutting_down()) {
-    if (!strm.wait_writable()) {
-      return false;
-    } else if (!content_provider(offset, 0, data_sink)) {
-      return false;
-    } else if (!ok) {
-      return false;
-    }
-  }
-  return true;
-}
-
-template <typename T, typename U>
-inline bool
-write_content_chunked(Stream &strm, const ContentProvider &content_provider,
-                      const T &is_shutting_down, U &compressor, Error &error) {
-  size_t offset = 0;
-  auto data_available = true;
-  auto ok = true;
-  DataSink data_sink;
-
-  data_sink.write = [&](const char *d, size_t l) -> bool {
-    if (ok) {
-      data_available = l > 0;
-      offset += l;
-
-      std::string payload;
-      if (compressor.compress(d, l, false,
-                              [&](const char *data, size_t data_len) {
-                                payload.append(data, data_len);
-                                return true;
-                              })) {
-        if (!payload.empty()) {
-          // Emit chunked response header and footer for each chunk
-          auto chunk =
-              from_i_to_hex(payload.size()) + "\r\n" + payload + "\r\n";
-          if (!write_data(strm, chunk.data(), chunk.size())) { ok = false; }
-        }
-      } else {
-        ok = false;
-      }
-    }
-    return ok;
-  };
-
-  data_sink.is_writable = [&]() -> bool { return strm.wait_writable(); };
-
-  auto done_with_trailer = [&](const Headers *trailer) {
-    if (!ok) { return; }
-
-    data_available = false;
-
-    std::string payload;
-    if (!compressor.compress(nullptr, 0, true,
-                             [&](const char *data, size_t data_len) {
-                               payload.append(data, data_len);
-                               return true;
-                             })) {
-      ok = false;
-      return;
-    }
-
-    if (!payload.empty()) {
-      // Emit chunked response header and footer for each chunk
-      auto chunk = from_i_to_hex(payload.size()) + "\r\n" + payload + "\r\n";
-      if (!write_data(strm, chunk.data(), chunk.size())) {
-        ok = false;
-        return;
-      }
-    }
-
-    constexpr const char done_marker[] = "0\r\n";
-    if (!write_data(strm, done_marker, str_len(done_marker))) { ok = false; }
-
-    // Trailer
-    if (trailer) {
-      for (const auto &kv : *trailer) {
-        std::string field_line = kv.first + ": " + kv.second + "\r\n";
-        if (!write_data(strm, field_line.data(), field_line.size())) {
-          ok = false;
-        }
-      }
-    }
-
-    constexpr const char crlf[] = "\r\n";
-    if (!write_data(strm, crlf, str_len(crlf))) { ok = false; }
-  };
-
-  data_sink.done = [&](void) { done_with_trailer(nullptr); };
-
-  data_sink.done_with_trailer = [&](const Headers &trailer) {
-    done_with_trailer(&trailer);
-  };
-
-  while (data_available && !is_shutting_down()) {
-    if (!strm.wait_writable()) {
-      error = Error::Write;
-      return false;
-    } else if (!content_provider(offset, 0, data_sink)) {
-      error = Error::Canceled;
-      return false;
-    } else if (!ok) {
-      error = Error::Write;
-      return false;
-    }
-  }
-
-  error = Error::Success;
-  return true;
-}
-
-template <typename T, typename U>
-inline bool write_content_chunked(Stream &strm,
-                                  const ContentProvider &content_provider,
-                                  const T &is_shutting_down, U &compressor) {
-  auto error = Error::Success;
-  return write_content_chunked(strm, content_provider, is_shutting_down,
-                               compressor, error);
-}
-
-template <typename T>
-inline bool redirect(T &cli, Request &req, Response &res,
-                     const std::string &path, const std::string &location,
-                     Error &error) {
-  Request new_req = req;
-  new_req.path = path;
-  new_req.redirect_count_ -= 1;
-
-  if (res.status == StatusCode::SeeOther_303 &&
-      (req.method != "GET" && req.method != "HEAD")) {
-    new_req.method = "GET";
-    new_req.body.clear();
-    new_req.headers.clear();
-  }
-
-  Response new_res;
-
-  auto ret = cli.send(new_req, new_res, error);
-  if (ret) {
-    req = new_req;
-    res = new_res;
-
-    if (res.location.empty()) { res.location = location; }
-  }
-  return ret;
-}
-
-inline std::string params_to_query_str(const Params &params) {
-  std::string query;
-
-  for (auto it = params.begin(); it != params.end(); ++it) {
-    if (it != params.begin()) { query += "&"; }
-    query += encode_query_component(it->first);
-    query += "=";
-    query += encode_query_component(it->second);
-  }
-  return query;
-}
-
-inline void parse_query_text(const char *data, std::size_t size,
-                             Params &params) {
-  std::set<std::string> cache;
-  split(data, data + size, '&', [&](const char *b, const char *e) {
-    std::string kv(b, e);
-    if (cache.find(kv) != cache.end()) { return; }
-    cache.insert(std::move(kv));
-
-    std::string key;
-    std::string val;
-    divide(b, static_cast<std::size_t>(e - b), '=',
-           [&](const char *lhs_data, std::size_t lhs_size, const char *rhs_data,
-               std::size_t rhs_size) {
-             key.assign(lhs_data, lhs_size);
-             val.assign(rhs_data, rhs_size);
-           });
-
-    if (!key.empty()) {
-      params.emplace(decode_query_component(key), decode_query_component(val));
-    }
-  });
-}
-
-inline void parse_query_text(const std::string &s, Params &params) {
-  parse_query_text(s.data(), s.size(), params);
-}
-
-inline bool parse_multipart_boundary(const std::string &content_type,
-                                     std::string &boundary) {
-  auto boundary_keyword = "boundary=";
-  auto pos = content_type.find(boundary_keyword);
-  if (pos == std::string::npos) { return false; }
-  auto end = content_type.find(';', pos);
-  auto beg = pos + strlen(boundary_keyword);
-  boundary = trim_double_quotes_copy(content_type.substr(beg, end - beg));
-  return !boundary.empty();
-}
-
-inline void parse_disposition_params(const std::string &s, Params &params) {
-  std::set<std::string> cache;
-  split(s.data(), s.data() + s.size(), ';', [&](const char *b, const char *e) {
-    std::string kv(b, e);
-    if (cache.find(kv) != cache.end()) { return; }
-    cache.insert(kv);
-
-    std::string key;
-    std::string val;
-    split(b, e, '=', [&](const char *b2, const char *e2) {
-      if (key.empty()) {
-        key.assign(b2, e2);
-      } else {
-        val.assign(b2, e2);
-      }
-    });
-
-    if (!key.empty()) {
-      params.emplace(trim_double_quotes_copy((key)),
-                     trim_double_quotes_copy((val)));
-    }
-  });
-}
-
-#ifdef CPPHTTPLIB_NO_EXCEPTIONS
-inline bool parse_range_header(const std::string &s, Ranges &ranges) {
-#else
-inline bool parse_range_header(const std::string &s, Ranges &ranges) try {
-#endif
-  auto is_valid = [](const std::string &str) {
-    return std::all_of(str.cbegin(), str.cend(),
-                       [](unsigned char c) { return std::isdigit(c); });
-  };
-
-  if (s.size() > 7 && s.compare(0, 6, "bytes=") == 0) {
-    const auto pos = static_cast<size_t>(6);
-    const auto len = static_cast<size_t>(s.size() - 6);
-    auto all_valid_ranges = true;
-    split(&s[pos], &s[pos + len], ',', [&](const char *b, const char *e) {
-      if (!all_valid_ranges) { return; }
-
-      const auto it = std::find(b, e, '-');
-      if (it == e) {
-        all_valid_ranges = false;
-        return;
-      }
-
-      const auto lhs = std::string(b, it);
-      const auto rhs = std::string(it + 1, e);
-      if (!is_valid(lhs) || !is_valid(rhs)) {
-        all_valid_ranges = false;
-        return;
-      }
-
-      const auto first =
-          static_cast<ssize_t>(lhs.empty() ? -1 : std::stoll(lhs));
-      const auto last =
-          static_cast<ssize_t>(rhs.empty() ? -1 : std::stoll(rhs));
-      if ((first == -1 && last == -1) ||
-          (first != -1 && last != -1 && first > last)) {
-        all_valid_ranges = false;
-        return;
-      }
-
-      ranges.emplace_back(first, last);
-    });
-    return all_valid_ranges && !ranges.empty();
-  }
-  return false;
-#ifdef CPPHTTPLIB_NO_EXCEPTIONS
-}
-#else
-} catch (...) { return false; }
-#endif
-
-inline bool parse_accept_header(const std::string &s,
-                                std::vector<std::string> &content_types) {
-  content_types.clear();
-
-  // Empty string is considered valid (no preference)
-  if (s.empty()) { return true; }
-
-  // Check for invalid patterns: leading/trailing commas or consecutive commas
-  if (s.front() == ',' || s.back() == ',' ||
-      s.find(",,") != std::string::npos) {
-    return false;
-  }
-
-  struct AcceptEntry {
-    std::string media_type;
-    double quality;
-    int order; // Original order in header
-  };
-
-  std::vector<AcceptEntry> entries;
-  int order = 0;
-  bool has_invalid_entry = false;
-
-  // Split by comma and parse each entry
-  split(s.data(), s.data() + s.size(), ',', [&](const char *b, const char *e) {
-    std::string entry(b, e);
-    entry = trim_copy(entry);
-
-    if (entry.empty()) {
-      has_invalid_entry = true;
-      return;
-    }
-
-    AcceptEntry accept_entry;
-    accept_entry.quality = 1.0; // Default quality
-    accept_entry.order = order++;
-
-    // Find q= parameter
-    auto q_pos = entry.find(";q=");
-    if (q_pos == std::string::npos) { q_pos = entry.find("; q="); }
-
-    if (q_pos != std::string::npos) {
-      // Extract media type (before q parameter)
-      accept_entry.media_type = trim_copy(entry.substr(0, q_pos));
-
-      // Extract quality value
-      auto q_start = entry.find('=', q_pos) + 1;
-      auto q_end = entry.find(';', q_start);
-      if (q_end == std::string::npos) { q_end = entry.length(); }
-
-      std::string quality_str =
-          trim_copy(entry.substr(q_start, q_end - q_start));
-      if (quality_str.empty()) {
-        has_invalid_entry = true;
-        return;
-      }
-
-#ifdef CPPHTTPLIB_NO_EXCEPTIONS
-      {
-        std::istringstream iss(quality_str);
-        iss >> accept_entry.quality;
-
-        // Check if conversion was successful and entire string was consumed
-        if (iss.fail() || !iss.eof()) {
-          has_invalid_entry = true;
-          return;
-        }
-      }
-#else
-      try {
-        accept_entry.quality = std::stod(quality_str);
-      } catch (...) {
-        has_invalid_entry = true;
-        return;
-      }
-#endif
-      // Check if quality is in valid range [0.0, 1.0]
-      if (accept_entry.quality < 0.0 || accept_entry.quality > 1.0) {
-        has_invalid_entry = true;
-        return;
-      }
-    } else {
-      // No quality parameter, use entire entry as media type
-      accept_entry.media_type = entry;
-    }
-
-    // Remove additional parameters from media type
-    auto param_pos = accept_entry.media_type.find(';');
-    if (param_pos != std::string::npos) {
-      accept_entry.media_type =
-          trim_copy(accept_entry.media_type.substr(0, param_pos));
-    }
-
-    // Basic validation of media type format
-    if (accept_entry.media_type.empty()) {
-      has_invalid_entry = true;
-      return;
-    }
-
-    // Check for basic media type format (should contain '/' or be '*')
-    if (accept_entry.media_type != "*" &&
-        accept_entry.media_type.find('/') == std::string::npos) {
-      has_invalid_entry = true;
-      return;
-    }
-
-    entries.push_back(accept_entry);
-  });
-
-  // Return false if any invalid entry was found
-  if (has_invalid_entry) { return false; }
-
-  // Sort by quality (descending), then by original order (ascending)
-  std::sort(entries.begin(), entries.end(),
-            [](const AcceptEntry &a, const AcceptEntry &b) {
-              if (a.quality != b.quality) {
-                return a.quality > b.quality; // Higher quality first
-              }
-              return a.order < b.order; // Earlier order first for same quality
-            });
-
-  // Extract sorted media types
-  content_types.reserve(entries.size());
-  for (const auto &entry : entries) {
-    content_types.push_back(entry.media_type);
-  }
-
-  return true;
-}
-
-class FormDataParser {
-public:
-  FormDataParser() = default;
-
-  void set_boundary(std::string &&boundary) {
-    boundary_ = boundary;
-    dash_boundary_crlf_ = dash_ + boundary_ + crlf_;
-    crlf_dash_boundary_ = crlf_ + dash_ + boundary_;
-  }
-
-  bool is_valid() const { return is_valid_; }
-
-  bool parse(const char *buf, size_t n, const FormDataHeader &header_callback,
-             const ContentReceiver &content_callback) {
-
-    buf_append(buf, n);
-
-    while (buf_size() > 0) {
-      switch (state_) {
-      case 0: { // Initial boundary
-        auto pos = buf_find(dash_boundary_crlf_);
-        if (pos == buf_size()) { return true; }
-        buf_erase(pos + dash_boundary_crlf_.size());
-        state_ = 1;
-        break;
-      }
-      case 1: { // New entry
-        clear_file_info();
-        state_ = 2;
-        break;
-      }
-      case 2: { // Headers
-        auto pos = buf_find(crlf_);
-        if (pos > CPPHTTPLIB_HEADER_MAX_LENGTH) { return false; }
-        while (pos < buf_size()) {
-          // Empty line
-          if (pos == 0) {
-            if (!header_callback(file_)) {
-              is_valid_ = false;
-              return false;
-            }
-            buf_erase(crlf_.size());
-            state_ = 3;
-            break;
-          }
-
-          const auto header = buf_head(pos);
-
-          if (!parse_header(header.data(), header.data() + header.size(),
-                            [&](const std::string &, const std::string &) {})) {
-            is_valid_ = false;
-            return false;
-          }
-
-          // Parse and emplace space trimmed headers into a map
-          if (!parse_header(
-                  header.data(), header.data() + header.size(),
-                  [&](const std::string &key, const std::string &val) {
-                    file_.headers.emplace(key, val);
-                  })) {
-            is_valid_ = false;
-            return false;
-          }
-
-          constexpr const char header_content_type[] = "Content-Type:";
-
-          if (start_with_case_ignore(header, header_content_type)) {
-            file_.content_type =
-                trim_copy(header.substr(str_len(header_content_type)));
-          } else {
-            thread_local const std::regex re_content_disposition(
-                R"~(^Content-Disposition:\s*form-data;\s*(.*)$)~",
-                std::regex_constants::icase);
-
-            std::smatch m;
-            if (std::regex_match(header, m, re_content_disposition)) {
-              Params params;
-              parse_disposition_params(m[1], params);
-
-              auto it = params.find("name");
-              if (it != params.end()) {
-                file_.name = it->second;
-              } else {
-                is_valid_ = false;
-                return false;
-              }
-
-              it = params.find("filename");
-              if (it != params.end()) { file_.filename = it->second; }
-
-              it = params.find("filename*");
-              if (it != params.end()) {
-                // Only allow UTF-8 encoding...
-                thread_local const std::regex re_rfc5987_encoding(
-                    R"~(^UTF-8''(.+?)$)~", std::regex_constants::icase);
-
-                std::smatch m2;
-                if (std::regex_match(it->second, m2, re_rfc5987_encoding)) {
-                  file_.filename = decode_path_component(m2[1]); // override...
-                } else {
-                  is_valid_ = false;
-                  return false;
-                }
-              }
-            }
-          }
-          buf_erase(pos + crlf_.size());
-          pos = buf_find(crlf_);
-        }
-        if (state_ != 3) { return true; }
-        break;
-      }
-      case 3: { // Body
-        if (crlf_dash_boundary_.size() > buf_size()) { return true; }
-        auto pos = buf_find(crlf_dash_boundary_);
-        if (pos < buf_size()) {
-          if (!content_callback(buf_data(), pos)) {
-            is_valid_ = false;
-            return false;
-          }
-          buf_erase(pos + crlf_dash_boundary_.size());
-          state_ = 4;
-        } else {
-          auto len = buf_size() - crlf_dash_boundary_.size();
-          if (len > 0) {
-            if (!content_callback(buf_data(), len)) {
-              is_valid_ = false;
-              return false;
-            }
-            buf_erase(len);
-          }
-          return true;
-        }
-        break;
-      }
-      case 4: { // Boundary
-        if (crlf_.size() > buf_size()) { return true; }
-        if (buf_start_with(crlf_)) {
-          buf_erase(crlf_.size());
-          state_ = 1;
-        } else {
-          if (dash_.size() > buf_size()) { return true; }
-          if (buf_start_with(dash_)) {
-            buf_erase(dash_.size());
-            is_valid_ = true;
-            buf_erase(buf_size()); // Remove epilogue
-          } else {
-            return true;
-          }
-        }
-        break;
-      }
-      }
-    }
-
-    return true;
-  }
-
-private:
-  void clear_file_info() {
-    file_.name.clear();
-    file_.filename.clear();
-    file_.content_type.clear();
-    file_.headers.clear();
-  }
-
-  bool start_with_case_ignore(const std::string &a, const char *b) const {
-    const auto b_len = strlen(b);
-    if (a.size() < b_len) { return false; }
-    for (size_t i = 0; i < b_len; i++) {
-      if (case_ignore::to_lower(a[i]) != case_ignore::to_lower(b[i])) {
-        return false;
-      }
-    }
-    return true;
-  }
-
-  const std::string dash_ = "--";
-  const std::string crlf_ = "\r\n";
-  std::string boundary_;
-  std::string dash_boundary_crlf_;
-  std::string crlf_dash_boundary_;
-
-  size_t state_ = 0;
-  bool is_valid_ = false;
-  FormData file_;
-
-  // Buffer
-  bool start_with(const std::string &a, size_t spos, size_t epos,
-                  const std::string &b) const {
-    if (epos - spos < b.size()) { return false; }
-    for (size_t i = 0; i < b.size(); i++) {
-      if (a[i + spos] != b[i]) { return false; }
-    }
-    return true;
-  }
-
-  size_t buf_size() const { return buf_epos_ - buf_spos_; }
-
-  const char *buf_data() const { return &buf_[buf_spos_]; }
-
-  std::string buf_head(size_t l) const { return buf_.substr(buf_spos_, l); }
-
-  bool buf_start_with(const std::string &s) const {
-    return start_with(buf_, buf_spos_, buf_epos_, s);
-  }
-
-  size_t buf_find(const std::string &s) const {
-    auto c = s.front();
-
-    size_t off = buf_spos_;
-    while (off < buf_epos_) {
-      auto pos = off;
-      while (true) {
-        if (pos == buf_epos_) { return buf_size(); }
-        if (buf_[pos] == c) { break; }
-        pos++;
-      }
-
-      auto remaining_size = buf_epos_ - pos;
-      if (s.size() > remaining_size) { return buf_size(); }
-
-      if (start_with(buf_, pos, buf_epos_, s)) { return pos - buf_spos_; }
-
-      off = pos + 1;
-    }
-
-    return buf_size();
-  }
-
-  void buf_append(const char *data, size_t n) {
-    auto remaining_size = buf_size();
-    if (remaining_size > 0 && buf_spos_ > 0) {
-      for (size_t i = 0; i < remaining_size; i++) {
-        buf_[i] = buf_[buf_spos_ + i];
-      }
-    }
-    buf_spos_ = 0;
-    buf_epos_ = remaining_size;
-
-    if (remaining_size + n > buf_.size()) { buf_.resize(remaining_size + n); }
-
-    for (size_t i = 0; i < n; i++) {
-      buf_[buf_epos_ + i] = data[i];
-    }
-    buf_epos_ += n;
-  }
-
-  void buf_erase(size_t size) { buf_spos_ += size; }
-
-  std::string buf_;
-  size_t buf_spos_ = 0;
-  size_t buf_epos_ = 0;
-};
-
-inline std::string random_string(size_t length) {
-  constexpr const char data[] =
-      "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz";
-
-  thread_local auto engine([]() {
-    // std::random_device might actually be deterministic on some
-    // platforms, but due to lack of support in the c++ standard library,
-    // doing better requires either some ugly hacks or breaking portability.
-    std::random_device seed_gen;
-    // Request 128 bits of entropy for initialization
-    std::seed_seq seed_sequence{seed_gen(), seed_gen(), seed_gen(), seed_gen()};
-    return std::mt19937(seed_sequence);
-  }());
-
-  std::string result;
-  for (size_t i = 0; i < length; i++) {
-    result += data[engine() % (sizeof(data) - 1)];
-  }
-  return result;
-}
-
-inline std::string make_multipart_data_boundary() {
-  return "--cpp-httplib-multipart-data-" + detail::random_string(16);
-}
-
-inline bool is_multipart_boundary_chars_valid(const std::string &boundary) {
-  auto valid = true;
-  for (size_t i = 0; i < boundary.size(); i++) {
-    auto c = boundary[i];
-    if (!std::isalnum(c) && c != '-' && c != '_') {
-      valid = false;
-      break;
-    }
-  }
-  return valid;
-}
-
-template <typename T>
-inline std::string
-serialize_multipart_formdata_item_begin(const T &item,
-                                        const std::string &boundary) {
-  std::string body = "--" + boundary + "\r\n";
-  body += "Content-Disposition: form-data; name=\"" + item.name + "\"";
-  if (!item.filename.empty()) {
-    body += "; filename=\"" + item.filename + "\"";
-  }
-  body += "\r\n";
-  if (!item.content_type.empty()) {
-    body += "Content-Type: " + item.content_type + "\r\n";
-  }
-  body += "\r\n";
-
-  return body;
-}
-
-inline std::string serialize_multipart_formdata_item_end() { return "\r\n"; }
-
-inline std::string
-serialize_multipart_formdata_finish(const std::string &boundary) {
-  return "--" + boundary + "--\r\n";
-}
-
-inline std::string
-serialize_multipart_formdata_get_content_type(const std::string &boundary) {
-  return "multipart/form-data; boundary=" + boundary;
-}
-
-inline std::string
-serialize_multipart_formdata(const UploadFormDataItems &items,
-                             const std::string &boundary, bool finish = true) {
-  std::string body;
-
-  for (const auto &item : items) {
-    body += serialize_multipart_formdata_item_begin(item, boundary);
-    body += item.content + serialize_multipart_formdata_item_end();
-  }
-
-  if (finish) { body += serialize_multipart_formdata_finish(boundary); }
-
-  return body;
-}
-
-inline void coalesce_ranges(Ranges &ranges, size_t content_length) {
-  if (ranges.size() <= 1) return;
-
-  // Sort ranges by start position
-  std::sort(ranges.begin(), ranges.end(),
-            [](const Range &a, const Range &b) { return a.first < b.first; });
-
-  Ranges coalesced;
-  coalesced.reserve(ranges.size());
-
-  for (auto &r : ranges) {
-    auto first_pos = r.first;
-    auto last_pos = r.second;
-
-    // Handle special cases like in range_error
-    if (first_pos == -1 && last_pos == -1) {
-      first_pos = 0;
-      last_pos = static_cast<ssize_t>(content_length);
-    }
-
-    if (first_pos == -1) {
-      first_pos = static_cast<ssize_t>(content_length) - last_pos;
-      last_pos = static_cast<ssize_t>(content_length) - 1;
-    }
-
-    if (last_pos == -1 || last_pos >= static_cast<ssize_t>(content_length)) {
-      last_pos = static_cast<ssize_t>(content_length) - 1;
-    }
-
-    // Skip invalid ranges
-    if (!(0 <= first_pos && first_pos <= last_pos &&
-          last_pos < static_cast<ssize_t>(content_length))) {
-      continue;
-    }
-
-    // Coalesce with previous range if overlapping or adjacent (but not
-    // identical)
-    if (!coalesced.empty()) {
-      auto &prev = coalesced.back();
-      // Check if current range overlaps or is adjacent to previous range
-      // but don't coalesce identical ranges (allow duplicates)
-      if (first_pos <= prev.second + 1 &&
-          !(first_pos == prev.first && last_pos == prev.second)) {
-        // Extend the previous range
-        prev.second = (std::max)(prev.second, last_pos);
-        continue;
-      }
-    }
-
-    // Add new range
-    coalesced.emplace_back(first_pos, last_pos);
-  }
-
-  ranges = std::move(coalesced);
-}
-
-inline bool range_error(Request &req, Response &res) {
-  if (!req.ranges.empty() && 200 <= res.status && res.status < 300) {
-    ssize_t content_len = static_cast<ssize_t>(
-        res.content_length_ ? res.content_length_ : res.body.size());
-
-    std::vector<std::pair<ssize_t, ssize_t>> processed_ranges;
-    size_t overwrapping_count = 0;
-
-    // NOTE: The following Range check is based on '14.2. Range' in RFC 9110
-    // 'HTTP Semantics' to avoid potential denial-of-service attacks.
-    // https://www.rfc-editor.org/rfc/rfc9110#section-14.2
-
-    // Too many ranges
-    if (req.ranges.size() > CPPHTTPLIB_RANGE_MAX_COUNT) { return true; }
-
-    for (auto &r : req.ranges) {
-      auto &first_pos = r.first;
-      auto &last_pos = r.second;
-
-      if (first_pos == -1 && last_pos == -1) {
-        first_pos = 0;
-        last_pos = content_len;
-      }
-
-      if (first_pos == -1) {
-        first_pos = content_len - last_pos;
-        last_pos = content_len - 1;
-      }
-
-      // NOTE: RFC-9110 '14.1.2. Byte Ranges':
-      // A client can limit the number of bytes requested without knowing the
-      // size of the selected representation. If the last-pos value is absent,
-      // or if the value is greater than or equal to the current length of the
-      // representation data, the byte range is interpreted as the remainder of
-      // the representation (i.e., the server replaces the value of last-pos
-      // with a value that is one less than the current length of the selected
-      // representation).
-      // https://www.rfc-editor.org/rfc/rfc9110.html#section-14.1.2-6
-      if (last_pos == -1 || last_pos >= content_len) {
-        last_pos = content_len - 1;
-      }
-
-      // Range must be within content length
-      if (!(0 <= first_pos && first_pos <= last_pos &&
-            last_pos <= content_len - 1)) {
-        return true;
-      }
-
-      // Request must not have more than two overlapping ranges
-      for (const auto &processed_range : processed_ranges) {
-        if (!(last_pos < processed_range.first ||
-              first_pos > processed_range.second)) {
-          overwrapping_count++;
-          if (overwrapping_count > 2) { return true; }
-          break; // Only count once per range
-        }
-      }
-
-      processed_ranges.emplace_back(first_pos, last_pos);
-    }
-
-    // After validation, coalesce overlapping ranges as per RFC 9110
-    coalesce_ranges(req.ranges, static_cast<size_t>(content_len));
-  }
-
-  return false;
-}
-
-inline std::pair<size_t, size_t>
-get_range_offset_and_length(Range r, size_t content_length) {
-  assert(r.first != -1 && r.second != -1);
-  assert(0 <= r.first && r.first < static_cast<ssize_t>(content_length));
-  assert(r.first <= r.second &&
-         r.second < static_cast<ssize_t>(content_length));
-  (void)(content_length);
-  return std::make_pair(r.first, static_cast<size_t>(r.second - r.first) + 1);
-}
-
-inline std::string make_content_range_header_field(
-    const std::pair<size_t, size_t> &offset_and_length, size_t content_length) {
-  auto st = offset_and_length.first;
-  auto ed = st + offset_and_length.second - 1;
-
-  std::string field = "bytes ";
-  field += std::to_string(st);
-  field += "-";
-  field += std::to_string(ed);
-  field += "/";
-  field += std::to_string(content_length);
-  return field;
-}
-
-template <typename SToken, typename CToken, typename Content>
-bool process_multipart_ranges_data(const Request &req,
-                                   const std::string &boundary,
-                                   const std::string &content_type,
-                                   size_t content_length, SToken stoken,
-                                   CToken ctoken, Content content) {
-  for (size_t i = 0; i < req.ranges.size(); i++) {
-    ctoken("--");
-    stoken(boundary);
-    ctoken("\r\n");
-    if (!content_type.empty()) {
-      ctoken("Content-Type: ");
-      stoken(content_type);
-      ctoken("\r\n");
-    }
-
-    auto offset_and_length =
-        get_range_offset_and_length(req.ranges[i], content_length);
-
-    ctoken("Content-Range: ");
-    stoken(make_content_range_header_field(offset_and_length, content_length));
-    ctoken("\r\n");
-    ctoken("\r\n");
-
-    if (!content(offset_and_length.first, offset_and_length.second)) {
-      return false;
-    }
-    ctoken("\r\n");
-  }
-
-  ctoken("--");
-  stoken(boundary);
-  ctoken("--");
-
-  return true;
-}
-
-inline void make_multipart_ranges_data(const Request &req, Response &res,
-                                       const std::string &boundary,
-                                       const std::string &content_type,
-                                       size_t content_length,
-                                       std::string &data) {
-  process_multipart_ranges_data(
-      req, boundary, content_type, content_length,
-      [&](const std::string &token) { data += token; },
-      [&](const std::string &token) { data += token; },
-      [&](size_t offset, size_t length) {
-        assert(offset + length <= content_length);
-        data += res.body.substr(offset, length);
-        return true;
-      });
-}
-
-inline size_t get_multipart_ranges_data_length(const Request &req,
-                                               const std::string &boundary,
-                                               const std::string &content_type,
-                                               size_t content_length) {
-  size_t data_length = 0;
-
-  process_multipart_ranges_data(
-      req, boundary, content_type, content_length,
-      [&](const std::string &token) { data_length += token.size(); },
-      [&](const std::string &token) { data_length += token.size(); },
-      [&](size_t /*offset*/, size_t length) {
-        data_length += length;
-        return true;
-      });
-
-  return data_length;
-}
-
-template <typename T>
-inline bool
-write_multipart_ranges_data(Stream &strm, const Request &req, Response &res,
-                            const std::string &boundary,
-                            const std::string &content_type,
-                            size_t content_length, const T &is_shutting_down) {
-  return process_multipart_ranges_data(
-      req, boundary, content_type, content_length,
-      [&](const std::string &token) { strm.write(token); },
-      [&](const std::string &token) { strm.write(token); },
-      [&](size_t offset, size_t length) {
-        return write_content(strm, res.content_provider_, offset, length,
-                             is_shutting_down);
-      });
-}
-
-inline bool expect_content(const Request &req) {
-  if (req.method == "POST" || req.method == "PUT" || req.method == "PATCH" ||
-      req.method == "DELETE") {
-    return true;
-  }
-  if (req.has_header("Content-Length") &&
-      req.get_header_value_u64("Content-Length") > 0) {
-    return true;
-  }
-  if (is_chunked_transfer_encoding(req.headers)) { return true; }
-  return false;
-}
-
-inline bool has_crlf(const std::string &s) {
-  auto p = s.c_str();
-  while (*p) {
-    if (*p == '\r' || *p == '\n') { return true; }
-    p++;
-  }
-  return false;
-}
-
-#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
-inline std::string message_digest(const std::string &s, const EVP_MD *algo) {
-  auto context = std::unique_ptr<EVP_MD_CTX, decltype(&EVP_MD_CTX_free)>(
-      EVP_MD_CTX_new(), EVP_MD_CTX_free);
-
-  unsigned int hash_length = 0;
-  unsigned char hash[EVP_MAX_MD_SIZE];
-
-  EVP_DigestInit_ex(context.get(), algo, nullptr);
-  EVP_DigestUpdate(context.get(), s.c_str(), s.size());
-  EVP_DigestFinal_ex(context.get(), hash, &hash_length);
-
-  std::stringstream ss;
-  for (auto i = 0u; i < hash_length; ++i) {
-    ss << std::hex << std::setw(2) << std::setfill('0')
-       << static_cast<unsigned int>(hash[i]);
-  }
-
-  return ss.str();
-}
-
-inline std::string MD5(const std::string &s) {
-  return message_digest(s, EVP_md5());
-}
-
-inline std::string SHA_256(const std::string &s) {
-  return message_digest(s, EVP_sha256());
-}
-
-inline std::string SHA_512(const std::string &s) {
-  return message_digest(s, EVP_sha512());
-}
-
-inline std::pair<std::string, std::string> make_digest_authentication_header(
-    const Request &req, const std::map<std::string, std::string> &auth,
-    size_t cnonce_count, const std::string &cnonce, const std::string &username,
-    const std::string &password, bool is_proxy = false) {
-  std::string nc;
-  {
-    std::stringstream ss;
-    ss << std::setfill('0') << std::setw(8) << std::hex << cnonce_count;
-    nc = ss.str();
-  }
-
-  std::string qop;
-  if (auth.find("qop") != auth.end()) {
-    qop = auth.at("qop");
-    if (qop.find("auth-int") != std::string::npos) {
-      qop = "auth-int";
-    } else if (qop.find("auth") != std::string::npos) {
-      qop = "auth";
-    } else {
-      qop.clear();
-    }
-  }
-
-  std::string algo = "MD5";
-  if (auth.find("algorithm") != auth.end()) { algo = auth.at("algorithm"); }
-
-  std::string response;
-  {
-    auto H = algo == "SHA-256"   ? detail::SHA_256
-             : algo == "SHA-512" ? detail::SHA_512
-                                 : detail::MD5;
-
-    auto A1 = username + ":" + auth.at("realm") + ":" + password;
-
-    auto A2 = req.method + ":" + req.path;
-    if (qop == "auth-int") { A2 += ":" + H(req.body); }
-
-    if (qop.empty()) {
-      response = H(H(A1) + ":" + auth.at("nonce") + ":" + H(A2));
-    } else {
-      response = H(H(A1) + ":" + auth.at("nonce") + ":" + nc + ":" + cnonce +
-                   ":" + qop + ":" + H(A2));
-    }
-  }
-
-  auto opaque = (auth.find("opaque") != auth.end()) ? auth.at("opaque") : "";
-
-  auto field = "Digest username=\"" + username + "\", realm=\"" +
-               auth.at("realm") + "\", nonce=\"" + auth.at("nonce") +
-               "\", uri=\"" + req.path + "\", algorithm=" + algo +
-               (qop.empty() ? ", response=\""
-                            : ", qop=" + qop + ", nc=" + nc + ", cnonce=\"" +
-                                  cnonce + "\", response=\"") +
-               response + "\"" +
-               (opaque.empty() ? "" : ", opaque=\"" + opaque + "\"");
-
-  auto key = is_proxy ? "Proxy-Authorization" : "Authorization";
-  return std::make_pair(key, field);
-}
-
-inline bool is_ssl_peer_could_be_closed(SSL *ssl, socket_t sock) {
-  detail::set_nonblocking(sock, true);
-  auto se = detail::scope_exit([&]() { detail::set_nonblocking(sock, false); });
-
-  char buf[1];
-  return !SSL_peek(ssl, buf, 1) &&
-         SSL_get_error(ssl, 0) == SSL_ERROR_ZERO_RETURN;
-}
-
-#ifdef _WIN32
-// NOTE: This code came up with the following stackoverflow post:
-// https://stackoverflow.com/questions/9507184/can-openssl-on-windows-use-the-system-certificate-store
-inline bool load_system_certs_on_windows(X509_STORE *store) {
-  auto hStore = CertOpenSystemStoreW((HCRYPTPROV_LEGACY)NULL, L"ROOT");
-  if (!hStore) { return false; }
-
-  auto result = false;
-  PCCERT_CONTEXT pContext = NULL;
-  while ((pContext = CertEnumCertificatesInStore(hStore, pContext)) !=
-         nullptr) {
-    auto encoded_cert =
-        static_cast<const unsigned char *>(pContext->pbCertEncoded);
-
-    auto x509 = d2i_X509(NULL, &encoded_cert, pContext->cbCertEncoded);
-    if (x509) {
-      X509_STORE_add_cert(store, x509);
-      X509_free(x509);
-      result = true;
-    }
-  }
-
-  CertFreeCertificateContext(pContext);
-  CertCloseStore(hStore, 0);
-
-  return result;
-}
-#elif defined(CPPHTTPLIB_USE_CERTS_FROM_MACOSX_KEYCHAIN) && TARGET_OS_MAC
-template <typename T>
-using CFObjectPtr =
-    std::unique_ptr<typename std::remove_pointer<T>::type, void (*)(CFTypeRef)>;
-
-inline void cf_object_ptr_deleter(CFTypeRef obj) {
-  if (obj) { CFRelease(obj); }
-}
-
-inline bool retrieve_certs_from_keychain(CFObjectPtr<CFArrayRef> &certs) {
-  CFStringRef keys[] = {kSecClass, kSecMatchLimit, kSecReturnRef};
-  CFTypeRef values[] = {kSecClassCertificate, kSecMatchLimitAll,
-                        kCFBooleanTrue};
-
-  CFObjectPtr<CFDictionaryRef> query(
-      CFDictionaryCreate(nullptr, reinterpret_cast<const void **>(keys), values,
-                         sizeof(keys) / sizeof(keys[0]),
-                         &kCFTypeDictionaryKeyCallBacks,
-                         &kCFTypeDictionaryValueCallBacks),
-      cf_object_ptr_deleter);
-
-  if (!query) { return false; }
-
-  CFTypeRef security_items = nullptr;
-  if (SecItemCopyMatching(query.get(), &security_items) != errSecSuccess ||
-      CFArrayGetTypeID() != CFGetTypeID(security_items)) {
-    return false;
-  }
-
-  certs.reset(reinterpret_cast<CFArrayRef>(security_items));
-  return true;
-}
-
-inline bool retrieve_root_certs_from_keychain(CFObjectPtr<CFArrayRef> &certs) {
-  CFArrayRef root_security_items = nullptr;
-  if (SecTrustCopyAnchorCertificates(&root_security_items) != errSecSuccess) {
-    return false;
-  }
-
-  certs.reset(root_security_items);
-  return true;
-}
-
-inline bool add_certs_to_x509_store(CFArrayRef certs, X509_STORE *store) {
-  auto result = false;
-  for (auto i = 0; i < CFArrayGetCount(certs); ++i) {
-    const auto cert = reinterpret_cast<const __SecCertificate *>(
-        CFArrayGetValueAtIndex(certs, i));
-
-    if (SecCertificateGetTypeID() != CFGetTypeID(cert)) { continue; }
-
-    CFDataRef cert_data = nullptr;
-    if (SecItemExport(cert, kSecFormatX509Cert, 0, nullptr, &cert_data) !=
-        errSecSuccess) {
-      continue;
-    }
-
-    CFObjectPtr<CFDataRef> cert_data_ptr(cert_data, cf_object_ptr_deleter);
-
-    auto encoded_cert = static_cast<const unsigned char *>(
-        CFDataGetBytePtr(cert_data_ptr.get()));
-
-    auto x509 =
-        d2i_X509(NULL, &encoded_cert, CFDataGetLength(cert_data_ptr.get()));
-
-    if (x509) {
-      X509_STORE_add_cert(store, x509);
-      X509_free(x509);
-      result = true;
-    }
-  }
-
-  return result;
-}
-
-inline bool load_system_certs_on_macos(X509_STORE *store) {
-  auto result = false;
-  CFObjectPtr<CFArrayRef> certs(nullptr, cf_object_ptr_deleter);
-  if (retrieve_certs_from_keychain(certs) && certs) {
-    result = add_certs_to_x509_store(certs.get(), store);
-  }
-
-  if (retrieve_root_certs_from_keychain(certs) && certs) {
-    result = add_certs_to_x509_store(certs.get(), store) || result;
-  }
-
-  return result;
-}
-#endif // _WIN32
-#endif // CPPHTTPLIB_OPENSSL_SUPPORT
-
-#ifdef _WIN32
-class WSInit {
-public:
-  WSInit() {
-    WSADATA wsaData;
-    if (WSAStartup(0x0002, &wsaData) == 0) is_valid_ = true;
-  }
-
-  ~WSInit() {
-    if (is_valid_) WSACleanup();
-  }
-
-  bool is_valid_ = false;
-};
-
-static WSInit wsinit_;
-#endif
-
-inline bool parse_www_authenticate(const Response &res,
-                                   std::map<std::string, std::string> &auth,
-                                   bool is_proxy) {
-  auto auth_key = is_proxy ? "Proxy-Authenticate" : "WWW-Authenticate";
-  if (res.has_header(auth_key)) {
-    thread_local auto re =
-        std::regex(R"~((?:(?:,\s*)?(.+?)=(?:"(.*?)"|([^,]*))))~");
-    auto s = res.get_header_value(auth_key);
-    auto pos = s.find(' ');
-    if (pos != std::string::npos) {
-      auto type = s.substr(0, pos);
-      if (type == "Basic") {
-        return false;
-      } else if (type == "Digest") {
-        s = s.substr(pos + 1);
-        auto beg = std::sregex_iterator(s.begin(), s.end(), re);
-        for (auto i = beg; i != std::sregex_iterator(); ++i) {
-          const auto &m = *i;
-          auto key = s.substr(static_cast<size_t>(m.position(1)),
-                              static_cast<size_t>(m.length(1)));
-          auto val = m.length(2) > 0
-                         ? s.substr(static_cast<size_t>(m.position(2)),
-                                    static_cast<size_t>(m.length(2)))
-                         : s.substr(static_cast<size_t>(m.position(3)),
-                                    static_cast<size_t>(m.length(3)));
-          auth[key] = val;
-        }
-        return true;
-      }
-    }
-  }
-  return false;
-}
-
-class ContentProviderAdapter {
-public:
-  explicit ContentProviderAdapter(
-      ContentProviderWithoutLength &&content_provider)
-      : content_provider_(content_provider) {}
-
-  bool operator()(size_t offset, size_t, DataSink &sink) {
-    return content_provider_(offset, sink);
-  }
-
-private:
-  ContentProviderWithoutLength content_provider_;
-};
-
-} // namespace detail
-
-inline std::string hosted_at(const std::string &hostname) {
-  std::vector<std::string> addrs;
-  hosted_at(hostname, addrs);
-  if (addrs.empty()) { return std::string(); }
-  return addrs[0];
-}
-
-inline void hosted_at(const std::string &hostname,
-                      std::vector<std::string> &addrs) {
-  struct addrinfo hints;
-  struct addrinfo *result;
-
-  memset(&hints, 0, sizeof(struct addrinfo));
-  hints.ai_family = AF_UNSPEC;
-  hints.ai_socktype = SOCK_STREAM;
-  hints.ai_protocol = 0;
-
-  if (detail::getaddrinfo_with_timeout(hostname.c_str(), nullptr, &hints,
-                                       &result, 0)) {
-#if defined __linux__ && !defined __ANDROID__
-    res_init();
-#endif
-    return;
-  }
-  auto se = detail::scope_exit([&] { freeaddrinfo(result); });
-
-  for (auto rp = result; rp; rp = rp->ai_next) {
-    const auto &addr =
-        *reinterpret_cast<struct sockaddr_storage *>(rp->ai_addr);
-    std::string ip;
-    auto dummy = -1;
-    if (detail::get_ip_and_port(addr, sizeof(struct sockaddr_storage), ip,
-                                dummy)) {
-      addrs.push_back(ip);
-    }
-  }
-}
-
-inline std::string encode_uri_component(const std::string &value) {
-  std::ostringstream escaped;
-  escaped.fill('0');
-  escaped << std::hex;
-
-  for (auto c : value) {
-    if (std::isalnum(static_cast<uint8_t>(c)) || c == '-' || c == '_' ||
-        c == '.' || c == '!' || c == '~' || c == '*' || c == '\'' || c == '(' ||
-        c == ')') {
-      escaped << c;
-    } else {
-      escaped << std::uppercase;
-      escaped << '%' << std::setw(2)
-              << static_cast<int>(static_cast<unsigned char>(c));
-      escaped << std::nouppercase;
-    }
-  }
-
-  return escaped.str();
-}
-
-inline std::string encode_uri(const std::string &value) {
-  std::ostringstream escaped;
-  escaped.fill('0');
-  escaped << std::hex;
-
-  for (auto c : value) {
-    if (std::isalnum(static_cast<uint8_t>(c)) || c == '-' || c == '_' ||
-        c == '.' || c == '!' || c == '~' || c == '*' || c == '\'' || c == '(' ||
-        c == ')' || c == ';' || c == '/' || c == '?' || c == ':' || c == '@' ||
-        c == '&' || c == '=' || c == '+' || c == '$' || c == ',' || c == '#') {
-      escaped << c;
-    } else {
-      escaped << std::uppercase;
-      escaped << '%' << std::setw(2)
-              << static_cast<int>(static_cast<unsigned char>(c));
-      escaped << std::nouppercase;
-    }
-  }
-
-  return escaped.str();
-}
-
-inline std::string decode_uri_component(const std::string &value) {
-  std::string result;
-
-  for (size_t i = 0; i < value.size(); i++) {
-    if (value[i] == '%' && i + 2 < value.size()) {
-      auto val = 0;
-      if (detail::from_hex_to_i(value, i + 1, 2, val)) {
-        result += static_cast<char>(val);
-        i += 2;
-      } else {
-        result += value[i];
-      }
-    } else {
-      result += value[i];
-    }
-  }
-
-  return result;
-}
-
-inline std::string decode_uri(const std::string &value) {
-  std::string result;
-
-  for (size_t i = 0; i < value.size(); i++) {
-    if (value[i] == '%' && i + 2 < value.size()) {
-      auto val = 0;
-      if (detail::from_hex_to_i(value, i + 1, 2, val)) {
-        result += static_cast<char>(val);
-        i += 2;
-      } else {
-        result += value[i];
-      }
-    } else {
-      result += value[i];
-    }
-  }
-
-  return result;
-}
-
-inline std::string encode_path_component(const std::string &component) {
-  std::string result;
-  result.reserve(component.size() * 3);
-
-  for (size_t i = 0; i < component.size(); i++) {
-    auto c = static_cast<unsigned char>(component[i]);
-
-    // Unreserved characters per RFC 3986: ALPHA / DIGIT / "-" / "." / "_" / "~"
-    if (std::isalnum(c) || c == '-' || c == '.' || c == '_' || c == '~') {
-      result += static_cast<char>(c);
-    }
-    // Path-safe sub-delimiters: "!" / "$" / "&" / "'" / "(" / ")" / "*" / "+" /
-    // "," / ";" / "="
-    else if (c == '!' || c == '$' || c == '&' || c == '\'' || c == '(' ||
-             c == ')' || c == '*' || c == '+' || c == ',' || c == ';' ||
-             c == '=') {
-      result += static_cast<char>(c);
-    }
-    // Colon is allowed in path segments except first segment
-    else if (c == ':') {
-      result += static_cast<char>(c);
-    }
-    // @ is allowed in path
-    else if (c == '@') {
-      result += static_cast<char>(c);
-    } else {
-      result += '%';
-      char hex[3];
-      snprintf(hex, sizeof(hex), "%02X", c);
-      result.append(hex, 2);
-    }
-  }
-  return result;
-}
-
-inline std::string decode_path_component(const std::string &component) {
-  std::string result;
-  result.reserve(component.size());
-
-  for (size_t i = 0; i < component.size(); i++) {
-    if (component[i] == '%' && i + 1 < component.size()) {
-      if (component[i + 1] == 'u') {
-        // Unicode %uXXXX encoding
-        auto val = 0;
-        if (detail::from_hex_to_i(component, i + 2, 4, val)) {
-          // 4 digits Unicode codes
-          char buff[4];
-          size_t len = detail::to_utf8(val, buff);
-          if (len > 0) { result.append(buff, len); }
-          i += 5; // 'u0000'
-        } else {
-          result += component[i];
-        }
-      } else {
-        // Standard %XX encoding
-        auto val = 0;
-        if (detail::from_hex_to_i(component, i + 1, 2, val)) {
-          // 2 digits hex codes
-          result += static_cast<char>(val);
-          i += 2; // 'XX'
-        } else {
-          result += component[i];
-        }
-      }
-    } else {
-      result += component[i];
-    }
-  }
-  return result;
-}
-
-inline std::string encode_query_component(const std::string &component,
-                                          bool space_as_plus) {
-  std::string result;
-  result.reserve(component.size() * 3);
-
-  for (size_t i = 0; i < component.size(); i++) {
-    auto c = static_cast<unsigned char>(component[i]);
-
-    // Unreserved characters per RFC 3986
-    if (std::isalnum(c) || c == '-' || c == '.' || c == '_' || c == '~') {
-      result += static_cast<char>(c);
-    }
-    // Space handling
-    else if (c == ' ') {
-      if (space_as_plus) {
-        result += '+';
-      } else {
-        result += "%20";
-      }
-    }
-    // Plus sign handling
-    else if (c == '+') {
-      if (space_as_plus) {
-        result += "%2B";
-      } else {
-        result += static_cast<char>(c);
-      }
-    }
-    // Query-safe sub-delimiters (excluding & and = which are query delimiters)
-    else if (c == '!' || c == '$' || c == '\'' || c == '(' || c == ')' ||
-             c == '*' || c == ',' || c == ';') {
-      result += static_cast<char>(c);
-    }
-    // Colon and @ are allowed in query
-    else if (c == ':' || c == '@') {
-      result += static_cast<char>(c);
-    }
-    // Forward slash is allowed in query values
-    else if (c == '/') {
-      result += static_cast<char>(c);
-    }
-    // Question mark is allowed in query values (after first ?)
-    else if (c == '?') {
-      result += static_cast<char>(c);
-    } else {
-      result += '%';
-      char hex[3];
-      snprintf(hex, sizeof(hex), "%02X", c);
-      result.append(hex, 2);
-    }
-  }
-  return result;
-}
-
-inline std::string decode_query_component(const std::string &component,
-                                          bool plus_as_space) {
-  std::string result;
-  result.reserve(component.size());
-
-  for (size_t i = 0; i < component.size(); i++) {
-    if (component[i] == '%' && i + 2 < component.size()) {
-      std::string hex = component.substr(i + 1, 2);
-      char *end;
-      unsigned long value = std::strtoul(hex.c_str(), &end, 16);
-      if (end == hex.c_str() + 2) {
-        result += static_cast<char>(value);
-        i += 2;
-      } else {
-        result += component[i];
-      }
-    } else if (component[i] == '+' && plus_as_space) {
-      result += ' '; // + becomes space in form-urlencoded
-    } else {
-      result += component[i];
-    }
-  }
-  return result;
-}
-
-inline std::string append_query_params(const std::string &path,
-                                       const Params &params) {
-  std::string path_with_query = path;
-  thread_local const std::regex re("[^?]+\\?.*");
-  auto delm = std::regex_match(path, re) ? '&' : '?';
-  path_with_query += delm + detail::params_to_query_str(params);
-  return path_with_query;
-}
-
-// Header utilities
-inline std::pair<std::string, std::string>
-make_range_header(const Ranges &ranges) {
-  std::string field = "bytes=";
-  auto i = 0;
-  for (const auto &r : ranges) {
-    if (i != 0) { field += ", "; }
-    if (r.first != -1) { field += std::to_string(r.first); }
-    field += '-';
-    if (r.second != -1) { field += std::to_string(r.second); }
-    i++;
-  }
-  return std::make_pair("Range", std::move(field));
-}
-
-inline std::pair<std::string, std::string>
-make_basic_authentication_header(const std::string &username,
-                                 const std::string &password, bool is_proxy) {
-  auto field = "Basic " + detail::base64_encode(username + ":" + password);
-  auto key = is_proxy ? "Proxy-Authorization" : "Authorization";
-  return std::make_pair(key, std::move(field));
-}
-
-inline std::pair<std::string, std::string>
-make_bearer_token_authentication_header(const std::string &token,
-                                        bool is_proxy = false) {
-  auto field = "Bearer " + token;
-  auto key = is_proxy ? "Proxy-Authorization" : "Authorization";
-  return std::make_pair(key, std::move(field));
-}
-
-// Request implementation
-inline bool Request::has_header(const std::string &key) const {
-  return detail::has_header(headers, key);
-}
-
-inline std::string Request::get_header_value(const std::string &key,
-                                             const char *def, size_t id) const {
-  return detail::get_header_value(headers, key, def, id);
-}
-
-inline size_t Request::get_header_value_count(const std::string &key) const {
-  auto r = headers.equal_range(key);
-  return static_cast<size_t>(std::distance(r.first, r.second));
-}
-
-inline void Request::set_header(const std::string &key,
-                                const std::string &val) {
-  if (detail::fields::is_field_name(key) &&
-      detail::fields::is_field_value(val)) {
-    headers.emplace(key, val);
-  }
-}
-
-inline bool Request::has_trailer(const std::string &key) const {
-  return trailers.find(key) != trailers.end();
-}
-
-inline std::string Request::get_trailer_value(const std::string &key,
-                                              size_t id) const {
-  auto rng = trailers.equal_range(key);
-  auto it = rng.first;
-  std::advance(it, static_cast<ssize_t>(id));
-  if (it != rng.second) { return it->second; }
-  return std::string();
-}
-
-inline size_t Request::get_trailer_value_count(const std::string &key) const {
-  auto r = trailers.equal_range(key);
-  return static_cast<size_t>(std::distance(r.first, r.second));
-}
-
-inline bool Request::has_param(const std::string &key) const {
-  return params.find(key) != params.end();
-}
-
-inline std::string Request::get_param_value(const std::string &key,
-                                            size_t id) const {
-  auto rng = params.equal_range(key);
-  auto it = rng.first;
-  std::advance(it, static_cast<ssize_t>(id));
-  if (it != rng.second) { return it->second; }
-  return std::string();
-}
-
-inline size_t Request::get_param_value_count(const std::string &key) const {
-  auto r = params.equal_range(key);
-  return static_cast<size_t>(std::distance(r.first, r.second));
-}
-
-inline bool Request::is_multipart_form_data() const {
-  const auto &content_type = get_header_value("Content-Type");
-  return !content_type.rfind("multipart/form-data", 0);
-}
-
-// Multipart FormData implementation
-inline std::string MultipartFormData::get_field(const std::string &key,
-                                                size_t id) const {
-  auto rng = fields.equal_range(key);
-  auto it = rng.first;
-  std::advance(it, static_cast<ssize_t>(id));
-  if (it != rng.second) { return it->second.content; }
-  return std::string();
-}
-
-inline std::vector<std::string>
-MultipartFormData::get_fields(const std::string &key) const {
-  std::vector<std::string> values;
-  auto rng = fields.equal_range(key);
-  for (auto it = rng.first; it != rng.second; it++) {
-    values.push_back(it->second.content);
-  }
-  return values;
-}
-
-inline bool MultipartFormData::has_field(const std::string &key) const {
-  return fields.find(key) != fields.end();
-}
-
-inline size_t MultipartFormData::get_field_count(const std::string &key) const {
-  auto r = fields.equal_range(key);
-  return static_cast<size_t>(std::distance(r.first, r.second));
-}
-
-inline FormData MultipartFormData::get_file(const std::string &key,
-                                            size_t id) const {
-  auto rng = files.equal_range(key);
-  auto it = rng.first;
-  std::advance(it, static_cast<ssize_t>(id));
-  if (it != rng.second) { return it->second; }
-  return FormData();
-}
-
-inline std::vector<FormData>
-MultipartFormData::get_files(const std::string &key) const {
-  std::vector<FormData> values;
-  auto rng = files.equal_range(key);
-  for (auto it = rng.first; it != rng.second; it++) {
-    values.push_back(it->second);
-  }
-  return values;
-}
-
-inline bool MultipartFormData::has_file(const std::string &key) const {
-  return files.find(key) != files.end();
-}
-
-inline size_t MultipartFormData::get_file_count(const std::string &key) const {
-  auto r = files.equal_range(key);
-  return static_cast<size_t>(std::distance(r.first, r.second));
-}
-
-// Response implementation
-inline bool Response::has_header(const std::string &key) const {
-  return headers.find(key) != headers.end();
-}
-
-inline std::string Response::get_header_value(const std::string &key,
-                                              const char *def,
-                                              size_t id) const {
-  return detail::get_header_value(headers, key, def, id);
-}
-
-inline size_t Response::get_header_value_count(const std::string &key) const {
-  auto r = headers.equal_range(key);
-  return static_cast<size_t>(std::distance(r.first, r.second));
-}
-
-inline void Response::set_header(const std::string &key,
-                                 const std::string &val) {
-  if (detail::fields::is_field_name(key) &&
-      detail::fields::is_field_value(val)) {
-    headers.emplace(key, val);
-  }
-}
-inline bool Response::has_trailer(const std::string &key) const {
-  return trailers.find(key) != trailers.end();
-}
-
-inline std::string Response::get_trailer_value(const std::string &key,
-                                               size_t id) const {
-  auto rng = trailers.equal_range(key);
-  auto it = rng.first;
-  std::advance(it, static_cast<ssize_t>(id));
-  if (it != rng.second) { return it->second; }
-  return std::string();
-}
-
-inline size_t Response::get_trailer_value_count(const std::string &key) const {
-  auto r = trailers.equal_range(key);
-  return static_cast<size_t>(std::distance(r.first, r.second));
-}
-
-inline void Response::set_redirect(const std::string &url, int stat) {
-  if (detail::fields::is_field_value(url)) {
-    set_header("Location", url);
-    if (300 <= stat && stat < 400) {
-      this->status = stat;
-    } else {
-      this->status = StatusCode::Found_302;
-    }
-  }
-}
-
-inline void Response::set_content(const char *s, size_t n,
-                                  const std::string &content_type) {
-  body.assign(s, n);
-
-  auto rng = headers.equal_range("Content-Type");
-  headers.erase(rng.first, rng.second);
-  set_header("Content-Type", content_type);
-}
-
-inline void Response::set_content(const std::string &s,
-                                  const std::string &content_type) {
-  set_content(s.data(), s.size(), content_type);
-}
-
-inline void Response::set_content(std::string &&s,
-                                  const std::string &content_type) {
-  body = std::move(s);
-
-  auto rng = headers.equal_range("Content-Type");
-  headers.erase(rng.first, rng.second);
-  set_header("Content-Type", content_type);
-}
-
-inline void Response::set_content_provider(
-    size_t in_length, const std::string &content_type, ContentProvider provider,
-    ContentProviderResourceReleaser resource_releaser) {
-  set_header("Content-Type", content_type);
-  content_length_ = in_length;
-  if (in_length > 0) { content_provider_ = std::move(provider); }
-  content_provider_resource_releaser_ = std::move(resource_releaser);
-  is_chunked_content_provider_ = false;
-}
-
-inline void Response::set_content_provider(
-    const std::string &content_type, ContentProviderWithoutLength provider,
-    ContentProviderResourceReleaser resource_releaser) {
-  set_header("Content-Type", content_type);
-  content_length_ = 0;
-  content_provider_ = detail::ContentProviderAdapter(std::move(provider));
-  content_provider_resource_releaser_ = std::move(resource_releaser);
-  is_chunked_content_provider_ = false;
-}
-
-inline void Response::set_chunked_content_provider(
-    const std::string &content_type, ContentProviderWithoutLength provider,
-    ContentProviderResourceReleaser resource_releaser) {
-  set_header("Content-Type", content_type);
-  content_length_ = 0;
-  content_provider_ = detail::ContentProviderAdapter(std::move(provider));
-  content_provider_resource_releaser_ = std::move(resource_releaser);
-  is_chunked_content_provider_ = true;
-}
-
-inline void Response::set_file_content(const std::string &path,
-                                       const std::string &content_type) {
-  file_content_path_ = path;
-  file_content_content_type_ = content_type;
-}
-
-inline void Response::set_file_content(const std::string &path) {
-  file_content_path_ = path;
-}
-
-// Result implementation
-inline bool Result::has_request_header(const std::string &key) const {
-  return request_headers_.find(key) != request_headers_.end();
-}
-
-inline std::string Result::get_request_header_value(const std::string &key,
-                                                    const char *def,
-                                                    size_t id) const {
-  return detail::get_header_value(request_headers_, key, def, id);
-}
-
-inline size_t
-Result::get_request_header_value_count(const std::string &key) const {
-  auto r = request_headers_.equal_range(key);
-  return static_cast<size_t>(std::distance(r.first, r.second));
-}
-
-// Stream implementation
-inline ssize_t Stream::write(const char *ptr) {
-  return write(ptr, strlen(ptr));
-}
-
-inline ssize_t Stream::write(const std::string &s) {
-  return write(s.data(), s.size());
-}
-
-namespace detail {
-
-inline void calc_actual_timeout(time_t max_timeout_msec, time_t duration_msec,
-                                time_t timeout_sec, time_t timeout_usec,
-                                time_t &actual_timeout_sec,
-                                time_t &actual_timeout_usec) {
-  auto timeout_msec = (timeout_sec * 1000) + (timeout_usec / 1000);
-
-  auto actual_timeout_msec =
-      (std::min)(max_timeout_msec - duration_msec, timeout_msec);
-
-  if (actual_timeout_msec < 0) { actual_timeout_msec = 0; }
-
-  actual_timeout_sec = actual_timeout_msec / 1000;
-  actual_timeout_usec = (actual_timeout_msec % 1000) * 1000;
-}
-
-// Socket stream implementation
-inline SocketStream::SocketStream(
-    socket_t sock, time_t read_timeout_sec, time_t read_timeout_usec,
-    time_t write_timeout_sec, time_t write_timeout_usec,
-    time_t max_timeout_msec,
-    std::chrono::time_point<std::chrono::steady_clock> start_time)
-    : sock_(sock), read_timeout_sec_(read_timeout_sec),
-      read_timeout_usec_(read_timeout_usec),
-      write_timeout_sec_(write_timeout_sec),
-      write_timeout_usec_(write_timeout_usec),
-      max_timeout_msec_(max_timeout_msec), start_time_(start_time),
-      read_buff_(read_buff_size_, 0) {}
-
-inline SocketStream::~SocketStream() = default;
-
-inline bool SocketStream::is_readable() const {
-  return read_buff_off_ < read_buff_content_size_;
-}
-
-inline bool SocketStream::wait_readable() const {
-  if (max_timeout_msec_ <= 0) {
-    return select_read(sock_, read_timeout_sec_, read_timeout_usec_) > 0;
-  }
-
-  time_t read_timeout_sec;
-  time_t read_timeout_usec;
-  calc_actual_timeout(max_timeout_msec_, duration(), read_timeout_sec_,
-                      read_timeout_usec_, read_timeout_sec, read_timeout_usec);
-
-  return select_read(sock_, read_timeout_sec, read_timeout_usec) > 0;
-}
-
-inline bool SocketStream::wait_writable() const {
-  return select_write(sock_, write_timeout_sec_, write_timeout_usec_) > 0 &&
-         is_socket_alive(sock_);
-}
-
-inline ssize_t SocketStream::read(char *ptr, size_t size) {
-#ifdef _WIN32
-  size =
-      (std::min)(size, static_cast<size_t>((std::numeric_limits<int>::max)()));
-#else
-  size = (std::min)(size,
-                    static_cast<size_t>((std::numeric_limits<ssize_t>::max)()));
-#endif
-
-  if (read_buff_off_ < read_buff_content_size_) {
-    auto remaining_size = read_buff_content_size_ - read_buff_off_;
-    if (size <= remaining_size) {
-      memcpy(ptr, read_buff_.data() + read_buff_off_, size);
-      read_buff_off_ += size;
-      return static_cast<ssize_t>(size);
-    } else {
-      memcpy(ptr, read_buff_.data() + read_buff_off_, remaining_size);
-      read_buff_off_ += remaining_size;
-      return static_cast<ssize_t>(remaining_size);
-    }
-  }
-
-  if (!wait_readable()) { return -1; }
-
-  read_buff_off_ = 0;
-  read_buff_content_size_ = 0;
-
-  if (size < read_buff_size_) {
-    auto n = read_socket(sock_, read_buff_.data(), read_buff_size_,
-                         CPPHTTPLIB_RECV_FLAGS);
-    if (n <= 0) {
-      return n;
-    } else if (n <= static_cast<ssize_t>(size)) {
-      memcpy(ptr, read_buff_.data(), static_cast<size_t>(n));
-      return n;
-    } else {
-      memcpy(ptr, read_buff_.data(), size);
-      read_buff_off_ = size;
-      read_buff_content_size_ = static_cast<size_t>(n);
-      return static_cast<ssize_t>(size);
-    }
-  } else {
-    return read_socket(sock_, ptr, size, CPPHTTPLIB_RECV_FLAGS);
-  }
-}
-
-inline ssize_t SocketStream::write(const char *ptr, size_t size) {
-  if (!wait_writable()) { return -1; }
-
-#if defined(_WIN32) && !defined(_WIN64)
-  size =
-      (std::min)(size, static_cast<size_t>((std::numeric_limits<int>::max)()));
-#endif
-
-  return send_socket(sock_, ptr, size, CPPHTTPLIB_SEND_FLAGS);
-}
-
-inline void SocketStream::get_remote_ip_and_port(std::string &ip,
-                                                 int &port) const {
-  return detail::get_remote_ip_and_port(sock_, ip, port);
-}
-
-inline void SocketStream::get_local_ip_and_port(std::string &ip,
-                                                int &port) const {
-  return detail::get_local_ip_and_port(sock_, ip, port);
-}
-
-inline socket_t SocketStream::socket() const { return sock_; }
-
-inline time_t SocketStream::duration() const {
-  return std::chrono::duration_cast<std::chrono::milliseconds>(
-             std::chrono::steady_clock::now() - start_time_)
-      .count();
-}
-
-// Buffer stream implementation
-inline bool BufferStream::is_readable() const { return true; }
-
-inline bool BufferStream::wait_readable() const { return true; }
-
-inline bool BufferStream::wait_writable() const { return true; }
-
-inline ssize_t BufferStream::read(char *ptr, size_t size) {
-#if defined(_MSC_VER) && _MSC_VER < 1910
-  auto len_read = buffer._Copy_s(ptr, size, size, position);
-#else
-  auto len_read = buffer.copy(ptr, size, position);
-#endif
-  position += static_cast<size_t>(len_read);
-  return static_cast<ssize_t>(len_read);
-}
-
-inline ssize_t BufferStream::write(const char *ptr, size_t size) {
-  buffer.append(ptr, size);
-  return static_cast<ssize_t>(size);
-}
-
-inline void BufferStream::get_remote_ip_and_port(std::string & /*ip*/,
-                                                 int & /*port*/) const {}
-
-inline void BufferStream::get_local_ip_and_port(std::string & /*ip*/,
-                                                int & /*port*/) const {}
-
-inline socket_t BufferStream::socket() const { return 0; }
-
-inline time_t BufferStream::duration() const { return 0; }
-
-inline const std::string &BufferStream::get_buffer() const { return buffer; }
-
-inline PathParamsMatcher::PathParamsMatcher(const std::string &pattern)
-    : MatcherBase(pattern) {
-  constexpr const char marker[] = "/:";
-
-  // One past the last ending position of a path param substring
-  std::size_t last_param_end = 0;
-
-#ifndef CPPHTTPLIB_NO_EXCEPTIONS
-  // Needed to ensure that parameter names are unique during matcher
-  // construction
-  // If exceptions are disabled, only last duplicate path
-  // parameter will be set
-  std::unordered_set<std::string> param_name_set;
-#endif
-
-  while (true) {
-    const auto marker_pos = pattern.find(
-        marker, last_param_end == 0 ? last_param_end : last_param_end - 1);
-    if (marker_pos == std::string::npos) { break; }
-
-    static_fragments_.push_back(
-        pattern.substr(last_param_end, marker_pos - last_param_end + 1));
-
-    const auto param_name_start = marker_pos + str_len(marker);
-
-    auto sep_pos = pattern.find(separator, param_name_start);
-    if (sep_pos == std::string::npos) { sep_pos = pattern.length(); }
-
-    auto param_name =
-        pattern.substr(param_name_start, sep_pos - param_name_start);
-
-#ifndef CPPHTTPLIB_NO_EXCEPTIONS
-    if (param_name_set.find(param_name) != param_name_set.cend()) {
-      std::string msg = "Encountered path parameter '" + param_name +
-                        "' multiple times in route pattern '" + pattern + "'.";
-      throw std::invalid_argument(msg);
-    }
-#endif
-
-    param_names_.push_back(std::move(param_name));
-
-    last_param_end = sep_pos + 1;
-  }
-
-  if (last_param_end < pattern.length()) {
-    static_fragments_.push_back(pattern.substr(last_param_end));
-  }
-}
-
-inline bool PathParamsMatcher::match(Request &request) const {
-  request.matches = std::smatch();
-  request.path_params.clear();
-  request.path_params.reserve(param_names_.size());
-
-  // One past the position at which the path matched the pattern last time
-  std::size_t starting_pos = 0;
-  for (size_t i = 0; i < static_fragments_.size(); ++i) {
-    const auto &fragment = static_fragments_[i];
-
-    if (starting_pos + fragment.length() > request.path.length()) {
-      return false;
-    }
-
-    // Avoid unnecessary allocation by using strncmp instead of substr +
-    // comparison
-    if (std::strncmp(request.path.c_str() + starting_pos, fragment.c_str(),
-                     fragment.length()) != 0) {
-      return false;
-    }
-
-    starting_pos += fragment.length();
-
-    // Should only happen when we have a static fragment after a param
-    // Example: '/users/:id/subscriptions'
-    // The 'subscriptions' fragment here does not have a corresponding param
-    if (i >= param_names_.size()) { continue; }
-
-    auto sep_pos = request.path.find(separator, starting_pos);
-    if (sep_pos == std::string::npos) { sep_pos = request.path.length(); }
-
-    const auto &param_name = param_names_[i];
-
-    request.path_params.emplace(
-        param_name, request.path.substr(starting_pos, sep_pos - starting_pos));
-
-    // Mark everything up to '/' as matched
-    starting_pos = sep_pos + 1;
-  }
-  // Returns false if the path is longer than the pattern
-  return starting_pos >= request.path.length();
-}
-
-inline bool RegexMatcher::match(Request &request) const {
-  request.path_params.clear();
-  return std::regex_match(request.path, request.matches, regex_);
-}
-
-inline std::string make_host_and_port_string(const std::string &host, int port,
-                                             bool is_ssl) {
-  std::string result;
-
-  // Enclose IPv6 address in brackets (but not if already enclosed)
-  if (host.find(':') == std::string::npos ||
-      (!host.empty() && host[0] == '[')) {
-    // IPv4, hostname, or already bracketed IPv6
-    result = host;
-  } else {
-    // IPv6 address without brackets
-    result = "[" + host + "]";
-  }
-
-  // Append port if not default
-  if ((!is_ssl && port == 80) || (is_ssl && port == 443)) {
-    ; // do nothing
-  } else {
-    result += ":" + std::to_string(port);
-  }
-
-  return result;
-}
-
-} // namespace detail
-
-// HTTP server implementation
-inline Server::Server()
-    : new_task_queue(
-          [] { return new ThreadPool(CPPHTTPLIB_THREAD_POOL_COUNT); }) {
-#ifndef _WIN32
-  signal(SIGPIPE, SIG_IGN);
-#endif
-}
-
-inline Server::~Server() = default;
-
-inline std::unique_ptr<detail::MatcherBase>
-Server::make_matcher(const std::string &pattern) {
-  if (pattern.find("/:") != std::string::npos) {
-    return detail::make_unique<detail::PathParamsMatcher>(pattern);
-  } else {
-    return detail::make_unique<detail::RegexMatcher>(pattern);
-  }
-}
-
-inline Server &Server::Get(const std::string &pattern, Handler handler) {
-  get_handlers_.emplace_back(make_matcher(pattern), std::move(handler));
-  return *this;
-}
-
-inline Server &Server::Post(const std::string &pattern, Handler handler) {
-  post_handlers_.emplace_back(make_matcher(pattern), std::move(handler));
-  return *this;
-}
-
-inline Server &Server::Post(const std::string &pattern,
-                            HandlerWithContentReader handler) {
-  post_handlers_for_content_reader_.emplace_back(make_matcher(pattern),
-                                                 std::move(handler));
-  return *this;
-}
-
-inline Server &Server::Put(const std::string &pattern, Handler handler) {
-  put_handlers_.emplace_back(make_matcher(pattern), std::move(handler));
-  return *this;
-}
-
-inline Server &Server::Put(const std::string &pattern,
-                           HandlerWithContentReader handler) {
-  put_handlers_for_content_reader_.emplace_back(make_matcher(pattern),
-                                                std::move(handler));
-  return *this;
-}
-
-inline Server &Server::Patch(const std::string &pattern, Handler handler) {
-  patch_handlers_.emplace_back(make_matcher(pattern), std::move(handler));
-  return *this;
-}
-
-inline Server &Server::Patch(const std::string &pattern,
-                             HandlerWithContentReader handler) {
-  patch_handlers_for_content_reader_.emplace_back(make_matcher(pattern),
-                                                  std::move(handler));
-  return *this;
-}
-
-inline Server &Server::Delete(const std::string &pattern, Handler handler) {
-  delete_handlers_.emplace_back(make_matcher(pattern), std::move(handler));
-  return *this;
-}
-
-inline Server &Server::Delete(const std::string &pattern,
-                              HandlerWithContentReader handler) {
-  delete_handlers_for_content_reader_.emplace_back(make_matcher(pattern),
-                                                   std::move(handler));
-  return *this;
-}
-
-inline Server &Server::Options(const std::string &pattern, Handler handler) {
-  options_handlers_.emplace_back(make_matcher(pattern), std::move(handler));
-  return *this;
-}
-
-inline bool Server::set_base_dir(const std::string &dir,
-                                 const std::string &mount_point) {
-  return set_mount_point(mount_point, dir);
-}
-
-inline bool Server::set_mount_point(const std::string &mount_point,
-                                    const std::string &dir, Headers headers) {
-  detail::FileStat stat(dir);
-  if (stat.is_dir()) {
-    std::string mnt = !mount_point.empty() ? mount_point : "/";
-    if (!mnt.empty() && mnt[0] == '/') {
-      base_dirs_.push_back({mnt, dir, std::move(headers)});
-      return true;
-    }
-  }
-  return false;
-}
-
-inline bool Server::remove_mount_point(const std::string &mount_point) {
-  for (auto it = base_dirs_.begin(); it != base_dirs_.end(); ++it) {
-    if (it->mount_point == mount_point) {
-      base_dirs_.erase(it);
-      return true;
-    }
-  }
-  return false;
-}
-
-inline Server &
-Server::set_file_extension_and_mimetype_mapping(const std::string &ext,
-                                                const std::string &mime) {
-  file_extension_and_mimetype_map_[ext] = mime;
-  return *this;
-}
-
-inline Server &Server::set_default_file_mimetype(const std::string &mime) {
-  default_file_mimetype_ = mime;
-  return *this;
-}
-
-inline Server &Server::set_file_request_handler(Handler handler) {
-  file_request_handler_ = std::move(handler);
-  return *this;
-}
-
-inline Server &Server::set_error_handler_core(HandlerWithResponse handler,
-                                              std::true_type) {
-  error_handler_ = std::move(handler);
-  return *this;
-}
-
-inline Server &Server::set_error_handler_core(Handler handler,
-                                              std::false_type) {
-  error_handler_ = [handler](const Request &req, Response &res) {
-    handler(req, res);
-    return HandlerResponse::Handled;
-  };
-  return *this;
-}
-
-inline Server &Server::set_exception_handler(ExceptionHandler handler) {
-  exception_handler_ = std::move(handler);
-  return *this;
-}
-
-inline Server &Server::set_pre_routing_handler(HandlerWithResponse handler) {
-  pre_routing_handler_ = std::move(handler);
-  return *this;
-}
-
-inline Server &Server::set_post_routing_handler(Handler handler) {
-  post_routing_handler_ = std::move(handler);
-  return *this;
-}
-
-inline Server &Server::set_pre_request_handler(HandlerWithResponse handler) {
-  pre_request_handler_ = std::move(handler);
-  return *this;
-}
-
-inline Server &Server::set_logger(Logger logger) {
-  logger_ = std::move(logger);
-  return *this;
-}
-
-inline Server &Server::set_error_logger(ErrorLogger error_logger) {
-  error_logger_ = std::move(error_logger);
-  return *this;
-}
-
-inline Server &Server::set_pre_compression_logger(Logger logger) {
-  pre_compression_logger_ = std::move(logger);
-  return *this;
-}
-
-inline Server &
-Server::set_expect_100_continue_handler(Expect100ContinueHandler handler) {
-  expect_100_continue_handler_ = std::move(handler);
-  return *this;
-}
-
-inline Server &Server::set_address_family(int family) {
-  address_family_ = family;
-  return *this;
-}
-
-inline Server &Server::set_tcp_nodelay(bool on) {
-  tcp_nodelay_ = on;
-  return *this;
-}
-
-inline Server &Server::set_ipv6_v6only(bool on) {
-  ipv6_v6only_ = on;
-  return *this;
-}
-
-inline Server &Server::set_socket_options(SocketOptions socket_options) {
-  socket_options_ = std::move(socket_options);
-  return *this;
-}
-
-inline Server &Server::set_default_headers(Headers headers) {
-  default_headers_ = std::move(headers);
-  return *this;
-}
-
-inline Server &Server::set_header_writer(
-    std::function<ssize_t(Stream &, Headers &)> const &writer) {
-  header_writer_ = writer;
-  return *this;
-}
-
-inline Server &
-Server::set_trusted_proxies(const std::vector<std::string> &proxies) {
-  trusted_proxies_ = proxies;
-  return *this;
-}
-
-inline Server &Server::set_keep_alive_max_count(size_t count) {
-  keep_alive_max_count_ = count;
-  return *this;
-}
-
-inline Server &Server::set_keep_alive_timeout(time_t sec) {
-  keep_alive_timeout_sec_ = sec;
-  return *this;
-}
-
-inline Server &Server::set_read_timeout(time_t sec, time_t usec) {
-  read_timeout_sec_ = sec;
-  read_timeout_usec_ = usec;
-  return *this;
-}
-
-inline Server &Server::set_write_timeout(time_t sec, time_t usec) {
-  write_timeout_sec_ = sec;
-  write_timeout_usec_ = usec;
-  return *this;
-}
-
-inline Server &Server::set_idle_interval(time_t sec, time_t usec) {
-  idle_interval_sec_ = sec;
-  idle_interval_usec_ = usec;
-  return *this;
-}
-
-inline Server &Server::set_payload_max_length(size_t length) {
-  payload_max_length_ = length;
-  return *this;
-}
-
-inline bool Server::bind_to_port(const std::string &host, int port,
-                                 int socket_flags) {
-  auto ret = bind_internal(host, port, socket_flags);
-  if (ret == -1) { is_decommissioned = true; }
-  return ret >= 0;
-}
-inline int Server::bind_to_any_port(const std::string &host, int socket_flags) {
-  auto ret = bind_internal(host, 0, socket_flags);
-  if (ret == -1) { is_decommissioned = true; }
-  return ret;
-}
-
-inline bool Server::listen_after_bind() { return listen_internal(); }
-
-inline bool Server::listen(const std::string &host, int port,
-                           int socket_flags) {
-  return bind_to_port(host, port, socket_flags) && listen_internal();
-}
-
-inline bool Server::is_running() const { return is_running_; }
-
-inline void Server::wait_until_ready() const {
-  while (!is_running_ && !is_decommissioned) {
-    std::this_thread::sleep_for(std::chrono::milliseconds{1});
-  }
-}
-
-inline void Server::stop() {
-  if (is_running_) {
-    assert(svr_sock_ != INVALID_SOCKET);
-    std::atomic<socket_t> sock(svr_sock_.exchange(INVALID_SOCKET));
-    detail::shutdown_socket(sock);
-    detail::close_socket(sock);
-  }
-  is_decommissioned = false;
-}
-
-inline void Server::decommission() { is_decommissioned = true; }
-
-inline bool Server::parse_request_line(const char *s, Request &req) const {
-  auto len = strlen(s);
-  if (len < 2 || s[len - 2] != '\r' || s[len - 1] != '\n') { return false; }
-  len -= 2;
-
-  {
-    size_t count = 0;
-
-    detail::split(s, s + len, ' ', [&](const char *b, const char *e) {
-      switch (count) {
-      case 0: req.method = std::string(b, e); break;
-      case 1: req.target = std::string(b, e); break;
-      case 2: req.version = std::string(b, e); break;
-      default: break;
-      }
-      count++;
-    });
-
-    if (count != 3) { return false; }
-  }
-
-  thread_local const std::set<std::string> methods{
-      "GET",     "HEAD",    "POST",  "PUT",   "DELETE",
-      "CONNECT", "OPTIONS", "TRACE", "PATCH", "PRI"};
-
-  if (methods.find(req.method) == methods.end()) {
-    output_error_log(Error::InvalidHTTPMethod, &req);
-    return false;
-  }
-
-  if (req.version != "HTTP/1.1" && req.version != "HTTP/1.0") {
-    output_error_log(Error::InvalidHTTPVersion, &req);
-    return false;
-  }
-
-  {
-    // Skip URL fragment
-    for (size_t i = 0; i < req.target.size(); i++) {
-      if (req.target[i] == '#') {
-        req.target.erase(i);
-        break;
-      }
-    }
-
-    detail::divide(req.target, '?',
-                   [&](const char *lhs_data, std::size_t lhs_size,
-                       const char *rhs_data, std::size_t rhs_size) {
-                     req.path =
-                         decode_path_component(std::string(lhs_data, lhs_size));
-                     detail::parse_query_text(rhs_data, rhs_size, req.params);
-                   });
-  }
-
-  return true;
-}
-
-inline bool Server::write_response(Stream &strm, bool close_connection,
-                                   Request &req, Response &res) {
-  // NOTE: `req.ranges` should be empty, otherwise it will be applied
-  // incorrectly to the error content.
-  req.ranges.clear();
-  return write_response_core(strm, close_connection, req, res, false);
-}
-
-inline bool Server::write_response_with_content(Stream &strm,
-                                                bool close_connection,
-                                                const Request &req,
-                                                Response &res) {
-  return write_response_core(strm, close_connection, req, res, true);
-}
-
-inline bool Server::write_response_core(Stream &strm, bool close_connection,
-                                        const Request &req, Response &res,
-                                        bool need_apply_ranges) {
-  assert(res.status != -1);
-
-  if (400 <= res.status && error_handler_ &&
-      error_handler_(req, res) == HandlerResponse::Handled) {
-    need_apply_ranges = true;
-  }
-
-  std::string content_type;
-  std::string boundary;
-  if (need_apply_ranges) { apply_ranges(req, res, content_type, boundary); }
-
-  // Prepare additional headers
-  if (close_connection || req.get_header_value("Connection") == "close") {
-    res.set_header("Connection", "close");
-  } else {
-    std::string s = "timeout=";
-    s += std::to_string(keep_alive_timeout_sec_);
-    s += ", max=";
-    s += std::to_string(keep_alive_max_count_);
-    res.set_header("Keep-Alive", s);
-  }
-
-  if ((!res.body.empty() || res.content_length_ > 0 || res.content_provider_) &&
-      !res.has_header("Content-Type")) {
-    res.set_header("Content-Type", "text/plain");
-  }
-
-  if (res.body.empty() && !res.content_length_ && !res.content_provider_ &&
-      !res.has_header("Content-Length")) {
-    res.set_header("Content-Length", "0");
-  }
-
-  if (req.method == "HEAD" && !res.has_header("Accept-Ranges")) {
-    res.set_header("Accept-Ranges", "bytes");
-  }
-
-  if (post_routing_handler_) { post_routing_handler_(req, res); }
-
-  // Response line and headers
-  {
-    detail::BufferStream bstrm;
-    if (!detail::write_response_line(bstrm, res.status)) { return false; }
-    if (!header_writer_(bstrm, res.headers)) { return false; }
-
-    // Flush buffer
-    auto &data = bstrm.get_buffer();
-    detail::write_data(strm, data.data(), data.size());
-  }
-
-  // Body
-  auto ret = true;
-  if (req.method != "HEAD") {
-    if (!res.body.empty()) {
-      if (!detail::write_data(strm, res.body.data(), res.body.size())) {
-        ret = false;
-      }
-    } else if (res.content_provider_) {
-      if (write_content_with_provider(strm, req, res, boundary, content_type)) {
-        res.content_provider_success_ = true;
-      } else {
-        ret = false;
-      }
-    }
-  }
-
-  // Log
-  output_log(req, res);
-
-  return ret;
-}
-
-inline bool
-Server::write_content_with_provider(Stream &strm, const Request &req,
-                                    Response &res, const std::string &boundary,
-                                    const std::string &content_type) {
-  auto is_shutting_down = [this]() {
-    return this->svr_sock_ == INVALID_SOCKET;
-  };
-
-  if (res.content_length_ > 0) {
-    if (req.ranges.empty()) {
-      return detail::write_content(strm, res.content_provider_, 0,
-                                   res.content_length_, is_shutting_down);
-    } else if (req.ranges.size() == 1) {
-      auto offset_and_length = detail::get_range_offset_and_length(
-          req.ranges[0], res.content_length_);
-
-      return detail::write_content(strm, res.content_provider_,
-                                   offset_and_length.first,
-                                   offset_and_length.second, is_shutting_down);
-    } else {
-      return detail::write_multipart_ranges_data(
-          strm, req, res, boundary, content_type, res.content_length_,
-          is_shutting_down);
-    }
-  } else {
-    if (res.is_chunked_content_provider_) {
-      auto type = detail::encoding_type(req, res);
-
-      std::unique_ptr<detail::compressor> compressor;
-      if (type == detail::EncodingType::Gzip) {
-#ifdef CPPHTTPLIB_ZLIB_SUPPORT
-        compressor = detail::make_unique<detail::gzip_compressor>();
-#endif
-      } else if (type == detail::EncodingType::Brotli) {
-#ifdef CPPHTTPLIB_BROTLI_SUPPORT
-        compressor = detail::make_unique<detail::brotli_compressor>();
-#endif
-      } else if (type == detail::EncodingType::Zstd) {
-#ifdef CPPHTTPLIB_ZSTD_SUPPORT
-        compressor = detail::make_unique<detail::zstd_compressor>();
-#endif
-      } else {
-        compressor = detail::make_unique<detail::nocompressor>();
-      }
-      assert(compressor != nullptr);
-
-      return detail::write_content_chunked(strm, res.content_provider_,
-                                           is_shutting_down, *compressor);
-    } else {
-      return detail::write_content_without_length(strm, res.content_provider_,
-                                                  is_shutting_down);
-    }
-  }
-}
-
-inline bool Server::read_content(Stream &strm, Request &req, Response &res) {
-  FormFields::iterator cur_field;
-  FormFiles::iterator cur_file;
-  auto is_text_field = false;
-  size_t count = 0;
-  if (read_content_core(
-          strm, req, res,
-          // Regular
-          [&](const char *buf, size_t n) {
-            if (req.body.size() + n > req.body.max_size()) { return false; }
-            req.body.append(buf, n);
-            return true;
-          },
-          // Multipart FormData
-          [&](const FormData &file) {
-            if (count++ == CPPHTTPLIB_MULTIPART_FORM_DATA_FILE_MAX_COUNT) {
-              output_error_log(Error::TooManyFormDataFiles, &req);
-              return false;
-            }
-
-            if (file.filename.empty()) {
-              cur_field = req.form.fields.emplace(
-                  file.name, FormField{file.name, file.content, file.headers});
-              is_text_field = true;
-            } else {
-              cur_file = req.form.files.emplace(file.name, file);
-              is_text_field = false;
-            }
-            return true;
-          },
-          [&](const char *buf, size_t n) {
-            if (is_text_field) {
-              auto &content = cur_field->second.content;
-              if (content.size() + n > content.max_size()) { return false; }
-              content.append(buf, n);
-            } else {
-              auto &content = cur_file->second.content;
-              if (content.size() + n > content.max_size()) { return false; }
-              content.append(buf, n);
-            }
-            return true;
-          })) {
-    const auto &content_type = req.get_header_value("Content-Type");
-    if (!content_type.find("application/x-www-form-urlencoded")) {
-      if (req.body.size() > CPPHTTPLIB_FORM_URL_ENCODED_PAYLOAD_MAX_LENGTH) {
-        res.status = StatusCode::PayloadTooLarge_413; // NOTE: should be 414?
-        output_error_log(Error::ExceedMaxPayloadSize, &req);
-        return false;
-      }
-      detail::parse_query_text(req.body, req.params);
-    }
-    return true;
-  }
-  return false;
-}
-
-inline bool Server::read_content_with_content_receiver(
-    Stream &strm, Request &req, Response &res, ContentReceiver receiver,
-    FormDataHeader multipart_header, ContentReceiver multipart_receiver) {
-  return read_content_core(strm, req, res, std::move(receiver),
-                           std::move(multipart_header),
-                           std::move(multipart_receiver));
-}
-
-inline bool Server::read_content_core(
-    Stream &strm, Request &req, Response &res, ContentReceiver receiver,
-    FormDataHeader multipart_header, ContentReceiver multipart_receiver) const {
-  detail::FormDataParser multipart_form_data_parser;
-  ContentReceiverWithProgress out;
-
-  if (req.is_multipart_form_data()) {
-    const auto &content_type = req.get_header_value("Content-Type");
-    std::string boundary;
-    if (!detail::parse_multipart_boundary(content_type, boundary)) {
-      res.status = StatusCode::BadRequest_400;
-      output_error_log(Error::MultipartParsing, &req);
-      return false;
-    }
-
-    multipart_form_data_parser.set_boundary(std::move(boundary));
-    out = [&](const char *buf, size_t n, size_t /*off*/, size_t /*len*/) {
-      return multipart_form_data_parser.parse(buf, n, multipart_header,
-                                              multipart_receiver);
-    };
-  } else {
-    out = [receiver](const char *buf, size_t n, size_t /*off*/,
-                     size_t /*len*/) { return receiver(buf, n); };
-  }
-
-  if (req.method == "DELETE" && !req.has_header("Content-Length")) {
-    return true;
-  }
-
-  if (!detail::read_content(strm, req, payload_max_length_, res.status, nullptr,
-                            out, true)) {
-    return false;
-  }
-
-  if (req.is_multipart_form_data()) {
-    if (!multipart_form_data_parser.is_valid()) {
-      res.status = StatusCode::BadRequest_400;
-      output_error_log(Error::MultipartParsing, &req);
-      return false;
-    }
-  }
-
-  return true;
-}
-
-inline bool Server::handle_file_request(const Request &req, Response &res) {
-  for (const auto &entry : base_dirs_) {
-    // Prefix match
-    if (!req.path.compare(0, entry.mount_point.size(), entry.mount_point)) {
-      std::string sub_path = "/" + req.path.substr(entry.mount_point.size());
-      if (detail::is_valid_path(sub_path)) {
-        auto path = entry.base_dir + sub_path;
-        if (path.back() == '/') { path += "index.html"; }
-
-        detail::FileStat stat(path);
-
-        if (stat.is_dir()) {
-          res.set_redirect(sub_path + "/", StatusCode::MovedPermanently_301);
-          return true;
-        }
-
-        if (stat.is_file()) {
-          for (const auto &kv : entry.headers) {
-            res.set_header(kv.first, kv.second);
-          }
-
-          auto mm = std::make_shared<detail::mmap>(path.c_str());
-          if (!mm->is_open()) {
-            output_error_log(Error::OpenFile, &req);
-            return false;
-          }
-
-          res.set_content_provider(
-              mm->size(),
-              detail::find_content_type(path, file_extension_and_mimetype_map_,
-                                        default_file_mimetype_),
-              [mm](size_t offset, size_t length, DataSink &sink) -> bool {
-                sink.write(mm->data() + offset, length);
-                return true;
-              });
-
-          if (req.method != "HEAD" && file_request_handler_) {
-            file_request_handler_(req, res);
-          }
-
-          return true;
-        } else {
-          output_error_log(Error::OpenFile, &req);
-        }
-      }
-    }
-  }
-  return false;
-}
-
-inline socket_t
-Server::create_server_socket(const std::string &host, int port,
-                             int socket_flags,
-                             SocketOptions socket_options) const {
-  return detail::create_socket(
-      host, std::string(), port, address_family_, socket_flags, tcp_nodelay_,
-      ipv6_v6only_, std::move(socket_options),
-      [&](socket_t sock, struct addrinfo &ai, bool & /*quit*/) -> bool {
-        if (::bind(sock, ai.ai_addr, static_cast<socklen_t>(ai.ai_addrlen))) {
-          output_error_log(Error::BindIPAddress, nullptr);
-          return false;
-        }
-        if (::listen(sock, CPPHTTPLIB_LISTEN_BACKLOG)) {
-          output_error_log(Error::Listen, nullptr);
-          return false;
-        }
-        return true;
-      });
-}
-
-inline int Server::bind_internal(const std::string &host, int port,
-                                 int socket_flags) {
-  if (is_decommissioned) { return -1; }
-
-  if (!is_valid()) { return -1; }
-
-  svr_sock_ = create_server_socket(host, port, socket_flags, socket_options_);
-  if (svr_sock_ == INVALID_SOCKET) { return -1; }
-
-  if (port == 0) {
-    struct sockaddr_storage addr;
-    socklen_t addr_len = sizeof(addr);
-    if (getsockname(svr_sock_, reinterpret_cast<struct sockaddr *>(&addr),
-                    &addr_len) == -1) {
-      output_error_log(Error::GetSockName, nullptr);
-      return -1;
-    }
-    if (addr.ss_family == AF_INET) {
-      return ntohs(reinterpret_cast<struct sockaddr_in *>(&addr)->sin_port);
-    } else if (addr.ss_family == AF_INET6) {
-      return ntohs(reinterpret_cast<struct sockaddr_in6 *>(&addr)->sin6_port);
-    } else {
-      output_error_log(Error::UnsupportedAddressFamily, nullptr);
-      return -1;
-    }
-  } else {
-    return port;
-  }
-}
-
-inline bool Server::listen_internal() {
-  if (is_decommissioned) { return false; }
-
-  auto ret = true;
-  is_running_ = true;
-  auto se = detail::scope_exit([&]() { is_running_ = false; });
-
-  {
-    std::unique_ptr<TaskQueue> task_queue(new_task_queue());
-
-    while (svr_sock_ != INVALID_SOCKET) {
-#ifndef _WIN32
-      if (idle_interval_sec_ > 0 || idle_interval_usec_ > 0) {
-#endif
-        auto val = detail::select_read(svr_sock_, idle_interval_sec_,
-                                       idle_interval_usec_);
-        if (val == 0) { // Timeout
-          task_queue->on_idle();
-          continue;
-        }
-#ifndef _WIN32
-      }
-#endif
-
-#if defined _WIN32
-      // sockets connected via WASAccept inherit flags NO_HANDLE_INHERIT,
-      // OVERLAPPED
-      socket_t sock = WSAAccept(svr_sock_, nullptr, nullptr, nullptr, 0);
-#elif defined SOCK_CLOEXEC
-      socket_t sock = accept4(svr_sock_, nullptr, nullptr, SOCK_CLOEXEC);
-#else
-      socket_t sock = accept(svr_sock_, nullptr, nullptr);
-#endif
-
-      if (sock == INVALID_SOCKET) {
-        if (errno == EMFILE) {
-          // The per-process limit of open file descriptors has been reached.
-          // Try to accept new connections after a short sleep.
-          std::this_thread::sleep_for(std::chrono::microseconds{1});
-          continue;
-        } else if (errno == EINTR || errno == EAGAIN) {
-          continue;
-        }
-        if (svr_sock_ != INVALID_SOCKET) {
-          detail::close_socket(svr_sock_);
-          ret = false;
-          output_error_log(Error::Connection, nullptr);
-        } else {
-          ; // The server socket was closed by user.
-        }
-        break;
-      }
-
-      detail::set_socket_opt_time(sock, SOL_SOCKET, SO_RCVTIMEO,
-                                  read_timeout_sec_, read_timeout_usec_);
-      detail::set_socket_opt_time(sock, SOL_SOCKET, SO_SNDTIMEO,
-                                  write_timeout_sec_, write_timeout_usec_);
-
-      if (!task_queue->enqueue(
-              [this, sock]() { process_and_close_socket(sock); })) {
-        output_error_log(Error::ResourceExhaustion, nullptr);
-        detail::shutdown_socket(sock);
-        detail::close_socket(sock);
-      }
-    }
-
-    task_queue->shutdown();
-  }
-
-  is_decommissioned = !ret;
-  return ret;
-}
-
-inline bool Server::routing(Request &req, Response &res, Stream &strm) {
-  if (pre_routing_handler_ &&
-      pre_routing_handler_(req, res) == HandlerResponse::Handled) {
-    return true;
-  }
-
-  // File handler
-  if ((req.method == "GET" || req.method == "HEAD") &&
-      handle_file_request(req, res)) {
-    return true;
-  }
-
-  if (detail::expect_content(req)) {
-    // Content reader handler
-    {
-      ContentReader reader(
-          [&](ContentReceiver receiver) {
-            auto result = read_content_with_content_receiver(
-                strm, req, res, std::move(receiver), nullptr, nullptr);
-            if (!result) { output_error_log(Error::Read, &req); }
-            return result;
-          },
-          [&](FormDataHeader header, ContentReceiver receiver) {
-            auto result = read_content_with_content_receiver(
-                strm, req, res, nullptr, std::move(header),
-                std::move(receiver));
-            if (!result) { output_error_log(Error::Read, &req); }
-            return result;
-          });
-
-      if (req.method == "POST") {
-        if (dispatch_request_for_content_reader(
-                req, res, std::move(reader),
-                post_handlers_for_content_reader_)) {
-          return true;
-        }
-      } else if (req.method == "PUT") {
-        if (dispatch_request_for_content_reader(
-                req, res, std::move(reader),
-                put_handlers_for_content_reader_)) {
-          return true;
-        }
-      } else if (req.method == "PATCH") {
-        if (dispatch_request_for_content_reader(
-                req, res, std::move(reader),
-                patch_handlers_for_content_reader_)) {
-          return true;
-        }
-      } else if (req.method == "DELETE") {
-        if (dispatch_request_for_content_reader(
-                req, res, std::move(reader),
-                delete_handlers_for_content_reader_)) {
-          return true;
-        }
-      }
-    }
-
-    // Read content into `req.body`
-    if (!read_content(strm, req, res)) {
-      output_error_log(Error::Read, &req);
-      return false;
-    }
-  }
-
-  // Regular handler
-  if (req.method == "GET" || req.method == "HEAD") {
-    return dispatch_request(req, res, get_handlers_);
-  } else if (req.method == "POST") {
-    return dispatch_request(req, res, post_handlers_);
-  } else if (req.method == "PUT") {
-    return dispatch_request(req, res, put_handlers_);
-  } else if (req.method == "DELETE") {
-    return dispatch_request(req, res, delete_handlers_);
-  } else if (req.method == "OPTIONS") {
-    return dispatch_request(req, res, options_handlers_);
-  } else if (req.method == "PATCH") {
-    return dispatch_request(req, res, patch_handlers_);
-  }
-
-  res.status = StatusCode::BadRequest_400;
-  return false;
-}
-
-inline bool Server::dispatch_request(Request &req, Response &res,
-                                     const Handlers &handlers) const {
-  for (const auto &x : handlers) {
-    const auto &matcher = x.first;
-    const auto &handler = x.second;
-
-    if (matcher->match(req)) {
-      req.matched_route = matcher->pattern();
-      if (!pre_request_handler_ ||
-          pre_request_handler_(req, res) != HandlerResponse::Handled) {
-        handler(req, res);
-      }
-      return true;
-    }
-  }
-  return false;
-}
-
-inline void Server::apply_ranges(const Request &req, Response &res,
-                                 std::string &content_type,
-                                 std::string &boundary) const {
-  if (req.ranges.size() > 1 && res.status == StatusCode::PartialContent_206) {
-    auto it = res.headers.find("Content-Type");
-    if (it != res.headers.end()) {
-      content_type = it->second;
-      res.headers.erase(it);
-    }
-
-    boundary = detail::make_multipart_data_boundary();
-
-    res.set_header("Content-Type",
-                   "multipart/byteranges; boundary=" + boundary);
-  }
-
-  auto type = detail::encoding_type(req, res);
-
-  if (res.body.empty()) {
-    if (res.content_length_ > 0) {
-      size_t length = 0;
-      if (req.ranges.empty() || res.status != StatusCode::PartialContent_206) {
-        length = res.content_length_;
-      } else if (req.ranges.size() == 1) {
-        auto offset_and_length = detail::get_range_offset_and_length(
-            req.ranges[0], res.content_length_);
-
-        length = offset_and_length.second;
-
-        auto content_range = detail::make_content_range_header_field(
-            offset_and_length, res.content_length_);
-        res.set_header("Content-Range", content_range);
-      } else {
-        length = detail::get_multipart_ranges_data_length(
-            req, boundary, content_type, res.content_length_);
-      }
-      res.set_header("Content-Length", std::to_string(length));
-    } else {
-      if (res.content_provider_) {
-        if (res.is_chunked_content_provider_) {
-          res.set_header("Transfer-Encoding", "chunked");
-          if (type == detail::EncodingType::Gzip) {
-            res.set_header("Content-Encoding", "gzip");
-          } else if (type == detail::EncodingType::Brotli) {
-            res.set_header("Content-Encoding", "br");
-          } else if (type == detail::EncodingType::Zstd) {
-            res.set_header("Content-Encoding", "zstd");
-          }
-        }
-      }
-    }
-  } else {
-    if (req.ranges.empty() || res.status != StatusCode::PartialContent_206) {
-      ;
-    } else if (req.ranges.size() == 1) {
-      auto offset_and_length =
-          detail::get_range_offset_and_length(req.ranges[0], res.body.size());
-      auto offset = offset_and_length.first;
-      auto length = offset_and_length.second;
-
-      auto content_range = detail::make_content_range_header_field(
-          offset_and_length, res.body.size());
-      res.set_header("Content-Range", content_range);
-
-      assert(offset + length <= res.body.size());
-      res.body = res.body.substr(offset, length);
-    } else {
-      std::string data;
-      detail::make_multipart_ranges_data(req, res, boundary, content_type,
-                                         res.body.size(), data);
-      res.body.swap(data);
-    }
-
-    if (type != detail::EncodingType::None) {
-      output_pre_compression_log(req, res);
-
-      std::unique_ptr<detail::compressor> compressor;
-      std::string content_encoding;
-
-      if (type == detail::EncodingType::Gzip) {
-#ifdef CPPHTTPLIB_ZLIB_SUPPORT
-        compressor = detail::make_unique<detail::gzip_compressor>();
-        content_encoding = "gzip";
-#endif
-      } else if (type == detail::EncodingType::Brotli) {
-#ifdef CPPHTTPLIB_BROTLI_SUPPORT
-        compressor = detail::make_unique<detail::brotli_compressor>();
-        content_encoding = "br";
-#endif
-      } else if (type == detail::EncodingType::Zstd) {
-#ifdef CPPHTTPLIB_ZSTD_SUPPORT
-        compressor = detail::make_unique<detail::zstd_compressor>();
-        content_encoding = "zstd";
-#endif
-      }
-
-      if (compressor) {
-        std::string compressed;
-        if (compressor->compress(res.body.data(), res.body.size(), true,
-                                 [&](const char *data, size_t data_len) {
-                                   compressed.append(data, data_len);
-                                   return true;
-                                 })) {
-          res.body.swap(compressed);
-          res.set_header("Content-Encoding", content_encoding);
-        }
-      }
-    }
-
-    auto length = std::to_string(res.body.size());
-    res.set_header("Content-Length", length);
-  }
-}
-
-inline bool Server::dispatch_request_for_content_reader(
-    Request &req, Response &res, ContentReader content_reader,
-    const HandlersForContentReader &handlers) const {
-  for (const auto &x : handlers) {
-    const auto &matcher = x.first;
-    const auto &handler = x.second;
-
-    if (matcher->match(req)) {
-      req.matched_route = matcher->pattern();
-      if (!pre_request_handler_ ||
-          pre_request_handler_(req, res) != HandlerResponse::Handled) {
-        handler(req, res, content_reader);
-      }
-      return true;
-    }
-  }
-  return false;
-}
-
-inline std::string
-get_client_ip(const std::string &x_forwarded_for,
-              const std::vector<std::string> &trusted_proxies) {
-  // X-Forwarded-For is a comma-separated list per RFC 7239
-  std::vector<std::string> ip_list;
-  detail::split(x_forwarded_for.data(),
-                x_forwarded_for.data() + x_forwarded_for.size(), ',',
-                [&](const char *b, const char *e) {
-                  auto r = detail::trim(b, e, 0, static_cast<size_t>(e - b));
-                  ip_list.emplace_back(std::string(b + r.first, b + r.second));
-                });
-
-  for (size_t i = 0; i < ip_list.size(); ++i) {
-    auto ip = ip_list[i];
-
-    auto is_trusted_proxy =
-        std::any_of(trusted_proxies.begin(), trusted_proxies.end(),
-                    [&](const std::string &proxy) { return ip == proxy; });
-
-    if (is_trusted_proxy) {
-      if (i == 0) {
-        // If the trusted proxy is the first IP, there's no preceding client IP
-        return ip;
-      } else {
-        // Return the IP immediately before the trusted proxy
-        return ip_list[i - 1];
-      }
-    }
-  }
-
-  // If no trusted proxy is found, return the first IP in the list
-  return ip_list.front();
-}
-
-inline bool
-Server::process_request(Stream &strm, const std::string &remote_addr,
-                        int remote_port, const std::string &local_addr,
-                        int local_port, bool close_connection,
-                        bool &connection_closed,
-                        const std::function<void(Request &)> &setup_request) {
-  std::array<char, 2048> buf{};
-
-  detail::stream_line_reader line_reader(strm, buf.data(), buf.size());
-
-  // Connection has been closed on client
-  if (!line_reader.getline()) { return false; }
-
-  Request req;
-  req.start_time_ = std::chrono::steady_clock::now();
-
-  Response res;
-  res.version = "HTTP/1.1";
-  res.headers = default_headers_;
-
-#ifdef __APPLE__
-  // Socket file descriptor exceeded FD_SETSIZE...
-  if (strm.socket() >= FD_SETSIZE) {
-    Headers dummy;
-    detail::read_headers(strm, dummy);
-    res.status = StatusCode::InternalServerError_500;
-    output_error_log(Error::ExceedMaxSocketDescriptorCount, &req);
-    return write_response(strm, close_connection, req, res);
-  }
-#endif
-
-  // Request line and headers
-  if (!parse_request_line(line_reader.ptr(), req)) {
-    res.status = StatusCode::BadRequest_400;
-    output_error_log(Error::InvalidRequestLine, &req);
-    return write_response(strm, close_connection, req, res);
-  }
-
-  // Request headers
-  if (!detail::read_headers(strm, req.headers)) {
-    res.status = StatusCode::BadRequest_400;
-    output_error_log(Error::InvalidHeaders, &req);
-    return write_response(strm, close_connection, req, res);
-  }
-
-  // Check if the request URI doesn't exceed the limit
-  if (req.target.size() > CPPHTTPLIB_REQUEST_URI_MAX_LENGTH) {
-    Headers dummy;
-    detail::read_headers(strm, dummy);
-    res.status = StatusCode::UriTooLong_414;
-    output_error_log(Error::ExceedUriMaxLength, &req);
-    return write_response(strm, close_connection, req, res);
-  }
-
-  if (req.get_header_value("Connection") == "close") {
-    connection_closed = true;
-  }
-
-  if (req.version == "HTTP/1.0" &&
-      req.get_header_value("Connection") != "Keep-Alive") {
-    connection_closed = true;
-  }
-
-  if (!trusted_proxies_.empty() && req.has_header("X-Forwarded-For")) {
-    auto x_forwarded_for = req.get_header_value("X-Forwarded-For");
-    req.remote_addr = get_client_ip(x_forwarded_for, trusted_proxies_);
-  } else {
-    req.remote_addr = remote_addr;
-  }
-  req.remote_port = remote_port;
-
-  req.local_addr = local_addr;
-  req.local_port = local_port;
-
-  if (req.has_header("Accept")) {
-    const auto &accept_header = req.get_header_value("Accept");
-    if (!detail::parse_accept_header(accept_header, req.accept_content_types)) {
-      res.status = StatusCode::BadRequest_400;
-      output_error_log(Error::HTTPParsing, &req);
-      return write_response(strm, close_connection, req, res);
-    }
-  }
-
-  if (req.has_header("Range")) {
-    const auto &range_header_value = req.get_header_value("Range");
-    if (!detail::parse_range_header(range_header_value, req.ranges)) {
-      res.status = StatusCode::RangeNotSatisfiable_416;
-      output_error_log(Error::InvalidRangeHeader, &req);
-      return write_response(strm, close_connection, req, res);
-    }
-  }
-
-  if (setup_request) { setup_request(req); }
-
-  if (req.get_header_value("Expect") == "100-continue") {
-    int status = StatusCode::Continue_100;
-    if (expect_100_continue_handler_) {
-      status = expect_100_continue_handler_(req, res);
-    }
-    switch (status) {
-    case StatusCode::Continue_100:
-    case StatusCode::ExpectationFailed_417:
-      detail::write_response_line(strm, status);
-      strm.write("\r\n");
-      break;
-    default:
-      connection_closed = true;
-      return write_response(strm, true, req, res);
-    }
-  }
-
-  // Setup `is_connection_closed` method
-  auto sock = strm.socket();
-  req.is_connection_closed = [sock]() {
-    return !detail::is_socket_alive(sock);
-  };
-
-  // Routing
-  auto routed = false;
-#ifdef CPPHTTPLIB_NO_EXCEPTIONS
-  routed = routing(req, res, strm);
-#else
-  try {
-    routed = routing(req, res, strm);
-  } catch (std::exception &e) {
-    if (exception_handler_) {
-      auto ep = std::current_exception();
-      exception_handler_(req, res, ep);
-      routed = true;
-    } else {
-      res.status = StatusCode::InternalServerError_500;
-      std::string val;
-      auto s = e.what();
-      for (size_t i = 0; s[i]; i++) {
-        switch (s[i]) {
-        case '\r': val += "\\r"; break;
-        case '\n': val += "\\n"; break;
-        default: val += s[i]; break;
-        }
-      }
-      res.set_header("EXCEPTION_WHAT", val);
-    }
-  } catch (...) {
-    if (exception_handler_) {
-      auto ep = std::current_exception();
-      exception_handler_(req, res, ep);
-      routed = true;
-    } else {
-      res.status = StatusCode::InternalServerError_500;
-      res.set_header("EXCEPTION_WHAT", "UNKNOWN");
-    }
-  }
-#endif
-  if (routed) {
-    if (res.status == -1) {
-      res.status = req.ranges.empty() ? StatusCode::OK_200
-                                      : StatusCode::PartialContent_206;
-    }
-
-    // Serve file content by using a content provider
-    if (!res.file_content_path_.empty()) {
-      const auto &path = res.file_content_path_;
-      auto mm = std::make_shared<detail::mmap>(path.c_str());
-      if (!mm->is_open()) {
-        res.body.clear();
-        res.content_length_ = 0;
-        res.content_provider_ = nullptr;
-        res.status = StatusCode::NotFound_404;
-        output_error_log(Error::OpenFile, &req);
-        return write_response(strm, close_connection, req, res);
-      }
-
-      auto content_type = res.file_content_content_type_;
-      if (content_type.empty()) {
-        content_type = detail::find_content_type(
-            path, file_extension_and_mimetype_map_, default_file_mimetype_);
-      }
-
-      res.set_content_provider(
-          mm->size(), content_type,
-          [mm](size_t offset, size_t length, DataSink &sink) -> bool {
-            sink.write(mm->data() + offset, length);
-            return true;
-          });
-    }
-
-    if (detail::range_error(req, res)) {
-      res.body.clear();
-      res.content_length_ = 0;
-      res.content_provider_ = nullptr;
-      res.status = StatusCode::RangeNotSatisfiable_416;
-      return write_response(strm, close_connection, req, res);
-    }
-
-    return write_response_with_content(strm, close_connection, req, res);
-  } else {
-    if (res.status == -1) { res.status = StatusCode::NotFound_404; }
-
-    return write_response(strm, close_connection, req, res);
-  }
-}
-
-inline bool Server::is_valid() const { return true; }
-
-inline bool Server::process_and_close_socket(socket_t sock) {
-  std::string remote_addr;
-  int remote_port = 0;
-  detail::get_remote_ip_and_port(sock, remote_addr, remote_port);
-
-  std::string local_addr;
-  int local_port = 0;
-  detail::get_local_ip_and_port(sock, local_addr, local_port);
-
-  auto ret = detail::process_server_socket(
-      svr_sock_, sock, keep_alive_max_count_, keep_alive_timeout_sec_,
-      read_timeout_sec_, read_timeout_usec_, write_timeout_sec_,
-      write_timeout_usec_,
-      [&](Stream &strm, bool close_connection, bool &connection_closed) {
-        return process_request(strm, remote_addr, remote_port, local_addr,
-                               local_port, close_connection, connection_closed,
-                               nullptr);
-      });
-
-  detail::shutdown_socket(sock);
-  detail::close_socket(sock);
-  return ret;
-}
-
-inline void Server::output_log(const Request &req, const Response &res) const {
-  if (logger_) {
-    std::lock_guard<std::mutex> guard(logger_mutex_);
-    logger_(req, res);
-  }
-}
-
-inline void Server::output_pre_compression_log(const Request &req,
-                                               const Response &res) const {
-  if (pre_compression_logger_) {
-    std::lock_guard<std::mutex> guard(logger_mutex_);
-    pre_compression_logger_(req, res);
-  }
-}
-
-inline void Server::output_error_log(const Error &err,
-                                     const Request *req) const {
-  if (error_logger_) {
-    std::lock_guard<std::mutex> guard(logger_mutex_);
-    error_logger_(err, req);
-  }
-}
-
-// HTTP client implementation
-inline ClientImpl::ClientImpl(const std::string &host)
-    : ClientImpl(host, 80, std::string(), std::string()) {}
-
-inline ClientImpl::ClientImpl(const std::string &host, int port)
-    : ClientImpl(host, port, std::string(), std::string()) {}
-
-inline ClientImpl::ClientImpl(const std::string &host, int port,
-                              const std::string &client_cert_path,
-                              const std::string &client_key_path)
-    : host_(detail::escape_abstract_namespace_unix_domain(host)), port_(port),
-      host_and_port_(detail::make_host_and_port_string(host_, port, is_ssl())),
-      client_cert_path_(client_cert_path), client_key_path_(client_key_path) {}
-
-inline ClientImpl::~ClientImpl() {
-  // Wait until all the requests in flight are handled.
-  size_t retry_count = 10;
-  while (retry_count-- > 0) {
-    {
-      std::lock_guard<std::mutex> guard(socket_mutex_);
-      if (socket_requests_in_flight_ == 0) { break; }
-    }
-    std::this_thread::sleep_for(std::chrono::milliseconds{1});
-  }
-
-  std::lock_guard<std::mutex> guard(socket_mutex_);
-  shutdown_socket(socket_);
-  close_socket(socket_);
-}
-
-inline bool ClientImpl::is_valid() const { return true; }
-
-inline void ClientImpl::copy_settings(const ClientImpl &rhs) {
-  client_cert_path_ = rhs.client_cert_path_;
-  client_key_path_ = rhs.client_key_path_;
-  connection_timeout_sec_ = rhs.connection_timeout_sec_;
-  read_timeout_sec_ = rhs.read_timeout_sec_;
-  read_timeout_usec_ = rhs.read_timeout_usec_;
-  write_timeout_sec_ = rhs.write_timeout_sec_;
-  write_timeout_usec_ = rhs.write_timeout_usec_;
-  max_timeout_msec_ = rhs.max_timeout_msec_;
-  basic_auth_username_ = rhs.basic_auth_username_;
-  basic_auth_password_ = rhs.basic_auth_password_;
-  bearer_token_auth_token_ = rhs.bearer_token_auth_token_;
-#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
-  digest_auth_username_ = rhs.digest_auth_username_;
-  digest_auth_password_ = rhs.digest_auth_password_;
-#endif
-  keep_alive_ = rhs.keep_alive_;
-  follow_location_ = rhs.follow_location_;
-  path_encode_ = rhs.path_encode_;
-  address_family_ = rhs.address_family_;
-  tcp_nodelay_ = rhs.tcp_nodelay_;
-  ipv6_v6only_ = rhs.ipv6_v6only_;
-  socket_options_ = rhs.socket_options_;
-  compress_ = rhs.compress_;
-  decompress_ = rhs.decompress_;
-  interface_ = rhs.interface_;
-  proxy_host_ = rhs.proxy_host_;
-  proxy_port_ = rhs.proxy_port_;
-  proxy_basic_auth_username_ = rhs.proxy_basic_auth_username_;
-  proxy_basic_auth_password_ = rhs.proxy_basic_auth_password_;
-  proxy_bearer_token_auth_token_ = rhs.proxy_bearer_token_auth_token_;
-#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
-  proxy_digest_auth_username_ = rhs.proxy_digest_auth_username_;
-  proxy_digest_auth_password_ = rhs.proxy_digest_auth_password_;
-#endif
-#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
-  ca_cert_file_path_ = rhs.ca_cert_file_path_;
-  ca_cert_dir_path_ = rhs.ca_cert_dir_path_;
-  ca_cert_store_ = rhs.ca_cert_store_;
-#endif
-#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
-  server_certificate_verification_ = rhs.server_certificate_verification_;
-  server_hostname_verification_ = rhs.server_hostname_verification_;
-  server_certificate_verifier_ = rhs.server_certificate_verifier_;
-#endif
-  logger_ = rhs.logger_;
-  error_logger_ = rhs.error_logger_;
-}
-
-inline socket_t ClientImpl::create_client_socket(Error &error) const {
-  if (!proxy_host_.empty() && proxy_port_ != -1) {
-    return detail::create_client_socket(
-        proxy_host_, std::string(), proxy_port_, address_family_, tcp_nodelay_,
-        ipv6_v6only_, socket_options_, connection_timeout_sec_,
-        connection_timeout_usec_, read_timeout_sec_, read_timeout_usec_,
-        write_timeout_sec_, write_timeout_usec_, interface_, error);
-  }
-
-  // Check is custom IP specified for host_
-  std::string ip;
-  auto it = addr_map_.find(host_);
-  if (it != addr_map_.end()) { ip = it->second; }
-
-  return detail::create_client_socket(
-      host_, ip, port_, address_family_, tcp_nodelay_, ipv6_v6only_,
-      socket_options_, connection_timeout_sec_, connection_timeout_usec_,
-      read_timeout_sec_, read_timeout_usec_, write_timeout_sec_,
-      write_timeout_usec_, interface_, error);
-}
-
-inline bool ClientImpl::create_and_connect_socket(Socket &socket,
-                                                  Error &error) {
-  auto sock = create_client_socket(error);
-  if (sock == INVALID_SOCKET) { return false; }
-  socket.sock = sock;
-  return true;
-}
-
-inline void ClientImpl::shutdown_ssl(Socket & /*socket*/,
-                                     bool /*shutdown_gracefully*/) {
-  // If there are any requests in flight from threads other than us, then it's
-  // a thread-unsafe race because individual ssl* objects are not thread-safe.
-  assert(socket_requests_in_flight_ == 0 ||
-         socket_requests_are_from_thread_ == std::this_thread::get_id());
-}
-
-inline void ClientImpl::shutdown_socket(Socket &socket) const {
-  if (socket.sock == INVALID_SOCKET) { return; }
-  detail::shutdown_socket(socket.sock);
-}
-
-inline void ClientImpl::close_socket(Socket &socket) {
-  // If there are requests in flight in another thread, usually closing
-  // the socket will be fine and they will simply receive an error when
-  // using the closed socket, but it is still a bug since rarely the OS
-  // may reassign the socket id to be used for a new socket, and then
-  // suddenly they will be operating on a live socket that is different
-  // than the one they intended!
-  assert(socket_requests_in_flight_ == 0 ||
-         socket_requests_are_from_thread_ == std::this_thread::get_id());
-
-  // It is also a bug if this happens while SSL is still active
-#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
-  assert(socket.ssl == nullptr);
-#endif
-  if (socket.sock == INVALID_SOCKET) { return; }
-  detail::close_socket(socket.sock);
-  socket.sock = INVALID_SOCKET;
-}
-
-inline bool ClientImpl::read_response_line(Stream &strm, const Request &req,
-                                           Response &res) const {
-  std::array<char, 2048> buf{};
-
-  detail::stream_line_reader line_reader(strm, buf.data(), buf.size());
-
-  if (!line_reader.getline()) { return false; }
-
-#ifdef CPPHTTPLIB_ALLOW_LF_AS_LINE_TERMINATOR
-  thread_local const std::regex re("(HTTP/1\\.[01]) (\\d{3})(?: (.*?))?\r?\n");
-#else
-  thread_local const std::regex re("(HTTP/1\\.[01]) (\\d{3})(?: (.*?))?\r\n");
-#endif
-
-  std::cmatch m;
-  if (!std::regex_match(line_reader.ptr(), m, re)) {
-    return req.method == "CONNECT";
-  }
-  res.version = std::string(m[1]);
-  res.status = std::stoi(std::string(m[2]));
-  res.reason = std::string(m[3]);
-
-  // Ignore '100 Continue'
-  while (res.status == StatusCode::Continue_100) {
-    if (!line_reader.getline()) { return false; } // CRLF
-    if (!line_reader.getline()) { return false; } // next response line
-
-    if (!std::regex_match(line_reader.ptr(), m, re)) { return false; }
-    res.version = std::string(m[1]);
-    res.status = std::stoi(std::string(m[2]));
-    res.reason = std::string(m[3]);
-  }
-
-  return true;
-}
-
-inline bool ClientImpl::send(Request &req, Response &res, Error &error) {
-  std::lock_guard<std::recursive_mutex> request_mutex_guard(request_mutex_);
-  auto ret = send_(req, res, error);
-  if (error == Error::SSLPeerCouldBeClosed_) {
-    assert(!ret);
-    ret = send_(req, res, error);
-  }
-  return ret;
-}
-
-inline bool ClientImpl::send_(Request &req, Response &res, Error &error) {
-  {
-    std::lock_guard<std::mutex> guard(socket_mutex_);
-
-    // Set this to false immediately - if it ever gets set to true by the end
-    // of the request, we know another thread instructed us to close the
-    // socket.
-    socket_should_be_closed_when_request_is_done_ = false;
-
-    auto is_alive = false;
-    if (socket_.is_open()) {
-      is_alive = detail::is_socket_alive(socket_.sock);
-
-#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
-      if (is_alive && is_ssl()) {
-        if (detail::is_ssl_peer_could_be_closed(socket_.ssl, socket_.sock)) {
-          is_alive = false;
-        }
-      }
-#endif
-
-      if (!is_alive) {
-        // Attempt to avoid sigpipe by shutting down non-gracefully if it
-        // seems like the other side has already closed the connection Also,
-        // there cannot be any requests in flight from other threads since we
-        // locked request_mutex_, so safe to close everything immediately
-        const bool shutdown_gracefully = false;
-        shutdown_ssl(socket_, shutdown_gracefully);
-        shutdown_socket(socket_);
-        close_socket(socket_);
-      }
-    }
-
-    if (!is_alive) {
-      if (!create_and_connect_socket(socket_, error)) {
-        output_error_log(error, &req);
-        return false;
-      }
-
-#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
-      // TODO: refactoring
-      if (is_ssl()) {
-        auto &scli = static_cast<SSLClient &>(*this);
-        if (!proxy_host_.empty() && proxy_port_ != -1) {
-          auto success = false;
-          if (!scli.connect_with_proxy(socket_, req.start_time_, res, success,
-                                       error)) {
-            if (!success) { output_error_log(error, &req); }
-            return success;
-          }
-        }
-
-        if (!scli.initialize_ssl(socket_, error)) {
-          output_error_log(error, &req);
-          return false;
-        }
-      }
-#endif
-    }
-
-    // Mark the current socket as being in use so that it cannot be closed by
-    // anyone else while this request is ongoing, even though we will be
-    // releasing the mutex.
-    if (socket_requests_in_flight_ > 1) {
-      assert(socket_requests_are_from_thread_ == std::this_thread::get_id());
-    }
-    socket_requests_in_flight_ += 1;
-    socket_requests_are_from_thread_ = std::this_thread::get_id();
-  }
-
-  for (const auto &header : default_headers_) {
-    if (req.headers.find(header.first) == req.headers.end()) {
-      req.headers.insert(header);
-    }
-  }
-
-  auto ret = false;
-  auto close_connection = !keep_alive_;
-
-  auto se = detail::scope_exit([&]() {
-    // Briefly lock mutex in order to mark that a request is no longer ongoing
-    std::lock_guard<std::mutex> guard(socket_mutex_);
-    socket_requests_in_flight_ -= 1;
-    if (socket_requests_in_flight_ <= 0) {
-      assert(socket_requests_in_flight_ == 0);
-      socket_requests_are_from_thread_ = std::thread::id();
-    }
-
-    if (socket_should_be_closed_when_request_is_done_ || close_connection ||
-        !ret) {
-      shutdown_ssl(socket_, true);
-      shutdown_socket(socket_);
-      close_socket(socket_);
-    }
-  });
-
-  ret = process_socket(socket_, req.start_time_, [&](Stream &strm) {
-    return handle_request(strm, req, res, close_connection, error);
-  });
-
-  if (!ret) {
-    if (error == Error::Success) {
-      error = Error::Unknown;
-      output_error_log(error, &req);
-    }
-  }
-
-  return ret;
-}
-
-inline Result ClientImpl::send(const Request &req) {
-  auto req2 = req;
-  return send_(std::move(req2));
-}
-
-inline Result ClientImpl::send_(Request &&req) {
-  auto res = detail::make_unique<Response>();
-  auto error = Error::Success;
-  auto ret = send(req, *res, error);
-#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
-  return Result{ret ? std::move(res) : nullptr, error, std::move(req.headers),
-                last_ssl_error_, last_openssl_error_};
-#else
-  return Result{ret ? std::move(res) : nullptr, error, std::move(req.headers)};
-#endif
-}
-
-inline bool ClientImpl::handle_request(Stream &strm, Request &req,
-                                       Response &res, bool close_connection,
-                                       Error &error) {
-  if (req.path.empty()) {
-    error = Error::Connection;
-    output_error_log(error, &req);
-    return false;
-  }
-
-  auto req_save = req;
-
-  bool ret;
-
-  if (!is_ssl() && !proxy_host_.empty() && proxy_port_ != -1) {
-    auto req2 = req;
-    req2.path = "http://" + host_and_port_ + req.path;
-    ret = process_request(strm, req2, res, close_connection, error);
-    req = req2;
-    req.path = req_save.path;
-  } else {
-    ret = process_request(strm, req, res, close_connection, error);
-  }
-
-  if (!ret) { return false; }
-
-  if (res.get_header_value("Connection") == "close" ||
-      (res.version == "HTTP/1.0" && res.reason != "Connection established")) {
-    // TODO this requires a not-entirely-obvious chain of calls to be correct
-    // for this to be safe.
-
-    // This is safe to call because handle_request is only called by send_
-    // which locks the request mutex during the process. It would be a bug
-    // to call it from a different thread since it's a thread-safety issue
-    // to do these things to the socket if another thread is using the socket.
-    std::lock_guard<std::mutex> guard(socket_mutex_);
-    shutdown_ssl(socket_, true);
-    shutdown_socket(socket_);
-    close_socket(socket_);
-  }
-
-  if (300 < res.status && res.status < 400 && follow_location_) {
-    req = req_save;
-    ret = redirect(req, res, error);
-  }
-
-#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
-  if ((res.status == StatusCode::Unauthorized_401 ||
-       res.status == StatusCode::ProxyAuthenticationRequired_407) &&
-      req.authorization_count_ < 5) {
-    auto is_proxy = res.status == StatusCode::ProxyAuthenticationRequired_407;
-    const auto &username =
-        is_proxy ? proxy_digest_auth_username_ : digest_auth_username_;
-    const auto &password =
-        is_proxy ? proxy_digest_auth_password_ : digest_auth_password_;
-
-    if (!username.empty() && !password.empty()) {
-      std::map<std::string, std::string> auth;
-      if (detail::parse_www_authenticate(res, auth, is_proxy)) {
-        Request new_req = req;
-        new_req.authorization_count_ += 1;
-        new_req.headers.erase(is_proxy ? "Proxy-Authorization"
-                                       : "Authorization");
-        new_req.headers.insert(detail::make_digest_authentication_header(
-            req, auth, new_req.authorization_count_, detail::random_string(10),
-            username, password, is_proxy));
-
-        Response new_res;
-
-        ret = send(new_req, new_res, error);
-        if (ret) { res = new_res; }
-      }
-    }
-  }
-#endif
-
-  return ret;
-}
-
-inline bool ClientImpl::redirect(Request &req, Response &res, Error &error) {
-  if (req.redirect_count_ == 0) {
-    error = Error::ExceedRedirectCount;
-    output_error_log(error, &req);
-    return false;
-  }
-
-  auto location = res.get_header_value("location");
-  if (location.empty()) { return false; }
-
-  thread_local const std::regex re(
-      R"((?:(https?):)?(?://(?:\[([a-fA-F\d:]+)\]|([^:/?#]+))(?::(\d+))?)?([^?#]*)(\?[^#]*)?(?:#.*)?)");
-
-  std::smatch m;
-  if (!std::regex_match(location, m, re)) { return false; }
-
-  auto scheme = is_ssl() ? "https" : "http";
-
-  auto next_scheme = m[1].str();
-  auto next_host = m[2].str();
-  if (next_host.empty()) { next_host = m[3].str(); }
-  auto port_str = m[4].str();
-  auto next_path = m[5].str();
-  auto next_query = m[6].str();
-
-  auto next_port = port_;
-  if (!port_str.empty()) {
-    next_port = std::stoi(port_str);
-  } else if (!next_scheme.empty()) {
-    next_port = next_scheme == "https" ? 443 : 80;
-  }
-
-  if (next_scheme.empty()) { next_scheme = scheme; }
-  if (next_host.empty()) { next_host = host_; }
-  if (next_path.empty()) { next_path = "/"; }
-
-  auto path = decode_query_component(next_path, true) + next_query;
-
-  // Same host redirect - use current client
-  if (next_scheme == scheme && next_host == host_ && next_port == port_) {
-    return detail::redirect(*this, req, res, path, location, error);
-  }
-
-  // Cross-host/scheme redirect - create new client with robust setup
-  return create_redirect_client(next_scheme, next_host, next_port, req, res,
-                                path, location, error);
-}
-
-// New method for robust redirect client creation
-inline bool ClientImpl::create_redirect_client(
-    const std::string &scheme, const std::string &host, int port, Request &req,
-    Response &res, const std::string &path, const std::string &location,
-    Error &error) {
-  // Determine if we need SSL
-  auto need_ssl = (scheme == "https");
-
-  // Clean up request headers that are host/client specific
-  // Remove headers that should not be carried over to new host
-  auto headers_to_remove =
-      std::vector<std::string>{"Host", "Proxy-Authorization", "Authorization"};
-
-  for (const auto &header_name : headers_to_remove) {
-    auto it = req.headers.find(header_name);
-    while (it != req.headers.end()) {
-      it = req.headers.erase(it);
-      it = req.headers.find(header_name);
-    }
-  }
-
-  // Create appropriate client type and handle redirect
-  if (need_ssl) {
-#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
-    // Create SSL client for HTTPS redirect
-    SSLClient redirect_client(host, port);
-
-    // Setup basic client configuration first
-    setup_redirect_client(redirect_client);
-
-    // SSL-specific configuration for proxy environments
-    if (!proxy_host_.empty() && proxy_port_ != -1) {
-      // Critical: Disable SSL verification for proxy environments
-      redirect_client.enable_server_certificate_verification(false);
-      redirect_client.enable_server_hostname_verification(false);
-    } else {
-      // For direct SSL connections, copy SSL verification settings
-      redirect_client.enable_server_certificate_verification(
-          server_certificate_verification_);
-      redirect_client.enable_server_hostname_verification(
-          server_hostname_verification_);
-    }
-
-    // Handle CA certificate store and paths if available
-    if (ca_cert_store_ && X509_STORE_up_ref(ca_cert_store_)) {
-      redirect_client.set_ca_cert_store(ca_cert_store_);
-    }
-    if (!ca_cert_file_path_.empty()) {
-      redirect_client.set_ca_cert_path(ca_cert_file_path_, ca_cert_dir_path_);
-    }
-
-    // Client certificates are set through constructor for SSLClient
-    // NOTE: SSLClient constructor already takes client_cert_path and
-    // client_key_path so we need to create it properly if client certs are
-    // needed
-
-    // Execute the redirect
-    return detail::redirect(redirect_client, req, res, path, location, error);
-#else
-    // SSL not supported - set appropriate error
-    error = Error::SSLConnection;
-    output_error_log(error, &req);
-    return false;
-#endif
-  } else {
-    // HTTP redirect
-    ClientImpl redirect_client(host, port);
-
-    // Setup client with robust configuration
-    setup_redirect_client(redirect_client);
-
-    // Execute the redirect
-    return detail::redirect(redirect_client, req, res, path, location, error);
-  }
-}
-
-// New method for robust client setup (based on basic_manual_redirect.cpp
-// logic)
-template <typename ClientType>
-inline void ClientImpl::setup_redirect_client(ClientType &client) {
-  // Copy basic settings first
-  client.set_connection_timeout(connection_timeout_sec_);
-  client.set_read_timeout(read_timeout_sec_, read_timeout_usec_);
-  client.set_write_timeout(write_timeout_sec_, write_timeout_usec_);
-  client.set_keep_alive(keep_alive_);
-  client.set_follow_location(
-      true); // Enable redirects to handle multi-step redirects
-  client.set_path_encode(path_encode_);
-  client.set_compress(compress_);
-  client.set_decompress(decompress_);
-
-  // Copy authentication settings BEFORE proxy setup
-  if (!basic_auth_username_.empty()) {
-    client.set_basic_auth(basic_auth_username_, basic_auth_password_);
-  }
-  if (!bearer_token_auth_token_.empty()) {
-    client.set_bearer_token_auth(bearer_token_auth_token_);
-  }
-#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
-  if (!digest_auth_username_.empty()) {
-    client.set_digest_auth(digest_auth_username_, digest_auth_password_);
-  }
-#endif
-
-  // Setup proxy configuration (CRITICAL ORDER - proxy must be set
-  // before proxy auth)
-  if (!proxy_host_.empty() && proxy_port_ != -1) {
-    // First set proxy host and port
-    client.set_proxy(proxy_host_, proxy_port_);
-
-    // Then set proxy authentication (order matters!)
-    if (!proxy_basic_auth_username_.empty()) {
-      client.set_proxy_basic_auth(proxy_basic_auth_username_,
-                                  proxy_basic_auth_password_);
-    }
-    if (!proxy_bearer_token_auth_token_.empty()) {
-      client.set_proxy_bearer_token_auth(proxy_bearer_token_auth_token_);
-    }
-#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
-    if (!proxy_digest_auth_username_.empty()) {
-      client.set_proxy_digest_auth(proxy_digest_auth_username_,
-                                   proxy_digest_auth_password_);
-    }
-#endif
-  }
-
-  // Copy network and socket settings
-  client.set_address_family(address_family_);
-  client.set_tcp_nodelay(tcp_nodelay_);
-  client.set_ipv6_v6only(ipv6_v6only_);
-  if (socket_options_) { client.set_socket_options(socket_options_); }
-  if (!interface_.empty()) { client.set_interface(interface_); }
-
-  // Copy logging and headers
-  if (logger_) { client.set_logger(logger_); }
-  if (error_logger_) { client.set_error_logger(error_logger_); }
-
-  // NOTE: DO NOT copy default_headers_ as they may contain stale Host headers
-  // Each new client should generate its own headers based on its target host
-}
-
-inline bool ClientImpl::write_content_with_provider(Stream &strm,
-                                                    const Request &req,
-                                                    Error &error) const {
-  auto is_shutting_down = []() { return false; };
-
-  if (req.is_chunked_content_provider_) {
-    // TODO: Brotli support
-    std::unique_ptr<detail::compressor> compressor;
-#ifdef CPPHTTPLIB_ZLIB_SUPPORT
-    if (compress_) {
-      compressor = detail::make_unique<detail::gzip_compressor>();
-    } else
-#endif
-    {
-      compressor = detail::make_unique<detail::nocompressor>();
-    }
-
-    return detail::write_content_chunked(strm, req.content_provider_,
-                                         is_shutting_down, *compressor, error);
-  } else {
-    return detail::write_content_with_progress(
-        strm, req.content_provider_, 0, req.content_length_, is_shutting_down,
-        req.upload_progress, error);
-  }
-}
-
-inline bool ClientImpl::write_request(Stream &strm, Request &req,
-                                      bool close_connection, Error &error) {
-  // Prepare additional headers
-  if (close_connection) {
-    if (!req.has_header("Connection")) {
-      req.set_header("Connection", "close");
-    }
-  }
-
-  if (!req.has_header("Host")) {
-    // For Unix socket connections, use "localhost" as Host header (similar to
-    // curl behavior)
-    if (address_family_ == AF_UNIX) {
-      req.set_header("Host", "localhost");
-    } else {
-      req.set_header("Host", host_and_port_);
-    }
-  }
-
-  if (!req.has_header("Accept")) { req.set_header("Accept", "*/*"); }
-
-  if (!req.content_receiver) {
-    if (!req.has_header("Accept-Encoding")) {
-      std::string accept_encoding;
-#ifdef CPPHTTPLIB_BROTLI_SUPPORT
-      accept_encoding = "br";
-#endif
-#ifdef CPPHTTPLIB_ZLIB_SUPPORT
-      if (!accept_encoding.empty()) { accept_encoding += ", "; }
-      accept_encoding += "gzip, deflate";
-#endif
-#ifdef CPPHTTPLIB_ZSTD_SUPPORT
-      if (!accept_encoding.empty()) { accept_encoding += ", "; }
-      accept_encoding += "zstd";
-#endif
-      req.set_header("Accept-Encoding", accept_encoding);
-    }
-
-#ifndef CPPHTTPLIB_NO_DEFAULT_USER_AGENT
-    if (!req.has_header("User-Agent")) {
-      auto agent = std::string("cpp-httplib/") + CPPHTTPLIB_VERSION;
-      req.set_header("User-Agent", agent);
-    }
-#endif
-  };
-
-  if (req.body.empty()) {
-    if (req.content_provider_) {
-      if (!req.is_chunked_content_provider_) {
-        if (!req.has_header("Content-Length")) {
-          auto length = std::to_string(req.content_length_);
-          req.set_header("Content-Length", length);
-        }
-      }
-    } else {
-      if (req.method == "POST" || req.method == "PUT" ||
-          req.method == "PATCH") {
-        req.set_header("Content-Length", "0");
-      }
-    }
-  } else {
-    if (!req.has_header("Content-Type")) {
-      req.set_header("Content-Type", "text/plain");
-    }
-
-    if (!req.has_header("Content-Length")) {
-      auto length = std::to_string(req.body.size());
-      req.set_header("Content-Length", length);
-    }
-  }
-
-  if (!basic_auth_password_.empty() || !basic_auth_username_.empty()) {
-    if (!req.has_header("Authorization")) {
-      req.headers.insert(make_basic_authentication_header(
-          basic_auth_username_, basic_auth_password_, false));
-    }
-  }
-
-  if (!proxy_basic_auth_username_.empty() &&
-      !proxy_basic_auth_password_.empty()) {
-    if (!req.has_header("Proxy-Authorization")) {
-      req.headers.insert(make_basic_authentication_header(
-          proxy_basic_auth_username_, proxy_basic_auth_password_, true));
-    }
-  }
-
-  if (!bearer_token_auth_token_.empty()) {
-    if (!req.has_header("Authorization")) {
-      req.headers.insert(make_bearer_token_authentication_header(
-          bearer_token_auth_token_, false));
-    }
-  }
-
-  if (!proxy_bearer_token_auth_token_.empty()) {
-    if (!req.has_header("Proxy-Authorization")) {
-      req.headers.insert(make_bearer_token_authentication_header(
-          proxy_bearer_token_auth_token_, true));
-    }
-  }
-
-  // Request line and headers
-  {
-    detail::BufferStream bstrm;
-
-    // Extract path and query from req.path
-    std::string path_part, query_part;
-    auto query_pos = req.path.find('?');
-    if (query_pos != std::string::npos) {
-      path_part = req.path.substr(0, query_pos);
-      query_part = req.path.substr(query_pos + 1);
-    } else {
-      path_part = req.path;
-      query_part = "";
-    }
-
-    // Encode path and query
-    auto path_with_query =
-        path_encode_ ? detail::encode_path(path_part) : path_part;
-
-    detail::parse_query_text(query_part, req.params);
-    if (!req.params.empty()) {
-      path_with_query = append_query_params(path_with_query, req.params);
-    }
-
-    // Write request line and headers
-    detail::write_request_line(bstrm, req.method, path_with_query);
-    header_writer_(bstrm, req.headers);
-
-    // Flush buffer
-    auto &data = bstrm.get_buffer();
-    if (!detail::write_data(strm, data.data(), data.size())) {
-      error = Error::Write;
-      output_error_log(error, &req);
-      return false;
-    }
-  }
-
-  // Body
-  if (req.body.empty()) {
-    return write_content_with_provider(strm, req, error);
-  }
-
-  if (req.upload_progress) {
-    auto body_size = req.body.size();
-    size_t written = 0;
-    auto data = req.body.data();
-
-    while (written < body_size) {
-      size_t to_write = (std::min)(CPPHTTPLIB_SEND_BUFSIZ, body_size - written);
-      if (!detail::write_data(strm, data + written, to_write)) {
-        error = Error::Write;
-        output_error_log(error, &req);
-        return false;
-      }
-      written += to_write;
-
-      if (!req.upload_progress(written, body_size)) {
-        error = Error::Canceled;
-        output_error_log(error, &req);
-        return false;
-      }
-    }
-  } else {
-    if (!detail::write_data(strm, req.body.data(), req.body.size())) {
-      error = Error::Write;
-      output_error_log(error, &req);
-      return false;
-    }
-  }
-
-  return true;
-}
-
-inline std::unique_ptr<Response> ClientImpl::send_with_content_provider(
-    Request &req, const char *body, size_t content_length,
-    ContentProvider content_provider,
-    ContentProviderWithoutLength content_provider_without_length,
-    const std::string &content_type, Error &error) {
-  if (!content_type.empty()) { req.set_header("Content-Type", content_type); }
-
-#ifdef CPPHTTPLIB_ZLIB_SUPPORT
-  if (compress_) { req.set_header("Content-Encoding", "gzip"); }
-#endif
-
-#ifdef CPPHTTPLIB_ZLIB_SUPPORT
-  if (compress_ && !content_provider_without_length) {
-    // TODO: Brotli support
-    detail::gzip_compressor compressor;
-
-    if (content_provider) {
-      auto ok = true;
-      size_t offset = 0;
-      DataSink data_sink;
-
-      data_sink.write = [&](const char *data, size_t data_len) -> bool {
-        if (ok) {
-          auto last = offset + data_len == content_length;
-
-          auto ret = compressor.compress(
-              data, data_len, last,
-              [&](const char *compressed_data, size_t compressed_data_len) {
-                req.body.append(compressed_data, compressed_data_len);
-                return true;
-              });
-
-          if (ret) {
-            offset += data_len;
-          } else {
-            ok = false;
-          }
-        }
-        return ok;
-      };
-
-      while (ok && offset < content_length) {
-        if (!content_provider(offset, content_length - offset, data_sink)) {
-          error = Error::Canceled;
-          output_error_log(error, &req);
-          return nullptr;
-        }
-      }
-    } else {
-      if (!compressor.compress(body, content_length, true,
-                               [&](const char *data, size_t data_len) {
-                                 req.body.append(data, data_len);
-                                 return true;
-                               })) {
-        error = Error::Compression;
-        output_error_log(error, &req);
-        return nullptr;
-      }
-    }
-  } else
-#endif
-  {
-    if (content_provider) {
-      req.content_length_ = content_length;
-      req.content_provider_ = std::move(content_provider);
-      req.is_chunked_content_provider_ = false;
-    } else if (content_provider_without_length) {
-      req.content_length_ = 0;
-      req.content_provider_ = detail::ContentProviderAdapter(
-          std::move(content_provider_without_length));
-      req.is_chunked_content_provider_ = true;
-      req.set_header("Transfer-Encoding", "chunked");
-    } else {
-      req.body.assign(body, content_length);
-    }
-  }
-
-  auto res = detail::make_unique<Response>();
-  return send(req, *res, error) ? std::move(res) : nullptr;
-}
-
-inline Result ClientImpl::send_with_content_provider(
-    const std::string &method, const std::string &path, const Headers &headers,
-    const char *body, size_t content_length, ContentProvider content_provider,
-    ContentProviderWithoutLength content_provider_without_length,
-    const std::string &content_type, UploadProgress progress) {
-  Request req;
-  req.method = method;
-  req.headers = headers;
-  req.path = path;
-  req.upload_progress = std::move(progress);
-  if (max_timeout_msec_ > 0) {
-    req.start_time_ = std::chrono::steady_clock::now();
-  }
-
-  auto error = Error::Success;
-
-  auto res = send_with_content_provider(
-      req, body, content_length, std::move(content_provider),
-      std::move(content_provider_without_length), content_type, error);
-
-#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
-  return Result{std::move(res), error, std::move(req.headers), last_ssl_error_,
-                last_openssl_error_};
-#else
-  return Result{std::move(res), error, std::move(req.headers)};
-#endif
-}
-
-inline void ClientImpl::output_log(const Request &req,
-                                   const Response &res) const {
-  if (logger_) {
-    std::lock_guard<std::mutex> guard(logger_mutex_);
-    logger_(req, res);
-  }
-}
-
-inline void ClientImpl::output_error_log(const Error &err,
-                                         const Request *req) const {
-  if (error_logger_) {
-    std::lock_guard<std::mutex> guard(logger_mutex_);
-    error_logger_(err, req);
-  }
-}
-
-inline bool ClientImpl::process_request(Stream &strm, Request &req,
-                                        Response &res, bool close_connection,
-                                        Error &error) {
-  // Send request
-  if (!write_request(strm, req, close_connection, error)) { return false; }
-
-#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
-  if (is_ssl()) {
-    auto is_proxy_enabled = !proxy_host_.empty() && proxy_port_ != -1;
-    if (!is_proxy_enabled) {
-      if (detail::is_ssl_peer_could_be_closed(socket_.ssl, socket_.sock)) {
-        error = Error::SSLPeerCouldBeClosed_;
-        output_error_log(error, &req);
-        return false;
-      }
-    }
-  }
-#endif
-
-  // Receive response and headers
-  if (!read_response_line(strm, req, res) ||
-      !detail::read_headers(strm, res.headers)) {
-    error = Error::Read;
-    output_error_log(error, &req);
-    return false;
-  }
-
-  // Body
-  if ((res.status != StatusCode::NoContent_204) && req.method != "HEAD" &&
-      req.method != "CONNECT") {
-    auto redirect = 300 < res.status && res.status < 400 &&
-                    res.status != StatusCode::NotModified_304 &&
-                    follow_location_;
-
-    if (req.response_handler && !redirect) {
-      if (!req.response_handler(res)) {
-        error = Error::Canceled;
-        output_error_log(error, &req);
-        return false;
-      }
-    }
-
-    auto out =
-        req.content_receiver
-            ? static_cast<ContentReceiverWithProgress>(
-                  [&](const char *buf, size_t n, size_t off, size_t len) {
-                    if (redirect) { return true; }
-                    auto ret = req.content_receiver(buf, n, off, len);
-                    if (!ret) {
-                      error = Error::Canceled;
-                      output_error_log(error, &req);
-                    }
-                    return ret;
-                  })
-            : static_cast<ContentReceiverWithProgress>(
-                  [&](const char *buf, size_t n, size_t /*off*/,
-                      size_t /*len*/) {
-                    assert(res.body.size() + n <= res.body.max_size());
-                    res.body.append(buf, n);
-                    return true;
-                  });
-
-    auto progress = [&](size_t current, size_t total) {
-      if (!req.download_progress || redirect) { return true; }
-      auto ret = req.download_progress(current, total);
-      if (!ret) {
-        error = Error::Canceled;
-        output_error_log(error, &req);
-      }
-      return ret;
-    };
-
-    if (res.has_header("Content-Length")) {
-      if (!req.content_receiver) {
-        auto len = res.get_header_value_u64("Content-Length");
-        if (len > res.body.max_size()) {
-          error = Error::Read;
-          output_error_log(error, &req);
-          return false;
-        }
-        res.body.reserve(static_cast<size_t>(len));
-      }
-    }
-
-    if (res.status != StatusCode::NotModified_304) {
-      int dummy_status;
-      if (!detail::read_content(strm, res, (std::numeric_limits<size_t>::max)(),
-                                dummy_status, std::move(progress),
-                                std::move(out), decompress_)) {
-        if (error != Error::Canceled) { error = Error::Read; }
-        output_error_log(error, &req);
-        return false;
-      }
-    }
-  }
-
-  // Log
-  output_log(req, res);
-
-  return true;
-}
-
-inline ContentProviderWithoutLength ClientImpl::get_multipart_content_provider(
-    const std::string &boundary, const UploadFormDataItems &items,
-    const FormDataProviderItems &provider_items) const {
-  size_t cur_item = 0;
-  size_t cur_start = 0;
-  // cur_item and cur_start are copied to within the std::function and
-  // maintain state between successive calls
-  return [&, cur_item, cur_start](size_t offset,
-                                  DataSink &sink) mutable -> bool {
-    if (!offset && !items.empty()) {
-      sink.os << detail::serialize_multipart_formdata(items, boundary, false);
-      return true;
-    } else if (cur_item < provider_items.size()) {
-      if (!cur_start) {
-        const auto &begin = detail::serialize_multipart_formdata_item_begin(
-            provider_items[cur_item], boundary);
-        offset += begin.size();
-        cur_start = offset;
-        sink.os << begin;
-      }
-
-      DataSink cur_sink;
-      auto has_data = true;
-      cur_sink.write = sink.write;
-      cur_sink.done = [&]() { has_data = false; };
-
-      if (!provider_items[cur_item].provider(offset - cur_start, cur_sink)) {
-        return false;
-      }
-
-      if (!has_data) {
-        sink.os << detail::serialize_multipart_formdata_item_end();
-        cur_item++;
-        cur_start = 0;
-      }
-      return true;
-    } else {
-      sink.os << detail::serialize_multipart_formdata_finish(boundary);
-      sink.done();
-      return true;
-    }
-  };
-}
-
-inline bool ClientImpl::process_socket(
-    const Socket &socket,
-    std::chrono::time_point<std::chrono::steady_clock> start_time,
-    std::function<bool(Stream &strm)> callback) {
-  return detail::process_client_socket(
-      socket.sock, read_timeout_sec_, read_timeout_usec_, write_timeout_sec_,
-      write_timeout_usec_, max_timeout_msec_, start_time, std::move(callback));
-}
-
-inline bool ClientImpl::is_ssl() const { return false; }
-
-inline Result ClientImpl::Get(const std::string &path,
-                              DownloadProgress progress) {
-  return Get(path, Headers(), std::move(progress));
-}
-
-inline Result ClientImpl::Get(const std::string &path, const Params &params,
-                              const Headers &headers,
-                              DownloadProgress progress) {
-  if (params.empty()) { return Get(path, headers); }
-
-  std::string path_with_query = append_query_params(path, params);
-  return Get(path_with_query, headers, std::move(progress));
-}
-
-inline Result ClientImpl::Get(const std::string &path, const Headers &headers,
-                              DownloadProgress progress) {
-  Request req;
-  req.method = "GET";
-  req.path = path;
-  req.headers = headers;
-  req.download_progress = std::move(progress);
-  if (max_timeout_msec_ > 0) {
-    req.start_time_ = std::chrono::steady_clock::now();
-  }
-
-  return send_(std::move(req));
-}
-
-inline Result ClientImpl::Get(const std::string &path,
-                              ContentReceiver content_receiver,
-                              DownloadProgress progress) {
-  return Get(path, Headers(), nullptr, std::move(content_receiver),
-             std::move(progress));
-}
-
-inline Result ClientImpl::Get(const std::string &path, const Headers &headers,
-                              ContentReceiver content_receiver,
-                              DownloadProgress progress) {
-  return Get(path, headers, nullptr, std::move(content_receiver),
-             std::move(progress));
-}
-
-inline Result ClientImpl::Get(const std::string &path,
-                              ResponseHandler response_handler,
-                              ContentReceiver content_receiver,
-                              DownloadProgress progress) {
-  return Get(path, Headers(), std::move(response_handler),
-             std::move(content_receiver), std::move(progress));
-}
-
-inline Result ClientImpl::Get(const std::string &path, const Headers &headers,
-                              ResponseHandler response_handler,
-                              ContentReceiver content_receiver,
-                              DownloadProgress progress) {
-  Request req;
-  req.method = "GET";
-  req.path = path;
-  req.headers = headers;
-  req.response_handler = std::move(response_handler);
-  req.content_receiver =
-      [content_receiver](const char *data, size_t data_length,
-                         size_t /*offset*/, size_t /*total_length*/) {
-        return content_receiver(data, data_length);
-      };
-  req.download_progress = std::move(progress);
-  if (max_timeout_msec_ > 0) {
-    req.start_time_ = std::chrono::steady_clock::now();
-  }
-
-  return send_(std::move(req));
-}
-
-inline Result ClientImpl::Get(const std::string &path, const Params &params,
-                              const Headers &headers,
-                              ContentReceiver content_receiver,
-                              DownloadProgress progress) {
-  return Get(path, params, headers, nullptr, std::move(content_receiver),
-             std::move(progress));
-}
-
-inline Result ClientImpl::Get(const std::string &path, const Params &params,
-                              const Headers &headers,
-                              ResponseHandler response_handler,
-                              ContentReceiver content_receiver,
-                              DownloadProgress progress) {
-  if (params.empty()) {
-    return Get(path, headers, std::move(response_handler),
-               std::move(content_receiver), std::move(progress));
-  }
-
-  std::string path_with_query = append_query_params(path, params);
-  return Get(path_with_query, headers, std::move(response_handler),
-             std::move(content_receiver), std::move(progress));
-}
-
-inline Result ClientImpl::Head(const std::string &path) {
-  return Head(path, Headers());
-}
-
-inline Result ClientImpl::Head(const std::string &path,
-                               const Headers &headers) {
-  Request req;
-  req.method = "HEAD";
-  req.headers = headers;
-  req.path = path;
-  if (max_timeout_msec_ > 0) {
-    req.start_time_ = std::chrono::steady_clock::now();
-  }
-
-  return send_(std::move(req));
-}
-
-inline Result ClientImpl::Post(const std::string &path) {
-  return Post(path, std::string(), std::string());
-}
-
-inline Result ClientImpl::Post(const std::string &path,
-                               const Headers &headers) {
-  return Post(path, headers, nullptr, 0, std::string());
-}
-
-inline Result ClientImpl::Post(const std::string &path, const char *body,
-                               size_t content_length,
-                               const std::string &content_type,
-                               UploadProgress progress) {
-  return Post(path, Headers(), body, content_length, content_type, progress);
-}
-
-inline Result ClientImpl::Post(const std::string &path, const std::string &body,
-                               const std::string &content_type,
-                               UploadProgress progress) {
-  return Post(path, Headers(), body, content_type, progress);
-}
-
-inline Result ClientImpl::Post(const std::string &path, const Params &params) {
-  return Post(path, Headers(), params);
-}
-
-inline Result ClientImpl::Post(const std::string &path, size_t content_length,
-                               ContentProvider content_provider,
-                               const std::string &content_type,
-                               UploadProgress progress) {
-  return Post(path, Headers(), content_length, std::move(content_provider),
-              content_type, progress);
-}
-
-inline Result ClientImpl::Post(const std::string &path,
-                               ContentProviderWithoutLength content_provider,
-                               const std::string &content_type,
-                               UploadProgress progress) {
-  return Post(path, Headers(), std::move(content_provider), content_type,
-              progress);
-}
-
-inline Result ClientImpl::Post(const std::string &path, const Headers &headers,
-                               const Params &params) {
-  auto query = detail::params_to_query_str(params);
-  return Post(path, headers, query, "application/x-www-form-urlencoded");
-}
-
-inline Result ClientImpl::Post(const std::string &path,
-                               const UploadFormDataItems &items,
-                               UploadProgress progress) {
-  return Post(path, Headers(), items, progress);
-}
-
-inline Result ClientImpl::Post(const std::string &path, const Headers &headers,
-                               const UploadFormDataItems &items,
-                               UploadProgress progress) {
-  const auto &boundary = detail::make_multipart_data_boundary();
-  const auto &content_type =
-      detail::serialize_multipart_formdata_get_content_type(boundary);
-  const auto &body = detail::serialize_multipart_formdata(items, boundary);
-  return Post(path, headers, body, content_type, progress);
-}
-
-inline Result ClientImpl::Post(const std::string &path, const Headers &headers,
-                               const UploadFormDataItems &items,
-                               const std::string &boundary,
-                               UploadProgress progress) {
-  if (!detail::is_multipart_boundary_chars_valid(boundary)) {
-    return Result{nullptr, Error::UnsupportedMultipartBoundaryChars};
-  }
-
-  const auto &content_type =
-      detail::serialize_multipart_formdata_get_content_type(boundary);
-  const auto &body = detail::serialize_multipart_formdata(items, boundary);
-  return Post(path, headers, body, content_type, progress);
-}
-
-inline Result ClientImpl::Post(const std::string &path, const Headers &headers,
-                               const char *body, size_t content_length,
-                               const std::string &content_type,
-                               UploadProgress progress) {
-  return send_with_content_provider("POST", path, headers, body, content_length,
-                                    nullptr, nullptr, content_type, progress);
-}
-
-inline Result ClientImpl::Post(const std::string &path, const Headers &headers,
-                               const std::string &body,
-                               const std::string &content_type,
-                               UploadProgress progress) {
-  return send_with_content_provider("POST", path, headers, body.data(),
-                                    body.size(), nullptr, nullptr, content_type,
-                                    progress);
-}
-
-inline Result ClientImpl::Post(const std::string &path, const Headers &headers,
-                               size_t content_length,
-                               ContentProvider content_provider,
-                               const std::string &content_type,
-                               UploadProgress progress) {
-  return send_with_content_provider("POST", path, headers, nullptr,
-                                    content_length, std::move(content_provider),
-                                    nullptr, content_type, progress);
-}
-
-inline Result ClientImpl::Post(const std::string &path, const Headers &headers,
-                               ContentProviderWithoutLength content_provider,
-                               const std::string &content_type,
-                               UploadProgress progress) {
-  return send_with_content_provider("POST", path, headers, nullptr, 0, nullptr,
-                                    std::move(content_provider), content_type,
-                                    progress);
-}
-
-inline Result ClientImpl::Post(const std::string &path, const Headers &headers,
-                               const UploadFormDataItems &items,
-                               const FormDataProviderItems &provider_items,
-                               UploadProgress progress) {
-  const auto &boundary = detail::make_multipart_data_boundary();
-  const auto &content_type =
-      detail::serialize_multipart_formdata_get_content_type(boundary);
-  return send_with_content_provider(
-      "POST", path, headers, nullptr, 0, nullptr,
-      get_multipart_content_provider(boundary, items, provider_items),
-      content_type, progress);
-}
-
-inline Result ClientImpl::Post(const std::string &path, const Headers &headers,
-                               const std::string &body,
-                               const std::string &content_type,
-                               ContentReceiver content_receiver,
-                               DownloadProgress progress) {
-  Request req;
-  req.method = "POST";
-  req.path = path;
-  req.headers = headers;
-  req.body = body;
-  req.content_receiver =
-      [content_receiver](const char *data, size_t data_length,
-                         size_t /*offset*/, size_t /*total_length*/) {
-        return content_receiver(data, data_length);
-      };
-  req.download_progress = std::move(progress);
-
-  if (max_timeout_msec_ > 0) {
-    req.start_time_ = std::chrono::steady_clock::now();
-  }
-
-  if (!content_type.empty()) { req.set_header("Content-Type", content_type); }
-
-  return send_(std::move(req));
-}
-
-inline Result ClientImpl::Put(const std::string &path) {
-  return Put(path, std::string(), std::string());
-}
-
-inline Result ClientImpl::Put(const std::string &path, const Headers &headers) {
-  return Put(path, headers, nullptr, 0, std::string());
-}
-
-inline Result ClientImpl::Put(const std::string &path, const char *body,
-                              size_t content_length,
-                              const std::string &content_type,
-                              UploadProgress progress) {
-  return Put(path, Headers(), body, content_length, content_type, progress);
-}
-
-inline Result ClientImpl::Put(const std::string &path, const std::string &body,
-                              const std::string &content_type,
-                              UploadProgress progress) {
-  return Put(path, Headers(), body, content_type, progress);
-}
-
-inline Result ClientImpl::Put(const std::string &path, const Params &params) {
-  return Put(path, Headers(), params);
-}
-
-inline Result ClientImpl::Put(const std::string &path, size_t content_length,
-                              ContentProvider content_provider,
-                              const std::string &content_type,
-                              UploadProgress progress) {
-  return Put(path, Headers(), content_length, std::move(content_provider),
-             content_type, progress);
-}
-
-inline Result ClientImpl::Put(const std::string &path,
-                              ContentProviderWithoutLength content_provider,
-                              const std::string &content_type,
-                              UploadProgress progress) {
-  return Put(path, Headers(), std::move(content_provider), content_type,
-             progress);
-}
-
-inline Result ClientImpl::Put(const std::string &path, const Headers &headers,
-                              const Params &params) {
-  auto query = detail::params_to_query_str(params);
-  return Put(path, headers, query, "application/x-www-form-urlencoded");
-}
-
-inline Result ClientImpl::Put(const std::string &path,
-                              const UploadFormDataItems &items,
-                              UploadProgress progress) {
-  return Put(path, Headers(), items, progress);
-}
-
-inline Result ClientImpl::Put(const std::string &path, const Headers &headers,
-                              const UploadFormDataItems &items,
-                              UploadProgress progress) {
-  const auto &boundary = detail::make_multipart_data_boundary();
-  const auto &content_type =
-      detail::serialize_multipart_formdata_get_content_type(boundary);
-  const auto &body = detail::serialize_multipart_formdata(items, boundary);
-  return Put(path, headers, body, content_type, progress);
-}
-
-inline Result ClientImpl::Put(const std::string &path, const Headers &headers,
-                              const UploadFormDataItems &items,
-                              const std::string &boundary,
-                              UploadProgress progress) {
-  if (!detail::is_multipart_boundary_chars_valid(boundary)) {
-    return Result{nullptr, Error::UnsupportedMultipartBoundaryChars};
-  }
-
-  const auto &content_type =
-      detail::serialize_multipart_formdata_get_content_type(boundary);
-  const auto &body = detail::serialize_multipart_formdata(items, boundary);
-  return Put(path, headers, body, content_type, progress);
-}
-
-inline Result ClientImpl::Put(const std::string &path, const Headers &headers,
-                              const char *body, size_t content_length,
-                              const std::string &content_type,
-                              UploadProgress progress) {
-  return send_with_content_provider("PUT", path, headers, body, content_length,
-                                    nullptr, nullptr, content_type, progress);
-}
-
-inline Result ClientImpl::Put(const std::string &path, const Headers &headers,
-                              const std::string &body,
-                              const std::string &content_type,
-                              UploadProgress progress) {
-  return send_with_content_provider("PUT", path, headers, body.data(),
-                                    body.size(), nullptr, nullptr, content_type,
-                                    progress);
-}
-
-inline Result ClientImpl::Put(const std::string &path, const Headers &headers,
-                              size_t content_length,
-                              ContentProvider content_provider,
-                              const std::string &content_type,
-                              UploadProgress progress) {
-  return send_with_content_provider("PUT", path, headers, nullptr,
-                                    content_length, std::move(content_provider),
-                                    nullptr, content_type, progress);
-}
-
-inline Result ClientImpl::Put(const std::string &path, const Headers &headers,
-                              ContentProviderWithoutLength content_provider,
-                              const std::string &content_type,
-                              UploadProgress progress) {
-  return send_with_content_provider("PUT", path, headers, nullptr, 0, nullptr,
-                                    std::move(content_provider), content_type,
-                                    progress);
-}
-
-inline Result ClientImpl::Put(const std::string &path, const Headers &headers,
-                              const UploadFormDataItems &items,
-                              const FormDataProviderItems &provider_items,
-                              UploadProgress progress) {
-  const auto &boundary = detail::make_multipart_data_boundary();
-  const auto &content_type =
-      detail::serialize_multipart_formdata_get_content_type(boundary);
-  return send_with_content_provider(
-      "PUT", path, headers, nullptr, 0, nullptr,
-      get_multipart_content_provider(boundary, items, provider_items),
-      content_type, progress);
-}
-
-inline Result ClientImpl::Put(const std::string &path, const Headers &headers,
-                              const std::string &body,
-                              const std::string &content_type,
-                              ContentReceiver content_receiver,
-                              DownloadProgress progress) {
-  Request req;
-  req.method = "PUT";
-  req.path = path;
-  req.headers = headers;
-  req.body = body;
-  req.content_receiver =
-      [content_receiver](const char *data, size_t data_length,
-                         size_t /*offset*/, size_t /*total_length*/) {
-        return content_receiver(data, data_length);
-      };
-  req.download_progress = std::move(progress);
-
-  if (max_timeout_msec_ > 0) {
-    req.start_time_ = std::chrono::steady_clock::now();
-  }
-
-  if (!content_type.empty()) { req.set_header("Content-Type", content_type); }
-
-  return send_(std::move(req));
-}
-
-inline Result ClientImpl::Patch(const std::string &path) {
-  return Patch(path, std::string(), std::string());
-}
-
-inline Result ClientImpl::Patch(const std::string &path, const Headers &headers,
-                                UploadProgress progress) {
-  return Patch(path, headers, nullptr, 0, std::string(), progress);
-}
-
-inline Result ClientImpl::Patch(const std::string &path, const char *body,
-                                size_t content_length,
-                                const std::string &content_type,
-                                UploadProgress progress) {
-  return Patch(path, Headers(), body, content_length, content_type, progress);
-}
-
-inline Result ClientImpl::Patch(const std::string &path,
-                                const std::string &body,
-                                const std::string &content_type,
-                                UploadProgress progress) {
-  return Patch(path, Headers(), body, content_type, progress);
-}
-
-inline Result ClientImpl::Patch(const std::string &path, const Params &params) {
-  return Patch(path, Headers(), params);
-}
-
-inline Result ClientImpl::Patch(const std::string &path, size_t content_length,
-                                ContentProvider content_provider,
-                                const std::string &content_type,
-                                UploadProgress progress) {
-  return Patch(path, Headers(), content_length, std::move(content_provider),
-               content_type, progress);
-}
-
-inline Result ClientImpl::Patch(const std::string &path,
-                                ContentProviderWithoutLength content_provider,
-                                const std::string &content_type,
-                                UploadProgress progress) {
-  return Patch(path, Headers(), std::move(content_provider), content_type,
-               progress);
-}
-
-inline Result ClientImpl::Patch(const std::string &path, const Headers &headers,
-                                const Params &params) {
-  auto query = detail::params_to_query_str(params);
-  return Patch(path, headers, query, "application/x-www-form-urlencoded");
-}
-
-inline Result ClientImpl::Patch(const std::string &path,
-                                const UploadFormDataItems &items,
-                                UploadProgress progress) {
-  return Patch(path, Headers(), items, progress);
-}
-
-inline Result ClientImpl::Patch(const std::string &path, const Headers &headers,
-                                const UploadFormDataItems &items,
-                                UploadProgress progress) {
-  const auto &boundary = detail::make_multipart_data_boundary();
-  const auto &content_type =
-      detail::serialize_multipart_formdata_get_content_type(boundary);
-  const auto &body = detail::serialize_multipart_formdata(items, boundary);
-  return Patch(path, headers, body, content_type, progress);
-}
-
-inline Result ClientImpl::Patch(const std::string &path, const Headers &headers,
-                                const UploadFormDataItems &items,
-                                const std::string &boundary,
-                                UploadProgress progress) {
-  if (!detail::is_multipart_boundary_chars_valid(boundary)) {
-    return Result{nullptr, Error::UnsupportedMultipartBoundaryChars};
-  }
-
-  const auto &content_type =
-      detail::serialize_multipart_formdata_get_content_type(boundary);
-  const auto &body = detail::serialize_multipart_formdata(items, boundary);
-  return Patch(path, headers, body, content_type, progress);
-}
-
-inline Result ClientImpl::Patch(const std::string &path, const Headers &headers,
-                                const char *body, size_t content_length,
-                                const std::string &content_type,
-                                UploadProgress progress) {
-  return send_with_content_provider("PATCH", path, headers, body,
-                                    content_length, nullptr, nullptr,
-                                    content_type, progress);
-}
-
-inline Result ClientImpl::Patch(const std::string &path, const Headers &headers,
-                                const std::string &body,
-                                const std::string &content_type,
-                                UploadProgress progress) {
-  return send_with_content_provider("PATCH", path, headers, body.data(),
-                                    body.size(), nullptr, nullptr, content_type,
-                                    progress);
-}
-
-inline Result ClientImpl::Patch(const std::string &path, const Headers &headers,
-                                size_t content_length,
-                                ContentProvider content_provider,
-                                const std::string &content_type,
-                                UploadProgress progress) {
-  return send_with_content_provider("PATCH", path, headers, nullptr,
-                                    content_length, std::move(content_provider),
-                                    nullptr, content_type, progress);
-}
-
-inline Result ClientImpl::Patch(const std::string &path, const Headers &headers,
-                                ContentProviderWithoutLength content_provider,
-                                const std::string &content_type,
-                                UploadProgress progress) {
-  return send_with_content_provider("PATCH", path, headers, nullptr, 0, nullptr,
-                                    std::move(content_provider), content_type,
-                                    progress);
-}
-
-inline Result ClientImpl::Patch(const std::string &path, const Headers &headers,
-                                const UploadFormDataItems &items,
-                                const FormDataProviderItems &provider_items,
-                                UploadProgress progress) {
-  const auto &boundary = detail::make_multipart_data_boundary();
-  const auto &content_type =
-      detail::serialize_multipart_formdata_get_content_type(boundary);
-  return send_with_content_provider(
-      "PATCH", path, headers, nullptr, 0, nullptr,
-      get_multipart_content_provider(boundary, items, provider_items),
-      content_type, progress);
-}
-
-inline Result ClientImpl::Patch(const std::string &path, const Headers &headers,
-                                const std::string &body,
-                                const std::string &content_type,
-                                ContentReceiver content_receiver,
-                                DownloadProgress progress) {
-  Request req;
-  req.method = "PATCH";
-  req.path = path;
-  req.headers = headers;
-  req.body = body;
-  req.content_receiver =
-      [content_receiver](const char *data, size_t data_length,
-                         size_t /*offset*/, size_t /*total_length*/) {
-        return content_receiver(data, data_length);
-      };
-  req.download_progress = std::move(progress);
-
-  if (max_timeout_msec_ > 0) {
-    req.start_time_ = std::chrono::steady_clock::now();
-  }
-
-  if (!content_type.empty()) { req.set_header("Content-Type", content_type); }
-
-  return send_(std::move(req));
-}
-
-inline Result ClientImpl::Delete(const std::string &path,
-                                 DownloadProgress progress) {
-  return Delete(path, Headers(), std::string(), std::string(), progress);
-}
-
-inline Result ClientImpl::Delete(const std::string &path,
-                                 const Headers &headers,
-                                 DownloadProgress progress) {
-  return Delete(path, headers, std::string(), std::string(), progress);
-}
-
-inline Result ClientImpl::Delete(const std::string &path, const char *body,
-                                 size_t content_length,
-                                 const std::string &content_type,
-                                 DownloadProgress progress) {
-  return Delete(path, Headers(), body, content_length, content_type, progress);
-}
-
-inline Result ClientImpl::Delete(const std::string &path,
-                                 const std::string &body,
-                                 const std::string &content_type,
-                                 DownloadProgress progress) {
-  return Delete(path, Headers(), body.data(), body.size(), content_type,
-                progress);
-}
-
-inline Result ClientImpl::Delete(const std::string &path,
-                                 const Headers &headers,
-                                 const std::string &body,
-                                 const std::string &content_type,
-                                 DownloadProgress progress) {
-  return Delete(path, headers, body.data(), body.size(), content_type,
-                progress);
-}
-
-inline Result ClientImpl::Delete(const std::string &path, const Params &params,
-                                 DownloadProgress progress) {
-  return Delete(path, Headers(), params, progress);
-}
-
-inline Result ClientImpl::Delete(const std::string &path,
-                                 const Headers &headers, const Params &params,
-                                 DownloadProgress progress) {
-  auto query = detail::params_to_query_str(params);
-  return Delete(path, headers, query, "application/x-www-form-urlencoded",
-                progress);
-}
-
-inline Result ClientImpl::Delete(const std::string &path,
-                                 const Headers &headers, const char *body,
-                                 size_t content_length,
-                                 const std::string &content_type,
-                                 DownloadProgress progress) {
-  Request req;
-  req.method = "DELETE";
-  req.headers = headers;
-  req.path = path;
-  req.download_progress = std::move(progress);
-  if (max_timeout_msec_ > 0) {
-    req.start_time_ = std::chrono::steady_clock::now();
-  }
-
-  if (!content_type.empty()) { req.set_header("Content-Type", content_type); }
-  req.body.assign(body, content_length);
-
-  return send_(std::move(req));
-}
-
-inline Result ClientImpl::Options(const std::string &path) {
-  return Options(path, Headers());
-}
-
-inline Result ClientImpl::Options(const std::string &path,
-                                  const Headers &headers) {
-  Request req;
-  req.method = "OPTIONS";
-  req.headers = headers;
-  req.path = path;
-  if (max_timeout_msec_ > 0) {
-    req.start_time_ = std::chrono::steady_clock::now();
-  }
-
-  return send_(std::move(req));
-}
-
-inline void ClientImpl::stop() {
-  std::lock_guard<std::mutex> guard(socket_mutex_);
-
-  // If there is anything ongoing right now, the ONLY thread-safe thing we can
-  // do is to shutdown_socket, so that threads using this socket suddenly
-  // discover they can't read/write any more and error out. Everything else
-  // (closing the socket, shutting ssl down) is unsafe because these actions
-  // are not thread-safe.
-  if (socket_requests_in_flight_ > 0) {
-    shutdown_socket(socket_);
-
-    // Aside from that, we set a flag for the socket to be closed when we're
-    // done.
-    socket_should_be_closed_when_request_is_done_ = true;
-    return;
-  }
-
-  // Otherwise, still holding the mutex, we can shut everything down ourselves
-  shutdown_ssl(socket_, true);
-  shutdown_socket(socket_);
-  close_socket(socket_);
-}
-
-inline std::string ClientImpl::host() const { return host_; }
-
-inline int ClientImpl::port() const { return port_; }
-
-inline size_t ClientImpl::is_socket_open() const {
-  std::lock_guard<std::mutex> guard(socket_mutex_);
-  return socket_.is_open();
-}
-
-inline socket_t ClientImpl::socket() const { return socket_.sock; }
-
-inline void ClientImpl::set_connection_timeout(time_t sec, time_t usec) {
-  connection_timeout_sec_ = sec;
-  connection_timeout_usec_ = usec;
-}
-
-inline void ClientImpl::set_read_timeout(time_t sec, time_t usec) {
-  read_timeout_sec_ = sec;
-  read_timeout_usec_ = usec;
-}
-
-inline void ClientImpl::set_write_timeout(time_t sec, time_t usec) {
-  write_timeout_sec_ = sec;
-  write_timeout_usec_ = usec;
-}
-
-inline void ClientImpl::set_max_timeout(time_t msec) {
-  max_timeout_msec_ = msec;
-}
-
-inline void ClientImpl::set_basic_auth(const std::string &username,
-                                       const std::string &password) {
-  basic_auth_username_ = username;
-  basic_auth_password_ = password;
-}
-
-inline void ClientImpl::set_bearer_token_auth(const std::string &token) {
-  bearer_token_auth_token_ = token;
-}
-
-#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
-inline void ClientImpl::set_digest_auth(const std::string &username,
-                                        const std::string &password) {
-  digest_auth_username_ = username;
-  digest_auth_password_ = password;
-}
-#endif
-
-inline void ClientImpl::set_keep_alive(bool on) { keep_alive_ = on; }
-
-inline void ClientImpl::set_follow_location(bool on) { follow_location_ = on; }
-
-inline void ClientImpl::set_path_encode(bool on) { path_encode_ = on; }
-
-inline void
-ClientImpl::set_hostname_addr_map(std::map<std::string, std::string> addr_map) {
-  addr_map_ = std::move(addr_map);
-}
-
-inline void ClientImpl::set_default_headers(Headers headers) {
-  default_headers_ = std::move(headers);
-}
-
-inline void ClientImpl::set_header_writer(
-    std::function<ssize_t(Stream &, Headers &)> const &writer) {
-  header_writer_ = writer;
-}
-
-inline void ClientImpl::set_address_family(int family) {
-  address_family_ = family;
-}
-
-inline void ClientImpl::set_tcp_nodelay(bool on) { tcp_nodelay_ = on; }
-
-inline void ClientImpl::set_ipv6_v6only(bool on) { ipv6_v6only_ = on; }
-
-inline void ClientImpl::set_socket_options(SocketOptions socket_options) {
-  socket_options_ = std::move(socket_options);
-}
-
-inline void ClientImpl::set_compress(bool on) { compress_ = on; }
-
-inline void ClientImpl::set_decompress(bool on) { decompress_ = on; }
-
-inline void ClientImpl::set_interface(const std::string &intf) {
-  interface_ = intf;
-}
-
-inline void ClientImpl::set_proxy(const std::string &host, int port) {
-  proxy_host_ = host;
-  proxy_port_ = port;
-}
-
-inline void ClientImpl::set_proxy_basic_auth(const std::string &username,
-                                             const std::string &password) {
-  proxy_basic_auth_username_ = username;
-  proxy_basic_auth_password_ = password;
-}
-
-inline void ClientImpl::set_proxy_bearer_token_auth(const std::string &token) {
-  proxy_bearer_token_auth_token_ = token;
-}
-
-#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
-inline void ClientImpl::set_proxy_digest_auth(const std::string &username,
-                                              const std::string &password) {
-  proxy_digest_auth_username_ = username;
-  proxy_digest_auth_password_ = password;
-}
-
-inline void ClientImpl::set_ca_cert_path(const std::string &ca_cert_file_path,
-                                         const std::string &ca_cert_dir_path) {
-  ca_cert_file_path_ = ca_cert_file_path;
-  ca_cert_dir_path_ = ca_cert_dir_path;
-}
-
-inline void ClientImpl::set_ca_cert_store(X509_STORE *ca_cert_store) {
-  if (ca_cert_store && ca_cert_store != ca_cert_store_) {
-    ca_cert_store_ = ca_cert_store;
-  }
-}
-
-inline X509_STORE *ClientImpl::create_ca_cert_store(const char *ca_cert,
-                                                    std::size_t size) const {
-  auto mem = BIO_new_mem_buf(ca_cert, static_cast<int>(size));
-  auto se = detail::scope_exit([&] { BIO_free_all(mem); });
-  if (!mem) { return nullptr; }
-
-  auto inf = PEM_X509_INFO_read_bio(mem, nullptr, nullptr, nullptr);
-  if (!inf) { return nullptr; }
-
-  auto cts = X509_STORE_new();
-  if (cts) {
-    for (auto i = 0; i < static_cast<int>(sk_X509_INFO_num(inf)); i++) {
-      auto itmp = sk_X509_INFO_value(inf, i);
-      if (!itmp) { continue; }
-
-      if (itmp->x509) { X509_STORE_add_cert(cts, itmp->x509); }
-      if (itmp->crl) { X509_STORE_add_crl(cts, itmp->crl); }
-    }
-  }
-
-  sk_X509_INFO_pop_free(inf, X509_INFO_free);
-  return cts;
-}
-
-inline void ClientImpl::enable_server_certificate_verification(bool enabled) {
-  server_certificate_verification_ = enabled;
-}
-
-inline void ClientImpl::enable_server_hostname_verification(bool enabled) {
-  server_hostname_verification_ = enabled;
-}
-
-inline void ClientImpl::set_server_certificate_verifier(
-    std::function<SSLVerifierResponse(SSL *ssl)> verifier) {
-  server_certificate_verifier_ = verifier;
-}
-#endif
-
-inline void ClientImpl::set_logger(Logger logger) {
-  logger_ = std::move(logger);
-}
-
-inline void ClientImpl::set_error_logger(ErrorLogger error_logger) {
-  error_logger_ = std::move(error_logger);
-}
-
-/*
- * SSL Implementation
- */
-#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
-namespace detail {
-
-inline bool is_ip_address(const std::string &host) {
-  struct in_addr addr4;
-  struct in6_addr addr6;
-  return inet_pton(AF_INET, host.c_str(), &addr4) == 1 ||
-         inet_pton(AF_INET6, host.c_str(), &addr6) == 1;
-}
-
-template <typename U, typename V>
-inline SSL *ssl_new(socket_t sock, SSL_CTX *ctx, std::mutex &ctx_mutex,
-                    U SSL_connect_or_accept, V setup) {
-  SSL *ssl = nullptr;
-  {
-    std::lock_guard<std::mutex> guard(ctx_mutex);
-    ssl = SSL_new(ctx);
-  }
-
-  if (ssl) {
-    set_nonblocking(sock, true);
-    auto bio = BIO_new_socket(static_cast<int>(sock), BIO_NOCLOSE);
-    BIO_set_nbio(bio, 1);
-    SSL_set_bio(ssl, bio, bio);
-
-    if (!setup(ssl) || SSL_connect_or_accept(ssl) != 1) {
-      SSL_shutdown(ssl);
-      {
-        std::lock_guard<std::mutex> guard(ctx_mutex);
-        SSL_free(ssl);
-      }
-      set_nonblocking(sock, false);
-      return nullptr;
-    }
-    BIO_set_nbio(bio, 0);
-    set_nonblocking(sock, false);
-  }
-
-  return ssl;
-}
-
-inline void ssl_delete(std::mutex &ctx_mutex, SSL *ssl, socket_t sock,
-                       bool shutdown_gracefully) {
-  // sometimes we may want to skip this to try to avoid SIGPIPE if we know
-  // the remote has closed the network connection
-  // Note that it is not always possible to avoid SIGPIPE, this is merely a
-  // best-efforts.
-  if (shutdown_gracefully) {
-    (void)(sock);
-    // SSL_shutdown() returns 0 on first call (indicating close_notify alert
-    // sent) and 1 on subsequent call (indicating close_notify alert received)
-    if (SSL_shutdown(ssl) == 0) {
-      // Expected to return 1, but even if it doesn't, we free ssl
-      SSL_shutdown(ssl);
-    }
-  }
-
-  std::lock_guard<std::mutex> guard(ctx_mutex);
-  SSL_free(ssl);
-}
-
-template <typename U>
-bool ssl_connect_or_accept_nonblocking(socket_t sock, SSL *ssl,
-                                       U ssl_connect_or_accept,
-                                       time_t timeout_sec, time_t timeout_usec,
-                                       int *ssl_error) {
-  auto res = 0;
-  while ((res = ssl_connect_or_accept(ssl)) != 1) {
-    auto err = SSL_get_error(ssl, res);
-    switch (err) {
-    case SSL_ERROR_WANT_READ:
-      if (select_read(sock, timeout_sec, timeout_usec) > 0) { continue; }
-      break;
-    case SSL_ERROR_WANT_WRITE:
-      if (select_write(sock, timeout_sec, timeout_usec) > 0) { continue; }
-      break;
-    default: break;
-    }
-    if (ssl_error) { *ssl_error = err; }
-    return false;
-  }
-  return true;
-}
-
-template <typename T>
-inline bool process_server_socket_ssl(
-    const std::atomic<socket_t> &svr_sock, SSL *ssl, socket_t sock,
-    size_t keep_alive_max_count, time_t keep_alive_timeout_sec,
-    time_t read_timeout_sec, time_t read_timeout_usec, time_t write_timeout_sec,
-    time_t write_timeout_usec, T callback) {
-  return process_server_socket_core(
-      svr_sock, sock, keep_alive_max_count, keep_alive_timeout_sec,
-      [&](bool close_connection, bool &connection_closed) {
-        SSLSocketStream strm(sock, ssl, read_timeout_sec, read_timeout_usec,
-                             write_timeout_sec, write_timeout_usec);
-        return callback(strm, close_connection, connection_closed);
-      });
-}
-
-template <typename T>
-inline bool process_client_socket_ssl(
-    SSL *ssl, socket_t sock, time_t read_timeout_sec, time_t read_timeout_usec,
-    time_t write_timeout_sec, time_t write_timeout_usec,
-    time_t max_timeout_msec,
-    std::chrono::time_point<std::chrono::steady_clock> start_time, T callback) {
-  SSLSocketStream strm(sock, ssl, read_timeout_sec, read_timeout_usec,
-                       write_timeout_sec, write_timeout_usec, max_timeout_msec,
-                       start_time);
-  return callback(strm);
-}
-
-// SSL socket stream implementation
-inline SSLSocketStream::SSLSocketStream(
-    socket_t sock, SSL *ssl, time_t read_timeout_sec, time_t read_timeout_usec,
-    time_t write_timeout_sec, time_t write_timeout_usec,
-    time_t max_timeout_msec,
-    std::chrono::time_point<std::chrono::steady_clock> start_time)
-    : sock_(sock), ssl_(ssl), read_timeout_sec_(read_timeout_sec),
-      read_timeout_usec_(read_timeout_usec),
-      write_timeout_sec_(write_timeout_sec),
-      write_timeout_usec_(write_timeout_usec),
-      max_timeout_msec_(max_timeout_msec), start_time_(start_time) {
-  SSL_clear_mode(ssl, SSL_MODE_AUTO_RETRY);
-}
-
-inline SSLSocketStream::~SSLSocketStream() = default;
-
-inline bool SSLSocketStream::is_readable() const {
-  return SSL_pending(ssl_) > 0;
-}
-
-inline bool SSLSocketStream::wait_readable() const {
-  if (max_timeout_msec_ <= 0) {
-    return select_read(sock_, read_timeout_sec_, read_timeout_usec_) > 0;
-  }
-
-  time_t read_timeout_sec;
-  time_t read_timeout_usec;
-  calc_actual_timeout(max_timeout_msec_, duration(), read_timeout_sec_,
-                      read_timeout_usec_, read_timeout_sec, read_timeout_usec);
-
-  return select_read(sock_, read_timeout_sec, read_timeout_usec) > 0;
-}
-
-inline bool SSLSocketStream::wait_writable() const {
-  return select_write(sock_, write_timeout_sec_, write_timeout_usec_) > 0 &&
-         is_socket_alive(sock_) && !is_ssl_peer_could_be_closed(ssl_, sock_);
-}
-
-inline ssize_t SSLSocketStream::read(char *ptr, size_t size) {
-  if (SSL_pending(ssl_) > 0) {
-    return SSL_read(ssl_, ptr, static_cast<int>(size));
-  } else if (wait_readable()) {
-    auto ret = SSL_read(ssl_, ptr, static_cast<int>(size));
-    if (ret < 0) {
-      auto err = SSL_get_error(ssl_, ret);
-      auto n = 1000;
-#ifdef _WIN32
-      while (--n >= 0 && (err == SSL_ERROR_WANT_READ ||
-                          (err == SSL_ERROR_SYSCALL &&
-                           WSAGetLastError() == WSAETIMEDOUT))) {
-#else
-      while (--n >= 0 && err == SSL_ERROR_WANT_READ) {
-#endif
-        if (SSL_pending(ssl_) > 0) {
-          return SSL_read(ssl_, ptr, static_cast<int>(size));
-        } else if (wait_readable()) {
-          std::this_thread::sleep_for(std::chrono::microseconds{10});
-          ret = SSL_read(ssl_, ptr, static_cast<int>(size));
-          if (ret >= 0) { return ret; }
-          err = SSL_get_error(ssl_, ret);
-        } else {
-          break;
-        }
-      }
-      assert(ret < 0);
-    }
-    return ret;
-  } else {
-    return -1;
-  }
-}
-
-inline ssize_t SSLSocketStream::write(const char *ptr, size_t size) {
-  if (wait_writable()) {
-    auto handle_size = static_cast<int>(
-        std::min<size_t>(size, (std::numeric_limits<int>::max)()));
-
-    auto ret = SSL_write(ssl_, ptr, static_cast<int>(handle_size));
-    if (ret < 0) {
-      auto err = SSL_get_error(ssl_, ret);
-      auto n = 1000;
-#ifdef _WIN32
-      while (--n >= 0 && (err == SSL_ERROR_WANT_WRITE ||
-                          (err == SSL_ERROR_SYSCALL &&
-                           WSAGetLastError() == WSAETIMEDOUT))) {
-#else
-      while (--n >= 0 && err == SSL_ERROR_WANT_WRITE) {
-#endif
-        if (wait_writable()) {
-          std::this_thread::sleep_for(std::chrono::microseconds{10});
-          ret = SSL_write(ssl_, ptr, static_cast<int>(handle_size));
-          if (ret >= 0) { return ret; }
-          err = SSL_get_error(ssl_, ret);
-        } else {
-          break;
-        }
-      }
-      assert(ret < 0);
-    }
-    return ret;
-  }
-  return -1;
-}
-
-inline void SSLSocketStream::get_remote_ip_and_port(std::string &ip,
-                                                    int &port) const {
-  detail::get_remote_ip_and_port(sock_, ip, port);
-}
-
-inline void SSLSocketStream::get_local_ip_and_port(std::string &ip,
-                                                   int &port) const {
-  detail::get_local_ip_and_port(sock_, ip, port);
-}
-
-inline socket_t SSLSocketStream::socket() const { return sock_; }
-
-inline time_t SSLSocketStream::duration() const {
-  return std::chrono::duration_cast<std::chrono::milliseconds>(
-             std::chrono::steady_clock::now() - start_time_)
-      .count();
-}
-
-} // namespace detail
-
-// SSL HTTP server implementation
-inline SSLServer::SSLServer(const char *cert_path, const char *private_key_path,
-                            const char *client_ca_cert_file_path,
-                            const char *client_ca_cert_dir_path,
-                            const char *private_key_password) {
-  ctx_ = SSL_CTX_new(TLS_server_method());
-
-  if (ctx_) {
-    SSL_CTX_set_options(ctx_,
-                        SSL_OP_NO_COMPRESSION |
-                            SSL_OP_NO_SESSION_RESUMPTION_ON_RENEGOTIATION);
-
-    SSL_CTX_set_min_proto_version(ctx_, TLS1_2_VERSION);
-
-    if (private_key_password != nullptr && (private_key_password[0] != '\0')) {
-      SSL_CTX_set_default_passwd_cb_userdata(
-          ctx_,
-          reinterpret_cast<void *>(const_cast<char *>(private_key_password)));
-    }
-
-    if (SSL_CTX_use_certificate_chain_file(ctx_, cert_path) != 1 ||
-        SSL_CTX_use_PrivateKey_file(ctx_, private_key_path, SSL_FILETYPE_PEM) !=
-            1 ||
-        SSL_CTX_check_private_key(ctx_) != 1) {
-      last_ssl_error_ = static_cast<int>(ERR_get_error());
-      SSL_CTX_free(ctx_);
-      ctx_ = nullptr;
-    } else if (client_ca_cert_file_path || client_ca_cert_dir_path) {
-      SSL_CTX_load_verify_locations(ctx_, client_ca_cert_file_path,
-                                    client_ca_cert_dir_path);
-
-      // Set client CA list to be sent to clients during TLS handshake
-      if (client_ca_cert_file_path) {
-        auto ca_list = SSL_load_client_CA_file(client_ca_cert_file_path);
-        if (ca_list != nullptr) {
-          SSL_CTX_set_client_CA_list(ctx_, ca_list);
-        } else {
-          // Failed to load client CA list, but we continue since
-          // SSL_CTX_load_verify_locations already succeeded and
-          // certificate verification will still work
-          last_ssl_error_ = static_cast<int>(ERR_get_error());
-        }
-      }
-
-      SSL_CTX_set_verify(
-          ctx_, SSL_VERIFY_PEER | SSL_VERIFY_FAIL_IF_NO_PEER_CERT, nullptr);
-    }
-  }
-}
-
-inline SSLServer::SSLServer(X509 *cert, EVP_PKEY *private_key,
-                            X509_STORE *client_ca_cert_store) {
-  ctx_ = SSL_CTX_new(TLS_server_method());
-
-  if (ctx_) {
-    SSL_CTX_set_options(ctx_,
-                        SSL_OP_NO_COMPRESSION |
-                            SSL_OP_NO_SESSION_RESUMPTION_ON_RENEGOTIATION);
-
-    SSL_CTX_set_min_proto_version(ctx_, TLS1_2_VERSION);
-
-    if (SSL_CTX_use_certificate(ctx_, cert) != 1 ||
-        SSL_CTX_use_PrivateKey(ctx_, private_key) != 1) {
-      SSL_CTX_free(ctx_);
-      ctx_ = nullptr;
-    } else if (client_ca_cert_store) {
-      SSL_CTX_set_cert_store(ctx_, client_ca_cert_store);
-
-      // Extract CA names from the store and set them as the client CA list
-      auto ca_list = extract_ca_names_from_x509_store(client_ca_cert_store);
-      if (ca_list) {
-        SSL_CTX_set_client_CA_list(ctx_, ca_list);
-      } else {
-        // Failed to extract CA names, record the error
-        last_ssl_error_ = static_cast<int>(ERR_get_error());
-      }
-
-      SSL_CTX_set_verify(
-          ctx_, SSL_VERIFY_PEER | SSL_VERIFY_FAIL_IF_NO_PEER_CERT, nullptr);
-    }
-  }
-}
-
-inline SSLServer::SSLServer(
-    const std::function<bool(SSL_CTX &ssl_ctx)> &setup_ssl_ctx_callback) {
-  ctx_ = SSL_CTX_new(TLS_method());
-  if (ctx_) {
-    if (!setup_ssl_ctx_callback(*ctx_)) {
-      SSL_CTX_free(ctx_);
-      ctx_ = nullptr;
-    }
-  }
-}
-
-inline SSLServer::~SSLServer() {
-  if (ctx_) { SSL_CTX_free(ctx_); }
-}
-
-inline bool SSLServer::is_valid() const { return ctx_; }
-
-inline SSL_CTX *SSLServer::ssl_context() const { return ctx_; }
-
-inline void SSLServer::update_certs(X509 *cert, EVP_PKEY *private_key,
-                                    X509_STORE *client_ca_cert_store) {
-
-  std::lock_guard<std::mutex> guard(ctx_mutex_);
-
-  SSL_CTX_use_certificate(ctx_, cert);
-  SSL_CTX_use_PrivateKey(ctx_, private_key);
-
-  if (client_ca_cert_store != nullptr) {
-    SSL_CTX_set_cert_store(ctx_, client_ca_cert_store);
-  }
-}
-
-inline bool SSLServer::process_and_close_socket(socket_t sock) {
-  auto ssl = detail::ssl_new(
-      sock, ctx_, ctx_mutex_,
-      [&](SSL *ssl2) {
-        return detail::ssl_connect_or_accept_nonblocking(
-            sock, ssl2, SSL_accept, read_timeout_sec_, read_timeout_usec_,
-            &last_ssl_error_);
-      },
-      [](SSL * /*ssl2*/) { return true; });
-
-  auto ret = false;
-  if (ssl) {
-    std::string remote_addr;
-    int remote_port = 0;
-    detail::get_remote_ip_and_port(sock, remote_addr, remote_port);
-
-    std::string local_addr;
-    int local_port = 0;
-    detail::get_local_ip_and_port(sock, local_addr, local_port);
-
-    ret = detail::process_server_socket_ssl(
-        svr_sock_, ssl, sock, keep_alive_max_count_, keep_alive_timeout_sec_,
-        read_timeout_sec_, read_timeout_usec_, write_timeout_sec_,
-        write_timeout_usec_,
-        [&](Stream &strm, bool close_connection, bool &connection_closed) {
-          return process_request(strm, remote_addr, remote_port, local_addr,
-                                 local_port, close_connection,
-                                 connection_closed,
-                                 [&](Request &req) { req.ssl = ssl; });
-        });
-
-    // Shutdown gracefully if the result seemed successful, non-gracefully if
-    // the connection appeared to be closed.
-    const bool shutdown_gracefully = ret;
-    detail::ssl_delete(ctx_mutex_, ssl, sock, shutdown_gracefully);
-  }
-
-  detail::shutdown_socket(sock);
-  detail::close_socket(sock);
-  return ret;
-}
-
-inline STACK_OF(X509_NAME) * SSLServer::extract_ca_names_from_x509_store(
-                                 X509_STORE *store) {
-  if (!store) { return nullptr; }
-
-  auto ca_list = sk_X509_NAME_new_null();
-  if (!ca_list) { return nullptr; }
-
-  // Get all objects from the store
-  auto objs = X509_STORE_get0_objects(store);
-  if (!objs) {
-    sk_X509_NAME_free(ca_list);
-    return nullptr;
-  }
-
-  // Iterate through objects and extract certificate subject names
-  for (int i = 0; i < sk_X509_OBJECT_num(objs); i++) {
-    auto obj = sk_X509_OBJECT_value(objs, i);
-    if (X509_OBJECT_get_type(obj) == X509_LU_X509) {
-      auto cert = X509_OBJECT_get0_X509(obj);
-      if (cert) {
-        auto subject = X509_get_subject_name(cert);
-        if (subject) {
-          auto name_dup = X509_NAME_dup(subject);
-          if (name_dup) { sk_X509_NAME_push(ca_list, name_dup); }
-        }
-      }
-    }
-  }
-
-  // If no names were extracted, free the list and return nullptr
-  if (sk_X509_NAME_num(ca_list) == 0) {
-    sk_X509_NAME_free(ca_list);
-    return nullptr;
-  }
-
-  return ca_list;
-}
-
-// SSL HTTP client implementation
-inline SSLClient::SSLClient(const std::string &host)
-    : SSLClient(host, 443, std::string(), std::string()) {}
-
-inline SSLClient::SSLClient(const std::string &host, int port)
-    : SSLClient(host, port, std::string(), std::string()) {}
-
-inline SSLClient::SSLClient(const std::string &host, int port,
-                            const std::string &client_cert_path,
-                            const std::string &client_key_path,
-                            const std::string &private_key_password)
-    : ClientImpl(host, port, client_cert_path, client_key_path) {
-  ctx_ = SSL_CTX_new(TLS_client_method());
-
-  SSL_CTX_set_min_proto_version(ctx_, TLS1_2_VERSION);
-
-  detail::split(&host_[0], &host_[host_.size()], '.',
-                [&](const char *b, const char *e) {
-                  host_components_.emplace_back(b, e);
-                });
-
-  if (!client_cert_path.empty() && !client_key_path.empty()) {
-    if (!private_key_password.empty()) {
-      SSL_CTX_set_default_passwd_cb_userdata(
-          ctx_, reinterpret_cast<void *>(
-                    const_cast<char *>(private_key_password.c_str())));
-    }
-
-    if (SSL_CTX_use_certificate_file(ctx_, client_cert_path.c_str(),
-                                     SSL_FILETYPE_PEM) != 1 ||
-        SSL_CTX_use_PrivateKey_file(ctx_, client_key_path.c_str(),
-                                    SSL_FILETYPE_PEM) != 1) {
-      last_openssl_error_ = ERR_get_error();
-      SSL_CTX_free(ctx_);
-      ctx_ = nullptr;
-    }
-  }
-}
-
-inline SSLClient::SSLClient(const std::string &host, int port,
-                            X509 *client_cert, EVP_PKEY *client_key,
-                            const std::string &private_key_password)
-    : ClientImpl(host, port) {
-  ctx_ = SSL_CTX_new(TLS_client_method());
-
-  detail::split(&host_[0], &host_[host_.size()], '.',
-                [&](const char *b, const char *e) {
-                  host_components_.emplace_back(b, e);
-                });
-
-  if (client_cert != nullptr && client_key != nullptr) {
-    if (!private_key_password.empty()) {
-      SSL_CTX_set_default_passwd_cb_userdata(
-          ctx_, reinterpret_cast<void *>(
-                    const_cast<char *>(private_key_password.c_str())));
-    }
-
-    if (SSL_CTX_use_certificate(ctx_, client_cert) != 1 ||
-        SSL_CTX_use_PrivateKey(ctx_, client_key) != 1) {
-      last_openssl_error_ = ERR_get_error();
-      SSL_CTX_free(ctx_);
-      ctx_ = nullptr;
-    }
-  }
-}
-
-inline SSLClient::~SSLClient() {
-  if (ctx_) { SSL_CTX_free(ctx_); }
-  // Make sure to shut down SSL since shutdown_ssl will resolve to the
-  // base function rather than the derived function once we get to the
-  // base class destructor, and won't free the SSL (causing a leak).
-  shutdown_ssl_impl(socket_, true);
-}
-
-inline bool SSLClient::is_valid() const { return ctx_; }
-
-inline void SSLClient::set_ca_cert_store(X509_STORE *ca_cert_store) {
-  if (ca_cert_store) {
-    if (ctx_) {
-      if (SSL_CTX_get_cert_store(ctx_) != ca_cert_store) {
-        // Free memory allocated for old cert and use new store
-        // `ca_cert_store`
-        SSL_CTX_set_cert_store(ctx_, ca_cert_store);
-        ca_cert_store_ = ca_cert_store;
-      }
-    } else {
-      X509_STORE_free(ca_cert_store);
-    }
-  }
-}
-
-inline void SSLClient::load_ca_cert_store(const char *ca_cert,
-                                          std::size_t size) {
-  set_ca_cert_store(ClientImpl::create_ca_cert_store(ca_cert, size));
-}
-
-inline long SSLClient::get_openssl_verify_result() const {
-  return verify_result_;
-}
-
-inline SSL_CTX *SSLClient::ssl_context() const { return ctx_; }
-
-inline bool SSLClient::create_and_connect_socket(Socket &socket, Error &error) {
-  if (!is_valid()) {
-    error = Error::SSLConnection;
-    return false;
-  }
-  return ClientImpl::create_and_connect_socket(socket, error);
-}
-
-// Assumes that socket_mutex_ is locked and that there are no requests in
-// flight
-inline bool SSLClient::connect_with_proxy(
-    Socket &socket,
-    std::chrono::time_point<std::chrono::steady_clock> start_time,
-    Response &res, bool &success, Error &error) {
-  success = true;
-  Response proxy_res;
-  if (!detail::process_client_socket(
-          socket.sock, read_timeout_sec_, read_timeout_usec_,
-          write_timeout_sec_, write_timeout_usec_, max_timeout_msec_,
-          start_time, [&](Stream &strm) {
-            Request req2;
-            req2.method = "CONNECT";
-            req2.path = host_and_port_;
-            if (max_timeout_msec_ > 0) {
-              req2.start_time_ = std::chrono::steady_clock::now();
-            }
-            return process_request(strm, req2, proxy_res, false, error);
-          })) {
-    // Thread-safe to close everything because we are assuming there are no
-    // requests in flight
-    shutdown_ssl(socket, true);
-    shutdown_socket(socket);
-    close_socket(socket);
-    success = false;
-    return false;
-  }
-
-  if (proxy_res.status == StatusCode::ProxyAuthenticationRequired_407) {
-    if (!proxy_digest_auth_username_.empty() &&
-        !proxy_digest_auth_password_.empty()) {
-      std::map<std::string, std::string> auth;
-      if (detail::parse_www_authenticate(proxy_res, auth, true)) {
-        // Close the current socket and create a new one for the authenticated
-        // request
-        shutdown_ssl(socket, true);
-        shutdown_socket(socket);
-        close_socket(socket);
-
-        // Create a new socket for the authenticated CONNECT request
-        if (!create_and_connect_socket(socket, error)) {
-          success = false;
-          output_error_log(error, nullptr);
-          return false;
-        }
-
-        proxy_res = Response();
-        if (!detail::process_client_socket(
-                socket.sock, read_timeout_sec_, read_timeout_usec_,
-                write_timeout_sec_, write_timeout_usec_, max_timeout_msec_,
-                start_time, [&](Stream &strm) {
-                  Request req3;
-                  req3.method = "CONNECT";
-                  req3.path = host_and_port_;
-                  req3.headers.insert(detail::make_digest_authentication_header(
-                      req3, auth, 1, detail::random_string(10),
-                      proxy_digest_auth_username_, proxy_digest_auth_password_,
-                      true));
-                  if (max_timeout_msec_ > 0) {
-                    req3.start_time_ = std::chrono::steady_clock::now();
-                  }
-                  return process_request(strm, req3, proxy_res, false, error);
-                })) {
-          // Thread-safe to close everything because we are assuming there are
-          // no requests in flight
-          shutdown_ssl(socket, true);
-          shutdown_socket(socket);
-          close_socket(socket);
-          success = false;
-          return false;
-        }
-      }
-    }
-  }
-
-  // If status code is not 200, proxy request is failed.
-  // Set error to ProxyConnection and return proxy response
-  // as the response of the request
-  if (proxy_res.status != StatusCode::OK_200) {
-    error = Error::ProxyConnection;
-    output_error_log(error, nullptr);
-    res = std::move(proxy_res);
-    // Thread-safe to close everything because we are assuming there are
-    // no requests in flight
-    shutdown_ssl(socket, true);
-    shutdown_socket(socket);
-    close_socket(socket);
-    return false;
-  }
-
-  return true;
-}
-
-inline bool SSLClient::load_certs() {
-  auto ret = true;
-
-  std::call_once(initialize_cert_, [&]() {
-    std::lock_guard<std::mutex> guard(ctx_mutex_);
-    if (!ca_cert_file_path_.empty()) {
-      if (!SSL_CTX_load_verify_locations(ctx_, ca_cert_file_path_.c_str(),
-                                         nullptr)) {
-        last_openssl_error_ = ERR_get_error();
-        ret = false;
-      }
-    } else if (!ca_cert_dir_path_.empty()) {
-      if (!SSL_CTX_load_verify_locations(ctx_, nullptr,
-                                         ca_cert_dir_path_.c_str())) {
-        last_openssl_error_ = ERR_get_error();
-        ret = false;
-      }
-    } else {
-      auto loaded = false;
-#ifdef _WIN32
-      loaded =
-          detail::load_system_certs_on_windows(SSL_CTX_get_cert_store(ctx_));
-#elif defined(CPPHTTPLIB_USE_CERTS_FROM_MACOSX_KEYCHAIN) && TARGET_OS_MAC
-      loaded = detail::load_system_certs_on_macos(SSL_CTX_get_cert_store(ctx_));
-#endif // _WIN32
-      if (!loaded) { SSL_CTX_set_default_verify_paths(ctx_); }
-    }
-  });
-
-  return ret;
-}
-
-inline bool SSLClient::initialize_ssl(Socket &socket, Error &error) {
-  auto ssl = detail::ssl_new(
-      socket.sock, ctx_, ctx_mutex_,
-      [&](SSL *ssl2) {
-        if (server_certificate_verification_) {
-          if (!load_certs()) {
-            error = Error::SSLLoadingCerts;
-            output_error_log(error, nullptr);
-            return false;
-          }
-          SSL_set_verify(ssl2, SSL_VERIFY_NONE, nullptr);
-        }
-
-        if (!detail::ssl_connect_or_accept_nonblocking(
-                socket.sock, ssl2, SSL_connect, connection_timeout_sec_,
-                connection_timeout_usec_, &last_ssl_error_)) {
-          error = Error::SSLConnection;
-          output_error_log(error, nullptr);
-          return false;
-        }
-
-        if (server_certificate_verification_) {
-          auto verification_status = SSLVerifierResponse::NoDecisionMade;
-
-          if (server_certificate_verifier_) {
-            verification_status = server_certificate_verifier_(ssl2);
-          }
-
-          if (verification_status == SSLVerifierResponse::CertificateRejected) {
-            last_openssl_error_ = ERR_get_error();
-            error = Error::SSLServerVerification;
-            output_error_log(error, nullptr);
-            return false;
-          }
-
-          if (verification_status == SSLVerifierResponse::NoDecisionMade) {
-            verify_result_ = SSL_get_verify_result(ssl2);
-
-            if (verify_result_ != X509_V_OK) {
-              last_openssl_error_ = static_cast<unsigned long>(verify_result_);
-              error = Error::SSLServerVerification;
-              output_error_log(error, nullptr);
-              return false;
-            }
-
-            auto server_cert = SSL_get1_peer_certificate(ssl2);
-            auto se = detail::scope_exit([&] { X509_free(server_cert); });
-
-            if (server_cert == nullptr) {
-              last_openssl_error_ = ERR_get_error();
-              error = Error::SSLServerVerification;
-              output_error_log(error, nullptr);
-              return false;
-            }
-
-            if (server_hostname_verification_) {
-              if (!verify_host(server_cert)) {
-                last_openssl_error_ = X509_V_ERR_HOSTNAME_MISMATCH;
-                error = Error::SSLServerHostnameVerification;
-                output_error_log(error, nullptr);
-                return false;
-              }
-            }
-          }
-        }
-
-        return true;
-      },
-      [&](SSL *ssl2) {
-        // Set SNI only if host is not IP address
-        if (!detail::is_ip_address(host_)) {
-#if defined(OPENSSL_IS_BORINGSSL)
-          SSL_set_tlsext_host_name(ssl2, host_.c_str());
-#else
-          // NOTE: Direct call instead of using the OpenSSL macro to suppress
-          // -Wold-style-cast warning
-          SSL_ctrl(ssl2, SSL_CTRL_SET_TLSEXT_HOSTNAME,
-                   TLSEXT_NAMETYPE_host_name,
-                   static_cast<void *>(const_cast<char *>(host_.c_str())));
-#endif
-        }
-        return true;
-      });
-
-  if (ssl) {
-    socket.ssl = ssl;
-    return true;
-  }
-
-  if (ctx_ == nullptr) {
-    error = Error::SSLConnection;
-    last_openssl_error_ = ERR_get_error();
-  }
-
-  shutdown_socket(socket);
-  close_socket(socket);
-  return false;
-}
-
-inline void SSLClient::shutdown_ssl(Socket &socket, bool shutdown_gracefully) {
-  shutdown_ssl_impl(socket, shutdown_gracefully);
-}
-
-inline void SSLClient::shutdown_ssl_impl(Socket &socket,
-                                         bool shutdown_gracefully) {
-  if (socket.sock == INVALID_SOCKET) {
-    assert(socket.ssl == nullptr);
-    return;
-  }
-  if (socket.ssl) {
-    detail::ssl_delete(ctx_mutex_, socket.ssl, socket.sock,
-                       shutdown_gracefully);
-    socket.ssl = nullptr;
-  }
-  assert(socket.ssl == nullptr);
-}
-
-inline bool SSLClient::process_socket(
-    const Socket &socket,
-    std::chrono::time_point<std::chrono::steady_clock> start_time,
-    std::function<bool(Stream &strm)> callback) {
-  assert(socket.ssl);
-  return detail::process_client_socket_ssl(
-      socket.ssl, socket.sock, read_timeout_sec_, read_timeout_usec_,
-      write_timeout_sec_, write_timeout_usec_, max_timeout_msec_, start_time,
-      std::move(callback));
-}
-
-inline bool SSLClient::is_ssl() const { return true; }
-
-inline bool SSLClient::verify_host(X509 *server_cert) const {
-  /* Quote from RFC2818 section 3.1 "Server Identity"
-
-     If a subjectAltName extension of type dNSName is present, that MUST
-     be used as the identity. Otherwise, the (most specific) Common Name
-     field in the Subject field of the certificate MUST be used. Although
-     the use of the Common Name is existing practice, it is deprecated and
-     Certification Authorities are encouraged to use the dNSName instead.
-
-     Matching is performed using the matching rules specified by
-     [RFC2459].  If more than one identity of a given type is present in
-     the certificate (e.g., more than one dNSName name, a match in any one
-     of the set is considered acceptable.) Names may contain the wildcard
-     character * which is considered to match any single domain name
-     component or component fragment. E.g., *.a.com matches foo.a.com but
-     not bar.foo.a.com. f*.com matches foo.com but not bar.com.
-
-     In some cases, the URI is specified as an IP address rather than a
-     hostname. In this case, the iPAddress subjectAltName must be present
-     in the certificate and must exactly match the IP in the URI.
-
-  */
-  return verify_host_with_subject_alt_name(server_cert) ||
-         verify_host_with_common_name(server_cert);
-}
-
-inline bool
-SSLClient::verify_host_with_subject_alt_name(X509 *server_cert) const {
-  auto ret = false;
-
-  auto type = GEN_DNS;
-
-  struct in6_addr addr6 = {};
-  struct in_addr addr = {};
-  size_t addr_len = 0;
-
-#ifndef __MINGW32__
-  if (inet_pton(AF_INET6, host_.c_str(), &addr6)) {
-    type = GEN_IPADD;
-    addr_len = sizeof(struct in6_addr);
-  } else if (inet_pton(AF_INET, host_.c_str(), &addr)) {
-    type = GEN_IPADD;
-    addr_len = sizeof(struct in_addr);
-  }
-#endif
-
-  auto alt_names = static_cast<const struct stack_st_GENERAL_NAME *>(
-      X509_get_ext_d2i(server_cert, NID_subject_alt_name, nullptr, nullptr));
-
-  if (alt_names) {
-    auto dsn_matched = false;
-    auto ip_matched = false;
-
-    auto count = sk_GENERAL_NAME_num(alt_names);
-
-    for (decltype(count) i = 0; i < count && !dsn_matched; i++) {
-      auto val = sk_GENERAL_NAME_value(alt_names, i);
-      if (!val || val->type != type) { continue; }
-
-      auto name =
-          reinterpret_cast<const char *>(ASN1_STRING_get0_data(val->d.ia5));
-      if (name == nullptr) { continue; }
-
-      auto name_len = static_cast<size_t>(ASN1_STRING_length(val->d.ia5));
-
-      switch (type) {
-      case GEN_DNS: dsn_matched = check_host_name(name, name_len); break;
-
-      case GEN_IPADD:
-        if (!memcmp(&addr6, name, addr_len) || !memcmp(&addr, name, addr_len)) {
-          ip_matched = true;
-        }
-        break;
-      }
-    }
-
-    if (dsn_matched || ip_matched) { ret = true; }
-  }
-
-  GENERAL_NAMES_free(const_cast<STACK_OF(GENERAL_NAME) *>(
-      reinterpret_cast<const STACK_OF(GENERAL_NAME) *>(alt_names)));
-  return ret;
-}
-
-inline bool SSLClient::verify_host_with_common_name(X509 *server_cert) const {
-  const auto subject_name = X509_get_subject_name(server_cert);
-
-  if (subject_name != nullptr) {
-    char name[BUFSIZ];
-    auto name_len = X509_NAME_get_text_by_NID(subject_name, NID_commonName,
-                                              name, sizeof(name));
-
-    if (name_len != -1) {
-      return check_host_name(name, static_cast<size_t>(name_len));
-    }
-  }
-
-  return false;
-}
-
-inline bool SSLClient::check_host_name(const char *pattern,
-                                       size_t pattern_len) const {
-  if (host_.size() == pattern_len && host_ == pattern) { return true; }
-
-  // Wildcard match
-  // https://bugs.launchpad.net/ubuntu/+source/firefox-3.0/+bug/376484
-  std::vector<std::string> pattern_components;
-  detail::split(&pattern[0], &pattern[pattern_len], '.',
-                [&](const char *b, const char *e) {
-                  pattern_components.emplace_back(b, e);
-                });
-
-  if (host_components_.size() != pattern_components.size()) { return false; }
-
-  auto itr = pattern_components.begin();
-  for (const auto &h : host_components_) {
-    auto &p = *itr;
-    if (p != h && p != "*") {
-      auto partial_match = (p.size() > 0 && p[p.size() - 1] == '*' &&
-                            !p.compare(0, p.size() - 1, h));
-      if (!partial_match) { return false; }
-    }
-    ++itr;
-  }
-
-  return true;
-}
-#endif
-
-// Universal client implementation
-inline Client::Client(const std::string &scheme_host_port)
-    : Client(scheme_host_port, std::string(), std::string()) {}
-
-inline Client::Client(const std::string &scheme_host_port,
-                      const std::string &client_cert_path,
-                      const std::string &client_key_path) {
-  const static std::regex re(
-      R"((?:([a-z]+):\/\/)?(?:\[([a-fA-F\d:]+)\]|([^:/?#]+))(?::(\d+))?)");
-
-  std::smatch m;
-  if (std::regex_match(scheme_host_port, m, re)) {
-    auto scheme = m[1].str();
-
-#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
-    if (!scheme.empty() && (scheme != "http" && scheme != "https")) {
-#else
-    if (!scheme.empty() && scheme != "http") {
-#endif
-#ifndef CPPHTTPLIB_NO_EXCEPTIONS
-      std::string msg = "'" + scheme + "' scheme is not supported.";
-      throw std::invalid_argument(msg);
-#endif
-      return;
-    }
-
-    auto is_ssl = scheme == "https";
-
-    auto host = m[2].str();
-    if (host.empty()) { host = m[3].str(); }
-
-    auto port_str = m[4].str();
-    auto port = !port_str.empty() ? std::stoi(port_str) : (is_ssl ? 443 : 80);
-
-    if (is_ssl) {
-#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
-      cli_ = detail::make_unique<SSLClient>(host, port, client_cert_path,
-                                            client_key_path);
-      is_ssl_ = is_ssl;
-#endif
-    } else {
-      cli_ = detail::make_unique<ClientImpl>(host, port, client_cert_path,
-                                             client_key_path);
-    }
-  } else {
-    // NOTE: Update TEST(UniversalClientImplTest, Ipv6LiteralAddress)
-    // if port param below changes.
-    cli_ = detail::make_unique<ClientImpl>(scheme_host_port, 80,
-                                           client_cert_path, client_key_path);
-  }
-} // namespace detail
-
-inline Client::Client(const std::string &host, int port)
-    : cli_(detail::make_unique<ClientImpl>(host, port)) {}
-
-inline Client::Client(const std::string &host, int port,
-                      const std::string &client_cert_path,
-                      const std::string &client_key_path)
-    : cli_(detail::make_unique<ClientImpl>(host, port, client_cert_path,
-                                           client_key_path)) {}
-
-inline Client::~Client() = default;
-
-inline bool Client::is_valid() const {
-  return cli_ != nullptr && cli_->is_valid();
-}
-
-inline Result Client::Get(const std::string &path, DownloadProgress progress) {
-  return cli_->Get(path, std::move(progress));
-}
-inline Result Client::Get(const std::string &path, const Headers &headers,
-                          DownloadProgress progress) {
-  return cli_->Get(path, headers, std::move(progress));
-}
-inline Result Client::Get(const std::string &path,
-                          ContentReceiver content_receiver,
-                          DownloadProgress progress) {
-  return cli_->Get(path, std::move(content_receiver), std::move(progress));
-}
-inline Result Client::Get(const std::string &path, const Headers &headers,
-                          ContentReceiver content_receiver,
-                          DownloadProgress progress) {
-  return cli_->Get(path, headers, std::move(content_receiver),
-                   std::move(progress));
-}
-inline Result Client::Get(const std::string &path,
-                          ResponseHandler response_handler,
-                          ContentReceiver content_receiver,
-                          DownloadProgress progress) {
-  return cli_->Get(path, std::move(response_handler),
-                   std::move(content_receiver), std::move(progress));
-}
-inline Result Client::Get(const std::string &path, const Headers &headers,
-                          ResponseHandler response_handler,
-                          ContentReceiver content_receiver,
-                          DownloadProgress progress) {
-  return cli_->Get(path, headers, std::move(response_handler),
-                   std::move(content_receiver), std::move(progress));
-}
-inline Result Client::Get(const std::string &path, const Params &params,
-                          const Headers &headers, DownloadProgress progress) {
-  return cli_->Get(path, params, headers, std::move(progress));
-}
-inline Result Client::Get(const std::string &path, const Params &params,
-                          const Headers &headers,
-                          ContentReceiver content_receiver,
-                          DownloadProgress progress) {
-  return cli_->Get(path, params, headers, std::move(content_receiver),
-                   std::move(progress));
-}
-inline Result Client::Get(const std::string &path, const Params &params,
-                          const Headers &headers,
-                          ResponseHandler response_handler,
-                          ContentReceiver content_receiver,
-                          DownloadProgress progress) {
-  return cli_->Get(path, params, headers, std::move(response_handler),
-                   std::move(content_receiver), std::move(progress));
-}
-
-inline Result Client::Head(const std::string &path) { return cli_->Head(path); }
-inline Result Client::Head(const std::string &path, const Headers &headers) {
-  return cli_->Head(path, headers);
-}
-
-inline Result Client::Post(const std::string &path) { return cli_->Post(path); }
-inline Result Client::Post(const std::string &path, const Headers &headers) {
-  return cli_->Post(path, headers);
-}
-inline Result Client::Post(const std::string &path, const char *body,
-                           size_t content_length,
-                           const std::string &content_type,
-                           UploadProgress progress) {
-  return cli_->Post(path, body, content_length, content_type, progress);
-}
-inline Result Client::Post(const std::string &path, const Headers &headers,
-                           const char *body, size_t content_length,
-                           const std::string &content_type,
-                           UploadProgress progress) {
-  return cli_->Post(path, headers, body, content_length, content_type,
-                    progress);
-}
-inline Result Client::Post(const std::string &path, const std::string &body,
-                           const std::string &content_type,
-                           UploadProgress progress) {
-  return cli_->Post(path, body, content_type, progress);
-}
-inline Result Client::Post(const std::string &path, const Headers &headers,
-                           const std::string &body,
-                           const std::string &content_type,
-                           UploadProgress progress) {
-  return cli_->Post(path, headers, body, content_type, progress);
-}
-inline Result Client::Post(const std::string &path, size_t content_length,
-                           ContentProvider content_provider,
-                           const std::string &content_type,
-                           UploadProgress progress) {
-  return cli_->Post(path, content_length, std::move(content_provider),
-                    content_type, progress);
-}
-inline Result Client::Post(const std::string &path,
-                           ContentProviderWithoutLength content_provider,
-                           const std::string &content_type,
-                           UploadProgress progress) {
-  return cli_->Post(path, std::move(content_provider), content_type, progress);
-}
-inline Result Client::Post(const std::string &path, const Headers &headers,
-                           size_t content_length,
-                           ContentProvider content_provider,
-                           const std::string &content_type,
-                           UploadProgress progress) {
-  return cli_->Post(path, headers, content_length, std::move(content_provider),
-                    content_type, progress);
-}
-inline Result Client::Post(const std::string &path, const Headers &headers,
-                           ContentProviderWithoutLength content_provider,
-                           const std::string &content_type,
-                           UploadProgress progress) {
-  return cli_->Post(path, headers, std::move(content_provider), content_type,
-                    progress);
-}
-inline Result Client::Post(const std::string &path, const Params &params) {
-  return cli_->Post(path, params);
-}
-inline Result Client::Post(const std::string &path, const Headers &headers,
-                           const Params &params) {
-  return cli_->Post(path, headers, params);
-}
-inline Result Client::Post(const std::string &path,
-                           const UploadFormDataItems &items,
-                           UploadProgress progress) {
-  return cli_->Post(path, items, progress);
-}
-inline Result Client::Post(const std::string &path, const Headers &headers,
-                           const UploadFormDataItems &items,
-                           UploadProgress progress) {
-  return cli_->Post(path, headers, items, progress);
-}
-inline Result Client::Post(const std::string &path, const Headers &headers,
-                           const UploadFormDataItems &items,
-                           const std::string &boundary,
-                           UploadProgress progress) {
-  return cli_->Post(path, headers, items, boundary, progress);
-}
-inline Result Client::Post(const std::string &path, const Headers &headers,
-                           const UploadFormDataItems &items,
-                           const FormDataProviderItems &provider_items,
-                           UploadProgress progress) {
-  return cli_->Post(path, headers, items, provider_items, progress);
-}
-inline Result Client::Post(const std::string &path, const Headers &headers,
-                           const std::string &body,
-                           const std::string &content_type,
-                           ContentReceiver content_receiver,
-                           DownloadProgress progress) {
-  return cli_->Post(path, headers, body, content_type, content_receiver,
-                    progress);
-}
-
-inline Result Client::Put(const std::string &path) { return cli_->Put(path); }
-inline Result Client::Put(const std::string &path, const Headers &headers) {
-  return cli_->Put(path, headers);
-}
-inline Result Client::Put(const std::string &path, const char *body,
-                          size_t content_length,
-                          const std::string &content_type,
-                          UploadProgress progress) {
-  return cli_->Put(path, body, content_length, content_type, progress);
-}
-inline Result Client::Put(const std::string &path, const Headers &headers,
-                          const char *body, size_t content_length,
-                          const std::string &content_type,
-                          UploadProgress progress) {
-  return cli_->Put(path, headers, body, content_length, content_type, progress);
-}
-inline Result Client::Put(const std::string &path, const std::string &body,
-                          const std::string &content_type,
-                          UploadProgress progress) {
-  return cli_->Put(path, body, content_type, progress);
-}
-inline Result Client::Put(const std::string &path, const Headers &headers,
-                          const std::string &body,
-                          const std::string &content_type,
-                          UploadProgress progress) {
-  return cli_->Put(path, headers, body, content_type, progress);
-}
-inline Result Client::Put(const std::string &path, size_t content_length,
-                          ContentProvider content_provider,
-                          const std::string &content_type,
-                          UploadProgress progress) {
-  return cli_->Put(path, content_length, std::move(content_provider),
-                   content_type, progress);
-}
-inline Result Client::Put(const std::string &path,
-                          ContentProviderWithoutLength content_provider,
-                          const std::string &content_type,
-                          UploadProgress progress) {
-  return cli_->Put(path, std::move(content_provider), content_type, progress);
-}
-inline Result Client::Put(const std::string &path, const Headers &headers,
-                          size_t content_length,
-                          ContentProvider content_provider,
-                          const std::string &content_type,
-                          UploadProgress progress) {
-  return cli_->Put(path, headers, content_length, std::move(content_provider),
-                   content_type, progress);
-}
-inline Result Client::Put(const std::string &path, const Headers &headers,
-                          ContentProviderWithoutLength content_provider,
-                          const std::string &content_type,
-                          UploadProgress progress) {
-  return cli_->Put(path, headers, std::move(content_provider), content_type,
-                   progress);
-}
-inline Result Client::Put(const std::string &path, const Params &params) {
-  return cli_->Put(path, params);
-}
-inline Result Client::Put(const std::string &path, const Headers &headers,
-                          const Params &params) {
-  return cli_->Put(path, headers, params);
-}
-inline Result Client::Put(const std::string &path,
-                          const UploadFormDataItems &items,
-                          UploadProgress progress) {
-  return cli_->Put(path, items, progress);
-}
-inline Result Client::Put(const std::string &path, const Headers &headers,
-                          const UploadFormDataItems &items,
-                          UploadProgress progress) {
-  return cli_->Put(path, headers, items, progress);
-}
-inline Result Client::Put(const std::string &path, const Headers &headers,
-                          const UploadFormDataItems &items,
-                          const std::string &boundary,
-                          UploadProgress progress) {
-  return cli_->Put(path, headers, items, boundary, progress);
-}
-inline Result Client::Put(const std::string &path, const Headers &headers,
-                          const UploadFormDataItems &items,
-                          const FormDataProviderItems &provider_items,
-                          UploadProgress progress) {
-  return cli_->Put(path, headers, items, provider_items, progress);
-}
-inline Result Client::Put(const std::string &path, const Headers &headers,
-                          const std::string &body,
-                          const std::string &content_type,
-                          ContentReceiver content_receiver,
-                          DownloadProgress progress) {
-  return cli_->Put(path, headers, body, content_type, content_receiver,
-                   progress);
-}
-
-inline Result Client::Patch(const std::string &path) {
-  return cli_->Patch(path);
-}
-inline Result Client::Patch(const std::string &path, const Headers &headers) {
-  return cli_->Patch(path, headers);
-}
-inline Result Client::Patch(const std::string &path, const char *body,
-                            size_t content_length,
-                            const std::string &content_type,
-                            UploadProgress progress) {
-  return cli_->Patch(path, body, content_length, content_type, progress);
-}
-inline Result Client::Patch(const std::string &path, const Headers &headers,
-                            const char *body, size_t content_length,
-                            const std::string &content_type,
-                            UploadProgress progress) {
-  return cli_->Patch(path, headers, body, content_length, content_type,
-                     progress);
-}
-inline Result Client::Patch(const std::string &path, const std::string &body,
-                            const std::string &content_type,
-                            UploadProgress progress) {
-  return cli_->Patch(path, body, content_type, progress);
-}
-inline Result Client::Patch(const std::string &path, const Headers &headers,
-                            const std::string &body,
-                            const std::string &content_type,
-                            UploadProgress progress) {
-  return cli_->Patch(path, headers, body, content_type, progress);
-}
-inline Result Client::Patch(const std::string &path, size_t content_length,
-                            ContentProvider content_provider,
-                            const std::string &content_type,
-                            UploadProgress progress) {
-  return cli_->Patch(path, content_length, std::move(content_provider),
-                     content_type, progress);
-}
-inline Result Client::Patch(const std::string &path,
-                            ContentProviderWithoutLength content_provider,
-                            const std::string &content_type,
-                            UploadProgress progress) {
-  return cli_->Patch(path, std::move(content_provider), content_type, progress);
-}
-inline Result Client::Patch(const std::string &path, const Headers &headers,
-                            size_t content_length,
-                            ContentProvider content_provider,
-                            const std::string &content_type,
-                            UploadProgress progress) {
-  return cli_->Patch(path, headers, content_length, std::move(content_provider),
-                     content_type, progress);
-}
-inline Result Client::Patch(const std::string &path, const Headers &headers,
-                            ContentProviderWithoutLength content_provider,
-                            const std::string &content_type,
-                            UploadProgress progress) {
-  return cli_->Patch(path, headers, std::move(content_provider), content_type,
-                     progress);
-}
-inline Result Client::Patch(const std::string &path, const Params &params) {
-  return cli_->Patch(path, params);
-}
-inline Result Client::Patch(const std::string &path, const Headers &headers,
-                            const Params &params) {
-  return cli_->Patch(path, headers, params);
-}
-inline Result Client::Patch(const std::string &path,
-                            const UploadFormDataItems &items,
-                            UploadProgress progress) {
-  return cli_->Patch(path, items, progress);
-}
-inline Result Client::Patch(const std::string &path, const Headers &headers,
-                            const UploadFormDataItems &items,
-                            UploadProgress progress) {
-  return cli_->Patch(path, headers, items, progress);
-}
-inline Result Client::Patch(const std::string &path, const Headers &headers,
-                            const UploadFormDataItems &items,
-                            const std::string &boundary,
-                            UploadProgress progress) {
-  return cli_->Patch(path, headers, items, boundary, progress);
-}
-inline Result Client::Patch(const std::string &path, const Headers &headers,
-                            const UploadFormDataItems &items,
-                            const FormDataProviderItems &provider_items,
-                            UploadProgress progress) {
-  return cli_->Patch(path, headers, items, provider_items, progress);
-}
-inline Result Client::Patch(const std::string &path, const Headers &headers,
-                            const std::string &body,
-                            const std::string &content_type,
-                            ContentReceiver content_receiver,
-                            DownloadProgress progress) {
-  return cli_->Patch(path, headers, body, content_type, content_receiver,
-                     progress);
-}
-
-inline Result Client::Delete(const std::string &path,
-                             DownloadProgress progress) {
-  return cli_->Delete(path, progress);
-}
-inline Result Client::Delete(const std::string &path, const Headers &headers,
-                             DownloadProgress progress) {
-  return cli_->Delete(path, headers, progress);
-}
-inline Result Client::Delete(const std::string &path, const char *body,
-                             size_t content_length,
-                             const std::string &content_type,
-                             DownloadProgress progress) {
-  return cli_->Delete(path, body, content_length, content_type, progress);
-}
-inline Result Client::Delete(const std::string &path, const Headers &headers,
-                             const char *body, size_t content_length,
-                             const std::string &content_type,
-                             DownloadProgress progress) {
-  return cli_->Delete(path, headers, body, content_length, content_type,
-                      progress);
-}
-inline Result Client::Delete(const std::string &path, const std::string &body,
-                             const std::string &content_type,
-                             DownloadProgress progress) {
-  return cli_->Delete(path, body, content_type, progress);
-}
-inline Result Client::Delete(const std::string &path, const Headers &headers,
-                             const std::string &body,
-                             const std::string &content_type,
-                             DownloadProgress progress) {
-  return cli_->Delete(path, headers, body, content_type, progress);
-}
-inline Result Client::Delete(const std::string &path, const Params &params,
-                             DownloadProgress progress) {
-  return cli_->Delete(path, params, progress);
-}
-inline Result Client::Delete(const std::string &path, const Headers &headers,
-                             const Params &params, DownloadProgress progress) {
-  return cli_->Delete(path, headers, params, progress);
-}
-
-inline Result Client::Options(const std::string &path) {
-  return cli_->Options(path);
-}
-inline Result Client::Options(const std::string &path, const Headers &headers) {
-  return cli_->Options(path, headers);
-}
-
-inline bool Client::send(Request &req, Response &res, Error &error) {
-  return cli_->send(req, res, error);
-}
-
-inline Result Client::send(const Request &req) { return cli_->send(req); }
-
-inline void Client::stop() { cli_->stop(); }
-
-inline std::string Client::host() const { return cli_->host(); }
-
-inline int Client::port() const { return cli_->port(); }
-
-inline size_t Client::is_socket_open() const { return cli_->is_socket_open(); }
-
-inline socket_t Client::socket() const { return cli_->socket(); }
-
-inline void
-Client::set_hostname_addr_map(std::map<std::string, std::string> addr_map) {
-  cli_->set_hostname_addr_map(std::move(addr_map));
-}
-
-inline void Client::set_default_headers(Headers headers) {
-  cli_->set_default_headers(std::move(headers));
-}
-
-inline void Client::set_header_writer(
-    std::function<ssize_t(Stream &, Headers &)> const &writer) {
-  cli_->set_header_writer(writer);
-}
-
-inline void Client::set_address_family(int family) {
-  cli_->set_address_family(family);
-}
-
-inline void Client::set_tcp_nodelay(bool on) { cli_->set_tcp_nodelay(on); }
-
-inline void Client::set_socket_options(SocketOptions socket_options) {
-  cli_->set_socket_options(std::move(socket_options));
-}
-
-inline void Client::set_connection_timeout(time_t sec, time_t usec) {
-  cli_->set_connection_timeout(sec, usec);
-}
-
-inline void Client::set_read_timeout(time_t sec, time_t usec) {
-  cli_->set_read_timeout(sec, usec);
-}
-
-inline void Client::set_write_timeout(time_t sec, time_t usec) {
-  cli_->set_write_timeout(sec, usec);
-}
-
-inline void Client::set_basic_auth(const std::string &username,
-                                   const std::string &password) {
-  cli_->set_basic_auth(username, password);
-}
-inline void Client::set_bearer_token_auth(const std::string &token) {
-  cli_->set_bearer_token_auth(token);
-}
-#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
-inline void Client::set_digest_auth(const std::string &username,
-                                    const std::string &password) {
-  cli_->set_digest_auth(username, password);
-}
-#endif
-
-inline void Client::set_keep_alive(bool on) { cli_->set_keep_alive(on); }
-inline void Client::set_follow_location(bool on) {
-  cli_->set_follow_location(on);
-}
-
-inline void Client::set_path_encode(bool on) { cli_->set_path_encode(on); }
-
-[[deprecated("Use set_path_encode instead")]]
-inline void Client::set_url_encode(bool on) {
-  cli_->set_path_encode(on);
-}
-
-inline void Client::set_compress(bool on) { cli_->set_compress(on); }
-
-inline void Client::set_decompress(bool on) { cli_->set_decompress(on); }
-
-inline void Client::set_interface(const std::string &intf) {
-  cli_->set_interface(intf);
-}
-
-inline void Client::set_proxy(const std::string &host, int port) {
-  cli_->set_proxy(host, port);
-}
-inline void Client::set_proxy_basic_auth(const std::string &username,
-                                         const std::string &password) {
-  cli_->set_proxy_basic_auth(username, password);
-}
-inline void Client::set_proxy_bearer_token_auth(const std::string &token) {
-  cli_->set_proxy_bearer_token_auth(token);
-}
-#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
-inline void Client::set_proxy_digest_auth(const std::string &username,
-                                          const std::string &password) {
-  cli_->set_proxy_digest_auth(username, password);
-}
-#endif
-
-#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
-inline void Client::enable_server_certificate_verification(bool enabled) {
-  cli_->enable_server_certificate_verification(enabled);
-}
-
-inline void Client::enable_server_hostname_verification(bool enabled) {
-  cli_->enable_server_hostname_verification(enabled);
-}
-
-inline void Client::set_server_certificate_verifier(
-    std::function<SSLVerifierResponse(SSL *ssl)> verifier) {
-  cli_->set_server_certificate_verifier(verifier);
-}
-#endif
-
-inline void Client::set_logger(Logger logger) {
-  cli_->set_logger(std::move(logger));
-}
-
-inline void Client::set_error_logger(ErrorLogger error_logger) {
-  cli_->set_error_logger(std::move(error_logger));
-}
-
-#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
-inline void Client::set_ca_cert_path(const std::string &ca_cert_file_path,
-                                     const std::string &ca_cert_dir_path) {
-  cli_->set_ca_cert_path(ca_cert_file_path, ca_cert_dir_path);
-}
-
-inline void Client::set_ca_cert_store(X509_STORE *ca_cert_store) {
-  if (is_ssl_) {
-    static_cast<SSLClient &>(*cli_).set_ca_cert_store(ca_cert_store);
-  } else {
-    cli_->set_ca_cert_store(ca_cert_store);
-  }
-}
-
-inline void Client::load_ca_cert_store(const char *ca_cert, std::size_t size) {
-  set_ca_cert_store(cli_->create_ca_cert_store(ca_cert, size));
-}
-
-inline long Client::get_openssl_verify_result() const {
-  if (is_ssl_) {
-    return static_cast<SSLClient &>(*cli_).get_openssl_verify_result();
-  }
-  return -1; // NOTE: -1 doesn't match any of X509_V_ERR_???
-}
-
-inline SSL_CTX *Client::ssl_context() const {
-  if (is_ssl_) { return static_cast<SSLClient &>(*cli_).ssl_context(); }
-  return nullptr;
-}
-#endif
 
-// ----------------------------------------------------------------------------
 
 } // namespace httplib
 

From 3fe36c32389ade876ec505f32df08f5121cf597f Mon Sep 17 00:00:00 2001
From: sudhiarm <sudhi.sathyavathy@arm.com>
Date: Tue, 11 Nov 2025 15:58:05 +0000
Subject: [PATCH 160/185] ci: add Arm-hosted Graviton4 runner (#17021)

* ci: add Arm-hosted Graviton4 runner

* ci: add missing dependencies for graviton4 build

* ci: enable LFS checkout on graviton4

* ci: move git-lfs install to dependencies in Graviton4 workflow
---
 .github/workflows/build.yml | 47 +++++++++++++++++++++++++++++++++++++
 ci/run.sh                   |  7 +++++-
 2 files changed, 53 insertions(+), 1 deletion(-)

diff --git a/.github/workflows/build.yml b/.github/workflows/build.yml
index 36084c55078..0112fc323f7 100644
--- a/.github/workflows/build.yml
+++ b/.github/workflows/build.yml
@@ -1651,3 +1651,50 @@ jobs:
          run: |
            GG_BUILD_KLEIDIAI=1 GG_BUILD_EXTRA_TESTS_0=1 bash ./ci/run.sh ./tmp/results ./tmp/mnt
 
+  ggml-ci-arm64-graviton4-kleidiai:
+     runs-on: ah-ubuntu_22_04-c8g_8x
+
+     steps:
+       - name: Clone
+         id: checkout
+         uses: actions/checkout@v4
+
+       - name: Dependencies
+         id: depends
+         run: |
+           set -euxo pipefail
+           sudo apt-get update
+           sudo DEBIAN_FRONTEND=noninteractive NEEDRESTART_MODE=a \
+           apt-get install -y \
+            build-essential \
+            libcurl4-openssl-dev \
+            python3-venv \
+            gpg \
+            wget \
+            time \
+            git-lfs
+
+           git lfs install
+
+           # install the latest cmake
+           sudo install -d /usr/share/keyrings
+           wget -O - https://apt.kitware.com/keys/kitware-archive-latest.asc \
+            | gpg --dearmor \
+            | sudo tee /usr/share/keyrings/kitware-archive-keyring.gpg >/dev/null
+           echo 'deb [signed-by=/usr/share/keyrings/kitware-archive-keyring.gpg] https://apt.kitware.com/ubuntu/ jammy main' \
+            | sudo tee /etc/apt/sources.list.d/kitware.list
+           sudo apt-get update
+           sudo apt-get install -y cmake
+
+       - name: ccache
+         uses: ggml-org/ccache-action@v1.2.16
+         with:
+           key: ggml-ci-arm64-graviton4-kleidiai
+           evict-old-files: 1d
+
+       - name: Test
+         id: ggml-ci
+         run: |
+           GG_BUILD_KLEIDIAI=1 \
+           GG_BUILD_EXTRA_TESTS_0=1 \
+           bash ./ci/run.sh ./tmp/results ./tmp/mnt
diff --git a/ci/run.sh b/ci/run.sh
index 1a4806976aa..3fec8e9110f 100755
--- a/ci/run.sh
+++ b/ci/run.sh
@@ -121,7 +121,12 @@ fi
 if [ -n "${GG_BUILD_KLEIDIAI}" ]; then
     echo ">>===== Enabling KleidiAI support"
 
-    CANDIDATES=("armv9-a+dotprod+i8mm" "armv8.6-a+dotprod+i8mm" "armv8.2-a+dotprod")
+    CANDIDATES=(
+        "armv9-a+dotprod+i8mm+sve2"
+        "armv9-a+dotprod+i8mm"
+        "armv8.6-a+dotprod+i8mm"
+        "armv8.2-a+dotprod"
+    )
     CPU=""
 
     for cpu in "${CANDIDATES[@]}"; do

From 7d019cff744b73084b15ca81ba9916f3efab1223 Mon Sep 17 00:00:00 2001
From: Eve <139727413+netrunnereve@users.noreply.github.com>
Date: Tue, 11 Nov 2025 18:53:30 +0000
Subject: [PATCH 161/185] disable rms norm mul rope for chips with no fp16 rte
 (#17134)

---
 ggml/src/ggml-vulkan/ggml-vulkan.cpp | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/ggml/src/ggml-vulkan/ggml-vulkan.cpp b/ggml/src/ggml-vulkan/ggml-vulkan.cpp
index e4b7e1ea9e5..c6503f03260 100644
--- a/ggml/src/ggml-vulkan/ggml-vulkan.cpp
+++ b/ggml/src/ggml-vulkan/ggml-vulkan.cpp
@@ -12670,6 +12670,12 @@ static bool ggml_vk_can_fuse_rms_norm_mul_rope(ggml_backend_vk_context * ctx, co
         return false;
     }
 
+    // conditions for pipeline creation
+    if (!(ctx->device->float_controls_rte_fp16 &&
+        sizeof(vk_op_rms_norm_mul_rope_push_constants) <= ctx->device->properties.limits.maxPushConstantsSize)) {
+        return false;
+    }
+
     return true;
 }
 

From c273d7537503e47f7be8c293b767ebad1adbc5d0 Mon Sep 17 00:00:00 2001
From: Max Krasnyansky <maxk@qti.qualcomm.com>
Date: Tue, 11 Nov 2025 15:25:04 -0800
Subject: [PATCH 162/185] hexagon:  various Op fixes (#17135)

* hexagon: explicitly check for ops with zero nrows

llm_graph_context::build_inp_out_ids() can generate tensors with zero nrows.
Somehow other backends seems to handle this without obvious explicit checks.
In the hexagon case we need to check explicitly and skip them.

* hexagon: introduce fastdiv, fix test-backend-ops for ADD/SUB/MUL

Co-authored-by: chraac <chraac@gmail.com>

* hexagon: use fastdiv in ADD_ID

* hexagon: use ggml_op_is_empty and ggml_is_empty to check for NOPs

---------

Co-authored-by: chraac <chraac@gmail.com>
---
 ggml/src/ggml-hexagon/ggml-hexagon.cpp | 37 ++++---------
 ggml/src/ggml-hexagon/htp/binary-ops.c | 76 ++++++++++++++++----------
 ggml/src/ggml-hexagon/htp/htp-msg.h    |  8 +--
 ggml/src/ggml-hexagon/htp/htp-ops.h    | 11 ++++
 ggml/src/ggml-hexagon/htp/ops-utils.h  | 33 +++++++++++
 5 files changed, 106 insertions(+), 59 deletions(-)

diff --git a/ggml/src/ggml-hexagon/ggml-hexagon.cpp b/ggml/src/ggml-hexagon/ggml-hexagon.cpp
index 7064b7486f2..cabd301ad35 100644
--- a/ggml/src/ggml-hexagon/ggml-hexagon.cpp
+++ b/ggml/src/ggml-hexagon/ggml-hexagon.cpp
@@ -3156,26 +3156,17 @@ static inline bool op_reuse_src1(const ggml_tensor * op1, const ggml_tensor * op
     return (op0 && op0->src[1] == op1->src[1]);
 }
 
+static inline bool is_compute_op(ggml_tensor *node)
+{
+    return !(ggml_op_is_empty(node->op) || ggml_is_empty(node));
+}
+
 // scan the graph and figure out last compute op index
 static inline int last_compute_op(ggml_cgraph * graph) {
-    int last;
+    int last = 0;
     for (int i = 0; i < graph->n_nodes; ++i) {
-        ggml_tensor * node = graph->nodes[i];
-
-        switch (node->op) {
-            case GGML_OP_MUL_MAT:
-            case GGML_OP_MUL_MAT_ID:
-            case GGML_OP_MUL:
-            case GGML_OP_ADD:
-            case GGML_OP_SUB:
-            case GGML_OP_RMS_NORM:
-            case GGML_OP_GLU:
-            case GGML_OP_ADD_ID:
-                last = i;
-                break;
-
-            default:
-                break;
+        if (is_compute_op(graph->nodes[i])) {
+            last = i;
         }
     }
 
@@ -3194,6 +3185,10 @@ static ggml_status ggml_backend_hexagon_graph_compute(ggml_backend_t backend, gg
     for (int i = 0; i < graph->n_nodes; ++i) {
         ggml_tensor * node = graph->nodes[i];
 
+        if (!is_compute_op(node)) {
+            continue;
+        }
+
         uint32_t flags = 0;
 
         // skip quantizer if src1 is reused
@@ -3245,14 +3240,6 @@ static ggml_status ggml_backend_hexagon_graph_compute(ggml_backend_t backend, gg
                 ggml_hexagon_rope(node, flags);
                 break;
 
-            // non-compute ops
-            case GGML_OP_NONE:
-            case GGML_OP_RESHAPE:
-            case GGML_OP_VIEW:
-            case GGML_OP_PERMUTE:
-            case GGML_OP_TRANSPOSE:
-                break;
-
             default:
                 GGML_ABORT("\nggml-hex: graph-compute %s is not supported\n", ggml_op_desc(node));
         }
diff --git a/ggml/src/ggml-hexagon/htp/binary-ops.c b/ggml/src/ggml-hexagon/htp/binary-ops.c
index 92c0109d287..8ed7f67d9c8 100644
--- a/ggml/src/ggml-hexagon/htp/binary-ops.c
+++ b/ggml/src/ggml-hexagon/htp/binary-ops.c
@@ -34,6 +34,11 @@ static hvx_elemwise_f32_func func_table_HVX[]     = { hvx_mul_f32, hvx_add_f32,
 static hvx_elemwise_f32_func func_table_HVX_opt[] = { hvx_mul_f32_opt, hvx_add_f32_opt, hvx_sub_f32_opt };
 
 #define htp_binary_preamble            \
+    const struct htp_tensor * src0 = &octx->src0; \
+    const struct htp_tensor * src1 = &octx->src1; \
+    const struct htp_tensor * src2 = &octx->src2; \
+    struct htp_tensor *       dst  = &octx->dst;  \
+                                       \
     const uint32_t ne00 = src0->ne[0]; \
     const uint32_t ne01 = src0->ne[1]; \
     const uint32_t ne02 = src0->ne[2]; \
@@ -62,16 +67,15 @@ static hvx_elemwise_f32_func func_table_HVX_opt[] = { hvx_mul_f32_opt, hvx_add_f
     const uint32_t nb0 = dst->nb[0];   \
     const uint32_t nb1 = dst->nb[1];   \
     const uint32_t nb2 = dst->nb[2];   \
-    const uint32_t nb3 = dst->nb[3];
-
-static void binary_job_f32_per_thread(const struct htp_tensor * src0,
-                                      const struct htp_tensor * src1,
-                                      struct htp_tensor *       dst,
-                                      uint8_t *                 spad_data,
-                                      uint32_t                  nth,
-                                      uint32_t                  ith,
-                                      uint32_t                  src0_nrows_per_thread,
-                                      enum htp_op               op) {
+    const uint32_t nb3 = dst->nb[3];   \
+                                       \
+    const uint32_t src0_nrows_per_thread = octx->src0_nrows_per_thread;
+
+static void binary_job_f32_per_thread(struct htp_ops_context * octx,
+                                      uint8_t *                spad_data,
+                                      uint32_t                 nth,
+                                      uint32_t                 ith,
+                                      enum htp_op              op) {
     htp_binary_preamble;
 
     const size_t src0_row_size = nb01;
@@ -107,16 +111,23 @@ static void binary_job_f32_per_thread(const struct htp_tensor * src0,
 
     uint8_t * restrict spad_data_th = spad_data + (ith * src0_row_size);
 
-    const uint32_t nr0 = ne00 / ne10;
-
     const uint8_t * restrict src0_ptr = (const uint8_t *) src0->data + (src0_start_row * src0_row_size);
     uint8_t * restrict dst_ptr        = (uint8_t *) dst->data + (src0_start_row * dst_row_size);
 
     const uint8_t * restrict data_src1 = (const uint8_t *) src1->data;
-    const uint8_t * restrict src1_ptr  = NULL;
+
+    const uint32_t ne02_ne01 = ne02 * ne01;
 
     for (uint32_t ir = src0_start_row; ir < src0_end_row; ir++) {
-        src1_ptr = data_src1 + (ir % src1_nrows) * src1_row_size;
+        const uint32_t i03 = fastdiv(ir, &octx->src0_div21);
+        const uint32_t i02 = fastdiv(ir - i03 * ne02_ne01, &octx->src0_div1);
+        const uint32_t i01 = (ir - i03 * ne02_ne01 - i02 * ne01);
+
+        const uint32_t i13 = fastmodulo(i03, ne13, &octx->src1_div3);
+        const uint32_t i12 = fastmodulo(i02, ne12, &octx->src1_div2);
+        const uint32_t i11 = fastmodulo(i01, ne11, &octx->src1_div1);
+
+        const uint8_t * restrict src1_ptr = data_src1 + i13 * nb13 + i12 * nb12 + i11 * src1_row_size;
 
         if (ir + 1 < src0_end_row) {
             htp_l2fetch(src0_ptr + ne00, 1, src0_row_size, src0_row_size);
@@ -125,6 +136,7 @@ static void binary_job_f32_per_thread(const struct htp_tensor * src0,
             }
         }
 
+        const uint32_t nr0 = ne00 / ne10;
         if (nr0 > 1) {
             if ((1 == is_aligned) && (nr0 == ne00)) {
                 hvx_bcast_fp32_a(spad_data_th, *(float *) src1_ptr, nr0);
@@ -149,22 +161,17 @@ static void binary_job_f32_per_thread(const struct htp_tensor * src0,
          (unsigned) HAP_perf_qtimer_count_to_us(t2 - t1));
 }
 
-static void binary_add_id_job_f32_per_thread(const struct htp_tensor * src0,
-                                             const struct htp_tensor * src1,
-                                             const struct htp_tensor * src2,
-                                             struct htp_tensor *       dst,
-                                             uint8_t *                 spad_data,
-                                             uint32_t                  nth,
-                                             uint32_t                  ith,
-                                             uint32_t                  src0_nrows_per_thread,
-                                             hvx_elemwise_f32_func     func_HVX) {
+static void binary_add_id_job_f32_per_thread(struct htp_ops_context * octx,
+                                             uint8_t *                spad_data,
+                                             uint32_t                 nth,
+                                             uint32_t                 ith,
+                                             hvx_elemwise_f32_func    func_HVX) {
     htp_binary_preamble;
 
     const size_t src0_row_size = nb01;
     const size_t src1_row_size = nb11;
     const size_t dst_row_size  = nb1;
 
-    const uint32_t ne02_ne01  = ne02 * ne01;
     const uint32_t src0_nrows = ne01 * ne02 * ne03;  // src0 rows
 
     const uint32_t src0_start_row = src0_nrows_per_thread * ith;
@@ -187,10 +194,11 @@ static void binary_add_id_job_f32_per_thread(const struct htp_tensor * src0,
     const uint8_t * restrict data_src1 = (const uint8_t *) src1->data;
     uint8_t * restrict data_dst        = (uint8_t *) dst->data;
 
+    const uint32_t ne02_ne01  = ne02 * ne01;
     for (uint32_t ir = src0_start_row; ir < src0_end_row; ir++) {
         // src0 indices
-        const uint32_t i03 = ir / ne02_ne01;
-        const uint32_t i02 = (ir - i03 * ne02_ne01) / ne01;
+        const uint32_t i03 = fastdiv(ir, &octx->src0_div21);
+        const uint32_t i02 = fastdiv(ir - i03 * ne02_ne01, &octx->src0_div1);
         const uint32_t i01 = (ir - i03 * ne02_ne01 - i02 * ne01);
 
         // src1 indices
@@ -234,13 +242,11 @@ static void binary_job_dispatcher_f32(unsigned int n, unsigned int i, void * dat
         case HTP_OP_MUL:
         case HTP_OP_ADD:
         case HTP_OP_SUB:
-            binary_job_f32_per_thread(&octx->src0, &octx->src1, &octx->dst, octx->src1_spad.data, n, i,
-                                      octx->src0_nrows_per_thread, octx->op);
+            binary_job_f32_per_thread(octx, octx->src1_spad.data, n, i, octx->op);
             break;
 
         case HTP_OP_ADD_ID:
-            binary_add_id_job_f32_per_thread(&octx->src0, &octx->src1, &octx->src2, &octx->dst, octx->src0_spad.data, n,
-                                             i, octx->src0_nrows_per_thread, hvx_add_f32);
+            binary_add_id_job_f32_per_thread(octx, octx->src0_spad.data, n, i, hvx_add_f32);
             break;
 
         default:
@@ -321,6 +327,16 @@ static int execute_op_binary_f32(struct htp_ops_context * octx) {
 
         octx->src0_nrows_per_thread = (src0_nrows + n_jobs - 1) / n_jobs;
 
+        octx->src0_div21 = init_fastdiv_values(src0->ne[2] * src0->ne[1]);
+        octx->src0_div3  = init_fastdiv_values(src0->ne[3]);
+        octx->src0_div2  = init_fastdiv_values(src0->ne[2]);
+        octx->src0_div1  = init_fastdiv_values(src0->ne[1]);
+
+        octx->src1_div21 = init_fastdiv_values(src1->ne[2] * src1->ne[1]);
+        octx->src1_div3  = init_fastdiv_values(src1->ne[3]);
+        octx->src1_div2  = init_fastdiv_values(src1->ne[2]);
+        octx->src1_div1  = init_fastdiv_values(src1->ne[1]);
+
         worker_pool_run_func(octx->ctx->worker_pool, binary_op_func, octx, n_jobs);
     }
 
diff --git a/ggml/src/ggml-hexagon/htp/htp-msg.h b/ggml/src/ggml-hexagon/htp/htp-msg.h
index f23d5788068..9278f41f4e1 100644
--- a/ggml/src/ggml-hexagon/htp/htp-msg.h
+++ b/ggml/src/ggml-hexagon/htp/htp-msg.h
@@ -119,10 +119,10 @@ static const char * htp_type_name(uint32_t t) {
 #define HTP_MAX_DIMS 4
 
 struct htp_tensor {
-    uint32_t data;              // Buffer offset in the messages, and data pointer on the NSP
-    uint32_t type;              // Data type
-    uint32_t ne[HTP_MAX_DIMS];  // Number of elements
-    uint32_t nb[HTP_MAX_DIMS];  // Stride in bytes (see ggml.h ggml_tensor)
+    uint32_t data;                // Buffer offset in the messages, and data pointer on the NSP
+    uint32_t type;                // Data type
+    uint32_t ne[HTP_MAX_DIMS];    // Number of elements
+    uint32_t nb[HTP_MAX_DIMS];    // Stride in bytes (see ggml.h ggml_tensor)
 };
 
 #define HTP_MAX_OP_PARAMS 64
diff --git a/ggml/src/ggml-hexagon/htp/htp-ops.h b/ggml/src/ggml-hexagon/htp/htp-ops.h
index 45723196791..e87657436f0 100644
--- a/ggml/src/ggml-hexagon/htp/htp-ops.h
+++ b/ggml/src/ggml-hexagon/htp/htp-ops.h
@@ -4,6 +4,7 @@
 #include "htp-ctx.h"
 #include "htp-msg.h"
 #include "worker-pool.h"
+#include "ops-utils.h"
 
 #include <assert.h>
 #include <stdint.h>
@@ -38,6 +39,16 @@ struct htp_ops_context {
     uint32_t src0_nrows_per_thread;
     uint32_t src1_nrows_per_thread;
 
+    struct fastdiv_values src0_div1;  // fastdiv values for ne1
+    struct fastdiv_values src0_div2;  // fastdiv values for ne2
+    struct fastdiv_values src0_div3;  // fastdiv values for ne3
+    struct fastdiv_values src0_div21; // fastdiv values for ne2 * ne1
+
+    struct fastdiv_values src1_div1;  // fastdiv values for ne1
+    struct fastdiv_values src1_div2;  // fastdiv values for ne2
+    struct fastdiv_values src1_div3;  // fastdiv values for ne3
+    struct fastdiv_values src1_div21; // fastdiv values for ne2 * ne1
+
     uint32_t flags;
 };
 
diff --git a/ggml/src/ggml-hexagon/htp/ops-utils.h b/ggml/src/ggml-hexagon/htp/ops-utils.h
index 302f1625216..af9c3305f61 100644
--- a/ggml/src/ggml-hexagon/htp/ops-utils.h
+++ b/ggml/src/ggml-hexagon/htp/ops-utils.h
@@ -31,6 +31,39 @@ static inline uint32_t htp_round_up(uint32_t n, uint32_t m) {
     return m * ((n + m - 1) / m);
 }
 
+// See https://gmplib.org/~tege/divcnst-pldi94.pdf figure 4.1.
+// Precompute mp (m' in the paper) and L such that division
+// can be computed using a multiply (high 32b of 64b result)
+// and a shift:
+//
+// n/d = (mulhi(n, mp) + n) >> L;
+struct fastdiv_values {
+    uint32_t mp;
+    uint32_t l;
+};
+
+static inline struct fastdiv_values init_fastdiv_values(uint32_t d) {
+    struct fastdiv_values result = { 0, 0 };
+    // compute L = ceil(log2(d));
+    while (result.l < 32 && ((uint32_t) 1 << result.l) < d) {
+        ++(result.l);
+    }
+
+    result.mp = (uint32_t) (((uint64_t) 1 << 32) * (((uint64_t) 1 << result.l) - d) / d + 1);
+    return result;
+}
+
+static inline uint32_t fastdiv(uint32_t n, const struct fastdiv_values * vals) {
+    // Compute high 32 bits of n * mp
+    const uint32_t hi = (uint32_t) (((uint64_t) n * vals->mp) >> 32);  // mulhi(n, mp)
+    // add n, apply bit shift
+    return (hi + n) >> vals->l;
+}
+
+static inline uint32_t fastmodulo(uint32_t n, uint32_t d, const struct fastdiv_values * vals) {
+    return n - fastdiv(n, vals) * d;
+}
+
 static inline void htp_l2fetch(const void * p, uint32_t height, uint32_t width, uint32_t stride) {
     const uint64_t control = Q6_P_combine_RR(stride, Q6_R_combine_RlRl(width, height));
     asm volatile(" l2fetch(%0,%1) " : : "r"(p), "r"(control));

From 23a46ce972cd1fa08e967f17ee9e024e87dcaadb Mon Sep 17 00:00:00 2001
From: Raul Torres <138264735+rauletorresc@users.noreply.github.com>
Date: Wed, 12 Nov 2025 06:37:52 +0000
Subject: [PATCH 163/185] CANN: GGML_CANN_ACL_GRAPH works only USE_ACL_GRAPH
 enabled (#16861)

The documentation should state that `GGML_CANN_ACL_GRAPH` is only effective if `USE_ACL_GRAPH` was enabled at compilation time.
---
 docs/backend/CANN.md | 7 ++++++-
 1 file changed, 6 insertions(+), 1 deletion(-)

diff --git a/docs/backend/CANN.md b/docs/backend/CANN.md
index e45fc7dd28f..37dcfaef9a8 100755
--- a/docs/backend/CANN.md
+++ b/docs/backend/CANN.md
@@ -313,7 +313,12 @@ Converting the matmul weight format from ND to NZ to improve performance. Enable
 
 ### GGML_CANN_ACL_GRAPH
 
-Operators are executed using ACL graph execution, rather than in op-by-op (eager) mode. Enabled by default.
+Operators are executed using ACL graph execution, rather than in op-by-op (eager) mode. Enabled by default. This option is only effective if `USE_ACL_GRAPH` was enabled at compilation time. To enable it, recompile using:
+
+```sh
+cmake -B build -DGGML_CANN=on -DCMAKE_BUILD_TYPE=release -DUSE_ACL_GRAPH=ON
+cmake --build build --config release
+```
 
 ### GGML_CANN_GRAPH_CACHE_CAPACITY
 

From 5da7664960f93a5602d166326f6375dd7cc112ad Mon Sep 17 00:00:00 2001
From: Neo Zhang Jianyu <jianyu.zhang@intel.com>
Date: Wed, 12 Nov 2025 14:44:29 +0800
Subject: [PATCH 164/185] [SYCL]fix ci crash about SSM_CONV (#17169)
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

* fix ci crash

* Update ggml-sycl.cpp

* Update ggml/src/ggml-sycl/ggml-sycl.cpp

Co-authored-by: Sigbjørn Skjæret <sigbjorn.skjaeret@scala.com>

---------

Co-authored-by: Zhang Jianyu <zhang.jianyu@outlook.com>
Co-authored-by: Sigbjørn Skjæret <sigbjorn.skjaeret@scala.com>
---
 ggml/src/ggml-sycl/ggml-sycl.cpp | 1 +
 1 file changed, 1 insertion(+)

diff --git a/ggml/src/ggml-sycl/ggml-sycl.cpp b/ggml/src/ggml-sycl/ggml-sycl.cpp
index f3b3e365740..941fd41c0d0 100644
--- a/ggml/src/ggml-sycl/ggml-sycl.cpp
+++ b/ggml/src/ggml-sycl/ggml-sycl.cpp
@@ -3933,6 +3933,7 @@ static bool ggml_sycl_compute_forward(ggml_backend_sycl_context & ctx, struct gg
             break;
         case GGML_OP_SSM_CONV:
             ggml_sycl_ssm_conv(ctx, dst);
+            break;
         case GGML_OP_ROLL:
             ggml_sycl_roll(ctx, dst);
             break;

From 655cddd174ab49643aaa6b8e20ca28fd3be254a6 Mon Sep 17 00:00:00 2001
From: TecJesh <qdvm5gl@163.com>
Date: Wed, 12 Nov 2025 15:11:42 +0800
Subject: [PATCH 165/185] CANN: Add L2_NORM op support (#16856)

* update L2_NORM op support

* update L2_NORM op support

* remove extra whitespace
---
 ggml/src/ggml-cann/aclnn_ops.cpp | 29 +++++++++++++++++++++++++++++
 ggml/src/ggml-cann/aclnn_ops.h   | 24 ++++++++++++++++++++++++
 ggml/src/ggml-cann/ggml-cann.cpp |  4 ++++
 3 files changed, 57 insertions(+)

diff --git a/ggml/src/ggml-cann/aclnn_ops.cpp b/ggml/src/ggml-cann/aclnn_ops.cpp
index 5df6dc96a3b..4835c5c0387 100644
--- a/ggml/src/ggml-cann/aclnn_ops.cpp
+++ b/ggml/src/ggml-cann/aclnn_ops.cpp
@@ -448,6 +448,35 @@ void ggml_cann_norm(ggml_backend_cann_context & ctx, ggml_tensor * dst) {
     ggml_cann_release_resources(ctx, norm, acl_src, acl_dst);
 }
 
+void ggml_cann_l2_norm(ggml_backend_cann_context & ctx, ggml_tensor * dst) {
+    ggml_tensor * src = dst->src[0];
+
+    aclTensor * acl_src = ggml_cann_create_tensor(src);
+    aclTensor * acl_dst = ggml_cann_create_tensor(dst);
+
+    size_t  type_size = ggml_type_size(src->type);
+    int64_t n_bytes   = src->ne[3]* src->ne[2]* src->ne[1]* type_size;
+    ggml_cann_pool_alloc temp_buffer_allocator(ctx.pool(), n_bytes);
+    void *               buffer       = temp_buffer_allocator.get();
+
+    int64_t div_ne[] = {1, src->ne[1], src->ne[2], src->ne[3]};
+    size_t  div_nb[GGML_MAX_DIMS];
+    div_nb[0] = sizeof(float);
+    for (int i = 1; i < GGML_MAX_DIMS; ++i) {
+        div_nb[i] = div_nb[i - 1] * div_ne[i - 1];
+    }
+    aclTensor *          acl_div      = ggml_cann_create_tensor(buffer, ACL_FLOAT, type_size, div_ne, div_nb, GGML_MAX_DIMS);
+
+    std::vector<int64_t> norm_dims = { 3 };
+    aclIntArray * dims_array = aclCreateIntArray(norm_dims.data(), norm_dims.size());
+
+    float p_value = 2.0f;
+    aclScalar * p_scalar = aclCreateScalar(&p_value, aclDataType::ACL_FLOAT);
+    GGML_CANN_CALL_ACLNN_OP(ctx, Norm, acl_src, p_scalar, dims_array, true, acl_div);
+    GGML_CANN_CALL_ACLNN_OP(ctx, Div, acl_src, acl_div, acl_dst);
+    ggml_cann_release_resources(ctx, dims_array, p_scalar, acl_src, acl_dst, acl_div);
+}
+
 void ggml_cann_group_norm(ggml_backend_cann_context & ctx, ggml_tensor * dst) {
     ggml_tensor * src = dst->src[0];
 
diff --git a/ggml/src/ggml-cann/aclnn_ops.h b/ggml/src/ggml-cann/aclnn_ops.h
index ec7455af88c..060eedbbb02 100644
--- a/ggml/src/ggml-cann/aclnn_ops.h
+++ b/ggml/src/ggml-cann/aclnn_ops.h
@@ -46,6 +46,7 @@
 #include <aclnnop/aclnn_cos.h>
 #include <aclnnop/aclnn_log.h>
 #include <aclnnop/aclnn_sign.h>
+#include <aclnnop/aclnn_norm.h>
 #include "acl_tensor.h"
 #include "common.h"
 
@@ -187,6 +188,29 @@ void ggml_cann_argsort(ggml_backend_cann_context & ctx, ggml_tensor * dst);
  */
 void ggml_cann_norm(ggml_backend_cann_context & ctx, ggml_tensor * dst);
 
+/**
+ * @brief   Computes the L2 Normalization for a ggml tensor using the CANN
+ *          backend.
+ *
+ * @details This function applies the L2 Normalization operation on the
+ *          input tensor `src` and stores the result in the destination tensor
+ *          `dst`. L2 Normalization scales the input tensor such that the
+ *          L2 norm along the specified dimension equals 1. This operation
+ *          is commonly used in neural networks for feature normalization
+ *          and vector scaling.
+ *          The operation is defined as:
+ *          \f[
+ *              \text{out} = \frac{x}{\sqrt{\sum{x^2}}}
+ *          \f]
+ *          The normalization is performed along the last dimension by default.
+ *
+ * @param ctx The CANN context used for operations.
+ * @param dst The destination tensor where the normalized values will be stored.
+ * @attention The normalization is performed along the last dimension of the
+ *            input tensor by default.
+ */
+void ggml_cann_l2_norm(ggml_backend_cann_context & ctx, ggml_tensor * dst);
+
 /**
  * @brief  Computes the Group Normalization for a ggml tensor using the CANN
  *         backend.
diff --git a/ggml/src/ggml-cann/ggml-cann.cpp b/ggml/src/ggml-cann/ggml-cann.cpp
index 51345742ee5..9de9440ac65 100644
--- a/ggml/src/ggml-cann/ggml-cann.cpp
+++ b/ggml/src/ggml-cann/ggml-cann.cpp
@@ -1777,6 +1777,9 @@ static bool ggml_cann_compute_forward(ggml_backend_cann_context & ctx, struct gg
         case GGML_OP_GROUP_NORM:
             ggml_cann_group_norm(ctx, dst);
             break;
+        case GGML_OP_L2_NORM:
+            ggml_cann_l2_norm(ctx, dst);
+            break;
         case GGML_OP_CONCAT:
             ggml_cann_concat(ctx, dst);
             break;
@@ -2515,6 +2518,7 @@ static bool ggml_backend_cann_supports_op(ggml_backend_dev_t dev, const ggml_ten
                 // value of paddingW should be at most half of kernelW
                 return (p0 <= (k0 / 2)) && (p1 <= (k1 / 2));
             }
+        case GGML_OP_L2_NORM:
         case GGML_OP_DUP:
         case GGML_OP_SUM:
         case GGML_OP_IM2COL:

From 78010a0d52ad03cd469448df89101579b225582c Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Adrien=20Gallou=C3=ABt?= <angt@huggingface.co>
Date: Wed, 12 Nov 2025 12:32:50 +0100
Subject: [PATCH 166/185] cmake : move OpenSSL linking to vendor/cpp-httplib
 (#17177)
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

* cmake : move OpenSSL linking to vendor/cpp-httplib

Signed-off-by: Adrien Gallouët <angt@huggingface.co>

* bring back httplib 0.27.0

* add -DLLAMA_HTTPLIB

* update cmake config for visionos

---------

Signed-off-by: Adrien Gallouët <angt@huggingface.co>
Co-authored-by: Xuan Son Nguyen <son@huggingface.co>
---
 CMakeLists.txt                    |    5 +-
 build-xcframework.sh              |    4 +
 common/CMakeLists.txt             |   40 +-
 common/download.cpp               |   76 +-
 scripts/sync_vendor.py            |    2 +-
 tools/server/CMakeLists.txt       |    4 +
 vendor/cpp-httplib/CMakeLists.txt |   38 +-
 vendor/cpp-httplib/httplib.cpp    | 3147 +++++++++++++++++++++--------
 vendor/cpp-httplib/httplib.h      |  842 ++++----
 9 files changed, 2866 insertions(+), 1292 deletions(-)

diff --git a/CMakeLists.txt b/CMakeLists.txt
index e7410184dfa..3278c4a72c1 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -92,6 +92,7 @@ option(LLAMA_TOOLS_INSTALL  "llama: install tools"        ${LLAMA_TOOLS_INSTALL_
 
 # 3rd party libs
 option(LLAMA_CURL       "llama: use libcurl to download model from an URL" ON)
+option(LLAMA_HTTPLIB    "llama: if libcurl is disabled, use httplib to download model from an URL" ON)
 option(LLAMA_OPENSSL    "llama: use openssl to support HTTPS" OFF)
 option(LLAMA_LLGUIDANCE "llama-common: include LLGuidance library for structured output in common utils" OFF)
 
@@ -200,7 +201,9 @@ endif()
 
 if (LLAMA_BUILD_COMMON)
     add_subdirectory(common)
-    add_subdirectory(vendor/cpp-httplib)
+    if (LLAMA_HTTPLIB)
+        add_subdirectory(vendor/cpp-httplib)
+    endif()
 endif()
 
 if (LLAMA_BUILD_COMMON AND LLAMA_BUILD_TESTS AND NOT CMAKE_JS_VERSION)
diff --git a/build-xcframework.sh b/build-xcframework.sh
index 796f8016ca6..81280f74977 100755
--- a/build-xcframework.sh
+++ b/build-xcframework.sh
@@ -454,6 +454,8 @@ cmake -B build-visionos -G Xcode \
     -DCMAKE_C_FLAGS="-D_XOPEN_SOURCE=700 ${COMMON_C_FLAGS}" \
     -DCMAKE_CXX_FLAGS="-D_XOPEN_SOURCE=700 ${COMMON_CXX_FLAGS}" \
     -DLLAMA_CURL=OFF \
+    -DLLAMA_HTTPLIB=OFF \
+    -DLLAMA_BUILD_SERVER=OFF \
     -S .
 cmake --build build-visionos --config Release -- -quiet
 
@@ -468,6 +470,8 @@ cmake -B build-visionos-sim -G Xcode \
     -DCMAKE_C_FLAGS="-D_XOPEN_SOURCE=700 ${COMMON_C_FLAGS}" \
     -DCMAKE_CXX_FLAGS="-D_XOPEN_SOURCE=700 ${COMMON_CXX_FLAGS}" \
     -DLLAMA_CURL=OFF \
+    -DLLAMA_HTTPLIB=OFF \
+    -DLLAMA_BUILD_SERVER=OFF \
     -S .
 cmake --build build-visionos-sim --config Release -- -quiet
 
diff --git a/common/CMakeLists.txt b/common/CMakeLists.txt
index 1d260507ad5..0c34ce1151c 100644
--- a/common/CMakeLists.txt
+++ b/common/CMakeLists.txt
@@ -91,47 +91,13 @@ if (LLAMA_CURL)
     target_compile_definitions(${TARGET} PUBLIC LLAMA_USE_CURL)
     include_directories(${CURL_INCLUDE_DIRS})
     set(LLAMA_COMMON_EXTRA_LIBS ${LLAMA_COMMON_EXTRA_LIBS} ${CURL_LIBRARIES})
-else()
+elseif (LLAMA_HTTPLIB)
     # otherwise, use cpp-httplib
+    message(FATAL "test")
+    target_compile_definitions(${TARGET} PUBLIC LLAMA_USE_HTTPLIB)
     set(LLAMA_COMMON_EXTRA_LIBS ${LLAMA_COMMON_EXTRA_LIBS} cpp-httplib)
 endif()
 
-if (LLAMA_OPENSSL)
-    find_package(OpenSSL)
-    if (OpenSSL_FOUND)
-        include(CheckCSourceCompiles)
-        set(SAVED_CMAKE_REQUIRED_INCLUDES ${CMAKE_REQUIRED_INCLUDES})
-        set(CMAKE_REQUIRED_INCLUDES ${OPENSSL_INCLUDE_DIR})
-        check_c_source_compiles("
-        #include <openssl/opensslv.h>
-        #if defined(OPENSSL_IS_BORINGSSL) || defined(LIBRESSL_VERSION_NUMBER)
-        #    if OPENSSL_VERSION_NUMBER < 0x1010107f
-        #        error bad version
-        #    endif
-        #else
-        #    if OPENSSL_VERSION_NUMBER < 0x30000000L
-        #        error bad version
-        #    endif
-        #endif
-        int main() { return 0; }
-        " OPENSSL_VERSION_SUPPORTED)
-        set(CMAKE_REQUIRED_INCLUDES ${SAVED_CMAKE_REQUIRED_INCLUDES})
-        if (OPENSSL_VERSION_SUPPORTED)
-            message(STATUS "OpenSSL found: ${OPENSSL_VERSION}")
-            target_compile_definitions(${TARGET} PUBLIC CPPHTTPLIB_OPENSSL_SUPPORT)
-            target_link_libraries(${TARGET} PUBLIC OpenSSL::SSL OpenSSL::Crypto)
-            if (APPLE AND CMAKE_SYSTEM_NAME STREQUAL "Darwin")
-                target_compile_definitions(${TARGET} PUBLIC CPPHTTPLIB_USE_CERTS_FROM_MACOSX_KEYCHAIN)
-                find_library(CORE_FOUNDATION_FRAMEWORK CoreFoundation REQUIRED)
-                find_library(SECURITY_FRAMEWORK Security REQUIRED)
-                target_link_libraries(${TARGET} PUBLIC ${CORE_FOUNDATION_FRAMEWORK} ${SECURITY_FRAMEWORK})
-            endif()
-        endif()
-    else()
-        message(STATUS "OpenSSL not found, SSL support disabled")
-    endif()
-endif()
-
 if (LLAMA_LLGUIDANCE)
     include(ExternalProject)
     set(LLGUIDANCE_SRC ${CMAKE_BINARY_DIR}/llguidance/source)
diff --git a/common/download.cpp b/common/download.cpp
index 57308a5c6d5..eeb32b6a863 100644
--- a/common/download.cpp
+++ b/common/download.cpp
@@ -20,7 +20,7 @@
 #if defined(LLAMA_USE_CURL)
 #include <curl/curl.h>
 #include <curl/easy.h>
-#else
+#elif defined(LLAMA_USE_HTTPLIB)
 #include "http.h"
 #endif
 
@@ -467,7 +467,7 @@ std::pair<long, std::vector<char>> common_remote_get_content(const std::string &
     return { res_code, std::move(res_buffer) };
 }
 
-#else
+#elif defined(LLAMA_USE_HTTPLIB)
 
 static bool is_output_a_tty() {
 #if defined(_WIN32)
@@ -713,6 +713,8 @@ std::pair<long, std::vector<char>> common_remote_get_content(const std::string
 
 #endif // LLAMA_USE_CURL
 
+#if defined(LLAMA_USE_CURL) || defined(LLAMA_USE_HTTPLIB)
+
 static bool common_download_file_single(const std::string & url,
                                         const std::string & path,
                                         const std::string & bearer_token,
@@ -907,33 +909,6 @@ common_hf_file_res common_get_hf_file(const std::string & hf_repo_with_tag, cons
     return { hf_repo, ggufFile, mmprojFile };
 }
 
-std::vector<common_cached_model_info> common_list_cached_models() {
-    std::vector<common_cached_model_info> models;
-    const std::string cache_dir = fs_get_cache_directory();
-    const std::vector<common_file_info> files = fs_list_files(cache_dir);
-    for (const auto & file : files) {
-        if (string_starts_with(file.name, "manifest=") && string_ends_with(file.name, ".json")) {
-            common_cached_model_info model_info;
-            model_info.manifest_path = file.path;
-            std::string fname = file.name;
-            string_replace_all(fname, ".json", ""); // remove extension
-            auto parts = string_split<std::string>(fname, '=');
-            if (parts.size() == 4) {
-                // expect format: manifest=<user>=<model>=<tag>=<other>
-                model_info.user  = parts[1];
-                model_info.model = parts[2];
-                model_info.tag   = parts[3];
-            } else {
-                // invalid format
-                continue;
-            }
-            model_info.size = 0; // TODO: get GGUF size, not manifest size
-            models.push_back(model_info);
-        }
-    }
-    return models;
-}
-
 //
 // Docker registry functions
 //
@@ -1052,3 +1027,46 @@ std::string common_docker_resolve_model(const std::string & docker) {
         throw;
     }
 }
+
+#else
+
+common_hf_file_res common_get_hf_file(const std::string &, const std::string &, bool) {
+    throw std::runtime_error("download functionality is not enabled in this build");
+}
+
+bool common_download_model(const common_params_model &, const std::string &, bool) {
+    throw std::runtime_error("download functionality is not enabled in this build");
+}
+
+std::string common_docker_resolve_model(const std::string &) {
+    throw std::runtime_error("download functionality is not enabled in this build");
+}
+
+#endif // LLAMA_USE_CURL || LLAMA_USE_HTTPLIB
+
+std::vector<common_cached_model_info> common_list_cached_models() {
+    std::vector<common_cached_model_info> models;
+    const std::string cache_dir = fs_get_cache_directory();
+    const std::vector<common_file_info> files = fs_list_files(cache_dir);
+    for (const auto & file : files) {
+        if (string_starts_with(file.name, "manifest=") && string_ends_with(file.name, ".json")) {
+            common_cached_model_info model_info;
+            model_info.manifest_path = file.path;
+            std::string fname = file.name;
+            string_replace_all(fname, ".json", ""); // remove extension
+            auto parts = string_split<std::string>(fname, '=');
+            if (parts.size() == 4) {
+                // expect format: manifest=<user>=<model>=<tag>=<other>
+                model_info.user  = parts[1];
+                model_info.model = parts[2];
+                model_info.tag   = parts[3];
+            } else {
+                // invalid format
+                continue;
+            }
+            model_info.size = 0; // TODO: get GGUF size, not manifest size
+            models.push_back(model_info);
+        }
+    }
+    return models;
+}
diff --git a/scripts/sync_vendor.py b/scripts/sync_vendor.py
index b578cf1e6af..ac94387dd2f 100755
--- a/scripts/sync_vendor.py
+++ b/scripts/sync_vendor.py
@@ -14,7 +14,7 @@
 
     "https://github.com/mackron/miniaudio/raw/refs/tags/0.11.22/miniaudio.h": "vendor/miniaudio/miniaudio.h",
 
-    "https://raw.githubusercontent.com/yhirose/cpp-httplib/refs/tags/v0.20.1/httplib.h": "vendor/cpp-httplib/httplib.h",
+    "https://raw.githubusercontent.com/yhirose/cpp-httplib/refs/tags/v0.27.0/httplib.h": "vendor/cpp-httplib/httplib.h",
 }
 
 for url, filename in vendor.items():
diff --git a/tools/server/CMakeLists.txt b/tools/server/CMakeLists.txt
index 5f8a50320d1..c801e84c3d4 100644
--- a/tools/server/CMakeLists.txt
+++ b/tools/server/CMakeLists.txt
@@ -7,6 +7,10 @@ if (MINGW)
     add_compile_definitions(_WIN32_WINNT=${GGML_WIN_VER})
 endif()
 
+if (NOT LLAMA_HTTPLIB)
+    message(FATAL_ERROR "LLAMA_HTTPLIB is OFF, cannot build llama-server. Hint: to skip building server, set -DLLAMA_BUILD_SERVER=OFF")
+endif()
+
 set(TARGET_SRCS
     server.cpp
     utils.hpp
diff --git a/vendor/cpp-httplib/CMakeLists.txt b/vendor/cpp-httplib/CMakeLists.txt
index 0033d52371f..3b42fc8c1dc 100644
--- a/vendor/cpp-httplib/CMakeLists.txt
+++ b/vendor/cpp-httplib/CMakeLists.txt
@@ -22,7 +22,39 @@ target_compile_definitions(${TARGET} PRIVATE
     CPPHTTPLIB_TCP_NODELAY=1
 )
 
-if (${CMAKE_SYSTEM_NAME} MATCHES "visionOS")
-    # quick fix for https://github.com/ggml-org/llama.cpp/actions/runs/19247291428/job/55024294176?pr=17150
-    target_compile_definitions(${TARGET} PRIVATE NI_MAXHOST=1025)
+if (LLAMA_OPENSSL)
+    find_package(OpenSSL)
+    if (OpenSSL_FOUND)
+        include(CheckCSourceCompiles)
+        set(SAVED_CMAKE_REQUIRED_INCLUDES ${CMAKE_REQUIRED_INCLUDES})
+        set(CMAKE_REQUIRED_INCLUDES ${OPENSSL_INCLUDE_DIR})
+        check_c_source_compiles("
+        #include <openssl/opensslv.h>
+        #if defined(OPENSSL_IS_BORINGSSL) || defined(LIBRESSL_VERSION_NUMBER)
+        #    if OPENSSL_VERSION_NUMBER < 0x1010107f
+        #        error bad version
+        #    endif
+        #else
+        #    if OPENSSL_VERSION_NUMBER < 0x30000000L
+        #        error bad version
+        #    endif
+        #endif
+        int main() { return 0; }
+        " OPENSSL_VERSION_SUPPORTED)
+        set(CMAKE_REQUIRED_INCLUDES ${SAVED_CMAKE_REQUIRED_INCLUDES})
+        if (OPENSSL_VERSION_SUPPORTED)
+            message(STATUS "OpenSSL found: ${OPENSSL_VERSION}")
+            target_compile_definitions(${TARGET} PUBLIC CPPHTTPLIB_OPENSSL_SUPPORT)
+            target_link_libraries(${TARGET} PUBLIC OpenSSL::SSL OpenSSL::Crypto)
+            if (APPLE AND CMAKE_SYSTEM_NAME STREQUAL "Darwin")
+                target_compile_definitions(${TARGET} PUBLIC CPPHTTPLIB_USE_CERTS_FROM_MACOSX_KEYCHAIN)
+                find_library(CORE_FOUNDATION_FRAMEWORK CoreFoundation REQUIRED)
+                find_library(SECURITY_FRAMEWORK Security REQUIRED)
+                target_link_libraries(${TARGET} PUBLIC ${CORE_FOUNDATION_FRAMEWORK} ${SECURITY_FRAMEWORK})
+            endif()
+        endif()
+    else()
+        message(STATUS "OpenSSL not found, SSL support disabled")
+    endif()
 endif()
+
diff --git a/vendor/cpp-httplib/httplib.cpp b/vendor/cpp-httplib/httplib.cpp
index e5c84d2b221..5432db69b4b 100644
--- a/vendor/cpp-httplib/httplib.cpp
+++ b/vendor/cpp-httplib/httplib.cpp
@@ -168,28 +168,7 @@ bool FileStat::is_dir() const {
   return ret_ >= 0 && S_ISDIR(st_.st_mode);
 }
 
-std::string encode_query_param(const std::string &value) {
-  std::ostringstream escaped;
-  escaped.fill('0');
-  escaped << std::hex;
-
-  for (auto c : value) {
-    if (std::isalnum(static_cast<uint8_t>(c)) || c == '-' || c == '_' ||
-        c == '.' || c == '!' || c == '~' || c == '*' || c == '\'' || c == '(' ||
-        c == ')') {
-      escaped << c;
-    } else {
-      escaped << std::uppercase;
-      escaped << '%' << std::setw(2)
-              << static_cast<int>(static_cast<unsigned char>(c));
-      escaped << std::nouppercase;
-    }
-  }
-
-  return escaped.str();
-}
-
-std::string encode_url(const std::string &s) {
+std::string encode_path(const std::string &s) {
   std::string result;
   result.reserve(s.size());
 
@@ -221,43 +200,6 @@ std::string encode_url(const std::string &s) {
   return result;
 }
 
-std::string decode_url(const std::string &s,
-                              bool convert_plus_to_space) {
-  std::string result;
-
-  for (size_t i = 0; i < s.size(); i++) {
-    if (s[i] == '%' && i + 1 < s.size()) {
-      if (s[i + 1] == 'u') {
-        auto val = 0;
-        if (from_hex_to_i(s, i + 2, 4, val)) {
-          // 4 digits Unicode codes
-          char buff[4];
-          size_t len = to_utf8(val, buff);
-          if (len > 0) { result.append(buff, len); }
-          i += 5; // 'u0000'
-        } else {
-          result += s[i];
-        }
-      } else {
-        auto val = 0;
-        if (from_hex_to_i(s, i + 1, 2, val)) {
-          // 2 digits hex codes
-          result += static_cast<char>(val);
-          i += 2; // '00'
-        } else {
-          result += s[i];
-        }
-      }
-    } else if (convert_plus_to_space && s[i] == '+') {
-      result += ' ';
-    } else {
-      result += s[i];
-    }
-  }
-
-  return result;
-}
-
 std::string file_extension(const std::string &path) {
   std::smatch m;
   thread_local auto re = std::regex("\\.([a-zA-Z0-9]+)$");
@@ -428,13 +370,8 @@ bool mmap::open(const char *path) {
   auto wpath = u8string_to_wstring(path);
   if (wpath.empty()) { return false; }
 
-#if _WIN32_WINNT >= _WIN32_WINNT_WIN8
   hFile_ = ::CreateFile2(wpath.c_str(), GENERIC_READ, FILE_SHARE_READ,
                          OPEN_EXISTING, NULL);
-#else
-  hFile_ = ::CreateFileW(wpath.c_str(), GENERIC_READ, FILE_SHARE_READ, NULL,
-                         OPEN_EXISTING, FILE_ATTRIBUTE_NORMAL, NULL);
-#endif
 
   if (hFile_ == INVALID_HANDLE_VALUE) { return false; }
 
@@ -450,12 +387,8 @@ bool mmap::open(const char *path) {
   }
   size_ = static_cast<size_t>(size.QuadPart);
 
-#if _WIN32_WINNT >= _WIN32_WINNT_WIN8
   hMapping_ =
       ::CreateFileMappingFromApp(hFile_, NULL, PAGE_READONLY, size_, NULL);
-#else
-  hMapping_ = ::CreateFileMappingW(hFile_, NULL, PAGE_READONLY, 0, 0, NULL);
-#endif
 
   // Special treatment for an empty file...
   if (hMapping_ == NULL && size_ == 0) {
@@ -469,11 +402,7 @@ bool mmap::open(const char *path) {
     return false;
   }
 
-#if _WIN32_WINNT >= _WIN32_WINNT_WIN8
   addr_ = ::MapViewOfFileFromApp(hMapping_, FILE_MAP_READ, 0, 0);
-#else
-  addr_ = ::MapViewOfFile(hMapping_, FILE_MAP_READ, 0, 0, 0);
-#endif
 
   if (addr_ == nullptr) {
     close();
@@ -600,6 +529,23 @@ int poll_wrapper(struct pollfd *fds, nfds_t nfds, int timeout) {
 
 template <bool Read>
 ssize_t select_impl(socket_t sock, time_t sec, time_t usec) {
+#ifdef __APPLE__
+  if (sock >= FD_SETSIZE) { return -1; }
+
+  fd_set fds, *rfds, *wfds;
+  FD_ZERO(&fds);
+  FD_SET(sock, &fds);
+  rfds = (Read ? &fds : nullptr);
+  wfds = (Read ? nullptr : &fds);
+
+  timeval tv;
+  tv.tv_sec = static_cast<long>(sec);
+  tv.tv_usec = static_cast<decltype(tv.tv_usec)>(usec);
+
+  return handle_EINTR([&]() {
+    return select(static_cast<int>(sock + 1), rfds, wfds, nullptr, &tv);
+  });
+#else
   struct pollfd pfd;
   pfd.fd = sock;
   pfd.events = (Read ? POLLIN : POLLOUT);
@@ -607,6 +553,7 @@ ssize_t select_impl(socket_t sock, time_t sec, time_t usec) {
   auto timeout = static_cast<int>(sec * 1000 + usec / 1000);
 
   return handle_EINTR([&]() { return poll_wrapper(&pfd, 1, timeout); });
+#endif
 }
 
 ssize_t select_read(socket_t sock, time_t sec, time_t usec) {
@@ -619,6 +566,36 @@ ssize_t select_write(socket_t sock, time_t sec, time_t usec) {
 
 Error wait_until_socket_is_ready(socket_t sock, time_t sec,
                                         time_t usec) {
+#ifdef __APPLE__
+  if (sock >= FD_SETSIZE) { return Error::Connection; }
+
+  fd_set fdsr, fdsw;
+  FD_ZERO(&fdsr);
+  FD_ZERO(&fdsw);
+  FD_SET(sock, &fdsr);
+  FD_SET(sock, &fdsw);
+
+  timeval tv;
+  tv.tv_sec = static_cast<long>(sec);
+  tv.tv_usec = static_cast<decltype(tv.tv_usec)>(usec);
+
+  auto ret = handle_EINTR([&]() {
+    return select(static_cast<int>(sock + 1), &fdsr, &fdsw, nullptr, &tv);
+  });
+
+  if (ret == 0) { return Error::ConnectionTimeout; }
+
+  if (ret > 0 && (FD_ISSET(sock, &fdsr) || FD_ISSET(sock, &fdsw))) {
+    auto error = 0;
+    socklen_t len = sizeof(error);
+    auto res = getsockopt(sock, SOL_SOCKET, SO_ERROR,
+                          reinterpret_cast<char *>(&error), &len);
+    auto successful = res >= 0 && !error;
+    return successful ? Error::Success : Error::Connection;
+  }
+
+  return Error::Connection;
+#else
   struct pollfd pfd_read;
   pfd_read.fd = sock;
   pfd_read.events = POLLIN | POLLOUT;
@@ -640,6 +617,7 @@ Error wait_until_socket_is_ready(socket_t sock, time_t sec,
   }
 
   return Error::Connection;
+#endif
 }
 
 bool is_socket_alive(socket_t sock) {
@@ -827,11 +805,339 @@ unescape_abstract_namespace_unix_domain(const std::string &s) {
   return s;
 }
 
+int getaddrinfo_with_timeout(const char *node, const char *service,
+                                    const struct addrinfo *hints,
+                                    struct addrinfo **res, time_t timeout_sec) {
+#ifdef CPPHTTPLIB_USE_NON_BLOCKING_GETADDRINFO
+  if (timeout_sec <= 0) {
+    // No timeout specified, use standard getaddrinfo
+    return getaddrinfo(node, service, hints, res);
+  }
+
+#ifdef _WIN32
+  // Windows-specific implementation using GetAddrInfoEx with overlapped I/O
+  OVERLAPPED overlapped = {0};
+  HANDLE event = CreateEventW(nullptr, TRUE, FALSE, nullptr);
+  if (!event) { return EAI_FAIL; }
+
+  overlapped.hEvent = event;
+
+  PADDRINFOEXW result_addrinfo = nullptr;
+  HANDLE cancel_handle = nullptr;
+
+  ADDRINFOEXW hints_ex = {0};
+  if (hints) {
+    hints_ex.ai_flags = hints->ai_flags;
+    hints_ex.ai_family = hints->ai_family;
+    hints_ex.ai_socktype = hints->ai_socktype;
+    hints_ex.ai_protocol = hints->ai_protocol;
+  }
+
+  auto wnode = u8string_to_wstring(node);
+  auto wservice = u8string_to_wstring(service);
+
+  auto ret = ::GetAddrInfoExW(wnode.data(), wservice.data(), NS_DNS, nullptr,
+                              hints ? &hints_ex : nullptr, &result_addrinfo,
+                              nullptr, &overlapped, nullptr, &cancel_handle);
+
+  if (ret == WSA_IO_PENDING) {
+    auto wait_result =
+        ::WaitForSingleObject(event, static_cast<DWORD>(timeout_sec * 1000));
+    if (wait_result == WAIT_TIMEOUT) {
+      if (cancel_handle) { ::GetAddrInfoExCancel(&cancel_handle); }
+      ::CloseHandle(event);
+      return EAI_AGAIN;
+    }
+
+    DWORD bytes_returned;
+    if (!::GetOverlappedResult((HANDLE)INVALID_SOCKET, &overlapped,
+                               &bytes_returned, FALSE)) {
+      ::CloseHandle(event);
+      return ::WSAGetLastError();
+    }
+  }
+
+  ::CloseHandle(event);
+
+  if (ret == NO_ERROR || ret == WSA_IO_PENDING) {
+    *res = reinterpret_cast<struct addrinfo *>(result_addrinfo);
+    return 0;
+  }
+
+  return ret;
+#elif TARGET_OS_MAC
+  // macOS implementation using CFHost API for asynchronous DNS resolution
+  CFStringRef hostname_ref = CFStringCreateWithCString(
+      kCFAllocatorDefault, node, kCFStringEncodingUTF8);
+  if (!hostname_ref) { return EAI_MEMORY; }
+
+  CFHostRef host_ref = CFHostCreateWithName(kCFAllocatorDefault, hostname_ref);
+  CFRelease(hostname_ref);
+  if (!host_ref) { return EAI_MEMORY; }
+
+  // Set up context for callback
+  struct CFHostContext {
+    bool completed = false;
+    bool success = false;
+    CFArrayRef addresses = nullptr;
+    std::mutex mutex;
+    std::condition_variable cv;
+  } context;
+
+  CFHostClientContext client_context;
+  memset(&client_context, 0, sizeof(client_context));
+  client_context.info = &context;
+
+  // Set callback
+  auto callback = [](CFHostRef theHost, CFHostInfoType /*typeInfo*/,
+                     const CFStreamError *error, void *info) {
+    auto ctx = static_cast<CFHostContext *>(info);
+    std::lock_guard<std::mutex> lock(ctx->mutex);
+
+    if (error && error->error != 0) {
+      ctx->success = false;
+    } else {
+      Boolean hasBeenResolved;
+      ctx->addresses = CFHostGetAddressing(theHost, &hasBeenResolved);
+      if (ctx->addresses && hasBeenResolved) {
+        CFRetain(ctx->addresses);
+        ctx->success = true;
+      } else {
+        ctx->success = false;
+      }
+    }
+    ctx->completed = true;
+    ctx->cv.notify_one();
+  };
+
+  if (!CFHostSetClient(host_ref, callback, &client_context)) {
+    CFRelease(host_ref);
+    return EAI_SYSTEM;
+  }
+
+  // Schedule on run loop
+  CFRunLoopRef run_loop = CFRunLoopGetCurrent();
+  CFHostScheduleWithRunLoop(host_ref, run_loop, kCFRunLoopDefaultMode);
+
+  // Start resolution
+  CFStreamError stream_error;
+  if (!CFHostStartInfoResolution(host_ref, kCFHostAddresses, &stream_error)) {
+    CFHostUnscheduleFromRunLoop(host_ref, run_loop, kCFRunLoopDefaultMode);
+    CFRelease(host_ref);
+    return EAI_FAIL;
+  }
+
+  // Wait for completion with timeout
+  auto timeout_time =
+      std::chrono::steady_clock::now() + std::chrono::seconds(timeout_sec);
+  bool timed_out = false;
+
+  {
+    std::unique_lock<std::mutex> lock(context.mutex);
+
+    while (!context.completed) {
+      auto now = std::chrono::steady_clock::now();
+      if (now >= timeout_time) {
+        timed_out = true;
+        break;
+      }
+
+      // Run the runloop for a short time
+      lock.unlock();
+      CFRunLoopRunInMode(kCFRunLoopDefaultMode, 0.1, true);
+      lock.lock();
+    }
+  }
+
+  // Clean up
+  CFHostUnscheduleFromRunLoop(host_ref, run_loop, kCFRunLoopDefaultMode);
+  CFHostSetClient(host_ref, nullptr, nullptr);
+
+  if (timed_out || !context.completed) {
+    CFHostCancelInfoResolution(host_ref, kCFHostAddresses);
+    CFRelease(host_ref);
+    return EAI_AGAIN;
+  }
+
+  if (!context.success || !context.addresses) {
+    CFRelease(host_ref);
+    return EAI_NODATA;
+  }
+
+  // Convert CFArray to addrinfo
+  CFIndex count = CFArrayGetCount(context.addresses);
+  if (count == 0) {
+    CFRelease(context.addresses);
+    CFRelease(host_ref);
+    return EAI_NODATA;
+  }
+
+  struct addrinfo *result_addrinfo = nullptr;
+  struct addrinfo **current = &result_addrinfo;
+
+  for (CFIndex i = 0; i < count; i++) {
+    CFDataRef addr_data =
+        static_cast<CFDataRef>(CFArrayGetValueAtIndex(context.addresses, i));
+    if (!addr_data) continue;
+
+    const struct sockaddr *sockaddr_ptr =
+        reinterpret_cast<const struct sockaddr *>(CFDataGetBytePtr(addr_data));
+    socklen_t sockaddr_len = static_cast<socklen_t>(CFDataGetLength(addr_data));
+
+    // Allocate addrinfo structure
+    *current = static_cast<struct addrinfo *>(malloc(sizeof(struct addrinfo)));
+    if (!*current) {
+      freeaddrinfo(result_addrinfo);
+      CFRelease(context.addresses);
+      CFRelease(host_ref);
+      return EAI_MEMORY;
+    }
+
+    memset(*current, 0, sizeof(struct addrinfo));
+
+    // Set up addrinfo fields
+    (*current)->ai_family = sockaddr_ptr->sa_family;
+    (*current)->ai_socktype = hints ? hints->ai_socktype : SOCK_STREAM;
+    (*current)->ai_protocol = hints ? hints->ai_protocol : IPPROTO_TCP;
+    (*current)->ai_addrlen = sockaddr_len;
+
+    // Copy sockaddr
+    (*current)->ai_addr = static_cast<struct sockaddr *>(malloc(sockaddr_len));
+    if (!(*current)->ai_addr) {
+      freeaddrinfo(result_addrinfo);
+      CFRelease(context.addresses);
+      CFRelease(host_ref);
+      return EAI_MEMORY;
+    }
+    memcpy((*current)->ai_addr, sockaddr_ptr, sockaddr_len);
+
+    // Set port if service is specified
+    if (service && strlen(service) > 0) {
+      int port = atoi(service);
+      if (port > 0) {
+        if (sockaddr_ptr->sa_family == AF_INET) {
+          reinterpret_cast<struct sockaddr_in *>((*current)->ai_addr)
+              ->sin_port = htons(static_cast<uint16_t>(port));
+        } else if (sockaddr_ptr->sa_family == AF_INET6) {
+          reinterpret_cast<struct sockaddr_in6 *>((*current)->ai_addr)
+              ->sin6_port = htons(static_cast<uint16_t>(port));
+        }
+      }
+    }
+
+    current = &((*current)->ai_next);
+  }
+
+  CFRelease(context.addresses);
+  CFRelease(host_ref);
+
+  *res = result_addrinfo;
+  return 0;
+#elif defined(_GNU_SOURCE) && defined(__GLIBC__) &&                            \
+    (__GLIBC__ > 2 || (__GLIBC__ == 2 && __GLIBC_MINOR__ >= 2))
+  // Linux implementation using getaddrinfo_a for asynchronous DNS resolution
+  struct gaicb request;
+  struct gaicb *requests[1] = {&request};
+  struct sigevent sevp;
+  struct timespec timeout;
+
+  // Initialize the request structure
+  memset(&request, 0, sizeof(request));
+  request.ar_name = node;
+  request.ar_service = service;
+  request.ar_request = hints;
+
+  // Set up timeout
+  timeout.tv_sec = timeout_sec;
+  timeout.tv_nsec = 0;
+
+  // Initialize sigevent structure (not used, but required)
+  memset(&sevp, 0, sizeof(sevp));
+  sevp.sigev_notify = SIGEV_NONE;
+
+  // Start asynchronous resolution
+  int start_result = getaddrinfo_a(GAI_NOWAIT, requests, 1, &sevp);
+  if (start_result != 0) { return start_result; }
+
+  // Wait for completion with timeout
+  int wait_result =
+      gai_suspend((const struct gaicb *const *)requests, 1, &timeout);
+
+  if (wait_result == 0 || wait_result == EAI_ALLDONE) {
+    // Completed successfully, get the result
+    int gai_result = gai_error(&request);
+    if (gai_result == 0) {
+      *res = request.ar_result;
+      return 0;
+    } else {
+      // Clean up on error
+      if (request.ar_result) { freeaddrinfo(request.ar_result); }
+      return gai_result;
+    }
+  } else if (wait_result == EAI_AGAIN) {
+    // Timeout occurred, cancel the request
+    gai_cancel(&request);
+    return EAI_AGAIN;
+  } else {
+    // Other error occurred
+    gai_cancel(&request);
+    return wait_result;
+  }
+#else
+  // Fallback implementation using thread-based timeout for other Unix systems
+
+  struct GetAddrInfoState {
+    std::mutex mutex;
+    std::condition_variable result_cv;
+    bool completed = false;
+    int result = EAI_SYSTEM;
+    std::string node = node;
+    std::string service = service;
+    struct addrinfo hints = hints;
+    struct addrinfo *info = nullptr;
+  };
+
+  // Allocate on the heap, so the resolver thread can keep using the data.
+  auto state = std::make_shared<GetAddrInfoState>();
+
+  std::thread resolve_thread([=]() {
+    auto thread_result = getaddrinfo(
+        state->node.c_str(), state->service.c_str(), hints, &state->info);
+
+    std::lock_guard<std::mutex> lock(state->mutex);
+    state->result = thread_result;
+    state->completed = true;
+    state->result_cv.notify_one();
+  });
+
+  // Wait for completion or timeout
+  std::unique_lock<std::mutex> lock(state->mutex);
+  auto finished =
+      state->result_cv.wait_for(lock, std::chrono::seconds(timeout_sec),
+                                [&] { return state->completed; });
+
+  if (finished) {
+    // Operation completed within timeout
+    resolve_thread.join();
+    *res = state->info;
+    return state->result;
+  } else {
+    // Timeout occurred
+    resolve_thread.detach(); // Let the thread finish in background
+    return EAI_AGAIN;        // Return timeout error
+  }
+#endif
+#else
+  (void)(timeout_sec); // Unused parameter for non-blocking getaddrinfo
+  return getaddrinfo(node, service, hints, res);
+#endif
+}
+
 template <typename BindOrConnect>
 socket_t create_socket(const std::string &host, const std::string &ip, int port,
                        int address_family, int socket_flags, bool tcp_nodelay,
                        bool ipv6_v6only, SocketOptions socket_options,
-                       BindOrConnect bind_or_connect) {
+                       BindOrConnect bind_or_connect, time_t timeout_sec = 0) {
   // Get address info
   const char *node = nullptr;
   struct addrinfo hints;
@@ -852,6 +1158,7 @@ socket_t create_socket(const std::string &host, const std::string &ip, int port,
     hints.ai_flags = socket_flags;
   }
 
+#if !defined(_WIN32) || defined(CPPHTTPLIB_HAVE_AFUNIX_H)
   if (hints.ai_family == AF_UNIX) {
     const auto addrlen = host.length();
     if (addrlen > sizeof(sockaddr_un::sun_path)) { return INVALID_SOCKET; }
@@ -896,10 +1203,12 @@ socket_t create_socket(const std::string &host, const std::string &ip, int port,
     }
     return sock;
   }
+#endif
 
   auto service = std::to_string(port);
 
-  if (getaddrinfo(node, service.c_str(), &hints, &result)) {
+  if (getaddrinfo_with_timeout(node, service.c_str(), &hints, &result,
+                               timeout_sec)) {
 #if defined __linux__ && !defined __ANDROID__
     res_init();
 #endif
@@ -997,7 +1306,10 @@ bool bind_ip_address(socket_t sock, const std::string &host) {
   hints.ai_socktype = SOCK_STREAM;
   hints.ai_protocol = 0;
 
-  if (getaddrinfo(host.c_str(), "0", &hints, &result)) { return false; }
+  if (getaddrinfo_with_timeout(host.c_str(), "0", &hints, &result, 0)) {
+    return false;
+  }
+
   auto se = detail::scope_exit([&] { freeaddrinfo(result); });
 
   auto ret = false;
@@ -1102,7 +1414,8 @@ socket_t create_client_socket(
 
         error = Error::Success;
         return true;
-      });
+      },
+      connection_timeout_sec); // Pass DNS timeout
 
   if (sock != INVALID_SOCKET) {
     error = Error::Success;
@@ -1158,7 +1471,7 @@ void get_remote_ip_and_port(socket_t sock, std::string &ip, int &port) {
       if (getsockopt(sock, SOL_SOCKET, SO_PEERCRED, &ucred, &len) == 0) {
         port = ucred.pid;
       }
-#elif defined(SOL_LOCAL) && defined(SO_PEERPID) // __APPLE__
+#elif defined(SOL_LOCAL) && defined(SO_PEERPID)
       pid_t pid;
       socklen_t len = sizeof(pid);
       if (getsockopt(sock, SOL_LOCAL, SO_PEERPID, &pid, &len) == 0) {
@@ -1570,13 +1883,35 @@ bool zstd_decompressor::decompress(const char *data, size_t data_length,
 }
 #endif
 
+bool is_prohibited_header_name(const std::string &name) {
+  using udl::operator""_t;
+
+  switch (str2tag(name)) {
+  case "REMOTE_ADDR"_t:
+  case "REMOTE_PORT"_t:
+  case "LOCAL_ADDR"_t:
+  case "LOCAL_PORT"_t: return true;
+  default: return false;
+  }
+}
+
 bool has_header(const Headers &headers, const std::string &key) {
+  if (is_prohibited_header_name(key)) { return false; }
   return headers.find(key) != headers.end();
 }
 
 const char *get_header_value(const Headers &headers,
                                     const std::string &key, const char *def,
                                     size_t id) {
+  if (is_prohibited_header_name(key)) {
+#ifndef CPPHTTPLIB_NO_EXCEPTIONS
+    std::string msg = "Prohibited header name '" + key + "' is specified.";
+    throw std::invalid_argument(msg);
+#else
+    return "";
+#endif
+  }
+
   auto rng = headers.equal_range(key);
   auto it = rng.first;
   std::advance(it, static_cast<ssize_t>(id));
@@ -1622,7 +1957,7 @@ bool parse_header(const char *beg, const char *end, T fn) {
         case_ignore::equal(key, "Referer")) {
       fn(key, val);
     } else {
-      fn(key, decode_url(val, false));
+      fn(key, decode_path_component(val));
     }
 
     return true;
@@ -1636,6 +1971,8 @@ bool read_headers(Stream &strm, Headers &headers) {
   char buf[bufsiz];
   stream_line_reader line_reader(strm, buf, bufsiz);
 
+  size_t header_count = 0;
+
   for (;;) {
     if (!line_reader.getline()) { return false; }
 
@@ -1656,6 +1993,9 @@ bool read_headers(Stream &strm, Headers &headers) {
 
     if (line_reader.size() > CPPHTTPLIB_HEADER_MAX_LENGTH) { return false; }
 
+    // Check header count limit
+    if (header_count >= CPPHTTPLIB_HEADER_MAX_COUNT) { return false; }
+
     // Exclude line terminator
     auto end = line_reader.ptr() + line_reader.size() - line_terminator_len;
 
@@ -1665,24 +2005,26 @@ bool read_headers(Stream &strm, Headers &headers) {
                       })) {
       return false;
     }
+
+    header_count++;
   }
 
   return true;
 }
 
-bool read_content_with_length(Stream &strm, uint64_t len,
-                                     Progress progress,
+bool read_content_with_length(Stream &strm, size_t len,
+                                     DownloadProgress progress,
                                      ContentReceiverWithProgress out) {
   char buf[CPPHTTPLIB_RECV_BUFSIZ];
 
-  uint64_t r = 0;
+  size_t r = 0;
   while (r < len) {
     auto read_len = static_cast<size_t>(len - r);
     auto n = strm.read(buf, (std::min)(read_len, CPPHTTPLIB_RECV_BUFSIZ));
     if (n <= 0) { return false; }
 
     if (!out(buf, static_cast<size_t>(n), r, len)) { return false; }
-    r += static_cast<uint64_t>(n);
+    r += static_cast<size_t>(n);
 
     if (progress) {
       if (!progress(r, len)) { return false; }
@@ -1692,63 +2034,90 @@ bool read_content_with_length(Stream &strm, uint64_t len,
   return true;
 }
 
-void skip_content_with_length(Stream &strm, uint64_t len) {
+void skip_content_with_length(Stream &strm, size_t len) {
   char buf[CPPHTTPLIB_RECV_BUFSIZ];
-  uint64_t r = 0;
+  size_t r = 0;
   while (r < len) {
     auto read_len = static_cast<size_t>(len - r);
     auto n = strm.read(buf, (std::min)(read_len, CPPHTTPLIB_RECV_BUFSIZ));
     if (n <= 0) { return; }
-    r += static_cast<uint64_t>(n);
+    r += static_cast<size_t>(n);
   }
 }
 
-bool read_content_without_length(Stream &strm,
-                                        ContentReceiverWithProgress out) {
+enum class ReadContentResult {
+  Success,         // Successfully read the content
+  PayloadTooLarge, // The content exceeds the specified payload limit
+  Error            // An error occurred while reading the content
+};
+
+ReadContentResult
+read_content_without_length(Stream &strm, size_t payload_max_length,
+                            ContentReceiverWithProgress out) {
   char buf[CPPHTTPLIB_RECV_BUFSIZ];
-  uint64_t r = 0;
+  size_t r = 0;
   for (;;) {
     auto n = strm.read(buf, CPPHTTPLIB_RECV_BUFSIZ);
-    if (n == 0) { return true; }
-    if (n < 0) { return false; }
+    if (n == 0) { return ReadContentResult::Success; }
+    if (n < 0) { return ReadContentResult::Error; }
+
+    // Check if adding this data would exceed the payload limit
+    if (r > payload_max_length ||
+        payload_max_length - r < static_cast<size_t>(n)) {
+      return ReadContentResult::PayloadTooLarge;
+    }
 
-    if (!out(buf, static_cast<size_t>(n), r, 0)) { return false; }
-    r += static_cast<uint64_t>(n);
+    if (!out(buf, static_cast<size_t>(n), r, 0)) {
+      return ReadContentResult::Error;
+    }
+    r += static_cast<size_t>(n);
   }
 
-  return true;
+  return ReadContentResult::Success;
 }
 
 template <typename T>
-bool read_content_chunked(Stream &strm, T &x,
-                                 ContentReceiverWithProgress out) {
+ReadContentResult read_content_chunked(Stream &strm, T &x,
+                                              size_t payload_max_length,
+                                              ContentReceiverWithProgress out) {
   const auto bufsiz = 16;
   char buf[bufsiz];
 
   stream_line_reader line_reader(strm, buf, bufsiz);
 
-  if (!line_reader.getline()) { return false; }
+  if (!line_reader.getline()) { return ReadContentResult::Error; }
 
   unsigned long chunk_len;
+  size_t total_len = 0;
   while (true) {
     char *end_ptr;
 
     chunk_len = std::strtoul(line_reader.ptr(), &end_ptr, 16);
 
-    if (end_ptr == line_reader.ptr()) { return false; }
-    if (chunk_len == ULONG_MAX) { return false; }
+    if (end_ptr == line_reader.ptr()) { return ReadContentResult::Error; }
+    if (chunk_len == ULONG_MAX) { return ReadContentResult::Error; }
 
     if (chunk_len == 0) { break; }
 
+    // Check if adding this chunk would exceed the payload limit
+    if (total_len > payload_max_length ||
+        payload_max_length - total_len < chunk_len) {
+      return ReadContentResult::PayloadTooLarge;
+    }
+
+    total_len += chunk_len;
+
     if (!read_content_with_length(strm, chunk_len, nullptr, out)) {
-      return false;
+      return ReadContentResult::Error;
     }
 
-    if (!line_reader.getline()) { return false; }
+    if (!line_reader.getline()) { return ReadContentResult::Error; }
 
-    if (strcmp(line_reader.ptr(), "\r\n") != 0) { return false; }
+    if (strcmp(line_reader.ptr(), "\r\n") != 0) {
+      return ReadContentResult::Error;
+    }
 
-    if (!line_reader.getline()) { return false; }
+    if (!line_reader.getline()) { return ReadContentResult::Error; }
   }
 
   assert(chunk_len == 0);
@@ -1765,10 +2134,54 @@ bool read_content_chunked(Stream &strm, T &x,
   //
   // According to the reference code in RFC 9112, cpp-httplib now allows
   // chunked transfer coding data without the final CRLF.
-  if (!line_reader.getline()) { return true; }
+  if (!line_reader.getline()) { return ReadContentResult::Success; }
+
+  // RFC 7230 Section 4.1.2 - Headers prohibited in trailers
+  thread_local case_ignore::unordered_set<std::string> prohibited_trailers = {
+      // Message framing
+      "transfer-encoding", "content-length",
+
+      // Routing
+      "host",
+
+      // Authentication
+      "authorization", "www-authenticate", "proxy-authenticate",
+      "proxy-authorization", "cookie", "set-cookie",
+
+      // Request modifiers
+      "cache-control", "expect", "max-forwards", "pragma", "range", "te",
+
+      // Response control
+      "age", "expires", "date", "location", "retry-after", "vary", "warning",
 
+      // Payload processing
+      "content-encoding", "content-type", "content-range", "trailer"};
+
+  // Parse declared trailer headers once for performance
+  case_ignore::unordered_set<std::string> declared_trailers;
+  if (has_header(x.headers, "Trailer")) {
+    auto trailer_header = get_header_value(x.headers, "Trailer", "", 0);
+    auto len = std::strlen(trailer_header);
+
+    split(trailer_header, trailer_header + len, ',',
+          [&](const char *b, const char *e) {
+            std::string key(b, e);
+            if (prohibited_trailers.find(key) == prohibited_trailers.end()) {
+              declared_trailers.insert(key);
+            }
+          });
+  }
+
+  size_t trailer_header_count = 0;
   while (strcmp(line_reader.ptr(), "\r\n") != 0) {
-    if (line_reader.size() > CPPHTTPLIB_HEADER_MAX_LENGTH) { return false; }
+    if (line_reader.size() > CPPHTTPLIB_HEADER_MAX_LENGTH) {
+      return ReadContentResult::Error;
+    }
+
+    // Check trailer header count limit
+    if (trailer_header_count >= CPPHTTPLIB_HEADER_MAX_COUNT) {
+      return ReadContentResult::Error;
+    }
 
     // Exclude line terminator
     constexpr auto line_terminator_len = 2;
@@ -1776,13 +2189,16 @@ bool read_content_chunked(Stream &strm, T &x,
 
     parse_header(line_reader.ptr(), end,
                  [&](const std::string &key, const std::string &val) {
-                   x.headers.emplace(key, val);
+                   if (declared_trailers.find(key) != declared_trailers.end()) {
+                     x.trailers.emplace(key, val);
+                     trailer_header_count++;
+                   }
                  });
 
-    if (!line_reader.getline()) { return false; }
+    if (!line_reader.getline()) { return ReadContentResult::Error; }
   }
 
-  return true;
+  return ReadContentResult::Success;
 }
 
 bool is_chunked_transfer_encoding(const Headers &headers) {
@@ -1824,7 +2240,7 @@ bool prepare_content_receiver(T &x, int &status,
     if (decompressor) {
       if (decompressor->is_valid()) {
         ContentReceiverWithProgress out = [&](const char *buf, size_t n,
-                                              uint64_t off, uint64_t len) {
+                                              size_t off, size_t len) {
           return decompressor->decompress(buf, n,
                                           [&](const char *buf2, size_t n2) {
                                             return receiver(buf2, n2, off, len);
@@ -1838,8 +2254,8 @@ bool prepare_content_receiver(T &x, int &status,
     }
   }
 
-  ContentReceiverWithProgress out = [&](const char *buf, size_t n, uint64_t off,
-                                        uint64_t len) {
+  ContentReceiverWithProgress out = [&](const char *buf, size_t n, size_t off,
+                                        size_t len) {
     return receiver(buf, n, off, len);
   };
   return callback(std::move(out));
@@ -1847,8 +2263,8 @@ bool prepare_content_receiver(T &x, int &status,
 
 template <typename T>
 bool read_content(Stream &strm, T &x, size_t payload_max_length, int &status,
-                  Progress progress, ContentReceiverWithProgress receiver,
-                  bool decompress) {
+                  DownloadProgress progress,
+                  ContentReceiverWithProgress receiver, bool decompress) {
   return prepare_content_receiver(
       x, status, std::move(receiver), decompress,
       [&](const ContentReceiverWithProgress &out) {
@@ -1856,14 +2272,31 @@ bool read_content(Stream &strm, T &x, size_t payload_max_length, int &status,
         auto exceed_payload_max_length = false;
 
         if (is_chunked_transfer_encoding(x.headers)) {
-          ret = read_content_chunked(strm, x, out);
+          auto result = read_content_chunked(strm, x, payload_max_length, out);
+          if (result == ReadContentResult::Success) {
+            ret = true;
+          } else if (result == ReadContentResult::PayloadTooLarge) {
+            exceed_payload_max_length = true;
+            ret = false;
+          } else {
+            ret = false;
+          }
         } else if (!has_header(x.headers, "Content-Length")) {
-          ret = read_content_without_length(strm, out);
+          auto result =
+              read_content_without_length(strm, payload_max_length, out);
+          if (result == ReadContentResult::Success) {
+            ret = true;
+          } else if (result == ReadContentResult::PayloadTooLarge) {
+            exceed_payload_max_length = true;
+            ret = false;
+          } else {
+            ret = false;
+          }
         } else {
           auto is_invalid_value = false;
-          auto len = get_header_value_u64(
-              x.headers, "Content-Length",
-              (std::numeric_limits<uint64_t>::max)(), 0, is_invalid_value);
+          auto len = get_header_value_u64(x.headers, "Content-Length",
+                                          (std::numeric_limits<size_t>::max)(),
+                                          0, is_invalid_value);
 
           if (is_invalid_value) {
             ret = false;
@@ -1932,10 +2365,14 @@ bool write_data(Stream &strm, const char *d, size_t l) {
 }
 
 template <typename T>
-bool write_content(Stream &strm, const ContentProvider &content_provider,
-                          size_t offset, size_t length, T is_shutting_down,
-                          Error &error) {
+bool write_content_with_progress(Stream &strm,
+                                        const ContentProvider &content_provider,
+                                        size_t offset, size_t length,
+                                        T is_shutting_down,
+                                        const UploadProgress &upload_progress,
+                                        Error &error) {
   size_t end_offset = offset + length;
+  size_t start_offset = offset;
   auto ok = true;
   DataSink data_sink;
 
@@ -1943,6 +2380,14 @@ bool write_content(Stream &strm, const ContentProvider &content_provider,
     if (ok) {
       if (write_data(strm, d, l)) {
         offset += l;
+
+        if (upload_progress && length > 0) {
+          size_t current_written = offset - start_offset;
+          if (!upload_progress(current_written, length)) {
+            ok = false;
+            return false;
+          }
+        }
       } else {
         ok = false;
       }
@@ -1969,6 +2414,14 @@ bool write_content(Stream &strm, const ContentProvider &content_provider,
   return true;
 }
 
+template <typename T>
+bool write_content(Stream &strm, const ContentProvider &content_provider,
+                          size_t offset, size_t length, T is_shutting_down,
+                          Error &error) {
+  return write_content_with_progress<T>(strm, content_provider, offset, length,
+                                        is_shutting_down, nullptr, error);
+}
+
 template <typename T>
 bool write_content(Stream &strm, const ContentProvider &content_provider,
                           size_t offset, size_t length,
@@ -2152,9 +2605,9 @@ std::string params_to_query_str(const Params &params) {
 
   for (auto it = params.begin(); it != params.end(); ++it) {
     if (it != params.begin()) { query += "&"; }
-    query += it->first;
+    query += encode_query_component(it->first);
     query += "=";
-    query += encode_query_param(it->second);
+    query += encode_query_component(it->second);
   }
   return query;
 }
@@ -2177,7 +2630,7 @@ void parse_query_text(const char *data, std::size_t size,
            });
 
     if (!key.empty()) {
-      params.emplace(decode_url(key, true), decode_url(val, true));
+      params.emplace(decode_query_component(key), decode_query_component(val));
     }
   });
 }
@@ -2272,37 +2725,166 @@ bool parse_range_header(const std::string &s, Ranges &ranges) try {
 } catch (...) { return false; }
 #endif
 
-class MultipartFormDataParser {
-public:
-  MultipartFormDataParser() = default;
+bool parse_accept_header(const std::string &s,
+                                std::vector<std::string> &content_types) {
+  content_types.clear();
 
-  void set_boundary(std::string &&boundary) {
-    boundary_ = boundary;
-    dash_boundary_crlf_ = dash_ + boundary_ + crlf_;
-    crlf_dash_boundary_ = crlf_ + dash_ + boundary_;
+  // Empty string is considered valid (no preference)
+  if (s.empty()) { return true; }
+
+  // Check for invalid patterns: leading/trailing commas or consecutive commas
+  if (s.front() == ',' || s.back() == ',' ||
+      s.find(",,") != std::string::npos) {
+    return false;
   }
 
-  bool is_valid() const { return is_valid_; }
+  struct AcceptEntry {
+    std::string media_type;
+    double quality;
+    int order; // Original order in header
+  };
 
-  bool parse(const char *buf, size_t n, const ContentReceiver &content_callback,
-             const MultipartContentHeader &header_callback) {
+  std::vector<AcceptEntry> entries;
+  int order = 0;
+  bool has_invalid_entry = false;
 
-    buf_append(buf, n);
+  // Split by comma and parse each entry
+  split(s.data(), s.data() + s.size(), ',', [&](const char *b, const char *e) {
+    std::string entry(b, e);
+    entry = trim_copy(entry);
 
-    while (buf_size() > 0) {
-      switch (state_) {
-      case 0: { // Initial boundary
-        buf_erase(buf_find(dash_boundary_crlf_));
-        if (dash_boundary_crlf_.size() > buf_size()) { return true; }
-        if (!buf_start_with(dash_boundary_crlf_)) { return false; }
-        buf_erase(dash_boundary_crlf_.size());
-        state_ = 1;
-        break;
+    if (entry.empty()) {
+      has_invalid_entry = true;
+      return;
+    }
+
+    AcceptEntry accept_entry;
+    accept_entry.quality = 1.0; // Default quality
+    accept_entry.order = order++;
+
+    // Find q= parameter
+    auto q_pos = entry.find(";q=");
+    if (q_pos == std::string::npos) { q_pos = entry.find("; q="); }
+
+    if (q_pos != std::string::npos) {
+      // Extract media type (before q parameter)
+      accept_entry.media_type = trim_copy(entry.substr(0, q_pos));
+
+      // Extract quality value
+      auto q_start = entry.find('=', q_pos) + 1;
+      auto q_end = entry.find(';', q_start);
+      if (q_end == std::string::npos) { q_end = entry.length(); }
+
+      std::string quality_str =
+          trim_copy(entry.substr(q_start, q_end - q_start));
+      if (quality_str.empty()) {
+        has_invalid_entry = true;
+        return;
       }
-      case 1: { // New entry
-        clear_file_info();
-        state_ = 2;
-        break;
+
+#ifdef CPPHTTPLIB_NO_EXCEPTIONS
+      {
+        std::istringstream iss(quality_str);
+        iss >> accept_entry.quality;
+
+        // Check if conversion was successful and entire string was consumed
+        if (iss.fail() || !iss.eof()) {
+          has_invalid_entry = true;
+          return;
+        }
+      }
+#else
+      try {
+        accept_entry.quality = std::stod(quality_str);
+      } catch (...) {
+        has_invalid_entry = true;
+        return;
+      }
+#endif
+      // Check if quality is in valid range [0.0, 1.0]
+      if (accept_entry.quality < 0.0 || accept_entry.quality > 1.0) {
+        has_invalid_entry = true;
+        return;
+      }
+    } else {
+      // No quality parameter, use entire entry as media type
+      accept_entry.media_type = entry;
+    }
+
+    // Remove additional parameters from media type
+    auto param_pos = accept_entry.media_type.find(';');
+    if (param_pos != std::string::npos) {
+      accept_entry.media_type =
+          trim_copy(accept_entry.media_type.substr(0, param_pos));
+    }
+
+    // Basic validation of media type format
+    if (accept_entry.media_type.empty()) {
+      has_invalid_entry = true;
+      return;
+    }
+
+    // Check for basic media type format (should contain '/' or be '*')
+    if (accept_entry.media_type != "*" &&
+        accept_entry.media_type.find('/') == std::string::npos) {
+      has_invalid_entry = true;
+      return;
+    }
+
+    entries.push_back(accept_entry);
+  });
+
+  // Return false if any invalid entry was found
+  if (has_invalid_entry) { return false; }
+
+  // Sort by quality (descending), then by original order (ascending)
+  std::sort(entries.begin(), entries.end(),
+            [](const AcceptEntry &a, const AcceptEntry &b) {
+              if (a.quality != b.quality) {
+                return a.quality > b.quality; // Higher quality first
+              }
+              return a.order < b.order; // Earlier order first for same quality
+            });
+
+  // Extract sorted media types
+  content_types.reserve(entries.size());
+  for (const auto &entry : entries) {
+    content_types.push_back(entry.media_type);
+  }
+
+  return true;
+}
+
+class FormDataParser {
+public:
+  FormDataParser() = default;
+
+  void set_boundary(std::string &&boundary) {
+    boundary_ = boundary;
+    dash_boundary_crlf_ = dash_ + boundary_ + crlf_;
+    crlf_dash_boundary_ = crlf_ + dash_ + boundary_;
+  }
+
+  bool is_valid() const { return is_valid_; }
+
+  bool parse(const char *buf, size_t n, const FormDataHeader &header_callback,
+             const ContentReceiver &content_callback) {
+
+    buf_append(buf, n);
+
+    while (buf_size() > 0) {
+      switch (state_) {
+      case 0: { // Initial boundary
+        auto pos = buf_find(dash_boundary_crlf_);
+        if (pos == buf_size()) { return true; }
+        buf_erase(pos + dash_boundary_crlf_.size());
+        state_ = 1;
+        break;
+      }
+      case 1: { // New entry
+        clear_file_info();
+        state_ = 2;
+        break;
       }
       case 2: { // Headers
         auto pos = buf_find(crlf_);
@@ -2327,6 +2909,16 @@ class MultipartFormDataParser {
             return false;
           }
 
+          // Parse and emplace space trimmed headers into a map
+          if (!parse_header(
+                  header.data(), header.data() + header.size(),
+                  [&](const std::string &key, const std::string &val) {
+                    file_.headers.emplace(key, val);
+                  })) {
+            is_valid_ = false;
+            return false;
+          }
+
           constexpr const char header_content_type[] = "Content-Type:";
 
           if (start_with_case_ignore(header, header_content_type)) {
@@ -2361,7 +2953,7 @@ class MultipartFormDataParser {
 
                 std::smatch m2;
                 if (std::regex_match(it->second, m2, re_rfc5987_encoding)) {
-                  file_.filename = decode_url(m2[1], false); // override...
+                  file_.filename = decode_path_component(m2[1]); // override...
                 } else {
                   is_valid_ = false;
                   return false;
@@ -2426,6 +3018,7 @@ class MultipartFormDataParser {
     file_.name.clear();
     file_.filename.clear();
     file_.content_type.clear();
+    file_.headers.clear();
   }
 
   bool start_with_case_ignore(const std::string &a, const char *b) const {
@@ -2447,7 +3040,7 @@ class MultipartFormDataParser {
 
   size_t state_ = 0;
   bool is_valid_ = false;
-  MultipartFormData file_;
+  FormData file_;
 
   // Buffer
   bool start_with(const std::string &a, size_t spos, size_t epos,
@@ -2585,7 +3178,7 @@ serialize_multipart_formdata_get_content_type(const std::string &boundary) {
 }
 
 std::string
-serialize_multipart_formdata(const MultipartFormDataItems &items,
+serialize_multipart_formdata(const UploadFormDataItems &items,
                              const std::string &boundary, bool finish = true) {
   std::string body;
 
@@ -2599,13 +3192,68 @@ serialize_multipart_formdata(const MultipartFormDataItems &items,
   return body;
 }
 
+void coalesce_ranges(Ranges &ranges, size_t content_length) {
+  if (ranges.size() <= 1) return;
+
+  // Sort ranges by start position
+  std::sort(ranges.begin(), ranges.end(),
+            [](const Range &a, const Range &b) { return a.first < b.first; });
+
+  Ranges coalesced;
+  coalesced.reserve(ranges.size());
+
+  for (auto &r : ranges) {
+    auto first_pos = r.first;
+    auto last_pos = r.second;
+
+    // Handle special cases like in range_error
+    if (first_pos == -1 && last_pos == -1) {
+      first_pos = 0;
+      last_pos = static_cast<ssize_t>(content_length);
+    }
+
+    if (first_pos == -1) {
+      first_pos = static_cast<ssize_t>(content_length) - last_pos;
+      last_pos = static_cast<ssize_t>(content_length) - 1;
+    }
+
+    if (last_pos == -1 || last_pos >= static_cast<ssize_t>(content_length)) {
+      last_pos = static_cast<ssize_t>(content_length) - 1;
+    }
+
+    // Skip invalid ranges
+    if (!(0 <= first_pos && first_pos <= last_pos &&
+          last_pos < static_cast<ssize_t>(content_length))) {
+      continue;
+    }
+
+    // Coalesce with previous range if overlapping or adjacent (but not
+    // identical)
+    if (!coalesced.empty()) {
+      auto &prev = coalesced.back();
+      // Check if current range overlaps or is adjacent to previous range
+      // but don't coalesce identical ranges (allow duplicates)
+      if (first_pos <= prev.second + 1 &&
+          !(first_pos == prev.first && last_pos == prev.second)) {
+        // Extend the previous range
+        prev.second = (std::max)(prev.second, last_pos);
+        continue;
+      }
+    }
+
+    // Add new range
+    coalesced.emplace_back(first_pos, last_pos);
+  }
+
+  ranges = std::move(coalesced);
+}
+
 bool range_error(Request &req, Response &res) {
   if (!req.ranges.empty() && 200 <= res.status && res.status < 300) {
     ssize_t content_len = static_cast<ssize_t>(
         res.content_length_ ? res.content_length_ : res.body.size());
 
-    ssize_t prev_first_pos = -1;
-    ssize_t prev_last_pos = -1;
+    std::vector<std::pair<ssize_t, ssize_t>> processed_ranges;
     size_t overwrapping_count = 0;
 
     // NOTE: The following Range check is based on '14.2. Range' in RFC 9110
@@ -2648,18 +3296,21 @@ bool range_error(Request &req, Response &res) {
         return true;
       }
 
-      // Ranges must be in ascending order
-      if (first_pos <= prev_first_pos) { return true; }
-
       // Request must not have more than two overlapping ranges
-      if (first_pos <= prev_last_pos) {
-        overwrapping_count++;
-        if (overwrapping_count > 2) { return true; }
+      for (const auto &processed_range : processed_ranges) {
+        if (!(last_pos < processed_range.first ||
+              first_pos > processed_range.second)) {
+          overwrapping_count++;
+          if (overwrapping_count > 2) { return true; }
+          break; // Only count once per range
+        }
       }
 
-      prev_first_pos = (std::max)(prev_first_pos, first_pos);
-      prev_last_pos = (std::max)(prev_last_pos, last_pos);
+      processed_ranges.emplace_back(first_pos, last_pos);
     }
+
+    // After validation, coalesce overlapping ranges as per RFC 9110
+    coalesce_ranges(req.ranges, static_cast<size_t>(content_len));
   }
 
   return false;
@@ -2927,8 +3578,7 @@ bool load_system_certs_on_windows(X509_STORE *store) {
 
   return result;
 }
-#elif defined(CPPHTTPLIB_USE_CERTS_FROM_MACOSX_KEYCHAIN) && defined(__APPLE__)
-#if TARGET_OS_OSX
+#elif defined(CPPHTTPLIB_USE_CERTS_FROM_MACOSX_KEYCHAIN) && TARGET_OS_MAC
 template <typename T>
 using CFObjectPtr =
     std::unique_ptr<typename std::remove_pointer<T>::type, void (*)(CFTypeRef)>;
@@ -3016,7 +3666,6 @@ bool load_system_certs_on_macos(X509_STORE *store) {
 
   return result;
 }
-#endif // TARGET_OS_OSX
 #endif // _WIN32
 #endif // CPPHTTPLIB_OPENSSL_SUPPORT
 
@@ -3105,7 +3754,8 @@ void hosted_at(const std::string &hostname,
   hints.ai_socktype = SOCK_STREAM;
   hints.ai_protocol = 0;
 
-  if (getaddrinfo(hostname.c_str(), nullptr, &hints, &result)) {
+  if (detail::getaddrinfo_with_timeout(hostname.c_str(), nullptr, &hints,
+                                       &result, 0)) {
 #if defined __linux__ && !defined __ANDROID__
     res_init();
 #endif
@@ -3125,6 +3775,239 @@ void hosted_at(const std::string &hostname,
   }
 }
 
+std::string encode_uri_component(const std::string &value) {
+  std::ostringstream escaped;
+  escaped.fill('0');
+  escaped << std::hex;
+
+  for (auto c : value) {
+    if (std::isalnum(static_cast<uint8_t>(c)) || c == '-' || c == '_' ||
+        c == '.' || c == '!' || c == '~' || c == '*' || c == '\'' || c == '(' ||
+        c == ')') {
+      escaped << c;
+    } else {
+      escaped << std::uppercase;
+      escaped << '%' << std::setw(2)
+              << static_cast<int>(static_cast<unsigned char>(c));
+      escaped << std::nouppercase;
+    }
+  }
+
+  return escaped.str();
+}
+
+std::string encode_uri(const std::string &value) {
+  std::ostringstream escaped;
+  escaped.fill('0');
+  escaped << std::hex;
+
+  for (auto c : value) {
+    if (std::isalnum(static_cast<uint8_t>(c)) || c == '-' || c == '_' ||
+        c == '.' || c == '!' || c == '~' || c == '*' || c == '\'' || c == '(' ||
+        c == ')' || c == ';' || c == '/' || c == '?' || c == ':' || c == '@' ||
+        c == '&' || c == '=' || c == '+' || c == '$' || c == ',' || c == '#') {
+      escaped << c;
+    } else {
+      escaped << std::uppercase;
+      escaped << '%' << std::setw(2)
+              << static_cast<int>(static_cast<unsigned char>(c));
+      escaped << std::nouppercase;
+    }
+  }
+
+  return escaped.str();
+}
+
+std::string decode_uri_component(const std::string &value) {
+  std::string result;
+
+  for (size_t i = 0; i < value.size(); i++) {
+    if (value[i] == '%' && i + 2 < value.size()) {
+      auto val = 0;
+      if (detail::from_hex_to_i(value, i + 1, 2, val)) {
+        result += static_cast<char>(val);
+        i += 2;
+      } else {
+        result += value[i];
+      }
+    } else {
+      result += value[i];
+    }
+  }
+
+  return result;
+}
+
+std::string decode_uri(const std::string &value) {
+  std::string result;
+
+  for (size_t i = 0; i < value.size(); i++) {
+    if (value[i] == '%' && i + 2 < value.size()) {
+      auto val = 0;
+      if (detail::from_hex_to_i(value, i + 1, 2, val)) {
+        result += static_cast<char>(val);
+        i += 2;
+      } else {
+        result += value[i];
+      }
+    } else {
+      result += value[i];
+    }
+  }
+
+  return result;
+}
+
+std::string encode_path_component(const std::string &component) {
+  std::string result;
+  result.reserve(component.size() * 3);
+
+  for (size_t i = 0; i < component.size(); i++) {
+    auto c = static_cast<unsigned char>(component[i]);
+
+    // Unreserved characters per RFC 3986: ALPHA / DIGIT / "-" / "." / "_" / "~"
+    if (std::isalnum(c) || c == '-' || c == '.' || c == '_' || c == '~') {
+      result += static_cast<char>(c);
+    }
+    // Path-safe sub-delimiters: "!" / "$" / "&" / "'" / "(" / ")" / "*" / "+" /
+    // "," / ";" / "="
+    else if (c == '!' || c == '$' || c == '&' || c == '\'' || c == '(' ||
+             c == ')' || c == '*' || c == '+' || c == ',' || c == ';' ||
+             c == '=') {
+      result += static_cast<char>(c);
+    }
+    // Colon is allowed in path segments except first segment
+    else if (c == ':') {
+      result += static_cast<char>(c);
+    }
+    // @ is allowed in path
+    else if (c == '@') {
+      result += static_cast<char>(c);
+    } else {
+      result += '%';
+      char hex[3];
+      snprintf(hex, sizeof(hex), "%02X", c);
+      result.append(hex, 2);
+    }
+  }
+  return result;
+}
+
+std::string decode_path_component(const std::string &component) {
+  std::string result;
+  result.reserve(component.size());
+
+  for (size_t i = 0; i < component.size(); i++) {
+    if (component[i] == '%' && i + 1 < component.size()) {
+      if (component[i + 1] == 'u') {
+        // Unicode %uXXXX encoding
+        auto val = 0;
+        if (detail::from_hex_to_i(component, i + 2, 4, val)) {
+          // 4 digits Unicode codes
+          char buff[4];
+          size_t len = detail::to_utf8(val, buff);
+          if (len > 0) { result.append(buff, len); }
+          i += 5; // 'u0000'
+        } else {
+          result += component[i];
+        }
+      } else {
+        // Standard %XX encoding
+        auto val = 0;
+        if (detail::from_hex_to_i(component, i + 1, 2, val)) {
+          // 2 digits hex codes
+          result += static_cast<char>(val);
+          i += 2; // 'XX'
+        } else {
+          result += component[i];
+        }
+      }
+    } else {
+      result += component[i];
+    }
+  }
+  return result;
+}
+
+std::string encode_query_component(const std::string &component,
+                                          bool space_as_plus) {
+  std::string result;
+  result.reserve(component.size() * 3);
+
+  for (size_t i = 0; i < component.size(); i++) {
+    auto c = static_cast<unsigned char>(component[i]);
+
+    // Unreserved characters per RFC 3986
+    if (std::isalnum(c) || c == '-' || c == '.' || c == '_' || c == '~') {
+      result += static_cast<char>(c);
+    }
+    // Space handling
+    else if (c == ' ') {
+      if (space_as_plus) {
+        result += '+';
+      } else {
+        result += "%20";
+      }
+    }
+    // Plus sign handling
+    else if (c == '+') {
+      if (space_as_plus) {
+        result += "%2B";
+      } else {
+        result += static_cast<char>(c);
+      }
+    }
+    // Query-safe sub-delimiters (excluding & and = which are query delimiters)
+    else if (c == '!' || c == '$' || c == '\'' || c == '(' || c == ')' ||
+             c == '*' || c == ',' || c == ';') {
+      result += static_cast<char>(c);
+    }
+    // Colon and @ are allowed in query
+    else if (c == ':' || c == '@') {
+      result += static_cast<char>(c);
+    }
+    // Forward slash is allowed in query values
+    else if (c == '/') {
+      result += static_cast<char>(c);
+    }
+    // Question mark is allowed in query values (after first ?)
+    else if (c == '?') {
+      result += static_cast<char>(c);
+    } else {
+      result += '%';
+      char hex[3];
+      snprintf(hex, sizeof(hex), "%02X", c);
+      result.append(hex, 2);
+    }
+  }
+  return result;
+}
+
+std::string decode_query_component(const std::string &component,
+                                          bool plus_as_space) {
+  std::string result;
+  result.reserve(component.size());
+
+  for (size_t i = 0; i < component.size(); i++) {
+    if (component[i] == '%' && i + 2 < component.size()) {
+      std::string hex = component.substr(i + 1, 2);
+      char *end;
+      unsigned long value = std::strtoul(hex.c_str(), &end, 16);
+      if (end == hex.c_str() + 2) {
+        result += static_cast<char>(value);
+        i += 2;
+      } else {
+        result += component[i];
+      }
+    } else if (component[i] == '+' && plus_as_space) {
+      result += ' '; // + becomes space in form-urlencoded
+    } else {
+      result += component[i];
+    }
+  }
+  return result;
+}
+
 std::string append_query_params(const std::string &path,
                                        const Params &params) {
   std::string path_with_query = path;
@@ -3188,6 +4071,24 @@ void Request::set_header(const std::string &key,
   }
 }
 
+bool Request::has_trailer(const std::string &key) const {
+  return trailers.find(key) != trailers.end();
+}
+
+std::string Request::get_trailer_value(const std::string &key,
+                                              size_t id) const {
+  auto rng = trailers.equal_range(key);
+  auto it = rng.first;
+  std::advance(it, static_cast<ssize_t>(id));
+  if (it != rng.second) { return it->second; }
+  return std::string();
+}
+
+size_t Request::get_trailer_value_count(const std::string &key) const {
+  auto r = trailers.equal_range(key);
+  return static_cast<size_t>(std::distance(r.first, r.second));
+}
+
 bool Request::has_param(const std::string &key) const {
   return params.find(key) != params.end();
 }
@@ -3211,19 +4112,47 @@ bool Request::is_multipart_form_data() const {
   return !content_type.rfind("multipart/form-data", 0);
 }
 
-bool Request::has_file(const std::string &key) const {
-  return files.find(key) != files.end();
+// Multipart FormData implementation
+std::string MultipartFormData::get_field(const std::string &key,
+                                                size_t id) const {
+  auto rng = fields.equal_range(key);
+  auto it = rng.first;
+  std::advance(it, static_cast<ssize_t>(id));
+  if (it != rng.second) { return it->second.content; }
+  return std::string();
+}
+
+std::vector<std::string>
+MultipartFormData::get_fields(const std::string &key) const {
+  std::vector<std::string> values;
+  auto rng = fields.equal_range(key);
+  for (auto it = rng.first; it != rng.second; it++) {
+    values.push_back(it->second.content);
+  }
+  return values;
+}
+
+bool MultipartFormData::has_field(const std::string &key) const {
+  return fields.find(key) != fields.end();
+}
+
+size_t MultipartFormData::get_field_count(const std::string &key) const {
+  auto r = fields.equal_range(key);
+  return static_cast<size_t>(std::distance(r.first, r.second));
 }
 
-MultipartFormData Request::get_file_value(const std::string &key) const {
-  auto it = files.find(key);
-  if (it != files.end()) { return it->second; }
-  return MultipartFormData();
+FormData MultipartFormData::get_file(const std::string &key,
+                                            size_t id) const {
+  auto rng = files.equal_range(key);
+  auto it = rng.first;
+  std::advance(it, static_cast<ssize_t>(id));
+  if (it != rng.second) { return it->second; }
+  return FormData();
 }
 
-std::vector<MultipartFormData>
-Request::get_file_values(const std::string &key) const {
-  std::vector<MultipartFormData> values;
+std::vector<FormData>
+MultipartFormData::get_files(const std::string &key) const {
+  std::vector<FormData> values;
   auto rng = files.equal_range(key);
   for (auto it = rng.first; it != rng.second; it++) {
     values.push_back(it->second);
@@ -3231,6 +4160,15 @@ Request::get_file_values(const std::string &key) const {
   return values;
 }
 
+bool MultipartFormData::has_file(const std::string &key) const {
+  return files.find(key) != files.end();
+}
+
+size_t MultipartFormData::get_file_count(const std::string &key) const {
+  auto r = files.equal_range(key);
+  return static_cast<size_t>(std::distance(r.first, r.second));
+}
+
 // Response implementation
 bool Response::has_header(const std::string &key) const {
   return headers.find(key) != headers.end();
@@ -3254,6 +4192,23 @@ void Response::set_header(const std::string &key,
     headers.emplace(key, val);
   }
 }
+bool Response::has_trailer(const std::string &key) const {
+  return trailers.find(key) != trailers.end();
+}
+
+std::string Response::get_trailer_value(const std::string &key,
+                                               size_t id) const {
+  auto rng = trailers.equal_range(key);
+  auto it = rng.first;
+  std::advance(it, static_cast<ssize_t>(id));
+  if (it != rng.second) { return it->second; }
+  return std::string();
+}
+
+size_t Response::get_trailer_value_count(const std::string &key) const {
+  auto r = trailers.equal_range(key);
+  return static_cast<size_t>(std::distance(r.first, r.second));
+}
 
 void Response::set_redirect(const std::string &url, int stat) {
   if (detail::fields::is_field_value(url)) {
@@ -3518,7 +4473,8 @@ time_t BufferStream::duration() const { return 0; }
 
 const std::string &BufferStream::get_buffer() const { return buffer; }
 
-PathParamsMatcher::PathParamsMatcher(const std::string &pattern) {
+PathParamsMatcher::PathParamsMatcher(const std::string &pattern)
+    : MatcherBase(pattern) {
   constexpr const char marker[] = "/:";
 
   // One past the last ending position of a path param substring
@@ -3614,9 +4570,33 @@ bool RegexMatcher::match(Request &request) const {
   return std::regex_match(request.path, request.matches, regex_);
 }
 
-} // namespace detail
+std::string make_host_and_port_string(const std::string &host, int port,
+                                             bool is_ssl) {
+  std::string result;
 
-// HTTP server implementation
+  // Enclose IPv6 address in brackets (but not if already enclosed)
+  if (host.find(':') == std::string::npos ||
+      (!host.empty() && host[0] == '[')) {
+    // IPv4, hostname, or already bracketed IPv6
+    result = host;
+  } else {
+    // IPv6 address without brackets
+    result = "[" + host + "]";
+  }
+
+  // Append port if not default
+  if ((!is_ssl && port == 80) || (is_ssl && port == 443)) {
+    ; // do nothing
+  } else {
+    result += ":" + std::to_string(port);
+  }
+
+  return result;
+}
+
+} // namespace detail
+
+// HTTP server implementation
 Server::Server()
     : new_task_queue(
           [] { return new ThreadPool(CPPHTTPLIB_THREAD_POOL_COUNT); }) {
@@ -3769,11 +4749,26 @@ Server &Server::set_post_routing_handler(Handler handler) {
   return *this;
 }
 
+Server &Server::set_pre_request_handler(HandlerWithResponse handler) {
+  pre_request_handler_ = std::move(handler);
+  return *this;
+}
+
 Server &Server::set_logger(Logger logger) {
   logger_ = std::move(logger);
   return *this;
 }
 
+Server &Server::set_error_logger(ErrorLogger error_logger) {
+  error_logger_ = std::move(error_logger);
+  return *this;
+}
+
+Server &Server::set_pre_compression_logger(Logger logger) {
+  pre_compression_logger_ = std::move(logger);
+  return *this;
+}
+
 Server &
 Server::set_expect_100_continue_handler(Expect100ContinueHandler handler) {
   expect_100_continue_handler_ = std::move(handler);
@@ -3811,6 +4806,12 @@ Server &Server::set_header_writer(
   return *this;
 }
 
+Server &
+Server::set_trusted_proxies(const std::vector<std::string> &proxies) {
+  trusted_proxies_ = proxies;
+  return *this;
+}
+
 Server &Server::set_keep_alive_max_count(size_t count) {
   keep_alive_max_count_ = count;
   return *this;
@@ -3908,9 +4909,15 @@ bool Server::parse_request_line(const char *s, Request &req) const {
       "GET",     "HEAD",    "POST",  "PUT",   "DELETE",
       "CONNECT", "OPTIONS", "TRACE", "PATCH", "PRI"};
 
-  if (methods.find(req.method) == methods.end()) { return false; }
+  if (methods.find(req.method) == methods.end()) {
+    output_error_log(Error::InvalidHTTPMethod, &req);
+    return false;
+  }
 
-  if (req.version != "HTTP/1.1" && req.version != "HTTP/1.0") { return false; }
+  if (req.version != "HTTP/1.1" && req.version != "HTTP/1.0") {
+    output_error_log(Error::InvalidHTTPVersion, &req);
+    return false;
+  }
 
   {
     // Skip URL fragment
@@ -3924,8 +4931,8 @@ bool Server::parse_request_line(const char *s, Request &req) const {
     detail::divide(req.target, '?',
                    [&](const char *lhs_data, std::size_t lhs_size,
                        const char *rhs_data, std::size_t rhs_size) {
-                     req.path = detail::decode_url(
-                         std::string(lhs_data, lhs_size), false);
+                     req.path =
+                         decode_path_component(std::string(lhs_data, lhs_size));
                      detail::parse_query_text(rhs_data, rhs_size, req.params);
                    });
   }
@@ -4017,7 +5024,7 @@ bool Server::write_response_core(Stream &strm, bool close_connection,
   }
 
   // Log
-  if (logger_) { logger_(req, res); }
+  output_log(req, res);
 
   return ret;
 }
@@ -4078,8 +5085,10 @@ Server::write_content_with_provider(Stream &strm, const Request &req,
 }
 
 bool Server::read_content(Stream &strm, Request &req, Response &res) {
-  MultipartFormDataMap::iterator cur;
-  auto file_count = 0;
+  FormFields::iterator cur_field;
+  FormFiles::iterator cur_file;
+  auto is_text_field = false;
+  size_t count = 0;
   if (read_content_core(
           strm, req, res,
           // Regular
@@ -4088,24 +5097,40 @@ bool Server::read_content(Stream &strm, Request &req, Response &res) {
             req.body.append(buf, n);
             return true;
           },
-          // Multipart
-          [&](const MultipartFormData &file) {
-            if (file_count++ == CPPHTTPLIB_MULTIPART_FORM_DATA_FILE_MAX_COUNT) {
+          // Multipart FormData
+          [&](const FormData &file) {
+            if (count++ == CPPHTTPLIB_MULTIPART_FORM_DATA_FILE_MAX_COUNT) {
+              output_error_log(Error::TooManyFormDataFiles, &req);
               return false;
             }
-            cur = req.files.emplace(file.name, file);
+
+            if (file.filename.empty()) {
+              cur_field = req.form.fields.emplace(
+                  file.name, FormField{file.name, file.content, file.headers});
+              is_text_field = true;
+            } else {
+              cur_file = req.form.files.emplace(file.name, file);
+              is_text_field = false;
+            }
             return true;
           },
           [&](const char *buf, size_t n) {
-            auto &content = cur->second.content;
-            if (content.size() + n > content.max_size()) { return false; }
-            content.append(buf, n);
+            if (is_text_field) {
+              auto &content = cur_field->second.content;
+              if (content.size() + n > content.max_size()) { return false; }
+              content.append(buf, n);
+            } else {
+              auto &content = cur_file->second.content;
+              if (content.size() + n > content.max_size()) { return false; }
+              content.append(buf, n);
+            }
             return true;
           })) {
     const auto &content_type = req.get_header_value("Content-Type");
     if (!content_type.find("application/x-www-form-urlencoded")) {
       if (req.body.size() > CPPHTTPLIB_FORM_URL_ENCODED_PAYLOAD_MAX_LENGTH) {
         res.status = StatusCode::PayloadTooLarge_413; // NOTE: should be 414?
+        output_error_log(Error::ExceedMaxPayloadSize, &req);
         return false;
       }
       detail::parse_query_text(req.body, req.params);
@@ -4117,19 +5142,16 @@ bool Server::read_content(Stream &strm, Request &req, Response &res) {
 
 bool Server::read_content_with_content_receiver(
     Stream &strm, Request &req, Response &res, ContentReceiver receiver,
-    MultipartContentHeader multipart_header,
-    ContentReceiver multipart_receiver) {
+    FormDataHeader multipart_header, ContentReceiver multipart_receiver) {
   return read_content_core(strm, req, res, std::move(receiver),
                            std::move(multipart_header),
                            std::move(multipart_receiver));
 }
 
-bool
-Server::read_content_core(Stream &strm, Request &req, Response &res,
-                          ContentReceiver receiver,
-                          MultipartContentHeader multipart_header,
-                          ContentReceiver multipart_receiver) const {
-  detail::MultipartFormDataParser multipart_form_data_parser;
+bool Server::read_content_core(
+    Stream &strm, Request &req, Response &res, ContentReceiver receiver,
+    FormDataHeader multipart_header, ContentReceiver multipart_receiver) const {
+  detail::FormDataParser multipart_form_data_parser;
   ContentReceiverWithProgress out;
 
   if (req.is_multipart_form_data()) {
@@ -4137,28 +5159,18 @@ Server::read_content_core(Stream &strm, Request &req, Response &res,
     std::string boundary;
     if (!detail::parse_multipart_boundary(content_type, boundary)) {
       res.status = StatusCode::BadRequest_400;
+      output_error_log(Error::MultipartParsing, &req);
       return false;
     }
 
     multipart_form_data_parser.set_boundary(std::move(boundary));
-    out = [&](const char *buf, size_t n, uint64_t /*off*/, uint64_t /*len*/) {
-      /* For debug
-      size_t pos = 0;
-      while (pos < n) {
-        auto read_size = (std::min)<size_t>(1, n - pos);
-        auto ret = multipart_form_data_parser.parse(
-            buf + pos, read_size, multipart_receiver, multipart_header);
-        if (!ret) { return false; }
-        pos += read_size;
-      }
-      return true;
-      */
-      return multipart_form_data_parser.parse(buf, n, multipart_receiver,
-                                              multipart_header);
+    out = [&](const char *buf, size_t n, size_t /*off*/, size_t /*len*/) {
+      return multipart_form_data_parser.parse(buf, n, multipart_header,
+                                              multipart_receiver);
     };
   } else {
-    out = [receiver](const char *buf, size_t n, uint64_t /*off*/,
-                     uint64_t /*len*/) { return receiver(buf, n); };
+    out = [receiver](const char *buf, size_t n, size_t /*off*/,
+                     size_t /*len*/) { return receiver(buf, n); };
   }
 
   if (req.method == "DELETE" && !req.has_header("Content-Length")) {
@@ -4173,6 +5185,7 @@ Server::read_content_core(Stream &strm, Request &req, Response &res,
   if (req.is_multipart_form_data()) {
     if (!multipart_form_data_parser.is_valid()) {
       res.status = StatusCode::BadRequest_400;
+      output_error_log(Error::MultipartParsing, &req);
       return false;
     }
   }
@@ -4180,8 +5193,7 @@ Server::read_content_core(Stream &strm, Request &req, Response &res,
   return true;
 }
 
-bool Server::handle_file_request(const Request &req, Response &res,
-                                        bool head) {
+bool Server::handle_file_request(const Request &req, Response &res) {
   for (const auto &entry : base_dirs_) {
     // Prefix match
     if (!req.path.compare(0, entry.mount_point.size(), entry.mount_point)) {
@@ -4203,7 +5215,10 @@ bool Server::handle_file_request(const Request &req, Response &res,
           }
 
           auto mm = std::make_shared<detail::mmap>(path.c_str());
-          if (!mm->is_open()) { return false; }
+          if (!mm->is_open()) {
+            output_error_log(Error::OpenFile, &req);
+            return false;
+          }
 
           res.set_content_provider(
               mm->size(),
@@ -4214,11 +5229,13 @@ bool Server::handle_file_request(const Request &req, Response &res,
                 return true;
               });
 
-          if (!head && file_request_handler_) {
+          if (req.method != "HEAD" && file_request_handler_) {
             file_request_handler_(req, res);
           }
 
           return true;
+        } else {
+          output_error_log(Error::OpenFile, &req);
         }
       }
     }
@@ -4233,11 +5250,15 @@ Server::create_server_socket(const std::string &host, int port,
   return detail::create_socket(
       host, std::string(), port, address_family_, socket_flags, tcp_nodelay_,
       ipv6_v6only_, std::move(socket_options),
-      [](socket_t sock, struct addrinfo &ai, bool & /*quit*/) -> bool {
+      [&](socket_t sock, struct addrinfo &ai, bool & /*quit*/) -> bool {
         if (::bind(sock, ai.ai_addr, static_cast<socklen_t>(ai.ai_addrlen))) {
+          output_error_log(Error::BindIPAddress, nullptr);
+          return false;
+        }
+        if (::listen(sock, CPPHTTPLIB_LISTEN_BACKLOG)) {
+          output_error_log(Error::Listen, nullptr);
           return false;
         }
-        if (::listen(sock, CPPHTTPLIB_LISTEN_BACKLOG)) { return false; }
         return true;
       });
 }
@@ -4256,6 +5277,7 @@ int Server::bind_internal(const std::string &host, int port,
     socklen_t addr_len = sizeof(addr);
     if (getsockname(svr_sock_, reinterpret_cast<struct sockaddr *>(&addr),
                     &addr_len) == -1) {
+      output_error_log(Error::GetSockName, nullptr);
       return -1;
     }
     if (addr.ss_family == AF_INET) {
@@ -4263,6 +5285,7 @@ int Server::bind_internal(const std::string &host, int port,
     } else if (addr.ss_family == AF_INET6) {
       return ntohs(reinterpret_cast<struct sockaddr_in6 *>(&addr)->sin6_port);
     } else {
+      output_error_log(Error::UnsupportedAddressFamily, nullptr);
       return -1;
     }
   } else {
@@ -4316,6 +5339,7 @@ bool Server::listen_internal() {
         if (svr_sock_ != INVALID_SOCKET) {
           detail::close_socket(svr_sock_);
           ret = false;
+          output_error_log(Error::Connection, nullptr);
         } else {
           ; // The server socket was closed by user.
         }
@@ -4329,6 +5353,7 @@ bool Server::listen_internal() {
 
       if (!task_queue->enqueue(
               [this, sock]() { process_and_close_socket(sock); })) {
+        output_error_log(Error::ResourceExhaustion, nullptr);
         detail::shutdown_socket(sock);
         detail::close_socket(sock);
       }
@@ -4348,9 +5373,8 @@ bool Server::routing(Request &req, Response &res, Stream &strm) {
   }
 
   // File handler
-  auto is_head_request = req.method == "HEAD";
-  if ((req.method == "GET" || is_head_request) &&
-      handle_file_request(req, res, is_head_request)) {
+  if ((req.method == "GET" || req.method == "HEAD") &&
+      handle_file_request(req, res)) {
     return true;
   }
 
@@ -4359,13 +5383,17 @@ bool Server::routing(Request &req, Response &res, Stream &strm) {
     {
       ContentReader reader(
           [&](ContentReceiver receiver) {
-            return read_content_with_content_receiver(
+            auto result = read_content_with_content_receiver(
                 strm, req, res, std::move(receiver), nullptr, nullptr);
+            if (!result) { output_error_log(Error::Read, &req); }
+            return result;
           },
-          [&](MultipartContentHeader header, ContentReceiver receiver) {
-            return read_content_with_content_receiver(strm, req, res, nullptr,
-                                                      std::move(header),
-                                                      std::move(receiver));
+          [&](FormDataHeader header, ContentReceiver receiver) {
+            auto result = read_content_with_content_receiver(
+                strm, req, res, nullptr, std::move(header),
+                std::move(receiver));
+            if (!result) { output_error_log(Error::Read, &req); }
+            return result;
           });
 
       if (req.method == "POST") {
@@ -4396,7 +5424,10 @@ bool Server::routing(Request &req, Response &res, Stream &strm) {
     }
 
     // Read content into `req.body`
-    if (!read_content(strm, req, res)) { return false; }
+    if (!read_content(strm, req, res)) {
+      output_error_log(Error::Read, &req);
+      return false;
+    }
   }
 
   // Regular handler
@@ -4425,7 +5456,11 @@ bool Server::dispatch_request(Request &req, Response &res,
     const auto &handler = x.second;
 
     if (matcher->match(req)) {
-      handler(req, res);
+      req.matched_route = matcher->pattern();
+      if (!pre_request_handler_ ||
+          pre_request_handler_(req, res) != HandlerResponse::Handled) {
+        handler(req, res);
+      }
       return true;
     }
   }
@@ -4506,6 +5541,8 @@ void Server::apply_ranges(const Request &req, Response &res,
     }
 
     if (type != detail::EncodingType::None) {
+      output_pre_compression_log(req, res);
+
       std::unique_ptr<detail::compressor> compressor;
       std::string content_encoding;
 
@@ -4552,13 +5589,51 @@ bool Server::dispatch_request_for_content_reader(
     const auto &handler = x.second;
 
     if (matcher->match(req)) {
-      handler(req, res, content_reader);
+      req.matched_route = matcher->pattern();
+      if (!pre_request_handler_ ||
+          pre_request_handler_(req, res) != HandlerResponse::Handled) {
+        handler(req, res, content_reader);
+      }
       return true;
     }
   }
   return false;
 }
 
+std::string
+get_client_ip(const std::string &x_forwarded_for,
+              const std::vector<std::string> &trusted_proxies) {
+  // X-Forwarded-For is a comma-separated list per RFC 7239
+  std::vector<std::string> ip_list;
+  detail::split(x_forwarded_for.data(),
+                x_forwarded_for.data() + x_forwarded_for.size(), ',',
+                [&](const char *b, const char *e) {
+                  auto r = detail::trim(b, e, 0, static_cast<size_t>(e - b));
+                  ip_list.emplace_back(std::string(b + r.first, b + r.second));
+                });
+
+  for (size_t i = 0; i < ip_list.size(); ++i) {
+    auto ip = ip_list[i];
+
+    auto is_trusted_proxy =
+        std::any_of(trusted_proxies.begin(), trusted_proxies.end(),
+                    [&](const std::string &proxy) { return ip == proxy; });
+
+    if (is_trusted_proxy) {
+      if (i == 0) {
+        // If the trusted proxy is the first IP, there's no preceding client IP
+        return ip;
+      } else {
+        // Return the IP immediately before the trusted proxy
+        return ip_list[i - 1];
+      }
+    }
+  }
+
+  // If no trusted proxy is found, return the first IP in the list
+  return ip_list.front();
+}
+
 bool
 Server::process_request(Stream &strm, const std::string &remote_addr,
                         int remote_port, const std::string &local_addr,
@@ -4573,15 +5648,34 @@ Server::process_request(Stream &strm, const std::string &remote_addr,
   if (!line_reader.getline()) { return false; }
 
   Request req;
+  req.start_time_ = std::chrono::steady_clock::now();
 
   Response res;
   res.version = "HTTP/1.1";
   res.headers = default_headers_;
 
+#ifdef __APPLE__
+  // Socket file descriptor exceeded FD_SETSIZE...
+  if (strm.socket() >= FD_SETSIZE) {
+    Headers dummy;
+    detail::read_headers(strm, dummy);
+    res.status = StatusCode::InternalServerError_500;
+    output_error_log(Error::ExceedMaxSocketDescriptorCount, &req);
+    return write_response(strm, close_connection, req, res);
+  }
+#endif
+
   // Request line and headers
-  if (!parse_request_line(line_reader.ptr(), req) ||
-      !detail::read_headers(strm, req.headers)) {
+  if (!parse_request_line(line_reader.ptr(), req)) {
+    res.status = StatusCode::BadRequest_400;
+    output_error_log(Error::InvalidRequestLine, &req);
+    return write_response(strm, close_connection, req, res);
+  }
+
+  // Request headers
+  if (!detail::read_headers(strm, req.headers)) {
     res.status = StatusCode::BadRequest_400;
+    output_error_log(Error::InvalidHeaders, &req);
     return write_response(strm, close_connection, req, res);
   }
 
@@ -4590,6 +5684,7 @@ Server::process_request(Stream &strm, const std::string &remote_addr,
     Headers dummy;
     detail::read_headers(strm, dummy);
     res.status = StatusCode::UriTooLong_414;
+    output_error_log(Error::ExceedUriMaxLength, &req);
     return write_response(strm, close_connection, req, res);
   }
 
@@ -4602,20 +5697,31 @@ Server::process_request(Stream &strm, const std::string &remote_addr,
     connection_closed = true;
   }
 
-  req.remote_addr = remote_addr;
+  if (!trusted_proxies_.empty() && req.has_header("X-Forwarded-For")) {
+    auto x_forwarded_for = req.get_header_value("X-Forwarded-For");
+    req.remote_addr = get_client_ip(x_forwarded_for, trusted_proxies_);
+  } else {
+    req.remote_addr = remote_addr;
+  }
   req.remote_port = remote_port;
-  req.set_header("REMOTE_ADDR", req.remote_addr);
-  req.set_header("REMOTE_PORT", std::to_string(req.remote_port));
 
   req.local_addr = local_addr;
   req.local_port = local_port;
-  req.set_header("LOCAL_ADDR", req.local_addr);
-  req.set_header("LOCAL_PORT", std::to_string(req.local_port));
+
+  if (req.has_header("Accept")) {
+    const auto &accept_header = req.get_header_value("Accept");
+    if (!detail::parse_accept_header(accept_header, req.accept_content_types)) {
+      res.status = StatusCode::BadRequest_400;
+      output_error_log(Error::HTTPParsing, &req);
+      return write_response(strm, close_connection, req, res);
+    }
+  }
 
   if (req.has_header("Range")) {
     const auto &range_header_value = req.get_header_value("Range");
     if (!detail::parse_range_header(range_header_value, req.ranges)) {
       res.status = StatusCode::RangeNotSatisfiable_416;
+      output_error_log(Error::InvalidRangeHeader, &req);
       return write_response(strm, close_connection, req, res);
     }
   }
@@ -4696,6 +5802,7 @@ Server::process_request(Stream &strm, const std::string &remote_addr,
         res.content_length_ = 0;
         res.content_provider_ = nullptr;
         res.status = StatusCode::NotFound_404;
+        output_error_log(Error::OpenFile, &req);
         return write_response(strm, close_connection, req, res);
       }
 
@@ -4755,6 +5862,29 @@ bool Server::process_and_close_socket(socket_t sock) {
   return ret;
 }
 
+void Server::output_log(const Request &req, const Response &res) const {
+  if (logger_) {
+    std::lock_guard<std::mutex> guard(logger_mutex_);
+    logger_(req, res);
+  }
+}
+
+void Server::output_pre_compression_log(const Request &req,
+                                               const Response &res) const {
+  if (pre_compression_logger_) {
+    std::lock_guard<std::mutex> guard(logger_mutex_);
+    pre_compression_logger_(req, res);
+  }
+}
+
+void Server::output_error_log(const Error &err,
+                                     const Request *req) const {
+  if (error_logger_) {
+    std::lock_guard<std::mutex> guard(logger_mutex_);
+    error_logger_(err, req);
+  }
+}
+
 // HTTP client implementation
 ClientImpl::ClientImpl(const std::string &host)
     : ClientImpl(host, 80, std::string(), std::string()) {}
@@ -4766,7 +5896,7 @@ ClientImpl::ClientImpl(const std::string &host, int port,
                               const std::string &client_cert_path,
                               const std::string &client_key_path)
     : host_(detail::escape_abstract_namespace_unix_domain(host)), port_(port),
-      host_and_port_(adjust_host_string(host_) + ":" + std::to_string(port)),
+      host_and_port_(detail::make_host_and_port_string(host_, port, is_ssl())),
       client_cert_path_(client_cert_path), client_key_path_(client_key_path) {}
 
 ClientImpl::~ClientImpl() {
@@ -4805,7 +5935,7 @@ void ClientImpl::copy_settings(const ClientImpl &rhs) {
 #endif
   keep_alive_ = rhs.keep_alive_;
   follow_location_ = rhs.follow_location_;
-  url_encode_ = rhs.url_encode_;
+  path_encode_ = rhs.path_encode_;
   address_family_ = rhs.address_family_;
   tcp_nodelay_ = rhs.tcp_nodelay_;
   ipv6_v6only_ = rhs.ipv6_v6only_;
@@ -4833,6 +5963,7 @@ void ClientImpl::copy_settings(const ClientImpl &rhs) {
   server_certificate_verifier_ = rhs.server_certificate_verifier_;
 #endif
   logger_ = rhs.logger_;
+  error_logger_ = rhs.error_logger_;
 }
 
 socket_t ClientImpl::create_client_socket(Error &error) const {
@@ -4946,8 +6077,9 @@ bool ClientImpl::send_(Request &req, Response &res, Error &error) {
   {
     std::lock_guard<std::mutex> guard(socket_mutex_);
 
-    // Set this to false immediately - if it ever gets set to true by the end of
-    // the request, we know another thread instructed us to close the socket.
+    // Set this to false immediately - if it ever gets set to true by the end
+    // of the request, we know another thread instructed us to close the
+    // socket.
     socket_should_be_closed_when_request_is_done_ = false;
 
     auto is_alive = false;
@@ -4963,10 +6095,10 @@ bool ClientImpl::send_(Request &req, Response &res, Error &error) {
 #endif
 
       if (!is_alive) {
-        // Attempt to avoid sigpipe by shutting down non-gracefully if it seems
-        // like the other side has already closed the connection Also, there
-        // cannot be any requests in flight from other threads since we locked
-        // request_mutex_, so safe to close everything immediately
+        // Attempt to avoid sigpipe by shutting down non-gracefully if it
+        // seems like the other side has already closed the connection Also,
+        // there cannot be any requests in flight from other threads since we
+        // locked request_mutex_, so safe to close everything immediately
         const bool shutdown_gracefully = false;
         shutdown_ssl(socket_, shutdown_gracefully);
         shutdown_socket(socket_);
@@ -4975,7 +6107,10 @@ bool ClientImpl::send_(Request &req, Response &res, Error &error) {
     }
 
     if (!is_alive) {
-      if (!create_and_connect_socket(socket_, error)) { return false; }
+      if (!create_and_connect_socket(socket_, error)) {
+        output_error_log(error, &req);
+        return false;
+      }
 
 #ifdef CPPHTTPLIB_OPENSSL_SUPPORT
       // TODO: refactoring
@@ -4985,11 +6120,15 @@ bool ClientImpl::send_(Request &req, Response &res, Error &error) {
           auto success = false;
           if (!scli.connect_with_proxy(socket_, req.start_time_, res, success,
                                        error)) {
+            if (!success) { output_error_log(error, &req); }
             return success;
           }
         }
 
-        if (!scli.initialize_ssl(socket_, error)) { return false; }
+        if (!scli.initialize_ssl(socket_, error)) {
+          output_error_log(error, &req);
+          return false;
+        }
       }
 #endif
     }
@@ -5035,7 +6174,10 @@ bool ClientImpl::send_(Request &req, Response &res, Error &error) {
   });
 
   if (!ret) {
-    if (error == Error::Success) { error = Error::Unknown; }
+    if (error == Error::Success) {
+      error = Error::Unknown;
+      output_error_log(error, &req);
+    }
   }
 
   return ret;
@@ -5050,7 +6192,12 @@ Result ClientImpl::send_(Request &&req) {
   auto res = detail::make_unique<Response>();
   auto error = Error::Success;
   auto ret = send(req, *res, error);
+#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
+  return Result{ret ? std::move(res) : nullptr, error, std::move(req.headers),
+                last_ssl_error_, last_openssl_error_};
+#else
   return Result{ret ? std::move(res) : nullptr, error, std::move(req.headers)};
+#endif
 }
 
 bool ClientImpl::handle_request(Stream &strm, Request &req,
@@ -5058,6 +6205,7 @@ bool ClientImpl::handle_request(Stream &strm, Request &req,
                                        Error &error) {
   if (req.path.empty()) {
     error = Error::Connection;
+    output_error_log(error, &req);
     return false;
   }
 
@@ -5133,6 +6281,7 @@ bool ClientImpl::handle_request(Stream &strm, Request &req,
 bool ClientImpl::redirect(Request &req, Response &res, Error &error) {
   if (req.redirect_count_ == 0) {
     error = Error::ExceedRedirectCount;
+    output_error_log(error, &req);
     return false;
   }
 
@@ -5165,26 +6314,157 @@ bool ClientImpl::redirect(Request &req, Response &res, Error &error) {
   if (next_host.empty()) { next_host = host_; }
   if (next_path.empty()) { next_path = "/"; }
 
-  auto path = detail::decode_url(next_path, true) + next_query;
+  auto path = decode_query_component(next_path, true) + next_query;
 
+  // Same host redirect - use current client
   if (next_scheme == scheme && next_host == host_ && next_port == port_) {
     return detail::redirect(*this, req, res, path, location, error);
-  } else {
-    if (next_scheme == "https") {
+  }
+
+  // Cross-host/scheme redirect - create new client with robust setup
+  return create_redirect_client(next_scheme, next_host, next_port, req, res,
+                                path, location, error);
+}
+
+// New method for robust redirect client creation
+bool ClientImpl::create_redirect_client(
+    const std::string &scheme, const std::string &host, int port, Request &req,
+    Response &res, const std::string &path, const std::string &location,
+    Error &error) {
+  // Determine if we need SSL
+  auto need_ssl = (scheme == "https");
+
+  // Clean up request headers that are host/client specific
+  // Remove headers that should not be carried over to new host
+  auto headers_to_remove =
+      std::vector<std::string>{"Host", "Proxy-Authorization", "Authorization"};
+
+  for (const auto &header_name : headers_to_remove) {
+    auto it = req.headers.find(header_name);
+    while (it != req.headers.end()) {
+      it = req.headers.erase(it);
+      it = req.headers.find(header_name);
+    }
+  }
+
+  // Create appropriate client type and handle redirect
+  if (need_ssl) {
 #ifdef CPPHTTPLIB_OPENSSL_SUPPORT
-      SSLClient cli(next_host, next_port);
-      cli.copy_settings(*this);
-      if (ca_cert_store_) { cli.set_ca_cert_store(ca_cert_store_); }
-      return detail::redirect(cli, req, res, path, location, error);
+    // Create SSL client for HTTPS redirect
+    SSLClient redirect_client(host, port);
+
+    // Setup basic client configuration first
+    setup_redirect_client(redirect_client);
+
+    // SSL-specific configuration for proxy environments
+    if (!proxy_host_.empty() && proxy_port_ != -1) {
+      // Critical: Disable SSL verification for proxy environments
+      redirect_client.enable_server_certificate_verification(false);
+      redirect_client.enable_server_hostname_verification(false);
+    } else {
+      // For direct SSL connections, copy SSL verification settings
+      redirect_client.enable_server_certificate_verification(
+          server_certificate_verification_);
+      redirect_client.enable_server_hostname_verification(
+          server_hostname_verification_);
+    }
+
+    // Handle CA certificate store and paths if available
+    if (ca_cert_store_ && X509_STORE_up_ref(ca_cert_store_)) {
+      redirect_client.set_ca_cert_store(ca_cert_store_);
+    }
+    if (!ca_cert_file_path_.empty()) {
+      redirect_client.set_ca_cert_path(ca_cert_file_path_, ca_cert_dir_path_);
+    }
+
+    // Client certificates are set through constructor for SSLClient
+    // NOTE: SSLClient constructor already takes client_cert_path and
+    // client_key_path so we need to create it properly if client certs are
+    // needed
+
+    // Execute the redirect
+    return detail::redirect(redirect_client, req, res, path, location, error);
 #else
-      return false;
+    // SSL not supported - set appropriate error
+    error = Error::SSLConnection;
+    output_error_log(error, &req);
+    return false;
 #endif
-    } else {
-      ClientImpl cli(next_host, next_port);
-      cli.copy_settings(*this);
-      return detail::redirect(cli, req, res, path, location, error);
+  } else {
+    // HTTP redirect
+    ClientImpl redirect_client(host, port);
+
+    // Setup client with robust configuration
+    setup_redirect_client(redirect_client);
+
+    // Execute the redirect
+    return detail::redirect(redirect_client, req, res, path, location, error);
+  }
+}
+
+// New method for robust client setup (based on basic_manual_redirect.cpp
+// logic)
+template <typename ClientType>
+void ClientImpl::setup_redirect_client(ClientType &client) {
+  // Copy basic settings first
+  client.set_connection_timeout(connection_timeout_sec_);
+  client.set_read_timeout(read_timeout_sec_, read_timeout_usec_);
+  client.set_write_timeout(write_timeout_sec_, write_timeout_usec_);
+  client.set_keep_alive(keep_alive_);
+  client.set_follow_location(
+      true); // Enable redirects to handle multi-step redirects
+  client.set_path_encode(path_encode_);
+  client.set_compress(compress_);
+  client.set_decompress(decompress_);
+
+  // Copy authentication settings BEFORE proxy setup
+  if (!basic_auth_username_.empty()) {
+    client.set_basic_auth(basic_auth_username_, basic_auth_password_);
+  }
+  if (!bearer_token_auth_token_.empty()) {
+    client.set_bearer_token_auth(bearer_token_auth_token_);
+  }
+#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
+  if (!digest_auth_username_.empty()) {
+    client.set_digest_auth(digest_auth_username_, digest_auth_password_);
+  }
+#endif
+
+  // Setup proxy configuration (CRITICAL ORDER - proxy must be set
+  // before proxy auth)
+  if (!proxy_host_.empty() && proxy_port_ != -1) {
+    // First set proxy host and port
+    client.set_proxy(proxy_host_, proxy_port_);
+
+    // Then set proxy authentication (order matters!)
+    if (!proxy_basic_auth_username_.empty()) {
+      client.set_proxy_basic_auth(proxy_basic_auth_username_,
+                                  proxy_basic_auth_password_);
+    }
+    if (!proxy_bearer_token_auth_token_.empty()) {
+      client.set_proxy_bearer_token_auth(proxy_bearer_token_auth_token_);
     }
+#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
+    if (!proxy_digest_auth_username_.empty()) {
+      client.set_proxy_digest_auth(proxy_digest_auth_username_,
+                                   proxy_digest_auth_password_);
+    }
+#endif
   }
+
+  // Copy network and socket settings
+  client.set_address_family(address_family_);
+  client.set_tcp_nodelay(tcp_nodelay_);
+  client.set_ipv6_v6only(ipv6_v6only_);
+  if (socket_options_) { client.set_socket_options(socket_options_); }
+  if (!interface_.empty()) { client.set_interface(interface_); }
+
+  // Copy logging and headers
+  if (logger_) { client.set_logger(logger_); }
+  if (error_logger_) { client.set_error_logger(error_logger_); }
+
+  // NOTE: DO NOT copy default_headers_ as they may contain stale Host headers
+  // Each new client should generate its own headers based on its target host
 }
 
 bool ClientImpl::write_content_with_provider(Stream &strm,
@@ -5207,8 +6487,9 @@ bool ClientImpl::write_content_with_provider(Stream &strm,
     return detail::write_content_chunked(strm, req.content_provider_,
                                          is_shutting_down, *compressor, error);
   } else {
-    return detail::write_content(strm, req.content_provider_, 0,
-                                 req.content_length_, is_shutting_down, error);
+    return detail::write_content_with_progress(
+        strm, req.content_provider_, 0, req.content_length_, is_shutting_down,
+        req.upload_progress, error);
   }
 }
 
@@ -5222,18 +6503,12 @@ bool ClientImpl::write_request(Stream &strm, Request &req,
   }
 
   if (!req.has_header("Host")) {
-    if (is_ssl()) {
-      if (port_ == 443) {
-        req.set_header("Host", host_);
-      } else {
-        req.set_header("Host", host_and_port_);
-      }
+    // For Unix socket connections, use "localhost" as Host header (similar to
+    // curl behavior)
+    if (address_family_ == AF_UNIX) {
+      req.set_header("Host", "localhost");
     } else {
-      if (port_ == 80) {
-        req.set_header("Host", host_);
-      } else {
-        req.set_header("Host", host_and_port_);
-      }
+      req.set_header("Host", host_and_port_);
     }
   }
 
@@ -5322,21 +6597,35 @@ bool ClientImpl::write_request(Stream &strm, Request &req,
   {
     detail::BufferStream bstrm;
 
-    const auto &path_with_query =
-        req.params.empty() ? req.path
-                           : append_query_params(req.path, req.params);
+    // Extract path and query from req.path
+    std::string path_part, query_part;
+    auto query_pos = req.path.find('?');
+    if (query_pos != std::string::npos) {
+      path_part = req.path.substr(0, query_pos);
+      query_part = req.path.substr(query_pos + 1);
+    } else {
+      path_part = req.path;
+      query_part = "";
+    }
 
-    const auto &path =
-        url_encode_ ? detail::encode_url(path_with_query) : path_with_query;
+    // Encode path and query
+    auto path_with_query =
+        path_encode_ ? detail::encode_path(path_part) : path_part;
 
-    detail::write_request_line(bstrm, req.method, path);
+    detail::parse_query_text(query_part, req.params);
+    if (!req.params.empty()) {
+      path_with_query = append_query_params(path_with_query, req.params);
+    }
 
+    // Write request line and headers
+    detail::write_request_line(bstrm, req.method, path_with_query);
     header_writer_(bstrm, req.headers);
 
     // Flush buffer
     auto &data = bstrm.get_buffer();
     if (!detail::write_data(strm, data.data(), data.size())) {
       error = Error::Write;
+      output_error_log(error, &req);
       return false;
     }
   }
@@ -5346,9 +6635,32 @@ bool ClientImpl::write_request(Stream &strm, Request &req,
     return write_content_with_provider(strm, req, error);
   }
 
-  if (!detail::write_data(strm, req.body.data(), req.body.size())) {
-    error = Error::Write;
-    return false;
+  if (req.upload_progress) {
+    auto body_size = req.body.size();
+    size_t written = 0;
+    auto data = req.body.data();
+
+    while (written < body_size) {
+      size_t to_write = (std::min)(CPPHTTPLIB_SEND_BUFSIZ, body_size - written);
+      if (!detail::write_data(strm, data + written, to_write)) {
+        error = Error::Write;
+        output_error_log(error, &req);
+        return false;
+      }
+      written += to_write;
+
+      if (!req.upload_progress(written, body_size)) {
+        error = Error::Canceled;
+        output_error_log(error, &req);
+        return false;
+      }
+    }
+  } else {
+    if (!detail::write_data(strm, req.body.data(), req.body.size())) {
+      error = Error::Write;
+      output_error_log(error, &req);
+      return false;
+    }
   }
 
   return true;
@@ -5398,6 +6710,7 @@ std::unique_ptr<Response> ClientImpl::send_with_content_provider(
       while (ok && offset < content_length) {
         if (!content_provider(offset, content_length - offset, data_sink)) {
           error = Error::Canceled;
+          output_error_log(error, &req);
           return nullptr;
         }
       }
@@ -5408,6 +6721,7 @@ std::unique_ptr<Response> ClientImpl::send_with_content_provider(
                                  return true;
                                })) {
         error = Error::Compression;
+        output_error_log(error, &req);
         return nullptr;
       }
     }
@@ -5437,12 +6751,12 @@ Result ClientImpl::send_with_content_provider(
     const std::string &method, const std::string &path, const Headers &headers,
     const char *body, size_t content_length, ContentProvider content_provider,
     ContentProviderWithoutLength content_provider_without_length,
-    const std::string &content_type, Progress progress) {
+    const std::string &content_type, UploadProgress progress) {
   Request req;
   req.method = method;
   req.headers = headers;
   req.path = path;
-  req.progress = progress;
+  req.upload_progress = std::move(progress);
   if (max_timeout_msec_ > 0) {
     req.start_time_ = std::chrono::steady_clock::now();
   }
@@ -5453,13 +6767,28 @@ Result ClientImpl::send_with_content_provider(
       req, body, content_length, std::move(content_provider),
       std::move(content_provider_without_length), content_type, error);
 
+#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
+  return Result{std::move(res), error, std::move(req.headers), last_ssl_error_,
+                last_openssl_error_};
+#else
   return Result{std::move(res), error, std::move(req.headers)};
+#endif
 }
 
-std::string
-ClientImpl::adjust_host_string(const std::string &host) const {
-  if (host.find(':') != std::string::npos) { return "[" + host + "]"; }
-  return host;
+void ClientImpl::output_log(const Request &req,
+                                   const Response &res) const {
+  if (logger_) {
+    std::lock_guard<std::mutex> guard(logger_mutex_);
+    logger_(req, res);
+  }
+}
+
+void ClientImpl::output_error_log(const Error &err,
+                                         const Request *req) const {
+  if (error_logger_) {
+    std::lock_guard<std::mutex> guard(logger_mutex_);
+    error_logger_(err, req);
+  }
 }
 
 bool ClientImpl::process_request(Stream &strm, Request &req,
@@ -5474,6 +6803,7 @@ bool ClientImpl::process_request(Stream &strm, Request &req,
     if (!is_proxy_enabled) {
       if (detail::is_ssl_peer_could_be_closed(socket_.ssl, socket_.sock)) {
         error = Error::SSLPeerCouldBeClosed_;
+        output_error_log(error, &req);
         return false;
       }
     }
@@ -5484,6 +6814,7 @@ bool ClientImpl::process_request(Stream &strm, Request &req,
   if (!read_response_line(strm, req, res) ||
       !detail::read_headers(strm, res.headers)) {
     error = Error::Read;
+    output_error_log(error, &req);
     return false;
   }
 
@@ -5497,6 +6828,7 @@ bool ClientImpl::process_request(Stream &strm, Request &req,
     if (req.response_handler && !redirect) {
       if (!req.response_handler(res)) {
         error = Error::Canceled;
+        output_error_log(error, &req);
         return false;
       }
     }
@@ -5504,24 +6836,30 @@ bool ClientImpl::process_request(Stream &strm, Request &req,
     auto out =
         req.content_receiver
             ? static_cast<ContentReceiverWithProgress>(
-                  [&](const char *buf, size_t n, uint64_t off, uint64_t len) {
+                  [&](const char *buf, size_t n, size_t off, size_t len) {
                     if (redirect) { return true; }
                     auto ret = req.content_receiver(buf, n, off, len);
-                    if (!ret) { error = Error::Canceled; }
+                    if (!ret) {
+                      error = Error::Canceled;
+                      output_error_log(error, &req);
+                    }
                     return ret;
                   })
             : static_cast<ContentReceiverWithProgress>(
-                  [&](const char *buf, size_t n, uint64_t /*off*/,
-                      uint64_t /*len*/) {
+                  [&](const char *buf, size_t n, size_t /*off*/,
+                      size_t /*len*/) {
                     assert(res.body.size() + n <= res.body.max_size());
                     res.body.append(buf, n);
                     return true;
                   });
 
-    auto progress = [&](uint64_t current, uint64_t total) {
-      if (!req.progress || redirect) { return true; }
-      auto ret = req.progress(current, total);
-      if (!ret) { error = Error::Canceled; }
+    auto progress = [&](size_t current, size_t total) {
+      if (!req.download_progress || redirect) { return true; }
+      auto ret = req.download_progress(current, total);
+      if (!ret) {
+        error = Error::Canceled;
+        output_error_log(error, &req);
+      }
       return ret;
     };
 
@@ -5530,6 +6868,7 @@ bool ClientImpl::process_request(Stream &strm, Request &req,
         auto len = res.get_header_value_u64("Content-Length");
         if (len > res.body.max_size()) {
           error = Error::Read;
+          output_error_log(error, &req);
           return false;
         }
         res.body.reserve(static_cast<size_t>(len));
@@ -5542,24 +6881,25 @@ bool ClientImpl::process_request(Stream &strm, Request &req,
                                 dummy_status, std::move(progress),
                                 std::move(out), decompress_)) {
         if (error != Error::Canceled) { error = Error::Read; }
+        output_error_log(error, &req);
         return false;
       }
     }
   }
 
   // Log
-  if (logger_) { logger_(req, res); }
+  output_log(req, res);
 
   return true;
 }
 
 ContentProviderWithoutLength ClientImpl::get_multipart_content_provider(
-    const std::string &boundary, const MultipartFormDataItems &items,
-    const MultipartFormDataProviderItems &provider_items) const {
+    const std::string &boundary, const UploadFormDataItems &items,
+    const FormDataProviderItems &provider_items) const {
   size_t cur_item = 0;
   size_t cur_start = 0;
-  // cur_item and cur_start are copied to within the std::function and maintain
-  // state between successive calls
+  // cur_item and cur_start are copied to within the std::function and
+  // maintain state between successive calls
   return [&, cur_item, cur_start](size_t offset,
                                   DataSink &sink) mutable -> bool {
     if (!offset && !items.empty()) {
@@ -5608,25 +6948,27 @@ bool ClientImpl::process_socket(
 
 bool ClientImpl::is_ssl() const { return false; }
 
-Result ClientImpl::Get(const std::string &path) {
-  return Get(path, Headers(), Progress());
-}
-
-Result ClientImpl::Get(const std::string &path, Progress progress) {
+Result ClientImpl::Get(const std::string &path,
+                              DownloadProgress progress) {
   return Get(path, Headers(), std::move(progress));
 }
 
-Result ClientImpl::Get(const std::string &path, const Headers &headers) {
-  return Get(path, headers, Progress());
+Result ClientImpl::Get(const std::string &path, const Params &params,
+                              const Headers &headers,
+                              DownloadProgress progress) {
+  if (params.empty()) { return Get(path, headers); }
+
+  std::string path_with_query = append_query_params(path, params);
+  return Get(path_with_query, headers, std::move(progress));
 }
 
 Result ClientImpl::Get(const std::string &path, const Headers &headers,
-                              Progress progress) {
+                              DownloadProgress progress) {
   Request req;
   req.method = "GET";
   req.path = path;
   req.headers = headers;
-  req.progress = std::move(progress);
+  req.download_progress = std::move(progress);
   if (max_timeout_msec_ > 0) {
     req.start_time_ = std::chrono::steady_clock::now();
   }
@@ -5634,48 +6976,24 @@ Result ClientImpl::Get(const std::string &path, const Headers &headers,
   return send_(std::move(req));
 }
 
-Result ClientImpl::Get(const std::string &path,
-                              ContentReceiver content_receiver) {
-  return Get(path, Headers(), nullptr, std::move(content_receiver), nullptr);
-}
-
 Result ClientImpl::Get(const std::string &path,
                               ContentReceiver content_receiver,
-                              Progress progress) {
+                              DownloadProgress progress) {
   return Get(path, Headers(), nullptr, std::move(content_receiver),
              std::move(progress));
 }
 
-Result ClientImpl::Get(const std::string &path, const Headers &headers,
-                              ContentReceiver content_receiver) {
-  return Get(path, headers, nullptr, std::move(content_receiver), nullptr);
-}
-
 Result ClientImpl::Get(const std::string &path, const Headers &headers,
                               ContentReceiver content_receiver,
-                              Progress progress) {
+                              DownloadProgress progress) {
   return Get(path, headers, nullptr, std::move(content_receiver),
              std::move(progress));
 }
 
-Result ClientImpl::Get(const std::string &path,
-                              ResponseHandler response_handler,
-                              ContentReceiver content_receiver) {
-  return Get(path, Headers(), std::move(response_handler),
-             std::move(content_receiver), nullptr);
-}
-
-Result ClientImpl::Get(const std::string &path, const Headers &headers,
-                              ResponseHandler response_handler,
-                              ContentReceiver content_receiver) {
-  return Get(path, headers, std::move(response_handler),
-             std::move(content_receiver), nullptr);
-}
-
 Result ClientImpl::Get(const std::string &path,
                               ResponseHandler response_handler,
                               ContentReceiver content_receiver,
-                              Progress progress) {
+                              DownloadProgress progress) {
   return Get(path, Headers(), std::move(response_handler),
              std::move(content_receiver), std::move(progress));
 }
@@ -5683,7 +7001,7 @@ Result ClientImpl::Get(const std::string &path,
 Result ClientImpl::Get(const std::string &path, const Headers &headers,
                               ResponseHandler response_handler,
                               ContentReceiver content_receiver,
-                              Progress progress) {
+                              DownloadProgress progress) {
   Request req;
   req.method = "GET";
   req.path = path;
@@ -5691,10 +7009,10 @@ Result ClientImpl::Get(const std::string &path, const Headers &headers,
   req.response_handler = std::move(response_handler);
   req.content_receiver =
       [content_receiver](const char *data, size_t data_length,
-                         uint64_t /*offset*/, uint64_t /*total_length*/) {
+                         size_t /*offset*/, size_t /*total_length*/) {
         return content_receiver(data, data_length);
       };
-  req.progress = std::move(progress);
+  req.download_progress = std::move(progress);
   if (max_timeout_msec_ > 0) {
     req.start_time_ = std::chrono::steady_clock::now();
   }
@@ -5702,18 +7020,10 @@ Result ClientImpl::Get(const std::string &path, const Headers &headers,
   return send_(std::move(req));
 }
 
-Result ClientImpl::Get(const std::string &path, const Params &params,
-                              const Headers &headers, Progress progress) {
-  if (params.empty()) { return Get(path, headers); }
-
-  std::string path_with_query = append_query_params(path, params);
-  return Get(path_with_query, headers, std::move(progress));
-}
-
 Result ClientImpl::Get(const std::string &path, const Params &params,
                               const Headers &headers,
                               ContentReceiver content_receiver,
-                              Progress progress) {
+                              DownloadProgress progress) {
   return Get(path, params, headers, nullptr, std::move(content_receiver),
              std::move(progress));
 }
@@ -5722,7 +7032,7 @@ Result ClientImpl::Get(const std::string &path, const Params &params,
                               const Headers &headers,
                               ResponseHandler response_handler,
                               ContentReceiver content_receiver,
-                              Progress progress) {
+                              DownloadProgress progress) {
   if (params.empty()) {
     return Get(path, headers, std::move(response_handler),
                std::move(content_receiver), std::move(progress));
@@ -5761,85 +7071,35 @@ Result ClientImpl::Post(const std::string &path,
 
 Result ClientImpl::Post(const std::string &path, const char *body,
                                size_t content_length,
-                               const std::string &content_type) {
-  return Post(path, Headers(), body, content_length, content_type, nullptr);
-}
-
-Result ClientImpl::Post(const std::string &path, const Headers &headers,
-                               const char *body, size_t content_length,
-                               const std::string &content_type) {
-  return send_with_content_provider("POST", path, headers, body, content_length,
-                                    nullptr, nullptr, content_type, nullptr);
-}
-
-Result ClientImpl::Post(const std::string &path, const Headers &headers,
-                               const char *body, size_t content_length,
                                const std::string &content_type,
-                               Progress progress) {
-  return send_with_content_provider("POST", path, headers, body, content_length,
-                                    nullptr, nullptr, content_type, progress);
-}
-
-Result ClientImpl::Post(const std::string &path, const std::string &body,
-                               const std::string &content_type) {
-  return Post(path, Headers(), body, content_type);
+                               UploadProgress progress) {
+  return Post(path, Headers(), body, content_length, content_type, progress);
 }
 
 Result ClientImpl::Post(const std::string &path, const std::string &body,
                                const std::string &content_type,
-                               Progress progress) {
+                               UploadProgress progress) {
   return Post(path, Headers(), body, content_type, progress);
 }
 
-Result ClientImpl::Post(const std::string &path, const Headers &headers,
-                               const std::string &body,
-                               const std::string &content_type) {
-  return send_with_content_provider("POST", path, headers, body.data(),
-                                    body.size(), nullptr, nullptr, content_type,
-                                    nullptr);
-}
-
-Result ClientImpl::Post(const std::string &path, const Headers &headers,
-                               const std::string &body,
-                               const std::string &content_type,
-                               Progress progress) {
-  return send_with_content_provider("POST", path, headers, body.data(),
-                                    body.size(), nullptr, nullptr, content_type,
-                                    progress);
-}
-
 Result ClientImpl::Post(const std::string &path, const Params &params) {
   return Post(path, Headers(), params);
 }
 
 Result ClientImpl::Post(const std::string &path, size_t content_length,
                                ContentProvider content_provider,
-                               const std::string &content_type) {
+                               const std::string &content_type,
+                               UploadProgress progress) {
   return Post(path, Headers(), content_length, std::move(content_provider),
-              content_type);
+              content_type, progress);
 }
 
 Result ClientImpl::Post(const std::string &path,
                                ContentProviderWithoutLength content_provider,
-                               const std::string &content_type) {
-  return Post(path, Headers(), std::move(content_provider), content_type);
-}
-
-Result ClientImpl::Post(const std::string &path, const Headers &headers,
-                               size_t content_length,
-                               ContentProvider content_provider,
-                               const std::string &content_type) {
-  return send_with_content_provider("POST", path, headers, nullptr,
-                                    content_length, std::move(content_provider),
-                                    nullptr, content_type, nullptr);
-}
-
-Result ClientImpl::Post(const std::string &path, const Headers &headers,
-                               ContentProviderWithoutLength content_provider,
-                               const std::string &content_type) {
-  return send_with_content_provider("POST", path, headers, nullptr, 0, nullptr,
-                                    std::move(content_provider), content_type,
-                                    nullptr);
+                               const std::string &content_type,
+                               UploadProgress progress) {
+  return Post(path, Headers(), std::move(content_provider), content_type,
+              progress);
 }
 
 Result ClientImpl::Post(const std::string &path, const Headers &headers,
@@ -5848,30 +7108,26 @@ Result ClientImpl::Post(const std::string &path, const Headers &headers,
   return Post(path, headers, query, "application/x-www-form-urlencoded");
 }
 
-Result ClientImpl::Post(const std::string &path, const Headers &headers,
-                               const Params &params, Progress progress) {
-  auto query = detail::params_to_query_str(params);
-  return Post(path, headers, query, "application/x-www-form-urlencoded",
-              progress);
-}
-
 Result ClientImpl::Post(const std::string &path,
-                               const MultipartFormDataItems &items) {
-  return Post(path, Headers(), items);
+                               const UploadFormDataItems &items,
+                               UploadProgress progress) {
+  return Post(path, Headers(), items, progress);
 }
 
 Result ClientImpl::Post(const std::string &path, const Headers &headers,
-                               const MultipartFormDataItems &items) {
+                               const UploadFormDataItems &items,
+                               UploadProgress progress) {
   const auto &boundary = detail::make_multipart_data_boundary();
   const auto &content_type =
       detail::serialize_multipart_formdata_get_content_type(boundary);
   const auto &body = detail::serialize_multipart_formdata(items, boundary);
-  return Post(path, headers, body, content_type);
+  return Post(path, headers, body, content_type, progress);
 }
 
 Result ClientImpl::Post(const std::string &path, const Headers &headers,
-                               const MultipartFormDataItems &items,
-                               const std::string &boundary) {
+                               const UploadFormDataItems &items,
+                               const std::string &boundary,
+                               UploadProgress progress) {
   if (!detail::is_multipart_boundary_chars_valid(boundary)) {
     return Result{nullptr, Error::UnsupportedMultipartBoundaryChars};
   }
@@ -5879,107 +7135,123 @@ Result ClientImpl::Post(const std::string &path, const Headers &headers,
   const auto &content_type =
       detail::serialize_multipart_formdata_get_content_type(boundary);
   const auto &body = detail::serialize_multipart_formdata(items, boundary);
-  return Post(path, headers, body, content_type);
+  return Post(path, headers, body, content_type, progress);
+}
+
+Result ClientImpl::Post(const std::string &path, const Headers &headers,
+                               const char *body, size_t content_length,
+                               const std::string &content_type,
+                               UploadProgress progress) {
+  return send_with_content_provider("POST", path, headers, body, content_length,
+                                    nullptr, nullptr, content_type, progress);
+}
+
+Result ClientImpl::Post(const std::string &path, const Headers &headers,
+                               const std::string &body,
+                               const std::string &content_type,
+                               UploadProgress progress) {
+  return send_with_content_provider("POST", path, headers, body.data(),
+                                    body.size(), nullptr, nullptr, content_type,
+                                    progress);
+}
+
+Result ClientImpl::Post(const std::string &path, const Headers &headers,
+                               size_t content_length,
+                               ContentProvider content_provider,
+                               const std::string &content_type,
+                               UploadProgress progress) {
+  return send_with_content_provider("POST", path, headers, nullptr,
+                                    content_length, std::move(content_provider),
+                                    nullptr, content_type, progress);
+}
+
+Result ClientImpl::Post(const std::string &path, const Headers &headers,
+                               ContentProviderWithoutLength content_provider,
+                               const std::string &content_type,
+                               UploadProgress progress) {
+  return send_with_content_provider("POST", path, headers, nullptr, 0, nullptr,
+                                    std::move(content_provider), content_type,
+                                    progress);
 }
 
-Result
-ClientImpl::Post(const std::string &path, const Headers &headers,
-                 const MultipartFormDataItems &items,
-                 const MultipartFormDataProviderItems &provider_items) {
+Result ClientImpl::Post(const std::string &path, const Headers &headers,
+                               const UploadFormDataItems &items,
+                               const FormDataProviderItems &provider_items,
+                               UploadProgress progress) {
   const auto &boundary = detail::make_multipart_data_boundary();
   const auto &content_type =
       detail::serialize_multipart_formdata_get_content_type(boundary);
   return send_with_content_provider(
       "POST", path, headers, nullptr, 0, nullptr,
       get_multipart_content_provider(boundary, items, provider_items),
-      content_type, nullptr);
+      content_type, progress);
 }
 
-Result ClientImpl::Put(const std::string &path) {
-  return Put(path, std::string(), std::string());
-}
+Result ClientImpl::Post(const std::string &path, const Headers &headers,
+                               const std::string &body,
+                               const std::string &content_type,
+                               ContentReceiver content_receiver,
+                               DownloadProgress progress) {
+  Request req;
+  req.method = "POST";
+  req.path = path;
+  req.headers = headers;
+  req.body = body;
+  req.content_receiver =
+      [content_receiver](const char *data, size_t data_length,
+                         size_t /*offset*/, size_t /*total_length*/) {
+        return content_receiver(data, data_length);
+      };
+  req.download_progress = std::move(progress);
 
-Result ClientImpl::Put(const std::string &path, const char *body,
-                              size_t content_length,
-                              const std::string &content_type) {
-  return Put(path, Headers(), body, content_length, content_type);
+  if (max_timeout_msec_ > 0) {
+    req.start_time_ = std::chrono::steady_clock::now();
+  }
+
+  if (!content_type.empty()) { req.set_header("Content-Type", content_type); }
+
+  return send_(std::move(req));
 }
 
-Result ClientImpl::Put(const std::string &path, const Headers &headers,
-                              const char *body, size_t content_length,
-                              const std::string &content_type) {
-  return send_with_content_provider("PUT", path, headers, body, content_length,
-                                    nullptr, nullptr, content_type, nullptr);
+Result ClientImpl::Put(const std::string &path) {
+  return Put(path, std::string(), std::string());
 }
 
-Result ClientImpl::Put(const std::string &path, const Headers &headers,
-                              const char *body, size_t content_length,
-                              const std::string &content_type,
-                              Progress progress) {
-  return send_with_content_provider("PUT", path, headers, body, content_length,
-                                    nullptr, nullptr, content_type, progress);
+Result ClientImpl::Put(const std::string &path, const Headers &headers) {
+  return Put(path, headers, nullptr, 0, std::string());
 }
 
-Result ClientImpl::Put(const std::string &path, const std::string &body,
-                              const std::string &content_type) {
-  return Put(path, Headers(), body, content_type);
+Result ClientImpl::Put(const std::string &path, const char *body,
+                              size_t content_length,
+                              const std::string &content_type,
+                              UploadProgress progress) {
+  return Put(path, Headers(), body, content_length, content_type, progress);
 }
 
 Result ClientImpl::Put(const std::string &path, const std::string &body,
                               const std::string &content_type,
-                              Progress progress) {
+                              UploadProgress progress) {
   return Put(path, Headers(), body, content_type, progress);
 }
 
-Result ClientImpl::Put(const std::string &path, const Headers &headers,
-                              const std::string &body,
-                              const std::string &content_type) {
-  return send_with_content_provider("PUT", path, headers, body.data(),
-                                    body.size(), nullptr, nullptr, content_type,
-                                    nullptr);
-}
-
-Result ClientImpl::Put(const std::string &path, const Headers &headers,
-                              const std::string &body,
-                              const std::string &content_type,
-                              Progress progress) {
-  return send_with_content_provider("PUT", path, headers, body.data(),
-                                    body.size(), nullptr, nullptr, content_type,
-                                    progress);
+Result ClientImpl::Put(const std::string &path, const Params &params) {
+  return Put(path, Headers(), params);
 }
 
 Result ClientImpl::Put(const std::string &path, size_t content_length,
                               ContentProvider content_provider,
-                              const std::string &content_type) {
+                              const std::string &content_type,
+                              UploadProgress progress) {
   return Put(path, Headers(), content_length, std::move(content_provider),
-             content_type);
+             content_type, progress);
 }
 
 Result ClientImpl::Put(const std::string &path,
                               ContentProviderWithoutLength content_provider,
-                              const std::string &content_type) {
-  return Put(path, Headers(), std::move(content_provider), content_type);
-}
-
-Result ClientImpl::Put(const std::string &path, const Headers &headers,
-                              size_t content_length,
-                              ContentProvider content_provider,
-                              const std::string &content_type) {
-  return send_with_content_provider("PUT", path, headers, nullptr,
-                                    content_length, std::move(content_provider),
-                                    nullptr, content_type, nullptr);
-}
-
-Result ClientImpl::Put(const std::string &path, const Headers &headers,
-                              ContentProviderWithoutLength content_provider,
-                              const std::string &content_type) {
-  return send_with_content_provider("PUT", path, headers, nullptr, 0, nullptr,
-                                    std::move(content_provider), content_type,
-                                    nullptr);
-}
-
-Result ClientImpl::Put(const std::string &path, const Params &params) {
-  return Put(path, Headers(), params);
+                              const std::string &content_type,
+                              UploadProgress progress) {
+  return Put(path, Headers(), std::move(content_provider), content_type,
+             progress);
 }
 
 Result ClientImpl::Put(const std::string &path, const Headers &headers,
@@ -5988,30 +7260,26 @@ Result ClientImpl::Put(const std::string &path, const Headers &headers,
   return Put(path, headers, query, "application/x-www-form-urlencoded");
 }
 
-Result ClientImpl::Put(const std::string &path, const Headers &headers,
-                              const Params &params, Progress progress) {
-  auto query = detail::params_to_query_str(params);
-  return Put(path, headers, query, "application/x-www-form-urlencoded",
-             progress);
-}
-
 Result ClientImpl::Put(const std::string &path,
-                              const MultipartFormDataItems &items) {
-  return Put(path, Headers(), items);
+                              const UploadFormDataItems &items,
+                              UploadProgress progress) {
+  return Put(path, Headers(), items, progress);
 }
 
 Result ClientImpl::Put(const std::string &path, const Headers &headers,
-                              const MultipartFormDataItems &items) {
+                              const UploadFormDataItems &items,
+                              UploadProgress progress) {
   const auto &boundary = detail::make_multipart_data_boundary();
   const auto &content_type =
       detail::serialize_multipart_formdata_get_content_type(boundary);
   const auto &body = detail::serialize_multipart_formdata(items, boundary);
-  return Put(path, headers, body, content_type);
+  return Put(path, headers, body, content_type, progress);
 }
 
 Result ClientImpl::Put(const std::string &path, const Headers &headers,
-                              const MultipartFormDataItems &items,
-                              const std::string &boundary) {
+                              const UploadFormDataItems &items,
+                              const std::string &boundary,
+                              UploadProgress progress) {
   if (!detail::is_multipart_boundary_chars_valid(boundary)) {
     return Result{nullptr, Error::UnsupportedMultipartBoundaryChars};
   }
@@ -6019,150 +7287,297 @@ Result ClientImpl::Put(const std::string &path, const Headers &headers,
   const auto &content_type =
       detail::serialize_multipart_formdata_get_content_type(boundary);
   const auto &body = detail::serialize_multipart_formdata(items, boundary);
-  return Put(path, headers, body, content_type);
+  return Put(path, headers, body, content_type, progress);
+}
+
+Result ClientImpl::Put(const std::string &path, const Headers &headers,
+                              const char *body, size_t content_length,
+                              const std::string &content_type,
+                              UploadProgress progress) {
+  return send_with_content_provider("PUT", path, headers, body, content_length,
+                                    nullptr, nullptr, content_type, progress);
+}
+
+Result ClientImpl::Put(const std::string &path, const Headers &headers,
+                              const std::string &body,
+                              const std::string &content_type,
+                              UploadProgress progress) {
+  return send_with_content_provider("PUT", path, headers, body.data(),
+                                    body.size(), nullptr, nullptr, content_type,
+                                    progress);
+}
+
+Result ClientImpl::Put(const std::string &path, const Headers &headers,
+                              size_t content_length,
+                              ContentProvider content_provider,
+                              const std::string &content_type,
+                              UploadProgress progress) {
+  return send_with_content_provider("PUT", path, headers, nullptr,
+                                    content_length, std::move(content_provider),
+                                    nullptr, content_type, progress);
+}
+
+Result ClientImpl::Put(const std::string &path, const Headers &headers,
+                              ContentProviderWithoutLength content_provider,
+                              const std::string &content_type,
+                              UploadProgress progress) {
+  return send_with_content_provider("PUT", path, headers, nullptr, 0, nullptr,
+                                    std::move(content_provider), content_type,
+                                    progress);
 }
 
-Result
-ClientImpl::Put(const std::string &path, const Headers &headers,
-                const MultipartFormDataItems &items,
-                const MultipartFormDataProviderItems &provider_items) {
+Result ClientImpl::Put(const std::string &path, const Headers &headers,
+                              const UploadFormDataItems &items,
+                              const FormDataProviderItems &provider_items,
+                              UploadProgress progress) {
   const auto &boundary = detail::make_multipart_data_boundary();
   const auto &content_type =
       detail::serialize_multipart_formdata_get_content_type(boundary);
   return send_with_content_provider(
       "PUT", path, headers, nullptr, 0, nullptr,
       get_multipart_content_provider(boundary, items, provider_items),
-      content_type, nullptr);
+      content_type, progress);
+}
+
+Result ClientImpl::Put(const std::string &path, const Headers &headers,
+                              const std::string &body,
+                              const std::string &content_type,
+                              ContentReceiver content_receiver,
+                              DownloadProgress progress) {
+  Request req;
+  req.method = "PUT";
+  req.path = path;
+  req.headers = headers;
+  req.body = body;
+  req.content_receiver =
+      [content_receiver](const char *data, size_t data_length,
+                         size_t /*offset*/, size_t /*total_length*/) {
+        return content_receiver(data, data_length);
+      };
+  req.download_progress = std::move(progress);
+
+  if (max_timeout_msec_ > 0) {
+    req.start_time_ = std::chrono::steady_clock::now();
+  }
+
+  if (!content_type.empty()) { req.set_header("Content-Type", content_type); }
+
+  return send_(std::move(req));
 }
+
 Result ClientImpl::Patch(const std::string &path) {
   return Patch(path, std::string(), std::string());
 }
 
-Result ClientImpl::Patch(const std::string &path, const char *body,
-                                size_t content_length,
-                                const std::string &content_type) {
-  return Patch(path, Headers(), body, content_length, content_type);
+Result ClientImpl::Patch(const std::string &path, const Headers &headers,
+                                UploadProgress progress) {
+  return Patch(path, headers, nullptr, 0, std::string(), progress);
 }
 
 Result ClientImpl::Patch(const std::string &path, const char *body,
                                 size_t content_length,
                                 const std::string &content_type,
-                                Progress progress) {
+                                UploadProgress progress) {
   return Patch(path, Headers(), body, content_length, content_type, progress);
 }
 
+Result ClientImpl::Patch(const std::string &path,
+                                const std::string &body,
+                                const std::string &content_type,
+                                UploadProgress progress) {
+  return Patch(path, Headers(), body, content_type, progress);
+}
+
+Result ClientImpl::Patch(const std::string &path, const Params &params) {
+  return Patch(path, Headers(), params);
+}
+
+Result ClientImpl::Patch(const std::string &path, size_t content_length,
+                                ContentProvider content_provider,
+                                const std::string &content_type,
+                                UploadProgress progress) {
+  return Patch(path, Headers(), content_length, std::move(content_provider),
+               content_type, progress);
+}
+
+Result ClientImpl::Patch(const std::string &path,
+                                ContentProviderWithoutLength content_provider,
+                                const std::string &content_type,
+                                UploadProgress progress) {
+  return Patch(path, Headers(), std::move(content_provider), content_type,
+               progress);
+}
+
+Result ClientImpl::Patch(const std::string &path, const Headers &headers,
+                                const Params &params) {
+  auto query = detail::params_to_query_str(params);
+  return Patch(path, headers, query, "application/x-www-form-urlencoded");
+}
+
+Result ClientImpl::Patch(const std::string &path,
+                                const UploadFormDataItems &items,
+                                UploadProgress progress) {
+  return Patch(path, Headers(), items, progress);
+}
+
 Result ClientImpl::Patch(const std::string &path, const Headers &headers,
-                                const char *body, size_t content_length,
-                                const std::string &content_type) {
-  return Patch(path, headers, body, content_length, content_type, nullptr);
+                                const UploadFormDataItems &items,
+                                UploadProgress progress) {
+  const auto &boundary = detail::make_multipart_data_boundary();
+  const auto &content_type =
+      detail::serialize_multipart_formdata_get_content_type(boundary);
+  const auto &body = detail::serialize_multipart_formdata(items, boundary);
+  return Patch(path, headers, body, content_type, progress);
+}
+
+Result ClientImpl::Patch(const std::string &path, const Headers &headers,
+                                const UploadFormDataItems &items,
+                                const std::string &boundary,
+                                UploadProgress progress) {
+  if (!detail::is_multipart_boundary_chars_valid(boundary)) {
+    return Result{nullptr, Error::UnsupportedMultipartBoundaryChars};
+  }
+
+  const auto &content_type =
+      detail::serialize_multipart_formdata_get_content_type(boundary);
+  const auto &body = detail::serialize_multipart_formdata(items, boundary);
+  return Patch(path, headers, body, content_type, progress);
 }
 
 Result ClientImpl::Patch(const std::string &path, const Headers &headers,
                                 const char *body, size_t content_length,
                                 const std::string &content_type,
-                                Progress progress) {
+                                UploadProgress progress) {
   return send_with_content_provider("PATCH", path, headers, body,
                                     content_length, nullptr, nullptr,
                                     content_type, progress);
 }
 
-Result ClientImpl::Patch(const std::string &path,
-                                const std::string &body,
-                                const std::string &content_type) {
-  return Patch(path, Headers(), body, content_type);
-}
-
-Result ClientImpl::Patch(const std::string &path,
-                                const std::string &body,
-                                const std::string &content_type,
-                                Progress progress) {
-  return Patch(path, Headers(), body, content_type, progress);
-}
-
-Result ClientImpl::Patch(const std::string &path, const Headers &headers,
-                                const std::string &body,
-                                const std::string &content_type) {
-  return Patch(path, headers, body, content_type, nullptr);
-}
-
 Result ClientImpl::Patch(const std::string &path, const Headers &headers,
                                 const std::string &body,
                                 const std::string &content_type,
-                                Progress progress) {
+                                UploadProgress progress) {
   return send_with_content_provider("PATCH", path, headers, body.data(),
                                     body.size(), nullptr, nullptr, content_type,
                                     progress);
 }
 
-Result ClientImpl::Patch(const std::string &path, size_t content_length,
-                                ContentProvider content_provider,
-                                const std::string &content_type) {
-  return Patch(path, Headers(), content_length, std::move(content_provider),
-               content_type);
-}
-
-Result ClientImpl::Patch(const std::string &path,
-                                ContentProviderWithoutLength content_provider,
-                                const std::string &content_type) {
-  return Patch(path, Headers(), std::move(content_provider), content_type);
-}
-
 Result ClientImpl::Patch(const std::string &path, const Headers &headers,
                                 size_t content_length,
                                 ContentProvider content_provider,
-                                const std::string &content_type) {
+                                const std::string &content_type,
+                                UploadProgress progress) {
   return send_with_content_provider("PATCH", path, headers, nullptr,
                                     content_length, std::move(content_provider),
-                                    nullptr, content_type, nullptr);
+                                    nullptr, content_type, progress);
 }
 
 Result ClientImpl::Patch(const std::string &path, const Headers &headers,
                                 ContentProviderWithoutLength content_provider,
-                                const std::string &content_type) {
+                                const std::string &content_type,
+                                UploadProgress progress) {
   return send_with_content_provider("PATCH", path, headers, nullptr, 0, nullptr,
                                     std::move(content_provider), content_type,
-                                    nullptr);
+                                    progress);
+}
+
+Result ClientImpl::Patch(const std::string &path, const Headers &headers,
+                                const UploadFormDataItems &items,
+                                const FormDataProviderItems &provider_items,
+                                UploadProgress progress) {
+  const auto &boundary = detail::make_multipart_data_boundary();
+  const auto &content_type =
+      detail::serialize_multipart_formdata_get_content_type(boundary);
+  return send_with_content_provider(
+      "PATCH", path, headers, nullptr, 0, nullptr,
+      get_multipart_content_provider(boundary, items, provider_items),
+      content_type, progress);
 }
 
-Result ClientImpl::Delete(const std::string &path) {
-  return Delete(path, Headers(), std::string(), std::string());
+Result ClientImpl::Patch(const std::string &path, const Headers &headers,
+                                const std::string &body,
+                                const std::string &content_type,
+                                ContentReceiver content_receiver,
+                                DownloadProgress progress) {
+  Request req;
+  req.method = "PATCH";
+  req.path = path;
+  req.headers = headers;
+  req.body = body;
+  req.content_receiver =
+      [content_receiver](const char *data, size_t data_length,
+                         size_t /*offset*/, size_t /*total_length*/) {
+        return content_receiver(data, data_length);
+      };
+  req.download_progress = std::move(progress);
+
+  if (max_timeout_msec_ > 0) {
+    req.start_time_ = std::chrono::steady_clock::now();
+  }
+
+  if (!content_type.empty()) { req.set_header("Content-Type", content_type); }
+
+  return send_(std::move(req));
 }
 
 Result ClientImpl::Delete(const std::string &path,
-                                 const Headers &headers) {
-  return Delete(path, headers, std::string(), std::string());
+                                 DownloadProgress progress) {
+  return Delete(path, Headers(), std::string(), std::string(), progress);
 }
 
-Result ClientImpl::Delete(const std::string &path, const char *body,
-                                 size_t content_length,
-                                 const std::string &content_type) {
-  return Delete(path, Headers(), body, content_length, content_type);
+Result ClientImpl::Delete(const std::string &path,
+                                 const Headers &headers,
+                                 DownloadProgress progress) {
+  return Delete(path, headers, std::string(), std::string(), progress);
 }
 
 Result ClientImpl::Delete(const std::string &path, const char *body,
                                  size_t content_length,
                                  const std::string &content_type,
-                                 Progress progress) {
+                                 DownloadProgress progress) {
   return Delete(path, Headers(), body, content_length, content_type, progress);
 }
 
 Result ClientImpl::Delete(const std::string &path,
-                                 const Headers &headers, const char *body,
-                                 size_t content_length,
-                                 const std::string &content_type) {
-  return Delete(path, headers, body, content_length, content_type, nullptr);
+                                 const std::string &body,
+                                 const std::string &content_type,
+                                 DownloadProgress progress) {
+  return Delete(path, Headers(), body.data(), body.size(), content_type,
+                progress);
+}
+
+Result ClientImpl::Delete(const std::string &path,
+                                 const Headers &headers,
+                                 const std::string &body,
+                                 const std::string &content_type,
+                                 DownloadProgress progress) {
+  return Delete(path, headers, body.data(), body.size(), content_type,
+                progress);
+}
+
+Result ClientImpl::Delete(const std::string &path, const Params &params,
+                                 DownloadProgress progress) {
+  return Delete(path, Headers(), params, progress);
+}
+
+Result ClientImpl::Delete(const std::string &path,
+                                 const Headers &headers, const Params &params,
+                                 DownloadProgress progress) {
+  auto query = detail::params_to_query_str(params);
+  return Delete(path, headers, query, "application/x-www-form-urlencoded",
+                progress);
 }
 
 Result ClientImpl::Delete(const std::string &path,
                                  const Headers &headers, const char *body,
                                  size_t content_length,
                                  const std::string &content_type,
-                                 Progress progress) {
+                                 DownloadProgress progress) {
   Request req;
   req.method = "DELETE";
   req.headers = headers;
   req.path = path;
-  req.progress = progress;
+  req.download_progress = std::move(progress);
   if (max_timeout_msec_ > 0) {
     req.start_time_ = std::chrono::steady_clock::now();
   }
@@ -6173,36 +7588,6 @@ Result ClientImpl::Delete(const std::string &path,
   return send_(std::move(req));
 }
 
-Result ClientImpl::Delete(const std::string &path,
-                                 const std::string &body,
-                                 const std::string &content_type) {
-  return Delete(path, Headers(), body.data(), body.size(), content_type);
-}
-
-Result ClientImpl::Delete(const std::string &path,
-                                 const std::string &body,
-                                 const std::string &content_type,
-                                 Progress progress) {
-  return Delete(path, Headers(), body.data(), body.size(), content_type,
-                progress);
-}
-
-Result ClientImpl::Delete(const std::string &path,
-                                 const Headers &headers,
-                                 const std::string &body,
-                                 const std::string &content_type) {
-  return Delete(path, headers, body.data(), body.size(), content_type);
-}
-
-Result ClientImpl::Delete(const std::string &path,
-                                 const Headers &headers,
-                                 const std::string &body,
-                                 const std::string &content_type,
-                                 Progress progress) {
-  return Delete(path, headers, body.data(), body.size(), content_type,
-                progress);
-}
-
 Result ClientImpl::Options(const std::string &path) {
   return Options(path, Headers());
 }
@@ -6226,8 +7611,8 @@ void ClientImpl::stop() {
   // If there is anything ongoing right now, the ONLY thread-safe thing we can
   // do is to shutdown_socket, so that threads using this socket suddenly
   // discover they can't read/write any more and error out. Everything else
-  // (closing the socket, shutting ssl down) is unsafe because these actions are
-  // not thread-safe.
+  // (closing the socket, shutting ssl down) is unsafe because these actions
+  // are not thread-safe.
   if (socket_requests_in_flight_ > 0) {
     shutdown_socket(socket_);
 
@@ -6295,7 +7680,7 @@ void ClientImpl::set_keep_alive(bool on) { keep_alive_ = on; }
 
 void ClientImpl::set_follow_location(bool on) { follow_location_ = on; }
 
-void ClientImpl::set_url_encode(bool on) { url_encode_ = on; }
+void ClientImpl::set_path_encode(bool on) { path_encode_ = on; }
 
 void
 ClientImpl::set_hostname_addr_map(std::map<std::string, std::string> addr_map) {
@@ -6407,12 +7792,23 @@ void ClientImpl::set_logger(Logger logger) {
   logger_ = std::move(logger);
 }
 
+void ClientImpl::set_error_logger(ErrorLogger error_logger) {
+  error_logger_ = std::move(error_logger);
+}
+
 /*
  * SSL Implementation
  */
 #ifdef CPPHTTPLIB_OPENSSL_SUPPORT
 namespace detail {
 
+bool is_ip_address(const std::string &host) {
+  struct in_addr addr4;
+  struct in6_addr addr6;
+  return inet_pton(AF_INET, host.c_str(), &addr4) == 1 ||
+         inet_pton(AF_INET6, host.c_str(), &addr6) == 1;
+}
+
 template <typename U, typename V>
 SSL *ssl_new(socket_t sock, SSL_CTX *ctx, std::mutex &ctx_mutex,
                     U SSL_connect_or_accept, V setup) {
@@ -6467,8 +7863,8 @@ void ssl_delete(std::mutex &ctx_mutex, SSL *ssl, socket_t sock,
 template <typename U>
 bool ssl_connect_or_accept_nonblocking(socket_t sock, SSL *ssl,
                                        U ssl_connect_or_accept,
-                                       time_t timeout_sec,
-                                       time_t timeout_usec) {
+                                       time_t timeout_sec, time_t timeout_usec,
+                                       int *ssl_error) {
   auto res = 0;
   while ((res = ssl_connect_or_accept(ssl)) != 1) {
     auto err = SSL_get_error(ssl, res);
@@ -6481,6 +7877,7 @@ bool ssl_connect_or_accept_nonblocking(socket_t sock, SSL *ssl,
       break;
     default: break;
     }
+    if (ssl_error) { *ssl_error = err; }
     return false;
   }
   return true;
@@ -6574,9 +7971,10 @@ ssize_t SSLSocketStream::read(char *ptr, size_t size) {
           if (ret >= 0) { return ret; }
           err = SSL_get_error(ssl_, ret);
         } else {
-          return -1;
+          break;
         }
       }
+      assert(ret < 0);
     }
     return ret;
   } else {
@@ -6606,9 +8004,10 @@ ssize_t SSLSocketStream::write(const char *ptr, size_t size) {
           if (ret >= 0) { return ret; }
           err = SSL_get_error(ssl_, ret);
         } else {
-          return -1;
+          break;
         }
       }
+      assert(ret < 0);
     }
     return ret;
   }
@@ -6659,12 +8058,26 @@ SSLServer::SSLServer(const char *cert_path, const char *private_key_path,
         SSL_CTX_use_PrivateKey_file(ctx_, private_key_path, SSL_FILETYPE_PEM) !=
             1 ||
         SSL_CTX_check_private_key(ctx_) != 1) {
+      last_ssl_error_ = static_cast<int>(ERR_get_error());
       SSL_CTX_free(ctx_);
       ctx_ = nullptr;
     } else if (client_ca_cert_file_path || client_ca_cert_dir_path) {
       SSL_CTX_load_verify_locations(ctx_, client_ca_cert_file_path,
                                     client_ca_cert_dir_path);
 
+      // Set client CA list to be sent to clients during TLS handshake
+      if (client_ca_cert_file_path) {
+        auto ca_list = SSL_load_client_CA_file(client_ca_cert_file_path);
+        if (ca_list != nullptr) {
+          SSL_CTX_set_client_CA_list(ctx_, ca_list);
+        } else {
+          // Failed to load client CA list, but we continue since
+          // SSL_CTX_load_verify_locations already succeeded and
+          // certificate verification will still work
+          last_ssl_error_ = static_cast<int>(ERR_get_error());
+        }
+      }
+
       SSL_CTX_set_verify(
           ctx_, SSL_VERIFY_PEER | SSL_VERIFY_FAIL_IF_NO_PEER_CERT, nullptr);
     }
@@ -6689,6 +8102,15 @@ SSLServer::SSLServer(X509 *cert, EVP_PKEY *private_key,
     } else if (client_ca_cert_store) {
       SSL_CTX_set_cert_store(ctx_, client_ca_cert_store);
 
+      // Extract CA names from the store and set them as the client CA list
+      auto ca_list = extract_ca_names_from_x509_store(client_ca_cert_store);
+      if (ca_list) {
+        SSL_CTX_set_client_CA_list(ctx_, ca_list);
+      } else {
+        // Failed to extract CA names, record the error
+        last_ssl_error_ = static_cast<int>(ERR_get_error());
+      }
+
       SSL_CTX_set_verify(
           ctx_, SSL_VERIFY_PEER | SSL_VERIFY_FAIL_IF_NO_PEER_CERT, nullptr);
     }
@@ -6732,7 +8154,8 @@ bool SSLServer::process_and_close_socket(socket_t sock) {
       sock, ctx_, ctx_mutex_,
       [&](SSL *ssl2) {
         return detail::ssl_connect_or_accept_nonblocking(
-            sock, ssl2, SSL_accept, read_timeout_sec_, read_timeout_usec_);
+            sock, ssl2, SSL_accept, read_timeout_sec_, read_timeout_usec_,
+            &last_ssl_error_);
       },
       [](SSL * /*ssl2*/) { return true; });
 
@@ -6768,6 +8191,44 @@ bool SSLServer::process_and_close_socket(socket_t sock) {
   return ret;
 }
 
+STACK_OF(X509_NAME) * SSLServer::extract_ca_names_from_x509_store(
+                                 X509_STORE *store) {
+  if (!store) { return nullptr; }
+
+  auto ca_list = sk_X509_NAME_new_null();
+  if (!ca_list) { return nullptr; }
+
+  // Get all objects from the store
+  auto objs = X509_STORE_get0_objects(store);
+  if (!objs) {
+    sk_X509_NAME_free(ca_list);
+    return nullptr;
+  }
+
+  // Iterate through objects and extract certificate subject names
+  for (int i = 0; i < sk_X509_OBJECT_num(objs); i++) {
+    auto obj = sk_X509_OBJECT_value(objs, i);
+    if (X509_OBJECT_get_type(obj) == X509_LU_X509) {
+      auto cert = X509_OBJECT_get0_X509(obj);
+      if (cert) {
+        auto subject = X509_get_subject_name(cert);
+        if (subject) {
+          auto name_dup = X509_NAME_dup(subject);
+          if (name_dup) { sk_X509_NAME_push(ca_list, name_dup); }
+        }
+      }
+    }
+  }
+
+  // If no names were extracted, free the list and return nullptr
+  if (sk_X509_NAME_num(ca_list) == 0) {
+    sk_X509_NAME_free(ca_list);
+    return nullptr;
+  }
+
+  return ca_list;
+}
+
 // SSL HTTP client implementation
 SSLClient::SSLClient(const std::string &host)
     : SSLClient(host, 443, std::string(), std::string()) {}
@@ -6800,6 +8261,7 @@ SSLClient::SSLClient(const std::string &host, int port,
                                      SSL_FILETYPE_PEM) != 1 ||
         SSL_CTX_use_PrivateKey_file(ctx_, client_key_path.c_str(),
                                     SSL_FILETYPE_PEM) != 1) {
+      last_openssl_error_ = ERR_get_error();
       SSL_CTX_free(ctx_);
       ctx_ = nullptr;
     }
@@ -6826,6 +8288,7 @@ SSLClient::SSLClient(const std::string &host, int port,
 
     if (SSL_CTX_use_certificate(ctx_, client_cert) != 1 ||
         SSL_CTX_use_PrivateKey(ctx_, client_key) != 1) {
+      last_openssl_error_ = ERR_get_error();
       SSL_CTX_free(ctx_);
       ctx_ = nullptr;
     }
@@ -6846,8 +8309,10 @@ void SSLClient::set_ca_cert_store(X509_STORE *ca_cert_store) {
   if (ca_cert_store) {
     if (ctx_) {
       if (SSL_CTX_get_cert_store(ctx_) != ca_cert_store) {
-        // Free memory allocated for old cert and use new store `ca_cert_store`
+        // Free memory allocated for old cert and use new store
+        // `ca_cert_store`
         SSL_CTX_set_cert_store(ctx_, ca_cert_store);
+        ca_cert_store_ = ca_cert_store;
       }
     } else {
       X509_STORE_free(ca_cert_store);
@@ -6867,10 +8332,15 @@ long SSLClient::get_openssl_verify_result() const {
 SSL_CTX *SSLClient::ssl_context() const { return ctx_; }
 
 bool SSLClient::create_and_connect_socket(Socket &socket, Error &error) {
-  return is_valid() && ClientImpl::create_and_connect_socket(socket, error);
+  if (!is_valid()) {
+    error = Error::SSLConnection;
+    return false;
+  }
+  return ClientImpl::create_and_connect_socket(socket, error);
 }
 
-// Assumes that socket_mutex_ is locked and that there are no requests in flight
+// Assumes that socket_mutex_ is locked and that there are no requests in
+// flight
 bool SSLClient::connect_with_proxy(
     Socket &socket,
     std::chrono::time_point<std::chrono::steady_clock> start_time,
@@ -6903,6 +8373,19 @@ bool SSLClient::connect_with_proxy(
         !proxy_digest_auth_password_.empty()) {
       std::map<std::string, std::string> auth;
       if (detail::parse_www_authenticate(proxy_res, auth, true)) {
+        // Close the current socket and create a new one for the authenticated
+        // request
+        shutdown_ssl(socket, true);
+        shutdown_socket(socket);
+        close_socket(socket);
+
+        // Create a new socket for the authenticated CONNECT request
+        if (!create_and_connect_socket(socket, error)) {
+          success = false;
+          output_error_log(error, nullptr);
+          return false;
+        }
+
         proxy_res = Response();
         if (!detail::process_client_socket(
                 socket.sock, read_timeout_sec_, read_timeout_usec_,
@@ -6937,6 +8420,7 @@ bool SSLClient::connect_with_proxy(
   // as the response of the request
   if (proxy_res.status != StatusCode::OK_200) {
     error = Error::ProxyConnection;
+    output_error_log(error, nullptr);
     res = std::move(proxy_res);
     // Thread-safe to close everything because we are assuming there are
     // no requests in flight
@@ -6957,11 +8441,13 @@ bool SSLClient::load_certs() {
     if (!ca_cert_file_path_.empty()) {
       if (!SSL_CTX_load_verify_locations(ctx_, ca_cert_file_path_.c_str(),
                                          nullptr)) {
+        last_openssl_error_ = ERR_get_error();
         ret = false;
       }
     } else if (!ca_cert_dir_path_.empty()) {
       if (!SSL_CTX_load_verify_locations(ctx_, nullptr,
                                          ca_cert_dir_path_.c_str())) {
+        last_openssl_error_ = ERR_get_error();
         ret = false;
       }
     } else {
@@ -6969,10 +8455,8 @@ bool SSLClient::load_certs() {
 #ifdef _WIN32
       loaded =
           detail::load_system_certs_on_windows(SSL_CTX_get_cert_store(ctx_));
-#elif defined(CPPHTTPLIB_USE_CERTS_FROM_MACOSX_KEYCHAIN) && defined(__APPLE__)
-#if TARGET_OS_OSX
+#elif defined(CPPHTTPLIB_USE_CERTS_FROM_MACOSX_KEYCHAIN) && TARGET_OS_MAC
       loaded = detail::load_system_certs_on_macos(SSL_CTX_get_cert_store(ctx_));
-#endif // TARGET_OS_OSX
 #endif // _WIN32
       if (!loaded) { SSL_CTX_set_default_verify_paths(ctx_); }
     }
@@ -6988,6 +8472,7 @@ bool SSLClient::initialize_ssl(Socket &socket, Error &error) {
         if (server_certificate_verification_) {
           if (!load_certs()) {
             error = Error::SSLLoadingCerts;
+            output_error_log(error, nullptr);
             return false;
           }
           SSL_set_verify(ssl2, SSL_VERIFY_NONE, nullptr);
@@ -6995,8 +8480,9 @@ bool SSLClient::initialize_ssl(Socket &socket, Error &error) {
 
         if (!detail::ssl_connect_or_accept_nonblocking(
                 socket.sock, ssl2, SSL_connect, connection_timeout_sec_,
-                connection_timeout_usec_)) {
+                connection_timeout_usec_, &last_ssl_error_)) {
           error = Error::SSLConnection;
+          output_error_log(error, nullptr);
           return false;
         }
 
@@ -7008,7 +8494,9 @@ bool SSLClient::initialize_ssl(Socket &socket, Error &error) {
           }
 
           if (verification_status == SSLVerifierResponse::CertificateRejected) {
+            last_openssl_error_ = ERR_get_error();
             error = Error::SSLServerVerification;
+            output_error_log(error, nullptr);
             return false;
           }
 
@@ -7016,7 +8504,9 @@ bool SSLClient::initialize_ssl(Socket &socket, Error &error) {
             verify_result_ = SSL_get_verify_result(ssl2);
 
             if (verify_result_ != X509_V_OK) {
+              last_openssl_error_ = static_cast<unsigned long>(verify_result_);
               error = Error::SSLServerVerification;
+              output_error_log(error, nullptr);
               return false;
             }
 
@@ -7024,13 +8514,17 @@ bool SSLClient::initialize_ssl(Socket &socket, Error &error) {
             auto se = detail::scope_exit([&] { X509_free(server_cert); });
 
             if (server_cert == nullptr) {
+              last_openssl_error_ = ERR_get_error();
               error = Error::SSLServerVerification;
+              output_error_log(error, nullptr);
               return false;
             }
 
             if (server_hostname_verification_) {
               if (!verify_host(server_cert)) {
+                last_openssl_error_ = X509_V_ERR_HOSTNAME_MISMATCH;
                 error = Error::SSLServerHostnameVerification;
+                output_error_log(error, nullptr);
                 return false;
               }
             }
@@ -7040,14 +8534,18 @@ bool SSLClient::initialize_ssl(Socket &socket, Error &error) {
         return true;
       },
       [&](SSL *ssl2) {
+        // Set SNI only if host is not IP address
+        if (!detail::is_ip_address(host_)) {
 #if defined(OPENSSL_IS_BORINGSSL)
-        SSL_set_tlsext_host_name(ssl2, host_.c_str());
+          SSL_set_tlsext_host_name(ssl2, host_.c_str());
 #else
-        // NOTE: Direct call instead of using the OpenSSL macro to suppress
-        // -Wold-style-cast warning
-        SSL_ctrl(ssl2, SSL_CTRL_SET_TLSEXT_HOSTNAME, TLSEXT_NAMETYPE_host_name,
-                 static_cast<void *>(const_cast<char *>(host_.c_str())));
+          // NOTE: Direct call instead of using the OpenSSL macro to suppress
+          // -Wold-style-cast warning
+          SSL_ctrl(ssl2, SSL_CTRL_SET_TLSEXT_HOSTNAME,
+                   TLSEXT_NAMETYPE_host_name,
+                   static_cast<void *>(const_cast<char *>(host_.c_str())));
 #endif
+        }
         return true;
       });
 
@@ -7056,6 +8554,11 @@ bool SSLClient::initialize_ssl(Socket &socket, Error &error) {
     return true;
   }
 
+  if (ctx_ == nullptr) {
+    error = Error::SSLConnection;
+    last_openssl_error_ = ERR_get_error();
+  }
+
   shutdown_socket(socket);
   close_socket(socket);
   return false;
@@ -7149,21 +8652,22 @@ SSLClient::verify_host_with_subject_alt_name(X509 *server_cert) const {
 
     for (decltype(count) i = 0; i < count && !dsn_matched; i++) {
       auto val = sk_GENERAL_NAME_value(alt_names, i);
-      if (val->type == type) {
-        auto name =
-            reinterpret_cast<const char *>(ASN1_STRING_get0_data(val->d.ia5));
-        auto name_len = static_cast<size_t>(ASN1_STRING_length(val->d.ia5));
-
-        switch (type) {
-        case GEN_DNS: dsn_matched = check_host_name(name, name_len); break;
-
-        case GEN_IPADD:
-          if (!memcmp(&addr6, name, addr_len) ||
-              !memcmp(&addr, name, addr_len)) {
-            ip_matched = true;
-          }
-          break;
+      if (!val || val->type != type) { continue; }
+
+      auto name =
+          reinterpret_cast<const char *>(ASN1_STRING_get0_data(val->d.ia5));
+      if (name == nullptr) { continue; }
+
+      auto name_len = static_cast<size_t>(ASN1_STRING_length(val->d.ia5));
+
+      switch (type) {
+      case GEN_DNS: dsn_matched = check_host_name(name, name_len); break;
+
+      case GEN_IPADD:
+        if (!memcmp(&addr6, name, addr_len) || !memcmp(&addr, name, addr_len)) {
+          ip_matched = true;
         }
+        break;
       }
     }
 
@@ -7287,72 +8791,54 @@ bool Client::is_valid() const {
   return cli_ != nullptr && cli_->is_valid();
 }
 
-Result Client::Get(const std::string &path) { return cli_->Get(path); }
-Result Client::Get(const std::string &path, const Headers &headers) {
-  return cli_->Get(path, headers);
-}
-Result Client::Get(const std::string &path, Progress progress) {
+Result Client::Get(const std::string &path, DownloadProgress progress) {
   return cli_->Get(path, std::move(progress));
 }
 Result Client::Get(const std::string &path, const Headers &headers,
-                          Progress progress) {
+                          DownloadProgress progress) {
   return cli_->Get(path, headers, std::move(progress));
 }
 Result Client::Get(const std::string &path,
-                          ContentReceiver content_receiver) {
-  return cli_->Get(path, std::move(content_receiver));
-}
-Result Client::Get(const std::string &path, const Headers &headers,
-                          ContentReceiver content_receiver) {
-  return cli_->Get(path, headers, std::move(content_receiver));
-}
-Result Client::Get(const std::string &path,
-                          ContentReceiver content_receiver, Progress progress) {
+                          ContentReceiver content_receiver,
+                          DownloadProgress progress) {
   return cli_->Get(path, std::move(content_receiver), std::move(progress));
 }
 Result Client::Get(const std::string &path, const Headers &headers,
-                          ContentReceiver content_receiver, Progress progress) {
+                          ContentReceiver content_receiver,
+                          DownloadProgress progress) {
   return cli_->Get(path, headers, std::move(content_receiver),
                    std::move(progress));
 }
 Result Client::Get(const std::string &path,
                           ResponseHandler response_handler,
-                          ContentReceiver content_receiver) {
-  return cli_->Get(path, std::move(response_handler),
-                   std::move(content_receiver));
-}
-Result Client::Get(const std::string &path, const Headers &headers,
-                          ResponseHandler response_handler,
-                          ContentReceiver content_receiver) {
-  return cli_->Get(path, headers, std::move(response_handler),
-                   std::move(content_receiver));
-}
-Result Client::Get(const std::string &path,
-                          ResponseHandler response_handler,
-                          ContentReceiver content_receiver, Progress progress) {
+                          ContentReceiver content_receiver,
+                          DownloadProgress progress) {
   return cli_->Get(path, std::move(response_handler),
                    std::move(content_receiver), std::move(progress));
 }
 Result Client::Get(const std::string &path, const Headers &headers,
                           ResponseHandler response_handler,
-                          ContentReceiver content_receiver, Progress progress) {
+                          ContentReceiver content_receiver,
+                          DownloadProgress progress) {
   return cli_->Get(path, headers, std::move(response_handler),
                    std::move(content_receiver), std::move(progress));
 }
 Result Client::Get(const std::string &path, const Params &params,
-                          const Headers &headers, Progress progress) {
+                          const Headers &headers, DownloadProgress progress) {
   return cli_->Get(path, params, headers, std::move(progress));
 }
 Result Client::Get(const std::string &path, const Params &params,
                           const Headers &headers,
-                          ContentReceiver content_receiver, Progress progress) {
+                          ContentReceiver content_receiver,
+                          DownloadProgress progress) {
   return cli_->Get(path, params, headers, std::move(content_receiver),
                    std::move(progress));
 }
 Result Client::Get(const std::string &path, const Params &params,
                           const Headers &headers,
                           ResponseHandler response_handler,
-                          ContentReceiver content_receiver, Progress progress) {
+                          ContentReceiver content_receiver,
+                          DownloadProgress progress) {
   return cli_->Get(path, params, headers, std::move(response_handler),
                    std::move(content_receiver), std::move(progress));
 }
@@ -7368,60 +8854,55 @@ Result Client::Post(const std::string &path, const Headers &headers) {
 }
 Result Client::Post(const std::string &path, const char *body,
                            size_t content_length,
-                           const std::string &content_type) {
-  return cli_->Post(path, body, content_length, content_type);
+                           const std::string &content_type,
+                           UploadProgress progress) {
+  return cli_->Post(path, body, content_length, content_type, progress);
 }
 Result Client::Post(const std::string &path, const Headers &headers,
                            const char *body, size_t content_length,
-                           const std::string &content_type) {
-  return cli_->Post(path, headers, body, content_length, content_type);
-}
-Result Client::Post(const std::string &path, const Headers &headers,
-                           const char *body, size_t content_length,
-                           const std::string &content_type, Progress progress) {
+                           const std::string &content_type,
+                           UploadProgress progress) {
   return cli_->Post(path, headers, body, content_length, content_type,
                     progress);
 }
 Result Client::Post(const std::string &path, const std::string &body,
-                           const std::string &content_type) {
-  return cli_->Post(path, body, content_type);
-}
-Result Client::Post(const std::string &path, const std::string &body,
-                           const std::string &content_type, Progress progress) {
+                           const std::string &content_type,
+                           UploadProgress progress) {
   return cli_->Post(path, body, content_type, progress);
 }
 Result Client::Post(const std::string &path, const Headers &headers,
                            const std::string &body,
-                           const std::string &content_type) {
-  return cli_->Post(path, headers, body, content_type);
-}
-Result Client::Post(const std::string &path, const Headers &headers,
-                           const std::string &body,
-                           const std::string &content_type, Progress progress) {
+                           const std::string &content_type,
+                           UploadProgress progress) {
   return cli_->Post(path, headers, body, content_type, progress);
 }
 Result Client::Post(const std::string &path, size_t content_length,
                            ContentProvider content_provider,
-                           const std::string &content_type) {
+                           const std::string &content_type,
+                           UploadProgress progress) {
   return cli_->Post(path, content_length, std::move(content_provider),
-                    content_type);
+                    content_type, progress);
 }
 Result Client::Post(const std::string &path,
                            ContentProviderWithoutLength content_provider,
-                           const std::string &content_type) {
-  return cli_->Post(path, std::move(content_provider), content_type);
+                           const std::string &content_type,
+                           UploadProgress progress) {
+  return cli_->Post(path, std::move(content_provider), content_type, progress);
 }
 Result Client::Post(const std::string &path, const Headers &headers,
                            size_t content_length,
                            ContentProvider content_provider,
-                           const std::string &content_type) {
+                           const std::string &content_type,
+                           UploadProgress progress) {
   return cli_->Post(path, headers, content_length, std::move(content_provider),
-                    content_type);
+                    content_type, progress);
 }
 Result Client::Post(const std::string &path, const Headers &headers,
                            ContentProviderWithoutLength content_provider,
-                           const std::string &content_type) {
-  return cli_->Post(path, headers, std::move(content_provider), content_type);
+                           const std::string &content_type,
+                           UploadProgress progress) {
+  return cli_->Post(path, headers, std::move(content_provider), content_type,
+                    progress);
 }
 Result Client::Post(const std::string &path, const Params &params) {
   return cli_->Post(path, params);
@@ -7430,85 +8911,91 @@ Result Client::Post(const std::string &path, const Headers &headers,
                            const Params &params) {
   return cli_->Post(path, headers, params);
 }
-Result Client::Post(const std::string &path, const Headers &headers,
-                           const Params &params, Progress progress) {
-  return cli_->Post(path, headers, params, progress);
-}
 Result Client::Post(const std::string &path,
-                           const MultipartFormDataItems &items) {
-  return cli_->Post(path, items);
+                           const UploadFormDataItems &items,
+                           UploadProgress progress) {
+  return cli_->Post(path, items, progress);
+}
+Result Client::Post(const std::string &path, const Headers &headers,
+                           const UploadFormDataItems &items,
+                           UploadProgress progress) {
+  return cli_->Post(path, headers, items, progress);
 }
 Result Client::Post(const std::string &path, const Headers &headers,
-                           const MultipartFormDataItems &items) {
-  return cli_->Post(path, headers, items);
+                           const UploadFormDataItems &items,
+                           const std::string &boundary,
+                           UploadProgress progress) {
+  return cli_->Post(path, headers, items, boundary, progress);
 }
 Result Client::Post(const std::string &path, const Headers &headers,
-                           const MultipartFormDataItems &items,
-                           const std::string &boundary) {
-  return cli_->Post(path, headers, items, boundary);
+                           const UploadFormDataItems &items,
+                           const FormDataProviderItems &provider_items,
+                           UploadProgress progress) {
+  return cli_->Post(path, headers, items, provider_items, progress);
 }
-Result
-Client::Post(const std::string &path, const Headers &headers,
-             const MultipartFormDataItems &items,
-             const MultipartFormDataProviderItems &provider_items) {
-  return cli_->Post(path, headers, items, provider_items);
+Result Client::Post(const std::string &path, const Headers &headers,
+                           const std::string &body,
+                           const std::string &content_type,
+                           ContentReceiver content_receiver,
+                           DownloadProgress progress) {
+  return cli_->Post(path, headers, body, content_type, content_receiver,
+                    progress);
 }
+
 Result Client::Put(const std::string &path) { return cli_->Put(path); }
+Result Client::Put(const std::string &path, const Headers &headers) {
+  return cli_->Put(path, headers);
+}
 Result Client::Put(const std::string &path, const char *body,
                           size_t content_length,
-                          const std::string &content_type) {
-  return cli_->Put(path, body, content_length, content_type);
-}
-Result Client::Put(const std::string &path, const Headers &headers,
-                          const char *body, size_t content_length,
-                          const std::string &content_type) {
-  return cli_->Put(path, headers, body, content_length, content_type);
+                          const std::string &content_type,
+                          UploadProgress progress) {
+  return cli_->Put(path, body, content_length, content_type, progress);
 }
 Result Client::Put(const std::string &path, const Headers &headers,
                           const char *body, size_t content_length,
-                          const std::string &content_type, Progress progress) {
+                          const std::string &content_type,
+                          UploadProgress progress) {
   return cli_->Put(path, headers, body, content_length, content_type, progress);
 }
 Result Client::Put(const std::string &path, const std::string &body,
-                          const std::string &content_type) {
-  return cli_->Put(path, body, content_type);
-}
-Result Client::Put(const std::string &path, const std::string &body,
-                          const std::string &content_type, Progress progress) {
+                          const std::string &content_type,
+                          UploadProgress progress) {
   return cli_->Put(path, body, content_type, progress);
 }
 Result Client::Put(const std::string &path, const Headers &headers,
                           const std::string &body,
-                          const std::string &content_type) {
-  return cli_->Put(path, headers, body, content_type);
-}
-Result Client::Put(const std::string &path, const Headers &headers,
-                          const std::string &body,
-                          const std::string &content_type, Progress progress) {
+                          const std::string &content_type,
+                          UploadProgress progress) {
   return cli_->Put(path, headers, body, content_type, progress);
 }
 Result Client::Put(const std::string &path, size_t content_length,
                           ContentProvider content_provider,
-                          const std::string &content_type) {
+                          const std::string &content_type,
+                          UploadProgress progress) {
   return cli_->Put(path, content_length, std::move(content_provider),
-                   content_type);
+                   content_type, progress);
 }
 Result Client::Put(const std::string &path,
                           ContentProviderWithoutLength content_provider,
-                          const std::string &content_type) {
-  return cli_->Put(path, std::move(content_provider), content_type);
+                          const std::string &content_type,
+                          UploadProgress progress) {
+  return cli_->Put(path, std::move(content_provider), content_type, progress);
 }
 Result Client::Put(const std::string &path, const Headers &headers,
                           size_t content_length,
                           ContentProvider content_provider,
-                          const std::string &content_type) {
+                          const std::string &content_type,
+                          UploadProgress progress) {
   return cli_->Put(path, headers, content_length, std::move(content_provider),
-                   content_type);
+                   content_type, progress);
 }
 Result Client::Put(const std::string &path, const Headers &headers,
                           ContentProviderWithoutLength content_provider,
-                          const std::string &content_type) {
-  return cli_->Put(path, headers, std::move(content_provider), content_type);
+                          const std::string &content_type,
+                          UploadProgress progress) {
+  return cli_->Put(path, headers, std::move(content_provider), content_type,
+                   progress);
 }
 Result Client::Put(const std::string &path, const Params &params) {
   return cli_->Put(path, params);
@@ -7517,147 +9004,174 @@ Result Client::Put(const std::string &path, const Headers &headers,
                           const Params &params) {
   return cli_->Put(path, headers, params);
 }
-Result Client::Put(const std::string &path, const Headers &headers,
-                          const Params &params, Progress progress) {
-  return cli_->Put(path, headers, params, progress);
-}
 Result Client::Put(const std::string &path,
-                          const MultipartFormDataItems &items) {
-  return cli_->Put(path, items);
+                          const UploadFormDataItems &items,
+                          UploadProgress progress) {
+  return cli_->Put(path, items, progress);
 }
 Result Client::Put(const std::string &path, const Headers &headers,
-                          const MultipartFormDataItems &items) {
-  return cli_->Put(path, headers, items);
+                          const UploadFormDataItems &items,
+                          UploadProgress progress) {
+  return cli_->Put(path, headers, items, progress);
 }
 Result Client::Put(const std::string &path, const Headers &headers,
-                          const MultipartFormDataItems &items,
-                          const std::string &boundary) {
-  return cli_->Put(path, headers, items, boundary);
+                          const UploadFormDataItems &items,
+                          const std::string &boundary,
+                          UploadProgress progress) {
+  return cli_->Put(path, headers, items, boundary, progress);
 }
-Result
-Client::Put(const std::string &path, const Headers &headers,
-            const MultipartFormDataItems &items,
-            const MultipartFormDataProviderItems &provider_items) {
-  return cli_->Put(path, headers, items, provider_items);
+Result Client::Put(const std::string &path, const Headers &headers,
+                          const UploadFormDataItems &items,
+                          const FormDataProviderItems &provider_items,
+                          UploadProgress progress) {
+  return cli_->Put(path, headers, items, provider_items, progress);
+}
+Result Client::Put(const std::string &path, const Headers &headers,
+                          const std::string &body,
+                          const std::string &content_type,
+                          ContentReceiver content_receiver,
+                          DownloadProgress progress) {
+  return cli_->Put(path, headers, body, content_type, content_receiver,
+                   progress);
 }
+
 Result Client::Patch(const std::string &path) {
   return cli_->Patch(path);
 }
-Result Client::Patch(const std::string &path, const char *body,
-                            size_t content_length,
-                            const std::string &content_type) {
-  return cli_->Patch(path, body, content_length, content_type);
+Result Client::Patch(const std::string &path, const Headers &headers) {
+  return cli_->Patch(path, headers);
 }
 Result Client::Patch(const std::string &path, const char *body,
                             size_t content_length,
                             const std::string &content_type,
-                            Progress progress) {
+                            UploadProgress progress) {
   return cli_->Patch(path, body, content_length, content_type, progress);
 }
-Result Client::Patch(const std::string &path, const Headers &headers,
-                            const char *body, size_t content_length,
-                            const std::string &content_type) {
-  return cli_->Patch(path, headers, body, content_length, content_type);
-}
 Result Client::Patch(const std::string &path, const Headers &headers,
                             const char *body, size_t content_length,
                             const std::string &content_type,
-                            Progress progress) {
+                            UploadProgress progress) {
   return cli_->Patch(path, headers, body, content_length, content_type,
                      progress);
 }
-Result Client::Patch(const std::string &path, const std::string &body,
-                            const std::string &content_type) {
-  return cli_->Patch(path, body, content_type);
-}
 Result Client::Patch(const std::string &path, const std::string &body,
                             const std::string &content_type,
-                            Progress progress) {
+                            UploadProgress progress) {
   return cli_->Patch(path, body, content_type, progress);
 }
-Result Client::Patch(const std::string &path, const Headers &headers,
-                            const std::string &body,
-                            const std::string &content_type) {
-  return cli_->Patch(path, headers, body, content_type);
-}
 Result Client::Patch(const std::string &path, const Headers &headers,
                             const std::string &body,
                             const std::string &content_type,
-                            Progress progress) {
+                            UploadProgress progress) {
   return cli_->Patch(path, headers, body, content_type, progress);
 }
 Result Client::Patch(const std::string &path, size_t content_length,
                             ContentProvider content_provider,
-                            const std::string &content_type) {
+                            const std::string &content_type,
+                            UploadProgress progress) {
   return cli_->Patch(path, content_length, std::move(content_provider),
-                     content_type);
+                     content_type, progress);
 }
 Result Client::Patch(const std::string &path,
                             ContentProviderWithoutLength content_provider,
-                            const std::string &content_type) {
-  return cli_->Patch(path, std::move(content_provider), content_type);
+                            const std::string &content_type,
+                            UploadProgress progress) {
+  return cli_->Patch(path, std::move(content_provider), content_type, progress);
 }
 Result Client::Patch(const std::string &path, const Headers &headers,
                             size_t content_length,
                             ContentProvider content_provider,
-                            const std::string &content_type) {
+                            const std::string &content_type,
+                            UploadProgress progress) {
   return cli_->Patch(path, headers, content_length, std::move(content_provider),
-                     content_type);
+                     content_type, progress);
 }
 Result Client::Patch(const std::string &path, const Headers &headers,
                             ContentProviderWithoutLength content_provider,
-                            const std::string &content_type) {
-  return cli_->Patch(path, headers, std::move(content_provider), content_type);
+                            const std::string &content_type,
+                            UploadProgress progress) {
+  return cli_->Patch(path, headers, std::move(content_provider), content_type,
+                     progress);
 }
-Result Client::Delete(const std::string &path) {
-  return cli_->Delete(path);
+Result Client::Patch(const std::string &path, const Params &params) {
+  return cli_->Patch(path, params);
 }
-Result Client::Delete(const std::string &path, const Headers &headers) {
-  return cli_->Delete(path, headers);
+Result Client::Patch(const std::string &path, const Headers &headers,
+                            const Params &params) {
+  return cli_->Patch(path, headers, params);
 }
-Result Client::Delete(const std::string &path, const char *body,
-                             size_t content_length,
-                             const std::string &content_type) {
-  return cli_->Delete(path, body, content_length, content_type);
+Result Client::Patch(const std::string &path,
+                            const UploadFormDataItems &items,
+                            UploadProgress progress) {
+  return cli_->Patch(path, items, progress);
+}
+Result Client::Patch(const std::string &path, const Headers &headers,
+                            const UploadFormDataItems &items,
+                            UploadProgress progress) {
+  return cli_->Patch(path, headers, items, progress);
+}
+Result Client::Patch(const std::string &path, const Headers &headers,
+                            const UploadFormDataItems &items,
+                            const std::string &boundary,
+                            UploadProgress progress) {
+  return cli_->Patch(path, headers, items, boundary, progress);
+}
+Result Client::Patch(const std::string &path, const Headers &headers,
+                            const UploadFormDataItems &items,
+                            const FormDataProviderItems &provider_items,
+                            UploadProgress progress) {
+  return cli_->Patch(path, headers, items, provider_items, progress);
+}
+Result Client::Patch(const std::string &path, const Headers &headers,
+                            const std::string &body,
+                            const std::string &content_type,
+                            ContentReceiver content_receiver,
+                            DownloadProgress progress) {
+  return cli_->Patch(path, headers, body, content_type, content_receiver,
+                     progress);
+}
+
+Result Client::Delete(const std::string &path,
+                             DownloadProgress progress) {
+  return cli_->Delete(path, progress);
+}
+Result Client::Delete(const std::string &path, const Headers &headers,
+                             DownloadProgress progress) {
+  return cli_->Delete(path, headers, progress);
 }
 Result Client::Delete(const std::string &path, const char *body,
                              size_t content_length,
                              const std::string &content_type,
-                             Progress progress) {
+                             DownloadProgress progress) {
   return cli_->Delete(path, body, content_length, content_type, progress);
 }
-Result Client::Delete(const std::string &path, const Headers &headers,
-                             const char *body, size_t content_length,
-                             const std::string &content_type) {
-  return cli_->Delete(path, headers, body, content_length, content_type);
-}
 Result Client::Delete(const std::string &path, const Headers &headers,
                              const char *body, size_t content_length,
                              const std::string &content_type,
-                             Progress progress) {
+                             DownloadProgress progress) {
   return cli_->Delete(path, headers, body, content_length, content_type,
                       progress);
 }
-Result Client::Delete(const std::string &path, const std::string &body,
-                             const std::string &content_type) {
-  return cli_->Delete(path, body, content_type);
-}
 Result Client::Delete(const std::string &path, const std::string &body,
                              const std::string &content_type,
-                             Progress progress) {
+                             DownloadProgress progress) {
   return cli_->Delete(path, body, content_type, progress);
 }
-Result Client::Delete(const std::string &path, const Headers &headers,
-                             const std::string &body,
-                             const std::string &content_type) {
-  return cli_->Delete(path, headers, body, content_type);
-}
 Result Client::Delete(const std::string &path, const Headers &headers,
                              const std::string &body,
                              const std::string &content_type,
-                             Progress progress) {
+                             DownloadProgress progress) {
   return cli_->Delete(path, headers, body, content_type, progress);
 }
+Result Client::Delete(const std::string &path, const Params &params,
+                             DownloadProgress progress) {
+  return cli_->Delete(path, params, progress);
+}
+Result Client::Delete(const std::string &path, const Headers &headers,
+                             const Params &params, DownloadProgress progress) {
+  return cli_->Delete(path, headers, params, progress);
+}
+
 Result Client::Options(const std::string &path) {
   return cli_->Options(path);
 }
@@ -7736,7 +9250,12 @@ void Client::set_follow_location(bool on) {
   cli_->set_follow_location(on);
 }
 
-void Client::set_url_encode(bool on) { cli_->set_url_encode(on); }
+void Client::set_path_encode(bool on) { cli_->set_path_encode(on); }
+
+[[deprecated("Use set_path_encode instead")]]
+void Client::set_url_encode(bool on) {
+  cli_->set_path_encode(on);
+}
 
 void Client::set_compress(bool on) { cli_->set_compress(on); }
 
@@ -7782,6 +9301,10 @@ void Client::set_logger(Logger logger) {
   cli_->set_logger(std::move(logger));
 }
 
+void Client::set_error_logger(ErrorLogger error_logger) {
+  cli_->set_error_logger(std::move(error_logger));
+}
+
 #ifdef CPPHTTPLIB_OPENSSL_SUPPORT
 void Client::set_ca_cert_path(const std::string &ca_cert_file_path,
                                      const std::string &ca_cert_dir_path) {
diff --git a/vendor/cpp-httplib/httplib.h b/vendor/cpp-httplib/httplib.h
index 7ee219380f9..083f7950364 100644
--- a/vendor/cpp-httplib/httplib.h
+++ b/vendor/cpp-httplib/httplib.h
@@ -8,7 +8,35 @@
 #ifndef CPPHTTPLIB_HTTPLIB_H
 #define CPPHTTPLIB_HTTPLIB_H
 
-#define CPPHTTPLIB_VERSION "0.20.1"
+#define CPPHTTPLIB_VERSION "0.27.0"
+#define CPPHTTPLIB_VERSION_NUM "0x001B00"
+
+/*
+ * Platform compatibility check
+ */
+
+#if defined(_WIN32) && !defined(_WIN64)
+#if defined(_MSC_VER)
+#pragma message(                                                               \
+    "cpp-httplib doesn't support 32-bit Windows. Please use a 64-bit compiler.")
+#else
+#warning                                                                       \
+    "cpp-httplib doesn't support 32-bit Windows. Please use a 64-bit compiler."
+#endif
+#elif defined(__SIZEOF_POINTER__) && __SIZEOF_POINTER__ < 8
+#warning                                                                       \
+    "cpp-httplib doesn't support 32-bit platforms. Please use a 64-bit compiler."
+#elif defined(__SIZEOF_SIZE_T__) && __SIZEOF_SIZE_T__ < 8
+#warning                                                                       \
+    "cpp-httplib doesn't support platforms where size_t is less than 64 bits."
+#endif
+
+#ifdef _WIN32
+#if defined(_WIN32_WINNT) && _WIN32_WINNT < 0x0A00
+#error                                                                         \
+    "cpp-httplib doesn't support Windows 8 or lower. Please use Windows 10 or later."
+#endif
+#endif
 
 /*
  * Configuration
@@ -76,7 +104,7 @@
 
 #ifndef CPPHTTPLIB_IDLE_INTERVAL_USECOND
 #ifdef _WIN32
-#define CPPHTTPLIB_IDLE_INTERVAL_USECOND 10000
+#define CPPHTTPLIB_IDLE_INTERVAL_USECOND 1000
 #else
 #define CPPHTTPLIB_IDLE_INTERVAL_USECOND 0
 #endif
@@ -90,6 +118,10 @@
 #define CPPHTTPLIB_HEADER_MAX_LENGTH 8192
 #endif
 
+#ifndef CPPHTTPLIB_HEADER_MAX_COUNT
+#define CPPHTTPLIB_HEADER_MAX_COUNT 100
+#endif
+
 #ifndef CPPHTTPLIB_REDIRECT_MAX_COUNT
 #define CPPHTTPLIB_REDIRECT_MAX_COUNT 20
 #endif
@@ -122,6 +154,10 @@
 #define CPPHTTPLIB_RECV_BUFSIZ size_t(16384u)
 #endif
 
+#ifndef CPPHTTPLIB_SEND_BUFSIZ
+#define CPPHTTPLIB_SEND_BUFSIZ size_t(16384u)
+#endif
+
 #ifndef CPPHTTPLIB_COMPRESSION_BUFSIZ
 #define CPPHTTPLIB_COMPRESSION_BUFSIZ size_t(16384u)
 #endif
@@ -169,11 +205,7 @@
 
 #pragma comment(lib, "ws2_32.lib")
 
-#ifdef _WIN64
 using ssize_t = __int64;
-#else
-using ssize_t = long;
-#endif
 #endif // _MSC_VER
 
 #ifndef S_ISREG
@@ -192,8 +224,13 @@ using ssize_t = long;
 #include <winsock2.h>
 #include <ws2tcpip.h>
 
+#if defined(__has_include)
+#if __has_include(<afunix.h>)
 // afunix.h uses types declared in winsock2.h, so has to be included after it.
 #include <afunix.h>
+#define CPPHTTPLIB_HAVE_AFUNIX_H 1
+#endif
+#endif
 
 #ifndef WSA_FLAG_NO_HANDLE_INHERIT
 #define WSA_FLAG_NO_HANDLE_INHERIT 0x80
@@ -236,6 +273,10 @@ using socket_t = int;
 #endif
 #endif //_WIN32
 
+#if defined(__APPLE__)
+#include <TargetConditionals.h>
+#endif
+
 #include <algorithm>
 #include <array>
 #include <atomic>
@@ -265,6 +306,15 @@ using socket_t = int;
 #include <unordered_set>
 #include <utility>
 
+#if defined(CPPHTTPLIB_USE_NON_BLOCKING_GETADDRINFO) ||                        \
+    defined(CPPHTTPLIB_USE_CERTS_FROM_MACOSX_KEYCHAIN)
+#if TARGET_OS_MAC
+#include <CFNetwork/CFHost.h>
+#include <CoreFoundation/CoreFoundation.h>
+#endif
+#endif // CPPHTTPLIB_USE_NON_BLOCKING_GETADDRINFO or
+       // CPPHTTPLIB_USE_CERTS_FROM_MACOSX_KEYCHAIN
+
 #ifdef CPPHTTPLIB_OPENSSL_SUPPORT
 #ifdef _WIN32
 #include <wincrypt.h>
@@ -279,14 +329,14 @@ using socket_t = int;
 #ifdef _MSC_VER
 #pragma comment(lib, "crypt32.lib")
 #endif
-#elif defined(CPPHTTPLIB_USE_CERTS_FROM_MACOSX_KEYCHAIN) && defined(__APPLE__)
-#include <TargetConditionals.h>
-#if TARGET_OS_OSX
-#include <CoreFoundation/CoreFoundation.h>
-#include <Security/Security.h>
-#endif // TARGET_OS_OSX
 #endif // _WIN32
 
+#if defined(CPPHTTPLIB_USE_CERTS_FROM_MACOSX_KEYCHAIN)
+#if TARGET_OS_MAC
+#include <Security/Security.h>
+#endif
+#endif // CPPHTTPLIB_USE_NON_BLOCKING_GETADDRINFO
+
 #include <openssl/err.h>
 #include <openssl/evp.h>
 #include <openssl/ssl.h>
@@ -308,7 +358,7 @@ using socket_t = int;
 #error Sorry, OpenSSL versions prior to 3.0.0 are not supported
 #endif
 
-#endif
+#endif // CPPHTTPLIB_OPENSSL_SUPPORT
 
 #ifdef CPPHTTPLIB_ZLIB_SUPPORT
 #include <zlib.h>
@@ -406,6 +456,10 @@ struct hash {
   }
 };
 
+template <typename T>
+using unordered_set = std::unordered_set<T, detail::case_ignore::hash,
+                                         detail::case_ignore::equal_to>;
+
 } // namespace case_ignore
 
 // This is based on
@@ -529,19 +583,53 @@ using Headers =
 using Params = std::multimap<std::string, std::string>;
 using Match = std::smatch;
 
-using Progress = std::function<bool(uint64_t current, uint64_t total)>;
+using DownloadProgress = std::function<bool(size_t current, size_t total)>;
+using UploadProgress = std::function<bool(size_t current, size_t total)>;
 
 struct Response;
 using ResponseHandler = std::function<bool(const Response &response)>;
 
+struct FormData {
+  std::string name;
+  std::string content;
+  std::string filename;
+  std::string content_type;
+  Headers headers;
+};
+
+struct FormField {
+  std::string name;
+  std::string content;
+  Headers headers;
+};
+using FormFields = std::multimap<std::string, FormField>;
+
+using FormFiles = std::multimap<std::string, FormData>;
+
 struct MultipartFormData {
+  FormFields fields; // Text fields from multipart
+  FormFiles files;   // Files from multipart
+
+  // Text field access
+  std::string get_field(const std::string &key, size_t id = 0) const;
+  std::vector<std::string> get_fields(const std::string &key) const;
+  bool has_field(const std::string &key) const;
+  size_t get_field_count(const std::string &key) const;
+
+  // File access
+  FormData get_file(const std::string &key, size_t id = 0) const;
+  std::vector<FormData> get_files(const std::string &key) const;
+  bool has_file(const std::string &key) const;
+  size_t get_file_count(const std::string &key) const;
+};
+
+struct UploadFormData {
   std::string name;
   std::string content;
   std::string filename;
   std::string content_type;
 };
-using MultipartFormDataItems = std::vector<MultipartFormData>;
-using MultipartFormDataMap = std::multimap<std::string, MultipartFormData>;
+using UploadFormDataItems = std::vector<UploadFormData>;
 
 class DataSink {
 public:
@@ -584,37 +672,34 @@ using ContentProviderWithoutLength =
 
 using ContentProviderResourceReleaser = std::function<void(bool success)>;
 
-struct MultipartFormDataProvider {
+struct FormDataProvider {
   std::string name;
   ContentProviderWithoutLength provider;
   std::string filename;
   std::string content_type;
 };
-using MultipartFormDataProviderItems = std::vector<MultipartFormDataProvider>;
+using FormDataProviderItems = std::vector<FormDataProvider>;
 
-using ContentReceiverWithProgress =
-    std::function<bool(const char *data, size_t data_length, uint64_t offset,
-                       uint64_t total_length)>;
+using ContentReceiverWithProgress = std::function<bool(
+    const char *data, size_t data_length, size_t offset, size_t total_length)>;
 
 using ContentReceiver =
     std::function<bool(const char *data, size_t data_length)>;
 
-using MultipartContentHeader =
-    std::function<bool(const MultipartFormData &file)>;
+using FormDataHeader = std::function<bool(const FormData &file)>;
 
 class ContentReader {
 public:
   using Reader = std::function<bool(ContentReceiver receiver)>;
-  using MultipartReader = std::function<bool(MultipartContentHeader header,
-                                             ContentReceiver receiver)>;
+  using FormDataReader =
+      std::function<bool(FormDataHeader header, ContentReceiver receiver)>;
 
-  ContentReader(Reader reader, MultipartReader multipart_reader)
+  ContentReader(Reader reader, FormDataReader multipart_reader)
       : reader_(std::move(reader)),
-        multipart_reader_(std::move(multipart_reader)) {}
+        formdata_reader_(std::move(multipart_reader)) {}
 
-  bool operator()(MultipartContentHeader header,
-                  ContentReceiver receiver) const {
-    return multipart_reader_(std::move(header), std::move(receiver));
+  bool operator()(FormDataHeader header, ContentReceiver receiver) const {
+    return formdata_reader_(std::move(header), std::move(receiver));
   }
 
   bool operator()(ContentReceiver receiver) const {
@@ -622,7 +707,7 @@ class ContentReader {
   }
 
   Reader reader_;
-  MultipartReader multipart_reader_;
+  FormDataReader formdata_reader_;
 };
 
 using Range = std::pair<ssize_t, ssize_t>;
@@ -631,8 +716,10 @@ using Ranges = std::vector<Range>;
 struct Request {
   std::string method;
   std::string path;
+  std::string matched_route;
   Params params;
   Headers headers;
+  Headers trailers;
   std::string body;
 
   std::string remote_addr;
@@ -643,16 +730,18 @@ struct Request {
   // for server
   std::string version;
   std::string target;
-  MultipartFormDataMap files;
+  MultipartFormData form;
   Ranges ranges;
   Match matches;
   std::unordered_map<std::string, std::string> path_params;
   std::function<bool()> is_connection_closed = []() { return true; };
 
   // for client
+  std::vector<std::string> accept_content_types;
   ResponseHandler response_handler;
   ContentReceiverWithProgress content_receiver;
-  Progress progress;
+  DownloadProgress download_progress;
+  UploadProgress upload_progress;
 #ifdef CPPHTTPLIB_OPENSSL_SUPPORT
   const SSL *ssl = nullptr;
 #endif
@@ -660,21 +749,21 @@ struct Request {
   bool has_header(const std::string &key) const;
   std::string get_header_value(const std::string &key, const char *def = "",
                                size_t id = 0) const;
-  uint64_t get_header_value_u64(const std::string &key, uint64_t def = 0,
-                                size_t id = 0) const;
+  size_t get_header_value_u64(const std::string &key, size_t def = 0,
+                              size_t id = 0) const;
   size_t get_header_value_count(const std::string &key) const;
   void set_header(const std::string &key, const std::string &val);
 
+  bool has_trailer(const std::string &key) const;
+  std::string get_trailer_value(const std::string &key, size_t id = 0) const;
+  size_t get_trailer_value_count(const std::string &key) const;
+
   bool has_param(const std::string &key) const;
   std::string get_param_value(const std::string &key, size_t id = 0) const;
   size_t get_param_value_count(const std::string &key) const;
 
   bool is_multipart_form_data() const;
 
-  bool has_file(const std::string &key) const;
-  MultipartFormData get_file_value(const std::string &key) const;
-  std::vector<MultipartFormData> get_file_values(const std::string &key) const;
-
   // private members...
   size_t redirect_count_ = CPPHTTPLIB_REDIRECT_MAX_COUNT;
   size_t content_length_ = 0;
@@ -690,17 +779,22 @@ struct Response {
   int status = -1;
   std::string reason;
   Headers headers;
+  Headers trailers;
   std::string body;
   std::string location; // Redirect location
 
   bool has_header(const std::string &key) const;
   std::string get_header_value(const std::string &key, const char *def = "",
                                size_t id = 0) const;
-  uint64_t get_header_value_u64(const std::string &key, uint64_t def = 0,
-                                size_t id = 0) const;
+  size_t get_header_value_u64(const std::string &key, size_t def = 0,
+                              size_t id = 0) const;
   size_t get_header_value_count(const std::string &key) const;
   void set_header(const std::string &key, const std::string &val);
 
+  bool has_trailer(const std::string &key) const;
+  std::string get_trailer_value(const std::string &key, size_t id = 0) const;
+  size_t get_trailer_value_count(const std::string &key) const;
+
   void set_redirect(const std::string &url, int status = StatusCode::Found_302);
   void set_content(const char *s, size_t n, const std::string &content_type);
   void set_content(const std::string &s, const std::string &content_type);
@@ -860,6 +954,10 @@ class ThreadPool final : public TaskQueue {
 
 using Logger = std::function<void(const Request &, const Response &)>;
 
+// Forward declaration for Error type
+enum class Error;
+using ErrorLogger = std::function<void(const Error &, const Request *)>;
+
 using SocketOptions = std::function<void(socket_t sock)>;
 
 namespace detail {
@@ -882,10 +980,16 @@ namespace detail {
 
 class MatcherBase {
 public:
+  MatcherBase(std::string pattern) : pattern_(pattern) {}
   virtual ~MatcherBase() = default;
 
+  const std::string &pattern() const { return pattern_; }
+
   // Match request path and populate its matches and
   virtual bool match(Request &request) const = 0;
+
+private:
+  std::string pattern_;
 };
 
 /**
@@ -937,7 +1041,8 @@ class PathParamsMatcher final : public MatcherBase {
  */
 class RegexMatcher final : public MatcherBase {
 public:
-  RegexMatcher(const std::string &pattern) : regex_(pattern) {}
+  RegexMatcher(const std::string &pattern)
+      : MatcherBase(pattern), regex_(pattern) {}
 
   bool match(Request &request) const override;
 
@@ -947,6 +1052,9 @@ class RegexMatcher final : public MatcherBase {
 
 ssize_t write_headers(Stream &strm, const Headers &headers);
 
+std::string make_host_and_port_string(const std::string &host, int port,
+                                      bool is_ssl);
+
 } // namespace detail
 
 class Server {
@@ -1004,11 +1112,16 @@ class Server {
   }
 
   Server &set_exception_handler(ExceptionHandler handler);
+
   Server &set_pre_routing_handler(HandlerWithResponse handler);
   Server &set_post_routing_handler(Handler handler);
 
+  Server &set_pre_request_handler(HandlerWithResponse handler);
+
   Server &set_expect_100_continue_handler(Expect100ContinueHandler handler);
   Server &set_logger(Logger logger);
+  Server &set_pre_compression_logger(Logger logger);
+  Server &set_error_logger(ErrorLogger error_logger);
 
   Server &set_address_family(int family);
   Server &set_tcp_nodelay(bool on);
@@ -1019,6 +1132,8 @@ class Server {
   Server &
   set_header_writer(std::function<ssize_t(Stream &, Headers &)> const &writer);
 
+  Server &set_trusted_proxies(const std::vector<std::string> &proxies);
+
   Server &set_keep_alive_max_count(size_t count);
   Server &set_keep_alive_timeout(time_t sec);
 
@@ -1057,6 +1172,9 @@ class Server {
                        const std::function<void(Request &)> &setup_request);
 
   std::atomic<socket_t> svr_sock_{INVALID_SOCKET};
+
+  std::vector<std::string> trusted_proxies_;
+
   size_t keep_alive_max_count_ = CPPHTTPLIB_KEEPALIVE_MAX_COUNT;
   time_t keep_alive_timeout_sec_ = CPPHTTPLIB_KEEPALIVE_TIMEOUT_SECOND;
   time_t read_timeout_sec_ = CPPHTTPLIB_SERVER_READ_TIMEOUT_SECOND;
@@ -1087,8 +1205,7 @@ class Server {
   bool listen_internal();
 
   bool routing(Request &req, Response &res, Stream &strm);
-  bool handle_file_request(const Request &req, Response &res,
-                           bool head = false);
+  bool handle_file_request(const Request &req, Response &res);
   bool dispatch_request(Request &req, Response &res,
                         const Handlers &handlers) const;
   bool dispatch_request_for_content_reader(
@@ -1109,18 +1226,23 @@ class Server {
                                    Response &res, const std::string &boundary,
                                    const std::string &content_type);
   bool read_content(Stream &strm, Request &req, Response &res);
-  bool
-  read_content_with_content_receiver(Stream &strm, Request &req, Response &res,
-                                     ContentReceiver receiver,
-                                     MultipartContentHeader multipart_header,
-                                     ContentReceiver multipart_receiver);
+  bool read_content_with_content_receiver(Stream &strm, Request &req,
+                                          Response &res,
+                                          ContentReceiver receiver,
+                                          FormDataHeader multipart_header,
+                                          ContentReceiver multipart_receiver);
   bool read_content_core(Stream &strm, Request &req, Response &res,
                          ContentReceiver receiver,
-                         MultipartContentHeader multipart_header,
+                         FormDataHeader multipart_header,
                          ContentReceiver multipart_receiver) const;
 
   virtual bool process_and_close_socket(socket_t sock);
 
+  void output_log(const Request &req, const Response &res) const;
+  void output_pre_compression_log(const Request &req,
+                                  const Response &res) const;
+  void output_error_log(const Error &err, const Request *req) const;
+
   std::atomic<bool> is_running_{false};
   std::atomic<bool> is_decommissioned{false};
 
@@ -1149,9 +1271,13 @@ class Server {
   ExceptionHandler exception_handler_;
   HandlerWithResponse pre_routing_handler_;
   Handler post_routing_handler_;
+  HandlerWithResponse pre_request_handler_;
   Expect100ContinueHandler expect_100_continue_handler_;
 
+  mutable std::mutex logger_mutex_;
   Logger logger_;
+  Logger pre_compression_logger_;
+  ErrorLogger error_logger_;
 
   int address_family_ = AF_UNSPEC;
   bool tcp_nodelay_ = CPPHTTPLIB_TCP_NODELAY;
@@ -1180,6 +1306,22 @@ enum class Error {
   Compression,
   ConnectionTimeout,
   ProxyConnection,
+  ResourceExhaustion,
+  TooManyFormDataFiles,
+  ExceedMaxPayloadSize,
+  ExceedUriMaxLength,
+  ExceedMaxSocketDescriptorCount,
+  InvalidRequestLine,
+  InvalidHTTPMethod,
+  InvalidHTTPVersion,
+  InvalidHeaders,
+  MultipartParsing,
+  OpenFile,
+  Listen,
+  GetSockName,
+  UnsupportedAddressFamily,
+  HTTPParsing,
+  InvalidRangeHeader,
 
   // For internal use only
   SSLPeerCouldBeClosed_,
@@ -1196,6 +1338,17 @@ class Result {
          Headers &&request_headers = Headers{})
       : res_(std::move(res)), err_(err),
         request_headers_(std::move(request_headers)) {}
+#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
+  Result(std::unique_ptr<Response> &&res, Error err, Headers &&request_headers,
+         int ssl_error)
+      : res_(std::move(res)), err_(err),
+        request_headers_(std::move(request_headers)), ssl_error_(ssl_error) {}
+  Result(std::unique_ptr<Response> &&res, Error err, Headers &&request_headers,
+         int ssl_error, unsigned long ssl_openssl_error)
+      : res_(std::move(res)), err_(err),
+        request_headers_(std::move(request_headers)), ssl_error_(ssl_error),
+        ssl_openssl_error_(ssl_openssl_error) {}
+#endif
   // Response
   operator bool() const { return res_ != nullptr; }
   bool operator==(std::nullptr_t) const { return res_ == nullptr; }
@@ -1210,19 +1363,30 @@ class Result {
   // Error
   Error error() const { return err_; }
 
+#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
+  // SSL Error
+  int ssl_error() const { return ssl_error_; }
+  // OpenSSL Error
+  unsigned long ssl_openssl_error() const { return ssl_openssl_error_; }
+#endif
+
   // Request Headers
   bool has_request_header(const std::string &key) const;
   std::string get_request_header_value(const std::string &key,
                                        const char *def = "",
                                        size_t id = 0) const;
-  uint64_t get_request_header_value_u64(const std::string &key,
-                                        uint64_t def = 0, size_t id = 0) const;
+  size_t get_request_header_value_u64(const std::string &key, size_t def = 0,
+                                      size_t id = 0) const;
   size_t get_request_header_value_count(const std::string &key) const;
 
 private:
   std::unique_ptr<Response> res_;
   Error err_ = Error::Unknown;
   Headers request_headers_;
+#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
+  int ssl_error_ = 0;
+  unsigned long ssl_openssl_error_ = 0;
+#endif
 };
 
 class ClientImpl {
@@ -1239,185 +1403,86 @@ class ClientImpl {
 
   virtual bool is_valid() const;
 
-  Result Get(const std::string &path);
-  Result Get(const std::string &path, const Headers &headers);
-  Result Get(const std::string &path, Progress progress);
-  Result Get(const std::string &path, const Headers &headers,
-             Progress progress);
-  Result Get(const std::string &path, ContentReceiver content_receiver);
-  Result Get(const std::string &path, const Headers &headers,
-             ContentReceiver content_receiver);
-  Result Get(const std::string &path, ContentReceiver content_receiver,
-             Progress progress);
-  Result Get(const std::string &path, const Headers &headers,
-             ContentReceiver content_receiver, Progress progress);
-  Result Get(const std::string &path, ResponseHandler response_handler,
-             ContentReceiver content_receiver);
-  Result Get(const std::string &path, const Headers &headers,
-             ResponseHandler response_handler,
-             ContentReceiver content_receiver);
-  Result Get(const std::string &path, ResponseHandler response_handler,
-             ContentReceiver content_receiver, Progress progress);
-  Result Get(const std::string &path, const Headers &headers,
-             ResponseHandler response_handler, ContentReceiver content_receiver,
-             Progress progress);
-
-  Result Get(const std::string &path, const Params &params,
-             const Headers &headers, Progress progress = nullptr);
-  Result Get(const std::string &path, const Params &params,
-             const Headers &headers, ContentReceiver content_receiver,
-             Progress progress = nullptr);
-  Result Get(const std::string &path, const Params &params,
-             const Headers &headers, ResponseHandler response_handler,
-             ContentReceiver content_receiver, Progress progress = nullptr);
+  // clang-format off
+  Result Get(const std::string &path, DownloadProgress progress = nullptr);
+  Result Get(const std::string &path, ContentReceiver content_receiver, DownloadProgress progress = nullptr);
+  Result Get(const std::string &path, ResponseHandler response_handler, ContentReceiver content_receiver, DownloadProgress progress = nullptr);
+  Result Get(const std::string &path, const Headers &headers, DownloadProgress progress = nullptr);
+  Result Get(const std::string &path, const Headers &headers, ContentReceiver content_receiver, DownloadProgress progress = nullptr);
+  Result Get(const std::string &path, const Headers &headers, ResponseHandler response_handler, ContentReceiver content_receiver, DownloadProgress progress = nullptr);
+  Result Get(const std::string &path, const Params &params, const Headers &headers, DownloadProgress progress = nullptr);
+  Result Get(const std::string &path, const Params &params, const Headers &headers, ContentReceiver content_receiver, DownloadProgress progress = nullptr);
+  Result Get(const std::string &path, const Params &params, const Headers &headers, ResponseHandler response_handler, ContentReceiver content_receiver, DownloadProgress progress = nullptr);
 
   Result Head(const std::string &path);
   Result Head(const std::string &path, const Headers &headers);
 
   Result Post(const std::string &path);
-  Result Post(const std::string &path, const Headers &headers);
-  Result Post(const std::string &path, const char *body, size_t content_length,
-              const std::string &content_type);
-  Result Post(const std::string &path, const Headers &headers, const char *body,
-              size_t content_length, const std::string &content_type);
-  Result Post(const std::string &path, const Headers &headers, const char *body,
-              size_t content_length, const std::string &content_type,
-              Progress progress);
-  Result Post(const std::string &path, const std::string &body,
-              const std::string &content_type);
-  Result Post(const std::string &path, const std::string &body,
-              const std::string &content_type, Progress progress);
-  Result Post(const std::string &path, const Headers &headers,
-              const std::string &body, const std::string &content_type);
-  Result Post(const std::string &path, const Headers &headers,
-              const std::string &body, const std::string &content_type,
-              Progress progress);
-  Result Post(const std::string &path, size_t content_length,
-              ContentProvider content_provider,
-              const std::string &content_type);
-  Result Post(const std::string &path,
-              ContentProviderWithoutLength content_provider,
-              const std::string &content_type);
-  Result Post(const std::string &path, const Headers &headers,
-              size_t content_length, ContentProvider content_provider,
-              const std::string &content_type);
-  Result Post(const std::string &path, const Headers &headers,
-              ContentProviderWithoutLength content_provider,
-              const std::string &content_type);
+  Result Post(const std::string &path, const char *body, size_t content_length, const std::string &content_type, UploadProgress progress = nullptr);
+  Result Post(const std::string &path, const std::string &body, const std::string &content_type, UploadProgress progress = nullptr);
+  Result Post(const std::string &path, size_t content_length, ContentProvider content_provider, const std::string &content_type, UploadProgress progress = nullptr);
+  Result Post(const std::string &path, ContentProviderWithoutLength content_provider, const std::string &content_type, UploadProgress progress = nullptr);
   Result Post(const std::string &path, const Params &params);
-  Result Post(const std::string &path, const Headers &headers,
-              const Params &params);
-  Result Post(const std::string &path, const Headers &headers,
-              const Params &params, Progress progress);
-  Result Post(const std::string &path, const MultipartFormDataItems &items);
-  Result Post(const std::string &path, const Headers &headers,
-              const MultipartFormDataItems &items);
-  Result Post(const std::string &path, const Headers &headers,
-              const MultipartFormDataItems &items, const std::string &boundary);
-  Result Post(const std::string &path, const Headers &headers,
-              const MultipartFormDataItems &items,
-              const MultipartFormDataProviderItems &provider_items);
+  Result Post(const std::string &path, const UploadFormDataItems &items, UploadProgress progress = nullptr);
+  Result Post(const std::string &path, const Headers &headers);
+  Result Post(const std::string &path, const Headers &headers, const char *body, size_t content_length, const std::string &content_type, UploadProgress progress = nullptr);
+  Result Post(const std::string &path, const Headers &headers, const std::string &body, const std::string &content_type, UploadProgress progress = nullptr);
+  Result Post(const std::string &path, const Headers &headers, size_t content_length, ContentProvider content_provider, const std::string &content_type, UploadProgress progress = nullptr);
+  Result Post(const std::string &path, const Headers &headers, ContentProviderWithoutLength content_provider, const std::string &content_type, UploadProgress progress = nullptr);
+  Result Post(const std::string &path, const Headers &headers, const Params &params);
+  Result Post(const std::string &path, const Headers &headers, const UploadFormDataItems &items, UploadProgress progress = nullptr);
+  Result Post(const std::string &path, const Headers &headers, const UploadFormDataItems &items, const std::string &boundary, UploadProgress progress = nullptr);
+  Result Post(const std::string &path, const Headers &headers, const UploadFormDataItems &items, const FormDataProviderItems &provider_items, UploadProgress progress = nullptr);
+  Result Post(const std::string &path, const Headers &headers, const std::string &body, const std::string &content_type, ContentReceiver content_receiver, DownloadProgress progress = nullptr);
 
   Result Put(const std::string &path);
-  Result Put(const std::string &path, const char *body, size_t content_length,
-             const std::string &content_type);
-  Result Put(const std::string &path, const Headers &headers, const char *body,
-             size_t content_length, const std::string &content_type);
-  Result Put(const std::string &path, const Headers &headers, const char *body,
-             size_t content_length, const std::string &content_type,
-             Progress progress);
-  Result Put(const std::string &path, const std::string &body,
-             const std::string &content_type);
-  Result Put(const std::string &path, const std::string &body,
-             const std::string &content_type, Progress progress);
-  Result Put(const std::string &path, const Headers &headers,
-             const std::string &body, const std::string &content_type);
-  Result Put(const std::string &path, const Headers &headers,
-             const std::string &body, const std::string &content_type,
-             Progress progress);
-  Result Put(const std::string &path, size_t content_length,
-             ContentProvider content_provider, const std::string &content_type);
-  Result Put(const std::string &path,
-             ContentProviderWithoutLength content_provider,
-             const std::string &content_type);
-  Result Put(const std::string &path, const Headers &headers,
-             size_t content_length, ContentProvider content_provider,
-             const std::string &content_type);
-  Result Put(const std::string &path, const Headers &headers,
-             ContentProviderWithoutLength content_provider,
-             const std::string &content_type);
+  Result Put(const std::string &path, const char *body, size_t content_length, const std::string &content_type, UploadProgress progress = nullptr);
+  Result Put(const std::string &path, const std::string &body, const std::string &content_type, UploadProgress progress = nullptr);
+  Result Put(const std::string &path, size_t content_length, ContentProvider content_provider, const std::string &content_type, UploadProgress progress = nullptr);
+  Result Put(const std::string &path, ContentProviderWithoutLength content_provider, const std::string &content_type, UploadProgress progress = nullptr);
   Result Put(const std::string &path, const Params &params);
-  Result Put(const std::string &path, const Headers &headers,
-             const Params &params);
-  Result Put(const std::string &path, const Headers &headers,
-             const Params &params, Progress progress);
-  Result Put(const std::string &path, const MultipartFormDataItems &items);
-  Result Put(const std::string &path, const Headers &headers,
-             const MultipartFormDataItems &items);
-  Result Put(const std::string &path, const Headers &headers,
-             const MultipartFormDataItems &items, const std::string &boundary);
-  Result Put(const std::string &path, const Headers &headers,
-             const MultipartFormDataItems &items,
-             const MultipartFormDataProviderItems &provider_items);
+  Result Put(const std::string &path, const UploadFormDataItems &items, UploadProgress progress = nullptr);
+  Result Put(const std::string &path, const Headers &headers);
+  Result Put(const std::string &path, const Headers &headers, const char *body, size_t content_length, const std::string &content_type, UploadProgress progress = nullptr);
+  Result Put(const std::string &path, const Headers &headers, const std::string &body, const std::string &content_type, UploadProgress progress = nullptr);
+  Result Put(const std::string &path, const Headers &headers, size_t content_length, ContentProvider content_provider, const std::string &content_type, UploadProgress progress = nullptr);
+  Result Put(const std::string &path, const Headers &headers, ContentProviderWithoutLength content_provider, const std::string &content_type, UploadProgress progress = nullptr);
+  Result Put(const std::string &path, const Headers &headers, const Params &params);
+  Result Put(const std::string &path, const Headers &headers, const UploadFormDataItems &items, UploadProgress progress = nullptr);
+  Result Put(const std::string &path, const Headers &headers, const UploadFormDataItems &items, const std::string &boundary, UploadProgress progress = nullptr);
+  Result Put(const std::string &path, const Headers &headers, const UploadFormDataItems &items, const FormDataProviderItems &provider_items, UploadProgress progress = nullptr);
+  Result Put(const std::string &path, const Headers &headers, const std::string &body, const std::string &content_type, ContentReceiver content_receiver, DownloadProgress progress = nullptr);
 
   Result Patch(const std::string &path);
-  Result Patch(const std::string &path, const char *body, size_t content_length,
-               const std::string &content_type);
-  Result Patch(const std::string &path, const char *body, size_t content_length,
-               const std::string &content_type, Progress progress);
-  Result Patch(const std::string &path, const Headers &headers,
-               const char *body, size_t content_length,
-               const std::string &content_type);
-  Result Patch(const std::string &path, const Headers &headers,
-               const char *body, size_t content_length,
-               const std::string &content_type, Progress progress);
-  Result Patch(const std::string &path, const std::string &body,
-               const std::string &content_type);
-  Result Patch(const std::string &path, const std::string &body,
-               const std::string &content_type, Progress progress);
-  Result Patch(const std::string &path, const Headers &headers,
-               const std::string &body, const std::string &content_type);
-  Result Patch(const std::string &path, const Headers &headers,
-               const std::string &body, const std::string &content_type,
-               Progress progress);
-  Result Patch(const std::string &path, size_t content_length,
-               ContentProvider content_provider,
-               const std::string &content_type);
-  Result Patch(const std::string &path,
-               ContentProviderWithoutLength content_provider,
-               const std::string &content_type);
-  Result Patch(const std::string &path, const Headers &headers,
-               size_t content_length, ContentProvider content_provider,
-               const std::string &content_type);
-  Result Patch(const std::string &path, const Headers &headers,
-               ContentProviderWithoutLength content_provider,
-               const std::string &content_type);
-
-  Result Delete(const std::string &path);
-  Result Delete(const std::string &path, const Headers &headers);
-  Result Delete(const std::string &path, const char *body,
-                size_t content_length, const std::string &content_type);
-  Result Delete(const std::string &path, const char *body,
-                size_t content_length, const std::string &content_type,
-                Progress progress);
-  Result Delete(const std::string &path, const Headers &headers,
-                const char *body, size_t content_length,
-                const std::string &content_type);
-  Result Delete(const std::string &path, const Headers &headers,
-                const char *body, size_t content_length,
-                const std::string &content_type, Progress progress);
-  Result Delete(const std::string &path, const std::string &body,
-                const std::string &content_type);
-  Result Delete(const std::string &path, const std::string &body,
-                const std::string &content_type, Progress progress);
-  Result Delete(const std::string &path, const Headers &headers,
-                const std::string &body, const std::string &content_type);
-  Result Delete(const std::string &path, const Headers &headers,
-                const std::string &body, const std::string &content_type,
-                Progress progress);
+  Result Patch(const std::string &path, const char *body, size_t content_length, const std::string &content_type, UploadProgress progress = nullptr);
+  Result Patch(const std::string &path, const std::string &body, const std::string &content_type, UploadProgress progress = nullptr);
+  Result Patch(const std::string &path, size_t content_length, ContentProvider content_provider, const std::string &content_type, UploadProgress progress = nullptr);
+  Result Patch(const std::string &path, ContentProviderWithoutLength content_provider, const std::string &content_type, UploadProgress progress = nullptr);
+  Result Patch(const std::string &path, const Params &params);
+  Result Patch(const std::string &path, const UploadFormDataItems &items, UploadProgress progress = nullptr);
+  Result Patch(const std::string &path, const Headers &headers, UploadProgress progress = nullptr);
+  Result Patch(const std::string &path, const Headers &headers, const char *body, size_t content_length, const std::string &content_type, UploadProgress progress = nullptr);
+  Result Patch(const std::string &path, const Headers &headers, const std::string &body, const std::string &content_type, UploadProgress progress = nullptr);
+  Result Patch(const std::string &path, const Headers &headers, size_t content_length, ContentProvider content_provider, const std::string &content_type, UploadProgress progress = nullptr);
+  Result Patch(const std::string &path, const Headers &headers, ContentProviderWithoutLength content_provider, const std::string &content_type, UploadProgress progress = nullptr);
+  Result Patch(const std::string &path, const Headers &headers, const Params &params);
+  Result Patch(const std::string &path, const Headers &headers, const UploadFormDataItems &items, UploadProgress progress = nullptr);
+  Result Patch(const std::string &path, const Headers &headers, const UploadFormDataItems &items, const std::string &boundary, UploadProgress progress = nullptr);
+  Result Patch(const std::string &path, const Headers &headers, const UploadFormDataItems &items, const FormDataProviderItems &provider_items, UploadProgress progress = nullptr);
+  Result Patch(const std::string &path, const Headers &headers, const std::string &body, const std::string &content_type, ContentReceiver content_receiver, DownloadProgress progress = nullptr);
+
+  Result Delete(const std::string &path, DownloadProgress progress = nullptr);
+  Result Delete(const std::string &path, const char *body, size_t content_length, const std::string &content_type, DownloadProgress progress = nullptr);
+  Result Delete(const std::string &path, const std::string &body, const std::string &content_type, DownloadProgress progress = nullptr);
+  Result Delete(const std::string &path, const Params &params, DownloadProgress progress = nullptr);
+  Result Delete(const std::string &path, const Headers &headers, DownloadProgress progress = nullptr);
+  Result Delete(const std::string &path, const Headers &headers, const char *body, size_t content_length, const std::string &content_type, DownloadProgress progress = nullptr);
+  Result Delete(const std::string &path, const Headers &headers, const std::string &body, const std::string &content_type, DownloadProgress progress = nullptr);
+  Result Delete(const std::string &path, const Headers &headers, const Params &params, DownloadProgress progress = nullptr);
 
   Result Options(const std::string &path);
   Result Options(const std::string &path, const Headers &headers);
+  // clang-format on
 
   bool send(Request &req, Response &res, Error &error);
   Result send(const Request &req);
@@ -1469,7 +1534,7 @@ class ClientImpl {
   void set_keep_alive(bool on);
   void set_follow_location(bool on);
 
-  void set_url_encode(bool on);
+  void set_path_encode(bool on);
 
   void set_compress(bool on);
 
@@ -1501,6 +1566,7 @@ class ClientImpl {
 #endif
 
   void set_logger(Logger logger);
+  void set_error_logger(ErrorLogger error_logger);
 
 protected:
   struct Socket {
@@ -1533,6 +1599,9 @@ class ClientImpl {
 
   void copy_settings(const ClientImpl &rhs);
 
+  void output_log(const Request &req, const Response &res) const;
+  void output_error_log(const Error &err, const Request *req) const;
+
   // Socket endpoint information
   const std::string host_;
   const int port_;
@@ -1581,7 +1650,7 @@ class ClientImpl {
   bool keep_alive_ = false;
   bool follow_location_ = false;
 
-  bool url_encode_ = true;
+  bool path_encode_ = true;
 
   int address_family_ = AF_UNSPEC;
   bool tcp_nodelay_ = CPPHTTPLIB_TCP_NODELAY;
@@ -1617,7 +1686,14 @@ class ClientImpl {
   std::function<SSLVerifierResponse(SSL *ssl)> server_certificate_verifier_;
 #endif
 
+  mutable std::mutex logger_mutex_;
   Logger logger_;
+  ErrorLogger error_logger_;
+
+#ifdef CPPHTTPLIB_OPENSSL_SUPPORT
+  int last_ssl_error_ = 0;
+  unsigned long last_openssl_error_ = 0;
+#endif
 
 private:
   bool send_(Request &req, Response &res, Error &error);
@@ -1629,6 +1705,11 @@ class ClientImpl {
   bool write_request(Stream &strm, Request &req, bool close_connection,
                      Error &error);
   bool redirect(Request &req, Response &res, Error &error);
+  bool create_redirect_client(const std::string &scheme,
+                              const std::string &host, int port, Request &req,
+                              Response &res, const std::string &path,
+                              const std::string &location, Error &error);
+  template <typename ClientType> void setup_redirect_client(ClientType &client);
   bool handle_request(Stream &strm, Request &req, Response &res,
                       bool close_connection, Error &error);
   std::unique_ptr<Response> send_with_content_provider(
@@ -1641,12 +1722,10 @@ class ClientImpl {
       const Headers &headers, const char *body, size_t content_length,
       ContentProvider content_provider,
       ContentProviderWithoutLength content_provider_without_length,
-      const std::string &content_type, Progress progress);
+      const std::string &content_type, UploadProgress progress);
   ContentProviderWithoutLength get_multipart_content_provider(
-      const std::string &boundary, const MultipartFormDataItems &items,
-      const MultipartFormDataProviderItems &provider_items) const;
-
-  std::string adjust_host_string(const std::string &host) const;
+      const std::string &boundary, const UploadFormDataItems &items,
+      const FormDataProviderItems &provider_items) const;
 
   virtual bool
   process_socket(const Socket &socket,
@@ -1678,185 +1757,86 @@ class Client {
 
   bool is_valid() const;
 
-  Result Get(const std::string &path);
-  Result Get(const std::string &path, const Headers &headers);
-  Result Get(const std::string &path, Progress progress);
-  Result Get(const std::string &path, const Headers &headers,
-             Progress progress);
-  Result Get(const std::string &path, ContentReceiver content_receiver);
-  Result Get(const std::string &path, const Headers &headers,
-             ContentReceiver content_receiver);
-  Result Get(const std::string &path, ContentReceiver content_receiver,
-             Progress progress);
-  Result Get(const std::string &path, const Headers &headers,
-             ContentReceiver content_receiver, Progress progress);
-  Result Get(const std::string &path, ResponseHandler response_handler,
-             ContentReceiver content_receiver);
-  Result Get(const std::string &path, const Headers &headers,
-             ResponseHandler response_handler,
-             ContentReceiver content_receiver);
-  Result Get(const std::string &path, const Headers &headers,
-             ResponseHandler response_handler, ContentReceiver content_receiver,
-             Progress progress);
-  Result Get(const std::string &path, ResponseHandler response_handler,
-             ContentReceiver content_receiver, Progress progress);
-
-  Result Get(const std::string &path, const Params &params,
-             const Headers &headers, Progress progress = nullptr);
-  Result Get(const std::string &path, const Params &params,
-             const Headers &headers, ContentReceiver content_receiver,
-             Progress progress = nullptr);
-  Result Get(const std::string &path, const Params &params,
-             const Headers &headers, ResponseHandler response_handler,
-             ContentReceiver content_receiver, Progress progress = nullptr);
+  // clang-format off
+  Result Get(const std::string &path, DownloadProgress progress = nullptr);
+  Result Get(const std::string &path, ContentReceiver content_receiver, DownloadProgress progress = nullptr);
+  Result Get(const std::string &path, ResponseHandler response_handler, ContentReceiver content_receiver, DownloadProgress progress = nullptr);
+  Result Get(const std::string &path, const Headers &headers, DownloadProgress progress = nullptr);
+  Result Get(const std::string &path, const Headers &headers, ContentReceiver content_receiver, DownloadProgress progress = nullptr);
+  Result Get(const std::string &path, const Headers &headers, ResponseHandler response_handler, ContentReceiver content_receiver, DownloadProgress progress = nullptr);
+  Result Get(const std::string &path, const Params &params, const Headers &headers, DownloadProgress progress = nullptr);
+  Result Get(const std::string &path, const Params &params, const Headers &headers, ContentReceiver content_receiver, DownloadProgress progress = nullptr);
+  Result Get(const std::string &path, const Params &params, const Headers &headers, ResponseHandler response_handler, ContentReceiver content_receiver, DownloadProgress progress = nullptr);
 
   Result Head(const std::string &path);
   Result Head(const std::string &path, const Headers &headers);
 
   Result Post(const std::string &path);
-  Result Post(const std::string &path, const Headers &headers);
-  Result Post(const std::string &path, const char *body, size_t content_length,
-              const std::string &content_type);
-  Result Post(const std::string &path, const Headers &headers, const char *body,
-              size_t content_length, const std::string &content_type);
-  Result Post(const std::string &path, const Headers &headers, const char *body,
-              size_t content_length, const std::string &content_type,
-              Progress progress);
-  Result Post(const std::string &path, const std::string &body,
-              const std::string &content_type);
-  Result Post(const std::string &path, const std::string &body,
-              const std::string &content_type, Progress progress);
-  Result Post(const std::string &path, const Headers &headers,
-              const std::string &body, const std::string &content_type);
-  Result Post(const std::string &path, const Headers &headers,
-              const std::string &body, const std::string &content_type,
-              Progress progress);
-  Result Post(const std::string &path, size_t content_length,
-              ContentProvider content_provider,
-              const std::string &content_type);
-  Result Post(const std::string &path,
-              ContentProviderWithoutLength content_provider,
-              const std::string &content_type);
-  Result Post(const std::string &path, const Headers &headers,
-              size_t content_length, ContentProvider content_provider,
-              const std::string &content_type);
-  Result Post(const std::string &path, const Headers &headers,
-              ContentProviderWithoutLength content_provider,
-              const std::string &content_type);
+  Result Post(const std::string &path, const char *body, size_t content_length, const std::string &content_type, UploadProgress progress = nullptr);
+  Result Post(const std::string &path, const std::string &body, const std::string &content_type, UploadProgress progress = nullptr);
+  Result Post(const std::string &path, size_t content_length, ContentProvider content_provider, const std::string &content_type, UploadProgress progress = nullptr);
+  Result Post(const std::string &path, ContentProviderWithoutLength content_provider, const std::string &content_type, UploadProgress progress = nullptr);
   Result Post(const std::string &path, const Params &params);
-  Result Post(const std::string &path, const Headers &headers,
-              const Params &params);
-  Result Post(const std::string &path, const Headers &headers,
-              const Params &params, Progress progress);
-  Result Post(const std::string &path, const MultipartFormDataItems &items);
-  Result Post(const std::string &path, const Headers &headers,
-              const MultipartFormDataItems &items);
-  Result Post(const std::string &path, const Headers &headers,
-              const MultipartFormDataItems &items, const std::string &boundary);
-  Result Post(const std::string &path, const Headers &headers,
-              const MultipartFormDataItems &items,
-              const MultipartFormDataProviderItems &provider_items);
+  Result Post(const std::string &path, const UploadFormDataItems &items, UploadProgress progress = nullptr);
+  Result Post(const std::string &path, const Headers &headers);
+  Result Post(const std::string &path, const Headers &headers, const char *body, size_t content_length, const std::string &content_type, UploadProgress progress = nullptr);
+  Result Post(const std::string &path, const Headers &headers, const std::string &body, const std::string &content_type, UploadProgress progress = nullptr);
+  Result Post(const std::string &path, const Headers &headers, size_t content_length, ContentProvider content_provider, const std::string &content_type, UploadProgress progress = nullptr);
+  Result Post(const std::string &path, const Headers &headers, ContentProviderWithoutLength content_provider, const std::string &content_type, UploadProgress progress = nullptr);
+  Result Post(const std::string &path, const Headers &headers, const Params &params);
+  Result Post(const std::string &path, const Headers &headers, const UploadFormDataItems &items, UploadProgress progress = nullptr);
+  Result Post(const std::string &path, const Headers &headers, const UploadFormDataItems &items, const std::string &boundary, UploadProgress progress = nullptr);
+  Result Post(const std::string &path, const Headers &headers, const UploadFormDataItems &items, const FormDataProviderItems &provider_items, UploadProgress progress = nullptr);
+  Result Post(const std::string &path, const Headers &headers, const std::string &body, const std::string &content_type, ContentReceiver content_receiver, DownloadProgress progress = nullptr);
 
   Result Put(const std::string &path);
-  Result Put(const std::string &path, const char *body, size_t content_length,
-             const std::string &content_type);
-  Result Put(const std::string &path, const Headers &headers, const char *body,
-             size_t content_length, const std::string &content_type);
-  Result Put(const std::string &path, const Headers &headers, const char *body,
-             size_t content_length, const std::string &content_type,
-             Progress progress);
-  Result Put(const std::string &path, const std::string &body,
-             const std::string &content_type);
-  Result Put(const std::string &path, const std::string &body,
-             const std::string &content_type, Progress progress);
-  Result Put(const std::string &path, const Headers &headers,
-             const std::string &body, const std::string &content_type);
-  Result Put(const std::string &path, const Headers &headers,
-             const std::string &body, const std::string &content_type,
-             Progress progress);
-  Result Put(const std::string &path, size_t content_length,
-             ContentProvider content_provider, const std::string &content_type);
-  Result Put(const std::string &path,
-             ContentProviderWithoutLength content_provider,
-             const std::string &content_type);
-  Result Put(const std::string &path, const Headers &headers,
-             size_t content_length, ContentProvider content_provider,
-             const std::string &content_type);
-  Result Put(const std::string &path, const Headers &headers,
-             ContentProviderWithoutLength content_provider,
-             const std::string &content_type);
+  Result Put(const std::string &path, const char *body, size_t content_length, const std::string &content_type, UploadProgress progress = nullptr);
+  Result Put(const std::string &path, const std::string &body, const std::string &content_type, UploadProgress progress = nullptr);
+  Result Put(const std::string &path, size_t content_length, ContentProvider content_provider, const std::string &content_type, UploadProgress progress = nullptr);
+  Result Put(const std::string &path, ContentProviderWithoutLength content_provider, const std::string &content_type, UploadProgress progress = nullptr);
   Result Put(const std::string &path, const Params &params);
-  Result Put(const std::string &path, const Headers &headers,
-             const Params &params);
-  Result Put(const std::string &path, const Headers &headers,
-             const Params &params, Progress progress);
-  Result Put(const std::string &path, const MultipartFormDataItems &items);
-  Result Put(const std::string &path, const Headers &headers,
-             const MultipartFormDataItems &items);
-  Result Put(const std::string &path, const Headers &headers,
-             const MultipartFormDataItems &items, const std::string &boundary);
-  Result Put(const std::string &path, const Headers &headers,
-             const MultipartFormDataItems &items,
-             const MultipartFormDataProviderItems &provider_items);
+  Result Put(const std::string &path, const UploadFormDataItems &items, UploadProgress progress = nullptr);
+  Result Put(const std::string &path, const Headers &headers);
+  Result Put(const std::string &path, const Headers &headers, const char *body, size_t content_length, const std::string &content_type, UploadProgress progress = nullptr);
+  Result Put(const std::string &path, const Headers &headers, const std::string &body, const std::string &content_type, UploadProgress progress = nullptr);
+  Result Put(const std::string &path, const Headers &headers, size_t content_length, ContentProvider content_provider, const std::string &content_type, UploadProgress progress = nullptr);
+  Result Put(const std::string &path, const Headers &headers, ContentProviderWithoutLength content_provider, const std::string &content_type, UploadProgress progress = nullptr);
+  Result Put(const std::string &path, const Headers &headers, const Params &params);
+  Result Put(const std::string &path, const Headers &headers, const UploadFormDataItems &items, UploadProgress progress = nullptr);
+  Result Put(const std::string &path, const Headers &headers, const UploadFormDataItems &items, const std::string &boundary, UploadProgress progress = nullptr);
+  Result Put(const std::string &path, const Headers &headers, const UploadFormDataItems &items, const FormDataProviderItems &provider_items, UploadProgress progress = nullptr);
+  Result Put(const std::string &path, const Headers &headers, const std::string &body, const std::string &content_type, ContentReceiver content_receiver, DownloadProgress progress = nullptr);
 
   Result Patch(const std::string &path);
-  Result Patch(const std::string &path, const char *body, size_t content_length,
-               const std::string &content_type);
-  Result Patch(const std::string &path, const char *body, size_t content_length,
-               const std::string &content_type, Progress progress);
-  Result Patch(const std::string &path, const Headers &headers,
-               const char *body, size_t content_length,
-               const std::string &content_type);
-  Result Patch(const std::string &path, const Headers &headers,
-               const char *body, size_t content_length,
-               const std::string &content_type, Progress progress);
-  Result Patch(const std::string &path, const std::string &body,
-               const std::string &content_type);
-  Result Patch(const std::string &path, const std::string &body,
-               const std::string &content_type, Progress progress);
-  Result Patch(const std::string &path, const Headers &headers,
-               const std::string &body, const std::string &content_type);
-  Result Patch(const std::string &path, const Headers &headers,
-               const std::string &body, const std::string &content_type,
-               Progress progress);
-  Result Patch(const std::string &path, size_t content_length,
-               ContentProvider content_provider,
-               const std::string &content_type);
-  Result Patch(const std::string &path,
-               ContentProviderWithoutLength content_provider,
-               const std::string &content_type);
-  Result Patch(const std::string &path, const Headers &headers,
-               size_t content_length, ContentProvider content_provider,
-               const std::string &content_type);
-  Result Patch(const std::string &path, const Headers &headers,
-               ContentProviderWithoutLength content_provider,
-               const std::string &content_type);
-
-  Result Delete(const std::string &path);
-  Result Delete(const std::string &path, const Headers &headers);
-  Result Delete(const std::string &path, const char *body,
-                size_t content_length, const std::string &content_type);
-  Result Delete(const std::string &path, const char *body,
-                size_t content_length, const std::string &content_type,
-                Progress progress);
-  Result Delete(const std::string &path, const Headers &headers,
-                const char *body, size_t content_length,
-                const std::string &content_type);
-  Result Delete(const std::string &path, const Headers &headers,
-                const char *body, size_t content_length,
-                const std::string &content_type, Progress progress);
-  Result Delete(const std::string &path, const std::string &body,
-                const std::string &content_type);
-  Result Delete(const std::string &path, const std::string &body,
-                const std::string &content_type, Progress progress);
-  Result Delete(const std::string &path, const Headers &headers,
-                const std::string &body, const std::string &content_type);
-  Result Delete(const std::string &path, const Headers &headers,
-                const std::string &body, const std::string &content_type,
-                Progress progress);
+  Result Patch(const std::string &path, const char *body, size_t content_length, const std::string &content_type, UploadProgress progress = nullptr);
+  Result Patch(const std::string &path, const std::string &body, const std::string &content_type, UploadProgress progress = nullptr);
+  Result Patch(const std::string &path, size_t content_length, ContentProvider content_provider, const std::string &content_type, UploadProgress progress = nullptr);
+  Result Patch(const std::string &path, ContentProviderWithoutLength content_provider, const std::string &content_type, UploadProgress progress = nullptr);
+  Result Patch(const std::string &path, const Params &params);
+  Result Patch(const std::string &path, const UploadFormDataItems &items, UploadProgress progress = nullptr);
+  Result Patch(const std::string &path, const Headers &headers);
+  Result Patch(const std::string &path, const Headers &headers, const char *body, size_t content_length, const std::string &content_type, UploadProgress progress = nullptr);
+  Result Patch(const std::string &path, const Headers &headers, const std::string &body, const std::string &content_type, UploadProgress progress = nullptr);
+  Result Patch(const std::string &path, const Headers &headers, size_t content_length, ContentProvider content_provider, const std::string &content_type, UploadProgress progress = nullptr);
+  Result Patch(const std::string &path, const Headers &headers, ContentProviderWithoutLength content_provider, const std::string &content_type, UploadProgress progress = nullptr);
+  Result Patch(const std::string &path, const Headers &headers, const Params &params);
+  Result Patch(const std::string &path, const Headers &headers, const UploadFormDataItems &items, UploadProgress progress = nullptr);
+  Result Patch(const std::string &path, const Headers &headers, const UploadFormDataItems &items, const std::string &boundary, UploadProgress progress = nullptr);
+  Result Patch(const std::string &path, const Headers &headers, const UploadFormDataItems &items, const FormDataProviderItems &provider_items, UploadProgress progress = nullptr);
+  Result Patch(const std::string &path, const Headers &headers, const std::string &body, const std::string &content_type, ContentReceiver content_receiver, DownloadProgress progress = nullptr);
+
+  Result Delete(const std::string &path, DownloadProgress progress = nullptr);
+  Result Delete(const std::string &path, const char *body, size_t content_length, const std::string &content_type, DownloadProgress progress = nullptr);
+  Result Delete(const std::string &path, const std::string &body, const std::string &content_type, DownloadProgress progress = nullptr);
+  Result Delete(const std::string &path, const Params &params, DownloadProgress progress = nullptr);
+  Result Delete(const std::string &path, const Headers &headers, DownloadProgress progress = nullptr);
+  Result Delete(const std::string &path, const Headers &headers, const char *body, size_t content_length, const std::string &content_type, DownloadProgress progress = nullptr);
+  Result Delete(const std::string &path, const Headers &headers, const std::string &body, const std::string &content_type, DownloadProgress progress = nullptr);
+  Result Delete(const std::string &path, const Headers &headers, const Params &params, DownloadProgress progress = nullptr);
 
   Result Options(const std::string &path);
   Result Options(const std::string &path, const Headers &headers);
+  // clang-format on
 
   bool send(Request &req, Response &res, Error &error);
   Result send(const Request &req);
@@ -1907,6 +1887,7 @@ class Client {
   void set_keep_alive(bool on);
   void set_follow_location(bool on);
 
+  void set_path_encode(bool on);
   void set_url_encode(bool on);
 
   void set_compress(bool on);
@@ -1932,6 +1913,7 @@ class Client {
 #endif
 
   void set_logger(Logger logger);
+  void set_error_logger(ErrorLogger error_logger);
 
   // SSL
 #ifdef CPPHTTPLIB_OPENSSL_SUPPORT
@@ -1977,11 +1959,17 @@ class SSLServer : public Server {
   void update_certs(X509 *cert, EVP_PKEY *private_key,
                     X509_STORE *client_ca_cert_store = nullptr);
 
+  int ssl_last_error() const { return last_ssl_error_; }
+
 private:
   bool process_and_close_socket(socket_t sock) override;
 
+  STACK_OF(X509_NAME) * extract_ca_names_from_x509_store(X509_STORE *store);
+
   SSL_CTX *ctx_;
   std::mutex ctx_mutex_;
+
+  int last_ssl_error_ = 0;
 };
 
 class SSLClient final : public ClientImpl {
@@ -2066,12 +2054,14 @@ template <size_t N> inline constexpr size_t str_len(const char (&)[N]) {
 }
 
 inline bool is_numeric(const std::string &str) {
-  return !str.empty() && std::all_of(str.begin(), str.end(), ::isdigit);
+  return !str.empty() &&
+         std::all_of(str.cbegin(), str.cend(),
+                     [](unsigned char c) { return std::isdigit(c); });
 }
 
-inline uint64_t get_header_value_u64(const Headers &headers,
-                                     const std::string &key, uint64_t def,
-                                     size_t id, bool &is_invalid_value) {
+inline size_t get_header_value_u64(const Headers &headers,
+                                   const std::string &key, size_t def,
+                                   size_t id, bool &is_invalid_value) {
   is_invalid_value = false;
   auto rng = headers.equal_range(key);
   auto it = rng.first;
@@ -2086,22 +2076,22 @@ inline uint64_t get_header_value_u64(const Headers &headers,
   return def;
 }
 
-inline uint64_t get_header_value_u64(const Headers &headers,
-                                     const std::string &key, uint64_t def,
-                                     size_t id) {
-  bool dummy = false;
+inline size_t get_header_value_u64(const Headers &headers,
+                                   const std::string &key, size_t def,
+                                   size_t id) {
+  auto dummy = false;
   return get_header_value_u64(headers, key, def, id, dummy);
 }
 
 } // namespace detail
 
-inline uint64_t Request::get_header_value_u64(const std::string &key,
-                                              uint64_t def, size_t id) const {
+inline size_t Request::get_header_value_u64(const std::string &key, size_t def,
+                                            size_t id) const {
   return detail::get_header_value_u64(headers, key, def, id);
 }
 
-inline uint64_t Response::get_header_value_u64(const std::string &key,
-                                               uint64_t def, size_t id) const {
+inline size_t Response::get_header_value_u64(const std::string &key, size_t def,
+                                             size_t id) const {
   return detail::get_header_value_u64(headers, key, def, id);
 }
 
@@ -2258,6 +2248,7 @@ Server::set_idle_interval(const std::chrono::duration<Rep, Period> &duration) {
 inline std::string to_string(const Error error) {
   switch (error) {
   case Error::Success: return "Success (no error)";
+  case Error::Unknown: return "Unknown";
   case Error::Connection: return "Could not establish connection";
   case Error::BindIPAddress: return "Failed to bind IP address";
   case Error::Read: return "Failed to read connection";
@@ -2274,7 +2265,23 @@ inline std::string to_string(const Error error) {
   case Error::Compression: return "Compression failed";
   case Error::ConnectionTimeout: return "Connection timed out";
   case Error::ProxyConnection: return "Proxy connection failed";
-  case Error::Unknown: return "Unknown";
+  case Error::ResourceExhaustion: return "Resource exhaustion";
+  case Error::TooManyFormDataFiles: return "Too many form data files";
+  case Error::ExceedMaxPayloadSize: return "Exceeded maximum payload size";
+  case Error::ExceedUriMaxLength: return "Exceeded maximum URI length";
+  case Error::ExceedMaxSocketDescriptorCount:
+    return "Exceeded maximum socket descriptor count";
+  case Error::InvalidRequestLine: return "Invalid request line";
+  case Error::InvalidHTTPMethod: return "Invalid HTTP method";
+  case Error::InvalidHTTPVersion: return "Invalid HTTP version";
+  case Error::InvalidHeaders: return "Invalid headers";
+  case Error::MultipartParsing: return "Multipart parsing failed";
+  case Error::OpenFile: return "Failed to open file";
+  case Error::Listen: return "Failed to listen on socket";
+  case Error::GetSockName: return "Failed to get socket name";
+  case Error::UnsupportedAddressFamily: return "Unsupported address family";
+  case Error::HTTPParsing: return "HTTP parsing failed";
+  case Error::InvalidRangeHeader: return "Invalid Range header";
   default: break;
   }
 
@@ -2287,9 +2294,9 @@ inline std::ostream &operator<<(std::ostream &os, const Error &obj) {
   return os;
 }
 
-inline uint64_t Result::get_request_header_value_u64(const std::string &key,
-                                                     uint64_t def,
-                                                     size_t id) const {
+inline size_t Result::get_request_header_value_u64(const std::string &key,
+                                                   size_t def,
+                                                   size_t id) const {
   return detail::get_header_value_u64(request_headers_, key, def, id);
 }
 
@@ -2341,6 +2348,10 @@ Client::set_write_timeout(const std::chrono::duration<Rep, Period> &duration) {
   cli_->set_write_timeout(duration);
 }
 
+inline void Client::set_max_timeout(time_t msec) {
+  cli_->set_max_timeout(msec);
+}
+
 template <class Rep, class Period>
 inline void
 Client::set_max_timeout(const std::chrono::duration<Rep, Period> &duration) {
@@ -2356,6 +2367,20 @@ std::string hosted_at(const std::string &hostname);
 
 void hosted_at(const std::string &hostname, std::vector<std::string> &addrs);
 
+// JavaScript-style URL encoding/decoding functions
+std::string encode_uri_component(const std::string &value);
+std::string encode_uri(const std::string &value);
+std::string decode_uri_component(const std::string &value);
+std::string decode_uri(const std::string &value);
+
+// RFC 3986 compliant URL component encoding/decoding functions
+std::string encode_path_component(const std::string &component);
+std::string decode_path_component(const std::string &component);
+std::string encode_query_component(const std::string &component,
+                                   bool space_as_plus = true);
+std::string decode_query_component(const std::string &component,
+                                   bool plus_as_space = true);
+
 std::string append_query_params(const std::string &path, const Params &params);
 
 std::pair<std::string, std::string> make_range_header(const Ranges &ranges);
@@ -2397,10 +2422,6 @@ struct FileStat {
   int ret_ = -1;
 };
 
-std::string encode_query_param(const std::string &value);
-
-std::string decode_url(const std::string &s, bool convert_plus_to_space);
-
 std::string trim_copy(const std::string &s);
 
 void divide(
@@ -2450,6 +2471,9 @@ bool parse_multipart_boundary(const std::string &content_type,
 
 bool parse_range_header(const std::string &s, Ranges &ranges);
 
+bool parse_accept_header(const std::string &s,
+                         std::vector<std::string> &content_types);
+
 int close_socket(socket_t sock);
 
 ssize_t send_socket(socket_t sock, const void *ptr, size_t size, int flags);

From 52cf111b312d6747fd553782bee7f9fc808bf564 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Adrien=20Gallou=C3=ABt?= <angt@huggingface.co>
Date: Wed, 12 Nov 2025 13:48:30 +0100
Subject: [PATCH 167/185] cmake : cleanup (#17199)

---
 common/CMakeLists.txt | 1 -
 1 file changed, 1 deletion(-)

diff --git a/common/CMakeLists.txt b/common/CMakeLists.txt
index 0c34ce1151c..706fa32eed0 100644
--- a/common/CMakeLists.txt
+++ b/common/CMakeLists.txt
@@ -93,7 +93,6 @@ if (LLAMA_CURL)
     set(LLAMA_COMMON_EXTRA_LIBS ${LLAMA_COMMON_EXTRA_LIBS} ${CURL_LIBRARIES})
 elseif (LLAMA_HTTPLIB)
     # otherwise, use cpp-httplib
-    message(FATAL "test")
     target_compile_definitions(${TARGET} PUBLIC LLAMA_USE_HTTPLIB)
     set(LLAMA_COMMON_EXTRA_LIBS ${LLAMA_COMMON_EXTRA_LIBS} cpp-httplib)
 endif()

From 1c398dc9eca9c366ce98deb0e6f3538e444ebc8a Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Alberto=20Cabrera=20P=C3=A9rez?= <alberto.cabrera@liquid.ai>
Date: Wed, 12 Nov 2025 12:52:19 +0000
Subject: [PATCH 168/185] ggml-cpu: handle 3d tensors in repack mat_mul
 (#17030)

* ggml-cpu: handle 3d tensors in repack mul_mat

* Removed unnecessary branch, removed need for <algorithm>

* Fixed dst_ptr pointer in chunk + clang_format

* GGML_ASSERT to check wdata within bounds

* Accidental ggml.h inclusion

* Improved GGML_ASSERT on wdata boundaries
---
 ggml/src/ggml-cpu/repack.cpp | 132 ++++++++++++++++++++++++-----------
 1 file changed, 90 insertions(+), 42 deletions(-)

diff --git a/ggml/src/ggml-cpu/repack.cpp b/ggml/src/ggml-cpu/repack.cpp
index 8421c84ce09..274be146dc5 100644
--- a/ggml/src/ggml-cpu/repack.cpp
+++ b/ggml/src/ggml-cpu/repack.cpp
@@ -1600,29 +1600,52 @@ template <typename BLOC_TYPE, int64_t INTER_SIZE, int64_t NB_COLS, ggml_type PAR
         return false;
     }
 
-    void forward_mul_mat_one_chunk(ggml_compute_params * params, ggml_tensor * op, int64_t src0_start, int64_t src0_end) {
+    void forward_mul_mat_one_chunk(ggml_compute_params * params,
+                                   ggml_tensor *         op,
+                                   int64_t               src0_start,
+                                   int64_t               src0_end,
+                                   int64_t               src1_start,
+                                   int64_t               src1_end) {
         const ggml_tensor * src0 = op->src[0];
         const ggml_tensor * src1 = op->src[1];
         ggml_tensor *       dst  = op;
 
         GGML_TENSOR_BINARY_OP_LOCALS
 
-        const void * src1_wdata      = params->wdata;
         const size_t src1_col_stride = ggml_row_size(PARAM_TYPE, ne10);
 
+        GGML_ASSERT(ne03 == 1 && ne13 == 1);
+        GGML_ASSERT(ne12 % ne02 == 0);
+        const int64_t r2 = ne12 / ne02;
+
+        const int64_t i12 = src1_start / ne1;
+        const int64_t i11 = src1_start - i12 * ne1;
+
+        // Determine batch index
+        const int64_t i02 = i12 / r2;
+
+        const int64_t i1 = i11;
+        const int64_t i2 = i12;
+
+        const char * src0_ptr = (const char *) src0->data + i02 * nb02;
+        const char * src1_ptr = (const char *) params->wdata + (i11 + i12 * ne11) * src1_col_stride;
+        char *       dst_ptr  = ((char *) dst->data + (i1 * nb1 + i2 * nb2));
+
+        const int64_t nrows = src1_end - src1_start;
+        const int64_t ncols = src0_end - src0_start;
+
+        GGML_ASSERT(src1_ptr + src1_col_stride * nrows <= (const char *) params->wdata + params->wsize);
+
         // If there are more than three rows in src1, use gemm; otherwise, use gemv.
-        if (ne11 > 3) {
-            gemm<BLOC_TYPE, INTER_SIZE, NB_COLS, PARAM_TYPE>(ne00,
-                    (float *) ((char *) dst->data) + src0_start, ne01,
-                    (const char *) src0->data + src0_start * nb01,
-                    (const char *) src1_wdata, ne11 - ne11 % 4, src0_end - src0_start);
+        if (nrows > 3) {
+            gemm<BLOC_TYPE, INTER_SIZE, NB_COLS, PARAM_TYPE>(ne00, (float *) (dst_ptr) + src0_start, nb1 / nb0,
+                                                             src0_ptr + src0_start * nb01, src1_ptr,
+                                                             nrows - (nrows % 4), ncols);
         }
-        for (int iter = ne11 - ne11 % 4; iter < ne11; iter++) {
-            gemv<BLOC_TYPE, INTER_SIZE, NB_COLS, PARAM_TYPE>(ne00,
-                    (float *) ((char *) dst->data + (iter * nb1)) + src0_start, ne01,
-                    (const char *) src0->data + src0_start * nb01,
-                    (const char *) src1_wdata + (src1_col_stride * iter), 1,
-                    src0_end - src0_start);
+        for (int iter = nrows - (nrows % 4); iter < nrows; iter++) {
+            gemv<BLOC_TYPE, INTER_SIZE, NB_COLS, PARAM_TYPE>(ne00, (float *) (dst_ptr + (iter * nb1)) + src0_start,
+                                                             ne01, src0_ptr + src0_start * nb01,
+                                                             src1_ptr + (src1_col_stride * iter), 1 /* nrows */, ncols);
         }
     }
 
@@ -1647,6 +1670,12 @@ template <typename BLOC_TYPE, int64_t INTER_SIZE, int64_t NB_COLS, ggml_type PAR
         GGML_ASSERT(nb1 <= nb2);
         GGML_ASSERT(nb2 <= nb3);
 
+        // TODO: General batched mul mat for 4D tensors
+        // Currently only supports 3D tensors
+        GGML_ASSERT(ne03 == 1);
+        GGML_ASSERT(ne13 == 1);
+        GGML_ASSERT(ne3 == 1);
+
         GGML_ASSERT(src1->type == GGML_TYPE_F32);
 
         GGML_ASSERT(ggml_n_dims(op->src[0]) == 2);
@@ -1654,47 +1683,60 @@ template <typename BLOC_TYPE, int64_t INTER_SIZE, int64_t NB_COLS, ggml_type PAR
 
         char *       wdata = static_cast<char *>(params->wdata);
         const size_t nbw1  = ggml_row_size(PARAM_TYPE, ne10);
+        const size_t nbw2  = nbw1 * ne11;
 
-        assert(params->wsize >= nbw1 * ne11);
+        assert(params->wsize >= nbw2 * ne12);
 
         const ggml_from_float_t from_float = ggml_get_type_traits_cpu(PARAM_TYPE)->from_float;
 
-        int64_t i11_processed = 0;
-        for (int64_t i11 = ith * 4; i11 < ne11 - ne11 % 4; i11 += nth * 4) {
-            ggml_quantize_mat_t<INTER_SIZE, PARAM_TYPE>((float *) ((char *) src1->data + i11 * nb11), (void *) (wdata + i11 * nbw1), 4, ne10);
-        }
+        for (int64_t i12 = 0; i12 < ne12; i12++) {
+            char * data_ptr  = (char *) src1->data + i12 * nb12;
+            char * wdata_ptr = wdata + i12 * nbw2;
 
-        i11_processed = ne11 - ne11 % 4;
-        for (int64_t i11 = i11_processed + ith; i11 < ne11; i11 += nth) {
-            from_float((float *) ((char *) src1->data + i11 * nb11), (void *) (wdata + i11 * nbw1), ne10);
+            for (int64_t i11 = ith * 4; i11 < ne11 - ne11 % 4; i11 += nth * 4) {
+                ggml_quantize_mat_t<INTER_SIZE, PARAM_TYPE>((float *) (data_ptr + i11 * nb11),
+                                                            (void *) (wdata_ptr + i11 * nbw1), 4, ne10);
+            }
+
+            const int64_t i11_processed = ne11 - ne11 % 4;
+            for (int64_t i11 = i11_processed + ith; i11 < ne11; i11 += nth) {
+                from_float((float *) (data_ptr + i11 * nb11), (void *) (wdata_ptr + i11 * nbw1), ne10);
+            }
         }
 
         // disable for NUMA
         const bool disable_chunking = ggml_is_numa();
 
         // 4x chunks per thread
-        int64_t nr = ggml_nrows(op->src[0]);
-        int nth_scaled = nth * 4;
-        int64_t chunk_size = (nr + nth_scaled - 1) / nth_scaled;
-        int64_t nchunk     = (nr + chunk_size - 1) / chunk_size;
+        const int64_t nr0 = ggml_nrows(op->src[0]);
+        const int64_t nr1 = ne1 * ne2 * ne3;
+
+        int     nth_scaled  = nth * 4;
+        int64_t chunk_size0 = (nr0 + nth_scaled - 1) / nth_scaled;
+        // avoid too small chunks for narrow src1
+        int64_t chunk_size1 = MAX(16, (nr1 + nth - 1) / nth);
+        int64_t nchunk0     = (nr0 + chunk_size0 - 1) / chunk_size0;
+        int64_t nchunk1     = (nr1 + chunk_size1 - 1) / chunk_size1;
 
         // Ensure minimum chunk size to avoid alignment issues with high thread counts
         // Minimum chunk size should be at least NB_COLS to prevent overlapping chunks after alignment
         const int64_t min_chunk_size = NB_COLS;
-        if (nchunk > 0 && (nr / nchunk) < min_chunk_size && nr >= min_chunk_size) {
-            nchunk = (nr + min_chunk_size - 1) / min_chunk_size;
+        if (nchunk0 > 0 && (nr0 / nchunk0) < min_chunk_size && nr0 >= min_chunk_size) {
+            nchunk0 = (nr0 + min_chunk_size - 1) / min_chunk_size;
         }
 
-        if (nth == 1 || nchunk < nth || disable_chunking) {
-            nchunk = nth;
+        if (nth == 1 || nchunk0 * nchunk1 < nth || disable_chunking) {
+            nchunk0 = nr0 > nr1 ? nth : 1;
+            nchunk1 = nr0 > nr1 ? 1 : nth;
         }
 
+        const int64_t dr0 = (nr0 + nchunk0 - 1) / nchunk0;
+        const int64_t dr1 = (nr1 + nchunk1 - 1) / nchunk1;
+
         // Ensure nchunk doesn't exceed the number of rows divided by minimum chunk size
         // This prevents creating too many tiny chunks that could overlap after alignment
-        const int64_t max_nchunk = (nr + min_chunk_size - 1) / min_chunk_size;
-        if (nchunk > max_nchunk) {
-            nchunk = max_nchunk;
-        }
+        const int64_t max_nchunk = (nr0 + min_chunk_size - 1) / min_chunk_size;
+        nchunk0                  = MIN(nchunk0, max_nchunk);
 
         if (ith == 0) {
             // Every thread starts at ith, so the first unprocessed chunk is nth.  This save a bit of coordination right at the start.
@@ -1706,23 +1748,29 @@ template <typename BLOC_TYPE, int64_t INTER_SIZE, int64_t NB_COLS, ggml_type PAR
         // The first chunk comes from our thread_id, the rest will get auto-assigned.
         int current_chunk = ith;
 
-        while (current_chunk < nchunk) {
-            int64_t src0_start = (current_chunk * ne01) / nchunk;
-            int64_t src0_end   = ((current_chunk + 1) * ne01) / nchunk;
+        while (current_chunk < nchunk0 * nchunk1) {
+            const int64_t ith0 = current_chunk % nchunk0;
+            const int64_t ith1 = current_chunk / nchunk0;
+
+            int64_t src0_start = dr0 * ith0;
+            int64_t src0_end   = MIN(src0_start + dr0, nr0);
+
+            int64_t src1_start = dr1 * ith1;
+            int64_t src1_end   = MIN(src1_start + dr1, nr1);
 
             // Align boundaries to NB_COLS - round up to ensure all data is included
             // The chunk size limiting above ensures chunks are large enough to prevent overlaps
             src0_start = (src0_start % NB_COLS) ? src0_start + NB_COLS - (src0_start % NB_COLS) : src0_start;
-            src0_end   = (src0_end   % NB_COLS) ? src0_end   + NB_COLS - (src0_end   % NB_COLS) : src0_end;
-            if (src0_end > ne01) {
-                src0_end = ne01;
-            }
+            src0_end   = (src0_end % NB_COLS) ? src0_end + NB_COLS - (src0_end % NB_COLS) : src0_end;
+            src0_end   = MIN(src0_end, ne01);
 
+            // Make sure current plane is the last one before exiting
             if (src0_start >= src0_end) {
-                break;
+                current_chunk = ggml_threadpool_chunk_add(params->threadpool, 1);
+                continue;
             }
 
-            forward_mul_mat_one_chunk(params, dst, src0_start, src0_end);
+            forward_mul_mat_one_chunk(params, dst, src0_start, src0_end, src1_start, src1_end);
 
             current_chunk = ggml_threadpool_chunk_add(params->threadpool, 1);
         }

From ee8dd5c6583b25bd7542ef7956ca96e1e81f67a9 Mon Sep 17 00:00:00 2001
From: Xuan-Son Nguyen <son@huggingface.co>
Date: Wed, 12 Nov 2025 14:17:24 +0100
Subject: [PATCH 169/185] server: move res_error/res_ok to static function
 (#17167)

---
 tools/server/server.cpp | 61 ++++++++++++++++++++---------------------
 1 file changed, 30 insertions(+), 31 deletions(-)

diff --git a/tools/server/server.cpp b/tools/server/server.cpp
index 6bd4be3cc17..0cf2f767b33 100644
--- a/tools/server/server.cpp
+++ b/tools/server/server.cpp
@@ -4432,6 +4432,17 @@ static void log_server_request(const httplib::Request & req, const httplib::Resp
     SRV_DBG("response: %s\n", res.body.c_str());
 }
 
+static void res_error(httplib::Response & res, const json & error_data) {
+    json final_response {{"error", error_data}};
+    res.set_content(safe_json_to_str(final_response), MIMETYPE_JSON);
+    res.status = json_value(error_data, "code", 500);
+}
+
+static void res_ok(httplib::Response & res, const json & data) {
+    res.set_content(safe_json_to_str(data), MIMETYPE_JSON);
+    res.status = 200;
+}
+
 std::function<void(int)> shutdown_handler;
 std::atomic_flag is_terminating = ATOMIC_FLAG_INIT;
 
@@ -4501,19 +4512,7 @@ int main(int argc, char ** argv) {
 
     svr->set_default_headers({{"Server", "llama.cpp"}});
     svr->set_logger(log_server_request);
-
-    auto res_error = [](httplib::Response & res, const json & error_data) {
-        json final_response {{"error", error_data}};
-        res.set_content(safe_json_to_str(final_response), MIMETYPE_JSON);
-        res.status = json_value(error_data, "code", 500);
-    };
-
-    auto res_ok = [](httplib::Response & res, const json & data) {
-        res.set_content(safe_json_to_str(data), MIMETYPE_JSON);
-        res.status = 200;
-    };
-
-    svr->set_exception_handler([&res_error](const httplib::Request &, httplib::Response & res, const std::exception_ptr & ep) {
+    svr->set_exception_handler([](const httplib::Request &, httplib::Response & res, const std::exception_ptr & ep) {
         std::string message;
         try {
             std::rethrow_exception(ep);
@@ -4532,7 +4531,7 @@ int main(int argc, char ** argv) {
         }
     });
 
-    svr->set_error_handler([&res_error](const httplib::Request &, httplib::Response & res) {
+    svr->set_error_handler([](const httplib::Request &, httplib::Response & res) {
         if (res.status == 404) {
             res_error(res, format_error_response("File Not Found", ERROR_TYPE_NOT_FOUND));
         }
@@ -4562,7 +4561,7 @@ int main(int argc, char ** argv) {
     // Middlewares
     //
 
-    auto middleware_validate_api_key = [&params, &res_error](const httplib::Request & req, httplib::Response & res) {
+    auto middleware_validate_api_key = [&params](const httplib::Request & req, httplib::Response & res) {
         static const std::unordered_set<std::string> public_endpoints = {
             "/health",
             "/v1/health",
@@ -4600,7 +4599,7 @@ int main(int argc, char ** argv) {
         return false;
     };
 
-    auto middleware_server_state = [&res_error, &state](const httplib::Request & req, httplib::Response & res) {
+    auto middleware_server_state = [&state](const httplib::Request & req, httplib::Response & res) {
         server_state current_state = state.load();
         if (current_state == SERVER_STATE_LOADING_MODEL) {
             auto tmp = string_split<std::string>(req.path, '.');
@@ -4788,7 +4787,7 @@ int main(int argc, char ** argv) {
         res.status = 200; // HTTP OK
     };
 
-    const auto handle_slots_save = [&ctx_server, &res_error, &res_ok, &params](const httplib::Request & req, httplib::Response & res, int id_slot) {
+    const auto handle_slots_save = [&ctx_server, &params](const httplib::Request & req, httplib::Response & res, int id_slot) {
         json request_data = json::parse(req.body);
         std::string filename = request_data.at("filename");
         if (!fs_validate_filename(filename)) {
@@ -4820,7 +4819,7 @@ int main(int argc, char ** argv) {
         res_ok(res, result->to_json());
     };
 
-    const auto handle_slots_restore = [&ctx_server, &res_error, &res_ok, &params](const httplib::Request & req, httplib::Response & res, int id_slot) {
+    const auto handle_slots_restore = [&ctx_server, &params](const httplib::Request & req, httplib::Response & res, int id_slot) {
         json request_data = json::parse(req.body);
         std::string filename = request_data.at("filename");
         if (!fs_validate_filename(filename)) {
@@ -4853,7 +4852,7 @@ int main(int argc, char ** argv) {
         res_ok(res, result->to_json());
     };
 
-    const auto handle_slots_erase = [&ctx_server, &res_error, &res_ok](const httplib::Request & /* req */, httplib::Response & res, int id_slot) {
+    const auto handle_slots_erase = [&ctx_server](const httplib::Request & /* req */, httplib::Response & res, int id_slot) {
         int task_id = ctx_server.queue_tasks.get_new_id();
         {
             server_task task(SERVER_TASK_TYPE_SLOT_ERASE);
@@ -4876,7 +4875,7 @@ int main(int argc, char ** argv) {
         res_ok(res, result->to_json());
     };
 
-    const auto handle_slots_action = [&params, &res_error, &handle_slots_save, &handle_slots_restore, &handle_slots_erase](const httplib::Request & req, httplib::Response & res) {
+    const auto handle_slots_action = [&params, &handle_slots_save, &handle_slots_restore, &handle_slots_erase](const httplib::Request & req, httplib::Response & res) {
         if (params.slot_save_path.empty()) {
             res_error(res, format_error_response("This server does not support slots action. Start it with `--slot-save-path`", ERROR_TYPE_NOT_SUPPORTED));
             return;
@@ -4905,7 +4904,7 @@ int main(int argc, char ** argv) {
         }
     };
 
-    const auto handle_props = [&params, &ctx_server, &res_ok](const httplib::Request &, httplib::Response & res) {
+    const auto handle_props = [&params, &ctx_server](const httplib::Request &, httplib::Response & res) {
         json default_generation_settings_for_props;
 
         {
@@ -4947,7 +4946,7 @@ int main(int argc, char ** argv) {
         res_ok(res, data);
     };
 
-    const auto handle_props_change = [&ctx_server, &res_error, &res_ok](const httplib::Request & req, httplib::Response & res) {
+    const auto handle_props_change = [&ctx_server](const httplib::Request & req, httplib::Response & res) {
         if (!ctx_server.params_base.endpoint_props) {
             res_error(res, format_error_response("This server does not support changing global properties. Start it with `--props`", ERROR_TYPE_NOT_SUPPORTED));
             return;
@@ -4960,7 +4959,7 @@ int main(int argc, char ** argv) {
         res_ok(res, {{ "success", true }});
     };
 
-    const auto handle_api_show = [&ctx_server, &res_ok](const httplib::Request &, httplib::Response & res) {
+    const auto handle_api_show = [&ctx_server](const httplib::Request &, httplib::Response & res) {
         bool has_mtmd = ctx_server.mctx != nullptr;
         json data = {
             {
@@ -4991,7 +4990,7 @@ int main(int argc, char ** argv) {
 
     // handle completion-like requests (completion, chat, infill)
     // we can optionally provide a custom format for partial results and final results
-    const auto handle_completions_impl = [&ctx_server, &res_error, &res_ok](
+    const auto handle_completions_impl = [&ctx_server](
             server_task_type type,
             json & data,
             const std::vector<raw_buffer> & files,
@@ -5139,7 +5138,7 @@ int main(int argc, char ** argv) {
             OAICOMPAT_TYPE_COMPLETION);
     };
 
-    const auto handle_infill = [&ctx_server, &res_error, &handle_completions_impl](const httplib::Request & req, httplib::Response & res) {
+    const auto handle_infill = [&ctx_server, &handle_completions_impl](const httplib::Request & req, httplib::Response & res) {
         // check model compatibility
         std::string err;
         if (llama_vocab_fim_pre(ctx_server.vocab) == LLAMA_TOKEN_NULL) {
@@ -5238,7 +5237,7 @@ int main(int argc, char ** argv) {
     };
 
     // same with handle_chat_completions, but without inference part
-    const auto handle_apply_template = [&ctx_server, &res_ok](const httplib::Request & req, httplib::Response & res) {
+    const auto handle_apply_template = [&ctx_server](const httplib::Request & req, httplib::Response & res) {
         auto body = json::parse(req.body);
         std::vector<raw_buffer> files; // dummy, unused
         json data = oaicompat_chat_params_parse(
@@ -5248,7 +5247,7 @@ int main(int argc, char ** argv) {
         res_ok(res, {{ "prompt", std::move(data.at("prompt")) }});
     };
 
-    const auto handle_models = [&params, &ctx_server, &state, &res_ok](const httplib::Request &, httplib::Response & res) {
+    const auto handle_models = [&params, &ctx_server, &state](const httplib::Request &, httplib::Response & res) {
         server_state current_state = state.load();
         json model_meta = nullptr;
         if (current_state == SERVER_STATE_READY) {
@@ -5293,7 +5292,7 @@ int main(int argc, char ** argv) {
         res_ok(res, models);
     };
 
-    const auto handle_tokenize = [&ctx_server, &res_ok](const httplib::Request & req, httplib::Response & res) {
+    const auto handle_tokenize = [&ctx_server](const httplib::Request & req, httplib::Response & res) {
         const json body = json::parse(req.body);
 
         json tokens_response = json::array();
@@ -5334,7 +5333,7 @@ int main(int argc, char ** argv) {
         res_ok(res, data);
     };
 
-    const auto handle_detokenize = [&ctx_server, &res_ok](const httplib::Request & req, httplib::Response & res) {
+    const auto handle_detokenize = [&ctx_server](const httplib::Request & req, httplib::Response & res) {
         const json body = json::parse(req.body);
 
         std::string content;
@@ -5347,7 +5346,7 @@ int main(int argc, char ** argv) {
         res_ok(res, data);
     };
 
-    const auto handle_embeddings_impl = [&ctx_server, &res_error, &res_ok](const httplib::Request & req, httplib::Response & res, oaicompat_type oaicompat) {
+    const auto handle_embeddings_impl = [&ctx_server](const httplib::Request & req, httplib::Response & res, oaicompat_type oaicompat) {
         if (!ctx_server.params_base.embedding) {
             res_error(res, format_error_response("This server does not support embeddings. Start it with `--embeddings`", ERROR_TYPE_NOT_SUPPORTED));
             return;
@@ -5457,7 +5456,7 @@ int main(int argc, char ** argv) {
         handle_embeddings_impl(req, res, OAICOMPAT_TYPE_EMBEDDING);
     };
 
-    const auto handle_rerank = [&ctx_server, &res_error, &res_ok](const httplib::Request & req, httplib::Response & res) {
+    const auto handle_rerank = [&ctx_server](const httplib::Request & req, httplib::Response & res) {
         if (!ctx_server.params_base.embedding || ctx_server.params_base.pooling_type != LLAMA_POOLING_TYPE_RANK) {
             res_error(res, format_error_response("This server does not support reranking. Start it with `--reranking`", ERROR_TYPE_NOT_SUPPORTED));
             return;

From 017eceed61e885b79f6cf3542e0879be68c6e922 Mon Sep 17 00:00:00 2001
From: Xuan-Son Nguyen <son@huggingface.co>
Date: Wed, 12 Nov 2025 14:56:02 +0100
Subject: [PATCH 170/185] ci: add check vendor job (#17179)

* ci: add check vendor job

* use dev version of miniaudio

* move to dedicated workflow, only run on related files changed
---
 .github/workflows/check-vendor.yml | 52 ++++++++++++++++++++++++++++++
 scripts/sync_vendor.py             |  4 ++-
 2 files changed, 55 insertions(+), 1 deletion(-)
 create mode 100644 .github/workflows/check-vendor.yml

diff --git a/.github/workflows/check-vendor.yml b/.github/workflows/check-vendor.yml
new file mode 100644
index 00000000000..7b3016079cc
--- /dev/null
+++ b/.github/workflows/check-vendor.yml
@@ -0,0 +1,52 @@
+name: Check vendor
+
+on:
+  workflow_dispatch: # allows manual triggering
+  push:
+    branches:
+      - master
+    paths: [
+      'vendor/**',
+      'scripts/sync_vendor.py'
+    ]
+
+  pull_request:
+    types: [opened, synchronize, reopened]
+    paths: [
+      'vendor/**',
+      'scripts/sync_vendor.py'
+    ]
+
+jobs:
+  check-vendor:
+    runs-on: ubuntu-latest
+
+    steps:
+      - name: Checkout
+        uses: actions/checkout@v4
+        with:
+          fetch-depth: 0
+
+      - name: Setup Python
+        uses: actions/setup-python@v4
+        with:
+          python-version: '3.x'
+
+      - name: Run vendor sync
+        run: |
+          set -euo pipefail
+          python3 scripts/sync_vendor.py
+
+      - name: Check for changes
+        run: |
+          set -euo pipefail
+          # detect modified or untracked files
+          changed=$(git status --porcelain --untracked-files=all || true)
+          if [ -n "$changed" ]; then
+            echo "Vendor sync modified files:"
+            echo "$changed" | awk '{ print $2 }' | sed '/^$/d'
+            echo "Failing because vendor files mismatch. Please update scripts/sync_vendor.py"
+            exit 1
+          else
+            echo "Vendor files are up-to-date."
+          fi
diff --git a/scripts/sync_vendor.py b/scripts/sync_vendor.py
index ac94387dd2f..4a89d08f805 100755
--- a/scripts/sync_vendor.py
+++ b/scripts/sync_vendor.py
@@ -12,7 +12,9 @@
 
     "https://raw.githubusercontent.com/nothings/stb/refs/heads/master/stb_image.h": "vendor/stb/stb_image.h",
 
-    "https://github.com/mackron/miniaudio/raw/refs/tags/0.11.22/miniaudio.h": "vendor/miniaudio/miniaudio.h",
+    # not using latest tag to avoid this issue: https://github.com/ggml-org/llama.cpp/pull/17179#discussion_r2515877926
+    # "https://github.com/mackron/miniaudio/raw/refs/tags/0.11.23/miniaudio.h": "vendor/miniaudio/miniaudio.h",
+    "https://github.com/mackron/miniaudio/raw/669ed3e844524fcd883231b13095baee9f6de304/miniaudio.h": "vendor/miniaudio/miniaudio.h",
 
     "https://raw.githubusercontent.com/yhirose/cpp-httplib/refs/tags/v0.27.0/httplib.h": "vendor/cpp-httplib/httplib.h",
 }

From 00c94083b3ffd51bb81cd5cb5cf1177168ce286c Mon Sep 17 00:00:00 2001
From: Xuan-Son Nguyen <son@huggingface.co>
Date: Wed, 12 Nov 2025 18:50:52 +0100
Subject: [PATCH 171/185] server: (refactor) implement generator-based API for
 task results (#17174)

* server: (refactor) implement generator-based API for task results

* improve

* moving some code

* fix "Response ended prematurely"

* add sink.done before return false

* rm redundant check

* rm unused var

* rename generator --> reader
---
 tools/server/server.cpp | 399 +++++++++++++++++++++-------------------
 tools/server/utils.hpp  |  26 ++-
 2 files changed, 232 insertions(+), 193 deletions(-)

diff --git a/tools/server/server.cpp b/tools/server/server.cpp
index 0cf2f767b33..0b3c77879c2 100644
--- a/tools/server/server.cpp
+++ b/tools/server/server.cpp
@@ -684,7 +684,7 @@ struct server_task_result {
     }
     virtual bool is_stop() {
         // only used by server_task_result_cmpl_*
-        return false;
+        return true;
     }
     virtual int get_index() {
         return -1;
@@ -3238,105 +3238,6 @@ struct server_context {
         queue_results.send(std::move(res));
     }
 
-    //
-    // Functions to create new task(s) and receive result(s)
-    //
-
-    void cancel_tasks(const std::unordered_set<int> & id_tasks) {
-        std::vector<server_task> cancel_tasks;
-        cancel_tasks.reserve(id_tasks.size());
-        for (const auto & id_task : id_tasks) {
-            SRV_WRN("cancel task, id_task = %d\n", id_task);
-
-            server_task task(SERVER_TASK_TYPE_CANCEL);
-            task.id_target = id_task;
-            queue_results.remove_waiting_task_id(id_task);
-            cancel_tasks.push_back(std::move(task));
-        }
-        // push to beginning of the queue, so it has highest priority
-        queue_tasks.post(std::move(cancel_tasks), true);
-    }
-
-    // receive the results from task(s)
-    void receive_multi_results(
-            const std::unordered_set<int> & id_tasks,
-            const std::function<void(std::vector<server_task_result_ptr>&)> & result_handler,
-            const std::function<void(json)> & error_handler,
-            const std::function<bool()> & is_connection_closed) {
-        std::vector<server_task_result_ptr> results(id_tasks.size());
-        for (int i = 0; i < (int)id_tasks.size(); i++) {
-            server_task_result_ptr result = queue_results.recv_with_timeout(id_tasks, HTTP_POLLING_SECONDS);
-
-            if (is_connection_closed()) {
-                cancel_tasks(id_tasks);
-                return;
-            }
-
-            if (result == nullptr) {
-                i--; // retry
-                continue;
-            }
-
-            if (result->is_error()) {
-                error_handler(result->to_json());
-                cancel_tasks(id_tasks);
-                return;
-            }
-
-            GGML_ASSERT(
-                dynamic_cast<server_task_result_cmpl_final*>(result.get()) != nullptr
-                || dynamic_cast<server_task_result_embd*>(result.get()) != nullptr
-                || dynamic_cast<server_task_result_rerank*>(result.get()) != nullptr
-            );
-            const size_t idx = result->get_index();
-            GGML_ASSERT(idx < results.size() && "index out of range");
-            results[idx] = std::move(result);
-        }
-        result_handler(results);
-    }
-
-    // receive the results from task(s), in stream mode
-    void receive_cmpl_results_stream(
-            const std::unordered_set<int> & id_tasks,
-            const std::function<bool(server_task_result_ptr&)> & result_handler,
-            const std::function<void(json)> & error_handler,
-            const std::function<bool()> & is_connection_closed) {
-        size_t n_finished = 0;
-        while (true) {
-            server_task_result_ptr result = queue_results.recv_with_timeout(id_tasks, HTTP_POLLING_SECONDS);
-
-            if (is_connection_closed()) {
-                cancel_tasks(id_tasks);
-                return;
-            }
-
-            if (result == nullptr) {
-                continue; // retry
-            }
-
-            if (result->is_error()) {
-                error_handler(result->to_json());
-                cancel_tasks(id_tasks);
-                return;
-            }
-
-            GGML_ASSERT(
-                dynamic_cast<server_task_result_cmpl_partial*>(result.get()) != nullptr
-                || dynamic_cast<server_task_result_cmpl_final*>(result.get()) != nullptr
-            );
-            if (!result_handler(result)) {
-                cancel_tasks(id_tasks);
-                break;
-            }
-
-            if (result->is_stop()) {
-                if (++n_finished == id_tasks.size()) {
-                    break;
-                }
-            }
-        }
-    }
-
     //
     // Functions to process the task
     //
@@ -4418,6 +4319,104 @@ struct server_context {
     }
 };
 
+// generator-like API for server responses, support pooling connection state and aggregating results
+struct server_response_reader {
+    std::unordered_set<int> id_tasks;
+    server_context & ctx_server;
+    size_t received_count = 0;
+    bool cancelled = false;
+
+    server_response_reader(server_context & ctx_server) : ctx_server(ctx_server) {}
+    ~server_response_reader() {
+        stop();
+    }
+
+    void post_tasks(std::vector<server_task> && tasks) {
+        id_tasks = server_task::get_list_id(tasks);
+        ctx_server.queue_results.add_waiting_tasks(tasks);
+        ctx_server.queue_tasks.post(std::move(tasks));
+    }
+
+    bool has_next() {
+        return !cancelled && received_count < id_tasks.size();
+    }
+
+    // return nullptr if should_stop() is true before receiving a result
+    // note: if one error is received, it will stop further processing and return error result
+    server_task_result_ptr next(const std::function<bool()> & should_stop) {
+        while (true) {
+            server_task_result_ptr result = ctx_server.queue_results.recv_with_timeout(id_tasks, HTTP_POLLING_SECONDS);
+            if (result == nullptr) {
+                // timeout, check stop condition
+                if (should_stop()) {
+                    SRV_DBG("%s", "stopping wait for next result due to should_stop condition\n");
+                    return nullptr;
+                }
+            } else {
+                if (result->is_error()) {
+                    stop(); // cancel remaining tasks
+                    SRV_DBG("%s", "received error result, stopping further processing\n");
+                    return result;
+                }
+                if (result->is_stop()) {
+                    received_count++;
+                }
+                return result;
+            }
+        }
+
+        // should not reach here
+    }
+
+    struct batch_response {
+        bool is_terminated = false; // if true, indicates that processing was stopped before all results were received
+        std::vector<server_task_result_ptr> results;
+        server_task_result_ptr error; // nullptr if no error
+    };
+
+    batch_response wait_for_all(const std::function<bool()> & should_stop) {
+        batch_response batch_res;
+        batch_res.results.resize(id_tasks.size());
+        while (has_next()) {
+            auto res = next(should_stop);
+            if (res == nullptr) {
+                batch_res.is_terminated = true;
+                return batch_res;
+            }
+            if (res->is_error()) {
+                batch_res.error = std::move(res);
+                return batch_res;
+            }
+            const size_t idx = res->get_index();
+            GGML_ASSERT(idx < batch_res.results.size() && "index out of range");
+            GGML_ASSERT(batch_res.results[idx] == nullptr && "duplicate result received");
+            batch_res.results[idx] = std::move(res);
+        }
+        return batch_res;
+    }
+
+    void stop() {
+        ctx_server.queue_results.remove_waiting_task_ids(id_tasks);
+        if (has_next() && !cancelled) {
+            // if tasks is not finished yet, cancel them
+            cancelled = true;
+            std::vector<server_task> cancel_tasks;
+            cancel_tasks.reserve(id_tasks.size());
+            for (const auto & id_task : id_tasks) {
+                SRV_WRN("cancel task, id_task = %d\n", id_task);
+                server_task task(SERVER_TASK_TYPE_CANCEL);
+                task.id_target = id_task;
+                ctx_server.queue_results.remove_waiting_task_id(id_task);
+                cancel_tasks.push_back(std::move(task));
+            }
+            // push to beginning of the queue, so it has highest priority
+            ctx_server.queue_tasks.post(std::move(cancel_tasks), true);
+        } else {
+            SRV_DBG("%s", "all tasks already finished, no need to cancel\n");
+        }
+    }
+};
+
 static void log_server_request(const httplib::Request & req, const httplib::Response & res) {
     // skip GH copilot requests when using default port
     if (req.path == "/v1/health") {
@@ -5000,7 +4999,10 @@ int main(int argc, char ** argv) {
         GGML_ASSERT(type == SERVER_TASK_TYPE_COMPLETION || type == SERVER_TASK_TYPE_INFILL);
 
         auto completion_id = gen_chatcmplid();
-        std::unordered_set<int> task_ids;
+        // need to store the reader as a pointer, so that it won't be destroyed when the handle returns
+        // use shared_ptr as it's shared between the chunked_content_provider() and on_complete()
+        const auto rd = std::make_shared<server_response_reader>(ctx_server);
+
         try {
             std::vector<server_task> tasks;
 
@@ -5018,17 +5020,8 @@ int main(int argc, char ** argv) {
                 // Everything else, including multimodal completions.
                 inputs = tokenize_input_prompts(ctx_server.vocab, ctx_server.mctx, prompt, true, true);
             }
-            const size_t n_ctx_slot = ctx_server.slots.front().n_ctx;
             tasks.reserve(inputs.size());
             for (size_t i = 0; i < inputs.size(); i++) {
-                auto n_prompt_tokens = inputs[i].size();
-                if (n_prompt_tokens >= n_ctx_slot) {
-                    json error_data = format_error_response("the request exceeds the available context size, try increasing it", ERROR_TYPE_EXCEED_CONTEXT_SIZE);
-                    error_data["n_prompt_tokens"] = n_prompt_tokens;
-                    error_data["n_ctx"] = n_ctx_slot;
-                    res_error(res, error_data);
-                    return;
-                }
                 server_task task = server_task(type);
 
                 task.id    = ctx_server.queue_tasks.get_new_id();
@@ -5049,9 +5042,7 @@ int main(int argc, char ** argv) {
                 tasks.push_back(std::move(task));
             }
 
-            task_ids = server_task::get_list_id(tasks);
-            ctx_server.queue_results.add_waiting_tasks(tasks);
-            ctx_server.queue_tasks.post(std::move(tasks));
+            rd->post_tasks(std::move(tasks));
         } catch (const std::exception & e) {
             res_error(res, format_error_response(e.what(), ERROR_TYPE_INVALID_REQUEST));
             return;
@@ -5060,54 +5051,95 @@ int main(int argc, char ** argv) {
         bool stream = json_value(data, "stream", false);
 
         if (!stream) {
-            ctx_server.receive_multi_results(task_ids, [&](std::vector<server_task_result_ptr> & results) {
-                if (results.size() == 1) {
-                    // single result
-                    res_ok(res, results[0]->to_json());
-                } else {
-                    // multiple results (multitask)
-                    json arr = json::array();
-                    for (auto & res : results) {
-                        arr.push_back(res->to_json());
-                    }
-                    res_ok(res, arr);
+            // non-stream, wait for the results
+            auto all_results = rd->wait_for_all(is_connection_closed);
+            if (all_results.is_terminated) {
+                return; // connection is closed
+            } else if (all_results.error) {
+                res_error(res, all_results.error->to_json());
+                return;
+            } else {
+                json arr = json::array();
+                for (auto & res : all_results.results) {
+                    GGML_ASSERT(dynamic_cast<server_task_result_cmpl_final*>(res.get()) != nullptr);
+                    arr.push_back(res->to_json());
                 }
-            }, [&](const json & error_data) {
-                res_error(res, error_data);
-            }, is_connection_closed);
+                // if single request, return single object instead of array
+                res_ok(res, arr.size() == 1 ? arr[0] : arr);
+            }
 
-            ctx_server.queue_results.remove_waiting_task_ids(task_ids);
         } else {
-            const auto chunked_content_provider = [task_ids, &ctx_server, oaicompat](size_t, httplib::DataSink & sink) {
-                ctx_server.receive_cmpl_results_stream(task_ids, [&](server_task_result_ptr & result) -> bool {
-                    json res_json = result->to_json();
-                    if (res_json.is_array()) {
-                        for (const auto & res : res_json) {
-                            if (!server_sent_event(sink, res)) {
-                                // sending failed (HTTP connection closed), cancel the generation
-                                return false;
-                            }
-                        }
-                        return true;
-                    } else {
-                        return server_sent_event(sink, res_json);
+            // in streaming mode, the first error must be treated as non-stream response
+            // this is to match the OAI API behavior
+            // ref: https://github.com/ggml-org/llama.cpp/pull/16486#discussion_r2419657309
+            server_task_result_ptr first_result = rd->next(is_connection_closed);
+            if (first_result == nullptr) {
+                return; // connection is closed
+            } else if (first_result->is_error()) {
+                res_error(res, first_result->to_json());
+                return;
+            } else {
+                GGML_ASSERT(
+                    dynamic_cast<server_task_result_cmpl_partial*>(first_result.get()) != nullptr
+                    || dynamic_cast<server_task_result_cmpl_final*>(first_result.get()) != nullptr
+                );
+            }
+
+            // next responses are streamed
+            json first_result_json = first_result->to_json();
+            const auto chunked_content_provider = [first_result_json, rd, oaicompat](size_t, httplib::DataSink & sink) mutable -> bool {
+                // flush the first result as it's not an error
+                if (!first_result_json.empty()) {
+                    if (!server_sent_event(sink, first_result_json)) {
+                        sink.done();
+                        return false; // sending failed, go to on_complete()
                     }
-                }, [&](const json & error_data) {
-                    server_sent_event(sink, json{{"error", error_data}});
-                }, [&sink]() {
-                    // note: do not use req.is_connection_closed here because req is already destroyed
-                    return !sink.is_writable();
-                });
-                if (oaicompat != OAICOMPAT_TYPE_NONE) {
-                    static const std::string ev_done = "data: [DONE]\n\n";
-                    sink.write(ev_done.data(), ev_done.size());
+                    first_result_json.clear(); // mark as sent
                 }
-                sink.done();
-                return false;
+
+                // receive subsequent results
+                auto result = rd->next([&sink]{ return !sink.is_writable(); });
+                if (result == nullptr) {
+                    sink.done();
+                    return false; // connection is closed, go to on_complete()
+                }
+
+                // send the results
+                json res_json = result->to_json();
+                bool ok = false;
+                if (result->is_error()) {
+                    ok = server_sent_event(sink, json {{ "error", result->to_json() }});
+                    sink.done();
+                    return false; // go to on_complete()
+                } else {
+                    GGML_ASSERT(
+                        dynamic_cast<server_task_result_cmpl_partial*>(result.get()) != nullptr
+                        || dynamic_cast<server_task_result_cmpl_final*>(result.get()) != nullptr
+                    );
+                    ok = server_sent_event(sink, res_json);
+                }
+
+                if (!ok) {
+                    sink.done();
+                    return false; // sending failed, go to on_complete()
+                }
+
+                // check if there is more data
+                if (!rd->has_next()) {
+                    if (oaicompat != OAICOMPAT_TYPE_NONE) {
+                        static const std::string ev_done = "data: [DONE]\n\n";
+                        sink.write(ev_done.data(), ev_done.size());
+                    }
+                    sink.done();
+                    return false; // no more data, go to on_complete()
+                }
+
+                // has next data, continue
+                return true;
             };
 
-            auto on_complete = [task_ids, &ctx_server] (bool) {
-                ctx_server.queue_results.remove_waiting_task_ids(task_ids);
+            auto on_complete = [rd](bool) {
+                rd->stop();
             };
 
             res.set_chunked_content_provider("text/event-stream", chunked_content_provider, on_complete);
@@ -5401,8 +5433,7 @@ int main(int argc, char ** argv) {
 
         // create and queue the task
         json responses = json::array();
-        bool error = false;
-        std::unordered_set<int> task_ids;
+        server_response_reader rd(ctx_server);
         {
             std::vector<server_task> tasks;
             for (size_t i = 0; i < tokenized_prompts.size(); i++) {
@@ -5418,27 +5449,23 @@ int main(int argc, char ** argv) {
 
                 tasks.push_back(std::move(task));
             }
-
-            task_ids = server_task::get_list_id(tasks);
-            ctx_server.queue_results.add_waiting_tasks(tasks);
-            ctx_server.queue_tasks.post(std::move(tasks));
+            rd.post_tasks(std::move(tasks));
         }
 
-        // get the result
-        ctx_server.receive_multi_results(task_ids, [&](std::vector<server_task_result_ptr> & results) {
-            for (auto & res : results) {
+        // wait for the results
+        auto all_results = rd.wait_for_all(req.is_connection_closed);
+
+        // collect results
+        if (all_results.is_terminated) {
+            return; // connection is closed
+        } else if (all_results.error) {
+            res_error(res, all_results.error->to_json());
+            return;
+        } else {
+            for (auto & res : all_results.results) {
                 GGML_ASSERT(dynamic_cast<server_task_result_embd*>(res.get()) != nullptr);
                 responses.push_back(res->to_json());
             }
-        }, [&](const json & error_data) {
-            res_error(res, error_data);
-            error = true;
-        }, req.is_connection_closed);
-
-        ctx_server.queue_results.remove_waiting_task_ids(task_ids);
-
-        if (error) {
-            return;
         }
 
         // write JSON response
@@ -5492,8 +5519,7 @@ int main(int argc, char ** argv) {
 
         // create and queue the task
         json responses = json::array();
-        bool error = false;
-        std::unordered_set<int> task_ids;
+        server_response_reader rd(ctx_server);
         {
             std::vector<server_task> tasks;
             tasks.reserve(documents.size());
@@ -5505,24 +5531,23 @@ int main(int argc, char ** argv) {
                 task.tokens = std::move(tmp);
                 tasks.push_back(std::move(task));
             }
-
-            task_ids = server_task::get_list_id(tasks);
-            ctx_server.queue_results.add_waiting_tasks(tasks);
-            ctx_server.queue_tasks.post(std::move(tasks));
+            rd.post_tasks(std::move(tasks));
         }
 
-        ctx_server.receive_multi_results(task_ids, [&](std::vector<server_task_result_ptr> & results) {
-            for (auto & res : results) {
+        // wait for the results
+        auto all_results = rd.wait_for_all(req.is_connection_closed);
+
+        // collect results
+        if (all_results.is_terminated) {
+            return; // connection is closed
+        } else if (all_results.error) {
+            res_error(res, all_results.error->to_json());
+            return;
+        } else {
+            for (auto & res : all_results.results) {
                 GGML_ASSERT(dynamic_cast<server_task_result_rerank*>(res.get()) != nullptr);
                 responses.push_back(res->to_json());
             }
-        }, [&](const json & error_data) {
-            res_error(res, error_data);
-            error = true;
-        }, req.is_connection_closed);
-
-        if (error) {
-            return;
         }
 
         // write JSON response
diff --git a/tools/server/utils.hpp b/tools/server/utils.hpp
index e9d4431ddfb..b1ecc5af5ed 100644
--- a/tools/server/utils.hpp
+++ b/tools/server/utils.hpp
@@ -453,15 +453,29 @@ static std::string tokens_to_output_formatted_string(const llama_context * ctx,
     return out;
 }
 
+// note: if data is a json array, it will be sent as multiple events, one per item
 static bool server_sent_event(httplib::DataSink & sink, const json & data) {
-    const std::string str =
-        "data: " +
-        data.dump(-1, ' ', false, json::error_handler_t::replace) +
-        "\n\n"; // required by RFC 8895 - A message is terminated by a blank line (two line terminators in a row).
+    static auto send_single = [](httplib::DataSink & sink, const json & data) -> bool {
+        const std::string str =
+            "data: " +
+            data.dump(-1, ' ', false, json::error_handler_t::replace) +
+            "\n\n"; // required by RFC 8895 - A message is terminated by a blank line (two line terminators in a row).
+
+        LOG_DBG("data stream, to_send: %s", str.c_str());
+        return sink.write(str.c_str(), str.size());
+    };
 
-    LOG_DBG("data stream, to_send: %s", str.c_str());
+    if (data.is_array()) {
+        for (const auto & item : data) {
+            if (!send_single(sink, item)) {
+                return false;
+            }
+        }
+    } else {
+        return send_single(sink, data);
+    }
 
-    return sink.write(str.c_str(), str.size());
+    return true;
 }
 
 //

From 8e878f0cb4c893de23455dd0a6bfbbb21bcaad89 Mon Sep 17 00:00:00 2001
From: Aleksander Grygier <aleksander.grygier@gmail.com>
Date: Wed, 12 Nov 2025 19:01:48 +0100
Subject: [PATCH 172/185] Update packages + upgrade Storybook to v10 (#17201)

* chore: Update packages + upgrade Storybook to v10

* fix: Increase timeout for UI tests
---
 .github/workflows/server.yml                  |   2 +-
 tools/server/webui/.storybook/preview.ts      |   8 +
 tools/server/webui/.storybook/vitest.setup.ts |   3 +-
 tools/server/webui/package-lock.json          | 491 +++++++-----------
 tools/server/webui/package.json               |  26 +-
 .../webui/src/stories/ChatForm.stories.svelte |   2 +-
 .../src/stories/ChatSidebar.stories.svelte    |   2 +-
 .../stories/MarkdownContent.stories.svelte    |  51 +-
 8 files changed, 234 insertions(+), 351 deletions(-)

diff --git a/.github/workflows/server.yml b/.github/workflows/server.yml
index 1ea1300c2e4..ebcd6424bc0 100644
--- a/.github/workflows/server.yml
+++ b/.github/workflows/server.yml
@@ -209,7 +209,7 @@ jobs:
         working-directory: tools/server/webui
 
       - name: Run UI tests
-        run: npm run test:ui
+        run: npm run test:ui -- --testTimeout=60000
         working-directory: tools/server/webui
 
       - name: Run E2E tests
diff --git a/tools/server/webui/.storybook/preview.ts b/tools/server/webui/.storybook/preview.ts
index fb91386af46..8d530e43e37 100644
--- a/tools/server/webui/.storybook/preview.ts
+++ b/tools/server/webui/.storybook/preview.ts
@@ -11,8 +11,16 @@ const preview: Preview = {
 				date: /Date$/i
 			}
 		},
+
 		backgrounds: {
 			disable: true
+		},
+
+		a11y: {
+			// 'todo' - show a11y violations in the test UI only
+			// 'error' - fail CI on a11y violations
+			// 'off' - skip a11y checks entirely
+			test: 'todo'
 		}
 	},
 	decorators: [
diff --git a/tools/server/webui/.storybook/vitest.setup.ts b/tools/server/webui/.storybook/vitest.setup.ts
index e0c1753c849..14715728989 100644
--- a/tools/server/webui/.storybook/vitest.setup.ts
+++ b/tools/server/webui/.storybook/vitest.setup.ts
@@ -1,8 +1,9 @@
+import * as a11yAddonAnnotations from '@storybook/addon-a11y/preview';
 import { setProjectAnnotations } from '@storybook/sveltekit';
 import * as previewAnnotations from './preview';
 import { beforeAll } from 'vitest';
 
-const project = setProjectAnnotations([previewAnnotations]);
+const project = setProjectAnnotations([a11yAddonAnnotations, previewAnnotations]);
 
 beforeAll(async () => {
 	if (project.beforeAll) {
diff --git a/tools/server/webui/package-lock.json b/tools/server/webui/package-lock.json
index 8fab38f6f14..a11b87ad509 100644
--- a/tools/server/webui/package-lock.json
+++ b/tools/server/webui/package-lock.json
@@ -22,20 +22,20 @@
 				"unist-util-visit": "^5.0.0"
 			},
 			"devDependencies": {
-				"@chromatic-com/storybook": "^4.0.1",
+				"@chromatic-com/storybook": "^4.1.2",
 				"@eslint/compat": "^1.2.5",
 				"@eslint/js": "^9.18.0",
 				"@internationalized/date": "^3.8.2",
 				"@lucide/svelte": "^0.515.0",
 				"@playwright/test": "^1.49.1",
-				"@storybook/addon-a11y": "^9.0.17",
-				"@storybook/addon-docs": "^9.0.17",
-				"@storybook/addon-svelte-csf": "^5.0.7",
-				"@storybook/addon-vitest": "^9.0.17",
-				"@storybook/sveltekit": "^9.0.17",
-				"@sveltejs/adapter-static": "^3.0.8",
-				"@sveltejs/kit": "^2.22.0",
-				"@sveltejs/vite-plugin-svelte": "^6.0.0",
+				"@storybook/addon-a11y": "^10.0.7",
+				"@storybook/addon-docs": "^10.0.7",
+				"@storybook/addon-svelte-csf": "^5.0.10",
+				"@storybook/addon-vitest": "^10.0.7",
+				"@storybook/sveltekit": "^10.0.7",
+				"@sveltejs/adapter-static": "^3.0.10",
+				"@sveltejs/kit": "^2.48.4",
+				"@sveltejs/vite-plugin-svelte": "^6.2.1",
 				"@tailwindcss/forms": "^0.5.9",
 				"@tailwindcss/typography": "^0.5.15",
 				"@tailwindcss/vite": "^4.0.0",
@@ -46,21 +46,21 @@
 				"dexie": "^4.0.11",
 				"eslint": "^9.18.0",
 				"eslint-config-prettier": "^10.0.1",
-				"eslint-plugin-storybook": "^9.0.17",
+				"eslint-plugin-storybook": "^10.0.7",
 				"eslint-plugin-svelte": "^3.0.0",
 				"fflate": "^0.8.2",
 				"globals": "^16.0.0",
 				"http-server": "^14.1.1",
 				"mdast": "^3.0.0",
 				"mdsvex": "^0.12.3",
-				"playwright": "^1.53.0",
+				"playwright": "^1.56.1",
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+			"version": "0.7.45",
+			"resolved": "https://registry.npmjs.org/svelte2tsx/-/svelte2tsx-0.7.45.tgz",
+			"integrity": "sha512-cSci+mYGygYBHIZLHlm/jYlEc1acjAHqaQaDFHdEBpUueM9kSTnPpvPtSl5VkJOU1qSJ7h1K+6F/LIUYiqC8VA==",
 			"dev": true,
 			"license": "MIT",
 			"dependencies": {
 				"dedent-js": "^1.0.1",
-				"pascal-case": "^3.1.1"
+				"scule": "^1.3.0"
 			},
 			"peerDependencies": {
 				"svelte": "^3.55 || ^4.0.0-next.0 || ^4.0 || ^5.0.0-next.0",
@@ -8535,14 +8408,14 @@
 			"license": "MIT"
 		},
 		"node_modules/tinyglobby": {
-			"version": "0.2.14",
-			"resolved": "https://registry.npmjs.org/tinyglobby/-/tinyglobby-0.2.14.tgz",
-			"integrity": "sha512-tX5e7OM1HnYr2+a2C/4V0htOcSQcoSTH9KgJnVvNm5zm/cyEWKJ7j7YutsH9CxMdtOkkLFy2AHrMci9IM8IPZQ==",
+			"version": "0.2.15",
+			"resolved": "https://registry.npmjs.org/tinyglobby/-/tinyglobby-0.2.15.tgz",
+			"integrity": "sha512-j2Zq4NyQYG5XMST4cbs02Ak8iJUdxRM0XI5QyxXuZOzKOINmWurp3smXu3y5wDcJrptwpSjgXHzIQxR0omXljQ==",
 			"dev": true,
 			"license": "MIT",
 			"dependencies": {
-				"fdir": "^6.4.4",
-				"picomatch": "^4.0.2"
+				"fdir": "^6.5.0",
+				"picomatch": "^4.0.3"
 			},
 			"engines": {
 				"node": ">=12.0.0"
@@ -8918,17 +8791,19 @@
 			}
 		},
 		"node_modules/unplugin": {
-			"version": "1.16.1",
-			"resolved": "https://registry.npmjs.org/unplugin/-/unplugin-1.16.1.tgz",
-			"integrity": "sha512-4/u/j4FrCKdi17jaxuJA0jClGxB1AvU2hw/IuayPc4ay1XGaJs/rbb4v5WKwAjNifjmXK9PIFyuPiaK8azyR9w==",
+			"version": "2.3.10",
+			"resolved": "https://registry.npmjs.org/unplugin/-/unplugin-2.3.10.tgz",
+			"integrity": "sha512-6NCPkv1ClwH+/BGE9QeoTIl09nuiAt0gS28nn1PvYXsGKRwM2TCbFA2QiilmehPDTXIe684k4rZI1yl3A1PCUw==",
 			"dev": true,
 			"license": "MIT",
 			"dependencies": {
-				"acorn": "^8.14.0",
+				"@jridgewell/remapping": "^2.3.5",
+				"acorn": "^8.15.0",
+				"picomatch": "^4.0.3",
 				"webpack-virtual-modules": "^0.6.2"
 			},
 			"engines": {
-				"node": ">=14.0.0"
+				"node": ">=18.12.0"
 			}
 		},
 		"node_modules/uri-js": {
@@ -9054,18 +8929,18 @@
 			}
 		},
 		"node_modules/vite": {
-			"version": "7.0.5",
-			"resolved": "https://registry.npmjs.org/vite/-/vite-7.0.5.tgz",
-			"integrity": "sha512-1mncVwJxy2C9ThLwz0+2GKZyEXuC3MyWtAAlNftlZZXZDP3AJt5FmwcMit/IGGaNZ8ZOB2BNO/HFUB+CpN0NQw==",
+			"version": "7.2.2",
+			"resolved": "https://registry.npmjs.org/vite/-/vite-7.2.2.tgz",
+			"integrity": "sha512-BxAKBWmIbrDgrokdGZH1IgkIk/5mMHDreLDmCJ0qpyJaAteP8NvMhkwr/ZCQNqNH97bw/dANTE9PDzqwJghfMQ==",
 			"dev": true,
 			"license": "MIT",
 			"dependencies": {
 				"esbuild": "^0.25.0",
-				"fdir": "^6.4.6",
-				"picomatch": "^4.0.2",
+				"fdir": "^6.5.0",
+				"picomatch": "^4.0.3",
 				"postcss": "^8.5.6",
-				"rollup": "^4.40.0",
-				"tinyglobby": "^0.2.14"
+				"rollup": "^4.43.0",
+				"tinyglobby": "^0.2.15"
 			},
 			"bin": {
 				"vite": "bin/vite.js"
diff --git a/tools/server/webui/package.json b/tools/server/webui/package.json
index 92c7457bd31..8b88f691a43 100644
--- a/tools/server/webui/package.json
+++ b/tools/server/webui/package.json
@@ -24,20 +24,20 @@
 		"cleanup": "rm -rf .svelte-kit build node_modules test-results"
 	},
 	"devDependencies": {
-		"@chromatic-com/storybook": "^4.0.1",
+		"@chromatic-com/storybook": "^4.1.2",
 		"@eslint/compat": "^1.2.5",
 		"@eslint/js": "^9.18.0",
 		"@internationalized/date": "^3.8.2",
 		"@lucide/svelte": "^0.515.0",
 		"@playwright/test": "^1.49.1",
-		"@storybook/addon-a11y": "^9.0.17",
-		"@storybook/addon-docs": "^9.0.17",
-		"@storybook/addon-svelte-csf": "^5.0.7",
-		"@storybook/addon-vitest": "^9.0.17",
-		"@storybook/sveltekit": "^9.0.17",
-		"@sveltejs/adapter-static": "^3.0.8",
-		"@sveltejs/kit": "^2.22.0",
-		"@sveltejs/vite-plugin-svelte": "^6.0.0",
+		"@storybook/addon-a11y": "^10.0.7",
+		"@storybook/addon-docs": "^10.0.7",
+		"@storybook/addon-svelte-csf": "^5.0.10",
+		"@storybook/addon-vitest": "^10.0.7",
+		"@storybook/sveltekit": "^10.0.7",
+		"@sveltejs/adapter-static": "^3.0.10",
+		"@sveltejs/kit": "^2.48.4",
+		"@sveltejs/vite-plugin-svelte": "^6.2.1",
 		"@tailwindcss/forms": "^0.5.9",
 		"@tailwindcss/typography": "^0.5.15",
 		"@tailwindcss/vite": "^4.0.0",
@@ -48,21 +48,21 @@
 		"dexie": "^4.0.11",
 		"eslint": "^9.18.0",
 		"eslint-config-prettier": "^10.0.1",
-		"eslint-plugin-storybook": "^9.0.17",
+		"eslint-plugin-storybook": "^10.0.7",
 		"eslint-plugin-svelte": "^3.0.0",
 		"fflate": "^0.8.2",
 		"globals": "^16.0.0",
 		"http-server": "^14.1.1",
 		"mdast": "^3.0.0",
 		"mdsvex": "^0.12.3",
-		"playwright": "^1.53.0",
+		"playwright": "^1.56.1",
 		"prettier": "^3.4.2",
 		"prettier-plugin-svelte": "^3.3.3",
 		"prettier-plugin-tailwindcss": "^0.6.11",
 		"rehype-katex": "^7.0.1",
 		"remark-math": "^6.0.0",
 		"sass": "^1.93.3",
-		"storybook": "^9.0.17",
+		"storybook": "^10.0.7",
 		"svelte": "^5.0.0",
 		"svelte-check": "^4.0.0",
 		"tailwind-merge": "^3.3.1",
@@ -73,7 +73,7 @@
 		"typescript-eslint": "^8.20.0",
 		"unified": "^11.0.5",
 		"uuid": "^13.0.0",
-		"vite": "^7.0.4",
+		"vite": "^7.2.2",
 		"vite-plugin-devtools-json": "^0.2.0",
 		"vitest": "^3.2.3",
 		"vitest-browser-svelte": "^0.1.0"
diff --git a/tools/server/webui/src/stories/ChatForm.stories.svelte b/tools/server/webui/src/stories/ChatForm.stories.svelte
index 6a0fc087019..82848e4fbf1 100644
--- a/tools/server/webui/src/stories/ChatForm.stories.svelte
+++ b/tools/server/webui/src/stories/ChatForm.stories.svelte
@@ -1,7 +1,7 @@
 <script module lang="ts">
 	import { defineMeta } from '@storybook/addon-svelte-csf';
 	import ChatForm from '$lib/components/app/chat/ChatForm/ChatForm.svelte';
-	import { expect } from 'storybook/internal/test';
+	import { expect } from 'storybook/test';
 	import { mockServerProps, mockConfigs } from './fixtures/storybook-mocks';
 	import jpgAsset from './fixtures/assets/1.jpg?url';
 	import svgAsset from './fixtures/assets/hf-logo.svg?url';
diff --git a/tools/server/webui/src/stories/ChatSidebar.stories.svelte b/tools/server/webui/src/stories/ChatSidebar.stories.svelte
index 1b1754f9d37..b74b246b1d1 100644
--- a/tools/server/webui/src/stories/ChatSidebar.stories.svelte
+++ b/tools/server/webui/src/stories/ChatSidebar.stories.svelte
@@ -1,7 +1,7 @@
 <script module lang="ts">
 	import { defineMeta } from '@storybook/addon-svelte-csf';
 	import ChatSidebar from '$lib/components/app/chat/ChatSidebar/ChatSidebar.svelte';
-	import { waitFor } from 'storybook/internal/test';
+	import { waitFor } from 'storybook/test';
 	import { screen } from 'storybook/test';
 
 	const { Story } = defineMeta({
diff --git a/tools/server/webui/src/stories/MarkdownContent.stories.svelte b/tools/server/webui/src/stories/MarkdownContent.stories.svelte
index c8294ba0d98..90aa90bb046 100644
--- a/tools/server/webui/src/stories/MarkdownContent.stories.svelte
+++ b/tools/server/webui/src/stories/MarkdownContent.stories.svelte
@@ -1,5 +1,6 @@
 <script module lang="ts">
 	import { defineMeta } from '@storybook/addon-svelte-csf';
+	import { expect } from 'storybook/test';
 	import { MarkdownContent } from '$lib/components/app';
 	import { AI_TUTORIAL_MD } from './fixtures/ai-tutorial.js';
 	import { API_DOCS_MD } from './fixtures/api-docs.js';
@@ -68,64 +69,62 @@ All links should have \`target="_blank"\` and \`rel="noopener noreferrer"\` attr
 		class: 'max-w-[56rem] w-[calc(100vw-2rem)]'
 	}}
 	play={async ({ canvasElement }) => {
-		const { expect } = await import('storybook/internal/test');
-		
 		// Wait for component to render
-		await new Promise(resolve => setTimeout(resolve, 100));
-		
+		await new Promise((resolve) => setTimeout(resolve, 100));
+
 		// Find all links in the rendered content
 		const links = canvasElement.querySelectorAll('a[href]');
-		
+
 		// Test that we have the expected number of links
 		expect(links.length).toBeGreaterThan(0);
-		
+
 		// Test each link for proper attributes
 		links.forEach((link) => {
 			const href = link.getAttribute('href');
-			
+
 			// Test that external links have proper security attributes
 			if (href && (href.startsWith('http://') || href.startsWith('https://'))) {
 				expect(link.getAttribute('target')).toBe('_blank');
 				expect(link.getAttribute('rel')).toBe('noopener noreferrer');
 			}
 		});
-		
+
 		// Test specific links exist
-		const hugginFaceLink = Array.from(links).find(link => 
-			link.getAttribute('href') === 'https://huggingface.co'
+		const hugginFaceLink = Array.from(links).find(
+			(link) => link.getAttribute('href') === 'https://huggingface.co'
 		);
 		expect(hugginFaceLink).toBeTruthy();
 		expect(hugginFaceLink?.textContent).toBe('Hugging Face Homepage');
-		
-		const githubLink = Array.from(links).find(link => 
-			link.getAttribute('href') === 'https://github.com/ggml-org/llama.cpp'
+
+		const githubLink = Array.from(links).find(
+			(link) => link.getAttribute('href') === 'https://github.com/ggml-org/llama.cpp'
 		);
 		expect(githubLink).toBeTruthy();
 		expect(githubLink?.textContent).toBe('GitHub Repository');
-		
-		const openaiLink = Array.from(links).find(link => 
-			link.getAttribute('href') === 'https://openai.com'
+
+		const openaiLink = Array.from(links).find(
+			(link) => link.getAttribute('href') === 'https://openai.com'
 		);
 		expect(openaiLink).toBeTruthy();
 		expect(openaiLink?.textContent).toBe('OpenAI Website');
-		
-		const googleLink = Array.from(links).find(link => 
-			link.getAttribute('href') === 'https://www.google.com'
+
+		const googleLink = Array.from(links).find(
+			(link) => link.getAttribute('href') === 'https://www.google.com'
 		);
 		expect(googleLink).toBeTruthy();
 		expect(googleLink?.textContent).toBe('Google Search');
-		
+
 		// Test inline links (auto-linked URLs)
-		const exampleLink = Array.from(links).find(link => 
-			link.getAttribute('href') === 'https://example.com'
+		const exampleLink = Array.from(links).find(
+			(link) => link.getAttribute('href') === 'https://example.com'
 		);
 		expect(exampleLink).toBeTruthy();
-		
-		const pythonDocsLink = Array.from(links).find(link => 
-			link.getAttribute('href') === 'https://docs.python.org'
+
+		const pythonDocsLink = Array.from(links).find(
+			(link) => link.getAttribute('href') === 'https://docs.python.org'
 		);
 		expect(pythonDocsLink).toBeTruthy();
-		
+
 		console.log(`✅ URL Links test passed - Found ${links.length} links with proper attributes`);
 	}}
 />

From 374fe09cdd4a9d7ebaec6fde87ac2b9b75f019c4 Mon Sep 17 00:00:00 2001
From: Georgi Gerganov <ggerganov@gmail.com>
Date: Wed, 12 Nov 2025 20:43:38 +0200
Subject: [PATCH 173/185] ggml : use std::sort in ggml_argsort CPU
 implementation (#17211)

* ggml : use std::sort in ggml_argsort CPU implementation

* cont : add missing header
---
 ggml/src/ggml-cpu/ops.cpp | 25 +++++++++++++------------
 1 file changed, 13 insertions(+), 12 deletions(-)

diff --git a/ggml/src/ggml-cpu/ops.cpp b/ggml/src/ggml-cpu/ops.cpp
index 5a272b9abc5..9f1e5f8d646 100644
--- a/ggml/src/ggml-cpu/ops.cpp
+++ b/ggml/src/ggml-cpu/ops.cpp
@@ -7,8 +7,9 @@
 #include "unary-ops.h"
 #include "vec.h"
 
-#include <float.h>
+#include <cfloat>
 #include <algorithm>
+#include <functional>
 
 // ggml_compute_forward_dup
 
@@ -7682,24 +7683,24 @@ static void ggml_compute_forward_argsort_f32(
     ggml_sort_order order = (ggml_sort_order) ggml_get_op_params_i32(dst, 0);
 
     for (int64_t i = ith; i < nr; i += nth) {
-        int32_t * dst_data = (int32_t *)((char *) dst->data + i*nb1);
         const float * src_data = (float *)((char *) src0->data + i*nb01);
 
+        int32_t * dst_data = (int32_t *)((char *) dst->data + i*nb1);
+
         for (int64_t j = 0; j < ne0; j++) {
             dst_data[j] = j;
         }
 
-        // C doesn't have a functional sort, so we do a bubble sort instead
-        for (int64_t j = 0; j < ne0; j++) {
-            for (int64_t k = j + 1; k < ne0; k++) {
-                if ((order == GGML_SORT_ORDER_ASC  && src_data[dst_data[j]] > src_data[dst_data[k]]) ||
-                    (order == GGML_SORT_ORDER_DESC && src_data[dst_data[j]] < src_data[dst_data[k]])) {
-                    int32_t tmp = dst_data[j];
-                    dst_data[j] = dst_data[k];
-                    dst_data[k] = tmp;
-                }
-            }
+        std::function<bool(int32_t, int32_t)> cmp;
+
+        // note: this might be causing memory allocations? ideally should be avoided if it's the case
+        switch (order) {
+            case GGML_SORT_ORDER_ASC:  cmp = [src_data](int32_t a, int32_t b) { return src_data[a] < src_data[b]; }; break;
+            case GGML_SORT_ORDER_DESC: cmp = [src_data](int32_t a, int32_t b) { return src_data[a] > src_data[b]; }; break;
+            default: GGML_ABORT("invalid sort order");
         }
+
+        std::sort(dst_data, dst_data + ne0, cmp);
     }
 }
 

From 92bb442ad999a0d52df0af2730cd861012e8ac5c Mon Sep 17 00:00:00 2001
From: Mike Abbott <michael.abbott@lvt.com>
Date: Wed, 12 Nov 2025 12:33:55 -0700
Subject: [PATCH 174/185] docker : preserve .so symlinks for docker container
 builds (#17214)

---
 .devops/cann.Dockerfile   | 2 +-
 .devops/cpu.Dockerfile    | 2 +-
 .devops/cuda.Dockerfile   | 2 +-
 .devops/intel.Dockerfile  | 2 +-
 .devops/musa.Dockerfile   | 2 +-
 .devops/rocm.Dockerfile   | 2 +-
 .devops/vulkan.Dockerfile | 2 +-
 7 files changed, 7 insertions(+), 7 deletions(-)

diff --git a/.devops/cann.Dockerfile b/.devops/cann.Dockerfile
index 02f3e03b5e2..9d9fabf887f 100644
--- a/.devops/cann.Dockerfile
+++ b/.devops/cann.Dockerfile
@@ -49,7 +49,7 @@ RUN source /usr/local/Ascend/ascend-toolkit/set_env.sh --force \
 # -- Organize build artifacts for copying in later stages --
 # Create a lib directory to store all .so files
 RUN mkdir -p /app/lib && \
-    find build -name "*.so" -exec cp {} /app/lib \;
+    find build -name "*.so*" -exec cp -P {} /app/lib \;
 
 # Create a full directory to store all executables and Python scripts
 RUN mkdir -p /app/full && \
diff --git a/.devops/cpu.Dockerfile b/.devops/cpu.Dockerfile
index e1bb7d4675d..6e16ecda44f 100644
--- a/.devops/cpu.Dockerfile
+++ b/.devops/cpu.Dockerfile
@@ -20,7 +20,7 @@ RUN if [ "$TARGETARCH" = "amd64" ] || [ "$TARGETARCH" = "arm64" ]; then \
     cmake --build build -j $(nproc)
 
 RUN mkdir -p /app/lib && \
-    find build -name "*.so" -exec cp {} /app/lib \;
+    find build -name "*.so*" -exec cp -P {} /app/lib \;
 
 RUN mkdir -p /app/full \
     && cp build/bin/* /app/full \
diff --git a/.devops/cuda.Dockerfile b/.devops/cuda.Dockerfile
index 4b708ae278d..54f793d0a3f 100644
--- a/.devops/cuda.Dockerfile
+++ b/.devops/cuda.Dockerfile
@@ -25,7 +25,7 @@ RUN if [ "${CUDA_DOCKER_ARCH}" != "default" ]; then \
     cmake --build build --config Release -j$(nproc)
 
 RUN mkdir -p /app/lib && \
-    find build -name "*.so" -exec cp {} /app/lib \;
+    find build -name "*.so*" -exec cp -P {} /app/lib \;
 
 RUN mkdir -p /app/full \
     && cp build/bin/* /app/full \
diff --git a/.devops/intel.Dockerfile b/.devops/intel.Dockerfile
index cd2f9aa79bd..d1a8fbed4cf 100644
--- a/.devops/intel.Dockerfile
+++ b/.devops/intel.Dockerfile
@@ -21,7 +21,7 @@ RUN if [ "${GGML_SYCL_F16}" = "ON" ]; then \
     cmake --build build --config Release -j$(nproc)
 
 RUN mkdir -p /app/lib && \
-    find build -name "*.so" -exec cp {} /app/lib \;
+    find build -name "*.so*" -exec cp -P {} /app/lib \;
 
 RUN mkdir -p /app/full \
     && cp build/bin/* /app/full \
diff --git a/.devops/musa.Dockerfile b/.devops/musa.Dockerfile
index ec44b229143..faa3500e619 100644
--- a/.devops/musa.Dockerfile
+++ b/.devops/musa.Dockerfile
@@ -32,7 +32,7 @@ RUN if [ "${MUSA_DOCKER_ARCH}" != "default" ]; then \
     cmake --build build --config Release -j$(nproc)
 
 RUN mkdir -p /app/lib && \
-    find build -name "*.so" -exec cp {} /app/lib \;
+    find build -name "*.so*" -exec cp -P {} /app/lib \;
 
 RUN mkdir -p /app/full \
     && cp build/bin/* /app/full \
diff --git a/.devops/rocm.Dockerfile b/.devops/rocm.Dockerfile
index df9058d946a..d6bf28b1058 100644
--- a/.devops/rocm.Dockerfile
+++ b/.devops/rocm.Dockerfile
@@ -45,7 +45,7 @@ RUN HIPCXX="$(hipconfig -l)/clang" HIP_PATH="$(hipconfig -R)" \
     && cmake --build build --config Release -j$(nproc)
 
 RUN mkdir -p /app/lib \
-    && find build -name "*.so" -exec cp {} /app/lib \;
+    && find build -name "*.so*" -exec cp -P {} /app/lib \;
 
 RUN mkdir -p /app/full \
     && cp build/bin/* /app/full \
diff --git a/.devops/vulkan.Dockerfile b/.devops/vulkan.Dockerfile
index 75924684037..b6b802a7c6e 100644
--- a/.devops/vulkan.Dockerfile
+++ b/.devops/vulkan.Dockerfile
@@ -20,7 +20,7 @@ RUN cmake -B build -DGGML_NATIVE=OFF -DGGML_VULKAN=ON -DLLAMA_BUILD_TESTS=OFF -D
     cmake --build build --config Release -j$(nproc)
 
 RUN mkdir -p /app/lib && \
-    find build -name "*.so" -exec cp {} /app/lib \;
+    find build -name "*.so*" -exec cp -P {} /app/lib \;
 
 RUN mkdir -p /app/full \
     && cp build/bin/* /app/full \

From 5d6838b74f151443ef126a6efda46e93f3b721e3 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Johannes=20G=C3=A4=C3=9Fler?= <johannesg@5d6.de>
Date: Wed, 12 Nov 2025 23:13:55 +0100
Subject: [PATCH 175/185] CUDA: static assert to prevent misuse of memcpy_1
 (#17198)

---
 ggml/src/ggml-cuda/common.cuh | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/ggml/src/ggml-cuda/common.cuh b/ggml/src/ggml-cuda/common.cuh
index ca876459d40..25e9308d756 100644
--- a/ggml/src/ggml-cuda/common.cuh
+++ b/ggml/src/ggml-cuda/common.cuh
@@ -586,6 +586,12 @@ static __device__ __forceinline__ void ggml_cuda_mad(half2 & acc, const half2 v,
 //     If dst and src point at different address spaces then they are guaranteed to not be aliased.
 template <int nbytes, int alignment = 0>
 static __device__ __forceinline__ void ggml_cuda_memcpy_1(void * __restrict__ dst, const void * __restrict__ src) {
+    static_assert(
+        nbytes <= ggml_cuda_get_max_cpy_bytes() || alignment == 0,
+        "You are misusing the alignment parameter for ggml_cuda_memcpy_1. "
+        "The intent is for the parameter is only as a workaround if either one of the pointers is not properly aligned. "
+        "If you use it to do more bytes per copy than ggml_cuda_max_cpy_bytes() the reads and writes may not be coalesced. "
+        "Call ggml_cuda_memcpy_1 in a loop instead.");
     if constexpr (alignment != 0) {
         static_assert(nbytes % alignment == 0, "bad alignment");
     }

From ffb6f3d921bbc64d559164e23671a710a4dd9de5 Mon Sep 17 00:00:00 2001
From: o7si <32285332+o7si@users.noreply.github.com>
Date: Thu, 13 Nov 2025 06:41:02 +0800
Subject: [PATCH 176/185] vocab : correct bounds check for UGM XCDA array
 access (#17215)

---
 src/llama-vocab.cpp | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/llama-vocab.cpp b/src/llama-vocab.cpp
index 735c5d547f9..97f374eac95 100644
--- a/src/llama-vocab.cpp
+++ b/src/llama-vocab.cpp
@@ -1013,7 +1013,7 @@ struct llm_tokenizer_ugm_session {
         }
     private:
         uint32_t get_node(size_t index) {
-            if (index > xcda_array_size) {
+            if (index >= xcda_array_size) {
                 throw std::runtime_error("Index out of array bounds in XCDA array!");
             }
             return xcda_array[index];

From 07751f8d446e2d05d069e8d77d984dd64c1a5878 Mon Sep 17 00:00:00 2001
From: Neo Zhang Jianyu <jianyu.zhang@intel.com>
Date: Thu, 13 Nov 2025 08:42:23 +0800
Subject: [PATCH 177/185] update SYCL support OPs (#17208)

Co-authored-by: Zhang Jianyu <zhang.jianyu@outlook.com>
---
 docs/ops.md       |   22 +-
 docs/ops/SYCL.csv | 4693 +++++++++++++++++++++++----------------------
 2 files changed, 2415 insertions(+), 2300 deletions(-)

diff --git a/docs/ops.md b/docs/ops.md
index 775b938bd12..0c4f7ef5c81 100644
--- a/docs/ops.md
+++ b/docs/ops.md
@@ -19,10 +19,10 @@ Legend:
 |                              ADD | ❌ | ✅ | ✅ | ✅ | 🟡 | 🟡 | ✅ | ✅ | ❌ |
 |                             ADD1 | ❌ | ✅ | ✅ | ✅ | ❌ | ❌ | ✅ | ❌ | ❌ |
 |                           ADD_ID | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
-|                           ARANGE | ❌ | ✅ | ✅ | ✅ | ✅ | ❌ | ❌ | ❌ | ❌ |
+|                           ARANGE | ❌ | ✅ | ✅ | ✅ | ✅ | ❌ | ✅ | ❌ | ❌ |
 |                           ARGMAX | ❌ | ✅ | ✅ | ✅ | ✅ | ❌ | ✅ | ✅ | ❌ |
 |                          ARGSORT | ❌ | ✅ | ✅ | ✅ | ✅ | ✅ | ✅ | ✅ | ❌ |
-|                             CEIL | ❌ | ❌ | ✅ | 🟡 | ❌ | ❌ | ✅ | ❌ | ❌ |
+|                             CEIL | ❌ | ❌ | ✅ | 🟡 | ❌ | ❌ | 🟡 | ❌ | ❌ |
 |                            CLAMP | ❌ | ✅ | ✅ | ✅ | 🟡 | 🟡 | ✅ | 🟡 | ❌ |
 |                           CONCAT | ❌ | ✅ | ✅ | 🟡 | ✅ | 🟡 | ✅ | ✅ | ❌ |
 |                             CONT | ❌ | 🟡 | ✅ | ✅ | ✅ | 🟡 | 🟡 | 🟡 | ❌ |
@@ -42,7 +42,7 @@ Legend:
 |                              ELU | ❌ | ✅ | ✅ | 🟡 | 🟡 | ❌ | 🟡 | ❌ | ❌ |
 |                              EXP | ❌ | ✅ | ✅ | 🟡 | 🟡 | ❌ | 🟡 | ❌ | ❌ |
 |                   FLASH_ATTN_EXT | ❌ | 🟡 | ✅ | 🟡 | 🟡 | ❌ | ❌ | 🟡 | ❌ |
-|                            FLOOR | ❌ | ❌ | ✅ | 🟡 | ❌ | ❌ | ✅ | ❌ | ❌ |
+|                            FLOOR | ❌ | ❌ | ✅ | 🟡 | ❌ | ❌ | 🟡 | ❌ | ❌ |
 |                GATED_LINEAR_ATTN | ❌ | ❌ | ✅ | ✅ | ❌ | ❌ | ✅ | ❌ | ❌ |
 |                            GEGLU | ❌ | ✅ | ✅ | ✅ | 🟡 | ✅ | ✅ | 🟡 | ❌ |
 |                        GEGLU_ERF | ❌ | ✅ | ✅ | ✅ | 🟡 | ✅ | ✅ | 🟡 | ❌ |
@@ -61,7 +61,7 @@ Legend:
 |                          L2_NORM | ❌ | ❌ | ✅ | ✅ | ✅ | ❌ | ✅ | ✅ | ❌ |
 |                       LEAKY_RELU | ❌ | ✅ | ✅ | ✅ | ✅ | ❌ | ✅ | ✅ | ❌ |
 |                              LOG | ❌ | ✅ | ✅ | ✅ | ❌ | ❌ | ✅ | ❌ | ❌ |
-|                             MEAN | ❌ | ✅ | ✅ | ✅ | ✅ | ❌ | ❌ | ❌ | ❌ |
+|                             MEAN | ❌ | ✅ | ✅ | ✅ | ✅ | ❌ | ✅ | ❌ | ❌ |
 |                              MUL | ❌ | ✅ | ✅ | ✅ | 🟡 | 🟡 | ✅ | ✅ | ❌ |
 |                          MUL_MAT | 🟡 | 🟡 | 🟡 | 🟡 | 🟡 | 🟡 | 🟡 | 🟡 | 🟡 |
 |                       MUL_MAT_ID | ❌ | 🟡 | ✅ | ✅ | ✅ | 🟡 | 🟡 | ✅ | ❌ |
@@ -77,18 +77,18 @@ Legend:
 |                            REGLU | ❌ | ✅ | ✅ | ✅ | 🟡 | ✅ | ✅ | 🟡 | ❌ |
 |                             RELU | ❌ | ✅ | ✅ | 🟡 | 🟡 | 🟡 | 🟡 | 🟡 | ❌ |
 |                           REPEAT | ❌ | ✅ | ✅ | 🟡 | ✅ | 🟡 | ✅ | 🟡 | ❌ |
-|                      REPEAT_BACK | ❌ | ❌ | ✅ | ✅ | ❌ | ❌ | ❌ | ✅ | ❌ |
+|                      REPEAT_BACK | ❌ | ❌ | ✅ | ✅ | ❌ | ❌ | ✅ | ✅ | ❌ |
 |                         RMS_NORM | ❌ | ✅ | ✅ | ✅ | 🟡 | ✅ | ✅ | ✅ | ❌ |
 |                    RMS_NORM_BACK | ❌ | ❌ | ✅ | ✅ | ❌ | ❌ | ✅ | ✅ | ❌ |
 |                 RMS_NORM_MUL_ADD | ❌ | ✅ | ✅ | ✅ | ✅ | ✅ | ✅ | ✅ | ❌ |
-|                             ROLL | ❌ | ❌ | ✅ | ❌ | ❌ | ❌ | ❌ | ✅ | ❌ |
+|                             ROLL | ❌ | ❌ | ✅ | ❌ | ❌ | ❌ | ✅ | ✅ | ❌ |
 |                             ROPE | ❌ | 🟡 | ✅ | ✅ | ✅ | ✅ | ✅ | ✅ | ❌ |
 |                        ROPE_BACK | ❌ | ❌ | ✅ | ✅ | ❌ | ❌ | ❌ | ✅ | ❌ |
-|                            ROUND | ❌ | ❌ | ✅ | 🟡 | ❌ | ❌ | ✅ | ❌ | ❌ |
+|                            ROUND | ❌ | ❌ | ✅ | 🟡 | ❌ | ❌ | 🟡 | ❌ | ❌ |
 |                        RWKV_WKV6 | ❌ | ❌ | ✅ | ✅ | ✅ | ❌ | ✅ | ✅ | ❌ |
 |                        RWKV_WKV7 | ❌ | ❌ | ✅ | ✅ | ✅ | ❌ | ✅ | ✅ | ❌ |
 |                            SCALE | ❌ | 🟡 | ✅ | ✅ | ✅ | ✅ | ✅ | ✅ | ❌ |
-|                              SET | ❌ | ❌ | ✅ | ❌ | ✅ | ❌ | ❌ | ❌ | ❌ |
+|                              SET | ❌ | ❌ | ✅ | ❌ | ✅ | ❌ | 🟡 | ❌ | ❌ |
 |                         SET_ROWS | ❌ | ❌ | 🟡 | 🟡 | 🟡 | 🟡 | 🟡 | 🟡 | ❌ |
 |                              SGN | ❌ | ✅ | ✅ | 🟡 | 🟡 | ❌ | 🟡 | ❌ | ❌ |
 |                          SIGMOID | ❌ | ✅ | ✅ | 🟡 | 🟡 | 🟡 | 🟡 | 🟡 | ❌ |
@@ -100,17 +100,17 @@ Legend:
 |                    SOFT_MAX_BACK | ❌ | ❌ | 🟡 | 🟡 | ❌ | ❌ | 🟡 | ✅ | ❌ |
 |                              SQR | ❌ | ✅ | ✅ | ✅ | 🟡 | ❌ | ✅ | 🟡 | ❌ |
 |                             SQRT | ❌ | ✅ | ✅ | ✅ | 🟡 | ❌ | ✅ | ❌ | ❌ |
-|                         SSM_CONV | ❌ | ❌ | ✅ | ✅ | ✅ | ❌ | ❌ | ✅ | ❌ |
+|                         SSM_CONV | ❌ | ❌ | ✅ | ✅ | ✅ | ❌ | ✅ | ✅ | ❌ |
 |                         SSM_SCAN | ❌ | ❌ | ✅ | ✅ | ✅ | ❌ | ❌ | ✅ | ❌ |
 |                             STEP | ❌ | ✅ | ✅ | 🟡 | 🟡 | ❌ | 🟡 | ❌ | ❌ |
 |                              SUB | ❌ | ✅ | ✅ | ✅ | 🟡 | 🟡 | ✅ | ✅ | ❌ |
-|                              SUM | ❌ | ✅ | ✅ | ✅ | ❌ | ❌ | ✅ | ✅ | ❌ |
+|                              SUM | ❌ | ✅ | ✅ | ✅ | ❌ | ❌ | 🟡 | ✅ | ❌ |
 |                         SUM_ROWS | ❌ | ✅ | ✅ | ✅ | ✅ | ✅ | 🟡 | ✅ | ❌ |
 |                           SWIGLU | ❌ | ✅ | ✅ | ✅ | 🟡 | ✅ | ✅ | 🟡 | ❌ |
 |                       SWIGLU_OAI | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
 |                             TANH | ❌ | ✅ | ✅ | 🟡 | 🟡 | ✅ | 🟡 | 🟡 | ❌ |
 |               TIMESTEP_EMBEDDING | ❌ | ✅ | ✅ | ✅ | ✅ | ✅ | ✅ | ✅ | ❌ |
 |                         TOPK_MOE | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ | ✅ | ❌ | ❌ |
-|                            TRUNC | ❌ | ❌ | ✅ | 🟡 | ❌ | ❌ | ✅ | ❌ | ❌ |
+|                            TRUNC | ❌ | ❌ | ✅ | 🟡 | ❌ | ❌ | 🟡 | ❌ | ❌ |
 |                          UPSCALE | ❌ | 🟡 | ✅ | ✅ | 🟡 | ✅ | 🟡 | ✅ | ❌ |
 |                            XIELU | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ | ❌ |
diff --git a/docs/ops/SYCL.csv b/docs/ops/SYCL.csv
index d7e71990a88..f52324b24b2 100644
--- a/docs/ops/SYCL.csv
+++ b/docs/ops/SYCL.csv
@@ -71,6 +71,14 @@
 "SYCL0","GELU_ERF","type=f16,ne_a=[5,7,11,13],v=1","support","0","no","SYCL"
 "SYCL0","XIELU","type=f16,ne_a=[128,2,2,2],v=1","support","0","no","SYCL"
 "SYCL0","XIELU","type=f16,ne_a=[5,7,11,13],v=1","support","0","no","SYCL"
+"SYCL0","FLOOR","type=f16,ne_a=[128,2,2,2],v=1","support","0","no","SYCL"
+"SYCL0","FLOOR","type=f16,ne_a=[5,7,11,13],v=1","support","0","no","SYCL"
+"SYCL0","CEIL","type=f16,ne_a=[128,2,2,2],v=1","support","0","no","SYCL"
+"SYCL0","CEIL","type=f16,ne_a=[5,7,11,13],v=1","support","0","no","SYCL"
+"SYCL0","ROUND","type=f16,ne_a=[128,2,2,2],v=1","support","0","no","SYCL"
+"SYCL0","ROUND","type=f16,ne_a=[5,7,11,13],v=1","support","0","no","SYCL"
+"SYCL0","TRUNC","type=f16,ne_a=[128,2,2,2],v=1","support","0","no","SYCL"
+"SYCL0","TRUNC","type=f16,ne_a=[5,7,11,13],v=1","support","0","no","SYCL"
 "SYCL0","ABS","type=f32,ne_a=[128,2,2,2],v=0","support","1","yes","SYCL"
 "SYCL0","ABS","type=f32,ne_a=[5,7,11,13],v=0","support","1","yes","SYCL"
 "SYCL0","SGN","type=f32,ne_a=[128,2,2,2],v=0","support","1","yes","SYCL"
@@ -143,6 +151,14 @@
 "SYCL0","GELU_ERF","type=f32,ne_a=[5,7,11,13],v=1","support","0","no","SYCL"
 "SYCL0","XIELU","type=f32,ne_a=[128,2,2,2],v=1","support","0","no","SYCL"
 "SYCL0","XIELU","type=f32,ne_a=[5,7,11,13],v=1","support","0","no","SYCL"
+"SYCL0","FLOOR","type=f32,ne_a=[128,2,2,2],v=1","support","0","no","SYCL"
+"SYCL0","FLOOR","type=f32,ne_a=[5,7,11,13],v=1","support","0","no","SYCL"
+"SYCL0","CEIL","type=f32,ne_a=[128,2,2,2],v=1","support","0","no","SYCL"
+"SYCL0","CEIL","type=f32,ne_a=[5,7,11,13],v=1","support","0","no","SYCL"
+"SYCL0","ROUND","type=f32,ne_a=[128,2,2,2],v=1","support","0","no","SYCL"
+"SYCL0","ROUND","type=f32,ne_a=[5,7,11,13],v=1","support","0","no","SYCL"
+"SYCL0","TRUNC","type=f32,ne_a=[128,2,2,2],v=1","support","0","no","SYCL"
+"SYCL0","TRUNC","type=f32,ne_a=[5,7,11,13],v=1","support","0","no","SYCL"
 "SYCL0","REGLU","type=f16,ne_a=[128,2,2,2],v=0,swapped=0","support","1","yes","SYCL"
 "SYCL0","REGLU","type=f16,ne_a=[5,7,11,13],v=0,swapped=0","support","1","yes","SYCL"
 "SYCL0","REGLU","type=f16,ne_a=[128,2,2,2],v=0,swapped=1","support","1","yes","SYCL"
@@ -4963,16 +4979,16 @@
 "SYCL0","REPEAT","type=f32,ne=[10,5,4,3],nr=[1,1,1,2]","support","1","yes","SYCL"
 "SYCL0","REPEAT","type=i32,ne=[10,5,4,3],nr=[2,1,1,1]","support","1","yes","SYCL"
 "SYCL0","REPEAT","type=i16,ne=[10,5,4,3],nr=[1,1,1,2]","support","1","yes","SYCL"
-"SYCL0","REPEAT_BACK","type=f32,ne=[8,6,4,2],nr=[1,1,1,1],v=0","support","0","no","SYCL"
-"SYCL0","REPEAT_BACK","type=f32,ne=[8,6,4,2],nr=[2,1,1,1],v=0","support","0","no","SYCL"
-"SYCL0","REPEAT_BACK","type=f32,ne=[8,6,4,2],nr=[1,2,1,1],v=0","support","0","no","SYCL"
-"SYCL0","REPEAT_BACK","type=f32,ne=[8,6,4,2],nr=[1,1,2,1],v=0","support","0","no","SYCL"
-"SYCL0","REPEAT_BACK","type=f32,ne=[8,6,4,2],nr=[1,1,1,2],v=0","support","0","no","SYCL"
-"SYCL0","REPEAT_BACK","type=f32,ne=[8,6,4,2],nr=[1,1,1,1],v=1","support","0","no","SYCL"
-"SYCL0","REPEAT_BACK","type=f32,ne=[8,6,4,2],nr=[2,1,1,1],v=1","support","0","no","SYCL"
-"SYCL0","REPEAT_BACK","type=f32,ne=[8,6,4,2],nr=[1,2,1,1],v=1","support","0","no","SYCL"
-"SYCL0","REPEAT_BACK","type=f32,ne=[8,6,4,2],nr=[1,1,2,1],v=1","support","0","no","SYCL"
-"SYCL0","REPEAT_BACK","type=f32,ne=[8,6,4,2],nr=[1,1,1,2],v=1","support","0","no","SYCL"
+"SYCL0","REPEAT_BACK","type=f32,ne=[8,6,4,2],nr=[1,1,1,1],v=0","support","1","yes","SYCL"
+"SYCL0","REPEAT_BACK","type=f32,ne=[8,6,4,2],nr=[2,1,1,1],v=0","support","1","yes","SYCL"
+"SYCL0","REPEAT_BACK","type=f32,ne=[8,6,4,2],nr=[1,2,1,1],v=0","support","1","yes","SYCL"
+"SYCL0","REPEAT_BACK","type=f32,ne=[8,6,4,2],nr=[1,1,2,1],v=0","support","1","yes","SYCL"
+"SYCL0","REPEAT_BACK","type=f32,ne=[8,6,4,2],nr=[1,1,1,2],v=0","support","1","yes","SYCL"
+"SYCL0","REPEAT_BACK","type=f32,ne=[8,6,4,2],nr=[1,1,1,1],v=1","support","1","yes","SYCL"
+"SYCL0","REPEAT_BACK","type=f32,ne=[8,6,4,2],nr=[2,1,1,1],v=1","support","1","yes","SYCL"
+"SYCL0","REPEAT_BACK","type=f32,ne=[8,6,4,2],nr=[1,2,1,1],v=1","support","1","yes","SYCL"
+"SYCL0","REPEAT_BACK","type=f32,ne=[8,6,4,2],nr=[1,1,2,1],v=1","support","1","yes","SYCL"
+"SYCL0","REPEAT_BACK","type=f32,ne=[8,6,4,2],nr=[1,1,1,2],v=1","support","1","yes","SYCL"
 "SYCL0","DUP","type=f32,ne=[10,10,20,1]","support","1","yes","SYCL"
 "SYCL0","DUP","type=f16,ne=[10,10,20,1]","support","1","yes","SYCL"
 "SYCL0","DUP","type=i32,ne=[10,10,20,1]","support","1","yes","SYCL"
@@ -4983,411 +4999,419 @@
 "SYCL0","DUP","type=f16,ne=[10,10,5,1],permute=[1,0,2,3]","support","1","yes","SYCL"
 "SYCL0","DUP","type=i16,ne=[10,8,3,1],permute=[0,2,1,3]","support","1","yes","SYCL"
 "SYCL0","DUP","type=i16,ne=[10,8,3,1],permute=[1,2,0,3]","support","1","yes","SYCL"
-"SYCL0","SET","type_src=f32,type_dst=f32,ne=[6,5,4,3],dim=1","support","0","no","SYCL"
-"SYCL0","SET","type_src=f32,type_dst=f32,ne=[6,5,4,3],dim=2","support","0","no","SYCL"
-"SYCL0","SET","type_src=f32,type_dst=f32,ne=[6,5,4,3],dim=3","support","0","no","SYCL"
+"SYCL0","SET","type_src=f32,type_dst=f32,ne=[6,5,4,3],dim=1","support","1","yes","SYCL"
+"SYCL0","SET","type_src=f32,type_dst=f32,ne=[6,5,4,3],dim=2","support","1","yes","SYCL"
+"SYCL0","SET","type_src=f32,type_dst=f32,ne=[6,5,4,3],dim=3","support","1","yes","SYCL"
 "SYCL0","SET","type_src=i32,type_dst=i32,ne=[6,5,4,3],dim=1","support","0","no","SYCL"
 "SYCL0","SET","type_src=i32,type_dst=i32,ne=[6,5,4,3],dim=2","support","0","no","SYCL"
 "SYCL0","SET","type_src=i32,type_dst=i32,ne=[6,5,4,3],dim=3","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=f32,ne=[1,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=f32,ne=[1,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=f32,ne=[1,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=f32,ne=[2,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=f32,ne=[2,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=f32,ne=[2,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=f32,ne=[3,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=f32,ne=[3,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=f32,ne=[3,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=f16,ne=[1,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=f16,ne=[1,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=f16,ne=[1,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=f16,ne=[2,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=f16,ne=[2,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=f16,ne=[2,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=f16,ne=[3,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=f16,ne=[3,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=f16,ne=[3,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=bf16,ne=[1,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=bf16,ne=[1,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=bf16,ne=[1,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=bf16,ne=[2,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=bf16,ne=[2,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=bf16,ne=[2,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=bf16,ne=[3,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=bf16,ne=[3,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=bf16,ne=[3,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=q4_0,type_dst=q4_0,ne=[32,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q4_0,type_dst=q4_0,ne=[32,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q4_0,type_dst=q4_0,ne=[32,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q4_0,type_dst=q4_0,ne=[64,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q4_0,type_dst=q4_0,ne=[64,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q4_0,type_dst=q4_0,ne=[64,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q4_0,type_dst=q4_0,ne=[96,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q4_0,type_dst=q4_0,ne=[96,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q4_0,type_dst=q4_0,ne=[96,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q4_1,type_dst=q4_1,ne=[32,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q4_1,type_dst=q4_1,ne=[32,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q4_1,type_dst=q4_1,ne=[32,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q4_1,type_dst=q4_1,ne=[64,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q4_1,type_dst=q4_1,ne=[64,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q4_1,type_dst=q4_1,ne=[64,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q4_1,type_dst=q4_1,ne=[96,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q4_1,type_dst=q4_1,ne=[96,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q4_1,type_dst=q4_1,ne=[96,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q5_0,type_dst=q5_0,ne=[32,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q5_0,type_dst=q5_0,ne=[32,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q5_0,type_dst=q5_0,ne=[32,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q5_0,type_dst=q5_0,ne=[64,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q5_0,type_dst=q5_0,ne=[64,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q5_0,type_dst=q5_0,ne=[64,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q5_0,type_dst=q5_0,ne=[96,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q5_0,type_dst=q5_0,ne=[96,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q5_0,type_dst=q5_0,ne=[96,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q5_1,type_dst=q5_1,ne=[32,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q5_1,type_dst=q5_1,ne=[32,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q5_1,type_dst=q5_1,ne=[32,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q5_1,type_dst=q5_1,ne=[64,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q5_1,type_dst=q5_1,ne=[64,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q5_1,type_dst=q5_1,ne=[64,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q5_1,type_dst=q5_1,ne=[96,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q5_1,type_dst=q5_1,ne=[96,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q5_1,type_dst=q5_1,ne=[96,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q8_0,type_dst=q8_0,ne=[32,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q8_0,type_dst=q8_0,ne=[32,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q8_0,type_dst=q8_0,ne=[32,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q8_0,type_dst=q8_0,ne=[64,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q8_0,type_dst=q8_0,ne=[64,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q8_0,type_dst=q8_0,ne=[64,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q8_0,type_dst=q8_0,ne=[96,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q8_0,type_dst=q8_0,ne=[96,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q8_0,type_dst=q8_0,ne=[96,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=mxfp4,type_dst=mxfp4,ne=[32,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=mxfp4,type_dst=mxfp4,ne=[32,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=mxfp4,type_dst=mxfp4,ne=[32,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=mxfp4,type_dst=mxfp4,ne=[64,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=mxfp4,type_dst=mxfp4,ne=[64,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=mxfp4,type_dst=mxfp4,ne=[64,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=mxfp4,type_dst=mxfp4,ne=[96,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=mxfp4,type_dst=mxfp4,ne=[96,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=mxfp4,type_dst=mxfp4,ne=[96,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=q2_K,type_dst=q2_K,ne=[256,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q2_K,type_dst=q2_K,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=q2_K,type_dst=q2_K,ne=[256,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=q2_K,type_dst=q2_K,ne=[512,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q2_K,type_dst=q2_K,ne=[512,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=q2_K,type_dst=q2_K,ne=[512,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=q2_K,type_dst=q2_K,ne=[768,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q2_K,type_dst=q2_K,ne=[768,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=q2_K,type_dst=q2_K,ne=[768,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=q3_K,type_dst=q3_K,ne=[256,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q3_K,type_dst=q3_K,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=q3_K,type_dst=q3_K,ne=[256,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=q3_K,type_dst=q3_K,ne=[512,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q3_K,type_dst=q3_K,ne=[512,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=q3_K,type_dst=q3_K,ne=[512,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=q3_K,type_dst=q3_K,ne=[768,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q3_K,type_dst=q3_K,ne=[768,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=q3_K,type_dst=q3_K,ne=[768,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=q4_K,type_dst=q4_K,ne=[256,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q4_K,type_dst=q4_K,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=q4_K,type_dst=q4_K,ne=[256,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=q4_K,type_dst=q4_K,ne=[512,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q4_K,type_dst=q4_K,ne=[512,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=q4_K,type_dst=q4_K,ne=[512,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=q4_K,type_dst=q4_K,ne=[768,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q4_K,type_dst=q4_K,ne=[768,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=q4_K,type_dst=q4_K,ne=[768,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=q5_K,type_dst=q5_K,ne=[256,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q5_K,type_dst=q5_K,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=q5_K,type_dst=q5_K,ne=[256,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=q5_K,type_dst=q5_K,ne=[512,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q5_K,type_dst=q5_K,ne=[512,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=q5_K,type_dst=q5_K,ne=[512,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=q5_K,type_dst=q5_K,ne=[768,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q5_K,type_dst=q5_K,ne=[768,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=q5_K,type_dst=q5_K,ne=[768,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=q6_K,type_dst=q6_K,ne=[256,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q6_K,type_dst=q6_K,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=q6_K,type_dst=q6_K,ne=[256,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=q6_K,type_dst=q6_K,ne=[512,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q6_K,type_dst=q6_K,ne=[512,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=q6_K,type_dst=q6_K,ne=[512,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=q6_K,type_dst=q6_K,ne=[768,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q6_K,type_dst=q6_K,ne=[768,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=q6_K,type_dst=q6_K,ne=[768,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq2_xxs,type_dst=iq2_xxs,ne=[256,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=iq2_xxs,type_dst=iq2_xxs,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq2_xxs,type_dst=iq2_xxs,ne=[256,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq2_xxs,type_dst=iq2_xxs,ne=[512,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=iq2_xxs,type_dst=iq2_xxs,ne=[512,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq2_xxs,type_dst=iq2_xxs,ne=[512,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq2_xxs,type_dst=iq2_xxs,ne=[768,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=iq2_xxs,type_dst=iq2_xxs,ne=[768,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq2_xxs,type_dst=iq2_xxs,ne=[768,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq2_xs,type_dst=iq2_xs,ne=[256,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=iq2_xs,type_dst=iq2_xs,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq2_xs,type_dst=iq2_xs,ne=[256,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq2_xs,type_dst=iq2_xs,ne=[512,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=iq2_xs,type_dst=iq2_xs,ne=[512,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq2_xs,type_dst=iq2_xs,ne=[512,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq2_xs,type_dst=iq2_xs,ne=[768,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=iq2_xs,type_dst=iq2_xs,ne=[768,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq2_xs,type_dst=iq2_xs,ne=[768,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq2_s,type_dst=iq2_s,ne=[256,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=iq2_s,type_dst=iq2_s,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq2_s,type_dst=iq2_s,ne=[256,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq2_s,type_dst=iq2_s,ne=[512,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=iq2_s,type_dst=iq2_s,ne=[512,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq2_s,type_dst=iq2_s,ne=[512,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq2_s,type_dst=iq2_s,ne=[768,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=iq2_s,type_dst=iq2_s,ne=[768,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq2_s,type_dst=iq2_s,ne=[768,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq3_xxs,type_dst=iq3_xxs,ne=[256,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=iq3_xxs,type_dst=iq3_xxs,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq3_xxs,type_dst=iq3_xxs,ne=[256,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq3_xxs,type_dst=iq3_xxs,ne=[512,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=iq3_xxs,type_dst=iq3_xxs,ne=[512,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq3_xxs,type_dst=iq3_xxs,ne=[512,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq3_xxs,type_dst=iq3_xxs,ne=[768,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=iq3_xxs,type_dst=iq3_xxs,ne=[768,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq3_xxs,type_dst=iq3_xxs,ne=[768,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq1_s,type_dst=iq1_s,ne=[256,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=iq1_s,type_dst=iq1_s,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq1_s,type_dst=iq1_s,ne=[256,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq1_s,type_dst=iq1_s,ne=[512,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=iq1_s,type_dst=iq1_s,ne=[512,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq1_s,type_dst=iq1_s,ne=[512,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq1_s,type_dst=iq1_s,ne=[768,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=iq1_s,type_dst=iq1_s,ne=[768,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq1_s,type_dst=iq1_s,ne=[768,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq1_m,type_dst=iq1_m,ne=[256,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=iq1_m,type_dst=iq1_m,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq1_m,type_dst=iq1_m,ne=[256,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq1_m,type_dst=iq1_m,ne=[512,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=iq1_m,type_dst=iq1_m,ne=[512,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq1_m,type_dst=iq1_m,ne=[512,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq1_m,type_dst=iq1_m,ne=[768,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=iq1_m,type_dst=iq1_m,ne=[768,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq1_m,type_dst=iq1_m,ne=[768,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq4_nl,type_dst=iq4_nl,ne=[32,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=iq4_nl,type_dst=iq4_nl,ne=[32,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq4_nl,type_dst=iq4_nl,ne=[32,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq4_nl,type_dst=iq4_nl,ne=[64,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=iq4_nl,type_dst=iq4_nl,ne=[64,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq4_nl,type_dst=iq4_nl,ne=[64,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq4_nl,type_dst=iq4_nl,ne=[96,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=iq4_nl,type_dst=iq4_nl,ne=[96,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq4_nl,type_dst=iq4_nl,ne=[96,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq3_s,type_dst=iq3_s,ne=[256,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=iq3_s,type_dst=iq3_s,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq3_s,type_dst=iq3_s,ne=[256,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq3_s,type_dst=iq3_s,ne=[512,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=iq3_s,type_dst=iq3_s,ne=[512,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq3_s,type_dst=iq3_s,ne=[512,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq3_s,type_dst=iq3_s,ne=[768,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=iq3_s,type_dst=iq3_s,ne=[768,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq3_s,type_dst=iq3_s,ne=[768,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq4_xs,type_dst=iq4_xs,ne=[256,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=iq4_xs,type_dst=iq4_xs,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq4_xs,type_dst=iq4_xs,ne=[256,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq4_xs,type_dst=iq4_xs,ne=[512,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=iq4_xs,type_dst=iq4_xs,ne=[512,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq4_xs,type_dst=iq4_xs,ne=[512,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq4_xs,type_dst=iq4_xs,ne=[768,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=iq4_xs,type_dst=iq4_xs,ne=[768,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq4_xs,type_dst=iq4_xs,ne=[768,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=f32,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=f32,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=f16,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=f16,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=bf16,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=bf16,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=q4_0,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=q4_0,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=q4_1,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=q4_1,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=q5_0,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=q5_0,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=q5_1,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=q5_1,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=q8_0,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=q8_0,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=mxfp4,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=mxfp4,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=q2_K,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=q2_K,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=q3_K,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=q3_K,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=q4_K,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=q4_K,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=q5_K,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=q5_K,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=q6_K,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=q6_K,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=iq2_xxs,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=iq2_xxs,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=iq2_xs,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=iq2_xs,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=iq2_s,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=iq2_s,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=iq3_xxs,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=iq3_xxs,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=iq1_s,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=iq1_s,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=iq1_m,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=iq1_m,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=iq4_nl,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=iq4_nl,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=iq3_s,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=iq3_s,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=iq4_xs,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=iq4_xs,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=f32,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=f32,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=f16,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=f16,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=bf16,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=bf16,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=q4_0,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=q4_0,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=q4_1,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=q4_1,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=q5_0,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=q5_0,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=q5_1,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=q5_1,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=q8_0,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=q8_0,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=mxfp4,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=mxfp4,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=q2_K,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=q2_K,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=q3_K,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=q3_K,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=q4_K,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=q4_K,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=q5_K,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=q5_K,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=q6_K,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=q6_K,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=iq2_xxs,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=iq2_xxs,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=iq2_xs,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=iq2_xs,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=iq2_s,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=iq2_s,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=iq3_xxs,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=iq3_xxs,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=iq1_s,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=iq1_s,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=iq1_m,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=iq1_m,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=iq4_nl,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=iq4_nl,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=iq3_s,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=iq3_s,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=iq4_xs,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=iq4_xs,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=f32,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=f32,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=f16,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=f16,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=bf16,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=bf16,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=q4_0,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=q4_0,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=q4_1,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=q4_1,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=q5_0,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=q5_0,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=q5_1,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=q5_1,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=q8_0,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=q8_0,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=mxfp4,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=mxfp4,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=q2_K,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=q2_K,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=q3_K,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=q3_K,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=q4_K,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=q4_K,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=q5_K,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=q5_K,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=q6_K,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=q6_K,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=iq2_xxs,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=iq2_xxs,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=iq2_xs,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=iq2_xs,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=iq2_s,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=iq2_s,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=iq3_xxs,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=iq3_xxs,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=iq1_s,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=iq1_s,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=iq1_m,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=iq1_m,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=iq4_nl,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=iq4_nl,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=iq3_s,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=iq3_s,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=iq4_xs,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=iq4_xs,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=f32,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=f32,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=f32,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=f32,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=f32,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=bf16,type_dst=f32,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=q4_0,type_dst=f32,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q4_0,type_dst=f32,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q4_1,type_dst=f32,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q4_1,type_dst=f32,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q5_0,type_dst=f32,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q5_0,type_dst=f32,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q5_1,type_dst=f32,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q5_1,type_dst=f32,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q8_0,type_dst=f32,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=q8_0,type_dst=f32,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=mxfp4,type_dst=f32,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=mxfp4,type_dst=f32,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=q2_K,type_dst=f32,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=q2_K,type_dst=f32,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=q3_K,type_dst=f32,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=q3_K,type_dst=f32,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=q4_K,type_dst=f32,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=q4_K,type_dst=f32,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=q5_K,type_dst=f32,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=q5_K,type_dst=f32,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=q6_K,type_dst=f32,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=q6_K,type_dst=f32,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq2_xxs,type_dst=f32,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq2_xxs,type_dst=f32,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq2_xs,type_dst=f32,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq2_xs,type_dst=f32,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq2_s,type_dst=f32,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq2_s,type_dst=f32,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq3_xxs,type_dst=f32,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq3_xxs,type_dst=f32,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq1_s,type_dst=f32,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq1_s,type_dst=f32,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq1_m,type_dst=f32,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq1_m,type_dst=f32,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq4_nl,type_dst=f32,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq4_nl,type_dst=f32,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq3_s,type_dst=f32,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq3_s,type_dst=f32,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq4_xs,type_dst=f32,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=iq4_xs,type_dst=f32,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=f16,ne=[256,2,3,4],permute_src=[1,0,2,3],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=f16,type_dst=f32,ne=[256,2,3,4],permute_src=[1,0,2,3],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=f16,ne=[256,2,3,4],permute_src=[1,0,2,3],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=f32,ne=[256,2,3,4],permute_src=[1,0,2,3],permute_dst=[0,0,0,0]","support","1","yes","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=i32,ne=[256,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=f32,type_dst=i32,ne=[256,2,3,4],permute_src=[1,0,2,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=i32,type_dst=f32,ne=[256,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0]","support","0","no","SYCL"
-"SYCL0","CPY","type_src=i32,type_dst=f32,ne=[256,2,3,4],permute_src=[1,0,2,3],permute_dst=[0,0,0,0]","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=f32,ne=[1,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=f32,ne=[1,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=f32,ne=[1,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=f32,ne=[2,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=f32,ne=[2,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=f32,ne=[2,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=f32,ne=[3,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=f32,ne=[3,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=f32,ne=[3,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=f16,ne=[1,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=f16,ne=[1,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=f16,ne=[1,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=f16,ne=[2,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=f16,ne=[2,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=f16,ne=[2,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=f16,ne=[3,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=f16,ne=[3,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=f16,ne=[3,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=bf16,ne=[1,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=bf16,ne=[1,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=bf16,ne=[1,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=bf16,ne=[2,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=bf16,ne=[2,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=bf16,ne=[2,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=bf16,ne=[3,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=bf16,ne=[3,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=bf16,ne=[3,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=q4_0,type_dst=q4_0,ne=[32,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q4_0,type_dst=q4_0,ne=[32,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q4_0,type_dst=q4_0,ne=[32,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q4_0,type_dst=q4_0,ne=[64,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q4_0,type_dst=q4_0,ne=[64,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q4_0,type_dst=q4_0,ne=[64,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q4_0,type_dst=q4_0,ne=[96,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q4_0,type_dst=q4_0,ne=[96,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q4_0,type_dst=q4_0,ne=[96,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q4_1,type_dst=q4_1,ne=[32,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q4_1,type_dst=q4_1,ne=[32,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q4_1,type_dst=q4_1,ne=[32,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q4_1,type_dst=q4_1,ne=[64,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q4_1,type_dst=q4_1,ne=[64,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q4_1,type_dst=q4_1,ne=[64,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q4_1,type_dst=q4_1,ne=[96,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q4_1,type_dst=q4_1,ne=[96,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q4_1,type_dst=q4_1,ne=[96,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q5_0,type_dst=q5_0,ne=[32,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q5_0,type_dst=q5_0,ne=[32,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q5_0,type_dst=q5_0,ne=[32,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q5_0,type_dst=q5_0,ne=[64,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q5_0,type_dst=q5_0,ne=[64,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q5_0,type_dst=q5_0,ne=[64,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q5_0,type_dst=q5_0,ne=[96,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q5_0,type_dst=q5_0,ne=[96,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q5_0,type_dst=q5_0,ne=[96,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q5_1,type_dst=q5_1,ne=[32,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q5_1,type_dst=q5_1,ne=[32,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q5_1,type_dst=q5_1,ne=[32,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q5_1,type_dst=q5_1,ne=[64,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q5_1,type_dst=q5_1,ne=[64,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q5_1,type_dst=q5_1,ne=[64,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q5_1,type_dst=q5_1,ne=[96,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q5_1,type_dst=q5_1,ne=[96,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q5_1,type_dst=q5_1,ne=[96,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q8_0,type_dst=q8_0,ne=[32,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q8_0,type_dst=q8_0,ne=[32,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q8_0,type_dst=q8_0,ne=[32,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q8_0,type_dst=q8_0,ne=[64,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q8_0,type_dst=q8_0,ne=[64,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q8_0,type_dst=q8_0,ne=[64,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q8_0,type_dst=q8_0,ne=[96,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q8_0,type_dst=q8_0,ne=[96,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q8_0,type_dst=q8_0,ne=[96,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=mxfp4,type_dst=mxfp4,ne=[32,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=mxfp4,type_dst=mxfp4,ne=[32,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=mxfp4,type_dst=mxfp4,ne=[32,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=mxfp4,type_dst=mxfp4,ne=[64,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=mxfp4,type_dst=mxfp4,ne=[64,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=mxfp4,type_dst=mxfp4,ne=[64,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=mxfp4,type_dst=mxfp4,ne=[96,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=mxfp4,type_dst=mxfp4,ne=[96,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=mxfp4,type_dst=mxfp4,ne=[96,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=q2_K,type_dst=q2_K,ne=[256,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q2_K,type_dst=q2_K,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=q2_K,type_dst=q2_K,ne=[256,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=q2_K,type_dst=q2_K,ne=[512,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q2_K,type_dst=q2_K,ne=[512,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=q2_K,type_dst=q2_K,ne=[512,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=q2_K,type_dst=q2_K,ne=[768,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q2_K,type_dst=q2_K,ne=[768,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=q2_K,type_dst=q2_K,ne=[768,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=q3_K,type_dst=q3_K,ne=[256,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q3_K,type_dst=q3_K,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=q3_K,type_dst=q3_K,ne=[256,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=q3_K,type_dst=q3_K,ne=[512,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q3_K,type_dst=q3_K,ne=[512,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=q3_K,type_dst=q3_K,ne=[512,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=q3_K,type_dst=q3_K,ne=[768,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q3_K,type_dst=q3_K,ne=[768,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=q3_K,type_dst=q3_K,ne=[768,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=q4_K,type_dst=q4_K,ne=[256,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q4_K,type_dst=q4_K,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=q4_K,type_dst=q4_K,ne=[256,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=q4_K,type_dst=q4_K,ne=[512,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q4_K,type_dst=q4_K,ne=[512,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=q4_K,type_dst=q4_K,ne=[512,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=q4_K,type_dst=q4_K,ne=[768,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q4_K,type_dst=q4_K,ne=[768,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=q4_K,type_dst=q4_K,ne=[768,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=q5_K,type_dst=q5_K,ne=[256,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q5_K,type_dst=q5_K,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=q5_K,type_dst=q5_K,ne=[256,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=q5_K,type_dst=q5_K,ne=[512,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q5_K,type_dst=q5_K,ne=[512,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=q5_K,type_dst=q5_K,ne=[512,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=q5_K,type_dst=q5_K,ne=[768,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q5_K,type_dst=q5_K,ne=[768,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=q5_K,type_dst=q5_K,ne=[768,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=q6_K,type_dst=q6_K,ne=[256,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q6_K,type_dst=q6_K,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=q6_K,type_dst=q6_K,ne=[256,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=q6_K,type_dst=q6_K,ne=[512,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q6_K,type_dst=q6_K,ne=[512,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=q6_K,type_dst=q6_K,ne=[512,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=q6_K,type_dst=q6_K,ne=[768,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q6_K,type_dst=q6_K,ne=[768,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=q6_K,type_dst=q6_K,ne=[768,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq2_xxs,type_dst=iq2_xxs,ne=[256,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=iq2_xxs,type_dst=iq2_xxs,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq2_xxs,type_dst=iq2_xxs,ne=[256,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq2_xxs,type_dst=iq2_xxs,ne=[512,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=iq2_xxs,type_dst=iq2_xxs,ne=[512,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq2_xxs,type_dst=iq2_xxs,ne=[512,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq2_xxs,type_dst=iq2_xxs,ne=[768,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=iq2_xxs,type_dst=iq2_xxs,ne=[768,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq2_xxs,type_dst=iq2_xxs,ne=[768,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq2_xs,type_dst=iq2_xs,ne=[256,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=iq2_xs,type_dst=iq2_xs,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq2_xs,type_dst=iq2_xs,ne=[256,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq2_xs,type_dst=iq2_xs,ne=[512,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=iq2_xs,type_dst=iq2_xs,ne=[512,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq2_xs,type_dst=iq2_xs,ne=[512,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq2_xs,type_dst=iq2_xs,ne=[768,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=iq2_xs,type_dst=iq2_xs,ne=[768,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq2_xs,type_dst=iq2_xs,ne=[768,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq2_s,type_dst=iq2_s,ne=[256,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=iq2_s,type_dst=iq2_s,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq2_s,type_dst=iq2_s,ne=[256,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq2_s,type_dst=iq2_s,ne=[512,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=iq2_s,type_dst=iq2_s,ne=[512,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq2_s,type_dst=iq2_s,ne=[512,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq2_s,type_dst=iq2_s,ne=[768,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=iq2_s,type_dst=iq2_s,ne=[768,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq2_s,type_dst=iq2_s,ne=[768,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq3_xxs,type_dst=iq3_xxs,ne=[256,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=iq3_xxs,type_dst=iq3_xxs,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq3_xxs,type_dst=iq3_xxs,ne=[256,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq3_xxs,type_dst=iq3_xxs,ne=[512,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=iq3_xxs,type_dst=iq3_xxs,ne=[512,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq3_xxs,type_dst=iq3_xxs,ne=[512,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq3_xxs,type_dst=iq3_xxs,ne=[768,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=iq3_xxs,type_dst=iq3_xxs,ne=[768,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq3_xxs,type_dst=iq3_xxs,ne=[768,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq1_s,type_dst=iq1_s,ne=[256,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=iq1_s,type_dst=iq1_s,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq1_s,type_dst=iq1_s,ne=[256,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq1_s,type_dst=iq1_s,ne=[512,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=iq1_s,type_dst=iq1_s,ne=[512,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq1_s,type_dst=iq1_s,ne=[512,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq1_s,type_dst=iq1_s,ne=[768,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=iq1_s,type_dst=iq1_s,ne=[768,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq1_s,type_dst=iq1_s,ne=[768,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq1_m,type_dst=iq1_m,ne=[256,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=iq1_m,type_dst=iq1_m,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq1_m,type_dst=iq1_m,ne=[256,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq1_m,type_dst=iq1_m,ne=[512,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=iq1_m,type_dst=iq1_m,ne=[512,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq1_m,type_dst=iq1_m,ne=[512,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq1_m,type_dst=iq1_m,ne=[768,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=iq1_m,type_dst=iq1_m,ne=[768,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq1_m,type_dst=iq1_m,ne=[768,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq4_nl,type_dst=iq4_nl,ne=[32,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=iq4_nl,type_dst=iq4_nl,ne=[32,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq4_nl,type_dst=iq4_nl,ne=[32,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq4_nl,type_dst=iq4_nl,ne=[64,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=iq4_nl,type_dst=iq4_nl,ne=[64,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq4_nl,type_dst=iq4_nl,ne=[64,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq4_nl,type_dst=iq4_nl,ne=[96,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=iq4_nl,type_dst=iq4_nl,ne=[96,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq4_nl,type_dst=iq4_nl,ne=[96,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq3_s,type_dst=iq3_s,ne=[256,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=iq3_s,type_dst=iq3_s,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq3_s,type_dst=iq3_s,ne=[256,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq3_s,type_dst=iq3_s,ne=[512,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=iq3_s,type_dst=iq3_s,ne=[512,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq3_s,type_dst=iq3_s,ne=[512,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq3_s,type_dst=iq3_s,ne=[768,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=iq3_s,type_dst=iq3_s,ne=[768,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq3_s,type_dst=iq3_s,ne=[768,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq4_xs,type_dst=iq4_xs,ne=[256,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=iq4_xs,type_dst=iq4_xs,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq4_xs,type_dst=iq4_xs,ne=[256,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq4_xs,type_dst=iq4_xs,ne=[512,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=iq4_xs,type_dst=iq4_xs,ne=[512,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq4_xs,type_dst=iq4_xs,ne=[512,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq4_xs,type_dst=iq4_xs,ne=[768,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=iq4_xs,type_dst=iq4_xs,ne=[768,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq4_xs,type_dst=iq4_xs,ne=[768,2,3,4],permute_src=[0,3,1,2],permute_dst=[0,2,1,3],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=f32,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=f32,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=f16,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=f16,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=bf16,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=bf16,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=q4_0,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=q4_0,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=q4_1,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=q4_1,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=q5_0,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=q5_0,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=q5_1,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=q5_1,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=q8_0,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=q8_0,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=mxfp4,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=mxfp4,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=q2_K,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=q2_K,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=q3_K,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=q3_K,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=q4_K,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=q4_K,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=q5_K,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=q5_K,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=q6_K,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=q6_K,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=iq2_xxs,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=iq2_xxs,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=iq2_xs,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=iq2_xs,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=iq2_s,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=iq2_s,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=iq3_xxs,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=iq3_xxs,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=iq1_s,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=iq1_s,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=iq1_m,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=iq1_m,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=iq4_nl,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=iq4_nl,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=iq3_s,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=iq3_s,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=iq4_xs,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=iq4_xs,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=f32,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=f32,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=f16,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=f16,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=bf16,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=bf16,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=q4_0,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=q4_0,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=q4_1,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=q4_1,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=q5_0,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=q5_0,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=q5_1,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=q5_1,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=q8_0,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=q8_0,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=mxfp4,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=mxfp4,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=q2_K,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=q2_K,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=q3_K,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=q3_K,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=q4_K,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=q4_K,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=q5_K,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=q5_K,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=q6_K,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=q6_K,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=iq2_xxs,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=iq2_xxs,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=iq2_xs,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=iq2_xs,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=iq2_s,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=iq2_s,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=iq3_xxs,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=iq3_xxs,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=iq1_s,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=iq1_s,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=iq1_m,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=iq1_m,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=iq4_nl,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=iq4_nl,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=iq3_s,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=iq3_s,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=iq4_xs,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=iq4_xs,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=f32,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=f32,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=f16,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=f16,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=bf16,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=bf16,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=q4_0,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=q4_0,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=q4_1,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=q4_1,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=q5_0,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=q5_0,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=q5_1,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=q5_1,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=q8_0,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=q8_0,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=mxfp4,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=mxfp4,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=q2_K,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=q2_K,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=q3_K,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=q3_K,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=q4_K,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=q4_K,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=q5_K,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=q5_K,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=q6_K,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=q6_K,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=iq2_xxs,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=iq2_xxs,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=iq2_xs,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=iq2_xs,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=iq2_s,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=iq2_s,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=iq3_xxs,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=iq3_xxs,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=iq1_s,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=iq1_s,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=iq1_m,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=iq1_m,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=iq4_nl,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=iq4_nl,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=iq3_s,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=iq3_s,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=iq4_xs,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=iq4_xs,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=f32,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=f32,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=f32,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=f32,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=f32,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=f32,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=q4_0,type_dst=f32,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q4_0,type_dst=f32,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q4_1,type_dst=f32,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q4_1,type_dst=f32,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q5_0,type_dst=f32,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q5_0,type_dst=f32,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q5_1,type_dst=f32,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q5_1,type_dst=f32,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q8_0,type_dst=f32,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=q8_0,type_dst=f32,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=mxfp4,type_dst=f32,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=mxfp4,type_dst=f32,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=q2_K,type_dst=f32,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=q2_K,type_dst=f32,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=q3_K,type_dst=f32,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=q3_K,type_dst=f32,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=q4_K,type_dst=f32,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=q4_K,type_dst=f32,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=q5_K,type_dst=f32,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=q5_K,type_dst=f32,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=q6_K,type_dst=f32,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=q6_K,type_dst=f32,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq2_xxs,type_dst=f32,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq2_xxs,type_dst=f32,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq2_xs,type_dst=f32,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq2_xs,type_dst=f32,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq2_s,type_dst=f32,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq2_s,type_dst=f32,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq3_xxs,type_dst=f32,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq3_xxs,type_dst=f32,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq1_s,type_dst=f32,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq1_s,type_dst=f32,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq1_m,type_dst=f32,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq1_m,type_dst=f32,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq4_nl,type_dst=f32,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq4_nl,type_dst=f32,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq3_s,type_dst=f32,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq3_s,type_dst=f32,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq4_xs,type_dst=f32,ne=[256,4,4,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=iq4_xs,type_dst=f32,ne=[256,2,3,4],permute_src=[0,2,1,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=f16,ne=[256,2,3,4],permute_src=[1,0,2,3],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=f32,ne=[256,2,3,4],permute_src=[1,0,2,3],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=f16,ne=[256,2,3,4],permute_src=[1,0,2,3],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=f32,ne=[256,2,3,4],permute_src=[1,0,2,3],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=i32,ne=[256,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=i32,ne=[256,2,3,4],permute_src=[1,0,2,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=i32,type_dst=f32,ne=[256,2,3,4],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=i32,type_dst=f32,ne=[256,2,3,4],permute_src=[1,0,2,3],permute_dst=[0,0,0,0],_src_transpose=0","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=f16,ne=[256,4,3,1],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=1","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=f32,ne=[256,4,3,1],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=1","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=f32,ne=[256,4,3,3],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=1","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=bf16,ne=[256,4,3,1],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=1","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f16,type_dst=f16,ne=[256,4,1,1],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=1","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=f32,ne=[256,4,1,1],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=1","support","1","yes","SYCL"
+"SYCL0","CPY","type_src=bf16,type_dst=bf16,ne=[256,4,1,1],permute_src=[0,0,0,0],permute_dst=[0,0,0,0],_src_transpose=1","support","0","no","SYCL"
+"SYCL0","CPY","type_src=f32,type_dst=f32,ne=[256,1,4,1],permute_src=[1,2,0,3],permute_dst=[0,0,0,0],_src_transpose=0","support","1","yes","SYCL"
 "SYCL0","CONT","type=f32,ne=[10,10,10,1]","support","1","yes","SYCL"
 "SYCL0","CONT","type=f32,ne=[2,1,1,1]","support","1","yes","SYCL"
 "SYCL0","CONT","type=f32,ne=[2,1,3,5]","support","1","yes","SYCL"
@@ -5689,24 +5713,24 @@
 "SYCL0","RMS_NORM_MUL_ADD","type=f32,ne=[16896,1,1,1],eps=0.000001,broadcast=0,multi_add=0","support","1","yes","SYCL"
 "SYCL0","RMS_NORM_MUL_ADD","type=f32,ne=[16896,1,1,1],eps=0.000001,broadcast=0,multi_add=1","support","1","yes","SYCL"
 "SYCL0","L2_NORM","type=f32,ne=[64,5,4,3]","support","1","yes","SYCL"
-"SYCL0","SSM_CONV","type=f32,ne_a=[4,1024,1,1],ne_b=[3,1024,1,1]","support","0","no","SYCL"
-"SYCL0","SSM_CONV","type=f32,ne_a=[8,1024,1,1],ne_b=[3,1024,1,1]","support","0","no","SYCL"
-"SYCL0","SSM_CONV","type=f32,ne_a=[4,1024,4,1],ne_b=[3,1024,1,1]","support","0","no","SYCL"
-"SYCL0","SSM_CONV","type=f32,ne_a=[4,1536,1,1],ne_b=[3,1536,1,1]","support","0","no","SYCL"
-"SYCL0","SSM_CONV","type=f32,ne_a=[8,1536,1,1],ne_b=[3,1536,1,1]","support","0","no","SYCL"
-"SYCL0","SSM_CONV","type=f32,ne_a=[4,1536,4,1],ne_b=[3,1536,1,1]","support","0","no","SYCL"
-"SYCL0","SSM_CONV","type=f32,ne_a=[4,2048,1,1],ne_b=[3,2048,1,1]","support","0","no","SYCL"
-"SYCL0","SSM_CONV","type=f32,ne_a=[8,2048,1,1],ne_b=[3,2048,1,1]","support","0","no","SYCL"
-"SYCL0","SSM_CONV","type=f32,ne_a=[4,2048,4,1],ne_b=[3,2048,1,1]","support","0","no","SYCL"
-"SYCL0","SSM_CONV","type=f32,ne_a=[4,1024,1,1],ne_b=[4,1024,1,1]","support","0","no","SYCL"
-"SYCL0","SSM_CONV","type=f32,ne_a=[8,1024,1,1],ne_b=[4,1024,1,1]","support","0","no","SYCL"
-"SYCL0","SSM_CONV","type=f32,ne_a=[4,1024,4,1],ne_b=[4,1024,1,1]","support","0","no","SYCL"
-"SYCL0","SSM_CONV","type=f32,ne_a=[4,1536,1,1],ne_b=[4,1536,1,1]","support","0","no","SYCL"
-"SYCL0","SSM_CONV","type=f32,ne_a=[8,1536,1,1],ne_b=[4,1536,1,1]","support","0","no","SYCL"
-"SYCL0","SSM_CONV","type=f32,ne_a=[4,1536,4,1],ne_b=[4,1536,1,1]","support","0","no","SYCL"
-"SYCL0","SSM_CONV","type=f32,ne_a=[4,2048,1,1],ne_b=[4,2048,1,1]","support","0","no","SYCL"
-"SYCL0","SSM_CONV","type=f32,ne_a=[8,2048,1,1],ne_b=[4,2048,1,1]","support","0","no","SYCL"
-"SYCL0","SSM_CONV","type=f32,ne_a=[4,2048,4,1],ne_b=[4,2048,1,1]","support","0","no","SYCL"
+"SYCL0","SSM_CONV","type=f32,ne_a=[4,1024,1,1],ne_b=[3,1024,1,1]","support","1","yes","SYCL"
+"SYCL0","SSM_CONV","type=f32,ne_a=[8,1024,1,1],ne_b=[3,1024,1,1]","support","1","yes","SYCL"
+"SYCL0","SSM_CONV","type=f32,ne_a=[4,1024,4,1],ne_b=[3,1024,1,1]","support","1","yes","SYCL"
+"SYCL0","SSM_CONV","type=f32,ne_a=[4,1536,1,1],ne_b=[3,1536,1,1]","support","1","yes","SYCL"
+"SYCL0","SSM_CONV","type=f32,ne_a=[8,1536,1,1],ne_b=[3,1536,1,1]","support","1","yes","SYCL"
+"SYCL0","SSM_CONV","type=f32,ne_a=[4,1536,4,1],ne_b=[3,1536,1,1]","support","1","yes","SYCL"
+"SYCL0","SSM_CONV","type=f32,ne_a=[4,2048,1,1],ne_b=[3,2048,1,1]","support","1","yes","SYCL"
+"SYCL0","SSM_CONV","type=f32,ne_a=[8,2048,1,1],ne_b=[3,2048,1,1]","support","1","yes","SYCL"
+"SYCL0","SSM_CONV","type=f32,ne_a=[4,2048,4,1],ne_b=[3,2048,1,1]","support","1","yes","SYCL"
+"SYCL0","SSM_CONV","type=f32,ne_a=[4,1024,1,1],ne_b=[4,1024,1,1]","support","1","yes","SYCL"
+"SYCL0","SSM_CONV","type=f32,ne_a=[8,1024,1,1],ne_b=[4,1024,1,1]","support","1","yes","SYCL"
+"SYCL0","SSM_CONV","type=f32,ne_a=[4,1024,4,1],ne_b=[4,1024,1,1]","support","1","yes","SYCL"
+"SYCL0","SSM_CONV","type=f32,ne_a=[4,1536,1,1],ne_b=[4,1536,1,1]","support","1","yes","SYCL"
+"SYCL0","SSM_CONV","type=f32,ne_a=[8,1536,1,1],ne_b=[4,1536,1,1]","support","1","yes","SYCL"
+"SYCL0","SSM_CONV","type=f32,ne_a=[4,1536,4,1],ne_b=[4,1536,1,1]","support","1","yes","SYCL"
+"SYCL0","SSM_CONV","type=f32,ne_a=[4,2048,1,1],ne_b=[4,2048,1,1]","support","1","yes","SYCL"
+"SYCL0","SSM_CONV","type=f32,ne_a=[8,2048,1,1],ne_b=[4,2048,1,1]","support","1","yes","SYCL"
+"SYCL0","SSM_CONV","type=f32,ne_a=[4,2048,4,1],ne_b=[4,2048,1,1]","support","1","yes","SYCL"
 "SYCL0","SSM_SCAN","type=f32,d_state=16,head_dim=1,n_head=1024,n_group=1,n_seq_tokens=32,n_seqs=4","support","0","no","SYCL"
 "SYCL0","SSM_SCAN","type=f32,d_state=128,head_dim=64,n_head=16,n_group=2,n_seq_tokens=32,n_seqs=4","support","0","no","SYCL"
 "SYCL0","SSM_SCAN","type=f32,d_state=256,head_dim=64,n_head=8,n_group=2,n_seq_tokens=32,n_seqs=4","support","0","no","SYCL"
@@ -5722,1836 +5746,1852 @@
 "SYCL0","GATED_LINEAR_ATTN","type=f32,head_count=32,head_size=64,n_seq_tokens=32,n_seqs=1","support","1","yes","SYCL"
 "SYCL0","GATED_LINEAR_ATTN","type=f32,head_count=32,head_size=64,n_seq_tokens=32,n_seqs=4","support","1","yes","SYCL"
 "SYCL0","GATED_LINEAR_ATTN","type=f32,head_count=32,head_size=64,n_seq_tokens=128,n_seqs=4","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=2,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=3,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=4,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=5,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=6,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=7,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=8,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=9,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=2,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=3,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=4,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=5,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=6,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=7,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=8,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=9,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=16,n=2,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=16,n=3,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=16,n=4,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=16,n=5,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=16,n=6,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=16,n=7,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=16,n=8,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=16,n=9,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=2,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=3,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=4,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=5,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=6,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=7,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=8,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=9,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=2,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=3,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=4,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=5,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=6,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=7,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=8,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=9,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q5_0,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q5_0,type_b=f32,m=16,n=2,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q5_0,type_b=f32,m=16,n=3,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q5_0,type_b=f32,m=16,n=4,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q5_0,type_b=f32,m=16,n=5,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q5_0,type_b=f32,m=16,n=6,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q5_0,type_b=f32,m=16,n=7,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q5_0,type_b=f32,m=16,n=8,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q5_0,type_b=f32,m=16,n=9,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q5_1,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q5_1,type_b=f32,m=16,n=2,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q5_1,type_b=f32,m=16,n=3,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q5_1,type_b=f32,m=16,n=4,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q5_1,type_b=f32,m=16,n=5,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q5_1,type_b=f32,m=16,n=6,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q5_1,type_b=f32,m=16,n=7,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q5_1,type_b=f32,m=16,n=8,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q5_1,type_b=f32,m=16,n=9,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=2,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=3,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=4,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=5,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=6,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=7,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=8,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=9,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=2,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=3,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=4,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=5,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=6,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=7,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=8,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=9,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q2_K,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q2_K,type_b=f32,m=16,n=2,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q2_K,type_b=f32,m=16,n=3,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q2_K,type_b=f32,m=16,n=4,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q2_K,type_b=f32,m=16,n=5,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q2_K,type_b=f32,m=16,n=6,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q2_K,type_b=f32,m=16,n=7,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q2_K,type_b=f32,m=16,n=8,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q2_K,type_b=f32,m=16,n=9,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q3_K,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q3_K,type_b=f32,m=16,n=2,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q3_K,type_b=f32,m=16,n=3,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q3_K,type_b=f32,m=16,n=4,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q3_K,type_b=f32,m=16,n=5,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q3_K,type_b=f32,m=16,n=6,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q3_K,type_b=f32,m=16,n=7,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q3_K,type_b=f32,m=16,n=8,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q3_K,type_b=f32,m=16,n=9,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=2,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=3,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=4,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=5,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=6,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=7,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=8,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=9,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q5_K,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q5_K,type_b=f32,m=16,n=2,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q5_K,type_b=f32,m=16,n=3,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q5_K,type_b=f32,m=16,n=4,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q5_K,type_b=f32,m=16,n=5,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q5_K,type_b=f32,m=16,n=6,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q5_K,type_b=f32,m=16,n=7,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q5_K,type_b=f32,m=16,n=8,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q5_K,type_b=f32,m=16,n=9,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q6_K,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q6_K,type_b=f32,m=16,n=2,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q6_K,type_b=f32,m=16,n=3,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q6_K,type_b=f32,m=16,n=4,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q6_K,type_b=f32,m=16,n=5,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q6_K,type_b=f32,m=16,n=6,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q6_K,type_b=f32,m=16,n=7,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q6_K,type_b=f32,m=16,n=8,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q6_K,type_b=f32,m=16,n=9,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=2,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=3,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=4,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=5,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=6,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=7,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=8,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=9,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xs,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xs,type_b=f32,m=16,n=2,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xs,type_b=f32,m=16,n=3,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xs,type_b=f32,m=16,n=4,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xs,type_b=f32,m=16,n=5,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xs,type_b=f32,m=16,n=6,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xs,type_b=f32,m=16,n=7,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xs,type_b=f32,m=16,n=8,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xs,type_b=f32,m=16,n=9,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_s,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_s,type_b=f32,m=16,n=2,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_s,type_b=f32,m=16,n=3,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_s,type_b=f32,m=16,n=4,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_s,type_b=f32,m=16,n=5,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_s,type_b=f32,m=16,n=6,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_s,type_b=f32,m=16,n=7,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_s,type_b=f32,m=16,n=8,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_s,type_b=f32,m=16,n=9,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq3_xxs,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq3_xxs,type_b=f32,m=16,n=2,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq3_xxs,type_b=f32,m=16,n=3,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq3_xxs,type_b=f32,m=16,n=4,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq3_xxs,type_b=f32,m=16,n=5,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq3_xxs,type_b=f32,m=16,n=6,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq3_xxs,type_b=f32,m=16,n=7,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq3_xxs,type_b=f32,m=16,n=8,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq3_xxs,type_b=f32,m=16,n=9,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq1_s,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq1_s,type_b=f32,m=16,n=2,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq1_s,type_b=f32,m=16,n=3,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq1_s,type_b=f32,m=16,n=4,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq1_s,type_b=f32,m=16,n=5,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq1_s,type_b=f32,m=16,n=6,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq1_s,type_b=f32,m=16,n=7,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq1_s,type_b=f32,m=16,n=8,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq1_s,type_b=f32,m=16,n=9,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq1_m,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq1_m,type_b=f32,m=16,n=2,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq1_m,type_b=f32,m=16,n=3,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq1_m,type_b=f32,m=16,n=4,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq1_m,type_b=f32,m=16,n=5,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq1_m,type_b=f32,m=16,n=6,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq1_m,type_b=f32,m=16,n=7,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq1_m,type_b=f32,m=16,n=8,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq1_m,type_b=f32,m=16,n=9,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq4_nl,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq4_nl,type_b=f32,m=16,n=2,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq4_nl,type_b=f32,m=16,n=3,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq4_nl,type_b=f32,m=16,n=4,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq4_nl,type_b=f32,m=16,n=5,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq4_nl,type_b=f32,m=16,n=6,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq4_nl,type_b=f32,m=16,n=7,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq4_nl,type_b=f32,m=16,n=8,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq4_nl,type_b=f32,m=16,n=9,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq3_s,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq3_s,type_b=f32,m=16,n=2,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq3_s,type_b=f32,m=16,n=3,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq3_s,type_b=f32,m=16,n=4,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq3_s,type_b=f32,m=16,n=5,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq3_s,type_b=f32,m=16,n=6,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq3_s,type_b=f32,m=16,n=7,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq3_s,type_b=f32,m=16,n=8,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq3_s,type_b=f32,m=16,n=9,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq4_xs,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq4_xs,type_b=f32,m=16,n=2,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq4_xs,type_b=f32,m=16,n=3,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq4_xs,type_b=f32,m=16,n=4,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq4_xs,type_b=f32,m=16,n=5,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq4_xs,type_b=f32,m=16,n=6,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq4_xs,type_b=f32,m=16,n=7,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq4_xs,type_b=f32,m=16,n=8,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq4_xs,type_b=f32,m=16,n=9,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=1,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=1,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=16,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=16,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=16,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=16,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=16,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=1,k=4,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=1,k=4,bs=[1,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=1,k=4,bs=[1,1],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=1,k=4,bs=[3,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=1,k=4,bs=[3,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=1,k=4,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=1,k=4,bs=[3,2],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=1,k=4,bs=[3,2],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=1,k=4,bs=[3,2],nr=[2,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=16,k=4,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=16,k=4,bs=[1,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=16,k=4,bs=[1,1],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=16,k=4,bs=[3,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=16,k=4,bs=[3,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=16,k=4,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=16,k=4,bs=[3,2],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=16,k=4,bs=[3,2],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=16,k=4,bs=[3,2],nr=[2,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=1,k=4,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=1,k=4,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=1,k=4,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=8,k=4,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=8,k=4,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=8,k=4,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=16,k=4,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=16,k=4,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=16,k=4,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=1,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=8,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=16,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=1,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=1,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=1,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=1,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=16,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=16,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=16,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=16,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=16,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=1,k=4,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=1,k=4,bs=[1,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=1,k=4,bs=[1,1],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=1,k=4,bs=[3,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=1,k=4,bs=[3,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=1,k=4,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=1,k=4,bs=[3,2],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=1,k=4,bs=[3,2],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=1,k=4,bs=[3,2],nr=[2,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=16,k=4,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=16,k=4,bs=[1,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=16,k=4,bs=[1,1],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=16,k=4,bs=[3,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=16,k=4,bs=[3,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=16,k=4,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=16,k=4,bs=[3,2],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=16,k=4,bs=[3,2],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=16,k=4,bs=[3,2],nr=[2,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=1,k=4,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=1,k=4,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=1,k=4,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=8,k=4,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=8,k=4,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=8,k=4,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=16,k=4,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=16,k=4,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=16,k=4,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=1,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=8,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=16,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=1,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=1,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=16,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=16,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=16,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=16,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=16,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=1,k=4,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=1,k=4,bs=[1,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=1,k=4,bs=[1,1],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=1,k=4,bs=[3,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=1,k=4,bs=[3,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=1,k=4,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=1,k=4,bs=[3,2],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=1,k=4,bs=[3,2],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=1,k=4,bs=[3,2],nr=[2,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=16,k=4,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=16,k=4,bs=[1,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=16,k=4,bs=[1,1],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=16,k=4,bs=[3,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=16,k=4,bs=[3,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=16,k=4,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=16,k=4,bs=[3,2],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=16,k=4,bs=[3,2],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=16,k=4,bs=[3,2],nr=[2,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=1,k=4,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=1,k=4,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=1,k=4,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=8,k=4,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=8,k=4,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=8,k=4,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=16,k=4,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=16,k=4,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=16,k=4,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=1,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=8,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=16,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=1,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=1,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=1,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=1,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=16,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=16,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=16,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=16,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=16,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=1,k=4,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=1,k=4,bs=[1,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=1,k=4,bs=[1,1],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=1,k=4,bs=[3,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=1,k=4,bs=[3,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=1,k=4,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=1,k=4,bs=[3,2],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=1,k=4,bs=[3,2],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=1,k=4,bs=[3,2],nr=[2,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=16,k=4,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=16,k=4,bs=[1,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=16,k=4,bs=[1,1],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=16,k=4,bs=[3,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=16,k=4,bs=[3,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=16,k=4,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=16,k=4,bs=[3,2],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=16,k=4,bs=[3,2],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=16,k=4,bs=[3,2],nr=[2,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=1,k=4,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=1,k=4,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=1,k=4,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=8,k=4,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=8,k=4,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=8,k=4,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=16,k=4,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=16,k=4,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=16,k=4,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=1,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=8,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=16,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=1,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=1,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=16,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=16,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=16,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=16,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=16,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=1,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=8,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=16,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=1,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=1,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=1,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=1,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=16,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=16,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=16,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=16,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=16,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=1,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=8,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=16,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=1,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=1,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=16,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=16,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=16,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=16,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=16,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=1,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=8,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=16,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=1,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=1,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=1,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=1,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=16,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=16,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=16,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=16,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=16,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=1,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=8,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=16,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=1,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=1,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=16,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=16,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=16,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=16,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=16,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=1,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=8,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=16,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=1,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=1,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=1,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=1,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=16,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=16,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=16,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=16,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=16,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=1,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=8,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=16,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=1,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=1,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=16,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=16,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=16,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=16,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=16,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=1,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=8,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=16,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=1,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=1,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=1,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=1,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=16,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=16,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=16,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=16,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=16,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=1,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=8,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=16,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=1,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=1,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=16,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=16,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=16,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=16,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=16,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=1,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=8,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=16,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=1,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=1,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=1,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=1,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=16,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=16,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=16,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=16,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=16,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=1,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=8,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=16,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=1,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=1,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=16,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=16,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=16,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=16,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=16,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=1,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=8,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=16,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=1,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=1,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=1,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=1,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=16,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=16,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=16,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=16,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=16,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=1,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=8,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=16,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=1,k=32,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q5_0,type_b=f32,m=16,n=1,k=32,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q5_0,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q5_1,type_b=f32,m=16,n=1,k=32,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q5_1,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=1,k=32,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q2_K,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q3_K,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q5_K,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=q6_K,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_xs,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq2_s,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq3_xxs,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq1_s,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq1_m,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq4_nl,type_b=f32,m=16,n=1,k=32,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq4_nl,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq3_s,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=iq4_xs,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=16,n=1,k=1,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=64,n=2,k=128,bs=[8,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=83,n=2,k=128,bs=[8,1],nr=[4,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=64,n=2,k=64,bs=[8,1],nr=[4,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=83,n=2,k=64,bs=[8,1],nr=[4,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=64,n=45,k=128,bs=[8,1],nr=[4,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=45,k=64,bs=[8,1],nr=[4,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=193,bs=[1,1],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=67,bs=[1,1],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=32,k=32,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=1,o=3","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=64,n=77,k=77,bs=[12,1],nr=[1,1],per=[0,1,2,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=128,bs=[1,1],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1056,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=128,bs=[1,1],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1056,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=128,bs=[1,1],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1056,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=129,bs=[1,1],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1057,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=129,bs=[1,1],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1057,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=129,bs=[1,1],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1057,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=128,bs=[1,1],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1056,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=128,bs=[1,1],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1056,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=128,bs=[1,1],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1056,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=129,bs=[1,1],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1057,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=129,bs=[1,1],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1057,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=129,bs=[1,1],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1057,bs=[1,1],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=128,bs=[1,1],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1056,bs=[1,1],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=128,bs=[1,1],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1056,bs=[1,1],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=128,bs=[1,1],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1056,bs=[1,1],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=129,bs=[1,1],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1057,bs=[1,1],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=129,bs=[1,1],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1057,bs=[1,1],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=129,bs=[1,1],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1057,bs=[1,1],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=128,bs=[1,1],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1056,bs=[1,1],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=128,bs=[1,1],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1056,bs=[1,1],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=128,bs=[1,1],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1056,bs=[1,1],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=129,bs=[1,1],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1057,bs=[1,1],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=129,bs=[1,1],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1057,bs=[1,1],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=129,bs=[1,1],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1057,bs=[1,1],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=128,bs=[2,1],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1056,bs=[2,1],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=128,bs=[2,1],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1056,bs=[2,1],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=128,bs=[2,1],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1056,bs=[2,1],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=129,bs=[2,1],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1057,bs=[2,1],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=129,bs=[2,1],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1057,bs=[2,1],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=129,bs=[2,1],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1057,bs=[2,1],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=128,bs=[2,1],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1056,bs=[2,1],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=128,bs=[2,1],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1056,bs=[2,1],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=128,bs=[2,1],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1056,bs=[2,1],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=129,bs=[2,1],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1057,bs=[2,1],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=129,bs=[2,1],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1057,bs=[2,1],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=129,bs=[2,1],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1057,bs=[2,1],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=128,bs=[2,1],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1056,bs=[2,1],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=128,bs=[2,1],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1056,bs=[2,1],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=128,bs=[2,1],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1056,bs=[2,1],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=129,bs=[2,1],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1057,bs=[2,1],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=129,bs=[2,1],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1057,bs=[2,1],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=129,bs=[2,1],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1057,bs=[2,1],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=128,bs=[2,1],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1056,bs=[2,1],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=128,bs=[2,1],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1056,bs=[2,1],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=128,bs=[2,1],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1056,bs=[2,1],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=129,bs=[2,1],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1057,bs=[2,1],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=129,bs=[2,1],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1057,bs=[2,1],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=129,bs=[2,1],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1057,bs=[2,1],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=128,bs=[4,1],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1056,bs=[4,1],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=128,bs=[4,1],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1056,bs=[4,1],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=128,bs=[4,1],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1056,bs=[4,1],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=129,bs=[4,1],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1057,bs=[4,1],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=129,bs=[4,1],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1057,bs=[4,1],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=129,bs=[4,1],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1057,bs=[4,1],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=128,bs=[4,1],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1056,bs=[4,1],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=128,bs=[4,1],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1056,bs=[4,1],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=128,bs=[4,1],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1056,bs=[4,1],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=129,bs=[4,1],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1057,bs=[4,1],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=129,bs=[4,1],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1057,bs=[4,1],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=129,bs=[4,1],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1057,bs=[4,1],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=128,bs=[4,1],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1056,bs=[4,1],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=128,bs=[4,1],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1056,bs=[4,1],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=128,bs=[4,1],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1056,bs=[4,1],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=129,bs=[4,1],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1057,bs=[4,1],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=129,bs=[4,1],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1057,bs=[4,1],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=129,bs=[4,1],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1057,bs=[4,1],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=128,bs=[4,1],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1056,bs=[4,1],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=128,bs=[4,1],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1056,bs=[4,1],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=128,bs=[4,1],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1056,bs=[4,1],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=129,bs=[4,1],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1057,bs=[4,1],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=129,bs=[4,1],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1057,bs=[4,1],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=129,bs=[4,1],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1057,bs=[4,1],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=128,bs=[8,1],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1056,bs=[8,1],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=128,bs=[8,1],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1056,bs=[8,1],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=128,bs=[8,1],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1056,bs=[8,1],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=129,bs=[8,1],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1057,bs=[8,1],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=129,bs=[8,1],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1057,bs=[8,1],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=129,bs=[8,1],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1057,bs=[8,1],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=128,bs=[8,1],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1056,bs=[8,1],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=128,bs=[8,1],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1056,bs=[8,1],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=128,bs=[8,1],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1056,bs=[8,1],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=129,bs=[8,1],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1057,bs=[8,1],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=129,bs=[8,1],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1057,bs=[8,1],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=129,bs=[8,1],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1057,bs=[8,1],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=128,bs=[8,1],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1056,bs=[8,1],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=128,bs=[8,1],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1056,bs=[8,1],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=128,bs=[8,1],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1056,bs=[8,1],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=129,bs=[8,1],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1057,bs=[8,1],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=129,bs=[8,1],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1057,bs=[8,1],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=129,bs=[8,1],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1057,bs=[8,1],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=128,bs=[8,1],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1056,bs=[8,1],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=128,bs=[8,1],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1056,bs=[8,1],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=128,bs=[8,1],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1056,bs=[8,1],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=129,bs=[8,1],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1057,bs=[8,1],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=129,bs=[8,1],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1057,bs=[8,1],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=129,bs=[8,1],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1057,bs=[8,1],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=128,bs=[1,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1056,bs=[1,3],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=128,bs=[1,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1056,bs=[1,3],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=128,bs=[1,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1056,bs=[1,3],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=129,bs=[1,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1057,bs=[1,3],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=129,bs=[1,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1057,bs=[1,3],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=129,bs=[1,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1057,bs=[1,3],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=128,bs=[1,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1056,bs=[1,3],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=128,bs=[1,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1056,bs=[1,3],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=128,bs=[1,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1056,bs=[1,3],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=129,bs=[1,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1057,bs=[1,3],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=129,bs=[1,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1057,bs=[1,3],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=129,bs=[1,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1057,bs=[1,3],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=128,bs=[1,3],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1056,bs=[1,3],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=128,bs=[1,3],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1056,bs=[1,3],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=128,bs=[1,3],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1056,bs=[1,3],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=129,bs=[1,3],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1057,bs=[1,3],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=129,bs=[1,3],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1057,bs=[1,3],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=129,bs=[1,3],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1057,bs=[1,3],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=128,bs=[1,3],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1056,bs=[1,3],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=128,bs=[1,3],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1056,bs=[1,3],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=128,bs=[1,3],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1056,bs=[1,3],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=129,bs=[1,3],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1057,bs=[1,3],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=129,bs=[1,3],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1057,bs=[1,3],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=129,bs=[1,3],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1057,bs=[1,3],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=128,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1056,bs=[2,3],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=128,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1056,bs=[2,3],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=128,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1056,bs=[2,3],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=129,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1057,bs=[2,3],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=129,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1057,bs=[2,3],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=129,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1057,bs=[2,3],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=128,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1056,bs=[2,3],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=128,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1056,bs=[2,3],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=128,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1056,bs=[2,3],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=129,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1057,bs=[2,3],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=129,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1057,bs=[2,3],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=129,bs=[2,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1057,bs=[2,3],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=128,bs=[2,3],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1056,bs=[2,3],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=128,bs=[2,3],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1056,bs=[2,3],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=128,bs=[2,3],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1056,bs=[2,3],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=129,bs=[2,3],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1057,bs=[2,3],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=129,bs=[2,3],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1057,bs=[2,3],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=129,bs=[2,3],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1057,bs=[2,3],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=128,bs=[2,3],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1056,bs=[2,3],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=128,bs=[2,3],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1056,bs=[2,3],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=128,bs=[2,3],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1056,bs=[2,3],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=129,bs=[2,3],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1057,bs=[2,3],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=129,bs=[2,3],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1057,bs=[2,3],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=129,bs=[2,3],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1057,bs=[2,3],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=128,bs=[4,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1056,bs=[4,3],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=128,bs=[4,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1056,bs=[4,3],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=128,bs=[4,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1056,bs=[4,3],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=129,bs=[4,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1057,bs=[4,3],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=129,bs=[4,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1057,bs=[4,3],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=129,bs=[4,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1057,bs=[4,3],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=128,bs=[4,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1056,bs=[4,3],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=128,bs=[4,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1056,bs=[4,3],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=128,bs=[4,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1056,bs=[4,3],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=129,bs=[4,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1057,bs=[4,3],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=129,bs=[4,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1057,bs=[4,3],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=129,bs=[4,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1057,bs=[4,3],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=128,bs=[4,3],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1056,bs=[4,3],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=128,bs=[4,3],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1056,bs=[4,3],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=128,bs=[4,3],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1056,bs=[4,3],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=129,bs=[4,3],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1057,bs=[4,3],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=129,bs=[4,3],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1057,bs=[4,3],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=129,bs=[4,3],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1057,bs=[4,3],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=128,bs=[4,3],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1056,bs=[4,3],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=128,bs=[4,3],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1056,bs=[4,3],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=128,bs=[4,3],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1056,bs=[4,3],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=129,bs=[4,3],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1057,bs=[4,3],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=129,bs=[4,3],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1057,bs=[4,3],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=129,bs=[4,3],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1057,bs=[4,3],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=128,bs=[8,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1056,bs=[8,3],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=128,bs=[8,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1056,bs=[8,3],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=128,bs=[8,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1056,bs=[8,3],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=129,bs=[8,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1057,bs=[8,3],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=129,bs=[8,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1057,bs=[8,3],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=129,bs=[8,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1057,bs=[8,3],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=128,bs=[8,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1056,bs=[8,3],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=128,bs=[8,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1056,bs=[8,3],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=128,bs=[8,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1056,bs=[8,3],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=129,bs=[8,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1057,bs=[8,3],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=129,bs=[8,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1057,bs=[8,3],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=129,bs=[8,3],nr=[1,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1057,bs=[8,3],nr=[1,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=128,bs=[8,3],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1056,bs=[8,3],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=128,bs=[8,3],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1056,bs=[8,3],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=128,bs=[8,3],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1056,bs=[8,3],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=129,bs=[8,3],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1057,bs=[8,3],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=129,bs=[8,3],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1057,bs=[8,3],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=129,bs=[8,3],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1057,bs=[8,3],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=128,bs=[8,3],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1056,bs=[8,3],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=128,bs=[8,3],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1056,bs=[8,3],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=128,bs=[8,3],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1056,bs=[8,3],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=129,bs=[8,3],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1057,bs=[8,3],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=129,bs=[8,3],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1057,bs=[8,3],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=129,bs=[8,3],nr=[4,1],per=[0,2,1,3],v=0,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1057,bs=[8,3],nr=[4,1],per=[0,1,2,3],v=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=16,n_used=16,b=0,m=32,n=1024,k=16,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=2,n_used=2,b=0,m=32,n=8192,k=64,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=16,n_used=16,b=0,m=50,n=200,k=64,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=16,n_used=16,b=1,m=32,n=1024,k=16,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=2,n_used=2,b=1,m=32,n=8192,k=64,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=16,n_used=16,b=1,m=50,n=200,k=64,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=1,n_used=1,b=0,m=8,n=16,k=1,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=16,n_used=16,b=0,m=32,n=32,k=32,o=3","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=1,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=1,b=0,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=1,b=0,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=1,b=0,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=1,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=1,b=0,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=8,n_used=1,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=8,n_used=1,b=0,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=8,n_used=1,b=0,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=8,n_used=1,b=0,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=8,n_used=1,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=8,n_used=1,b=0,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=8,n_used=1,b=1,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=8,n_used=1,b=1,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=8,n_used=1,b=1,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=8,n_used=1,b=1,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=8,n_used=1,b=1,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=8,n_used=1,b=1,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=8,n_used=2,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=8,n_used=2,b=0,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=8,n_used=2,b=0,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=8,n_used=2,b=0,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=8,n_used=2,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=8,n_used=2,b=0,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=8,n_used=2,b=1,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=8,n_used=2,b=1,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=8,n_used=2,b=1,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=8,n_used=2,b=1,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=8,n_used=2,b=1,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=8,n_used=2,b=1,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=8,n_used=4,b=1,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=8,n_used=4,b=1,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=8,n_used=4,b=1,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=8,n_used=4,b=1,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=8,n_used=4,b=1,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=8,n_used=4,b=1,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=4,n_used=1,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=4,n_used=1,b=0,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=4,n_used=1,b=0,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=4,n_used=1,b=0,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=4,n_used=1,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=4,n_used=1,b=0,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=8,n_used=1,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=8,n_used=1,b=0,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=8,n_used=1,b=0,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=8,n_used=1,b=0,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=8,n_used=1,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=8,n_used=1,b=0,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=8,n_used=1,b=1,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=8,n_used=1,b=1,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=8,n_used=1,b=1,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=8,n_used=1,b=1,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=8,n_used=1,b=1,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=8,n_used=1,b=1,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=8,n_used=2,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=8,n_used=2,b=0,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=8,n_used=2,b=0,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=8,n_used=2,b=0,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=8,n_used=2,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=8,n_used=2,b=0,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=8,n_used=2,b=1,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=8,n_used=2,b=1,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=8,n_used=2,b=1,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=8,n_used=2,b=1,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=8,n_used=2,b=1,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=8,n_used=2,b=1,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=8,n_used=4,b=1,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=8,n_used=4,b=1,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=8,n_used=4,b=1,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=8,n_used=4,b=1,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=8,n_used=4,b=1,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=8,n_used=4,b=1,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=4,n_used=1,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=4,n_used=1,b=0,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=4,n_used=1,b=0,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=4,n_used=1,b=0,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=4,n_used=1,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=4,n_used=1,b=0,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=8,n_used=1,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=8,n_used=1,b=0,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=8,n_used=1,b=0,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=8,n_used=1,b=0,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=8,n_used=1,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=8,n_used=1,b=0,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=8,n_used=1,b=1,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=8,n_used=1,b=1,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=8,n_used=1,b=1,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=8,n_used=1,b=1,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=8,n_used=1,b=1,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=8,n_used=1,b=1,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=8,n_used=2,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=8,n_used=2,b=0,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=8,n_used=2,b=0,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=8,n_used=2,b=0,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=8,n_used=2,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=8,n_used=2,b=0,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=8,n_used=2,b=1,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=8,n_used=2,b=1,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=8,n_used=2,b=1,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=8,n_used=2,b=1,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=8,n_used=2,b=1,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=8,n_used=2,b=1,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=8,n_used=4,b=1,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=8,n_used=4,b=1,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=8,n_used=4,b=1,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=8,n_used=4,b=1,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=8,n_used=4,b=1,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=8,n_used=4,b=1,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=4,n_used=1,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=4,n_used=1,b=0,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=4,n_used=1,b=0,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=4,n_used=1,b=0,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=4,n_used=1,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=4,n_used=1,b=0,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=8,n_used=1,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=8,n_used=1,b=0,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=8,n_used=1,b=0,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=8,n_used=1,b=0,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=8,n_used=1,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=8,n_used=1,b=0,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=8,n_used=1,b=1,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=8,n_used=1,b=1,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=8,n_used=1,b=1,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=8,n_used=1,b=1,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=8,n_used=1,b=1,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=8,n_used=1,b=1,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=8,n_used=2,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=8,n_used=2,b=0,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=8,n_used=2,b=0,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=8,n_used=2,b=0,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=8,n_used=2,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=8,n_used=2,b=0,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=8,n_used=2,b=1,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=8,n_used=2,b=1,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=8,n_used=2,b=1,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=8,n_used=2,b=1,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=8,n_used=2,b=1,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=8,n_used=2,b=1,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=8,n_used=4,b=1,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=8,n_used=4,b=1,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=8,n_used=4,b=1,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=8,n_used=4,b=1,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=8,n_used=4,b=1,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_0,type_b=f32,n_mats=8,n_used=4,b=1,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=4,n_used=1,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=4,n_used=1,b=0,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=4,n_used=1,b=0,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=4,n_used=1,b=0,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=4,n_used=1,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=4,n_used=1,b=0,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=8,n_used=1,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=8,n_used=1,b=0,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=8,n_used=1,b=0,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=8,n_used=1,b=0,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=8,n_used=1,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=8,n_used=1,b=0,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=8,n_used=1,b=1,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=8,n_used=1,b=1,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=8,n_used=1,b=1,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=8,n_used=1,b=1,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=8,n_used=1,b=1,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=8,n_used=1,b=1,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=8,n_used=2,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=8,n_used=2,b=0,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=8,n_used=2,b=0,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=8,n_used=2,b=0,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=8,n_used=2,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=8,n_used=2,b=0,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=8,n_used=2,b=1,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=8,n_used=2,b=1,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=8,n_used=2,b=1,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=8,n_used=2,b=1,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=8,n_used=2,b=1,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=8,n_used=2,b=1,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=8,n_used=4,b=1,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=8,n_used=4,b=1,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=8,n_used=4,b=1,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=8,n_used=4,b=1,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=8,n_used=4,b=1,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=8,n_used=4,b=1,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=4,n_used=1,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=4,n_used=1,b=0,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=4,n_used=1,b=0,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=4,n_used=1,b=0,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=4,n_used=1,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=4,n_used=1,b=0,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=8,n_used=1,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=8,n_used=1,b=0,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=8,n_used=1,b=0,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=8,n_used=1,b=0,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=8,n_used=1,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=8,n_used=1,b=0,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=8,n_used=1,b=1,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=8,n_used=1,b=1,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=8,n_used=1,b=1,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=8,n_used=1,b=1,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=8,n_used=1,b=1,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=8,n_used=1,b=1,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=8,n_used=2,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=8,n_used=2,b=0,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=8,n_used=2,b=0,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=8,n_used=2,b=0,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=8,n_used=2,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=8,n_used=2,b=0,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=8,n_used=2,b=1,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=8,n_used=2,b=1,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=8,n_used=2,b=1,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=8,n_used=2,b=1,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=8,n_used=2,b=1,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=8,n_used=2,b=1,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=8,n_used=4,b=1,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=8,n_used=4,b=1,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=8,n_used=4,b=1,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=8,n_used=4,b=1,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=8,n_used=4,b=1,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=8,n_used=4,b=1,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=4,n_used=1,b=0,m=512,n=1,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=4,n_used=1,b=0,m=512,n=4,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=4,n_used=1,b=0,m=512,n=5,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=4,n_used=1,b=0,m=512,n=17,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=4,n_used=1,b=0,m=512,n=32,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=4,n_used=1,b=0,m=512,n=129,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=1,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=4,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=5,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=17,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=32,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=129,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=1,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=4,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=5,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=17,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=32,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=129,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=1,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=4,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=5,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=17,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=32,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=129,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=1,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=4,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=5,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=17,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=32,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=129,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=1,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=4,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=5,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=17,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=32,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=129,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=8,n_used=1,b=0,m=512,n=1,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=8,n_used=1,b=0,m=512,n=4,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=8,n_used=1,b=0,m=512,n=5,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=8,n_used=1,b=0,m=512,n=17,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=8,n_used=1,b=0,m=512,n=32,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=8,n_used=1,b=0,m=512,n=129,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=8,n_used=1,b=1,m=512,n=1,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=8,n_used=1,b=1,m=512,n=4,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=8,n_used=1,b=1,m=512,n=5,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=8,n_used=1,b=1,m=512,n=17,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=8,n_used=1,b=1,m=512,n=32,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=8,n_used=1,b=1,m=512,n=129,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=8,n_used=2,b=0,m=512,n=1,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=8,n_used=2,b=0,m=512,n=4,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=8,n_used=2,b=0,m=512,n=5,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=8,n_used=2,b=0,m=512,n=17,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=8,n_used=2,b=0,m=512,n=32,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=8,n_used=2,b=0,m=512,n=129,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=8,n_used=2,b=1,m=512,n=1,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=8,n_used=2,b=1,m=512,n=4,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=8,n_used=2,b=1,m=512,n=5,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=8,n_used=2,b=1,m=512,n=17,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=8,n_used=2,b=1,m=512,n=32,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=8,n_used=2,b=1,m=512,n=129,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=1,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=4,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=5,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=17,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=32,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=129,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=8,n_used=4,b=1,m=512,n=1,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=8,n_used=4,b=1,m=512,n=4,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=8,n_used=4,b=1,m=512,n=5,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=8,n_used=4,b=1,m=512,n=17,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=8,n_used=4,b=1,m=512,n=32,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=8,n_used=4,b=1,m=512,n=129,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=1,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=1,b=0,m=512,n=4,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=1,b=0,m=512,n=5,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=1,b=0,m=512,n=17,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=1,b=0,m=512,n=32,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=1,b=0,m=512,n=129,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=4,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=5,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=17,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=32,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=129,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=4,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=5,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=17,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=32,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=129,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=4,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=5,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=17,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=32,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=129,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=1,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=1,b=0,m=512,n=4,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=1,b=0,m=512,n=5,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=1,b=0,m=512,n=17,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=1,b=0,m=512,n=32,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=1,b=0,m=512,n=129,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=1,b=1,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=1,b=1,m=512,n=4,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=1,b=1,m=512,n=5,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=1,b=1,m=512,n=17,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=1,b=1,m=512,n=32,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=1,b=1,m=512,n=129,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=2,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=2,b=0,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=2,b=0,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=2,b=0,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=2,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=2,b=0,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=2,b=1,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=2,b=1,m=512,n=4,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=2,b=1,m=512,n=5,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=2,b=1,m=512,n=17,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=2,b=1,m=512,n=32,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=2,b=1,m=512,n=129,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=4,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=5,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=17,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=129,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=4,b=1,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=4,b=1,m=512,n=4,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=4,b=1,m=512,n=5,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=4,b=1,m=512,n=17,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=4,b=1,m=512,n=32,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=4,b=1,m=512,n=129,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q5_0,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q5_0,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q5_1,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q5_1,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q2_K,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q2_K,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q3_K,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q3_K,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q5_K,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q5_K,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q6_K,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=q6_K,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xs,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_xs,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_s,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq2_s,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq3_xxs,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq3_xxs,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq1_s,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq1_s,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq1_m,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq1_m,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq4_nl,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq4_nl,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq3_s,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq3_s,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq4_xs,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=1,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=iq4_xs,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=32,k=256,o=1","support","1","yes","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=bf16,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=1,k=256,o=1","support","0","no","SYCL"
-"SYCL0","MUL_MAT_ID","type_a=bf16,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=32,k=256,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=2,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=3,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=4,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=5,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=6,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=7,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=8,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=9,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=2,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=3,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=4,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=5,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=6,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=7,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=8,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=9,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=16,n=2,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=16,n=3,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=16,n=4,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=16,n=5,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=16,n=6,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=16,n=7,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=16,n=8,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=16,n=9,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=2,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=3,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=4,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=5,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=6,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=7,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=8,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=9,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=2,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=3,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=4,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=5,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=6,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=7,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=8,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=9,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q5_0,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q5_0,type_b=f32,m=16,n=2,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q5_0,type_b=f32,m=16,n=3,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q5_0,type_b=f32,m=16,n=4,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q5_0,type_b=f32,m=16,n=5,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q5_0,type_b=f32,m=16,n=6,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q5_0,type_b=f32,m=16,n=7,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q5_0,type_b=f32,m=16,n=8,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q5_0,type_b=f32,m=16,n=9,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q5_1,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q5_1,type_b=f32,m=16,n=2,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q5_1,type_b=f32,m=16,n=3,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q5_1,type_b=f32,m=16,n=4,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q5_1,type_b=f32,m=16,n=5,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q5_1,type_b=f32,m=16,n=6,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q5_1,type_b=f32,m=16,n=7,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q5_1,type_b=f32,m=16,n=8,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q5_1,type_b=f32,m=16,n=9,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=2,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=3,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=4,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=5,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=6,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=7,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=8,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=9,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=2,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=3,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=4,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=5,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=6,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=7,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=8,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=9,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q2_K,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q2_K,type_b=f32,m=16,n=2,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q2_K,type_b=f32,m=16,n=3,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q2_K,type_b=f32,m=16,n=4,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q2_K,type_b=f32,m=16,n=5,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q2_K,type_b=f32,m=16,n=6,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q2_K,type_b=f32,m=16,n=7,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q2_K,type_b=f32,m=16,n=8,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q2_K,type_b=f32,m=16,n=9,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q3_K,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q3_K,type_b=f32,m=16,n=2,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q3_K,type_b=f32,m=16,n=3,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q3_K,type_b=f32,m=16,n=4,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q3_K,type_b=f32,m=16,n=5,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q3_K,type_b=f32,m=16,n=6,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q3_K,type_b=f32,m=16,n=7,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q3_K,type_b=f32,m=16,n=8,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q3_K,type_b=f32,m=16,n=9,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=2,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=3,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=4,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=5,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=6,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=7,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=8,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=9,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q5_K,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q5_K,type_b=f32,m=16,n=2,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q5_K,type_b=f32,m=16,n=3,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q5_K,type_b=f32,m=16,n=4,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q5_K,type_b=f32,m=16,n=5,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q5_K,type_b=f32,m=16,n=6,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q5_K,type_b=f32,m=16,n=7,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q5_K,type_b=f32,m=16,n=8,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q5_K,type_b=f32,m=16,n=9,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q6_K,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q6_K,type_b=f32,m=16,n=2,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q6_K,type_b=f32,m=16,n=3,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q6_K,type_b=f32,m=16,n=4,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q6_K,type_b=f32,m=16,n=5,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q6_K,type_b=f32,m=16,n=6,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q6_K,type_b=f32,m=16,n=7,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q6_K,type_b=f32,m=16,n=8,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q6_K,type_b=f32,m=16,n=9,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=2,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=3,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=4,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=5,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=6,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=7,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=8,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=9,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xs,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xs,type_b=f32,m=16,n=2,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xs,type_b=f32,m=16,n=3,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xs,type_b=f32,m=16,n=4,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xs,type_b=f32,m=16,n=5,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xs,type_b=f32,m=16,n=6,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xs,type_b=f32,m=16,n=7,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xs,type_b=f32,m=16,n=8,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xs,type_b=f32,m=16,n=9,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_s,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_s,type_b=f32,m=16,n=2,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_s,type_b=f32,m=16,n=3,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_s,type_b=f32,m=16,n=4,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_s,type_b=f32,m=16,n=5,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_s,type_b=f32,m=16,n=6,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_s,type_b=f32,m=16,n=7,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_s,type_b=f32,m=16,n=8,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_s,type_b=f32,m=16,n=9,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq3_xxs,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq3_xxs,type_b=f32,m=16,n=2,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq3_xxs,type_b=f32,m=16,n=3,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq3_xxs,type_b=f32,m=16,n=4,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq3_xxs,type_b=f32,m=16,n=5,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq3_xxs,type_b=f32,m=16,n=6,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq3_xxs,type_b=f32,m=16,n=7,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq3_xxs,type_b=f32,m=16,n=8,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq3_xxs,type_b=f32,m=16,n=9,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq1_s,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq1_s,type_b=f32,m=16,n=2,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq1_s,type_b=f32,m=16,n=3,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq1_s,type_b=f32,m=16,n=4,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq1_s,type_b=f32,m=16,n=5,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq1_s,type_b=f32,m=16,n=6,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq1_s,type_b=f32,m=16,n=7,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq1_s,type_b=f32,m=16,n=8,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq1_s,type_b=f32,m=16,n=9,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq1_m,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq1_m,type_b=f32,m=16,n=2,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq1_m,type_b=f32,m=16,n=3,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq1_m,type_b=f32,m=16,n=4,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq1_m,type_b=f32,m=16,n=5,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq1_m,type_b=f32,m=16,n=6,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq1_m,type_b=f32,m=16,n=7,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq1_m,type_b=f32,m=16,n=8,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq1_m,type_b=f32,m=16,n=9,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq4_nl,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq4_nl,type_b=f32,m=16,n=2,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq4_nl,type_b=f32,m=16,n=3,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq4_nl,type_b=f32,m=16,n=4,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq4_nl,type_b=f32,m=16,n=5,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq4_nl,type_b=f32,m=16,n=6,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq4_nl,type_b=f32,m=16,n=7,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq4_nl,type_b=f32,m=16,n=8,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq4_nl,type_b=f32,m=16,n=9,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq3_s,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq3_s,type_b=f32,m=16,n=2,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq3_s,type_b=f32,m=16,n=3,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq3_s,type_b=f32,m=16,n=4,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq3_s,type_b=f32,m=16,n=5,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq3_s,type_b=f32,m=16,n=6,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq3_s,type_b=f32,m=16,n=7,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq3_s,type_b=f32,m=16,n=8,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq3_s,type_b=f32,m=16,n=9,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq4_xs,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq4_xs,type_b=f32,m=16,n=2,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq4_xs,type_b=f32,m=16,n=3,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq4_xs,type_b=f32,m=16,n=4,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq4_xs,type_b=f32,m=16,n=5,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq4_xs,type_b=f32,m=16,n=6,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq4_xs,type_b=f32,m=16,n=7,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq4_xs,type_b=f32,m=16,n=8,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq4_xs,type_b=f32,m=16,n=9,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=1,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=1,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=16,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=16,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=16,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=16,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=16,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=1,k=4,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=1,k=4,bs=[1,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=1,k=4,bs=[1,1],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=1,k=4,bs=[3,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=1,k=4,bs=[3,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=1,k=4,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=1,k=4,bs=[3,2],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=1,k=4,bs=[3,2],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=1,k=4,bs=[3,2],nr=[2,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=16,k=4,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=16,k=4,bs=[1,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=16,k=4,bs=[1,1],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=16,k=4,bs=[3,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=16,k=4,bs=[3,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=16,k=4,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=16,k=4,bs=[3,2],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=16,k=4,bs=[3,2],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=16,k=4,bs=[3,2],nr=[2,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=1,k=4,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=1,k=4,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=1,k=4,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=8,k=4,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=8,k=4,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=8,k=4,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=16,k=4,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=16,k=4,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=16,k=4,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=1,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=8,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=16,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=16,n=8,k=256,bs=[1536,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=1,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=1,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=1,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=1,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=16,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=16,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=16,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=16,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=16,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=1,k=4,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=1,k=4,bs=[1,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=1,k=4,bs=[1,1],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=1,k=4,bs=[3,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=1,k=4,bs=[3,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=1,k=4,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=1,k=4,bs=[3,2],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=1,k=4,bs=[3,2],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=1,k=4,bs=[3,2],nr=[2,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=16,k=4,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=16,k=4,bs=[1,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=16,k=4,bs=[1,1],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=16,k=4,bs=[3,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=16,k=4,bs=[3,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=16,k=4,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=16,k=4,bs=[3,2],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=16,k=4,bs=[3,2],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=16,k=4,bs=[3,2],nr=[2,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=1,k=4,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=1,k=4,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=1,k=4,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=8,k=4,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=8,k=4,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=8,k=4,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=16,k=4,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=16,k=4,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=16,k=4,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=1,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=8,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=16,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f16,m=16,n=8,k=256,bs=[1536,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=1,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=1,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=16,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=16,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=16,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=16,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=16,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=1,k=4,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=1,k=4,bs=[1,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=1,k=4,bs=[1,1],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=1,k=4,bs=[3,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=1,k=4,bs=[3,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=1,k=4,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=1,k=4,bs=[3,2],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=1,k=4,bs=[3,2],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=1,k=4,bs=[3,2],nr=[2,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=16,k=4,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=16,k=4,bs=[1,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=16,k=4,bs=[1,1],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=16,k=4,bs=[3,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=16,k=4,bs=[3,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=16,k=4,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=16,k=4,bs=[3,2],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=16,k=4,bs=[3,2],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=16,k=4,bs=[3,2],nr=[2,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=1,k=4,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=1,k=4,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=1,k=4,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=8,k=4,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=8,k=4,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=8,k=4,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=16,k=4,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=16,k=4,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=16,k=4,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=1,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=8,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=16,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=16,n=8,k=256,bs=[1536,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=1,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=1,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=1,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=1,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=16,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=16,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=16,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=16,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=16,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=1,k=4,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=1,k=4,bs=[1,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=1,k=4,bs=[1,1],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=1,k=4,bs=[3,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=1,k=4,bs=[3,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=1,k=4,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=1,k=4,bs=[3,2],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=1,k=4,bs=[3,2],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=1,k=4,bs=[3,2],nr=[2,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=16,k=4,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=16,k=4,bs=[1,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=16,k=4,bs=[1,1],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=16,k=4,bs=[3,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=16,k=4,bs=[3,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=16,k=4,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=16,k=4,bs=[3,2],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=16,k=4,bs=[3,2],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=16,k=4,bs=[3,2],nr=[2,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=1,k=4,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=1,k=4,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=1,k=4,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=8,k=4,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=8,k=4,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=8,k=4,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=16,k=4,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=16,k=4,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=16,k=4,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=1,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=8,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=16,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f16,m=16,n=8,k=256,bs=[1536,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=1,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=1,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=16,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=16,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=16,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=16,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=16,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=1,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=8,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=16,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=8,k=256,bs=[1536,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=1,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=1,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=1,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=1,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=16,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=16,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=16,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=16,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=16,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=1,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=8,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=16,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f16,m=16,n=8,k=256,bs=[1536,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=1,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=1,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=16,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=16,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=16,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=16,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=16,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=1,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=8,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=16,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=16,n=8,k=256,bs=[1536,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=1,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=1,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=1,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=1,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=16,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=16,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=16,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=16,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=16,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=1,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=8,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=16,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f16,m=16,n=8,k=256,bs=[1536,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=1,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=1,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=16,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=16,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=16,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=16,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=16,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=1,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=8,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=16,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=8,k=256,bs=[1536,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=1,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=1,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=1,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=1,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=16,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=16,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=16,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=16,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=16,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=1,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=8,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=16,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f16,m=16,n=8,k=256,bs=[1536,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=1,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=1,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=16,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=16,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=16,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=16,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=16,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=1,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=8,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=16,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f32,m=16,n=8,k=256,bs=[1536,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=1,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=1,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=1,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=1,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=16,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=16,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=16,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=16,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=16,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=1,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=8,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=16,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_K,type_b=f16,m=16,n=8,k=256,bs=[1536,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=1,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=1,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=16,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=16,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=16,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=16,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=16,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=1,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=8,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=16,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f32,m=16,n=8,k=256,bs=[1536,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=1,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=1,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=1,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=1,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=16,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=16,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=16,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=16,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=16,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=1,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=8,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=16,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=mxfp4,type_b=f16,m=16,n=8,k=256,bs=[1536,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=1,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=1,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=1,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=16,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=16,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=16,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=16,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=16,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=16,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=1,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=8,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=16,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f32,m=16,n=8,k=256,bs=[1536,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=1,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=1,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=1,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=1,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=1,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=16,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=16,k=256,bs=[1,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=16,k=256,bs=[1,1],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=16,k=256,bs=[3,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=16,k=256,bs=[3,1],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[2,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[1,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=16,k=256,bs=[3,2],nr=[2,2],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=1,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=8,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,1,3,2],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=16,k=256,bs=[2,3],nr=[1,1],per=[0,3,2,1],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=1,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=8,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=16,k=1024,bs=[3,2],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xxs,type_b=f16,m=16,n=8,k=256,bs=[1536,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=1,k=32,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_1,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q5_0,type_b=f32,m=16,n=1,k=32,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q5_0,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q5_1,type_b=f32,m=16,n=1,k=32,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q5_1,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=1,k=32,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q8_0,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q2_K,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q3_K,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q5_K,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q6_K,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_xs,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq2_s,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq3_xxs,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq1_s,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq1_m,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq4_nl,type_b=f32,m=16,n=1,k=32,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq4_nl,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq3_s,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=iq4_xs,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=16,n=1,k=1,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=16,n=1,k=256,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=64,n=2,k=128,bs=[8,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=83,n=2,k=128,bs=[8,1],nr=[4,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=64,n=2,k=64,bs=[8,1],nr=[4,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=83,n=2,k=64,bs=[8,1],nr=[4,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=64,n=45,k=128,bs=[8,1],nr=[4,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=45,k=64,bs=[8,1],nr=[4,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=193,bs=[1,1],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=67,bs=[1,1],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=64,n=77,k=77,bs=[12,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=q4_0,type_b=f32,m=576,n=512,k=576,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=128,bs=[1,1],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1056,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=128,bs=[1,1],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1056,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=2112,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=128,bs=[1,1],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1056,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=129,bs=[1,1],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1057,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=129,bs=[1,1],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1057,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=2113,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=129,bs=[1,1],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1057,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=128,bs=[1,1],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1056,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=128,bs=[1,1],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1056,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=2112,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=128,bs=[1,1],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1056,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=129,bs=[1,1],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1057,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=129,bs=[1,1],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1057,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=2113,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=129,bs=[1,1],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1057,bs=[1,1],nr=[1,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=128,bs=[1,1],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1056,bs=[1,1],nr=[4,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=128,bs=[1,1],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1056,bs=[1,1],nr=[4,1],per=[0,1,2,3],k_v=2112,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=128,bs=[1,1],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1056,bs=[1,1],nr=[4,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=129,bs=[1,1],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1057,bs=[1,1],nr=[4,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=129,bs=[1,1],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1057,bs=[1,1],nr=[4,1],per=[0,1,2,3],k_v=2113,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=129,bs=[1,1],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1057,bs=[1,1],nr=[4,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=128,bs=[1,1],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1056,bs=[1,1],nr=[4,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=128,bs=[1,1],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1056,bs=[1,1],nr=[4,1],per=[0,1,2,3],k_v=2112,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=128,bs=[1,1],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1056,bs=[1,1],nr=[4,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=129,bs=[1,1],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1057,bs=[1,1],nr=[4,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=129,bs=[1,1],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1057,bs=[1,1],nr=[4,1],per=[0,1,2,3],k_v=2113,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=129,bs=[1,1],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1057,bs=[1,1],nr=[4,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=128,bs=[2,1],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1056,bs=[2,1],nr=[1,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=128,bs=[2,1],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1056,bs=[2,1],nr=[1,1],per=[0,1,2,3],k_v=2112,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=128,bs=[2,1],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1056,bs=[2,1],nr=[1,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=129,bs=[2,1],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1057,bs=[2,1],nr=[1,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=129,bs=[2,1],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1057,bs=[2,1],nr=[1,1],per=[0,1,2,3],k_v=2113,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=129,bs=[2,1],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1057,bs=[2,1],nr=[1,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=128,bs=[2,1],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1056,bs=[2,1],nr=[1,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=128,bs=[2,1],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1056,bs=[2,1],nr=[1,1],per=[0,1,2,3],k_v=2112,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=128,bs=[2,1],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1056,bs=[2,1],nr=[1,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=129,bs=[2,1],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1057,bs=[2,1],nr=[1,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=129,bs=[2,1],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1057,bs=[2,1],nr=[1,1],per=[0,1,2,3],k_v=2113,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=129,bs=[2,1],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1057,bs=[2,1],nr=[1,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=128,bs=[2,1],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1056,bs=[2,1],nr=[4,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=128,bs=[2,1],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1056,bs=[2,1],nr=[4,1],per=[0,1,2,3],k_v=2112,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=128,bs=[2,1],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1056,bs=[2,1],nr=[4,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=129,bs=[2,1],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1057,bs=[2,1],nr=[4,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=129,bs=[2,1],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1057,bs=[2,1],nr=[4,1],per=[0,1,2,3],k_v=2113,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=129,bs=[2,1],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1057,bs=[2,1],nr=[4,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=128,bs=[2,1],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1056,bs=[2,1],nr=[4,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=128,bs=[2,1],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1056,bs=[2,1],nr=[4,1],per=[0,1,2,3],k_v=2112,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=128,bs=[2,1],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1056,bs=[2,1],nr=[4,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=129,bs=[2,1],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1057,bs=[2,1],nr=[4,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=129,bs=[2,1],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1057,bs=[2,1],nr=[4,1],per=[0,1,2,3],k_v=2113,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=129,bs=[2,1],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1057,bs=[2,1],nr=[4,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=128,bs=[4,1],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1056,bs=[4,1],nr=[1,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=128,bs=[4,1],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1056,bs=[4,1],nr=[1,1],per=[0,1,2,3],k_v=2112,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=128,bs=[4,1],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1056,bs=[4,1],nr=[1,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=129,bs=[4,1],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1057,bs=[4,1],nr=[1,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=129,bs=[4,1],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1057,bs=[4,1],nr=[1,1],per=[0,1,2,3],k_v=2113,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=129,bs=[4,1],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1057,bs=[4,1],nr=[1,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=128,bs=[4,1],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1056,bs=[4,1],nr=[1,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=128,bs=[4,1],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1056,bs=[4,1],nr=[1,1],per=[0,1,2,3],k_v=2112,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=128,bs=[4,1],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1056,bs=[4,1],nr=[1,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=129,bs=[4,1],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1057,bs=[4,1],nr=[1,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=129,bs=[4,1],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1057,bs=[4,1],nr=[1,1],per=[0,1,2,3],k_v=2113,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=129,bs=[4,1],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1057,bs=[4,1],nr=[1,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=128,bs=[4,1],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1056,bs=[4,1],nr=[4,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=128,bs=[4,1],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1056,bs=[4,1],nr=[4,1],per=[0,1,2,3],k_v=2112,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=128,bs=[4,1],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1056,bs=[4,1],nr=[4,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=129,bs=[4,1],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1057,bs=[4,1],nr=[4,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=129,bs=[4,1],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1057,bs=[4,1],nr=[4,1],per=[0,1,2,3],k_v=2113,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=129,bs=[4,1],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1057,bs=[4,1],nr=[4,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=128,bs=[4,1],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1056,bs=[4,1],nr=[4,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=128,bs=[4,1],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1056,bs=[4,1],nr=[4,1],per=[0,1,2,3],k_v=2112,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=128,bs=[4,1],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1056,bs=[4,1],nr=[4,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=129,bs=[4,1],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1057,bs=[4,1],nr=[4,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=129,bs=[4,1],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1057,bs=[4,1],nr=[4,1],per=[0,1,2,3],k_v=2113,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=129,bs=[4,1],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1057,bs=[4,1],nr=[4,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=128,bs=[8,1],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1056,bs=[8,1],nr=[1,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=128,bs=[8,1],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1056,bs=[8,1],nr=[1,1],per=[0,1,2,3],k_v=2112,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=128,bs=[8,1],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1056,bs=[8,1],nr=[1,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=129,bs=[8,1],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1057,bs=[8,1],nr=[1,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=129,bs=[8,1],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1057,bs=[8,1],nr=[1,1],per=[0,1,2,3],k_v=2113,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=129,bs=[8,1],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1057,bs=[8,1],nr=[1,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=128,bs=[8,1],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1056,bs=[8,1],nr=[1,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=128,bs=[8,1],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1056,bs=[8,1],nr=[1,1],per=[0,1,2,3],k_v=2112,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=128,bs=[8,1],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1056,bs=[8,1],nr=[1,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=129,bs=[8,1],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1057,bs=[8,1],nr=[1,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=129,bs=[8,1],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1057,bs=[8,1],nr=[1,1],per=[0,1,2,3],k_v=2113,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=129,bs=[8,1],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1057,bs=[8,1],nr=[1,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=128,bs=[8,1],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1056,bs=[8,1],nr=[4,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=128,bs=[8,1],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1056,bs=[8,1],nr=[4,1],per=[0,1,2,3],k_v=2112,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=128,bs=[8,1],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1056,bs=[8,1],nr=[4,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=129,bs=[8,1],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1057,bs=[8,1],nr=[4,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=129,bs=[8,1],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1057,bs=[8,1],nr=[4,1],per=[0,1,2,3],k_v=2113,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=129,bs=[8,1],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1057,bs=[8,1],nr=[4,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=128,bs=[8,1],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1056,bs=[8,1],nr=[4,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=128,bs=[8,1],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1056,bs=[8,1],nr=[4,1],per=[0,1,2,3],k_v=2112,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=128,bs=[8,1],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1056,bs=[8,1],nr=[4,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=129,bs=[8,1],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1057,bs=[8,1],nr=[4,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=129,bs=[8,1],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1057,bs=[8,1],nr=[4,1],per=[0,1,2,3],k_v=2113,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=129,bs=[8,1],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1057,bs=[8,1],nr=[4,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=128,bs=[1,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1056,bs=[1,3],nr=[1,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=128,bs=[1,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1056,bs=[1,3],nr=[1,1],per=[0,1,2,3],k_v=2112,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=128,bs=[1,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1056,bs=[1,3],nr=[1,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=129,bs=[1,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1057,bs=[1,3],nr=[1,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=129,bs=[1,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1057,bs=[1,3],nr=[1,1],per=[0,1,2,3],k_v=2113,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=129,bs=[1,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1057,bs=[1,3],nr=[1,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=128,bs=[1,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1056,bs=[1,3],nr=[1,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=128,bs=[1,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1056,bs=[1,3],nr=[1,1],per=[0,1,2,3],k_v=2112,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=128,bs=[1,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1056,bs=[1,3],nr=[1,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=129,bs=[1,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1057,bs=[1,3],nr=[1,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=129,bs=[1,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1057,bs=[1,3],nr=[1,1],per=[0,1,2,3],k_v=2113,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=129,bs=[1,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1057,bs=[1,3],nr=[1,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=128,bs=[1,3],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1056,bs=[1,3],nr=[4,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=128,bs=[1,3],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1056,bs=[1,3],nr=[4,1],per=[0,1,2,3],k_v=2112,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=128,bs=[1,3],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1056,bs=[1,3],nr=[4,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=129,bs=[1,3],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1057,bs=[1,3],nr=[4,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=129,bs=[1,3],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1057,bs=[1,3],nr=[4,1],per=[0,1,2,3],k_v=2113,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=129,bs=[1,3],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1057,bs=[1,3],nr=[4,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=128,bs=[1,3],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1056,bs=[1,3],nr=[4,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=128,bs=[1,3],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1056,bs=[1,3],nr=[4,1],per=[0,1,2,3],k_v=2112,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=128,bs=[1,3],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1056,bs=[1,3],nr=[4,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=129,bs=[1,3],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1057,bs=[1,3],nr=[4,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=129,bs=[1,3],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1057,bs=[1,3],nr=[4,1],per=[0,1,2,3],k_v=2113,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=129,bs=[1,3],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1057,bs=[1,3],nr=[4,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=128,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1056,bs=[2,3],nr=[1,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=128,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1056,bs=[2,3],nr=[1,1],per=[0,1,2,3],k_v=2112,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=128,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1056,bs=[2,3],nr=[1,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=129,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1057,bs=[2,3],nr=[1,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=129,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1057,bs=[2,3],nr=[1,1],per=[0,1,2,3],k_v=2113,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=129,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1057,bs=[2,3],nr=[1,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=128,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1056,bs=[2,3],nr=[1,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=128,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1056,bs=[2,3],nr=[1,1],per=[0,1,2,3],k_v=2112,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=128,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1056,bs=[2,3],nr=[1,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=129,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1057,bs=[2,3],nr=[1,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=129,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1057,bs=[2,3],nr=[1,1],per=[0,1,2,3],k_v=2113,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=129,bs=[2,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1057,bs=[2,3],nr=[1,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=128,bs=[2,3],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1056,bs=[2,3],nr=[4,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=128,bs=[2,3],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1056,bs=[2,3],nr=[4,1],per=[0,1,2,3],k_v=2112,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=128,bs=[2,3],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1056,bs=[2,3],nr=[4,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=129,bs=[2,3],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1057,bs=[2,3],nr=[4,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=129,bs=[2,3],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1057,bs=[2,3],nr=[4,1],per=[0,1,2,3],k_v=2113,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=129,bs=[2,3],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1057,bs=[2,3],nr=[4,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=128,bs=[2,3],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1056,bs=[2,3],nr=[4,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=128,bs=[2,3],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1056,bs=[2,3],nr=[4,1],per=[0,1,2,3],k_v=2112,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=128,bs=[2,3],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1056,bs=[2,3],nr=[4,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=129,bs=[2,3],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1057,bs=[2,3],nr=[4,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=129,bs=[2,3],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1057,bs=[2,3],nr=[4,1],per=[0,1,2,3],k_v=2113,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=129,bs=[2,3],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1057,bs=[2,3],nr=[4,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=128,bs=[4,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1056,bs=[4,3],nr=[1,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=128,bs=[4,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1056,bs=[4,3],nr=[1,1],per=[0,1,2,3],k_v=2112,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=128,bs=[4,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1056,bs=[4,3],nr=[1,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=129,bs=[4,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1057,bs=[4,3],nr=[1,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=129,bs=[4,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1057,bs=[4,3],nr=[1,1],per=[0,1,2,3],k_v=2113,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=129,bs=[4,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1057,bs=[4,3],nr=[1,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=128,bs=[4,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1056,bs=[4,3],nr=[1,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=128,bs=[4,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1056,bs=[4,3],nr=[1,1],per=[0,1,2,3],k_v=2112,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=128,bs=[4,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1056,bs=[4,3],nr=[1,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=129,bs=[4,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1057,bs=[4,3],nr=[1,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=129,bs=[4,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1057,bs=[4,3],nr=[1,1],per=[0,1,2,3],k_v=2113,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=129,bs=[4,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1057,bs=[4,3],nr=[1,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=128,bs=[4,3],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1056,bs=[4,3],nr=[4,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=128,bs=[4,3],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1056,bs=[4,3],nr=[4,1],per=[0,1,2,3],k_v=2112,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=128,bs=[4,3],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1056,bs=[4,3],nr=[4,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=129,bs=[4,3],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1057,bs=[4,3],nr=[4,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=129,bs=[4,3],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1057,bs=[4,3],nr=[4,1],per=[0,1,2,3],k_v=2113,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=129,bs=[4,3],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1057,bs=[4,3],nr=[4,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=128,bs=[4,3],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1056,bs=[4,3],nr=[4,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=128,bs=[4,3],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1056,bs=[4,3],nr=[4,1],per=[0,1,2,3],k_v=2112,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=128,bs=[4,3],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1056,bs=[4,3],nr=[4,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=129,bs=[4,3],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1057,bs=[4,3],nr=[4,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=129,bs=[4,3],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1057,bs=[4,3],nr=[4,1],per=[0,1,2,3],k_v=2113,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=129,bs=[4,3],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1057,bs=[4,3],nr=[4,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=128,bs=[8,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1056,bs=[8,3],nr=[1,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=128,bs=[8,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1056,bs=[8,3],nr=[1,1],per=[0,1,2,3],k_v=2112,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=128,bs=[8,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1056,bs=[8,3],nr=[1,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=129,bs=[8,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1057,bs=[8,3],nr=[1,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=129,bs=[8,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1057,bs=[8,3],nr=[1,1],per=[0,1,2,3],k_v=2113,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=129,bs=[8,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1057,bs=[8,3],nr=[1,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=128,bs=[8,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1056,bs=[8,3],nr=[1,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=128,bs=[8,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1056,bs=[8,3],nr=[1,1],per=[0,1,2,3],k_v=2112,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=128,bs=[8,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1056,bs=[8,3],nr=[1,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=129,bs=[8,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1057,bs=[8,3],nr=[1,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=129,bs=[8,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1057,bs=[8,3],nr=[1,1],per=[0,1,2,3],k_v=2113,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=129,bs=[8,3],nr=[1,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1057,bs=[8,3],nr=[1,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=128,bs=[8,3],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1056,bs=[8,3],nr=[4,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=128,bs=[8,3],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1056,bs=[8,3],nr=[4,1],per=[0,1,2,3],k_v=2112,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=128,bs=[8,3],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1056,bs=[8,3],nr=[4,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1056,n=1,k=129,bs=[8,3],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=128,n=1,k=1057,bs=[8,3],nr=[4,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1056,n=1,k=129,bs=[8,3],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=128,n=1,k=1057,bs=[8,3],nr=[4,1],per=[0,1,2,3],k_v=2113,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1056,n=1,k=129,bs=[8,3],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=128,n=1,k=1057,bs=[8,3],nr=[4,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=128,bs=[8,3],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1056,bs=[8,3],nr=[4,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=128,bs=[8,3],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1056,bs=[8,3],nr=[4,1],per=[0,1,2,3],k_v=2112,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=128,bs=[8,3],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1056,bs=[8,3],nr=[4,1],per=[0,1,2,3],k_v=2112,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=1057,n=1,k=129,bs=[8,3],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f16,type_b=f32,m=129,n=1,k=1057,bs=[8,3],nr=[4,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=1057,n=1,k=129,bs=[8,3],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=bf16,type_b=f32,m=129,n=1,k=1057,bs=[8,3],nr=[4,1],per=[0,1,2,3],k_v=2113,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=1057,n=1,k=129,bs=[8,3],nr=[4,1],per=[0,2,1,3],k_v=0,o=1","support","0","no","SYCL"
+"SYCL0","MUL_MAT","type_a=f32,type_b=f32,m=129,n=1,k=1057,bs=[8,3],nr=[4,1],per=[0,1,2,3],k_v=2113,o=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=16,n_used=16,b=0,m=32,n=1024,k=16","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=2,n_used=2,b=0,m=32,n=8192,k=64","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=16,n_used=16,b=0,m=50,n=200,k=64","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=16,n_used=16,b=1,m=32,n=1024,k=16","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=2,n_used=2,b=1,m=32,n=8192,k=64","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=16,n_used=16,b=1,m=50,n=200,k=64","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=f16,type_b=f32,n_mats=1,n_used=1,b=0,m=8,n=16,k=1","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=mxfp4,type_b=f32,n_mats=32,n_used=2,b=0,m=2880,n=32,k=2880","support","0","no","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=1,b=0,m=512,n=1,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=1,b=0,m=512,n=4,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=1,b=0,m=512,n=5,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=1,b=0,m=512,n=17,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=1,b=0,m=512,n=32,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=1,b=0,m=512,n=129,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=1,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=4,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=5,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=17,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=32,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=129,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=1,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=4,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=5,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=17,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=32,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=129,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=1,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=4,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=5,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=17,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=32,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=129,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=1,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=4,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=5,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=17,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=32,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=129,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=1,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=4,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=5,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=17,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=32,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=f32,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=129,k=256","support","1","yes","SYCL"
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+"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=1,k=256","support","1","yes","SYCL"
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+"SYCL0","MUL_MAT_ID","type_a=q4_K,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=32,k=256","support","1","yes","SYCL"
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+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=1,b=0,m=512,n=129,k=256","support","0","no","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=1,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=4,k=256","support","0","no","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=5,k=256","support","0","no","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=17,k=256","support","0","no","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=32,k=256","support","0","no","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=1,b=1,m=512,n=129,k=256","support","0","no","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=1,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=4,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=5,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=17,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=32,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=129,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=1,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=4,k=256","support","0","no","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=5,k=256","support","0","no","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=17,k=256","support","0","no","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=32,k=256","support","0","no","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=2,b=1,m=512,n=129,k=256","support","0","no","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=1,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=4,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=5,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=17,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=32,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=4,b=0,m=512,n=129,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=1,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=4,k=256","support","0","no","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=5,k=256","support","0","no","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=17,k=256","support","0","no","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=32,k=256","support","0","no","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=4,n_used=4,b=1,m=512,n=129,k=256","support","0","no","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=1,b=0,m=512,n=1,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=1,b=0,m=512,n=4,k=256","support","0","no","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=1,b=0,m=512,n=5,k=256","support","0","no","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=1,b=0,m=512,n=17,k=256","support","0","no","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=1,b=0,m=512,n=32,k=256","support","0","no","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=1,b=0,m=512,n=129,k=256","support","0","no","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=1,b=1,m=512,n=1,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=1,b=1,m=512,n=4,k=256","support","0","no","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=1,b=1,m=512,n=5,k=256","support","0","no","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=1,b=1,m=512,n=17,k=256","support","0","no","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=1,b=1,m=512,n=32,k=256","support","0","no","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=1,b=1,m=512,n=129,k=256","support","0","no","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=2,b=0,m=512,n=1,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=2,b=0,m=512,n=4,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=2,b=0,m=512,n=5,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=2,b=0,m=512,n=17,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=2,b=0,m=512,n=32,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=2,b=0,m=512,n=129,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=2,b=1,m=512,n=1,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=2,b=1,m=512,n=4,k=256","support","0","no","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=2,b=1,m=512,n=5,k=256","support","0","no","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=2,b=1,m=512,n=17,k=256","support","0","no","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=2,b=1,m=512,n=32,k=256","support","0","no","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=2,b=1,m=512,n=129,k=256","support","0","no","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=1,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=4,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=5,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=17,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=32,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=4,b=0,m=512,n=129,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=4,b=1,m=512,n=1,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=4,b=1,m=512,n=4,k=256","support","0","no","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=4,b=1,m=512,n=5,k=256","support","0","no","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=4,b=1,m=512,n=17,k=256","support","0","no","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=4,b=1,m=512,n=32,k=256","support","0","no","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xxs,type_b=f32,n_mats=8,n_used=4,b=1,m=512,n=129,k=256","support","0","no","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=1,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=q4_1,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=32,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=q5_0,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=1,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=q5_0,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=32,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=q5_1,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=1,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=q5_1,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=32,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=1,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=q8_0,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=32,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=q2_K,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=1,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=q2_K,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=32,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=q3_K,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=1,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=q3_K,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=32,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=q5_K,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=1,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=q5_K,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=32,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=q6_K,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=1,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=q6_K,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=32,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xs,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=1,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_xs,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=32,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_s,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=1,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq2_s,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=32,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq3_xxs,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=1,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq3_xxs,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=32,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq1_s,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=1,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq1_s,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=32,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq1_m,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=1,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq1_m,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=32,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq4_nl,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=1,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq4_nl,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=32,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq3_s,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=1,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq3_s,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=32,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq4_xs,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=1,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=iq4_xs,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=32,k=256","support","1","yes","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=bf16,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=1,k=256","support","0","no","SYCL"
+"SYCL0","MUL_MAT_ID","type_a=bf16,type_b=f32,n_mats=4,n_used=2,b=0,m=512,n=32,k=256","support","0","no","SYCL"
 "SYCL0","OUT_PROD","type_a=f32,type_b=f32,m=256,n=1,k=1,bs=[1,1],nr=[1,1],trans_b=0","support","1","yes","SYCL"
 "SYCL0","OUT_PROD","type_a=f32,type_b=f32,m=256,n=1,k=1,bs=[1,1],nr=[1,2],trans_b=0","support","0","no","SYCL"
 "SYCL0","OUT_PROD","type_a=f32,type_b=f32,m=256,n=1,k=1,bs=[1,1],nr=[2,1],trans_b=0","support","0","no","SYCL"
@@ -8619,6 +8659,10 @@
 "SYCL0","COS","type=f16,ne=[10,2,2,2]","support","1","yes","SYCL"
 "SYCL0","CLAMP","type=f16,ne=[10,5,4,3],min=-0.500000,max=0.500000","support","1","yes","SYCL"
 "SYCL0","LEAKY_RELU","type=f16,ne_a=[10,5,4,3],negative_slope=0.100000","support","1","yes","SYCL"
+"SYCL0","FLOOR","type=f16,ne=[10,2,2,2]","support","1","yes","SYCL"
+"SYCL0","CEIL","type=f16,ne=[10,2,2,2]","support","1","yes","SYCL"
+"SYCL0","ROUND","type=f16,ne=[10,2,2,2]","support","1","yes","SYCL"
+"SYCL0","TRUNC","type=f16,ne=[10,2,2,2]","support","1","yes","SYCL"
 "SYCL0","SQR","type=f16,ne=[7,1,5,3]","support","1","yes","SYCL"
 "SYCL0","SQRT","type=f16,ne=[7,1,5,3]","support","1","yes","SYCL"
 "SYCL0","LOG","type=f16,ne=[7,1,5,3]","support","1","yes","SYCL"
@@ -8626,6 +8670,10 @@
 "SYCL0","COS","type=f16,ne=[7,1,5,3]","support","1","yes","SYCL"
 "SYCL0","CLAMP","type=f16,ne=[7,1,5,3],min=-0.500000,max=0.500000","support","1","yes","SYCL"
 "SYCL0","LEAKY_RELU","type=f16,ne_a=[7,1,5,3],negative_slope=0.100000","support","1","yes","SYCL"
+"SYCL0","FLOOR","type=f16,ne=[7,1,5,3]","support","1","yes","SYCL"
+"SYCL0","CEIL","type=f16,ne=[7,1,5,3]","support","1","yes","SYCL"
+"SYCL0","ROUND","type=f16,ne=[7,1,5,3]","support","1","yes","SYCL"
+"SYCL0","TRUNC","type=f16,ne=[7,1,5,3]","support","1","yes","SYCL"
 "SYCL0","SQR","type=f32,ne=[10,5,4,3]","support","1","yes","SYCL"
 "SYCL0","SQRT","type=f32,ne=[10,3,3,2]","support","1","yes","SYCL"
 "SYCL0","LOG","type=f32,ne=[10,5,4,3]","support","1","yes","SYCL"
@@ -8633,6 +8681,10 @@
 "SYCL0","COS","type=f32,ne=[10,2,2,2]","support","1","yes","SYCL"
 "SYCL0","CLAMP","type=f32,ne=[10,5,4,3],min=-0.500000,max=0.500000","support","1","yes","SYCL"
 "SYCL0","LEAKY_RELU","type=f32,ne_a=[10,5,4,3],negative_slope=0.100000","support","1","yes","SYCL"
+"SYCL0","FLOOR","type=f32,ne=[10,2,2,2]","support","1","yes","SYCL"
+"SYCL0","CEIL","type=f32,ne=[10,2,2,2]","support","1","yes","SYCL"
+"SYCL0","ROUND","type=f32,ne=[10,2,2,2]","support","1","yes","SYCL"
+"SYCL0","TRUNC","type=f32,ne=[10,2,2,2]","support","1","yes","SYCL"
 "SYCL0","SQR","type=f32,ne=[7,1,5,3]","support","1","yes","SYCL"
 "SYCL0","SQRT","type=f32,ne=[7,1,5,3]","support","1","yes","SYCL"
 "SYCL0","LOG","type=f32,ne=[7,1,5,3]","support","1","yes","SYCL"
@@ -8640,6 +8692,10 @@
 "SYCL0","COS","type=f32,ne=[7,1,5,3]","support","1","yes","SYCL"
 "SYCL0","CLAMP","type=f32,ne=[7,1,5,3],min=-0.500000,max=0.500000","support","1","yes","SYCL"
 "SYCL0","LEAKY_RELU","type=f32,ne_a=[7,1,5,3],negative_slope=0.100000","support","1","yes","SYCL"
+"SYCL0","FLOOR","type=f32,ne=[7,1,5,3]","support","1","yes","SYCL"
+"SYCL0","CEIL","type=f32,ne=[7,1,5,3]","support","1","yes","SYCL"
+"SYCL0","ROUND","type=f32,ne=[7,1,5,3]","support","1","yes","SYCL"
+"SYCL0","TRUNC","type=f32,ne=[7,1,5,3]","support","1","yes","SYCL"
 "SYCL0","DIAG_MASK_INF","type=f32,ne=[10,10,1,1],n_past=5","support","1","yes","SYCL"
 "SYCL0","DIAG_MASK_INF","type=f32,ne=[10,10,3,1],n_past=5","support","1","yes","SYCL"
 "SYCL0","DIAG_MASK_INF","type=f32,ne=[10,10,3,2],n_past=5","support","1","yes","SYCL"
@@ -8915,7 +8971,12 @@
 "SYCL0","ROPE","type=f32,ne_a=[128,28,2,1],n_dims=128,mode=8,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=0,v=0,inplace=0","support","1","yes","SYCL"
 "SYCL0","ROPE","type=f32,ne_a=[128,12,2,1],n_dims=20,mode=8,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=0,v=0,inplace=0","support","1","yes","SYCL"
 "SYCL0","ROPE","type=f32,ne_a=[128,28,2,1],n_dims=32,mode=8,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=0,v=0,inplace=0","support","1","yes","SYCL"
+"SYCL0","ROPE","type=f32,ne_a=[128,12,2,1],n_dims=128,mode=40,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=0,v=0,inplace=0","support","1","yes","SYCL"
+"SYCL0","ROPE","type=f32,ne_a=[128,28,2,1],n_dims=128,mode=40,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=0,v=0,inplace=0","support","1","yes","SYCL"
+"SYCL0","ROPE","type=f32,ne_a=[128,12,2,1],n_dims=20,mode=40,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=0,v=0,inplace=0","support","1","yes","SYCL"
+"SYCL0","ROPE","type=f32,ne_a=[128,28,2,1],n_dims=32,mode=40,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=0,v=0,inplace=0","support","1","yes","SYCL"
 "SYCL0","ROPE","type=f32,ne_a=[80,16,2,1],n_dims=80,mode=24,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=0,v=0,inplace=0","support","1","yes","SYCL"
+"SYCL0","ROPE","type=f32,ne_a=[128,16,2,1],n_dims=128,mode=40,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=0,v=0,inplace=0","support","1","yes","SYCL"
 "SYCL0","ROPE","type=f32,ne_a=[64,128,2,1],n_dims=64,mode=2,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=0,v=0,inplace=0","support","1","yes","SYCL"
 "SYCL0","ROPE","type=f32,ne_a=[128,32,2,1],n_dims=128,mode=0,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=0,v=1,inplace=0","support","1","yes","SYCL"
 "SYCL0","ROPE","type=f32,ne_a=[128,40,2,1],n_dims=128,mode=0,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=0,v=1,inplace=0","support","1","yes","SYCL"
@@ -8934,7 +8995,12 @@
 "SYCL0","ROPE","type=f32,ne_a=[128,28,2,1],n_dims=128,mode=8,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=0,v=1,inplace=0","support","1","yes","SYCL"
 "SYCL0","ROPE","type=f32,ne_a=[128,12,2,1],n_dims=20,mode=8,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=0,v=1,inplace=0","support","1","yes","SYCL"
 "SYCL0","ROPE","type=f32,ne_a=[128,28,2,1],n_dims=32,mode=8,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=0,v=1,inplace=0","support","1","yes","SYCL"
+"SYCL0","ROPE","type=f32,ne_a=[128,12,2,1],n_dims=128,mode=40,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=0,v=1,inplace=0","support","1","yes","SYCL"
+"SYCL0","ROPE","type=f32,ne_a=[128,28,2,1],n_dims=128,mode=40,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=0,v=1,inplace=0","support","1","yes","SYCL"
+"SYCL0","ROPE","type=f32,ne_a=[128,12,2,1],n_dims=20,mode=40,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=0,v=1,inplace=0","support","1","yes","SYCL"
+"SYCL0","ROPE","type=f32,ne_a=[128,28,2,1],n_dims=32,mode=40,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=0,v=1,inplace=0","support","1","yes","SYCL"
 "SYCL0","ROPE","type=f32,ne_a=[80,16,2,1],n_dims=80,mode=24,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=0,v=1,inplace=0","support","1","yes","SYCL"
+"SYCL0","ROPE","type=f32,ne_a=[128,16,2,1],n_dims=128,mode=40,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=0,v=1,inplace=0","support","1","yes","SYCL"
 "SYCL0","ROPE","type=f32,ne_a=[64,128,2,1],n_dims=64,mode=2,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=0,v=1,inplace=0","support","1","yes","SYCL"
 "SYCL0","ROPE","type=f32,ne_a=[128,32,2,1],n_dims=128,mode=0,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=1,v=0,inplace=0","support","1","yes","SYCL"
 "SYCL0","ROPE","type=f32,ne_a=[128,40,2,1],n_dims=128,mode=0,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=1,v=0,inplace=0","support","1","yes","SYCL"
@@ -8953,7 +9019,12 @@
 "SYCL0","ROPE","type=f32,ne_a=[128,28,2,1],n_dims=128,mode=8,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=1,v=0,inplace=0","support","1","yes","SYCL"
 "SYCL0","ROPE","type=f32,ne_a=[128,12,2,1],n_dims=20,mode=8,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=1,v=0,inplace=0","support","1","yes","SYCL"
 "SYCL0","ROPE","type=f32,ne_a=[128,28,2,1],n_dims=32,mode=8,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=1,v=0,inplace=0","support","1","yes","SYCL"
+"SYCL0","ROPE","type=f32,ne_a=[128,12,2,1],n_dims=128,mode=40,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=1,v=0,inplace=0","support","1","yes","SYCL"
+"SYCL0","ROPE","type=f32,ne_a=[128,28,2,1],n_dims=128,mode=40,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=1,v=0,inplace=0","support","1","yes","SYCL"
+"SYCL0","ROPE","type=f32,ne_a=[128,12,2,1],n_dims=20,mode=40,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=1,v=0,inplace=0","support","1","yes","SYCL"
+"SYCL0","ROPE","type=f32,ne_a=[128,28,2,1],n_dims=32,mode=40,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=1,v=0,inplace=0","support","1","yes","SYCL"
 "SYCL0","ROPE","type=f32,ne_a=[80,16,2,1],n_dims=80,mode=24,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=1,v=0,inplace=0","support","1","yes","SYCL"
+"SYCL0","ROPE","type=f32,ne_a=[128,16,2,1],n_dims=128,mode=40,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=1,v=0,inplace=0","support","1","yes","SYCL"
 "SYCL0","ROPE","type=f32,ne_a=[64,128,2,1],n_dims=64,mode=2,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=1,v=0,inplace=0","support","1","yes","SYCL"
 "SYCL0","ROPE","type=f32,ne_a=[128,32,2,1],n_dims=128,mode=0,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=1,v=1,inplace=0","support","1","yes","SYCL"
 "SYCL0","ROPE","type=f32,ne_a=[128,40,2,1],n_dims=128,mode=0,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=1,v=1,inplace=0","support","1","yes","SYCL"
@@ -8972,7 +9043,12 @@
 "SYCL0","ROPE","type=f32,ne_a=[128,28,2,1],n_dims=128,mode=8,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=1,v=1,inplace=0","support","1","yes","SYCL"
 "SYCL0","ROPE","type=f32,ne_a=[128,12,2,1],n_dims=20,mode=8,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=1,v=1,inplace=0","support","1","yes","SYCL"
 "SYCL0","ROPE","type=f32,ne_a=[128,28,2,1],n_dims=32,mode=8,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=1,v=1,inplace=0","support","1","yes","SYCL"
+"SYCL0","ROPE","type=f32,ne_a=[128,12,2,1],n_dims=128,mode=40,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=1,v=1,inplace=0","support","1","yes","SYCL"
+"SYCL0","ROPE","type=f32,ne_a=[128,28,2,1],n_dims=128,mode=40,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=1,v=1,inplace=0","support","1","yes","SYCL"
+"SYCL0","ROPE","type=f32,ne_a=[128,12,2,1],n_dims=20,mode=40,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=1,v=1,inplace=0","support","1","yes","SYCL"
+"SYCL0","ROPE","type=f32,ne_a=[128,28,2,1],n_dims=32,mode=40,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=1,v=1,inplace=0","support","1","yes","SYCL"
 "SYCL0","ROPE","type=f32,ne_a=[80,16,2,1],n_dims=80,mode=24,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=1,v=1,inplace=0","support","1","yes","SYCL"
+"SYCL0","ROPE","type=f32,ne_a=[128,16,2,1],n_dims=128,mode=40,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=1,v=1,inplace=0","support","1","yes","SYCL"
 "SYCL0","ROPE","type=f32,ne_a=[64,128,2,1],n_dims=64,mode=2,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=1,v=1,inplace=0","support","1","yes","SYCL"
 "SYCL0","ROPE","type=f16,ne_a=[128,32,2,1],n_dims=128,mode=0,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=0,v=0,inplace=0","support","1","yes","SYCL"
 "SYCL0","ROPE","type=f16,ne_a=[64,128,2,1],n_dims=64,mode=2,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=0,v=0,inplace=0","support","1","yes","SYCL"
@@ -9111,7 +9187,12 @@
 "SYCL0","ROPE_BACK","type=f32,ne_a=[128,28,2,1],n_dims=128,mode=8,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=0,v=0,inplace=0","support","0","no","SYCL"
 "SYCL0","ROPE_BACK","type=f32,ne_a=[128,12,2,1],n_dims=20,mode=8,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=0,v=0,inplace=0","support","0","no","SYCL"
 "SYCL0","ROPE_BACK","type=f32,ne_a=[128,28,2,1],n_dims=32,mode=8,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=0,v=0,inplace=0","support","0","no","SYCL"
+"SYCL0","ROPE_BACK","type=f32,ne_a=[128,12,2,1],n_dims=128,mode=40,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=0,v=0,inplace=0","support","0","no","SYCL"
+"SYCL0","ROPE_BACK","type=f32,ne_a=[128,28,2,1],n_dims=128,mode=40,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=0,v=0,inplace=0","support","0","no","SYCL"
+"SYCL0","ROPE_BACK","type=f32,ne_a=[128,12,2,1],n_dims=20,mode=40,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=0,v=0,inplace=0","support","0","no","SYCL"
+"SYCL0","ROPE_BACK","type=f32,ne_a=[128,28,2,1],n_dims=32,mode=40,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=0,v=0,inplace=0","support","0","no","SYCL"
 "SYCL0","ROPE_BACK","type=f32,ne_a=[80,16,2,1],n_dims=80,mode=24,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=0,v=0,inplace=0","support","0","no","SYCL"
+"SYCL0","ROPE_BACK","type=f32,ne_a=[128,16,2,1],n_dims=128,mode=40,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=0,v=0,inplace=0","support","0","no","SYCL"
 "SYCL0","ROPE_BACK","type=f32,ne_a=[64,128,2,1],n_dims=64,mode=2,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=0,v=0,inplace=0","support","0","no","SYCL"
 "SYCL0","ROPE_BACK","type=f32,ne_a=[128,32,2,1],n_dims=128,mode=0,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=0,v=1,inplace=0","support","0","no","SYCL"
 "SYCL0","ROPE_BACK","type=f32,ne_a=[128,40,2,1],n_dims=128,mode=0,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=0,v=1,inplace=0","support","0","no","SYCL"
@@ -9130,7 +9211,12 @@
 "SYCL0","ROPE_BACK","type=f32,ne_a=[128,28,2,1],n_dims=128,mode=8,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=0,v=1,inplace=0","support","0","no","SYCL"
 "SYCL0","ROPE_BACK","type=f32,ne_a=[128,12,2,1],n_dims=20,mode=8,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=0,v=1,inplace=0","support","0","no","SYCL"
 "SYCL0","ROPE_BACK","type=f32,ne_a=[128,28,2,1],n_dims=32,mode=8,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=0,v=1,inplace=0","support","0","no","SYCL"
+"SYCL0","ROPE_BACK","type=f32,ne_a=[128,12,2,1],n_dims=128,mode=40,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=0,v=1,inplace=0","support","0","no","SYCL"
+"SYCL0","ROPE_BACK","type=f32,ne_a=[128,28,2,1],n_dims=128,mode=40,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=0,v=1,inplace=0","support","0","no","SYCL"
+"SYCL0","ROPE_BACK","type=f32,ne_a=[128,12,2,1],n_dims=20,mode=40,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=0,v=1,inplace=0","support","0","no","SYCL"
+"SYCL0","ROPE_BACK","type=f32,ne_a=[128,28,2,1],n_dims=32,mode=40,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=0,v=1,inplace=0","support","0","no","SYCL"
 "SYCL0","ROPE_BACK","type=f32,ne_a=[80,16,2,1],n_dims=80,mode=24,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=0,v=1,inplace=0","support","0","no","SYCL"
+"SYCL0","ROPE_BACK","type=f32,ne_a=[128,16,2,1],n_dims=128,mode=40,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=0,v=1,inplace=0","support","0","no","SYCL"
 "SYCL0","ROPE_BACK","type=f32,ne_a=[64,128,2,1],n_dims=64,mode=2,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=0,v=1,inplace=0","support","0","no","SYCL"
 "SYCL0","ROPE_BACK","type=f32,ne_a=[128,32,2,1],n_dims=128,mode=0,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=1,v=0,inplace=0","support","0","no","SYCL"
 "SYCL0","ROPE_BACK","type=f32,ne_a=[128,40,2,1],n_dims=128,mode=0,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=1,v=0,inplace=0","support","0","no","SYCL"
@@ -9149,7 +9235,12 @@
 "SYCL0","ROPE_BACK","type=f32,ne_a=[128,28,2,1],n_dims=128,mode=8,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=1,v=0,inplace=0","support","0","no","SYCL"
 "SYCL0","ROPE_BACK","type=f32,ne_a=[128,12,2,1],n_dims=20,mode=8,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=1,v=0,inplace=0","support","0","no","SYCL"
 "SYCL0","ROPE_BACK","type=f32,ne_a=[128,28,2,1],n_dims=32,mode=8,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=1,v=0,inplace=0","support","0","no","SYCL"
+"SYCL0","ROPE_BACK","type=f32,ne_a=[128,12,2,1],n_dims=128,mode=40,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=1,v=0,inplace=0","support","0","no","SYCL"
+"SYCL0","ROPE_BACK","type=f32,ne_a=[128,28,2,1],n_dims=128,mode=40,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=1,v=0,inplace=0","support","0","no","SYCL"
+"SYCL0","ROPE_BACK","type=f32,ne_a=[128,12,2,1],n_dims=20,mode=40,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=1,v=0,inplace=0","support","0","no","SYCL"
+"SYCL0","ROPE_BACK","type=f32,ne_a=[128,28,2,1],n_dims=32,mode=40,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=1,v=0,inplace=0","support","0","no","SYCL"
 "SYCL0","ROPE_BACK","type=f32,ne_a=[80,16,2,1],n_dims=80,mode=24,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=1,v=0,inplace=0","support","0","no","SYCL"
+"SYCL0","ROPE_BACK","type=f32,ne_a=[128,16,2,1],n_dims=128,mode=40,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=1,v=0,inplace=0","support","0","no","SYCL"
 "SYCL0","ROPE_BACK","type=f32,ne_a=[64,128,2,1],n_dims=64,mode=2,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=1,v=0,inplace=0","support","0","no","SYCL"
 "SYCL0","ROPE_BACK","type=f32,ne_a=[128,32,2,1],n_dims=128,mode=0,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=1,v=1,inplace=0","support","0","no","SYCL"
 "SYCL0","ROPE_BACK","type=f32,ne_a=[128,40,2,1],n_dims=128,mode=0,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=1,v=1,inplace=0","support","0","no","SYCL"
@@ -9168,7 +9259,12 @@
 "SYCL0","ROPE_BACK","type=f32,ne_a=[128,28,2,1],n_dims=128,mode=8,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=1,v=1,inplace=0","support","0","no","SYCL"
 "SYCL0","ROPE_BACK","type=f32,ne_a=[128,12,2,1],n_dims=20,mode=8,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=1,v=1,inplace=0","support","0","no","SYCL"
 "SYCL0","ROPE_BACK","type=f32,ne_a=[128,28,2,1],n_dims=32,mode=8,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=1,v=1,inplace=0","support","0","no","SYCL"
+"SYCL0","ROPE_BACK","type=f32,ne_a=[128,12,2,1],n_dims=128,mode=40,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=1,v=1,inplace=0","support","0","no","SYCL"
+"SYCL0","ROPE_BACK","type=f32,ne_a=[128,28,2,1],n_dims=128,mode=40,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=1,v=1,inplace=0","support","0","no","SYCL"
+"SYCL0","ROPE_BACK","type=f32,ne_a=[128,12,2,1],n_dims=20,mode=40,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=1,v=1,inplace=0","support","0","no","SYCL"
+"SYCL0","ROPE_BACK","type=f32,ne_a=[128,28,2,1],n_dims=32,mode=40,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=1,v=1,inplace=0","support","0","no","SYCL"
 "SYCL0","ROPE_BACK","type=f32,ne_a=[80,16,2,1],n_dims=80,mode=24,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=1,v=1,inplace=0","support","0","no","SYCL"
+"SYCL0","ROPE_BACK","type=f32,ne_a=[128,16,2,1],n_dims=128,mode=40,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=1,v=1,inplace=0","support","0","no","SYCL"
 "SYCL0","ROPE_BACK","type=f32,ne_a=[64,128,2,1],n_dims=64,mode=2,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=1,v=1,inplace=0","support","0","no","SYCL"
 "SYCL0","ROPE_BACK","type=f16,ne_a=[128,32,2,1],n_dims=128,mode=0,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=0,v=0,inplace=0","support","0","no","SYCL"
 "SYCL0","ROPE_BACK","type=f16,ne_a=[64,128,2,1],n_dims=64,mode=2,n_ctx=512,fs=1.000000,ef=0.000000,af=1.000000,ff=0,v=0,inplace=0","support","0","no","SYCL"
@@ -9296,6 +9392,8 @@
 "SYCL0","ROPE","type=f32,ne_a=[128,32,2,1],n_dims=128,mode=2,n_ctx=512,fs=1.424500,ef=0.746500,af=1.424500,ff=1,v=0,inplace=1","support","1","yes","SYCL"
 "SYCL0","ROPE","type=f32,ne_a=[128,32,2,1],n_dims=128,mode=8,n_ctx=512,fs=1.424500,ef=0.746500,af=1.424500,ff=0,v=0,inplace=1","support","1","yes","SYCL"
 "SYCL0","ROPE","type=f32,ne_a=[128,32,2,1],n_dims=128,mode=8,n_ctx=512,fs=1.424500,ef=0.746500,af=1.424500,ff=1,v=0,inplace=1","support","1","yes","SYCL"
+"SYCL0","ROPE","type=f32,ne_a=[128,32,2,1],n_dims=128,mode=40,n_ctx=512,fs=1.424500,ef=0.746500,af=1.424500,ff=0,v=0,inplace=1","support","1","yes","SYCL"
+"SYCL0","ROPE","type=f32,ne_a=[128,32,2,1],n_dims=128,mode=40,n_ctx=512,fs=1.424500,ef=0.746500,af=1.424500,ff=1,v=0,inplace=1","support","1","yes","SYCL"
 "SYCL0","ROPE","type=f32,ne_a=[128,32,2,1],n_dims=128,mode=24,n_ctx=512,fs=1.424500,ef=0.746500,af=1.424500,ff=0,v=0,inplace=1","support","1","yes","SYCL"
 "SYCL0","ROPE","type=f32,ne_a=[128,32,2,1],n_dims=128,mode=24,n_ctx=512,fs=1.424500,ef=0.746500,af=1.424500,ff=1,v=0,inplace=1","support","1","yes","SYCL"
 "SYCL0","ROPE","type=f16,ne_a=[128,32,2,1],n_dims=128,mode=0,n_ctx=512,fs=1.424500,ef=0.746500,af=1.424500,ff=0,v=0,inplace=1","support","1","yes","SYCL"
@@ -9304,74 +9402,91 @@
 "SYCL0","ROPE","type=f16,ne_a=[128,32,2,1],n_dims=128,mode=2,n_ctx=512,fs=1.424500,ef=0.746500,af=1.424500,ff=1,v=0,inplace=1","support","1","yes","SYCL"
 "SYCL0","ROPE","type=f16,ne_a=[128,32,2,1],n_dims=128,mode=8,n_ctx=512,fs=1.424500,ef=0.746500,af=1.424500,ff=0,v=0,inplace=1","support","1","yes","SYCL"
 "SYCL0","ROPE","type=f16,ne_a=[128,32,2,1],n_dims=128,mode=8,n_ctx=512,fs=1.424500,ef=0.746500,af=1.424500,ff=1,v=0,inplace=1","support","1","yes","SYCL"
+"SYCL0","ROPE","type=f16,ne_a=[128,32,2,1],n_dims=128,mode=40,n_ctx=512,fs=1.424500,ef=0.746500,af=1.424500,ff=0,v=0,inplace=1","support","1","yes","SYCL"
+"SYCL0","ROPE","type=f16,ne_a=[128,32,2,1],n_dims=128,mode=40,n_ctx=512,fs=1.424500,ef=0.746500,af=1.424500,ff=1,v=0,inplace=1","support","1","yes","SYCL"
 "SYCL0","ROPE","type=f16,ne_a=[128,32,2,1],n_dims=128,mode=24,n_ctx=512,fs=1.424500,ef=0.746500,af=1.424500,ff=0,v=0,inplace=1","support","1","yes","SYCL"
 "SYCL0","ROPE","type=f16,ne_a=[128,32,2,1],n_dims=128,mode=24,n_ctx=512,fs=1.424500,ef=0.746500,af=1.424500,ff=1,v=0,inplace=1","support","1","yes","SYCL"
 "SYCL0","CONCAT","type=f32,ne_a=[11,12,13,14],ne_b_d=7,dim=0,v=0","support","1","yes","SYCL"
-"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=0,v=0","support","0","yes","SYCL"
+"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=0,v=0","support","1","yes","SYCL"
 "SYCL0","CONCAT","type=f32,ne_a=[11,12,13,14],ne_b_d=7,dim=1,v=0","support","1","yes","SYCL"
-"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=1,v=0","support","0","yes","SYCL"
+"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=1,v=0","support","1","yes","SYCL"
 "SYCL0","CONCAT","type=f32,ne_a=[11,12,13,14],ne_b_d=7,dim=2,v=0","support","1","yes","SYCL"
-"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=2,v=0","support","0","yes","SYCL"
+"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=2,v=0","support","1","yes","SYCL"
 "SYCL0","CONCAT","type=f32,ne_a=[11,12,13,14],ne_b_d=7,dim=3,v=0","support","1","yes","SYCL"
-"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=3,v=0","support","0","yes","SYCL"
+"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=3,v=0","support","1","yes","SYCL"
 "SYCL0","CONCAT","type=f32,ne_a=[11,12,13,14],ne_b_d=7,dim=0,v=1","support","1","yes","SYCL"
-"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=0,v=1","support","0","yes","SYCL"
+"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=0,v=1","support","1","yes","SYCL"
 "SYCL0","CONCAT","type=f32,ne_a=[11,12,13,14],ne_b_d=7,dim=1,v=1","support","1","yes","SYCL"
-"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=1,v=1","support","0","yes","SYCL"
+"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=1,v=1","support","1","yes","SYCL"
 "SYCL0","CONCAT","type=f32,ne_a=[11,12,13,14],ne_b_d=7,dim=2,v=1","support","1","yes","SYCL"
-"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=2,v=1","support","0","yes","SYCL"
+"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=2,v=1","support","1","yes","SYCL"
 "SYCL0","CONCAT","type=f32,ne_a=[11,12,13,14],ne_b_d=7,dim=3,v=1","support","1","yes","SYCL"
-"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=3,v=1","support","0","yes","SYCL"
+"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=3,v=1","support","1","yes","SYCL"
 "SYCL0","CONCAT","type=f32,ne_a=[11,12,13,14],ne_b_d=7,dim=0,v=2","support","1","yes","SYCL"
-"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=0,v=2","support","0","yes","SYCL"
+"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=0,v=2","support","1","yes","SYCL"
 "SYCL0","CONCAT","type=f32,ne_a=[11,12,13,14],ne_b_d=7,dim=1,v=2","support","1","yes","SYCL"
-"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=1,v=2","support","0","yes","SYCL"
+"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=1,v=2","support","1","yes","SYCL"
 "SYCL0","CONCAT","type=f32,ne_a=[11,12,13,14],ne_b_d=7,dim=2,v=2","support","1","yes","SYCL"
-"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=2,v=2","support","0","yes","SYCL"
+"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=2,v=2","support","1","yes","SYCL"
 "SYCL0","CONCAT","type=f32,ne_a=[11,12,13,14],ne_b_d=7,dim=3,v=2","support","1","yes","SYCL"
-"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=3,v=2","support","0","yes","SYCL"
+"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=3,v=2","support","1","yes","SYCL"
 "SYCL0","CONCAT","type=f32,ne_a=[11,12,13,14],ne_b_d=7,dim=0,v=3","support","1","yes","SYCL"
-"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=0,v=3","support","0","yes","SYCL"
+"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=0,v=3","support","1","yes","SYCL"
 "SYCL0","CONCAT","type=f32,ne_a=[11,12,13,14],ne_b_d=7,dim=1,v=3","support","1","yes","SYCL"
-"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=1,v=3","support","0","yes","SYCL"
+"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=1,v=3","support","1","yes","SYCL"
 "SYCL0","CONCAT","type=f32,ne_a=[11,12,13,14],ne_b_d=7,dim=2,v=3","support","1","yes","SYCL"
-"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=2,v=3","support","0","yes","SYCL"
+"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=2,v=3","support","1","yes","SYCL"
 "SYCL0","CONCAT","type=f32,ne_a=[11,12,13,14],ne_b_d=7,dim=3,v=3","support","1","yes","SYCL"
-"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=3,v=3","support","0","yes","SYCL"
+"SYCL0","CONCAT","type=i32,ne_a=[11,12,13,14],ne_b_d=7,dim=3,v=3","support","1","yes","SYCL"
 "SYCL0","ARGSORT","type=f32,ne=[8,1,1,1],order=0","support","1","yes","SYCL"
 "SYCL0","ARGSORT","type=f32,ne=[16,10,10,10],order=0","support","1","yes","SYCL"
 "SYCL0","ARGSORT","type=f32,ne=[60,10,10,10],order=0","support","1","yes","SYCL"
 "SYCL0","ARGSORT","type=f32,ne=[1024,1,1,1],order=0","support","1","yes","SYCL"
 "SYCL0","ARGSORT","type=f32,ne=[16384,1,1,1],order=0","support","1","yes","SYCL"
+"SYCL0","ARGSORT","type=f32,ne=[2,8,8192,1],order=0","support","1","yes","SYCL"
 "SYCL0","ARGSORT","type=f32,ne=[8,1,1,1],order=1","support","1","yes","SYCL"
 "SYCL0","ARGSORT","type=f32,ne=[16,10,10,10],order=1","support","1","yes","SYCL"
 "SYCL0","ARGSORT","type=f32,ne=[60,10,10,10],order=1","support","1","yes","SYCL"
 "SYCL0","ARGSORT","type=f32,ne=[1024,1,1,1],order=1","support","1","yes","SYCL"
 "SYCL0","ARGSORT","type=f32,ne=[16384,1,1,1],order=1","support","1","yes","SYCL"
+"SYCL0","ARGSORT","type=f32,ne=[2,8,8192,1],order=1","support","1","yes","SYCL"
 "SYCL0","UPSCALE","type=f32,ne=[512,512,3,2],scale_factor=2,mode=nearest,transpose=0","support","1","yes","SYCL"
 "SYCL0","UPSCALE","type=f32,ne=[512,512,3,2],scale_factor=2,mode=nearest,transpose=1","support","1","yes","SYCL"
-"SYCL0","UPSCALE","type=f32,ne=[2,5,7,11],ne_tgt=[5,7,11,13],mode=0","support","1","yes","SYCL"
-"SYCL0","UPSCALE","type=f32,ne=[5,7,11,13],ne_tgt=[2,5,7,11],mode=0","support","1","yes","SYCL"
+"SYCL0","UPSCALE","type=f32,ne=[2,5,7,11],ne_tgt=[5,7,11,13],mode=nearest,flags=none","support","1","yes","SYCL"
+"SYCL0","UPSCALE","type=f32,ne=[5,7,11,13],ne_tgt=[2,5,7,11],mode=nearest,flags=none","support","1","yes","SYCL"
 "SYCL0","UPSCALE","type=f32,ne=[512,512,3,2],scale_factor=2,mode=bilinear,transpose=0","support","0","no","SYCL"
 "SYCL0","UPSCALE","type=f32,ne=[512,512,3,2],scale_factor=2,mode=bilinear,transpose=1","support","0","no","SYCL"
-"SYCL0","UPSCALE","type=f32,ne=[2,5,7,11],ne_tgt=[5,7,11,13],mode=1","support","0","no","SYCL"
-"SYCL0","UPSCALE","type=f32,ne=[5,7,11,13],ne_tgt=[2,5,7,11],mode=1","support","0","no","SYCL"
-"SYCL0","UPSCALE","type=f32,ne=[2,5,7,11],ne_tgt=[5,7,11,13],mode=257","support","0","no","SYCL"
+"SYCL0","UPSCALE","type=f32,ne=[2,5,7,11],ne_tgt=[5,7,11,13],mode=bilinear,flags=none","support","0","no","SYCL"
+"SYCL0","UPSCALE","type=f32,ne=[5,7,11,13],ne_tgt=[2,5,7,11],mode=bilinear,flags=none","support","0","no","SYCL"
+"SYCL0","UPSCALE","type=f32,ne=[512,512,3,2],scale_factor=2,mode=bicubic,transpose=0","support","0","no","SYCL"
+"SYCL0","UPSCALE","type=f32,ne=[512,512,3,2],scale_factor=2,mode=bicubic,transpose=1","support","0","no","SYCL"
+"SYCL0","UPSCALE","type=f32,ne=[2,5,7,11],ne_tgt=[5,7,11,13],mode=bicubic,flags=none","support","0","no","SYCL"
+"SYCL0","UPSCALE","type=f32,ne=[5,7,11,13],ne_tgt=[2,5,7,11],mode=bicubic,flags=none","support","0","no","SYCL"
+"SYCL0","UPSCALE","type=f32,ne=[2,5,7,11],ne_tgt=[5,7,11,13],mode=bilinear,flags=align_corners","support","0","no","SYCL"
+"SYCL0","UPSCALE","type=f32,ne=[1,4,3,2],ne_tgt=[2,8,3,2],mode=bilinear,flags=align_corners","support","0","no","SYCL"
+"SYCL0","UPSCALE","type=f32,ne=[4,1,3,2],ne_tgt=[1,1,3,2],mode=bilinear,flags=align_corners","support","0","no","SYCL"
+"SYCL0","UPSCALE","type=f32,ne=[2,5,7,11],ne_tgt=[5,7,11,13],mode=bicubic,flags=align_corners","support","0","no","SYCL"
+"SYCL0","UPSCALE","type=f32,ne=[1,4,3,2],ne_tgt=[2,8,3,2],mode=bicubic,flags=align_corners","support","0","no","SYCL"
+"SYCL0","UPSCALE","type=f32,ne=[4,1,3,2],ne_tgt=[1,1,3,2],mode=bicubic,flags=align_corners","support","0","no","SYCL"
 "SYCL0","SUM","type=f32,ne=[10,5,4,3]","support","1","yes","SYCL"
 "SYCL0","SUM_ROWS","type=f32,ne=[10,5,4,3],permute=0,slice=0","support","1","yes","SYCL"
+"SYCL0","SUM","type=f32,ne=[11,5,6,3],permute=[0,2,1,3]","support","0","no","SYCL"
+"SYCL0","SUM","type=f32,ne=[11,5,6,3],permute=[0,3,2,1]","support","0","no","SYCL"
+"SYCL0","SUM","type=f32,ne=[11,5,6,3],permute=[0,1,3,2]","support","0","no","SYCL"
 "SYCL0","SUM_ROWS","type=f32,ne=[11,5,6,3],permute=1,slice=0","support","0","no","SYCL"
 "SYCL0","SUM_ROWS","type=f32,ne=[11,5,6,3],permute=0,slice=1","support","0","no","SYCL"
 "SYCL0","SUM_ROWS","type=f32,ne=[11,5,6,3],permute=1,slice=1","support","0","no","SYCL"
-"SYCL0","MEAN","type=f32,ne=[10,5,4,3]","support","0","no","SYCL"
+"SYCL0","MEAN","type=f32,ne=[10,5,4,3]","support","1","yes","SYCL"
 "SYCL0","SUM","type=f32,ne=[33,1,1,1]","support","1","yes","SYCL"
 "SYCL0","SUM_ROWS","type=f32,ne=[33,1,1,1],permute=0,slice=0","support","1","yes","SYCL"
-"SYCL0","MEAN","type=f32,ne=[33,1,1,1]","support","0","no","SYCL"
+"SYCL0","MEAN","type=f32,ne=[33,1,1,1]","support","1","yes","SYCL"
 "SYCL0","SUM","type=f32,ne=[33,1024,1,1]","support","1","yes","SYCL"
 "SYCL0","SUM_ROWS","type=f32,ne=[33,1024,1,1],permute=0,slice=0","support","1","yes","SYCL"
 "SYCL0","SUM","type=f32,ne=[33,256,1,1]","support","1","yes","SYCL"
+"SYCL0","SUM","type=f32,ne=[33,256,1,1],permute=[1,0,2,3]","support","0","no","SYCL"
 "SYCL0","SUM_ROWS","type=f32,ne=[33,256,1,1],permute=0,slice=0","support","1","yes","SYCL"
-"SYCL0","MEAN","type=f32,ne=[33,256,1,1]","support","0","no","SYCL"
-"SYCL0","MEAN","type=f32,ne=[32769,1,1,1]","support","0","no","SYCL"
+"SYCL0","MEAN","type=f32,ne=[33,256,1,1]","support","1","yes","SYCL"
+"SYCL0","MEAN","type=f32,ne=[32769,1,1,1]","support","1","yes","SYCL"
 "SYCL0","GROUP_NORM","type=f32,ne=[64,64,320,1],num_groups=32,eps=0.000001","support","1","yes","SYCL"
 "SYCL0","GROUP_NORM","type=f32,ne=[9,9,1280,1],num_groups=32,eps=0.000001","support","1","yes","SYCL"
 "SYCL0","GROUP_NORM_MUL_ADD","type=f32,ne=[64,64,320,1],num_groups=4,eps=0.000010","support","1","yes","SYCL"
@@ -9379,10 +9494,10 @@
 "SYCL0","ACC","type=f32,ne_a=[256,17,1,1],ne_b=[256,16,1,1]","support","1","yes","SYCL"
 "SYCL0","PAD","type=f32,ne_a=[512,512,1,1],pad_0=1,pad_1=1","support","1","yes","SYCL"
 "SYCL0","PAD","type=f32,ne_a=[512,512,3,1],lp0=1,rp0=1,lp1=1,rp1=1,lp2=1,rp2=1,lp3=1,rp3=1,v=0","support","1","yes","SYCL"
-"SYCL0","PAD_REFLECT_1D","type=f32,ne_a=[3000,384,4,1],pad_0=10,pad_1=9","support","0","yes","SYCL"
-"SYCL0","PAD_REFLECT_1D","type=f32,ne_a=[512,34,2,1],pad_0=10,pad_1=9","support","0","yes","SYCL"
-"SYCL0","ROLL","shift0=3,shift1=-2,shift3=1,shift4=-1","support","0","no","SYCL"
-"SYCL0","ARANGE","type=f32,start=0.000000,stop=10.000000,step=1.000000","support","0","no","SYCL"
+"SYCL0","PAD_REFLECT_1D","type=f32,ne_a=[512,34,2,1],pad_0=10,pad_1=9","support","1","yes","SYCL"
+"SYCL0","PAD_REFLECT_1D","type=f32,ne_a=[3000,384,4,1],pad_0=10,pad_1=9","support","1","yes","SYCL"
+"SYCL0","ROLL","shift0=3,shift1=-2,shift3=1,shift4=-1","support","1","yes","SYCL"
+"SYCL0","ARANGE","type=f32,start=0.000000,stop=10.000000,step=1.000000","support","1","yes","SYCL"
 "SYCL0","TIMESTEP_EMBEDDING","type=f32,ne_a=[2,1,1,1],dim=320,max_period=10000","support","1","yes","SYCL"
 "SYCL0","LEAKY_RELU","type=f32,ne_a=[10,5,4,3],negative_slope=0.100000","support","1","yes","SYCL"
 "SYCL0","PAD","type=f32,ne_a=[512,512,1,1],lp0=0,rp0=1,lp1=0,rp1=1,lp2=0,rp2=0,lp3=0,rp3=0,v=0","support","1","yes","SYCL"

From a90eb94ca9ec19f049a1c8e4958e71d9da777569 Mon Sep 17 00:00:00 2001
From: Aman Gupta <amangupta052@gmail.com>
Date: Thu, 13 Nov 2025 08:50:01 +0800
Subject: [PATCH 178/185] CUDA: fuse rope + set_rows (#16884)

* CUDA: add fused rope

* move k forward_expand up

* create helper function instead of re-using params

* make assert statement more in line with comment

* rope_norm: coalesced writes to global mem
---
 ggml/src/ggml-cuda/ggml-cuda.cu |  49 +++++++
 ggml/src/ggml-cuda/rope.cu      | 222 +++++++++++++++++++++++---------
 ggml/src/ggml-cuda/rope.cuh     |   2 +
 src/llama-graph.cpp             |   3 +-
 4 files changed, 215 insertions(+), 61 deletions(-)

diff --git a/ggml/src/ggml-cuda/ggml-cuda.cu b/ggml/src/ggml-cuda/ggml-cuda.cu
index 68dc57843e4..41de87c0999 100644
--- a/ggml/src/ggml-cuda/ggml-cuda.cu
+++ b/ggml/src/ggml-cuda/ggml-cuda.cu
@@ -2992,6 +2992,36 @@ static void update_cuda_graph_executable(ggml_backend_cuda_context * cuda_ctx) {
 }
 #endif
 
+static bool ggml_cuda_should_fuse_rope_set_rows(const ggml_tensor * rope,
+                                                const ggml_tensor * view,
+                                                const ggml_tensor * set_rows) {
+    // ne3 not tested
+    if (rope->src[0]->ne[3] != 1) {
+        return false;
+    }
+
+    if (set_rows->type != GGML_TYPE_F32 && set_rows->type != GGML_TYPE_F16) {
+        return false;
+    }
+
+    if (set_rows->src[1]->type != GGML_TYPE_I64) {
+        return false;
+    }
+
+    // The view should flatten two dims of rope into one dim
+    if (!ggml_is_contiguous(view) || view->ne[0] != rope->ne[0] * rope->ne[1]) {
+        return false;
+    }
+
+    // Only norm/neox shaders have the fusion code
+    const int mode = ((const int32_t *) rope->op_params)[2];
+    if (mode != GGML_ROPE_TYPE_NORMAL && mode != GGML_ROPE_TYPE_NEOX) {
+        return false;
+    }
+
+    return true;
+}
+
 static bool ggml_cuda_can_fuse(const struct ggml_cgraph * cgraph, int node_idx, std::initializer_list<enum ggml_op> ops, std::initializer_list<enum ggml_unary_op> unary_ops) {
 #ifndef NDEBUG
     const size_t num_unary = std::count(ops.begin(), ops.end(), GGML_OP_UNARY);
@@ -3067,6 +3097,16 @@ static bool ggml_cuda_can_fuse(const struct ggml_cgraph * cgraph, int node_idx,
         }
     }
 
+    if (ops.size() == 3 && ggml_can_fuse_subgraph(cgraph, node_idx, ops, { node_idx + 2 })) {
+        const ggml_tensor * rope     = cgraph->nodes[node_idx];
+        const ggml_tensor * view     = cgraph->nodes[node_idx + 1];
+        const ggml_tensor * set_rows = cgraph->nodes[node_idx + 2];
+
+        if (ggml_cuda_should_fuse_rope_set_rows(rope, view, set_rows)) {
+            return true;
+        }
+    }
+
     if (!ggml_can_fuse(cgraph, node_idx, ops)) {
         return false;
     }
@@ -3196,6 +3236,15 @@ static void evaluate_and_capture_cuda_graph(ggml_backend_cuda_context * cuda_ctx
                         continue;
                     }
 
+                    if (ggml_cuda_can_fuse(cgraph, i, { GGML_OP_ROPE, GGML_OP_VIEW, GGML_OP_SET_ROWS }, {})) {
+                        ggml_tensor * rope = cgraph->nodes[i];
+                        ggml_tensor * set_rows = cgraph->nodes[i + 2];
+
+                        ggml_cuda_op_rope_fused(*cuda_ctx, rope, set_rows);
+                        i += 2;
+                        continue;
+                    }
+
                     if (node->op == GGML_OP_ADD) {
                         int n_fuse = 0;
                         ggml_op ops[8];
diff --git a/ggml/src/ggml-cuda/rope.cu b/ggml/src/ggml-cuda/rope.cu
index 78ed7f519ab..88ed79111a1 100644
--- a/ggml/src/ggml-cuda/rope.cu
+++ b/ggml/src/ggml-cuda/rope.cu
@@ -1,3 +1,6 @@
+#include "convert.cuh"
+#include "ggml-cuda/common.cuh"
+#include "ggml.h"
 #include "rope.cuh"
 
 struct rope_corr_dims {
@@ -37,11 +40,23 @@ static __device__ void rope_yarn(
     }
 }
 
-template<bool forward, bool has_ff, typename T>
-static __global__ void rope_norm(
-        const T * x, T * dst, const int ne0, const int ne1, const int s1, const int s2, const int n_dims,
-        const int32_t * pos, const float freq_scale, const float ext_factor, const float attn_factor,
-        const rope_corr_dims corr_dims, const float theta_scale, const float * freq_factors) {
+template <bool forward, bool has_ff, typename T, typename D>
+static __global__ void rope_norm(const T *            x,
+                                 D *                  dst,
+                                 const int            ne0,
+                                 const int            ne1,
+                                 const int            s1,
+                                 const int            s2,
+                                 const int            n_dims,
+                                 const int32_t *      pos,
+                                 const float          freq_scale,
+                                 const float          ext_factor,
+                                 const float          attn_factor,
+                                 const rope_corr_dims corr_dims,
+                                 const float          theta_scale,
+                                 const float *        freq_factors,
+                                 const int64_t *      row_indices,
+                                 const int            set_rows_stride) {
     const int i0 = 2*(blockDim.y*blockIdx.y + threadIdx.y);
 
     if (i0 >= ne0) {
@@ -53,13 +68,27 @@ static __global__ void rope_norm(
     const int row_x     = row_dst % ne1;
     const int channel_x = row_dst / ne1;
 
-    const int idst = row_dst*ne0 + i0;
+    int       idst = row_dst * ne0 + i0;
     const int ix   = channel_x*s2 + row_x*s1 + i0;
 
-    if (i0 >= n_dims) {
-        dst[idst + 0] = x[ix + 0];
-        dst[idst + 1] = x[ix + 1];
+    // Fusion optimization: ROPE + VIEW + SET_ROWS.
+    // The rope output is viewed as a 1D tensor and offset based on a row index in row_indices.
+    if (set_rows_stride != 0) {
+        idst = row_x * ne0 + i0;
+        idst += row_indices[channel_x] * set_rows_stride;
+    }
 
+    const auto & store_coaelsced = [&](float x0, float x1) {
+        if constexpr (std::is_same_v<float, D>) {
+            float2 v = make_float2(x0, x1);
+            ggml_cuda_memcpy_1<8>(dst + idst, &v);
+        } else if constexpr (std::is_same_v<half, D>) {
+            half2 v = make_half2(x0, x1);
+            ggml_cuda_memcpy_1<4>(dst + idst, &v);
+        }
+    };
+    if (i0 >= n_dims) {
+        store_coaelsced(x[ix + 0], x[ix + 1]);
         return;
     }
 
@@ -75,15 +104,26 @@ static __global__ void rope_norm(
     const float x0 = x[ix + 0];
     const float x1 = x[ix + 1];
 
-    dst[idst + 0] = x0*cos_theta - x1*sin_theta;
-    dst[idst + 1] = x0*sin_theta + x1*cos_theta;
+    store_coaelsced(x0 * cos_theta - x1 * sin_theta, x0 * sin_theta + x1 * cos_theta);
 }
 
-template<bool forward, bool has_ff, typename T>
-static __global__ void rope_neox(
-        const T * x, T * dst, const int ne0, const int ne1, const int s1, const int s2, const int n_dims,
-        const int32_t * pos, const float freq_scale, const float ext_factor, const float attn_factor,
-        const rope_corr_dims corr_dims, const float theta_scale, const float * freq_factors) {
+template <bool forward, bool has_ff, typename T, typename D>
+static __global__ void rope_neox(const T *            x,
+                                 D *                  dst,
+                                 const int            ne0,
+                                 const int            ne1,
+                                 const int            s1,
+                                 const int            s2,
+                                 const int            n_dims,
+                                 const int32_t *      pos,
+                                 const float          freq_scale,
+                                 const float          ext_factor,
+                                 const float          attn_factor,
+                                 const rope_corr_dims corr_dims,
+                                 const float          theta_scale,
+                                 const float *        freq_factors,
+                                 const int64_t *      row_indices,
+                                 const int            set_rows_stride) {
     const int i0 = 2*(blockDim.y*blockIdx.y + threadIdx.y);
 
     if (i0 >= ne0) {
@@ -95,12 +135,19 @@ static __global__ void rope_neox(
     const int row_x     = row_dst % ne1;
     const int channel_x = row_dst / ne1;
 
-    const int idst = row_dst*ne0 + i0/2;
+    int       idst = row_dst * ne0 + i0 / 2;
     const int ix   = channel_x*s2 + row_x*s1 + i0/2;
 
+    // Fusion optimization: ROPE + VIEW + SET_ROWS.
+    // The rope output is viewed as a 1D tensor and offset based on a row index in row_indices.
+    if (set_rows_stride != 0) {
+        idst = row_x * ne0 + i0 / 2;
+        idst += row_indices[channel_x] * set_rows_stride;
+    }
+
     if (i0 >= n_dims) {
-        dst[idst + i0/2 + 0] = x[ix + i0/2 + 0];
-        dst[idst + i0/2 + 1] = x[ix + i0/2 + 1];
+        dst[idst + i0 / 2 + 0] = ggml_cuda_cast<D>(x[ix + i0 / 2 + 0]);
+        dst[idst + i0 / 2 + 1] = ggml_cuda_cast<D>(x[ix + i0 / 2 + 1]);
 
         return;
     }
@@ -117,8 +164,8 @@ static __global__ void rope_neox(
     const float x0 = x[ix + 0];
     const float x1 = x[ix + n_dims/2];
 
-    dst[idst + 0]        = x0*cos_theta - x1*sin_theta;
-    dst[idst + n_dims/2] = x0*sin_theta + x1*cos_theta;
+    dst[idst + 0]          = ggml_cuda_cast<D>(x0 * cos_theta - x1 * sin_theta);
+    dst[idst + n_dims / 2] = ggml_cuda_cast<D>(x0 * sin_theta + x1 * cos_theta);
 }
 
 template<bool forward, bool has_ff, typename T>
@@ -238,11 +285,25 @@ static __global__ void rope_vision(
     dst[idst + n_dims] = x0*sin_theta + x1*cos_theta;
 }
 
-template<bool forward, typename T>
-static void rope_norm_cuda(
-        const T * x, T * dst, const int ne0, const int ne1, const int s1, const int s2, const int n_dims, const int nr,
-        const int32_t * pos, const float freq_scale, const float freq_base, const float ext_factor, const float attn_factor,
-        const rope_corr_dims corr_dims, const float * freq_factors, cudaStream_t stream) {
+template <bool forward, typename T, typename D>
+static void rope_norm_cuda(const T *            x,
+                           D *                  dst,
+                           const int            ne0,
+                           const int            ne1,
+                           const int            s1,
+                           const int            s2,
+                           const int            n_dims,
+                           const int            nr,
+                           const int32_t *      pos,
+                           const float          freq_scale,
+                           const float          freq_base,
+                           const float          ext_factor,
+                           const float          attn_factor,
+                           const rope_corr_dims corr_dims,
+                           const float *        freq_factors,
+                           const int64_t *      row_indices,
+                           const int            set_rows_stride,
+                           cudaStream_t         stream) {
     GGML_ASSERT(ne0 % 2 == 0);
     const dim3 block_dims(1, CUDA_ROPE_BLOCK_SIZE, 1);
     const int n_blocks_x = (ne0 + 2*CUDA_ROPE_BLOCK_SIZE - 1) / (2*CUDA_ROPE_BLOCK_SIZE);
@@ -252,20 +313,34 @@ static void rope_norm_cuda(
 
     if (freq_factors == nullptr) {
         rope_norm<forward, false><<<block_nums, block_dims, 0, stream>>>(
-            x, dst, ne0, ne1, s1, s2, n_dims, pos, freq_scale, ext_factor,
-            attn_factor, corr_dims, theta_scale, freq_factors);
+            x, dst, ne0, ne1, s1, s2, n_dims, pos, freq_scale, ext_factor, attn_factor, corr_dims, theta_scale,
+            freq_factors, row_indices, set_rows_stride);
     } else {
         rope_norm<forward, true><<<block_nums, block_dims, 0, stream>>>(
-            x, dst, ne0, ne1, s1, s2, n_dims, pos, freq_scale, ext_factor,
-            attn_factor, corr_dims, theta_scale, freq_factors);
+            x, dst, ne0, ne1, s1, s2, n_dims, pos, freq_scale, ext_factor, attn_factor, corr_dims, theta_scale,
+            freq_factors, row_indices, set_rows_stride);
     }
 }
 
-template<bool forward, typename T>
-static void rope_neox_cuda(
-        const T * x, T * dst, const int ne0, const int ne1, const int s1, const int s2, const int n_dims, const int nr,
-        const int32_t * pos, const float freq_scale, const float freq_base, const float ext_factor, const float attn_factor,
-        const rope_corr_dims corr_dims, const float * freq_factors, cudaStream_t stream) {
+template <bool forward, typename T, typename D>
+static void rope_neox_cuda(const T *            x,
+                           D *                  dst,
+                           const int            ne0,
+                           const int            ne1,
+                           const int            s1,
+                           const int            s2,
+                           const int            n_dims,
+                           const int            nr,
+                           const int32_t *      pos,
+                           const float          freq_scale,
+                           const float          freq_base,
+                           const float          ext_factor,
+                           const float          attn_factor,
+                           const rope_corr_dims corr_dims,
+                           const float *        freq_factors,
+                           const int64_t *      row_indices,
+                           const int            set_rows_stride,
+                           cudaStream_t         stream) {
     GGML_ASSERT(ne0 % 2 == 0);
     const dim3 block_dims(1, CUDA_ROPE_BLOCK_SIZE, 1);
     const int n_blocks_x = (ne0 + 2*CUDA_ROPE_BLOCK_SIZE - 1) / (2*CUDA_ROPE_BLOCK_SIZE);
@@ -274,13 +349,13 @@ static void rope_neox_cuda(
     const float theta_scale = powf(freq_base, -2.0f/n_dims);
 
     if (freq_factors == nullptr) {
-        rope_neox<forward, false, T><<<block_nums, block_dims, 0, stream>>>(
-            x, dst, ne0, ne1, s1, s2, n_dims, pos, freq_scale, ext_factor,
-            attn_factor, corr_dims, theta_scale, freq_factors);
+        rope_neox<forward, false><<<block_nums, block_dims, 0, stream>>>(
+            x, dst, ne0, ne1, s1, s2, n_dims, pos, freq_scale, ext_factor, attn_factor, corr_dims, theta_scale,
+            freq_factors, row_indices, set_rows_stride);
     } else {
-        rope_neox<forward, true, T><<<block_nums, block_dims, 0, stream>>>(
-            x, dst, ne0, ne1, s1, s2, n_dims, pos, freq_scale, ext_factor,
-            attn_factor, corr_dims, theta_scale, freq_factors);
+        rope_neox<forward, true><<<block_nums, block_dims, 0, stream>>>(
+            x, dst, ne0, ne1, s1, s2, n_dims, pos, freq_scale, ext_factor, attn_factor, corr_dims, theta_scale,
+            freq_factors, row_indices, set_rows_stride);
     }
 }
 
@@ -333,7 +408,9 @@ static void rope_vision_cuda(
 }
 
 template <bool forward>
-void ggml_cuda_op_rope_impl(ggml_backend_cuda_context & ctx, ggml_tensor * dst) {
+void ggml_cuda_op_rope_impl(ggml_backend_cuda_context & ctx,
+                            ggml_tensor *               dst,
+                            const ggml_tensor *         set_rows = nullptr) {
     const ggml_tensor * src0 = dst->src[0];
     const ggml_tensor * src1 = dst->src[1];
     const ggml_tensor * src2 = dst->src[2];
@@ -341,12 +418,25 @@ void ggml_cuda_op_rope_impl(ggml_backend_cuda_context & ctx, ggml_tensor * dst)
     const float * src0_d = (const float *)src0->data;
     const float * src1_d = (const float *)src1->data;
 
-    float * dst_d = (float *)dst->data;
+    void *          dst_d           = dst->data;
+    const int64_t * row_indices     = nullptr;
+    ggml_type       dst_type        = dst->type;
+    int             set_rows_stride = 0;
+
+    if (set_rows != nullptr) {
+        GGML_ASSERT(forward);
+        dst_d           = set_rows->data;
+        row_indices     = (const int64_t *) set_rows->src[1]->data;
+        dst_type        = set_rows->type;
+        set_rows_stride = set_rows->nb[1] / ggml_type_size(set_rows->type);
+    }
     cudaStream_t stream = ctx.stream();
 
     GGML_ASSERT(src0->type == GGML_TYPE_F32 || src0->type == GGML_TYPE_F16);
     GGML_ASSERT( dst->type == GGML_TYPE_F32 ||  dst->type == GGML_TYPE_F16);
-    GGML_ASSERT(src0->type == dst->type);
+    // When not fused, src0 and dst types must match
+    // When fused (ROPE+VIEW+SET_ROWS), src0 may be F32 and dst may be F16
+    GGML_ASSERT(src0->type == dst->type || (src0->type == GGML_TYPE_F32 && dst->type == GGML_TYPE_F16));
 
     const int64_t ne00 = src0->ne[0]; // head dims
     const int64_t ne01 = src0->ne[1]; // num heads
@@ -404,14 +494,18 @@ void ggml_cuda_op_rope_impl(ggml_backend_cuda_context & ctx, ggml_tensor * dst)
 
     // compute
     if (is_neox) {
-        if (src0->type == GGML_TYPE_F32) {
-            rope_neox_cuda<forward>(
-                (const float *) src0_d, (float *) dst_d, ne00, ne01, s01, s02, n_dims, nr, pos, freq_scale,
-                freq_base, ext_factor, attn_factor, corr_dims, freq_factors, stream);
-        } else if (src0->type == GGML_TYPE_F16) {
-            rope_neox_cuda<forward>(
-                (const half *) src0_d, (half *) dst_d, ne00, ne01, s01, s02, n_dims, nr, pos, freq_scale,
-                freq_base, ext_factor, attn_factor, corr_dims, freq_factors, stream);
+        if (src0->type == GGML_TYPE_F32 && dst_type == GGML_TYPE_F32) {
+            rope_neox_cuda<forward, float, float>((const float *) src0_d, (float *) dst_d, ne00, ne01, s01, s02, n_dims,
+                                                  nr, pos, freq_scale, freq_base, ext_factor, attn_factor, corr_dims,
+                                                  freq_factors, row_indices, set_rows_stride, stream);
+        } else if (src0->type == GGML_TYPE_F32 && dst_type == GGML_TYPE_F16) {
+            rope_neox_cuda<forward, float, half>((const float *) src0_d, (half *) dst_d, ne00, ne01, s01, s02, n_dims,
+                                                 nr, pos, freq_scale, freq_base, ext_factor, attn_factor, corr_dims,
+                                                 freq_factors, row_indices, set_rows_stride, stream);
+        } else if (src0->type == GGML_TYPE_F16 && dst_type == GGML_TYPE_F16) {
+            rope_neox_cuda<forward, half, half>((const half *) src0_d, (half *) dst_d, ne00, ne01, s01, s02, n_dims, nr,
+                                                pos, freq_scale, freq_base, ext_factor, attn_factor, corr_dims,
+                                                freq_factors, row_indices, set_rows_stride, stream);
         } else {
             GGML_ABORT("fatal error");
         }
@@ -440,14 +534,18 @@ void ggml_cuda_op_rope_impl(ggml_backend_cuda_context & ctx, ggml_tensor * dst)
             GGML_ABORT("fatal error");
         }
     } else {
-        if (src0->type == GGML_TYPE_F32) {
-            rope_norm_cuda<forward>(
-                (const float *) src0_d, (float *) dst_d, ne00, ne01, s01, s02, n_dims, nr, pos, freq_scale,
-                freq_base, ext_factor, attn_factor, corr_dims, freq_factors, stream);
-        } else if (src0->type == GGML_TYPE_F16) {
-            rope_norm_cuda<forward>(
-                (const half *) src0_d, (half *) dst_d, ne00, ne01, s01, s02, n_dims, nr, pos, freq_scale,
-                freq_base, ext_factor, attn_factor, corr_dims, freq_factors, stream);
+        if (src0->type == GGML_TYPE_F32 && dst_type == GGML_TYPE_F32) {
+            rope_norm_cuda<forward, float, float>((const float *) src0_d, (float *) dst_d, ne00, ne01, s01, s02, n_dims,
+                                                  nr, pos, freq_scale, freq_base, ext_factor, attn_factor, corr_dims,
+                                                  freq_factors, row_indices, set_rows_stride, stream);
+        } else if (src0->type == GGML_TYPE_F32 && dst_type == GGML_TYPE_F16) {
+            rope_norm_cuda<forward, float, half>((const float *) src0_d, (half *) dst_d, ne00, ne01, s01, s02, n_dims,
+                                                 nr, pos, freq_scale, freq_base, ext_factor, attn_factor, corr_dims,
+                                                 freq_factors, row_indices, set_rows_stride, stream);
+        } else if (src0->type == GGML_TYPE_F16 && dst_type == GGML_TYPE_F16) {
+            rope_norm_cuda<forward, half, half>((const half *) src0_d, (half *) dst_d, ne00, ne01, s01, s02, n_dims, nr,
+                                                pos, freq_scale, freq_base, ext_factor, attn_factor, corr_dims,
+                                                freq_factors, row_indices, set_rows_stride, stream);
         } else {
             GGML_ABORT("fatal error");
         }
@@ -461,3 +559,7 @@ void ggml_cuda_op_rope(ggml_backend_cuda_context & ctx, ggml_tensor * dst) {
 void ggml_cuda_op_rope_back(ggml_backend_cuda_context & ctx, ggml_tensor * dst) {
     ggml_cuda_op_rope_impl<false>(ctx, dst);
 }
+
+void ggml_cuda_op_rope_fused(ggml_backend_cuda_context & ctx, ggml_tensor * rope, ggml_tensor * set_rows) {
+    ggml_cuda_op_rope_impl<true>(ctx, rope, set_rows);
+}
diff --git a/ggml/src/ggml-cuda/rope.cuh b/ggml/src/ggml-cuda/rope.cuh
index 9139f3b220d..72af086cd1b 100644
--- a/ggml/src/ggml-cuda/rope.cuh
+++ b/ggml/src/ggml-cuda/rope.cuh
@@ -5,3 +5,5 @@
 void ggml_cuda_op_rope(ggml_backend_cuda_context & ctx, ggml_tensor * dst);
 
 void ggml_cuda_op_rope_back(ggml_backend_cuda_context & ctx, ggml_tensor * dst);
+
+void ggml_cuda_op_rope_fused(ggml_backend_cuda_context & ctx, ggml_tensor * dst, ggml_tensor * set_rows);
diff --git a/src/llama-graph.cpp b/src/llama-graph.cpp
index b199e94628f..650e40ec6ff 100644
--- a/src/llama-graph.cpp
+++ b/src/llama-graph.cpp
@@ -1592,9 +1592,10 @@ ggml_tensor * llm_graph_context::build_attn(
             int       il) const {
     // these nodes are added to the graph together so that they are not reordered
     // by doing so, the number of splits in the graph is reduced
+    // expand k later to enable rope fusion which directly writes into k-v cache
     ggml_build_forward_expand(gf, q_cur);
-    ggml_build_forward_expand(gf, k_cur);
     ggml_build_forward_expand(gf, v_cur);
+    ggml_build_forward_expand(gf, k_cur);
 
     const auto * mctx_cur = inp->mctx;
 

From 97d5117217e4ad904493345e2f71dfe441a08e25 Mon Sep 17 00:00:00 2001
From: TecJesh <qdvm5gl@163.com>
Date: Thu, 13 Nov 2025 09:39:51 +0800
Subject: [PATCH 179/185] CANN: Add cross_entropy_loss op support (#16886)

* update L2_NORM op support

* update L2_NORM op support

* remove extra whitespace

* cann: update cross_entropy_loss op support

* remove trailing whitespaces

* rebase the latest code in the main repository and remove the l2_norm operator that already exists in another pull request.

* undo the l2_norm operator deletion
---
 ggml/src/ggml-cann/aclnn_ops.cpp | 86 ++++++++++++++++++++++++++++++++
 ggml/src/ggml-cann/aclnn_ops.h   | 38 ++++++++++++++
 ggml/src/ggml-cann/ggml-cann.cpp |  4 ++
 3 files changed, 128 insertions(+)

diff --git a/ggml/src/ggml-cann/aclnn_ops.cpp b/ggml/src/ggml-cann/aclnn_ops.cpp
index 4835c5c0387..6d8b4a5f0eb 100644
--- a/ggml/src/ggml-cann/aclnn_ops.cpp
+++ b/ggml/src/ggml-cann/aclnn_ops.cpp
@@ -477,6 +477,92 @@ void ggml_cann_l2_norm(ggml_backend_cann_context & ctx, ggml_tensor * dst) {
     ggml_cann_release_resources(ctx, dims_array, p_scalar, acl_src, acl_dst, acl_div);
 }
 
+void ggml_cann_cross_entropy_loss(ggml_backend_cann_context & ctx, ggml_tensor * dst) {
+    ggml_tensor * src0 = dst->src[0];
+    ggml_tensor * src1 = dst->src[1];
+
+    const int64_t nc = src0->ne[0];
+    const int64_t nr = ggml_nrows(src0);
+
+    int64_t logits_ne[] = {nc, nr};
+    size_t logits_nb[2];
+    logits_nb[0] = ggml_type_size(src0->type);
+    logits_nb[1] = logits_nb[0] * logits_ne[0];
+    aclTensor * acl_logits = ggml_cann_create_tensor(src0->data, ACL_FLOAT, sizeof(float), logits_ne, logits_nb, 2);
+
+    size_t log_softmax_type_size = sizeof(float);
+    int64_t log_softmax_n_bytes = nr * nc * log_softmax_type_size;
+    ggml_cann_pool_alloc log_softmax_allocator(ctx.pool(), log_softmax_n_bytes);
+    void * log_softmax_buffer = log_softmax_allocator.get();
+
+    int64_t log_softmax_ne[] = {nc, nr};
+    size_t log_softmax_nb[2];
+    log_softmax_nb[0] = log_softmax_type_size;
+    log_softmax_nb[1] = log_softmax_nb[0] * log_softmax_ne[0];
+    aclTensor * acl_log_softmax = ggml_cann_create_tensor(log_softmax_buffer, ACL_FLOAT, log_softmax_type_size, log_softmax_ne, log_softmax_nb, 2);
+
+    GGML_CANN_CALL_ACLNN_OP(ctx, LogSoftmax, acl_logits, 1, acl_log_softmax);
+
+    int64_t labels_ne[] = {nc, nr};
+    size_t labels_nb[2];
+    labels_nb[0] = ggml_type_size(src1->type);
+    labels_nb[1] = labels_nb[0] * labels_ne[0];
+    aclTensor * acl_labels = ggml_cann_create_tensor(src1->data, ACL_FLOAT, sizeof(float), labels_ne, labels_nb, 2);
+
+    size_t mul_type_size = sizeof(float);
+    int64_t mul_n_bytes = nr * nc * mul_type_size;
+    ggml_cann_pool_alloc mul_allocator(ctx.pool(), mul_n_bytes);
+    void * mul_buffer = mul_allocator.get();
+
+    int64_t mul_ne[] = {nc, nr};
+    size_t mul_nb[2];
+    mul_nb[0] = mul_type_size;
+    mul_nb[1] = mul_nb[0] * mul_ne[0];
+    aclTensor * acl_mul_result = ggml_cann_create_tensor(mul_buffer, ACL_FLOAT, mul_type_size, mul_ne, mul_nb, 2);
+
+    GGML_CANN_CALL_ACLNN_OP(ctx, Mul, acl_log_softmax, acl_labels, acl_mul_result);
+
+    size_t sum_per_sample_type_size = sizeof(float);
+    int64_t sum_per_sample_n_bytes = nr * sum_per_sample_type_size;
+    ggml_cann_pool_alloc sum_per_sample_allocator(ctx.pool(), sum_per_sample_n_bytes);
+    void * sum_per_sample_buffer = sum_per_sample_allocator.get();
+
+    int64_t sum_per_sample_ne[] = {nr};
+    size_t sum_per_sample_nb[1];
+    sum_per_sample_nb[0] = sum_per_sample_type_size;
+    aclTensor * acl_sum_per_sample = ggml_cann_create_tensor(sum_per_sample_buffer, ACL_FLOAT, sum_per_sample_type_size, sum_per_sample_ne, sum_per_sample_nb, 1);
+
+    std::vector<int64_t> sum_dims = {1};
+    aclIntArray * dims_array = aclCreateIntArray(sum_dims.data(), sum_dims.size());
+    bool keep_dims = false;
+
+    GGML_CANN_CALL_ACLNN_OP(ctx, ReduceSum, acl_mul_result, dims_array, keep_dims, ACL_FLOAT, acl_sum_per_sample);
+
+    size_t total_sum_type_size = sizeof(float);
+    int64_t total_sum_n_bytes = 1 * total_sum_type_size;
+    ggml_cann_pool_alloc total_sum_allocator(ctx.pool(), total_sum_n_bytes);
+    void * total_sum_buffer = total_sum_allocator.get();
+
+    int64_t total_sum_ne[] = {1};
+    size_t total_sum_nb[1];
+    total_sum_nb[0] = total_sum_type_size;
+
+    aclTensor * acl_total_sum = ggml_cann_create_tensor(total_sum_buffer, ACL_FLOAT, total_sum_type_size, total_sum_ne, total_sum_nb, 1);
+
+    std::vector<int64_t> total_sum_dims = {0};
+    aclIntArray * total_sum_dims_array = aclCreateIntArray(total_sum_dims.data(), total_sum_dims.size());
+
+    GGML_CANN_CALL_ACLNN_OP(ctx, ReduceSum, acl_sum_per_sample, total_sum_dims_array, keep_dims, ACL_FLOAT, acl_total_sum);
+
+    float value = -1.0f / static_cast<float>(nr);
+    aclScalar * scale_factor = aclCreateScalar(&value, aclDataType::ACL_FLOAT);
+    aclTensor * acl_dst = ggml_cann_create_tensor(dst->data, ACL_FLOAT, sizeof(float), total_sum_ne, total_sum_nb, 1);
+
+    GGML_CANN_CALL_ACLNN_OP(ctx, Muls, acl_total_sum, scale_factor, acl_dst);
+
+    ggml_cann_release_resources(ctx, acl_logits, acl_log_softmax, acl_labels, acl_mul_result, acl_sum_per_sample, acl_total_sum, acl_dst, scale_factor, dims_array, total_sum_dims_array);
+}
+
 void ggml_cann_group_norm(ggml_backend_cann_context & ctx, ggml_tensor * dst) {
     ggml_tensor * src = dst->src[0];
 
diff --git a/ggml/src/ggml-cann/aclnn_ops.h b/ggml/src/ggml-cann/aclnn_ops.h
index 060eedbbb02..c1ea1b153fc 100644
--- a/ggml/src/ggml-cann/aclnn_ops.h
+++ b/ggml/src/ggml-cann/aclnn_ops.h
@@ -47,6 +47,7 @@
 #include <aclnnop/aclnn_log.h>
 #include <aclnnop/aclnn_sign.h>
 #include <aclnnop/aclnn_norm.h>
+#include <aclnnop/aclnn_logsoftmax.h>
 #include "acl_tensor.h"
 #include "common.h"
 
@@ -211,6 +212,43 @@ void ggml_cann_norm(ggml_backend_cann_context & ctx, ggml_tensor * dst);
  */
 void ggml_cann_l2_norm(ggml_backend_cann_context & ctx, ggml_tensor * dst);
 
+/**
+ * @brief   Computes the Cross Entropy Loss for a ggml tensor using the CANN
+ *          backend.
+ *
+ * @details This function computes the cross entropy loss between the predicted
+ *          logits and target probability distributions. The operation follows
+ *          the same computation pattern as the CPU implementation:
+ *          1. Applies log_softmax to the logits along the class dimension
+ *          2. Element-wise multiplication with target distributions
+ *          3. Summation along the class dimension to get per-sample losses
+ *          4. Global summation and scaling by -1/nr to get final loss
+ *
+ *          The computation can be expressed as:
+ *          \f[
+ *              \text{loss} = -\frac{1}{N} \sum_{i=1}^{N} \sum_{j=1}^{C} y_{ij} \cdot \log(\text{softmax}(x_{ij}))
+ *          \f]
+ *          where \f$N\f$ is the total number of samples, \f$C\f$ is the number
+ *          of classes, \f$x\f$ are the logits, and \f$y\f$ are the target
+ *          probability distributions.
+ *
+ * @param ctx The CANN context used for operations.
+ * @param dst The destination tensor where the computed loss will be stored.
+ *            This should be a scalar tensor containing the final loss value.
+ *
+ * @note This implementation computes cross entropy between probability
+ *       distributions, not the typical classification cross entropy that
+ *       expects class indices as targets. Both input tensors (src0 and src1)
+ *       should have the same shape and represent probability distributions
+ *       over the class dimension.
+ * @note The function expects two source tensors:
+ *       - dst->src[0]: Logits tensor (before softmax)
+ *       - dst->src[1]: Target probability distributions tensor
+ * @note The computation is performed using CANN backend operators including
+ *       LogSoftmax, Mul, ReduceSum, and Muls for the final scaling.
+ */
+void ggml_cann_cross_entropy_loss(ggml_backend_cann_context & ctx, ggml_tensor * dst);
+
 /**
  * @brief  Computes the Group Normalization for a ggml tensor using the CANN
  *         backend.
diff --git a/ggml/src/ggml-cann/ggml-cann.cpp b/ggml/src/ggml-cann/ggml-cann.cpp
index 9de9440ac65..da7aede702a 100644
--- a/ggml/src/ggml-cann/ggml-cann.cpp
+++ b/ggml/src/ggml-cann/ggml-cann.cpp
@@ -1780,6 +1780,9 @@ static bool ggml_cann_compute_forward(ggml_backend_cann_context & ctx, struct gg
         case GGML_OP_L2_NORM:
             ggml_cann_l2_norm(ctx, dst);
             break;
+        case GGML_OP_CROSS_ENTROPY_LOSS:
+            ggml_cann_cross_entropy_loss(ctx, dst);
+            break;
         case GGML_OP_CONCAT:
             ggml_cann_concat(ctx, dst);
             break;
@@ -2519,6 +2522,7 @@ static bool ggml_backend_cann_supports_op(ggml_backend_dev_t dev, const ggml_ten
                 return (p0 <= (k0 / 2)) && (p1 <= (k1 / 2));
             }
         case GGML_OP_L2_NORM:
+        case GGML_OP_CROSS_ENTROPY_LOSS:
         case GGML_OP_DUP:
         case GGML_OP_SUM:
         case GGML_OP_IM2COL:

From 879dec341a528be90fb03bbc9bd3bea7da0b11de Mon Sep 17 00:00:00 2001
From: Diego Devesa <slarengh@gmail.com>
Date: Thu, 13 Nov 2025 00:59:05 -0800
Subject: [PATCH 180/185] ggml-cpu : use template for argsort (#17222)

---
 ggml/src/ggml-cpu/ops.cpp  | 30 ++++++++++++++++++++++--------
 tests/test-backend-ops.cpp |  2 ++
 2 files changed, 24 insertions(+), 8 deletions(-)

diff --git a/ggml/src/ggml-cpu/ops.cpp b/ggml/src/ggml-cpu/ops.cpp
index 9f1e5f8d646..09f53b470b2 100644
--- a/ggml/src/ggml-cpu/ops.cpp
+++ b/ggml/src/ggml-cpu/ops.cpp
@@ -7665,6 +7665,18 @@ void ggml_compute_forward_timestep_embedding(
 
 // ggml_compute_forward_argsort
 
+template<enum ggml_sort_order order>
+struct argsort_cmp {
+    const float * data;
+    bool operator()(int32_t a, int32_t b) const {
+        if constexpr (order == GGML_SORT_ORDER_ASC) {
+            return data[a] < data[b];
+        } else {
+            return data[a] > data[b];
+        }
+    }
+};
+
 static void ggml_compute_forward_argsort_f32(
     const ggml_compute_params * params,
     ggml_tensor * dst) {
@@ -7691,16 +7703,18 @@ static void ggml_compute_forward_argsort_f32(
             dst_data[j] = j;
         }
 
-        std::function<bool(int32_t, int32_t)> cmp;
-
-        // note: this might be causing memory allocations? ideally should be avoided if it's the case
         switch (order) {
-            case GGML_SORT_ORDER_ASC:  cmp = [src_data](int32_t a, int32_t b) { return src_data[a] < src_data[b]; }; break;
-            case GGML_SORT_ORDER_DESC: cmp = [src_data](int32_t a, int32_t b) { return src_data[a] > src_data[b]; }; break;
-            default: GGML_ABORT("invalid sort order");
-        }
+            case GGML_SORT_ORDER_ASC:
+                std::sort(dst_data, dst_data + ne0, argsort_cmp<GGML_SORT_ORDER_ASC>{src_data});
+                break;
 
-        std::sort(dst_data, dst_data + ne0, cmp);
+            case GGML_SORT_ORDER_DESC:
+                std::sort(dst_data, dst_data + ne0, argsort_cmp<GGML_SORT_ORDER_DESC>{src_data});
+                break;
+
+            default:
+                GGML_ABORT("invalid sort order");
+        }
     }
 }
 
diff --git a/tests/test-backend-ops.cpp b/tests/test-backend-ops.cpp
index 92c17ac4399..38b7ddf2217 100644
--- a/tests/test-backend-ops.cpp
+++ b/tests/test-backend-ops.cpp
@@ -7631,6 +7631,8 @@ static std::vector<std::unique_ptr<test_case>> make_test_cases_perf() {
         test_cases.emplace_back(new test_sum(GGML_TYPE_F32, it));
     }
 
+    test_cases.emplace_back(new test_argsort(GGML_TYPE_F32, {65000, 16, 1, 1}));
+
     return test_cases;
 }
 

From 2776db6c810cc08b44b68326204a6c6a228ad4ff Mon Sep 17 00:00:00 2001
From: Georgi Gerganov <ggerganov@gmail.com>
Date: Thu, 13 Nov 2025 12:59:37 +0200
Subject: [PATCH 181/185] Revert "ggml-cpu: handle 3d tensors in repack mat_mul
 (#17030)" (#17233)

This reverts commit 1c398dc9eca9c366ce98deb0e6f3538e444ebc8a.
---
 ggml/src/ggml-cpu/repack.cpp | 132 +++++++++++------------------------
 1 file changed, 42 insertions(+), 90 deletions(-)

diff --git a/ggml/src/ggml-cpu/repack.cpp b/ggml/src/ggml-cpu/repack.cpp
index 274be146dc5..8421c84ce09 100644
--- a/ggml/src/ggml-cpu/repack.cpp
+++ b/ggml/src/ggml-cpu/repack.cpp
@@ -1600,52 +1600,29 @@ template <typename BLOC_TYPE, int64_t INTER_SIZE, int64_t NB_COLS, ggml_type PAR
         return false;
     }
 
-    void forward_mul_mat_one_chunk(ggml_compute_params * params,
-                                   ggml_tensor *         op,
-                                   int64_t               src0_start,
-                                   int64_t               src0_end,
-                                   int64_t               src1_start,
-                                   int64_t               src1_end) {
+    void forward_mul_mat_one_chunk(ggml_compute_params * params, ggml_tensor * op, int64_t src0_start, int64_t src0_end) {
         const ggml_tensor * src0 = op->src[0];
         const ggml_tensor * src1 = op->src[1];
         ggml_tensor *       dst  = op;
 
         GGML_TENSOR_BINARY_OP_LOCALS
 
+        const void * src1_wdata      = params->wdata;
         const size_t src1_col_stride = ggml_row_size(PARAM_TYPE, ne10);
 
-        GGML_ASSERT(ne03 == 1 && ne13 == 1);
-        GGML_ASSERT(ne12 % ne02 == 0);
-        const int64_t r2 = ne12 / ne02;
-
-        const int64_t i12 = src1_start / ne1;
-        const int64_t i11 = src1_start - i12 * ne1;
-
-        // Determine batch index
-        const int64_t i02 = i12 / r2;
-
-        const int64_t i1 = i11;
-        const int64_t i2 = i12;
-
-        const char * src0_ptr = (const char *) src0->data + i02 * nb02;
-        const char * src1_ptr = (const char *) params->wdata + (i11 + i12 * ne11) * src1_col_stride;
-        char *       dst_ptr  = ((char *) dst->data + (i1 * nb1 + i2 * nb2));
-
-        const int64_t nrows = src1_end - src1_start;
-        const int64_t ncols = src0_end - src0_start;
-
-        GGML_ASSERT(src1_ptr + src1_col_stride * nrows <= (const char *) params->wdata + params->wsize);
-
         // If there are more than three rows in src1, use gemm; otherwise, use gemv.
-        if (nrows > 3) {
-            gemm<BLOC_TYPE, INTER_SIZE, NB_COLS, PARAM_TYPE>(ne00, (float *) (dst_ptr) + src0_start, nb1 / nb0,
-                                                             src0_ptr + src0_start * nb01, src1_ptr,
-                                                             nrows - (nrows % 4), ncols);
+        if (ne11 > 3) {
+            gemm<BLOC_TYPE, INTER_SIZE, NB_COLS, PARAM_TYPE>(ne00,
+                    (float *) ((char *) dst->data) + src0_start, ne01,
+                    (const char *) src0->data + src0_start * nb01,
+                    (const char *) src1_wdata, ne11 - ne11 % 4, src0_end - src0_start);
         }
-        for (int iter = nrows - (nrows % 4); iter < nrows; iter++) {
-            gemv<BLOC_TYPE, INTER_SIZE, NB_COLS, PARAM_TYPE>(ne00, (float *) (dst_ptr + (iter * nb1)) + src0_start,
-                                                             ne01, src0_ptr + src0_start * nb01,
-                                                             src1_ptr + (src1_col_stride * iter), 1 /* nrows */, ncols);
+        for (int iter = ne11 - ne11 % 4; iter < ne11; iter++) {
+            gemv<BLOC_TYPE, INTER_SIZE, NB_COLS, PARAM_TYPE>(ne00,
+                    (float *) ((char *) dst->data + (iter * nb1)) + src0_start, ne01,
+                    (const char *) src0->data + src0_start * nb01,
+                    (const char *) src1_wdata + (src1_col_stride * iter), 1,
+                    src0_end - src0_start);
         }
     }
 
@@ -1670,12 +1647,6 @@ template <typename BLOC_TYPE, int64_t INTER_SIZE, int64_t NB_COLS, ggml_type PAR
         GGML_ASSERT(nb1 <= nb2);
         GGML_ASSERT(nb2 <= nb3);
 
-        // TODO: General batched mul mat for 4D tensors
-        // Currently only supports 3D tensors
-        GGML_ASSERT(ne03 == 1);
-        GGML_ASSERT(ne13 == 1);
-        GGML_ASSERT(ne3 == 1);
-
         GGML_ASSERT(src1->type == GGML_TYPE_F32);
 
         GGML_ASSERT(ggml_n_dims(op->src[0]) == 2);
@@ -1683,60 +1654,47 @@ template <typename BLOC_TYPE, int64_t INTER_SIZE, int64_t NB_COLS, ggml_type PAR
 
         char *       wdata = static_cast<char *>(params->wdata);
         const size_t nbw1  = ggml_row_size(PARAM_TYPE, ne10);
-        const size_t nbw2  = nbw1 * ne11;
 
-        assert(params->wsize >= nbw2 * ne12);
+        assert(params->wsize >= nbw1 * ne11);
 
         const ggml_from_float_t from_float = ggml_get_type_traits_cpu(PARAM_TYPE)->from_float;
 
-        for (int64_t i12 = 0; i12 < ne12; i12++) {
-            char * data_ptr  = (char *) src1->data + i12 * nb12;
-            char * wdata_ptr = wdata + i12 * nbw2;
-
-            for (int64_t i11 = ith * 4; i11 < ne11 - ne11 % 4; i11 += nth * 4) {
-                ggml_quantize_mat_t<INTER_SIZE, PARAM_TYPE>((float *) (data_ptr + i11 * nb11),
-                                                            (void *) (wdata_ptr + i11 * nbw1), 4, ne10);
-            }
+        int64_t i11_processed = 0;
+        for (int64_t i11 = ith * 4; i11 < ne11 - ne11 % 4; i11 += nth * 4) {
+            ggml_quantize_mat_t<INTER_SIZE, PARAM_TYPE>((float *) ((char *) src1->data + i11 * nb11), (void *) (wdata + i11 * nbw1), 4, ne10);
+        }
 
-            const int64_t i11_processed = ne11 - ne11 % 4;
-            for (int64_t i11 = i11_processed + ith; i11 < ne11; i11 += nth) {
-                from_float((float *) (data_ptr + i11 * nb11), (void *) (wdata_ptr + i11 * nbw1), ne10);
-            }
+        i11_processed = ne11 - ne11 % 4;
+        for (int64_t i11 = i11_processed + ith; i11 < ne11; i11 += nth) {
+            from_float((float *) ((char *) src1->data + i11 * nb11), (void *) (wdata + i11 * nbw1), ne10);
         }
 
         // disable for NUMA
         const bool disable_chunking = ggml_is_numa();
 
         // 4x chunks per thread
-        const int64_t nr0 = ggml_nrows(op->src[0]);
-        const int64_t nr1 = ne1 * ne2 * ne3;
-
-        int     nth_scaled  = nth * 4;
-        int64_t chunk_size0 = (nr0 + nth_scaled - 1) / nth_scaled;
-        // avoid too small chunks for narrow src1
-        int64_t chunk_size1 = MAX(16, (nr1 + nth - 1) / nth);
-        int64_t nchunk0     = (nr0 + chunk_size0 - 1) / chunk_size0;
-        int64_t nchunk1     = (nr1 + chunk_size1 - 1) / chunk_size1;
+        int64_t nr = ggml_nrows(op->src[0]);
+        int nth_scaled = nth * 4;
+        int64_t chunk_size = (nr + nth_scaled - 1) / nth_scaled;
+        int64_t nchunk     = (nr + chunk_size - 1) / chunk_size;
 
         // Ensure minimum chunk size to avoid alignment issues with high thread counts
         // Minimum chunk size should be at least NB_COLS to prevent overlapping chunks after alignment
         const int64_t min_chunk_size = NB_COLS;
-        if (nchunk0 > 0 && (nr0 / nchunk0) < min_chunk_size && nr0 >= min_chunk_size) {
-            nchunk0 = (nr0 + min_chunk_size - 1) / min_chunk_size;
+        if (nchunk > 0 && (nr / nchunk) < min_chunk_size && nr >= min_chunk_size) {
+            nchunk = (nr + min_chunk_size - 1) / min_chunk_size;
         }
 
-        if (nth == 1 || nchunk0 * nchunk1 < nth || disable_chunking) {
-            nchunk0 = nr0 > nr1 ? nth : 1;
-            nchunk1 = nr0 > nr1 ? 1 : nth;
+        if (nth == 1 || nchunk < nth || disable_chunking) {
+            nchunk = nth;
         }
 
-        const int64_t dr0 = (nr0 + nchunk0 - 1) / nchunk0;
-        const int64_t dr1 = (nr1 + nchunk1 - 1) / nchunk1;
-
         // Ensure nchunk doesn't exceed the number of rows divided by minimum chunk size
         // This prevents creating too many tiny chunks that could overlap after alignment
-        const int64_t max_nchunk = (nr0 + min_chunk_size - 1) / min_chunk_size;
-        nchunk0                  = MIN(nchunk0, max_nchunk);
+        const int64_t max_nchunk = (nr + min_chunk_size - 1) / min_chunk_size;
+        if (nchunk > max_nchunk) {
+            nchunk = max_nchunk;
+        }
 
         if (ith == 0) {
             // Every thread starts at ith, so the first unprocessed chunk is nth.  This save a bit of coordination right at the start.
@@ -1748,29 +1706,23 @@ template <typename BLOC_TYPE, int64_t INTER_SIZE, int64_t NB_COLS, ggml_type PAR
         // The first chunk comes from our thread_id, the rest will get auto-assigned.
         int current_chunk = ith;
 
-        while (current_chunk < nchunk0 * nchunk1) {
-            const int64_t ith0 = current_chunk % nchunk0;
-            const int64_t ith1 = current_chunk / nchunk0;
-
-            int64_t src0_start = dr0 * ith0;
-            int64_t src0_end   = MIN(src0_start + dr0, nr0);
-
-            int64_t src1_start = dr1 * ith1;
-            int64_t src1_end   = MIN(src1_start + dr1, nr1);
+        while (current_chunk < nchunk) {
+            int64_t src0_start = (current_chunk * ne01) / nchunk;
+            int64_t src0_end   = ((current_chunk + 1) * ne01) / nchunk;
 
             // Align boundaries to NB_COLS - round up to ensure all data is included
             // The chunk size limiting above ensures chunks are large enough to prevent overlaps
             src0_start = (src0_start % NB_COLS) ? src0_start + NB_COLS - (src0_start % NB_COLS) : src0_start;
-            src0_end   = (src0_end % NB_COLS) ? src0_end + NB_COLS - (src0_end % NB_COLS) : src0_end;
-            src0_end   = MIN(src0_end, ne01);
+            src0_end   = (src0_end   % NB_COLS) ? src0_end   + NB_COLS - (src0_end   % NB_COLS) : src0_end;
+            if (src0_end > ne01) {
+                src0_end = ne01;
+            }
 
-            // Make sure current plane is the last one before exiting
             if (src0_start >= src0_end) {
-                current_chunk = ggml_threadpool_chunk_add(params->threadpool, 1);
-                continue;
+                break;
             }
 
-            forward_mul_mat_one_chunk(params, dst, src0_start, src0_end, src1_start, src1_end);
+            forward_mul_mat_one_chunk(params, dst, src0_start, src0_end);
 
             current_chunk = ggml_threadpool_chunk_add(params->threadpool, 1);
         }

From 0cfb19166b39a8c8ff2421bfcef7c3a595161367 Mon Sep 17 00:00:00 2001
From: bagheera <59658056+bghira@users.noreply.github.com>
Date: Thu, 13 Nov 2025 05:32:44 -0600
Subject: [PATCH 182/185] metal: accelerated conv2d (#17175)

* metal: accelerated conv2d

* cont : cleanup

---------

Co-authored-by: bghira <bghira@users.github.com>
Co-authored-by: Georgi Gerganov <ggerganov@gmail.com>
---
 ggml/src/ggml-metal/ggml-metal-device.cpp |  24 +++++
 ggml/src/ggml-metal/ggml-metal-device.h   |   1 +
 ggml/src/ggml-metal/ggml-metal-device.m   |   5 +
 ggml/src/ggml-metal/ggml-metal-impl.h     |  30 ++++++
 ggml/src/ggml-metal/ggml-metal-ops.cpp    |  88 ++++++++++++++++-
 ggml/src/ggml-metal/ggml-metal-ops.h      |   1 +
 ggml/src/ggml-metal/ggml-metal.metal      | 114 ++++++++++++++++++++++
 7 files changed, 258 insertions(+), 5 deletions(-)

diff --git a/ggml/src/ggml-metal/ggml-metal-device.cpp b/ggml/src/ggml-metal/ggml-metal-device.cpp
index 5607deaf414..08095dcf060 100644
--- a/ggml/src/ggml-metal/ggml-metal-device.cpp
+++ b/ggml/src/ggml-metal/ggml-metal-device.cpp
@@ -1438,6 +1438,30 @@ ggml_metal_pipeline_t ggml_metal_library_get_pipeline_conv_transpose_2d(ggml_met
     return res;
 }
 
+ggml_metal_pipeline_t ggml_metal_library_get_pipeline_conv_2d(ggml_metal_library_t lib, const ggml_tensor * op) {
+    assert(op->op == GGML_OP_CONV_2D);
+
+    GGML_ASSERT(ggml_is_contiguous(op->src[0]));
+    GGML_ASSERT(op->src[0]->type == GGML_TYPE_F16 || op->src[0]->type == GGML_TYPE_F32);
+    GGML_ASSERT(op->src[1]->type == GGML_TYPE_F32);
+    GGML_ASSERT(op->type         == GGML_TYPE_F32);
+
+    char base[256];
+    char name[256];
+
+    snprintf(base, 256, "kernel_conv_2d_%s_%s", ggml_type_name(op->src[0]->type), ggml_type_name(op->src[1]->type));
+    snprintf(name, 256, "%s", base);
+
+    ggml_metal_pipeline_t res = ggml_metal_library_get_pipeline(lib, name);
+    if (res) {
+        return res;
+    }
+
+    res = ggml_metal_library_compile_pipeline(lib, base, name, nullptr);
+
+    return res;
+}
+
 ggml_metal_pipeline_t ggml_metal_library_get_pipeline_upscale(ggml_metal_library_t lib, const ggml_tensor * op) {
     assert(op->op == GGML_OP_UPSCALE);
 
diff --git a/ggml/src/ggml-metal/ggml-metal-device.h b/ggml/src/ggml-metal/ggml-metal-device.h
index cb27dca9892..5a8bc0c1ccd 100644
--- a/ggml/src/ggml-metal/ggml-metal-device.h
+++ b/ggml/src/ggml-metal/ggml-metal-device.h
@@ -133,6 +133,7 @@ ggml_metal_pipeline_t ggml_metal_library_get_pipeline_rope              (ggml_me
 ggml_metal_pipeline_t ggml_metal_library_get_pipeline_im2col            (ggml_metal_library_t lib, const struct ggml_tensor * op);
 ggml_metal_pipeline_t ggml_metal_library_get_pipeline_conv_transpose_1d (ggml_metal_library_t lib, const struct ggml_tensor * op);
 ggml_metal_pipeline_t ggml_metal_library_get_pipeline_conv_transpose_2d (ggml_metal_library_t lib, const struct ggml_tensor * op);
+ggml_metal_pipeline_t ggml_metal_library_get_pipeline_conv_2d           (ggml_metal_library_t lib, const struct ggml_tensor * op);
 ggml_metal_pipeline_t ggml_metal_library_get_pipeline_upscale           (ggml_metal_library_t lib, const struct ggml_tensor * op);
 ggml_metal_pipeline_t ggml_metal_library_get_pipeline_pad               (ggml_metal_library_t lib, const struct ggml_tensor * op);
 ggml_metal_pipeline_t ggml_metal_library_get_pipeline_pad_reflect_1d    (ggml_metal_library_t lib, const struct ggml_tensor * op);
diff --git a/ggml/src/ggml-metal/ggml-metal-device.m b/ggml/src/ggml-metal/ggml-metal-device.m
index 3471225ab47..69c8820854a 100644
--- a/ggml/src/ggml-metal/ggml-metal-device.m
+++ b/ggml/src/ggml-metal/ggml-metal-device.m
@@ -885,6 +885,11 @@ bool ggml_metal_device_supports_op(ggml_metal_device_t dev, const struct ggml_te
             return true;
         case GGML_OP_IM2COL:
             return ggml_is_contiguous(op->src[1]) && op->src[1]->type == GGML_TYPE_F32 && (op->type == GGML_TYPE_F16 || op->type == GGML_TYPE_F32);
+        case GGML_OP_CONV_2D:
+            return ggml_is_contiguous(op->src[0]) &&
+                   op->src[1]->type == GGML_TYPE_F32 &&
+                   op->type == GGML_TYPE_F32 &&
+                   (op->src[0]->type == GGML_TYPE_F16 || op->src[0]->type == GGML_TYPE_F32);
         case GGML_OP_POOL_1D:
             return false;
         case GGML_OP_UPSCALE:
diff --git a/ggml/src/ggml-metal/ggml-metal-impl.h b/ggml/src/ggml-metal/ggml-metal-impl.h
index 7a878a657bc..6d02befa97d 100644
--- a/ggml/src/ggml-metal/ggml-metal-impl.h
+++ b/ggml/src/ggml-metal/ggml-metal-impl.h
@@ -528,6 +528,36 @@ typedef struct {
     uint64_t nb2;
 } ggml_metal_kargs_conv_transpose_2d;
 
+typedef struct {
+    uint64_t nb00;
+    uint64_t nb01;
+    uint64_t nb02;
+    uint64_t nb03;
+    uint64_t nb10;
+    uint64_t nb11;
+    uint64_t nb12;
+    uint64_t nb13;
+    uint64_t nb0;
+    uint64_t nb1;
+    uint64_t nb2;
+    uint64_t nb3;
+    int32_t  IW;
+    int32_t  IH;
+    int32_t  KW;
+    int32_t  KH;
+    int32_t  IC;
+    int32_t  OC;
+    int32_t  OW;
+    int32_t  OH;
+    int32_t  N;
+    int32_t  s0;
+    int32_t  s1;
+    int32_t  p0;
+    int32_t  p1;
+    int32_t  d0;
+    int32_t  d1;
+} ggml_metal_kargs_conv_2d;
+
 typedef struct {
     uint64_t  ofs0;
     uint64_t  ofs1;
diff --git a/ggml/src/ggml-metal/ggml-metal-ops.cpp b/ggml/src/ggml-metal/ggml-metal-ops.cpp
index 5a8f150a71d..d9811e31159 100644
--- a/ggml/src/ggml-metal/ggml-metal-ops.cpp
+++ b/ggml/src/ggml-metal/ggml-metal-ops.cpp
@@ -10,6 +10,7 @@
 
 #include <cassert>
 #include <algorithm>
+#include <limits>
 
 static ggml_metal_buffer_id ggml_metal_get_buffer_id(const ggml_tensor * t) {
     if (!t) {
@@ -364,6 +365,10 @@ static int ggml_metal_op_encode_impl(ggml_metal_op_t ctx, int idx) {
             {
                 n_fuse = ggml_metal_op_im2col(ctx, idx);
             } break;
+        case GGML_OP_CONV_2D:
+            {
+                n_fuse = ggml_metal_op_conv_2d(ctx, idx);
+            } break;
         case GGML_OP_CONV_TRANSPOSE_1D:
             {
                 n_fuse = ggml_metal_op_conv_transpose_1d(ctx, idx);
@@ -1036,11 +1041,6 @@ int ggml_metal_op_set_rows(ggml_metal_op_t ctx, int idx) {
 
     nth = std::min(nth, nk0);
 
-    if (nth*nrptg > ggml_metal_pipeline_max_theads_per_threadgroup(pipeline)) {
-        nth = ggml_metal_pipeline_max_theads_per_threadgroup(pipeline);
-        nrptg = 1;
-    }
-
     ggml_metal_kargs_set_rows args = {
         /*.nk0  =*/ nk0,
         /*.ne01 =*/ ne01,
@@ -3082,6 +3082,84 @@ int ggml_metal_op_im2col(ggml_metal_op_t ctx, int idx) {
     return 1;
 }
 
+int ggml_metal_op_conv_2d(ggml_metal_op_t ctx, int idx) {
+    ggml_tensor * op = ctx->node(idx);
+
+    ggml_metal_library_t lib = ctx->lib;
+    ggml_metal_encoder_t enc = ctx->enc;
+
+    GGML_TENSOR_LOCALS( int32_t, ne0, op->src[0], ne);
+    GGML_TENSOR_LOCALS(uint64_t, nb0, op->src[0], nb);
+    GGML_TENSOR_LOCALS( int32_t, ne1, op->src[1], ne);
+    GGML_TENSOR_LOCALS(uint64_t, nb1, op->src[1], nb);
+    GGML_TENSOR_LOCALS( int32_t, ne,  op,         ne);
+    GGML_TENSOR_LOCALS(uint64_t, nb,  op,         nb);
+
+    GGML_ASSERT(ggml_is_contiguous(op->src[0]));
+    GGML_ASSERT(op->src[1]->type == GGML_TYPE_F32);
+    GGML_ASSERT(op->type == GGML_TYPE_F32);
+    GGML_ASSERT(op->src[0]->type == GGML_TYPE_F16 || op->src[0]->type == GGML_TYPE_F32);
+
+    const int32_t s0 = ((const int32_t *) op->op_params)[0];
+    const int32_t s1 = ((const int32_t *) op->op_params)[1];
+    const int32_t p0 = ((const int32_t *) op->op_params)[2];
+    const int32_t p1 = ((const int32_t *) op->op_params)[3];
+    const int32_t d0 = ((const int32_t *) op->op_params)[4];
+    const int32_t d1 = ((const int32_t *) op->op_params)[5];
+
+    ggml_metal_kargs_conv_2d args = {
+        /*.nb00 =*/ nb00,
+        /*.nb01 =*/ nb01,
+        /*.nb02 =*/ nb02,
+        /*.nb03 =*/ nb03,
+        /*.nb10 =*/ nb10,
+        /*.nb11 =*/ nb11,
+        /*.nb12 =*/ nb12,
+        /*.nb13 =*/ nb13,
+        /*.nb0  =*/ nb0,
+        /*.nb1  =*/ nb1,
+        /*.nb2  =*/ nb2,
+        /*.nb3  =*/ nb3,
+        /*.IW   =*/ ne10,
+        /*.IH   =*/ ne11,
+        /*.KW   =*/ ne00,
+        /*.KH   =*/ ne01,
+        /*.IC   =*/ ne02,
+        /*.OC   =*/ ne03,
+        /*.OW   =*/ ne0,
+        /*.OH   =*/ ne1,
+        /*.N    =*/ ne3,
+        /*.s0   =*/ s0,
+        /*.s1   =*/ s1,
+        /*.p0   =*/ p0,
+        /*.p1   =*/ p1,
+        /*.d0   =*/ d0,
+        /*.d1   =*/ d1,
+    };
+
+    ggml_metal_pipeline_t pipeline = ggml_metal_library_get_pipeline_conv_2d(lib, op);
+
+    int nth = ggml_metal_pipeline_max_theads_per_threadgroup(pipeline);
+    nth = std::min(nth, 256);
+    nth = std::max(nth, 1);
+
+    const uint64_t n_out = ggml_nelements(op);
+
+    uint64_t tg = (n_out + nth - 1)/nth;
+    tg = std::max<uint64_t>(tg, 1);
+    tg = std::min<uint64_t>(tg, (uint64_t) std::numeric_limits<int>::max());
+
+    ggml_metal_encoder_set_pipeline(enc, pipeline);
+    ggml_metal_encoder_set_bytes   (enc, &args, sizeof(args), 0);
+    ggml_metal_encoder_set_buffer  (enc, ggml_metal_get_buffer_id(op->src[0]), 1);
+    ggml_metal_encoder_set_buffer  (enc, ggml_metal_get_buffer_id(op->src[1]), 2);
+    ggml_metal_encoder_set_buffer  (enc, ggml_metal_get_buffer_id(op),         3);
+
+    ggml_metal_encoder_dispatch_threadgroups(enc, tg, 1, 1, nth, 1, 1);
+
+    return 1;
+}
+
 int ggml_metal_op_conv_transpose_1d(ggml_metal_op_t ctx, int idx) {
     ggml_tensor * op = ctx->node(idx);
 
diff --git a/ggml/src/ggml-metal/ggml-metal-ops.h b/ggml/src/ggml-metal/ggml-metal-ops.h
index 0d9cb8af7c1..3cf400dc45c 100644
--- a/ggml/src/ggml-metal/ggml-metal-ops.h
+++ b/ggml/src/ggml-metal/ggml-metal-ops.h
@@ -70,6 +70,7 @@ int ggml_metal_op_group_norm        (ggml_metal_op_t ctx, int idx);
 int ggml_metal_op_norm              (ggml_metal_op_t ctx, int idx);
 int ggml_metal_op_rope              (ggml_metal_op_t ctx, int idx);
 int ggml_metal_op_im2col            (ggml_metal_op_t ctx, int idx);
+int ggml_metal_op_conv_2d           (ggml_metal_op_t ctx, int idx);
 int ggml_metal_op_conv_transpose_1d (ggml_metal_op_t ctx, int idx);
 int ggml_metal_op_conv_transpose_2d (ggml_metal_op_t ctx, int idx);
 int ggml_metal_op_upscale           (ggml_metal_op_t ctx, int idx);
diff --git a/ggml/src/ggml-metal/ggml-metal.metal b/ggml/src/ggml-metal/ggml-metal.metal
index cea535ade74..7f94419c3ac 100644
--- a/ggml/src/ggml-metal/ggml-metal.metal
+++ b/ggml/src/ggml-metal/ggml-metal.metal
@@ -4146,6 +4146,120 @@ template [[host_name("kernel_im2col_f16")]] kernel im2col_t kernel_im2col<half>;
 //template [[host_name("kernel_im2col_ext_f32")]] kernel im2col_ext_t kernel_im2col_ext<float>;
 //template [[host_name("kernel_im2col_ext_f16")]] kernel im2col_ext_t kernel_im2col_ext<half>;
 
+template <typename TK>
+kernel void kernel_conv_2d(
+        constant ggml_metal_kargs_conv_2d & args,
+        device const char * weights,
+        device const char * src,
+        device       char * dst,
+        uint3   tgpig[[threadgroup_position_in_grid]],
+        uint3    tgpg[[threadgroups_per_grid]],
+        uint3   tpitg[[thread_position_in_threadgroup]],
+        uint3     ntg[[threads_per_threadgroup]]) {
+
+    const uint threads_per_tg = ntg.x * ntg.y * ntg.z;
+    const uint tg_index = (tgpig.z * tgpg.y + tgpig.y) * tgpg.x + tgpig.x;
+    const uint local_thread = tpitg.z * (ntg.x * ntg.y) + tpitg.y * ntg.x + tpitg.x;
+    const uint thread_index = tg_index * threads_per_tg + local_thread;
+    const uint64_t total_threads = (uint64_t) threads_per_tg * tgpg.x * tgpg.y * tgpg.z;
+    const uint64_t total_outputs = (uint64_t) args.N * args.OC * args.OH * args.OW;
+
+    for (uint64_t index = thread_index; index < total_outputs; index += total_threads) {
+        uint64_t tmp = index;
+
+        const int32_t ow = tmp % args.OW; tmp /= args.OW;
+        const int32_t oh = tmp % args.OH; tmp /= args.OH;
+        const int32_t oc = tmp % args.OC; tmp /= args.OC;
+        const int32_t  n = tmp;
+
+        float acc = 0.0f;
+
+        const int32_t base_x = ow*args.s0 - args.p0;
+        const int32_t base_y = oh*args.s1 - args.p1;
+
+        int32_t ky_start = 0;
+        if (base_y < 0) {
+            ky_start = (-base_y + args.d1 - 1)/args.d1;
+        }
+        int32_t ky_end = args.KH;
+        const int32_t y_max = args.IH - 1 - base_y;
+        if (y_max < 0) {
+            ky_end = ky_start;
+        } else if (base_y + (args.KH - 1)*args.d1 >= args.IH) {
+            ky_end = min(ky_end, y_max/args.d1 + 1);
+        }
+
+        int32_t kx_start = 0;
+        if (base_x < 0) {
+            kx_start = (-base_x + args.d0 - 1)/args.d0;
+        }
+        int32_t kx_end = args.KW;
+        const int32_t x_max = args.IW - 1 - base_x;
+        if (x_max < 0) {
+            kx_end = kx_start;
+        } else if (base_x + (args.KW - 1)*args.d0 >= args.IW) {
+            kx_end = min(kx_end, x_max/args.d0 + 1);
+        }
+
+        if (ky_start < ky_end && kx_start < kx_end) {
+            const uint64_t src_base_n = (uint64_t) n  * args.nb13;
+            const uint64_t w_base_oc  = (uint64_t) oc * args.nb03;
+
+            for (int32_t ic = 0; ic < args.IC; ++ic) {
+                const uint64_t src_base_nc = src_base_n + (uint64_t) ic * args.nb12;
+                const uint64_t w_base_ocic = w_base_oc  + (uint64_t) ic * args.nb02;
+
+                for (int32_t ky = ky_start; ky < ky_end; ++ky) {
+                    const int32_t iy = base_y + ky*args.d1;
+                    const uint64_t src_base_row = src_base_nc + (uint64_t) iy * args.nb11;
+                    const uint64_t w_base_row   = w_base_ocic + (uint64_t) ky * args.nb01;
+
+                    for (int32_t kx = kx_start; kx < kx_end; ++kx) {
+                        const int32_t ix = base_x + kx*args.d0;
+                        const uint64_t src_offs = src_base_row + (uint64_t) ix * args.nb10;
+                        const uint64_t w_offs   = w_base_row   + (uint64_t) kx * args.nb00;
+
+                        const float x = *(device const float *)(src + src_offs);
+                        const float w = (float) (*(device const TK *)(weights + w_offs));
+
+                        acc += x * w;
+                    }
+                }
+            }
+        }
+
+        const uint64_t dst_offs =
+            (uint64_t) n  * args.nb3 +
+            (uint64_t) oc * args.nb2 +
+            (uint64_t) oh * args.nb1 +
+            (uint64_t) ow * args.nb0;
+
+        *(device float *)(dst + dst_offs) = acc;
+    }
+}
+
+template [[host_name("kernel_conv_2d_f32_f32")]]
+kernel void kernel_conv_2d<float>(
+        constant ggml_metal_kargs_conv_2d & args,
+        device const char * weights,
+        device const char * src,
+        device       char * dst,
+        uint3   tgpig[[threadgroup_position_in_grid]],
+        uint3    tgpg[[threadgroups_per_grid]],
+        uint3   tpitg[[thread_position_in_threadgroup]],
+        uint3     ntg[[threads_per_threadgroup]]);
+
+template [[host_name("kernel_conv_2d_f16_f32")]]
+kernel void kernel_conv_2d<half>(
+        constant ggml_metal_kargs_conv_2d & args,
+        device const char * weights,
+        device const char * src,
+        device       char * dst,
+        uint3   tgpig[[threadgroup_position_in_grid]],
+        uint3    tgpg[[threadgroups_per_grid]],
+        uint3   tpitg[[thread_position_in_threadgroup]],
+        uint3     ntg[[threads_per_threadgroup]]);
+
 typedef void (conv_transpose_1d_t)(
         constant ggml_metal_kargs_conv_transpose_1d & args,
         device const float * src0,

From 1215dde7b0ee02114d074b0b785eedd3052b0006 Mon Sep 17 00:00:00 2001
From: ixgbe <1113177880@qq.com>
Date: Thu, 13 Nov 2025 20:13:32 +0800
Subject: [PATCH 183/185] ggml-cpu : add RISC-V vector intrinsic support for
 silu and cvar operations (#17227)

Signed-off-by: Wang Yang <yangwang@iscas.ac.cn>
---
 ggml/src/ggml-cpu/vec.cpp | 17 +++++++++++++++++
 1 file changed, 17 insertions(+)

diff --git a/ggml/src/ggml-cpu/vec.cpp b/ggml/src/ggml-cpu/vec.cpp
index 43dc7537c33..ac8633e2128 100644
--- a/ggml/src/ggml-cpu/vec.cpp
+++ b/ggml/src/ggml-cpu/vec.cpp
@@ -360,6 +360,13 @@ void ggml_vec_silu_f32(const int n, float * y, const float * x) {
     for (; i + 3 < n; i += 4) {
         vst1q_f32(y + i, ggml_v_silu(vld1q_f32(x + i)));
     }
+#elif defined(__riscv_v_intrinsic)
+    for (int vl; i < n; i += vl) {
+        vl = __riscv_vsetvl_e32m2(n - i);
+        vfloat32m2_t vx = __riscv_vle32_v_f32m2(&x[i], vl);
+        vfloat32m2_t vy = ggml_v_silu_m2(vx, vl);
+        __riscv_vse32_v_f32m2(&y[i], vy, vl);
+    }
 #endif
     for (; i < n; ++i) {
         y[i] = ggml_silu_f32(x[i]);
@@ -460,6 +467,16 @@ ggml_float ggml_vec_cvar_f32(const int n, float * y, const float * x, const floa
         val = vec_mul(val, val);
         sum += (ggml_float)vec_hsum_f32x4(val);
     }
+#elif defined(__riscv_v_intrinsic)
+    vfloat64m1_t vsum = __riscv_vfmv_v_f_f64m1(0, 1);
+    for (int vl; i < n; i += vl) {
+        vl = __riscv_vsetvl_e32m2(n - i);
+        vfloat32m2_t val = __riscv_vfsub_vf_f32m2(__riscv_vle32_v_f32m2(&x[i], vl), mean, vl);
+        __riscv_vse32_v_f32m2(&y[i], val, vl);
+        val = __riscv_vfmul_vv_f32m2(val, val, vl);
+        vsum = __riscv_vfwredusum_vs_f32m2_f64m1(val, vsum, vl);
+    }
+    sum = (ggml_float)__riscv_vfmv_f_s_f64m1_f64(vsum);
 #endif
     for (; i < n; ++i) {
         float val = x[i] - mean;

From dd091e52f886d8b851658c38b8ce8a98e70cd45d Mon Sep 17 00:00:00 2001
From: Diego Devesa <slarengh@gmail.com>
Date: Thu, 13 Nov 2025 04:14:02 -0800
Subject: [PATCH 184/185] sched : fix reserve ignoring user tensor assignments
 (#17232)

---
 ggml/src/ggml-backend.cpp | 2 --
 1 file changed, 2 deletions(-)

diff --git a/ggml/src/ggml-backend.cpp b/ggml/src/ggml-backend.cpp
index ff9135fe2d8..eeaf35c169f 100644
--- a/ggml/src/ggml-backend.cpp
+++ b/ggml/src/ggml-backend.cpp
@@ -1698,8 +1698,6 @@ bool ggml_backend_sched_reserve(ggml_backend_sched_t sched, struct ggml_cgraph *
     GGML_ASSERT(sched);
     GGML_ASSERT((int)sched->hash_set.size >= measure_graph->n_nodes + measure_graph->n_leafs);
 
-    ggml_backend_sched_reset(sched);
-
     ggml_backend_sched_synchronize(sched);
 
     ggml_backend_sched_split_graph(sched, measure_graph);

From a19bd6f7ce7e7b76e0dd7a614668a3042f5c1bfe Mon Sep 17 00:00:00 2001
From: Ruben Ortlam <picard12@live.de>
Date: Thu, 13 Nov 2025 14:51:21 +0100
Subject: [PATCH 185/185] vulkan: remove shell call from vulkan-shaders-gen
 tool, revert file check (#17219)

* vulkan: remove shell call from vulkan-shaders-gen tool

* use string vector for command execution

* Fix condition

* use string, remove const_cast

* Fix dependency file quotation on Windows

---------

Co-authored-by: Jeff Bolz <jbolz@nvidia.com>
---
 .../vulkan-shaders/vulkan-shaders-gen.cpp     | 53 ++++++++++++-------
 1 file changed, 33 insertions(+), 20 deletions(-)

diff --git a/ggml/src/ggml-vulkan/vulkan-shaders/vulkan-shaders-gen.cpp b/ggml/src/ggml-vulkan/vulkan-shaders/vulkan-shaders-gen.cpp
index c8a6f97ecff..1423f772403 100644
--- a/ggml/src/ggml-vulkan/vulkan-shaders/vulkan-shaders-gen.cpp
+++ b/ggml/src/ggml-vulkan/vulkan-shaders/vulkan-shaders-gen.cpp
@@ -76,7 +76,7 @@ enum MatMulIdType {
 
 namespace {
 
-void execute_command(const std::string& command, std::string& stdout_str, std::string& stderr_str) {
+void execute_command(std::vector<std::string>& command, std::string& stdout_str, std::string& stderr_str) {
 #ifdef _WIN32
     HANDLE stdout_read, stdout_write;
     HANDLE stderr_read, stderr_write;
@@ -99,8 +99,10 @@ void execute_command(const std::string& command, std::string& stdout_str, std::s
     si.hStdOutput = stdout_write;
     si.hStdError = stderr_write;
 
-    std::vector<char> cmd(command.begin(), command.end());
-    cmd.push_back('\0');
+    std::string cmd;
+    for (const auto& part : command) {
+        cmd += part + " ";
+    }
 
     if (!CreateProcessA(NULL, cmd.data(), NULL, NULL, TRUE, 0, NULL, NULL, &si, &pi)) {
         throw std::runtime_error("Failed to create process");
@@ -138,6 +140,12 @@ void execute_command(const std::string& command, std::string& stdout_str, std::s
         throw std::runtime_error("Failed to fork process");
     }
 
+    std::vector<char*> argv;
+    for (std::string& part : command) {
+        argv.push_back(part.data());
+    }
+    argv.push_back(nullptr);
+
     if (pid == 0) {
         close(stdout_pipe[0]);
         close(stderr_pipe[0]);
@@ -145,7 +153,7 @@ void execute_command(const std::string& command, std::string& stdout_str, std::s
         dup2(stderr_pipe[1], STDERR_FILENO);
         close(stdout_pipe[1]);
         close(stderr_pipe[1]);
-        execl("/bin/sh", "sh", "-c", command.c_str(), (char*) nullptr);
+        execvp(argv[0], argv.data());
         _exit(EXIT_FAILURE);
     } else {
         close(stdout_pipe[1]);
@@ -316,21 +324,27 @@ compile_count_guard acquire_compile_slot() {
 void string_to_spv_func(std::string name, std::string in_path, std::string out_path, std::map<std::string, std::string> defines, bool coopmat, bool dep_file, compile_count_guard slot) {
     std::string target_env = (name.find("_cm2") != std::string::npos) ? "--target-env=vulkan1.3" : "--target-env=vulkan1.2";
 
-    // disable spirv-opt for coopmat shaders for https://github.com/ggerganov/llama.cpp/issues/10734
-    // disable spirv-opt for bf16 shaders for https://github.com/ggml-org/llama.cpp/issues/15344
-    // disable spirv-opt for rope shaders for https://github.com/ggml-org/llama.cpp/issues/16860
-    std::string opt_level = (coopmat || name.find("bf16") != std::string::npos || name.find("rope") != std::string::npos) ? "" : "-O";
-
     #ifdef _WIN32
-        std::vector<std::string> cmd = {GLSLC, "-fshader-stage=compute", target_env, opt_level, "\"" + in_path + "\"", "-o", "\"" + out_path + "\""};
+        std::vector<std::string> cmd = {GLSLC, "-fshader-stage=compute", target_env, "\"" + in_path + "\"", "-o", "\"" + out_path + "\""};
     #else
-        std::vector<std::string> cmd = {GLSLC, "-fshader-stage=compute", target_env, opt_level, in_path, "-o",  out_path};
+        std::vector<std::string> cmd = {GLSLC, "-fshader-stage=compute", target_env, in_path, "-o", out_path};
     #endif
 
+    // disable spirv-opt for coopmat shaders for https://github.com/ggerganov/llama.cpp/issues/10734
+    // disable spirv-opt for bf16 shaders for https://github.com/ggml-org/llama.cpp/issues/15344
+    // disable spirv-opt for rope shaders for https://github.com/ggml-org/llama.cpp/issues/16860
+    if (!coopmat && name.find("bf16") == std::string::npos && name.find("rope") == std::string::npos) {
+        cmd.push_back("-O");
+    }
+
     if (dep_file) {
         cmd.push_back("-MD");
         cmd.push_back("-MF");
+#ifdef _WIN32
         cmd.push_back("\"" + target_cpp + ".d\"");
+#else
+        cmd.push_back(target_cpp + ".d");
+#endif
     }
 
     #ifdef GGML_VULKAN_SHADER_DEBUG_INFO
@@ -354,9 +368,13 @@ void string_to_spv_func(std::string name, std::string in_path, std::string out_p
         // }
         // std::cout << std::endl;
 
-        execute_command(command, stdout_str, stderr_str);
+        execute_command(cmd, stdout_str, stderr_str);
         if (!stderr_str.empty()) {
-            std::cerr << "cannot compile " << name << "\n\n" << command << "\n\n" << stderr_str << std::endl;
+            std::cerr << "cannot compile " << name << "\n\n";
+            for (const auto& part : cmd) {
+                std::cerr << part << " ";
+            }
+            std::cerr << "\n\n" << stderr_str << std::endl;
             return;
         }
 
@@ -430,7 +448,7 @@ void matmul_shaders(bool fp16, MatMulIdType matmul_id_type, bool coopmat, bool c
     base_dict["ACC_TYPE"     ] = f16acc ? "float16_t" : "float";
     base_dict["ACC_TYPE_VEC2"] = f16acc ? "f16vec2"   : "vec2";
     if (f16acc) {
-        base_dict["ACC_TYPE_MAX"] = "\"float16_t(65504.0)\"";
+        base_dict["ACC_TYPE_MAX"] = "float16_t(65504.0)";
     }
 
     if (coopmat) {
@@ -610,7 +628,7 @@ void process_shaders() {
         fa_base_dict["ACC_TYPE"] = f16acc ? "float16_t" : "float";
         fa_base_dict["ACC_TYPEV4"] = f16acc ? "f16vec4" : "vec4";
         if (f16acc) {
-            fa_base_dict["ACC_TYPE_MAX"] = "\"float16_t(65504.0)\"";
+            fa_base_dict["ACC_TYPE_MAX"] = "float16_t(65504.0)";
         }
 
         for (const auto& tname : type_names) {
@@ -1081,11 +1099,6 @@ int main(int argc, char** argv) {
 
     if (args.find("--glslc") != args.end()) {
         GLSLC = args["--glslc"]; // Path to glslc
-
-        if (!std::filesystem::exists(GLSLC) || !std::filesystem::is_regular_file(GLSLC)) {
-            std::cerr << "Error: glslc not found at " << GLSLC << std::endl;
-            return EXIT_FAILURE;
-        }
     }
     if (args.find("--source") != args.end()) {
         input_filepath = args["--source"]; // The shader source file to compile